.. _physics-cosmologicalVelocityField:

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\ :math:`^{-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 :math:`\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 :math:`\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``

.. _physics-cosmologicalVelocityFieldFilteredPower:

``cosmologicalVelocityFieldFilteredPower``
------------------------------------------

Cosmological velocity field computed by filtering the linear theory power spectrum. The growth factor for velocities is :math:`D_\mathrm{v}(t) = a(t) D(t) H(t) f(t)`, where :math:`D(t)` is the usual growth factor for density, and :math:`f(t) = \mathrm{d}\log D / \mathrm{d} \log a`. Note that the factor of :math:`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 :math:`\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. :cite:t:`sheth_peculiar_2001`.
* ``peakCorrection`` — Compute the peak correction term for the velocity dispersion of halos of given ``mass``, e.g. :cite:t:`sheth_peculiar_2001`, and :cite:t:`bardeen_statistics_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.