Astr 328/428 Homework #4 -- Due Nov 17th
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.
- the globular cluster M13
- the Milky Way galaxy
- the Coma Cluster
- the Bootes void
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
2. Growth of Structure
We are going to look at the growth
structure in simulations with differing cosmological parameters. The
simulations are the "Hubble Volume Simulations" and more information
can be found at http://www.mpa-garching.mpg.de/Virgo/hubble.html.
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.
- LCDM: H0=70 km/s/Mpc, OM=0.3, OL=0.7
- tauCDM: H0=50 km/s/Mpc, OM=1.0, OL=0.0
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
dvol=np.diff(vol) # THIS GETS THE TOTAL VOLUME WITHIN 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 http://www.mpa-garching.mpg.de/Virgo/data_download.html 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?)
- Plot up x vs y for all galaxies to give a feel for what the
data look like (remember to set the aspect ratio properly on your plots!). Then do the same thing just for E's and just for
S's. Describe any differences and explain whether or not it makes sense.
- Now calculate the two point correlation function for all the
galaxies (see below for how to do this). Do this for seperations
between 1 and 10 Mpc, then fit a power law and derive the clustering
length, r0. Also describe qualitatively what this is telling you about
how galaxies are distributed.
- Now do the same thing just looking at 2 point correlation
function for spirals only, and again for ellipticals only. Plot them
up, fit power laws, and derive the clustering lengths. Describe the
differences you find in the clustering lengths for each sample. What
does this tell you about the clustering of different types of galaxies
in the universe, and does this make sense qualitatively based on what
you know about galaxies?
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.