Assessing luminosity correlations via cluster analysis: Evidence for   dual tracks in the radio/X-ray domain of black hole X-ray binaries
  [abridged] The radio:X-ray correlation for hard and quiescent state black hole X-ray binaries is critically investigated in this paper. New observations of known sources, along with newly discovered ones, have resulted in an increasingly large number of outliers lying well outside the scatter about the quoted best-fit relation. Here, we employ and compare state of the art data clustering techniques in order to identify and characterize different data groupings within the radio:X-ray luminosity plane for 18 hard and quiescent state black hole X-ray binaries with nearly simultaneous multi-wavelength coverage. Linear regression is then carried out on the clustered data to infer the parameters of a relationship of the form {ell}_{r}=alpha+beta {ell}_x through a Bayesian approach (where {ell} denotes log lum). We conclude that the two cluster model, with independent linear fits, is a significant improvement over fitting all points as a single cluster. While the upper track slope (0.63\pm0.03) is consistent, within the errors, with the fitted slope for the 2003 relation (0.7\pm0.1), the lower track slope (0.98\pm0.08) is not consistent with the upper track, nor it is with the widely adopted value of ~1.4 for the neutron stars. The two luminosity tracks do not reflect systematic differences in black hole spins as estimated either from reflection, or continuum fitting method. These results are insensitive to the selection of sub-samples, accuracy in the distances, and to the treatment of upper limits. Besides introducing a further level of complexity in understanding the interplay between synchrotron and Comptonised emission from black hole X-ray binaries, the existence of two tracks in the radio:X-ray domain underscores that a high level of caution must be exercised when employing black hole luminosity relations for the purpose of estimating a third parameter, such as distance or mass. 
Elena Gallo, Brendan Miller, Rob Fender
astro-ph.HE