Non-linear shock acceleration and high energy gamma rays from clusters of galaxies

Merger and accretion shocks in clusters of galaxies can accelerate particles via first order Fermi process. Since this mechanism is believed to be intrinsically efficient, shocks are expected to be modified by the backreaction of the accelerated particles. Such a modification might induce appreciable effects on the non--thermal emission from clusters and a suppression of the heating of the gas at strong shocks. Here we consider in particular the gamma ray emission and we discuss the capability of Cherenkov telescopes such as HESS to detect clusters at TeV energies.Comment: 6 pages, to appear in the proceedings of the Gamma 2004 Symposium on High Energy Gamma Ray Astronomy, Heidelberg, July 2004 (AIP Proceedings Series

Dynamics and High Energy Emission of the Flaring HST-1 Knot in the M 87 Jet

Stimulated by recent observations of a radio-to-X-ray synchrotron flare from HST-1, the innermost knot of the M 87 jet, as well as by a detection of a very high energy gamma-ray emission from M 87, we investigated the dynamics and multiwavelength emission of the HST-1 region. We study thermal pressure of the hot interstellar medium in M 87 and argue for a presence of a gaseous condensation in its central parts. Interaction of the jet with such a feature is likely to result in formation of a converging reconfinement shock in the innermost parts of the M 87 jet. We show that for a realistic set of the outflow parameters, a stationary and a flaring part of the HST-1 knot located \~100 pc away from the active center can be associated with the decelerated portion of the jet matter placed immediately downstream of the point where the reconfinement shock reaches the jet axis. We discuss a possible scenario explaining a broad-band brightening of the HST-1 region related to the variable activity of the central core. We show that assuming a previous epoch of the high central black hole activity resulting in ejection of excess particles and photons down along the jet, one may first expect a high-energy flare of HST-1 due to inverse-Comptonisation of the nuclear radiation, followed after a few years by an increase in the synchrotron continuum of this region. If this is the case, then the recently observed increase in the knot luminosity in all spectral bands could be regarded as an unusual echo of the outburst that had happened previously in the active core of the M 87 radio galaxy.Comment: 30 pages, 7 figures included. Accepted for publication in MNRA

Self-Similar Collisionless Shocks

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<s_B<=0, that the spectrum of accelerated particles is dn/dE \propto E^{-2/(s_B+1)}, and that the scaling of the magnetic correlation function is \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 \mu of momentum p in diffusive shock acceleration models must satisfy D_{\mu\mu}(p,D) = D^{-1}D'_{\mu\mu}(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).Comment: 16 pages, 1 figure, accepted for publication in Ap

Analytical Study of Diffusive Relativistic Shock Acceleration

Particle acceleration in relativistic shocks is studied analytically in the test-particle, small-angle scattering limit, for an arbitrary velocity-angle diffusion function D. Accurate analytic expressions for the spectral index s are derived using few (2-6) low-order moments of the shock-frame angular distribution. For isotropic diffusion, previous results are reproduced and justified. For anisotropic diffusion, s is shown to be sensitive to D, particularly downstream and at certain angles, and a wide range of s values is attainable. The analysis, confirmed numerically, can be used to test collisionless shock models and to observationally constrain D. For example, strongly forward- or backward-enhanced diffusion downstream is ruled out by GRB afterglow observations.Comment: 4 pages, 2 figures, PRL accepted, minor change

On the Interaction of the PKS B1358-113 Radio Galaxy with the Abell 1836 Cluster

[abridged] Here we present the analysis of multifrequency data gathered for the FRII radio galaxy PKS B1358-113, hosted in the brightest cluster galaxy of Abell 1836. The galaxy harbors one of the most massive black holes known to date and our analysis of the optical data reveals that this black hole is only weakly active. Based on new Chandra and XMM-Newton X-ray observations and archival radio data we derive the preferred range for the jet kinetic luminosity $\sim (0.5-3) \times 10^{45}$ erg s$^{-1}$. This is above the values implied by various scaling relations proposed for radio sources in galaxy clusters, being instead very close to the maximum jet power allowed for the given accretion rate. We constrain the radio source lifetime as $\sim 40-70$ Myrs, and the total amount of deposited jet energy $\sim (2-8) \times 10^{60}$\,ergs. The detailed analysis of the X-ray data provides indication for the presence of a bow-shock driven by the expanding radio lobes into the Abell 1836 cluster environment, with the corresponding Mach number $\sim 2-4$. This, together with the recently growing evidence that powerful FRII radio galaxies may not be uncommon in the centers of clusters at higher redshifts, supports the idea that jet-induced shock heating may indeed play an important role in shaping the properties of clusters, galaxy groups, and galaxies in formation. We speculate on a possible bias against detecting jet-driven shocks in poorer environments, resulting from an inefficient electron heating at the shock front, combined with a relatively long electron-ion equilibration timescale.Comment: Version accepted to Ap

A differentiable characterization of local contractions on Banach spaces

This note provides a differentiable characterization of local contractions on an arbitrary Banach space. As a corollary, a refinement to Ostrowski’s sufficient condition for local convergence in finite spaces is obtained, which applies to many models, e.g. in economics, ecology or game theory, where one has an interest in fixed point iterations and local stability of discrete dynamic processes. We show that for the local contraction property to hold, continuity of the derivative at the fixed point is indispensable

No Tradeoff between Coherence and Sub-Poissonianity for Heisenberg-Limited Lasers

The Heisenberg limit to laser coherence $\mathfrak{C}$ -- the number of photons in the maximally populated mode of the laser beam -- is the fourth power of the number of excitations inside the laser. We generalize the previous proof of this upper bound scaling by dropping the requirement that the beam photon statistics be Poissonian (i.e., Mandel's $Q=0$). We then show that the relation between $\mathfrak{C}$ and sub-Poissonianity ($Q<0$) is win-win, not a tradeoff. For both regular (non-Markovian) pumping with semi-unitary gain (which allows $Q\xrightarrow{}-1$), and random (Markovian) pumping with optimized gain, $\mathfrak{C}$ is maximized when $Q$ is minimized.Comment: This is a companion letter to the manuscript entitled "Optimized Laser Models with Heisenberg-Limited Coherence and Sub-Poissonian Beam Photon Statistics", arxiv:2208.14082. 6 pages, 2 figure

Optimized Laser Models with Heisenberg-Limited Coherence and Sub-Poissonian Beam Photon Statistics

Recently it has been shown that it is possible for a laser to produce a stationary beam with a coherence (quantified as the mean photon number at spectral peak) which scales as the fourth power of the mean number of excitations stored within the laser, this being quadratically larger than the standard or Schawlow-Townes limit [1]. Moreover, this was analytically proven to be the ultimate quantum limit (Heisenberg limit) scaling under defining conditions for CW lasers, plus a strong assumption about the properties of the output beam. In Ref. [2], we show that the latter can be replaced by a weaker assumption, which allows for highly sub-Poissonian output beams, without changing the upper bound scaling or its achievability. In this Paper, we provide details of the calculations in Ref. [2], and introduce three new families of laser models which may be considered as generalizations of those presented in that work. Each of these families of laser models is parameterized by a real number, $p$, with $p=4$ corresponding to the original models. The parameter space of these laser families is numerically investigated in detail, where we explore the influence of these parameters on both the coherence and photon statistics of the laser beams. Two distinct regimes for the coherence may be identified based on the choice of $p$, where for $p>3$, each family of models exhibits Heisenberg-limited beam coherence, while for $p<3$, the Heisenberg limit is no longer attained. Moreover, in the former regime, we derive formulae for the beam coherence of each of these three laser families which agree with the numerics. We find that the optimal parameter is in fact $p\approx4.15$, not $p=4$.Comment: This is a companion manuscript to the letter entitled "No Tradeoff between Coherence and Sub-Poissonianity for Heisenberg-Limited Lasers", arxiv:2208.14081. 22 pages, 11 figure