Chimera states in networks of phase oscillators: the case of two small populations

Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators and analyzed in the continuum limit, chimeras may also occur in systems with finite (and small) numbers of oscillators. Focusing on networks of $2N$ phase oscillators that are organized in two groups, we find that chimera states, corresponding to attracting periodic orbits, appear with as few as two oscillators per group and demonstrate that for $N>2$ the bifurcations that create them are analogous to those observed in the continuum limit. These findings suggest that chimeras, which bear striking similarities to dynamical patterns in nature, are observable and robust in small networks that are relevant to a variety of real-world systems.Comment: 13 pages, 16 figure

An Attempt to Probe the Radio Jet Collimation Regions in NGC 4278, NGC 4374 (M84), and NGC 6166

NRAO Very Long Baseline Array (VLBA) observations of NGC 4278, NGC 4374 (M84), NGC 6166, and M87 (NGC 4486) have been made at 43 GHz in an effort to image the jet collimation region. This is the first attempt to image the first three sources at 43 GHz using Very Long Baseline Interferometry (VLBI) techniques. These three sources were chosen because their estimated black hole mass and distance implied a Schwarzschild radius with large angular size, giving hope that the jet collimation regions could be studied. Phase referencing was utilize for the three sources because of their expected low flux densities. M87 was chosen as the calibrator for NGC 4374 because it satisfied the phase referencing requirements: nearby to the source and sufficiently strong. Having observed M87 for a long integration time, we have detected its sub-parsec jet, allowing us to confirm previous high resolution observations made by Junor, Biretta & Livio, who have indicated that a wide opening angle was seen near the base of the jet. Phase referencing successfully improved our image sensitivity, yielding detections and providing accurate positions for NGC 4278, NGC 4374 and NGC 6166. These sources are point dominated, but show suggestions of extended structure in the direction of the large-scale jets. However, higher sensitivity will be required to study their sub-parsec jet structure

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

A relativistic model of the radio jets in NGC 315

We apply our intrinsically symmetrical, decelerating relativistic jet model to deep VLA imaging of the inner 140 arcsec of the giant low-luminosity radio galaxy NGC 315. An optimized model accurately fits the data in both total intensity and linear polarization. We infer that the velocity, emissivity and field structure in NGC 315 are very similar to those of the other low-luminosity sources we have modelled, but that all of the physical scales are larger by a factor of about 5. We derive an inclination to the line of sight of 38 degrees for the jets. Where they first brighten, their on-axis velocity is approximately v/c = 0.9. They decelerate to v/c = 0.4 between 8 and 18 kpc from the nucleus and the velocity thereafter remains constant. The speed at the edge of the jet is roughly 0.6 of the on-axis value where it is best constrained, but the transverse velocity profile may deviate systematically from the Gaussian form we assume. The proper emissivity profile is split into three power-law regions separated by shorter transition zones. In the first of these, at 3 kpc (the flaring point) the jets expand rapidly at constant emissivity, leading to a large increase in the observed brightness on the approaching side. At 10 kpc, the emissivity drops abruptly by a factor of 2. Where the jets are well resolved their rest-frame emission is centre-brightened. The magnetic field is modelled as random on small scales but anisotropic and we rule out a globally ordered helical configuration. To a first approximation, the field evolves from a mixture of longitudinal and toroidal components to predominantly toroidal, but it also shows variations in structure along and across the jets, with a significant radial component in places. Simple adiabatic models fail to fit the emissivity variations.Comment: 20 pages, 17 figures, MNRAS (in press

Asymmetry of jets, lobe size and spectral index in radio galaxies and quasars

We investigate the correlations between spectral index, jet side and extent of the radio lobes for a sample of nearby FRII radio galaxies. In Dennett-Thorpe et al. (1997) we studied a sample of quasars and found that the high surface brightness regions had flatter spectra on the jet side (explicable as a result of Doppler beaming) whilst the extended regions had spectral asymmetries dependent on lobe length. Unified schemes predict that asymmetries due to beaming will be much smaller in narrow-line radio galaxies than in quasars: we therefore investigate in a similar manner, a sample of radio galaxies with detected jets. We find that spectral asymmetries in these objects are uncorrelated with jet sidedness at all brightness levels, but depend on relative lobe volume. Our results are not in conflict with unified schemes, but suggest that the differences between the two samples are due primarily to power or redshift, rather than to orientation. We also show directly that hotspot spectra steepen as a function of radio power or redshift. Whilst a shift in observed frequency due to the redshift may account for some of the steepening, it cannot account for all of it, and a dependence on radio power is required.Comment: accepted for publication in MNRAS, 10 pages; typos/minor correctio

The magnetized medium around the radio galaxy B2 0755+37: an interaction with the intra-group gas

We explore the magneto-ionic environment of the isolated radio galaxy B2 0755+37 using detailed imaging of the distributions of Faraday rotation and depolarization over the radio source from Very Large Array observations at 1385,1465 and 4860 MHz and new X-ray data from XMM-Newton. The Rotation Measure (RM) distribution is complex, with evidence for anisotropic fluctuations in two regions. The approaching lobe shows low and uniform RM in an unusual `stripe' along an extension of the jet axis and a linear gradient transverse to this axis over its Northern half. The leading edge of the receding lobe shows arc-like RM structures with sign reversals. Elsewhere, the RM structures are reasonably isotropic. The RM power spectra are well described by cut-off power laws with slopes ranging from 2.1 to 3.2 in different sub-regions. The corresponding magnetic-field autocorrelation lengths, where well-determined, range from 0.25 to 1.4 kpc. It is likely that the fluctuations are mostly produced by compressed gas and field around the leading edges of the lobes. We identify areas of high depolarization around the jets and inner lobes. These could be produced by dense gas immediately surrounding the radio emission containing a magnetic field which is tangled on small scales. We also identify four ways in which the well known depolarization (Faraday depth) asymmetry between jetted and counter-jetted lobes of extended radio sources can be modified by interactions with the surrounding medium.Comment: 16 pages, 13 figures, accepted for publication in MNRAS. Full resolution paper available at: ftp://ftp.ira.inaf.it/pub/outgoing/guidetti/ Subjects: Cosmology and Extragalactic Astrophysics (astro-ph.CO

Dynamical Phase Transitions In Driven Integrate-And-Fire Neurons

We explore the dynamics of an integrate-and-fire neuron with an oscillatory stimulus. The frustration due to the competition between the neuron's natural firing period and that of the oscillatory rhythm, leads to a rich structure of asymptotic phase locking patterns and ordering dynamics. The phase transitions between these states can be classified as either tangent or discontinuous bifurcations, each with its own characteristic scaling laws. The discontinuous bifurcations exhibit a new kind of phase transition that may be viewed as intermediate between continuous and first order, while tangent bifurcations behave like continuous transitions with a diverging coherence scale.Comment: 4 pages, 5 figure

The IRAS Revised Bright Galaxy Sample (RBGS)

IRAS flux densities, redshifts, and infrared luminosities are reported for all sources identified in the IRAS Revised Bright Galaxy Sample (RBGS), a complete flux-limited survey of all extragalactic objects with total 60 micron flux density greater than 5.24 Jy, covering the entire sky surveyed by IRAS at Galactic latitude |b| > 5 degrees. The RBGS includes 629 objects, with a median (mean) sample redshift of 0.0082 (0.0126) and a maximum redshift of 0.0876. The RBGS supersedes the previous two-part IRAS Bright Galaxy Samples, which were compiled before the final ("Pass 3") calibration of the IRAS Level 1 Archive in May 1990. The RBGS also makes use of more accurate and consistent automated methods to measure the flux of objects with extended emission. Basic properties of the RBGS sources are summarized, including estimated total infrared luminosities, as well as updates to cross-identifications with sources from optical galaxy catalogs established using the NASA/IPAC Extragalactic Database (NED). In addition, an atlas of images from the Digitized Sky Survey with overlays of the IRAS position uncertainty ellipse and annotated scale bars is provided for ease in visualizing the optical morphology in context with the angular and metric size of each object. The revised bolometric infrared luminosity function, phi(L_ir), for infrared bright galaxies in the local Universe remains best fit by a double power law, phi(L_ir) ~ L_ir^alpha, with alpha = -0.6 (+/- 0.1), and alpha = -2.2 (+/- 0.1) below and above the "characteristic" infrared luminosity L_ir ~ 10^{10.5} L_solar, respectively. (Abridged)Comment: Accepted for publication in the Astronomical Journal. Contains 50 pages, 7 tables, 16 figures. Due to astro-ph space limits, only 1 of 26 pages of Figure 1, and 1 of 11 pages of Table 7, are included; full resolution Postscript files are available at http://nedwww.ipac.caltech.edu/level5/March03/IRAS_RBGS/Figures/ . Replacement: Corrected insertion of Fig. 15 (MethodCodes.ps) in LaTe