1. The dark matter self-interaction and its impact on the critical mass for dark matter evaporations inside the Sun Yen-Hsun Lin Institute of Physics Nati’l Chiao Tung Univ., Taiwan in collaboration with C.-S. Chen, F.-F. Lee and G.-L. Lin To be submitted!

2. Outline Introduction Dark matter (DM) self-interaction (SI) DM evolution equation in the Sun Solution with the presence of both SI & evaporation Effects of self-interacting dark matter (SIDM) Crucial region for SIDM in σ χp - σ χχ parameter space SIDM σ χχ sensitivity Testing SIDM by IceCube-PINGU Summary

3. INTRODUCTION ICHEP2014, Valencia, Spain

4. Motivation of SIDM Allowing interactions between DMs can alleviate core/cusp problem [1] Particular focus on 1-10 GeV DM mass: Evaporation is inevitable [2] Self-interaction (SI) enhances the DM number accumulating in the Sun [3] SI will makes critical mass, m EV, smaller Low mass also favored by Asymmetric DM [4] Assuming neutrinos are produced after DM annihilation in the Sun Part 1 Introduction 1.D. N. Spergel and P. J. Steinhardtd, PRL 84, 3760 (2000); L. Hui, PRL 86, 3467 (2001). 2.D. N. Spergel and W. H. Press, Ap. J. 294, 663 (1985); A. Gould, Ap. J. 321, 560 (1987). 3.A. Zentner, PRD 80, 063501 (2009). 4.K. M. Zurek, Phys. Rept. 537, 91 (2014).

5. DM-DM self-interaction: DM-DM annihilation: DM-nucleon scattering (experimental σ χp constraints): Dark matter interactions Elastic-scattering between DM particles, only kinetic energy exchanges. + χ(p1)χ(p1) χ(p2)χ(p2) χ(k1)χ(k1) χ(k2)χ(k2) σ χχ + χ χ ℓ+ℓ+ ℓ−ℓ− συ + χ(p1)χ(p1) N(p2)N(p2) χ(k1)χ(k1) N(k2)N(k2) σχpσχp Annihilation between two DM particles and Standard Model (SM) particles produced. Elastic-scattering between DM particle and atomic nucleon. Recoil energy gained by nucleon. Part 1 Introduction

6. Current experimental σ χp constraints LUX XENON100 Spin-independent σ χp Spin-dependent σ χp M. G. Aartsen et al. [IceCube Collaboration], PRL 110, 131302 (2013) D. S. Akerib et al. [LUX Colla- boration], PRL 112, 091303 (2014)

7. DM particles in the Sun Capture, C c Attracted by Sun’s gravity and scattered with nucleus via [5-9] : Spin-dependent interaction: Spin-independent interaction: Part 1 Introduction 5.D. N. Spergel and W. H. Press, Ap. J. 296, 679 (1985); J. Faulkner and R. L. Gilliland, Ap. J. 299, 994 (1985). 6.K. Griest and D. Seckek, Nucl. Phys. B 283, 681 (1987). 7.A. Gould, Ap. J. 321, 571 (1987). 8.G. Jungman, M. Kamionskowski and K. Griest, Phys. Rept. 267, 195 (1996). 9.G. Bertone, D. Hooper and J. Silk, Phys. Rept. 405, 279 (2005).

8. DM particles in the Sun Self-interaction, C s Schematic view of SIDM: DM particle in the Halo near the Sun with υ χ > υ esc Collision happens between the Halo and the captured DMs The Halo one loses kinetic and the captured one gain additional velocity Part 1 Introduction χ χ χ χ χ χ χ χ χ χ χ χ χ χ υ χ > υ esc χ χ χ χ χ χ χ χ χ χ χ χ χ χ υ χ < υ esc υ ʹ χ < υ esc BeforeAfter

9. DM particles in the Sun After DM-DM scattering: Both captured After scattering, both One captured, the other escapes After scattering one the other All escape After scattering, both The possibilities for the last two are rare [3]. The self-interaction rate, C s, is proportional to: Part 1 Introduction 3.A. Zentner, PRD 80, 063501 (2009).

10. DM particles in the Sun Evaporation, C e, and annihilation, C a Evaporation: If DM mass m χ is below the critical mass, m EV, the evaporation will take over No signals from DM annihilation will be observed The rate of evaporation C e [6,10,11] : Annihilation: High dense DM particles in the Sun’s core will trigger DM annihilation into SM particles The rate of annihilation [6] : Part 1 Introduction 10.A. Gould, Ap. J. 321, 560 (1987). 11.G. Busoni, A. D. Simone and W.-C. Huang, JCAP 1307, 010 (2013).

11. DARK MATTER EVOLUTION EQUATION ICHEP2014, Valencia, Spain

12. Generalized DM evolution equation in the Sun The general evolution equation of DM in the Sun is given by The coefficients: C c : for capture C s : for self-interaction C e : for evaporation C a : for annihilation Part 2 DM Evolution Equation

13. Solution to the evolution equation The DM number inside the Sun is: where τ A is the time-scale reaching equilibrium If the state achieves equilibrium, tanh(t/τ A ) ~1, N χ number becomes Part 2 DM Evolution Equation

14. Comparisons to recent studies Absence of self-interaction [6] Absence of evaporation [3] Absence of both [8,9] Part 2 DM Evolution Equation

15. EFFECTS OF DARK MATTER SELF-INTERACTION ICHEP2014, Valencia, Spain

16. When does self-interaction or evaporation become crucial? Parameter R se in the DM number N χ,eq : For convenience, we have Whether SI or evaporation becomes significant depends on the critical mass m EV Part 3 Effects of SI- DM R se > 1, SI or evap. is important R se < 1, SI or evap. is not important N χ,eq w/o SI & evap.

17. Crucial region for SIDM in σ χp - σ χχ para- meter space m χ = 3 GeV Colors represent log 10 R se m χ = 20 GeV IC-SD constraint: σ χp < 10 −40 cm 2 @ m χ ~ 10 2 GeV

18. Spin-dependent N χ NχNχ m χ [GeV] NχNχ

19. Enhancement via self-interaction to total annihilation rate Γ A The total annihilation rate Γ A : C s and C e are present: Part 3 Effects of SI- DM σ χp = 10 − 41 cm 2 spin-dependent m χ [GeV]

20. CONSTRAINTS ON SELF- INTERACTING DARK MATTER ICHEP2014, Valencia, Spain

21. Testing SIDM by IceCube-PINGU Part 4 Constraints on SIDM PINGU module designed to detect E ν as low as a few GeV [12] Large detector volume ~ MTon Performance: Angular resolution: Δθ ~ 10 º for ν e, E ν @ 5 GeV Δθ ~ 10 º for ν μ, E ν @ 5 GeV ν τ & NC are similar to ν e Energy resolution: ΔE/E ~ 0.25 for ν e, E ν @ 5 GeV ΔE/E ~ 0.25 for ν μ, E ν @ 5 GeV ν τ & NC are similar to ν e 12.M. G. Aartsen et al. [IceCube-PINGU Colla- boration], arXiv:1401.2046 (2014).

22. Neutrino signals from DM annihilation in the Sun The differential neutrino flux: generated by WimpSim [13] and where: : neutrino oscillation probability : 1 A.U. Γ A : total annihilation rate B f : branching ratio : neutrino spectrum at production point Event rate N ν : Part 4 Constraints on SIDM Detector eff. area 13.M. Blennow, J. Edsjö and T. Ohlsson, JCAP 0801, 021 (2008)

23. Detector effective area, detection significance and ATM backgrounds Detector effective area can be estimated: We consider 2 σ detection significance in 5 years: The ATM backgrounds: Part 4 Constraints on SIDM ATM fluxes, Honda et al. 14.M. Honda et al., PRD 75, 043006 (2007). IC-PINGU eff. vol.

24. Sensitivity of σ χχ Spin-dependent σ χp = 10 − 41 cm 2 τ channel ν channel 15.S.W. Randall et al., Ap. J. 679, 1173 (2008). 16.A. H. G. Peter et al., arXiv:1208.3026 (2012). 17.J. Zavala, M. Vogelsberger and M.G. Walker, Mon. Not. Roy. Astron. Soc. 431 (2013) L20. Observational constraint [15-17] 1.0 < σ χχ /m χ < 0.1 cm 2 /g IC-SD constraint: σ χp < 10 −40 cm 2 @ m χ ~ 10 2 GeV m χ [GeV] σ χχ [cm 2 ] m χ [GeV] Too weak to alleviate core/cusp problem [16]

25. Sensitivity of σ χχ Spin-dependent σ χp = 10 − 43 cm 2 τ channel ν channel Too weak to alleviate core/cusp problem [16] m χ [GeV] σ χχ [cm 2 ] m χ [GeV] Observational constraint [15-17] 1.0 < σ χχ /m χ < 0.1 cm 2 /g IC-SD constraint: σ χp < 10 −40 cm 2 @ m χ ~ 10 2 GeV

26. SUMMARY ICHEP2014, Valencia, Spain

27. Summary Generalized DM evolution equation with C s and C e can be exactly solved SI effect is significant in m χ ~ O (1GeV) SI enhances Γ A and causes evaporation to occur at lighter mass SI accelerates the DM evolution eq. – reaching equilibrium state more quickly SIDM can be tested in IceCube-PINGU at smaller ‹συ› In the σ χp allowed region, a narrow σ χχ space can be examined via DM annihilation to τ and ν channels Part 5 Summary

28. ADDITIONAL SLIDES ICHEP2014, Valencia, Spain

29. N χ & R se Part 6 Additional Slides Assume C s >> C e :

30. Crucial region for SIDM in σ χp - σ χχ para- meter space: Spin-independent Colors represent log 10 R se m χ = 3 GeV m χ = 20 GeV σ χp [cm 2 ] σ χχ [cm 2 ] σ χp [cm 2 ] σ χχ [cm 2 ] LUX exclusion

31. Spin-independent N χ σ χp = 10 − 45 cm 2 Part 6 Additional Slides m χ [GeV] NχNχ

32. Sensitivity of σ χχ Spin-independent σ χp = 10 − 45 cm 2 τ channel ν channel Observational constraint [14-16] 1.0 < σ χχ /m χ < 0.1 cm 2 /g LUX exclusion m χ [GeV] σ χχ [cm 2 ] m χ [GeV] Too weak to alleviate core/cusp problem [16]