Alfven Wave Reflection and Turbulent Heating in the Solar Wind from 1 Solar Radius to 1 AU: an Analytical Treatment

We study the propagation, reflection, and turbulent dissipation of Alfven waves in coronal holes and the solar wind. We start with the Heinemann-Olbert equations, which describe non-compressive magnetohydrodynamic fluctuations in an inhomogeneous medium with a background flow parallel to the background magnetic field. Following the approach of Dmitruk et al, we model the nonlinear terms in these equations using a simple phenomenology for the cascade and dissipation of wave energy, and assume that there is much more energy in waves propagating away from the Sun than waves propagating towards the Sun. We then solve the equations analytically for waves with periods of hours and longer to obtain expressions for the wave amplitudes and turbulent heating rate as a function of heliocentric distance. We also develop a second approximate model that includes waves with periods of roughly one minute to one hour, which undergo less reflection than the longer-period waves, and compare our models to observations. Our models generalize the phenomenological model of Dmitruk et al by accounting for the solar wind velocity, so that the turbulent heating rate can be evaluated from the coronal base out past the Alfven critical point - that is, throughout the region in which most of the heating and acceleration occurs. The simple analytical expressions that we obtain can be used to incorporate Alfven-wave reflection and turbulent heating into fluid models of the solar wind.Comment: 9 pages, 9 figures, accepted for publication in Ap

Perpendicular Ion Heating by Low-Frequency Alfven-Wave Turbulence in the Solar Wind

We consider ion heating by turbulent Alfven waves (AWs) and kinetic Alfven waves (KAWs) with perpendicular wavelengths comparable to the ion gyroradius and frequencies smaller than the ion cyclotron frequency. When the turbulence amplitude exceeds a certain threshold, an ion's orbit becomes chaotic. The ion then interacts stochastically with the time-varying electrostatic potential, and the ion's energy undergoes a random walk. Using phenomenological arguments, we derive an analytic expression for the rates at which different ion species are heated, which we test by simulating test particles interacting with a spectrum of randomly phased AWs and KAWs. We find that the stochastic heating rate depends sensitively on the quantity epsilon = dv/vperp, where vperp is the component of the ion velocity perpendicular to the background magnetic field B0, and dv (dB) is the rms amplitude of the velocity (magnetic-field) fluctuations at the gyroradius scale. In the case of thermal protons, when epsilon << eps1, where eps1 is a constant, a proton's magnetic moment is nearly conserved and stochastic heating is extremely weak. However, when epsilon > eps1, the proton heating rate exceeds the cascade power that would be present in strong balanced KAW turbulence with the same value of dv, and magnetic-moment conservation is violated. For the random-phase waves in our test-particle simulations, eps1 is approximately 0.2. For protons in low-beta plasmas, epsilon is approximately dB/B0 divided by the square root of beta, and epsilon can exceed eps1 even when dB/B0 << eps1. At comparable temperatures, alpha particles and minor ions have larger values of epsilon than protons and are heated more efficiently as a result. We discuss the implications of our results for ion heating in coronal holes and the solar wind.Comment: 14 pages, 5 figures, submitted to Ap

Resonance Broadening and Heating of Charged Particles in Magnetohydrodynamic Turbulence

The heating, acceleration, and pitch-angle scattering of charged particles by MHD turbulence are important in a wide range of astrophysical environments, including the solar wind, accreting black holes, and galaxy clusters. We simulate the interaction of high-gyrofrequency test particles with fully dynamical simulations of subsonic MHD turbulence, focusing on the parameter regime with beta ~ 1, where beta is the ratio of gas to magnetic pressure. We use the simulation results to calibrate analytical expressions for test particle velocity-space diffusion coefficients and provide simple fits that can be used in other work. The test particle velocity diffusion in our simulations is due to a combination of two processes: interactions between particles and magnetic compressions in the turbulence (as in linear transit-time damping; TTD) and what we refer to as Fermi Type-B (FTB) interactions, in which charged particles moving on field lines may be thought of as beads spiralling around moving wires. We show that test particle heating rates are consistent with a TTD resonance which is broadened according to a decorrelation prescription that is Gaussian in time. TTD dominates the heating for v_s >> v_A (e.g. electrons), where v_s is the thermal speed of species s and v_A is the Alfven speed, while FTB dominates for v_s << v_A (e.g. minor ions). Proton heating rates for beta ~ 1 are comparable to the turbulent cascade rate. Finally, we show that velocity diffusion of collisionless, large gyrofrequency particles due to large-scale MHD turbulence does not produce a power-law distribution function.Comment: 20 pages, 15 figures; accepted by The Astrophysical Journal; added clarifying appendices, but no major changes to result

Stochastic Weighted Graphs: Flexible Model Specification and Simulation

In most domains of network analysis researchers consider networks that arise in nature with weighted edges. Such networks are routinely dichotomized in the interest of using available methods for statistical inference with networks. The generalized exponential random graph model (GERGM) is a recently proposed method used to simulate and model the edges of a weighted graph. The GERGM specifies a joint distribution for an exponential family of graphs with continuous-valued edge weights. However, current estimation algorithms for the GERGM only allow inference on a restricted family of model specifications. To address this issue, we develop a Metropolis--Hastings method that can be used to estimate any GERGM specification, thereby significantly extending the family of weighted graphs that can be modeled with the GERGM. We show that new flexible model specifications are capable of avoiding likelihood degeneracy and efficiently capturing network structure in applications where such models were not previously available. We demonstrate the utility of this new class of GERGMs through application to two real network data sets, and we further assess the effectiveness of our proposed methodology by simulating non-degenerate model specifications from the well-studied two-stars model. A working R version of the GERGM code is available in the supplement and will be incorporated in the gergm CRAN package.Comment: 33 pages, 6 figures. To appear in Social Network

Constraining Low-Frequency Alfvenic Turbulence in the Solar Wind Using Density Fluctuation Measurements

One proposed mechanism for heating the solar wind, from close to the sun to beyond 10 AU, invokes low-frequency, oblique, Alfven-wave turbulence. Because small-scale oblique Alfven waves (kinetic Alfven waves) are compressive, the measured density fluctuations in the solar wind place an upper limit on the amplitude of kinetic Alfven waves and hence an upper limit on the rate at which the solar wind can be heated by low-frequency, Alfvenic turbulence. We evaluate this upper limit for both coronal holes at 5 solar radii and in the near-Earth solar wind. At both radii, the upper limit we find is consistent with models in which the solar wind is heated by low-frequency Alfvenic turbulence. At 1 AU, the upper limit on the turbulent heating rate derived from the measured density fluctuations is within a factor of 2 of the measured solar wind heating rate. Thus if low-frequency Alfvenic turbulence contributes to heating the near-Earth solar wind, kinetic Alfven waves must be one of the dominant sources of solar wind density fluctuations at frequencies of order 1 Hz. We also present a simple argument for why density fluctuation measurements do appear to rule out models in which the solar wind is heated by non-turbulent high-frequency waves ``sweeping'' through the ion-cyclotron resonance, but are compatible with heating by low-frequency Alfvenic turbulence.Comment: 8 pages, 3 figures, submitted to Ap

Dominant next-to-leading order QCD corrections to Higgs plus three jet production in vector-boson fusion

We present the calculation of the dominant next to leading order QCD corrections to Higgs boson production in association with three jets via vector boson fusion in the form of a NLO parton-level Monte Carlo program. QCD corrections to integrated cross sections are modest, while the shapes of some kinematical distributions change appreciably at NLO. Scale uncertainties are shown to be reduced at NLO for the total cross section and for distributions. We consider a central jet veto at the LHC and analyze the veto probability for typical vector boson fusion cuts. Scale uncertainties of the veto probability are sufficiently small at NLO for precise Higgs coupling measurements at the LHC.Comment: 40 pages, 17 figures, 2 tables, published versio

A Stellar Rotation Census of B Stars: from ZAMS to TAMS

Two recent observing campaigns provide us with moderate dispersion spectra of more than 230 cluster and 370 field B stars. Combining them and the spectra of the B stars from our previous investigations ($\sim$430 cluster and $\sim$100 field B stars) yields a large, homogeneous sample for studying the rotational properties of B stars. We derive the projected rotational velocity $V\sin i$, effective temperature, gravity, mass, and critical rotation speed $V_{\rm crit}$ for each star. We find that the average $V\sin i$ is significantly lower among field stars because they are systematically more evolved and spun down than their cluster counterparts. The rotational distribution functions of $V_{\rm eq}/V_{\rm crit}$ for the least evolved B stars show that lower mass B stars are born with a larger proportion of rapid rotators than higher mass B stars. However, the upper limit of $V_{\rm eq}/V_{\rm crit}$ that may separate normal B stars from emission line Be stars (where rotation promotes mass loss into a circumstellar disk) is smaller among the higher mass B stars. We compare the evolutionary trends of rotation (measured according to the polar gravity of the star) with recent models that treat internal mixing. The spin-down rates observed in the high mass subset ($\sim 9 M_\odot$) agree with predictions, but the rates are larger for the low mass group ($\sim 3 M_\odot$). The faster spin down in the low mass B stars matches well with the predictions based on conservation of angular momentum in individual spherical shells. Our results suggest the fastest rotators (that probably correspond to the emission line Be stars) are probably formed by evolutionary spin up (for the more massive stars) and by mass transfer in binaries (for the full range of B star masses).Comment: 44 pages, 10 figures, accepted for publication in Ap