On the estimation of galaxy structural parameters: the Sersic model

Abstract

This paper addresses some questions which have arisen from the use of the Sérsic r1/n law in modelling the luminosity profiles of early‐type galaxies. The first issue deals with the trend between the half‐light radius and the structural parameter n. We show that the correlation between these two parameters is not only real, but also a natural consequence from the previous relations found to exist between the model‐independent parameters: total luminosity, effective radius and effective surface brightness. We also define a new galaxy concentration index which is largely independent of the image exposure depth, and is shown to be monotonically related with n. The second question concerns the curious coincidence between the form of the Fundamental Plane and the coupling between 〈I〉e and re when modelling a light profile. We explain, through a mathematical analysis of the Sérsic law, why the quantity re〈I〉e0.7 appears almost constant for an individual galaxy, regardless of the value of n (over a large range) adopted in the fit to the light profile. Consequently, Fundamental Planes of the form re〈I〉e0.7∝σ0x (for any x, and where σ0 is the central galaxy velocity dispersion) are insensitive to galaxy structure. Finally, we address the problematic issue of the use of model‐dependent galaxy light‐profile parameters versus model‐independent quantities for the half‐light radii, mean surface brightness and total galaxy magnitude. The former implicitly assume that the light‐profile model can be extrapolated to infinity, while the latter quantities, in general, are derived from a signal‐to‐noise ratio truncated profile. We quantify (mathematically) how these parameters change as one reduces the outer radius of an r1/n profile, and reveal how these can vary substantially when n≥4.

Total mass distributions of Sersic galaxies from photometry and central velocity dispersion

“…Even when this factor in taken into account, the range of our models covers the programme galaxies of the ACSVCS. -Measurement of effective radius is waveband dependent (Temi et al 2008;Ko & Im 2005), so that for n = 3 and 4, our limits on the model X e values in the z-band, are compatible with observations (Ferrarese et al 2006;Trujillo et al 2001;La Barbera et al 2005). -At high redshifts, systems display evolution towards higher compactness (Buitrago et al 2008).…”

“…Additionally, we question the relevance of the upper limits on the effective radii at n = 3 and 4, which are smaller than the range permitted for higher values of n. As far as the correlation between the shape parameter n and log of effective radius is concerned, it is well known that in general, half-light radius decreases with decreasing n (Boselli et al 2008;Côté et al 2008;Naab & Trujillo 2006;Brown et al 2003;Trujillo et al 2001). In fact, such a correlation is physical and is hinted at by the global relations between structural parameters; it is not merely a reflection of the fitting procedure (Trujillo et al 2001).…”

Evidence for an Outer Disk in the Prototype “Compact Elliptical” Galaxy M32

“…Kormendy & Gebhardt (2001) used the words "compact" and "fluffy" when referring to bulges. It should be noted that this has no reference at all to varying profile "shape" (or equivalently "concentration," according to the mathematical definition given in Trujillo et al 2001, their Bekki et al's (2001) N-body/smooth particle hydrodynamic simulations of tidal interactions between M31 and an orbiting early-type spiral galaxy predict either a complete stripping of the satellite's disk or at least a vertical heating of the disk to create a thick disk. As we have seen, it would appear that a faint disk, with very little gas (Welch & Sage 2001), still surrounds M32.…”

Structural properties of dwarf ellipticals and the connection with (ordinary) elliptical galaxies

“…However, as noted in Djorgovski & Kormendy (1989), it fits best elliptical galaxies with M B ∼ −21 mag; brighter and fainter galaxies having different curvature than described by the R 1/4 model. Thanks to the pioneering work of Capaccioli and collaborators, most notably Caon, Capaccioli & D'Onofrio (1993), numerous studies have now shown that Sérsic's (1963Sérsic's ( , 1968) R 1/n generalisation † accommodates for the real (Trujillo, Graham & Caon 2001; their section 2) and systematic changes in light-profile shape n with absolute magnitude (e.g., D'Onofrio, Capaccioli, & Caon 1994;Graham et al 1996;Vennik et al 1996). Similarly, the stellar distribution in dwarf elliptical galaxies is also a function of absolute magnitude (e.g., Davies et al 1988;Cellone, Forte, & Geisler 1994;Vennik & Richter 1994;Young & Currie 1994, 1995Karachentseva et al 1996;Jerjen & Binggeli 1997).…”

“…Presumably the actual level of scatter is less than seen here. One may alternatively plot concentration, rather than profile shape, as done in Graham, Trujillo & Caon (2001).…”