Stackelberg security game models and associated computational tools have seen deployment in a number of high-consequence security settings, such as LAX canine patrols and Federal Air Marshal Service. These models focus on isolated systems with only o
ne defender, despite being part of a more complex system with multiple players. Furthermore, many real systems such as transportation networks and the power grid exhibit interdependencies between targets and, consequently, between decision makers jointly charged with protecting them. To understand such multidefender strategic interactions present in security, we investigate game theoretic models of security games with multiple defenders. Unlike most prior analysis, we focus on the situations in which each defender must protect multiple targets, so that even a single defenders best response decision is, in general, highly non-trivial. We start with an analytical investigation of multidefender security games with independent targets, offering an equilibrium and price-of-anarchy analysis of three models with increasing generality. In all models, we find that defenders have the incentive to over-protect targets, at times significantly. Additionally, in the simpler models, we find that the price of anarchy is unbounded, linearly increasing both in the number of defenders and the number of targets per defender. Considering interdependencies among targets, we develop a novel mixed-integer linear programming formulation to compute a defenders best response, and make use of this formulation in approximating Nash equilibria of the game. We apply this approach towards computational strategic analysis of several models of networks representing interdependencies, including real-world power networks. Our analysis shows how network structure and the probability of failure spread determine the propensity of defenders to over- or under-invest in security.
Due to its extraordinarily high concentration of known relativistic particle accelerators such as pulsar wind nebula, supernova remnants, dense molecular cloud regions, and the supermassive black hole (Sgr A*); the center of the Milky Way galaxy has
long been an ideal target for high energy (HE, 0.1-100 GeV) and very high energy ( VHE, 50 GeV-50 TeV) gamma-ray emission. Indeed, detections of Sgr A* and other nearby regions of gamma-ray emission have been reported by EGRET and Fermi-LAT in the HE band, as well as CANGAROO, Whipple, HESS, VERITAS, and MAGIC in the VHE band. Here we report on the results of extended observations of the region with VERITAS between 2010-2014. Due to the visibility of the source for VERITAS in the Northern Hemisphere, these observations provide the most sensitive probe of gamma-ray emission above 2 TeV in one of the most complicated and interesting regions of our home galaxy.
We present the results of a multiwavelength observational campaign on the TeV binary system LS I +61 303 with the VERITAS telescope array (>200 GeV), Fermi-LAT (0.3-300 GeV), and Swift-XRT (2-10 keV). The data were taken from December 2011 through Ja
nuary 2012 and show a strong detection in all three wavebands. During this period VERITAS obtained 24.9 hours of quality selected livetime data in which LS I +61 303 was detected at a statistical sig- nificance of 11.9 sigma. These TeV observations show evidence for nightly variability in the TeV regime at a post-trial significance of 3.6 sigma. The combination of the simultaneously obtained TeV and X-ray fluxes do not demonstrate any evidence for a correlation between emission in the two bands. For the first time since the launch of the Fermi satellite in 2008, this TeV detection allows the construction of a detailed MeV-TeV spectral energy distribution from LS I +61 303. This spectrum shows a distinct cutoff in emission near 4 GeV, with emission seen by the VERITAS observations following a simple power-law above 200 GeV. This feature in the spectrum of LS I +61 303, obtained from overlapping observations with Fermi-LAT and VERITAS, may indicate that there are two distinct populations of accelerated particles producing the GeV and TeV emission.
Since the commissioning of the array in Spring 2007, the VERITAS array (sensitive in the 0.1-50 TeV energy range) has acquired over 300 hours of observations investigating the TeV emission from X-ray binary star systems, in particular focusing on the
known TeV binary targets LS I +61 303 and HESS J0632+057. Both TeV binaries have been monitored by VERITAS for several years and the resulting dataset is continuing to yield important results in the characterization of these poorly understood systems. We present these results, as well as the contemporaneous observations of these sources taken with Fermi-LAT and Swift-XRT. In the case of LS I +61 303, simultaneous observations taken with VERITAS and Fermi-LAT reveal a break in emission in the 10-200 GeV range. For HESS J0632 057, the extended VERITAS observations have allowed for the first identification of a binary system through TeV gamma-ray observations.
In this white paper, submitted as a part of Snowmass 2013 (subgroup CF2), we examine the current status and future prospects of the VERITAS indirect dark matter detection program. The VERITAS array of imaging atmospheric Cherenkov telescopes (IACTs),
sensitive in the 0.1-50 TeV regime, is in the process of completing a multi-year program aimed at detecting signatures of neutralino dark matter. This program is spread out over a range of astrophysical targets which can potentially yield definitive signatures of neutralino self-annihilation such as dwarf spheroidal galaxies (dSphs) and the center of the Milky Way galaxy. While the program is still in progress, initial results on dSphs have produced very competitive upper limits on the thermally averaged cross-section of neutralino self-annihilation as well as strongly constraining leptophillic dark matter models (such as those inferred from the PAMELA and AMS positron fraction results). As the program continues over the next 5 years, VERITAS observations will yield some of the strongest constraints available from IACTs, pushing down the limit on the thermally averaged cross-section of neutralino self-annihilation to the expected natural thermal relic scale.
We present observations of the BL Lac object 1ES 0414+009 in the >200 GeV gamma-ray band by the VERITAS array of Cherenkov telescopes. 1ES 0414+009 was observed by VERITAS between January 2008 and February 2011, resulting in 56.2 hours of good qualit
y pointed observations. These observations resulted in a detection of 822 events from the source corresponding to a statistical significance of 6.4 standard deviations (6.4 sigma) above the background. The source flux, showing no evidence for variability, is measured as 5.2 +/- 1.1_stat +/- 2.6_sys * 10^-12 photons cm^-2 s^-1 above 200 GeV, equivalent to approximately 2% of the Crab Nebula flux above this energy. The differential photon spectrum from 230 GeV to 850 GeV is well fit by a power law with an photon index of Gamma 3.4 +/- 0.5_stat +/- 0.3_sys and a flux normalization of 1.6 +/- 0.3_stat +/- 0.8_sys * 10^-11 photons cm^-2 s^-1 at 300 GeV. We also present multiwavelength results taken in the optical (MDM), X-ray (Swift-XRT), and GeV (Fermi-LAT) bands and use these results to construct a broadband spectral energy distribution (SED). Modeling of this SED indicates that homogenous one-zone leptonic scenarios are not adequate to describe emission from the system, with a lepto-hadronic model providing a better fit to the data.
We present the results of observations of the TeV binary LS I +61 303 with the VERITAS telescope array between 2008 and 2010, at energies above 300 GeV. In the past, both ground-based gamma-ray telescopes VERITAS and MAGIC have reported detections of
TeV emission near the apastron phases of the binary orbit. The observations presented here show no strong evidence for TeV emission during these orbital phases; however, during observations taken in late 2010, significant emission was detected from the source close to the phase of superior conjunction (much closer to periastron passage) at a 5.6 standard deviation (5.6 sigma) post-trials significance. In total, between October 2008 and December 2010 a total exposure of 64.5 hours was accumulated with VERITAS on LS I +61 303, resulting in an excess at the 3.3 sigma significance level for constant emission over the entire integrated dataset. The flux upper limits derived for emission during the previously reliably active TeV phases (i.e. close to apastron) are less than 5% of the Crab Nebula flux in the same energy range. This result stands in apparent contrast to previous observations by both MAGIC and VERITAS which detected the source during these phases at >10% of the Crab Nebula flux. During the two year span of observations, a large amount of X-ray data were also accrued on LS I +61 303 by the Swift X-ray Telescope (XRT) and the Rossi X-ray Timing Explorer Timing (RXTE) Proportional Counter Array (PCA). We find no evidence for a correlation between emission in the X-ray and TeV regimes during 20 directly overlapping observations. We also comment on data obtained contemporaneously by the Fermi Large Area Telescope (LAT).
We present results from a long-term monitoring campaign on the TeV binary LSI +61 303 with VERITAS at energies above 500 GeV, and in the 2-10 keV hard X-ray bands with RXTE and Swift, sampling nine 26.5 day orbital cycles between September 2006 and F
ebruary 2008. The binary was observed by VERITAS to be variable, with all integrated observations resulting in a detection at the 8.8 sigma (2006/2007) and 7.3 sigma (2007/2008) significance level for emission above 500 GeV. The source was detected during active periods with flux values ranging from 5 to 20% of the Crab Nebula, varying over the course of a single orbital cycle. Additionally, the observations conducted in the 2007-2008 observing season show marginal evidence (at the 3.6 sigma significance level) for TeV emission outside of the apastron passage of the compact object around the Be star. Contemporaneous hard X-ray observations with RXTE and Swift show large variability with flux values typically varying between 0.5 and 3.0*10^-11 ergs cm^-2 s^-1 over a single orbital cycle. The contemporaneous X-ray and TeV data are examined and it is shown that the TeV sampling is not dense enough to detect a correlation between the two bands.
A long term, multi-wavelength monitoring campaign on the TeV binary LS I +61 303 has been performed utilizing >300 GeV observations with VERITAS along with monitoring in the 0.2-10 keV band by RXTE and Swift between September 2006 and February 2008.
The source was detected by VERITAS as a variable TeV source with flux values ranging from 5-20% of the Crab Nebula flux with the strongest flux levels appearing around apastron. X-ray observations by RXTE and Swift show the source as a highly variable hard X-ray source with flux values varying in the range of 0.5-3*10^-11 ergs cm^-2 s^-1 over a single orbital cycle. The 2007-2008 RXTE data set also shows the presence of several extremely large flaring episodes presenting a flux of up to 7.2*10^-11 ergs cm^-2 s^-1, the largest such flare recorded from this source. Comparison of the contemporaneous TeV and X-ray data does not show a correlation at this time, however, the sparsity of data sets do not preclude the existence of such a correlation.
