‘Dark Matter Tomography' Measuring the DM velocity distribution with directional detection Bradley J. Kavanagh LPTHE (Paris) & IPhT (CEA/Saclay) University of Sheffield - 15th June 2016 bradley.kavanagh@lpthe.jussieu.fr @BradleyKavanagh NewDark
Direct detection DM m χ & 1 GeV N N v ∼ 10 − 3 χ χ Measure energy (and possibly direction) of recoiling nucleus Reconstruct the mass and cross section of DM? Need to know the velocity distribution of the DM particles. Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
The WIMP wind WIMP: Weakly Interacting In the halo: Massive Particle v sun ∼ 220 km s − 1 Cygnus constellation v DM ∼ 220 km s − 1 Detector In the lab: ‘WIMP wind from Cygnus’ Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
The WIMP wind WIMP: Weakly Interacting In the halo: Massive Particle v sun ∼ 220 km s − 1 Cygnus constellation But we don’t know the velocity distribution exactly! v DM ∼ 220 km s − 1 Detector In the lab: ‘WIMP wind from Cygnus’ Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
What could go wrong? Correct distribution Incorrect distribution Benchmark Best fit Astrophysical uncertainties need to be accounted for! While we’re at it, why not try to reconstruct the velocity distribution too?! Need directionality! Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
Outline Directional event rate in DD Mayet et al. [1602.03781] Reconstructing f(v) in non-directional experiments BJK, Green [1207.2039, 1303.6868,1312.1852]; BJK, Fornasa, Green [1410.8051] Discretising the DM velocity distribution BJK [1502.04224] Reconstructing f(v) in directional experiments BJK, O’Hare [in preparation] Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
Directional recoil rate Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
Directional recoil rate Flux of particles with velocity : m χ m N v ✓ ρ χ ◆ f ( v ) d 3 v v m χ ~ v ~ q Differential cross section for recoil energy : E R d σ ∼ 1 v 2 d E R Kinematic constraint for recoil with momentum : q q = v min /v v · ˆ ˆ ρ χ ∼ 0 . 2 − 0 . 6 GeV cm − 3 s m N E R Read (2014) v min = where 2 µ 2 [arXiv:1404.1938] χ N Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
Directional recoil spectrum d R ρ 0 σ p C N F 2 ( E R ) ˆ = f ( v min , ˆ q ) 4 π µ 2 d E R d Ω q χ p m χ s m N E R v min = 2 µ 2 χ N Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
Directional recoil spectrum d σ d E R d R ρ 0 σ p C N F 2 ( E R ) ˆ = f ( v min , ˆ q ) 4 π µ 2 d E R d Ω q χ p m χ s m N E R v min = 2 µ 2 χ N Enhancement for nucleus : N ( | Z + ( f p /f n )( A � Z ) | 2 SI interactions C N = | h S p i + ( a p /a n ) h S n i | 2 4 J +1 SD interactions 3 J NB: May get interesting directional signatures from other operators Form factor: F 2 ( E R ) BJK [1505.07406] Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
Directional recoil spectrum d R ρ 0 σ p C N F 2 ( E R ) ˆ = f ( v min , ˆ q ) 4 π µ 2 d E R d Ω q χ p m χ s m N E R v min = 2 µ 2 χ N Enhancement for nucleus : N ( | Z + ( f p /f n )( A � Z ) | 2 SI interactions C N = | h S p i + ( a p /a n ) h S n i | 2 4 J +1 SD interactions 3 J NB: May get interesting directional signatures from other operators Form factor: F 2 ( E R ) BJK [1505.07406] Radon Transform (RT): Z ˆ q − v min ) d 3 v f ( v min , ˆ q ) = R 3 f ( v ) δ ( v · ˆ Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
Radon Transform Radon Transform (RT): Z ˆ q − v min ) d 3 v f ( v min , ˆ q ) = R 3 f ( v ) δ ( v · ˆ v ˆ q v min Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
What do we know about the velocity distribution? Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
Standard Halo Model Standard Halo Model (SHM) is typically assumed: isotropic, ρ ( r ) ∝ r − 2 spherically symmetric distribution of particles with . Maxwell-Boltzmann distribution: − ( v − v e ) 2 � v ) − 3 / 2 exp f Lab ( v ) = (2 πσ 2 Θ ( | v − v e | − v esc ) 2 σ 2 v v e - Earth’s Velocity I f 1 ( v ) = v 2 v e ∼ 220 − 250 km s − 1 f ( v ) d Ω v σ v ∼ 155 − 175 km s − 1 Feast et al. [astro-ph/9706293], Bovy et al. [1209.0759] − 41 km s − 1 v esc = 533 +54 Piffl et al. (RAVE) [1309.4293] Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
Astrophysical uncertainties High resolution N-body simulations can be used to extract the DM speed distribution Non-Maxwellian Debris flows Dark disk structure 6 5 5 f 1 ( v ) [10 − 3 km − 1 s] Aq-A-1 5 4 4 4 3 3 f H v L * 10 3 f(v) × 10 -3 L 10 3 2 2 2 1 1 1 0 0 0 0 100 200 300 400 500 0 100 200 300 400 500 600 700 0 150 300 450 600 ê s L v H km ê s L v [km s -1 ] Pillepich et al. [1308.1703], 10 4 10 4 Vogelsberger et al. [0812.0362] Kuhlen et al. [1202.0007] Schaller et al. [1605.02770] 10 4 10 4 5000 5000 However, N-body simulations cannot probe down to the Counts Counts sub-milliparsec scales probes by direct detection… 1000 1000 500 500 Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016 100 100 0 100 200 300 400 500 0 100 200 300 400 500 600 700 ê s L ê s L
Local substructure May want to worry about ultra-local substructure - subhalos and streams which are not completely phase-mixed. But from N-body simulations, expect lots of ‘sub-streams’ to form a smooth halo. Helmi et al. [astro-ph/0201289], Vogelsberger et al. [0711.1105] www.cosmotography.com However, this does not exclude the possibility of a stream - e.g. due to the ongoing tidal disruption of the Sagittarius dwarf galaxy. Freese et al. [astro-ph/0309279, astro-ph/0310334] Measuring f(v) may tell us something about galaxy formation and the history of our Milky Way! Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
Tomography I ( θ ) θ θ www.fda.gov Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
Tomography I ( θ ) RT θ Invert www.fda.gov Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
DM Tomography d R f ( v ) d E R d cos θ θ θ Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
DM Tomography d R f ( v ) d E R d cos θ RT θ θ Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
DM Tomography d R f ( v ) d E R d cos θ RT θ θ Invert d 2 f ( v ) = − 1 Z q ) 2 ˆ f ( v · ˆ q , ˆ q ) d Ω q 8 π 2 d( v · ˆ Gondolo [hep-ph/0209110] Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
DM Tomography d R f ( v ) d E R d cos θ RT θ θ Invert But we don’t get to choose where to scan, we just get random samples! Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
1-D reconstructions (Energy only) Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
Reconstructing f(v) Many previous attempts to tackle this problem: Numerical inversion (‘measure’ f(v) from the data) Fox, Liu, Weiner [1011.915], Frandsen et al. [1111.0292], Feldstein, Kahlhoefer [1403.4606] Include uncertainties in SHM parameters in the fit Strigari, Trotta [0906.5361] Add extra components to the velocity distribution (and fit) Lee, Peter [1202.5035], O’Hare, Green [1410.2749] But can we be more general? Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
General empirical parametrisation Write a general parametrisation for the speed distribution: Peter [1103.5145] N − 1 ! X a k v k f ( v ) = exp − k =0 BJK & Green [1303.6868,1312.1852] f 1 ( v ) = v 2 f ( v ) This form guarantees a positive distribution function. Now we attempt to fit the particle ( m χ , σ p ) physics parameters , as well as the astrophysics parameters . { a k } Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
Testing the parametrisation 2 σ 1 σ Benchmark Best fit Best fit m χ = m rec Assuming incorrect distribution Tested for a number of different underlying speed distributions Bradley J Kavanagh (LPTHE & IPhT) ‘DM Tomography’ University of Sheffield - 15th June 2016
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