Open AccessCovariance of the one‐dimensional mass power spectrum
Author(s) -
Zhan Hu,
Eisenstein Daniel
Publication year - 2005
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2005.08776.x
Subject(s) - physics , covariance , covariance matrix , spectral density , covariance function , covariance mapping , gaussian , diagonal , field (mathematics) , cosmic variance , covariance intersection , statistical physics , gaussian random field , statistics , astrophysics , computational physics , galaxy , gaussian process , mathematics , quantum mechanics , geometry , redshift , pure mathematics
We analyse the covariance of the one‐dimensional mass power spectrum along lines of sight. The covariance reveals the correlation between different modes of fluctuations in the cosmic density field and gives the sample variance error for measurements of the mass power spectrum. For Gaussian random fields, the covariance matrix is diagonal. As expected, the variance of the measured one‐dimensional mass power spectrum is inversely proportional to the number of lines of sight that are sampled from each random field. The correlation between lines of sight in a single field may alter the covariance. However, lines of sight that are sampled far apart are only weakly correlated, so that they can be treated as independent samples. Using N ‐body simulations, we find that the covariance matrix of the one‐dimensional mass power spectrum is not diagonal for the cosmic density field due to the non‐Gaussianity and that the variance is much higher than that of Gaussian random fields. From the covariance, one will be able to determine the cosmic variance in the measured one‐dimensional mass power spectrum as well as to estimate how many lines of sight are needed to achieve a target precision.