盖亚400，894 QSO对低频引力波能量密度的约束
Gaia 400,894 QSO constraint on the energy density of low-frequency gravitational waves
摘要：
低频引力波（GWs）是理解宇宙膨胀和黑洞合并形成超大质量黑洞（SMBH）的关键，但由于地震噪声的影响，利用先进的LIGO（aLIGO）和VIRGO等地面GWs实验难以识别低频GWs。虽然低频GWs产生的准恒星物体（QSO）自行是通过具有良好位置精度的甚长基线干涉测量（VLBI）观测的开创性研究来测量的，但低频GWs并不受711个QSO的小统计数据的强烈约束（Darling等人，2018）。本文给出了斯隆数字巡天（SDSS）的400，894个类星体的自行场图，用光学的{ \it Gaia} EDR 3自行测量，其位置精度为$< 0.4$毫角秒，与射电VLBI观测相当。我们得到的最佳拟合球谐函数与典型的磁场强度的$\mathcal{O}(0.1)\, μ$ arcsec，并放置一个严格的约束的能量密度的GW，$Ω_{\rm gw}=(0.964 \pm 3.804) \times 10^{-4}$（95 \%的置信水平），这是显着强于两个数量级的脉冲星定时技术未探索的$f <10^{-9}\,{\rm [Hz]}\simeq (30\,{\rm yr})^{-1}$的低频制度比以前的VLBI研究之一。我们的上限排除了SMBH双星系统的存在距离$r < 400$ kpc从地球的银河系中心和本地集团星系。证明我们的光学类星体研究给出的限制，我们声称，天体测量卫星数据，包括即将到来的{ \it盖亚} DR 5数据与小系统误差是强大的约束低频GWs。
英文摘要：
Low frequency gravitational waves (GWs) are keys to understanding cosmological inflation and super massive blackhole (SMBH) formation via blackhole mergers, while it is difficult to identify the low frequency GWs with ground-based GW experiments such as the advanced LIGO (aLIGO) and VIRGO due to the seismic noise. Although quasi-stellar object (QSO) proper motions produced by the low frequency GWs are measured by pioneering studies of very long baseline interferometry (VLBI) observations with good positional accuracy, the low frequency GWs are not strongly constrained by the small statistics with 711 QSOs (Darling et al. 2018). Here we present the proper motion field map of 400,894 QSOs of the Sloan Digital Sky Survey (SDSS) with optical {\it Gaia} EDR3 proper motion measurements whose positional accuracy is $< 0.4$ milli-arcsec comparable with the one of the radio VLBI observations. We obtain the best-fit spherical harmonics with the typical field strength of $\mathcal{O}(0.1)\, μ$arcsec, and place a tight constraint on the energy density of GWs, $Ω_{\rm gw}=(0.964 \pm 3.804) \times 10^{-4}$ (95 \% confidence level), that is significantly stronger than the one of the previous VLBI study by two orders of magnitude at the low frequency regime of $f <10^{-9}\,{\rm [Hz]}\simeq (30\,{\rm yr})^{-1}$ unexplored by the pulsar timing technique. Our upper limit rules out the existence of SMBH binary systems at the distance $r < 400$ kpc from the Earth where the Milky Way center and local group galaxies are included. Demonstrating the limit given by our optical QSO study, we claim that astrometric satellite data including the forthcoming {\it Gaia} DR5 data with small systematic errors are powerful to constrain low frequency GWs.
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