3. Galactic distribution, extinction
To extrapolate from a local X/O nova rate to a galactic population of low mass BHB systems, one needs a distribution model. Here it is assumed the black holes are distributed similarly to other high mass star products at birth, namely the Galactic neutron stars. To minimize the extrapolation to the Galactic center, the BH systems are distributed according to the model of Johnston (1994) for the pulsar Galactic surface density
with kpc and kpc, which provides a good fit to the observed pulsar distribution, and avoids a large excess inside the kpc molecular gas ring. The thickness z of this disk is modeled as a Gaussian distribution with pc. This model follows recent high mass star formation; it might be argued that this under-counts old systems produced by the bulge. For example, in Sect. 6 the classical novae are considered, which have a significant bulge population. These are observed to follow the distribution of light in external galaxies, so Shafter (1997) models the Galactic population as
The scale heights of these populations are 100pc and 200pc respectively (Warner 1995) and, following the surface brightness distribution, 12% of the systems are found in the bulge.
The observed low mass BHB transients are discovered in X-rays, but confirmed via radial velocity studies in the optical. The quiescent counterparts are generally very faint, and optical extinction is a serious impediment to their study (Table 1). Extinction will, of course affect their outburst magnitudes and can be a very significant limit on detectability, even for systems with kpc. To follow the distribution of optical extinction with l, b and d in the Solar neighborhood, one may use the compilation of Galactic reddening from stellar observations described in Guarinos (1992). From this compilation of 15,500 measurements one may extract stars close to any given and follow the increase of with d to model the local extinction. In practice, regions of radius were used along the Galactic plane, and the top tercile of in each distance bin was selected to minimize bias against rare high lines of sight. These data allowed estimates out to kpc in the plane. When were needed at larger d than covered by the data for a given line of sight, an exponential dust disk of height 100pc and mean extinction in the plane of mag/kpc was assumed (cf. Burton and Deul 1987). There are, of course, long interarm regions that are relatively dust free in the galaxy. To model this 10% of the nominal disk's dust density was assigned randomly to 0.2 of the lines of sight beyond the local 2-3 kpc. This turned out to have a very small effect on the BHB statistics. This extinction model was checked against a number of measured extinctions, giving adequate estimates. While rare lines of sight through very large molecular clouds are not followed, the results should be reasonable for modeling of the nearby outburst sample.
© European Southern Observatory (ESO) 1998
Online publication: April 20, 1998