Apostolos Mastichiadis

X-Ray Spectral Formation in a Converging Fluid Flow: Spherical Accretion into Black Holes

We study Compton upscattering of low-frequency photons in a converging flow of thermal plasma. The photons escape diffusively, and electron scattering is the dominant source of opacity. We solve the equation of radiative transfer in the case of spherical, steady state accretion into black holes numerically and approximately analytically. Unlike previous work on this subject, we consider the inner boundary at a finite radius, and this has a significant effect on the emergent spectrum. It is shown that the bulk motion of the converging flow is more efficient in upscattering photons than thermal Comptonization, provided that the electron temperature in the flow is of order a few keV or less. In this case, the spectrum observed at infinity consists of a soft component coming from input photons that escaped after a few scatterings without any significant energy change and of a power law that extends to high energies and is made of those photons that underwent significant upscattering. The luminosity of the power law is relatively small compared to that of the soft component. The more reflective the inner boundary is, the flatter the power-law spectrum becomes. The spectral energy power-law index for black hole accretion is always higher than 1, and it is approximately 1.5 for high accretion rates. This result tempts us to say that bulk motion Comptonization might be the mechanism behind the power-law spectra seen in black hole X-ray sources.

The Beaming Pattern and Spectrum of Radiation from Inverse Compton Scattering in Blazars

By including Klein-Nishina effects, we generalize previous calculations of the beaming pattern of photons produced by inverse Compton scattering. For an isotropic distribution of soft photons upscattered by nonthermal electrons with a power-law density distribution n(γ) ∝ γ-p, embedded in a plasma moving with relativistic bulk speed, we show that the observed radiation intensity is proportional to D3+p, where D is the Doppler boosting factor. This agrees with previous computations performed in the Thomson limit, where the observed spectral index is α = (p - 1)/2 and the beaming pattern is D4+2α. Independent of D, Klein-Nishina effects limit the location of the peak energy peakmec2 of the observed spectral energy distribution such that peak 1/0, where 0 is the energy of the seed photons in units of mec2. Assuming that the seed photons originate in the broad-line region, we demonstrate that the GeV emission of blazars is significantly modified by Klein-Nishina effects, the spectrum being softer than that calculated in the Thomson limit. We further show that the change in the spectral index of the inverse Compton emission across peak can exceed the value of 0.5 predicted by computations performed in the Thomson limit. The model spectra agree with OSSE and COMPTEL limits on this break without invoking the effects of differential absorption at the edge of a gamma-ray photosphere.

Stochastic particle acceleration and synchrotron self-Compton radiation in TeV blazars

Aims. We analyse the influence of the stochastic particle accelera tion for the evolution of the electron spectrum. We assume that all investigated spectra are generated inside a spherical, homogeneous source and also analyse the synchrotron and inverse Compton emission generated by such an object. Methods. The stochastic acceleration is treated as the diffusion of the particle momentum and is described by the momentum‐diffusion equation. We investigate the stationary and time dependent solutions of the equation for several different evolutionary scenarios. The scenarios are divided into two general classes. First, we analyse a few cases without injection or escape of the particles during th e evolution. Then we investigate the scenarios where we assume continuous injection and simultaneous escape of the particles. Results. In the case of no injection and escape the acceleration process, competing with the radiative cooling, only modifies the i nitial particle spectrum. The competition leads to a thermal or quasi‐thermal distribution of the particle energy. In the case of the inj ection and simultaneous escape the resulting spectra depend mostly on the energy distribution of the injected particles. In the simplest case, w here the particles are injected at the lowest possible energies, the competition b etween the acceleration and the escape forms a power‐law energy distribution. We apply our modeling to the high energy activity of the blazar Mrk 501 observed in April 1997. Calculating the evolution of the electron spectrum self‐consistently we can reproduce the observed spectra well with a number of free parameters that is comparable to or less than in the “classic stationary” one‐zone synchrotron self‐Compton scenario.

Correlation between the TeV and X-ray emission in high-energy peaked BL Lac objects

We discuss the correlation between the evolution of the TeV emission and X-ray radiation observed in high-energy peaked BL Lac objects. We describe such a correlation by a simple power law FTeV (t) ∝ F x−ray (t). In the first part of this work we present correlations obtained for the activity of Mrk 501 observed in 1997 April and for the activity of Mrk 421 observed in 2000 February. Our results obtained for Mrk 501 show that the index of the correlation (x) may strongly depend on the width and position of the spectral bands used for the comparison. The result of the correlation which we have obtained for Mrk 421 is not informative. However, we discuss results of similar correlation obtained for this source by other authors. They report an almost quadratic (x ∼ 2) correlations observed between the evolution of the TeV and X-ray emission. In the second part of this paper we present a phenomenological model which describes the evolution of the synchrotron and inverse Compton emission of a simple spherical homogeneous source. Neglecting the radiative cooling of the particles we derive analytical expressions that describe the evolution. Then we use a numerical code to investigate the impact of radiative cooling on the evolution. We show that different forms of correlations can be obtained depending on the assumed evolution scenario and the spectral bands used for the calculation. However, the quadratic correlation observed during the decay phase of the flare observed in Mrk 421 on 2001 March 19 appears problematic for this basic modeling. The quadratic correlation can be explained only for specific choices of the spectral bands used for the calculation. Therefore, looking for more robust solutions, we investigate the evolution of the emission generated by a cylindrical source. However this model does not provide robust solutions for the problem of a quadratic correlation. In principle the problem could be solved by the TeV emission generated by the self Compton scattering in the Thomson limit. However, we show that such a process requires unacceptably large values of the Doppler factor. Finally we briefly discuss the possible influence of the light travel time effect on our results.

Photohadronic origin of

The recent IceCube discovery of 0.1-1 PeV neutrinos of astrophysical origin opens up a new era for high-energy astrophysics. Although there are various astrophysical candidate sources, a firm association of the detected neutrinos with one (or more) of them is still lacking. A recent analysis of plausible astrophysical counterparts within the error circles of IceCube events showed that likely counterparts for nine of the IceCube neutrinos include mostly BL Lacs, among which Mrk 421. Motivated by this result and a previous independent analysis on the neutrino emission from Mrk 421, we test the BL Lac-neutrino connection in the context of a specific theoretical model for BL Lac emission. We model the spectral energy distribution (SED) of the BL Lacs selected as counterparts of the IceCube neutrinos using a one-zone leptohadronic model and mostly nearly simultaneous data. The neutrino flux for each BL Lac is self-consistently calculated, using photon and proton distributions specifically derived for every individual source. We find that the SEDs of the sample, although different in shape and flux, are all well fitted by the model using reasonable parameter values. Moreover, the model-predicted neutrino flux and energy for these sources are of the same order of magnitude as those of the IceCube neutrinos. In two cases, namely Mrk 421 and H 1914-194, we find a suggestively good agreement between the model prediction and the detected neutrino flux. Our predictions for all the BL Lacs of the sample are in the range to be confirmed or disputed by IceCube in the next few years of data sampling.

\boldsymbol {\gamma }

We investigate the origin of high-energy emission in blazars within the context of the leptohadronic one-zone model. We find that γ -ray emission can be attributed to synchrotron radiation either from protons or from secondary leptons produced via photohadronic processes. These possibilities imply differences not only in the spectral energy distribution (SED) but also in the variability signatures, especially in the X- and γ -ray regime. Thus, the temporal behaviour of each leptohadronic scenario can be used to probe the particle population responsible for the high-energy emission as it can give extra information not available by spectral fits. In this work, we apply these ideas to the non-thermal emission of Mrk 421, which is one of the best monitored TeV blazars. We focus on the observations of 2001 March, since during that period Mrk 421 showed multiple flares that have been observed in detail both in X-rays and γ -rays. First, we obtain pre-flaring fits to the SED using the different types of leptohadronic scenarios. Then, we introduce random-walk-type, small-amplitude variations on the injection compactness or on the maximum energy of radiating particles and follow the subsequent response of the radiated photon spectrum. For each leptohadronic scenario, we calculate the X-ray and γ -ray fluxes and investigate their possible correlation. Whenever the ‘input’ variations lead, apart from flux variability, also to spectral variability, we present the resulting relations between the spectral index and the flux, both in X-rays and γ -rays. We find that proton synchrotron models are favoured energetically but require fine tuning between electron and proton parameters to reproduce the observed quadratic behaviour between X-rays and TeV γ -rays. On the other hand, models based on pion decay can reproduce this behaviour in a much more natural way.

-ray BL Lac emission: implications for IceCube neutrinos

We present a time-dependent approach to the one-zone hadronic model in the case where the photon spectrum is produced by ultrarelativistic protons interacting with soft photons that are produced from protons and low magnetic fields. Assuming that protons are injected at a certain rate in a homogeneous spherical volume containing a magnetic field, the evolution of the system can be described by five coupled kinetic equations, for protons, electrons, photons, neutrons, and neutrinos. Photopair and photopion interactions are modelled using the results of Monte-Carlo simulations and, in particular from the SOPHIA code for the latter. The coupling of energy losses and injection introduces a self-consistency in our approach and allows the study of the comparative relevancy of processes at various conditions, the efficiency of the conversion of proton luminosity to radiation, the resulting neutrino spectra, and the effects of time variability on proton injection, among other topics. We present some characteristic examples of the temporal behaviour of the system and show that this can be very different from the one exhibited by leptonic models. Furthermore, we argue that, contrary to the wide-held belief, there are parameter regimes where the hadronic models can become quite efficient. However, to keep the free parameters at a minimum and facilitate an in-depth study of the system, we have only concentrated on the case where protons are injected; i.e., we did not consider the effects of a co-accelerated leptonic component.

Mrk 421 as a case study for TeV and X-ray variability in leptohadronic models

We look for the expected signature of an accretion disc by examining the properties of the Hα emission line versus viewing angle in a sample of 22 superluminal (SL) quasars. The Doppler factor δ, jet velocity γ and viewing angle θ towards the jet are derived from published radio and X-ray data. Most of the Hα spectra (14) have been observed at the United Kingdom Infrared Telescope (UKIRT) and are reported here. About a quarter of the SL objects have weak or absent Hα emission lines, with small equivalent widths (EW). These have high optical polarization, radio core dominance and Doppler factor, and most of them have high apparent SL velocity and low viewing angles. Therefore these weak-EW objects almost certainly have relativistically beamed optical continua. The strong-EW objects also show a clear beaming effect, but a much weaker one, with line EW varying by only a factor of 3 while radio core dominance varies by a factor of several hundred. The correlation of EW with θ is quantitatively in good agreement with the prediction of a flat accretion disc with limb darkening. The weakand strong-EW sources also show an anticorrelation of line velocity width with the various beaming indicators. Again, the correlation with the derived viewing angle θ shows a quantitative agreement with the effect expected for an axisymmetric structure with velocity dominated by rotation. The line emission cannot come from the surface of the disc, or the line beaming would cancel the continuum beaming. However, it could come from an axisymmetric system of clouds corotating with the accretion disc.

The time-dependent one-zone hadronic model - First principles

Abstract The acceleration of electrons at a shock front can produce characteristic patterns in the variation of the spectral index of the synchrotron emission as a function of flux. Using a simple model of the acceleration process, we present a discussion of these patterns and show how they compare with the variations in the emission of the same electrons via inverse Compton scattering of isotropically distributed target photons from an external source. The “soft lag” behaviour is observed in synchrotron emission, and should also be present in the inverse Compton flux. Shock models can also show “hard lag” behaviour of the synchrotron emission, but this is more difficult to achieve in the inverse Compton emission, because of Klein-Nishina effects. In some cases, the time scales of rise and fall of both the synchrotron and inverse Compton fluxes can depend on the acceleration mechanism.

Is there a disc in the superluminal quasars

We show that relativistic bremsstrahlung and inverse Compton scattering of radio-emitting electrons can easily account for the observed γ-ray spectrum of 2EG J1857+0118 if the field strength in the shell is below ~30 μG. This source is located at the eastern border of the composite SNR W44, where the expanding radio shell is interacting with a dense molecular cloud. The nondetection of this remnant above 250 GeV implies a cutoff or steepening in the electron spectrum above ~100 GeV. The E-1.66 spectrum of this radio/γ-ray-emitting electron component is too flat to have its origin in standard first-order Fermi acceleration, but electron injection into the shell by the pulsar PSR B1853+01 over the 2 × 104 yr lifetime may explain why the Crab-like radio spectrum (Sν ∝ ν-0.33) is about the hardest of all shell-type remnants. The injected energy would be sufficient to account for the required energy of 6 × 1049 ergs if the initial spin-down power of PSR B1853+01 was about 10 times larger than the present spin-down power of the Crab pulsar. A steeper Fermi electron component may be present, but the observational data are not constraining enough to provide a meaningful limit on the presence of an additional ~E-2 shell-type electron component. The predicted γ-ray contribution from high-energy proton-gas interactions is about 20% of the observed EGRET flux above 100 MeV, which confirms our conclusion that the γ-ray emission from W44 is dominated by a leptonic component.