Synergy between CSST and future gravitational-wave detectors: Probing primordial black holes by cross-correlating dark sirens with galaxies

Author(s)

Du, Ya-Nan, Song, Ji-Yu, Zhang, Jing-Fei, Zhang, Xin

Abstract

Gravitational-wave (GW) events and galaxies both trace the cosmic matter distribution, but the mergers of astrophysical black holes and primordial black holes (PBHs) are expected to populate different environments and therefore to cluster with different biases. The GW clustering bias is thus a statistical observable that can separate the two populations. We assess how well this can be done by cross-correlating the photometric galaxy survey of the Chinese Space-station Survey Telescope (CSST) with mock GW catalogs from two future detector networks: the third-generation ET2CE network (the Einstein Telescope and two Cosmic Explorer detectors) and the multi-band BDET2CE network, which adds the space-based baseline Decihertz Interferometer Gravitational-Wave Observatory. We find that CSST combined with 10 years of ET2CE observations can reveal a PBH contribution once its fraction in the total merger rate exceeds about $40\%$, while the much sharper sky localization of BDET2CE lowers this threshold to about $20\%$. The improvement comes from recovering the small-scale clustering information that localization errors would otherwise erase. These results show that combining future GW detector networks with CSST galaxy clustering offers a promising and largely independent route to identifying PBHs statistically.

Figures

Caption

Detected GW number density and effective GW bias for different PBH fractions. The left panel shows the number density of detected GW sources as a function of luminosity distance for one year of observation, while the right panel shows the redshift evolution of the effective GW bias. Larger $f^{\mathrm{P}}$ values increase the high-redshift event density and flatten or lower the effective bias

Caption

Detected GW number density and effective GW bias for different PBH fractions. The left panel shows the number density of detected GW sources as a function of luminosity distance for one year of observation, while the right panel shows the redshift evolution of the effective GW bias. Larger $f^{\mathrm{P}}$ values increase the high-redshift event density and flatten or lower the effective bias

Caption

The theoretical angular power spectra with multipole $\ell$ in the seventh redshift bin, $z\in[0.65,0.73]$. The left panel shows the ET2CE galaxy-GW cross-spectrum $C_\ell^{\mathrm{gGW}}$ for different values of $f^{\mathrm{P}}$, illustrating the suppression of the signal as the effective GW bias decreases. The right panel fixes $f^{\mathrm{P}}=0.2$ and compares the galaxy auto-spectrum $C_\ell^{\mathrm{gg}}$, galaxy-GW cross-spectrum $C_\ell^{\mathrm{gGW}}$, and GW auto-spectrum $C_\ell^{\mathrm{GWGW}}$ for ET2CE and BDET2CE.

Caption

The theoretical angular power spectra with multipole $\ell$ in the seventh redshift bin, $z\in[0.65,0.73]$. The left panel shows the ET2CE galaxy-GW cross-spectrum $C_\ell^{\mathrm{gGW}}$ for different values of $f^{\mathrm{P}}$, illustrating the suppression of the signal as the effective GW bias decreases. The right panel fixes $f^{\mathrm{P}}=0.2$ and compares the galaxy auto-spectrum $C_\ell^{\mathrm{gg}}$, galaxy-GW cross-spectrum $C_\ell^{\mathrm{gGW}}$, and GW auto-spectrum $C_\ell^{\mathrm{GWGW}}$ for ET2CE and BDET2CE.

Caption

SNR for distinguishing the AP model from the A model as a function of $f^{\mathrm{P}}$. The left and right panels show 1-year and 10-year observations, respectively. Curves correspond to the GW auto-correlation (GWGW), the galaxy-GW cross-correlation (gGW), and the joint three-spectrum analysis including the galaxy auto-correlation (total).

Caption

GW effective bias compared with the $1\sigma$ A model bias constraints for 10-year observations. The panels show ET2CE GW auto-correlation only (left), ET2CE-CSST galaxy-GW cross-correlation (center), and BDET2CE-CSST galaxy-GW cross-correlation (right). The gray bands show the A model $1\sigma$ uncertainties, while the colored curves show AP model effective biases for different PBH fractions.

Caption

The $1\sigma$ posterior constraints on the AP model parameters $C$, $D$, and $f^{\mathrm{P}}$ for the fiducial case $f^{\mathrm{P}}=0.4$. The constraints use the 10-year BDET2CE GW sample and the CSST photometric galaxy sample. Results are compared for the GW auto-correlation only (GWGW), the galaxy-GW cross-correlation only (gGW), and the joint analysis including the galaxy auto-correlation (total).