Limits to Quantum Gravity Effects from Observations of TeV Flares in Active Galaxies

We have used data from the TeV gamma-ray flare associated with the active galaxy Markarian 421 observed on 15 May 1996 to place bounds on the possible energy-dependence of the speed of light in the context of an effective quantum gravitational energy scale. The possibility of an observable time dispersion in high energy radiation has recently received attention in the literature, with some suggestions that the relevant energy scale could be less than the Planck mass and perhaps as low as 10^16 GeV. The limits derived here indicate this energy scale to be in excess of 4x10^16 GeV at the 95% confidence level. To the best of our knowledge, this constitutes the first convincing limit on such phenomena in this energy regime.Comment: 6 pages, including 2 figure

Deformation of canonical morphisms and the moduli of surfaces of general type

In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite map can be deformed to a one--to--one map. We use this criterion to construct new simple canonical surfaces with different $c_1^2$ and $\chi$. Our general results enable us to describe some new components of the moduli of surfaces of general type. We also find infinitely many moduli spaces $\mathcal M_{(x',0,y)}$ having one component whose general point corresponds to a canonically embedded surface and another component whose general point corresponds to a surface whose canonical map is a degree 2 morphism.Comment: 32 pages. Final version with some simplifications and clarifications in the exposition. To appear in Invent. Math. (the final publication is available at springerlink.com

Geometric and homological finiteness in free abelian covers

We describe some of the connections between the Bieri-Neumann-Strebel-Renz invariants, the Dwyer-Fried invariants, and the cohomology support loci of a space X. Under suitable hypotheses, the geometric and homological finiteness properties of regular, free abelian covers of X can be expressed in terms of the resonance varieties, extracted from the cohomology ring of X. In general, though, translated components in the characteristic varieties affect the answer. We illustrate this theory in the setting of toric complexes, as well as smooth, complex projective and quasi-projective varieties, with special emphasis on configuration spaces of Riemann surfaces and complements of hyperplane arrangements.Comment: 30 pages; to appear in Configuration Spaces: Geometry, Combinatorics and Topology (Centro De Giorgi, 2010), Edizioni della Normale, Pisa, 201

On the nonthermal X-ray emission in blazar jets

We consider particle acceleration to high energy via diffusive shock acceleration in a simple, self-consistent shock in jet model for blazars. Electrons are assumed to be accelerated at a shock front in relativistic jets and radiate synchrotron emission in a post-shock region. The full time, space and momentum dependence of the electron distribution function is used for a calculation of the nonthermal synchrotron spectra. We discuss the evolution of the spectral index by varying the rate at which particles enter the acceleration process. The results indicate that the synchrotron spectral index displays a characteristic looplike behaviour with intensity (as has been observed in several blazars), where the orientation of the loop depends on whether the acceleration time scale is comparable to the synchrotron cooling time scale or not. We show that our model provides a good fit to the observed evolution of the spectral index of Mkn 421 during a flare in 1994.Comment: 6 pages, 3 figures, conference proceedin

Complex Spectral Variability from Intensive Multi-wavelength Monitoring of Mrk421 in 1998

We conducted a multi-frequency campaign for the TeV blazar Mrk~421 in 1998 April. The campaign started from a pronounced high amplitude flare recorded by SAX and Whipple; ASCA observation started three days later. In the X-ray data, we detected multiple flares, occuring on time scales of about one day. ASCA data clearly reveal spectral variability. The comparison of the data from ASCA, EUVE and RXTE indicates that the variability amplitudes in the low energy synchrotron component are larger at higher photon energies. In TeV Gamma-rays, large intra-day variations -- which were correlated with the X-ray flux -- were observed when results from three Cherenkov telescopes are combined. The RMS variability of TeV Gamma--rays was similar to that observed in hard X-rays, above 10 keV. The X-ray light curve reveals flares which are almost symmetric for most of cases, implying the dominant time scale is the light crossing time through the emitting region. The structure function analysis based on the continuous X-ray light curve of seven days indicates that the characteristic time scale is ~0.5 day. The analysis of ASCA light curves in various energy bands appears to show both soft (positive) and hard (negative) lags. These may not be real, as systematic effects could also produce these lags, which are all much smaller than an orbit. If the lags of both signs are real, these imply that the particle acceleration and X-ray cooling time scales are similar.Comment: 10 pages, 4 figures, accepted for publication in ApJ Letter

Correlated variability of Mkn 421 at X-ray and TeV wavelengths on timescales of hours

Mkn 421 was observed for about two days with BeppoSAX, prior to and partly overlapping the start of a 1 week continuous exposure with ASCA in April 1998, as part of a world-wide multiwavelength campaign. A pronounced, well defined, flare observed in X-rays was also observed simultaneously at TeV energies by the Whipple Observatory's 10 m gamma-ray telescope. These data provide the first evidence that the X-ray and TeV intensities are well correlated on time-scales of hours.Comment: 4 pages, 1 figure, presented at the VERITAS Workshop on the TeV Astrophysics of Extragalactic Object

The classification of isotrivially fibred surfaces with p_g=q=2

An isotrivially fibred surface is a smooth projective surface endowed with a morphism onto a curve such that all the smooth fibres are isomorphic to each other. The first goal of this paper is to classify the isotrivially fibred surfaces with $p_g=q=2$ completing and extending a result of Zucconi. As an important byproduct, we provide new examples of minimal surfaces of general type with $p_g=q=2$ and $K^2=4,5$ and a first example with $K^2=6$.Comment: Main paper by M.Penegini. Appendix by S.Rollenske. 31 pages, 6 Figures. v2 changed group relations in Theorem 5.2, changes in Theorem 5.7, new proof of Theorem 4.15, minor corrections of misprint

Search for TeV Gamma-Rays from Shell-Type Supernova Remnants

If cosmic rays with energies <100 TeV originate in the galaxy and are accelerated in shock waves in shell-type supernova remnants (SNRs), gamma-rays will be produced as the result of proton and electron interactions with the local interstellar medium, and by inverse Compton emission from electrons scattering soft photon fields. We report on observations of two supernova remnants with the Whipple Observatory's 10 m gamma-ray telescope. No significant detections have been made and upper limits on the >500 GeV flux are reported. Non-thermal X-ray emission detected from one of these remnants (Cassiopeia A) has been interpreted as synchrotron emission from electrons in the ambient magnetic fields. Gamma-ray emission detected from the Monoceros/Rosette Nebula region has been interpreted as evidence of cosmic-ray acceleration. We interpret our results in the context of these observations.Comment: 4 pages, 2 figures, to appear in the proceedings of 26th International Cosmic Ray Conference (Salt Lake City, 1999