arXiv subjects
Publications and source records attributed to Boaz Katz.
Simple expressions for the radius and magnetic field of a system emitting Synchrotron-self-absorbed radio and Inverse Compton X-rays are derived from first principles which involve observable quantities only. These expressions are useful for analyzing observations of Supernova blastwaves interacting with dense circumstellar material at early times.
Kozai-Lidov oscillations of Jupiter-mass planets, excited by comparable planetary or brown dwarf mass perturbers were recently shown in numerical experiments to be slowly modulated and to exhibit striking features, including extremely high eccentricities and the generation of retrograde orbits with respect to the perturber. Here we solve this problem analytically for the case of a test particle orbiting a host star and perturbed by a distant companion whose orbit is eccentric and highly inclined. We give analytic expressions for the conditions that produce retrograde orbits and high eccentricities. This mechanism likely operates in various systems thought to involve Kozai-Lidov oscillations such as tight binaries, mergers of compact objects, irregular moons of planets and many others. In particular, it could be responsible for exciting eccentricities and inclinations of exo-planetary orbits and be important for understanding the spin-orbit (mis)alignment of hot Jupiters.
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 10's of Mpc by km-scale neutrino telescopes.
The Kozai mechanism for exponentially exciting eccentricity of a Keplerian orbit by a distant perturber is extended to a general perturbing potential. In particular, the case of an axisymmetric potential is solved analytically. The analysis is applied to orbits around an oblate central object with a distant perturber. If the equatorial plane of the central object is aligned with the orbit of the distant perturber (axisymmetric potential), a single instability zone, in which eccentricity grows exponentially, is found between two critical inclinations; if misaligned (non-axisymmetric potential), a rich set of critical inclinations separating stable and unstable zones is obtained (Vashkoviak 1974). The analysis is also applied to a general quadratic potential. Similarly, for non-axisymmetric cases, multiple stability and instability zones are obtained. Here eccentricity can reach very high values in the instability zones even when the potential's deviation from axisymmetry is small.
Exact bolometric light curves of supernova shock breakouts are derived based on the universal, non relativistic, planar breakout solutions (Sapir et al. 2011), assuming spherical symmetry, constant Thomson scattering opacity, κ, and angular intensity corresponding to the steady state planar limit. These approximations are accurate for progenitors with a scale height much smaller than the radius. The light curves are insensitive to the density profile and are determined by the progenitor radius R, and the breakout velocity and density, v_0 and ρ_0 respectively, and κ. The total breakout energy, E_BO, and the maximal ejecta velocity, v_max, are shown to be E_BO=8.0πR^2κ^-1cv_0 and v_max=2.0v_0 respectively, to an accuracy of about 10%. The calculated light curves are valid up to the time of transition to spherical expansion, t_sph\approx R/4v_0. Approximate analytic expressions for the light curves are provided for breakouts in which the shock crossing time at breakout, t_0=c/κρ_0v_0^2, is << R/c (valid for R<10^14 cm). Modifications of the flux angular intensity distribution and differences in shock arrival times to the surface, Δt_asym, due to moderately asymmetric explosions, affect the early light curve but do not affect v_max and E_BO. For 4v_0<<c, valid for large (RSG) progenitors, L\propto t^{-4/3} at max(Δt_asym,R/c)< t<t_sph and R may be accurately estimated from R\approx 2*10^13 (L/10^43 erg s^-1)^{2/5}(t/1 hr)^{8/15}.
The problem of a non-steady planar radiation mediated shock (RMS) breaking out from a surface with a power-law density profile, ρ\propto 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 and on the steady RMS solutions, is constructed and shown to agree with the numerical solutions as long as the shock is far from the surface, τ>> c/v_{sh}. Approximate analytic expressions, calibrated based on the exact solutions, are provided, 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 (v_{sh}>~0.1) non-thermal breakouts, and show that it is few times smaller than inferred based on steady-state RMS solutions.
We derive expressions for the time integrated spectrum of Cosmic Rays (CRs) that are accelerated in a decelerating relativistic shock wave and escape ahead of the shock. It is assumed that at any given time the CRs have a power law form, carry a constant fraction of the energy E_tot of the shocked plasma, and escape continuously at the maximal energy attainable. The spectrum of escaping particles is highly sensitive to the instantaneous spectral index due to the fact that the minimal energy, E_min ~ Γ^2 m_pc^2 where Γis the shock Lorentz factor, changes with time. In particular, the escaping spectrum may be considerably harder than the canonical N(E)\propto E^-2 spectrum. For a shock expanding into a plasma of density n, a spectral break is expected at the maximal energy attainable at the transition to non relativistic velocities, E ~ 10^19 (ε_B/0.1)(n/1 cm^-3)^(1/6)(E_tot/10^51 erg)^(1/3) eV where ε_B is the fraction of the energy flux carried by the magnetic field. If ultra-high energy CRs are generated in decelerating relativistic blast waves arising from the explosion of stellar mass objects, their generation spectrum may therefore be different than the canonical N(E)\propto E^-2.
We present a simple analytic model for the structure of non-relativistic and relativistic radiation mediated shocks. At shock velocities β_s\equiv v_s/c\gtrsim 0.1, the shock transition region is far from thermal equilibrium, since the transition crossing time is too short for the production of a black-body photon density (by Bremsstrahlung emission). In this region, electrons and photons (and positrons) are in Compton (pair) equilibrium at temperatures T_s significantly exceeding the far downstream temperature, T_s\gg T_d\approx 2(\varepsilon n_u \hbar^3c^3)^{1/4}. T_s\gtrsim 10 keV is reached at shock velocities β_s\approx 0.2. At higher velocities, β_s\gtrsim0.6, the plasma is dominated in the transition region by e^\pm pairs and 60 keV\lesssim T_s \lesssim 200 keV. We argue that the spectrum emitted during the breaking out of supernova shocks from the stellar envelopes (or the surrounding winds) of Blue Super Giants and Wolf-Rayet stars, which reach β_s>0.1 for reasonable stellar parameters, may include a hard component with photon energies reaching tens or even hundreds of keV. This may account for the X-ray outburst associated with SN2008D, and possibly for other SN-associated outbursts with spectra not extending beyond few 100 keV (e.g. XRF060218/SN2006aj).
The growth rate of long wavelength kinetic instabilities arising due to the interaction of a collimated beam of relativistic particles and a cold unmagnetized plasma are calculated in the ultra relativistic limit. For sufficiently culminated beams, all long wave-length modes are shown to be Weibel-unstable, and a simple analytic expression for their growth rate is derived. For large transverse velocity spreads, these modes become stable. An analytic condition for stability is given. These analytic results, which generalize earlier ones given in the literature, are shown to be in agreement with numerical solutions of the dispersion equation and with the results of novel PIC simulations in which the electro-magnetic fields are restricted to a given k-mode. The results may describe the interaction of energetic cosmic rays, propagating into the far upstream of a relativistic collisionless shock, with a cold unmagnetized upstream. The long wavelength modes considered may be efficient in deflecting particles and could be important for diffusive shock acceleration. It is shown that while these modes grow in relativistic shocks propagating into electron-positron pair plasmas, they are damped in relativistic shocks propagating into electron-proton plasmas with moderate Lorenz factors Γ_{sh}\lesssim 100. If these modes dominate the deflection of energetic cosmic rays in electron-positron shocks, it is argued that particle acceleration is suppressed at shock frame energies that are larger than the downstream thermal energy by a factor greater than the shock Lorentz factor.
The structure of relativistic radiation mediated shocks (RRMS) 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 $Γ_u$ in the range $6\leΓ_u\le30$, 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 $ Γ$ drops from $ Γ_u $ to $ \sim 1 $, is characterized by high plasma temperatures $ T\sim Γm_ec^2 $ and highly anisotropic radiation, with characteristic shock-frame energy of upstream and downstream going photons of a few~$\times\, m_ec^2$ and $\sim Γ^2 m_ec^2$, respectively.Photon scattering is dominated by e$^\pm$ pairs, with pair to proton density ratio reaching $\approx10^2Γ_u$. The width of the deceleration region, in terms of Thomson optical depths for upstream going photons, is large, $Δτ\simΓ_u^2$ ($Δτ\sim1$ neglecting the contribution of pairs) due to Klein Nishina suppression of the scattering cross section. A high energy photon component, narrowly beamed in the downstream direction, with a nearly flat power-law like spectrum, $νI_ν\proptoν^0$, and an energy cutoff at $ \sim Γ_u^2 m_ec^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.
We present a critical analysis of the observational constraints on, and of the theoretical modeling of, aspects of cosmic ray (CR) generation and propagation in the Galaxy, which are relevant for the interpretation of recent positron and anti-proton measurements. We give simple, analytic, model independent expressions for the secondary pbar flux, and an upper limit for the secondary e+ flux, obtained by neglecting e+ radiative losses, e+/(e+ + e-)<0.2\pm0.1 up to ~300 GeV. These expressions are completely determined by the rigidity dependent grammage, which is measured from stable CR secondaries up to ~150 GeV/nuc, and by nuclear cross sections measured in the laboratory. pbar and e+ measurements, available up to ~100 GeV, are consistent with these estimates, implying that there is no need for new, non-secondary, pbar or e+ sources. The radiative loss suppression factor f_{s,e+} of the e+ flux depends on the e+ propagation in the Galaxy, which is not understood theoretically. A rough, model independent estimate of f_{s,e+} 1/3 can be obtained at a single energy, E\sim20 GeV, from unstable secondary decay and is found to be consistent with e+ measurements, including the positron fraction measured by PAMELA. We show that specific detailed models, that agree with compositional CR data, agree with our simple expressions for the e+ and pbar flux, and that the claims that the positron fraction measured by PAMELA requires new primary e+ sources are based on assumptions, that are not supported by observations. If PAMELA results are correct, they suggest that f_{s,e+} is slightly increasing with energy, which provides an interesting constraint on CR propagation models. We argue that measurements of the e+ to pbar ratio are more useful for challenging secondary production models than the positron fraction.
We argue that the observed correlation between the radio luminosity and the X-ray luminosity in 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>(8πa T_{CMB}^4)^{1/2}\simeq 3\muG. 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 beta_{core} between the CR energy (per logarithmic particle energy interval) and the thermal energy is beta_{core}\sim 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 \gtrsim100 kpc is not short compared to the Hubble time; Cluster magnetic fields are enhanced by mergers to \gtrsim 1 % of equipartition, and decay (to <1 muG) on 1 Gyr time scales. The inferred value of beta_{core} implies that high energy gamma-ray emission from secondaries at cluster cores will be difficult to detect with existing and planned instruments.
We derive simple analytic expressions for the flux and spectrum of ultra-high energy cosmic-rays (UHECRs) predicted in models where the CRs are protons produced by extra-Galactic sources. For a power-law scaling of the CR production rate with redshift and energy, d\dot{n} /dE\propto E^-α(1+z)^m, our results are accurate at high energy, E>10^18.7 eV, to better than 15%, providing a simple and straightforward method for inferring d\dot{n}/dE from the observed flux at E. We show that current measurements of the UHECR spectrum, including the latest Auger data, imply E^2d\dot{n}/dE(z=0)=(0.45\pm0.15)(α-1) 10^44 erg Mpc^-3 yr^-1 at E<10^19.5 eV with αroughly confined to 2\lesseqα<2.7. The uncertainty is dominated by the systematic and statistic errors in the experimental determination of individual CR event energy, (ΔE/E)_{sys} (ΔE/E)_{stat} ~20%. At lower energy, d\dot{n}/dE is uncertain due to the unknown Galactic contribution. Simple models in which α\simeq 2 and the transition from Galactic to extra-Galactic sources takes place at the "ankle", E ~10^19 eV, are consistent with the data. Models in which the transition occurs at lower energies require a high degree of fine tuning and a steep spectrum, α\simeq 2.7, which is disfavored by the data. We point out that in the absence of accurate composition measurements, the (all particle) energy spectrum alone cannot be used to infer the detailed spectral shapes of the Galactic and extra-Galactic contributions.
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.
For more than fifty years, it has been believed that cosmic ray (CR) nuclei are accelerated to high energies in the rapidly expanding shockwaves created by powerful supernova explosions. Yet observational proof of this conjecture is still lacking. Recently, Uchiyama and collaborators reported the detection of small-scale X-ray flares in one such supernova remnant, dubbed 'RX J1713-3946' (a.k.a. G347.3-0.5), which also emits very energetic, TeV (10^12 eV) range, gamma-rays. They contend that the variability of these X-ray 'hotspots' implies that the magnetic field in the remnant is about a hundred times larger than normally assumed; and this, they say, means that the detected TeV range photons were produced in energetic nuclear interactions, providing 'a strong argument for acceleration of protons and nuclei to energies of 1 PeV (10^15 eV) and beyond in young supernova remnants.' We point out here that the existing multiwavelength data on this object certainly do not support such conclusions. Though intriguing, the small-scale X-ray flares are not the long sought-after 'smoking gun' of nucleonic CR acceleration in SNRs.
We present a simple analytic model for the various contributions to the non-thermal emission from shell type SNRs, and show that this model's results reproduce well the results of previous detailed calculations. We show that the \geq 1 TeV gamma ray emission from the shell type SNRs RX J1713.7-3946 and RX J0852.0-4622 is dominated by inverse-Compton scattering of CMB photons (and possibly infra-red ambient photons) by accelerated electrons. Pion decay (due to proton-proton collisions) is shown to account for only a small fraction, \lesssim10^-2, of the observed flux, as assuming a larger fractional contribution would imply nonthermal radio and X-ray synchrotron emission and thermal X-ray Bremsstrahlung emission that far exceed the observed radio and X-ray fluxes. Models where pion decay dominates the \geq 1 TeV flux avoid the implied excessive synchrotron emission (but not the implied excessive thermal X-ray Bremsstrahlung emission) by assuming an extremely low efficiency of electron acceleration, K_ep \lesssim 10^-4 (K_ep is the ratio of the number of accelerated electrons and the number of accelerated protons at a given energy). We argue that observations of SNRs in nearby galaxies imply a lower limit of K_ep \gtrsim 10^-3, and thus rule out K_ep values \lesssim 10^-4 (assuming that SNRs share a common typical value of K_ep). It is suggested that SNRs with strong thermal X-ray emission, rather than strong non-thermal X-ray emission, are more suitable candidates for searches of gamma rays and neutrinos resulting from proton-proton collisions. In particular, it is shown that the neutrino flux from the SNRs above is probably too low to be detected by current and planned neutrino observatories (Abridged).
Observations of gamma-ray burst afterglows suggest that the correlation length of magnetic field fluctuations downstream of relativistic non-magnetized 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 \propto D^{s_B} with -1 \propto x^{2s_B} (for x>>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 s_B=0 and the scalings are completely determined (e.g. dn/dE \propto E^{-2} and B \propto D^0). Similar claims apply to non- relativistic 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 μof momentum p in diffusive shock acceleration models must satisfy D_{μμ}(p,D) = D^{-1}D'_{μμ}(p/D), 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 (Abridged).
The AdS/CFT correspondence relates deformations of the CFT by "multi-trace operators" to "non-local string theories". The deformed theories seem to have non-local interactions in the compact directions of space-time; in the gravity approximation the deformed theories involve modified boundary conditions on the fields which are explicitly non-local in the compact directions. In this note we exhibit a particular non-local property of the resulting space-time theory. We show that in the usual backgrounds appearing in the AdS/CFT correspondence, the commutator of two bulk scalar fields at points with a large enough distance between them in the compact directions and a small enough time-like distance between them in AdS vanishes, but this is not always true in the deformed theories. We discuss how this is consistent with causality.