profiles.density.HernquistDensityProfile.compute_cosmological_overdensity_radius#

HernquistDensityProfile.compute_cosmological_overdensity_radius(z: float, delta_target: float, rmin: float | unyt_quantity, rmax: float | unyt_quantity, units: str | Unit | None = 'kpc', cosmology: Cosmology | None = None, **kwargs)#

Find the radius enclosing a target overdensity relative to the critical density at redshift \(z\).

Numerically solves for radius \(r_{\Delta}\) satisfying:

\[\Delta(r_{\Delta}) = \Delta_{\mathrm{target}}\]
Parameters:

  • z (float) – Redshift at which to compute overdensity.

  • delta_target (float) – Desired overdensity value (must be positive).

  • rmin (float) – Lower bound for root-finding search interval, in units specified by units.

  • rmax (float) – Upper bound for root-finding search interval.

  • units (str or Unit, optional) – Units for rmin and rmax. Default is kpc.

  • cosmology (Cosmology, optional) – Cosmology used to compute \(\rho_{\mathrm{crit}}(z)\). Defaults to pisces_config.

  • **kwargs – Additional arguments passed to compute_enclosed_mass().

Returns:

r_delta – Radius enclosing the target overdensity.

Return type:

unyt_quantity

Raises:

ValueError – If inputs are invalid or critical density calculation fails.

Examples

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

profile = HernquistDensityProfile(
    rho_0=0.05, r_s=10
)

r_delta = profile.compute_cosmological_overdensity_radius(
    z=0.3,
    delta_target=200,
    rmin=1,
    rmax=500,
    units="kpc",
    cosmology=Planck18,
)

print(f"r_200 = {r_delta:.2f}")

See also

compute_cosmological_overdensity_profile(), compute_enclosed_mass(), scipy.optimize.brentq()