To the 100th anniversary of the birth of Ya.B. Zeldovich
How the theory of disk accretion was created
N. I. SHAKURA,
Doctor of Physical and Mathematical Sciences GAISH MSU
It was the summer of 1963. After the final exams at the secondary school of the urban village of Parichi in the Gomel region, on some business I went to the city of Bobruisk, went to a bookstore and saw there the book “Higher Mathematics for Beginners” by Ya.B. Zeldovich. Naturally, the name of the author did not mean anything to me, but the content of the book interested me for the following reason.
In those now distant times, secondary education in mathematics ended with the taking of limits. They were preceded by elementary functions, one of which is a parabola. It was necessary to find the position of the minimum (parabola with “horns” up) or maximum (parabola with “horns” down). Explaining how this is done according to the then existing methods using the Vietta formula, the school teacher of mathematics (as well as physics and astronomy) Alfred Viktorovich Baranovsky said the following: "But by the methods of higher mathematics, these minimaxes are calculated much faster and more beautifully." Alfred did not conduct special classes with the leaders of the school process. I received my individual development in mathematics by getting acquainted with the content of problems sent by mail from Moscow State University.
After buying the book, I went into a small cozy park on Ba-khareva street and started leafing through it. The first pages outlined school concepts: functions, schedules, speed, acceleration ...
More I am in the book of Ya.B. Zeldovich did not drop in, he had to go to Moscow to take the entrance exams at Moscow State University. I chose the astronomy department while already in the admissions office: only a little over two years have passed since Yu.A. Gagarin. Still, the decisive role was played by a book titled "Studies of the Universe", written by Professor BA. Vorontsov-Velyaminov. As a student, I listened to Boris Alexandrovich's lectures and, naturally, passed him an exam. At school we taught astronomy from his standard high school textbook, Astronomy. It didn't even occur to me then that only two or three years would pass and he would teach me a course in higher astronomy.
The first three years of training passed without Ya.B. Zeldovich. Moreover, I forgot about the book I bought in Bobruisk: it was not included in the standard university textbooks. It was intended for those who comprehend higher mathematics by self-
© Shakura N.I.
Academician Y.B. Zeldovich speaks at the seminar. 1974 year
of education. The academician addressed it to novice engineers and technicians. Moreover, there is a wonderful photo where he presents a two-volume edition of his selected works to Pope Paul-John II.
My scientific career began in my third year in the solar department of the GAISH MSU. Under the guidance of Olga Nikolaevna Mitropolskaya (wife of Professor Solomon Borisovich Pi-kellner) and Anna Ivanovna Kiryukhina, I studied the mechanisms of broadening of absorption lines in the solar spectrum.
When I was in my third year, I was lucky to see Yakov Borisovich. The dean's office of the Faculty of Physics organized a meeting of the students of the faculty with the editorial board of the journal in the Large Physical Auditorium
"Advances in Physical Sciences". The editor-in-chief, the brilliant Eduard Vladimirovich Shpolsky, made a strong impression. I WOULD. Zeldovich was present, but did not speak.
The first time I met an academician in person was a year later, when he began lecturing for fourth-year students. In the fall of 1966, we, students of the Astronomy Department of the Physics Faculty of Moscow State University, discovered a new special course in the class schedule - "The structure and evolution of stars", which was prepared by Ya.B. Zeldovich. Lectures were given on Fridays, and on Thursdays, under the leadership of YaB (as his fellow scientists called him), the Joint Astrophysical Seminar (OAS) was held at the Moscow State University of Astrophysics. It was attended not only by established scientists, but also
young people who have recently graduated from higher education. Students ran to this seminar whenever possible, since it was not on the schedule of training sessions. After his first lecture, Yakov Borisovich asked those wishing to get a topic from him for a term paper to stay late. Several students, myself included, stayed in the classroom. When it came to me, he asked if I was present at the SLA meeting yesterday. I answered in the affirmative. On the second question: did I listen to the report on the (then mysterious) sources of cosmic X-ray radiation, the answer was also in the affirmative. Then Ya.B. Zeldovich said: "Try to calculate the structure and emission spectrum of a powerful shock wave that occurs as a result of gas falling on a neutron star near its surface."
The first sources of cosmic X-ray radiation were discovered by a group of American scientists, headed by Professor Ricardo Giacco-ni, during the launch of the Aerobi geophysical rocket on June 18, 1962. By the early 1960s. one extraterrestrial source of X-ray radiation was already known - the corona of our Sun. It turned out that the coronal gas was heated by some mechanisms to a temperature of several million degrees and the luminosity of the solar corona in this range is approximately one millionth of the optical luminosity of the Sun (4x1033 erg / s). It was natural to assume that hot coronae exist around other stars as well. However, a simple calculation showed that the detectors of those times could not register even the corona of the nearest stars from a distance of several parsecs. Scientists were hoping for the discovery of X-rays from the moon! Of course, the Moon has no atmosphere. However, a possible mechanism consisted in the fluorescent glow of the lunar soil, irradiated
expected by X-rays coming from the solar corona. The Aerobi rocket reached an altitude of 225 km, the flight lasted 350 s. Of the three Geiger counters with a large area and good sensitivity in the energy range of 1.5-6 keV, two were constantly operating. In this range, the earth's atmosphere is completely opaque. Instead of X-rays from the Moon, they discovered a bright previously unknown source located far beyond the solar system in the direction of the constellation Scorpio, dubbed Sco X-1. Later, as a result of rocket launches, new X-ray sources began to be discovered. Gradually, a map of the X-ray sky was created with sources of different nature, they were named in accordance with the direction of which constellation they were (for example, Cyg X-1, Cyg X-2, Her X-1, Cep X-3). As it turned out later, their X-ray luminosity was thousands, or even tens of thousands of times higher than the optical luminosity of the Sun. Thus began the era of X-ray astronomy, the era of extraordinary discoveries in the Universe.
In the fall of 1966, a few weeks after the start of classes, Valentina Yakovlevna Alduseva, a scientific secretary of the Department of Astrophysics, a researcher at the GAISh, approached me to clarify the topic of my term paper. “Kolya, Academician Zeldovich has set the task for you to develop an accretion model,” she said. It was then that I first heard the mysteriously sounded word "accretion" and was extremely surprised. After all, the academician asked me to calculate the structure of the shock wave and at first did not use this term in his conversations with me, and in the standard astronomical courses of those times, the concept of accretion processes was absent.
Seeing my confusion, Valentina Yakovlevna invited me to use the scientific library
X-ray radiation
Accreting
Shock wave
Diagram explaining the occurrence of a shock wave near the surface of an accreting neutron star.
GAISH. I found out that the word "accretion" is of Latin origin (aoogeHo) and means increment, adding something. In astronomy, the term accretion means the processes of falling on gravitating centers of various natures of the rarefied matter surrounding them. Yes, then, more than half a century ago, the theoretical study of the processes of accretion of matter in the Universe was in its infancy. Moreover, in the 1950s. the stellar winds were discovered,
preventing interstellar matter from falling onto the surface of ordinary stars. The reasons for the generation of stellar winds in different classes of stars (including our Sun) are different, but there is no accretion onto ordinary single stars. The final stages of stellar evolution are a different matter: white dwarfs, neutron stars and black holes.
Two types of accretion disk formation in close binaries with relativistic stars.
goy - the famous American physicist E. Salpeter. They drew attention to the energy release in the shock wave arising from the supersonic motion of a black hole in an extensive gas cloud. Near a black hole, after the shock wave has passed, the gas heats up so much that it begins to emit energy in the X-ray and gamma ranges.
In the fall of 1966, under the guidance of Yakov Borisovich, I began to calculate the structure and emission spectrum of a strong shock wave that arises near the surface of an accreting neutron star. The complexity of the problem was that the path length of the incident particles to their complete stop is tens of times greater than the characteristic scale of interaction of radiation with matter. When solving many problems, there is no need to consider the structure of the shock wave - it is enough to set the jump in density, pressure, temperature, and other physical quantities depending on the rate of fall and the adiabatic index of the substance. In the task at hand, both the density, and the temperature, and other quantities varied in the deceleration zone with the release of energy. Moreover, in this zone, the emergence of collective plasma processes is not excluded with the arrival of the calculation at a more complex level of physical kinetics instead of the usual
hydrodynamics. Eventually, it was shown that the emission spectra of shock waves from accreting neutron stars explained the data obtained as a result of rocket launches.
In the 1960s. the first identifications of cosmic X-ray sources in the optical range appeared, which made it possible to estimate the distance to them and their luminosity. YaB and I became clear
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Many models of optical and X-ray emission of quasars are based on quasi-spherical, or disk, accretion onto black holes (Section 4). An important parameter in these models is the ratio of the fall time to the cooling time.If this ratio is much greater or much less than unity, then the efficiency of energy release will be low and the gravitational energy of the accreted matter will be swallowed by the hole in the form of kinetic or thermal energy. If that value can be large. For quasi-spherical accretion, most of the incident gas could be in the form of cold clouds with low angular momentum. If (ideally) these clouds collide very close to the hole, where their relative velocities reach c, then shock waves will arise in the clouds, producing effective dissipation. (We know from observations of galactic supernova remnants that shock waves with velocities c are efficient enough to accelerate relativistic electrons and that the resulting radiation efficiencies are quite plausible if this type of collision could actually occur.) As discussed above, disk accretion can also occur size
Instabilities, which are a disaster for the models of X-ray binaries, are fully present in the disk models of quasars. The innermost disk regions, surrounding a black hole with a mass accreting at the Eddington limit, should have temperatures of 10 V K. This means that the ratio of the radiation pressure to the gas pressure (see Section 4) is large and that the cooling in the lines (see, for example, ) the released gravitational energy is stored in the "corona" above the disk. Energy can be carried away in the form of a radiative or thermal driven wind mechanism - a scale-shifted version of the solar wind that carries away most of the energy stored in the solar corona. Similarity solutions were found in which a small part of the matter accreting in the disk is "taken" by the hole and can generate luminosity. The rest of the matter is carried away by radiation pressure. In this case, it becomes possible to obtain fluxes collimated parallel and antiparallel to the spin axis.
In an alternative scheme (see, as well as Blandorf's article in the book and the references therein), the energy and angular momentum of the accreting gas are extracted by electromagnetic torsional forces acting near the hole. In fact, this can be done with a fairly high efficiency even in axisymmetric geometry. Consider a magnetic field embedded in a disk. In the first approximation, the field will be “frozen” into the matter rotating in the disk (due to the huge electrical conductivity, which implies the “ideal MHD condition”. The rotor of this equation implies that it is directly interpreted as the freezing of the magnetic field into the matter). Magnetic lines of force emerging from the disk and “frozen” into the matter rotating in the disk will generate an electric field as it would be seen by locally non-rotating (stationary) observers. This electric field creates an electrical potential difference across the innermost parts of the disk and actually across the hole, just like in the Faraday disk. This potential difference will force currents
flow along the magnetic lines of force from the disk, establishing a magnetosphere around the hole. Eventually, these currents will generate a toroidal component of the magnetic field, so that the lines of force will be blown back by the movement of matter. Therefore, there will be a resisting moment of rotation acting on any matter near the hole, and this can lead to the transfer of angular momentum (and energy) not outward in the plane of the disk (as in conventional models with viscosity), but perpendicular to the disk in the form of an electromagnetic or hydromagnetic Poynting flux ...
The same mechanism can lead to the extraction of spin energy from the hole itself. From a Kerr black hole with a specific angular momentum a, in principle, it is possible to extract a fraction of the energy (varying from 0 to 29% as a increases from 0 to M). However, for this to be realized in practice, currents are required that freely flow across the horizon. Since the particles must move inward at the horizon and can apparently move outward at large distances, there must be some source of charges carrying current in the inner magnetosphere. It can be provided by breaking the vacuum above the horizon, as in a lightning strike. This leads to the fact that under the expected conditions inside the core of the quasar, there are simple mechanisms capable of producing this destruction. This provides an alternative way of releasing a significant part of the rest energy of the accreted matter. In fact, any accreting magnetized gas would appear to be unstable, so that most of the energy would be released rather in explosive flares. If the hole were massive enough, it could attract dense enough regions of the cluster, so as to provide fuel for even the brightest quasars)
