The Cepheid Period-Luminosity Relation (The Leavitt Law) at Mid-Infrared Wavelengths: IV. Cepheids in IC 1613
We present mid-infrared Period-Luminosity relations for Cepheids in the Local Group galaxy IC 1613. Using archival IRAC imaging data from Spitzer we were able to measure single-epoch magnitudes for five, 7 to 50-day, Cepheids at 3.6 and 4.5m. When fit to the calibrating relations, measured for the Large Magellanic Cloud Cepheids, the data give apparent distance moduli of 24.290.07 and 24.280.07 at 3.6 and 4.5m, respectively. A multi-wavelength fit to previously published BVRIJHK apparent moduli and the two IRAC moduli gives a true distance modulus of 24.27 0.02 mag with E(B-V) = 0.08 mag, and a corresponding metric distance of 715 kpc. Given that these results are based on single-phase observations derived from exposures having total integration times of only 1,000 sec/pixel we suggest that Cepheids out to about 2 Mpc are accessible to Spitzer with modest integration times during its warm mission. We identify the main limiting factor to this method to be crowding/contamination induced by the ubiquitous population of infrared-bright AGB stars.
The Local Group galaxy, IC 1613 is a highly-resolved dwarf of type IB(s)m (de Vaucouleurs et al. 1991). IC 1613 is rich in gas and is actively forming stars; as a consequence it also contains many Classical (Population I) Cepheid variables. These stars have been the subject of a variety of multi-wavelength distance determinations, which place the host galaxy at a distance of about 700 kpc, comparable to that of M31, the Andromeda nebula. Consistent with its high Galactic latitude, the foreground Galactic extinction towards IC 1613 appears to be low, with estimates ranging from E(B-V) = 0.025 mag (Schlegel et al. 1998) to E(B-V) = 0.005 mag (Burstein & Heiles 1982).
Cepheids in IC 1613 were first discovered by Hubble, Mayall and Baade in the 1930s (as reported by Sandage 1971), but it was not until about 40 years later that Sandage published Baade’s data on that galaxy. Of the 59 variable stars reported at least thirty-seven were considered to be bona fide Cepheids. Only B-band photographic photometry was available at that time. Carlson & Sandage (1990) updated the periods and the B-band light curves for 16 of the faintest Cepheids in IC 1613, extending the PL relation down to about 2 days. The first multi-wavelength CCD observations of Cepheids in IC 1613 were made by Freedman (1988), allowing a simultaneous fit for the reddening and true distance modulus which were determined to be E(B-V) = 0.040.04 mag and = 24.300.10 mag, respectively. In the meantime more recent optical studies of Cepheids in IC 1613 include the unfiltered (“white light”) CCD surveys by Antonello et al. (1999, 2000), Mantegazza, et al. (2001), and the VI CCD monitoring project of Udalski et al. (2001) which raised the numbers of known Cepheids in IC 1613 to at least 138), and the BVRI sparse-sampling, follow-up study of Antonello et al. (2006) which concluded that E(B-V) = 0.070.08 mag and = 24.230.20 mag. Near infrared H-band observations of 10 Cepheids in IC 1613 were first made by McAlary, Madore & Davis (1984) giving = 24.310.12 mag, and these were more recently complemented by a major survey of 29 Cepheids at J and K wavelengths published by Pietrzynski et al. (2006). They derived a reddening of E(B-V) = 0.090.02 mag and a true distance modulus of = 24.290.04 mag.
2 IRAC Observations and Mid-Infrared Period-Luminosity Relations
As part of Guaranteed Time observations Gehrz (PID: 128) obtained a series of observations of IC 1613 resulting in an average integration time of about 16 min/pixel for all four mid-IR channels. Six uncrowded Cepheids were measured at the shortest two wavelengths. All but two of the Cepheids were either undetected or confused at 8.0m. No Cepheids in IC 1613 were confidently measured in IC 1613 at 5.8m. The very long-period (146 day) Cepheid IC 1613:[S71] V22 was measured in all three bands; however its period puts it beyond the limits of our standard calibration and it was not used in this determination of a distance to IC 1613. We do note, however, that V22 does conform to the trend noticed for these very long-period Cepheids (known as Leavitt Variables, Grieve, Madore & Welch 1985) in that they are subluminous with respect to a linear extrapolation of period-luminosity relations calibrated on shorter-period (10 to 60-day) Cepheids.
Fluxed mosaics, known as “post-BCD mosaics”, were downloaded from the Spitzer archive. Aperture photometry was done using DAOPHOT with an R 2 native pixel source aperture, and an R 2.6 pixel annular sky aperture. Aperture corrections were taken from Table 5.7 of the IRAC Data Handbook. No color corrections were applied. The observations were reduced using DAOPHOT psf fitting techniques in exactly the same way as the IRAC observations of Cepheids in NGC 6822 (Madore et al. 2009b). The reader is referred to that paper for details. The final sample of Cepheids and their psf magnitudes are given in Table 1. The flux densities, converted to the IRAC magnitude system use the zero-points of Reach et al. (2005) which correspond to the SAGE zero points used for the LMC calibration. Errors on the individual data points are those returned by DAOPHOT and are based on photon statistics alone.
Fig. 1 – Mid-Infrared Period-Luminosity relations for Cepheids in IC 1613. Dashed lines are fits to the fiducial relations of Madore et al. (2009a) based on LMC data and an adopted true distance to the LMC of 18.50 mag. The flanking solid lines are offset from the fit by 0.20 mag and appear to represent the full width of each of the relations.
3 Multi-Wavelength Solutions
Table 2 contains apparent distance moduli to IC 1613 based on a variety of published Cepheid samples measured at optical through near-infrared wavelengths. These moduli are plotted as a function of inverse wavelength in Figure 2. The near flatness of the run of apparent moduli with inverse wavelength immediately attests to the fact that the total line-of-sight reddening towards IC 1613 and its Cepheids is indeed small. The plotted fit to a standard Galactic extinction curve (Cardelli et al. 1989) is scaled to a color excess of E(B-V) = 0.08 mag, and a true distance modulus of 24.270.02 mag, which corresponds to a metric distance of 7157 kpc.
Fig. 2 – A plot of apparent distance moduli as a function of inverse wavelength. Data points are individual Cepheid distance moduli. The solid line is a scaled and shifted Galactic extinction curve whose slope is the extinction and whose intercept is the true distance modulus. Individual bands contributing to the solution are given just above the bottom axis.
We note here that these observations were reduced in exactly the same manner as the IRAC observations of Cepheids in NGC 6822 (Madore et al. 2009b), although there are differences in the post-processing of the mosaics, with the SINGS images of NGC 6822 being enhanced over the standard post-bcd mosaics used here. In the NGC 6822 paper we noted a discrepancy between the mid-infrared distance moduli and the two near-infrared (J & K) moduli from (Gieren et al. 2006). No such discrepancy is seen in a comparison of these IRAC observations and the near-infrared (again J & K) moduli for IC 1613, this time published by Pietrzynski et al. (2006). As such we are still no closer to understanding the differences seen in the NGC 6822 near-infrared data sets.
4 Limits on IRAC
Given the sensitivity of IRAC, especially for the shortest wavelength bands, modest integration times (hours) could, in principle, allow one to press the application of mid-infrared period-luminosity relations in determining distances out to several megaparsecs. Scaling from the data on IC 1613, similar Cepheids at a distance of 2 Mpc could be measured to the same signal-to-noise in about three hours.
However, sensitivity is not the limiting factor: crowding is. The mid-infrared studies of the stellar populations in WLM and IC 1613 by Jackson et al. (2007a,b) have convincingly shown that the vast majority of stars resolved at the brightest magnitudes (i.e., above the tip of the red giant branch, M = -6.0 mag and brighter) are IR-AGB stars, a substantial component of which (40-45%) are not detected in the optical. From the data presented in Figure 5 of Jackson et al. (2007a) it is possible to estimate the areal density of these stars across the face of IC 1613. From that we deduce that the mean separation of stars brighter than -6 mag at 3.6m is 18 arcsec. Translated into practical terms this means that for a galaxy 10 times further than IC 1613 (i.e. 7-8 Mpc) the average separation of bright sources would be less than 2 arcsec, which is now comparable to the resolution of IRAC. Even at the distance of IC 1613 itself we found that upwards of half of the known Cepheids in this galaxy were visibly contaminated.
Thus we estimate that care must be taken in using IRAC to measure Cepheids in galaxies another factor of two or three further in distance than IC 1613. More than half of the Cepheids will be crowded but for a given pointing the total number of Cepheids that fit in the detector’s field of view will also go up so that the absolute yield of uncontaminated Cepheids might be maintained at this limit. Pressing this method beyond 2 Mpc is best left for JWST; but everything inside of that sphere is plausibly within reach.
Using short-exposure, archival data from Spitzer we have demonstrated the feasibility of measuring mid-infrared magnitudes for Cepheids out to one of the most distant galaxies in the Local Group. Exposures a factor of 10 or more longer would only amount to a couple of hours and are not unreasonably long. These could allow one to press observations of Cepheids using IRAC on Spitzer out to 2 Mpc and into the nearby Hubble flow. The main limiting factor is crowding and contamination of the Cepheid photometry by the rise of infrared-bright AGB and extended AGB.
The two short-wavelength IRAC distance moduli to IC 1613 give individual distance moduli of = 24.290.07 and = 24.280.07 mag. When combined with optical (BVRI) and near-infrared (JHK) data we derive a true distance modulus to IC 1613 of = 24.270.02 mag (715 kpc) and a reddening of E(B-V) = 0.08 mag. The uncorrected IRAC observations alone are each within 0.02 mag of the finally adopted true modulus of IC 1613.
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|IC 1613:[S71] V20||1.619||16.49||16.45||16.19|
|0.09||0.17||. . .|
|IC 1613:[U01] 07647||1.219||17.56||17.87||. . .|
|0.09||0.17||. . .|
|IC 1613:[S71] V16||1.019||18.34||18.42||. . .|
|0.09||0.17||. . .|
|IC 1613:[S71] V06||0.973||18.68||18.64||. . .|
|0.08||0.16||. . .|
|IC 1613:[S71] V24||0.829||19.20||19.03||. . .|
|0.07||0.16||. . .|
|IC 1613:[S71] V22||2.093||15.29||15.24||14.95|
|0.09||0.17||. . .|
|B||24.56 (0.10)||Freedman (1988)|
|V||24.54 (0.09)||Udalski et al. (2001)|
|R||24.48 (0.11)||Freedman (1988)|
|I||24.44 (0.11)||Udalski et al. (2001)|
|J||24.39 (0.04)||Pietrzynski et al. (2006)|
|H||24.31 (0.09)||McAlary, Madore & Davis (1984)|
|K||24.30 (0.05)||Pietrzynski et al. (2006)|
|3.6m||24.29 (0.07)||this paper|
|4.5m||24.28 (0.07)||this paper|