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Astron. Astrophys. 317, 689-693 (1997)

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4. The H distributions of sdB and sdO

We turn now from the small set of stars that both have known radial velocities and proper motions, to the larger set of stars that have known proper motions only.

To examine the relative population memberships of sdB and sdO we compared the reduced proper motions (Jones 1972) [FORMULA], where m and M are the apparent and absolute magnitudes, respectively, µ is the proper motion in [FORMULA] and T the tangential velocity in [FORMULA]. The resulting H distributions are seen in Fig. 2.

[FIGURE] Fig. 2. Reduced proper motions H for our sample of hot subdwarfs. [FORMULA], where m and M are the apparent and absolute magnitudes, respectively, µ is the proper motion in [FORMULA] and T the tangential velocity in [FORMULA].

Formally, the statistical significance of the different distributions of H is evaluated using Student's t test for distributions with possibly different variances. The probability that the two distributions have the same mean is found to be 0.0016 which we interpret as significant evidence that the two distributions of H are different. The [FORMULA] -test gives the probability that the two distributions of H are drawn from the same parent distribution - this has a probability of about 9%, calculated using the method in Press et al. (1992; Sect. 14.2). This also supports the idea that the sdB and sdO H distributions are different, although less stringently.

The distributions of H reflect both the velocity ellipsoid of the stars, the mean absolute magnitude of the stars as a group, and, importantly, the scatter in their absolute magnitude. To examine the H distributions further, we again assume that the stars belong to one of the four Galactic populations above, and calculate the expected H distribution for various assumptions about the mean absolute magnitude and scatter in absolute magnitude of the sdB and sdO.

As before, the stars are not optimally spread around the sky, but are in fact somewhat concentrated towards the galactic poles. We remove this bias as before by drawing stars from our simulated samples along the same lines-of-sight as in the observed sample.

We consider first the sdB because their absolute magnitude is more secure than the sdO.

A large number of simulations, over a grid in mean absolute magnitude [FORMULA] (sdB) and intrinsic scatter in the sdB absolute magnitude [FORMULA] (sdB), were run in order to smooth out statistical variations. For each of the four populations, the expected H distribution was simulated and compared to the H distribution of the real stars. The [FORMULA] statistic was calculated between the observed and model H distributions and the best fitting models found by minimizing this quantity. The results are shown in Table 3.


Table 3. Results of fitting the H -distribution for sdB.


Table 4. Hot subdwarf astrometry results. From the observations at the CAMC coordinates in epoch J2000.0 are given (coloumns 1-6). Proper motions have been calculated using the positions retrieved from the Astrographic Catalogue. Proper motions calculated by using a digitized version of the POSS, and the Guide Star Catalog are also given, when available. Double entries, such as for the star at (01 19 29.04 +24 25 31.86) gives first the values from the CAMC/AC and then secondly the GSC/POSS value. 7 stars in this table were only recoverable in the GSC/POSS system, and these are shown with the symbol ([FORMULA]) after the hh. Notes: a=PHL 678, b=PHL 2726=PB5795, c=PB6107, d=PHL 932, e=Feige 11=FB 13=PB 6252, f=Feige 19=PB 6715, g=TON 13=FB 55, h=GD299=FB 57, i=GD300=FB60, j=UVO1032+40=PB 385, k=Feige 34=FB 64=PB 462, l=TON 1273, m=TON 1281, n=LB1938, o=Feige 36, p=Feige 38, q=TON 1384, r=EG 81=Feige 46, s=PB3854, t=HZ 22, u=Feige 65, v=BD+18 2647, w=BD-7 3477=HW Vir, x=TON 139, y=HZ 38, z=LB27, aa=Feige 80, ab=Feige 87, ac=PB1207, ad=TON 183, ae=TON 194, af=Feige 95, ag=TON 209, ah=UVO1505+07, ai=TON 788, aj=TON 803, ak=LB9514, al=Feige 109, am=PB5333, an=GD314, and ao=GD108. The remainder of the tables of hot subdwarf astrometric data (Tables 5-9) is available at the CDS only (see footnote to the abstract).

As expected, the data could be well fitted for all four populations, by adjusting the mean absolute magnitude appropriately. However, since we know independently from the radial velocity analysis above that the sdB must be intermediate between old disk and thick disk in their kinematics, from this we estimate that the mean absolute V magnitude of the sdB is [FORMULA] (sdB) [FORMULA], with an intrinsic scatter in their absolute magnitude of 0.8 mag.

We have performed a similar analysis of the 28 sdO stars in our data. In this case, we are hampered significantly by not knowing the population type of the objects, essentially through having no radial velocity data. We can express our results relative to the sdB, however. We find that if the sdO stars are from the same kinematic population as the sdB (as would be the case in a scenario where sdB stars evolve to sdO stars) then the mean absolute magnitude of the sdO stars is [FORMULA] brighter than the sdB and the intrinsic scatter in the absolute V magnitudes [FORMULA] greater. These numbers have statistical errors of the order of [FORMULA], dominated by the effect of the smaller number of sdO. A significantly larger scatter in the sdO absolute magnitudes is very clearly indicated. This scatter is also seen when spectroscopically derived sdO temperatures and gravities are plotted using the assumption of a single mass (e.g. Thejll et al. 1994).

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Online publication: July 8, 1998