标题： 一颗宁静星系中的潮汐瓦解事件的恒星和气体动力学模型 显示英文标题

标题： Stellar and gas dynamical model for tidal disruption events in a quiescent galaxy

摘要： 利用包含黑洞（BH）质量$M_{\bullet}$、特定轨道能量$E$和角动量$J$、恒星质量$M_{\star}$和半径$R_{\star}$以及恒星轨道近日点$r_{p}(E,\hspace{1mm}J,\hspace{1mm}M_{\bullet})$的恒星动力学和气体动力学输入，构建了详细的潮汐瓦解事件（TDEs）模型。 我们利用标准的损失锥理论求解了适用于银河系密度分布剖面$\rho (r) \propto r^{-\gamma}$和恒星质量函数$\xi(m) $的定态 Fokker-Planck 方程，其中$m=M_{\star}/M_{\odot}$，并得到了归一化到相空间内的黑洞(BH)供能率$\dot{N}_{t} \propto M_{\bullet}^\beta$，其中$\beta= -0.3\pm 0.01$对于$M_{\bullet}>10^7 M_{\odot}$和$\sim 6.8 \hspace{1mm} \times 10^{-5}$年$^{-1}$对于$\gamma=0.7$。 我们用它来模拟被潮汐瓦解抛射物的吸积率，$\dot{M}(E,\hspace{1mm}J,\hspace{1mm}m,\hspace{1mm}t)$，并讨论盘状结构形成的条件，发现对于典型物理参量范围内的吸积盘几乎总是会形成。我们还研究了从具有超爱丁顿吸积阶段的恒星潮汐瓦解抛射物中形成的盘状结构的条件。我们已经模拟了相关的光学g波段和软X射线中的光变曲线轮廓，作为超爱丁顿和次爱丁顿吸积盘函数， $\dot{M}(E,\hspace{1mm}J,\hspace{1mm}t)$的函数。利用这些，标准宇宙学参数以及任务仪器细节，最终预测了各种即将到来的巡天探测中可检测到的TDE（潮汐瓦解事件）率作为 $\gamma$的函数。 显示英文摘要

摘要： A detailed model of the tidal disruption events (TDEs) has been constructed using stellar dynamical and gas dynamical inputs that include black hole (BH) mass $M_{\bullet}$, specific orbital energy $E$ and angular momentum $J$, star mass $M_{\star}$ and radius $R_{\star}$, and the pericenter of the star orbit $r_{p}(E,\hspace{1mm}J,\hspace{1mm}M_{\bullet})$. We solved the steady state Fokker--Planck equation using the standard loss cone theory for the galactic density profile $\rho (r) \propto r^{-\gamma}$ and stellar mass function $\xi(m) $ where $m=M_{\star}/M_{\odot}$ and obtained the feeding rate of stars to the BH integrated over the phase space as $\dot{N}_{t} \propto M_{\bullet}^\beta$, where $\beta= -0.3\pm 0.01$ for $M_{\bullet}>10^7 M_{\odot}$ and $\sim 6.8 \hspace{1mm} \times 10^{-5}$ Yr$^{-1}$ for $\gamma=0.7$. We use this to model the in-fall rate of the disrupted debris, $\dot{M}(E,\hspace{1mm}J,\hspace{1mm}m,\hspace{1mm}t)$, and discuss the conditions for the disk formation, finding that the accretion disk is almost always formed for the fiduciary range of the physical parameters. We also find the conditions under which the disk formed from the tidal debris of a given star with a super Eddington accretion phase. We have simulated the light curve profiles in the relevant optical g band and soft X-rays for both super and sub-Eddington accretion disks as a function of $\dot{M}(E,\hspace{1mm}J,\hspace{1mm}t)$. Using this, standard cosmological parameters, and mission instrument details, we predict the detectable TDE rates for various forthcoming surveys finally as a function of $\gamma$.