TY - JOUR

T1 - Bispectrum supersample covariance

AU - Chan, Kwan Chuen

AU - Moradinezhad Dizgah, Azadeh

AU - Noreña, Jorge

N1 - Funding Information:
Our work makes it clear that for the bispectrum covariance and the cross-covariance, the small-scale covariance is the dominant source, at least up to . For the bispectrum this is probably the highest scale we can hope to model. Thankfully, the small-scale non-Gaussian covariance can be studied using the standard periodic setup with a small box size, which is much more accessible in terms of computational resources. On the other hand, there have been few efforts so far to model the small-scale covariance . The perturbative approach only improves over the Gaussian covariance in the mildly nonlinear regime . To extend the perturbative calculation to higher , one possibility is to model the bispectrum covariance using the halo model. A useful way of organizing the computation is to expand the covariance in terms of the connected correlators , which in turn are computed using the halo model. ACKNOWLEDGMENTS for sharing the data with us. K. C. C. acknowledges the support from the Spanish Ministerio de Economia y Competitividad Grant No. ESP2013-48274-C3-1-P and the Juan de la Cierva fellowship. J. N. is supported by Fondecyt Grant No. 1171466.
Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/2/28

Y1 - 2018/2/28

N2 - Modes with wavelengths larger than the survey window can have significant impact on the covariance within the survey window. The supersample covariance has been recognized as an important source of covariance for the power spectrum on small scales, and it can potentially be important for the bispectrum covariance as well. In this paper, using the response function formalism, we model the supersample covariance contributions to the bispectrum covariance and the cross-covariance between the power spectrum and the bispectrum. The supersample covariances due to the long-wavelength density and tidal perturbations are investigated, and the tidal contribution is a few orders of magnitude smaller than the density one because in configuration space the bispectrum estimator involves angular averaging and the tidal response function is anisotropic. The impact of the super-survey modes is quantified using numerical measurements with periodic box and sub-box setups. For the matter bispectrum, the ratio between the supersample covariance correction and the small-scale covariance - which can be computed using a periodic box - is roughly an order of magnitude smaller than that for the matter power spectrum. This is because for the bispectrum, the small-scale non-Gaussian covariance is significantly larger than that for the power spectrum. For the cross-covariance, the supersample covariance is as important as for the power spectrum covariance. The supersample covariance prediction with the halo model response function is in good agreement with numerical results.

AB - Modes with wavelengths larger than the survey window can have significant impact on the covariance within the survey window. The supersample covariance has been recognized as an important source of covariance for the power spectrum on small scales, and it can potentially be important for the bispectrum covariance as well. In this paper, using the response function formalism, we model the supersample covariance contributions to the bispectrum covariance and the cross-covariance between the power spectrum and the bispectrum. The supersample covariances due to the long-wavelength density and tidal perturbations are investigated, and the tidal contribution is a few orders of magnitude smaller than the density one because in configuration space the bispectrum estimator involves angular averaging and the tidal response function is anisotropic. The impact of the super-survey modes is quantified using numerical measurements with periodic box and sub-box setups. For the matter bispectrum, the ratio between the supersample covariance correction and the small-scale covariance - which can be computed using a periodic box - is roughly an order of magnitude smaller than that for the matter power spectrum. This is because for the bispectrum, the small-scale non-Gaussian covariance is significantly larger than that for the power spectrum. For the cross-covariance, the supersample covariance is as important as for the power spectrum covariance. The supersample covariance prediction with the halo model response function is in good agreement with numerical results.

UR - http://www.scopus.com/inward/record.url?scp=85043683654&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.97.043532

DO - 10.1103/PhysRevD.97.043532

M3 - Article

AN - SCOPUS:85043683654

VL - 97

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 4

M1 - 043532

ER -