Assessing luminosity correlations via cluster analysis: evidence for dual tracks in the radio/X-ray domain of black hole X-ray binaries

Abstract

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 (since 2003), have resulted in an increasingly large number of outliers lying well outside the scatter about the quoted best-fitting relation. Most of these outliers tend to cluster below the best-fitting line, possibly indicative of two distinct tracks which might reflect different accretion regimes within the hard state. 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 multiwavelength coverage. Linear regression is then carried out on the clustered data to infer the parameters of a relationship of the form r = α + β x through a Bayesian approach (where denotes logarithmic luminosities). We conclude that the twocluster model, with independent linear fits, is a significant improvement over fitting all points as a single cluster. While the upper track slope (0.63 ± 0.03) is consistent, within the errors, with the fitted slope for the 2003 relation (0.7 ± 0.1), the lower track slope (0.98 ± 0.08) is not consistent with the upper track or 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. Additionally, there is evidence for at least two sources (H1743−322 and GRO J1655−500) jumping from the lower to the upper track as they fade towards quiescence, further indicating that black hole spin does not play any major role in defining the radio loudness of compact jets from hard black hole X-ray binaries. The results of the clustering and regression analysis are fairly insensitive to the selection of subsamples, accuracy in the distances and the treatment of upper limits. Besides introducing a further level of complexity in understanding the interplay between synchrotron and Comptonized 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-luminosity relations for the purpose of estimating a third parameter, such as distance or mass.

The black hole binary V404 Cygni: a highly accreting obscured AGN analogue

“…In this context, the fact that the reprocessed emission almost dominates the entire spectrum, implies that the emitted luminosity can be order of magnitudes higher than what is directly measured (see, e.g., Murphy & Yaqoob 2009), as our results suggest. This has strong implications in the context of X-ray/radio correlations (e.g., Gallo et al 2012). The large difference between observed and measured X-ray flux should be taken into account carefully, since while the X-ray emitting region could be almost completely obscured, the radio emitting region is most likely always visible as it is probably emitted from a few to tens of Rg away from the accretion disk midplane.…”

Gamma rays detected from Cygnus X-1 with likely jet origin

“…In addition, the HS generally displays relatively persistent relativistic jets emitting synchrotron radiation at GHz radio frequencies, whereas in the SS, where the disk comes up to the BH last stable circular orbit, such an emission is strongly quenched. A two-cluster non-linear correlation between the radio and the Xray fluxes, with slopes of ∼ 0.7 and ∼1, respectively, suggests that there is a close coupling between the X-ray and the radio emitters (Gallo et al 2003(Gallo et al , 2012. The existence of such a correlation was used to prove a possible synchrotron origin of the X-ray power-law tail (Markoff et al 2003).…”

Revealing the Nature of the Ulx and X-Ray Population of the Spiral Galaxy NGC 4088

“…If we assume for a moment that the source is residing in the low/hard state accreting at L < 10% Eddington (e.g., Done & Gierliński 2003), we are able to invoke the fundamental plane of accreting BHs (e.g., Merloni et al 2003;Körding et al 2006;Gallo et al 2012) and estimate a BH mass. For this, we use the 2-10 keV X-ray flux obtained from the Chandra spectral fitting and scale the 1.6 GHz flux density to 5 GHz using a radio spectral index α = 0.15 (a typical spectral index for flat cores used to estimate the BH mass from the Fundamental Plane, e.g., Falcke et al 2004).…”

“…In those cases where candidate radio counterparts have been identified, attempts have been made to obtain the BH mass using the Fundamental Plane of accreting BHs (e.g., Sánchez-Sutil et al 2006;Mezcua & Lobanov 2011;Webb et al 2012;Mezcua et al 2013a;Mezcua et al 2013c). The Fundamental Plane is a correlation between 2-10 keV Xray luminosity, 5 GHz radio luminosity, and BH mass that holds for sub-Eddington accreting BHs in the low/hard X-ray state and with steady jet emission (e.g., Merloni et al 2003;Körding et al 2006;Gallo et al 2012). The detection of compact core radio emission is required in order to locate a ULX in the Fundamental Plane, which can be achieved only by means of very long baseline interferometry (VLBI) radio observations.…”