Sommerfeld-Enhanced J-Factors for Dwarf Spheroidal Galaxies

Transcription

1 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

2 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 d 2 de d = J ( ) 1 4 X f h v rel i f 2m 2 dn f de

3 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 d 2 de d = J ( ) 1 Astrophysics 4 X Particle Physics Separate astrophysics from particle physics f h v rel i f 2m 2 dn f de J ( ) = J = Z Z los 2 DM(r) J ( ) d

4 J-FACTORS FOR DWARF SPHEROIDAL GALAXIES Fermi LAT, PRL 115, (2015) DES, ApJ 808, 95 (2015) Ursa Minor Draco Reticulum II log 10 [ J / (GeV 2 cm -5 )] 18.9 Coma Berenices Segue =

5 J-FACTORS FOR DWARF SPHEROIDAL GALAXIES Fermi LAT, PRL 115, (2015) DES, ApJ 808, 95 (2015) log 10 [ J / (GeV 2 cm -5 )] Ursa Minor Draco Reticulum II Coma Berenices Segue Potential signal Geringer-Sameth et al., PRL 115, (2015) =

6 J-FACTORS FOR DWARF SPHEROIDAL GALAXIES Fermi LAT, PRL 115, (2015) DES, ApJ 808, 95 (2015) log 10 [ J / (GeV 2 cm -5 )] Ursa Minor Draco Reticulum II Coma Berenices Segue Potential signal Geringer-Sameth et al., PRL 115, (2015) Why not here? Hold that thought. =

7 A CLOSER LOOK d 2 Velocity-averaged annihilation cross section h v rel i = Trivial integral for s-wave, no velocity dependence proceed as usual de d = J ( ) 1 Z 4 d 3 v 1 f(v 1 ) Z X f h v rel i f 2m 2 dn f de d 3 v 2 f(v 2 ) ~v 1 ~v 2

8 A CLOSER LOOK d 2 Velocity-averaged annihilation cross section h v rel i = Trivial integral for s-wave, no velocity dependence proceed as usual de d = J ( ) 1 Z 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 4 d 3 v 1 f(v 1 ) X (This is not specific to dsphs or Sommerfeld enhancement) Z f h v rel i f 2m 2 dn f de d 3 v 2 f(v 2 ) ~v 1 ~v 2

9 PROPERLY INCORPORATE DM VELOCITY DISTRIBUTION Eddington formula for isotropic distribution f( ) = 1 p 8 2 Z 0 d 2 DM d 2 d p = v2 2 + (r) Assume NFW profile NFW (r) = DM density s 2 r 1+ r r s r s Depends on ρ s and r s (or equivalently, V max and r max ) DM (r) =4 Z vesc 0 dv v 2 f(r, v)

10 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 (V max,r max ) relation from Aquarius simulation

11 2.0 Reticulum II 3.0 Coma Berenices 3.0 Segue 1 rmax[kpc] rmax[kpc] rmax[kpc] V max [km/s] V max [km/s] V max [km/s] 3.0 Draco 3.0 Ursa Minor rmax[kpc] rmax[kpc] V max [km/s] V max [km/s] From Aquarius From stellar velocity

12 SOMMERFELD ENHANCEMENT Yukawa potential V (r) = Long-range force causes distortion in incoming wave function, particularly at low relative velocities Annihilation cross section enhanced by S= ψ(0) 2 Rearrange: X r e m r v rel =( v rel ) 0 S d 2 de d =[...] 1 4 X f vrel 2 vrel/2 ( v rel ) 0,f 2m dn f de S m /m X X =10 2

13 SOMMERFELD-ENHANCED J-FACTORS J S = Z Z Z Z d 3 v 1 f(r(l, ), ~v 1 ) los d 3 v 2 f(r(l, ), ~v 2 )S( ~v 1 ~v 2 /2) Reticulum II Coma Berenices Segue JS [GeV 2 /cm 5 ] m /m X Draco m /m X Ursa Minor m /m X JS [GeV 2 /cm 5 ] m /m X m /m X X =10 2

14 ORDER FLIP EXAMPLE # JS [GeV 2 /cm 5 ] Reticulum II Coma Berenices Segue 1 Draco Ursa Minor m /m X X =10 2

15 ORDER FLIP EXAMPLE # JS [GeV 2 /cm 5 ] Reticulum II Coma Berenices Segue 1 Draco Ursa Minor m /m X X =10 2

16 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 J S -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