L-\sigma relation for H II Galaxies

# The L−σ relation for massive bursts of star formation ††thanks: Partially based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile, under program: 083.A-0347 and at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan.

R. Chávez, R. Terlevich, E. Terlevich, F. Bresolin, J. Melnick, M. Plionis and S. Basilakos.

Instituto Nacional de Astrofísica Óptica y Electrónica, AP 51 y 216, 72000, Puebla, México.
Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK.
Institute for Astronomy of the University of Hawaii, 2680 Woodlawn Drive, 96822 Honolulu,HI USA.
European Southern Observatory, Alonso de Cordova 3107, Santiago, Chile.
Physics Dept., Aristotle Univ. of Thessaloniki, Thessaloniki 54124, Greece
National Observatory of Athens, P.Pendeli, Athens, Greece
Academy of Athens, Research center for Astronomy and Applied Mathematics, Soranou Efesiou 4, 11527, Athens, Greece.
E-mail:ricardoc@inaoep.mx
v22RC —- Compiled at 15:39 hrs on July 20, 2019
###### Abstract

The validity of the emission line luminosity vs. ionised gas velocity dispersion () correlation for HII galaxies (HIIGx), and its potential as an accurate distance estimator are assessed.

For a sample of 128 local () compact HIIGx with high equivalent widths of their Balmer emission lines we obtained ionized gas velocity dispersion from high S/N high-dispersion spectroscopy (Subaru-HDS and ESO VLT-UVES) and integrated H fluxes from low dispersion wide aperture spectrophotometry.

We find that the  relation is strong and stable against restrictions in the sample (mostly based on the emission line profiles). The ‘gaussianity’ of the profile is important for reducing the rms uncertainty of the distance indicator, but at the expense of substantially reducing the sample.

By fitting other physical parameters into the correlation we are able to significantly decrease the scatter without reducing the sample. The size of the starforming region is an important second parameter, while adding the emission line equivalent width or the continuum colour and metallicity, produces the solution with the smallest rms scatter=.

The derived coefficients in the best  relation are very close to what is expected from virialized ionizing clusters, while the derived sum of the stellar and ionised gas masses are similar to the dynamical mass estimated using the HST corrected Petrosian radius. These results are compatible with gravity being the main mechanism causing the broadening of the emission lines in these very young and massive clusters. The derived masses range from about 2 M to M and their ‘corrected’ Petrosian radius, from a few tens to a few hundred parsecs.

###### keywords:
H ii galaxies – distance scale – cosmology: observations
pagerange: The relation for massive bursts of star formation thanks: Partially based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile, under program: 083.A-0347 and at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan.Referencespubyear: 2014

## 1 Introduction

Observational cosmology has witnessed in the last few years advances that resulted in the inception of what many consider the first precision cosmological model, involving a spatially flat geometry and an accelerated expansion of the Universe. To build a robust model of the Universe it is necessary not only to set the strongest possible constraints on the cosmological parameters, applying joint analyses of a variety of distinct methodologies, but also to confirm the results through extensive consistency checks, using independent measurements and different methods, in order to identify and remove possible systematic errors, related to either the methods themselves or the tracers used.

It is accepted that young massive star clusters, like those responsible for the ionisation in giant extragalactic HII regions (GEHR) and HII galaxies (HIIGx) display a correlation between the luminosity and the width of their emission lines, the relation (Terlevich & Melnick, 1981). The scatter in the relation is small enough that it can be used to determine cosmic distances independently of redshift (Melnick et al., 1987; Melnick et al., 1988; Siegel et al., 2005; Bordalo & Telles, 2011; Plionis et al., 2011; Chávez et al., 2012). Melnick et al. (1988) used this correlation to determine km sMpc and Chávez et al. (2012), using a subset of the sample of HIIGx that we will present in this work, found a value for km sMpc, which is consistent with, and independently confirms, the Riess et al. (2011, km sMpc) and more recent SNIa results (e.g.  Freedman et al., 2012, km sMpc).

GEHR are massive bursts of star formation generally located in the outer disk of late type galaxies. HIIGx are also massive bursts of star formation but in this case located in dwarf irregular galaxies and almost completely dominating the total luminosity output. The optical spectra of both GEHR and HIIGx, indistinguishable from each other, are characterized by strong emission lines produced by the gas ionized by a young massive star cluster (Searle & Sargent, 1972; Bergeron, 1977; Terlevich & Melnick, 1981; Kunth & Östlin, 2000). One important property is that, as the mass of the young stellar cluster increases, both the number of ionizing photons and the motion of the ionised gas, which is determined by the gravitational potential of the stellar cluster and gas complex, also increases. This fact induces the correlation between the luminosity of recombination lines, e.g. , which is proportional to the number of ionizing photons, and the ionized gas velocity dispersion (), which can be measured using the emission lines width as an indicator.

Recently Bordalo & Telles (2011) have explored the correlation and its systematic errors using a nearby sample selected from the Terlevich et al. (1991) spectrophotometric catalogue of HIIGx (). They conclude that considering only the objects with clearly gaussian profiles in their emission lines, they obtain something close to an relation with an rms scatter of . It is important to emphasise that the observed properties of HIIGx, in particular the derived  111L(H) is related to L(H) by the theoretical Case B recombination ratio = 2.86. relation, are mostly those of the young burst and not those of the parent galaxy. This is particularly true if one selects those systems with the largest equivalent width (EW) in their emission lines, i.e. EW(HÅ  as we will discuss in the body of the paper. The selection of those HIIGx having the strongest emission lines minimises the evolutionary effects in their luminosity (Copetti, Pastoriza & Dottori, 1986), which would introduce a systematic shift in the  relation due to the rapid drop of the ionising flux after 5 Myr of evolution. This selection minimises also any possible contamination in the observable due to the stellar populations of the parent galaxy.

A feature of the HIIGx optical spectrum, their strong and narrow emission lines, makes them readily observable with present instrumentation out to . Regarding such distant systems, Koo et al. (1995) and also Guzmán et al. (1996) have shown that a large fraction of the numerous compact star forming galaxies found at intermediate redshifts have kinematical properties similar to those of luminous local HIIGx. They exhibit fairly narrow emission line widths ( from 30 to 150 km/s) rather than the 200 km/s typical for galaxies of similar luminosities. In particular galaxies with 65 km/s seem to follow the same relations in , M and as the local ones.

From spectroscopy of Balmer emission lines in a few Lyman break galaxies at 3 Pettini et al. (1998) suggested that these systems adhere to the same relations but that the conclusions had to be confirmed for a larger sample. These results opened the important possibility of applying the distance estimator and mapping the Hubble flow up to extremely high redshifts and simultaneously to study the behaviour of starbursts of similar luminosities over a very large redshift range.

Using a sample of intermediate and high redshift HIIGx Melnick, Terlevich & Terlevich (2000) investigated the use of the  correlation as a high- distance indicator. They found a good correlation between the luminosity and velocity dispersion confirming that the  correlation for local HIIGx is valid up to 3. Indeed, our group (Plionis et al., 2011) showed that the HIIGx relation constitutes a viable alternative cosmic probe to SNe Ia. We also presented a general strategy to use HIIGx to trace the high- Hubble expansion in order to put stringent constrains on the dark energy equation of state and test its possible evolution with redshift. A first attempt by Siegel et al. (2005), using a sample of 15 high- HIIGx (), selected as in Melnick et al. (2000), with the original  calibration of Melnick et al. (1988), found a mass content of the universe of for a flat -dominated universe. Our recent reanalysis of the Siegel et al. (2005) sample (Plionis et al., 2011), using a revised zero-point of the original relation, provided a similar value of but with substantially smaller errors (see also Jarosik et al., 2011).

Recapitulating, we reassess in this paper the HIIGx  relation using new data obtained with modern instrumentation with the aim of reducing the impact of observational random and systematic errors onto the HIIGx Hubble diagram. To achieve this goal, we selected from the SDSS catalogue a sample of 128 local (), compact HIIGx with the highest equivalent width of their Balmer emission lines. We obtained high S/N high-dispersion echelle spectroscopic data with the VLT and Subaru telescopes to accurately measure the ionized gas velocity dispersion. We also obtained integrated H fluxes using low dispersion wide aperture spectrophotometry from the 2.1m telescopes at Cananea and San Pedro Mártir in Mexico, complemented with data from the SDSS spectroscopic survey.

The layout of the paper is as follows: we describe the sample selection procedure in §2, observations and data reduction in §3; an analysis in depth of the data error budget (observational and systematic) and the method for analysing the data are discussed in §4. The effect that different intrinsic physical parameters of the star-forming regions could have on the  relation is studied in §5. The results for the  relation is presented in §6, together with possible second parameters and systematic effects. Summary and conclusions are given in §7. Fittings to the line profiles are shown in the Appendix which is available electronically.

## 2 Sample selection

We observed 128 HIIGx selected from the SDSS DR7 spectroscopic catalogue (Abazajian et al., 2009) for having the strongest emission lines relative to the continuum (i.e. largest equivalent widths) and in the redshift range . The lower redshift limit was selected to avoid nearby objects that are more affected by local peculiar motions relative to the Hubble flow and the upper limit was set to minimize the cosmological non-linearity effects. Figure 1 shows the redshift distribution for the sample. The median of the distribution is also shown as a dashed line at , the corresponding recession velocity is .

Only those HIIGx with the largest equivalent width in their emission lines, were included in the sample. This relatively high lower limit in the observed equivalent width of the recombination hydrogen lines is of fundamental importance to guarantee that the sample is composed by systems in which a single very young starburst dominates the total luminosity. This selection criterion also minimizes the posible contamination due to an underlying older population or older clusters inside the spectrograph aperture [cf. Melnick et al. (2000); Dottori (1981); Dottori & Bica (1981)]. Figure 2 shows the distribution for the sample; the dashed line marks the median of the distribution, its value is .

Starbusrt99 (Leitherer et al., 1999, SB99) models indicate that an instantaneous burst with and Salpeter IMF has to be younger than about 5 Myr (see Figure 3). This is a strong upper limit because in the case that part of the continuum is produced by an underlying older stellar population, the derived cluster age will be even smaller.

The sample is also flux limited as it was selected from SDSS for having an line core . To discriminate against high velocity dispersion objects and also to avoid those that are dominated by rotation, we have selected only those objects with . From the values of the line core and of the line we can calculate that the flux limit in the line is which corresponds to an emission-free continuum magnitude of [cf. Terlevich & Melnick (1981) for the conversion].

To guarantee the best integrated spectrophotometry, only objects with Petrosian diameter less than 6″ were selected. In addition a visual inspection of the SDSS images was performed to avoid systems composed of multiple knots or extended haloes. Colour images from SDSS for a subset of objects in the sample are shown in Figure 4. The range in colour is related to the redshifts span of the objects and is due mainly to the dominant [OIII]4959,5007 doublet moving from the g to the r SDSS filters and to the RGB colour definition. The compactness of the sources can be appreciated in the figure.

## 3 Observations and Data Reduction

The data required for determining the  relation are of two kinds:

1. Wide slit low resolution spectrophotometry to obtain accurate integrated emission line fluxes.

2. High resolution spectroscopy to measure the velocity dispersion from the and [OIII] line profiles. Typical values of the FWHM range from 30 to about 200.

A journal of observations is given in table 1 where column (1) gives the observing date, column (2) the telescope, column (3) the instrument used, column (4) the detector and column (5) the projected slit width in arc seconds.

### 3.1 Low resolution spectroscopy

The low resolution spectroscopy was performed with two identical Boller & Chivens Cassegrain spectrographs (B&C) in long slit mode at similar 2 meter class telescopes, one of them at the Observatorio Astronómico Nacional (OAN) in San Pedro Mártir (Baja California) and the other one at the Observatorio Astrofísico Guillermo Haro (OAGH) in Cananea (Sonora) both in México.

The observations at OAN were performed using a grating with a blaze angle of . The grating was centred at and the slit width was 10″. The resolution obtained with this configuration is ( 2.07 Å/ pix) and the spectral coverage is . The data from OAGH was obtained using a grating with a blaze angle of centred at . With this configuration and a slit width of 8.14″, the spectral resolution is ( 7.88 Å/ pix).

At least four observations of three spectrophotometric standard stars were performed each night. Futhermore, to secure the photometric link between different nights at least one HIIGx was repeated every night during each run. All objects were observed at small zenith distance, but for optimal determination of the atmospheric extinction the first and the last standard stars of the night were also observed at high zenith distance.

The wide-slit spectra obtained at OAN and OAGH were reduced using standard IRAF333IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. tasks. The reduction procedure entailed the following steps: (1) bias, flat field and cosmetic corrections, (2) wavelength calibration, (3) background subtraction, (4) flux calibration and (5) 1d spectrum extraction. The spectrophotometric standard stars for each night were selected among , Feige 66, Hz 44, , GD 50, Hiltner 600, HR 3454, Feige 34 and GD 108.

We complemented our own wide-slit spectrophotometric observations with the SDSS DR7 spectroscopic data when available. SLOAN spectra are obtained with 3″diameter fibers, covering a range from and a resolution of . The comparison between our own and SDSS spectrophotometry is discussed later on in §4.1.

### 3.2 High resolution spectroscopy

High spectral resolution spectroscopy was obtained using echelle spectrographs at 8 meter class telescopes. The telescopes and instruments used are the Ultraviolet and Visual Echelle Spectrograph (UVES) at the European Southern Observatory (ESO) Very Large Telescope (VLT) in Paranal, Chile, and the High Dispersion Spectrograph (HDS) at the National Astronomical Observatory of Japan (NAOJ) Subaru Telescope in Mauna Kea, Hawaii (see Table 1 for the journal of observations).

UVES is a two-arm cross-disperser echelle spectrograph located at the Nasmyth B focus of ESO-VLT Unit Telescope 2 (UT2; Kueyen) (Dekker et al., 2000). The spectral range goes from to . The maximum spectral resolution is and in the blue and red arm respectively. We used the red arm ( grating, blaze angle) with cross disperser 3 configuration ( grating) centred at . The width of the slit was 2″, giving a spectral resolution of (0.014 Å/pix).

HDS is a high resolution cross-disperser echelle spectrograph located at the optical Nasmyth platform of NAOJ-Subaru Telescope (Noguchi et al., 2002; Sato et al., 2002). The instrument covers from to . The maximum spectral resolution is . The echelle grating used has with a blaze angle of . We used the red cross-disperser ( grating, blaze angle) centred at and a slit width of 4″, that provided a spectral resolution of (0.054 Å/ pix).

57 objects were observed with UVES and 76 with HDS. Five of them were observed with both instruments. During the UVES observing run 16 objects were observed more than once (three times for four objects and four times for another one) in order to estimate better the observational errors, and to link the different nights of the run. Two objects were observed twice with the HDS. The five galaxies observed at both telescopes also served as a link between the observing runs and to compare the performance of both telescopes/instruments and the quality of the nights.

Similarly, 59 sources were observed at OAGH and 59 at OAN, of which 15 were observed at both telescopes.

The UVES data reduction was carried out using the UVES pipeline V4.7.4 under the GASGANO V2.4.0 environment444GASGANO is a JAVA based Data File Organizer developed and maintained by ESO.. The reduction entailed the following steps and tasks: (1) master bias generation (uves_cal_mbias), (2) spectral orders reference table generation (uves_cal_predict and uves_cal_orderpos), (3) master flat generation (uves_cal_mflat), (4) wavelength calibration (uves_cal_wavecal), (5) flux calibration (uves_cal_response) and (6) science objects reduction (uves_obs_scired).

The HDS data were reduced using IRAF packages and a script for overscan removal and detector linearity corrections provided by the NAOJ-Subaru telescope team. The reduction procedure entailed the following steps: (1) bias subtraction, (2) generation of spectral order trace template, (3) scattered light removal, (4) flat fielding, (5) 1d spectrum extraction and (6) wavelength calibration.

Typical examples of the high dispersion spectra are shown in Figure 5. The instrumental profile of each setup is also shown on the left.

## 4 Data analysis.

We have already mentioned in §2 that we observed 128 HIIGx with EW(H) . From the observed sample we have removed 13 objects which presented problems in the data (low S/N) or showed evidence for a prominent underlying Balmer absorption. We also removed an extra object that presented highly asymmetric emission lines. After this we were left with 114 objects that comprise our ‘initial’ sample (S2).

It was shown by Melnick et al. (1988) that imposing an upper limit to the velocity dispersion such as H , minimizes the probability of including rotationally supported systems and/or objects with multiple young ionising clusters contributing to the total flux and affecting the line profiles. Therefore from S2 we selected all objects having H thus creating sample S3 – our ‘benchmark’ sample – composed of 107 objects.

A summary of the characteristics of the subsamples used in this paper can be found in Table 2 and is further discussed in section 6. Column (1) of Table 2 gives the reference name of the sample, column (2) lists its descriptive name, column (3) gives the constraints that led to the creation of the subsample and column (4) gives the number of objects left in it.

### 4.1 Emission line fluxes.

Given the importance of accurate measurements for our results, we will describe in detail our methods.

Total flux and equivalent width of the strongest emission lines were measured from our low dispersion wide-slit spectra. Three methods were used, we have obtained the total flux and equivalent width from single gaussian fits to the line profiles using both the IDL routine gaussfit and the IRAF task splot, and we also measured the fluxes integrated under the line, in order to have a measurement independent of the line shape.

Figure 6 shows a gaussian fit and the corresponding integrated flux measurement for an line from our low dispersion data. It is clear from the figure that in the cases when the line is asymmetric, the gaussian fit would not provide a good estimate of the actual flux. In the example shown the difference between the gaussian fit and the integration is in flux.

Table 3 shows the results of our wide-slit low resolution spectroscopy measurements. The data listed have not been corrected for internal extinction. Column (1) is our index number, column (2) is the SDSS name, column (3) is the integrated flux measured by us from the SDSS published spectra, columns (4) and (5) are the line fluxes as measured from a gaussian fit to the emission line and integrating the line respectively, columns (6) and (7) are the and line fluxes measured from a gaussian fit, column (8) gives the EW of the line as measured from the SDSS spectra and column (9) is a flag that indicates the origin of the data and is described in the table caption.

Figure 7 shows the comparison between SDSS and our low resolution spectra. Clearly most of the objects show an excess flux in our data which could easily be explained as an aperture effect, as the diameter fiber of SDSS in many cases does not cover all the object whereas our spectra were taken with apertures of in width, hence covering the entire compact object in all cases.

Fluxes and equivalent widths of , , , , and were also measured from the SDSS spectra when available. We have fitted single gaussians to the line profiles using both the IDL routine gaussfit and the IRAF task splot and, when necessary, we have de-blended lines by multiple gaussian fitting.

Table 4 shows the results for the SDSS spectra line flux measurements as intensity relative to . Columns are: (1) the index number, (2) the SDSS name, (3) and (4) the intensities of and , (5), (6) and (7) the intensities of and , (8) intensity, (9) intensity, (10) and (11) are the intensities of and and (12) and (13) the intensities of the and lines. The values given are as measured, not corrected for extinction. The 1 uncertainties for the fluxes are given in percentage.

In all cases, unless otherwise stated in the tables, the uncertainties and equivalent flux of the lines have been estimated from the expressions (Tresse et al., 1999):

 σF = σcD√2Npix+EW/D, (1) σEW = EWFσcD√EW/D+2Npix+(EW/D)2/Npix, (2)

where is the mean standard deviation per pixel of the continuum at each side of the line, is the spectral dispersion in , is the number of pixels covered by the line, is the line equivalent width in , is the flux in units of . When more than one observation was available, the 1 uncertainty was given as the standard deviation of the individual determinations.

In order to characterise further the sample, a BPT diagram was drawn for the 99 objects of S3 that have a good measurement of 5007/  and 6584/ ratios. The diagram is shown in figure 8 where it can be seen that clearly, all objects are located in a narrow strip just below the transition line (Kewley et al., 2001) indicating high excitation and suggesting low metal content and photoionisation by hot main sequence stars, consistent with the expectations for young HII regions.

### 4.2 Line profiles

From the two dimensional high dispersion spectra we have obtained the total flux, the position and the full width at half maximum (FWHM) of and Å in each spatial increment i.e. along the slit.

These measurements were used to map the trends in intensity, position, centroid wavelength and FWHM of those emission lines. The intensity or brightness distribution across the object provides information about the sizes of the line and continuum emitting regions. The brightness distribution was used to determine the centroid and FWHM of the line emitting region. On the other hand the trend in the central wavelength of the spectral profile along the spatial direction was used to determine the amount of rotation present.

The trend in FWHM along the slit help us also to verify that there is no FWHM gradient across the object; any important change along the slit could affect the global measurements. In general it was found that the FWHM of the non-rotating systems is almost constant. Those systems with significant gradient or change, were removed from S3 leaving us with the sample used in Chavez et al 2012 paper (S5). We call this procedure the ‘kinematic analysis’ of the emission line profiles and we will discuss in §6 whether this can affect the distance estimator.

The observed spatial FWHM of the emitting region was used to extract the one dimensional spectrum of each object. Three different fits were performed on the 1D spectra profiles (FWHM) of and the Å lines: a single gaussian, two asymmetric gaussians and 3 gaussians (a core plus a blue and a red wing). These fits were performed using the IDL routines gaussfit, arm_asymgaussfit and arm_multgaussfit respectively. Figure 9 shows a typical fit to ; the best fitting to all the sample objects is presented in Appendix A.

Multiple fittings with no initial restrictions are not unique, so we computed using an automatized IDL code, a grid of fits each with slightly different initial conditions. From this set of solutions we chose those that had the minimum . We begin with a blind grid of parameters from which the multiple gaussian fits are constructed, hence some of the resulting fits with small are not reasonable due to numerical divergence in the fitting procedure. We have eliminated unreasonable results by visual inspection.

The 1 uncertainties of the FWHM were estimated using a Montecarlo analysis. A set of random realizations of every spectrum was generated using the data poissonian 1 1-pixel uncertainty. Gaussian fitting for every synthetic spectrum in the set was performed afterwards, and we obtained a distribution of FWHM measurements from which the 1 uncertainty for the FWHM measured in the spectra follows. Average values obtained are 6.3% in H and 3.6% in [OIII].

Table 5 lists the FWHM measurements for the high resolution observations prior to any correction such as instrumental or thermal broadening. Column (1) is the index number, column (2) is the SDSS name, columns (3) and (4) are the right ascension and declination in degrees, column (5) is the heliocentric redshift as taken from the SDSS DR7 spectroscopic data, columns (6) and (7) are the measured and FWHM in Å.

### 4.3 Emission line widths

The observed velocity dispersions () – and their 1 uncertainties – have been derived from the FWHM measurements of the and lines on the high resolution spectra as:

 σo≡FWHM2√2 ln(2) (3)

Corrections for thermal (), instrumental () and fine structure () broadening have been applied. The corrected value is given by the expression:

 σ=√σ2o−σ2th−σ2i−σ2fs (4)

We have adopted the value of as published in García-Díaz et al. (2008). The 1 uncertainties for the velocity dispersion have been propagated from the values.

The high resolution spectra were obtained with two different slit widths. The slit size was initially defined as to cover part of the Petrosian diameter of the objects. For UVES data, for which the slit width was 2 and the slit was uniformly illuminated, was directly estimated from sky lines, as usual. The Subaru observations have shown that the 4 slit size used, combined with the excellent seeing during our observations has the unwanted consequence that the slit was not uniformly illuminated for the most compact HIIGx that tend to be also the most distant ones. Thus we have devised a simple procedure to calculate the instrumental broadening correction for the Subaru data. In this case, was estimated from the target size; we positioned a rectangular area representing the slit over the corresponding SDSS r band image and measured from the image the FWHM of the object along the dispersion direction. In Figure 10 we plot (after applying the broadening corrections as described above) for the five objects that have been observed with both instruments. It is clear that the results using both methods are consistent.

The thermal broadening was calculated assuming a Maxwellian velocity distribution of the hydrogen and oxygen ions, from the expression:

 σth≡√kTem, (5)

where is the Boltzmann constant, is the mass of the ion in question and is the electron temperature in degrees Kelvin as discussed in §6.4. For the H lines, an object with the sample median =37km/s, thermal broadening represents about 10%, =0.3% and =2% while =9%. For the [OIII] lines, thermal broadening is less than 1%, typically 0.3%.

The obtained velocity dispersions for the and lines are shown in Table 6, in columns (7) and (8) respectively. Figure 11 shows the distribution of the velocity dispersions for the S3 sample (see Table 2).

### 4.4 Extinction and underlying absorption

Reddening correction was performed using the coefficients derived from the Balmer decrement, with , and fluxes obtained from the SDSS DR7 spectra. However, contamination by the underlying stellar population produces Balmer stellar absorption lines under the Balmer nebular emission lines. This fact alters the observed emission line ratios in such a way that the Balmer decrement and the internal extinction are overestimated (see e.g. Olofsson, 1995).

To correct the extinction determinations for underlying absorption, we use the technique proposed by Rosa-González et al. (2002). The first step is to determine the underlying Balmer absorption () and the “true” visual extinction () from the observed one ().

The ratio between a specific line intensity, , and that of , , is given by

 F(λ)F(Hβ)=F0(λ)F0(Hβ)10−0.4AV[k(λ)−k(Hβ)]/RV, (6)

where is given by the adopted extinction law, is the optical total-to-selective extinction ratio and the subscript indicates unreddened intrinsic values.

We used as reference the theoretical ratios for Case B recombination and (Osterbrock, 1989). In the absence of underlying absorption, the observed flux ratios can be expressed as a function of the theoretical ratios and the visual extinction:

 logF(Hα)F(Hβ) =log2.86−0.4[k(Hα)−k(Hβ)]AV/RV, (7) logF(Hγ)F(Hβ) =log0.47−0.4[k(Hγ)−k(Hβ)]AV/RV. (8)

Including the underlying absorption and assuming that the absorption and emission lines have the same widths (González-Delgado et al., 1999), the observed ratio between and is given by

 F(Hα)F(Hβ)=2.86{1−PQ[W+(Hβ)/W+(Hα)]}1−Q, (9)

where and are the equivalent widths in emission for the lines, is the ratio between the equivalent widths of in absorption and in emission and is the ratio between and equivalent widths in absorption.

The value can be obtained theoretically from spectral evolution models. Olofsson (1995) has shown that for solar abundance and stellar mass in the range using a Salpeter IMF, the value of is close to with a dispersion for ages between . Since the variation of produces a change in the ratio of less than 2 % that, given the low extinction in HIIGx, translates in a flux uncertainty well below 1 %, we have assumed .

The ratio between and is

 F(Hγ)F(Hβ)=0.47−GQ1−Q, (10)

where is the ratio between the equivalent widths in absorption of and . Olofsson (1995, ; Tables 3a,b ) and González-Delgado et al. (1999, ; Table 1) suggest that the value of the parameter can also be taken as .

When the theoretical values for the ratios and , are chosen as the origin, the observed ratios can define a vector for the observed visual extinction (). From equations (7) and (8) and a set of values for , we define a vector for the “true” visual extinction, whereas from equations (9) and (10) and a set of values of , we define a vector for the underlying absorption . Assuming that the vector relation is satisfied, by minimizing the distance between the position of the vector and the sum for every pair of parameters , we obtain simultaneously the values for and that correspond to the observed visual extinction.

The de-reddened fluxes were obtained from the expression

 Fo(λ)=Fobs(λ)100.4AVk(λ)/RV, (11)

where the extinction law was taken from Calzetti et al. (2000). The 1 uncertainties were propagated by means of a Monte Carlo procedure.

Finally, the de-reddened fluxes were corrected for underlying absorption. For the correction is given by:

 F(Hβ)=Fo(Hβ)1−Q (12)

The 1 uncertainties were propagated straightforwardly. The results are shown in Table 6, columns (4), (5) and (6) where we give the values for , and respectively.