Spectral Problems for Quasinormal Modes of Black Holes

This is an unconventional review article on spectral problems in black hole perturbation theory. Our purpose is to explain how to apply various known techniques in quantum mechanics to such spectral problems. The article includes analytical/numerical treatments, semiclassical perturbation theory, the (uniform) WKB method and useful mathematical tools: Borel summations, Padé approximants, and so forth. The article is not comprehensive, but rather looks into a few examples from various points of view. The techniques in this article are widely applicable to many other examples.

Neutrino Transport with the Monte Carlo Method. II. Quantum Kinetic Equations

Neutrinos have a unique quantum feature as flavor conversions. Recent studies suggested that collective neutrino oscillations play important roles in high-energy astrophysical phenomena. The quantum kinetic equation (QKE) is capable of describing the neutrino flavor conversion, transport, and matter collision self-consistently. However, we have experienced many technical difficulties in their numerical implementation. In this paper, we present a new QKE solver based on a Monte Carlo (MC) approach. This is an upgraded version of our classical MC neutrino transport solver; in essence, a flavor degree of freedom including mixing state is added into each MC particle. This extension requires updating numerical treatments of collision terms, in particular for scattering processes. We deal with the technical problem by generating a new MC particle at each scattering event. To reduce statistical noise inherent in MC methods, we develop the effective mean free path method. This suppresses a sudden change of flavor state due to collisions without increasing the number of MC particles. We present a suite of code tests to validate these new modules with comparison to the results reported in previous studies. Our QKE-MC solver is developed with fundamentally different philosophy and design from other deterministic and mesh methods, suggesting that it will be complementary to others and potentially provide new insights into physical processes of neutrino dynamics.

The Development of a Split-tail Heliosphere and the Role of Non-ideal Processes: A Comparison of the BU and Moscow Models

Global models of the heliosphere are critical tools used in the interpretation of heliospheric observations. There are several three-dimensional magnetohydrodynamic (MHD) heliospheric models that rely on different strategies and assumptions. Until now only one paper has compared global heliosphere models, but without magnetic field effects. We compare the results of two different MHD models, the BU and Moscow models. Both models use identical boundary conditions to compare how different numerical approaches and physical assumptions contribute to the heliospheric solution. Based on the different numerical treatments of discontinuities, the BU model allows for the presence of magnetic reconnection, while the Moscow model does not. Both models predict collimation of the solar outflow in the heliosheath by the solar magnetic field and produce a split tail where the solar magnetic field confines the charged solar particles into distinct north and south columns that become lobes. In the BU model, the interstellar medium (ISM) flows between the two lobes at large distances due to MHD instabilities and reconnection. Reconnection in the BU model at the port flank affects the draping of the interstellar magnetic field in the immediate vicinity of the heliopause. Different draping in the models cause different ISM pressures, yielding different heliosheath thicknesses and boundary locations, with the largest effects at high latitudes. The BU model heliosheath is 15% thinner and the heliopause is 7% more inwards at the north pole relative to the Moscow model. These differences in the two plasma solutions may manifest themselves in energetic neutral atom measurements of the heliosphere.