53,973 research outputs found
Discretising the velocity distribution for directional dark matter experiments
Dark matter (DM) direct detection experiments which are
directionally-sensitive may be the only method of probing the full velocity
distribution function (VDF) of the Galactic DM halo. We present an angular
basis for the DM VDF which can be used to parametrise the distribution in order
to mitigate astrophysical uncertainties in future directional experiments and
extract information about the DM halo. This basis consists of discretising the
VDF in a series of angular bins, with the VDF being only a function of the DM
speed within each bin. In contrast to other methods, such as spherical
harmonic expansions, the use of this basis allows us to guarantee that the
resulting VDF is everywhere positive and therefore physical. We present a
recipe for calculating the event rates corresponding to the discrete VDF for an
arbitrary number of angular bins and investigate the discretisation error
which is introduced in this way. For smooth, Standard Halo Model-like
distribution functions, only angular bins are required to achieve an
accuracy of around in the number of events in each bin. Shortly after
confirmation of the DM origin of the signal with around 50 events, this
accuracy should be sufficient to allow the discretised velocity distribution to
be employed reliably. For more extreme VDFs (such as streams), the
discretisation error is typically much larger, but can be improved with
increasing . This method paves the way towards an astrophysics-independent
analysis framework for the directional detection of dark matter.Comment: 36 pages, 11 figures. Matches version accepted in JCAP. Python code
for Radon transform calculation available from the autho
SILC: a new Planck Internal Linear Combination CMB temperature map using directional wavelets
We present new clean maps of the CMB temperature anisotropies (as measured by
Planck) constructed with a novel internal linear combination (ILC) algorithm
using directional, scale-discretised wavelets --- Scale-discretised,
directional wavelet ILC or SILC. Directional wavelets, when convolved with
signals on the sphere, can separate the anisotropic filamentary structures
which are characteristic of both the CMB and foregrounds. Extending previous
component separation methods, which use the frequency, spatial and harmonic
signatures of foregrounds to separate them from the cosmological background
signal, SILC can additionally use morphological information in the foregrounds
and CMB to better localise the cleaning algorithm. We test the method on Planck
data and simulations, demonstrating consistency with existing component
separation algorithms, and discuss how to optimise the use of morphological
information by varying the number of directional wavelets as a function of
spatial scale. We find that combining the use of directional and axisymmetric
wavelets depending on scale could yield higher quality CMB temperature maps.
Our results set the stage for the application of SILC to polarisation
anisotropies through an extension to spin wavelets.Comment: 15 pages, 13 figures. Minor changes to match version published in
MNRAS. Map products available at http://www.silc-cmb.or
Fast directional correlation on the sphere with steerable filters
A fast algorithm is developed for the directional correlation of scalar
band-limited signals and band-limited steerable filters on the sphere. The
asymptotic complexity associated to it through simple quadrature is of order
O(L^5), where 2L stands for the square-root of the number of sampling points on
the sphere, also setting a band limit L for the signals and filters considered.
The filter steerability allows to compute the directional correlation uniquely
in terms of direct and inverse scalar spherical harmonics transforms, which
drive the overall asymptotic complexity. The separation of variables technique
for the scalar spherical harmonics transform produces an O(L^3) algorithm
independently of the pixelization. On equi-angular pixelizations, a sampling
theorem introduced by Driscoll and Healy implies the exactness of the
algorithm. The equi-angular and HEALPix implementations are compared in terms
of memory requirements, computation times, and numerical stability. The
computation times for the scalar transform, and hence for the directional
correlation, of maps of several megapixels on the sphere (L~10^3) are reduced
from years to tens of seconds in both implementations on a single standard
computer. These generic results for the scale-space signal processing on the
sphere are specifically developed in the perspective of the wavelet analysis of
the cosmic microwave background (CMB) temperature (T) and polarization (E and
B) maps of the WMAP and Planck experiments. As an illustration, we consider the
computation of the wavelet coefficients of a simulated temperature map of
several megapixels with the second Gaussian derivative wavelet.Comment: Version accepted in APJ. 14 pages, 2 figures, Revtex4 (emulateapj).
Changes include (a) a presentation of the algorithm as directly built on
blocks of standard spherical harmonics transforms, (b) a comparison between
the HEALPix and equi-angular implementation
Localisation of directional scale-discretised wavelets on the sphere
Scale-discretised wavelets yield a directional wavelet framework on the
sphere where a signal can be probed not only in scale and position but also in
orientation. Furthermore, a signal can be synthesised from its wavelet
coefficients exactly, in theory and practice (to machine precision).
Scale-discretised wavelets are closely related to spherical needlets (both were
developed independently at about the same time) but relax the axisymmetric
property of needlets so that directional signal content can be probed. Needlets
have been shown to satisfy important quasi-exponential localisation and
asymptotic uncorrelation properties. We show that these properties also hold
for directional scale-discretised wavelets on the sphere and derive similar
localisation and uncorrelation bounds in both the scalar and spin settings.
Scale-discretised wavelets can thus be considered as directional needlets.Comment: 28 pages, 8 figures, minor changes to match version accepted for
publication by ACH
Displaced path integral formulation for the momentum distribution of quantum particles
The proton momentum distribution, accessible by deep inelastic neutron
scattering, is a very sensitive probe of the potential of mean force
experienced by the protons in hydrogen-bonded systems. In this work we
introduce a novel estimator for the end to end distribution of the Feynman
paths, i.e. the Fourier transform of the momentum distribution. In this
formulation, free particle and environmental contributions factorize. Moreover,
the environmental contribution has a natural analogy to a free energy surface
in statistical mechanics, facilitating the interpretation of experiments. The
new formulation is not only conceptually but also computationally advantageous.
We illustrate the method with applications to an empirical water model,
ab-initio ice, and one dimensional model systems
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