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.
Using a hydrodynamic adaptive mesh refinement code, we simulate the growth and evolution of a galaxy, which could potentially host a supermassive black hole, within a cosmological volume. Reaching a dynamical range in excess of 10 million, the simula
tion follows the evolution of the gas structure from super-galactic scales all the way down to the outer edge of the accretion disk. Here, we focus on global instabilities in the self-gravitating, cold, turbulence-supported, molecular gas disk at the center of the model galaxy, which provide a natural mechanism for angular momentum transport down to sub-pc scales. The gas density profile follows a power-law scaling as r^-8/3, consistent with an analytic description of turbulence in a quasi-stationary circumnuclear disk. We analyze the properties of the disk which contribute to the instabilities, and investigate the significance of instability for the galaxys evolution and the growth of a supermassive black hole at the center.
