KB, J. Kumar, L. Strigari, M.-Y. Wang (2017) Sommerfeld-Enhanced J-Factors for Dwarf Spheroidal Galaxies Kimberly Boddy, University of Hawaii TeVPA 2017, Columbus, OH 9 August 2017 OVERVIEW OF INDIRECT DETECTION ➤ Search for DM by detecting annihilation/decay into SM particles (e.g., photons) ➤ Focus on DM annihilation in dwarf spheroidal galaxies (DM-dominated, good S/N) ➤ Differential flux d2Φ 1 σv dN = (⌦) h relif f dE d⌦ J 4⇡ 2m2 dE Xf OVERVIEW OF INDIRECT DETECTION ➤ Search for DM by detecting annihilation/decay into SM particles (e.g., photons) ➤ Focus on DM annihilation in dwarf spheroidal galaxies (DM-dominated, good S/N) ➤ Differential flux Particle Physics (⌦)= ⇢2 (r) d2Φ 1 σv dN J DM = (⌦) h relif f Zlos dE d⌦ J 4⇡ 2m2 dE f J = (⌦) d⌦ Astrophysics X J Z⌦ ➤ Separate astrophysics from particle physics J-FACTORS FOR DWARF SPHEROIDAL GALAXIES Fermi LAT, PRL 115, 231301 (2015) DES, ApJ 808, 95 (2015) 2 -5 log10[ J / (GeV cm )] ➤ Ursa Minor 18.8 ➤ Draco 18.8 ➤ Reticulum II 18.9 ➤ Coma Berenices 19.0 ➤ Segue 1 19.6 4 ⌦ =2.4 10− ⇥ J-FACTORS FOR DWARF SPHEROIDAL GALAXIES Fermi LAT, PRL 115, 231301 (2015) DES, ApJ 808, 95 (2015) 2 -5 log10[ J / (GeV cm )] ➤ Ursa Minor 18.8 ➤ Draco 18.8 ➤ Reticulum II 18.9 Potential signal‽ Geringer-Sameth et al., PRL 115, 081101 (2015) ➤ Coma Berenices 19.0 ➤ Segue 1 19.6 4 ⌦ =2.4 10− ⇥ J-FACTORS FOR DWARF SPHEROIDAL GALAXIES Fermi LAT, PRL 115, 231301 (2015) DES, ApJ 808, 95 (2015) 2 -5 log10[ J / (GeV cm )] ➤ Ursa Minor 18.8 ➤ Draco 18.8 ➤ Reticulum II 18.9 Potential signal‽ Geringer-Sameth et al., PRL 115, 081101 (2015) ➤ Coma Berenices 19.0 ➤ Segue 1 19.6 Why not here? Hold that thought. 4 ⌦ =2.4 10− ⇥ A CLOSER LOOK d2Φ 1 σv dN = (⌦) h relif f dE d⌦ J 4⇡ 2m2 dE f ➤ Velocity-averaged annihilation crossX section σv = d3v f(v ) d3v f(v )σ ~v ~v h reli 1 1 2 2 | 1 − 2| ➤ Trivial integral forZ s-wave, no velocityZ dependence ➞ proceed as usual A CLOSER LOOK d2Φ 1 σv dN = (⌦) h relif f dE d⌦ J 4⇡ 2m2 dE f ➤ Velocity-averaged annihilation crossX section σv = d3v f(v ) d3v f(v )σ ~v ~v h reli 1 1 2 2 | 1 − 2| ➤ Trivial integral forZ s-wave, no velocityZ dependence ➞ proceed as usual ➤ If there is velocity dependence, factorization of astrophysics and particle physics does not hold! ➤ DM velocity is dependent on location within the halo — relate to DM density profile ➤ (This is not specific to dSphs or Sommerfeld enhancement) PROPERLY INCORPORATE DM VELOCITY DISTRIBUTION v2 ➤ ✏ = + (r) Eddington formula for isotropic distribution 2 1 0 d2⇢ d f(✏)= DM p8⇡2 d 2 p✏ Z✏ − ➤ Assume NFW profile ⇢s ⇢NFW(r)= 2 r 1+ r Depends on !s and rs rs rs (or equivalently, Vmax and rmax) ➤ DM density ⇣ ⌘⇣ ⌘ vesc 2 ⇢DM(r)=4⇡ dv v f(r, v) Z0 DETERMINE NFW PROFILE PARAMETERS ➤ Constrain using average LOS stellar velocity distribution ➤ Assume Plummer profile ➤ Obtain stellar velocity distribution from Eddington formula ➤ Match average velocity dispersion to observed value ➤ Constrain using (Vmax,rmax) relation from Aquarius simulation Reticulum II Coma Berenices Segue 1 2.0 3.0 3.0 16.8 17.2 16.4 16.4 17.6 16.8 18.0 16.0 16.4 2.5 2.5 17.6 17.2 18.4 18.0 18.4 17.2 16.8 17.6 18.8 1.5 18.8 18.0 18.4 2.0 2.0 19.2 [kpc] 18.8 [kpc] [kpc] 19.6 1.0 1.5 19.2 1.5 19.2 20.0 max max max r r r 1.0 19.6 1.0 20.4 0.5 20.8 20.0 0.5 19.6 0.5 10 20 5 10 15 20 25 10 20 30 Vmax[km/s] Vmax[km/s] Vmax[km/s] Draco Ursa Minor 3.0 3.0 2.5 2.5 17.2 17.6 17.3 18.0 17.7 18.1 2.0 18.4 2.0 18.5 [kpc] 1.5 [kpc] 1.5 18.9 18.8 max max r 1.0 19.2 r 1.0 19.3 0.5 0.5 19.6 10 20 30 10 20 30 Vmax[km/s] Vmax[km/s] From Aquarius From stellar velocity SOMMERFELD ENHANCEMENT ➤ Yukawa potential 2 S 7 ↵X m r 10− 10 V (r)= e− φ − r 106 ➤ 3 Long-range force causes 10− distortion in incoming 105 4 10− wave function, particularly 104 2 / rel at low relative velocities v 103 5 10− vrel σvrel =(σvrel)0 S ⇥ 2 102 6 ⇣ ⌘ 10− ➤ Annihilation cross section 101 enhanced by S=|ψ(0)|2 100 6 5 4 3 2 1 10− 10− 10− 10− 10− 10− ➤ Rearrange: mφ/mX 2 d Φ 1 (σvrel)0,f dNf =[...] 2 2 dE d⌦ ⇥ 4⇡ 2m dE ↵X =10− Xf SOMMERFELD-ENHANCED J-FACTORS J = d3v f(r(l, ⌦),~v ) d3v f(r(l, ⌦),~v )S( ~v ~v /2) S 1 1 ⇥ 2 2 | 1 − 2| Z⌦ Zlos Z Z Reticulum II Coma Berenices Segue 1 1024 1023 ] 5 1022 cm / 2 1021 [GeV 1020 S J 1019 1018 6 5 4 3 2 1 0 6 5 4 3 2 1 0 6 5 4 3 2 1 0 10− 10− 10− 10− 10− 10− 10 10− 10− 10− 10− 10− 10− 10 10− 10− 10− 10− 10− 10− 10 mφ/mX mφ/mX mφ/mX Draco Ursa Minor 1024 1023 ] 5 1022 cm / 2 1021 [GeV 1020 S J 1019 1018 6 5 4 3 2 1 0 6 5 4 3 2 1 0 2 10− 10− 10− 10− 10− 10− 10 10− 10− 10− 10− 10− 10− 10 ↵X =10− mφ/mX mφ/mX ORDER FLIP EXAMPLE #1 1024 1023 1022 ] 5 cm / 2 1021 [GeV S J 1020 Reticulum II 1019 Coma Berenices Segue 1 Draco Ursa Minor 1018 6 5 4 3 2 1 0 10− 10− 10− 10− 10− 10− 10 mφ/mX 2 ↵X =10− ORDER FLIP EXAMPLE #2 1024 1023 1022 ] 5 cm / 2 1021 [GeV S J 1020 Reticulum II 1019 Coma Berenices Segue 1 Draco Ursa Minor 1018 6 5 4 3 2 1 0 10− 10− 10− 10− 10− 10− 10 mφ/mX 2 ↵X =10− SUMMARY ➤ Large variations in J-factors due to: ➤ Astrophysics: Form of density profile (and velocity distribution) ➤ Particle physics: Velocity dependence of annihilation cross section ➤ Proper velocity averaging may significantly impact limits (or derived quantities from a future detection) on particular models ➤ Ordering of dwarf spheroidal JS-factors is different in s-wave limit vs. Coulomb limit for Sommerfeld enhancement ➤ Beware naive consistency check: Possible signal could still have a DM interpretation, even if no signal is observed in another system with larger “s-wave” J-factor.