4 Extraction of excess fluxes

Following the same steps as in Paper I, Tables 1 and 2 list the adopted $T_{\rm eff}$ for the objects in this paper, based on the literature and our analysis shown in Fig. 1 (available on line).

 

Figure 1: The detected JHK fluxes, plotted with available UV and optical data on logarithmic scales. Along the horizontal axis wavelength is plotted in units of Å while the vertical axis shows $\lambda^4 \times F_{\lambda}$ in units of Å$^4 \times$ erg/cm2/s/Å, along with a model that represents the best estimates of $T_{\rm eff}$. In each frame the object identify is labeled at the bottom. Near the top there is a legend explaining at which wavelength point the model flux was normalized to the observations. A letter code identifies this point; UBV refers to Johnson magnitudes, uvby to Strömgren data, capital letters subscripted with lower case g refer to Geneva bands and "IUE" followed by a number indicates that the IUE flux was used at the given wavelength (see Thejll et al. 1995) for details

For extraction of excess IR fluxes we scale an appropriate model spectrum to some point in the range of photometric data that we believe is unaffected by radiation from the companion. We always pick the point at which we do the normalization as redward as possible since picking a point far into the UV range can lead to practical problems if the far-UV flux is heavily depressed by metal opacities. Usually this depression is most severe on the blue side of 2000 Å. The excess in any band, but in particular the JH and K bands is then simply calculated by subtraction of the normalized model flux from the observations. We use the Kurucz (1993) grid of metal-line blanketed model spectra distributed on CD-ROM disks.

Using Kurucz models has obvious advantages over the simple BB analysis of Paper I. However, it also poses two main drawbacks to our study, as follows: i) the maximum effective temperature available is 50000 K; and ii) no He-rich models are available. Both have an impact on our conclusions regarding the claim of excesses (see Table 7) and must be kept in mind when dealing with their interpretation, specially among the hottest O type sds: BD+28 4211, PG2102+037, PG2158+082 and PG2352+181. However, none of these four met the 2$\sigma$ requirement to be analysed for excess. From the February, 1994, data the following sdO objects had already been found as binary candidates in Paper I: BD+10 2357, Feige 34, Feige 80, GD 299, HD113001 and HD 128220. But constraints i) and ii) may lessen the now newly discovered excesses for BD+37 1977 and BD+48 1777. On the other hand and in general, where the excesses mainly rest, at the longer wavelengths, for both i) and ii) the impact is the least, as already argued in Paper I.

In converting observed magnitudes into physical absolute fluxes we use the zero-point definitions tabulated by Zombeck (1990) for the UBVRI and JHK data, while we used Oke & Gunn (1983) for Greenstein multichannel data and Table 7 (first column) in Heber et al.$\,$(1984) for uvby data (see Paper I). In Table 7 we list the extracted J flux for stars with at least 2 $\sigma$ significant excesses (in JHK simultaneously), and also the calculated J-H and J-K colors of the excesses.

Using the Bessel & Brett (1988) tables of J-H and J-K colors we estimate the range of dwarf spectral classes that correspond to the extracted excess colours. These too are shown in Table 7.

  

Table 7: The excess fluxes in significant cases. Column 1 gives the object's name, 2 contains the excess J flux and its error, in units of $10^{-24}\, \rm erg/cm^{2}/s/Hz$, in 3 and 4 are given the J-H and J-K colours, respectively, of the excess flux. The Bessel & Brett (1988) dwarf type (their Table II) corresponding to the J-H and J-K colour ranges is in 5. The overlap in types is given; both type-ranges are shown in all cases where an overlap was not found. "ve'' and "vl'' indicate ranges that are outside the ranges of the Bessel & Brett table - either "very early'' (i.e. before B8 type) or `very late'' (i.e. after M5). The use of the $\rightarrow$X notation indicates a range including all previous spectral type up to the X type. Only systems where the excesses were significant at the 2$\sigma$level in each of the J, H and K bands are included. As the analysis of individual stars in principle is independent of that in Paper I we repeat objects here that appeared first in Paper I; February 1994, objects are quoted with "F'' after the target's name

We next derive companion classes for the hot subdwarf by fitting a weighted sum of two model spectra (using Kurucz (1993) models) to the collected and observed photometric data. The fitted weights are proportional to the areas of the stars, so after a successful fit the weight ratio is proportional to the ratio of stellar radii squared. The fit also gives the temperature of the best-fitting cool model. The results are shown in Table 8.

The fitting procedure is a least-$\chi^{2}$ method and in principle tests the fit of all Kurucz (1993) models against all other models in the grid. In practise we restrict the range of the models to fit since it is prohibitively time-consuming to fit all 3576 Kurucz models against each other - see the caption of the table. The hot model should not be chosen freely as some stars have very accurate atmospheric parameters from the literature and we do not wish to stray far from these values - this is a complicated process as some stars have lots of published photometric data, the fitting of which agrees well with literature values, while other stars have little observed data to work with but may have atmospheric parameters based on spectroscopy, while yet other stars have neither good photometric data nor published atmospheric parameters but only a simple estimate of the spectral type from the literature - frequently based on visual inspections of low dispersion spectra during some classification project.

In a few cases (Feige 80 and GD 299), this method yields a best fit Kurucz effective temperature for the hot component discrepant from previous literature determinations.

  

Figure 2: Comparison of companion types determined by two methods. Along the horizontal axis is plotted the limits on spectral class that can be inferred from the extracted J-H and J-K colours and the Bessel & Brett (1988) tables for real stars, while the vertical axis displays the spectral type inferred from fits of Kurucz model spectra

In Fig. 2 we compare the dwarf class inferred from extracted colors (Table 7) and fitted models (Table 8). We see that the agreement is quite fair although not complete. Of the 28 stars that had companion-type estimates from both methods, we used 21 stars that have limits on the Bessel & Brett class - i.e., according to notation in Table 7 no "vl" or "$\rightarrow$X" ones were included. Of these, only BD+29 3070 deviates by more than one spectral class.

The conclusion we can draw from this comparison of derived log(g) limits is that we appear to have 2 methods that are able, when the data is good, to jointly find the spectral type of the companion to within one class in about 75% of all cases.

  

Table 8: Results of fitting Kurucz models to the observed fluxes and summary of literature data for hot subdwarf log(g) values, and/or luminosity classes of companions. The columns are: (1) Object name, (2) $T_{\rm eff}$ of the assumed or fitted hot model, (3) the $T_{\rm eff}$ of the fitted cool model, followed in parenthesis by the dwarf spectral type derived from the temperature and standard tables (Zombeck 1990), (4) The ratio $R^\prime=R$(cool star)/R(hot sd), (5) the derived gravity of the hot subdwarf (upper limit) calculated from an assumed sd mass of 0.55 $M_{\hbox{$\odot$}}$, $R^\prime$and a mass of the cool companion derived from the mass-radius-$T_{\rm eff}$relationship for ZAMS stars from Zombeck, (6) literature values for surface gravity (with reference in parenthesis, see Table 1 and below) and (7) luminosity class of the companion from the literature, if known. In all cases, except for BD+34 1543 ([-0.5]), we have used solar metallicity models. Whenever possible we have chosen the log(g)=5.0 model for the hot star. Notes: ^a= log(g) based on equivalent widths determination; ^b= log(g) based on R and I photometric determinations by Thejll et al. (1994b; Th94). All other log(g) determinations are spectroscopic. B82=Baschek et al.$\,$(1982). B93=Boffin et al.$\,$(1993). K88=Kilkenny et al.$\,$(1988), Ra93=Rauch (1993), WSp60=Wallerstein & Spinrad (1960), WSK63=Wallerstein et al.$\,$(1963), WW66=Wallerstein & Wolff (1966), WS83=Willis & Stickland (1983)