Gaia 400,894 QSO constraint on the energy density of low-frequency gravitational waves

TL;DR

This study uses Gaia EDR3 proper motion data of nearly 400,000 QSOs to set a new, stringent upper limit on the energy density of low-frequency gravitational waves, surpassing previous VLBI constraints and ruling out nearby SMBH binaries.

Contribution

It provides the first large-scale QSO proper motion map with Gaia data to constrain low-frequency GWs, significantly improving existing limits and demonstrating the potential of future Gaia data releases.

Findings

Placed the tightest constraint on GW energy density at low frequencies.

Ruled out SMBH binaries within 400 kpc of Earth.

Demonstrated the power of Gaia astrometry for GW detection.

Abstract

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 $\mathcal{O}(0.1)\, \mu$arcsec, and place a tight constraint on the energy density of GWs, $\Omega_{\rm gw}=(0.964 \pm 3.804) \times 10^{-4}$ (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.