- Definition
- Applications
- Generalizations of the Sérsic profile
- See also
- References
- External links
The Sérsic profile (or Sérsic model or Sérsic's law) is a mathematical function that describes how the intensity 
of a galaxy varies with distance 
from its center. It is a generalization of de Vaucouleurs' law. José Luis Sérsic first published his law in 1963.[1]
Definition
The Sérsic profile has the form
where 
is the intensity at 
.
The parameter 
, called the "Sérsic index," controls the degree of curvature of the profile (see figure). The smaller the value of , the less centrally concentrated the profile is
and the shallower (steeper) the logarithmic slope at small (large) radii is:
Today, it is more common to write this function in terms of the half-light radius, Re, and the intensity at that radius, Ie, such that
where b is approximately 2n-1/3.
It can be shown that 
satisfies 
, where 
and 
are respectively the Gamma function and lower incomplete Gamma function.
Many related expressions, in terms of the surface brightness, also exist.[2]
Applications
Most galaxies are fit by Sérsic profiles with indices in the range 1/2 < n < 10.
The best-fit value of n correlates with galaxy size and luminosity, such that bigger and brighter galaxies tend to be fit with larger n.
[4][5]Setting n = 4 gives the de Vaucouleurs profile:
which is a rough approximation of ordinary elliptical galaxies.
Setting n = 1 gives the exponential profile:
which is a good approximation of spiral galaxy disks and a rough approximation of dwarf elliptical galaxies. The correlation of Sérsic index (i.e. galaxy concentration[6]) with galaxy morphology is sometimes used in automated schemes to determine the Hubble type of distant galaxies.[7] Sérsic indices have also been shown to correlate with the mass of the supermassive black hole at the centers of the galaxies.
[8]Sérsic profiles can also be used to describe dark matter halos, where the Sérsic index correlates with halo mass.[9]
[10]Generalizations of the Sérsic profile
The brightest elliptical galaxies often have low-density cores that are not well described by Sérsic's law. The core-Sérsic family of models was introduced
[11][12][13] to describe such galaxies. Core-Sérsic models have an additional set of parameters that describe the core.
Dwarf elliptical galaxies and bulges often have point-like nuclei that are also not well described by Sérsic's law. These galaxies are often fit by a Sérsic model with an added central component representing the nucleus.
[14][15]The Einasto profile is mathematically identical to the Sérsic profile, except that is replaced by 
, the volume density, and is replaced by 
, the internal (not projected on the sky) distance from the center.
See also
- Elliptical galaxies
- Bulges
References
2. ^Graham, A.W. and Driver, S.P. (2005), A Concise Reference to (Projected) Sérsic R1/n Quantities, Including Concentration, Profile Slopes, Petrosian Indices, and Kron Magnitudes
3. ^ G. Savorgnan et al. (2013),The supermassive black hole mass-Sérsic index relations for bulges and elliptical galaxies
4. ^N. Caon et al. (1993), On the Shape of the Light Profiles of Early Type Galaxies
5. ^C. Young & M. Currie (1994), A New Extragalactic Distance Indicator Based on the Surface Brightness Profiles of Dwarf Elliptical Galaxies
6. ^Trujillo, I., Graham, Alister W., Caon, N. (2001), On the estimation of galaxy structural parameters: the Sérsic model
7. ^A. van der Wel (2008), The morphology-density relation: a constant of nature
8. ^A. Graham & S. Driver (2007), A Log-Quadratic Relation for Predicting Supermassive Black Hole Masses from the Host Bulge Sérsic Index
9. ^D. Merritt et al. (2005), A Universal Density Profile for Dark and Luminous Matter?
10. ^D. Merritt et al. (2006), Empirical Models for Dark Matter Halos. III. Nonparametric Construction of Density Profiles and Comparison with Parametric Models
11. ^A. Graham et al. (2003), A New Empirical Model for the Structural Analysis of Early-Type Galaxies, and A Critical Review of the Nuker Model
12. ^I. Trujillo et al. (2004), Evidence for a New Elliptical-Galaxy Paradigm: Sérsic and Core Galaxies
13. ^B. Terzić & A. W. Graham (2005), Density-potential pairs for spherical stellar systems with Sérsic light profiles and (optional) power-law cores
14. ^A. Graham & R. Guzmán (2003), HST Photometry of Dwarf Elliptical Galaxies in Coma
15. ^P. Cote et al. (2006), The ACS Virgo Cluster Survey. VIII. The Nuclei of Early-Type Galaxies
External links
- Stellar systems following the R exp 1/m luminosity law A comprehensive paper that derives many properties of Sérsic models.
- A Concise Reference to (Projected) Sérsic R1/n Quantities, Including Concentration, Profile Slopes, Petrosian Indices, and Kron Magnitudes.
- Barbhitha High School
- Barb Holland
- Barbi3
- Barbiani
- Barbican (beverage)
- Barbican (drink)
- Barbican FC
- Barbican F.C.
- Barbican Frieze
- Barbi (disambiguation)
- Barbie and Her Sisters in A Puppy Chase
- Barbie and Her Sisters in The Great Puppy Adventure
- Barbie and her Sisters: Puppy Rescue
- Barbie and the Rockers: Out of this World
- Barbie and The Sensations: Rockin' Back to Earth
- Barbie Beach Vacation
- Barbie Bones
- Barbiedoll
- Barbie Dolphin Magic
- Barbie: Dolphin Magic
- Barbie: Dream House Adventures
- Barbie Dreamhouse Adventures
- Barbie: Dreamhouse Adventures
- Barbie: Dreamhouse Party
- Barbie Dreams