884 research outputs found
Using hybrid GPU/CPU kernel splitting to accelerate spherical convolutions
We present a general method for accelerating by more than an order of
magnitude the convolution of pixelated functions on the sphere with a
radially-symmetric kernel. Our method splits the kernel into a compact
real-space component and a compact spherical harmonic space component. These
components can then be convolved in parallel using an inexpensive commodity GPU
and a CPU. We provide models for the computational cost of both real-space and
Fourier space convolutions and an estimate for the approximation error. Using
these models we can determine the optimum split that minimizes the wall clock
time for the convolution while satisfying the desired error bounds. We apply
this technique to the problem of simulating a cosmic microwave background (CMB)
anisotropy sky map at the resolution typical of the high resolution maps
produced by the Planck mission. For the main Planck CMB science channels we
achieve a speedup of over a factor of ten, assuming an acceptable fractional
rms error of order 1.e-5 in the power spectrum of the output map.Comment: 9 pages, 11 figures, 1 table, accepted by Astronomy & Computing w/
minor revisions. arXiv admin note: substantial text overlap with
arXiv:1211.355
Universal Density Profile for Cosmic Voids
We present a simple empirical function for the average density profile of
cosmic voids, identified via the watershed technique in CDM N-body
simulations. This function is universal across void size and redshift,
accurately describing a large radial range of scales around void centers with
only two free parameters. In analogy to halo density profiles, these parameters
describe the scale radius and the central density of voids. While we initially
start with a more general four-parameter model, we find two of its parameters
to be redundant, as they follow linear trends with the scale radius in two
distinct regimes of the void sample, separated by its compensation scale.
Assuming linear theory, we derive an analytic formula for the velocity profile
of voids and find an excellent agreement with the numerical data as well. In
our companion paper [Sutter et al., Mon. Not. R. Astron. Soc. 442, 462 (2014)]
the presented density profile is shown to be universal even across tracer type,
properly describing voids defined in halo and galaxy distributions of varying
sparsity, allowing us to relate various void populations by simple rescalings.
This provides a powerful framework to match theory and simulations with
observational data, opening up promising perspectives to constrain competing
models of cosmology and gravity.Comment: 5 pages, 3 figures. Matches PRL published version after minor
correction
Probing cosmology and gravity with redshift-space distortions around voids
Cosmic voids in the large-scale structure of the Universe affect the peculiar
motions of objects in their vicinity. Although these motions are difficult to
observe directly, the clustering pattern of their surrounding tracers in
redshift space is influenced in a unique way. This allows to investigate the
interplay between densities and velocities around voids, which is solely
dictated by the laws of gravity. With the help of -body simulations and
derived mock-galaxy catalogs we calculate the average density fluctuations
around voids identified with a watershed algorithm in redshift space and
compare the results with the expectation from general relativity and the
CDM model. We find linear theory to work remarkably well in describing
the dynamics of voids. Adopting a Bayesian inference framework, we explore the
full posterior of our model parameters and forecast the achievable accuracy on
measurements of the growth rate of structure and the geometric distortion
through the Alcock-Paczynski effect. Systematic errors in the latter are
reduced from to when peculiar velocities are taken into
account. The relative parameter uncertainties in galaxy surveys with number
densities comparable to the SDSS MAIN (CMASS) sample probing a volume of
yield () and
(), respectively. At this level of precision
the linear-theory model becomes systematics dominated, with parameter biases
that fall beyond these values. Nevertheless, the presented method is highly
model independent; its viability lies in the underlying assumption of
statistical isotropy of the Universe.Comment: 38 pages, 14 figures. Published in JCAP. Referee comments
incorporated, typos corrected, references added. Considerably improved
results thanks to consideration of full covariance matrix in the MCMC
analysi
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