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Systematic Uncertainties from Halo Asphericity in Dark Matter Searches

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Systematic Uncertainties from Halo Asphericity in Dark Matter Searches CORE Metadata, citation and similar papers at core.ac.uk Provided by Elsevier - Publisher Connector Available online at www.sciencedirect.com Nuclear and Particle Physics Proceedings 267–269 (2015) 345–352 www.elsevier.com/locate/nppp Systematic uncertainties from halo asphericity in dark matter searches Nicolas´ Bernala, Jaime E. Forero-Romerob, Raghuveer Garanic, Sergio Palomares-Ruizd aICTP South American Institute for Fundamental Research and Instituto de F´ısicaTe´orica,Universidade Estadual Paulista, S˜aoPaulo, Brazil bDepartamento de F´ısica,Universidad de los Andes, Cra. 1 No. 18A-10, Edificio Ip, Bogot´a,Colombia cBethe Center for Theoretical Physics and Physikalisches Institut, Universit¨atBonn, Nußallee 12, D-53115 Bonn, Germany dInstituto de F´ısicaCorpuscular (IFIC), CSIC-Universitat de Val`encia,Apartado de Correos 22085, E-46071 Val`encia,Spain Abstract Dark matter halos are predicted to be non-spherical by N-body simulations. Using data from the large N-body cos- mological simulation Bolshoi, we quantify the systematic uncertainties due to halo asphericity on the determination of local dark matter density and the J factors for dark matter annihilations and decay from the galactic center. Keywords: Dark matter, N-body Simulations, triaxial halos. 1. Introduction tion predict DM halos to be triaxial. In this talk we re- visit the question: “What is the impact of halo aspheric- The existence of non-luminous Dark Matter (DM) is ity on direct and indirect searches?” 1. To formulate a by now well established [1, 2]. In order to detect and sensible answer we analyze a sample of 105 DM-only constrain the nature of DM three complementary and Milky Way like halos from Bolshoi simulation [5]. competing strategies have been developed, namely: col- The remainder of the talk (based on Ref. [6]) is or- lider searches, direct and indirect searches. In contrast ganized as follows: In Sec. 2 we emphasize the de- to collider DM searches, direct and indirect methods de- pendence of direct and indirect methods on DM halo pend crucially on the properties of the Milky Way DM density profile. The data we select from the Bolshoi halo. For example: direct detection experiments depend simulation to construct the density profile is briefly dis- on the flux of halo DM particles streaming through the cussed in Sec. 3. In Sec. 4 we use three examples to detector, which naturally depends on the local density illustrate the impact of halo asphericity on the local DM of DM particles. Indirect detection experiments which density and on the so-called J factors. Sec. 5 is devoted measure the flux of gamma-rays and neutrinos that are to the observational priors used. The conclusions are products of DM annihilations or decays, depend on the presented in the last section. shape and orientation of DM halo in the direction of ob- servation. The Milky Way is usually modeled by decomposing 2. Direct and Indirect Searches the galaxy into three components: the bulge, the disc Direct detection experiments aim at detecting halo and the dark halo respectively; with the bulge and the DM particles by measuring nuclear recoils resulting disc embedded in a spherical DM halo. However, it is from scattering of DM with the nuclei in the detector. well known that N-body simulations of structure forma- Qualitatively, the event rate R is given by [7] Email addresses: [email protected] (Nicolas´ Bernal), 1The effects of triaxiality on the estimates for the local DM density [email protected] (Jaime E. Forero-Romero), have been studied in Ref. [3], using a simulation with only DM, and in [email protected] (Raghuveer Garani), Ref. [4], with simulations of two Milky-Way-like galaxies including [email protected] (Sergio Palomares-Ruiz) baryons. http://dx.doi.org/10.1016/j.nuclphysbps.2015.10.129 2405-6014/© 2015 Elsevier B.V. All rights reserved. 346 N. Bernal et al. / Nuclear and Particle Physics Proceedings 267–269 (2015) 345–352 simulation, are compatible with the results from the ρ σ v R ≈ . (1) ninth year data releases from the Wilkinson Microwave χ m mA Anisotropy Probe [10], with Ωm = 0.27, ΩΛ = 0.73, = . = . σ = . Here σ is the DM-nuclei scattering cross section, ρ is ns 0 95, h 0 70 and 8 0 82 for the matter the local DM density, v is the average relative speed of density, dark energy density, slope of the matter fluc- = DM with respect to the target, mχ is the DM mass and tuations, the Hubble parameter at z 0 in units of 100 −1 −1 mA is the mass of the target nuclei. Thus, the measure- km s Mpc and the normalization of the power spec- ment of recoil rate is directly proportional to the local trum, respectively. With these parameters the mass of a = . × 8 −1 DM density, ρ. simulation particle is mp 1 4 10 h M. The sim- For indirect detection of DM annihilations or decays ulation follows the non-linear evolution of DM density − from the galactic center (GC), the spatial distribution of fluctuations in a cube of length 250h 1 Mpc with 20483 DM in the halo is important. The differential flux of particles. The halos formed in this simulation are well resultant products (prompt gamma-ray or neutrinos) of fit by Navarro-Frenk-White (NFW) profile [11, 12]. DM annihilation (decays) in the smooth Milky Way DM The data set we analyze contains 87132 halos which halo coming from a direction within a solid angle ΔΩ, have virial masses in the Milky Way range, i.e., Mv = 12 can be written as [8] [0.7, 4.0] × 10 M. Typically a spherically symmetric DM density profile can be parametrized by two vari- ables, the virial mass M and concentration parameter i v dΦann σv dN ΔΩ (E, ΔΩ) = BR ann J¯ (Ω) , ca. However, in order to describe a triaxial halo two dE 2 m2 i dE ann 4 π χ i more variables are required which describe the shape: / / ≥ ≥ Φ i ΔΩ the axes ratios b a and c a. Here a b c are the d dec 1 dNdec (E, ΔΩ) = BRi J¯dec(Ω) . eigenvalues of the shape tensor for a given halo. dE mχ τχ dE 4 π i The standard spherically symmetric NFW profile is (2) given by σ ρ = N , Here v is the thermally averaged total DM anni- (r) 2 (4) (r/rs)[1+ (r/rs)] hilation cross section times the relative velocity, τχ is the DM lifetime, the discrete sum is over all DM an- and is generalized to a triaxial shape by re- nihilation (decay) channels, BRi is the branching ratio parameterizing r as, of DM annihilation (decay) into the i-th final state and i / i / ff 2 2 dNann dE (dNdec dE) is the di erential gamma-ray or 2 y z neutrino spectrum from the i-th channel. The quanti- r → re = x + + . b/a c/a ties J¯ann(Ω) and J¯dec(Ω), also known as J-factors, which depend on the DM distribution are defined as The resulting distributions for the parameters of triax- ial NFW profile are shown with the black lines in Fig. 1. 1 2 The average values of the parameters in this sample are: J¯ (Ω) = dΩ ρ r(s, Ω) ds , 12 ann ΔΩ M = 1.55 × 10 M, c = 8.9, b/a = 0.81 and ΔΩ los v e c/a = 0.66. ¯ Ω = 1 Ω ρ , Ω . Jdec( ) d r(s ) ds (3) Hierarchical structure formation predicts that massive ΔΩ ΔΩ los halos are formed by mergers of smaller halos. This fea- Here the integral of ρ(r)2 and ρ(r) is performed along ture is nicely illustrated in the probability distribution the line of sight within the solid angle of observation of Mv in Fig. 1. A larger number of halos exist for ΔΩ. low masses. This dependence of the halo abundance as a function of halo mass is well understood and is parametrized through the halo mass function. How- 3. Bolshoi Simulation ever, as for the Milky Way, its mass is quite uncertain The data used in this work is publicly available (within an order of magnitude). In order to avoid an un- through the MultiDark Database2 presented in Ref. [9]. fair weight to the low mass range due to cosmological ff The cosmological parameters, which are inputs to the e ects in the simulation, we also consider a flat prior on Mv by weighting all bins such that all values of Mv, 12 in the range Mv = [0.7, 4.0] × 10 M, are equiproba- 2http://www.multidark.org/MultiDark/MyDB ble. With this exercise we can study systematic effects N. Bernal et al. / Nuclear and Particle Physics Proceedings 267–269 (2015) 345–352 347 Figure 1: Probability distributions of the halo parameters: black Figure 2: Probability distributions of the halo parameters: black lines for our data sample and red lines when a flat prior on Mv is lines for our data sample and red lines when a flat prior on Mv is imposed. The upper panel depicts the probability distributions of the imposed. The upper panel depict the probability distributions of the halo mass Mv and the lower panel the probability distributions of the axes ratio b/a and the lower panel depict probability distributions of concentration parameter ca. the axes ratio c/a. independently of the cosmological bias. The probabil- significant variance with respect to the spherically aver- ity distributions of the parameters for this re-weighted aged value [13]. We show that there exists similar devi- sample, with a flat prior on the halo mass, are depicted ations from the spherically averaged value for J factors in Figs.
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