New PNe in the Large Magellanic Cloud (III): The PNLF

A New Population of Planetary Nebulae Discovered in the Large Magellanic Cloud (III): The Luminosity Function

Warren A. Reid and Quentin A. Parker
Department of Physics, Macquarie University, Sydney, NSW 2109, Australia
Anglo-Australian Observatory, PO Box 296, Epping, NSW 1710 Australia
e-Mail: warren@ics.mq.edu.au; war@aao.gov.au e-Mail: qap@ics.mq.edu.au
Abstract

Our previous identification and spectroscopic confirmation of 431 faint, new planetary nebulae in the central 25 deg region of the LMC permits us to now examine the shape of the LMC Planetary Nebula Luminosity Function (PNLF) through an unprecedented 10 magnitude range. The majority of our newly discovered and previously known PNe were observed using the 2dF, multi-object fibre spectroscopy system on the 3.9-m Anglo-Australian Telescope and the FLAMES multi-object spectrograph on the 8-m VLT. We present reliable [O iii]5007Å and H flux estimates based on calibrations to well established PN fluxes from previous surveys and spectroscopic standard stars. The bright cutoff (M) of the PNLF is found by fitting a truncated exponential curve to the bright end of the PNLF over a 3.4 magnitude range. This cutoff is used to estimate a new distance modulus of 18.46 to the LMC, in close agreement with previous PNLF studies and the best estimates by other indicators. The bright end cutoff is robust to small samples of bright PNe since significantly increased PN samples do not change this fiducial. We then fit a truncated exponential curve directly to the bright end of the function over a 6 magnitude range and test the curve’s ability to indicate the position of M. Because of the significant increase in the number of LMC PN, the shape of the PNLF is now examined in greater detail than has previously been possible. Newly discovered features include a small increase in the number of PNe over the brightest 4 magnitudes followed by a steep rise over 2 magnitudes, a peak at 6 magnitudes below the bright cutoff and an almost linear drop-off to the faint end. Dips at the bright end of the PNLF are examined in relation to the overall shape of the PNLF and the exponential increase in the number of PNe. Through cumulative functions, the new LMC PNLF is compared to those from the SMC and a new deep local Galactic sample revealing the effects of incompleteness. The new [O iii]5007Å LMC PNLF is then compared to our new H LMC PNLF using calibrated and measured fluxes for the same objects, revealing the effects of metallicity on the [O iii]5007Å line.

keywords:
surveys - planetary nebulae: general - luminosity function - galaxies: Magellanic Clouds.
pagerange: A New Population of Planetary Nebulae Discovered in the Large Magellanic Cloud (III): The Luminosity FunctionApubyear: 2002

1 Introduction

The PN luminosity function (PNLF) describes the number density of PNe within a given system over any given luminosity range based on a prominent emission line such as [O iii]. Its most frequent use is as an extragalactic distance indicator where it is the only standard candle that can be applied to all the large galaxies in the Local Supercluster (Jacoby, 1980, Ciardullo & Jacoby et al. 1989, Ciardullo & Jacoby, 1992, Ciardullo, 2006). In this role, the distance estimate relies on the shape created by the binning of [O iii] 5007Å fluxes at the bright end of the PNLF, which appears to be essentially invariant across all galaxies tested thus far, regardless of their morphological type or metallicity (Méndez et al. 1993; Ciardullo et al. 2004). There is a consistent [O iii] 5007Å high luminosity cut-off beyond which no PNe are observed. The bright cut-off point is identified by fitting an exponential curve to the bright end of the PNLF and is believed to be invariant for all PN systems in all galaxies (Stanghellini 1995, Ciardullo 2006).

The concept of using PNe as a cosmological distance indicator was first suggested in the 1960’s (Henize et al. 1963; Hodge 1966). It was slow to gain acceptance because individual PNe are not standard candles, distances to local Galactic PNe were very difficult to estimate and extragalactic PNe were severely under-sampled. The first study using an [O iii] 5007Å-emission-line based PN luminosity function as a distance indicator was performed in 1990 by Jacoby et al. (1990). Today, with large numbers of PNe being discovered in external galaxies (Kniazev et al. 2005, Ciardullo 2006, Jacoby 2006) it is recognised as one of the most important and resilient distance indicators in extragalactic astronomy (Ciardullo 2006). The PNLF method has been proven to be an accurate standard candle (Jacoby 1989; Ciardullo et al. 1989; Jacoby, Ciardullo, Ford, 1990; Jacoby, Walker, Ciardullo, 1990b) and appears to be extremely insensitive to parent stellar population (Ciardullo & Jacoby, 1992).

The PNLF has other uses apart from distance determination. Establishing the consistent shape of the function provides a basis for estimating the number of PNe in any galaxy, given only the number of PNe in the brightest 3 or 4 magnitudes. A PNLF which comprises a near complete sample of PNe across a galaxy can be used to estimate the luminosity-to-mass and dynamical age relations (Méndez et al. 1993). It has also been suggested as a valuable tool for studies of the initial-to-final mass relation and related mass loss processes in stars of early-type galaxies (Méndez et al. 1993). Lastly, the PNLF provides a unique probe into a galaxy’s chemical and dynamical evolution. The mass and metallicity of the progenitor star largely determines the maximum [O iii] line luminosity of the PN (Dopita et al. 1992). This makes the shape of the [O iii] PNLF an important diagnostic for galactic chemical evolution.

The first luminosity function for PNe in the LMC and SMC was constructed by Jacoby (1980). The advantage of using PNe in these local, external galaxies to create a luminosity function was clear since the distance to all the PNe was essentially equal, faint PNe could still be identified and each galactic system could be studied in its entirety. The majority of bright PNe in each galaxy had already been identified so the bright end of the PNLF was able to be modeled and successfully used as a distance indicator. However, with a faint cutoff only 6 magnitudes below the brightest, the overall shape of the PNLF, especially at the faint end, was still unknown.

The overall shape of the PNLF has previously been difficult to determine for any galaxy due to sample incompleteness at the faint end. With 431 medium to faint PNe together with 162 previously identified PNe now uncovered within the central 25 deg of the LMC (Reid & Parker, 2006b) [RPb] hereafter, we can now update the LMC PNLF and provide measured estimates to compare with previous theoretical simulations and other observed PNLFs. The RP PNe were discovered using an AAO/UKST H (+ effectively [N ii]) 40 field mini-survey of the entire LMC, SMC and surrounding regions. The details are provided in Reid & Parker (2006a) hence [RPa] and will not be repeated here. For details regarding the overall H survey, see Parker et al. (2005) and for the candidate selection technique and followup spectroscopic object confirmations, please see [RPb].

The new RP sample will enable both the shape and structure of the LMC PNLF to be analysed in detail for the first time over a much wider 10 magnitude range. The distance has always been estimated using an empirical (or theoretical) luminosity function and fitting this curve to the data using a statistically robust technique such as or the maximum likelihood method to give the appropriate bright-end position. The bright-end intersection of this curve with the magnitude plane gives the position of M (the brightest possible PN in the system) and the distance modulus. In this work, we use a cumulative function to determine the position of M. We also fit the truncated exponential curve directly to the very complete bright end of the PNLF over a 6 magnitude range to test it’s ability to depict PN evolution and indicate distance. Our ability to identify PNe to magnitudes as faint as 25 in [O iii], 10 magnitudes below M, gives us confidence that we are largely complete at the bright end of the PNLF. It also largely does away with the need to simulate and extrapolate the PNLF to account for unobserved, faint PNe with (M–M) 5.

A brief description of the PN spectra used in this study is provided in section 2 along with the data reduction procedure. The new method of flux calibration for fibre spectra together with the de-reddening procedure is outlined in section 3. In section 4 we present the new [O iii] PNLF for the LMC using 574 bright to faint PNe and compare the shape to the previous best LMC PNLF from Jacoby et al. (1990), and the empirical predictions of Ciadullo et al. (1989) and Méndez et al. (1993). In section 5 the PNLF is constructed using the H line, a good predictor of central star temperature, and compared to our new determination of the traditional [O iii]5007Å based PNLF.

2 2dF and FLAMES observations

2.1 Brief description

A five night observing run on the AAT using 2dF (Lewis et al. 2002) was undertaken in December 2004 to spectroscopically confirm LMC emission candidates as PNe and to eliminate contaminants such as H ii regions and emission line stars. 2dF was an ideal choice of instrument for the spectroscopic followup of large numbers of candidate emission objects due to its unique ability to simultaneously observe 400 targets (including objects, fiducial stars and sky positions) with 2 arcsec fibres over a wide 2 degree diameter field area. The large corrector lens incorporates an atmospheric dispersion compensator, which is essential for wide wavelength coverage using small diameter fibres.

The observations provided 4,000 spectra. Individual exposure times were mostly 1200s using the 300B grating with a central wavelength of 5852Å and wavelength range 3600-8000Å at a dispersion of 4.30Å/pixel. These low-resolution observations, at 9.0Å FWHM, were used as the primary means of object classification and provided the bright [O iii]5007 fluxes for this study. All fields were then re-observed using the 1200R grating for kinematic studies [RPb] and improved resolution of the [S ii] 6716,6731Å lines for determination of electron densities.

The 2dF raw data were processed using the AAO 2dF data reduction system, 2dFDR111http://www.aao.gov.au/AAO/2df/software.html#2dfdr. This software can probe the multifibre spectra creating the necessary calibration groups (eg. BIAS, DARK, FLAT, ARC etc). As a calibration exposure is reduced it is inserted into the appropriate group.

The software was instructed to perform a subtraction of background scattered light prior to the extraction. The background is determined by fitting a function through the ‘dead’ or unused fibres in the image.

A bias frame was obtained for each observed field. The mean of the bias frame has the bias strip removed. This strip is subtracted from the data and the bias strip is trimmed from the data frame. A variance array is then derived from the data with values determined from photon statistics and readout noise. The resulting frame was then used throughout the reduction process.

The data reduction system performs a wavelength calibration using the information from the spectrograph optical model. This is then refined using data from the arc lamp exposure. The lines in the arc lamp exposure are matched against a line list. A cubic fit for each fibre is then performed to the predicted and measured wavelengths of all lines which are non-blended, not too wide and not too weak. This fit is then used to further refine the wavelengths.

To perform the sky subtraction, the data is first corrected for the relative fibre throughput, based on a throughput map derived from the dedicated sky fibres. The relative intensities of the skylines in the object data frame are used to determine the relative fibre throughput. This method saves time, as no offset­sky observations are required. The median sky spectrum was calculated from the median of all the sky spectra normalized by their mean flux. Each of these spectra are continuum subtracted, using a boxcar median smoothing with a 201 pixel box to define the continuum. A robust least­squares fit of the counts was performed in the differential or continuum subtracted data fibres versus the counts in the differential or continuum subtracted median sky. Assuming that the sky was the dominant source of emission, the slope of this fit gives the fibre throughput. The robust fit is especially important when dealing with faint objects. The sky fibre spectra in the data were then combined and subtracted from each fibre. Cosmic rays were rejected automatically during the process of combining two or more observations.

Our data includes spectroscopic observations of a sub-sample of 21 PNe in dense regions of the LMC main bar, undertaken using the multi-object fibre spectroscopic system, FLAMES (Pasquini 2002) on the VLT UT2 over three nights in December 2004. Gratings LR2 and LR3 allowed us to cover the most important optical diagnostic lines for PNe in the blue including [O iii] 4363Å, He ii 4686Å, H and [O iii] 4959 & 5007Å. Grating LR6 covered the H, [N ii] 6548 and 6583Å lines as well as the [S ii] 6716 & 6731Å lines for electron densities. Details are provided in [RPa] and [RPb] but we will produce a separate paper examining all 420 objects (including PNe, H ii regions, and WR stars) observed using FLAMES.

The VLT FLAMES spectra were reduced using IRAF tasks IMRED, SPECRED and CCDRED for multi-spec files. Cosmic rays were rejected when combining frames. Using the weighted intensity of the continuum, the IRAF SCOMBINE task was then used to combine the three different wavelength portions of the spectrum into one spectral image.

2.2 Continuing Object followup

RP cat. RA DEC Previous Previous New New Reason
No. J2000 J2000 ID Prob. ID Prob.
5 05 40 28.18 -70 56 07.1 PN T H ii region T weak [O iii]5007 (1)
105 05 40 45.26 -70 28 06.7 PN T H ii region T Large angular size, Radio, IR
148 05 37 17.35 -70 07 49.3 PN L SNR L large size, strong [S ii] lines (1)
352 05 37 14.33 -66 26 54.61 PN P ELS L Low [O iii]5007/H (1)
490 05 37 31.73 -71 10 48.8 PN P symbiotic T continuum peaking at 7500Å(1)
641 05 37 06.38 -69 47 17.3 PN P H ii region T [O iii]5007/H = 60% (1)
667 05 30 26.20 -70 15 01.5 PN P ELS P Strong continuum (2)
782 05 28 18.80 -69 28 15.3 PN L Good PN lines, morphology (2)
798 05 26 13.74 -69 25 45.1 PN L ELS L Strong continuum (1)
841 05 28 08.09 -69 10 21.9 PN P ELS L Strong continuum (1)
856 05 24 38.82 -69 04 13.7 PN T PN P [O iii]5007/H =160%, crowded environ. (2)
872 05 24 25.18 -69 39 06.3 PN L H ii region T Strong continuum (1)
993 05 30 54.58 -68 34 22.4 PN L H ii region T Strong radio source, IR
1079 05 30 33.09 -66 57 41.5 PN L ELS L Strong continuum (1)
1113 05 22 49.80 -66 40 55.5 PN P H ii region T [O iii]5007 = H (2)
1192 05 19 56.77 -70 39 03.6 PN T symbiotic L Red continuum (1)
1434 05 20 16.84 -68 45 10.1 PN L symbiotic L Red continuum (1)
1495 05 19 06.88 -68 21 34.4 PN P H ii region T Radio
1534 05 21 29.65 -67 51 06.6 PN T PN + H ii L Radio, small PN 3” SE
1541 05 21 22.00 -67 47 28.6 PN L H ii region P Radio, IR, [O iii]5007/H = 60%
1691 05 00 32.23 -70 00 49.0 PN P ELS T Mostly H emission (2)
1716 04 54 24.49 -69 29 42.5 PN P H ii region T Large size (2)
1760 05 03 51.47 -68 57 23.7 PN L ELS L Strong continuum (1)
1783 04 54 33.78 -69 20 35.7 PN P ELS T Low [O iii]5007/H (2)
1933 05 04 47.34 -66 40 30.3 PN P H ii region T Strong radio source (2)
2194 05 19 18.44 -69 47 17.2 PN P H ii region T IR
Table 1: A list of 26 RP objects which have now been re-classified or had their status changed following new high resolution, higher S/N spectral observations and multi-wavelength analysis. ELS = Emission-line star; PN = Planetary Nebula; SNR = Supernova Remnant; Prob. refers to classification probability where T = True; L = Likely; P = Possible. Under the heading ‘Reason’, (1) refers to analysis using a 2.3m telescope optical spectrum, (2) refers to analysis using follow up observations on 2dF, ‘IR’ refers to false infrared colours at 3.6m and 4.5m 5.8m and 8m indicating H ii regions or hot stars, ‘Radio’ strong radio source (3mJy). Please see the text (section 2.2) for more details.

Every PN in the LMC sample, both previously known and new, has been re-analysed in order to identify and exclude interlopers which may effect the PNLF. This is particularly important at the bright end for distance determination. H and off-band red images were examined alongside high and low resolution optical spectra. In addition we have searched the SAGE (Meixner et al. 2006), Spitzer maps and overlaid false colours at 3.6, 4.5, 5.8 and 8m to assist verification. Finally, with mosaic radio maps of combined LMC data from ATCA and Parkes we were able to re-classify 3 ultra-bright ‘True’ PNe as contaminants due to their strong radio fluxes 3mJy (see Filipovic et al. 2009). This is despite optical spectra which would otherwise strongly indicate a PN. These compact emission objects are now classified as H ii regions. For a full list of re-classified objects, please see Table 1.

In order to provide independent checks of our 2dF data and create the most accurate LMC PN sample possible, we have undertaken a deep multi-wavelength study of PN candidates selected from our original discovery list that exhibited unusual characteristics and/or were deemed suspicious. In particular, due to the possibility of minor positioning errors, we have made 78 longslit observations of previous ‘possible’ and ‘likely’ PNe candidates in the RP sample using the MSSSO 2.3m telescope in order to firm-up their status. Using the double-beam spectrograph (DBS) on this telescope, the visible range (3200-9000Å), is split by a dichroic at around 6000Å and fed into two spectrographs, with red and blue optimized detectors. We used the 300B and 316R gratings to obtain a resolution of 4Å for each arm of the DBS. Reduction and extraction of 2.3m spectra were performed using the standard IRAF tasks IMRED, SPECRED, CCDRED and FIGARO’s task BCLEAN. One dimensional spectra were created and the background sky was subtracted. Final flux calibration used the standard stars, LTT7987, LTT9239, LTT2415 and LTT9491. Results are given in Table 1, where 8 ‘likely’ and 12 ‘possible’ PNe have been re-classified.

3 Flux Calibration and De-reddening of the 2dF Fibre Spectra

Figure 1: The uncorrected MCPN [O iii] 5007Å fluxes for 65 PNe are plotted against the [O iii] 5007Å 2dF 300B PN line intensities from all field exposures. General agreement is evident through an essentially log-linear relation with a turn-over at the bright end but the scatter is too wide (1 dex) to provide a reliable flux calibration. The line represents a least squares fit to the data.

Decent flux calibration of the 2dF LMC PN spectra was required in order to combine PN spectra from different 2dF fields and to make meaningful comparisons between fibre spectroscopy and long-slit observations of individual objects. A reliable flux calibration permits quick conversion to magnitudes for luminosity studies. It also permits a study into other nebula characteristics such as excitation class, temperature, density and mass. Since the majority of the spectra were gained by multi-fibre spectroscopy, it was necessary to verify the reliability of the measured line intensities. A comparison of the same objects observed in two or more overlapping 2dF field plate exposures revealed variations in line strengths of up to 35% from field to field, clearly rendering the standard reduced spectra unsuitable for combination in their raw state. A further comparison was made between combined 2dF line intensities and published fluxes from the Magellanic Cloud Planetary Nebulae spectral catalogue ([MCPN] thereafter) (Stanghellini et al. 2002)111Magellanic Cloud Planetary Nebula data is available from http://archive.stsci.edu/hst/mcpn/MCPN. The results, using all 65 MCPN which correspond with the RP sample, are shown in Figure 1. General agreement is evident through an essentially log-linear relation but the scatter is too wide (1 dex) to provide a reliable flux calibration. The variations in the [O iii] 5007Å line intensities shown are mainly due to the different relative strengths in the [O iii] 5007Å line from one 2dF field exposure to another in the raw, reddened spectra. A flux calibration of the spectra was required but to achieve this, a reliable method had to be found. This has proved quite difficult to do previously with fibre-based spectra (eg. Mortlock et al. 2001; Georgakakis et al. 2004). Below, an effective new method is described, which, in its careful application, is shown to be able to produce reliable flux calibration for the 2dF spectra.

Figure 2: Four examples of the flux calibration procedure. In each case, an excellent agreement has been found between previously published [O iii] and H line fluxes and 2dF line intensities. The graphs on the left provide the calibration for CCD1 and the graphs on the right provide the calibration for CCD2 from the same field-plate observation. Field C1 is calibrated to 7 PNe, C2 to 6 PNe, H1 to 20 PNe and H2 to 28 PNe. The equation shown in the top left of each graph has been applied to all [O iii] and H line intensities for spectra fed to that particular CCD and field-plate combination.

3.1 Flux calibration technique

Altogether, 18 overlapping 2dF field-plate exposures were taken in order to cover the entire central 25deg survey region of the LMC. A comparison of line intensities from overlapping areas revealed that each field plate/observational setup resulted in its own individual spectrum intensity scale. In addition, the 400 spectra from each field were fed to 2 identical spectrographs. Although they were well matched, small instrumental differences were noticeable. Overall, the combined use of 2 different field-plates, each sending spectra to 2 different spectrographs and CCD cameras resulted in the observed deviations seen when comparing previously published fluxes with line intensities for the same objects from multiple 2dF fields (Figure 1).

Experiments were undertaken in order to find the most reliable method of flux calibration using the observed line intensities. The best results were obtained by individually calibrating each spectral line on each field plate from each CCD camera to raw MCPN fluxes gained from HST exposures. The known PNe included and observed on each field plate were used as flux calibrators for each individual measured field. In order to extend the reliability of the [O iii]5007Å flux calibration to magnitudes 19, the [O iii]4959Å and H4861Å lines (Shaw et al. 2006) were included in the calibration. All three lines are close enough in the optical spectrum to produce reliable flux ratios. The individual H and [O iii]4959,5007Å 2dF line intensities for known PNe observed for each CCD and each field plate exposure were graphed against the individual published fluxes for the same lines (eg. Figure 2). The same method was applied to our multi-fibre spectra from VLT FLAMES. All 2dF and FLAMES fields purposefully contained sufficient PNe with well calibrated fluxes to enable this process. The agreement of flux calibrated PNe from each spectrograph/field plate combination was considered strong enough (within 0.2 dex, see Figure 2) to allow its application to all the H and [O iii]4959,5007Å emission lines for other PNe observed in the same field. In each case, a line of best fit was derived and the underlying linear equation extracted. This equation became the calibrator for each emission line in each uncalibrated PN from the CCD and individual 2dF field plate exposure used. The equation was applied to each spectrum with a detectable line intensity in that field.

Fluxes for LMC PNe from other catalogues (Jacoby et al. 1990, Leisy et al. private communication, Meatheringham et al. 1988) were also included in order to build up the number of calibrators per field. Where only a de-reddened flux value was published, a relative reddening was applied in order to make a better correlation. Where 2 or more published fluxes were found for the same PN, stronger comparisons could be made. Each independent survey showed a mean agreement to within 0.2 dex, slightly increasing as the magnitude grew fainter. A comparison between calibrated [O iii]5007Å fluxes from 2dF and published fluxes from the MCPN, Jacoby et al. (1990) and Leisy et al. are shown in Figure 3. The agreement ( dex) is very good across all surveys; especially since they represent space vs ground based observations in some cases with a variety of detectors and measurement methods. It also shows that the 2dF calibrated fluxes remain within the dex agreement. The mean slope of the fit (2dF/MCPN) is 1.01, where 1 would represent a perfect match. The median is exactly 1 and the standard deviation = 0.12 dex.

A spread in published line fluxes for the same PN is common but helps us to establish the uncertainties. Since the MCPN catalogue contained the largest number of PNe and the raw fluxes were ‘as measured’ (not de-reddened) these were given preference where irregularities became obvious. The MCPN set also includes some ground-based fluxes from ELCAT (Kaler et al. 1997) available at http://stsdas.stsci.edu/elcat/ where the spectra are uncorrected for extinction. The intention was to provide self consistent fluxes for all the 2dF observations.

A calibrated quality and consistency check was then performed where fluxes for several PNe observed on more than one field plate exposure (due to the overlaps in 2dF pointings across the survey) were compared for consistency once the new flux calibration had been applied to each field. Figure 4, shows an excellent match in the high as well as the low flux regimes, proving that reliable and consistent fluxes can in fact be achieved this way. The equation to convert line intensities to fluxes in each field was then applied to the 2dF and FLAMES [O iii] 5007Å line intensities for each corresponding field. Further line-to-flux calibration equations were then derived for other spectral lines such as H which, together with H, controls the de-reddening. A similar procedure was then carried out for each of the spectral lines to provide their individual flux calibration.

3.2 Reliability of the line intensities and fluxes

At the distance of the LMC, most PNe are compact and point-like in ground-based observations allowing most of the flux to fall within the 2 arcsec diameter 2dF fibre. This is despite the larger reported angular diameters, which suffer from point spread function growth as a function of source intensity and include the very faint surrounding halos. The extended outer halos typically represent about 1,000th of the flux of the inner PN (Corradi, 2003). Clearly, the central region of LMC PNe contains the majority of the light. There are 70 PNe out of our sample of 589 with inner shell diameters which exceed 2 arcsec by more than 1 arcsec. These are among the brightest LMC PNe and, despite the anticipated loss of light by 2dF spectroscopy, are still able to be accurately flux calibrated. For example, the loss of light from bright PNe is evidenced by the bright turnover in Figure 1. However, individual spectrograph calibration which includes the brightest PNe in each field (Figure 2), is able to largely correct for the assumed loss of light at the highest magnitude level. It does this by calibrating the increasing brightness received by the fibre directly to a well established flux level. This level will vary for each spectrograph/plate observation. For this reason, calibration of 2dF spectra to a single standard star would produce erroneously low fluxes for bright and extended LMC objects. In the same way, if a longslit is too narrow, flux levels will be underestimated (Jacoby & Kaler, 1993). This may be the cause of some small deviations in previously published fluxes for LMC PNe.

Flux ratios of doublet or close lines from the central shell of the PN, such as the [S ii] ratio used for the estimation of nebula densities, are largely consistent across the nebula and do not require flux calibration. The [S ii]6716,6731 lines were measured from the high resolution 1200R spectra. All other lines, into the blue, were measured from the 300B spectra.

3.2.1 Error estimations

The line intensities measured from 2dF 300B and 1200R spectra have two main sources of error. The first is due to an uncertainty in where to place the continuum level for line intensity measurement. Since the author performed all the line measurements, they were all performed in the same manner, at the same base positions for any line, relative to the continuum and/or noise. Repeated measurements however indicated an increased error estimate should apply to lines with a S/N of 5 or less. The error estimate increases from 10% at S/N = 5 to 40% at S/N = 3. About 5% of H intensities are low enough that the increased measurement error should be applied. This is never applied to the [O iii]5007 line used for the PNLF in this study. These lines mostly have intensities 4 H and have repeat error estimates no greater than 3% for the faintest PNe. This system however provides a general error estimate for the line measurements in all 631 PNe.

Figure 3: The calibrated [O iii] 5007Å 2dF 300B line fluxes are plotted against the published [O iii] 5007Å fluxes from the MCPN on-line catalogue [MCPN], Jacoby, Walker, Ciadullo 1990b, [JWC] and Leisy & Dennefeld 2006, [LD]. The sample of 85 calibrated data points from 2dF and 13 from VLT FLAMES are drawn from 21 different fibre field exposures. Extremely good agreement can be seen between all the combined data points and published fluxes. Through this calibration method, 2dF and VLT FLAMES line intensities for all the remaining PNe observed in a given 2dF or FLAMES field exposure are reliably calibrated to fainter magnitudes. The mean agreement flux (RP-MCPN) is 0.030.10 dex. A similar mean agreement is found between RP and JWC (-0.0040.11) and RP and LD (0.020.13).

Secondly, there are difficulties in placing exact errors on the individual lines, due to the inherent variations in detector response with wavelength. Luckily, this is the same for all objects on any given field plate exposure and can therefore be estimated from the response curve. The exposure times are also exactly the same across any given field and most of the exposures for the different fields are also of the same duration. With a small error included for these two variables, the remaining difficulty is the different absolute fluxes which cause a variation in the signal to noise. One fortunate aspect of having a relatively large number of PNe re-observed on different 2dF fields is that a comparison between two or more observations of the same object is possible. A comparison of line intensity ratios for the same PN, observed on two or more fields (Figure 4), gives an agreement to within 0.2 dex with =0.15 using a sample of 81 repeated PNe. This discrepancy includes ratios between strong lines and between strong to weak lines.

Figure 4: The [O iii] 5007Å calibrated fluxes for 81 PNe with multiple observations (due to overlapping fields) are plotted in order to check the integrity of the calibration across different observations including different CCD and field plate combinations. A good match (0.2 dex) along the line of equality has been found, where there is a mixture of fields and flux intensities represented over a 4 dex range.

In addition to the estimates for spectral line errors, the flux calibration adds an extra level of error. With a very good calibration of the 300B spectra to the MCPN fluxes (Figure 2), the average difference to the published fluxes following calibration is 0.18 dex with = 0.5. These published fluxes will themselves have both measurement and systematic errors and these have been estimated at 0.2 dex through direct comparison. An allowance is made for these errors to increase with decreasing flux. This estimated increase is based on the standard deviation in the calibrated fluxes, increasing to 0.3 = 0.2 dex.

With ground-based spectroscopy, atmospheric dispersion can produce an extended object on the slit where blue light is separated from red light, also received by the detector (Filippenko, 1982). This effect can cause a systematic difference when comparing standard stars observed at a lower air mass. It can also produce larger images in the blue than in the red due to more blue light being captured by the fibre. The increase is estimated as (1/) (Fried 1966; Boyd 1978). To overcome this problem, 2dF has an ‘Atmospheric Dispersion Compensator’ (ADC) which largely compensates for this. With our flux calibration technique, however, lines from different regions of the optical spectrum are individually calibrated to HST-based fluxes, largely circumventing problems of atmospheric dispersion and the differential air mass of standard stars. A correction for extinction is applied using the Balmer decrement, where the fixed ratio 1:2.86 applies between H and H in the absence of extinction. This corrected ratio is discussed in detail in the following subsection.

In addition to the photometric and flux calibration errors, an error estimate for the inclination of the LMC to the line of sight may be included. This could be as much as 0.04 mag (Jacoby et al. 1990) based on a 1 depth uncertainty.

One further problem can cause errors in flux estimations for LMC PNe. The LMC is filled with faint stars and diffuse emission of varying intensity. For individual slit spectroscopy, it can be extremely difficult to find a region of blank sky along the slit. In the case of 2dF fibre spectroscopy, we dedicated 40 fibres to specially selected sky positions. These positions represented average values of background sky in each field observed. The H map provided the most appropriate positions. For each field, the 2dfdr reduction program sampled and averaged these regions before applying the sky subtraction to the objects. The resulting error estimates for [O iii]5007 as a function of line measurement and flux calibration are based on results from Figures 3 and 4. Line measurement errors increase from 2% to 10% and flux calibration errors increase from 6% to 20%. The line measurement error also includes an estimated error based on a function of the discrepancy between repeated, field to field and line ratio measurements.

3.3 Corrections for extinction and reddening

Extinction of light from distant objects is mainly the result of interstellar dust. The light is both scattered and absorbed, which increases the interstellar extinction towards shorter wavelengths. The amount of extinction will differ for each object and needs to be corrected to gain true fluxes. In the optical regime, the H/H ratio was used to determine the extinction constant cH (i.e., the logarithmic extinction at H for each nebula. These hydrogen transitions are the strongest and easiest to accurately measure in the nebula spectrum and therefore provide a better estimate than other H lines. The observed H/H ratio, when compared to the recombination value of 2.86 (Aller 1984), gives a logarithmic extinction at H of:

(1)

This estimation is based on the relationship between observed and intrinsic intensities:

(2)

where[f (H)-f (H)] = –0.34 from the standard interstellar extinction curve given in Osterbrock (1989) and c(H) is the logarithmic extinction of H. The intrinsic ratio is mildly dependent on temperature: for T between 2,500 and 20,000 K, the ratio varies from 3.30 to 2.76 (Osterbrock, 2006).

The value of c and I() for all other lines was then used to correct for interstellar extinction using the galactic extinction law from Whitford (1958) in the form of Miller & Mathews (1972):

(3)

Reworking this equation for the H line all other lines could be corrected for reddening using:

(4)

Application of the Balmer decrement ratio 2.86 between the H and H lines is able to correct the spectrum in terms of the required ratios however the degree of c is dependent on flux calibration for each of these lines and any internal inconsistencies. For fibre-based observations, the uncertainty in c(H) is extremely difficult to estimate as there may be small inconsistencies between fibres resulting from light transmission and position of the fibre on the plate. These will have an effect on the reddening corrected fluxes. Calibration of both the red and blue sides of the spectra each show a maximum uncertainty of 0.2 dex. This is consistent with the uncertainty found comparing published fluxes, indicating that internal inconsistencies are low. The reddening law of Howarth (1983) where E(B-V) = 0.689c was also employed. It then follows that A = 3.5 E(B-V) and A = 3.63 E(B-V).

When estimating the errors, flux calibration is given predominant consideration together with the wide spectral range between the H and H lines. This is estimated for H using the same method of 2dF flux calibration described above where the H spectral line in each nebula was individually compared to published H fluxes for the same objects. The estimated uncertainty in c(H) as a result of combined maximum errors in line measurement and flux calibration estimations is 7%.

The optical image of every PN was inspected for the presence of diffuse H ii across its immediate field. This was used as a means of testing the environment of PNe with high values of c(H) in the range 1.4 to 2.0. The available 8m Spizer SAGE image (Meixner et al., 2006) was also examined for areas where IR emission extended across individual PNe. This was added confirmation that foreground dust could play a significant role in flux determination for some LMC PNe. The intensity of the ambient emission in H was then measured in counts, where, for a measure below 3 , the noise begins to have a significant effect on the observed PN flux. Velocity measurements (RPb) for PNe and the velocity for the HI disk in the vicinity of each PN were then examined to estimate whether the PN was foreground, within, or background to the bulk of observed emission. From the list of 292 newly discovered ‘true’ PNe, 11 were found in areas of relatively strong H ii emission. Of these, only 2 were identified as lying beyond the visible emission. Of the newly discovered PNe, all 4 ‘likely’ PNe in areas of strong, dense H ii emission (3 the noise) exist within or beyond the H i disk. All of these PNe have values of c(H) 0.8.

Figure 5: The range of derived values for c(H) using the RP and previously known LMC PNe from 2dF 300B spectra. A peak at 0.4 shows the low overall extinction of most LMC PNe. Most of the bright, previously known PNe occupy the range 0-0.4.

Due to the suspected low metallicity of many of the new, faint PNe in the RP LMC sample, as well as the generally low metallicity of all PNe in the LMC compared to the Galaxy (Leisy & Dennefeld, 1996), we also consider the effect of collisional excitation on the H line (Stasiska, 2002) and the effect it may have on the extinction calculation. Because PNe are excited by power-law photoionisation or shock-heating from the central star, collisional excitation and self-absorption can affect the intrinsic Balmer decrement. This can be caused by high T resulting in the H/H ratio no longer holding the canonical recombination value of 2.86 (Osterbrock & Ferland 2006). It is possible that this scenario applies to some PNe in the LMC. Since the de-reddening procedure involves H there may be some overestimation of the extinction c(H). It has been shown that this error, which is independent of extinction, can be large when the lines have far separated wavelengths (Stasiska, 2002). In low metallicity nebulae, there may be a range of evolutionary sequences where H/H is significantly larger than the accepted recombination value. The resulting error has been estimated to be as high as 10%. Since there is no precise means to estimate the amount of correction required, care was taken to identify faint, low mass PNe with high T and extremely high H/H 10 ratios which may have been affected by power-law photoionisation or shock-heating (see Stasiska, 2002 fig. 2). In the LMC sample, 6 PNe with c(H) 0.8 and T 25,000K have been identified. They are marked with a in column 3 of appendix tables 3 and 4. Where inconsistencies (such as ultra-low N/O abundances) are found in 1 of these PNe (RP1584), the cause can be traced to collisional excitation or self absorption affecting c(H).

The derived values for H) are shown in the histogram of Figure 5. Despite low extinction towards the LMC PNe we still find a few PNe with values of c reaching as high as 1.6. Most of the brighter previously known LMC PNe generally occupy the lower range from 0 to 0.6 however some fainter Jacoby (1980) PNe in dusty, nebulous areas have H) values up to 1.0. Results for bright LMC PNe agree with values derived using fluxes in the MCPN catalogue. The majority of these PNe have c(H) between 0 and 0.6 but also range as high as 1.6. For all the RP PNe, there is a peak at 0.4 with the largest proportion of PNe occupying the range 0.3 - 0.5. The mean extinction of 0.4 corresponds to E(B-V)=0.31 mag, which is considerably higher than the line-of-sight reddening of 0.074-0.11 for stars in the LMC (Caldwell & Coulson 1986). It is also higher than a value of 0.2 found for LMC PNe by Herrmann & Ciardullo (2009) using a pre-RP catalogue sample to produce a basic skeleton of our Figure 5 plot. They cover less than half the magnitude range with lower sampling and base the Balmer decrement on estimated H values. Nonetheless, their sample of the bright end also shows evidence of an increase in extinction beginning at 3 magnitudes below the brightest.

Somewhat higher values of H) in the RP sample are to be expected due to their faint magnitudes and often dusty environments. It does suggest that average internal dust reddening may be as great as 0.5 mag. Most of the dust is expected to consist of carbon-rich and dredged-up material, the quantity of which will have dependence on the mass and metallicity of the central star (Doptia et al. 1992). PNe at the bright end mainly occupy the medium excitation range (Reid & Parker 2006c) with central stars ranging in temperature from 80,000K to 126,000K making them very efficient at converting central star luminosity to luminosity in the nebula. Necessary corrections for H) were applied to the whole LMC sample on an individual object basis. The derived values of H) for each previously known and newly discovered PNe are given in appendix Tables 3 and 4 respectively.

When deriving the distance to an extragalactic source using the PNLF, we use the raw [O iii]5007Å fluxes corrected only for foreground reddening. This is because none of the measured PNLFs and simulations to date have included the effects of circumstellar dust. Most surveys have been based on the [O iii]5007Å line. The H line, required to derive c, is extremely difficult to measure from individual objects in external galaxies. Circumstellar dust therefore plays a large part in determining the observed brightness of the PNLF bright end. In order to make the correct comparison, our PNLF for distance determination has only been corrected for foreground reddening. The contribution of Galactic dust was removed assuming a foreground reddening value of E(B-V) = 0.074 (Caldwell & Coulson, 1985).

4 The new PNLF for the LMC

The PNLF is a plot of the total number of PNe in a defined volume at a particular magnitude at a given point of time. Since the [O iii] 5007Å line is generally the brightest line optically emitted by the nebula, it has traditionally been used to plot the PNLF. The raw fluxes are listed in Appendix Tables 4 and 5 for the 164 previously known and 432 newly discovered PNe respectively. The [O iii]5007Å fluxes for the observed PN sample, corrected only for foreground reddening have been transformed to the magnitude system using the relation provided by Jacoby (1989):

(5)

Using the magnitudes, the luminosity function can be displayed through several methods. In principle we can get an approximation to the luminosity function by plotting the number of PNe found within any number of equally spaced luminosity bins. Using this method, all previously known and new RP PNe within the central 25deg of the LMC have been plotted into one of 54 bins, each 0.2 magnitude wide. This luminosity function, based on the foreground de-reddened flux of the [O iii] 5007Å emission line, in magnitudes, is shown as a histogram in Figure 7. The magnitude assigned to each bin represents the magnitude at the central position of each bin. Poisson error bars have been included.

Figure 6: The foreground de-reddened planetary nebulae luminosity function for the central 25 deg of the LMC, with PNe separated into the categories of previously known and true, likely and possible RP PNe in the survey area for this study. The bins are 0.2 mags in width. Poisson error bars are shown. The errors are calculated individually for previously known, true, likely and possible PNe and combined for each bin.
Figure 7: The planetary nebulae luminosity function for the central 25 deg of the LMC, with PNe separated into the categories of previously known and true, likely and possible RP PNe in the survey area for this study. All PNe are individually corrected for internal extinction using the Balmer decrement. The bins are 0.2 mags in width. Poisson error bars are shown. The errors are calculated individually for previously known, true, likely and possible PNe and combined for each bin.
Figure 6: The foreground de-reddened planetary nebulae luminosity function for the central 25 deg of the LMC, with PNe separated into the categories of previously known and true, likely and possible RP PNe in the survey area for this study. The bins are 0.2 mags in width. Poisson error bars are shown. The errors are calculated individually for previously known, true, likely and possible PNe and combined for each bin.
Figure 8: In order to observe the effects of internal dust extinction within the LMC PNe, the foreground de-reddened [O iii]5007Å magnitudes are plotted against extinction. PNe in the brightest 4 magnitudes have low to medium extinction while PNe with medium to high extinction are only found less than 4 magnitudes below the brightest. These highly reddened faint PNe probably have intrinsically fainter cores which have evolved over a longer timescale. It is therefore possible that the dust properties of these objects may be rather different to those of the higher-core mass objects.

In the first PNLF derived for the Magellanic Clouds, Jacoby (1980) using a sample of 41 PNe, demonstrated the theoretical exponential function of Henize & Westerlund (1963), whereby a PN is treated as a uniformly expanding homogeneous sphere ionised by a non-evolving central star. It follows, therefore, that the number of PNe in each luminosity bin is proportional to the time those PNe spend at that luminosity (Jacoby, 1980, Ciardullo et al. 1989, Ciardullo et al. 2004). This may be represented by an exponential curve (Henize & Westerlund, 1963) with a sharp truncation designed to accommodate the bright end (Ciardullo et al. 1989). The resulting curve is described by:

(6)

In this equation, the key parameter  is the absolute magnitude of the brightest possible PN. The limit to the high luminosity of the [O iii] 5007Å line is mainly due to the initial mass of the progenitor star and its evolution to a white dwarf as a function of time in the ranges of 3-11 Gyrs (Jacoby, 1989; Méndez et al., 1993; Stanghellini, 1995; Richer et al., 1997; Jacoby, 1997). This PNLF model has been demonstrated as an excellent standard candle when compared to other distance indicators (Ciardullo, 2006).

It has been shown that there is a weak correlation between the luminosity of and the metallicity of a galaxy (Ciardullo & Jacoby, 1992; Dopita et al. 1992; Richer 1993; Ciardullo et al. 2002, 2005). This trend has been modeled by Dopita et al. (1992), showing that is bright for solar oxygen abundances but fades where metallicity increases or decreases away from solar. The correction for is given by:

(7)

where solar metallicity is assumed to be 12 + log (O/H) = 8.87 (Grevesse, Noels & Sauval 1996) (see Ciardullo et al. 2002 for additional details). The metallicity of the LMC has been determined from the emission lines of H ii regions. A mean value of (12 + log [O/H]) 8.45 0.11 from LMC H ii regions was found by averaging mean values from Dufour, Shields & Talbot (1982), Dennefeld (1989), Monk, Barlow & Clegg (1988) and Ferrarese et al. (2000a). With this value, using the metallicity dependence of Doptia et al. (1992) we find a metal dependence () of 0.1 mag.

In the LMC, the estimated metallicity is low compared to the Galaxy. The low oxygen abundance in LMC PNe, whether inherent or through depletion, also raises the electron temperature thereby increasing the rate of collisional excitations per ion. Since oxygen is a coolant, a decrease in oxygen abundance only decreases the [O iii] 5007Å flux by roughly the square root of the difference in abundance (Jacoby 1989). The central star at the core of a PN affects the luminosity the opposite way to low metallicity. Low metallicity in the progenitor star produces a more massive radius with greater UV flux (Lattanzio 1986). This energy compensates for the decreased emissivity of the nebula. The total [O iii] 5007Å flux then becomes somewhat independent of metallicity.

In order to reveal the effects of dust, internal to the LMC and the environment of each individual PN, we include another PNLF (see Figure 7) where the same objects have been corrected for what we will refer to as ‘internal extinction’ using the Balmer decrement. Both functions have been plotted on the same scale in order to clearly demonstrate the offset caused by extinction. A comparison of the foreground de-reddened (Figure 7) and internally de-reddened (Figure 7) plots shows a highly consistent shape in the function.

Unfortunately, with most external galaxies, it is almost impossible to correct each observed PN for the effects of internal extinction. Remarkably however, Figure 7 implies that if the foreground de-reddened PNLF is simply shifted by applying 1 magnitude of extinction to each object, the internally de-reddened PNLF is recovered, so that the shape of the observed and de-reddened PNLFs are essentially identical. This result is rather surprising since although individual object extinctions vary between 0 cH 1.3 (0 - 2 mag), from a global perspective, the PNLF responds as though each PN has cH = 0.4. The magnitude range and shape of the plot (Figure 7), corrected for internal extinction, has only shifted 1 magnitude brighter than that corrected for line of sight reddening. It implies that the one dimensional PNLF of external galaxies can be modeled by simply applying a mean offset.

In order to observe the effects of internal dust extinction within the LMC PNe, the foreground de-reddened [O iii]5007Å magnitudes are plotted against extinction in Figure 8. PNe in the brightest 4 magnitudes have low to medium extinction (0 to 0.6) while PNe with medium to high extinction (0.6) are only found  4 magnitudes below the brightest. These highly reddened faint PNe probably have intrinsically fainter cores which have evolved over a longer timescale. It is therefore possible that the dust properties of these objects may be rather different to those of the higher-core mass objects. Most of the PNe, across the full magnitude range, are located in the low to medium extinction range. This suggests that, regardless of the diminishing intrinsic luminosity as a consequence of age, a large proportion of these PNe with high-mass cores have evolved fairly rapidly and their surrounding circumstellar envelope, which provides the extinction, have remained of similar opacity.

This is not to say that there has not been evolution within each nebulae such as decreasing electron density against changes in mass. Although the trends shown in Figure 8 are strong, there are selection effects which may come into play. A further study including electron densities, masses and dynamical ages will be required in order to reveal these effects and understand the role played by circumstellar dust.

Figure 9: The planetary nebulae luminosity function for the central 25 deg of the LMC, derived from an homogeneous sample of previously known and RP LMC PNe. In order to use the PNLF for distance determination, the data have only been corrected for line of sight reddening. The data have been binned into 0.2 mag intervals and plotted in log space. The solid line is the log of the truncated exponential curve (Equation 6) as predicted by Ciardullo et al. (1989) convolved for errors and placed at the best-fit position to the bright end of the observed function. Poisson error bars are included. It is assumed that the decreasing number at magnitudes m  21 is due to incompleteness. This provides the first, direct estimation of for [O iii]5007 in the LMC using a 3.4 magnitude range at the bright end of the LMC PNLF.
Figure 10: The bright end of the planetary nebulae luminosity function to mag 19.3 for the central 25 deg of the LMC, binned into 0.2 mag intervals and plotted in linear space. In order to examine the true shape of the [O iii]5007-based PNLF, the data are fully corrected for internal extinction. The broken line is the theoretical truncated exponential curve (Equation 6) as predicted by Ciardullo et al. (1989). Error bars employ poisson statistics. The curve matches the bright end of the function very well. Data bins that exceed 2 away from the theoretical curve are shown as open circles. This provides the first, direct estimation of the extinction corrected value of for [O iii]5007 in the LMC using the bright end of the LMC PNLF.

4.1 New PNLF-based distance estimate to the LMC

The standard means of determining the distance to a galaxy using the PNLF has been previously confined to the brightest 1 or 2 magnitudes. We now extend this range to the brightest 3.4 magnitudes. With a good estimate of completeness to this magnitude depth, we avoid including the effects of any possible dip in the function, 4 magnitudes below the brightest.

To estimate the distance, we use the method to fit a model PNLF to the observed PNLF corrected for foreground reddening (Figure 9). The bright cut-off absolute magnitude () has been estimated as = –4.44 0.05 (Ciardullo et al. 1989, 2002; Jacoby et al. 1992). We adopt this value because it reflects the theoretical dependence of on metallicity (Dopita et al. 1992) and in order to make a direct comparison to previous LMC PNLF distance estimates using this value. This gives us a distance modulus of 18.460.2 for the LMC where the magnitude errors are used as systematic uncertainties for the distance modulus. The error estimate allows for errors in line measurement and calibration, a 1 error in the fit, uncertainties in the distance calibrator galaxy, M31 and the shape model of the PNLF. The previous best PNLF for the LMC using real LMC PNe for a distance estimate is shown as Figure 4 in Jacoby et al (1990b). This figure includes the model exponential curve of Ciardullo et al. (1989). Figure 7 shows that we have only added one extra PNe to the bright end of the function. This being the case, it is not surprising that the distance modulus does not deviate greatly from the distance modulus of 18.44 previously determined by Jacoby et al. (1990b).

Speculation has arisen as to whether the shape of the PNLF itself can be used for distance determinations (eg. Mendez & Soffner, 1997). Only a deep and complete survey can answer this question.

Although it is extremely difficult to place an exact limiting magnitude on our survey data, we are confident that we are complete to 7 mag below the brightest. We are, therefore, in a good position to test if the truncated exponential curve (Ciardullo et al. 1989) is a good predictor of PNLF shape and can be used as a distance indicator.

In order to test this, we fit the theoretical truncated exponential from Ciardullo et al. (1989), to the brightest 6 magnitudes of the PNLF using the Levenberg-Marquardt fit method to achieve the best fit position. To check how well the observed PNLF follows the theoretical exponential curve (equation 6) we ran the Kolmogorov-Smirnov (KS), Anderson Darling and tests since all three work very well with binned data. Three assumed distributions were tested in order to find the best fit. The results represent values of the 0.2 magnitude binning and no poor fitting data points have been smoothed or excluded. The KS test, based on the largest vertical difference between the theoretical and empirical cumulative distribution function, found a statistic of D=0.11 down the brightest 6 magnitudes assuming an exponential distribution.

The threshold value of the significance level (P-value) of 0.677 between the observed and theoretical functions means the null hypothesis (H) that the observed distribution does not match the theoretical distribution must be accepted with a 95% confidence limit. The major departure from the theoretical curve occurs 1.5 magnitudes below the brightest PN and lasts for 1.5 magnitudes. This may be referred to as a dip in the observed function and will be discussed in subsection 4.2. Despite peaks and troughs in the observed function, if one were to estimate PN populations simply by integrating equation 6 over 6 magnitudes one would over estimate the population by only 3%.

Extinction Distribution Kolmogorov Anderson
Smirnov Darling
Foreground Exponential 0.119 2.262 1.147
Normal 0.229 2.072 3.684
Johnson SB 0.074 11.119 N/A
Internal Exponential 0.134 0.781 0.909
Normal 0.257 2.523 4.418
Johnson SB 0.188 14.35 N/A
Table 2: Summary of the goodness of fit tests between the observed and empirical PNLFs.

The same objects, after correction for internal extinction, are plotted in linear space (Figure 10) in order to fit and test the truncated exponential curve while examining the bright end with increased detail. Error bars represent poisson statistics. The same truncated exponential curve, again has a mean bin-to-bin agreement of 87 53% against the observed data over 6 magnitudes. The goodness of fit tests between the observed and empirical PNLFs are summarised in Table 2. Clearly, the exponential increase in the number of PNe to be found with decreasing magnitude, first suggested by Henize & Westerlund et al. (1963) is equally invalid once internal extinction is removed. The close statistical results are also further proof of the identical shape of the observed and internally corrected PNLFs, discussed in section 4.

An up to date compendium of distance estimates to the LMC is shown in Table 3. These results represent a variety of calibration objects, methods and extinction estimates. The PNLF method has been shown to be a very robust method (Ciardullo et al. 2005) across all galaxies tested. Our confirmed distance estimate of 18.46 0.20 is in very good agreement with Cepheid and RR Lyrae distances derived from optical observations. It is also in close agreement with the previous PNLF distance estimate of 18.44 0.18 as found by Jacoby et al. (1990) where the underlying universal luminosity function is used as a probability distribution function. The estimated distance was given by the abscissa of graphed maximum likelihood solutions.

It is extremely encouraging that a direct fit to the bright end of the PNLF using our considerable new data over the first 6 magnitudes has produced a result in keeping with the previous LMC PNLF work using far fewer PNe. This important result shows that the bright end cut-off fit is robust to far less complete PN samples obtained for a galaxy and that its use as a standard candle is not compromised by modest sampling of the bright end of the PNLF.

The 1990 IAU LMC distance consensus of 50 kpc was presented by Mould (1990). Using an absolute magnitude of -4.44 for M in the LMC, the brightest PN would need to have an apparent magnitude of 14.05 to equal the 50 kpc distance. An increase in the value of M would move the PNLF-based distance toward higher distance estimates. Our new PNLF distance indicator places the LMC at precisely 49.2 kpc 0.2 kpc, very close to 48.7 kpc 2.32 kpc, which is the mean distance and mean error found from all the distance results shown in Table 3.

Method Survey Distance Distance
Modulus kpc
B stars Shobbrock and Visvanathan (1987) 18.3 0.2 45.7
Cepheids Feast and Walker (1987) 18.47 0.15 49.4
Cepheids Welch et al. (1987) 18.57 0.05 51.7
Cepheids Visvanathan (1989) 18.42 0.04 48.3
Cepheids Paturel et al. (1997) 18.7 0.02 54.9
Cepheids Luri and Torra et al. (1999) 18.35 0.13 46.7
Cepheids Bono et al. (2002) 18.53 0.08 50.8
Cepheids Keller and Wood (2006) 18.54 0.018 51.0
LT Eclipsing Binary Systems Pietrzyski et al. (2009) 18.50 3% 50.1
LPV & Miras Bergeat, Knapik and Rutily (1998) 18.50 0.17 50.1
Miras Feast (1988) 18.28 0.6 45.3
Model Atmospheres Eastman and Kirshner (1989) 18.45 0.28 48.9
MS fitting Chiosi and Pigatto (1986) 18.5 0.1 50.1
MS fitting Schommer et al. (1984) 18.2 0.2 43.6
MS fitting VandenBerg and Poll (1989) 18.4 47.8
Novae Capaccioli et al. (1990) 18.70 0.2 54.9
O stars Conti, Garmany and Massey (1986) 18.3 0.3 45.7
PNLF Jacoby, Walker and Ciardullo (1990) 18.44 0.18 48.7
PNLF Dopita, Jacoby, Vassiliadis (1992) 18.37 0.15 47.2
PNLF Reid and Parker (this work) (2009) 18.46 0.2 49.2
Red Clump stars Grocholski et al. (2007) 18.40 0.04 47.8
RR Lyraes Reid and Strugnell (1986) 18.37 0.15 47.2
RR Lyraes Walker and Mack (1987) 18.44 0.05 48.7
RR Lyraes Alcock, Alves, Axelrod et al. (2004) 18.43 1.6 48.5
RR Lyraes Catelan and Corts (2008) 18.44 0.11 48.7

LMC short distances.

Table 3: A 20 year compendium of distance estimates to the Large Magellanic Cloud including our new estimate using the LMC PNLF.

4.2 The shape of the PNLF

Since the PN population in the LMC is now one of the most complete, observed samples at fixed distance available, modeling of the PNLF can be undertaken using this population. Although this study has extended the luminosity range to far fainter limits than previously achievable, and is therefore more complete, there still exists the possibility that the most luminous PNe are over-represented due to all surveys being flux-limited. The large number of PNe now available from the RP sample has a strong effect on the shape of the PNLF fainter than 5 absolute magnitudes below the brightest. When examining the overall shape of the LMC PNLF, it is important to remember that the sample includes PNe that are both optically thick and optically thin, hydrogen burners and helium burners, type I and type II PNe (Peimbert 1978), young, middle-aged and old with different evolutionary characteristics and morphologies (Vassiliadis & Wood, 1994; Dopita et al. 1992). It is beyond the scope of this paper to undertake evolutionary modeling of the PNe at this stage, however, the shape of the PNLF can now be examined in detail. Unless specified, we use the PNLF, corrected for internal extinction when discussing the shape of the PNLF and any evolutionary models.

The peak number of PNe occurs at magnitude 19, which is half a magnitude fainter than half the magnitude range of the sample. The distribution on both sides of the peak is rather different. The bright end is relatively flat for the initial 3.5 mag before a steep and almost constant rise to the peak. The faint end drops off far more gradually with only three detections in the faintest bin.

The rapid rise at the bright end, from mag 17.5 (4 mag below the brightest) is a new major feature. It has not been seen before in an observed sample of PNe in any galaxy but was previously predicted due to the mean age of 3-8 Gyr for stars in the LMC (Stryker & Butcher 1981; Frogel & Blanco 1983; Hyland 1991). This places the largest number of PNe close to a luminosity of log (L/L) 3.65-3.75 in keeping with previous predictions (Dopita et al. 1992).

This rise in the function coincides with the faint end of a sudden dip or inflection point found in some extragalactic studies (Ciardullo 2006). Importantly, we don’t see a strong ‘dip’ (also known as the ‘Jacoby dip’) hinted at in the earlier but far more incomplete LMC PNLF (see Figure 7 and 7). Although there is a small decrease in the number of PNe between magnitudes 16.4 and 17.2 it is not a strong feature. Rather, the function is relatively flat until mag 17.2. The dip in the number of PNe occasionally seen at 3.5–4 mag below the bright cut-off (eg. Jacoby & De Marco, 2002) has been attributed to the decline in luminosity of the central star as it starts descending the White Dwarf (WD) cooling track (eg. Frew 2008). Alternatively, it may indicate that the PN evolutionary phase can occur at different luminosity levels for stars of different progenitor masses where 4 magnitudes below the brightest is representative of the largest group. It may also be evidence for the bimodal luminosity function expected from post-AGB stars (Vassiliadis & Wood, 1994). Interestingly, the PNe populations sampled in star forming galaxies exhibit a broad dip at 1.5-2 magnitudes below the brightest. Both PNLFs (Figures 7 and 7, corrected for foreground and internal extinction respectively, show some convincing evidence for the existence of this dip. This is characteristic of galaxies and models in which the evolution of [O iii] 5007Å in PNe is governed by the rapid evolution of a high mass core.

Figure 11: The planetary nebulae luminosity function for the central 25 deg of the LMC in 0.4 magnitude bins. The overall shape of the PNLF begins to resemble that simulated by Méndez et al (2008, Fig.7). The simulation resulted in a smooth distribution which may be close to the truth once all the bright PNe across the LMC are included in the PNLF. The truncated exponential curve (Ciadullo et al. 1989) has been included for comparison. Although we point out the broadly linear distribution at the faint end, no scientific conclusions can be drawn from this result as the faint end of the PNLF will suffer from incompleteness. It is however worth noting that our survey, to a depth of mag 25 in [O iii]5007, shows this linear decline.

By graphing the PNLF into 0.4 magnitude bins as a smoothed frequency distribution (Figure 11), it becomes easier to identify any possible evolutionary dips in the shape of the PNLF. By including the truncated exponential curve we have a clearer impression of the dip between magnitudes 15 and 16. Overall, however, we see a relatively flat distribution over the brightest 3 to 4 magnitudes followed by a steep rise in the function. It agrees very well with the theoretically simulated PNLF created by Méndez et al. (2008), where there is a sudden rise at the bright end followed by a very gradual decline for 4 magnitudes and a steep rise over 2 magnitudes to a peak in the function. The reason for the function remaining relatively flat for 4 magnitudes may be related to the bright LMC PNe being a combination of H-burning and He-burning central stars with a small proportion of low mass H-burners. Figure 7 in Méndez at el. (2008) shows that the function steadily rises with no dip if the simulation includes too many central stars with masses as low as 0.55M. It conversely dips too low if there are too many high mass central stars. The relatively steady distribution over the brightest 4 magnitudes of the LMC PNLF found through this study adds weight to probability that central star mass plays a major role in shaping the bright end; especially if we accept that the steep rise 4 mags in represents the point at which the central star starts its descent down the WD cooling track.

The number of PNe identified in our deep H survey begins to decline at magnitudes m 19. Is this due to incompleteness or is there a real turnover close to this point in the function? The decline begins rather steeply over the next 4 mag but clearly becomes increasingly incomplete in the faintest two magnitudes of the survey (mag 23 25). If the theoretical and empirical PNLFs (Jacoby 1989; Ciardullo et al. 1989) were employed beyond the peak magnitude of 19 as found in this work, they would predict the presence of a large number of PNe by magnitude 25. Are they there? Is there sufficient mass in the LMC to permit the co-existence of tens of thousands of faint PNe at this end of the function?

It would be very surprising if we have missed detecting hundreds of PNe more than 5 magnitudes brighter than our detection limit. Our PNe were selected using a deep H filter (see RPa) which includes the [N ii]6548 and 6583Å lines. Deep PN surveys of the LMC have already been conducted using [O iii] filters with enormous success (RPa). Our survey using H and [N ii] has allowed us to discover a large number of PNe with extremely low [O iii] levels. Where [O iii] is low in abundance, [N ii] is normally enhanced (RPa,b), permitting us to uncover a large population of PNe that would be very difficult to discover in an [O iii] survey. Even so, it is always possible that a deeper [O iii] survey and new extraction techniques may uncover more PNe. The only really hard constraint on the number of PNe to be found in the LMC comes from stellar evolutionary theory. The number of PNe shouldn’t be greater than the product of the stellar evolutionary flux (2E-11 stars yr L) times the LMC bolometric luminosity times the PN lifetime. Our previous work (RPb) estimates the existence of 956  141 PNe in the LMC, in close agreement with an earlier estimation of 996 by Jacoby (1980). The derived luminosity-specific number of PNe () in the LMC according to Buzzoni et al. (2006), is given as log = -6.57  0.04, representing 1040  60 PNe.

We therefore suggest that a turnover is likely to occur at some midpoint in the function. At this stage, we can safely say that equation 6 represents the bright end of the PNLF with a range of 6 magnitudes. After this initial 6 magnitudes and the peak in the PNLF, there is likely to be a flattening or even a decline in the number of PNe to be found. Only further deep surveys will be able to solve this issue conclusively.

4.3 Luminosity implied time

If we accept that the number of PNe in each luminosity bin is generally proportional to the time those PNe spend at that luminosity (Jacoby 1980; Ciardullo et al. 1989; Ciardullo et al. 2004), then we may conclude that PNe evolve away from the brightest 3 magnitudes at a proportionally fast pace. The time spent at each luminosity bin is plotted in Figure 12 where each luminosity bin is 1 magnitude wide. This histogram ignores the possible incompleteness of the faint end. It is also insensitive to any intrinsic variation and ‘birth-to-death’ luminosity range for a given PN as progenitors range between 1 and 8 M. Many PNe may have low-luminosity cores, and therefore join the luminosity function at fainter magnitudes. A simulated increase of the faintest 2 magnitudes would further decrease the percentages at the bright end. All this plot can effectively show is the number of PNe that may be found per luminosity bin at a single instant of time.

Each bin has been scaled as a percentage of the number of PNe in the whole sample. Figure 16 shows that the percentage of PNe in the brightest 4 magnitudes accounts for only 14.6% of all LMC PNe within the deep sample. In other words, 40% of the magnitude range contains only 14.6% of the PNe. It has been suggested that this drop in number density brighter than mag 18 is due to the negative slope of the initial mass function, especially effecting young stellar populations (Shaw, 1989) and the rapidly accelerating rate of evolution across the H-R diagram with increasing luminosity, particularly evident on the hydrogen-burning tracks (Dopita et al. 1992). Simulations conducted by Méndez et al. (1993) suggest that these PNe at the bright end are also predominantly optically thin.

Figure 12: The percentage of PNe at each luminosity bin represents the percentage of time PNe spend at that luminosity according to predictions of Jacoby (1980); Ciardullo et al. (1989) and Ciardullo et al. (2004). This plot ignores the possible incompleteness of the faint end. It is also insensitive to any intrinsic variation and ‘birth-to-death’ luminosity range for a given PN as progenitors range between 1 and 8 M. A simulated increase of the faintest 2 magnitudes would further decrease the percentages at the bright end.

4.4 The cumulative PNLF and comparisons with other galaxies

In order to compare the depth of our derived PNLF with previous LMC PNLF models and PNLF in other galaxies, we create a cumulative distribution of the function. We present the cumulative function as a percentage of PNe found at each magnitude and compare this to model cumulative functions. This approach helps to reveal the positions at which incompleteness begins to set in. It also shows the way in which incompleteness affects the overall shape of the cumulative function.

The cumulative LMC PNLF for [O iii]5007 is shown in Figure 13 where it is compared with the cumulative PNLFs calculated in the same way for the SMC, using data from Jacoby (2006) and for local PNe using the new highly complete local Galactic volume catalogue of Frew (2008) which includes PNe out to 3kpc. These objects are included in the MASH catalogue of Parker et al (2006). Although each PNLF is affected by incompleteness, compared to the LMC, the local and SMC samples have a larger percentage of PNe in the brightest 6 magnitude range (41% for the LMC, compared to 54% for the SMC and 55% for the local PNLFs). The shape of the bright end of the PNLF is therefore very sensitive to the relative number of PNe included at the very brightest magnitude. It is also sensitive to the peak number density, the flux limit of the survey and the decreasing number of PNe at the faint end.

The large increase in the number of LMC PNe between 4 and the peak at 7 magnitudes below the brightest causes the LMC PNLF to rise away from the predicted exponential curve. With an identical magnitude range, the local PNLF shows a more constant rise. The SMC PNLF, with its smaller magnitude range, shows a small dip between 4 and 5 mag below the brightest, after which it also rises steeply. The steepest section of each cumulative function represents a rise to the peak in number density. This feature is easiest to see in the LMC PNLF, however, it’s presence also in the SMC and between 6 and 7.5 magnitude ranges in the local PNLF suggests that it may be common to PN evolution in most galaxies.

The final three magnitudes of the LMC PNLF show a gradual turnover towards the faint drop-off. A stronger turnover is also seen in the local sample, affecting the final 2 magnitudes, with only 8% of PNe found in this range, prior to the faint drop-off. These turnovers are the result of incompleteness at the faint end, where we would expect the number of PNe to either rise or remain stable beyond the peak density (6 mag below the brightest). We do not discount the possibility that a certain drop in number density towards the faint end may be a real feature suggesting that most PNe spend the majority of their lifecycle between 4 and 7 magnitudes below the brightest. The SMC PNLF only shows a turnover (drop in number density) in the final magnitude of its faint end. This short turnover would normally indicate that the SMC PNLF is more complete up to its final magnitude drop-off than the other two PNLFs. The SMC faint turnover, however, also coincides with the drop-off from the peak number density in the LMC PNLF. The LMC contains a further 228 PNe fainter than this magnitude. Therefore, the faint end of the SMC PNLF is actually less complete than the other two and we predict more PNe be found 4 mag below the brightest and 3 magnitudes deeper than currently available.

Using equation 6, Méndez et al. (1993) have obtained the cumulative PNLF for any magnitude M fainter than the cutoff by integrating N(M) between and M using the following formula:

(8)

The dotted lines in Figure 13 represent this predicted cumulative PNLF from Eq. (8), adjusted to fit the magnitude range of PNe in the SMC and LMC. Comparing this predicted curve to the SMC PNLF suggests there is a lack of PNe in the range 4-6 below the brightest. This is affecting the overall shape of this PNLF and creating the upward ‘hump’ from 1 to 4 mag below the brightest. The cumulative curve from Eq. (8), when fitted to the LMC, agrees very well at the brightest 4 magnitudes. After this, it does not follow the strong peak in the function but continues at a steady exponential rate. A larger number of PNe at the faintest 3 magnitudes would effectively bring the LMC PNLF closer to the predicted curve. The local PNLF also shares a 10 mag range in [O iii] and so shares the same predicted curve as our LMC PNLF, but traces out a path much further to the bright end and away from the simulated PNLF. This position for the local PNLF, when compared to the LMC PNLF either suggests that there should be a great many more faint PNe (6 mag below the brightest) to be found within the local 3 kpc radii range or the local PNLF is affected by selection effects since it is only sampling a relatively small region of our Galaxy.

While the formula of Ciardullo et al. (1989) results in a constantly increasing PNLF towards fainter magnitudes, the simulated PNLF of Méndez et al. (1997) produces two rises and declines. The first decline is between [O iii] 5007Å magnitudes -3.5 and -2.5 (Méndez et al. 1997, fig. 4). It then rises again from mags fainter than -2.3 until it reaches a peak at –0.2. From this point, it begins a steady decline. This simulation however was re-worked to allow for PNe on cooling tracks by including a random distribution of the absorbing factor between 0.1 and 1. With this adjustment, the simulation fits the formula of Ciardullo et al. (1989) very well (see Méndez et al. 1997, fig 5). This was a prediction, where severe incompleteness hampered any true test with observations. The simulation of Méndez et al. (1997, fig. 5) after a correction to allow absorbing factors to tend to 0, shows a peak in the function at mag 6 and a faint end decline from that point. This is exactly what is seen in the LMC PNLF using the RP sample (Figure 13). This in turn strengthens the case for a strong rise in the function from 4 magnitudes below the brightest. This rise is the result of an evolutionary change where a young, high mass and luminous PN reaches a peak in its photoionisation potential. It then shifts towards the WD cooling track with increasingly lower density to mass ratios. The sudden rise in number density shows that this change occurs rapidly.

Figure 13: The cumulative PNLFs for [O iii]5007 using the new PNLF for the central LMC (solid line - this work), the revised deep SMC PNLF of Jacoby (2006) and a deep local sample from Frew (2008), to a volume radii of 3.0kpc, centred on the sun. The dotted lines are the plots of Eq. (8) from Méndez et al. (1993) with c = 12 for the SMC, c = 6 for the LMC and local PNLF to 3kpc, c = 0.307 for both.

The extension of the PNLF to fainter magnitudes describes complete population effects as predicted by the Shklovski model (1981) and permits us to observe what effect the faint PN population may reveal for successful PNLF modeling. It is hoped that this will in turn help to further refine PNLF simulations.

5 The potential of the LMC H Pnlf

The PNLF is essentially based on the evolution of the central ionising star (Jacoby, 1989). In particular, the H intensity is a measure of the central star’s ionising luminosity (Osterbrock, 1989) and can also indicate the heating of the nebula as long as it is optically thick. This would indicate that a hydrogen emission line would also be a natural choice for a PNLF. Since the evolution of the central star’s luminosity gives rise to the PN luminosity function, there should be a correlation between the relative strengths of the integrated [O iii] 5007Å and H fluxes. The H line is also less influenced by the metallicity of the parent galaxy, which could make it an ideal choice for distance determination. A PNLF was constructed using H in order to discover the bright cutoff and shape of the function. A comparison with the [O iii]5007 PNLF should then reveal broad influences of the LMC’s low metallicity. The H flux by comparison is typically  5 times fainter than [O iii]5007 in most PNe making it much more difficult to spectroscopically measure in external galaxies. This is why H is not generally used for distance determination. H has a bright cut-off at about 2.4 mag fainter than that of [O iii] 5007Å.

Figure 14: The H planetary nebulae luminosity function for the central 25 deg of the LMC, with PNe separated into the categories of previously known, true, likely and possible PNe in the survey area for this study. Only foreground de-reddening has been applied to the raw magnitudes. The bins are 0.2 mags in width. Poisson error bars are included. The errors are calculated individually for previously known, true, likely and possible PNe as shown in Tables 4 & 5 and then combined for each magnitude bin.
Figure 15: The H planetary nebulae luminosity function for the central 25 deg of the LMC, with PNe separated into the categories of previously known, true, likely and possible PNe in the survey area for this study. A correction for internal extinction has been applied to each PNe using the Balmer decrement. The bins are 0.2 mags in width. Poisson error bars have been included. The errors are calculated individually for previously known, true, likely and possible PNe as shown in Tables 4 & 5 and then combined for each magnitude bin.
Figure 14: The H planetary nebulae luminosity function for the central 25 deg of the LMC, with PNe separated into the categories of previously known, true, likely and possible PNe in the survey area for this study. Only foreground de-reddening has been applied to the raw magnitudes. The bins are 0.2 mags in width. Poisson error bars are included. The errors are calculated individually for previously known, true, likely and possible PNe as shown in Tables 4 & 5 and then combined for each magnitude bin.

For optically thick PNe, the H flux should be a reliable indicator of stellar luminosity. The maximum conversion efficiency from stellar luminosity to luminosity in the H line only varies by a factor of 2, even though a maximum of just under 1% of stellar luminosity is converted into H photons (Dopita et al. 1992). Dopita et al. (1992) have found the variation in this conversion efficiency to be even less.

In order to convert our H fluxes, expressed in ergs cm s, to magnitudes, we use the definition given by Jacoby (1989):

(9)

where f represents the flux to be roughly converted to the broad V-band magnitude. The close interval between the [O iii]5007Å and H lines allows use of the same definition to convert fluxes from ergs cm s, to magnitudes for both lines. This technique, previously adopted by Mndez et al. (1993), allows us to make a direct comparison between [O iii]5007Å and H magnitudes on the same scale. The luminosity function for the H line is shown in Figure 15 for foreground de-reddened objects where the brightest PN is found at an apparent magnitude of = 16.8 In Figure 15 the PNLF is shown following correction for internal extinction where the brightest PN is found at an apparent magnitude of 16.2.

In Figure 16 we show the H PNLF as a log plot with the truncated exponential curve of Ciardullo et al. (1989) added for comparison. The curve has been placed at the best fit to the bright end, using the Levenberg-Marquardt fit method. Using the bright intersection of the curve with the x-axis, a value of M = 16.80.21 was found. This corresponds to an absolute magnitude of -1.680.21 for M. Statistically, the goodness of fit tests to the theoretical exponential curve give F=1.31, a KS statistic of 0.13 and statistic of 2.85 providing 95% confidence limits that the observed PNLF is unlikely to be drawn from the empirical one. At present there is little data on extragalactic H fluxes available with which to compare these results. Stanghellini (1995) constructed an H PNLF for the Magellanic Clouds based on the fluxes of Richer (private communication) together with a simulation of 1000 optically thick PNe using Salpeter’s IMF and Weidemann’s initial mass-final mass relation, with M = 0.7 M (Weidemann 1987). This data produced very encouraging comparisons, however, variations in the mass truncation produced significantly different results. Using M = 0.7 M, the peak in the distribution occurred only 1 magnitude below the brightest PN. Increasing M to 1.4 M shifted the peak 2.2 magnitudes fainter but the entire distribution only covered a 4 magnitude range.

The bright end only is plotted in linear space in Figure 17 using the same data corrected for internal extinction. Analogous to the [O iii]5007Å function, the brightest PN in the H function also increases 0.8 magnitudes after correction. Assuming an exponential growth in the function, and comparing the empirical PNLF of Ciardullo et al. (1989), the KS statistic is 0.122 and the statistic is 5.0. This indicates that the observed PNLF is unlikely to be drawn from the extrapolated one at the 90% confidence level.

Improved simulations of the empirical PNLF were presented for both the [O iii]5007Å and H lines by Méndez and Soffner (1997). By varying the estimated fraction of stellar ionising luminosity absorbed by the nebula, better known as the absorbing factor , and using available evolutionary tracks to produce a good representation of varying , mass and log L for 3000 100 year intervals between 0 and 30,000 years, they produced good representations to the standard predictions of Ciardullo (1995). Their Fig.6 simulation of the H PNLF shows a peak in the distribution at precisely the same position of M = 3.8 found in this study using real LMC PNe. This remarkable match to model predictions proves that not all PNe on cooling tracks can have = 1, since that would create a strong hump at the peak and make fainter PNe extremely hard to find. The values of most likely vary between 0.1 and 1 between ages of 1 and 30,000 years.

Figure 16: The H planetary nebulae luminosity function for the central 25 deg of the LMC, derived from a homogeneous sample of LMC PNe with m 27.0. The data have been binned into 0.2 mag intervals and plotted in log space. Error bars are based on poisson statistics. The solid line is the truncated exponential curve as predicted by Ciardullo et al. (1989) convolved for errors and placed at the best fit position. It marks out magnitude 16.8 as the position of m. The curve matches the brightest 6 magnitudes of the function quite well. It is assumed that the falloff at magnitudes m 24 is due to incompleteness.
Figure 17: The bright end of the H planetary nebulae luminosity function to mag 21.4 for the central 25 deg of the LMC, binned into 0.2 mag intervals and plotted in linear space. The broken line is the truncated exponential curve as predicted by Ciardullo et al. (1989). Error bars are based on poisson statistics. The curve matches the bright end of the function well. This provides the first, direct estimation of H for the LMC using the bright end of the LMC PNLF.

5.1 PNe with low central star temperatures

It is important to note that we have found 3 PNe (SMP numbers 64, 31, 55) with very high H fluxes belonging to excitation class 1, the lowest category (Reid & Parker, 2009). In RPb, SMP64 and SMP31 were classified as possible PNe belonging to a class known as Very Low Excitation (VLE) PNe. They have central stars with T so low (31,200 K to 38,500 K) that the [O iii]5007Å is extremely low by comparison to H (details in RPb). A further 4 PNe (SMP67, 77, 76 and MG62) also have [O iii]5007/H flux ratios 3, low excitation classes from 2 to 3 and T between 46,500 K and 64,200 K. The presence of VLE PNe has previously been reported by Méndez et al. (1993) and can be seen in Fig. 4a of Doptia et al. (1992) for several Magellanic Cloud PNe.

In order for the H luminosity to remain constantly high in these PNe, the number of ionising photons from the central star must increase by a factor of 2.5 as the temperature increases from T 30,000 K to 70,000 K. If these nebulae were optically thick, we would expect a proportional increase in the H luminosity with increasing central star temperature. To keep these nebulae constantly bright on the horizontal portion of the post-AGB evolutionary tracks, Méndez et al. (1993) suggest they must be optically thin in the H Lyman continuum. The fraction of stellar ionising luminosity absorbed by the nebula, defined as the absorbing factor, , (Méndez et al. 1992) may also play a defining role here. Another possibility is that many of these central stars are burning He rather than H. This might account for a decrease in luminosity as T increases.

5.2 [O iii]5007 vs H magnitudes

Comparisons have been previously drawn between the [O iii]5007Å and H + [N ii] line ratios in a given population of extragalactic PNe (eg. Ciardullo et al. 2002, 2004). The H, being the brightest line in the Balmer series, is the easiest hydrogen line to measure in extra-galactic PNe. Unfortunately, due to filter responses, it usually includes the adjacent [N ii]6548Å + 6583Å lines. The LMC is close enough that the H line is easy to measure using our spectroscopic observations. Since it is cleanly separated and yet relatively close to the [O iii]5007 line in the optical spectrum, the ratios will be less affected by errors in flux calibration and extinction estimates.

The shape of the H PNLF has strong similarities to that of [O iii] Figure 7 but there some differences. Once again there is a peak to the distribution, however, it is not as strongly marked as its counterpart in [O iii]. With the H peak occurring at magnitude 22.4 (absolute mag 2.6), 5 magnitudes below the brightest, 48% or 287 PNe have fluxes occurring at the bright end. This may be compared with the [O iii] function where the peak occurs at magnitude 20.4 (absolute mag 0.4), however only 242 or 41% of PNe are found at the bright end of the peak. This is despite the [O iii] peak occurring 5.2 magnitudes below the brightest, which is relatively 0.2 magnitudes fainter than the peak in H. In general terms, across a broad range of evolution, this suggests that the H flux increases and fades at a steadier rate than [O iii] flux. The [O iii] flux appears to be highly sensitive to evolutionary spikes and dips whereas the H flux is more sensitive to the opacity of the nebula. It also suggests that the central star evolves over the dynamic lifetime of a PN as it ionises the uniformly expanding shells (Henize & Westerlund, 1963), affecting temperature, luminosity and excitation of the nebula. These parameters will be closely examined in a further paper in this series.

All the previously known and new PN in this survey are included in Figure 18 where the [O iii] 5007Å magnitudes are plotted against the H magnitudes, both de-reddened and corrected for extinction. The correction between the line fluxes is generally very small. Even for a huge reddening of E(B–V)=1.0, the differential reddening between [O iii] 5007Å and H is less than 0.06 dex (Schild, 1977).

Figure 18 shows that the [O iii] 5007Å line intensities span 10 magnitudes. The H line intensities on the other hand only span 8.5 magnitudes. A faint dotted line included in Figure 18 represents the H function, moved to the best fitting position with the [O iii]5007 function. Statistically, on a bin-to-bin basis, there is an agreement of 82% between them. This, however, should be viewed only in terms of overall shape of the PNLF since [O iii]5007/H in individual PNe may vary by as much as 2.5 magnitudes. With this in place, it becomes apparent that [O iii]5007 fluxes extend approximately 1 magnitude brighter than the bright end of the H function. Assuming an exponential distribution, the KS statistic is 0.10 and the statistic is 9.72 indicating a 92% probability that the two functions do not correspond. Nonetheless, we cannot statistically exclude the possibility that the two samples are essentially the same shape.

At the bright end, the H PNLF like that of [O iii] 5007Å starts to climb almost immediately without any strongly defined dips but a series of peaks and troughs. This may indicate that the central star’s progression onto the WD cooling track has little immediate impact on stellar luminosity. Although the stellar temperature begins to fall, causing a dip in the [O iii]5007Å line, the H flux is maintained longer, probably due to the higher ionisation potential of H.

Although the transition probability (3 to 1) between the [O iii]5007Å and 4959Å lines (Osterbrock & Ferland, 2006) remains constant, our measurements of PNe in the LMC show that the H flux varies widely by comparison to these lines. Combined [O iii]5007Å + 4959Å fluxes lie between 62 and 0.9 the strength of H PN fluxes in the LMC survey sample. Figure 19 directly compares the measured fluxes. A fitted trend line shows a steady regression towards the line of equality with fainter magnitudes. PNe at the brightest 4 magnitudes have consistently high 5007/4861Å ratios. The marked lack of low 5007/4861Å ratios in this region suggests that these PNe are young, optically thick, medium to high excitation PNe with central stars which have not yet reached the WD cooling track.

PNe with low [O iii] fluxes, -0.9 to 2 times H are found in both faint, highly evolved PNe and within magnitude ranges fainter than 18. Other diagnostics such as high [N ii]6583/H together with morphology, when available from HST images, help to distinguish these candidates as possible Very Low Excitation (VLE) PNe. The mean ratio ([O iii]5007,4959/H) across the entire central 25deg survey region is 8.937.31. By far, the majority (94%) of [O iii]5007 + 4959 fluxes are below 20  H fluxes.

Figure 18: The planetary nebulae luminosity functions of H and [O iii]5007, corrected for extinction, are directly compared using all PNe uncovered in the central 25 deg of the LMC. The data have been binned into 0.2 mag intervals and plotted according to their measured and corrected magnitudes. The bright cut-off for H occurs at magnitude 16.8, 2.4 magnitudes below that of [O iii]5007. At the peak of the distributions (shown) the magnitude (H-[O iii]5007) is reduced to 1.8 magnitudes and remains at approximately this level to the faint cut-off.
Figure 19: A direct comparison of [O iii]5007Å and H4861Å apparent magnitudes corrected for internal extinction shows a steady regression towards the line of equality with fainter magnitudes. The faint trend line marks out this regression while the darker line represents the line of equality where the 5007Å and 4861Å magnitudes would be equal. PNe in the brightest 4 magnitudes mainly exhibit high 5007/4861Å ratios.

The H bright cutoff occurs 2.4 magnitudes fainter than the equivalent position for [O iii]5007Å. Figure 19 shows that PNe with the brightest H fluxes also have strong [O iii]5007Å fluxes. In fact, sampling the brightest 50 H fluxes, the average [O iii]5007Å flux is 8.9 times H. These include mostly medium and some high excitation PNe with central star temperatures between T =31,800 K and 136,000 K.

Figure 20: The cumulative PNLF using the [O iii]5007 line (left) and H4861 line (right). The bright end of the PNLF, traditionally used for distance determination, is marked on both wavelengths. Both lines equally contribute to this section of the function, making either a good choice for modeling the bright end and distance estimations. The stronger peak in the [O iii]5007Å function results in the oscillation seen either side of the arrow, to the right and left of the central line.

The H PNLF shows the same rather flat distribution seen across the initial 2 brightest magnitudes of the [O iii]5007Å PNLF. The initial peak in the H distribution is only 1.8 magnitudes fainter than the equivalent position for [O iii]5007Å. Similarly the faintest PNe in each wavelength are generally 1.8 magnitudes in separation. Both of these PNLF estimates agree closely with the average magnitude difference of 1.7 0.9 by directly comparing 591 LMC PNe. By comparison, if we average the magnitude difference between [O iii]5007Å and H for the brightest 30 PNe in H, the result is a much higher 2.3 0.6 mag difference. The flat distribution at the bright end of the [O iii]5007Å PNLF is therefore the result of a bright extension, peculiar to the bright end of the [O iii]5007Å PNLF. This extension is an average 0.6 mag greater than the average difference for the remaining 95% of PNe. These results, despite the evolutionary effects, indicate that the temperature of the central star is the most dominant contributor to the PN luminosity function (eg. Jacoby 1989), giving rise to both the H and [O iii]5007Å luminosity.

The raw cumulative luminosity functions derived from the [O iii] and H magnitudes are shown in Figure 20. In each case, the bright end of the functions are fitted with a straight line, indicating the upper luminosity cutoff. This line traditionally represents the observational basis for distance estimates once corrections for reddening and luminosity efficiency of the [O iii] or H line photons are made. The graphs clearly show however, that most PNe follow the steeper slope which represents the greatest growth, peak and fall in the function. The number of PNe on this line is equal in [O iii]5007Å and H (70-75% for both). The stronger peak in the [O iii]5007Å function results in the oscillation seen either side of the arrow, to the right and left of the central line.

Tables 4 and 5 in the appendix provide a compendium of H and [O iii]5007Å raw flux estimates for previously known and newly discovered RP PNe respectively in the Large Magellanic Cloud. The tables also include the measured values of cH and the estimated errors. Table 5 includes the PN object probability where ‘T’ represents ‘True’, ‘L’ represents ‘Likely’ and ‘P’ represents ‘Possible’.

It is anticipated that once the RP survey is extended to the outer LMC, a similar shape for the PNLF to that newly obtained for the central 25 deg would be found. The increase in total numbers should create a much tighter fit to the exponential curve, providing a very accurate distance estimate. The combination of previously known and newly discovered PNe in this study currently provide the most accurate estimate for the shape of the LMC PNLF obtained thus far.

6 Conclusion

Due to the depth of the UKST multi-stacked H survey, the subsequently uncovered large RP PN sample is able to show the influence of population effects on the shape of the PNLF for the first time. We present details of a new technique for the flux calibration of fibre-based spectra. Using this technique, we provide carefully calibrated [O iii]5007Å and H flux estimates from 2dF and FLAMES spectra together with fluxes from calibrated longslit spectra for 584 LMC PNe. These fluxes are converted to magnitudes and used to construct a PNLF in [O iii] and in H. The PNe are separated into previously known and newly discovered PNe where a significant increase in the number of LMC PNe below an apparent magnitude of 18.6 in [O iii]5007 is possible thanks to this work. The [O iii]5007Å PNLF is used to directly estimate the distance to the LMC. By fitting an exponential curve to the bright end of the function over a 6 magnitude range, an m value of 14.02 is found. Applying the accepted M value of -4.44, we find a distance modulus of 18.46 for the LMC. This is in excellent agreement with the best recent calibrations (see table 2). The bright end cutoff is found to be robust to small samples of bright PNe since our significantly increased PN samples have no effect on this fiducial.

We find a peak in the [O iii]5007 PNLF 6 mags below the brightest. This peak was previously predicted but not seen in a real sample until now. The steep rise to the peak in the function over a 2 mag range was also not seen before but was also predicted due to the position of the WD cooling track and a mixture of H and He-burning stars in the LMC. Not withstanding incompleteness, the faint end of the PNLF can now be examined for the first time. Over a 4 mag range we find a linear drop-off in the number of PNe per mag bin.

A comparison of the foreground de-reddened [O iii]5007 PNLF with the same [O iii]5007 PNLF after correction for internal extinction reveals almost no change in the overall shape of the PNLF. If the observed PNLF is shifted by applying 1 magnitude of extinction to each object, then the de-reddened PNLF can be almost exactly recovered. This remarkable finding means that although the PN extinction ranges from 0 c(H) 1.3, from a global prospective, the PNLF acts as if each one has c(H) = 0.4. This will clearly make it easier to model the PNLF in distant galaxies, as it implies that, for a 1 dimensional analysis, there is only a mean offset to be applied.

We have constructed the first LMC PNLF in H using 591 measured PN spectra. We find a value of 16.8 for the m bright cut-off. This leads to an estimate of M = –1.68 for H-based PNLF distance estimates.

A clear relation is found between the shape of the [O iii] 5007Å and the H PNLF with a mean difference of 2.8 magnitudes at the bright cut-off decreasing to 1.8 magnitudes by the peak of the distributions or 6 magnitudes below m.

The new LMC PNLF is compared to a new PNLF constructed using local Galactic PNe to 3kpc and the newest sample from the SMC. The magnitude range is almost exactly the same for both the LMC and local surveys. A small dip 3 and 4 mag below the brightest is evident in the local and LMC surveys respectively. The rollover at the faint end of the PNLF is generally interpreted as a sign of incompleteness in the survey, where the rollover occurs across the faintest 1 or 2 magnitudes. Using 584 PNe in the RP sample from this survey, the rollover occurs over 1.5 magnitudes, causing the shape of the faint end to inversely reflect the shape of the PNLF at the bright end. This would indicate that the peak distribution found in this work is close to the true peak distribution for LMC PNe. This occurs at an absolute magnitude of 0.8. By comparison, the peak distribution of local Galactic PNe occurs at an absolute magnitude of 2, 1.2 magnitudes fainter than that found for the LMC.

Once we complete our survey by including the outer LMC, we expect the estimated extra 80 PNe at the bright end of the function will fill out much of the exponential curve. It should thereby clarify the position of the rise, 4 mags below the brightest and the position of any dip if they exist. The extra objects are not expected to alter the distance modulus of 18.46; similar to the result found by Jacoby (1989). Final results will largely depend on individual luminosities up to 6 magnitudes below m.

Acknowledgments

The authors wish to thank the AAO board for observing time on the AAT and UKST. The authors also thank the European Southern Observatory for observing time on the VLT and Australian National University along with their telescope time allocation committees for supporting our programme of follow-up spectroscopy. We thank Martin Cohen for making SAGE data available and assisting in the followup analysis of LMC PNe. We also thank Robin Ciardullo for very helpful comments and suggestions while carefully reviewing the paper. WR thanks Macquarie University, Sydney, for travel grants.

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Appendix A Appendix

RP Common cH Flux H Flux [O iii]
Ref. Nomenclature 4861Å 5007Å
(erg cm s) (erg cm s)
10 SMP88 WS27 0.56 4.63E-14 2.3E-15 2.02E-13 1.0E-14
12 SMP90 0.42 3.65E-14 1.8E-15 2.31E-13 1.1E-14
74 Mo35 0.46 4.94E-15 4.9E-16 3.78E-14 3.2E-14
75 Mo40 0.34 6.42E-15 5.4E-15 4.61E-14 2.5E-14
106 LM2-40 N217 0.65 1.28E-15 1.2E-16 4.12E-15 3.5E-15
133 SMP89 WS38 0.35 2.09E-13 1.0E-14 2.80E-12 1.4E-13
134 Mo39 0.48 3.51E-15 3.5E-16 2.66E-14 2.2E-14
152 Mo37 0.34 1.25E-14 6.2E-16 6.78E-14 3.3E-15
179 Mo36 0.32 6.13E-15 5.2E-15 5.71E-14 3.1E-14
209 SMP93 0.33 4.35E-14 2.1E-15 1.91E-13 9.5E-15
213 SMP92 WS39 0.12 2.10E-13 1.0E-14 3.70E-12 1.8E-13
214 MG73 0.36 8.81E-15 7.4E-15 4.37E-14 2.4E-14
215 MG76 0.45 1.39E-14 6.9E-16 7.60E-14 3.8E-15
267 MG68 0.19 2.28E-14 1.1E-15 7.06E-14 3.5E-15
269 SMP86 0.11 1.94E-14 9.6E-16 1.24E-13 6.2E-15
270 SMP91 0.02 2.86E-14 1.4E-15 1.98E-13 9.9E-15
271 MG75 0.41 8.15E-15 6.9E-15 6.14E-14 3.3E-14
272 MG77 0.30 9.05E-15 7.6E-15 4.17E-14 2.2E-14
273 MG78 0.32 2.48E-15 2.4E-16 1.61E-14 1.3E-14
316 Sa124 0.41 7.65E-15 6.5E-15 8.72E-14 4.3E-15
317 SMP83 WS35 0.01 1.70E-13 8.5E-15 1.85E-12 9.2E-14
318 SMP85 0.06 2.16E-13 1.0E-14 9.21E-13 4.6E-14 *
346 MG72 0.33 6.07E-15 5.1E-15 4.93E-14 2.7E-14 *
350 MG69 0.39 5.98E-15 5.0E-15 5.60E-14 3.0E-14
356 MG71 0.35 1.00E-14 5.0E-16 7.13E-14 3.5E-15
398 SMP55 0.41 6.36E-13 6.8E-15 1.40E-12 1.4E-14
399 SMP59 0.23 6.96E-14 3.4E-15 2.22E-13 1.1E-14 *
400 SMP60 0.18 6.89E-14 9.5E-16 4.62E-13 9.9E-15
401 SMP62 WS25 0.36 4.95E-13 1.8E-14 2.64E-12 2.4E-13
402 SMP65 0.65 3.19E-14 1.5E-15 2.59E-13 1.2E-14 *
403 SMP68 0.02 1.30E-13 6.5E-15 4.49E-13 2.2E-14
404 SMP71 0.31 1.48E-13 7.3E-15 1.38E-12 6.8E-14
405 SMP72 0.16 1.23E-14 6.1E-16 1.21E-13 6.0E-15
406 SMP73 0.32 3.72E-13 1.8E-14 5.52E-12 2.7E-13
407 SMP80 WS24 0.16 7.16E-14 3.5E-15 3.44E-13 1.7E-14
408 Sa120 0.51 9.81E-15 8.3E-15 9.32E-14 4.6E-15
409 Sa121 0.29 1.40E-14 6.9E-16 1.16E-13 5.7E-15
410 Sa123 LM2-36 0.11 1.56E-13 7.8E-15 7.22E-13 3.6E-14
411 MG51 0.32 9.79E-15 8.3E-15 7.34E-14 3.6E-15
412 Mo24 0.41 3.14E-14 5.7E-15 3.12E-13 3.2E-15
413 Mo28 0.44 5.53E-15 4.7E-15 6.42E-14 3.2E-15
414 Mo33 0.51 1.66E-14 8.3E-16 9.94E-14 4.9E-15
539 MG43 0.37 2.96E-14 1.4E-15 1.16E-13 5.8E-15
642 SMP56 0.33 1.07E-13 5.3E-15 4.28E-13 2.1E-14
643 SMP57 0.45 2.67E-14 1.3E-15 2.42E-13 1.2E-14
644 SMP58 WS23 0.08 2.97E-13 1.4E-14 1.93E-12 9.6E-14
646 SMP77 0.33 1.58E-13 7.9E-15 6.34E-13 3.1E-14 *
647 SMP78 WS33 0.41 3.17E-13 1.5E-14 3.36E-12 1.6E-13
648 SMP82 0.46 3.77E-14 1.8E-15 3.33E-13 1.6E-14
649 Sa117 0.45 1.98E-14 9.8E-16 1.28E-13 6.3E-15
650 Sa122 0.38 2.29E-14 1.1E-15 1.22E-13 6.1E-15
651 Sa116 LM2-24 0.32 2.97E-14 1.4E-15 2.19E-13 1.1E-14
652 Sa118 0.35 1.18E-14 5.9E-16 9.97E-14 4.9E-15
654 MG49 0.27 2.93E-14 1.4E-15 1.03E-13 5.1E-15
655 MG52 0.60 5.33E-15 4.5E-15 5.88E-14 3.2E-14
656 MG53 0.36 1.90E-14 9.5E-16 1.43E-13 7.1E-15
657 MG56 0.52 2.55E-15 2.5E-16 7.66E-15 6.5E-15
658 MG60 0.33 1.21E-14 6.0E-16 8.07E-14 4.0E-15
659 MG65 0.37 3.04E-14 1.5E-15 1.04E-13 5.2E-15
660 Mo23 0.05 1.16E-14 5.7E-16 3.68E-14 3.1E-14
661 Mo27 0.20 1.05E-14 5.2E-16 4.67E-14 2.5E-14
662 Mo30 0.42 1.22E-14 6.1E-16 6.02E-14 3.3E-14
663 Mo34 0.52 3.75E-14 1.8E-15 1.69E-13 8.4E-15
664 Mo32 0.46 1.62E-14 8.1E-16 9.82E-14 4.9E-15
668 Mo26 0.48 7.82E-15 6.6E-15 7.02E-14 3.5E-15
890 SMP63 WS26 0.40 3.24E-13 1.6E-14 3.90E-12 1.9E-13
891 SMP75 WS31 0.39 2.62E-13 1.3E-14 2.91E-12 1.4E-13
892 SMP76 WS32 0.38 3.55E-13 1.7E-14 1.85E-12 9.2E-14
893 MG40 0.31 2.92E-14 1.4E-15 2.18E-13 1.0E-14
894 MG54 0.32 9.75E-15 8.2E-15 8.42E-14 4.2E-15
895 MG62 0.31 2.81E-15 2.8E-16 1.06E-14 9.0E-15
1047 SMP66 0.01 2.89E-13 1.4E-14 2.19E-12 1.1E-13 *
1048 SMP67 0.14 1.61E-13 8.0E-15 5.15E-13 2.5E-14
1049 SMP69 0.29 4.24E-14 2.1E-15 3.44E-13 1.7E-14
1050 MG42 0.29 1.78E-15 1.7E-16 9.33E-15 7.9E-15
1051 MG50 0.27 2.31E-14 1.1E-15 8.66E-14 4.3E-15
Table 4: A compendium of H and [O iii]5007Å raw flux estimates for Large Magellanic Cloud PNe. * = A flux measured directly from long-slit spectra. = PNe with extremely high H/H 10 ratios which may have been affected by power-law photoionisation or shock-heating (see section 3.3).
RP Common cH Flux H Flux [O iii]
Ref. Nomenclature 4868Å 5007Å
(erg cm s) (erg cm s)
1052 MG58 0.35 1.27E-14 6.3E-16 7.15E-14 3.5E-15
1053 MG64 0.46 3.66E-15 3.6E-16 3.20E-14 2.7E-14
1114 SMP32 WS10 0.29 5.83E-13 3.4E-14 4.16E-12 4.5E-13
1115 SMP41 0.28 1.61E-13 8.0E-15 2.39E-12 1.2E-13
1116 SMP49 0.29 7.22E-14 2.2E-15 5.25E-13 2.9E-14
1117 MG30 0.26 9.15E-14 3.0E-15 3.36E-13 1.6E-14
1118 Mo20 0.16 3.88E-14 9.9E-16 1.49E-13 5.7E-15
1212 SMP38 WS15 0.22 2.06E-13 1.0E-14 3.03E-12 1.5E-13
1213 SMP43 0.46 9.53E-14 4.7E-15 1.20E-12 6.0E-14
1214 SMP47 WS18 0.55 2.57E-13 1.2E-14 2.77E-12 1.3E-13
1215 SMP48 WS19 0.50 2.41E-13 1.2E-14 1.88E-12 9.4E-14
1216 SMP51 0.44 6.08E-14 3.0E-15 9.21E-13 4.6E-14
1217 J-5 0.59 3.99E-14 2.0E-15 2.28E-13 1.1E-14
1218 J-04 0.27 6.59E-15 5.6E-15 3.52E-14 2.9E-14
1219 J-7 0.57 1.49E-16 1.4E-17 9.83E-16 8.3E-16
1220 J-12 0.54 7.53E-15 6.4E-15 3.96E-14 3.3E-14
1221 J-14 0.62 3.46E-15 3.4E-16 5.19E-14 2.8E-14
1222 J-15 0.85 3.50E-15 3.5E-16 3.69E-14 3.1E-14
1223 J-16 0.64 3.40E-15 3.4E-16 3.64E-14 3.0E-14
1224 J-17 0.70 3.43E-14 1.7E-15 6.98E-14 3.4E-15
1225 J-18 0.57 1.98E-15 1.9E-16 2.91E-14 2.4E-14
1227 J-20 0.33 1.94E-14 9.6E-16 1.12E-13 5.6E-15
1228 J-21 0.43 7.70E-15 6.5E-15 3.36E-14 2.8E-14
1229 J-22 0.39 8.64E-15 7.3E-15 4.92E-14 2.7E-14
1230 J-23 0.32 7.68E-14 3.8E-15 3.23E-13 1.6E-14
1231 J-24 0.53 9.13E-15 7.7E-15 4.71E-14 2.5E-14
1232 J-26 0.32 1.19E-14 5.9E-16 1.19E-13 5.9E-15
1234 J-32 0.57 5.38E-15 4.5E-15 6.12E-14 3.3E-14
1235 J-33 0.06 2.59E-14 1.2E-15 1.95E-13 9.74E-15
1236 MG28 0.32 1.07E-14 5.3E-16 7.48E-14 3.74E-15
1237 Mo19 0.26 1.44E-14 7.2E-16 1.75E-13 8.77E-15
1395 SMP28 0.39 3.15E-14 1.5E-15 2.06E-13 1.0E-14
1396 SMP29 WS9 0.34 1.59E-13 7.9E-15 1.67E-12 8.3E-14
1398 SMP33 WS11 0.47 1.24E-13 6.2E-15 1.74E-12 8.7E-14
1399 SMP34 0.36 1.05E-13 5.2E-15 6.58E-13 3.2E-14
1400 SMP36 WS13 0.26 5.73E-14 2.8E-15 8.88E-13 4.4E-14
1401 SMP37 WS14 0.37 8.72E-14 4.3E-15 1.44E-12 7.1E-14
1402 SMP39 0.48 5.35E-14 2.6E-15 6.92E-13 3.4E-14
1403 SMP42 0.00 6.46E-14 3.2E-15 8.25E-13 4.1E-14
1404 SMP46 0.51 3.43E-14 1.7E-15 4.55E-13 2.2E-14
1405 SMP52 WS21 0.22 3.27E-13 1.6E-14 4.59E-12 2.2E-13
1406 SMP54 J-35 0.36 3.85E-14 1.9E-15 3.32E-13 1.6E-14
1407 Sa110 0.28 1.46E-14 7.3E-16 2.15E-13 1.0E-14
1408 J-10 0.49 2.33E-15 2.3E-16 2.52E-14 2.1E-14
1409 MG19 0.37 1.10E-14 5.4E-16 8.75E-14 4.3E-15
1410 MG20 0.33 1.00E-14 5.0E-16 7.90E-14 3.9E-15
1411 MG23 0.46 2.24E-15 2.2E-16 2.07E-14 1.7E-14
1412 MG29 0.38 3.33E-14 1.6E-15 3.94E-13 1.9E-14
1413 MG31 0.40 9.48E-15 8.0E-15 8.81E-14 4.4E-15
1552 SMP30 0.44 3.11E-14 1.5E-15 2.35E-13 1.1E-14
1553 SMP44 0.33 3.91E-14 1.9E-15 3.40E-13 1.7E-14
1554 SMP45 WS17 0.53 8.25E-14 4.1E-15 1.17E-12 5.8E-14
1555 SMP50 WS20 0.39 1.68E-13 8.4E-15 1.38E-12 6.9E-14
1556 SMP53 WS22 0.25 5.96E-13 2.9E-14 3.30E-12 1.6E-13
1557 MG34 0.33 8.05E-15 6.8E-15 2.05E-14 1.7E-14
1558 MG35 0.45 1.72E-14 8.6E-16 4.20E-14 2.3E-14
1602 SMP13 WS4 0.33 1.57E-13 7.8E-15 1.64E-12 8.2E-14
1603 SMP14 WS2 0.35 1.85E-14 9.2E-16 1.29E-13 6.4E-15
1604 SMP15 WS5 0.41 1.66E-13 8.2E-15 2.28E-12 1.1E-13
1605 SMP19 WS6 0.33 3.36E-13 1.6E-14 1.50E-12 7.5E-14
1606 MG4 0.19 7.03E-15 5.9E-15 5.65E-14 3.1E-14 *
1607 Mo9 0.51 9.97E-15 8.4E-15 3.05E-14 2.5E-14
1608 Mo11 0.30 7.05E-15 5.9E-15 5.56E-14 3.0E-14
1609 Mo14 0.24 5.96E-15 5.0E-15 3.81E-14 3.2E-14
1677 SMP16 0.43 4.30E-14 2.1E-15 4.19E-13 2.0E-14
1678 SMP17 0.04 8.63E-15 7.3E-15 5.69E-14 3.1E-14
1679 SMP18 0.31 5.27E-14 2.6E-15 4.37E-13 2.1E-14
1680 SMP20 0.35 4.06E-14 2.0E-15 3.95E-13 1.9E-14
1681 SMP22 0.42 1.61E-14 8.0E-16 1.75E-13 8.7E-15
1682 SMP24 0.02 1.15E-14 5.7E-16 1.54E-13 7.6E-15
1683 SMP25 0.31 4.03E-13 2.0E-14 3.47E-12 1.7E-13
1684 Sa105 0.52 9.41E-15 8.0E-15 9.91E-14 4.9E-15
1685 Sa107 0.45 1.61E-14 8.0E-16 1.51E-13 7.5E-15
1686 MG14 0.28 3.12E-14 1.5E-15 3.17E-13 1.5E-14
1687 Mo12 0.41 5.92E-15 5.0E-15 4.75E-14 2.6E-14
1688 Mo13 0.26 5.41E-15 4.5E-15 3.42E-14 2.9E-14
1689 Mo16 0.14 4.90E-15 4.9E-16 4.15E-14 2.2E-14
1797 SMP21 WS7 0.46 1.68E-13 8.4E-15 1.95E-12 9.7E-14
1798 SMP23 WS8 0.11 2.14E-13 1.0E-14 1.67E-12 8.3E-14
1799 Sa106 0.33 1.66E-14 8.3E-16 1.38E-13 6.8E-15
RP Common cH Flux H Flux [O iii]
Ref. Nom. 4868Å 5007Å
(erg cm s) (erg cm s)
1800 MG8 0.38 1.52E-14 7.6E-16 1.24E-13 6.2E-15
1801 MG10 0.43 1.25E-14 6.2E-16 1.34E-13 6.7E-15
1802 MG15 0.34 4.46E-15 4.4E-16 1.78E-14 1.5E-14
1894 SMP27 0.26 1.72E-14 8.6E-16 2.24E-13 1.1E-14 *
1895 MG9 0.39 9.07E-15 7.7E-15 7.32E-14 3.6E-15
1896 MG11 0.41 1.23E-14 6.1E-16 5.88E-14 3.2E-14
1897 MG12 0.41 9.59E-15 8.1E-15 4.42E-14 2.4E-14
1898 Mo17 0.28 5.89E-15 5.0E-15 3.97E-14 3.3E-14

Explanation of abbreviations used: J: Jacoby (1980), LM2: Lindsay & Mullan (1963),  MG: Morgan & Good (1992),  Mo: Morgan (1994), N: Henize (1956), SMP: Sanduleak et al. (1978),  Sa: Sanduleak (1984),  WS: Westerlund & Smith (1964)

RP P cH Flux H Flux [O iii]
Ref. 4861Å 5007Å
(erg cm s) (erg cm s)
1 L 0.56 1.46E-15 7.29E-17 2.52E-15 1.26E-16
9 T 0.49 2.60E-15 1.30E-16 2.32E-14 1.16E-15
18 T 0.28 7.11E-15 3.56E-16 1.39E-14 6.96E-16
25 T 0.10 9.66E-16 8.21E-16 7.76E-15 3.88E-16
26 T 0.21 3.39E-15 1.69E-16 1.72E-14 8.58E-16
35 T 0.06 5.12E-15 2.56E-16 5.60E-15 2.80E-16
44 T 0.45 1.06E-14 5.32E-16 2.07E-14 1.04E-15
46 P 0.29 2.64E-13 1.32E-14 3.52E-13 1.76E-14 *
61 T 0.33 5.42E-15 2.71E-16 2.28E-14 1.14E-15
62 T 0.51 1.74E-15 8.69E-17 1.01E-14 5.04E-16
70 T 1.01 3.79E-16 3.79E-17 3.32E-15 1.66E-16
72 L 0.09 5.30E-15 2.65E-16 3.05E-14 1.53E-15 *
77 T 0.78 3.28E-16 3.28E-17 2.28E-15 1.14E-16
85 L 0.84 7.68E-15 3.84E-16 1.64E-14 8.20E-16
86 P 0.86 1.43E-15 7.16E-17 6.20E-15 3.10E-16
87 L 0.32 7.24E-16 7.24E-17 9.28E-16 9.28E-17
89 T 0.63 6.03E-15 3.02E-16 1.11E-14 5.54E-16
90 T 0.63 1.29E-15 6.46E-17 3.52E-15 1.76E-16
93 T 0.56 2.32E-15 1.16E-16 1.57E-14 7.84E-16
95 P 0.72 2.08E-15 1.04E-16 7.02E-15 3.51E-16
97 P 0.69 2.04E-15 1.02E-16 2.27E-15 1.13E-16
99 T 0.43 3.45E-15 1.73E-16 4.26E-14 2.13E-15
102 T 0.07 2.23E-15 1.12E-16 7.00E-15 3.50E-16
103 T 0.55 5.08E-15 2.54E-16 2.06E-14 1.03E-15
111 T 0.83 4.74E-15 2.37E-16 1.26E-14 6.28E-16
116 L 0.53 3.03E-14 1.51E-15 8.84E-14 4.42E-15 *
120 P 0.36 7.47E-15 3.74E-16 1.73E-14 8.67E-16
122 T 0.15 1.31E-15 6.55E-17 4.29E-15 2.15E-16
125 T 0.93 3.60E-16 3.60E-17 1.57E-15 1.34E-15
127 L 0.43 3.26E-15 1.63E-16 7.80E-15 3.90E-16
129 T 0.35 7.19E-15 3.60E-16 1.74E-14 8.72E-16
130 P 0.26 4.82E-15 2.41E-16 7.93E-15 3.97E-16
135 T 0.23 6.77E-15 3.38E-16 2.24E-14 1.12E-15
142 T 0.48 4.62E-15 2.31E-16 7.49E-15 3.75E-16
143 T 0.40 4.36E-15 2.18E-16 2.50E-14 1.25E-15
144 T 0.76 1.13E-15 5.65E-17 8.83E-15 4.42E-16
145 T 0.06 2.55E-15 1.28E-16 2.84E-15 1.42E-16
147 T 0.51 6.09E-16 6.09E-17 3.59E-15 1.79E-16
162 T 0.34 3.67E-15 1.84E-16 1.21E-14 6.05E-16
163 P 0.28 4.95E-15 2.47E-16 8.55E-15 4.28E-16
171 T 0.13 3.73E-15 1.87E-16 1.47E-14 7.34E-16 *
172 T 0.19 1.40E-15 6.98E-17 3.96E-15 1.98E-16
178 T 0.24 6.36E-15 3.18E-16 2.31E-14 1.16E-15
180 L 0.18 1.50E-15 7.49E-17 1.61E-15 8.04E-17
182 L 0.09 1.99E-15 9.93E-17 2.26E-15 1.13E-16
187 P 0.59 2.31E-15 1.15E-16 2.27E-14 1.13E-15
188 P 0.41 2.11E-15 1.05E-16 3.30E-15 1.65E-16
189 P 0.68 1.70E-15 8.52E-17 3.98E-15 1.99E-16
194 T 0.53 2.57E-15 1.28E-16 9.78E-15 4.89E-16
198 P 0.96 4.12E-15 2.06E-16 8.13E-15 4.07E-16 *
202 T 0.39 2.83E-15 1.42E-16 1.75E-14 8.75E-16
203 T 0.07 1.83E-15 9.17E-17 1.71E-14 8.53E-16
207 L 0.28 2.17E-15 1.08E-16 3.37E-15 1.68E-16
217 P 0.37 5.91E-15 2.96E-16 7.20E-15 3.60E-16
219 P 0.49 9.00E-15 4.50E-16 1.49E-14 7.45E-16
223 P 0.43 1.73E-14 8.66E-16 4.65E-14 2.32E-15
227 P 0.37 2.27E-14 1.14E-15 3.65E-14 1.82E-15
228 P 0.65 2.78E-15 1.39E-16 7.84E-15 3.92E-16
231 L 0.44 1.12E-14 5.58E-16 2.74E-14 1.37E-15
232 L 0.28 1.24E-14 6.19E-16 4.01E-14 2.00E-15
234 P 0.22 1.15E-14 5.74E-16 4.75E-14 2.38E-15
240 P 0.48 1.02E-14 5.08E-16 2.72E-14 1.36E-15
241 P 0.49 8.60E-15 4.30E-16 2.93E-14 1.46E-15
242 P 0.44 3.82E-14 1.91E-15 3.07E-14 1.54E-15
246 P 0.59 8.71E-15 4.36E-16 3.96E-14 1.98E-15
247 P 0.62 9.85E-15 4.92E-16 1.80E-14 8.98E-16
250 P 0.52 2.50E-14 1.25E-15 4.98E-14 2.49E-15
251 P 0.52 1.43E-14 7.15E-16 1.22E-14 6.12E-16
252 P 0.79 4.16E-15 2.08E-16 5.11E-15 2.56E-16
Table 5: A compendium of H and [O iii]5007Å raw flux estimates for RP PNe in the Large Magellanic Cloud. P = Probability where T = True, L = Likely, P = Possible. A detailed review of T, L and P is given in [RPb]. * = A flux measured directly from long-slit spectra. = PNe with extremely high H/H 10 ratios which may have been affected by power-law photoionisation or shock-heating (see section 3.3).
RP P cH Flux H Flux [O iii]
Ref. 4868Å 5007Å
(erg cm s) (erg cm s)
254 P 0.47 9.39E-15 4.70E-16 1.80E-14 9.01E-16
259 P 0.55 7.73E-15 3.86E-16 1.20E-14 5.98E-16
261 P 0.54 3.32E-14 1.66E-15 3.04E-14 1.52E-15
263 P 0.55 9.27E-15 4.64E-16 1.42E-14 7.08E-16
264 P 0.68 1.16E-14 5.80E-16 1.19E-14 5.96E-16
265 T 0.12 1.36E-14 6.80E-16 4.39E-14 2.20E-15
266 P 0.35 7.81E-14 3.90E-15 8.69E-14 4.35E-15
268 P 0.00 3.39E-14 1.69E-15 7.75E-14 3.87E-15
277 P 0.12 1.80E-15 9.02E-17 3.00E-15 1.50E-16
283 P 1.00 3.31E-15 1.66E-16 6.40E-15 3.20E-16
295 P 0.58 1.01E-14 5.07E-16 1.25E-14 6.23E-16
296 P 0.59 1.25E-15 6.25E-17 1.60E-15 7.99E-17
299 T 0.32 4.85E-15 2.42E-16 1.95E-14 9.73E-16
303 P 1.14 7.70E-16 7.70E-17 1.79E-15 8.95E-17 *
307 P 0.54 9.12E-15 4.56E-16 2.51E-14 1.26E-15
312 L 0.32 7.22E-15 3.61E-16 2.57E-14 1.29E-15
315 P 0.39 9.22E-15 4.61E-16 2.76E-14 1.38E-15
326 P 0.71 4.39E-15 2.19E-16 9.02E-15 4.51E-16
328 P 0.32 4.44E-16 4.44E-17 2.05E-15 1.03E-16
331 P 0.44 1.02E-15 5.12E-17 2.28E-15 1.14E-16
347 T 0.51 4.03E-15 2.01E-16 2.24E-14 1.12E-15
359 T 0.58 8.30E-16 8.30E-17 5.02E-15 2.51E-16
363 P 0.74 1.65E-16 1.65E-17 1.66E-15 8.29E-17
366 T 0.02 1.16E-15 5.79E-17 2.00E-15 1.00E-16
384 T 0.20 9.86E-16 8.38E-16 2.93E-15 1.46E-16
393 T 0.20 1.04E-15 5.20E-17 4.91E-15 2.46E-16 *
394 T 0.07 1.00E-15 5.02E-17 1.13E-15 9.61E-16 *
395 L 0.37 6.53E-16 6.53E-17 1.90E-15 9.48E-17
396 T 0.34 1.71E-15 8.57E-17 8.07E-15 4.03E-16
397 T 0.16 8.81E-16 8.81E-17 8.64E-16 8.64E-17
415 T 0.33 2.21E-14 1.10E-15 8.00E-14 4.00E-15
427 T 0.31 1.61E-14 8.05E-16 4.16E-14 2.08E-15
440 T 0.22 1.46E-14 7.28E-16 6.26E-14 3.13E-15 *
441 T 0.40 1.33E-15 6.65E-17 9.60E-15 4.80E-16
442 T 0.19 1.96E-14 9.78E-16 6.69E-14 3.34E-15
445 L 0.57 1.47E-15 7.37E-17 2.33E-14 1.16E-15
460 P 0.39 9.67E-16 8.22E-16 2.29E-15 1.15E-16
463 P 0.76 1.74E-15 8.68E-17 3.82E-15 1.91E-16
473 L 0.51 2.22E-15 1.11E-16 5.87E-15 2.94E-16 *
474 P 0.22 2.14E-16 2.14E-17 1.08E-15 9.16E-16
478 T 0.55 1.59E-15 7.96E-17 1.21E-14 6.05E-16
491 T 0.56 9.74E-15 4.87E-16 5.30E-14 2.65E-15
492 P 0.99 9.75E-15 4.88E-16 6.42E-14 3.21E-15 *
492 P 9.75E-15 4.88E-16 6.42E-14 3.21E-15
493 T 0.84 2.56E-14 1.28E-15 6.65E-14 3.32E-15
499 T 0.57 1.79E-15 8.96E-17 1.35E-14 6.76E-16
506 P 0.28 1.42E-15 7.10E-17 3.52E-15 1.76E-16 *
523 T 0.44 1.21E-15 6.07E-17 3.96E-15 1.98E-16
524 L 0.21 5.07E-15 2.54E-16 1.38E-14 6.89E-16
525 T 0.27 1.08E-15 5.40E-17 3.45E-15 1.72E-16
530 T 0.35 1.11E-14 5.56E-16 1.15E-13 5.73E-15
548 T 0.27 1.18E-14 5.91E-16 5.92E-14 2.96E-15
553 P 0.40 1.99E-15 9.93E-17 2.68E-15 1.34E-16
561 T 0.31 2.94E-15 1.47E-16 1.77E-14 8.85E-16
565 P 6.28E-15 3.14E-16 *
577 T 0.39 1.40E-15 7.00E-17 1.96E-14 9.79E-16
580 T 0.30 9.97E-16 8.48E-16 6.29E-15 3.14E-16
589 T 0.38 1.76E-15 8.80E-17 1.20E-14 5.98E-16
590 T 0.43 7.90E-15 3.95E-16 2.81E-14 1.40E-15
594 T 0.44 9.88E-15 4.94E-16 3.66E-14 1.83E-15
603 T 0.71 1.85E-14 9.27E-16 1.62E-13 8.09E-15
604 T 0.08 1.74E-15 8.68E-17 6.90E-15 3.45E-16
607 T 0.29 4.44E-15 2.22E-16 1.85E-14 9.26E-16
613 P 0.58 1.46E-15 7.31E-17 4.27E-15 2.14E-16
614 T 1.02 1.61E-16 1.61E-17 6.84E-16 6.84E-17
615 T 0.62 2.01E-14 1.00E-15 6.09E-14 3.05E-15
618 P 0.83 1.53E-15 7.64E-17 1.56E-15 9.88E-16
619 T 0.20 1.47E-15 7.36E-17 2.71E-15 1.36E-16
620 T 0.62 1.12E-15 5.58E-17 4.20E-15 2.10E-16
621 P 0.39 2.37E-15 1.18E-16 2.38E-15 1.19E-16
622 T 0.33 4.75E-15 2.38E-16 3.85E-14 1.93E-15
624 T 0.41 6.56E-16 6.56E-17 1.53E-15 1.30E-15
637 T 0.45 2.31E-15 1.16E-16 6.46E-15 3.23E-16
645 P 0.69 1.56E-13 7.82E-15 6.18E-14 3.09E-15
666 T 0.41 1.41E-14 7.03E-16 6.33E-14 3.16E-15
671 T 0.70 1.08E-15 5.41E-17 1.24E-14 6.18E-16
676 T 0.20 1.47E-15 7.35E-17 3.50E-15 1.75E-16
678 T 0.28 2.87E-15 1.43E-16 1.22E-14 6.11E-16
RP P cH Flux H Flux [O iii]
Ref. 4868Å 5007Å
(erg cm s) (erg cm s)
679 T 0.18 7.45E-15 3.73E-16 1.37E-14 6.87E-16
680 T 0.37 1.25E-14 6.27E-16 4.50E-14 2.25E-15 *
681 T 0.23 5.32E-15 2.66E-16 1.67E-14 8.34E-16 *
682 P 1.06 6.06E-16 6.06E-17 1.76E-15 8.79E-17
683 P 0.31 5.32E-15 2.66E-16 4.13E-15 2.06E-16
686 T 0.49 3.02E-15 1.51E-16 3.43E-14 1.72E-15
687 T 0.23 5.45E-15 2.72E-16 3.38E-14 1.69E-15
691 T 0.56 1.12E-15 5.62E-17 1.29E-14 6.43E-16 *
692 T 0.44 4.74E-15 2.37E-16 3.31E-14 1.66E-15
693 L 0.68 1.85E-15 9.24E-17 3.85E-15 1.92E-16
695 T 0.03 4.73E-15 2.37E-16 3.16E-14 1.58E-15 *
700 T 0.37 3.77E-15 1.88E-16 3.24E-15 1.62E-16
701 T 0.19 1.34E-14 6.69E-16 1.64E-14 8.19E-16
711 P 0.21 1.44E-15 7.21E-17 5.73E-15 2.87E-16
714 T 0.33 4.97E-15 2.49E-16 3.50E-14 1.75E-15
717 T 0.37 2.74E-15 1.37E-16 4.78E-15 2.39E-16
719 P 2.13 1.53E-15 7.63E-17 4.23E-15 2.11E-16 *
721 T 0.63 3.24E-15 1.62E-16 4.06E-14 2.03E-15
722 T 1.15 5.33E-16 5.33E-17 6.01E-15 3.00E-16
723 T 0.36 1.10E-14 5.49E-16 7.01E-14 3.50E-15
727 L 0.82 3.10E-15 1.55E-16 3.82E-15 1.91E-16
732 T 0.79 2.62E-15 1.31E-16 3.10E-14 1.55E-15
733 T 0.97 5.76E-16 5.76E-17 4.12E-15 2.06E-16
735 T 0.06 7.87E-15 3.93E-16 2.85E-14 1.42E-15
736 T 0.41 9.51E-15 4.75E-16 3.38E-14 1.69E-15
737 L 0.96 3.19E-15 1.59E-16 1.12E-14 5.62E-16
748 T 0.02 1.79E-14 8.95E-16 5.19E-14 2.59E-15
753 P 0.58 8.46E-14 4.23E-15 1.31E-13 6.55E-15
756 P 0.94 1.02E-14 5.09E-16 4.83E-14 2.41E-15 *
757 T 0.52 3.00E-15 1.50E-16 1.96E-14 9.79E-16
758 T 0.03 3.93E-14 1.96E-15 5.68E-14 2.84E-15
764 T 0.50 5.06E-15 2.53E-16 2.77E-14 1.38E-15
771 T 0.31 4.09E-15 2.04E-16 1.20E-14 5.99E-16
774 P 0.58 2.13E-14 1.06E-15 2.96E-14 1.48E-15
775 P 0.90 2.91E-15 1.45E-16 1.51E-14 7.54E-16
776 T 0.66 7.46E-15 3.73E-16 1.24E-14 6.19E-16
777 P 0.29 3.61E-14 1.81E-15 2.75E-14 1.38E-15
789 T 0.71 2.27E-15 1.13E-16 3.13E-14 1.56E-15
790 L 0.40 7.63E-15 3.81E-16 5.52E-14 2.76E-15
791 L 0.37 3.40E-15 1.70E-16 1.16E-14 5.82E-16
793 T 0.29 3.64E-15 1.82E-16 9.39E-15 4.69E-16
803 T 0.23 5.53E-15 2.76E-16 5.98E-14 2.99E-15
806 T 0.31 8.48E-16 8.48E-17 1.02E-15 8.67E-16
815 T 0.26 9.23E-15 4.61E-16 3.02E-14 1.51E-15
828 P 0.73 1.24E-14 6.22E-16 1.83E-14 9.16E-16
850 T 0.84 8.85E-16 8.85E-17 3.28E-15 1.64E-16
856 P 0.40 1.42E-14 7.09E-16 2.12E-14 1.06E-15
857 L 0.23 4.58E-15 2.29E-16 1.40E-14 7.01E-16
865 T 0.48 2.22E-15 1.11E-16 1.84E-14 9.21E-16
875 T 0.55 2.20E-15 1.10E-16 1.87E-14 9.35E-16
883 P 1.22 2.09E-14 1.04E-15 3.54E-14 1.77E-15
885 T 0.42 1.19E-14 5.93E-16 5.86E-14 2.93E-15
887 P 1.05 1.64E-15 8.21E-17 6.50E-15 3.25E-16
889 T 0.34 3.33E-14 1.67E-15 1.49E-13 7.45E-15
896 T 0.28 1.61E-14 8.03E-16 1.02E-13 5.11E-15
900 T 0.50 2.63E-16 2.63E-17 1.36E-15 1.16E-15
903 T 0.29 1.12E-14 5.60E-16 5.33E-14 2.67E-15
907 T 0.25 2.35E-14 1.18E-15 7.77E-14 3.89E-15
908 L 0.80 1.34E-15 6.70E-17 1.84E-15 9.18E-17
913 P 0.29 1.15E-14 5.75E-16 1.03E-14 5.17E-16
916 T 0.53 1.31E-14 6.53E-16 3.34E-14 1.67E-15
917 T 0.25 1.80E-14 9.00E-16 9.28E-14 4.64E-15
919 T 0.40 1.38E-15 6.89E-17 3.61E-15 1.81E-16
926 T 0.45 8.10E-15 4.05E-16 3.19E-14 1.59E-15
931 P 0.75 1.04E-15 5.22E-17 3.92E-16 3.92E-17
932 P 0.35 3.14E-15 1.57E-16 5.56E-15 2.78E-16
945 T 0.57 3.96E-16 3.96E-17 1.18E-15 1.01E-15
958 L 0.24 5.12E-16 5.12E-17 1.00E-15 8.51E-16
972 T 0.42 5.79E-15 2.89E-16 2.56E-14 1.28E-15
977 P 0.81 1.09E-14 5.47E-16 1.19E-14 5.97E-16
979 T 0.52 2.00E-14 1.00E-15 8.47E-14 4.24E-15
980 T 0.38 2.05E-13 1.03E-14 9.10E-13 4.55E-14
992 P 0.43 9.96E-14 4.98E-15 5.83E-14 2.91E-15
1006 T 0.35 3.24E-15 1.62E-16 2.84E-14 1.42E-15
1012 T 0.80 1.57E-14 7.86E-16 5.25E-14 2.62E-15
1018 P 0.57 2.48E-15 1.24E-16 4.46E-15 2.23E-16
1024 T 0.47 1.82E-15 9.09E-17 4.10E-15 2.05E-16
1037 T 0.47 4.44E-15 2.22E-16 1.60E-14 8.01E-16
RP P cH Flux H