Observational characteristics of accretion onto black holes

These notes resulted from a series of lectures at the IAC winter school. They are designed to help students, especially those just starting in subject, to get hold of the fundamental tools used to study accretion powered sources. As such, the references give a place to start reading, rather than representing a complete survey of work done in the field. I outline Compton scattering and blackbody radiation as the two predominant radiation mechanisms for accreting black holes, producing the hard X-ray tail and disc spectral components, respectively. The interaction of this radiation with matter can result in photo-electric absorption and/or reflection. While the basic processes can be found in any textbook, here I focus on how these can be used as a toolkit to interpret the spectra and variability of black hole binaries (hereafter BHB) and Active Galactic Nuclei (AGN). I also discuss how to use these to physically interpret real data using the publicly available XSPEC spectral fitting package (Arnaud et al 1996), and how this has led to current models (and controversies) of the accretion flow in both BHB and AGN.

💡 Research Summary

The manuscript is a pedagogical synthesis of material presented at the IAC winter school, aimed at newcomers who wish to learn how to interpret the X‑ray and multi‑wavelength spectra of accreting black holes. It begins by outlining the two dominant radiative processes that shape the observed spectra of both black‑hole binaries (BHBs) and active galactic nuclei (AGN). The first is inverse Compton scattering in a hot, optically thin corona, which up‑scatters soft photons from the accretion disc into a power‑law hard X‑ray tail. The spectral slope (Γ) and high‑energy cut‑off (E_cut) are directly linked to the electron temperature (kT_e) and optical depth (τ) through the Compton y‑parameter, providing a straightforward diagnostic of coronal physics. The second process is thermal emission from a geometrically thin, optically thick disc, described by the multi‑colour disc (MCD) model. The disc temperature profile follows T(r) ∝ r^‑3/4, leading to a characteristic ν^1/3 spectrum that peaks at kT_in. The peak temperature and inferred inner radius (R_in) give access to the black‑hole mass, spin, and accretion rate.

The paper then discusses how this radiation interacts with surrounding matter. Photo‑electric absorption imprints a series of low‑energy edges (e.g., O K, Fe L) that must be modeled to recover the intrinsic continuum. At higher energies, photons are reflected off the disc surface, producing a relativistically broadened Fe Kα line near 6.4 keV and a Compton hump around 20–30 keV. The shape of the line encodes the disc inclination, ionisation state, and the black‑hole spin through gravitational redshift and Doppler broadening. By fitting both absorption and reflection components simultaneously, one can constrain the ionisation parameter (ξ), reflection fraction (R), and geometry of the system.

A substantial portion of the manuscript is devoted to practical spectral fitting with XSPEC, the community standard software. The author walks the reader through the construction of a baseline model: “diskbb” for the disc blackbody, “nthcomp” (or “comptt”) for the coronal Comptonisation, and “pexrav/pexriv” or the more recent “relxill” family for relativistic reflection. Parameter linking (e.g., tying the seed photon temperature of nthcomp to the diskbb temperature) and strategies for dealing with degeneracies are explained with concrete examples from both BHB and AGN data sets. The author emphasizes the scaling differences: BHBs have masses of a few to tens of solar masses, rapid variability on seconds‑to‑minutes timescales, and disc temperatures in the keV range, whereas AGN host supermassive black holes (10⁶–10⁹ M⊙), vary on days‑to‑years, and emit disc photons primarily in the UV/optical band. Despite these differences, the same physical components can be applied across the mass scale, allowing a unified phenomenological framework.

Finally, the manuscript surveys current controversies. In the hard state of BHBs, the community debates whether the inner disc is truncated, giving way to a radiatively inefficient advection‑dominated flow (ADAF), or whether a compact “lamp‑post” corona sits above an intact disc, producing the observed reflection signatures. For AGN, the origin of the ubiquitous soft excess remains unsettled: is it a warm Comptonising layer, a blurred reflection component, or simply the high‑energy tail of the disc blackbody? The author points out that forthcoming high‑resolution X‑ray missions such as XRISM and Athena, together with coordinated multi‑wavelength campaigns, will be decisive in breaking these degeneracies. In summary, the paper serves as a concise yet thorough guide that equips beginners with the theoretical background, observational diagnostics, and practical tools needed to analyse accretion‑powered black‑hole systems and to engage with the ongoing debates in the field.