5 Results

5.1 Single-star spectra

Figure 1 shows the best fit model for the single sdB star PG0004+133.

Figure 1: Normalized blue spectrum of the single sdB star PG0004+133 (histogram) together with the best fit model spectrum (polyline). The symbol $\times$ marks a CCD defect.

In addition to results reported in Table 4, the following individual remarks are noted. PG0004+133: since only the H$\gamma$ line is available, we have assumed T $_{\rm eff}$ from Paper I.

PG0229+064: with y=0.33, this is a helium-rich sdB star (Heber et al. 1999). The metal lines imply a higher metal abundance than assumed in the model. This has also been found by Ramspeck et al. (2001) who, in particular, find C and N overabundant by nearly one dex.

PG0240+046: an even more helium-rich sdB star with 66$\%$ of He abundance, consistent with a previous abundance of 55$\%$ Thejll et al. (1994).

PG0342+026: C, Si and Mg appear to be underabundant relative to the assumed solar composition.

PG0839+399 and PG1233+426: the helium abundance is below the measurement threshold, and metals are underabundant.

PG2259+134: C appears to be underabundant.

5.2 Composite spectra

Results for sdB stars with composite spectra are shown in Table 5. Figures 2 and 3 show best fits for the composite sdB star, PG2110+127.

Figure 2: Normalized blue spectrum of the composite PG2110+127 a) together with the best fit composite model spectrum b) formed by adding models with c)  $\mbox{\it T$_{\rm eff}$ }_{1}=26\,500$ K, $\mbox{\,log $g$ }_{1}=5.20$, y=0.01, $\mbox{\,$v_{\rm t}$ }_1=5$  $\mbox{km}\,\mbox{s}^{-1}$ and d) $\mbox{\it T$_{\rm eff}$ }_{2}=5400$ K, $\mbox{\,log $g$ }_{2}=4.40$, $\mbox{${\rm [Fe/H]}$ }=0.00$, $\mbox{\,$v_{\rm t}$ }_2=2$  $\mbox{km}\,\mbox{s}^{-1}$ with radius ratio R2/R1=4.7. The model spectra have been velocity shifted and degraded to match the observations. The symbol $\times$ marks a CCD defect.

The radius ratios (R₂/R₁) and hence, by implication, the radii of the cool stars (R₂) are all smaller than measured previously.

In nearly all cases, the Hei lines are weaker than predicted by models with $\mbox{\,$n_{\rm He}$ }_1=0.01$, implying hot star He abundances below this value. In addition, metal lines from the hot star, (e.g. silicon, carbon and magnesium), appear to be too strong in the model compared with the observations. Since we assumed $\mbox{${\rm [Fe/H]}$ }_1=0.0$, this implies that metals are generally underabundant in the sdB stars in our sample. This requires confirmation from high-resolution spectroscopy. In addition to results reported in Table 5, the following individual remarks are noted.

PG0110+262 and PG0749+658: C underabundant

Figure 3: Normalized red spectrum of the composite PG2110+127 around the infrared calcium triplet (histogram) together with the best fit model spectrum (polyline).

PG1104+243: with $y=0.01\pm0.01$, this is the most helium-rich composite sdB in our sample. The strength of the Ca K line and other metallic lines in the blue spectrum indicates $\mbox{\it T$_{\rm eff}$ }_2 = 6400 \,\mbox{K}$, $\log g_2=4.3$, and $R_2/R_1 \sim 6$. However, assuming the same radius ratio and $\mbox{${\rm [Fe/H]}$ }_2=0.0$, the red spectrum gives $\mbox{\it T$_{\rm eff}$ }_2 = 4500 \,\mbox{K}$ and $\log g_2=4.6$. Since the blue spectrum provides very strong constraints on $\mbox{\it T$_{\rm eff}$ }_2$ and R₂/R₁, it was necessary to adopt a reduced value for $\mbox{${\rm [Fe/H]}$ }_2=-0.5$ to maintain consistency with Paper I.

PG1701+359 and PG1718+519: C, Mg and Si underabundant. R₂/R₁ significantly smaller than in Paper I. This could be due to the adoption of too high metallicity $\mbox{${\rm [Fe/H]}$ }_2$.

PG2110+127: C, Mg and Si underabundant.

PG2135+045: C, Mg and Si underabundant. R₂/R₁ significantly smaller than in Paper I. This is probably due to the absence of IUE LW and JHK photometry which led to particularly large errors in the Paper I $\mbox{\it T$_{\rm eff}$ }$ measurements.

PG2148+095: C, Mg and Si underabundant. R₂/R₁ significantly smaller than in Paper I probably due to significant differences in $\mbox{\it T$_{\rm eff}$ }$. The latter are probably due to the absence of an IUE LW spectrum and a possible anomaly in the J-band photometry.

Significant differences between the results of the spectroscopic ( SFIT) and photometric (Paper I) analyses have been discussed above. Tables 4 and 5 also include the results of earlier photometric and spectroscopic analyses. The current results agree well with previous spectroscopic analyses (Moehler et al. 1990a; Saffer et al. 1994; Heber et al. 1999) in the cases of PG0342+026, PG0839+399, PG1233+426 and PG0749+658. They do not agree well in the cases of PG0004+133, PG0229+064, PG2110+127 and PG2135+045.

The high helium abundance may contribute to the $\mbox{\it T$_{\rm eff}$ }$ discrepancy in PG0229+064, a cool He-rich subdwarf with a relatively low surface gravity. Saffer et al. (1994) did not recognize the composite nature of PG0749+658 and PG2135+045, and it is not clear how they modelled the spectrum of PG2110+127. When deriving the sdB parameters, Theissen et al. (1993, 1995) corrected for the continuum light of the cool companions, but not the (weaker) Balmer lines from the cool stars. Therefore these results may not be fully reliable.

5.3 (logg-T $_\mathsfsl{eff}$) diagram and helium abundances

Figure 5 compares the sdB stars analysed here with an homogeneous sample of sdB stars (Moehler, private communication) and the location of the helium main sequence (He-MS) and zero-age extreme horizontal branch (ZAEHB) (Moehler et al. 1990a).

Figure 4: As in Fig. 1 but for the composite sdB star PG2148+095.

The surface gravities of hot stars in composite sdBs lie in the range $4.80 \le \log g \le 6.00$, while our sample of single sdB stars have $4.35 \le \log g \le 6.25$. Although both log g and T $_{\rm eff}$ ranges for composite sdBs are slightly smaller than for the single-spectrum stars, there is essentially no difference between their distribution in the log g-T $_{\rm eff}$ diagram and that of larger samples of sdB stars analyzed previously.

A striking result of this study is that the majority of single-spectrum sdB stars have helium abundances of y=0.01 or higher, while the composite stars have y<0.01 (the minimum currently available in our model grid).

Low surface He abundances are expected in sdB stars because of the competition between gravitational settling and radiative levitation acting on different ions. The same diffusive processes may be responsible for the apparently low abundances of carbon, silicon and magnesium in our sample (cf. Bergeron et al. 1988).

Figure 5: Position of single sdB stars (filled circles) and composite sdB stars (filled triangles) in the ( $\mbox{\,log $g$ }_1$- $\mbox{\it T$_{\rm eff}$ }_1$) diagram as derived from the spectral analysis SFIT. Open circles represent the position of an homogeneous sample of sdB stars (Maxted et al. 2001). The position of the He-MS and ZAEHB are represented as solid and dash-dotted lines, respectively (Moehler et al. 1990a).

It has already been noted that sdB stars with composite spectra and, hence, F-, G- or K-type companions form a distinct group from those with no or unseen companions (Saffer et al. 2001). With a separate evolutionary history, a distinct surface abundance might be anticipated, but remains to be explained.

Two single-spectrum sdB stars (PG0229+064 and PG0240+046) have $y\gg 0.01$. It is interesting that these particular examples lie at the extremities of our sample. Recalling the three groups of sdBs introduced earlier (Saffer et al. 2001), such helium-rich sdBs may form a completely separate subgroup. They were identified in the PG survey (Green et al. 1986: spectral classes sdB-O, sdOA and sdOD) and subsequently (Moehler et al. 1990a: HesdB, Saffer et al. 1994). The latter found most of the He-rich sdBs to have $\mbox{\it T$_{\rm eff}$ }>30\,000\,\mbox{K}$, and commented that it was difficult to reconcile these stars with time-dependent diffusion calculations.

We do not currently know whether any He-rich sdB stars are members of short-period binary systems. The latter is particularly important - one scenario for the production of sdBs is the merger of two helium-white dwarfs (Iben 1990; Saio & Jeffery 2000). The surface layers of the product may be so helium-rich that diffusive processes could not completely remove the surface helium. A significant number of He-rich binary sdBs would demand an alternative explanation.

5.4 Composite sdB companions in the HR diagram

The cool companions in binary sdB stars have surface gravities in the range $4.30 \le \log g_2 \le 4.58$. Figure 6 shows the position of the cool companion in binary sdB stars in the (log g-T $_{\rm eff}$) diagram as derived from SFIT together with the location of the ZAMS and TAMS from stellar models with solar composition (Girardi et al. 2000).

Figure 6: Position of the cool companion in composite sdB stars in the ( $\mbox{\,log $g$ }_2$- $\mbox{\it T$_{\rm eff}$ }_2$) diagram as derived from the spectral analysis. The position of the ZAMS and TAMS from stellar models with solar composition (Girardi et al. 2000) are plotted as dash-dotted and dashed lines, respectively. Labels refer to identification numbers in Table 7.

The observations are consistent with surface gravities of main-sequence stars. This comparison may be taken further by assuming a canonical 0.5$M_\odot$ for the masses of the sdB stars. Using the sdB surface gravities and the measured radius ratios, the luminosities of both components can be calculated (Table 7).

   

Table 7: Spectroscopically determined luminosities and masses for composite sdB star companions compared with the photometric analysis (Paper I). The luminosities assume 0.5 $M_\odot$ for the sdB stars (Heber et al. 1984; Heber 1986).

Star	SFIT		Paper I
	$L_2/\mbox{\,$L_{\odot}$ }$	$\mbox{\it T$_{\rm eff}$ }_2/\,\mbox{K}$	$L_2/\mbox{\,$L_{\odot}$ }$	$\mbox{\it T$_{\rm eff}$ }_2/\,\mbox{K}$
1 PG0110+262	$0.64\pm0.40$	$5250\pm~800$	$0.19\pm0.04$	$5485\pm~200$
2 PG0749+658	$0.19\pm0.08$	$5000\pm~500$	$0.18\pm0.07$	$5600\pm~300$
3 PG1104+243	$2.85\pm1.78$	$6400\pm1000$	$4.90\pm0.77$	$5735\pm~150$
4 PG1701+359	$0.21\pm0.14$	$6000\pm1000$	$0.48\pm0.10$	$6450\pm~230$
5 PG1718+519	$0.21\pm0.06$	$5200\pm~400$	$1.02\pm0.15$	$5925\pm~~70$
6 PG2110+127	$1.45\pm0.44$	$5400\pm~400$	$0.03\pm0.02$	$5500\pm~575$
7 PG2135+045	$1.17\pm0.48$	$5000\pm~500$	$0.31\pm0.54$	$4375\pm1790$
8 PG2148+095	$1.47\pm0.44$	$5700\pm~400$	$0.11\pm0.03$	$4375\pm~200$

Table 7 presents the luminosities, effective temperature and masses of the cool companions of composite sdB stars. These results reinforce our conclusion (Paper I) that the cool companions in composite sdB systems are main-sequence stars with $M \sim 1.0\pm0.1 \mbox{\,$M_{\odot}$ }$.

5.5 Mass ratios in composite sdB systems

The mass ratio of a binary system containing a hot sdB star and a cool companion is given by q = M₂/M₁. From g = (G M)/R² and the radius ratio R₂/R₁, the mass ratio can be expressed as

 

q = (R₂/R₁)² (g₁/g₂). (6)

This method of measuring q is subject to the normally quite large errors in measuring $\log g$. Mass ratios for composite systems analysed by us lie in the range 0.52 < q < 3.83.

Assuming the cool companions in our sample to be main-sequence stars with effective temperatures $4500 < \mbox{\it T$_{\rm eff}$ }_2/\,\mbox{K} < 6500$, then their masses should be in the range $0.75\le M / \mbox{\,$M_{\odot}$ }\le1.32$ (Gray 1992). Hence, assuming that the hot components of the binary systems are sdB stars with typical masses of $\sim$ $0.5 ~M_{\odot}$ (Heber et al. 1984; Heber 1986), then the mass ratios should be in the range $1.50 \le q \le 2.65$. Clearly, the surface gravity ratio method is not yet sufficiently sensitive to yield the mass ratio directly.