# Entrainment in Superfluid Neutron Star Crusts: Hydrodynamic Description and Microscopic Origin [HEAP]

In spite of the absence of viscous drag, the neutron superfluid permeating the inner crust of a neutron star cannot flow freely, and is entrained by the nuclear lattice similarly to laboratory superfluid atomic gases in optical lattices. The role of entrainment on the neutron superfluid dynamics is reviewed. For this purpose, a minimal hydrodynamical model of superfluidity in neutron-star crusts is presented. This model relies on a fully four-dimensionally covariant action principle. The equivalence of this formulation with the more traditional approach is demonstrated. In addition, the different treatments of entrainment in terms of dynamical effective masses or superfluid density are clarified. The nuclear energy density functional theory employed for the calculations of all the necessary microscopic inputs is also reviewed, focusing on superfluid properties. In particular, the microscopic origin of entrainment and the different methods to estimate its importance are discussed.

N. Chamel
Wed, 26 Jul 17
55/68

# A signature of anisotropic cosmic-ray transport in the gamma-ray sky [HEAP]

A crucial process in Galactic cosmic-ray (CR) transport is the spatial diffusion due to the interaction with the interstellar turbulent magnetic field. Usually, CR diffusion is assumed to be uniform and isotropic all across the Galaxy. However, this picture is clearly inaccurate: Several data-driven and theoretical arguments, as well as dedicated numerical simulations, show that diffusion exhibits highly anisotropic properties with respect to the direction of a background (ordered) magnetic field (i.e., parallel or perpendicular to it).
In this paper we focus on a recently discovered anomaly in the hadronic CR spectrum inferred by the Fermi-LAT gamma-ray data at different positions in the Galaxy, i.e. the progressive hardening of the proton slope at low Galactocentric radii. We propose the idea that this feature can be interpreted as a signature of anisotropic diffusion in the complex Galactic magnetic field: In particular, the harder slope in the inner Galaxy is due, in our scenario, to the parallel diffusive escape along the poloidal component of the large-scale, regular, magnetic field.
We implement this idea in a numerical framework, based on the DRAGON code, and perform detailed numerical tests on the accuracy of our setup. We discuss how the effect proposed depends on the relevant free parameters involved. Based on low-energy extrapolation of the few focused numerical simulations aimed at determining the scalings of the anisotropic diffusion coefficients, we finally present a set of plausible models that reproduce the behavior of the CR proton slopes inferred by gamma-ray data.

S. Cerri, D. Gaggero, A. Vittino, et. al.
Wed, 26 Jul 17
57/68

# Perpendicular and parallel diffusion coefficients of energetic charged particles in the presence of adiabatic focusing [HEAP]

Understanding stochastic diffusion of energetic charged particles in non-uniform background magnetic field is one of the major problems in plasmas of space and fusion devices. In this paper by using the improved perturbation method developed by He \& Schlickeiser starting from the modified Fokker-Planck equation of energetic charged particles we derive an differential equation for isotropic distribution function with infinite iteration of anisotropic distribution function $g(\mu)$. And then new perpendicular and parallel diffusion coefficients are obtained which include the infinite iteration effect. It is demonstrated that the form of perpendicular diffusion coefficient is invariable with the iterations, but the parallel diffusion coefficient is modified by iterations. We also find that the parallel diffusion coefficient derived in some previous papers is the special case of which is derived in this paper.

J. Wang and G. Qin
Wed, 26 Jul 17
61/68

# Perpendicular and parallel diffusion coefficients of energetic charged particles in the presence of adiabatic focusing [HEAP]

Understanding stochastic diffusion of energetic charged particles in non-uniform background magnetic field is one of the major problems in plasmas of space and fusion devices. In this paper by using the improved perturbation method developed by He \& Schlickeiser starting from the modified Fokker-Planck equation of energetic charged particles we derive an differential equation for isotropic distribution function with infinite iteration of anisotropic distribution function $g(\mu)$. And then new perpendicular and parallel diffusion coefficients are obtained which include the infinite iteration effect. It is demonstrated that the form of perpendicular diffusion coefficient is invariable with the iterations, but the parallel diffusion coefficient is modified by iterations. We also find that the parallel diffusion coefficient derived in some previous papers is the special case of which is derived in this paper.

J. Wang and G. Qin
Wed, 26 Jul 17
61/68

# Acceleration of Cosmic Ray Electrons at Weak Shocks in Galaxy Clusters [HEAP]

According to structure formation simulations, weak shocks with typical Mach number, $M_{\rm s}\lesssim 3$, are expected to form in merging galaxy clusters. The presence of such shocks has been indicated by X-ray and radio observations of many merging clusters. In particular, diffuse radio sources known as radio relics could be explained by synchrotron-emitting electrons accelerated via diffusive shock acceleration (Fermi I) at quasi-perpendicular shocks. Here we also consider possible roles of stochastic acceleration (Fermi II) by compressive MHD turbulence downstream of the shock. Then we explore a puzzling discrepancy that for some radio relics, the shock Mach number inferred from the radio spectral index is substantially larger than that estimated from X-ray observations. This problem could be understood, if shock surfaces associated with radio relics consist of multiple shocks with different strengths.In that case, X-ray observations tend to pick up the part of shocks with lower Mach numbers and higher kinetic energy flux, while radio emissions come preferentially from the part of shocks with higher Mach numbers and higher cosmic ray (CR) production. We also show that the Fermi I reacceleration model with preexisting fossil electrons supplemented by Fermi II acceleration due to postshock turbulence could reproduce observed profiles of radio flux densities and integrated radio spectra of two giant radio relics. This study demonstrates the CR electrons can be accelerated at collisionless shocks in galaxy clusters just like supernova remnant shock in the interstellar medium and interplanetary shocks in the solar wind.

H. Kang, D. Ryu and T. Jones
Tue, 25 Jul 17
1/70

Comments: 8 pages, 35th International Cosmic Ray Conference, Busan, Korea

# Pulsar Wind Blowout from a Supernova [HEAP]

For pulsars born in supernovae, the expansion of the shocked pulsar wind nebula is initially in the freely expanding ejecta of the supernova. While the nebula is in the inner flat part of the ejecta density profile, the swept-up, accelerating shell is subject to the Rayleigh-Taylor instability. We carried out 2 and 3-dimensional simulations showing that the instability gives rise to filamentary structure during this initial phase but does not greatly change the dynamics of the expanding shell. The flow is effectively self-similar. If the shell is powered into the outer steep part of the density profile, the shell is subject to a robust Rayleigh-Taylor instability in which the shell is fragmented and the shocked pulsar wind breaks out through the shell. The flow is not self-similar in this phase. For a wind nebula to reach this phase requires that the deposited pulsar energy be greater than the supernova energy, or that the initial pulsar period be in the ms range for a typical 10^{51} erg supernova. These conditions are satisfied by some magnetar models for Type I superluminous supernovae. We also consider the Crab Nebula, which may be associated with a low energy supernova for which this scenario applies.

J. Blondin and R. Chevalier
Tue, 25 Jul 17
4/70