The dark matter self-interaction and its impact on the critical mass for dark matter evaporations inside the Sun

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!

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 σχχ} sensitivity

•

Testing SIDM by IceCube-PINGU

•

^Summary

INTRODUCTION

ICHEP2014, Valencia, Spain

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).

•

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(p₂)

χ(k₁) χ(k₂) σ_χχ

+

χ χ

ℓ⁺ ℓ⁻

⟨συ⟩

+

χ(p₁) N(p₂)

χ(k₁) N(k₂) σ_χp

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

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)

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).

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

υ_χ > υ_esc

χ χ

χ

χ χ χ

χ

υ_χ < υ_esc υʹ_χ< υ_esc

Before After

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).

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).

DARK MATTER EVOLUTION EQUATION

ICHEP2014, Valencia, Spain

Generalized DM evolution equation in the Sun

The general evolution equation of DM in the Sun is given by

The coefficients:

•

^Cc: for capture

•

^Cs: for self-interaction

•

^Ce: for evaporation

•

^Ca: for annihilation

Part 2

DM Evolution Equation

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

Comparisons to recent studies

•

Absence of self-interaction^[6]

•

Absence of evaporation^[3]

•

Absence of both^[8,9]

Part 2

DM Evolution Equation

EFFECTS OF DARK MATTER SELF-INTERACTION

ICHEP2014, Valencia, Spain

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.

Crucial region for SIDM in σ

_χp

- σ

_χχ

para- meter space

m_χ = 3GeV

Colors represent log₁₀R_se

m_χ = 20GeV

IC-SD constraint: σ_χp < 10⁻⁴⁰ cm² @ m_χ ~ 10² GeV

Spin-dependent N

_χ

Nχ

m_χ [GeV] m_χ [GeV]

Nχ

Enhancement via self-interaction to total annihilation rate Γ

_A

•

The total annihilation rate Γ_A:

•

^Cs and C_e are present:

Part 3

Effects of SI- DM

σ_χp = 10⁻⁴¹ cm²

spin-dependent

m_χ [GeV]

CONSTRAINTS ON SELF-

INTERACTING DARK MATTER

ICHEP2014, Valencia, Spain

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 ~ 10º for ν_e, E_ν @ 5 GeV

•

Δθ ~ 10º for ν_μ, E_ν @ 5 GeV

•

^ντ & 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

•

^ντ & NC are similar to ν_e

12. M. G. Aartsen et al. [IceCube-PINGU Colla- boration], arXiv:1401.2046 (2014).

Neutrino signals from DM annihilation in the Sun

•

The differential neutrino flux:

generated by WimpSim^[13] and where:

•

: neutrino oscillation probability

•

: 1 A.U.

•

^ΓA: total annihilation rate

•

^Bf: 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)

Detector effective area, detection significance and ATM backgrounds

•

Detector effective area can be estimated:

•

We consider 2σ 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.

Sensitivity of σ

_χχ

Spin-dependent σ_χp = 10⁻⁴¹ cm²

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 cm²/g IC-SD constraint:

σ_χp < 10⁻⁴⁰ cm² @ m_χ ~ 10² GeV

m_χ [GeV]

σ χχ[cm2 ] σ χχ[cm2 ]

m_χ [GeV]

Too weak to alleviate core/cusp problem^[16]

Sensitivity of σ

_χχ

Spin-dependent σ_χp = 10⁻⁴³ cm²

τ channel ν channel

Too weak to alleviate core/cusp problem^[16]

m_χ [GeV]

σ χχ[cm2 ] σ χχ[cm2 ]

m_χ [GeV]

Observational constraint^[15-17]

1.0 < σ_χχ/m_χ < 0.1 cm²/g IC-SD constraint:

σ_χp < 10⁻⁴⁰ cm² @ m_χ ~ 10² GeV

SUMMARY

ICHEP2014, Valencia, Spain

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

ADDITIONAL SLIDES

ICHEP2014, Valencia, Spain

N

_χ

& R

_se

Part 6

Additional Slides

Assume C_s>>C_e:

Crucial region for SIDM in σ

_χp

- σ

_χχ

para- meter space: Spin-independent

Colors represent log₁₀R_se

m_χ = 3GeV m_χ = 20GeV

σ_χp [cm²] σχχ [cm2 ]

σ_χp [cm²] σχχ [cm2 ]

LUX exclusion

Spin-independent N

_χ

σ_χp = 10⁻⁴⁵ cm²

Part 6

Additional Slides

m_χ [GeV]

Nχ

Sensitivity of σ

_χχ

Spin-independent σ_χp = 10⁻⁴⁵ cm²

τ channel ν channel

Observational constraint^[14-16]

1.0 < σ_χχ/m_χ < 0.1 cm²/g

LUX exclusion LUX exclusion

m_χ [GeV]

σ χχ[cm2 ] σ χχ[cm2 ]

m_χ [GeV]

Too weak to alleviate core/cusp problem^[16]