Dark matter detection: a closer look at the astrophysical uncertainties. Riccardo Catena. Institut für Theoretische Physik, Heidelberg - PDF

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Dark matter detection: a closer look at the astrophysical uncertainties Riccardo Catena Institut für Theoretische Physik, Heidelberg R. C. and P. Ullio, JCAP 1008 (2010) 004 R. C. and P. Ullio,

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Dark matter detection: a closer look at the astrophysical uncertainties Riccardo Catena Institut für Theoretische Physik, Heidelberg R. C. and P. Ullio, JCAP 1008 (2010) 004 R. C. and P. Ullio, in progress R. C.,C. Evoli,L. Maccione and P. Ullio, in progress Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Overview/Motivations Present dark matter detection strategies: - Direct detection - Indirect detection - Accelerators searches Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Overview/Motivations Direct detection - Signal: dr = σp ρ Z DM(R 0 ) f DM (v, t) de r 2µ 2 p,dm m dv A 2 F 2 (E r ) DM v min v - Assumptions: * The local density ρ DM (R 0 ) * The velocity distribution f DM (v, t) Indirect detection (gamma-rays) - Signal: Indirect detection (antimatter) - Signal: Φ(ψ, E) = σ v d N - Assumptions: 1 d E 4πm DM * The dark matter profile ρ 2 DM Z l.o.s. ds ρ 2 DM (r(s, ψ)) q p (r, z, T p ) = σv g(t p )! 2 ρ DM (r, z) m DM q p Φ TOA (solving the diffusion eq.) - Assumptions: * The diffusive model * The dark matter profile ρ 2 DM * The solar modulation Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Overview/Motivations This talk is devoted to: - The local density - The local velocity distribution (in progress) - The diffusion model (in progress) Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Outline 1 The local density The underlying Galactic Model The experimental constraints The method:bayesian inference with Markov Chain Monte Carlo Results 2 The velocity distribution 3 The diffusion model 4 Conclusions Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Outline 1 The local density The underlying Galactic Model The experimental constraints The method:bayesian inference with Markov Chain Monte Carlo Results 2 The velocity distribution 3 The diffusion model 4 Conclusions Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Outline 1 The local density The underlying Galactic Model The experimental constraints The method:bayesian inference with Markov Chain Monte Carlo Results 2 The velocity distribution 3 The diffusion model 4 Conclusions Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Outline 1 The local density The underlying Galactic Model The experimental constraints The method:bayesian inference with Markov Chain Monte Carlo Results 2 The velocity distribution 3 The diffusion model 4 Conclusions Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 The underlying Galactic Model Dark Halo Thick Disk Gas + Fluctuations Bulge/Bar Thin Disk Figure: Schematic representation of the Galaxy Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 The underlying Galactic Model Dark Halo Thick Disk Gas + Fluctuations Bulge/Bar Thin Disk Figure: Schematic representation of the assumed Galactic model Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 The underlying Galactic Model - The stellar disk: ρ d (R, z) = Σ ( ) d e R R z d sech 2 2z d z d with R R dm H. T. Freudenreich, Astrophys. J. 492, 495 (1998) - The dust layer: The distribution of the Interstellar Medium is assumed axisymmetric as well. T. M. Dame, AIP Conference Proceedings 278 (1993) 267. Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 The underlying Galactic Model - The stellar bulge/bar: [ ( ) ] ρ bb (x, y, z) = ρ bb (0) exp s2 b + sa 1.85 exp( s a ) 2 where s 2 a = q2 a (x 2 + y 2 ) + z 2 z 2 b [ ( ) 2 ( ) ] 2 2 ( ) 4 x y z sb 2 = + +. x b y b z b H. Zhao, arxiv:astro-ph/ Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 The underlying Galactic Model - The Dark Matter halo: where f is the Dark Matter profile. - M vir, and c vir as halo parameters: ( R ρ h (R) = ρ f a h ), ρ = ρ (M vir, c vir ) a h = a h (M vir, c vir ) Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 The underlying Galactic Model - The Dark Matter profile: [ ] f E (x) = exp 2 α E (x α E 1) J.F. Navarro et al., MNRAS 349 (2004) A.W. Graham, D. Merritt, B. Moore, J. Diemand and B. Terzic, Astron. J. 132 (2006) f NFW (x) = 1 x(1+x) 2 J.F. Navarro, C.S. Frenk and S.D.M. White, Astrophys. J. 462, 563 (1996); Astrophys. J. 490, 493 (1997). f B (x) = 1 (1+x) (1+x 2 ). A. Burkert, Astrophys. J. 447 (1995) L25. Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 The underlying Galactic Model 1e+07 1e+06 Dark matter profiles Einasto NFW Burkert Profiles [GeV/cm 3 ] Galactocentric distance [Kpc] Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Parameter space Galactic components Parameters Disk Disk Σ d R d Bulge/bar ρ bb (0) Halo Halo Halo α E M vir c vir All components R 0 All components β Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 The experimental constraints Constraints: - Oort s constants: A B = Θ 0 R 0 ; A + B = Θ(R 0) R - terminal velocities - total mean surface density within z 1.1kpc - local disk surface mass density - total mass inside 50 kpc and 100 kpc - l.s.r. velocity, proper motion and parallaxes distance of high mass star forming regions in the outer Galaxy - radial velocity dispersion of tracers from the SDSS - stellar motions around the massive black hole in the GC - peculiar motion of SgrA Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 The experimental constraints Constraints: - Oort s constants: A B = Θ 0 R 0 ; A + B = Θ(R 0) R - terminal velocities - total mean surface density within z 1.1kpc - local disk surface mass density - total mass inside 50 kpc and 100 kpc - l.s.r. velocity, proper motion and parallaxes distance of high mass star forming regions in the outer Galaxy - radial velocity dispersion of tracers from the SDSS - stellar motions around the massive black hole in the GC - peculiar motion of SgrA Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 The experimental constraints: Radial velocity dispersions -The dataset: population of stars with distances up to 60kpc from the Galactic center. The distances are accurate to 10% and the radial velocity errors are less than 30 km s 1. -It is a strong constraint in the range 10 kpc R 60 kpc -To compare the data to the predictions: Jeans Equation σ 2 r (r) = 1 r 2β ρ (r) r d r r 2β 1 ρ ( r)θ 2 ( r) - where β is the anisotropy parameter: β 1 σ 2 t /σ2 r. Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 The method: Bayesian approach Parametric model of the Galaxy Frequentist approach = Maximum Likelihood Bayesian approach = Posterior probability density - This work Bayesian approach Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 The method: Bayesian approach - Target: posterior pdf (Bayes theorem): p(η d) = L(d η)π(η) p(d) ; d = data; η = parameters - Output: the mean and the variance with respect to p(η d) of functions f(η). - We will focus on f = η and f = ρ DM (R 0 ). Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 The method: Markov Chain Monte Carlo - Monte Carlo expectation values: f(η) = dη f(η)p(η d) 1 N 1 f(η (t) ), N where η (t) was sampled from p(η d). t=0 - Monte Carlo technics require a method to sample η (t) = Markov chains. - Markov chains : p(η (0) ) T(η (t), η (t+1) ) = η(t) distributed according to p(η d). Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Convergence of the Markov chains R (Scale reduction factor). Convergence: R 1.1 and roughly constant. 1-R as a function of the iteration number: disc central surface density bulge-bar central mass density disc radial scale Sun s Galactocentric distance halo virial mass concentration parameter anisotropy beta parameter Multivariate Scale Reduction Fatcor Iteration number Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Figure: Marginal posterior pdf of the Galactic model parameters (NFW profile). Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Figure: Marginal posterior pdf of the Galactic model parameters (Einasto profile). Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 R 0 [Kpc] R 0 [kpc] c vir M [ M ] vir Θ c vir M [ M ] vir Θ Figure: Two dimensional marginal posterior pdf in the planes spanned by combinations of the Galactic model parameters (NFW profile). Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 R 0 [kpc] R 0 [kpc] M vir [10 12 M Θ ] M vir [ M Θ ] c vir α E c vir 15 c vir 15 α E M vir [ M Θ ] α E R 0 [kpc] Figure: Two dimensional marginal posterior pdf in the planes spanned by combinations of the Galactic model parameters (Einasto profile). Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Figure: Marginal posterior pdf for the local Dark Matter density. Top left panel: Einasto profile, applying different subsets of constraints. Top right panel: Einasto profile. Bottom left panel: NFW profile. Bottom right panel: Burkert profile. Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Numerical values - Numerically we find: ρ DM (R 0 ) = (0.385 ± 0.027) GeV cm 3 (Einasto) ρ DM (R 0 ) = (0.389 ± 0.025) GeV cm 3 (NFW) ρ DM (R 0 ) = (0.409 ± 0.029) GeV cm 3 (Burkert) - No strong dependences from the assumed halo profile. Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Comparison with other recent related works - Maximum Likelihood approach: M. Weber and W. de Boer, arxiv: [astro-ph.co]. * Only three free parameters (many fixed a priori) * For some choice of the fixed parameters (with reasonable M vir ): ρ DM (R 0 ) = (0.39 ± 0.05) GeV cm 3 - Poisson equation approach: P. Salucci, F. Nesti, G. Gentile and C. F. Martins, arxiv: [astro-ph.ga]. RΘ 2 K, R=R 0 * Strategy: ρ DM (R 0 ) = 1 4πGR 2 0 R ρ DM (R 0 ) = (0.43 ± 0.11 ± 0.10) GeV cm 3 - Fisher matrix forecasts: L. E. Strigari and R. Trotta, JCAP 0911 (2009) 019 [arxiv: [astro-ph.he]]. * Assumed a reference point in parameter space it tests the reconstruction capabilities of a future direct detection experiment accounting for astrophysical uncertainties. Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 A bayesian study of the velocity distribution function (in progress) - Isotropic phase space density from a given spherically symmetric mass profile F(E) = 1 Z E» d 2 ρ dψ p + 1 «dρ 8π 2 0 dψ 2 E ψ E dψ ψ=0 - Dark matter velocity distribution: f(v) = F DM (R 0 )/ρ DM (R 0 ) Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 A bayesian study of the diffusion model - The transport equation (the case of a stable nucleus) N i t (D v c) N i + ṗ p p 3 v c N i N i p p2 D pp p p = 2 = Q i (p, r, z) + X j i cβn gas(r, z)σ ji N j cβn gasσ in(e k )N i -The parameter space: D, v c, D pp, etc -The calculated signals (L.Maccione et al. (2010)) Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 A global scan with GALPROP R. Trotta et al. (2010) Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 A global scan with DRAGON (in progress) Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31 Conclusions We proved that Bayesian probabilistic inference is a good method to constrain the local dark matter density. For a given dark matter profile, and assuming spherical symmetry, we can therefore estimate the local dark matter density with an accuracy of roughly the 10%. This result does not include a number of systematic uncertainties which are related to the galactic model, e.g.: - baryonic compression - dark disk The possibility of applying similar technics to the study of the dark matter velocity distribution and the cosmic rays diffusion model is at present under investigation Riccardo Catena (ITP) MPIK, Heidelberg 29/11/ / 31
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