# Description of the model¶

## (MM, A) LIMEPY: (Multi-Mass, Anisotropic) Lowered Isothermal Model Explorer in Python¶

### Isotropic models¶

The isotropic distribution functions are defined as (Gomez-Leyton & Velazquez 2014)

where \(\displaystyle \hat{E} = (\phi(r_{\rm t}) - \phi - v^2/2)/s^2\), \(\phi\) is the potential, \(r_{\rm t}\) is the trunction radius, \(s\) is a velocity scale and

where \(0 <
\phi-\phi(r_{\rm t}) <\phi_0/s^2\) is the (positive) potential and \(P(a, x)\) is the
regularised lower incomplete gamma function \(P(a, x) =
\gamma(a, x)/\Gamma(x)\). For some integer values of *g* several well
known models are found

- g = 0 : Woolley (1954)
- g = 1 : King (1966)
- g = 2 : Wilson (1975)

### Anisotropic models¶

Radial anisotropy as in Michie (1963) can be included as follows

where \(\hat{J}^2 = (rv_t)^2/(2r_{\rm a}^2s^2)\), here \(r_{\rm a}\) is the user-defined anisotropy radius.

### Multi-mass model¶

Multi-mass models are found by summing the DFs of individual mass components and adopting for each component (following Gunn & Griffin (1979))

where \(\mu_j = m_j/\bar{m}\) and \(\bar{m}\) is the central density weighted mean mass.