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.

中文翻译：

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恒星+超大质量黑洞系统演化过程中的恒星破坏

摘要

在某些条件下，紧挨着超大质量黑洞（SMBH）的恒星可以与SMBH形成紧密的双星系统，其中恒星可能充满罗氏瓣，并且可能在SMBH上强烈积聚恒星物质。本文在黑洞主要从伴星吸收物质的假设下研究了恒星+ SMBH双星系统的演化。计算考虑了决定普通双星系统演化的所有过程，以及确定恒星辐射到恒星上的原因，恒星辐射是由于物质在SMBH上的积聚而产生的。恒星包膜中外部辐射通量的吸收是通过与用于计算恒星物质的不透明度相同的形式来计算的。此外，假定如果质量交换的特征时间小于恒星的热时间，则系统的轨道角动量与流向SMBH的物质的角动量之间不会发生交换。在我们先前的研究中进行的数值模拟表明，在所采用的假设下，这种双星系统存在三种可能的演化类型，这取决于SMBH和恒星的质量，以及恒星与恒星的初始距离SMBH。第一种演化类型导致恒星的毁灭。这是质量低于质量的低质量主序（MS）恒星发生的唯一情况 系统的轨道角动量与流向SMBH的物质的角动量之间没有交换。在我们先前的研究中进行的数值模拟表明，在所采用的假设下，这种双星系统存在三种可能的演化类型，这取决于SMBH和恒星的质量，以及恒星与恒星的初始距离SMBH。第一种演化类型导致恒星的毁灭。这是质量低于质量的低质量主序（MS）恒星发生的唯一情况 系统的轨道角动量与流向SMBH的物质的角动量之间没有交换。在我们先前的研究中进行的数值模拟表明，在所采用的假设下，这种双星系统存在三种可能的演化类型，这取决于SMBH和恒星的质量，以及恒星与恒星的初始距离SMBH。第一种演化类型导致恒星的毁灭。这是质量低于质量的低质量主序（MS）恒星发生的唯一情况 取决于SMBH和恒星的质量，以及恒星与SMBH的初始距离。第一种演化类型导致恒星的毁灭。这是质量低于质量的低质量主序（MS）恒星发生的唯一情况 取决于SMBH和恒星的质量，以及恒星与SMBH的初始距离。第一种演化类型导致恒星的毁灭。这是质量低于质量的低质量主序（MS）恒星发生的唯一情况\（\ sim {\ kern 1pt} 1 \，{{M} _ {\ odot}} \），即使SMBH质量相对较小，并且恒星与SMBH的初始距离也较大。如果SMBH质量较大且恒星与SMBH的初始距离足够小，则也将破坏MS巨星。第二种类型的演化可能发生于最初比第一种情况更远离SMBH的大质量MS恒星。在这种情况下，巨大的恒星在进化膨胀过程中充满了罗氏瓣，此后便开始了密集的物质交换阶段。第二类进化的特征是系统的轨道周期随时间增加。结果，在物质大量损失的阶段之后，恒星在罗氏叶下“撤退”。这颗恒星的残留物仍将是白矮星，并且可能最终与SMBH相距很远。第三种类型的演化可能发生于最初比第二种变体更远离SMBH的大质量MS恒星，以及已演化的大质量恒星。在这种情况下，保守的质量交换伴随着强烈的恒星风导致了恒星从SMBH移开而根本没有充满罗氏瓣的事实。在本文中，我们彻底检查了演化的第一种类型，这导致了恒星的破坏。根据计算结果，SMBH的质量越大，最大质量就越大 以及演化的大质量恒星。在这种情况下，保守的质量交换伴随着强烈的恒星风导致了恒星从SMBH移开而根本没有充满罗氏瓣的事实。在本文中，我们彻底检查了演化的第一种类型，这导致了恒星的破坏。根据计算结果，SMBH的质量越大，最大质量就越大 以及演化的大质量恒星。在这种情况下，保守的质量交换伴随着强烈的恒星风导致了恒星从SMBH移开而根本没有充满罗氏瓣的事实。在本文中，我们彻底检查了演化的第一种类型，这导致了恒星的破坏。根据计算结果，SMBH的质量越大，最大质量就越大\（{{M} _ {{\\ max}}} \）可以被摧毁的恒星。对于中等质量的黑洞，\（（{{10} ^ {3}} {-} {{10} ^ {5}}）\，{{M} _ {\ odot}} \），\（ {{M} _ {{\\ max}}} \）的值相对较小，等于（2–9）\（{{M} _ {\ odot}} \）。对于质量为\（{{10} ^ {6}} \，{{M} _ {\ odot}} \）的SMBH，\（{{M} _ {{\ max}}} \\）是接近的到25  \（{{M} _ {\ odot}} \）。对于质量为\（{{{10} ^ {7}} {-} {{10} ^ {9}}）\，{{M} _ {\ odot}} \）的大规模SMBH ，\（{{ M} _ {{\ max}}} \）超过50  \（{{M} _ {\ odot}} \）。如果恒星的质量小于\（{{M} _ {{\\ max}}} \）并且罗氏波瓣\（D \）的初始填充度大于边界值\（{{D} _ {{{\ text {destr}}}}} \\），该恒星将被破坏，而在\（D <{{{D} _ {{{\ text {destr}}}}} \）处，它将远离SMBH，并可以避免破坏。SMBH的质量越大，给定质量的恒星的\（{{D} _ {{\ text {destr}}}}} \\值就越低。恒星+ SMBH系统在恒星毁灭之前的演化特征取决于恒星质量。对于质量为\（M \ lesssim 1 \，{{M} _ {\ odot}} \\）的恒星在罗氏叶充盈后，破坏立即开始，物质损失率随之迅速增加。对于更大质量的恒星，罗氏瓣的填充之后是演化阶段，物质损失率相对较低。当轨道的半长轴减小到某个值时，该速率会迅速增加，这会导致恒星的辐射程度及其破坏增加。在破坏的初始阶段，恒星的物质损失速率增长得越快，SMBH的质量越大，恒星的初始质量就越小，并且恒星在初始时刻离SMBH越近。\（\ dot {M} \）增加的特征时间 在毁灭阶段开始的三个数量级，从数十年到数千年不等，这取决于恒星和SMBH的质量。