AI 中文总结
本研究针对辐射压主导黑洞吸积盘的热稳定性矛盾，通过分析净垂直磁通量对径向应力的热响应机制，推导局部稳定性条件并计算阈值，发现垂直磁场可缩小不稳定区间但无法完全消除，关键在于应力热响应而非磁压分数。
AI 中文摘要
经典的辐射压不稳定性理论预言，发光黑洞吸积盘会出现强烈的热变率，然而大多数以吸积盘为主的X射线双星软态却保持相对稳定。我们研究了净垂直磁通量是否能通过其对径向应力的贡献来削弱这种不稳定性。稳定性不仅取决于平衡磁应力，还取决于热扰动过程中该应力的变化方式。我们用对数加热响应$q_+<q_{+,\rm crit}$写出了局部稳定性条件，该条件无需明确湍流应力如何划分为参考分量和净通量分量。作为示例的闭合关系取$δ=ζ\bpol\btor/α$，其中$\rm \rmetad=-d\rm lnδ/d\rm lnH$描述分数应力修正的响应，而$\rm \rm Gnf=d\rm lnW_{\rm nf}/d\rm lnH$描述额外净通量应力本身的响应。对于一个质量为$10M_\rm \rm odot$的黑洞周围、位于$R=20\rg$处且吸积率$\rm \rm Mdot=0.5\rm MEdd$的吸积盘，我们采用热时标上的固定局部质量通量，取$(γ,\rm gp)=(1,0)$，且$d\rm lnζ/d\rm lnH=0$。此时，临界稳定状态对应的$\bpol^{\rm crit}$在$ζ=1$时为0.0176，在$ζ=0.25$时为0.1338。这些阈值取决于所采用的应力闭合关系和磁场响应预设，不应被解释为普适的磁压分数。采用稳态之间$B_φ$变化的独立关系得到的固定$B_z$平衡序列表明，增强垂直磁场会缩小热不稳定的吸积率区间，但在$H/R<0.1$或$H/R<0.2$的情况下都无法消除不稳定性。因此，与稳定作用相关的物理量是净垂直通量相关应力的热响应，而非单纯的垂直磁压分数。
英文摘要
The classical radiation-pressure instability predicts strong thermal variability in luminous black-hole accretion disks, whereas most disk-dominated X-ray binary soft states remain comparatively stable. We examine whether net vertical magnetic flux can weaken this instability through its contribution to the radial stress. The stability depends not only on the equilibrium magnetic stress but also on how that stress changes during a thermal perturbation. We write the local stability condition in terms of the logarithmic heating response, $q_+<q_{+,\rm crit}$, which avoids specifying how the turbulent stress is divided into reference and net-flux components. For the illustrative closure $δ=ζ\sqrt{\bpol\btor}/α$, $\etad=-d\lnδ/d\ln H$ describes the response of the fractional stress correction, while $\Gnf=d\ln W_{\rm nf}/d\ln H$ describes the response of the additional net-flux stress itself. For an accretion disk around a $10M_\odot$ black hole at $R=20\rg$ and $\Mdot=0.5\MEdd$, we adopt fixed local mass flux on the thermal timescale, $(γ,\gp)=(1,0)$, and $d\lnζ/d\ln H=0$. Marginal stability then occurs at $\bpol^{\rm crit}=0.0176$ for $ζ=1$ and $0.1338$ for $ζ=0.25$. These thresholds depend on the adopted stress closure and field-response prescription and should not be interpreted as universal magnetic-pressure fractions. Fixed-$B_z$ equilibrium sequences, using a separate relation for the variation of $B_φ$ between steady states, show that increasing vertical field narrows the thermally unstable accretion-rate interval but does not eliminate it for either $H/R<0.1$ or $H/R<0.2$. The relevant quantity for stabilization is therefore the thermal response of the stress associated with net vertical flux rather than the vertical magnetic-pressure fraction alone.
Comments12 pages, 5 figures, Accepted for publication in ApJ
