On the rapid TeV flaring activity of Markarian 501

Aims: We investigate the one-zone SSC model of TeV blazars in the presence of electron acceleration. In this picture electrons reach a maximum energy where acceleration saturates from a combination of synchrotron and inverse Compton scattering losses. Methods: We solve the spatially averaged kinetic equations which describe the simultaneous evolution of particles and photons, obtaining the multi-wavelength spectrum as a function of time. Results: We apply the model to the rapid flare of Mrk 501 of July 9, 2005 as this was observed by the MAGIC telescope and obtain the relevant parameters for the pre-flare quasi steady state and the ones during the flare. We show that a hard lag flare can be obtained with parameters which lie well within the range already accepted for this source. Especially the choice of a high value of the Doppler factor seems to be necessary.Comment: 4 pages, 4 figures, to appear in A&A (Letters

Magnetic field effects on neutrino production in microquasars

We investigate the effects of magnetic fields on neutrino production in microquasars. We calculate the steady particle distributions for the pions and muons generated in p-gamma and p-p interactions in the jet taking the effects of all energy losses into account. The obtained neutrino emission is significantly modified due to the synchrotron losses suffered by secondary pions and muons. The estimates made for neutrino fluxes arriving on the Earth imply that detection of high-energy neutrinos from the vicinity of the compact object can be difficult. However, in the case of windy microquasars, the interaction of energetic protons in the jet with matter of dense clumps of the wind could produce detectable neutrinos. This is because the pions and muons at larger distances from the compact object will not be affected by synchrotron losses.Comment: 12 pages, 11 figures, accepted for publication in A&

Spectral evolution of non-thermal electron distributions in intense radiation fields

(abridged) Models of many astrophysical gamma-ray sources assume they contain a homogeneous distribution of electrons that are injected as a power-law in energy and evolve by interacting with radiation fields, magnetic fields and particles in the source and by escaping. This problem is particularly complicated if the radiation fields have higher energy density than the magnetic field and are sufficiently energetic that inverse Compton scattering is not limited to the Thomson regime. We present a simple, time-dependent, semi-analytical solution of the electron kinetic equation that treats both continuous and impulsive injection, cooling via synchrotron and inverse Compton radiation, (taking into account Klein-Nishina effects) and energy dependent particle escape. The kinetic equation for an arbitrary, time-dependent source function is solved by the method of Laplace transformations. Using an approximate expression for the energy loss rate that takes into account synchrotron and inverse Compton losses including Klein-Nishina effects for scattering off an isotropic photon field with either a power-law or black-body distribution, we find explicit expressions for the cooling time and escape probability of individual electrons. This enables the full, time-dependent solution to be reduced to a single quadrature. From the electron distribution, we then construct the time-dependent, multi-wavelength emission spectrum. We compare our solutions with several limiting cases and discuss the general appearance and temporal behaviour of spectral features (i.e., cooling breaks, bumps etc.). As a specific example, we model the broad-band energy spectrum of the open stellar association Westerlund-2 at different times of its evolution, and compare it with observations.Comment: 14 pages, 8 figures, acccepted for publication in A&

The modulation of the gamma-ray emission from the binary LS 5039

Gamma-ray binaries, composed of a massive star and compact object, have been established as a new class of sources of very high energy (VHE) photons. The gamma-rays are produced by inverse Compton scattering of the stellar light by VHE electrons accelerated in the vicinity of the compact object. The VHE emission from LS 5039 displays an orbital modulation. The inverse Compton spectrum depends on the angle between the incoming and outgoing photon in the electron rest frame. Since the angle at which an observer sees the star and electrons changes with the orbit, a phase dependence of the spectrum is expected. The phase-dependent spectrum of LS 5039 is calculated, assuming a continuous injection of electrons. The shape of the electron distribution depends on the injected power-law and on the magnetic field intensity. Anisotropic scattering produces hard emission at inferior conjunction, when attenuation due to pair production of the VHE gamma-rays on star light is minimum. The computed lightcurve and spectra provide good fits to the HESS and EGRET observations, except at phases of maximum attenuation where pair cascade emission may be significant for HESS. Detailed predictions are made for a modulation in the GLAST energy range. The magnetic field intensity at periastron is 0.8+-0.2 G. Anisotropic inverse Compton scattering plays a major role in LS 5039. The derived magnetic field intensity, injection energy and slope suggest a rotation-powered pulsar wind nebula. Gamma-ray binaries are promising sources to study the environment of pulsars on small scales.Comment: 12 pages, 8 figures, accepted for publication in A&

High-energy emission from jet-clump interactions in microquasars

High-mass microquasars are binary systems consisting of a massive star and an accreting compact object from which relativistic jets are launched. There is considerable observational evidence that winds of massive stars are clumpy. Individual clumps may interact with the jets in high-mass microquasars to produce outbursts of high-energy emission. Gamma-ray flares have been detected in some high-mass X-ray binaries, such as Cygnus X-1, and probably in LS 5039 and LS I+61 303. We predict the high-energy emission produced by the interaction between a jet and a clump of the stellar wind in a high-mass microquasar. Assuming a hydrodynamic scenario for the jet-clump interaction, we calculate the spectral energy distributions produced by the dominant non-thermal processes: relativistic bremsstrahlung, synchrotron and inverse Compton radiation, for leptons, and for hadrons, proton-proton collisions. Significant levels of emission in X-rays (synchrotron), high-energy gamma rays (inverse Compton), and very high-energy gamma rays (from the decay of neutral pions) are predicted, with luminosities in the different domains in the range ~ 10^{32}-10^{35} erg/s. The spectral energy distributions vary strongly depending on the specific conditions. Jet-clump interactions may be detectable at high and very high energies, and provide an explanation for the fast TeV variability found in some high-mass X-ray binary systems. Our model can help to infer information about the properties of jets and clumpy winds by means of high-sensitivity gamma-ray astronomy.Comment: Accepted for publication in A&A (10 pages, 8 figures

Uniqueness of radial solutions for the fractional Laplacian

We prove general uniqueness results for radial solutions of linear and nonlinear equations involving the fractional Laplacian $(-\Delta)^s$ with $s \in (0,1)$ for any space dimensions $N \geq 1$. By extending a monotonicity formula found by Cabre and Sire \cite{CaSi-10}, we show that the linear equation $(-\Delta)^s u+ Vu = 0$ in $\mathbb{R}^N$ has at most one radial and bounded solution vanishing at infinity, provided that the potential $V$ is a radial and non-decreasing. In particular, this result implies that all radial eigenvalues of the corresponding fractional Schr\"odinger operator $H=(-\Delta)^s + V$ are simple. Furthermore, by combining these findings on linear equations with topological bounds for a related problem on the upper half-space $\mathbb{R}^{N+1}_+$, we show uniqueness and nondegeneracy of ground state solutions for the nonlinear equation $(-\Delta)^s Q + Q - |Q|^{\alpha} Q = 0$ in $\mathbb{R}^N$ for arbitrary space dimensions $N \geq 1$ and all admissible exponents $\alpha >0$. This generalizes the nondegeneracy and uniqueness result for dimension N=1 recently obtained by the first two authors in \cite{FrLe-10} and, in particular, the uniqueness result for solitary waves of the Benjamin--Ono equation found by Amick and Toland \cite{AmTo-91}.Comment: 38 pages; revised version; various typos corrected; proof of Lemma 8.1 corrected; discussion of case \kappa_* =1 in the proof of Theorem 2 corrected with new Lemma A.2; accepted for publication in Comm. Pure. Appl. Mat

Locating the VHE source in the Galactic Centre with milli-arcsecond accuracy

Very high-energy gamma-rays (VHE; E>100 GeV) have been detected from the direction of the Galactic Centre up to energies E>10 TeV. Up to now, the origin of this emission is unknown due to the limited positional accuracy of the observing instruments. One of the counterpart candidates is the super-massive black hole (SMBH) Sgr A*. If the VHE emission is produced within ~10^{15} cm ~1000 r_G (r_G=G M/c^2 is the Schwarzschild radius) of the SMBH, a decrease of the VHE photon flux in the energy range 100--300 GeV is expected whenever an early type or giant star approaches the line of sight within ~ milli-arcseconds (mas). The dimming of the flux is due to absorption by pair-production of the VHE photons in the soft photon field of the star, an effect we refer to as pair-production eclipse (PPE). Based upon the currently known orbits of stars in the inner arcsecond of the Galaxy we find that PPEs lead to a systematic dimming in the 100--300 GeV band at the level of a few per cent and lasts for several weeks. Since the PPE affects only a narrow energy band and is well correlated with the passage of the star, it can be clearly discriminated against other systematic or even source-intrinsic effects. While the effect is too small to be observable with the current generation of VHE detectors, upcoming high count-rate experiments like the Cherenkov telescope array (CTA) will be sufficiently sensitive. Measuring the temporal signature of the PPE bears the potential to locate the position and size of the VHE emitting region within the inner 1000 r_G or in the case of a non-detection exclude the immediate environment of the SMBH as the site of gamma-ray production altogether.Comment: 7 pages, published in MNRAS 402, pg. 1342-134

Spectral signature of a free pulsar wind in the gamma-ray binaries LS 5039 and LSI +61\degr303

LS 5039 and LSI +61\degr303 are two binaries that have been detected in the TeV energy domain. These binaries are composed of a massive star and a compact object, possibly a young pulsar. The gamma-ray emission would be due to particle acceleration at the collision site between the relativistic pulsar wind and the stellar wind of the massive star. Part of the emission may also originate from inverse Compton scattering of stellar photons on the unshocked (free) pulsar wind. The purpose of this work is to constrain the bulk Lorentz factor of the pulsar wind and the shock geometry in the compact pulsar wind nebula scenario for LS 5039 and LSI +61\degr303 by computing the unshocked wind emission and comparing it to observations. Anisotropic inverse Compton losses equations are derived and applied to the free pulsar wind in binaries. The unshocked wind spectra seen by the observer are calculated taking into account the gamma-gamma absorption and the shock geometry. A pulsar wind composed of monoenergetic pairs produces a typical sharp peak at an energy which depends on the bulk Lorentz factor and whose amplitude depends on the size of the emitting region. This emission from the free pulsar wind is found to be strong and difficult to avoid in LS 5039 and LSI +61\degr303. If the particles in the pulsar are monoenergetic then the observations constrain their energy to roughly 10-100 GeV. For more complex particle distributions, the free pulsar wind emission will be difficult to distinguish from the shocked pulsar wind emission.Comment: 11 pages, 10 figures, accepted for publication in Astronomy and Astrophysic

Limits on the extragalactic background light in the Fermi era

Very high energy (VHE, energy $E \gtrsim 100$\,GeV) \gamma-rays from cosmological sources are attenuated due to the interaction with photons of the extragalactic background light (EBL) in the ultraviolet to infrared wavelength band. The EBL, thus, leaves an imprint on the observed energy spectra of these objects. In the last four years, the number of extragalactic VHE sources discovered with imaging atmospheric Cherenkov telescopes (IACTs), such as MAGIC, H.E.S.S., and VERITAS, has doubled. Furthermore, the measurements of the \emph{Fermi} satellite brought new insights into the intrinsic spectra of the sources at GeV energies. In this paper, upper limits on the EBL intensity are derived by considering the most extensive VHE source sample ever used in this context. This is accomplished by constructing a large number of generic EBL shapes and combining spectral informations from \emph{Fermi} and IACTs together with minimal assumptions about the source physics at high and very high \gamma-ray energies. The evolution of the EBL with redshift is accounted for and the possibility of the formation of an electromagnetic cascade and the implications on the upper limits are explored. The EBL density at $z=0$ is constrained over a broad wavelength range between 0.4 and 100\,\mu m. At optical wavelengths, the EBL density is constrained below 24\,nW\,m$^{-2}$\,sr$^{-1}$ and below 5\,nW\,m$^{-2}$\,sr$^{-1}$ between 8\,\mu m and 31\,\mu m.Comment: 14 pages, 10 figures; accepted for publication in Astronomy & Astrophysic