The fundamental plane of black hole activity

artistic impression

There are a number of distinctive signatures of black hole-powered activity that are usually regarded as proxy of  black hole existence.  Relativistic jets emitting synchrotron radiation in the radio band are one such signature, the second most common being the presence of strong, compact power-law X-ray emission commonly associated with the inner part of an accretion flow. Observationally, jet morphologies and spectral properties of both radio and X-ray cores are remarkably similar in stellar mass black holes  (galactic black holes, hereafter GBH) and in their supermassive counterparts  in the nuclei of galaxies (hereafter SMBH).

In collaboration with S. Heinz and T. Di Matteo, from MPA, I have recently examined the disc--jet connection  in stellar mass and supermassive black holes by investigating the properties of their compact emission in the X-ray and radio bands.  By compiling and analysing a sample of 100 AGN with measured mass, 5 GHz core emission, and 2-10 keV luminosity, together with 8 GBH with a total of 50 simultaneous observations in the radio and X-ray bands, I studied the correlations between the radio (L_R) and the X-ray (L_X) luminosity and the black hole mass (M). We demonstrated that the sources define a ``fundamental plane'' in the three-dimensional (log L_R, log L_X, log M) space (see Fig. 1 below).  This important empirical correlation has an elegant theoretical interpretation in terms of scale invariant jet models and can be directly used to constrain the dynamics of the accretion flow.

edge-on view of the fundamental plane
Fig.1: Edge-on view of the fundamental plane

Among active black holes, growing interest has been given in recent years to low-luminosity sources. It has become more and more evident that in order to understand their properties, not only advection, but also the back-reaction of relativistic jets/outflows on the accretion flow  needs to be taken into account. As a matter of fact, one of the results of the work on the fundamental plane  of black hole activity was to demonstrate that the observed scaling relations between L_R, L_X and M imply that the X-ray emission from black holes accreting at less than a few per cent of the Eddington rate is unlikely to be produced by radiatively efficient accretion, and is marginally consistent with optically thin synchrotron emission from the jet itself. On the other hand, models for radiatively inefficient accretion flows do agree well with the data. The exact physical nature of such flows, however, remains unclear. Does advection of energy across the black hole horizon plays an important role in the flow dynamics, or are powerful jet/outflows completely dominant?

This, and related questions, are the subject of a number of current projects of mine, focussed both on the study and modeling of spectra and variability of individual sources (as the low luminosity X-ray transient XTE J1118+480, in collaboration with T. Di Matteo, J. Malzac and A. Fabian) and on larger samples of both GBH and low luminosity AGN, with collaborators at SISSA, Trieste, and at the University of Amsterdam.

The cosmological growth of supermassive black holes: the X-ray/Radio connection

The observed correlations between the masses of black holes in the nuclei of nearby galaxies and global galactic properties, as the bulge luminosity or the central velocity dispersion, point towards a direct link between the physical processes that contribute to the central black holes growth and the formation of their host galaxies. Therefore, it is crucial to recover the history of SMBH growth for the entire population as closely as possible, if we want to understand the physical nature of such a link. Comparison of the local remnant black hole mass distribution with either integrated luminosity densities from accretion processes (as derived from the X-ray and Infrared backgrounds, for example) and accreting black holes luminosity functions (AGN and/or Quasars) suggest that black holes grew chiefly due to accretion of gas, and that mergers did not significantly contribute to the current mass build up. Under this assumption, the growth history of SMBH would in principle be completely determined by the joint evolution of the black hole mass function (BHMF) and of the accretion rate distribution function (BHARF).

The fundamental plane of black hole activity allows, for the first time, to draw a self-consistent picture for the joint evolution of both the BHMF and the BHARF, given the simultaneous  evolution of the observed hard X-ray and radio luminosity functions of AGN, a project I am currently involved in. Preliminary results clearly indicate that supermassive black holes grew in an  anti-hierarchical fashion, namely that mass was first assembled in high mass objects and later in lower mass ones. Thus, although the total black hole mass density is a monotonically decreasing function of redshift, the average black hole mass increases as we look backwards in time, as does the average dimensionless accretion rate.

As a goal for the next future, the evolution of the  joint (or conditional) hard X-ray/Radio AGN luminosity function will provide an unequivocal test of such a picture, as well as a probe of the fundamental plane relation itself at high redshift. In general, combined hard X-ray/Radio studies of the most distant accreting sources will provide valuable information on the assembly of the first structures.

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These pages are maintained by Andrea Merloni; last update: December 2003