On the number of limit cycles of the Lienard equation

In this paper, we study a Lienard system of the form dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This sequence seems to converge to the exact equation of each limit cycle. We obtain also a sequence of polynomials R_n(x) whose roots of odd multiplicity are related to the number and location of the limit cycles of the system.Comment: 10 pages, 5 figures. Submitted to Physical Review

Galaxy Clusters as Reservoirs of Heavy Dark Matter and High-Energy Cosmic Rays: Constraints from Neutrino Observations

Galaxy Clusters (GCs) are the largest reservoirs of both dark matter and cosmic rays (CRs). Dark matter self-annihilation can lead to a high luminosity in gamma rays and neutrinos, enhanced by a strong degree of clustering in dark matter substructures. Hadronic CR interactions can also lead to a high luminosity in gamma rays and neutrinos, enhanced by the confinement of CRs from cluster accretion/merger shocks and active galactic nuclei. We show that IceCube/KM3Net observations of high-energy neutrinos can probe the nature of GCs and the separate dark matter and CR emission processes, taking into account how the results depend on the still-substantial uncertainties. Neutrino observations are relevant at high energies, especially at >10 TeV. Our results should be useful for improving experimental searches for high-energy neutrino emission. Neutrino telescopes are sensitive to extended sources formed by dark matter substructures and CRs distributed over large scales. Recent observations by Fermi and imaging atmospheric Cherenkov telescopes have placed interesting constraints on the gamma-ray emission from GCs. We also provide calculations of the gamma-ray fluxes, taking into account electromagnetic cascades inside GCs, which can be important for injections at sufficiently high energies. This also allows us to extend previous gamma-ray constraints to very high dark matter masses and significant CR injections at very high energies. Using both neutrinos and gamma rays, which can lead to comparable constraints, will allow more complete understandings of GCs. Neutrinos are essential for some dark matter annihilation channels, and for hadronic instead of electronic CRs. Our results suggest that the multi-messenger observations of GCs will be able to give useful constraints on specific models of dark matter and CRs. [Abstract abridged.]Comment: 31 pages, 20 figures, 1 table, accepted for publication in JCAP, references and discussions adde

HST Observations of the Stellar Distribution Near Sgr A*

We present HST/NICMOS data to study the surface brightness distribution of stellar light within the inner 10" of Sgr A* at 1.4, 1.7 and 1.9 microns. We use these data to independently examine the surface brightness distribution that had been measured previously with NICMOS and to determine whether there is a drop in the surface density of stars very near Sgr A*. Our analysis confirms that a previously reported drop in the surface brightness within 0.8" of Sgr A* is an artifact of bright and massive stars near that radius. We also show that the surface brightness profile within 5" or ~0.2 pc of Sgr A* can be fitted with broken power laws. The power laws are consistent with previous measurements, in that the profile becomes shallower at small radii. For radii > 0.7" the slope is beta=-0.34\pm0.04 where Sigma is proportional to r^beta and becomes flatter at smaller radii with beta=-0.13\pm0.04. Modeling of the surface brightness profile gives a stellar density that increases roughly as r^-1 within the inner 1" of Sgr A*. This slope confirms earlier measurements in that it is not consistent with that expected from an old, dynamically-relaxed stellar cluster with a central supermassive black hole. Assuming that the diffuse emission is not contaminated by a faint population of young stars down to the 17.1 magnitude limit of our imaging data at 1.70$\mu$, the shallow cusp profile is not consistent with a decline in stellar density in the inner arcsecond. In addition, converting our measured diffuse light profile to a stellar mass profile, with the assumption that the light is dominated by K0 dwarfs, the enclosed stellar mass within radius r < 0.1 pc of Sgr A* is ~ 3.2x10^4 M_solar (r/0.1 {pc})^2.1.Comment: 16 pages, 7 figures, ApJ, in pres

Magnetic Fields, Relativistic Particles, and Shock Waves in Cluster Outskirts

It is only now, with low-frequency radio telescopes, long exposures with high-resolution X-ray satellites and gamma-ray telescopes, that we are beginning to learn about the physics in the periphery of galaxy clusters. In the coming years, Sunyaev-Zeldovich telescopes are going to deliver further great insights into the plasma physics of these special regions in the Universe. The last years have already shown tremendous progress with detections of shocks, estimates of magnetic field strengths and constraints on the particle acceleration efficiency. X-ray observations have revealed shock fronts in cluster outskirts which have allowed inferences about the microphysical structure of shocks fronts in such extreme environments. The best indications for magnetic fields and relativistic particles in cluster outskirts come from observations of so-called radio relics, which are megaparsec-sized regions of radio emission from the edges of galaxy clusters. As these are difficult to detect due to their low surface brightness, only few of these objects are known. But they have provided unprecedented evidence for the acceleration of relativistic particles at shock fronts and the existence of muG strength fields as far out as the virial radius of clusters. In this review we summarise the observational and theoretical state of our knowledge of magnetic fields, relativistic particles and shocks in cluster outskirts.Comment: 34 pages, to be published in Space Science Review

Statistical Mechanics of Canonical-Dissipative Systems and Applications to Swarm Dynamics

We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the take-up/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of non-equilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e. for active motion, (b) interactions between the particles based on global couplings. We derive analytical expressions for the non-equilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.Comment: 14 pages incl. 13 figures. v2: misprints in Eq. (40) corrected, ref. updated. For related work see also: http://summa.physik.hu-berlin.de/~frank/active.htm

The Swift BAT Perspective on Non-thermal Emission in HIFLUGCS Galaxy Clusters

The search for diffuse non-thermal, inverse Compton (IC) emission from galaxy clusters at hard X-ray energies has been underway for many years, with most detections being either of low significance or controversial. In this work, we investigate 14-195 keV spectra from the Swift Burst Alert Telescope (BAT) all-sky survey for evidence of non-thermal excess emission above the exponentially decreasing tail of thermal emission in the flux-limited HIFLUGCS sample. To account for the thermal contribution at BAT energies, XMM-Newton EPIC spectra are extracted from coincident spatial regions so that both thermal and non-thermal spectral components can be determined simultaneously. We find marginally significant IC components in six clusters, though after closer inspection and consideration of systematic errors we are unable to claim a clear detection in any of them. The spectra of all clusters are also summed to enhance a cumulative non-thermal signal not quite detectable in individual clusters. After constructing a model based on single-temperature fits to the XMM-Newton data alone, we see no significant excess emission above that predicted by the thermal model determined at soft energies. This result also holds for the summed spectra of various subgroups, except for the subsample of clusters with diffuse radio emission. For clusters hosting a diffuse radio halo, a relic, or a mini-halo, non-thermal emission is initially detected at the \sim5-sigma confidence level - driven by clusters with mini-halos - but modeling and systematic uncertainties ultimately degrade this significance. In individual clusters, the non-thermal pressure of relativistic electrons is limited to \sim10% of the thermal electron pressure, with stricter limits for the more massive clusters, indicating that these electrons are likely not dynamically important in the central regions of clusters.Comment: 25 pages, 15 figures; some figure and table numbering differs from published ApJ version: please see that for superior formattin

Radio observations of ZwCl 2341.1+0000: a double radio relic cluster

Context: Hierarchal models of large scale structure (LSS) formation predict that galaxy clusters grow via gravitational infall and mergers of (smaller) mass concentrations, such as clusters and galaxy groups. Diffuse radio emission, in the form of radio halos and relics, is found in clusters undergoing a merger, indicating that shocks or turbulence associated with the merger are capable of accelerating electrons to highly relativistic energies. Here we report on radio observations of ZwCl 2341.1+0000, a complex merging structure of galaxies located at z=0.27, using Giant Metrewave Radio Telescope (GMRT) observations. Aims: The main aim of the observations is to study the nature of the diffuse radio emission in the galaxy cluster ZwCl 2341.1+0000. Methods: We have carried out GMRT 610, 241, and 157 MHz continuum observations of ZwCl 2341.1+0000. The radio observations are combined with X-ray and optical data of the cluster. Results: The GMRT observations show the presence of a double peripheral radio relic in the cluster ZwCl 2341.1+0000. The spectral index is -0.49 \pm 0.18 for the northern relic and -0.76 \pm 0.17 for the southern relic respectively. We have derived values of 0.48-0.93 microGauss for the equipartition magnetic field strength. The relics are probably associated with an outwards traveling merger shock waves.Comment: 14 pages, 10 figures, accepted for publication in A&A on July 30, 200

Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles

The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comparatively fast time scale, the main dynamical property of (strongly) monotone systems, convergence to steady states, is still valid. An application is worked out to a double-phosphorylation ``futile cycle'' motif which plays a central role in eukaryotic cell signaling.Comment: 21 pages, 3 figures, corrected typos, references remove

Intermediate Asymptotics of the Kerr Quasinormal Spectrum

We study analytically the quasinormal mode spectrum of near-extremal (rotating) Kerr black holes. We find an analytic expression for these black-hole resonances in terms of the black-hole physical parameters: its Bekenstein-Hawking temperature T_{BH} and its horizon's angular velocity \Omega, which is valid in the intermediate asymptotic regime 1<<\omega<<1/T_{BH}.Comment: 4 page

Indirect signals from light neutralinos in supersymmetric models without gaugino mass unification

We examine indirect signals produced by neutralino self-annihilations, in the galactic halo or inside celestial bodies, in the frame of an effective MSSM model without gaugino-mass unification at a grand unification scale. We compare our theoretical predictions with current experimental data of gamma-rays and antiprotons in space and of upgoing muons at neutrino telescopes. Results are presented for a wide range of the neutralino mass, though our discussions are focused on light neutralinos. We find that only the antiproton signal is potentially able to set constraints on very low-mass neutralinos, below 20 GeV. The gamma-ray signal, both from the galactic center and from high galactic latitudes, requires significantly steep profiles or substantial clumpiness in order to reach detectable levels. The up-going muon signal is largely below experimental sensitivities for the neutrino flux coming from the Sun; for the flux from the Earth an improvement of about one order of magnitude in experimental sensitivities (with a low energy threshold) can make accessible neutralino masses close to O, Si and Mg nuclei masses, for which resonant capture is operative.Comment: 17 pages, 1 tables and 5 figures, typeset with ReVTeX4. The paper may also be found at http://www.to.infn.it/~fornengo/papers/indirect04.ps.gz or through http://www.astroparticle.to.infn.it/. Limit from BR(Bs--> mu+ mu-) adde