39,892 research outputs found
Local functional principal component analysis
Covariance operators of random functions are crucial tools to study the way
random elements concentrate over their support. The principal component
analysis of a random function X is well-known from a theoretical viewpoint and
extensively used in practical situations. In this work we focus on local
covariance operators. They provide some pieces of information about the
distribution of X around a fixed point of the space x₀. A description of
the asymptotic behaviour of the theoretical and empirical counterparts is
carried out. Asymptotic developments are given under assumptions on the
location of x₀ and on the distributions of projections of the data on the
eigenspaces of the (non-local) covariance operator
Radiation-pressure Waves and Multiphase Quasar Outflows
We report on quasar outflow properties revealed by analyzing more than 60
composite outflow spectra built from CIV absorption troughs in
the SDSS-III/BOSS DR12QBAL catalog. We assess the dependences of the equivalent
widths of many outflow metal absorption features on outflow velocity, trough
width and position, and quasar magnitude and redshift. The evolution of the
equivalent widths of the OVI and NV lines with outflow velocity correlates with
that of the mean absorption-line width, the outflow electron density, and the
strength of lines arising from collisionally-excited meta-stable states. None
of these correlations is found for the other high- or low-ionization species,
and different behaviors with trough width are also suggested. We find no
dependence on quasar magnitude or redshift in any case. All the observed trends
can be reconciled by considering a multiphase stratified outflow structure,
where inner regions are colder, denser and host lower-ionization species. Given
the prevalence of radiative acceleration in quasar outflows found by Mas-Ribas
& Mauland (2019), we suggest that radiation pressure sweeps up and compresses
the outflowing gas outwards, creating waves or filaments where the multiphase
stratified structure could take form. This scenario is supported by the
suggested correlation between electron density and outflow velocity, and the
similar behavior observed for the line and line-locking components of the
absorption features. We show that this outflow structure is also consistent
with other X-ray, radiative transfer, and polarization results, and discuss the
implications of our findings for future observational and numerical quasar
outflow studies.Comment: Main results Figs. 3 and 7. ApJ accepte
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