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KB, J. Kumar, L. Strigari, M.-Y. Wang (2017)

Sommerfeld-Enhanced J-Factors for Dwarf Spheroidal 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

d2 1 v 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) d2 1 v 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 )] ➤ 18.8 ➤ 18.8 ➤ II 18.9 ➤ 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

d2 1 v dN = (⌦) h relif f dE d⌦ J 4⇡ 2m2 dE f ➤ Velocity-averaged annihilation crossX section v = d3v f(v ) d3v f(v ) ~v ~v h reli 1 1 2 2 | 1 2| ➤ Trivial integral forZ s-wave, no velocityZ dependence ➞ proceed as usual A CLOSER LOOK

d2 1 v dN = (⌦) h relif f dE d⌦ J 4⇡ 2m2 dE f ➤ Velocity-averaged annihilation crossX section v = d3v f(v ) d3v f(v ) ~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 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 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 vrel =(vrel)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: m/mX 2 d 1 (vrel)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 m/mX m/mX m/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 m/mX m/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 m/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 m/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