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 $\sim 60\,000$ 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