14.07.2016 – ECT* Doctoral Training Program Timon Emken (CP 3 -Origins, University of Southern Denmark, Odense) Collaborators: Chris Kouvaris (CP 3 -Origins)
A story of two predictions Prediction A Uranus Prediction of additional, Orbital undiscovered (dark?) Anomalies matter, i.e. a new planet. 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 2
¡ French Mathematician ¡ Tried to understand the anomalies using Newtonian Gravity. ¡ Predicted a new planet and its orbit. ¡ No one in France cared. ¡ On 18.09.1846 he sent his result to Berlin. 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 3
¡ German Astronomer ¡ He and his assistant started looking for the new planet on the day the letter arrived. ¡ It took them roughly 30 minutes to discover the planet. ¡ Its position was within 1º of Le Verrier’s prediction! 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 4
A story of two predictions Prediction A Uranus Prediction of additional, Orbital undiscovered (dark?) Anomalies matter, i.e. a new planet. 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 5
A story of two predictions Prediction A Uranus Discovery of Neptune Orbital Anomalies on 23.09.1846 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 6
A story of two predictions Prediction B Mercury Prediction of another new Orbital planet Anomalies 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 7
¡ He tried to repeat his success. ¡ Predicted a new planet and its orbit. ¡ Being very confident in his calculation he named it “Vulcan”. ¡ Despite great effort it was never found. 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 8
A story of two predictions Prediction B Mercury Prediction of another new Orbital planet Anomalies 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 9
A story of two predictions Prediction B Mercury 1915: General Relativity Orbital R µ ν − 1 Anomalies 2 Rg µ ν = 8 π GT µ ν 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 10
Observation of Gravitational Anomalies Situation I Situation II Additional, “dark” matter, New laws of physics, not not yet discovered. yet discovered. § Today we find ourselves in a somewhat similar situation as Urbain Le Verrier over 150 years ago. § We have good reason to assume that the explanation of the observed anomalies is of the first class: Dark Matter (DM). 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 11
1) Evidence for Dark Matter 2) Basics of Direct Detection Experiments 3) Simulation of DM Trajectories 4) Final Remarks 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 12
On a broad range of scales. Simulating DM Trajectories for Direct Detection Experiments 13 14/07/16
¡ Newtonian Dynamics: r GM ( r ) v ( r ) = r ¡ Beyond optical disc we might expect M ( r ) ∝ const ¡ Instead we observe: M ( r ) ∝ r Begeman et al, Mon. Not. Roy. Astron. Soc. 249 (1991) 523 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 14
2 Fig. 1.— Shown above in the top panel is a color image from the Magellan images of the merging cluster 1E0657 − 558, with the white bar indicating 200 kpc at the distance of the cluster. In the bottom panel is a 500 ks Chandra image of the cluster. Shown in green contours in both panels are the weak lensing κ reconstruction with the outer contour level at κ = 0.16 and increasing in steps of 0.07. The white contours show the errors on the positions of the κ peaks and correspond to 68 . 3%, 95 . 5%, and 99 . 7% confidence levels. The blue +s show the location of the centers used to measure the masses of the plasma clouds in Table 2. Clowe et al, Astrophys. J. 648 (2006) L109-L113 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 15
¡ From primordial density fluctuations to large scale structures. ¡ N-body simulations show that the additional gravitational force of DM is absolutely essential for LSS. ¡ DM needs to be “cold”. Springel et al, Nature 440 (2006),1137 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 16
l ∞ δ T X X T = a lm Y lm ( θ , φ ) l =2 m = − l Image Source: ESA and the Planck Collaboration 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 17
Constituents 5% Dark Energy 26% Dark Matter 69% Ordinary Matter Image Source: ESA and the Planck Collaboration 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 18
WHAT IT IS WHAT IT IS NOT ¡ Heavy ¡ Charged ¡ Stable (or long-lived) ¡ Baryonic ¡ Cold ¡ Strongly self-interacting Dark Matter Candidates: § SUSY particles (neutralinos, gravitinos, sneutrinos,…) § Sterile Neutrinos § Kaluza Klein particles § Axions § ? 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 19
Event Rates and Annual Modulations Recoil energy: E R 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 20
1. The earth is moving through a halo of DM particles. 2. These particles interact weakly with matter, i.e. they are a kind of WIMP. 3. The DM velocity distribution is approximately known. 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 21
(differential event rate) d R A = N T σ N v d n v esc Z v )d 3 v , d n = n χ f halo ( ~ such that d n = n χ 0 Cross Section and velocity distribution: µ 2 σ SI N, 0 = σ SI A A 2 σ N = σ N, 0 F 2 A ( q ) p, 0 µ 2 p v 2 ✓ ◆ v ) = 1 − ~ f halo ( ~ exp 2 � 2 k 0 f ⊕ ( ~ v s ) ≡ f halo ( ~ v s + ~ v ⊕ ) v ⊕ ) 2 1 ✓ − ( ~ v s + ~ ◆ = k ( v esc , v ⊕ ) exp Θ ( v esc − | v ⊕ + ~ v s | ) 2 � 2 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 22
Z d R A d 3 v f ⊕ ( ~ v ) m A = N T n � � N 2 µ 2 d E R v A v min( ER ) ≤ | ~ v | ≤ v max | {z } ≡ ⌘ ( v min ( E R ) ,t ) E cutoff Z d R A X (total event rate) R = f A d E R d E R A E thr 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 23
10 - 36 10 - 38 10 - 40 σ 0SI [ cm 2 ] 10 - 42 10 - 44 10 - 46 5 10 50 100 500 1000 m χ [ GeV ] 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 24
Image Source: Freese et al, Rev.Mod.Phys. 85 (2013) 1561-1581 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 25
0 . 05 2–6 keVee Residual Rate [cpd/kg/keVee] 0 . 04 0 . 03 0 . 02 0 . 01 0 − 0 . 01 − 0 . 02 − 0 . 03 − 0 . 04 DAMA/NaI DAMA/LIBRA Best-fit − 0 . 05 1996 1998 2000 2002 2004 2006 2008 2010 Image Source: Freese et al, Rev.Mod.Phys. 85 (2013) 1561-1581 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 26
Earth’s effect on DM Direct Detection Experiments 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 27
P ( L ) = 1 − e − L/ λ mfp (Probability to scatter after travelling a length L) START Initial Conditions No. Save ( t f , ˛ r f , ˛ v i ) . Enter Earth? ( t i , ˛ v i ) r i , ˛ Yes. Save point of entry ( t entry , ˛ r entry , ˛ v i ) . ˛ r i +1 = ˛ r i + L ˛ e v Yes. Calculate the DM free path L No. Is | ˛ v | ≥ v cuto ff ? Find new position ˛ r . Scattering: Calculate Inside the Earth? ( | ˛ r | < r ⊕ ?) new ˛ v and save ( t, ˛ r, ˛ v ) . Yes. No. Save point of exit ( t exit , ˛ v ) and the r exit , ˛ STOP final position ( t f , ˛ r ≡ v ) . ˛ r f , ˛ 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 28
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1. Filter out the trajectories passing a detector or the local neighborhood. 2. Obtain enough DM velocity data. 3. Fit the local velocity distribution function via Kernel Density Estimation (KDE). n f ( v ) = 1 ✓ v − v i ◆ ˆ X K nh h i =1 4. Calculate event rates, signal modulations, data for directional experiments,… 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 31
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There are many approaches we want to follow: 1. Implement a realistic earth model (PREM - preliminary reference earth model). 2. Run the simulations on a Super computer in order to be able to decrease the detector size an gather enough data. 3. Use more general non-relativistic DM-nucleus interaction operators 4. Include gravity (lensing effects, capture rates,…) 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 33
¡ There is a lot of evidence supporting that we are in a situation similar to Le Verrier’s in the 1840s. ¡ But this time the solution seems to take a little longer than 30 minutes. ¡ Direct Detection experiments are a promising approach to finally observe a DM particle from the galactic halo. ¡ Our simulations will investigate the effect of the earth on these experiments. 14/07/16 Simulating DM Trajectories for Direct Detection Experiments 34
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