# Chandrasekhar dynamical friction¶

class galpy.potential.ChandrasekharDynamicalFrictionForce(amp=1.0, GMs=0.1, gamma=1.0, rhm=0.0, dens=None, sigmar=None, const_lnLambda=False, minr=0.0001, maxr=25.0, nr=501, ro=None, vo=None)[source]

Class that implements the Chandrasekhar dynamical friction force

$\mathbf{F}(\mathbf{x},\mathbf{v}) = -2\pi\,[G\,M]\,[G\,\rho(\mathbf{x})]\,\ln[1+\Lambda^2] \,\left[\mathrm{erf}(X)-\frac{2X}{\sqrt{\pi}}\exp\left(-X^2\right)\right]\,\frac{\mathbf{v}}{|\mathbf{v}|^3}\,$

on a mass (e.g., a satellite galaxy or a black hole) $$M$$ at position $$\mathbf{x}$$ moving at velocity $$\mathbf{v}$$ through a background density $$\rho$$. The quantity $$X$$ is the usual $$X=|\mathbf{v}|/[\sqrt{2}\sigma_r(r)$$. The factor $$\Lambda$$ that goes into the Coulomb logarithm is taken to be

$\Lambda = \frac{r/\gamma}{\mathrm{max}\left(r_{\mathrm{hm}},GM/|\mathbf{v}|^2\right)}\,,$

where $$\gamma$$ is a constant. This $$\gamma$$ should be the absolute value of the logarithmic slope of the density $$\gamma = |\mathrm{d} \ln \rho / \mathrm{d} \ln r|$$, although for $$\gamma<1$$ it is advisable to set $$\gamma=1$$. Implementation here roughly follows 2016MNRAS.463..858P and earlier work.

__init__(amp=1.0, GMs=0.1, gamma=1.0, rhm=0.0, dens=None, sigmar=None, const_lnLambda=False, minr=0.0001, maxr=25.0, nr=501, ro=None, vo=None)[source]

NAME:

__init__

PURPOSE:

initialize a Chandrasekhar Dynamical Friction force

INPUT:

amp - amplitude to be applied to the potential (default: 1)

GMs - satellite mass; can be a Quantity with units of mass or Gxmass; can be adjusted after initialization by setting obj.GMs= where obj is your ChandrasekharDynamicalFrictionForce instance (note that the mass of the satellite can not be changed simply by multiplying the instance by a number, because he mass is not only used as an amplitude)

rhm - half-mass radius of the satellite (set to zero for a black hole; can be a Quantity); can be adjusted after initialization by setting obj.rhm= where obj is your ChandrasekharDynamicalFrictionForce instance

gamma - Free-parameter in $$\Lambda$$

dens - Potential instance or list thereof that represents the density [default: LogarithmicHaloPotential(normalize=1.,q=1.)]

sigmar= (None) function that gives the velocity dispersion as a function of r (has to be in natural units!); if None, computed from the dens potential using the spherical Jeans equation (in galpy.df.jeans) assuming zero anisotropy; if set to a lambda function, the object cannot be pickled (so set it to a real function)

cont_lnLambda= (False) if set to a number, use a constant ln(Lambda) instead with this value

minr= (0.0001) minimum r at which to apply dynamical friction: at r < minr, friction is set to zero (can be a Quantity)

Interpolation:

maxr= (25) maximum r for which sigmar gets interpolated; for best performance set this to the maximum r you will consider (can be a Quantity)

nr= (501) number of radii to use in the interpolation of sigmar

You can check that sigmar is interpolated correctly by comparing the methods sigmar [the interpolated version] and sigmar_orig [the original or directly computed version]

OUTPUT:

(none)

HISTORY:

2011-12-26 - Started - Bovy (NYU)

2018-03-18 - Re-started: updated to r dependent Lambda form and integrated into galpy framework - Bovy (UofT)

2018-07-23 - Calculate sigmar from the Jeans equation and interpolate it; allow GMs and rhm to be set on the fly - Bovy (UofT)