Destruction of a Star during the Evolution of a Star + Supermassive Black Hole System

Abstract

Stars located closely to supermassive black holes (SMBHs) can, under certain conditions, form close binary systems with the SMBHs, in which the star may fill the Roche lobe and intensive accretion of stellar matter onto the SMBH is possible. In this paper, the evolution of star + SMBH binary systems is studied under the assumption that the black hole mainly accretes the matter from the companion star. The calculations considered all the processes that determine the evolution of ordinary binary systems, as well as the irradiation of a star by a hard radiation flux arising from the accretion of its matter onto the SMBH. The absorption of the external radiation flux in the stellar envelope was calculated through the same formalism that is used to calculate the opacity of stellar matter. In addition, it was assumed that if the characteristic time of mass exchange is less than the thermal time of the star, the exchange between the orbital angular momentum of the system and the angular momentum of the matter flowing to the SMBH does not take place. The numerical simulations performed in our previous studies showed that, within the adopted assumptions, there are three possible evolution types of such a binary system, depending on the masses of the SMBH and the star, as well as on the initial distance of the star from the SMBH. The first type of the evolution results in the destruction of the star. This is the only scenario that takes place for low-mass main sequence (MS) stars with masses below $\sim {\kern 1pt} 1\,{{M}_{ \odot }}$, even if the SMBH mass is relatively small, and the initial distance of the star from the SMBH is large. Massive MS stars are destroyed as well, if the SMBH mass is large and the initial distance of the star from the SMBH is sufficiently small. The second type of the evolution may take place for massive MS stars that are initially located farther from the SMBH than in the first scenario. In this case, the massive star fills its Roche lobe during the evolutionary expansion, after which a stage of intensive exchange of matter begins. A characteristic property of the evolution of the second type is an increase in the orbital period of the system with time. As a result, after the stage of intensive loss of matter, the star “retreats” under the Roche lobe. The remnant of the star will remain as a white dwarf and may end up at a fairly large distance from the SMBH. The third type of the evolution may occur for massive MS stars that are initially located even farther from the SMBH than in the second variant, as well as for evolved massive stars. In this case, conservative mass exchange accompanied by intense stellar wind leads to the fact that the star moves away from the SMBH without filling its Roche lobe at all. In this paper, we thoroughly examine the first type of the evolution, which results in the destruction of the star. According to the calculation results, the greater the mass of the SMBH, the greater the maximum mass ${{M}_{{\max}}}$ of stars that can be destroyed. For black holes of intermediate mass, $({{10}^{3}}{-} {{10}^{5}})\,{{M}_{ \odot }}$, the ${{M}_{{\max}}}$ value is relatively small and amounts to (2–9)${{M}_{ \odot }}$. For SMBHs with a mass of ${{10}^{6}}\,{{M}_{ \odot }}$, ${{M}_{{\max}}}$ is close to 25 ${{M}_{ \odot }}$. For massive SMBHs with masses of $({{10}^{7}}{-} {{10}^{9}})\,{{M}_{ \odot }}$, ${{M}_{{\max}}}$ exceeds 50 ${{M}_{ \odot }}$. If the mass of the star is lower than ${{M}_{{\max}}}$ and the initial degree of filling of the Roche lobe $D$ is greater than the boundary value ${{D}_{{{\text{destr}}}}}$, the star will be destroyed, while at $D < {{D}_{{{\text{destr}}}}}$ it will move away from the SMBH and may avoid destruction. The greater the mass of the SMBH, the lower the ${{D}_{{{\text{destr}}}}}$, value for a star of a given mass. The character of the evolution of a star + SMBH system before the destruction of the star depends on the stellar mass. For stars with masses $M \lesssim 1\,{{M}_{ \odot }}$, destruction begins immediately after the filling of the Roche lobe and a corresponding rapid increase in the rate of matter loss. For more massive stars, the filling of the Roche lobe is followed by the evolutionary phase with a relatively low rate of matter loss. As the semimajor axis of the orbit decreases to a certain value, this rate increases rapidly, which leads to an increased degree of irradiation of the star and its destruction. At the initial phase of the destruction, the star’s rate of matter loss grows the faster, the greater the mass of the SMBH, the smaller the initial mass of the star, and the closer the star is to the SMBH at the initial moment. The characteristic times of increase in $\dot {M}$ by three orders of magnitude at the beginning of the destruction phase vary from tens to thousands of years, depending on the masses of the star and the SMBH.