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)
*R*^{1/4} model to an *R*^{1/n} model was not
merely something he
mentioned in passing, but something which he felt *should* be
done. Indeed, Sérsic fitted the *R*^{1/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
*R*^{1/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 *R*^{1/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 *R*^{1/4} bulge and an *R*^{1/1} disk
component. This mixture of bulge
and disk components produces a combined surface brightness profile
with an intermediary form, hence the *R*^{1/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 *R*^{1/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
*R*^{1/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 *R*^{1/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 *R*^{1/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 *R*^{1/n} model. Moreover, no one
reference provides more than a few of the relevant equations, and many
textbooks still only refer to the *R*^{1/4} 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
*R*^{1/n} model.

^{1} The Reynolds
telescope was sadly destroyed in the 2003 Canberra bush fires.
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