Problem set 5 for ASTR 323: The Local Universe

Due in class Fri Nov 13

(1) Find a paper which uses the Baade-Wesselink method to measure the distance to an open or globular cluster. Then find a paper which uses main-sequence fitting to obtain an independent estimate for the cluster distance. Compare them, and comment on possible reasons for any discrepancy. The authors of your papers may have done this already. You should write about two paragraphs.

(2) Sparke and Gallagher Problems 2.7 and 4.7 (there is a copy in the library: make sure you use the second edition). Note that the smaller diameter of the SN 1987A ring should be 1.18 arcsec, not 1.1 arcsec.

(3) (undergrads in groups, grads individually)
Carefully watch the simulation of the growth of a dark halo like the Milky Way's at this link -- use the one labeled "the formation of the via lactea halo" under VL-1 movies.
Note that this simulation is displayed in physical, not comoving coordinates; the expansion of the universe is shown. Also note what they say about how the color scale corresponds to mass density.
Look at the formation history from z=12 to 0. (The higher-resolution movies, in particular the 218 MB one, are much better for this)

Select 5 of the most massive sub-halos and watch what happens as they are accreted. Are they totally disrupted? If so, how many orbits does this take?

Make a careful estimate of where the edge of the halo is at z=5,4,3,2,1.5,1.0,0.5,0.3 and 0. Explain how you decided where the edge was.

Then make an estimate of how many sub-halos are accreted by the big halo in between each of these times, and how massive each one is, compared to the mass of the existing big halo. (You should decide to ignore the smallest halos, but say how you decide this). Plot up the increase of mass of the halo with time (in Gyr). (Graduate students should add error bars to this plot and describe how you arrived at them.) Note that making the plot will involve a lot of stepping through the movie, and some snapshots.

Diemand et al (ApJ 667, 859, 2007) analyze the growth of the Via Lactea halo. Their Figure 1 shows the growth with time of shells of different mass, between 3x1011 and 3x1012 solar masses. For each shell, the plot shows the maximum radius of the shell and the points where the particles in the shell reach 20% of their final radii as a function of time and redshift. Use this plot to derive Diemand's version of the plot of halo mass as a function of time, stating any assumptions you make, and compare this with your own plot. How do they compare?

(4) (Grad students only): Give two reasons why the very first stars to form might be more massive than current-day stars. Search the literature for a recent (last 20 years) paper on the metallicity distribution of the Milky Way halo at the low-metallicity end, and give a 1-2 paragraph summary of the paper's findings, discussing whether you think this convincingly demonstrates that there are no zero-metallicity low mass stars existing today.