215,758 research outputs found
Determine the galaxy bias factors on large scales using bispectrum method
We study whether the bias factors of galaxies can be unbiasedly recovered
from their power spectra and bispectra. We use a set of numerical N-body
simulations and construct large mock galaxy catalogs based upon the
semi-analytical model of Croton et al. (2006). We measure the reduced bispectra
for galaxies of different luminosity, and determine the linear and first
nonlinear bias factors from their bispectra. We find that on large scales down
to that of the wavenumber k=0.1h/Mpc, the bias factors b1 and b2 are nearly
constant, and b1 obtained with the bispectrum method agrees very well with the
expected value. The nonlinear bias factor b2 is negative, except for the most
luminous galaxies with M<-23 which have a positive b2. The behavior of b2 of
galaxies is consistent with the b2 mass dependence of their host halos. We show
that it is essential to have an accurate estimation of the dark matter
bispectrum in order to have an unbiased measurement of b1 and b2. We also test
the analytical approach of incorporating halo occupation distribution to model
the galaxy power spectrum and bispectrum. The halo model predictions do not fit
the simulation results well on the precision requirement of current
cosmological studies.Comment: 9 pages, 8 figures, accepted for publication in Ap
Rational points near planar curves and Diophantine approximation
In this paper, we establish asymptotic formulae with optimal errors for the
number of rational points that are close to a planar curve, which unify and
extend the results of Beresnevich-Dickinson-Velani and Vaughan-Velani.
Furthermore, we complete the Lebesgue theory of Diophantine approximation on
weakly non-degenerate planar curves that was initially developed by
Beresnevich-Zorin in the divergence case.Comment: 27 pages, corrected typos, to appear in Adv. Mat
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