Working with the 30-inch Reynolds telescope 1 at what was then Australia's Commonwealth Observatory, and today known as Mount Stromlo Observatory, Gérard de Vaucouleurs published in 1956 the most extensive southern galaxy Atlas of the day. In the following year, José Luis Sérsic commenced work at the 1.54-m telescope at the Astrophysical Station at Bosque Alegre in Argentina. His studies from 1957-1966 culminated in his 1968 southern-hemisphere galaxy Atlas `Galaxias Australes'. It too has proven an invaluable contribution to our understanding of galaxies, evidenced by its status as a top 1000 cited astronomy publication.
In the Introduction of Sérsic's Atlas, it not only states the merits for a visual representation of galaxies, but, like de Vaucouleurs', it stresses the necessity to go beyond this and obtain quantitative measures of the light distribution. This was not mere rhetoric as his Atlas consists of two parts, one pictorial in nature and the latter quantitative. It is apparent that his generalisation of de Vaucouleurs' (1948, 1959) R1/4 model to an R1/n model was not merely something he mentioned in passing, but something which he felt should be done. Indeed, Sérsic fitted the R1/n model to every (sufficiently large) galaxy in his Atlas. He derived expressions to compute total (extrapolated) galaxy magnitudes, provided tables of assorted structural parameters associated with the R1/n model, and showed how they correlated with galaxy morphological type (his Figure 3) and galaxy concentration (his Figure 4, page 145). Sérsic (1963) even provides a prescription to correct the R1/n model parameters for Gaussian seeing due to atmospheric and instrumental dispersion.
It is, however, of interest to note that Sérsic's conviction lay in the observation that different galaxies possessed differing degrees of an R1/4 bulge and an R1/1 disk component. This mixture of bulge and disk components produces a combined surface brightness profile with an intermediary form, hence the R1/n model.
Today, usually when the required resolution is lacking to properly decompose an image into its separate bulge and disk components, galaxies are modelled with a single R1/n profile, just as Sérsic proposed (e.g., Blanton et al. 2003). While such an approach certainly has its merits, we now know that dynamically hot stellar systems themselves posses a range of profile shapes that are well described with the R1/n model (e.g., Graham & Guzmán 2003, and references therein). Detailed studies of well resolved lenticular and disk galaxies are routinely fitted with the combination of an exponential-disk plus an R1/n-bulge (e.g., Andredakis, Peletier, & Balcells 1995; Seigar & James 1998; Iodice, D'Onofrio, & Capaccioli 1997, 1999; Khosroshahi, Wadadekar, & Kembhavi 2000; D'Onofrio 2001; Graham 2001a; Möllenhoff & Heidt 2001). In either case, since the work of Capaccioli in the late 1980s and in particular Caon, Capaccioli, & D'Onofrio (1993) and D'Onofrio, Capaccioli, & Caon (1994), the past decade has seen an explosion in the application of the R1/n model (e.g., Cellone, Forte, & Geisler 1994; Vennik & Richter 1994; Young & Currie 1994, 1995; Graham et al. 1996; Karachentseva et al. 1996, Vennik et al. 1996, to mention just a few early papers), yet no single resource exists for the expressions and quantities pertaining to the R1/n model. Moreover, no one reference provides more than a few of the relevant equations, and many textbooks still only refer to the R1/4 model.
This (largely review) article intends to provide a compendium of equations, numbers, and figures for ease of reference. The derivation of these also provide useful exercises for students. Where appropriate, we have endeavoured to cite the first, or at least a useful early, reference to any given equation. To the best of our knowledge, Figures (6) through (10), describing Petrosian indices and Kron magnitudes, have never been seen before. A brief reference to where readers can find deprojected expressions, and how to deal with practical issues such as seeing, is given at the end. No attempt has been made here to show the numerous scientific advances engendered via application of the R1/n model.
1 The Reynolds telescope was sadly destroyed in the 2003 Canberra bush fires. Back.