vcdisk.sersic

class vcdisk.sersic(mtot, re, n)

Class for Sersic profiles.

This class creates a [Sersic68] profile from the total mass, the effective radius (i.e. the radius containing 50% of the total mass), and the Sersic index. It has two implemented methods:

  • __call__ returns the value

\[I(R) = I_e \exp\left\{ -b_n\left[\left(\frac{R}{R_e}\right)^\frac{1}{n}-1\right] \right\},\]

  • deriv returns the first derivative

\[\frac{{\rm d}I(R)}{{\rm d}R} = -\frac{I_e\,b_n}{n\,R_e} \exp\left\{ -b_n\left[\left(\frac{R}{R_e}\right)^\frac{1}{n}-1\right] \right\} \left(\frac{R}{R_e}\right)^{\frac{1}{n}-1},\]

where \(b_n = 2n -1/3 + (4/405)n^{-1} + o(n^{-2})\) (see [CiottiBertin1999]) and \(I_e\) is the surface density at the effective radius \(R_e\) and it is related to the total mass as

\[I_e = \frac{M}{2\pi n R_e^2} \frac{b_n^{2n}}{e^{b_n}\Gamma(2n)},\]

where \(\Gamma\) is the complete gamma function (see [GrahamDriver05]).

Parameters

  • mtot (float) – total mass in \(\rm M_\odot\).

  • re (float) – effective radius in \(\rm kpc\).

  • n (float) – Sersic index \(0 < n \leq 8\).

References

CiottiBertin1999

Ciotti & Bertin, 1999, A&A, 352, 447. Analytical properties of the \(R^{1/m}\) law. https://ui.adsabs.harvard.edu/abs/1999A%26A…352..447C/

GrahamDriver05

Graham & Driver, 2005, PASA, 22, 118. A Concise Reference to (Projected) Sérsic \(R^{1/n}\) Quantities, Including Concentration, Profile Slopes, Petrosian Indices, and Kron Magnitudes https://doi.org/10.1071/AS05001

__init__(mtot, re, n)

Methods

__init__(mtot, re, n)

deriv(R)

Returns the value \(I'(R)\)
__call__(R)

Returns the value \(I(R)\)

deriv(R)

Returns the value \(I'(R)\)