ASTR/PHYS 328/428 HW #2

1. The K-correction

Quantitatively, the K correction is written as m-M = 5*log(dL) - 5 + K(z)
If you are observing through a filter that transmits from lambda1 to lambda2, the flux in the bandpass from a distant object is given by

where Llambda is the luminosity per unit wavelength, and te refers to the spectrum at time of emission.

Show that the K-correction is given by

If a galaxy emits a spectrum (where Lnu is the luminosity per unit frequency) 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

3. Redshifting M87

M87 is a giant elliptical galaxy in the Virgo Cluster. Use the NASA Extragalactic database to figure out the absolute V magnitude, physical size (radius in kiloparsecs of the mu=25 mag/arcsec2 isophote), and average surface brightness (in mag/arcsec2) of the galaxy. Now imagine redshifting it to higher and higher redshift and put the following curves all on one plot, plotting redshift from z=0 to z=2.

4. ASTR 428: Hubble's Law vs Cosmological Distances

In the very local universe, we often will use Hubble's Law (v=H0d) to get distances to galaxies using their observed recession velocity. But we've seen in class that distances take on different definition on cosmological scales. So let's see how far out in redshift we can go using Hubble's Law before the errors introduced by ignoring cosmological effects become big. Let's assume we are observing a galaxy with an absolute magnitude of MV=-21 and a size of r=20kpc. Adopt a cosmology of H0=72 km/s/Mpc, OmegaM=0.3, OmegaL=0.7 and make a plot of the following as a function of log(z) for log(z)=-2 to 0 (so z=0.01 to 1.0):

5. ASTR 428: Project

Pick two possible presentation topics, and give me a one page 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.

Possibilities would include:
You will be asked to write a 5 page critical summary of the topic (due Dec 1), and give a ~ 30 minute in-class presentation to the class (on Dec 8).