ASTR/PHYS 328/428
Cosmology
Problem Set 3
Due Thursday 10 Oct 2024

  1. Age-Redshift Relation

  2. Hubble's Law vs Cosmological Distances
    In the local universe, we often use Hubble's Law (V = H0Dp) to get distances to galaxies using their observed recession velocity. But we've seen that distances take on different definitions on cosmological scales. So how far out in redshift we can go using Hubble's Law before the errors introduced by ignoring cosmological effects become substantial? Let's imagine observing a Milky Way-like galaxy with an absolute magnitude of MV = -21 and a size of Rg = 20 kpc in a vanilla LCDM cosmology with H0 = 70 km/s/Mpc, Ωm0 = 0.3, and ΩΛ0 = 0.7.

    Make plots of the following quantities as a function of redshift [log(1+z) from z = 0.01 to 1.0 works well] in two cases: (i) using Hubble's Law and (ii) using the correct cosmological quantity:

    Put the results for each part on the same graph so you can see the difference. You'll end up with 3 plots (for a, b, and c), each with two lines.
    Note that 0.1 magnitudes is a large error for modern photometry (differences of < 0.01 mag. can be measured with care), so these effects are readily discernable.

  3. H0 and the Distance to Virgo
    Professor Fink returns excited from an observing run because he has discovered a nova in a galaxy in the Virgo cluster, a key step in the distance scale. He knows that novae can be used as standard candles since they obey a luminosity--fade-time relation
    MVpeak = -10.7 + 2.3 log(t2)
    where t2 is the time in days that it takes for a nova to fade 2 magnitudes from its peak. (That's a base ten logarithm, as is conventional in astronomy.) Professor Fink hands you the data in the graph, and asks you to determine The Answer.

    Was Fink's initial excitement justified?
    (Keep in mind that the modern goal is to measure H0 to better than 2%.)

    Light curve of nova in the Virgo cluster.

  4. Galaxy number counts

    Galaxy number counts.

    A portion of the Hubble Ultra Deep Field.