3 Radial velocities

The spectra in our sample included both single and composite systems. Their radial velocities were measured by cross-correlation with theoretical models for both hot and cool star spectra.

This process includes the subtraction of the continuum and the conversion of the wavelength scale to logarithmic units, before calculating the cross-correlation function (ccf). Several spectral regions were excluded from the ccf, including wavelengths corresponding to bad CCD columns, cool-star features in composite systems (e.g. the G-band at $\lambda$ 4200 Å), broad Balmer lines, or strong lines from the observed spectrum that didn't appear in the synthetic spectrum. The ccf was then converted to velocity units and the position of its peak was measured by fitting a Gaussian.

The cross-correlation templates used for measuring the radial velocities $v_{\rm rad}$ of each observed spectrum were taken to be the best-fit model spectrum for the total system as described below. Hence, for single spectrum sdBs, we obtain a single radial velocity. For composite systems, the blue spectrum is dominated by lines from the hot star and so provides the sdB star velocity. The red spectrum is dominated by calcium lines from the cool companion and hence gives the cool star velocity. The heliocentric velocities measured from each observation are given in Table 3.

 

 

Table 3: Heliocentric radial velocity measurements of single and composite sdB stars.

Star	HJD	sdB	K star
	(-2450000)	v	v	$\delta v$
Single
PG0004+133	705.704	-20.6 $\pm$ 4
PG0229+064	1091.702	7.6 $\pm$ 4
PG0240+046	1091.721	63.4 $\pm$ 2
PG0342+026	705.748	13.4 $\pm$ 8
PG0839+399	1265.387	25.7 $\pm$ 8
PG1233+427	1265.591	65.5 $\pm$ 8
PG2259+134	704.454	-14.4 $\pm$ 6
Composite
PG0110+262	704.639	1.0 $\pm$ 6	---	35.9
	705.733	---	36.9 $\pm$ 2
PG0749+658	1264.399	-21.0 $\pm$ 7	---	0.2
	1264.538	---	-21.2 $\pm$ 2
PG1104+243	1265.667	-4.6 $\pm$ 8	---	8.4
	1264.596	---	-13.0 $\pm$ 4
PG1701+359	704.359	-121.9 $\pm$ 3	---	13.9
	704.359	---	-135.8 $\pm$ 2
PG1718+519	705.377	-63.3 $\pm$ 3	---	14.7
	705.378	---	-48.6 $\pm$ 1
PG2110+127	704.399	27.0 $\pm$ 1	---	1.1
	696.543	---	25.9 $\pm$ 1
PG2135+045	1090.365	-30.0 $\pm$ 1	---	2.0
	696.580	---	-28.0 $\pm$ 2
PG2148+095	705.427	-152.7 $\pm$ 1	---	34.8
	705.426	---	-117.9 $\pm$ 2

Errors on individual velocities are the formal errors given by the least squares Gaussian fit to the ccf peaks. The actual errors are probably much larger, but difficult to determine quantitatively (the typical ccf width is 200-400  $\mbox{km}\,\mbox{s}^{-1}$). The standard deviation about the mean ($\sim$14  $\mbox{km}\,\mbox{s}^{-1}$) may be a better indication.

In composite systems, the difference $\delta v$ between the two component radial velocities would be a measure of the lower limit to the orbital velocity of the sdB star. Systems with large velocity differences between hot and cool components could be short-period systems, i.e. PG0110+262, PG1701+359, PG1718+519 and PG2148+095.

In the interim, other groups have used radial velocity studies to detect binary sdB stars (Maxted et al. 2001; Saffer et al. 2001). From our sample, the single-spectrum sdB PG0839+399 is a radial velocity binary (Maxted et al. 2001), while the composite-spectrum sdBs PG0749+658 and PG1701+359 do not show detectable velocity variations (ibid.). Consequently, our conclusions may be subject to unidentified systematic errors. In the case of PG0229+064 heliocentric radial velocities of $+8\pm2$ and $+8\pm3$  $\mbox{km}\,\mbox{s}^{-1}$ measured on 1998 July 20 and September 13 respectively (Ramspeck et al. 2001) are essentially identical with our own measurement. Additional velocities for PG1233+427 ($53\pm2$  $\mbox{km}\,\mbox{s}^{-1}$: 2000 January 30 and 31), PG0342+026 ($15\pm2$  $\mbox{km}\,\mbox{s}^{-1}$: 1998 Sep. 11, $14\pm2$  $\mbox{km}\,\mbox{s}^{-1}$: 2000 Jan. 30) and PG0749+658 ($-11\pm2$ $\mbox{km}\,\mbox{s}^{-1}$: 2000 Jan. 31) have also been communicated to us (Edelmann & Heber, private communication). These are not sufficiently different from our own measurements to make us suspect that any are short-period spectroscopic binaries.

Prior to analysis, the wavelengths of the observed spectra were corrected to the laboratory rest frame by applying these measured radial velocity shifts.