pyccl.tracers module

class pyccl.tracers.CMBLensingTracer(cosmo, z_source, n_samples=100)

Bases: pyccl.tracers.Tracer

A Tracer for CMB lensing.

Parameters:

• cosmo (Cosmology) – Cosmology object.
• z_source (float) – Redshift of source plane for CMB lensing.
• nsamples (int, optional) – number of samples over which the kernel is desired. These will be equi-spaced in radial distance. The kernel is quite smooth, so usually O(100) samples is enough.

class pyccl.tracers.NumberCountsTracer(cosmo, has_rsd, dndz, bias, mag_bias=None)

Bases: pyccl.tracers.Tracer

Specific Tracer associated to galaxy clustering with linear scale-independent bias, including redshift-space distortions and magnification.

Parameters:

• cosmo (Cosmology) – Cosmology object.
• has_rsd (bool) – Flag for whether the tracer has a redshift-space distortion term.
• dndz (tuple of arrays) – A tuple of arrays (z, N(z)) giving the redshift distribution of the objects. The units are arbitrary; N(z) will be normalized to unity.
• bias (tuple of arrays) – A tuple of arrays (z, b(z)) giving the galaxy bias. If None, this tracer won’t include a term proportional to the matter density contrast.
• mag_bias (tuple of arrays, optional) – A tuple of arrays (z, s(z)) giving the magnification bias as a function of redshift. If None, the tracer is assumed to not have magnification bias terms. Defaults to None.

class pyccl.tracers.Tracer

Bases: object

Tracers contain the information necessary to describe the contribution of a given sky observable to its cross-power spectrum with any other tracer. Tracers are composed of 4 main ingredients:

• A radial kernel: this expresses the support in redshift/distance over which this tracer extends.
• A transfer function: this is a function of wavenumber and scale factor that describes the connection between the tracer and the power spectrum on different scales and at different cosmic times.
• An ell-dependent prefactor: normally associated with angular derivatives of a given fundamental quantity.
• The order of the derivative of the Bessel functions with which they enter the computation of the angular power spectrum.

A Tracer object will in reality be a list of different such tracers that get combined linearly when computing power spectra. Further details can be found in Section 4.9 of the CCL note.

add_tracer(cosmo, kernel=None, transfer_ka=None, transfer_k=None, transfer_a=None, der_bessel=0, der_angles=0, is_logt=False, extrap_order_lok=0, extrap_order_hik=2)

Adds one more tracer to the list contained in this Tracer.

Parameters:

• cosmo (Cosmology) – cosmology object.
• kernel (tulple of arrays, optional) – A tuple of arrays (chi, w_chi) describing the radial kernel of this tracer. chi should contain values of the comoving radial distance in increasing order, and w_chi should contain the values of the kernel at those values of the radial distance. The kernel will be assumed to be zero outside the range of distances covered by chi. If kernel is None a constant kernel w(chi)=1 will be assumed everywhere.
• transfer_ka (tuple of arrays, optional) – a tuple of arrays (a,`lk`,`t_ka`) describing the most general transfer function for a tracer. a should be an array of scale factor values in increasing order. lk should be an array of values of the natural logarithm of the wave number (in units of inverse Mpc) in increasing order. t_ka should be an array of shape (na,nk), where na and nk are the sizes of a and lk respectively. t_ka should hold the values of the transfer function at the corresponding values of a and lk. If your transfer function is factorizable (i.e. T(a,k) = A(a) * K(k)), it is more efficient to set this to None and use transfer_k and transfer_a to describe K and A respectively. The transfer function will be assumed continuous and constant outside the range of scale factors covered by a. It will be extrapolated using polynomials of order extrap_order_lok and extrap_order_hik below and above the range of wavenumbers covered by lk respectively. If this argument is not None, the values of transfer_k and transfer_a will be ignored.
• transfer_k (tuple of arrays, optional) – a tuple of arrays (lk,`t_k`) describing the scale-dependent part of a factorizable transfer function. lk should be an array of values of the natural logarithm of the wave number (in units of inverse Mpc) in increasing order. t_k ` should be an array of the same size holding the values of the k-dependent part of the transfer function at those wavenumbers. It will be extrapolated using polynomials of order `extrap_order_lok and extrap_order_hik below and above the range of wavenumbers covered by lk respectively. If None, the k-dependent part of the transfer function will be set to 1 everywhere.
• transfer_a (tuple of arrays, optional) – a tuple of arrays (a,`t_a`) describing the time-dependent part of a factorizable transfer function. a should be an array of scale factor values in increasing order. t_a should contain the time-dependent part of the transfer function at those values of the scale factor. The time dependence will be assumed continuous and constant outside the range covered by a. If None, the time-dependent part of the transfer function will be set to 1 everywhere.
• der_bessel (int) – order of the derivative of the Bessel functions with which this tracer enters the calculation of the power spectrum. Allowed values are -1, 0, 1 and 2. 0, 1 and 2 correspond to the raw functions, their first derivatives or their second derivatives. -1 corresponds to the raw functions divided by the square of their argument. We enable this special value because this type of dependence is ubiquitous for many common tracers (lensing, IAs), and makes the corresponding transfer functions more stables for small k or chi.
• der_angles (int) – integer describing the ell-dependent prefactor associated with this tracer. Allowed values are 0, 1 and 2. 0 means no prefactor. 1 means a prefactor ell*(ell+1), associated with the angular laplacian and used e.g. for lensing convergence and magnification. 2 means a prefactor sqrt((ell+2)!/(ell-2)!), associated with the angular derivatives of spin-2 fields (e.g. cosmic shear, IAs).
• is_logt (bool) – if True, transfer_ka, transfer_k and transfer_a will contain the natural logarithm of the transfer function (or their factorizable parts). Default is False.
• extrap_order_lok (int) – polynomial order used to extrapolate the transfer functions for low wavenumbers not covered by the input arrays.
• extrap_order_hik (int) – polynomial order used to extrapolate the transfer functions for high wavenumbers not covered by the input arrays.

class pyccl.tracers.WeakLensingTracer(cosmo, dndz, has_shear=True, ia_bias=None)

Bases: pyccl.tracers.Tracer

Specific Tracer associated to galaxy shape distortions including lensing shear and intrinsic alignments within the L-NLA model.

Parameters:

• cosmo (Cosmology) – Cosmology object.
• dndz (tuple of arrays) – A tuple of arrays (z, N(z)) giving the redshift distribution of the objects. The units are arbitrary; N(z) will be normalized to unity.
• has_shear (bool) – set to False if you want to omit the lensing shear contribution from this tracer.
• ia_bias (tuple of arrays, optional) – A tuple of arrays (z, A_IA(z)) giving the intrinsic alignment amplitude A_IA(z). If None, the tracer is assumped to not have intrinsic alignments. Defaults to None.

pyccl.tracers.get_density_kernel(cosmo, dndz)

This convenience function returns the radial kernel for galaxy-clustering-like tracers. Given an unnormalized redshift distribution, it returns two arrays: chi, w(chi), where chi is an array of radial distances in units of Mpc and w(chi) = p(z) * H(z), where H(z) is the expansion rate in units of Mpc^-1 and p(z) is the normalized redshift distribution.

Parameters:

• cosmo (Cosmology) – cosmology object used to transform redshifts into distances.
• dndz (tulple of arrays) – A tuple of arrays (z, N(z)) giving the redshift distribution of the objects. The units are arbitrary; N(z) will be normalized to unity.

pyccl.tracers.get_kappa_kernel(cosmo, z_source, nsamples)

This convenience function returns the radial kernel for CMB-lensing-like tracers.

Parameters:

• cosmo (Cosmology) – Cosmology object.
• z_source (float) – Redshift of source plane for CMB lensing.
• nsamples (int) – number of samples over which the kernel is desired. These will be equi-spaced in radial distance. The kernel is quite smooth, so usually O(100) samples is enough.

pyccl.tracers.get_lensing_kernel(cosmo, dndz, mag_bias=None)

This convenience function returns the radial kernel for weak-lensing-like. Given an unnormalized redshift distribution and an optional magnification bias function, it returns two arrays: chi, w(chi), where chi is an array of radial distances in units of Mpc and w(chi) is the lensing shear kernel (or the magnification one if mag_bias is not None).

Parameters:

• cosmo (Cosmology) – cosmology object used to transform redshifts into distances.
• dndz (tulple of arrays) – A tuple of arrays (z, N(z)) giving the redshift distribution of the objects. The units are arbitrary; N(z) will be normalized to unity.
• mag_bias (tuple of arrays, optional) – A tuple of arrays (z, s(z)) giving the magnification bias as a function of redshift. If None, s=0 will be assumed