Surface photometry of galaxies (see e.g. [Jedrzejewski(1987)] for E galaxies and
[Kent(1985)] for D galaxies) is usually analysed by fitting ellipses to the
isophotes and by plotting their surface brightness versus their radius,
which is defined as the geometric mean of the ellipse's semi-axes and
,
i.e.
. The resulting plot is then called the surface brightness
radial profile of the galaxy.
In this context, the effective radius of the galaxy is defined as the radius
of the isophote encircling half of the light emitted by the galaxy, also
called the effective isophote.
The effective radius and the effective surface brightness, the latter being
the surface brightness of the effective isophote, are usually indicated with
and
, respectively.
Until the launch of HST, accurate measurements of the small angular sizes of faint galaxies were made virtually impossible by the phenomenon of seeing. The Medium Deep Survey ([Ratnatunga et al.(1999)]), the first survey project to be carried out with HST superb instrumentation, has recently brought to an end this long-standing lack of meaningful data, while [Im et al.(1995)] have demonstrated the potential of angular size measurements to discriminate between currently competing cosmological models.
[Casertano et al.(1995)] have obtained effective radii for about 10,000 galaxies
from Wide Field and Planetary Camera (WF/PC) parallel observations of random
fields in the band. As shown in their Figure 6, the observed angular size
distribution as function of
magnitude shows a large scatter about the
median value, mainly due to the intrinsic scatter in linear size and redshift
distribution.
The same figure also shows that the observed relation between the median
effective radius and
magnitude is well-fit by the theoretically predicted
relation for galaxies of constant central surface brightness
mag/arcsec
and absolute magnitude
in the context
of a mild luminosity evolution scenario.
This latter relation asymptotically approaches the linear relation in
vs.
that is measured in local samples of bright spiral
galaxies following Freeman's law, and was therefore taken as a description
of the relation between the galaxy effective radius and magnitude in our
model. Least-square polynomial fit showed that its accurate description
required a fourth-degree polynomial, which is represented in
Figure 3, together with the Euclidean extrapolation to faint
magnitudes of the local linear relation.
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mag | deg![]() ![]() |
deg![]() |
arcsec | ![]() |
10 | 0.008183 | 0.005151 | 44.72 | 5.350 |
11 | 0.03777 | 0.02458 | 28.64 | 10.93 |
12 | 0.1654 | 0.1114 | 18.29 | 21.15 |
13 | 0.6867 | 0.4791 | 11.68 | 38.88 |
14 | 2.705 | 1.958 | 7.468 | 68.08 |
15 | 10.10 | 7.596 | 4.801 | 114.0 |
16 | 35.79 | 27.99 | 3.115 | 183.6 |
17 | 120.3 | 98.00 | 2.049 | 285.9 |
18 | 383.3 | 325.9 | 1.374 | 433.3 |
19 | 1159 | 1030 | 0.9446 | 644.0 |
20 | 3322 | 3093 | 0.6707 | 946.5 |
21 | 9032 | 8826 | 0.4954 | 1389 |
22 | 23290 | 23940 | 0.3838 | 2060 |
23 | 56970 | 61760 | 0.3147 | 3132 |
24 | 132200 | 151500 | 0.2758 | 4969 |