AI 中文总结
本研究模拟鲁宾天文台对麦哲伦云的观测，预测孤立黑洞微引力透镜事件的探测数量、天体测量特征及参数误差，可对特定质量的孤立黑洞设定95%置信水平的排除上限。
AI 中文摘要
引力微引力透镜巡天可通过孤立黑洞（IBHs）对共线恒星的视亮度和运动的引力效应，在大距离上发现孤立黑洞。本文研究利用Vera C.鲁宾天文台对大小麦哲伦云（LMC和SMC）的未来观测，探测并表征质量范围为$[3,5000]M_{\rm{\bigodot}}$、起源为恒星或暗物质的孤立黑洞。我们考虑四种透镜质量函数（MFs：$dN/dM\boldsymbol{\times} M^{-\beta}$，其中$\beta=0,0.5,1,2$），并生成鲁宾可探测的孤立黑洞引起的长时标微引力透镜事件。假设孤立黑洞质量占银河系总质量的比例为$\boldsymbol{\textit{F}}$，当$\beta=1$且$\boldsymbol{\textit{F}}=5\times10^{-3}$时，鲁宾对SMC和LMC方向的孤立黑洞微引力透镜事件探测概率约为0.3和2，这些孤立黑洞位于银河系内的概率$\boldsymbol{\textit{\textgreater}70\%}$。这些事件的平均爱因斯坦角$\theta_{\rm{E}}\boldsymbol{\textasciitilde}30-50\rm{mas}$，因此通过鲁宾天体测量观测分辨其引力透镜诱导图像的概率对LMC和SMC分别约为1.4%和16.3%，其中约1.5.2%的事件可实现天体测量偏转，分辨其视差的概率约为40%和25%。我们通过模拟合成数据点并假设真实模型为最佳拟合模型来评估相对误差，得出对于对数均匀质量函数，LMC和SMC方向光度可探测的微引力透镜事件中，分别有$\boldsymbol{\textless}0.1\%$和0.3%的事件，其透镜质量、距离和速度的相对误差$\boldsymbol{\textless}3\%$。我们假设孤立黑洞完全贡献暗物质晕中的致密天体，计算可探测孤立黑洞的数量，得出当$\boldsymbol{\textit{F}}\boldsymbol{\textasciitilde}4\times10^{-3}$时，鲁宾在95%置信水平（C.L.）下可对质量$\boldsymbol{\textless}208M_{\rm{\bigodot}}$和$8M_{\rm{\bigodot}}$的孤立黑洞设定排除上限。
英文摘要
Gravitational microlensing surveys potentially discover isolated black holes (IBHs) at large distances through their gravitational effects on apparent brightness and motion of collinear stars. Here, we study detecting and characterizing IBHs within the mass range $[3,~5000]M_{\odot}$ with either stellar or dark matter origins in the upcoming observations by Vera~C.~Rubin Observatory towards the Large and Small Magellanic Clouds (LMC and SMC). We consider four lens mass functions (MFs:~$dN/dM\propto M^{-β}$ for $β=0,~0.5,~1,~2$), and generate long-duration microlensing events due to IBHs detectable by Rubin. By assuming the fraction of IBHs's mass in total Galactic mass as $\mathcal{F}$, Rubin potentially detects $\sim0.3,~\rm{and}~2$ microlensing events towards SMC and LMC due to IBHs if $β=1,~\rm{and}~\mathcal{F}=5\times10^{-3}$. These IBHs are inside our galaxy with the probability $\gtrsim70\%$. These events have on average $θ_{\rm{E}}\sim30-50~\rm{mas}$, so that the probabilities of resolving their lensing-induced images through the Rubin astrometric observations are $\sim1.4,~\rm{and}~16.3\%$ towards LMC and SMC. In $\sim1,~5.2\%$ of these events their astrometric deflections are realizable. The probabilities of discerning their parallax are $\sim40,~25\%$. We evaluate relative errors with simulating synthetic data points and by assuming the true models as the best-fitted ones. We conclude for a log-uniform MF for $\lesssim0.1,~\rm{and}~0.3\%$ of photometrically detectable microlensing events towards in LMC and SMC the relative errors in the lens mass, distance and velocity are $\lesssim3\%$. We calculate the number of detectable IBHs versus by assuming their complete contribution of compact objects in halos' darkmatter, and conclude Rubin specifies $95\%$~C.L. upper-limit on IBHs exclusion by masses $\lesssim208,~8M_{\odot}$ for $\mathcal{F}\simeq4\times10^{-3}$.
Comments27 pages, 10 figures, 6 tables
