[论文解读] Reinterpreting Low Frequency LIGO/Virgo Events as Magnified Stellar-Mass Black Holes at Cosmological Distances

Tom Broadhurst, J. M. Diego+1 more|arXiv (Cornell University)|Feb 14, 2018

Pulsars and Gravitational Waves Research参考文献 34被引用 28

一句话总结

本文提出，LIGO/Virgo探测到的四个最高质量双黑洞（BBH）事件——此前被解释为低红移处20–35M⊙的并合——实则为来自宇宙学距离（z ≈ 1–2.5）的恒星级黑洞（5–15M⊙）经中间星系引力透镜放大后的信号。中间星系的引力透镜效应使引力波应变放大√µ倍，导致探测器低估距离（低估√µ倍）并高估质量（放大1+z倍），从而调和了高推断质量与恒星起源黑洞群体之间的矛盾。

ABSTRACT

Gravitational waves can be focussed by the gravity of an intervening galaxy, just like light, thereby magnifying binary merging events in the far Universe. High magnification by galaxies is found to be responsible for the brightest sources detected in sky surveys, but the low angular resolution of LIGO/Virgo is insufficient to check this lensing possibility directly. Here we find that the first six binary black hole (BBH) merging events reported by LIGO/Virgo show clear evidence for lensing in the plane of observed mass and source distance. The four lowest frequency events follow an apparent locus in this plane, which we can reproduce by galaxy lensing, where the higher the magnification, the generally more distant the source so the wave train is stretched more by the Universal expansion, by factors of 2-4. This revises the reported BBH distances upwards by an order of magnitude, equal to the square root of the magnification. Furthermore, the reported black hole masses must be decreased by 2-4 to counter the larger stretch factor, since the orbital frequency is used to derive the black hole masses. This lowers the masses to 5-15 solar masses, well below the puzzlingly high values of 20-35 solar masses otherwise estimated, with the attraction of finding agreement in mass with black holes orbiting stars in our own Galaxy, thereby implying a stellar origin for the low frequency events in the far Universe. We also show that the other two BBH events of higher frequency detected by LIGO/VIRGO, lie well below the lensing locus, consistent with being nearby and unlensed. If this apparent division between local and distant lensed events is reinforced by new detections then the spins and masses of stellar black holes can be compared over a timespan of 10 billion years by LIGO/Virgo.

研究动机与目标

• 解决LIGO/Virgo首次BBH事件中推断出的高质​​量（20–35M⊙）与恒星演化预期的5–15M⊙质量之间的矛盾。
• 检验中间星系的引力透镜是否能解释LIGO/Virgo数据中观测到的质量-距离相关性。
• 评估透镜效应是否能调和高推断质量与银河系中已知的恒星级黑洞群体之间的关系。
• 评估透镜效应与观测到的啁啾质量分布及推断距离的一致性，特别是高质​​量事件沿特定轨迹聚集的现象。

提出的方法

• 利用LIGO/Virgo BBH事件的观测啁啾质量和推断的光度距离，检验其是否与透镜效应一致。
• 应用透镜放大关系 h(t) ∝ √µ，其中µ为放大因子，以校正因应变被高估而导致的距离低估。
• 通过将推断距离乘以√µ、推断质量乘以(1+z)，反向校正透镜效应偏差，重建真实源红移z与本征啁啾质量。
• 使用与银河系黑洞一致的对数正态分布和高斯质量函数，结合恒星形成率（SFR）演化模型，模拟BBH事件群体，以预测可探测事件。
• 利用µ−2定律建模透镜光学深度，针对折叠焦线，µ > 80的放大在紧致源靠近焦线时较为常见。
• 使用蒙特卡洛模拟，结合几何因子Θ的不确定性，在啁啾质量-距离平面中比较模拟的透镜与未透镜事件分布与观测数据。

实验结果

研究问题

• RQ1 中间星系的引力透镜效应能否解释LIGO/Virgo BBH事件在啁啾质量-距离平面中沿特定轨迹聚集的现象？
• RQ2 透镜效应在多大程度上解释了LIGO/Virgo数据中黑洞质量的高估（20–35M⊙）与距离的低估？
• RQ3 在考虑透镜效应后，BBH事件的观测分布是否更支持高红移（z ≈ 1–2.5）处的恒星级起源（5–15M⊙），而非原初或大质量双星前身星？
• RQ4 引入透镜效应后，BBH的本征质量函数与事件率演化如何变化？

主要发现

• 四个最高质量的LIGO/Virgo BBH事件（啁啾质量20–35M⊙）最合理的解释是：红移z ≈ 1–2.5处的透镜源，放大因子µ ≈ 2–4，而非近距离的高质​​量并合。
• 透镜效应使推断距离缩小√µ ≈ 1.4–2倍，导致真实光度距离提升一个数量级。
• 本征黑洞质量从20–35M⊙降低至5–15M⊙，与银河系中观测到的恒星级黑洞质量一致。
• 两个低质量事件（啁啾质量8–9M⊙）位于透镜轨迹之下，与近距离未透镜事件一致，支持本地与遥远事件的双峰分布。
• 采用对数正态质量函数（5–15M⊙）并增强z ≈ 2处的SFR的模型，可产生与观测数据一致的透镜事件分布，包括高质​​量尾部。
• 高放大因子（µ > 80）的概率与折叠焦线的µ−2定律一致，此类放大对靠近焦线的紧凑、高红移源是合理的。