# Density profiles

Source: https://pianistpy.com/docs/guide/profiles

`pianistpy.DoublePowerLaw`

`DoublePowerLaw(rho_alpha, rho_beta, rho_gamma)` is the analytical double-power-law density profile
\(\varrho(R) = C\,R^{-\gamma}\,(1 + R^{\alpha})^{(\gamma-\beta)/\alpha}\), with \(R\) the radius in units of
the scale radius and \(C\) a normalization constant. The class takes three arguments:

- `rho_alpha`, the sharpness \(\alpha\) of the transition between the inner and the outer slope, at least
1/2;

- `rho_beta`, the outer slope \(\beta\), greater than 2 for the profile and at least 3 for a component;

- `rho_gamma`, the inner slope \(\gamma\), with \(0 \leq \gamma < 2\), so that the central potential is
finite.

In internal units ([Units](https://pianistpy.com/docs/guide/units)), the scale radius and the central potential of a `DoublePowerLaw`
profile are 1. The NFW, Hernquist and Plummer profiles are parameter sets of `DoublePowerLaw`, not classes of
their own:

```python
pp.DoublePowerLaw.nfw()        # Navarro-Frenk-White
pp.DoublePowerLaw.hernquist()
pp.DoublePowerLaw.plummer()
pp.DoublePowerLaw(1.0, 3.0, 1.0)   # the NFW profile, given by (rho_alpha, rho_beta, rho_gamma)
```

The methods `rho(r)`, `mass(r)` and `p(r)` of a `DoublePowerLaw` profile return the density, the enclosed mass
and the relative potential in closed form.

A component (`pianistpy.Component`) of a model is a density profile together with a velocity anisotropy
([Velocity anisotropy](https://pianistpy.com/docs/guide/anisotropy)). The density profile of a component needs an outer slope
\(\beta \geq 3\). In ver. 1.0.0, a component whose profile has \(2 < \beta < 3\) raises
`InputError`, with a message that begins `OUTER SLOPE`.