halomod.integrate_corr.angular_corr_gal

halomod.integrate_corr.angular_corr_gal(theta, xi, p1, zmin, zmax, logu_min, logu_max, znum=100, unum=100, p2=None, check_p_norm=True, cosmo=None, p_of_z=True, **xi_kw)[source]

Calculate the angular correlation function w(theta).

From [1], Eq. 33. That is, this uses the Limber approximation. This does not hold either for wide angles, or thin radial distributions.

Parameters

  • theta (array_like) – Angles at which to calculate the angular correlation. In radians.

  • xi (callable) – A function of one variable: r [Mpc/h], which returns the 3D correlation function at the scale r.

  • p1 (callable) – The redshift distribution of sources. Should integrate to 1 between logz_min and logz_max. A callable function of a single variable, z.

  • zmin (float) – The redshift limits of the sample distribution. Note that this is in redshift, regardless of the value of p_of_z.

  • zmax (float) – The redshift limits of the sample distribution. Note that this is in redshift, regardless of the value of p_of_z.

  • logu_min (float) – min,max of the log10 of radial separation grid [Mpc/h]. Must be large enough to let the integral over the 3D correlation function to converge.

  • logu_max (float) – min,max of the log10 of radial separation grid [Mpc/h]. Must be large enough to let the integral over the 3D correlation function to converge.

  • znum (int, optional) – Number of steps in redshift grid.

  • unum (int, optional) – Number of steps in the u grid.

  • p2 (callable, optional) – The same as p1, but for a second, cross-correlating dataset. If not provided, defaults to p1 (i.e. auto-correlation).

  • check_p_norm (bool, optional) – If False, cancels checking the normalisation of p1 and p2.

  • p_of_z (bool, optional) – Whether p1 and p2 are functions of redshift.

  • cosmo (hmf.cosmo.Cosmology instance, optional) – A cosmology, used to generate comoving distance from redshift. Default is the default cosmology of the hmf package.

  • xi_kw (unpacked-dict) – Any arguments to xi other than r,z.

Returns

wtheta – The angular correlation function corresponding to theta.

Return type

array_like

References

1

Blake, C. et al., “Halo-model signatures from 380000 Sloan Digital Sky Survey luminous red galaxies with photometric redshifts”, https://ui.adsabs.harvard.edu/abs/2008MNRAS.385.1257B.