Higher Spin Alternating Sign Matrices

We define a higher spin alternating sign matrix to be an integer-entry square matrix in which, for a nonnegative integer r, all complete row and column sums are r, and all partial row and column sums extending from each end of the row or column are nonnegative. Such matrices correspond to configurations of spin r/2 statistical mechanical vertex models with domain-wall boundary conditions. The case r=1 gives standard alternating sign matrices, while the case in which all matrix entries are nonnegative gives semimagic squares. We show that the higher spin alternating sign matrices of size n are the integer points of the r-th dilate of an integral convex polytope of dimension (n-1)^2 whose vertices are the standard alternating sign matrices of size n. It then follows that, for fixed n, these matrices are enumerated by an Ehrhart polynomial in r.Comment: 41 pages; v2: minor change

Self-gravity at the scale of the polar cell

We present the exact calculus of the gravitational potential and acceleration along the symmetry axis of a plane, homogeneous, polar cell as a function of mean radius a, radial extension e, and opening angle f. Accurate approximations are derived in the limit of high numerical resolution at the geometrical mean of the inner and outer radii (a key-position in current FFT-based Poisson solvers). Our results are the full extension of the approximate formula given in the textbook of Binney & Tremaine to all resolutions. We also clarify definitely the question about the existence (or not) of self-forces in polar cells. We find that there is always a self-force at radius except if the shape factor a.f/e reaches ~ 3.531, asymptotically. Such cells are therefore well suited to build a polar mesh for high resolution simulations of self-gravitating media in two dimensions. A by-product of this study is a newly discovered indefinite integral involving complete elliptic integral of the first kind over modulus.Comment: 4 pages, 4 figures, A&A accepte

Local geometry of random geodesics on negatively curved surfaces

It is shown that the tessellation of a compact, negatively curved surface induced by a typical long geodesic segment, when properly scaled, looks locally like a Poisson line process. This implies that the global statistics of the tessellation -- for instance, the fraction of triangles -- approach those of the limiting Poisson line process.Comment: This version extends the results of the previous version to surfaces with possibly variable negative curvatur

MAGIC detection of short-term variability of the high-peaked BL Lac object 1ES 0806+524

The high-frequency-peaked BL Lac (HBL) 1ES 0806+524 (z = 0.138) was discovered in VHE $\gamma$ rays in 2008. Until now, the broad-band spectrum of 1ES 0806+524 has been only poorly characterized, in particular at high energies. We analysed multiwavelength observations from $\gamma$ rays to radio performed from 2011 January to March, which were triggered by the high activity detected at optical frequencies. These observations constitute the most precise determination of the broad-band emission of 1ES 0806+524 to date. The stereoscopic MAGIC observations yielded a $\gamma$-ray signal above 250 GeV of $(3.7 \pm 0.7)$ per cent of the Crab Nebula flux with a statistical significance of 9.9 $\sigma$. The multiwavelength observations showed significant variability in essentially all energy bands, including a VHE $\gamma$-ray flare that lasted less than one night, which provided unprecedented evidence for short-term variability in 1ES 0806+524. The spectrum of this flare is well described by a power law with a photon index of $2.97 \pm 0.29$ between $\sim$150 GeV and 1 TeV and an integral flux of $(9.3 \pm 1.9)$ per cent of the Crab Nebula flux above 250 GeV. The spectrum during the non-flaring VHE activity is compatible with the only available VHE observation performed in 2008 with VERITAS when the source was in a low optical state. The broad-band spectral energy distribution can be described with a one-zone Synchrotron Self Compton model with parameters typical for HBLs, indicating that 1ES 0806+524 is not substantially different from the HBLs previously detected.Comment: 12 pages, 8 figures, 3 tables, accepted 2015 April 20 for publication in Monthly Notices of the Royal Astronomical Society Main Journa

Semi-analytic modeling of the EBL and consequences for extragalactic gamma-ray spectra

Attenuation of high-energy gamma rays by pair-production with UV, optical and IR extragalactic background light (EBL) photons provides a link between the history of galaxy formation and high-energy astrophysics. We present results from our latest semi-analytic models (SAMs), which employ the main ingredients thought to be important to galaxy formation and evolution, as well as an improved model for reprocessing of starlight by dust to mid- and far-IR wavelengths. These SAMs are based upon a Lambda-CDM hierarchical structural formation scenario, and are successful in reproducing a large variety of observational constraints such as number counts, luminosity and mass functions, and color bimodality. Our fiducial model is based upon a WMAP5 cosmology, and treats dust emission using empirical templates. This model predicts a background flux considerably lower than optical and near-IR measurements that rely on subtraction of zodiacal and galactic foregrounds, and near the lower bounds set by number counts of resolvable sources at a large number of wavelengths. We also show the results of varying cosmological parameters and dust attenuation model used in our SAM. For each EBL prediction, we show how the optical depth due to electron-positron pair-production is affected by redshift and gamma-ray energy, and the effect of gamma-ray absorption on the spectra of a variety of extragalactic sources. We conclude with a discussion of the implications of our work, comparisons to other models and key measurements of the EBL and a discussion of how the burgeoning science of gamma-ray astronomy will continue to help constrain cosmology. The low EBL flux predicted by our fiducial model suggests an optimistic future for further studies of distant gamma-ray sources.Comment: 23 pages, 11 figures, 3 tables, accepted by MNRAS; this preprint matches accepted versio

Constraints to Energy Spectra of Blazars based on Recent EBL Limits from Galaxy Counts

We combine the recent estimate of the contribution of galaxies to the 3.6 micron intensity of the extragalactic background light (EBL) with optical and near-infrared (IR) galaxy counts to set new limits on intrinsic spectra of some of the most distant TeV blazars 1ES 0229+200, 1ES 1218+30.4, and 1ES 1101-232, located at redshifts 0.1396, 0.182, and 0.186, respectively. The new lower limit on the 3.6 micron EBL intensity is significantly higher than the previous one set by the cumulative emission from resolved Spitzer galaxies. Correcting for attenuation by the revised EBL, we show that the differential spectral index of the intrinsic spectrum of the three blazars is 1.28 +- 0.20 or harder. These results present blazar emission models with the challenge of producing extremely hard intrinsic spectra in the sub-TeV to multi-TeV regime. These results also question the reliability of recently derived upper limits on the near-IR EBL intensity that are solely based on the assumption that intrinsic blazar spectra should not be harder than 1.5.Comment: 13 pages, 2 figures, submitted to the Astrophysical Journa