Boaz Katz

MAGNETIC FIELD EVOLUTION IN RELATIVISTIC UNMAGNETIZED COLLISIONLESS SHOCKS

We study relativistic unmagnetized collisionless shocks using unprecedentedly large particle-in-cell simulations of two-dimensional pair plasma. High energy particles accelerated by the shock are found to drive magnetic field evolution on a timescale >10^4 plasma times. Progressively stronger magnetic fields are generated on larger scales in a growing region around the shock. Shock-generated magnetic fields and accelerated particles carry >1% and >10% of the downstream energy flux, respectively. Our results suggest limits on the magnetization of relativistic astrophysical flows.

SUPER-ECCENTRIC MIGRATING JUPITERS

An important class of formation theories for hot Jupiters involves the excitation of extreme orbital eccentricity (e = 0.99 or even larger) followed by tidal dissipation at periastron passage that eventually circularizes the planetary orbit at a period less than 10 days. In a steady state, this mechanism requires the existence of a significant population of super-eccentric (e > 0.9) migrating Jupiters with long orbital periods and periastron distances of only a few stellar radii. For these super-eccentric planets, the periastron is fixed due to conservation of orbital angular momentum and the energy dissipated per orbit is constant, implying that the rate of change in semi-major axis a is a-dot {proportional_to}a{sup 1/2} and consequently the number distribution satisfies dN/d log a{proportional_to}a{sup 1/2}. If this formation process produces most hot Jupiters, Kepler should detect several super-eccentric migrating progenitors of hot Jupiters, allowing for a test of high-eccentricity migration scenarios.

Cosmic Rays from Transrelativistic Supernovae

We derive constraints that must be satisfied by the sources of ~1015 to ~1018 eV cosmic rays, under the assumption that the sources are Galactic. We show that while these constraints are not satisfied by ordinary supernovae (SNe), which are believed to be the sources of 1015 eV cosmic rays, they may be satisfied by the recently discovered class of transrelativistic supernovae (TRSNe), which were observed in association with gamma-ray bursts. We define TRSNe as SNe that deposit a large fraction, -->fR > 10−2, of their kinetic energy in mildly relativistic, -->γ β > 1, ejecta. The high-velocity ejecta enable particle acceleration to ~1018 eV, and the large value of fR (compared to -->fR ~ 10−7 for ordinary SNe) ensures that if TRSNe produce the observed ~1018 eV cosmic-ray flux, they do not overproduce the flux at lower energies. This, combined with the estimated rate and energy production of TRSNe, imply that Galactic TRSNe may be the sources of cosmic rays with energies up to ~1018 eV.

Magnetic fields and cosmic rays in clusters of galaxies

We argue that the observed correlation between the radio luminosity and the thermal X-ray luminosity of radio emitting galaxy clusters implies that the radio emission is due to secondary electrons that are produced by p-p interactions and lose their energy by emitting synchrotron radiation in a strong magnetic field, B > (8πaTCMB4)1/2 3 μG. We construct a simple model that naturally explains the correlation, and show that the observations provide stringent constraints on cluster magnetic fields and cosmic rays (CRs): Within the cores of clusters, the ratio βcore between the CR energy (per logarithmic particle energy interval) and the thermal energy is βcore ~ 2 10−4; The source of these CRs is most likely the cluster accretion shock, which is inferred to deposit in CRs ~ 0.1 of the thermal energy it generates; The diffusion time of 100 GeV CRs over scales 100 kpc is not short compared to the Hubble time; Cluster magnetic fields are enhanced by mergers to 1% of equipartition, and decay (to < 1 μG) on 1 Gyr time scales. The inferred value of βcore implies that high energy gamma-ray emission from secondaries at cluster cores will be difficult to detect with existing and planned instruments.

AMS-02 Results Support the Secondary Origin of Cosmic Ray Positrons

We show that the recent AMS-02 positron fraction measurement is consistent with a secondary origin for positrons and does not require additional primary sources such as pulsars or dark matter. The measured positron fraction at high energy saturates the previously predicted upper bound for secondary production, obtained by neglecting radiative losses. This coincidence, which will be further tested by upcoming AMS-02 data at higher energy, is a compelling indication for a secondary source. Within the secondary model, the AMS-02 data imply a cosmic ray propagation time in the Galaxy of <10(6) yr and an average traversed interstellar matter density of ~1 cm(-3), comparable to the density of the Milky Way gaseous disk, at a rigidity of 300 GV.

RELATIVISTIC RADIATION MEDIATED SHOCKS

The structure of relativistic radiation mediated shocks (RRMSs) propagating into a cold electron-proton plasma is calculated and analyzed. A qualitative discussion of the physics of relativistic and non-relativistic shocks, including order of magnitude estimates for the relevant temperature and length scales, is presented. Detailed numerical solutions are derived for shock Lorentz factors ? u in the range 6 ? ? u ? 30, using a novel iteration technique solving the hydrodynamics and radiation transport equations (the protons, electrons, and positrons are argued to be coupled by collective plasma processes and are treated as a fluid). The shock transition (deceleration) region, where the Lorentz factor ? drops from ? u to ~1, is characterized by high plasma temperatures T ~ ?mec 2 and highly anisotropic radiation, with characteristic shock-frame energy of upstream (US) and downstream (DS) going photons of a few ? mec 2 and ~?2 mec 2, respectively. Photon scattering is dominated by e ? pairs, with the pair-to-proton density ratio reaching 102? u . The width of the deceleration region, in terms of Thomson optical depths for US-going photons, is large, ?? ~ ?2 u (?? ~ 1 neglecting the contribution of pairs) due to Klein-Nishina suppression of the scattering cross section. A high-energy photon component, narrowly beamed in the DS direction, with a nearly flat power-law-like spectrum, ?I ? ?0, and an energy cutoff at ~?2 u mec 2 carries a fair fraction of the energy flux at the end of the deceleration region. An approximate analytic model of RRMS, reproducing the main features of the numerical results, is provided.

X-rays, γ-rays and neutrinos from collisionless shocks in supernova wind breakouts

We show that a collisionless shock necessarily forms during the shock breakout of a supernova (SN) surrounded by an optically thick wind. An intense non-thermal flash of <~ MeV gamma rays, hard X-rays and multi-TeV neutrinos is produced simultaneously with and following the soft X-ray breakout emission, carrying similar or larger energy than the soft emission. The non-thermal flash is detectable by current X-ray telescopes and may be detectable out to 10s of Mpc by km-scale neutrino telescopes.

NON-RELATIVISTIC RADIATION-MEDIATED SHOCK BREAKOUTS. I. EXACT BOLOMETRIC PLANAR BREAKOUT SOLUTIONS

The problem of a non-steady planar radiation mediated shock (RMS) breaking out from a surface with a power-law density profile, �/ x n , is numerically solved in the approximation of diffusion with constant opacity. For an appropriate choice of time, length and energy scales, determined by the breakout opacity, velocity and density, the solution is universal, i.e. depends only on the density power law index n. The resulting luminosity depends weakly on the value of n. An approximate analytic solution, based on the self-similar hydrodynamic solutions (Sakurai 1960) and on the steady RMS solutions (e.g. Weaver 1976), is constructed and shown to agree with the numerical solutions as long as the shock is far from the surface, � � c/vsh. Approximate analytic expressions, calibrated based on the exact solutions, are p rovided, that describe the escaping luminosity as a function of time. These results can be used to calculate the bolometric properties of the bursts of radiation produced during supernova (SN) shock breakouts. For completeness, we also use the exact breakout solutions to provide an analytic approximation for the maximum surface temperature for fast (vsh & 0.1) non-thermal breakouts, and show that it is few times smaller than inferred based on steady-state RMS solutions. Subject headings:radiation hydrodynamics — shock waves — supernovae: general

Self-Similar Collisionless Shocks

Observations of γ-ray burst afterglows suggest that the correlation length of magnetic field fluctuations downstream of relativistic nonmagnetized collisionless shocks grows with distance from the shock to scales much larger than the plasma skin depth. We argue that this indicates that the plasma properties are described by a self-similar solution and derive constraints on the scaling properties of the solution. For example, we find that the scaling of the characteristic magnetic field amplitude with distance from the shock is B DsB, with -1 < sB ≤ 0; that the spectrum of accelerated particles is dn/dE E−2/(sB + 1); and that the scaling of the magnetic correlation function is Bi(x)Bj(x + Δx) Δx2sB (for Δx D). We show that the plasma may be approximated as a combination of two self-similar components: a kinetic component of energetic particles and an MHD-like component representing thermal particles. We argue that the latter may be considered as infinitely conducting, in which case sB = 0 and the scalings are completely determined (e.g., dn/dE E-2 and B D0, with possible logarithmic corrections). Similar claims apply to nonrelativistic shocks such as in supernova remnants, if the upstream magnetic field can be neglected. Self-similarity has important implications for any model of particle acceleration and/or field generation. For example, we show that the diffusion function in the angle μ of momentum p in diffusive shock acceleration models must satisfy Dμμ(p,D) = D-1μμ(p/D) (where p is the particle momentum) and that a previously suggested model for the generation of large-scale magnetic fields through a hierarchical merger of current filaments should be generalized. A numerical experiment testing our analysis is outlined.

NON-RELATIVISTIC RADIATION MEDIATED SHOCK BREAKOUTS. III. SPECTRAL PROPERTIES OF SUPERNOVA SHOCK BREAKOUT

The spectrum of radiation emitted following shock breakout from a star’s surface with a power-law density profile � ∝ x n is investigated. Assuming planar geometry, local Compton equilibrium and bremsstrahlung emission as the dominant photon production mechanism, numerical solutions are obtained for the photon number density and temperature profiles as a function of time, fo r hydrogen-helium envelopes. The temperature solutions are determined by the breakout shock velocity v0 and the pre-shock breakout density �0, and depend weakly on the value of n. Fitting formulas for the peak surface temperature at break out as a function of v0 and �0 are provided, with Tpeak ≈ 9.44 exp[12.63(v0/c) 1/2 ] eV, and the time dependence of the surface temperature is tabulated. The time integrated emitted spectrum is a robu st prediction of the model, determined by Tpeak and v0 alone and insensitive to details of light travel time or slig ht deviations from spherical symmetry. Adopting commonly assumed progenitor parameters, breakout luminosities of ≈ 10 45 erg s -1 and ≈ 10 44 erg s -1 in the 0.3-10 keV band are expected for BSG and RSG/He-WR progenitors respectively (Tpeak is well below the band for RSGs, unless their radius is ∼ 10 13 cm). > 30 detections of SN1987A-like (BSG) breakouts are expected over the lifetime of ROSAT and XMM-Newton. An absence of such detections would imply that either the typical parameters assumed for BSG progenitors are grossly incorrect or that their envelopes are not hydrostatic. The observed spectrum and duration of XRF 080109/SN2008D are in tension with a non-relativistic breakout from a stellar surface interpretation. Subject headings:radiation hydrodynamics — shock waves — supernovae: general