8,162 research outputs found
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to
distance-regular graphs for the reader who is unfamiliar with the subject, and
then give an overview of some developments in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page
An Optimal-Dimensionality Sampling for Spin- Functions on the Sphere
For the representation of spin- band-limited functions on the sphere, we
propose a sampling scheme with optimal number of samples equal to the number of
degrees of freedom of the function in harmonic space. In comparison to the
existing sampling designs, which require samples for the
representation of spin- functions band-limited at , the proposed scheme
requires samples for the accurate computation of the spin-
spherical harmonic transform~(-SHT). For the proposed sampling scheme, we
also develop a method to compute the -SHT. We place the samples in our
design scheme such that the matrices involved in the computation of -SHT are
well-conditioned. We also present a multi-pass -SHT to improve the accuracy
of the transform. We also show the proposed sampling design exhibits superior
geometrical properties compared to existing equiangular and Gauss-Legendre
sampling schemes, and enables accurate computation of the -SHT corroborated
through numerical experiments.Comment: 5 pages, 2 figure
Measuring the 3D shape of X-ray clusters
Observations and numerical simulations of galaxy clusters strongly indicate
that the hot intracluster x-ray emitting gas is not spherically symmetric. In
many earlier studies spherical symmetry has been assumed partly because of
limited data quality, however new deep observations and instrumental designs
will make it possible to go beyond that assumption. Measuring the temperature
and density profiles are of interest when observing the x-ray gas, however the
spatial shape of the gas itself also carries very useful information. For
example, it is believed that the x-ray gas shape in the inner parts of galaxy
clusters is greatly affected by feedback mechanisms, cooling and rotation, and
measuring this shape can therefore indirectly provide information on these
mechanisms. In this paper we present a novel method to measure the
three-dimensional shape of the intracluster x-ray emitting gas. We can measure
the shape from the x-ray observations only, i.e. the method does not require
combination with independent measurements of e.g. the cluster mass or density
profile. This is possible when one uses the full spectral information contained
in the observed spectra. We demonstrate the method by measuring radial
dependent shapes along the line of sight for CHANDRA mock data. We find that at
least 10^6 photons are required to get a 5-{\sigma} detection of shape for an
x-ray gas having realistic features such as a cool core and a double powerlaw
for the density profile. We illustrate how Bayes' theorem is used to find the
best fitting model of the x-ray gas, an analysis that is very important in a
real observational scenario where the true spatial shape is unknown. Not
including a shape in the fit may propagate to a mass bias if the x-ray is used
to estimate the total cluster mass. We discuss this mass bias for a class of
spacial shapes.Comment: 29 pages, 16 figure
Future constraints on halo thermodynamics from combined Sunyaev-Zel'dovich measurements
The improving sensitivity of measurements of the kinetic Sunyaev-Zel'dovich
(SZ) effect opens a new window into the thermodynamic properties of the baryons
in halos. We propose a methodology to constrain these thermodynamic properties
by combining the kinetic SZ, which is an unbiased probe of the free electron
density, and the thermal SZ, which probes their thermal pressure. We forecast
that our method constrains the average thermodynamic processes that govern the
energetics of galaxy evolution like energetic feedback across all redshift
ranges where viable halos sample are available. Current Stage-3 cosmic
microwave background (CMB) experiments like AdvACT and SPT-3G can measure the
kSZ and tSZ to greater than 100 if combined with a DESI-like
spectroscopic survey. Such measurements translate into percent-level
constraints on the baryonic density and pressure profiles and on the feedback
and non-thermal pressure support parameters for a given ICM model. This in turn
will provide critical thermodynamic tests for sub-grid models of feedback in
cosmological simulations of galaxy formation. The high fidelity measurements
promised by the next generation CMB experiment, CMB-S4, allow one to further
sub-divide these constraints beyond redshift into other classifications, like
stellar mass or galaxy type.Comment: 11 pages, 3 figures, Accepted to JCA
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