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The impact of the formation channel on gravitational-wave-galaxy cross-correlations

Kabir Chakravarti, Federico R. Urban

Abstract

The angular, harmonic cross-correlation between gravitational wave (GW) events and galaxy catalogues contains rich information on the large-scale structure and the origin of compact binary mergers. In this work, we study how uncertainties in the binary formation channel affect the predicted cross-correlation signal for both current-generation and next-generation networks of detectors. We generate five mock GW catalogues for which we vary the progenitor-to-remnant mass-transfer function and the time-delay probability distribution between progenitor and remnant. We then cross-correlate these catalogues with galaxy samples modelled on the 2MASS Photometric Redshift catalogue (2MPZ) and the Gaia-unWISE quasar catalogue (Quaia). We find that the mass-transfer function has negligible effect on the cross-correlation signal, with differences remaining within redshift uncertainties. In contrast, the time-delay distribution dramatically affects the redshift distribution of the GW events and, with it, the cross-correlation signal, particularly for shallow galaxy catalogues. In particular, current-generation facilities can achieve significant detections only for the longest time delays when cross-correlated with 2MPZ, whilst all cross-correlations with the deeper Quaia catalogue are marginally detectable or consistent with zero. Our exploratory results thus demonstrate that forecasts on cosmological or astrophysical parameters derived from GW-galaxy cross-correlations are, as expected, strongly sensitive to the assumed binary formation history.

The impact of the formation channel on gravitational-wave-galaxy cross-correlations

Abstract

The angular, harmonic cross-correlation between gravitational wave (GW) events and galaxy catalogues contains rich information on the large-scale structure and the origin of compact binary mergers. In this work, we study how uncertainties in the binary formation channel affect the predicted cross-correlation signal for both current-generation and next-generation networks of detectors. We generate five mock GW catalogues for which we vary the progenitor-to-remnant mass-transfer function and the time-delay probability distribution between progenitor and remnant. We then cross-correlate these catalogues with galaxy samples modelled on the 2MASS Photometric Redshift catalogue (2MPZ) and the Gaia-unWISE quasar catalogue (Quaia). We find that the mass-transfer function has negligible effect on the cross-correlation signal, with differences remaining within redshift uncertainties. In contrast, the time-delay distribution dramatically affects the redshift distribution of the GW events and, with it, the cross-correlation signal, particularly for shallow galaxy catalogues. In particular, current-generation facilities can achieve significant detections only for the longest time delays when cross-correlated with 2MPZ, whilst all cross-correlations with the deeper Quaia catalogue are marginally detectable or consistent with zero. Our exploratory results thus demonstrate that forecasts on cosmological or astrophysical parameters derived from GW-galaxy cross-correlations are, as expected, strongly sensitive to the assumed binary formation history.
Paper Structure (9 sections, 12 equations, 4 figures, 1 table)

This paper contains 9 sections, 12 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. The formalism
  3. The catalogues
  4. Gravitational Waves
  5. GW radial kernels
  6. GW beam factor
  7. Galaxies
  8. Results
  9. Conclusion and outlook

Figures (4)

  • Figure 1: Distribution of SNRs $\rho$ with the current-generation ($\rho\geq8$, left, solid) and the next-generation ($\rho\geq12$, right, dashed) detectors for our catalogues: catalogue 6 is in blue, catalogue 7 in green, catalogue 8 in red, catalogue 9 in orange, and catalogue 11 in purple. The vertical dotted lines represent the $97\%$ containment values of the distributions. The catalogues as shown here are not rescaled by $f_\mathrm{Res}$.
  • Figure 2: Scaling of the redshift errors $\delta z$ with redshift $z$ (left panel) and the SNR $\rho$ (right panel) for a pilot catalogue of $10$ events with current-generation (dark blue disks) and next-generation networks (light blue squares). The solid and dashed lines shows the best fits for these data points, respectively.
  • Figure 3: The GW radial kernel $\phi_\mathrm{GW}(\chi)$ with the current-generation (left column, solid) and the next-generation (right column, dshed) detectors. The top panels compare catalogues 6 and 7, whereas the bottom panels compare catalogues 8, 9 and 11. The colour coding is the same as in \ref{['fig:rhodets']}. The shaded light-blue areas show the range covered by applying the redshift errors of \ref{['fig:zerrs']} to catalogue 6; the shaded light-orange areas show the sampling errors from the limited number of events in a given observation campaign. In addition, we show the 2MPZ and Quaia radial kernels in solid and dashed black, respectively. The $y$-axis units are arbitrary but consistent within tracers.
  • Figure 4: Gravitational wave-galaxy XC signal $C_\ell$ for the five GW catalogues against the galaxy catalogues 2MPZ (top row) and Quaia (bottom row). On the left we show results for the current-generation detectors (solid lines), whereas the right are next-generation detectors (dashed lines). The error bars have been shifted along the x-axis for clarity.