2,321 research outputs found
Numerical approach for high precision 3-D relativistic star models
A multi-domain spectral method for computing very high precision 3-D stellar
models is presented. The boundary of each domain is chosen in order to coincide
with a physical discontinuity (e.g. the star's surface). In addition, a
regularization procedure is introduced to deal with the infinite derivatives on
the boundary that may appear in the density field when stiff equations of state
are used. Consequently all the physical fields are smooth functions on each
domain and the spectral method is absolutely free of any Gibbs phenomenon,
which yields to a very high precision. The power of this method is demonstrated
by direct comparison with analytical solutions such as MacLaurin spheroids and
Roche ellipsoids. The relative numerical error reveals to be of the order of
. This approach has been developed for the study of relativistic
inspiralling binaries. It may be applied to a wider class of astrophysical
problems such as the study of relativistic rotating stars too.Comment: Minor changes, Phys. Rev. D in pres
StaRMAP - A second order staggered grid method for spherical harmonics moment equations of radiative transfer
We present a simple method to solve spherical harmonics moment systems, such
as the the time-dependent and equations, of radiative transfer.
The method, which works for arbitrary moment order , makes use of the
specific coupling between the moments in the equations. This coupling
naturally induces staggered grids in space and time, which in turn give rise to
a canonical, second-order accurate finite difference scheme. While the scheme
does not possess TVD or realizability limiters, its simplicity allows for a
very efficient implementation in Matlab. We present several test cases, some of
which demonstrate that the code solves problems with ten million degrees of
freedom in space, angle, and time within a few seconds. The code for the
numerical scheme, called StaRMAP (Staggered grid Radiation Moment
Approximation), along with files for all presented test cases, can be
downloaded so that all results can be reproduced by the reader.Comment: 28 pages, 7 figures; StaRMAP code available at
http://www.math.temple.edu/~seibold/research/starma
A New Spherical Harmonics Scheme for Multi-Dimensional Radiation Transport I: Static Matter Configurations
Recent work by McClarren & Hauck [29] suggests that the filtered spherical
harmonics method represents an efficient, robust, and accurate method for
radiation transport, at least in the two-dimensional (2D) case. We extend their
work to the three-dimensional (3D) case and find that all of the advantages of
the filtering approach identified in 2D are present also in the 3D case. We
reformulate the filter operation in a way that is independent of the timestep
and of the spatial discretization. We also explore different second- and
fourth-order filters and find that the second-order ones yield significantly
better results. Overall, our findings suggest that the filtered spherical
harmonics approach represents a very promising method for 3D radiation
transport calculations.Comment: 29 pages, 13 figures. Version matching the one in Journal of
Computational Physic
The pulsar force-free magnetosphere linked to its striped wind: time-dependent pseudo-spectral simulations
(abridged) Pulsar activity and its related radiation mechanism are usually
explained by invoking some plasma processes occurring inside the magnetosphere.
Despite many detailed local investigations, the global electrodynamics around
those neutron stars remains poorly described. Better understanding of these
compact objects requires a deep and accurate knowledge of their immediate
electromagnetic surrounding within the magnetosphere and its link to the
relativistic pulsar wind.
The aim of this work is to present accurate solutions to the nearly
stationary force-free pulsar magnetosphere and its link to the striped wind,
for various spin periods and arbitrary inclination. To this end, the
time-dependent Maxwell equations are solved in spherical geometry in the
force-free approximation using a vector spherical harmonic expansion of the
electromagnetic field. An exact analytical enforcement of the divergenceless of
the magnetic part is obtained by a projection method. Special care has been
given to design an algorithm able to look deeply into the magnetosphere with
physically realistic ratios of stellar to light-cylinder \rlight
radius. We checked our code against several analytical solutions, like the
Deutsch vacuum rotator solution and the Michel monopole field. We also retrieve
energy losses comparable to the magneto-dipole radiation formula and consistent
with previous similar works. Finally, for arbitrary obliquity, we give an
expression for the total electric charge of the system. It does not vanish
except for the perpendicular rotator. This is due to the often ignored point
charge located at the centre of the neutron star. It is questionable if such
solutions with huge electric charges could exist in reality except for
configurations close to an orthogonal rotator. The charge spread over the
stellar crust is not a tunable parameter as is often hypothesized.Comment: 16 pages, 13 figures, accepted by MNRA
Spectral methods in general relativistic astrophysics
We present spectral methods developed in our group to solve three-dimensional
partial differential equations. The emphasis is put on equations arising from
astrophysical problems in the framework of general relativity.Comment: 51 pages, elsart (Elsevier Preprint), 19 PostScript figures,
submitted to Journal of Computational & Applied Mathematic
How to make a clean separation between CMB E and B modes with proper foreground masking
We investigate the E/B decomposition of CMB polarization on a masked sky. In
real space, operators of E and B mode decomposition involve only differentials
of CMB polarization. We may, therefore in principle, perform a clean E/B
decomposition from incomplete sky data. Since it is impractical to apply second
derivatives to observation data, we usually rely on spherical harmonic
transformation and inverse transformation, instead of using real-space
operators. In spherical harmonic representation, jump discontinuities in a cut
sky produces Gibbs phenomenon, unless a spherical harmonic expansion is made up
to an infinitely high multipole. By smoothing a foreground mask, we may
suppress the Gibbs phenomenon effectively in a similar manner to apodization of
a foreground mask discussed in other works. However, we incur foreground
contamination by smoothing a foreground mask, because zero-value pixels in the
original mask may be rendered non-zero by the smoothing process. In this work,
we investigate an optimal foreground mask, which ensures proper foreground
masking and suppresses Gibbs phenomenon. We apply our method to a simulated map
of the pixel resolution comparable to the Planck satellite. The simulation
shows that the leakage power is lower than unlensed CMB B mode power spectrum
of tensor-to-scalar ratio . We compare the result with
that of the original mask. We find that the leakage power is reduced by a
factor of at the cost of a sky fraction , and that
the enhancement is highest at lowest multipoles. We confirm that all the
zero-value pixels in the original mask remain zero in our mask. The application
of this method to the Planck data will improve the detectability of primordial
tensor perturbation.Comment: v2: typos corrected, v3: matched with the published version (the
clarity improved) v4: a typo corrected v5: a bibliography file error fixe
A Note on Spherical Needlets
Compared with the traditional spherical harmonics, the spherical needlets are
a new generation of spherical wavelets that possess several attractive
properties. Their double localization in both spatial and frequency domains
empowers them to easily and sparsely represent functions with small spatial
scale features. This paper is divided into two parts. First, it reviews the
spherical harmonics and discusses their limitations in representing functions
with small spatial scale features. To overcome the limitations, it introduces
the spherical needlets and their attractive properties. In the second part of
the paper, a Matlab package for the spherical needlets is presented. The
properties of the spherical needlets are demonstrated by several examples using
the package.Comment: 12 pages, 7 figures, technical repor
Obtaining Potential Field Solution with Spherical Harmonics and Finite Differences
Potential magnetic field solutions can be obtained based on the synoptic
magnetograms of the Sun. Traditionally, a spherical harmonics decomposition of
the magnetogram is used to construct the current and divergence free magnetic
field solution. This method works reasonably well when the order of spherical
harmonics is limited to be small relative to the resolution of the magnetogram,
although some artifacts, such as ringing, can arise around sharp features. When
the number of spherical harmonics is increased, however, using the raw
magnetogram data given on a grid that is uniform in the sine of the latitude
coordinate can result in inaccurate and unreliable results, especially in the
polar regions close to the Sun.
We discuss here two approaches that can mitigate or completely avoid these
problems: i) Remeshing the magnetogram onto a grid with uniform resolution in
latitude, and limiting the highest order of the spherical harmonics to the
anti-alias limit; ii) Using an iterative finite difference algorithm to solve
for the potential field. The naive and the improved numerical solutions are
compared for actual magnetograms, and the differences are found to be rather
dramatic.
We made our new Finite Difference Iterative Potential-field Solver (FDIPS) a
publically available code, so that other researchers can also use it as an
alternative to the spherical harmonics approach.Comment: This paper describes the publicly available Finite Difference
Iterative Potential field Solver (FDIPS). The code can be obtained from
http://csem.engin.umich.edu/FDIP
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