David Thomas Hill PhD Thesis - Research@StAndrews:FullText ...

Chapter 1. Introduction: The luminosity distribution and total luminosity density of
galaxies
where I(x) is the average surface brightness profile, and δr → 0. The Petrosian radius
is the radius at which P (this ratio is also referred to as 1
νRPetro
following Petrosian’s
original definition) drops below a certain value. The SDSS survey (Strauss et al., 2002)
and SExtractor Petrosian magnitudes are both calculated using 1
νRPetro
= 0.2. Using a
multiple of the Petrosian radius to define an aperture will enclose a significant fraction
of the total galactic emission (2RPetro theoretically encloses > 80% for a de Vaucouleurs
profile, and ∼ 98% of an exponential profile’s light). As with the Kron magnitude system,
an additional theoretical advantage of the Petrosian magnitude system is that it is redshift
independent. In practice, as seeing quality diminishes and distance increases, the SDSS
survey team (Blanton et al., 2001) have found that the fraction of light enclosed by 2RPetro
tends towards the return expected from a PSF profile source(∼ 95%).
A parameter called the Concentration Index can be defined that uses the Petrosian radius
that contains a fraction of the galaxy’s flux to calculate the Sérsic index of the source
(Graham & Driver, 2005). The Concentration index is a ratio of two radii (often R90;
the R50
radii that enclose 50% and 90% of the Petrosian flux of the galaxy), and varies with the
underlying light profile. Using this parameter, it is possible to calculate the morphology
of a galaxy, and to convert the Petrosian radius into an effective half light radius and the
Petrosian luminosity into a Sérsic total luminosity.
1.2.3 Sérsic magnitudes and the ’missing light’ problem
Thetwomagnitudesystemsintroducedsofarhaveanimportantflaw. Theyfailtoaccount
for the light emitted by a galaxy outside of the radius of the aperture, and the fraction of
light they miss varies with the surface brightness profile of the source. The ’missing light’
problem is an important issue when calculating the true total luminosity density of the
Universe, as it will force the apparent magnitude of every galaxy fainter by a potentially
significant factor. Unfortunately, it is not an easy bias to correct. Aperture size can not
be increased infinitely, as eventually it will cover other sources, leading to uncertainty in
the distribution of the observed flux. Additionally, at some distance from the centre of
each galaxy, the flux emission will drop so low that it will be contained within the noise
properties of the image. An alternative method must be theorised. Once such method
is to fit each galaxy to a theoretical surface brightness profile, and ascertain the total
luminosity from the model. The Sérsic magnitude system is one way of achieving this
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