Astr 328/428 Homework #4 -- Due Nov 17th

1. Overdensities

Calculate the overdensity (delta) of the following:
In each case, explain your reasoning, describe whether (and why) your number is an upper limit, a lower limit, or a reasonable estimate of a particular value, and also cite your information sources.

Note: "Information sources" should be either refereed journal articles or research-grade books -- things you would cite when writing a journal article. Wikipedia, SEDS, non-technical/popular textbooks, and other websites do not qualify.

2. Growth of Structure

We are going to look at the growth of structure in simulations with differing cosmological parameters. The simulations are the "Hubble Volume Simulations" and more information can be found at I have grabbed the cluster catalogs from two simulations: LCDM and tauCDM. A description of these files can be found here -- look under "Cluster Catalog Files". The cosmological parameters of the sims are given by:
Make a plot of the (log of the) comoving number density (logN in #/Mpc^3) of clusters as a function of z (from z=0 to z=2) in the two simulations, as well as the (log of the) ratio N(LCDM)/N(tauCDM) as a function of redshift. Describe why the shapes of the plots look like they do.

Repeat the calculation just for the most massive clusters -- those with velocity dispersions > 600 km/s. Comment on any differences you see from the first plot.

You'll need to make use of astropy's cosmology routines for this, in order to work out the comoving volume in each of your redshift bins. You can get this by grabbing the total volume out to the edge of each of your bins, then doing a np.diff to get the volume within the bin; this shows how to do it for the LCDM cosmology:

from astropy import cosmology
LCDM=cosmology.LambdaCDM(H0=70, Om0=0.3, Ode0=0.7)
zbins=np.linspace(0,2,21) # THIS SETS UP THE EDGES OF YOUR BINS
bincenters = (zbins[:-1] + zbins[1:]) / 2.0  # THIS CALCULATES THE CENTER OF THE BIN
vol=LCDM.comoving_volume(zbins).value  # THIS GETS THE TOTAL VOLUME OUT TO THE EDGE OF EACH BIN

3. The Galaxy Two Point Correlation Function

There is a "chunk of the Virgo consortium universe" available for you here. The data come from a massive simulation of a cube of the universe measuring 140 Mpc on a side. Details of the simulation and the galaxy creation can be found at The data give the x, y, and z coordinates in Mpc and star formation rate in solar masses per year of 8384 simulated galaxies.

We are going to define subsets of galaxies as "late types" (ie Sb/Sc spirals) and "early types" (ellipticals and S0's) based on their star formation rates. Let's say late types are things with SFR's > 1 Msun/yr, and early types are things w/ SFR's < 0.1 Msun/yr. (Does this definition make sense?)

Calculating the 2ptCF: First, install astroml if you haven't already. Then to calculate the 2ptCF of a sample of N galaxies with x,y,z coordinates, do the following:

from astroML.correlation import two_point
pos=np.array[x,y,z].T  # YOU WANT AN ARRAY WITH SHAPE (N,3), NOT (3,N)
bincenters = (bins[:-1] + bins[1:]) / 2.0

ASTR 428 -- this piece due 11/28.

I want a quality draft of your project writeup -- the writeup should be 5 pages (single spaced, full pages), not including figures, references, and equations.

Oral in-class presentations (25 mins) will be done the last day of class (Dec 8), and the final writeup will be due Dec 15. The draft due on the 28th of November is to ensure your project is on track, that you haven't missed any critical details, and that your emphasis is appropriate for your oral presentation.