The shape of the accretion disk around a black hole can be determined by the polarization of its X-ray emission.

A team of astronomers from the Sternberg Astronomical Institute of Moscow State University, together with their Italian colleagues, developed an original method for determining the shape of accretion disks around black holes in X-ray binaries and active galactic nuclei by analyzing the degree of polarization of their X-ray emission. It turned out that the X-ray emission from accretion disks is sensitive to the disk shape and should be linearly polarized if the disk has a thin "pancake" shape. These theoretical predictions were confirmed by observations: the method was tested on several X-ray binaries with black holes, as well as on a Seyfert I galaxy.

Compact cosmic objects such as black holes (BHs) remain mysterious and essentially hypothetical, despite the discovery of numerous "black hole candidates" about which astrophysicists have little doubt (see, for example, the news item " The Black Hole of the Galaxy M87: An Interior Portrait ," Elements, April 14, 2019). Their research raises numerous questions that remain unanswered. For example, there is no clear understanding of what occurs in the immediate vicinity of BHs. Specifically, until recently, scientists could only make theoretical guesses about the shape of disks of matter falling into BHs (see the problem "Disk Accretion "). Various theories of the structure of accretion disks were proposed decades ago, but experimental data allowing one to determine which best describes reality was still lacking. This situation changed after the launch of the Imaging X-ray Polarimetry Explorer ( IXPE ) space telescope, which helped scientists obtain data that could revolutionize astrophysics textbooks.

There are three main possible shapes for an accretion disk: a "cylinder," a "sphere," and a thin, flat "pancake" (Fig. 2). The first calculations by Soviet astrophysicists in the 1970s hinted at a flat shape, but it was impossible to verify this guess at the time: telescopes and data analysis methods were limited in their ability to penetrate so deeply into the vicinity of black holes.

Observations of black holes conducted with the IXPE have confirmed what scientists had previously only suspected: X-ray emission from accretion disks is polarized . Furthermore, their polarization is linear and depends on the optical thickness of the disk, as well as its spatial orientation. The latter was predicted by Soviet physicists R. Sunyaev and L. Titarchuk back in 1985 based on theoretical calculations in strict accordance with relativistic radiative transfer theory (R. Sunyaev, L. Titarchuk, 1985. Comptonization of low-frequency radiation in accretion disks: Angular distribution and polarization of hard radiation ).

Now, MSU scientists have verified the previously proposed relationship between the degree of polarization, optical thickness, and the angle between the disk plane and the observer's direction, using a wide range of polarimetric measurements and synchronous spectral observations conducted by the NICER , NuSTAR , and Swift space telescopes. Importantly, confirming the relationship between polarization, disk thickness, and its orientation immediately confirms the shape of the accretion disk: it is "flat"! But first things first.

Back in 1973, N. Shakura and R. Sunyaev put forward a pioneering idea about how X-ray emission is formed in binary systems consisting of a normal star and a compact object (e.g., a black hole, Fig. 3). This idea is now generally accepted by the global astronomical community. The essence lies in the release of X-ray quanta during the formation of an accretion disk around the black hole, taking into account the viscosity of the flowing matter from the donor star onto the black hole (N. Shakura, R. Sunyaev, 1973. Black holes in binary systems. Observational appearance ). The accretion disk is a giant "whirlpool" or "donut" of hot gas and cosmic dust that forms when matter from the star is pulled by the colossal gravity of the black hole. This matter does not fall directly into the black hole, but swirls around it, accelerating to enormous speeds and heating up to millions of degrees. It is the main source of information about black holes, and astronomers can use its bright light to study their properties.

The first to conclude that polarization of radiation could be observed in binary systems was made by Chandrasekhar in 1946 (S. Chandrasekhar, 1946. On the Radiative Equilibrium of a Stellar Atmosphere ). He showed that in a plane-parallel electron-scattering atmosphere, radiative transfer leads to its polarization. However, Chandrasekhar's solution was intended for pure scattering in a semi-infinite atmosphere and still did not take into account disk geometry and the scattering of radiation with the acquisition of photon energy (i.e., Comptonization). R. Sunyaev and L. Titarchuk (in the above-mentioned 1985 paper ) were the first to calculate the angular and spatial distribution of the scattered radiation (over a time greater than the averaging time) for any optical depth.

The polarization of the radiation depends on the temperature of the accretion disk and the degree of ionization of its plasma. Furthermore, the ionization state also depends on the density. In fact, a classical accretion disk emits radiation characteristic of a perfect blackbody (N. Shakura, R. Sunyaev, 1973. Black holes in binary systems. Observational appearance ). This radiation is repeatedly scattered in the hot Compton cloud , and only this radiation is scattered to energies of 2–8 keV (this is precisely the range in which IXPE measures polarization). That is, it is this radiation that undergoes Comptonization upon reflection from the flat surface of the disk, and it is sensitive to the physical parameters of the disk (Fig. 3).

What happens inside the disk? Is polarization of X-ray radiation possible there? Inside the disk, all radiation is in thermal equilibrium and is not scattered at all, but if a blackbody photon is emitted, it is immediately absorbed (see G. Rybicki, A. Lightman, 1979. Radiative Processes in Astrophysics ). But in the hot Compton cloud, blackbody photons are indeed scattered, gaining energy.

As mentioned at the beginning of this text, the shape of the accretion disk has long been a subject of debate among astrophysicists. According to various sources, it may be spheroidal, flat, or lenticular (convex or concave). This was in part due to optical observations of the polarization of X-ray radiation from galaxies in which accretion disks form around supermassive black holes. However, these observations did not allow us to understand where the polarization of X-ray radiation actually occurs (in the bulge , in the disk, or in some part of the disk) or the shape of the main "polarizer." It turned out that the outer parts of the disk, in a sense, have a life of their own and do not actively participate in polarization.

Interestingly, previous models, which used a rather crude approximation, treated the disk as a cylinder with flat upper and lower boundaries (a "flat" disk). This is because rotating matter falling onto a central object (e.g., a black hole) forms a disk, elongated in the plane of rotation, under the influence of centripetal force and tidal forces (this issue is discussed in detail in the "Flat" Universe problem).

As shown by R. Sunyaev and L. Titarchuk (in the same 1985 article ), polarization of X-ray emission from a binary system occurs only in the inner part of the disk (in the Compton cloud, CC)—where the interaction of "cold" radiation with hot electrons occurs. Moreover, the degree of polarization depends on the spectral state of the black hole: it is higher in a high-luminosity state with a soft spectrum and lower in a low-luminosity state with a hard spectrum (Fig. 4; the spectral states are discussed in detail in the article Spectral Signatures Distinguishing X-ray Binary Systems with Black Holes and Neutron Stars ).

Comparison of theoretical calculations with observational data for a number of X-ray binary systems and active galactic nuclei confirmed the correctness of the described approach and also brought certainty to the diversity of previously proposed disk shape models, leaving only the “flat disk”.

Indeed, a simple comparison of the degree of polarization \(P\) measured with IXPE, plotted along the vertical axis (Fig. 5, left), and the disk inclination angle \(i\) (more precisely, \(cos i\)), plotted along the horizontal axis (this angle is known from observations), for various X-ray binary systems with BHs, showed that the intersection of these quantities lies on the graph (dark green curves) in accordance with the theory for the case of flat disks. And there are no intersections outside the theoretically calculated curves. Moreover, each of the curves, accompanied by the optical depth value, again exactly agrees with the theoretical prediction for the case of a flat disk. This means that all these disks are flat!

The results obtained, even though they were predicted 40 years ago and then "set aside" due to the impossibility of observingly verifying the polarization effect, turned out to be unexpected. They will have to be taken into account—this will undoubtedly lead to a revision of many accretion disk models due to possible discrepancies with observational data. Thanks to the described results, astrophysicists can now verify the degree of polarization when calculating the parameters of X-ray emission models. IXPE revealed the secrets of polarization and the characteristics of not only stellar-mass black holes but also supermassive black holes, whose radiation was also linearly polarized during Comptonization in the hot plasma of a flat accretion disk. The dependence of the degree of polarization of supermassive black holes on the disk's spatial orientation was confirmed.

In summary, the long-standing theory has gained a solid experimental basis, and the work under discussion not only confirms old conjectures, but also opens up a new way to study the most extreme objects in the Universe.

Source: Lev Titarchuk, Paolo Soffitta, Elena Seifina, Enrico Costa, Fabio Muleri, Romana Mikusincova. X-ray linear polarization prediction in black hole binaries and active galactic nuclei and measurements of it by IXPE // Astronomy and Astrophysics . 2025. DOI: 10.1051/0004-6361/202554834.

Elena Seyfina