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)
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.
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)