Cosmological Velocity Field

Class providing models of the large-scale cosmological peculiar velocity field—the deviation from pure Hubble flow driven by gravitational collapse of density perturbations. Methods return the mean pairwise radial velocity (in km s\(^{-1}\)) between galaxy pairs at a given separation, and the one-dimensional velocity dispersion on a scale corresponding to a given mass. These quantities enter models of redshift-space distortions, pairwise statistics, and galaxy clustering in redshift surveys, and depend on the matter power spectrum, cosmological parameters, and, if applicable, the halo bias.

Default implementation: cosmologicalVelocityFieldFilteredPower

Methods

velocityRadialMeanPairwise → double precision

Return the mean radial velocity (averaged over all positions; in km/s) at a given separation (in units of Mpc) and time (in units of Gyr). If includeHubbleFlow is true then the Hubble flow is included, otherwise only the peculiar component of the mean radial velocity is computed.

  • double precision, intent(in ) :: separation, time

  • logical , intent(in ) :: includeHubbleFlow

velocityDispersion1D → double precision

Return the 1-D dispersion of the velocity field (in units of km/s) on a scale corresponding to the given mass (in units of \(\mathrm{M}_\odot\)) and the given time (in units of Gyr).

  • double precision, intent(in ) :: mass, time

velocityDispersion1DHaloPairwise → double precision

Return the 1-D dispersion of the velocity field (in units of km/s) for pairs of halos of the given mass1 and mass2 (in units of \(\mathrm{M}_\odot\)) at the given separation (in units of Mpc) and the given time (in units of Gyr).

  • double precision, intent(in ) :: mass1, mass2, separation, time

cosmologicalVelocityFieldFilteredPower

Cosmological velocity field computed by filtering the linear theory power spectrum. The growth factor for velocities is \(D_\mathrm{v}(t) = a(t) D(t) H(t) f(t)\), where \(D(t)\) is the usual growth factor for density, and \(f(t) = \mathrm{d}\log D / \mathrm{d} \log a\). Note that the factor of \(D(t)\) does not explicitly appear in expressions for the velocity dispersion since it is included in the linear theory power spectrum appearing in those expressions.

(Default implementation)

Methods

  • sigmaJ — Compute the function \(\sigma_j^2(m) = {1 \over 2 \pi^2} \int_0^\infty \mathrm{d}k k^{2+2j} P(k) W^2[kR(m)]\), e.g. Sheth and Diaferio (2001).

  • peakCorrection — Compute the peak correction term for the velocity dispersion of halos of given mass, e.g. Sheth and Diaferio (2001), and Bardeen et al. (1986).

Parameters

  • [wavenumberMaximum] (default huge(0.0d0)) — The maximum wavenumber to which to integrate the power spectrum. By default this in infinite. It can be useful to set a smaller value for power spectra with small-scale cut offs to avoid convergence issues in the integrals.