Correlation of Solar X-ray Flux and SID Modified VLF Signal Strength

This paper presents a quantitative comparison of the X-ray flux during solar flares, as measured by the GOES-15 satellite, and the associated effects on the ionization levels in the lower ionosphere as measured by Sudden Ionospheric Disturbance (SID) monitors around the globe. These monitors detect signals from a variety of different transmitting stations, each sending a unique Very Low Frequency (VLF) or Low Frequency (LF) radio wave signal ranging from 16.4 to 77.5 kHz. Global signal propagation distances are achieved via the Earth-ionosphere waveguide propagation mode. During a solar flare, the increased X-ray flux enhances the ionization response in the sunlit ionosphere. The resulting SID in the lower ionosphere alters LF and VLF signal propagation. The monitored signal strength increases as a result of increased conductivity of the layer and a decrease in height of the ionosphere boundary. X-ray flux and SID modified signal strength were analyzed from March 2010 to June 2014. Ionospheric incubation times, and duration and strength of signal enhancement are related to flare strength via the X-ray flux enhancement

Axiomatic Bargaining Theory on Opportunity Assignments

This paper discusses issues of axiomatic bargaining problems over opportunity assignments. The fair arbitrator uses the principle of "equal opportunity" for all players to make the recommendation on re- source allocations. A framework in such a context is developed and several classical solutions to standard bargaining problems are reformulated and axiomatically characterized. Working Paper 06-4

On the Core of Dynamic Cooperative Games

We consider dynamic cooperative games, where the worth of coalitions varies over time according to the history of allocations. When defining the core of a dynamic game, we allow the possibility for coalitions to deviate at any time and thereby to give rise to a new environment. A coalition that considers a deviation needs to take the consequences into account because from the deviation point on, the game is no longer played with the original set of players. The deviating coalition becomes the new grand coalition which, in turn, induces a new dynamic game. The stage games of the new dynamical game depend on all previous allocation including those that have materialized from the deviating time on. We define three types of core solutions: fair core, stable core and credible core. We characterize the first two in case where the instantaneous game depends on the last allocation (rather than on the whole history of allocations) and the third in the general case. The analysis and the results resembles to a great extent the theory of non-cooperative dynamic games.Comment: 25 page

A nilpotent IP polynomial multiple recurrence theorem

We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibman's result that polynomial mappings into a nilpotent group form a group and a multiparameter version of the nilpotent Hales-Jewett theorem due to Bergelson and Leibman.Comment: v4: switch to TeXlive 2016 and biblate

Helical motion and the origin of QPO in blazar-type sources

Recent observations and analysis of blazar sources provide strong evidence for (i) the presence of significant periodicities in their lightcurves and (ii) the occurrence of helical trajectories in their radio jets. In scenarios, where the periodicity is caused by differential Doppler boosting effects along a helical jet path, both of these facts may be naturally tied together. Here we discuss four possible driving mechanisms for the occurrence of helical trajectories: orbital motion in a binary system, Newtonian-driven jet precession, internal jet rotation and motion along a global helical magnetic field. We point out that for non-ballistic helical motion the observed period may appear strongly shortened due to classical travel time effects. Finally, the possible relevance of the above mentioned driving mechanisms is discussed for Mkn~501, OJ 287 and AO 0235+16.Comment: 6 pages, 1 figure; presented at the 5th Microquasar Workshop, Beijing, June 2004. Accepted for publication in the Chinese Journal of Astronomy and Astrophysic

Simultaneous X-Ray and TeV Gamma-Ray Observations of the TeV Blazar Markarian 421 during February and May 2000

In this paper we present the results of simultaneous observations of the TeV blazar Markarian 421 (Mrk 421) at X-ray and TeV Gamma-ray energies with the Rossi X-Ray Timing Explorer (RXTE) and the stereoscopic Cherenkov Telescope system of the HEGRA (High Energy Gamma Ray Astronomy) experiment, respectively. The source was monitored from February 2nd to February 16th and from May 3rd to May 8th, 2000. We discuss in detail the temporal and spectral properties of the source. Remarkably, the TeV observations of February 7th/8th showed statistically significant evidence for substantial TeV flux variability on 30 min time scale. We show the results of modeling the data with a time dependent homogeneous Synchrotron Self-Compton (SSC) model. The X-ray and TeV gamma-ray emission strengths and energy spectra together with the rapid flux variability strongly suggest that the emission volume is approaching the observer with a Doppler factor of 50 or higher. The different flux variability time scales observed at X-rays and TeV Gamma-rays indicate that a more detailed analysis will require inhomogeneous models with several emission zones.Comment: Accepted for Publication in ApJ, 21 Pages, 5 Figure

Rejection of the hypothesis that Markarian 501 TeV photons are pure Bose-Einstein condensates

The energy spectrum of the Blazar type galaxy Markarian 501 (Mrk 501) as measured by the High-Energy-Gamma-Ray Astronomy (HEGRA) air Cerenkov telescopes extends beyond 16 TeV and constitutes the most energetic photons observed from an extragalactic object. A fraction of the emitted spectrum is possibly absorbed in interactions with low energy photons of the diffuse extragalactic infrared radiation, which in turn offers the unique possibility to measure the diffuse infrared radiation density by TeV spectroscopy. The upper limit on the density of the extragalactic infrared radiation derived from the TeV observations imposes constraints on models of galaxy formation and stellar evolution. One of the recently published ideas to overcome severe absorption of TeV photons is based upon the assumption that sources like Mrk 501 could produce Bose-Einstein condensates of coherent photons. The condensates would have a higher survival probability during the transport in the diffuse radiation field and could mimic TeV air shower events. The powerful stereoscopic technique of the HEGRA air Cerenkov telescopes allows to test this hypothesis by reconstructing the penetration depths of TeV air shower events: Air showers initiated by Bose-Einstein condensates are expected to reach the maximum of the shower development in the atmosphere earlier than single photon events. By comparing the energy-dependent penetration depths of TeV photons from Mrk 501 with those from the TeV standard-candle Crab Nebula and simulated air shower events, we can reject the hypothesis that TeV photons from Mrk 501 are pure Bose-Einstein condensates.Comment: 9 pages, 2 figures, published by ApJ Letters, revised version (simulation results added

The TeV Energy Spectrum of Mkn 501 Measured with the Stereoscopic Telescope System of HEGRA during 1998 and 1999

During 1997, the BL Lac object Mkn 501 went into an extraordinary state of high X-ray and TeV gamma-ray activity, lasting more than 6 months. In this paper we report on the TeV emission characteristics of the source in the subsequent years of 1998 and 1999 as measured with the Stereoscopic Cherenkov Telescope System of HEGRA (La Palma, Canary Islands). Our observations reveal a 1998-1999 mean emission level at 1 TeV of 1/3 of the flux of the Crab Nebula, a factor of 10 lower than during the year of 1997. A dataset of 122 observations hours with the HEGRA telescope system makes it possible to assess for the first time the Mkn 501 TeV energy spectrum for a mean flux level substantially below that of the Crab Nebula with reasonable statistical accuracy. Excluding the data of a strong flare, we find evidence that the 1998--1999 low-flux spectrum is substantially softer (by 0.44+-0.1(stat) in spectral index) than the 1997 time averaged spectrum. The 500 GeV to 10 TeV energy spectrum can well be described by a power law model with exponential cutoff: dN/dE ~ E^(-alpha) exp(-E/E0) with alpha=2.31+-0.22(stat), and E0=5.1 (-2.3+7.8)(stat) TeV. Within statistical accuracy, also a pure power law model gives an acceptable fit to the data: dN/dE ~ E^(-Gamma) with Gamma=2.76+-0.08(stat). After presenting the 1998-1999 TeV characteristics of the source we discuss the implications of the results.Comment: Accepted for publication in The Astrophysical Journal, Part 1, on August 4th, 200

The unidentified TeV source (TeVJ2032+4130) and surrounding field: Final HEGRA IACT-System results

The unidentified TeV source in Cygnus is now confirmed by follow-up observations from 2002 with the HEGRA stereoscopic system of Cherenkov Telescopes. Using all data (1999 to 2002) we confirm this new source as steady in flux over the four years of data taking, extended with radius 6.2 arcmin (+-1.2 arcmin (stat) +-0.9 arcmin (sys)) and exhibiting a hard spectrum with photon index -1.9. It is located in the direction of the dense OB stellar association, Cygnus OB2. Its integral flux above energies E>1 TeV amounts to \~5% of the Crab assuming a Gaussian profile for the intrinsic source morphology. There is no obvious counterpart at radio, optical nor X-ray energies, leaving TeVJ2032+4130 presently unidentified. Observational parameters of this source are updated here and some astrophysical discussion is provided. Also included are upper limits for a number of other interesting sources in the FoV, including the famous microquasar Cygnus X-3.Comment: 7 pages, 3 figures. Accepted for publication in Astronomy & Astrophysic