Speeding up the detectability of the harmonic-space galaxy bispectrum
arXiv:2008.11131 · doi:10.1088/1475-7516/2021/01/002
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 triangle configurations in multipole space, corresponding to a computational speedup of a factor , 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 bring higher cumulative SNR than bins at lower redshifts . Our results for the largest cumulative SNR suggest that the harmonic-space bispectrum is detectable within narrow () 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-Loève transform, a detection analysis only requires a covariance matrix for a single redshift bin.
arXiv comment18 pages, 6 figures. New analysis with narrow redshift bins yields SNR ~ 15. Version accepted by JCAP
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