profiles.density.CoredPowerLawDensityProfile.compute_escape_velocity#

CoredPowerLawDensityProfile.compute_escape_velocity(r: unyt_array | unyt_quantity, units: str | Unit | None = None, G: unyt_quantity | None = None, **kwargs) → unyt_array | unyt_quantity#

Compute the escape velocity at radius \(r\).

The escape velocity is the minimum speed required for a test particle to escape to infinity from radius \(r\) in a spherically symmetric gravitational potential:

\[v_{\mathrm{esc}}(r) = \sqrt{ \frac{2 G M(r)}{r} },\]

where \(M(r)\) is the enclosed mass at radius \(r\).

Parameters:

  • r (unyt_quantity or unyt_array) – Radius or array of radii at which to compute the escape velocity (must carry length units).

  • units (str or Unit, optional) – Desired output units for the escape velocity. By default, uses the internal units determined by G and the profile parameters.

  • G (unyt_quantity, optional) – Gravitational constant to use. Defaults to gravitational_constant.

  • kwargs (dict) – Additional keyword arguments passed to compute_enclosed_mass().

Returns:

v_esc – Escape velocity at each input radius, with appropriate units.

Return type:

unyt_quantity or unyt_array

Example

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

profile = HernquistDensityProfile(
    rho_0=1.0, r_s=5.0
)

r = np.logspace(-1, 2, 50)  # kpc
v_esc = profile.compute_escape_velocity(
    r, units="km/s"
)

print(v_esc)