1. Galaxy Counts - get real
Your task is to begin with the galaxy-counts model from Problem Set 4, and modify it to fit the
observed galaxy counts as defined between K=10 and
K=23.5 in this figure.
This figure prescribes a simple, empirical analytic formula to
represent the observed counts. You may find useful in your
endeavor.
When you have matched the observed counts to your satisfaction,
- specify your model concisely but with sufficient detail
that others may reproduce your results;
- extrapolate the counts to K = 28;
- predict the z distribution for all sources brighter
than K = 18, K = 20, and K=22;
- compare your results for the redshift distributions to
whatever you can find in the literature (you are free to
comment on the reliability of the observational results).
As in Problem Set 4, please email me your data files for the counts
and redshift distributions.
Here are some hints for what is at your disposal.
Start by modifying the no-evolution parameters provided in Problem Set 4. The parameters that you may
choose from include:
-
(a) cosmological parameters Omegatotal and Omegalambda;
(b) single luminosity function (LF) parameters phi*, M* and alpha;
(c) K-corrections (beta). You may also consider beta(z), where beta changes with
rest-wavelength), or actually try and adopt real spectral energy
distributions (SEDs) and a filter transmission
function. Use these K-corrections
(d) realistic LF which takes into account multi-components with
separate phi*, M*, alpha and K-corrections;
We have discussed in class the relative sensitivity of counts on these
parameters. You are free to adopt whatever parameters you would
like, but you must note whether they are reasonable based upon what we
know about the real universe. For example, we know a lot about the
spectral energy distributions of galaxies, but their space density is
less well determined. (See the literature; the ARAA articles by Ellis
'97 and Koo and Kron '92 are a good place to start.)
Given the redshift distribution to K=23 predicted by the model
in Problem Set 4 (see solutions), it
would be remarkable if the galaxy population is not evolving
significantly at the look-back times probed by real observations. If
you have been successful with just the above modifications to a
'no-evolution' model, you have the opportunity to stop and join the
small ranks of heretics who claim that no-evolution models can fit the
counts. But be prepared to pursue some of the following.
-
(e) Evolution:
- pure luminosity evolution (PLE): M* changes with z
- pure density evolution (PDE): phi* changes with z
- steepening LF (luminosity-dependent luminosity evolution,
LDLE): alpha changes with z
- evolving SEDs / K-corrections: beta or SEDs change with z
- merging: luminosity and density can both change with z
You may construct simple models for various kinds of evolution
[typically parameterized by power-laws in (1+z)]. I will give some
hints in class about how to handle evolving SEDs in a reasonably
simple way.
Finally keep in mind that this is a fairly open-ended assignment but
that I recognize you have limited time. Your goal is to do the best
with what time you've got. When you can, think of clever ways to make
shortcuts, and ways to check that your calculations are correct. You
may discuss references or citations with each other, but not your
actual work and results until after you have submitted your work.
last update: Dec 04, 2000
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