Speeding up the detectability of the harmonic-space galaxy bispectrum

TL;DR

This paper introduces a fast method to estimate the signal-to-noise ratio of the harmonic-space galaxy bispectrum, enabling detection prospects with upcoming surveys by analyzing a limited set of configurations efficiently.

Contribution

The authors develop a computationally efficient approach to evaluate the galaxy bispectrum's detectability in harmonic space, significantly reducing processing time compared to previous methods.

Findings

Spectroscopic surveys outperform photometric surveys in detecting the bispectrum.

Higher redshift bins around z~1 yield greater cumulative SNR than lower redshift bins.

Detection of the bispectrum is feasible within narrow redshift bins with upcoming surveys.

Abstract

We present a method that allows us for the first time to estimate the signal-to-noise ratio (SNR) of the harmonic-space galaxy bispectrum induced by gravity, a complementary probe to already well established Fourier-space clustering analyses. We show how to do it considering only $\sim1000$ triangle configurations in multipole space, corresponding to a computational speedup of a factor $\mathcal{O}(10^2)-\mathcal{O}(10^3)$, depending on the redshift bin, when including mildly non-linear scales. Assuming observational specifications consistent with forthcoming spectroscopic and photometric galaxy surveys like the Euclid satellite and the Square Kilometre Array (phase 1), we show: that given a single redshift bin, spectroscopic surveys outperform photometric surveys; and that -- due to shot-noise and redshift bin width balance -- bins at redshifts $z\sim1$ bring higher cumulative SNR than bins at lower redshifts $z \sim 0.5$. Our results for the largest cumulative SNR $\sim 15$ suggest that the harmonic-space bispectrum is detectable within narrow ($\Delta z \sim 0.01$) spectroscopic redshift bins even when including only mildly non-linear scales. Tomographic reconstructions and inclusion of highly non-linear scales will further boost detectability with upcoming galaxy surveys. In addition, we discuss how, using the Karhunen-Lo\`eve transform, a detection analysis only requires a $1 \times 1$ covariance matrix for a single redshift bin.