profiles.density.NFWDensityProfile.compute_cosmological_overdensity_profile#

NFWDensityProfile.compute_cosmological_overdensity_profile(z: float, R: unyt_array | unyt_quantity, cosmology: Cosmology | None = None, **kwargs)#

Compute the spherical overdensity profile relative to the critical density at redshift \(z\).

The overdensity is defined as:

\[\Delta(R) = \frac{3 M(R)}{4 \pi R^3 \rho_{\mathrm{crit}}(z)}\]

where \(M(R)\) is the enclosed mass and \(\rho_{\mathrm{crit}}(z)\) is the critical density.

Parameters:

z (float) – Redshift at which to compute the critical density.
R (unyt_quantity or unyt_array) – Radius or array of radii where overdensity is computed (must carry length units).
cosmology (Cosmology, optional) – Cosmology used to compute \(\rho_{\mathrm{crit}}(z)\). Defaults to pisces_config['physics.default_cosmology'].
**kwargs – Additional arguments passed to compute_enclosed_mass().

Returns:

overdensity – Dimensionless overdensity \(\Delta(R)\) at each radius.

Return type:

ndarray

Raises:

ValueError – If cosmology cannot compute the critical density.

Examples

import unyt
from astropy.cosmology import Planck18
from pisces.profiles.density import (
    NFWDensityProfile,
)

profile = NFWDensityProfile(
    rho_0=0.05 * unyt.Msun / unyt.kpc**3,
    r_s=10 * unyt.kpc,
)

R = unyt.array.unyt_array([1, 10, 100], "kpc")
delta = profile.compute_cosmological_overdensity_profile(
    z=0.5, R=R, cosmology=Planck18
)

print(delta)

profiles.density.NFWDensityProfile.compute_cosmological_overdensity_profile#

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