Higher multipoles of the galaxy bispectrum in redshift space

Abstract

As a generalization of our previous work [Phys. Rev. D 95 043528 (2017)], in which an analytic model for the galaxy bispectrum in redshift space was developed on the basis of the halo approach, we here investigate its higher multipoles that have not been known so far. The redshift-space bispectrum includes the two variables ω and φ for the line-of-sight direction, and the higher multipole bispectra are defined by the coefficients in the expansion of the redshift-space bispectrum using the spherical harmonics. We find 6 new nonvanishing components out of 25 total components up to ℓ = 4, in addition to 3 components discussed in the previous work (monopole, quadruple, and hexadecapole of m = 0). The characteristic behaviors of the new nonvanishing multipoles are compared with the results of galaxy mock catalogs that match the halo occupation distribution of the Sloan Digital Sky Survey Baryonic Oscillation Spectroscopic Survey low-redshift sample. We find that the multipoles with m = 0 are also sensitive to redshift-space distortion (RSD) as well as those with m = 0 and thus are key ingredients in the RSD analysis using the galaxy bispectrum. Analytic approximation formulas for these nonzero components are also presented; these are useful for understanding the characteristic behaviors.

The dipole of the galaxy bispectrum

“…Then, use the identity µ2 = µ1 cos θ + 1 − µ 2 1 sin θ cos ϕ , where θ = θ12 (and we define µ = cos θnote that θ is the angle outside the triangle as the ka's are head-to-tail). We use standard orthonormal spherical harmonics with the triangle lying in the y − z plane, with k1 aligned along the z-axis (Nan et al 2018). Then we have Y m (µ1, ϕ), so that we can write Bg = m B m Y m (µ1, ϕ).…”

“…A natural question is: what about the galaxy bispectrum? In the standard 'Newtonian' approximation, with only RSD, the galaxy bispectrum for a single tracer at fixed redshift has no dipole, and only has even multipoles (Scoccimarro et al 1999;Nan et al 2018). But with a lightcone corrected galaxy density contrast, the 3-point correlator, even for a single tracer, will no longer be an even function of ka · n (a = 1, 2, 3).…”

GEOMAX: beyond linear compression for three-point galaxy clustering statistics

“…In preparation for future game-changing data-sets like DESI 2 (Levi et al 2013); Euclid 3 (Laureijs et al 2011); PFS 4 (Ellis et al 2014); SKA 5 (Bacon et al 2018) and LSST 6 (Abell et al 2009), the scientific community has been working on improving the modelling of 3pt statistics and extending their applications. Di Dio et al (2019) studied the full sky angular galaxy bispectrum beyond the flat sky approximation, Yamamoto et al (2017); Nan et al (2018) and Sugiyama et al (2019b) proposed a complete multipole decomposition for the galaxy bispectrum, Bertacca et al (2018); Clarkson et al (2019) studied relativistic effects and corrections. Sabiu et al (2019) proposed a technique to speed up the computation of 3pt and higher order statistics while D'Amico et al…”

Bispectrum as baryon acoustic oscillation interferometer

“…Many studies of the anisotropic bispectrum and 3PCF, which retain information about the line of sight, have also employed a multipole basis with respect to the line of sight in redshift space (e.g. Gagrani & Samushia 2017;Yamamoto et al 2017;Castorina & White 2018;Desjacques et al 2018;Nan et al 2018;Yankelevich & Porciani 2018). Slepian & Eisenstein (2018) and Sugiyama et al (2018) use a spherical harmonic expansion of the 3PCF and bispectrum, which includes information on both the internal angle and the angles to the line of sight.…”