Likelihood reconstruction method of real-space density and velocity
  power spectra from a redshift galaxy survey
  We develop a maximum likelihood based method of reconstructing band powers of
the density and velocity power spectra at each wavenumber bins from the
measured clustering features of galaxies in redshift space, including
marginalization over uncertainties inherent in the Fingers-of-God (FoG) effect.
The reconstruction can be done assuming that the density and velocity power
spectra depend on the redshift-space power spectrum having different angular
modulations of mu with mu^{2n} (n=0,1,2) and that the model FoG effect is given
as a multiplicative function in the redshift-space spectrum. By using N-body
simulations and the halo catalogs, we test our method by comparing the
reconstructed power spectra with the simulations. For the spectrum of mu^0 or
equivalently the density power spectrum P_dd(k), our method recovers the
amplitudes to a few percent accuracies up to k=0.3 h/Mpc for both dark matter
and halos. For the power spectrum of mu^2, which is equivalent to the
density-velocity spectrum P_dv(k) in the linear regime, our method can recover
the input power spectrum for dark matter up to k=0.2 h/Mpc and at both z=0 and
1, if using the adequate FoG model. However, for the halo spectrum, the
reconstructed spectrum shows greater amplitudes than the simulation P_dv(k). We
argue that the disagreement is ascribed to nonlinearity effect that arises from
the cross-bispectra of density and velocity perturbations. Using the
perturbation theory, we derive the nonlinear correction term, and find that the
leading-order correction term is proportional to mu^2 and increases the
mu^2-power spectrum amplitudes at larger k, at lower redshifts and for more
massive halos. We find that adding the nonlinearity correction term to the
simulation P_dv(k) can fairly well reproduce the reconstructed P_dv(k) for
halos up to k~0.2 h/Mpc.
