dsigma.physics module

Physics functions for the dsigma pipeline.

dsigma.physics.critical_surface_density(z_l, z_s, cosmology=None, comoving=True, d_l=None, d_s=None)

Compute the critical surface density.

Parameters:

z_lfloat or numpy.ndarray

Redshift of lens.

z_sfloat or numpy.ndarray

Redshift of source.

cosmologyastropy.cosmology or None, optional

Cosmology to assume for calculations. Only used if comoving distances are not passed. If None, use dsigma.default_cosmology. Default is None.

comovingbool, optional

Flag for using comoving instead of physical units.

d_lfloat or numpy.ndarray

Comoving transverse distance to the lens. If not given, it is calculated from the redshift provided.

d_sfloat or numpy.ndarray

Comoving transverse distance to the source. If not given, it is calculated from the redshift provided.

Returns:

sigma_critfloat or numpy.ndarray

Critical surface density for each lens-source pair.

dsigma.physics.effective_critical_surface_density(z_l, z_s, n_s, cosmology=None, comoving=True)

Compute the effective critical surface density.

Parameters:

z_lfloat or numpy.ndarray

Redshift of lens.

z_snumpy.ndarray

Redshifts of sources.

n_snumpy.ndarray

Fraction of source galaxies in each redshift bin. Does not need to be normalized.

cosmologyastropy.cosmology or None, optional

Cosmology to assume for calculations. If None, use dsigma.default_cosmology. Default is None.

comovingbool, optional

Flag for using comoving instead of physical unit.

Returns:

sigma_crit_efffloat or numpy.ndarray

Effective critical surface density for the lens redshift given the source redshift distribution.

dsigma.physics.lens_magnification_shear_bias(theta, alpha_l, z_l, z_s, camb_results, n_z=10, n_ell=200, bessel_function_zeros=100, k_max=1000.0)

Compute the lens magnification bias to the mean tangential shear.

This function is based on equations (13) and (14) in Unruh et al. (2020).

Parameters:

thetafloat or astropy.units.quantity.Quantity

Angular separation \(\theta\) from the lens sample. If not quantity is given, the separation is assumed to be in radians.

alpha_lfloat

Local slope of the flux distribution of lenses near the flux limit.

z_lfloat

Redshift of lens.

z_sfloat

Redshift of source.

camb_resultscamb.results.CAMBdata

CAMB results object that contains information on cosmology and the matter power spectrum.

n_zint, optional

Number of redshift bins used in the integral. Larger numbers will be more accurate.

n_ellint, optional

Number of \(\ell\) bins used in the integral. Larger numbers will be more accurate.

bessel_function_zerosint, optional

The calculation involves an integral over the second order Bessel function \(J_2 (\ell \theta)\) from \(\ell = 0\) to \(\ell = \infty\). In practice, this function replaces the upper bound with the bessel_function_zeros-th zero point of the Bessel function. Larger number should lead to more accurate results. However, in practice, this also requires larger n_ell. Particularly, n_ell should never fall below bessel_function_zeros.

k_maxfloat, optional

The maximum wavenumber beyond which the power spectrum is assumed to be 0.

Returns:

et_lmfloat

Bias in the mean tangential shear due to lens magnification effects.

dsigma.physics.mpc_per_degree(z, cosmology=None, comoving=False)

Estimate the angular scale in Mpc/degree at certain redshift.

Parameters:

cosmologyastropy.cosmology or None, optional

Cosmology to assume for calculations. If None, use dsigma.default_cosmology. Default is None.

zfloat or numpy.ndarray

Redshift of the object.

cosmologyastropy.cosmology, optional

Cosmology to assume for calculations.

comovingbool, optional

Use comoving distance instead of physical distance when True. Default is False.

Returns:

float or numpy.ndarray

Physical scale in unit of Mpc/degree.

dsigma.physics.projection_angle(ra_l, dec_l, ra_s, dec_s)

Calculate projection angle between lens and sources.

Parameters:

ra_l, dec_lfloat or numpy.ndarray

Coordinates of the lens galaxies in degrees.

ra_s, dec_sfloat or numpy.ndarray

Coordinates of the source galaxies in degrees.

Returns:

cos_2phi, sin_2phifloat or numpy.ndarray

The \(\cos\) and \(\sin\) of \(2 \phi\), where \(\phi\) is the angle measured from right ascension direction to a line connecting the lens and source galaxies.