3.3 X-Ray Variability

Active galactic nuclei vary most conspicuously in hard X-rays (2 - 10 keV). One might hope to use the variability timescale to constrain the size of the X-ray emitting region and hence to estimate the central mass. However, no simple pattern of variability emerges, and defining a meaningful timescale is ambiguous. One approach uses the ``fastest doubling time,'' t, to establish a maximum source size R c t. High-energy photons presumably come from the hot, inner regions of the accretion disk or in an overlying hot corona. For example, if R 5 R<sub>S</sub>, as deduced in some models, we obtain an upper limit to the mass, M<sub>BH</sub> (c<sup>3</sup> / 10G) t ~ 10<sup>4</sup> t M (t in s). Masses estimated in this way are generally consistent with those obtained from other virial arguments, but they are considerably less robust because of uncertainties in associating the variability timescale with a source size. For example, the x-ray intensity variations could originate from localized ``hotspots'' in the accretion flow.

X-ray reverberation mapping may in the future be a more powerful tool. The iron K line is widely believed to be produced by reprocessing of the hard X-ray continuum by the accretion disk. The strikingly large width and skewness of the line profiles (Figure 1), now routinely detected with ASCA, reflect the plasma bulk motion within 10 - 100 gravitational radii of the center. The temporal response of the line strength and line profile depends on a number of factors that, in principle, can be modeled theoretically; these include the geometry of the X-ray source, the structure of the disk, and the assumed (Schwarzschild or Kerr) metric of the black hole. Time-resolved X-ray spectroscopy should become feasible with the X-ray Multi-Mirror Mission (XMM) in the near future. We can then look forward to constraints both on the masses and the spins of BHs.