Primordial black holes, allegedly formed in the very early Universe, have been proposed as a possible viable dark matter candidate. In this work we characterize the expected gravitational wave signal detectable by the planned space-borne interferometer LISA and the proposed next generation space-borne interferometer $\mu \mathrm{Ares}$ arising from a population of primordial black holes orbiting Sgr ${\mathrm{A}}^{\star }$, the supermassive black hole at the Galactic Center. Assuming that such objects indeed form the entire diffuse mass allowed by the observed orbits of stars in the Galactic Center ($\lesssim 4\times {10}^3{\mathrm{M}}_{\odot }$ within a radius of $\simeq {10}^{-3}\mathrm{pc}$ from Sgr ${\mathrm{A}}^{\star }$), under the simplified assumption of circular orbits and monochromatic mass function, we assess the expected signal in gravitational waves, either from resolved and nonresolved sources. We estimate a small but non negligible chance of $\simeq 10\%$ of detecting one single $1{\mathrm{M}}_{\odot }$ primordial black hole with LISA in a 10-year-long data stream, while the background signal due to unresolved sources would essentially elude any reasonable chance of detection. On the contrary, $\mu \mathrm{Ares}$, with a $\simeq 3$ orders-of-magnitude better sensitivity at $\simeq {10}^{-5}\mathrm{Hz}$, would be able to resolve $\simeq 140$ solar mass primordial black holes in the same amount of time, while the unresolved background should be observable with an integrated signal-to-noise ratio $\gtrsim 100$. Allowing the typical PBH mass to be in the range $0.01–10{\mathrm{M}}_{\odot }$ would increase LISA chance of detection to $\simeq 40\%$ towards the lower limit of the mass spectrum. In the case of $\mu \mathrm{Ares}$, instead, we find a “sweet spot” just about $1{\mathrm{M}}_{\odot }$, a mass for which the number of resolvable events is indeed maximized.

中文翻译：

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绕人马座轨道运行的原始黑洞引力波的可探测性*

据称在宇宙早期形成的原始黑洞已被提议作为可能的可行暗物质候选者。在这项工作中，我们描述了计划中的星载干涉仪 LISA 和拟议的下一代星载干涉仪可检测到的预期引力波信号$\mu \mathrm{战神}$由一群围绕人马座运行的原始黑洞产生${\mathrm{一个}}^{\star }$，银河系中心的超大质量黑洞。假设这些天体确实形成了银河系中心观测到的恒星轨道所允许的整个弥散质量（$\lesssim 4\times {10}^3{\mathrm{米}}_{\odot }$半径范围内$\simeq {10}^{-3}\mathrm{个人电脑}$来自人马座${\mathrm{一个}}^{\star }$），在圆形轨道和单色质量函数的简化假设下，我们评估了引力波中的预期信号，无论是来自已解决的还是未解决的源。我们估计一个很小但不可忽略的机会$\simeq 10\%$检测一个单一的$1{\mathrm{米}}_{\odot }$LISA 在长达 10 年的数据流中发现了原始黑洞，而由于未解析的来源而产生的背景信号基本上无法检测到任何合理的机会。相反，$\mu \mathrm{战神}$，有一个$\simeq 3$数量级更好的灵敏度$\simeq {10}^{-5}\mathrm{赫兹}$, 能解决$\simeq 140$太阳质量的原始黑洞在相同的时间内，而未解析的背景应该可以通过综合信噪比观察到$\gtrsim 100$. 允许典型的 PBH 质量在范围内$0.01–10{\mathrm{米}}_{\odot }$将增加 LISA 的检测机会$\simeq 40\%$接近质谱的下限。如果是$\mu \mathrm{战神}$，相反，我们找到了一个“甜蜜点”$1{\mathrm{米}}_{\odot }$, 可解析事件的数量确实最大化的质量。