profiles.density.EinastoDensityProfile.compute_fractional_mass_radius

EinastoDensityProfile.compute_fractional_mass_radius(rmin: float | unyt_quantity, rmax: float | unyt_quantity, fraction: float = 0.5, units: str | Unit | None = 'kpc', **kwargs)

Find the radius enclosing a given fraction of the total mass.

Solves numerically for radius \(r_f\) such that:

\[M(r_f) = f \times M_{\mathrm{tot}}\]

where \(f\) is the desired mass fraction.

Parameters:

• rmin (float or unyt_quantity) – Lower bound for the radius search interval.

• rmax (float or unyt_quantity) – Upper bound for the radius search interval.

• fraction (float, optional) – Mass fraction to enclose, between 0 and 1. Default is 0.5 (half-mass radius).

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

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

Returns:

radius – Radius enclosing the specified mass fraction.

Return type:

unyt_quantity

Raises:

ValueError – If the mass fraction is outside (0, 1) or search bounds are invalid.

Examples

import unyt
from pisces.profiles.density import (
    HernquistDensityProfile,
)

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

half_mass_radius = (
    profile.compute_fractional_mass_radius(
        0.1, 100, fraction=0.5, units="kpc"
    )
)
print(f"Half-mass radius: {half_mass_radius:.2f}")

See also

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