5. The observability of accreting neutron stars in dark clusters
How many HNS and DCNS should be present per square degree in the halo at large galactic latitude? In the case of the HNS, by using the value , this number is in the range objects per square degree (depending on the assumed neutron star core radius), if we take . In the case of the DCNS, their total number is independently from the dark cluster parameters, so that we expect DCNS per square degree.
However, the gas constituting molecular clouds diminishes (due to X-ray absorption) the number of accreting neutron stars that can be seen by a satellite. In particular, the expected number of HNS and DCNS in the field of view of a X-ray satellite has to be computed considering only those sources whose unabsorbed flux in the instrumental energy interval is above the sensitivity limit. The ROSAT satellite operating in the energy range 0.1-2.4 keV is by far the more sensitive X-ray detector, having a sensitivity at the threshold of erg cm-2 s-1. For comparison, the energy flux on the Earth of an unabsorbed X-ray source at a distance D is erg cm-2 s-1, showing that absorption is a crucial effect for discussing the detectability of HNS.
The absorption cross section in the ROSAT energy band for incoming X-rays on gas with interstellar composition can be parameterized in terms of the energy E (expressed in keV) as cm-2 (Morrison & McCammon 1983 ) 5. The corresponding values of result to be in the range cm-2, implying that gas column densities of cm-2 could be sufficient to obscure the emitted X-rays. This column density, for a single molecular cloud with cm-3 corresponds to a distance of the order of and this makes more likely the observation of neutron stars located only in the outer layer of dark clusters.
Actually, the previous values for have to be considered as upper limits, since we expect that molecular clouds have a lower metallicity (up to with respect to the solar one, see De Paolis et al. 1996b ). Indeed, for a low metallicity gas decreases significantly (see Fig. 1 in Morrison & McCammon 1983 ). This has a substantial effect in the energy range keV but already at keV the effect of assuming a low metallicity gas reduces the absorption cross section of a factor .
It is also known that UV and X-ray emission from a neutron star accreting in a molecular cloud ionize the ambient gas producing a HII region of dimension up to pc (Kallman & McCray 1982 ) for a X-ray luminosity erg s-1. This is relevant for DCNS, while in the case of HNS which have lower luminosity and move with high velocity through the accreting matter, a cometary structure of HII gas is instead produced with transverse dimension pc. Since ionization of hydrogen and helium reduces significantly the X-ray absorption (ionization of metals is not influent), the formation of these HII regions should help the visibility of accreting neutron stars.
Therefore, effects of low metallicity, ambient ionization as well as consideration of geometrical filling factor for molecular clouds in dark clusters should make observable DCNS in any position inside dark clusters. On the contrary, HNS should be detectable (at least in the mid 0.5-0.9 keV and high 0.9-2.0 keV ROSAT bands) only if located in an external layer with thickness of a few pc. This reduces roughly to one half the number of observable HNS so that we expect objects per square degree in the ROSAT field of view.
Actually, the dark cluster parameters are largely unknown and the expected number of HNS could substantially change if we take different values for the mass and radius. Moreover, as we have seen, X-ray absorption (besides molecular cloud parameters) also depends on the typical expected X-ray spectrum which, in turn, for low luminosity objects shows an overall hardening with respect to the blackbody at the neutron star temperature in addition to a significant excess over the Wien tail (see Zampieri et al. 1995 ). In conclusion, to perform a more quantitative determination of the expected number of HNS in the ROSAT field of view one needs to select values for a number of parameters which at the moment are largely unknown.
So far we discussed the possibility to detect HNS as isolated objects. However, it is also possible that unabsorbed X-rays from (unresolved) HNS contribute to the diffuse XRB. Parameterizing a generic point in the halo by coordinates (r, , ) and taking the Earth as the origin, the expected X-ray flux per unit solid angle is given by
where the HNS number density is given by Eq. (4) with and the factor has been introduced to account for the X-rays absorption by the halo gas in the dark clusters. The best chance to detect X-rays in question (avoiding absorption from interstellar gas) is provided by observations at high galactic latitude, and so we take in Eq. (8). Therefore, if we assume and , we get erg cm-2 s-1 deg-2 in the case kpc and kpc, respectively. This flux, for the effective temperature values given by Eq. (7), prevalently falls within the ROSAT energy band.
As a final point we note that if absorption is relevant, reprocessing of X-rays into infrared (due to vibrational-rotational transition of H2) should give rise to an infrared luminosity (Lepp & MacCray 1983 ). Also radio observations of free-free continuum and recombination line emission in the HII regions around accreting neutron stars could also be observed together with X-rays.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998