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.
Acknowledgements
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.