Finite Opening Angle Research Articles

Luminosity selection for gamma-ray bursts

Aims.There exists inevitable scatter in the intrinsic luminosity of gamma-ray bursts (GRBs). If there is relativistic beaming in the source, viewing angle variation necessarily introduces variation in the intrinsic luminosity function (ILF). Scatter in the ILF can cause selection bias where sources detected at distance have a greater median luminosity than those detected close by. Median luminosity divides any given population into equal halves. When the functional form of a distribution is unknown, it can be a more robust diagnostic than those that use trial functional forms.Method.In this work, we employ a statistical test based on median luminosity and use it to test a class of models for GRBs. We assume that the GRB jet has a finite opening angle and that the orientation of the GRB jet is random relative to the observer. We calculateLmedianas a function of redshift by simulating GRBs empirically and theoretically, and use the luminosity-vs.-redshiftSwiftdata in order to compare the theoretical results with the observed ones. The method accounts for the fact that there may be GRBs that go undetected at some redshifts.Results.We find thatLmedianis extremely insensitive to the on-axis (i.e., maximal) luminosity of the jet.

Radiation beaming in the quantum regime

Classical theories of radiation reaction predict that the electron motion is confined to the plane defined by the electron's instantaneous momentum and the force exerted by the external electromagnetic field. However, in the quantum radiation reaction regime, where the recoil exerted by individual quanta becomes significant, the electron can scatter `out-of-plane', as the photon is emitted into a cone with finite opening angle. We show that Monte Carlo implementation of an angularly resolved emission rate leads to substantially improved agreement with exact QED calculations of nonlinear Compton scattering. Furthermore, we show that the transverse recoil caused by this finite beaming, while negligible in many high-intensity scenarios, can be identified in the increase in divergence, in the plane perpendicular to the polarization, of a high-energy electron beam that interacts with a linearly polarized, ultraintense laser.

Fast logarithmic Fourier-Laplace transform of nonintegrable functions.

We present an efficient and very flexible numerical fast Fourier-Laplace transform that extends the logarithmic Fourier transform introduced by Haines and Jones [Geophys. J. Int. 92, 171 (1988)GJINEA0956-540X10.1111/j.1365-246X.1988.tb01131.x] for functions varying over many scales to nonintegrable functions. In particular, these include cases of the asymptotic form f(ν→0)∼ν^{a} and f(|ν|→∞)∼ν^{b} with arbitrary real a>b. Furthermore, we prove that the numerical transform converges exponentially fast in the number of data points, provided that the function is analytic in a cone |Imν|<θ|Reν| with a finite opening angle θ around the real axis and satisfies |f(ν)f(1/ν)|<ν^{c} as ν→0 with a positive constant c, which is the case for the class of functions with power-law tails. Based on these properties we derive ideal transformation parameters and discuss how the logarithmic Fourier transform can be applied to convolutions. The ability of the logarithmic Fourier transform to perform these operations on multiscale (nonintegrable) functions with power-law tails with exponentially small errors makes it the method of choice for many physical applications, which we demonstrate on typical examples. These include benchmarks against known analytical results inaccessible to other numerical methods, as well as physical models near criticality.

Relativistic HD and MHD modelling for AGN jets

Relativistic hydro and magnetohydrodynamics (MHD) provide a continuum fluid description for plasma dynamics characterized by shock-dominated flows approaching the speed of light. Significant progress in its numerical modelling emerged in the last two decades; we highlight selected examples of modern grid-adaptive, massively parallel simulations realized by our open-source software MPI-AMRVAC (Keppens et al 2012 J. Comput. Phys. 231 718). Hydrodynamical models quantify how energy transfer from active galactic nuclei (AGN) jets to their surrounding interstellar/intergalactic medium (ISM/IGM) gets mediated through shocks and various fluid instability mechanisms (Monceau-Baroux et al 2012 Astron. Astrophys. 545 A62). With jet parameters representative for Fanaroff–Riley type-II jets with finite opening angles, we can quantify the ISM volumes affected by jet injection and distinguish the roles of mixing versus shock-heating in cocoon regions. This provides insight in energy feedback by AGN jets, usually incorporated parametrically in cosmological evolution scenarios. We discuss recent axisymmetric studies up to full 3D simulations for precessing relativistic jets, where synthetic radio maps can confront observations. While relativistic hydrodynamic models allow one to better constrain dynamical parameters like the Lorentz factor and density contrast between jets and their surroundings, the role of magnetic fields in AGN jet dynamics and propagation characteristics needs full relativistic MHD treatments. Then, we can demonstrate the collimating properties of an overal helical magnetic field backbone and study differences between poloidal versus toroidal field dominated scenarios (Keppens et al 2008 Astron. Astrophys. 486 663). Full 3D simulations allow one to consider the fate of non-axisymmetric perturbations on relativistic jet propagation from rotating magnetospheres (Porth 2013 Mon. Not. R. Astron. Soc. 429 2482). Self-stabilization mechanisms related to the detailed magnetic pitch variations are discussed.

The effect of angular opening on the dynamics of relativistic hydro jets

Context. Relativistic jets emerging from AGN cores transfer energy from the core to their surrounding ISM/IGM. Because jets are observed to have finite opening angles, one needs to quantify the role of conical versus cylindrical jet propagation in this energy transfer. Aims. We use FR-II AGN jets parameter with finite opening angles. We study the effect of the variation of the opening angle on the dynamics and energy transfer of the jet. We also point out how the characteristics of this external medium, such as its density profile, play a role in the dynamics. Methods. This study exploits our parallel AMR code MPI-AMRVAC with its special relativistic hydrodynamic model, incorporating an equation of state with varying effective polytropic index. We studied mildly under-dense jets up to opening angles of 10 degrees, at Lorentz factors of about 10, inspired by observations. Instantaneous quantification of the various ISM volumes and their energy content allows one to quantify the role of mixing versus shock-heated cocoon regions over the time intervals. Results. We show that a wider opening angle jet results in a faster deceleration of the jet and leads to a wider cocoon dominated by Kelvin-Helmholtz and Rayleigh-Taylor instabilities. The energy transfer mainly occurs in the shocked ISM region by both the frontal bow shock and cocoon-traversing shock waves, in a roughly 3 to 1 ratio to the energy transfer of the mixing zone, for a 5 degree opening angle jet. A rarefaction wave induces a dynamically formed layered structure of the jet beam. Conclusions. Finite opening angle jets can efficiently transfer significant fractions (25 % up to 70 %) of their injected energy over a growing region of shocked ISM matter. The role of the ISM stratification is prominent for determining the overall volume that is affected by relativistic jet injection.

ANGULAR ENERGY DISTRIBUTION OF COLLAPSAR-JETS

Collapsars are fast-spinning, massive stars, whose core collapse liberates an energy that can be channeled in the form of ultrarelativistic jets. These jets transport the energy from the collapsed core to large distances, where it is dissipated in the form of long-duration gamma-ray bursts. In this paper, we study the dynamics of ultrarelativistic jets produced in collapsars. Also we extrapolate our results to infer the angular energy distribution of the produced outflows in the afterglow phase. Our main focus is to look for global energetical properties which can be imprinted by the different structure of different progenitor stars. Thus, we employ a number of pre-supernova stellar models (with distinct masses and metallicities), and inject in all of them jets with fixed initial conditions. We assume that at the injection nozzle, the jet is mildly relativistic (Lorentz factor of {approx}5), has a finite half-opening angle (5 deg.), and carries a power of 10{sup 51} erg s{sup -1}. In all cases, well collimated jets propagate through the progenitor, blowing a high-pressure and high-temperature cocoon. These jets arrive intact to the stellar surface and break out of it. A large Lorentz factor region {gamma} {approx}> 100 develops well before the jet reaches themore » surface of the star, in the unshocked part of the beam located between the injection nozzle and the first recollimation shock. These high values of {gamma} are possible because the finite opening angle of the jet allows for free expansion toward the radial direction. We find a strong correlation between the angular energy distribution of the jet, after its eruption from the progenitor surface, and the mass of the progenitors. The angular energy distribution of the jets from light progenitor models is steeper than that of the jets injected in more massive progenitor stars. This trend is also imprinted in the angular distribution of isotropic equivalent energy.« less

GAMMA-RAY VARIABILITY FROM WIND CLUMPING IN HIGH-MASS X-RAY BINARIES WITH JETS

In the subclass of high-mass X-ray binaries known as "microquasars", relativistic hadrons in the jets launched by the compact object can interact with cold protons from the star's radiatively driven wind, producing pions that then quickly decay into gamma rays. Since the resulting gamma-ray emissivity depends on the target density, the detection of rapid variability in microquasars with GLAST and the new generation of Cherenkov imaging arrays could be used to probe the clumped structure of the stellar wind. We show here that the fluctuation in gamma rays can be modeled using a "porosity length" formalism, usually applied to characterize clumping effects. In particular, for a porosity length defined by h=l/f, i.e. as the ratio of the characteristic size l of clumps to their volume filling factor f, we find that the relative fluctuation in gamma-ray emission in a binary with orbital separation a scales as sqrt(h/pi a) in the "thin-jet" limit, and is reduced by a factor 1/sqrt(1 + phi a/(2 l)) for a jet with a finite opening angle phi. For a thin jet and quite moderate porosity length h ~ 0.03 a, this implies a ca. 10 % variation in the gamma-ray emission. Moreover, the illumination of individual large clumps might result in isolated flares, as has been recently observed in some massive gamma-ray binaries.

Do the Mildly Superluminal VLBI Knots Exclude Ultrarelativistic Blazar Jets?

We compute the effective values of apparent transverse velocity and flux boosting factors for the VLBI radio knots of blazar jets by integrating over the angular distributions of these quantities across the widths of jets with finite opening angles but constant velocities. For high bulk Lorentz factors (Γ > 10), variations across the jet can be quite large if the opening angle, ω, is even a few degrees on subparsec scales. The resulting apparent speeds are often much lower than those obtained from the usual analyses that ignore the finite jet opening angles. We can thus reconcile the usually observed subluminal or mildly superluminal speeds with the very high (20) Γ factors, required by the inverse Compton origin and rapid variability of TeV fluxes, as well as by intraday radio variability. Thus it is possible to associate the VLBI radio knots directly with shocks in the ultrarelativistic main jet flow, without invoking very rapid jet deceleration on parsec scales or extremely unlikely viewing angles.

On the order of singularity at V-shaped notches in anisotropic bodies

The self-similar problem of stress singularity at the notch in infinite two-dimensional elastic orthotropic body was considered. The considerations were restricted to the notches symmetrically oriented with respect to the axes of orthotropy. Both, the extension and shear modes were studied. It was confirmed that in the limiting case of zero opening angle (semi-infinite crack), the order of singularity is the same as in the case of isotropic material - r -1/2 . This is not true in the case of finite opening angles. If the orientation of the notch axis is parallel to the axis of maximal stiffness, the order of singularity is lower than that for the case of perpendicular orientation. In the last case, if the ratio E T / E L is small enough, then the order of singularity in tension does not practically decrease with growing opening angle 2 α up to α ~= π /4.

Re-examination of crack opening model of interface fracture

The complex singularity associated with a crack at the interface between two dissimilar, isotropic and homogeneous materials leads to mathematical artefacts, such as stress oscillations and crack face interpenetrations in the vicinity of the crack tip. To avoid these unrealistic features, Sinclair (Sinclair GB. On the stress singularity at an interface crack. International Journal of Fracture 1980;16(2):111–9) assumed a finite crack opening angle (COA) such that the singularity λ became real equal to 1/2. This paper extends the COA model by considering real singularities not necessarily equal to 1/2. When COA is 0°, the interface crack singularity is complex with a real part equal to 1/2. On increasing COA, the imaginary part of the singularity decreases and becomes zero at a threshold value of COA; at this point, the singularity is a real, repeated value. A further increase in COA results in a pair of real singularities. Different crack opening configurations and material combinations are studied, and results presented for threshold COAs and associated values of singularity. Stress analyses for these three regimes: (a) complex, (b) real pair and (c) real repeated singularities, are reported. It is seen that additional complexities are present in the last case. Typical results for stress fields are also included for comparing with standard fields.

The large-scale structure of FR-II radio sources

The large-scale flow produced by classical and relativistic jets in a uniform external medium is explored using a combination of general arguments and numerical simulations. We find that in both cases, jets with finite initial opening angles are recollimated by the high pressure in the cocoon and that the outer flow becomes approximately self-similar at large times. However, if the opening angle is significantly less than 20°, then there is an intermediate stage during which the working surface propagates at a constant speed, which is of the same order as that in the jet. The behaviour of the relativistic and classical jets is very similar, except that the relativistic jets generate lighter cocoons. Application of the model to Cygnus A gives estimates of the source age and advance speed which agree very well with spectral ageing observations. Quantitative estimates and general arguments suggest that the regularly spaced knots in the Cygnus A jet can be interpreted as shocks associated with reconfinement of an initially free jet, knot 3 of the Cygnus A jet being identified with the reflection point of the reconfinement shock. However, the model predicts too large an initial opening angle for the Cygnus A jets. It is possible that this discrepancy is due to our imposition of axisymmetry which allows the numerical jets to become much better collimated after the reconfinement than they would be in the three-dimensional case. Further study is needed to test this idea.

Model scattering envelopes of young stellar objects. I - Method and application to circumstellar disks

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Continuous distribution of αt relative kinetic energies in 7Li breakup reactions

A newly developed technique has been used to probe a previously inaccessible region of the continuum in the at channels of 7Li breakup reactions. This was used to investigate reactions of 63 MeV 7Li with 58Ni, 120Sn, 144Sm, and 208Pb targets. Breakup pairs of α-particles and tritons emitted within a finite opening angle were analyzed according to their magnetic rigidity using a K = 150 Enge split-pole spectrograph. The αt coincidences were taken with two single-wire proportional counters mounted at different positions along the focal plane of the spectrograph. The large energy acceptance (Emax/Emin ≈ 8) of the spectrograph is crucial to the present coincidence measurements involving two particles with different q/m values. Very small relative energy components were studied without any detection threshold. A pronounced bump was observed immediately above the αt particle threshold. No strong indication of the post Coulomb acceleration was observed. The excitation of the continuum states as well as the 7−2 state in 7Li is discussed in terms of the distorted-wave Born approximation. The astrophysical implications of the data are also discussed regarding the Coulomb excitation of the continuum. The present technique offers the promise of very high sensitivity at small relative energies if it were applied in conjunction with ray-tracing, a thin target, and a dispersion-matched beam.

Measuring the ISR Impedance at Very High Frequencies by Observing the Energy Loss of a Coasting Beam

A slow energy loss of unbunched protons and antiprotons in the ISR has been observed which is larger than expected for interactions with the residual gas and for synchrotron radiation., It can be explained as a parasitic mode loss due to the wall currents induced by the longitudinal Schottky noise. This noise as seen at the wall of a circular chamber of radius a extends to a typical frequency of the order ? ~ c?/a limited by the finite opening angle of ~1/? of the fields created by a relativisitic particle. Due to the statistical longitudinal distribution of the particles the total energy loss due to the induced wall current is proportional to the total number of particles and the loss per particle becomes independent of current. This loss leads to a steady decrease of the orbit radius which can be observed for long storage times. Using these results obtained at different energies, the frequency dependence of the resistive longitudinal impedance in the range of several tens of GHz is obtained. This impedance is compared with the prediction of the diffraction theory.

Diffraction of a shock wave on a thin wedge moving at supersonic speed under the conditions of sporadic wave interaction: PMM vol. 40, no. 5, 1976, pp. 857–864

The subject of present investigation is the diffraction of a shock wave of arbitrary intensity on a thin wedge moving at a supersonic speed. The plane of the shock wave forms an almost right angle with the symmetry plane of the wedge. The interaction between the fronts is assumed sporadic. Studying the pressure perturbation along the front, a singularity of the type similar to that appearing when a weak pressure jump is diffracted on a wedge of finite opening angle with an attached shock, is discovered. This case was dealt with in [1]. The boundary value problem which is solved here using the results of [2, 3] enables us to find the pressure perturbations at the wall and along the shock front, and obtain the expression for the front in terms of elementary functions. The above problem was analyzed for the case of regular interaction in [3], where a method of generalizing the solution to the case of sporadic interaction was also suggested. The method however turned out to be impracticable.

Spherical harmonic analysis of satellite anisotropy measurements

A method is described whereby a particle distribution measured by a detector telescope mounted on a spinning satellite can be represented by an equivalent set of spherical harmonics. The response of the telescope is determined for each term of the harmonic expansion, and fitted to a set of satellite data, enabling the zero order, and first and second harmonics to be found. The effects of sectoring are introduced, and the limitations of both the sectoring and the finite telescope opening angle upon the angular resolution are evaluated. A method is outlined for including particle scattering in the calculations.

Diffraction of a plane wave on a wedge moving at supersonic speed under conditions of sporadic shock interaction: PMM vol. 38, n≗ 3, 1974, pp. 484–493

The subject of present investigation is the diffraction in such ranges of angles between the fronts of weak incident pressure jump and of an oblique compression shock attached to a wedge of finite opening angle in which the intersection of these occurs at the distorted section of the jump. On the side of smaller angles these ranges border on regions of possible regular interaction between two shocks coming from opposite directions [1], while on the side of greater angles these border of regions of shock waves moving in the same direction, which admit uniform streams in the neighborhood of intersection of fronts [2, 3]. The resulting boundary value problem has much in common with the similar problem of regular counter-interaction which was considered in [4]. In that paper, as in the present one, the method of analysis is related to the problem of perturbations of a uniform stream behind a plane shock front considered by Lighthill [5, 6]. The effect of triple shock configuration is represented by the combined dynamic singularity at the triple point. Some of its properties were predicted by Landau [7]. The particular case of motion of a slender wedge at hypersonic speed was considered by Inger [8, 9]. However his analysis contains statements which contradict existing concepts.

Combination of magnetic analyzers in nuclear reaction experiments

Different ways to increase the counting rate in measurements with magnetic analyzing systems are investigated. It is assumed that a good energy resolution is desirable and that the energy spread of the beam from the accelerator is fairly large (cyclotron). The effect of combining the analyzers suitably, as well as the influence of the type and the setting of the target are discussed. Two types of systems are considered, namely analyzers with coincident and with perpendicular bending planes. In both of these cases the energy spread caused by the finite opening angle of the second analyzer is treated, being of importance for reactions with light nuclei. It is found that it should be possible to use a quite large spot and thick target layer if the measurement is arranged in the proper way. The following circumstances are then important: the dimensions of the system and type of reaction, the bending direction and field gradient of the second analyzer, the target orientation and density and the detector position. The calculations are illustrated by some numerical examples † † Most of the calculations were made in conjunction with the design of the equipment described in ref. 7). .