profiles.density.KingDensityProfile.compute_enclosed_mass#

KingDensityProfile.compute_enclosed_mass(r: unyt_array | unyt_quantity, units: str | Unit | None = None, **kwargs) → unyt_array | unyt_quantity#

Numerically compute the enclosed mass \(M(r)\) within radius \(r\).

The enclosed mass is given by:

\[M(r) = 4 \pi \int_0^r \rho(r') \, r'^2 \, dr',\]

where \(\rho(r)\) is the spherically symmetric density profile.

Parameters:

r (unyt_quantity or unyt_array) – Radius or array of radii at which to compute enclosed mass. Must carry length units (e.g., kpc, pc).
units (str or Unit, optional) – Desired output units for mass. If not provided, output units follow from the profile parameters.
**kwargs – Additional arguments passed to scipy.integrate.quad().

Returns:

mass – Enclosed mass at each radius with appropriate units.

Return type:

unyt_quantity or unyt_array

Notes

Assumes spherical symmetry.
Uses scipy.integrate.quad() for numerical integration.
Units are handled automatically using unyt.

Examples

Compute enclosed mass for a Hernquist profile:

import numpy as np
import unyt
from pisces.profiles.density import (
    HernquistDensityProfile,
)

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

radii = np.logspace(-1, 2, 100) * unyt.kpc
mass = profile.compute_enclosed_mass(
    radii, units="Msun"
)

print(mass)

profiles.density.KingDensityProfile.compute_enclosed_mass#

This Page