ASTR 422
Problem Set 3
Due Friday, October 12, 2007
1. The very best velocity resolution in astronomy exists in searches for extrasolar planets.
Doppler shifts of down to ∼1 m s−1can be detected in some cases. Given this:
If you could measure redshifts to that accuracy for a z= 0.1 quasar (i.e., a single
point source, with a unique redshift at any given time), derive how long would you
have to wait between observations such that the acceleration of the universe produced
a change in recession speed of 1 m s−1. Note that the current Hubble parameter is
H0= 72 km s−1Mpc−1, and assume Ω = 0.27, Ωk= 0, and ΩΛ= 0.73.
2. The Phillips relation for white dwarf supernovae is that longer supernovae
have a higher peak luminosity. Do some Web research to determine the state
of the theoretical understanding of this correlation. Use any Web resources you
like, but you must write the final description in your own words (no more than
one short paragraph, please!). Good places to start are Google, the Astrophysics
Data Service (http://adsabs.harvard.edu/abstract service.html), and astro-ph
(http://www.arxiv.org/find/astro-ph). Note that the official name for white dwarf
supernovae is “Type Ia supernovae”, where that is a Roman numeral I. Please also give me
the URLs for the one or two references you found most helpful.
3. Suppose that the universe currently has Ω = 0.3 (composed entirely of pressureless
matter), Ωk=−0.05 (so that the geometry is of a closed universe) and ΩΛ= 0.75.
Demonstrate that the universe will expand forever. Note that you do not have to take on
the far more difficult task of following the evolution in detail; all you need to prove is that
despite the closed geometry, expansion will continue indefinitely.
4. Dr. I. M. N. Sane has been applying his deep intellect to the study of gravitational
lensing. He is especially interested in strong lensing (i.e., multiple imaging) of background
quasars by the supermassive black holes found in the centers of essentially all big galaxies.
His calculations suggest that there will be hundreds of such lensing events in the Sloan
Digital Sky Survey, and he has issued a press release announcing the revolution in cosmology
and black hole astrophysics that will be precipitated by his discovery.
Ron Cowen, the main astronomy writer for Science News, has called you to determine
whether he should run with this story. Following Dr. Sane’s calculations, we assume that
the number density of big galaxies is 0.003 Mpc−3and that the relevant volume of the
