Chimera states in heterogeneous networks

Chimera states in networks of coupled oscillators occur when some fraction of the oscillators synchronise with one another, while the remaining oscillators are incoherent. Several groups have studied chimerae in networks of identical oscillators, but here we study these states in a heterogeneous model for which the natural frequencies of the oscillators are chosen from a distribution. We obtain exact results by reduction to a finite set of differential equations. We find that heterogeneity can destroy chimerae, destroy all states except chimerae, or destabilise chimerae in Hopf bifurcations, depending on the form of the heterogeneity.Comment: Revised text. To appear, Chao

Multifrequency VLA observations of the FR I radio galaxy 3C 31: morphology, spectrum and magnetic field

We present high-quality VLA images of the FR I radio galaxy 3C 31 in the frequency range 1365 to 8440 MHz with angular resolutions from 0.25 to 40 arcsec. Our new images reveal complex, well resolved filamentary substructure in the radio jets and tails. We also use these images to explore the spectral structure of 3C 31 on large and small scales. We infer the apparent magnetic field structure by correcting for Faraday rotation. Some of the intensity substructure in the jets is clearly related to structure in their apparent magnetic field: there are arcs of emission where the degree of linear polarization increases, with the apparent magnetic field parallel to the ridges of the arcs. The spectral indices are significantly steeper (0.62) within 7 arcsec of the nucleus than between 7 and 50 arcsec (0.52 - 0.57). The spectra of the jet edges are also slightly flatter than the average for their surroundings. At larger distances, the jets are clearly delimited from surrounding larger-scale emission both by their flatter radio spectra and by sharp brightness gradients. The spectral index of 0.62 in the first 7 arcsec of 3C 31's jets is very close to that found in other FR I galaxies where their jets first brighten in the radio and where X-ray synchrotron emission is most prominent. Farther from the nucleus, where the spectra flatten, X-ray emission is fainter relative to the radio. The brightest X-ray emission from FR I jets is therefore not associated with the flattest radio spectra, but with a particle-acceleration process whose characteristic energy index is 2.24. The spectral flattening with distance from the nucleus occurs where our relativistic jet models require deceleration, and the flatter-spectra at the jet edges may be associated with transverse velocity shear. (Slightly abridged)Comment: 17 pages, 13 figures, accepted for publication in MNRA

Chimeras in networks of planar oscillators

Chimera states occur in networks of coupled oscillators, and are characterized by having some fraction of the oscillators perfectly synchronized, while the remainder are desynchronized. Most chimera states have been observed in networks of phase oscillators with coupling via a sinusoidal function of phase differences, and it is only for such networks that any analysis has been performed. Here we present the first analysis of chimera states in a network of planar oscillators, each of which is described by both an amplitude and a phase. We find that as the attractivity of the underlying periodic orbit is reduced chimeras are destroyed in saddle-node bifurcations, and supercritical Hopf and homoclinic bifurcations of chimeras also occur.Comment: To appear, Phys. Rev.

Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities

In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model with Heaviside firing rate function we calculate symmetric one-bump and ring solutions explicitly and use an Evans function approach to predict the point of instability and the shapes of the dominant growing modes. Our predictions are shown to be in excellent agreement with direct numerical simulations. Moreover, beyond the instability our simulations demonstrate the emergence of multi-bump and labyrinthine patterns. With the addition of spike-frequency adaptation, numerical simulations of the resulting vector model show that it is possible for structures without rotational symmetry, and in particular multi-bumps, to undergo an instability to a rotating wave. We use a general argument, valid for smooth firing rate functions, to establish the conditions necessary to generate such a rotational instability. Numerical continuation of the rotating wave is used to quantify the emergent angular velocity as a bifurcation parameter is varied. Wave stability is found via the numerical evaluation of an associated eigenvalue problem

Polarization in the prompt emission of gamma-ray bursts and their afterglows

Synchrotron is considered the dominant emission mechanism in the production of gamma-ray burst photons in the prompt as well as in the afterglow phase. Polarization is a characteristic feature of synchrotron and its study can reveal a wealth of information on the properties of the magnetic field and of the energy distribution in gamma-ray burst jets. In this paper I will review the theory and observations of gamma-ray bursts polarization. While the theory is well established, observations have prove difficult to perform, due to the weakness of the signal. The discriminating power of polarization observations, however, cannot be overestimated.Comment: 16 pages, 9 figures, accepted for publication in the New Journal of Physics focus issue on Gamma Ray Burst

Energy Injection Episodes in Gamma Ray Bursts: The Light Curves and Polarization Properties of GRB 021004

Several GRB afterglow light curves deviate strongly from the power law decay observed in most bursts. We show that these variations can be accounted for by including refreshed shocks in the standard fireball model previously used to interpret the overall afterglow behavior. As an example we consider GRB 021004 that exhibited strong light curve variations and has a reasonably well time-resolved polarimetry. We show that the light curves in the R-band, X-rays and in the radio can be accounted for by four energy injection episodes in addition to the initial event. The polarization variations are shown to be a consequence of the injections.Comment: 4 pages, 2 figures. To appear in ApJ

The XMM-Newton Detection of Diffuse Inverse Compton X-rays from Lobes of the FR-II Radio Galaxy 3C98

The XMM-Newton observation of the nearby FR-II radio galaxy 3C 98 is reported. In two exposures on the target, faint diffuse X-ray emission associated with the radio lobes was significantly detected, together with a bright X-ray active nucleus, of which the 2 -- 10 keV intrinsic luminosity is (4 -- 8) \times 10^{42} erg s-1. The EPIC spectra of the northern and southern lobes are reproduced by a single power law model modified by the Galactic absorption, with a photon index of 2.2-0.5+0.6 and 1.7-0.6+0.7 respectively. These indices are consistent with that of the radio synchrotron spectrum, 1.73 +- 0.01 The luminosity of the northern and southern lobes are measured to be 8.3-2.6+3.3 \times 10^{40} erg s-1 and 9.2-4.3+5.7 \times 10^{40} erg s-1, respectively, in the 0.7 -- 7 keV range. The diffuse X-ray emission is interpreted as an inverse-Compton emission, produced when the synchrotron-emitting energetic electrons in the lobes scatter off the cosmic microwave background photons. The magnetic field in the lobes is calculated to be about 1.7 \mu G, which is about 2.5 times lower than the value estimated under the minimum energy condition. The energy density of the electrons is inferred to exceed that in the magnetic fields by a factor of 40 -- 50.Comment: 23 pages, 7 figures. Accepted for publication in the Astrophysical Journa

A Chandra detection of diffuse hard X-ray emission associated with the lobes of the radio galaxy 3C 452

An 80 ksec Chandra ACIS observation of the radio galaxy 3C 452 is reported. A diffuse X-ray emission associated with the lobes has been detected with high statistical significance, together with the X-ray nucleus of the host galaxy. The 0.5--5 keV ACIS spectrum of the diffuse emission is described by a two-component model, consisting of a soft thermal plasma emission from the host galaxy halo and a hard non-thermal power-law component. The hard component is ascribed to the inverse Comptonization of cosmic microwave background photons by the synchrotron emitting electrons in the lobes, because its spectral energy index, 0.68+-0.28, is consistent with the radio synchrotron index, 0.78. These results reveal a significant electron dominance in the lobes. The electrons are inferred to have a relatively uniform distribution, while the magnetic field is compressed toward the lobe periphery.Comment: 4 figures, 2 tables, Accepted by ApJL (to appear in the December 1 issue

Jet Acceleration by Tangled Magnetic Fields

We explore the possibility that extragalactic radio jets might be accelerated by highly disorganized magnetic fields that are strong enough to dominate the dynamics until the terminal Lorentz factor is reached. Following the twin-exhaust model by Blandford & Rees (1974), the collimation under this scenario is provided by the stratified thermal pressure from an external medium. The acceleration efficiency then depends on the pressure gradient of that medium. In order for this mechanism to work there must be continuous tangling of the magnetic field, changing the magnetic equation of state away from pure flux freezing (otherwise conversion of Poynting flux to kinetic energy flux is suppressed). This is a complementary approach to models in which the plasma is accelerated by large scale ordered fields. We include a simple prescription for magnetic dissipation, which leads to tradeoffs among conversion of magnetic energy into bulk kinetic energy, random particle energy, and radiation. We present analytic dynamical solutions of such jets, assess the effects of radiation drag, and comment on observational issues, such as the predicted polarization and synchrotron brightness. Finally, we try to make the connection to observed radio galaxies and gamma-ray bursts.Comment: 15 pages, 10 figures, accepted for publication in Ap

Multifrequency Polarimetry of the Nrao 140 Jet: Possible Detection of a Helical Magnetic Field and Constraints on its Pitch Angle

We present results from multifrequency polarimetry of NRAO 140 using the Very Long Baseline Array. These observations allow us to reveal the distributions of both the polarization position angle and the Faraday rotation measure (RM). These distributions are powerful tools to discern the projected and line-of-sight components of the magnetic field, respectively. We find a systematic gradient in the RM distribution, with its sign being opposite at either side of the jet with respect to the jet axis. The sign of the RM changes only with the direction of the magnetic field component along the line of sight, so this can be explained by the existence of helical magnetic components associated with the jet itself. We derive two constraints for the pitch angle of the helical magnetic field from the distributions of the RM and the projected magnetic field; the RM distribution indicates that the helical fields are tightly wound, while that of the projected magnetic field suggests they are loosely wound around the jet axis. This inconsistency may be explained if the Faraday rotator is not cospatial with theemitting region. Our results may point toward a physical picture in which an ultra-relativistic jet (spine) with a loosely wound helical magnetic field is surrounded by a sub-relativistic wind layer (sheath) with a tightly wound helical magnetic field.Comment: 12 pages, 4 figures, ApJ, in pres