# DF (galpy.df)¶

galpy.df contains tools for dealing with distribution functions of stars in galaxies. It mainly contains a number of classes that define different types of distribution function, but galpy.df.jeans also has some tools for solving the Jeans equations for equilibrium systems.

## Spherical distribution functions¶

Isotropic and anisotropic distribution functions for spherical systems. Documentation of these is limited at this point, but generally, one can use them as:

from galpy import potential
from galpy.df import isotropicNFWdf
np= potential.NFWPotential(amp=1.2,a=2.3)
ndf= isotropicNFWdf(pot=np)
# sample
sam= ndf.sample(n=int(1e6))
print(numpy.std(sam[numpy.fabs(sam.r()-1.2) < 0.1].vr()))
# 0.2156787374302913
# Compute vel. dispersion
print(ndf.sigmar(1.2))
# 0.21985277878647172


or:

from galpy.df import kingdf
kdf= kingdf(M=2.3,rt=1.4,W0=3.)
sam= kdf.sample(n=int(1e6))
print(numpy.amax(sam.r()))
# 1.3883460662897116
print(numpy.std(sam[numpy.fabs(sam.r()-0.2) < 0.01].vr()))
# 1.081298923132113
print(kdf.sigmar(0.2))
# 1.0939934290993467


Various spherical DFs are explicitly implemented (e.g., Hernquist, NFW using a new approximation, King, Plummer) in isotropic and various anisotropic forms. General methods for computing isotropic, constant-beta anisotropic, and Osipkov-Merritt anisotropic for any potential/density pair are also included.

### Specific distribution functions¶

The following are isotropic distribution functions

Anisotropic versions also exist:

## Two-dimensional, axisymmetric disk distribution functions¶

Distribution function for orbits in the plane of a galactic disk.

## Two-dimensional, non-axisymmetric disk distribution functions¶

Distribution function for orbits in the plane of a galactic disk in non-axisymmetric potentials. These are calculated using the technique of Dehnen 2000, where the DF at the current time is obtained as the evolution of an initially-axisymmetric DF at time to in the non-axisymmetric potential until the current time.

## Three-dimensional disk distribution functions¶

Distribution functions for orbits in galactic disks, including the vertical motion for stars reaching large heights above the plane. Currently only the quasi-isothermal DF.

## The distribution function of a gap in a tidal stream¶

From Sanders, Bovy, & Erkal 2015; see Modeling gaps in streams using action-angle coordinates. Implemented as a subclass of streamdf. No full implementation is available currently, but the model can be set up and sampled as in the above paper.

## The distribution function of a tidal stream using a particle-spray technique¶

Model from Fardal et al. (2015) with full details of the galpy implementation given in Qian et al. (2022); see NEW in v1.8 Particle-spray modeling of streams with streamspraydf.