847 research outputs found
STARRY: Analytic Occultation Light Curves
We derive analytic, closed form, numerically stable solutions for the total
flux received from a spherical planet, moon or star during an occultation if
the specific intensity map of the body is expressed as a sum of spherical
harmonics. Our expressions are valid to arbitrary degree and may be computed
recursively for speed. The formalism we develop here applies to the computation
of stellar transit light curves, planetary secondary eclipse light curves, and
planet-planet/planet-moon occultation light curves, as well as thermal
(rotational) phase curves. In this paper we also introduce STARRY, an
open-source package written in C++ and wrapped in Python that computes these
light curves. The algorithm in STARRY is six orders of magnitude faster than
direct numerical integration and several orders of magnitude more precise.
STARRY also computes analytic derivatives of the light curves with respect to
all input parameters for use in gradient-based optimization and inference, such
as Hamiltonian Monte Carlo (HMC), allowing users to quickly and efficiently fit
observed light curves to infer properties of a celestial body's surface map.Comment: 55 pages, 20 figures. Accepted to the Astronomical Journal. Check out
the code at https://github.com/rodluger/starr
Implementing an apparent-horizon finder in three dimensions
Locating apparent horizons is not only important for a complete understanding
of numerically generated spacetimes, but it may also be a crucial component of
the technique for evolving black-hole spacetimes accurately. A scheme proposed
by Libson et al., based on expanding the location of the apparent horizon in
terms of symmetric trace-free tensors, seems very promising for use with
three-dimensional numerical data sets. In this paper, we generalize this scheme
and perform a number of code tests to fully calibrate its behavior in
black-hole spacetimes similar to those we expect to encounter in solving the
binary black-hole coalescence problem. An important aspect of the
generalization is that we can compute the symmetric trace-free tensor expansion
to any order. This enables us to determine how far we must carry the expansion
to achieve results of a desired accuracy. To accomplish this generalization, we
describe a new and very convenient set of recurrence relations which apply to
symmetric trace-free tensors.Comment: 14 pages (RevTeX 3.0 with 3 figures
A fast multipole method for stellar dynamics
The approximate computation of all gravitational forces between
interacting particles via the fast multipole method (FMM) can be made as
accurate as direct summation, but requires less than
operations. FMM groups particles into spatially bounded cells and uses
cell-cell interactions to approximate the force at any position within the sink
cell by a Taylor expansion obtained from the multipole expansion of the source
cell. By employing a novel estimate for the errors incurred in this process, I
minimise the computational effort required for a given accuracy and obtain a
well-behaved distribution of force errors. For relative force errors of
, the computational costs exhibit an empirical scaling of . My implementation (running on a 16 core node) out-performs a
GPU-based direct summation with comparable force errors for .Comment: 21 pages, 15 figures, accepted for publication in Journal for
Computational Astrophysics and Cosmolog
- …