Open AccessLikelihood analysis of the Local Group acceleration revisited
Author(s) -
Cieciela̧g Paweł,
Chodorowski Michał J.
Publication year - 2004
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.1365-2966.2004.07569.x
Subject(s) - physics , acceleration , cmb cold spot , cosmic microwave background , spectral density , coherence (philosophical gambling strategy) , gaussian , nonlinear system , computational physics , astrophysics , classical mechanics , quantum mechanics , statistics , mathematics , anisotropy
We re‐examine likelihood analyses of the Local Group (LG) acceleration, paying particular attention to non‐linear effects. Under the approximation that the joint distribution of the LG acceleration and velocity is Gaussian, two quantities describing non‐linear effects enter these analyses. The first one is the coherence function, i.e. the cross‐correlation coefficient of the Fourier modes of gravity and velocity fields. The second one is the ratio of velocity power spectrum to gravity power spectrum. To date, in all analyses of the LG acceleration, the second quantity has not been accounted for. Extending our previous work, we study both the coherence function and the ratio of the power spectra. With the aid of numerical simulations we obtain expressions for the two as functions of wavevector and σ 8 . Adopting WMAP 's best determination of σ 8 , we estimate the most likely value of the parameter β and its errors. As the observed values of the LG velocity and gravity, we adopt respectively an estimate of the LG velocity based on the cosmic microwave background, and Schmoldt et al.'s estimate of the LG acceleration from the PSCz catalogue. We obtain β= 0.66 +0.21 −0.07 ; thus our error bars are significantly smaller than those of Schmoldt et al. This is not surprising, because the coherence function they used greatly overestimates actual decoherence between non‐linear gravity and velocity.