ASTRO 735 - Problem Set Solutions

Set 4

1. Galaxy Counts - a simple model

m as a function of redshift for an M* galaxy

for a variety of cosmologies (top panel) and K-corrections (bottom panel). The fiducial cosmology and K-correction is represented by the bold curves in both panels. The key points to take away from this are that (a) the expected redshifts of M* galaxies down to K=23 are very large even in the absence of evolution; (b) the effects of changing K-corrections are much more substantial than changing the cosmological density parameters. You should also note in this figure the redshifts where various spectral breaks are redshifted into the observed K band. These will substantially modify the K-corrections at, and above these redshifts, and hence are a critical ingredient to include in a more realistic modeling of the counts.

This figure shows the following quantities for the K band (A0V zeropoint) for the model specified in the problem set:

A(K) for K = 10 to 28 mag
Mean M_K in each bin of K

In addition to the above quantities, the redshift distributions are also displayed in several different ways. These panels repay some study. Other, related figures worthy of inspection include:

What you should take away from this: There appears to be a feature in the counts at around K=20 where the slope changes, i.e., there is a "break" in the counts. This corresponds to a feature in the mean absolute magnitude plot: At K=20 the mean absolute magnitude starts to rapidly increase (decreasing L_K) with increasing K. This is not a coincidence. At the same time, while the mean redshift continues to increase with increasing K, the redshift median and quartiles do begin to roll over. (The median is a more robust statistic of the redshift distribution because it is less affected by distribution tails than the mean.) At K=20 both the mean and median z are very similar, with values between 1 and 2.

Next, an inspection of the volume figures reveals that dV/dz and V roll-over at around z = 1-2 for this cosmology.

Putting this all together, it appears that the count roll-over, accompanied by a shift to larger absolute magnitudes (lower L_K), is consistent with being caused by the pinching off of the cosmological volume. In general, this is a generic result and feature of expanding cosmological models, i.e., there is a volume pinch-off for all reasonable values of the density parameters. However, the position of this roll-over in redshift should be somewhat dependent on the density parameters, but in a complicated way that depends on Omega_total and Omega_lambda. The position of this roll-over in apparent magnitude is more complicated, since it will also depend on M*, as well as other parameters describing the galaxy population and its evolution. Likewise, since the slow rise of V(z) with z beyond z = 2-20 is weakly dependent on cosmology, it is likely that the slope and normalization of the counts beyond the break will be highly effected by the faint end of the luminosity function (and its evolution).

last update: Dec 04, 2000

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