Einasto profile

The einasto module implements the Einasto (1965) density profile,

\[\rho(r) = \rho_\mathrm{s} \exp\left(-\frac2\alpha \left[\left(\frac{r}{r_\mathrm{s}}\right)^\alpha - 1\right] \right)\]

where \(\alpha>0\). The calling signature is

from profiley.einasto import Einasto
Einasto(rho_s, r_s, alpha, **kwargs)

Unlike the NFW profile, the mass profile derived from this density profile converges to a total mass

\[M_\mathrm{tot} = \frac{4\pi\rho_\mathrm{s}r_\mathrm{s}^3}{\alpha} \left(\frac\alpha2\right)^{3/\alpha}\Gamma(3/\alpha)\exp(2/\alpha)\]

and the mass profile is described by

\[M(x) = M_\mathrm{tot} \frac{\Gamma(3/\alpha) - \Gamma(3/\alpha,2x^\alpha/\alpha)} {\Gamma(3/\alpha)},\]

where as usual \(x=r/r_\mathrm{s}\); see Cardone, Piedipalumbo & Tortora (2005).