ASTR/PHYS 328/428 HW #2

1. The K-correction

Quantitatively, the K correction is written as m-M = 5*log(d_L) + 5 + K(z)
If the flux from a distant object is given by

Show that the K-correction is given by

If a galaxy emits a spectrum

show that

and that the k correction can be written simply as

Since quasars typically have a spectrum with alpha ~ -1, this gives them a negligible k-correction!

2. Galaxy counts

Using Figure 1 from Metcalfe et al 1996, calculate the slope of the galaxy number count function over the magnitude range m_B=20-25 for the following:

the observed number counts;
no evolution models.
evolution models for q₀=0.5 and q₀=0.05.

Using this dataset of counts from the Hubble Ultra Deep Field, create your own version of the Metcalfe plot, and calculate the sloped of the observed galaxy number count function over that same magnitude range. Note that the UDF covers 9 square arcmins of the sky.
Discuss the comparison of your plot with that of Metcalfe etal, in the following terms:

overall match in the curve
match of the slopes
evidence for galaxy evolution

3. More High Redshift Galaxies

(ignore bandshifting, etc for this. pretend these magnitudes are all bolometric...)

Plot the apparent magnitude, angular size, and average surface brightness of an M*=-21 galaxy 20 kpc in radius as a function of redshift from z=0.1-2 for a flat, matter-dominated universe. If the brightness of the night sky is mu=21.5 mag/arcsec², at what redshift does the mean surface brightness of the galaxy drop below 10% of sky? 1% of sky? What is the z=0 average surface brightness of the galaxy?

4. Grad Students

Pick two possible presentation topics, and give me a one paragraph written description for each. They should be focused on observational cosmology and/or structure/galaxy formation, and something that we aren't going to talk about in class. They also can't be your own research/thesis topic. I will look over your possibilities and recommend one for you to follow up on.

You will be asked to write a 10page critical review of the topic (due at the end of the semester), and give a ~ 30 minute in-class presentation (think: invited review) to the class (also near the end of the semester).