Collapse of a self-gravitating Bose-Einstein condensate with attractive self-interaction
Collapse of a self-gravitating Bose-Einstein condensate with attractive self-interaction
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具有吸引自相互作用的自引力玻色-爱因斯坦凝聚态的塌缩
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发表时间：
2016
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通讯作者：
P. Chavanis
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作者：
P. Chavanis
我们研究了具有吸引自相互作用的自引力玻色-爱因斯坦凝聚体的坍缩。只有在最大质量$M_{
m max}=1.012hbar/sqrt{Gm|a_s|}$以下才存在引力和自相互作用引起的引力被量子压力抵消的平衡状态，其中$a_s M_{
m max}$预计系统将坍缩并形成黑洞。我们通过对波函数进行高斯方差分析来研究坍缩动力学。我们发现坍缩时间尺度为$(M/M_{
M max}-1)^{-1/4}$对于$M
ightarrow M_{
M max}^+$和$M^{-1/2}$对于$Mgg M_{
M max}$。我们将结果应用于质量$m=10^{-4}, {
m eV}/c^2$和散射长度$a_s=-5.8倍10^{-53}，{
m m}$的标准轴子，其中$M_{
m max}=6.5倍10^{-14}M_{odot}$和$R=3.3倍10^{-4}，R_{odot}$。我们证实了我们之前的说法，即具有吸引力的自相互作用的玻色子，如标准轴子，可能形成低质量恒星，但不能形成相关质量和大小的暗物质晕。这些迷你轴子星可能是暗物质的组成部分。它们可以在几个小时内坍缩成质量为10^{-14}，M_{odot}$的迷你黑洞。在这种情况下，暗物质晕将由迷你黑洞组成。我们还将我们的结果应用于质量$m=1.93倍10^{-20}，{
m eV}/c^2$和散射长度$a_s=-8.29倍10^{-60}，{
m fm}$的超轻轴子，其中$M_{
m max}=0.39倍10^6，M_{odot}$和$R=33, {
m pc}$。这些超轻轴子可以聚集成暗物质晕。具有吸引力的自相互作用的轴子暗物质晕可以在大约100万年的时间里坍缩成质量为$sim 10^{6}, M_{odot}$的超大质量黑洞。
We study the collapse of a self-gravitating Bose-Einstein condensate with attractive self-interaction. Equilibrium states in which the gravitational attraction and the attraction due to the self-interaction are counterbalanced by the quantum pressure exist only below a maximum mass $M_{
m max}=1.012hbar/sqrt{Gm|a_s|}$ where $a_s M_{
m max}$ the system is expected to collapse and form a black hole. We study the collapse dynamics by making a Gaussian ansatz for the wave function. We find that the collapse time scales as $(M/M_{
m max}-1)^{-1/4}$ for $M
ightarrow M_{
m max}^+$ and as $M^{-1/2}$ for $Mgg M_{
m max}$. We apply our results to standard axions with mass $m=10^{-4}, {
m eV}/c^2$ and scattering length $a_s=-5.8 imes 10^{-53}, {
m m}$ for which $M_{
m max}=6.5 imes 10^{-14}M_{odot}$ and $R=3.3 imes 10^{-4}, R_{odot}$. We confirm our previous claim that bosons with attractive self-interaction, such as standard axions, may form low mass stars but cannot form dark matter halos of relevant mass and size. These mini axions stars could be the constituents of dark matter. They can collapse into mini black holes of mass $sim 10^{-14}, M_{odot}$ in a few hours. In that case, dark matter halos would be made of mini black holes. We also apply our results to ultralight axions with mass $m=1.93 imes 10^{-20}, {
m eV}/c^2$ and scattering length $a_s=-8.29 imes 10^{-60}, {
m fm}$ for which $M_{
m max}=0.39 imes 10^6, M_{odot}$ and $R=33, {
m pc}$. These ultralight axions could cluster into dark matter halos. Axionic dark matter halos with attractive self-interaction can collapse into supermassive black holes of mass $sim 10^{6}, M_{odot}$ in about one million years.