systematics uncertainties in the determination of the local dark - PowerPoint PPT Presentation

systematics uncertainties in the determination of the local dark matter density in collaboration with: G. Bertone, O. Agertz, B. Moore, R. Teyssier Miguel Pato Universita’ degli Studi di Padova / Institut d’Astrophysique de Paris Institute for Theroretical Physics, University Z¨ urich TeV Particle Astrophysics 2010 Paris, France July 19th-23rd 2010

[1] the relevance of the local dark matter density ρ 0 ≡ ρ dm ( R 0 ∼ 8 kpc ) :: ρ 0 is a main astrophysical unknown for DM searches :: key ingredient to compute DM signals and draw limits uncertainties on ρ 0 are crucial in interpreting positive DM detections scattering off nuclei capture in Sun/Earth halo annihilation/decay R ∞ v min dv f ( v ) dN dm d φ dE ∝ � σ ann v � n k dm ∝ ρ k dR dE ∝ n dm ∝ ρ 0 = C − 2Γ ann 0 v dt R v max dv f ( v ) C ∝ n dm ∝ ρ 0 signals: γ , e + , ¯ signal: nuclei recoils p , ν 0 v sensitive to � ρ 0 � mpc signal: ν from Sun/Earth sensitive to � ρ 0 � [not the largest unknown] sensitive to � ρ 0 �

[1] from dynamical observables to ρ 0 Milky Way mass model � 3 kpc ρ b ( x , y , z ) x b , y b , z b bulge(+bar) disk � 10 kpc ρ d ( r , z ) Σ d , r d , z d dark halo � 200 kpc ρ dm ( x , y , z ) ∝ ρ 0 +gas... a model fixes M i ( R ) , φ i ( R ) i M i ( < R ) = v 2 ( R ) d φ dR ( R ) ≡ G � � v 0 ≡ v ( R 0 ) i R 2 R spherical average local density � � � v 2 R � � 1 1 ∂ � − dM d � � ρ 0 ≃ ¯ � � 4 π R 2 G ∂ R dR � � 0 R 0 � R 0

[1] from dynamical observables to ρ 0 observables A + B = − v ′ R 0 , A − B = v 0 / R 0 , 0 [fix v 0 , v ′ 0 ] mass enclosed M ( < 50 kpc ) M ( < 100 kpc ) local surface density Σ | z | < 1 . 1 kpc Σ ∗ terminal velocities R < R 0 v ( R ) = v T ( l ) + v 0 sin ( l ) velocity dispersions R � R 0 (tracer populations) ∂ ( νσ 2 R ) + 2 βσ 2 R ν d φ i dR = − ν G = ν � � Jeans (sph., steady) i M i ( < R ) ∂ R R i R 2 σ los ∝ σ R microlensing τ LMC ∼ 10 − 7 τ bulge ∼ 10 − 6 [constrain M b ]

[1] from dynamical observables to ρ 0 aim: use observables to constrain mass model parameters selected references (different models/observables) ρ 0 = 0 . 23 ± × 2 GeV/cm 3 Caldwell & Ostriker ’81 − 0 . 11 GeV/cm 3 ρ 0 = 0 . 30 +0 . 12 Gates, Gyuk & Turner ’95 ρ 0 ≃ 0 . 18 − 0 . 30 GeV/cm 3 Moore et al ’01 ρ 0 ≃ 0 . 18 − 0 . 71 GeV/cm 3 (isoth.) Belli et al ’02 Strigari & Trotta ’09 ∆ ρ 0 /ρ 0 = 20% (projected; 2000 halo stars, v esc ) ρ 0 ≃ 0 . 39 ± 0 . 03 GeV/cm 3 Catena & Ullio ’09 ∆ ρ 0 /ρ 0 = 7% !! ρ 0 ≃ 0 . 43 ± 0 . 21 GeV/cm 3 Salucci et al ’10 usual assumptions: ρ dm = ρ dm ( r ), ρ dm from DM-only simulations

[1] the role of baryons on dark matter halos adiabatic contraction [Blumenthal et al 1986] spherical mass distribution M i ( < R i ): baryons + dark matter f b ∼ 0 . 17 baryons cool and contract slowly → M b ( < R ) circular orbits + L = const R ( M b ( < R ) + M dm ( < R )) = R i M i ( < R i ) = R i M dm ( < R ) / (1 − f b ) ρ dm ∝ R − 2 dM dm dR final DM profile is significantly contracted [+ Gnedin et al 2004, Gustafsson et al 2006] halo shape DM-only halos are prolate + baryons: more oblate halos (still triaxial) in any case, ρ dm � = ρ dm ( r ) aim address systematics on ρ 0 in light of recent N-body+hydro simulations a realistic pdf on ρ 0 is needed if we are to convincingly identify WIMPs

[2] our numerical framework difficult to obtain a MW-like galaxy at z = 0 with simulations usually large bulges and small disks result ( L problem) recent sucessful attempt: Agertz, Teyssier & Moore 2010 dark matter + gas + stars cosmological setup baryonic features WMAP 5yr cosmology star formation (Schmidt law; ǫ ff , n 0 ) ρ g select DM-only halo ρ g = − ǫ ff ˙ t ff M vir ∼ 10 12 M ⊙ R vir ∼ 205 kpc stellar feedback (SNII, SNIa, wind) no major merger for z < 1 numerical features m DM = 2 . 5 × 10 6 M ⊙ ∆ x = 340 pc main result MW-like galaxy with v c ∼ const , B / D ∼ 0 . 25 , r d ∼ 4 − 5 kpc

[2] our numerical framework to bracket uncertainties we consider: DM only, MW like, baryon+

[3] halo shape: a first look profiles of dark matter density SR6-n01e1ML :: MW like 10 7 M ⊙ / kpc 3 ∼ 0 . 38 GeV/cm 3

[3] halo shape: a first look profiles of dark matter density SR6-n01e1ML :: MW like approximately axisymmetric halo 10 7 M ⊙ / kpc 3 ∼ 0 . 38 GeV/cm 3

[3] halo shape: a first look

[3] halo shape: a first look

[3] halo shape: a first look local spherical shell: 7 . 5 < R < 8 . 5 kpc DM overdensity towards z ∼ 0 (i.e. stellar disk) bottomline baryons make DM halos rounder (but still non-spherical) and flattened along the stellar disk

[3] halo shape: getting more quantitative inertia calculations P Np k =1 m k x i , k x j , k for a set of N p particles, J ij = P Np k =1 m k principle axes: eigenvectors � j a (major), � j b (intermediate), � j c (minor) p p axis ratios: b / a = J b / J a , c / a = J c / J a triaxiality: T = 1 − b 2 / a 2 1 − c 2 / a 2 iterative procedure [’a la Katz et al ’91] q r < R → b / a , c / a , � x 2 + y 2 z 2 j a , b , c → q = ( b / a ) 2 + ( c / a ) 2 < R → ... convergence criterium: 0.5% change in b / a , c / a

[3] halo shape: getting more quantitative inclusion of baryons prolate → oblate halo shape flattening aligned with stellar disk for R � 20 kpc [MP, Agertz, Bertone, Moore & Teyssier ’10]

[3] halo shape: consequences for ρ 0 / many studies assume a spherical halo [e.g. Catena & Ullio, Strigari & Trotta] / data then constrains the spherical average local density ¯ ρ 0 : � � � ∂ ( v 2 R ) 1 1 � − dM d � ρ 0 ≃ ¯ � � 4 π R 2 G ∂ R dR R 0 0 � R 0 / model triaxial halo is tricky ( b / a , c / a not known nor constant) / to estimate systematic uncertainty compare ¯ ρ 0 ↔ ρ 0 in simulations strategy spherical shell 7 . 5 < R < 8 . 5 kpc select particles in 3 orthogonal rings divide rings into 8 portions ∆ ϕ = π/ 4 evaluate ρ along the ring, ρ ( ϕ )

[3] halo shape: consequences for ρ 0 [MP, Agertz, Bertone, Moore & Teyssier ’10]

[3] halo shape: consequences for ρ 0 MW like ρ 0 / ¯ ρ 0 = 1 . 01 − 1 . 41 baryon+ ρ 0 / ¯ ρ 0 = 1 . 21 − 1 . 60 DM only ρ 0 / ¯ ρ 0 = 0 . 39 − 1 . 94 / ρ ( ϕ ) > ¯ ρ 0 because halo is flattened / halo-to-halo scatter can change normalisation [MP, Agertz, Bertone, Moore & Teyssier ’10]

[3] halo shape: consequences for ρ 0 just an exercise... ρ 0 = 0 . 466 ± 0 . 033 (stat) ± 0 . 077( syst ) GeV / cm 3 :: syst > stat :: future: bayesian study with triaxial halo

[4] ρ 0 : why do we care? direct detection Z ∞ ρ 0 v E ; v esp , v 0 ) d σ χ N dR d 3 � dE R = v vf ( � v + � m χ m N dE R v min standard assumptions ρ 0 = 0 . 3 GeV / cm 3 f ( v ) ∝ e − v 2 / v 2 0 , v 0 ≃ 220 km/s, v esc ≃ 600 km/s exclusion limits are not rigid ρ 0 should really be treated as a nuisance parameter in direct DM searches

[4] ρ 0 : why do we care? direct detection Z ∞ ρ 0 v E ; v esp , v 0 ) d σ χ N dR d 3 � dE R = v vf ( � v + � m χ m N dE R v min standard assumptions ρ 0 = 0 . 3 GeV / cm 3 f ( v ) ∝ e − v 2 / v 2 0 , v 0 ≃ 220 km/s, v esc ≃ 600 km/s exclusion limits are not rigid ρ 0 should really be treated as a nuisance parameter in direct DM searches

[4] ρ 0 : why do we care? reconstruction capabilities direct + halo stars direct + LHC 3/4 halo parameters ρ χ ∝ ρ 0 Ω χ ∆¯ ρ 0 / ¯ ρ 0 ∼ 20% no uncertainty on ρ 0 next steps: include astro+nuclear uncertainties complementarity between different targets in direct detection [on-going work...]

[..] conclusions ρ 0 in light of recent N-body+hydro simulations > baryons turn DM halo from prolate to oblate > flattening is along the disk > ρ 0 / ¯ ρ 0 ≃ 1 . 21 ± 0 . 20 ρ 0 uncertainties: not an academic question! ultimately limit our ability to combine signals and distinguish particle physics models upcoming direct detection experiments and results urge for accurate control over systematics of astrophysical parameters

[+] halo profile DM-only simulations find NFW | Einasto profiles ∂ ln ρ ∂ lnR → − 1 | 0 as R → 0 baryons expected to contract DM profile ∂ ln ρ ∂ lnR < − 1 for R < 1 kpc but: no convergence; R > 2∆ x teaser if ρ dm ∝ R − 2 , extrapolation to pc (why not?) yields extreme annihilation signals e.g. for Fermi-LAT GC γ , � σ ann v � � 10 − 28 cm 3 /s @ m dm = 100 GeV

[+] halo profile significant contraction wrt DM-only case hint for an inner cusp

[+] halo profile: mass enclosed M dm ( < 3 − 8 kpc ): important for dynamical constraints ↓ insensitive to inner cusp: R − 1 . 97 , ˜ ∆ M dm ( < ˜ R = 3(8) kpc R ) = 3(1)% ρ 0 ( SR6-n01e1ML ) ¯ same M dm ( < 8 kpc ) for ≃ 0 . 9 ρ 0 ( DM-only ) ¯ but: A ± B , Σ ∗ constrain ¯ ρ 0 and M dm ( < R 0 ) ↓ using contracted profiles would lead to smaller c , but same ¯ ρ 0