VERITAS Search for VHE Gamma-ray Emission from Dwarf Spheroidal Galaxies
VERITAS Collaboration, V. A. Acciari, T. Arlen, T. Aune, M. Beilicke, W. Benbow, D. Boltuch, S. M. Bradbury, J. H. Buckley, V. Bugaev, K. Byrum, A. Cannon, A. Cesarini, J. L. Christiansen, L. Ciupik, W. Cui, R. Dickherber, C. Duke, J. P. Finley, G. Finnegan, A. Furniss, N. Galante, S. Godambe, J. Grube, R. Guenette, G. Gyuk, D. Hanna, J. Holder, C. M. Hui, T. B. Humensky, A. Imran, P. Kaaret, N. Karlsson, M. Kertzman, D. Kieda, A. Konopelko, H. Krawczynski, F. Krennrich, G. Maier, S. McArthur, A. McCann, M. McCutcheon, P. Moriarty, R. A. Ong, A. N. Otte, D. Pandel, J. S. Perkins, M. Pohl, J. Quinn, K. Ragan, L. C. Reyes, P. T. Reynolds, E. Roache, H. J. Rose, M. Schroedter, G. H. Sembroski, G. Demet Senturk, A. W. Smith, D. Steele, S. P. Swordy, G. Tešić, M. Theiling, S. Thibadeau, A. Varlotta, V. V. Vassiliev, S. Vincent, R. G. Wagner, S. P. Wakely, J. E. Ward, T. C. Weekes, A. Weinstein, T. Weisgarber, D. A. Williams, S. Wissel, M. D. Wood, B. Zitzer
aa r X i v : . [ a s t r o - ph . C O ] S e p Submitted to the Astrophysical Journal
VERITAS Search for VHE Gamma-ray Emission fromDwarf Spheroidal Galaxies
V. A. Acciari , T. Arlen , T. Aune , M. Beilicke , W. Benbow , D. Boltuch ,S. M. Bradbury , J. H. Buckley , V. Bugaev , K. Byrum , A. Cannon , A. Cesarini ,J. L. Christiansen , L. Ciupik , W. Cui , R. Dickherber , C. Duke , J. P. Finley ,G. Finnegan , A. Furniss , N. Galante , S. Godambe , J. Grube , R. Guenette ,G. Gyuk , D. Hanna , J. Holder , C. M. Hui , T. B. Humensky , A. Imran ,P. Kaaret , N. Karlsson , M. Kertzman , D. Kieda , A. Konopelko , H. Krawczynski ,F. Krennrich , G. Maier , ∐ , S. McArthur , A. McCann , M. McCutcheon ,P. Moriarty , R. A. Ong , A. N. Otte , D. Pandel , J. S. Perkins , M. Pohl , ℧ , J. Quinn ,K. Ragan , L. C. Reyes , P. T. Reynolds , E. Roache , H. J. Rose , M. Schroedter ,G. H. Sembroski , G. Demet Senturk , A. W. Smith , D. Steele , ⋄ , S. P. Swordy ,G. Teˇsi´c , M. Theiling , S. Thibadeau , A. Varlotta , V. V. Vassiliev , S. Vincent ,R. G. Wagner , S. P. Wakely , J. E. Ward , T. C. Weekes , A. Weinstein ,T. Weisgarber , D. A. Williams , S. Wissel , M. D. Wood , B. Zitzer [email protected] Fred Lawrence Whipple Observatory, Harvard-Smithsonian Center for Astrophysics, Amado, AZ 85645,USA Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA Santa Cruz Institute for Particle Physics and Department of Physics, University of California, SantaCruz, CA 95064, USA Department of Physics, Washington University, St. Louis, MO 63130, USA Department of Physics and Astronomy and the Bartol Research Institute, University of Delaware,Newark, DE 19716, USA School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, USA School of Physics, University College Dublin, Belfield, Dublin 4, Ireland School of Physics, National University of Ireland Galway, University Road, Galway, Ireland Physics Department, California Polytechnic State University, San Luis Obispo, CA 94307, USA Astronomy Department, Adler Planetarium and Astronomy Museum, Chicago, IL 60605, USA Department of Physics, Purdue University, West Lafayette, IN 47907, USA Department of Physics, Grinnell College, Grinnell, IA 50112-1690, USA Department of Physics and Astronomy, University of Utah, Salt Lake City, UT 84112, USA Physics Department, McGill University, Montreal, QC H3A 2T8, Canada Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA Department of Physics and Astronomy, University of Iowa, Van Allen Hall, Iowa City, IA 52242, USA Department of Physics and Astronomy, DePauw University, Greencastle, IN 46135-0037, USA Department of Physics, Pittsburg State University, 1701 South Broadway, Pittsburg, KS 66762, USA Department of Life and Physical Sciences, Galway-Mayo Institute of Technology, Dublin Road, Galway,Ireland Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA Department of Applied Physics and Instrumentation, Cork Institute of Technology, Bishopstown, Cork,Ireland Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA ∐ Now at DESY, Platanenallee 6, 15738 Zeuthen, Germany ℧ Now at Institut f¨ur Physik und Astronomie, Universit¨at Potsdam, 14476 Potsdam-Golm,Germany;
ABSTRACT
Indirect dark matter searches with ground-based gamma-ray observatoriesprovide an alternative for identifying the particle nature of dark matter that iscomplementary to that of direct search or accelerator production experiments.We present the results of observations of the dwarf spheroidal galaxies Draco,Ursa Minor, Bo¨otes 1, and Willman 1 conducted by the Very Energetic Radi-ation Imaging Telescope Array System (VERITAS). These galaxies are nearbydark matter dominated objects located at a typical distance of several tens ofkiloparsecs for which there are good measurements of the dark matter densityprofile from stellar velocity measurements. Since the conventional astrophysicalbackground of very high energy gamma rays from these objects appears to benegligible, they are good targets to search for the secondary gamma-ray pho-tons produced by interacting or decaying dark matter particles. No significantgamma-ray flux above 200 GeV was detected from these four dwarf galaxies for atypical exposure of ∼
20 hours. The 95% confidence upper limits on the integralgamma-ray flux are in the range 0 . − . × − photons cm − s − . We interpretthis limiting flux in the context of pair annihilation of weakly interacting massiveparticles (WIMPs) and derive constraints on the thermally averaged product ofthe total self-annihilation cross section and the relative velocity of the WIMPs( h σv i . − cm s − for m χ &
300 GeV / c ). This limit is obtained under con-servative assumptions regarding the dark matter distribution in dwarf galaxiesand is approximately three orders of magnitude above the generic theoretical pre-diction for WIMPs in the minimal supersymmetric standard model framework.However significant uncertainty exists in the dark matter distribution as well asthe neutralino cross sections which under favorable assumptions could furtherlower this limit. Subject headings: gamma rays: observations — dark matter — galaxies: dwarf
1. Introduction
The existence of astrophysical non-baryonic dark matter (DM) has been established byits gravitational effects on a wide range of spatial scales. Perhaps the most compelling evi-
DESY, Platanenallee 6, 15738 Zeuthen, Germany ⋄ Now at Los Alamos National Laboratory, MS H803, Los Alamos, NM 87545 et al. et al. et al. >
100 GeV) gamma rays resulting from the interaction or decay of DMparticles in astrophysical objects in which the gravitational potential is dominated by DM.Among many theoretical candidates for the DM particle (Taoso et al. et al. DM h = 0 . ± . DM h = 0 . ± . DM is the ratio ofdark matter density to the critical density for a flat universe and h is a dimensionless quantitydefined as the Hubble constant, H ◦ , normalized to 100km s − Mpc − (Komatsu et al. et al. et al. to possibly a few TeV/c .The self-annihilation of WIMPs produces a unique spectral signature of secondarygamma rays which is expected to significantly deviate from the standard power-law be-havior observed in most conventional astrophysical sources of VHE gamma rays and wouldhave a cutoff at the WIMP mass. In addition, it could exhibit a monoenergetic line at theWIMP mass or a considerable enhancement of gamma-ray photons at the endpoint of thespectrum due to the internal bremsstrahlung effect (Bringmann et al. et al. et al. et al. et al. et al. et al. et al. et al. et al.
2. Observational Targets
Three of the dSphs forming the subject of this paper, Draco, Ursa Minor, and Willman1, have been identified as the objects within the dSph class with potentially the highestgamma-ray self-annihilation flux, e.g. see Strigari et al. (2007, 2008). The modeling of theDM distribution of these galaxies usually is based on stellar kinematics assuming a sphericallysymmetric stellar population and an NFW profile for DM (Navarro et al. r s and scale density ρ s , ρ ( r ) = ρ s (cid:18) rr s (cid:19) − (cid:18) rr s (cid:19) − . (1) 6 –Table 1: Properties of the four dSphs. Preferred values for DM halo parameters, ρ s andr s , which are defined in the text are taken from Strigari et al. (2007) and Bringmann et al. (2009b). Values for L V , the visual luminosity, and r h , the half-light radius are taken fromWalker et al. (2009). R d is heliocentric distance of the dSph. The calculation of the dimen-sionless line of sight integral, J, which is normalized to the critical density squared times theHubble radius (3 . × GeV cm − ), is explained in Section 5. The J value for Bo¨oteswas calculated by G.D. Martinez and J.S. Bullock. As explained in the text, the elongationof Bo¨otes and the relative lack of stellar kinematic data lead to large uncertainties for r s or ρ s and no values are provided in this case.Quantity Draco Ursa Minor Bo¨otes 1 Willman 1 α [J2000.0] 17 h m s h m s h m s h m s δ [J2000.0] 57 ◦ ′ ′′ ◦ ′ ′′ ◦ ′ ′′ ◦ ′ ′′ L V [L ⊙ ] (2 . ± . × (2 . ± . × (3 . ± . × (1 . ± . × r h [pc] 221 ±
16 150 ±
18 242 ±
21 25 ± R d [kpc] 80 66 62 38 ρ s [M ⊙ / kpc ] 4 . × . × — 4 × r s [kpc] 0.79 0.79 — 0.18 J ( ρ s , r s ) 4 7 3 22 7 –The properties of these galaxies including constraints on r s and ρ s as found in Strigari et al. (2007) and Strigari et al. (2008) are summarized in Table 1.The Draco dSph is one of the most frequently studied objects for indirect DM detection(Baltz et al. et al. et al. et al. et al. et al. L ⊙ (Piatek et al. et al. et al. et al. ± et al. et al. et al. et al. et al. ′ (Bellazzini et al. et al. et al. et al. et al. et al. et al. r s and ρ s are unavailable in the litera-ture. The modeling of Bo¨otes 1 was done by G.D. Martinez and J.S. Bullock (2009, privatecommunication) for a range of NFW fits. The methodology is described in Martinez et al. (2009); Abdo et al. (2010). They produce a probability density function (pdf) for J , theastrophysical contribution to the flux (see Section 5), which is approximately Gaussian inlog( J ). The value given in Table 1 represents J at the peak of the pdf which is approx- 8 –imately the mean of the distribution. The estimates of the age of the stellar populationand metallicity suggest similarity with the old and metal-poor ([Fe/H] ∼ -2.5 – -2.1) stellardistribution of M92 (Belokurov et al. et al. et al. et al. r h ∼
25 pc) and least luminous ( L V ∼ L ⊙ ) dSphs known. Its half-light radius and absolute magnitude suggest that it may be an intermediate object betweendwarf galaxies and globular clusters (Belokurov et al. et al. et al. et al.
3. Data and Analysis3.1. The VERITAS Observatory
The VERITAS observatory is an array of four 12m imaging atmospheric Cherenkovtelescopes (IACTs) located at the Fred Lawrence Whipple Observatory (31 ◦ ′ N 111 ◦ ′ W)in southern Arizona at an altitude of 1.27 km above sea level (Weekes et al. < . ◦ per event. For themeasurements reported here, VERITAS had a point source sensitivity capable of detectinggamma rays with a flux of 5% (1%) of the Crab Nebula flux above 300 GeV at five standarddeviations in < . <
50) hours at 20 ◦ zenith angle. During summer, 2009 subsequentto the four dSph observations, the array configuration was changed, improving the pointsource sensitivity. Further technical description of the VERITAS observatory can be foundin Acciari et al. (2008). Observations of the Draco, Ursa Minor, Bo¨otes 1, and Willman 1 dSphs were performedduring 2007-2009 (see Table 2). Observations were taken in “wobble” mode (Berge et al. ◦ from the center of the field of view in order to obtain 9 –source and background measurement within the same observation. The direction of the offsetwas alternated between north, south, east, and west to minimize systematic errors. Reflected background regions are defined within the field of view at the same radius with respect to thecamera center as that of the targeted dwarf galaxy. Observations were made with varyingatmospheric conditions during moonless periods of the night. Data were quality selectedfor analysis based on the stability of the cosmic-ray trigger rate and the rms temperaturefluctuations observed by an FIR camera viewing the sky in the vicinty of the observed target( ≤ . ◦ C ). The total exposure on each source is given in Table 2. Data reduction follows the methods described in Acciari et al. (2008). A brief outline ofthe analysis flow follows. Images recorded by each of the VERITAS telescopes are character-ized by a second moment analysis giving the Hillas parameters (Hillas 1985). A stereoscopicanalysis of the image parameters is used to reconstruct the gamma ray arrival directionand shower core position. The background of cosmic rays is reduced by a factor of > utilizing cuts on the reconstructed arrival direction ( θ < .
013 deg ) and the image shapeparameters, mean scaled width and length (0 . ≤ msw ≤ .
16 and 0 . ≤ msl ≤ . . ◦ to avoidtruncation effects at the edge of the 3.5 ◦ field of view. The integrated charge recorded inat least two telescopes is further required to be >
75 photoelectrons (400 digital counts)which effectively sets the energy threshold of the analysis to be above ∼
200 GeV dependingon the zenith angle. The energy threshold quoted in our analyses is taken to be the energyat which the differential detection rate of gamma rays from the Crab Nebula peaks. Thecuts applied in this analysis were optimized to maximize significance of the detection fora hypothetical source with a power-law spectrum (dF/dE = 3.2 × − (E/TeV) − . cm − s − TeV − ) corresponding to 3% of the Crab Nebula flux. Two independent data analysispackages were used to analyze the data and yielded consistent results.Table 2: Summary of observation periods and exposures of dSphs by VERITAS.Source Period Exposure [hr] Zenith Angle [ ◦ ]Draco 2007 Apr-May 18.38 26 – 51Ursa Minor 2007 Feb-May 18.91 35 – 46Bo¨otes 1 2009 Apr-May 14.31 17 – 29Willman 1 2007 Dec-2008 Feb 13.68 19 – 28 10 –The significance of the detection was calculated by comparing the counts in the sourceregion to the expected background counts. The background in the source region is estimatedusing the reflected region model. In this model circular background regions, here of angularradius 0 . ◦ , are defined with an offset from the camera center equal to that of the putativesource. Eleven background regions can be accommodated within the VERITAS field of view.The absence of bright stars within any of the four dSph pointings allows all eleven regionsto be used in the background count estimation. The significance of any signal is computedusing the Li and Ma method (Li & Ma 1983, eqn. 17).
4. Results
Table 3 summarizes the results for each of the four dSphs. The effective energy thresholdfor each of the targets changes primarily due to the average zenith angle of observations. Thetable shows the average effective collecting area for gamma rays as calculated from a sampleof simulated gamma-ray showers. No significant excesses of counts above background weredetected from these observations. The 95% confidence level upper limits on the gamma-rayintegral flux were calculated using the bounded profile likelihood ratio statistic developed byRolke et al. (2005).As we have noted, Draco, Ursa Minor, and Willman I have been observed by otherIACTs and we briefly compare our flux limits to the other observations. For Draco, STACEE(Driscoll et al. . × − (cid:0) E (cid:1) − . cm − s − GeV − .The MAGIC flux limit (Albert et al. . × − cm − s − above a threshold of 140 GeV. MAGIC also has set flux limits for Willman 1 in the range5 . − . × − cm − s − above 100 GeV based on several benchmark models (Aliu et al. . × − cm − s − above a threshold of 320 GeV. The limitsfor the VERITAS observations of Draco and Ursa Minor are an improvement of about a factorof 40 over the earlier observations of the group on the Whipple 10m IACT (Wood et al. d φ /dE)as a function of energy. The upper limits were derived with four equidistant log energy binsper decade requiring 95% C.L. in each bin. 11 –
5. Limits on WIMP Parameter Space
The differential flux of gamma rays from WIMP self-annihilation is given by dφ (∆Ω) dE = h σv i πm χ (cid:20) dN ( E, m χ ) dE (cid:21) Z ∆Ω d Ω Z ρ ( λ, Ω) dλ, (2)where h σv i is the thermally averaged product of the total self-annihilation cross section andthe velocity of the WIMP, m χ is the WIMP mass, dN ( E, m χ ) /dE is the differential gamma-ray yield per annihilation, ∆Ω is the observed solid angle around the dwarf galaxy center, ρ is the DM mass density, and λ is the line-of-sight distance to the differential integrationvolume. The astrophysical contribution to the flux can be expressed by the dimensionlessfactor J J (∆Ω) = (cid:18) ρ c R H (cid:19) Z ∆Ω d Ω Z ρ ( λ, Ω) dλ, (3)which has been normalized to the product of the square of the critical density, ρ c = 9 . × − g cm − and the Hubble radius, R H = 4 .
16 Gpc following Wood et al. (2008).Based on equation 2, the upper limits on the gamma-ray rate, R γ (95% C.L.), constrainthe WIMP parameter space ( m χ , h σv i ) according to R γ (95% C.L.)hr − > J . × (cid:18) h σv i × − cm s − (cid:19) × Z ∞ A ( E )5 × cm (cid:18)
300 GeV / c m χ (cid:19) EdN/dE ( E, m χ )10 − dEE , (4)where A ( E ) is the energy-dependent gamma-ray collecting area. The expression has beencast as a product of dimensionless factors with the variables normalized to representativequantities, e.g. the cross section times velocity is normalized to 3 × − cm s − which is arough generic prediction for h σv i for a WIMP thermal relic in the absence of coannihilationsfor m χ >
100 GeV/c (c.f. figure 2). The main contribution to the integral comes fromthe energy range in the vicinity of the energy threshold ( E ≃
300 GeV for observationsin this paper) where A ( E ) changes rapidly. For VERITAS the effective area at 300 GeVis ∼ × cm . For a representative MSSM model, EdN/dE at 300 GeV is a functionof neutralino mass, m χ , and it changes in the range 10 − − − for m χ from 300 GeV/c to a few TeV/c . Although EdN/dE is a rapid function of m χ , this dependence is nearlycompensated by the (300 GeV / c /m χ ) prefactor. The product of these two contributionsand, consequently, the overall integral value, is weakly dependent on the neutralino masswithin the indicated range and is on the order of 1. It is evident from the inequality (Equation4) that for a typical upper limit on the detection rate of 1 gamma ray per hour, significantlyconstraining upper limits on h σv i could be established if J is on the order of 10 . 12 –Because the factor, J , is proportional to the DM density squared, it is subject to con-siderable uncertainty in its experimental determination. For example, the mass of a DMhalo is determined by the interaction of a galaxy with its neighbors and is concentratedin the outer regions of the galaxy. Unlike the DM halo mass, the neutralino annihilationflux is determined by the inner regions of the galaxy where the density is the highest. Forthese regions the stellar kinematic data do not fully constrain the DM density profile dueto limited statistics. Various parametrizations of the DM mass density profile have beenput forward (Navarro et al. et al. et al. et al. r s . The astrophysical factor, J , is then given by J (∆Ω) = (cid:18) πρ s ρ c R H (cid:19) Z . ◦ ) Z λ max λ min (cid:18) r ( λ ) r s (cid:19) − (cid:20) (cid:18) r ( λ ) r s (cid:19)(cid:21) − dλ d (cos θ ) , (5)where the lower integration bound of 0 . ◦ corresponds to the size of the signal integrationregion. The galactocentric distance, r ( λ ), is determined by r ( λ ) = q λ + R dSph − λR dSph cos θ, (6)where λ is the line of sight distance and R dSph is the distance of the dwarf galaxy from theEarth.Although the integration limits, λ min and λ max , are determined by the tidal radius ofthe dSph ( r t = 7 kpc was used for these calculations) (S´anchez-Conde et al. J (∆Ω) comes from the regions r < r s ≪ r t and therefore the choice of r t negligibly affects the J value. The main uncertainty for J computation is due to the choice of ρ s and r s . For Draco and Ursa Minor, ρ s and r s are taken as the midpoints of the range fromStrigari et al. (2007). For Willman 1, ρ s and r s are adopted from Bringmann et al. (2009b).The J value Bo¨otes 1 was calculated by Martinez and Bullock as discussed in section 2. Thesummary of the J values calculated for each object is given in Table 1.An estimated value of J of order 10 is representative for all observed dSphs, which isthree orders of magnitude below the value needed to constrain generic WIMP models with m χ &
100 GeV/c . Figure 2 shows the exclusion region in the ( m χ , h σv i ) parameter spacedue to the observations reported in this paper. MSSM models shown in the figure wereproduced with a random scan of the 7-parameter phase space defined in the DarkSUSYpackage (Gondolo et al. et al. J as compared to the conservativeestimates given in Table 1. First, the inner asymptotic behavior of the DM density may besteeper than ∝ r − predicted by the NFW profile due to unaccounted physical processesat small spatial scales. The extreme assumption would be the Moore profile (Moore et al. ∝ r − . asymptotically which generates a logarithmically divergent self-annihilationflux indicating that another physical process, for example self-annihilation, would limit theDM density in the central regions of the galaxy. A second factor that would increase thevalue of J is deviations of the DM distribution from a smooth average profile (substruc-tures). CDM N-body simulations predict substructures in DM halos (Silk & Stebbins 1993;Diemand et al. et al. (2007) find a maximum boost factor of order 10 while a more detailed cal-culation that accounts for the particle properties of the neutralino during formation of DMhalos suggests boost factors of order 10 and below (Martinez et al. et al. (2008) can significantly enhance dN/dE at the energies comparableto m χ for some MSSM models due to the absence of the helicity suppression factor. Effec-tively this increases the value of the integral in Equation 4, especially for the higher massneutralino models. In addition, the h σv i for self-annihilation at the present cosmologicaltime may be considerably larger than at the time of WIMP decoupling due to a velocity-dependent term in the cross-section and the reduction of the kinetic energy of the WIMPdue to the cosmological expansion of the universe (Robertson & Zentner 2009; Pieri et al.
6. Conclusions
We have carried out a search for VHE gamma rays from four dSphs: Draco, UrsaMinor, Bo¨otes 1, and Willman 1, as part of an indirect DM search program at the VERITASobservatory. The dSphs were selected for proximity to Earth and for favorable estimates ofthe J factor based on stellar kinematics data. No significant gamma-ray excess was observedfrom the four dSphs, and the derived upper limits on the gamma-ray flux constrain the h σv i
14 –for neutralino pair annihilation as a function of neutralino mass to be . − cm s − for m χ &
300 GeV/c . The obtained h σv i limits are three orders of magnitude above genericpredictions for MSSM models assuming an NFW DM density profile, no boost factor, andno additional particle-related gamma-ray flux enhancement factors. Should the neglectedeffects be included, the constraints on h σv i in the most optimistic regime could be pushedto . − cm s − .To begin confronting the predictions of generic MSSM models through observation ofpresently known dSphs, future ground-based observatories will need a sensitivity at leastan order of magnitude better than present-day instruments. The list of dSphs favorable forobservations of DM self-annihilation has grown over the last years by a factor of roughly two,and it is anticipated that newly discovered dSphs may offer a larger factor J. The ongoingsky survey conducted by the Fermi Gamma-ray Space Telescope (FGST) may also identifynearby higher DM density substructures within the MW galaxy which could be followed upby the IACT observatories. Typical current exposures accumulated on dSphs by IACTs areof order 20 hours, and ongoing observing programs could feasibly increase the depth of theseobservations by a factor of 10 (a sensitivity increase of ∼ dN/dE contribution by a factoras large as 10 thus providing an additional sensitivity improvement. With all these factorscombined, the h σv i limits for m χ &
300 GeV/c will begin to rule out the most favorableMSSM models assuming a moderate boost factor. Next generation IACT arrays now beingplanned such as the Advanced Gamma-ray Imaging System (AGIS) and the CherenkovTelescope Array (CTA) will provide an order of magnitude increase in sensitivity and lowerthe energy threshold by factor of ∼ m χ ≃ without strong assumptions regarding potential flux enhancement factors.This research is supported by grants from the US National Science Foundation, the USDepartment of Energy, and the Smithsonian Institution, by NSERC in Canada, by ScienceFoundation Ireland, and by STFC in the UK. We acknowledge the excellent work of thetechnical support staff at the FLWO and the collaborating institutions in the constructionand operation of the instrument. V.V.V. acknowledges the support of the U.S. NationalScience Foundation under CAREER program (Grant No. 0422093).
15 –
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This preprint was prepared with the AAS L A TEX macros v5.2.
19 –Table 3: Results of observations of dSphs by VERITAS.Quantity Draco Ursa Minor Bo¨otes 1 Willman 1Exposure [s] 66185 68080 51532 49255On Source [counts] 305 250 429 326Total Background [counts] 3667 3084 4405 3602Number of Background Regions 11 11 11 11Significance a -1.51 -1.77 1.35 -0.0895% C.L. [counts] b ] 5 . × . × . × . × Energy Threshold [GeV] c
340 380 300 320Flux Limit 95% C.L. [cm − s − ] 0 . × − . × − . × − . × − a Li and Ma method (Li & Ma 1983). b Rolke method (Rolke et al. c Definition given in text.
20 –
E (TeV) −1
10 1 10 ) − s d N / d E ( e r g s c m E −14 −13 −12 −11 −10 DracoBootes IWillman IUrsa Minor
Fig. 1.— 95% C.L. upper limits on the spectral energy density (erg cm − s − ) as a functionof gamma-ray energy for the four dSphs. 21 – (GeV) χ M − s − v > c m σ < −30 −29 −28 −27 −26 −25 −24 −23 −22 −21 −20 DracoWillman IUrsa MinorBootes I
Fig. 2.— Exclusion regions in the ( M χ , h σv i ) parameter space based on the results of theobservations. It is computed according to eq. 4 using a composite neutralino spectrum (seeWood et al. (2008)) and the values of J from Table 1. Black asterisks represent points fromMSSM models that fall within ± et al.et al.