Problem set 2 for ASTR 328/428: Cosmology and Large-Scale Structure

Due in class, Wed March 19. Both problems are individual: work in groups if you like, but hand in solutions in your own words and your own plots.

(1) 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 150 Mpc on a side. Details of the simulation and the galaxy creation can be found at http://star-www.dur.ac. uk/~frazerp/virgo/virgo.html .

The data give the x, y, and z coordinates in Mpc and star formation rate in solar masses per year of 8384 galaxies. Plot up x vs y to give yourself a feel for the distribution of galaxies. If your analysis tools dont like such big datasets, choose a subset *which has similar clustering behaviour* and work on that.

Measure both the angular and spatial two-point correlation function for the galaxies. (Decide where you want to put the Sun in x,y,z coordinates so you can calculate angles).

Edge effects are important in calculating the two-point correlation function from any survey. Although the cube is 150 Mpc on a side, there are no galaxies outside the cube, so if you simply calculate the two-point correlation function without making any allowance, it will reflect the presence of an *enormous* void outside the cube.
(i) What is the minimum distance from a point at x=y=z=75 Mpc to the edge of the cube? This will give the largest possible meaningful r value.
(ii) How far is a point at x=y=z=140 Mpc from the nearest edge?
You may choose to do something fancy like repeating the cube at all its edges to get around the problem, or you may choose the easier path of choosing a "safe" subset of the data and restricting the range of r that you calculate. If you look at the calculated examples of the two-point correlation function you will see that many of them stop at distances of tens of Mpc: most of the action is inside that.

Now repeat the process of calculating spatial and angular two-point correlation functions, this time for ellipticals (no star formation) and spirals (star formation rate on the order of a solar mass per year). Do you see any differences? If so, do they agree with the differences discussed in class?

(2) Some of the most useful measures of both the baryonic and dark mass of galaxy clusters come from studies of the cluster X-ray gas. In order to model the properties of the potential we need to know how both gas temperature and density vary with radial distance in the cluster. Give a summary of what spatial and spectral resolution X-ray satellites (including Einstein, Rosat, ASCA, Chandra and XMM) have given astronomers. Find a well-studied galaxy cluster with observations taken on two or more of these satellites (extra credit for all 4) and compare the conclusions reached by each team. How well did the early results pan out when data were obtained with more recent missions?