4.2. Three physical models for the ULXs
There are at least three models to explain the physical nature of the ULXs (having excluded the bright X-ray SNRs from this category):
The Eddington limit is proportional to the mass of the accreting object, hence a 100-M BH could have a persistent luminosity 1040 erg s-1. The first problem this model has to address is how to form them. It is still not known what the maximum mass is for BHs formed via SN explosions of single stars, and how this mass depends on the metallicity of the progenitor star. If BH masses 50 M are required to explain the observations, mergers of smaller-scale bodies in a dense environment are likely to be necessary. It has been shown (Sigurdsson & Hernquist 1993; Kulkarni, Hut, & McMillan 1993) that it is not possible to merge small (M 50 M) BHs in a globular cluster via three body interactions: recoils tend to kick the BHs out of the cluster before they can merge. However, mergers become possible if one considers four-body interactions (Miller & Hamilton 2002). The best chance to form an IMBH occurs if a number of progenitor stars coalesce first into a ~ 103 M star which would then undergo a SN explosion (Ebisuzaki et al. 2001). In this case, the formation process would be most likely to occur near the center of compact, young super-star clusters usually found in starburst galaxies. If super-star clusters are the progenitors of globular clusters, this could also explain the presence of IMBHs in the old globulars of elliptical galaxies. Yet another suggestion (Madau & Rees 2001) is that IMBHs could be pre-galactic remnants formed from the fragmentation of primordial molecular clouds. The second problem to address is how to feed them: a discussion on the mass transfer mechanism (Roche-lobe overflow or stellar wind) and allowed ranges of mass for the companion star is beyond the scope of this review. (See Zezas & Fabbiano 2002 for such a discussion regarding the ULXs in M82). Thirdly, how to observe them. The most reliable determination of the mass function for Galactic BHs comes from optical observations of photometric variations and line velocity shifts of the accretion disk and companion star over a binary period. It is of course more difficult to achieve that in other galaxies (for M83, distance modulus 28).
The classical Eddington limit assumes that the average opacity <> Th. However, this may not be the case if the radiating medium (accretion disk or stellar surface) is clumpy. It can be shown that the flux-weighted, volume-averaged opacity can be lower than the electron scattering opacity for an inhomogeneous medium (Shaviv 1998). If this is the case, more photons can escape without blowing away the accretion flow, so that steady-state luminosities ~ 1040 erg s-1 could in principle be attained by a stellar-mass BH with M 10M. Observational evidence for "super-Eddington" luminosities has been suggested in the case of novae (Shaviv 2001). Models of clumpy accretion disks based on the same principle have also been proposed (Begelman 2002). At L LEdd, all systems should develop strong radiation-driven winds, whose density and velocity could in principle be inferred from high-resolution UV and X-ray spectra.
If the X-ray emission is beamed towards us rather than isotropic, the estimated ULX luminosities can be scaled down, depending on the beaming factor. Beamed X-ray emission is known to occur in some microquasars (eg, GRS 1915+105). Such systems would appear highly super-Eddington if we happen to observe them pole-on (Fabrika & Mescheryakov 2001; King et al. 2001). It is sometimes possible to determine whether the X-ray emission is beamed by studying the optical spectral lines of the photoionized nebula around a ULX. A detailed discussion of this technique is presented by M. Pakull elsewhere in these Proceedings.
Thanks to Kinwah Wu, Rosanne Di Stefano, Albert Kong, Manfred Pakull, Andrea Prestwich, Doug Swartz for comments and discussions, to Stuart Ryder for the use of his AAT images, and to Reiner Beck for his VLA radio map.