5 Deriving gravities for the hot subdwarfs

Another result of our model fitting procedure is the determination of gravity estimates for the hot subdwarf, by specifying a mass-gravity-temperature relationship for the companion with the aid of Eq. (5) in Paper I. For purposes of comparing to other work we will use, throughout, the standard assumption of 0.55 $M_{\hbox{$\odot$}}$(see also Paper I) for the mass of the hot subdwarf.

We can chose whatever mass-gravity-temperature relationship we think is appropriate for the companions, but note that use of a ZAMS relationship will tend to give upper limits on $\log(g_{\rm sd})$ which is desirable, also for comparision purposes. Many companions of evolved luminosity classes have been found and there are selection effects having to do with the relative brightnesses of the two stars that may make sub-giant or giant companions easier to find, in at least optical surveys, but as we use the full range of available UV and our own JHK data we think it is appropriate to at least start with the assumption that most companions will be in their longest phase of evolution - on the MS, and for simplicity we represent the MS by the ZAMS. The ZAMS mass-gravity-temperature relationship we use is based on tabulations such as those in Zombeck (1990). We perform linear interpolations in these tables.

The results of fitting our data is shown in Table 8. For this analysis only data for systems showing a significant excess (2$\sigma$ level at least) and yielding a convincingly good fit was employed.

We sorted those stars that could be analyzed with the Kurucz model fitting method into the sdB and sdO cases and made histograms of the derived gravity distribution. The results are shown in Fig. 3. The distributions are nearly indistinguishable, given the low numbers involved and that our analysis method is based on assuming ZAMS companions and that if the companion is more luminous for its spectral class than a dwarf then we will overestimate the gravity of the hot subdwarf - the one outlier at high log(g) in the sdB case and the 2 highest in the sdO case can then be removed and the difference between the log(g) distributions is then the slight excess of low gravity cases for the sdB's.

  

Figure 3: Derived upper limits for log(g) of the sample sdB and sdO stars. The bin width is 0.5

Next, among those stars for which an estimate of log(g) is available through other means, or for which the luminosity class of the companion is known (Table 8 summarizes what is known), we find a few (i.e., HD 149382, HD 185510, PG2110+127, PHL 1079, Feige 80, GD 299, HD 128220 and MRK 509C) that yield new log(g) values which may be discrepant by more than about 0.8 from previous ones. Some may contain Giant or Subgiant instead of ZAMS companions; HD 128220, for example, is a well established sd+subgiant case (Howarth & Heber 1990). We discuss HD149382 because as a well studied case (Saffer et al. 1994), it provides an example of a contradiction between its known log(g) values, based on spectroscopic analysis, and our upper limits. Is should be bared in mind the possibility that the cool star in this case be subluminous -i.e., halo system (Heber, private communication).

All the "binary'' cases we have here could of course be cases of chance super-impositions of one star on another with a resulting error in the derived log(g). "Companion'' stars that are closer to us than the hot subdwarf will cause overestimation of the hot subdwarf log(g), while "companions'' that are behind the hot subdwarf will cause the opposite to happen. As super-impositions are not entirely unlikely, but hard to evaluate, it is at present of greater interest to scrutinize our own method, and the individual spectroscopic analyses, in detail. Spectroscopic analyses have, in the contradictory case above, been performed without compensation for the excess flux of the "companion'' star. As the super-positioning of stellar spectra can lead to enhancement of spectral lines when lines coincide, and obliteration of lines when the companion star is line-free or -weak, an estimate of the companion spectral class and flux-contribution is needed to evaluate each case.

Several of the stars we have found to be composite have considerable contributions at optical wavelengths from the companion, and we suggest that reanalysis of these spectra, by subtraction of a suitable companion spectrum, could be beneficial in improving the determined atmospheric parameters.

For the particular case of HD149382, the contribution from the companion to its spectrum of is small - less than 10% at 5000 Å - so here we do not think the spectroscopic analysis was influenced much by the presence of excess flux. There is no significant discrepancy between the two spectral line analyses carried out by Baschek et al.$\,$(1982) with non-LTE models and Saffer et al.$\,$(1994) with LTE models for HD149382 - both results are significantly above the upper limit we get. As the star is bright it is not possible to use various digitized sky surveys to inspect the region near the sky for clues to the origin of the excess flux we see - the size of the aperture we used covers an area entirely dominated by the flux of this star so we can not rule out that the "companion'' is rather far from the target and thus unlikely to be physically related. However, as explained in Sect. 2 no visual evidence for contamination was detected at the time of the observation with the CST.