3 Spectroscopy

Medium resolution (4-6 Å) spectra were obtained in 1993 at the Calar Alto 2.2m telescope equipped with the B&C Cassegrain spectrograph, and in 1998 at the same telescope but using the CAFOS spectrograph. Details of the observations are listed in Table 1. Besides the Balmer lines of hydrogen, He I lines and He II 4686Å are detected in all stars. The exposure times are much longer than their oscillation periods (see Table 3) and therefore the spectra are time-averaged. Due to the poor quality of the spectrum of HS0444+0458 we re-observed the star with the DFOSC at the Danish 1.5m telescope at ESO. Spectra with two grisms (#6 and #7) were taken to cover the whole Balmer series.

The available spectra of HS1824+5745 and HS2151+0857 are of lower quality than those of the other two stars, and cover a smaller wavelength range, which allows to use only H$\beta$ to H$\delta$ for the spectral analysis.

A grid of synthetic spectra derived from H-He line blanketed NLTE model atmospheres (Napiwotzki 1997) was matched to the data to simultaneously determine effective temperature, gravity and He abundance (Heber et al. 2000). The line profile fits are displayed in Fig. 1 and the resulting atmospheric parameters are listed in Table 2. Statistical fitting errors are low for HS0039+4302 and HS0444+0458. However, systematic errors, which can only be estimated quantitatively from repeated observations, contribute significantly to the error budget. The error estimates in Table 2 are based on our previous experience (see Østensen et al. 2001). Adopting the canonical mass of $0.5~M_\odot$ for the sdB, we can estimate their absolute visual magnitudes and distances (as listed in Table 2).

Figure 3: Observed and synthetic light curves for HS0039+4302. The scale on the x-axis above the plot shows time in seconds with an arbitrary zero point, and the scale on the bottom shows absolute time of observation in BJD when the numbers in parentheses are added.

3.1 Discussion

The determined temperatures, gravities and helium abundances are typical for pulsating sdB stars, as it can be seen when comparing with known sdBVs (Fig. 2). HS0039+4302 is located right in the centre of the sdBV ( $T_{\rm eff}$, log g) distribution at a position close to PG1336-018 (Kilkenny et al. 1998).

The position of HS0444+0408 is similar to that of KPD1930+2752 (Billères et al. 2000) to within the error bars.

HS1824+5745 has effective temperature and gravity close to that of EC10228-0905 (Stobie et al. 1997).

HS2151+0857 has similar effective temperature and gravity as the class prototype EC14026-2647 (Kilkenny et al. 1997), and forms the high gravity edge of the known sdB stars in the ( $T_{\rm eff}$, log g) diagram (see Fig. 2).

No indications of any binary companion stars are found in the spectra of any of these four sdB stars. Neither absorption lines such as the Mg I triplet, the G band or Ca I 4226Å can be detected nor is there any flux excess in the red part of the spectra which could be caused by late type companions. Any companion therefore must be considerably fainter than the sdB stars whose absolute visual magnitudes are in the range M_V=4-5 mag (see Table 2). The spectra are not suitable for radial velocity measurements and therefore we cannot test whether the star that we have multiple spectra of, HS0444+0408, is a radial velocity variable or not.

 

 

Table 4: Time-series photometry.

Object	Date	Observers	Start	Length
	(2000)		(UT)	(s)
HS0039+4302	Oct. 4	RØ, JES	23:07	3880
	Oct. 5	RØ, JES	23:15	7720
	Oct. 7	RØ, JES	01:35	9100
HS0444+0458	Oct. 6	RØ, JES	02:27	3240
	Oct. 7	RØ, JES	04:55	5560
	Oct. 8	RØ, JES	02:37	5260
HS1824+5745	Jul. 9	RØ, RS	00:52	4100
	Jul. 10	RØ, RS	00:23	3800
	Jul. 11	RØ, RS	00:22	2820
HS2151+0857	Jul. 9	RØ, RS	03:14	4360
	Jul. 10	RØ, RS	02:49	5040
	Jul. 11	RØ, RS	03:18	8400