4.1. X-ray observations
The maximum luminosity of an accreting source is known as Eddington limit:
where <> is the average flux-weighted opacity.
The term "ULX" is generally applied to X-ray sources outside a galactic nucleus which persistently exceed (when in an active state) the Eddington luminosity of a 7-M BH (thought to be the "canonical" BH mass value); some sources emit a luminosity of up to a few times 1040 erg s-1 (Roberts & Warwick 2000). In fact, it is necessary to distinguish between bright SNR (for which the Eddington limit does not apply) and accreting sources. Even in the absence of detailed spectral information, variability by a factor 2 is usually taken as a good indicator that a source is not an SNR. Correlation with a non-thermal radio source is another criterion to identify an SNR.
It is still unclear whether ultra-luminous accreting sources are simply the high-luminosity end of the X-ray binary population, or a different physical class of objects. No significant break or feature at L 1039 erg s-1 is found in the cumulative luminosity distribution of X-ray sources in galaxies which contain ULXs. However, the statistical error is large, due to the small number of sources in each galaxy above that luminosity.
ULXs are found in elliptical galaxies (eg, NGC 1553: Sarazin et al. 2000; NGC 4697: Blanton, Sarazin & Irwin 2001), associated with an old stellar population, often inside globuler clusters. Their location, and the steep slope of the high-luminosity end of the X-ray luminosity function suggest that, in this case, they are old systems accreting from a low-mass companion. On the other hand, ULXs are also often found in starburst or active star-forming galaxies (eg, M82: Matsumoto et al. 2001; the Antennae: Zezas & Fabbiano 2002). The X-ray luminosity function in these galaxies is typically an unbroken power-law with a flat slope, dominated at high luminosities by young high-mass XRBs. In this case, the ULXs appear to be associated with a very young stellar population.
X-ray spectral analyses do not provide a unique physical identification, either. Some ULXs can be fitted with a simple power law continuum (La Parola et al. 2001; Strickland et al. 2001). Others are better fitted with a disk-blackbody model (Makishima et al. 2000; Roberts et al. 2002) with color temperatures 1-1.5 keV (such high color temperatures can still be consistent with a high-mass accretor, if the spectral hardening factor is 3). Transitions from a hard to a soft state are seen in a few cases (Kubota et al. 2001), analogous to those detected in Galactic BH candidates. At least one ULX has a supersoft spectrum with a blackbody temperature of 80 eV (Swartz et al. 2002). Finally, X-ray variability studies have shown a range of different behaviours: most of the sources are persistent; a few are transients on timescales of a few months/years; others are highly variable on timescales of a few thousand seconds (a ULX in M74: M. Garcia 2002, priv. comm.)