One of the classic tests of observational cosmology is to determine the "shape" of the universe based on number counts of extragalactic objects (galaxies, radio sources, QSO's, etc.). Assuming that the population under consideration does not evolve substantially in the volume sampled, the number of objects with an observed flux is related to the geometry of space-time. Consider the simple case of objects of luminosity L in an Einstein-de Sitter Universe (flat-space).
The number of sources within a distance R is proportional to the volume of the sphere:
N = (4/3) pi R3 x density.
The flux from the faintest source up to a distance R is:
F = L / (4 pi R2).
Thus, within a distance R:
N2 F3 = constant
or, d log(N)/d log(F) = -1.5
In other words, N measures the volume and F-1/2 is the radius of a spherical region centered on the observer.
In magnitude space: d log(N) / dm = 0.6 for a Euclidean universe.
During the next several homework assignments, you will be exploring the shape of the universe as measured from deep multi-filter imaging observations obtained with the WIYN 3.5m. The series of homework questions are designed to build backwards from the final analysis and results to the extraction of the appropriate information from the processed images. Each homework problem will focus on a different field (11 fields were obtained for the scientific program, we will use 3 fields as part of this assignment). You will thus have the opportunity to explore whether the local universe is isotropic, or whether there are preferred directions in space.
For this analysis, you will be using the source extraction software known as SExtractor to create your galaxy/star catalogs, a perl script to apply the calibration information, and SuperMongo to identify contaminants and to create the final figures.
Along the way, you will need to think about: are there systematic errors associated with this analysis? what are the completeness limits and how should I correct for them? How can I separate stars and galaxies in a reliable manner? If my images were obtained under different seeing conditions, will that effect my colors? Are there color differences?
Your final presentation (HW 4 and 5) should include a coherent write-up of the data analysis you have completed, the figures you are presenting, etc.