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A Test of Galaxy Evolutionary Models Via Angular Sizes
M. Im
S. Casertano, R. E. Griffiths, & K. U. Ratnatunga (The Johns Hopkins University)
The relationship between angular size, magnitude, and redshift of faint galaxies is explored
as a potential tool to distinguish between different galaxy evolutionary models. Different
models, based on merging, mild luminosity evolution and no evolution, lead to different pre­
dictions of the angular size distribution, redshift­size relation, and magnitude­size relation.
The merging model predicts significantly smaller sizes for faint galaxies than the standard
model, because of the requirement for more intrinsically small faint objects at high redshift.
A dwarf­rich no evolution model also predicts small sizes for faint galaxies. The mild lumi­
nosity evolution model predicts more luminous galaxies of large angular size at high redshift,
as does a standard no evolution model.
Pre­refurbishment HST observations of magnitudes and sizes of faint galaxies indicate an
excess of small vs. large faint galaxies, favoring the dwarf rich, no evolution model with
respect to the merging model; the other two models are more discrepant with the data. While
these results cannot yet be used to rule out with certainty any of the proposed models, they
demonstrate the potential of angular size to discriminate between models of galaxy evolution,
especially with the high­resolution HST WFPC2 data.
Presented at Quantifying Galaxy Morphology at High Redshift, a workshop held at
the Space Telescope Science Institute, Baltimore MD, April 27--29 1994
1 Outline
We have studied what we can learn about galaxy evolution by using angular sizes of faint
galaxies. Section 2 list models we used for this analysis. Section 3 explains the tests to
distinguish evolutionary models. Section 4 compares the result from HST data with the
model predictions. Section 5 gives the summary.
1

Im et al. A Test of Galaxy Evolutionary Models Via Angular Sizes
2 Models
We tested the following 4 models by preforming Monte Carlo simulations of each model.
1) Merging Model (Broadhurst et al. 1992, with Q=4, b=4)
2) Mild luminosity evolution model (mild LE model; Guiderdonni & Rocca­Volmerange,
1987)
3) Standard no evolution (NE) model
4) Dward Rich NE model (Driver et al. 1994)
3 Results & Discussion
3.1 Angular size distribution test
Fig. 1 shows the angular size distribution from various models in the different apparent
magnitude ranges. The merging model and the dwarf rich NE model predict smaller angular
sizes compared to the standard NE model and the mild LE model. This is due to the lack
of high redshift galaxies which are larger than lower redshift galaxies at a fixed magnitude.
The merging model has some high redshift galaxies, but they are intrinsically small.
The difference between models becomes more evident at fainter magnitudes, until it reaches
the very faint magnitude limit where galaxy sizes converge to very small values.
In fig. 2, we plot the angular size vs. magnitude for the different models.
3.2 Angular size dependence on redshift distribution
The observed fraction of galaxies at z ? 1 in a magnitude limited sample is dependent
on their angular sizes. For a fixed apparent magnitude, the larger galaxy (lower surface
brightness) tends do have the larger redshift, mainly due to the surface brightness dimming
effect in the expanding universe.
In fig. 3, we see that galaxies selected with r ? 1 arcsec are about 3 times more likely to be
at high redshift than size­independently selected sample. This kind of selection criteria may
help detecting high redshift galaxies with less effort.

Im et al. A Test of Galaxy Evolutionary Models Via Angular Sizes
4 Comparison of models with data
In fig. 4, we compare the angular size distribution of galaxies obtained from the Medium
Deep Survey, a HST key project, with the model predictions. In fig. 4, we can see the lack
of large galaxies and the excess of small galaxies compared to the mild LE model and the
standard LE model. The dwarf rich NE model seems to match the distribution best, and
the merging model is not so far off by looking at ü 2 value.
The data is from only one field so far, therefore it is premature to claim that any of evolu­
tionary model is excluded by looking at fig. 4.
5 Summary
We have investigated possible tests for various evolutionary models using angular sizes of
galaxies. The dwarf rich NE model and the merging model favor the smaller sizes, and the
standard NE model and the mild LE models favor the larger sizes. For a fixed apparent
magnitude, larger and lower surface brightness galaxies tend to be at higher redshift because
of the surface brightness dimming effect.
The comparison of the data with the model predictions via angular size distribution shows
that the dwarf rich NE model and the merging model are prefered over the mild LE model and
the standard NE model, but greater numbers of galaxies are needed to get firmer conclusions.

Im et al. A Test of Galaxy Evolutionary Models Via Angular Sizes
Figure 1: The angular size distribution of galaxies predicted according to various models in
the apparent magnitude range (a) 20 ! V ! 23, (b) 23 ! V ! 25, (c) 25 ! V ! 26, (d)
26 ! V ! 27. Each line corresponds to a different model, as follows: solid for mild LE,
dotted for merging, dashed for standard NE, and dot­dashed for dwarf­rich NE.
Figure 2: Angular size vs. apparent magnitude for different evolutionary models. Each line
represents the median angular size as a function of apparent magnitude for an evolutionary
model as in Fig.1.

Im et al. A Test of Galaxy Evolutionary Models Via Angular Sizes
Figure 3: The fraction of galaxies (23 ! V ! 25) with redshift higher than z ? 1 for
size­independent selection (solid line), and for selection with r ? 1 arcsec (dotted line).
Figure 4: The angular size distribution of galaxies (21 ! V ! 24) from the HST Medium
Deep Survey is compared with the model predictions.