G. Paolo Di Benedetto
C. N. R. - Istituto di Fisica Cosmica, Via Bassini 15, 20133 Milano, Italy
The relevant advantages in using PLC relations for getting Cepheid distances have long been recognized. These notably include a lesser sensitivity to interstellar reddening along with a reduced intrinsic dispersion of individual data due to thermal compensation by a color term. Accurate stellar surface brightness data available by means of observational interferometry now enable a reliable representation of Cepheid luminosities to be done according to the period P and a color C. Hence, a more fundamental calibration of the cosmic distance scale can be established by ground-based and HST photometric observations of Cepheids.
Empirical pulsation parallaxes to Cepheids are derived by matching the photometric angular size of photosphere inferred by a surface brightness-color SC relation to the corresponding linear size determined by the period-radius PR relation (Di Benedetto 1994). According to the Stefan's LRTe law in the V-magnitude system, these distances can also be converted into PLC luminosities by
where and () are the coefficients of the PR relation and SC relation, respectively, to be calibrated independently. The pulsational approach, revisited according to fully empirical SC correlations, has several advantages with respect to the current calibrations by the ZAMS-fitting method. First, it fully decouples the contribution to luminosity due to Cepheid radius essentially independent of abundance and temperature variations, according to results of pulsation theory, from that due to Cepheid temperature which includes all of dependence on metallicity and reddening variations. At a constant slope , these effects would induce systematic shifts only on the zero-point. Second, the SC correlations of any ensemble of Cepheids, and then the corresponding PLC relations, can be investigated against these shifts by reference to a suitable unbiased color-index. This would avoid theoretical corrections for metallicity currently applied to the ZAMS equations.
Among several observational results now available by different techniques, the modern Michelson stellar interferometry has provided the empirical SC correlation in the IR color (V-K) by measuring accurate angular diameters of non variable giant and supergiant stars (Di Benedetto 1993). According to empirical and theoretical results, this IR relation was found to be an ideal reference for inferring unbiased stellar angular sizes. Since it notably covered the Cepheid color domain, it has been further applied for investigating the SC correlations of ensemble of Cepheids at different degree of metallicity (Di Benedetto 1995). Some relevant results achieved for optical PL(V) and PLC (V, B-V) relations are of major concern. First, the luminosities of GAL Cepheids were found to be remarkably consistent with those from the ZAMS calibrated equations (Feast & Walker 1987). By applying current best estimates of optical reddening to all Cepheids concerned, the average residuals amounted to mag (PLC) and mag (PL). Second, the overall PLC residuals with respect to the IR reference were found to be much less affected by the metallicity than PL ones. The PLC shifts amounted to less than 0.1 mag (LMC and SMC), whereas the PL ones resulted to be greater than 0.1 mag (LMC) and 0.2 mag (SMC). Third, the above findings were strongly supported by theoretical PLC and PL relations derived according to the composite PLTe relation along with empirical thermal scales and .
Since, notably, the Johnson-Cousins color (V-Ic) must be less affected by abundances than the (B-V) color, the PLC (V, V-Ic) relation calibrated according to the above outlined procedures (Di Benedetto 1996) is expected to yield Cepheid distances almost unbiased by the metallicity of the host Galaxy. This relation is given by
with the reddening correction due to visual absorption Av separated from the apparent color.
In order to derive distance moduli to external Galaxies, the published Cepheid photometry in the Johnson-Cousins V, Ic magnitude system has been widely adopted as fiducial. Table 1 summarizes the results achieved for the apparent PLC distance moduli together with the reddening corrections (Av/20) for yielding true data. The quoted errors are internal and an additional allowance of 0.07 mag should be made to take into account the error on the zero-point determination. Table 1 also reports the true PL distance moduli together with the Av data derived by means of the PL(V) and PL(Ic) relations. To be conservative with the currently published results, the PL zero-points were calibrated with reference to LMC data (Madore & Freedman 1991) and apparent moduli and along with estimates of reddening were determined according to available standard procedures (Freedman 1988, Freedman et al. 1991, Freedman et al. 1992, Freedman et al. 1994, Saha et al. 1994, Saha et al. 1995). Somewhat different values of and Av with respect to published data may be due to either the extinction best determined by our calibration or the use of only V, Ic photometry in ground-based observations.
The PLC and PL results are compared between each other in the last column of Table 1. It can be seen that the luminosity residuals show to be affected by a systematic shift likely due to a difference between the independent absolute calibrations. In addition, this shift is not of constant value for each sampled set of Cepheids, likely revealing a bad compensation of thermal effects induced by the host Galaxy. These uncompensated effects must be now ascribed to the use of PL relations critically sensitive to metallicity, notably the PL(V) one, as earlier reported.
Awaiting space astrometry for a quite fundamental approach to the absolute calibration of the cosmic distance scale, it seems likely, at present, to assume as real the shift of about 0.14 mag between the PLC and PL distances of LMC. The somewhat increased distance to LMC by recently revisited data of SN 1987A (Crotts et al. 1995) as well as the remarkably consistent PLC distance moduli now achieved through B, V, Ic, K photometry would also strengthen the actual conclusion. This would imply an overall correction of distance scale by HST observations of about 7 % towards longer distances. Of course, the most relevant improvement is related to a low sensitivity to the reddening and now to metallicity inherent in the use of PLC rather than PL relations.
Table 1: Cepheid distances to Galaxies by V, Ic photometry.
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