99,135 research outputs found
Accounting for Calibration Uncertainties in X-ray Analysis: Effective Areas in Spectral Fitting
While considerable advance has been made to account for statistical
uncertainties in astronomical analyses, systematic instrumental uncertainties
have been generally ignored. This can be crucial to a proper interpretation of
analysis results because instrumental calibration uncertainty is a form of
systematic uncertainty. Ignoring it can underestimate error bars and introduce
bias into the fitted values of model parameters. Accounting for such
uncertainties currently requires extensive case-specific simulations if using
existing analysis packages. Here we present general statistical methods that
incorporate calibration uncertainties into spectral analysis of high-energy
data. We first present a method based on multiple imputation that can be
applied with any fitting method, but is necessarily approximate. We then
describe a more exact Bayesian approach that works in conjunction with a Markov
chain Monte Carlo based fitting. We explore methods for improving computational
efficiency, and in particular detail a method of summarizing calibration
uncertainties with a principal component analysis of samples of plausible
calibration files. This method is implemented using recently codified Chandra
effective area uncertainties for low-resolution spectral analysis and is
verified using both simulated and actual Chandra data. Our procedure for
incorporating effective area uncertainty is easily generalized to other types
of calibration uncertainties.Comment: 61 pages double spaced, 8 figures, accepted for publication in Ap
Application of XFaster power spectrum and likelihood estimator to Planck
We develop the XFaster Cosmic Microwave Background (CMB) temperature and
polarization anisotropy power spectrum and likelihood technique for the Planck
CMB satellite mission. We give an overview of this estimator and its current
implementation and present the results of applying this algorithm to simulated
Planck data. We show that it can accurately extract the power spectrum of
Planck data for the high-l multipoles range. We compare the XFaster
approximation for the likelihood to other high-l likelihood approximations such
as Gaussian and Offset Lognormal and a low-l pixel-based likelihood. We show
that the XFaster likelihood is not only accurate at high-l, but also performs
well at moderately low multipoles. We also present results for cosmological
parameter Markov Chain Monte Carlo estimation with the XFaster likelihood. As
long as the low-l polarization and temperature power are properly accounted
for, e.g., by adding an adequate low-l likelihood ingredient, the input
parameters are recovered to a high level of accuracy.Comment: 25 pages, 20 figures, updated to reflect published version: slightly
extended account of XFaster technique, added improved plots and minor
corrections. Accepted for publication in MNRA
A Statistical Method for Estimating Luminosity Functions using Truncated Data
The observational limitations of astronomical surveys lead to significant
statistical inference challenges. One such challenge is the estimation of
luminosity functions given redshift and absolute magnitude measurements
from an irregularly truncated sample of objects. This is a bivariate density
estimation problem; we develop here a statistically rigorous method which (1)
does not assume a strict parametric form for the bivariate density; (2) does
not assume independence between redshift and absolute magnitude (and hence
allows evolution of the luminosity function with redshift); (3) does not
require dividing the data into arbitrary bins; and (4) naturally incorporates a
varying selection function. We accomplish this by decomposing the bivariate
density into nonparametric and parametric portions. There is a simple way of
estimating the integrated mean squared error of the estimator; smoothing
parameters are selected to minimize this quantity. Results are presented from
the analysis of a sample of quasars.Comment: 30 pages, 9 figures, Accepted for publication in Ap
Application of Bayesian graphs to SN Ia data analysis and compression
Bayesian graphical models are an efficient tool for modelling complex data
and derive self-consistent expressions of the posterior distribution of model
parameters. We apply Bayesian graphs to perform statistical analyses of Type Ia
supernova (SN Ia) luminosity distance measurements from the joint light-curve
analysis (JLA) data set. In contrast to the approach used in previous
studies, the Bayesian inference allows us to fully account for the
standard-candle parameter dependence of the data covariance matrix. Comparing
with analysis results, we find a systematic offset of the marginal
model parameter bounds. We demonstrate that the bias is statistically
significant in the case of the SN Ia standardization parameters with a maximal
6 shift of the SN light-curve colour correction. In addition, we find
that the evidence for a host galaxy correction is now only 2.4 .
Systematic offsets on the cosmological parameters remain small, but may
increase by combining constraints from complementary cosmological probes. The
bias of the analysis is due to neglecting the parameter-dependent
log-determinant of the data covariance, which gives more statistical weight to
larger values of the standardization parameters. We find a similar effect on
compressed distance modulus data. To this end, we implement a fully consistent
compression method of the JLA data set that uses a Gaussian approximation of
the posterior distribution for fast generation of compressed data. Overall, the
results of our analysis emphasize the need for a fully consistent Bayesian
statistical approach in the analysis of future large SN Ia data sets.Comment: 14 pages, 13 figures, 5 tables. Submitted to MNRAS. Compression
utility available at https://gitlab.com/congma/libsncompress/ and example
cosmology code with machine-readable version of Tables A1 & A2 at
https://gitlab.com/congma/sn-bayesian-model-example/ v2: corrected typo in
author's name. v3: 15 pages, incl. corrections, matches the accepted versio
Dipolar Relaxation in an ultra-cold Gas of magnetically trapped chromium atoms
We have investigated both theoretically and experimentally dipolar relaxation
in a gas of magnetically trapped chromium atoms. We have found that the large
magnetic moment of 6 results in an event rate coefficient for dipolar
relaxation processes of up to cms at a magnetic
field of 44 G. We present a theoretical model based on pure dipolar coupling,
which predicts dipolar relaxation rates in agreement with our experimental
observations. This very general approach can be applied to a large variety of
dipolar gases.Comment: 9 pages, 9 figure
The kinematics of the diffuse ionized gas in NGC 4666
The global properties of the interstellar medium with processes such as
infall and outflow of gas and a large scale circulation of matter and its
consequences for star formation and chemical enrichment are important for the
understanding of galaxy evolution. In this paper we studied the kinematics and
morphology of the diffuse ionized gas (DIG) in the disk and in the halo of the
star forming spiral galaxy NGC 4666 to derive information about its kinematical
properties. Especially, we searched for infalling and outflowing ionized gas.
We determined surface brightness, radial velocity, and velocity dispersion of
the warm ionized gas via high spectral resolution (R ~ 9000) Fabry-P\'erot
interferometry. This allows the determination of the global velocity field and
the detection of local deviations from this verlocity field. We calculated
models of the DIG distribution and its kinematics for comparison with the
measured data. In this way we determined fundamental parameters such as the
inclination and the scale height of NGC 4666, and established the need for an
additional gas component to fit our observed data. We found individual areas,
especially along the minor axis, with gas components reaching into the halo
which we interpret as an outflowing component of the diffuse ionized gas. As
the main result of our study, we were able to determine that the vertical
structure of the DIG distribution in NGC 4666 is best modeled with two
components of ionized gas, a thick and a thin disk with 0.8 kpc and 0.2 kpc
scale height, respectively. Therefore, the enhanced star formation in NGC 4666
drives an outflow and also maintains a thick ionized gas layer reminiscent of
the Reynold's layer in the Milky Way.Comment: 12 pages, 10 figures, 3 table
The velocity-density relation in the spherical model
We study the cosmic velocity-density relation using the spherical collapse
model (SCM) as a proxy to non-linear dynamics. Although the dependence of this
relation on cosmological parameters is known to be weak, we retain the density
parameter Omega_m in SCM equations, in order to study the limit Omega_m -> 0.
We show that in this regime the considered relation is strictly linear, for
arbitrary values of the density contrast, on the contrary to some claims in the
literature. On the other hand, we confirm that for realistic values of Omega_m
the exact relation in the SCM is well approximated by the classic formula of
Bernardeau (1992), both for voids (delta<0) and for overdensities up to delta ~
3. Inspired by this fact, we find further analytic approximations to the
relation for the whole range delta from -1 to infinity. Our formula for voids
accounts for the weak Omega_m-dependence of their maximal rate of expansion,
which for Omega_m < 1 is slightly smaller that 3/2. For positive density
contrasts, we find a simple relation div v = 3 H_0 (Omega_m)^(0.6) [
(1+delta)^(1/6) - (1+delta)^(1/2) ], that works very well up to the turn-around
(i.e. up to delta ~ 13.5 for Omega_m = 0.25 and neglected Omega_Lambda). Having
the same second-order expansion as the formula of Bernardeau, it can be
regarded as an extension of the latter for higher density contrasts. Moreover,
it gives a better fit to results of cosmological numerical simulations.Comment: 11 pages, 6 figures. Accepted for publication in MNRA
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