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arXiv 2204.01792gr-qcastro-ph.COastro-ph.GAastro-ph.HEhep-th
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星系中心超大质量暗天体的致密性

Compactness of supermassive dark objects at galactic centers

K. S. Virbhadra

AI总结:

本文通过将超大质量暗天体建模为史瓦西透镜,推导出透镜致密性与质量距离比和距离比相关的公式,证明仅观测相对论像即可无需其他信息精确给出物理致密性上限。

摘要:

我们将引力透镜的致密性定义为产生像的零测地线的按比例缩放的最接近距离(即 $r_0/M$)。我们将四十个超大质量暗天体建模为史瓦西透镜,并计算透镜的致密性(由一阶相对论像的形成决定)。然后,我们得到了一个关于透镜致密性的新公式,该公式是质量与距离之比($M/D_d$)以及透镜-源距离与观测者-源距离之比($D_{ds}/D_s$)的函数。该公式给出了一个非常重要的结果:仅凭对相对论像的观测,就能极其精确地给出透镜物理致密性(半径与质量之比)的上限,而无需知道透镜质量、角源位置以及观测者-源和透镜-源的距离。类似地,我们证明了对二阶相对论像的观测将给出物理致密性上限的更低值。这些结果虽然是为星系中心的超大质量暗天体获得的,但对任何足够致密以致能产生相对论像的天体都有效。

英文摘要:

We define compactness of a gravitational lens as the scaled closest distance of approach (i.e., $r_0/M$) of the null geodesic giving rise to an image. We model forty supermassive dark objects as Schwarzschild lenses and compute compactness of lenses (determined by the formation of the first order relativistic image). We then obtain a novel formula for the compactness of a lens as a function of mass to the distance ratio ($M/D_d$) and the ratio of lens-source to the observer-source distances ($D_{ds}/D_s$). This formula yields a very important result: Just an observation of a relativistic image would give an incredibly accurate upper bound to the physical compactness (the ratio of the radius to mass) of the lens without having any knowledge of mass of the lens, angular source position, and observer-source and lens-source distances. Similarly, we show that the observation of the second order relativistic image would give a lower value of upper bound to the physical compactness. These results, though obtained for supermassive dark objects at galactic centers, are valid for any object compact enough to give rise to relativistic images.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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