Cross-correlating galaxy catalogs and gravitational waves: A tomographic approach

Unveiling the origin of the coalescing binaries detected via gravitational waves (GWs) is challenging, notably if no multiwavelength counterpart is detected. One important diagnostic tool is the coalescing binary distribution with respect to the large-scale structures (LSSs) of the Universe, which we quantify via the cross-correlation of galaxy catalogs with GW ones. By using both existing and forthcoming galaxy catalogs and using realistic Monte Carlo simulations of GW events, we find that the cross-correlation signal should be marginally detectable in 10-year data taking of advanced LIGO-Virgo detectors at design sensitivity, at least for binary neutron star mergers. The expected addition of KAGRA and LIGO-India to the GW detector network would allow for a firmer detection of this signal, and, in combination with future cosmological surveys, would also permit the detection of cross-correlation for coalescing black holes. Such a measurement may unveil, for instance, a primordial origin of coalescing black holes. To attain this goal, we find that it is crucial to adopt a tomographic approach and to reach a sufficiently accurate localization of GW events. The depth of forthcoming surveys will be fully exploited by third-generation GW detectors such as the Einstein Telescope or the Cosmic Explorer, which will allow one to perform precision studies of the coalescing black hole LSS distribution and attain rather advanced model discrimination capabilities.

Figure 1

Redshift distribution of different classes of GW events for an SNR cut above 8, for HLV [panel (a)] and ET2CE [panel (b)].

Figure 2

Correlation between the relative error on $z$ and SNR for a sample of sources simulated with bayestar: about 300 events of the BNS class in the HLVIK case [panel (a)], about ${10}^3$ events of the BBH class in the HLVIK case [panel (b)], and about $1.4\times {10}^4$ events of the BBH class in case ET2CE [panel (c)].

Figure 3

Correlation between ${\sigma }_b$ and $z$ for the BNS and BBH class in the HLVIK case [panel (a) and panel (b), respectively], as well as for the BBH class in the ET2CE case [panel (c)], for the same sample of events considered in Fig. 2. The red line shows the adopted regression fit.

Figure 4

SNR distribution for different classes of events for the HLVIK case [panel (a)] and the ET2CE case [panel (b)], for the full sample of events in our 10-year data taking simulation.

Figure 5

Redshift distribution, $dN/dz$, of the galaxy catalogs used for the cross-correlation. All distributions are normalized to 1.

Figure 6

Expected autocorrelation power spectrum (APS) and errors for the three classes of binary mergers considered and for the HLVIK GW detector configuration. Note that the error bars for the BHNS and BBH cases have been slightly shifted in $\ell$ to improve the readability of the plot.

Figure 7

Expected CAPS and errors between the 2MPZ catalog and the three classes of binary mergers considered, for the HLV [panel (a)] and HLVIK [panel (b)] GW detector configurations. Note that the error bars for the BHNS and BBH cases have been slightly shifted in $\ell$ to improve the readability of the plot.

Figure 8

$\mathrm{\Delta }{\chi }^2$ values as a function of bias $b$ for the cross-correlation between GW events and the 2MPZ catalog, for the HLV [panel (a)] and HVLIK case [panel (b)].

Figure 9

Expected cross-correlation between BBH GW events and a EUCLID-like galaxy survey for the HLVIK case with 10-year data taking. Panel (a): no binning in $z$. Panel (b): case with three $z$ bins with the cross-correlation in each bin explicitly shown. The curves for the different cases have been slightly shifted in $\ell$ to improve the readability of the plot. Note the overall increase of the signal in the low-$z$ bin(s) and the improved determination of $C_{\ell }$ with respect to the panel (a).

Figure 10

$\mathrm{\Delta }{\chi }^2$ as function of $b$ for 10-year GW data taking for the cross-correlation between BBH GW events and EUCLID-like survey, for HLVIK [panel (a)] and ET2CE [panel (b)] cases, and for different binning in $z$. Each panel illustrates the power of the tomographic approach, with precision increasing (i.e., increasing curvature of the functions) with more redshift bins.

Figure 11

Constraint on the BBH bias from the cross-correlation with a EUCLID-like catalog, in each redshift bin separately (error bars) and globally (shaded region), for HLVIK [panel (a)] and ET2CE [panel (b)]. For comparison, the much less precise bias extracted for ET2CE from the autocorrelation is also shown in the [panel (c)].