Revisiting the escape speed impact on dark matter direct detection Stefano Magni Ph.D. Student - LUPM (Montpellier) Based on collaborations with Julien Lavalle, paper in preparation FFP14 Marseille July 15, 2014
Outline ● Introduction ● Astrophysical parameters and uncertainties ● Insights from the escape speed after the RAVE survey ● Consistent astrophysical modeling and impact on exclusion curves ● Conclusions
Direct detection rate and exclusion curves 90% C.L. v min ( E r )= √ LUX E r m A experiment 2 2m red E T = 2.76 keV AstroPhysics A 2 σ p,SI F 2 ( E r ) Detector dN v ' 1 ∫ d 3 ⃗ ( E r ) = ΔM Δt v ( ⃗ v ' ) v' f ⃗ ρ 0 dE r 2 2m red , p m χ v ' ∣ >v' min ( Er ) ∣⃗ ¿ Particle + hadronic + nuclear physics ρ 0 η ( E r )
Reference speed function: the Standard Halo Model (SHM) Maxwell-Boltzmann speed distribution Relies on isothermal assumption σ ∝ v 0 − ( 2 ) v 2 v )= 4v 2 v 0 f v ( v )= 4πv 2 f ⃗ v (⃗ 3 e π 1 / 2 v 0 ¿ v esc (plus exponential cutoff at ) Important parameters and their standard values 3 v 0 = 220 km / s ρ 0 = 0.3 GeV / cm v esc = 544 km / s
Impact of astrophysical parameters on exclusion curves ρ 0 v 0 E T = 2.76 keV E T = 2.76 keV ∣⃗ v +⃗ v ⊕ ∣ <v esc d v f v ( v ) dN ∫ dEr ( Er ) ∝ v v>v min v esc E T = 2.76 keV v min v min m χ small m χ large
Astrophysical uncertainties ● Astrophysical parameters should be correlated: gravitational dynamics ● Several studies based on kinametic data + mass models Fairbairn et al. ('12), Catena & Ullio ('12), Bozorgna et al. ('13), Fornasa & Green ('13), etc. ● We focus on the latest estimate of the escape speed (RAVE survey) which cannot be used blindly (relies on assumptions) ● We work out a consistent modeling, complementarity to kinematical studies ● Escape speed important at low WIMP masses
Why focus on the escape speed? Del Nobile et al, (2014) m χ v esc Several effects at work: Experimental treshold ➢ v > v min ( E r ) Energy resolution ➢ Escape speed! ➢
Escape speed from RAVE (Piffl et al '13) ● Based on a selection of some stars from a catalog of 420000. n ( v )∝( v esc − v ) k ● Assumptions: (Leonard & Tremaine '90) ➢ R 0 = 8.28 kpc ➢ Mass model (NFW + fixed baryons) ➢ DM ( r )+ Φ BAR ( R, z ) Φ MW ( R ,z )= Φ NFW 2 free parameters ● Different analyses: + 54 km / s v esc = 533 − 41 v 0 = 220 km / s 1) likelihood analysis at fixed + 64 km / s v esc = 544 − 46 (90% C.L.) Old RAVE: (Smith et al. '07) Piffl et al, (2013) 2) analysis with same ρ NFW ( r )= δ( c ) ρ c v 0 likelihood but free r s ( 1 + r r s ) 2 r
Reminder on mass models Density of matter ρ (⃗ r )= ρ DM (⃗ r )+ ρ baryons (⃗ r ) Gravitational Potential Φ (⃗ r )= Φ DM (⃗ r )+ Φ baryons (⃗ r ) • Local dark • Escape speed • Circular speed matter density 2 ( R ,0 )= R ∂ Φ ( R ,0 ) r )= √ 2 ∣ Φ (⃗ ρ 0 = ρ DM (⃗ r 0 ) v esc (⃗ r )− Φ (⃗ r max )∣ v c ∂ R v 0 ρ 0 v esc So the correlation between , , and is clear R ⊙
From RAVE's mass constraints to circular and escape speed
From RAVE's mass constraints to circular and escape speed
Impact on direct detection from uncorrelated astrophysical parameters 3 ≤ ρ 0 ≤ 0.5 GeV / cm 3 ➢ 0.2 GeV / cm v esc consistent (Bovy et al., 2012) with RAVE's ➢ − 1 kpc − 1 29.9 ± 1.7 ≤ v c / R 0 ≤ 31.6 ± 1.7 km s second analysis (Mc Millan & Binney, 2009) E T = 2.76 keV (Maxwell-Boltzmann assumed)
Correlating the astrophysical parameters consistently with the RAVE's results v c ( R 0 )∝ f 1 ( Φ ( R 0 )) v esc ( R 0 )∝ f 2 ( Φ ( R 0 )) and functions of the mass model E T = 2.76 keV ➔ Exclusion more severe 3 ≤ ρ 0 ≤ 0.5 GeV / cm 3 0.374 GeV / cm Now only − 45 cm 2 ( 6.2 ± 3.4 ) 10 @ m χ = 10 GeV ➔ Uncertainties reduced: 2 @ m χ = 100 GeV − 46 cm ( 4.3 ± 0.7 ) 10 v esc ➔ Consistent way to use RAVE estimate of
Beyond Maxwell-Boltzmann: ergodic speed distribution References: Vergados '14, Bozorgna et al. '13, etc. σ ∝ v 0 ● MB (where ) relies on isothermal assumption ● Eddington equation √ 8 π ² [ ∫ 0 d ψ ) ψ= 0 ] ψ=− Φ MW ( r ) 1 / 2 ( 2 ρ d ρ 1 d ψ d √ ε−ψ+ 1 1 ε ε =− E f (ε)= 2 ε d ψ ρ=ρ NFW ( r ) f (ε ) f ( v ,R Sun )
Beyond Maxwell-Boltzmann - Results E T = 2.76 keV − 45 cm 2 ( 6.9 ± 3.7 ) 10 @ m χ = 10 GeV ➔ Reference values and ncertainties: − 46 cm 2 ( 4.3 ± 0.6 ) 10 @ m χ = 100 GeV ➔ Less constraining at low masses w.r.t. MB, with more uncertainties
Comparison with Germanium (used in SUPER CDMS) m Xe = 131.29 a.m.u. Xe v min ( E r )= √ (most common isotope: ) A = 132 E r m A 2 2m red m G e = 72.63 a.m.u. Ge ¿ (most common isotope: ) A = 74 Ge Ge E T = 2.76 keV ➔ The exclusion curves are translated toward lower masses ➔ So for any given (low) uncertainties are reduced m χ
Conclusions and perspectives ● We have revisited RAVE's estimate of the escape speed ● It cannot be used blindly as it relies on assumptions ● We have converted the full information consistently into direct detection limits ➔ Astro parameters correlated + Maxwell-Boltzmann + ergodic distribution ➔ Stronger bounds ➔ Uncertainties: − 45 cm 2 ( 6.9 ± 3.7 ) 10 @ m χ = 10 GeV − 46 cm 2 ( 4.3 ± 0.6 ) 10 @ m χ = 100 GeV ➔ Complementary to kinematic methods ● RAVE's method is not free of systematic uncertainties (as the escape speed definition) ● Test the method with cosmological simulations (P. Mollitor, E. Nezri) ● Go beyond isotropic case with generalized ergodic functions
Recommend
More recommend
