As galaxy surveys become larger and more complex, keeping track of the completeness, magnitude limit, and other survey parameters as a function of direction on the sky becomes an increasingly challenging computational task. For example, typical angul
ar masks of the Sloan Digital Sky Survey contain about N=300,000 distinct spherical polygons. Managing masks with such large numbers of polygons becomes intractably slow, particularly for tasks that run in time O(N^2) with a naive algorithm, such as finding which polygons overlap each other. Here we present a divide-and-conquer solution to this challenge: we first split the angular mask into predefined regions called pixels, such that each polygon is in only one pixel, and then perform further computations, such as checking for overlap, on the polygons within each pixel separately. This reduces O(N^2) tasks to O(N), and also reduces the important task of determining in which polygon(s) a point on the sky lies from O(N) to O(1), resulting in significant computational speedup. Additionally, we present a method to efficiently convert any angular mask to and from the popular HEALPix format. This method can be generically applied to convert to and from any desired spherical pixelization. We have implemented these techniques in a new version of the mangle software package, which is freely available at http://space.mit.edu/home/tegmark/mangle/, along with complete documentation and example applications. These new methods should prove quite useful to the astronomical community, and since mangle is a generic tool for managing angular masks on a sphere, it has the potential to benefit terrestrial mapmaking applications as well.
Particles have tremendous potential as astronomical messengers, and conversely, studying the universe as a whole also teaches us about particle physics. This thesis encompasses both of these research directions. Many models predict a diffuse flux o
f high energy neutrinos from active galactic nuclei and other astrophysical sources. The Astrophysics Underground portion of this thesis describes a search for this neutrino flux performed by looking for very high energy upward-going muons using the Super-K detector. In addition to using particles to do astronomy, we can also use the universe itself as a particle physics lab. The Particle Physics in the Sky portion of this thesis focuses on extracting cosmological information from galaxy surveys. To overcome technical challenges faced by the latest galaxy surveys, we produced a comprehensive upgrade to mangle, a software package that processes the angular masks defining the survey area on the sky. We added dramatically faster algorithms and new useful features that are necessary for managing complex masks of current and next-generation galaxy surveys. With this software in hand, we utilized SDSS data to investigate the relation between galaxies and dark matter by studying relative bias, i.e., the relation between different types of galaxies. Separating galaxies by their luminosities and colors reveals a complicated picture: red galaxies are clustered more strongly than blue galaxies, with both the brightest and the faintest red galaxies showing the strongest clustering. Furthermore, red and blue galaxies tend to occupy different regions of space. In order to make precise measurements from the next generation of galaxy surveys, it will be essential to account for this complexity.
