pyccl.halos.pk_2pt module

pyccl.halos.pk_2pt.halomod_power_spectrum(cosmo, hmc, k, a, prof, *, prof2=None, prof_2pt=None, p_of_k_a=None, get_1h=True, get_2h=True, smooth_transition=None, suppress_1h=None, extrap_pk=False)[source]

Computes the halo model power spectrum for two quantities defined by their respective halo profiles. The halo model power spectrum for two profiles \(u\) and \(v\) is:

\[P_{u,v}(k,a) = I^0_2(k,a|u,v) + I^1_1(k,a|u)\,I^1_1(k,a|v)\,P_{\rm lin}(k,a)\]

where \(P_{\rm lin}(k,a)\) is the linear matter power spectrum, \(I^1_1\) is defined in the documentation of I_1_1(), and \(I^0_2\) is defined in the documentation of I_0_2().

Parameters:

  • cosmo (Cosmology) – a Cosmology object.

  • hmc (HMCalculator) – a halo model calculator.

  • k (float or array) – comoving wavenumber in Mpc^-1.

  • a (float or array) – scale factor.

  • prof (HaloProfile) – halo profile.

  • prof2 (HaloProfile) – a second halo profile. If None, prof will be used as prof2.

  • prof_2pt (Profile2pt) – a profile covariance object returning the the two-point moment of the two profiles being correlated. If None, the default second moment will be used, corresponding to the products of the means of both profiles.

  • p_of_k_a (Pk2D) – a Pk2D object to be used as the linear matter power spectrum. If None, the power spectrum stored within cosmo will be used.

  • get_1h (bool) – if False, the 1-halo term (i.e. the first term in the first equation above) won’t be computed.

  • get_2h (bool) – if False, the 2-halo term (i.e. the second term in the first equation above) won’t be computed.

  • smooth_transition (callable or None) – Modify the halo model 1-halo/2-halo transition region via a time-dependent function \(\alpha(a)\), defined as in HMCODE-2020: \(P(k,a)= (P_{1h}^{\alpha(a)}(k)+P_{2h}^{\alpha(a)}(k))^{1/\alpha}\). If None the extra factor is just 1.

  • suppress_1h (callable or None) –

    Suppress the 1-halo large scale contribution by a time- and scale-dependent function \(k_*(a)\), defined as in HMCODE-2020: \(1/[1+(k_*(a)/k)^4]\). If None the standard 1-halo term is returned with no damping.

  • extrap_pk (bool) – Whether to extrapolate p_of_k_a in case a is out of its support. If `False`, and the queried values are out of bounds, an error is raised.

Returns:

integral values evaluated at each combination of k and a. The shape of the output will be (N_a, N_k) where N_k and N_a are the sizes of k and a respectively. If k or a are scalars, the corresponding dimension will be squeezed out on output.

Return type:

(float or array)

pyccl.halos.pk_2pt.halomod_Pk2D(cosmo, hmc, prof, *, prof2=None, prof_2pt=None, p_of_k_a=None, get_1h=True, get_2h=True, lk_arr=None, a_arr=None, extrap_order_lok=1, extrap_order_hik=2, smooth_transition=None, suppress_1h=None, extrap_pk=False)[source]

Returns a Pk2D object containing the halo-model power spectrum for two quantities defined by their respective halo profiles. See halomod_power_spectrum() for more details about the actual calculation.

Parameters:

  • cosmo (Cosmology) – a Cosmology object.

  • hmc (HMCalculator) – a halo model calculator.

  • prof (HaloProfile) – halo profile.

  • prof2 (HaloProfile) – a second halo profile. If None, prof will be used as prof2.

  • prof_2pt (Profile2pt) – a profile covariance object returning the the two-point moment of the two profiles being correlated. If None, the default second moment will be used, corresponding to the products of the means of both profiles.

  • p_of_k_a (Pk2D) – a Pk2D object to be used as the linear matter power spectrum. If None, the power spectrum stored within cosmo will be used.

  • get_1h (bool) – if False, the 1-halo term (i.e. the first term in the first equation above) won’t be computed.

  • get_2h (bool) – if False, the 2-halo term (i.e. the second term in the first equation above) won’t be computed.

  • a_arr (array) – an array holding values of the scale factor at which the halo model power spectrum should be calculated for interpolation. If None, the internal values used by cosmo will be used.

  • lk_arr (array) – an array holding values of the natural logarithm of the wavenumber (in units of Mpc^-1) at which the halo model power spectrum should be calculated for interpolation. If None, the internal values used by cosmo will be used.

  • extrap_order_lok (int) – extrapolation order to be used on k-values below the minimum of the splines. See Pk2D.

  • extrap_order_hik (int) – extrapolation order to be used on k-values above the maximum of the splines. See Pk2D.

  • smooth_transition (callable or None) –

    Modify the halo model 1-halo/2-halo transition region via a time-dependent function \(\alpha(a)\), defined as in HMCODE-2020: \(P(k,a)= (P_{1h}^{\alpha(a)}(k)+P_{2h}^{\alpha(a)}(k))^{1/\alpha}\). If None the extra factor is just 1.

  • suppress_1h (callable or None) –

    Suppress the 1-halo large scale contribution by a time- and scale-dependent function \(k_*(a)\), defined as in HMCODE-2020: \(1/[1+(k_*(a)/k)^4]\). If None the standard 1-halo term is returned with no damping.

  • extrap_pk (bool) – Whether to extrapolate p_of_k_a in case a is out of its support. If `False`, and the queried values are out of bounds, an error is raised.

Returns:

halo model power spectrum.

Return type:

Pk2D