semi-annihilation + self-interactionDark matter Accumulated evidences from observations of the Universe Known properties - long-lived over the age of the Universe Ω dm h 2 ≃ 5Ω

Oct. 8, 2019 @ IBS-MultiDark-IPPP workshop

1

semi-annihilation + self-interactionSelf-heating dark matter:

Based onAK, Hee Jung Kim, Hyungjin Kim, and Toyokazu Sekiguchi, PRL, 2018AK and Hee Jung Kim (+ Hitoshi Murayama), in preparation

Ayuki Kamada (IBS-CTPU)

- accounting for about of the present energy density of the Universe

2

Dark matterAccumulated evidences from observations of the Universe

Known properties- long-lived over the age of the Universe

Ωdmh2 ≃ 5Ωbaryonh2 ≃ 0.12- feebly-interacting with photon and baryon

- not too hot to smear out primordial density contrast

- originate from electroweak-scale new physics solving the hierarchy problem

Weakly-interacting massive particle (WIMP) paradigm- satisfy above properties w/ new symmetryℤ2

- WIMP miracle

- intensively investigated in direct/indirect detection experiments

30 %

3

No naturalness so far…

LHC discovery of Higgs and null-detection of top partners- something wrong in the hierarchy problem and postulated

solutions (including but not only electroweak-scale SUSY)

WIMP is no more as a miracle as we expected…

- new theoretical reasoning for WIMP?

- observational hints: small-scale issues in structure formation?

- mini-split SUSY- sfermions ; gauginos

- Higgs - dark matter- precise grand unification

No convincing signals in direct/indirect detection experiments so far

Arkani-Hamed and Dimopoulos, JHEP, 2005

Giudice and Romanino, NPB, 2004

Wells, PRD, 2005

Bullock and Bolyan-Kolchin, Ann. Rev. Astron. Astrophys., 2018

> 100 TeV ∼ TeV

125 GeV

125 GeV

4

What I will discuss

- evaporation through semi-annihilation - no core collapse unlike pure SIDM

part 2

Self-interacting dark matter (SIDM)- observations of different size halos

part 1

Self-heating dark matter (SHDM): halos

- velocity dependence of the cross section

- suppression of the linear matter spectrum

part 3

M ∼ 109-14 M⊙

- thermal freeze-outSelf-heating dark matter: early Universe

Self-interacting dark matter

5

Observed dwarf/law-surface brightness (LSB) galaxies → cored profile

Oman et al., MNRAS, 2015

6

Core-cusp problem

a.k.a. inner mass deficit problem- overpredict the circular

velocity by a factor of ( in mass)

∼ 2∼ 4

Collisionless cold dark matter (CDM) → cuspy profile

normalized radiusno

rmal

ized

mas

s de

nsity

Oh et al., AstroJ, 2011

M ∼ 1010-11 M⊙

prediction

data

predictiondata

7

The issues may be attributed to incomplete understanding of complex astrophysical processes (subgrid physics)

The issues may indicate alternatives to CDM (WIMPs)

Self-interacting dark matter

- self-interacting dark matter (SIDM) σ/m ∼ 1 cm2/g

- reduce the central mass density

Elbert et al., MNRAS, 2015

IC 2574, c200:-2.5σ, M200:1.5×1011M⊙

*******************

******

*******

*********

**********

*******************

******

*******

*********

**********

0 2 4 6 8 10 12 140

20

40

60

80

100

Radius (kpc)

Vcir(km/s)

M ∼ 1010 M⊙

σ/m = 3 cm2/g

AK, Kaplinghat, Pace, and Yu, PRL, 2017

CDM

SIDM

8

npÆnp elastic scattering

10 100 1000 104

1

2

5

10

20

50

100

vrel HkmêsL

sêmHcm

2 êgL

SIDM cross section inferred by a variety of halos diminishes toward higher velocity

105

21

0.5

0.20.1

1 10 100 1000

dwarf/LSB galaxies

galaxy clusters

bullet cluster

- cores in galaxy clusters→ σ/m ∼ 0.1 cm2/g

SIDM

Kaplinghat, Tulin, and Yu, PRL, 2016

Dark matter halos as particle colliders

- offset of bullet cluster

BCG wobbles

→ σ/m ≲ 1 cm2/g

- offsets of brightest cluster galaxy (BCG)

Randall et al., ApJ, 2008

→ σ/m ≲ 0.2 cm2/gHarvey, Robertson, Massay, and McCarthy, MNRAS, 2019

M ∼ 1010-11 M⊙

M ∼ 1014-15 M⊙

- cores of dwarf/LSB galaxies→ σ/m ∼ 1 cm2/g

9

Origin of velocity dependenceLight mediator dw

0.1

dw1

dw10

MW 0.1

MW 1cl 0.1

cl 1

10-4 0.001 0.01 0.1 10.1

1

10

100

1000

104

mf HGeVL

mXHGeVL

Dark matter with relic density Hs-waveLnon-perturbative (classical)

non-perturbative (s-wave resonance)

perturbative (Born)

mϕ < mχ Tulin, Yu, and Zurek, PRD, 2013

- hierarchical two scales

vector

- visible decay of ϕ❌ indirect detection experiments if annihilates into via s-wave

→ composite asymmetric DM

Bringmann, Kahlhoefer, Schmidt-Hoberg, and Walia, PRL, 2017

Ibe, AK, Kobayashi, Kuwahara, and Nakano, PRD, 2019

- puffy dark matter

- resonant dark matter

Chu, Garcia-Cely, and Murayama, arXiv:1901.00075

Chu, Garcia-Cely, and Murayama, PRL, 2019

mχα

mϕ< 1

mχα

mϕ> 1

mχα

mϕ> 1

mχv

mϕ> 1

mχv

mϕ< 1

- suppressed at high velocity like the Rutherford scattering

mϕ < mχv

Others

ϕχ

σSIDM/m(v) ≃ σn-p/m /10(v/10)QCD

ΛQCD′� ∼ ΛQCD

k cot δ ≃ −1a

+12

k2r −a ≫ r- deuteron

- previous figure

Steve’s talk

vs

10

1 + 2 → 3 + 4 Δ = 1 −m3 + m4

m1 + m2> 0

dσdΩ

=|ℳ |2

64π2s

|pf |

|pi |pi ∝ v

Dark fusion

pf ≃ m (2Δ + v2)1/2

McDermott, PRL, 2018

pf ≃ m (2Δ + v2)

10 100 103

10

100

103

10 100 103

10

100

103

- dark nuclei

0 < Δ ≪ 1

Loeb and Weiner, PRL, 2011Schutz and Slatyer, JCAP, 2015

- eXciting dark matter (XDM)

Δ v2

m1 ≃ m2 ≃ m

m3 ≃ 2m≃ m

Exothermic dark matter

vs

11

1 + 2 → 3 + 4One more important effect: heating

- boosted w/ kinetic energy

- make a difference from pure SIDM

→ DM evaporation from (the inner region of) a halo∼ Δ

Vogelsberger, Zavala, Schutz and Slatyer, MNRAS, 2019

Δ v2 - bigger impact on a smaller-size halo

Simulation of a MW-size halo

- difficult to cover a wide range w/ a simulation

Inelastic self-interacting dark matter

10 most massive subhalos

num

ber o

f sub

halo

s

Self-heating dark matter: halos

12

13

Self-heating dark matter

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f2<latexit sha1_base64="2WRvOi8yGUXygK6z5gAxLNjwKa4=">AAACCXicbVDLSsNAFJ34rPUVdelmsAiuSlIEXRbduKxgH9DUMJlO2qGTSZi5EUrI1o2/4saFIm79A3f+jdM0C209MMzhnHu5954gEVyD43xbK6tr6xubla3q9s7u3r59cNjRcaooa9NYxKoXEM0El6wNHATrJYqRKBCsG0yuZ373gSnNY3kH04QNIjKSPOSUgJF8G3vAI6axFypCs9DPvITn91kjz7Ow+Hy75tSdAniZuCWpoRIt3/7yhjFNIyaBCqJ133USGGREAaeC5VUv1SwhdEJGrG+oJGb8ICsuyfGpUYY4jJV5EnCh/u7ISKT1NApMZURgrBe9mfif108hvBxkXCYpMEnng8JUYIjxLBY85IpREFNDCFXc7IrpmJhMwIRXNSG4iycvk06j7jp19/a81rwq46igY3SCzpCLLlAT3aAWaiOKHtEzekVv1pP1Yr1bH/PSFavsOUJ/YH3+AIRrmtk=</latexit><latexit sha1_base64="2WRvOi8yGUXygK6z5gAxLNjwKa4=">AAACCXicbVDLSsNAFJ34rPUVdelmsAiuSlIEXRbduKxgH9DUMJlO2qGTSZi5EUrI1o2/4saFIm79A3f+jdM0C209MMzhnHu5954gEVyD43xbK6tr6xubla3q9s7u3r59cNjRcaooa9NYxKoXEM0El6wNHATrJYqRKBCsG0yuZ373gSnNY3kH04QNIjKSPOSUgJF8G3vAI6axFypCs9DPvITn91kjz7Ow+Hy75tSdAniZuCWpoRIt3/7yhjFNIyaBCqJ133USGGREAaeC5VUv1SwhdEJGrG+oJGb8ICsuyfGpUYY4jJV5EnCh/u7ISKT1NApMZURgrBe9mfif108hvBxkXCYpMEnng8JUYIjxLBY85IpREFNDCFXc7IrpmJhMwIRXNSG4iycvk06j7jp19/a81rwq46igY3SCzpCLLlAT3aAWaiOKHtEzekVv1pP1Yr1bH/PSFavsOUJ/YH3+AIRrmtk=</latexit><latexit sha1_base64="2WRvOi8yGUXygK6z5gAxLNjwKa4=">AAACCXicbVDLSsNAFJ34rPUVdelmsAiuSlIEXRbduKxgH9DUMJlO2qGTSZi5EUrI1o2/4saFIm79A3f+jdM0C209MMzhnHu5954gEVyD43xbK6tr6xubla3q9s7u3r59cNjRcaooa9NYxKoXEM0El6wNHATrJYqRKBCsG0yuZ373gSnNY3kH04QNIjKSPOSUgJF8G3vAI6axFypCs9DPvITn91kjz7Ow+Hy75tSdAniZuCWpoRIt3/7yhjFNIyaBCqJ133USGGREAaeC5VUv1SwhdEJGrG+oJGb8ICsuyfGpUYY4jJV5EnCh/u7ISKT1NApMZURgrBe9mfif108hvBxkXCYpMEnng8JUYIjxLBY85IpREFNDCFXc7IrpmJhMwIRXNSG4iycvk06j7jp19/a81rwq46igY3SCzpCLLlAT3aAWaiOKHtEzekVv1pP1Yr1bH/PSFavsOUJ/YH3+AIRrmtk=</latexit><latexit sha1_base64="2WRvOi8yGUXygK6z5gAxLNjwKa4=">AAACCXicbVDLSsNAFJ34rPUVdelmsAiuSlIEXRbduKxgH9DUMJlO2qGTSZi5EUrI1o2/4saFIm79A3f+jdM0C209MMzhnHu5954gEVyD43xbK6tr6xubla3q9s7u3r59cNjRcaooa9NYxKoXEM0El6wNHATrJYqRKBCsG0yuZ373gSnNY3kH04QNIjKSPOSUgJF8G3vAI6axFypCs9DPvITn91kjz7Ow+Hy75tSdAniZuCWpoRIt3/7yhjFNIyaBCqJ133USGGREAaeC5VUv1SwhdEJGrG+oJGb8ICsuyfGpUYY4jJV5EnCh/u7ISKT1NApMZURgrBe9mfif108hvBxkXCYpMEnng8JUYIjxLBY85IpREFNDCFXc7IrpmJhMwIRXNSG4iycvk06j7jp19/a81rwq46igY3SCzpCLLlAT3aAWaiOKHtEzekVv1pP1Yr1bH/PSFavsOUJ/YH3+AIRrmtk=</latexit>

e.g. variant of strongly-interacting massive particles (SIMPs)

AK, Kim, and Sekiguchi, PRD, 2017

- -axion-like particle (ALP) mixing through the anomalous coupling → freeze-out through semi-annihilation

- hidden pions in a hidden confinement sector- unbroken flavor symmetry → the stability of pions

Hochberg, Kuflik, Murayama, Volansky, and Wacker, PRL, 2015

η′�

Self-heating dark matter (SHDM): elastic self-scattering + semi-annihilation

⟨σsemivrel⟩ = 6 × 10−26 cm3/sσself /m ∼ 1 cm2/g

14

Gravothermal evolution

∂M∂r

= 4πr2ρ - equation of continuity

DM fluid: Lagrangian picture

∂ (ρν2)∂r

+GMρ

r2= 0 - hydrostatic equilibrium

3ν ( ∂ν

∂t )M

−1ρ ( ∂ρ

∂t )M

=1ν2

δuδt - energy conservation

- nature of DMInitial condition: NFW profile

ρNFW =ρs

r/rs(1 + r/rs)2w/ concentration-mass relation ↔ -ρs rs

Dutton and Macciò, MNRAS, 2014

c.f. Chu and Garcia-Cely, JCAP, 2018

Eulerian pictureonly semi-annihilationν2(r, t) = const .

15

Self-heating: energy deposit

δusemi

δt=

ρ ⟨σsemivrel⟩m

ξδEm

ξ = b ×rλ r=rs

δE =m4

- deposit efficiency w/ a fudge factor

≃ 0.0002 b ( rs

3.43 kpc ) ( ρs

0.011 M⊙/pc3 ) ( σself /m0.1 cm2/g )

b

Energy deposit through semi-annihilation

Pure SIDM - heat conductionδucond

δt= −

14πr2ρ

∂L∂r

L4πr2

= − κm∂∂r

ν2 κ−1 = κ−1SMFP + κ−1

LMFP

κSMFP =75 π

64ρλ2

amtself- collisional limit

- free-streaming limit

tself =m

aρσselfν

Koda and Shapiro, MNRAS, 2011

a =16π

κLMFP =32

CρH2

mtself

H =ν2

4πGρ

C = 0.75λ =

mσself ρ

- conductivity

- free-streaming length

λ ≪ H

λ ≪ H

- Jeans (gravitational) length

103

104

16

18

20

22

24

26

103

104

10-3

10-2

10-1

100

NFWm = 3MeVm = 0.3MeVm = 0.03MeV

NFWm = 3MeVm = 0.3MeVm = 0.03MeV

h�semivreli = 6⇥ 10�26 cm3/s

�self/m = 0.1 cm2/gb = 1

16

Sample halosδu = δusemi + δucondSHDM

dwarf/LSB galaxy M ≃ 1010 M⊙

1d v

eloc

ity d

ispe

rsio

n

AK and Kim, in preparation

t𝒥 ≃17 Gyr

b ( M200

1010 M⊙ )0.68

( m0.1 MeV ) ( 6 × 10−26cm3/s

⟨σsemivrel⟩ ) ( 0.1 cm2/gσself /m )

1ν2

δusemi

δt=

ρ ⟨σsemivrel⟩m

ξδEmν2

= ( νNFW(rs)ν )

2

( ρρNFW(rs) ) 1

t𝒥- heating

time scale

For given and , smaller has a bigger impactσself /m ⟨σsemivrel⟩ m

17

Core size - cross sections

0.1

10-1 100

10-27

10-26

10-25

10-24

10-27

10-26

10-25

10-24

⇢s = 0.0012M�/pc3

rs = 187 kpc , b = 1

m = 10MeV

m = 1MeV

m = 0.1MeV

m = 100MeV

0.05

10-1 100

10-27

10-26

10-25

10-24

10-27

10-26

10-25

10-24

m = 10MeV

m = 1MeV

m = 0.1MeV

m = 100MeV

\⇢s = 0.011M�/pc

3

rs = 3.43 kpc , b = 1


dwarf/LSB galaxy galaxy cluster

rcore/rs

preferred by dwarf/LSB galaxies

preferred by galaxy clusters

Preferred parameter:

Given , smaller for larger , i.e., smaller

σself /m ∼ 0.1 cm2/g

rcore

rcore σself /m ⟨σsemivrel⟩/m m

m ∼ O(1) MeV

M ≃ 1010 M⊙ M ≃ 1014 M⊙

101 102 103

100

101

102

103

104

101 102 103

100

101

102

103

104

0.1cm

2 /g

1 cm2 /g

10 cm2 /g


�self/m = 0.1 cm2/g

100cm

2 /g

0.01 cm

2 /gh�semivreli = 6⇥ 10�26 cm3/s

0.1cm

2 /g

1 cm2 /g

10 cm2 /g

100cm

2 /g

0.01 cm

2 /g



m = 0.3MeV

m = 0.3MeV

m = 2MeV

h�self,e↵v r

eli/

m⇥ cm

2/g

⇥km

/s⇤

18

Effective velocity dependence

σself,eff

SHDM ↔ pure SIDM? No!


No solution to for rc(SHDM) = rc(pure SIDM) σself,eff /m > 10 cm2/g

defined so thatEffective self-scattering cross section σself,eff /m

rcore(SHDM) = rcore(pure SIDM)

Sharp increase toward a smaller-size halo

Elbert et al., MNRAS, 2015M ∼ 1010 M⊙

increasing σ/mcore collapse

19

SHDM ≠ pure SIDMTwo regimes of pure SIDM

- collisional limit

- free-streaming limit λ ≫ H

λ ≪ H

decreasing → CDMσ/m

increasing → CDM!σ/m

Ann and Shapiro, MNRAS, 2005

→ maximal core size rcore ≲ 0.5rs

Monotonically escalating impacts toward smaller-size halos in SHDM

- differentiate SHDM and pure SIDM by smaller-size halos

- heatingrcore(t) ≃ rs ⋅ (t/t𝒥)0.57

ρcore(t) ∼ ρs ⋅ (t𝒥 /t)t𝒥 ≃

17 Gyrb ( M200

1010 M⊙ )0.68

( m0.1 MeV ) ( 6 × 10−26cm3/s

⟨σsemivrel⟩ ) ( 0.1 cm2/gσself /m )

M200

Disfavored if

0.1

10-1 100

10-27

10-26

10-25

10-24

10-27

10-26

10-25

10-24

⇢s = 0.0012M�/pc3

rs = 187 kpc , b = 1

m = 10MeV

m = 1MeV

m = 0.1MeV

m = 100MeV

0.05

10-1 100

10-27

10-26

10-25

10-24

10-27

10-26

10-25

10-24

m = 10MeV

m = 1MeV

m = 0.1MeV

m = 100MeV

\⇢s = 0.011M�/pc

3

rs = 3.43 kpc , b = 1

r (kpc)

ρ(M

⊙pc

−3

)

Ursa Minor

Draco

LeoII

LeoI

Carina

Sextans1/r

10−1 10010−3

10−2

10−1

100

20

Milky-Way satellites

M ∼ 109 M⊙ Wolf et al., MNRAS, 2010

Infall (before tidal-stripping) mass: Gilmore et al., ApJ, 2007

ρcore < ρcore,obs

Self-heating (or generically exothermic) dark matter could not explain MW satellites, dwarf/LSB galaxies, and galaxy clusters at the same time

preferred by galaxy clusters

preferred by dwarf/LSB galaxies

disfavored by MW satellites

mas

s de

nsity

[kpc][M

⊙/p

c3 ]

100

10−1

10−2

10−3

radius10−1

100

Self-heating dark matter: early Universe

21

Co-evolution equations:

22

��

� �

�

� �

��

�

�

�

� �

Co-evolution equations

fχ =nχ

neqχ (Tχ)

exp(−Eχ /Tχ)

AK, Kim, Kim, and Sekiguchi, PRL, 2018

·nχ + 3Hnχ = − nχ⟨σsemiv⟩TχTχ[nχ − 𝒥(Tχ, Tϕ)neqχ (Tχ)]

efficient self-scattering

- adiabatic cooling- heating through semi-annihilation

·Tχ + 3HTχ (Tχ

σE )2

= − (Tχ

σE )2 neq

ϕ (Tχ)

neqχ (Tχ)

⟨ΔEσinvv⟩Tχ,Tϕ=Tχ

× [nχ − neqχ (Tχ)𝒦(Tχ, Tϕ)]

σ2E = ⟨E2

χ ⟩ − ⟨Eχ⟩2

σ2E = 3Tχ

non-relativistic: σ2E = 3/2Tχ

relativistic: Tχ ∝ 1/a→→ Tχ ∝ 1/a2

Tχ = Tϕ

Boltzmann equation for WIMP freeze-out

DM DM

DM TP

23

101 102 10310-12

10-10

10-8

10-6

10-4

10-2 m� = 1 GeVm�/m� = 0

(�semivrel) = 6⇥ 10�26cm3/s

m�/m� = 0

m�/m� = 0.7

m�/m� = 0.9

m� /m

� =1

10 100 1000 1040.050.10

0.501

510

xfo /x

AK, Kim, Kim, and Sekiguchi, PRL, 2018

�

�<latexit sha1_base64="TwKQu5I6W5bc9HOXn7rGty6B3x4=">AAAB63icbVBNSwMxEJ3Ur1q/qh69BIvgqeyKoMeiF48VbC20S8mm2W5okl2SrFCW/gUvHhTx6h/y5r8x2+5BWx8MPN6bYWZemApurOd9o8ra+sbmVnW7trO7t39QPzzqmiTTlHVoIhLdC4lhgivWsdwK1ks1IzIU7DGc3Bb+4xPThifqwU5TFkgyVjzilNhCGtCYD+sNr+nNgVeJX5IGlGgP61+DUUIzyZSlghjT973UBjnRllPBZrVBZlhK6ISMWd9RRSQzQT6/dYbPnDLCUaJdKYvn6u+JnEhjpjJ0nZLY2Cx7hfif189sdB3kXKWZZYouFkWZwDbBxeN4xDWjVkwdIVRzdyumMdGEWhdPzYXgL7+8SroXTd9r+veXjdZNGUcVTuAUzsGHK2jBHbShAxRieIZXeEMSvaB39LForaBy5hj+AH3+AP+rjjI=</latexit><latexit sha1_base64="TwKQu5I6W5bc9HOXn7rGty6B3x4=">AAAB63icbVBNSwMxEJ3Ur1q/qh69BIvgqeyKoMeiF48VbC20S8mm2W5okl2SrFCW/gUvHhTx6h/y5r8x2+5BWx8MPN6bYWZemApurOd9o8ra+sbmVnW7trO7t39QPzzqmiTTlHVoIhLdC4lhgivWsdwK1ks1IzIU7DGc3Bb+4xPThifqwU5TFkgyVjzilNhCGtCYD+sNr+nNgVeJX5IGlGgP61+DUUIzyZSlghjT973UBjnRllPBZrVBZlhK6ISMWd9RRSQzQT6/dYbPnDLCUaJdKYvn6u+JnEhjpjJ0nZLY2Cx7hfif189sdB3kXKWZZYouFkWZwDbBxeN4xDWjVkwdIVRzdyumMdGEWhdPzYXgL7+8SroXTd9r+veXjdZNGUcVTuAUzsGHK2jBHbShAxRieIZXeEMSvaB39LForaBy5hj+AH3+AP+rjjI=</latexit><latexit sha1_base64="TwKQu5I6W5bc9HOXn7rGty6B3x4=">AAAB63icbVBNSwMxEJ3Ur1q/qh69BIvgqeyKoMeiF48VbC20S8mm2W5okl2SrFCW/gUvHhTx6h/y5r8x2+5BWx8MPN6bYWZemApurOd9o8ra+sbmVnW7trO7t39QPzzqmiTTlHVoIhLdC4lhgivWsdwK1ks1IzIU7DGc3Bb+4xPThifqwU5TFkgyVjzilNhCGtCYD+sNr+nNgVeJX5IGlGgP61+DUUIzyZSlghjT973UBjnRllPBZrVBZlhK6ISMWd9RRSQzQT6/dYbPnDLCUaJdKYvn6u+JnEhjpjJ0nZLY2Cx7hfif189sdB3kXKWZZYouFkWZwDbBxeN4xDWjVkwdIVRzdyumMdGEWhdPzYXgL7+8SroXTd9r+veXjdZNGUcVTuAUzsGHK2jBHbShAxRieIZXeEMSvaB39LForaBy5hj+AH3+AP+rjjI=</latexit><latexit sha1_base64="TwKQu5I6W5bc9HOXn7rGty6B3x4=">AAAB63icbVBNSwMxEJ3Ur1q/qh69BIvgqeyKoMeiF48VbC20S8mm2W5okl2SrFCW/gUvHhTx6h/y5r8x2+5BWx8MPN6bYWZemApurOd9o8ra+sbmVnW7trO7t39QPzzqmiTTlHVoIhLdC4lhgivWsdwK1ks1IzIU7DGc3Bb+4xPThifqwU5TFkgyVjzilNhCGtCYD+sNr+nNgVeJX5IGlGgP61+DUUIzyZSlghjT973UBjnRllPBZrVBZlhK6ISMWd9RRSQzQT6/dYbPnDLCUaJdKYvn6u+JnEhjpjJ0nZLY2Cx7hfif189sdB3kXKWZZYouFkWZwDbBxeN4xDWjVkwdIVRzdyumMdGEWhdPzYXgL7+8SroXTd9r+veXjdZNGUcVTuAUzsGHK2jBHbShAxRieIZXeEMSvaB39LForaBy5hj+AH3+AP+rjjI=</latexit>



�

�

→ time

com

ovin

g nu

mbe

r den

sity

tem

pera

ture

ratio

in equilibrium

❌ inverse process

❌ semi-annihilation

Freeze-out

- difference from ∼ 30 %Tχ = Tϕ ∝ 1/a

- no conversion → adiabatic cooling

Tχ ∝ 1/a2

- mass deficit converted into the kinetic energy → self-heating Tχ ∝ 1/a

mwdm = 4.09 keV

mwdm = 5.3 keV

100 101 102 103

10-1

100

24

Irŝiĉ et al., PRD, 2017

Baur et al., JCAP, 2016m� = 0.1GeV

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m� = 1GeV<latexit sha1_base64="qTUE/dFm+xen54htTwnSw3FJKaQ=">AAACAnicbVBNS8NAEN34WetX1JN4WSyCBymJCHoRih70WMF+QBPKZjtpl+4mYXcjlBC8+Fe8eFDEq7/Cm//GbZuDtj4YeLw3w8y8IOFMacf5thYWl5ZXVktr5fWNza1te2e3qeJUUmjQmMeyHRAFnEXQ0ExzaCcSiAg4tILh9dhvPYBULI7u9SgBX5B+xEJGiTZS194X3cyjA5bjS+xi7wRnnhT4Bpp51644VWcCPE/cglRQgXrX/vJ6MU0FRJpyolTHdRLtZ0RqRjnkZS9VkBA6JH3oGBoRAcrPJi/k+MgoPRzG0lSk8UT9PZERodRIBKZTED1Qs95Y/M/rpDq88DMWJamGiE4XhSnHOsbjPHCPSaCajwwhVDJzK6YDIgnVJrWyCcGdfXmeNE+rrlN1784qtasijhI6QIfoGLnoHNXQLaqjBqLoET2jV/RmPVkv1rv1MW1dsIqZPfQH1ucP1HSVxA==</latexit><latexit sha1_base64="qTUE/dFm+xen54htTwnSw3FJKaQ=">AAACAnicbVBNS8NAEN34WetX1JN4WSyCBymJCHoRih70WMF+QBPKZjtpl+4mYXcjlBC8+Fe8eFDEq7/Cm//GbZuDtj4YeLw3w8y8IOFMacf5thYWl5ZXVktr5fWNza1te2e3qeJUUmjQmMeyHRAFnEXQ0ExzaCcSiAg4tILh9dhvPYBULI7u9SgBX5B+xEJGiTZS194X3cyjA5bjS+xi7wRnnhT4Bpp51644VWcCPE/cglRQgXrX/vJ6MU0FRJpyolTHdRLtZ0RqRjnkZS9VkBA6JH3oGBoRAcrPJi/k+MgoPRzG0lSk8UT9PZERodRIBKZTED1Qs95Y/M/rpDq88DMWJamGiE4XhSnHOsbjPHCPSaCajwwhVDJzK6YDIgnVJrWyCcGdfXmeNE+rrlN1784qtasijhI6QIfoGLnoHNXQLaqjBqLoET2jV/RmPVkv1rv1MW1dsIqZPfQH1ucP1HSVxA==</latexit><latexit sha1_base64="qTUE/dFm+xen54htTwnSw3FJKaQ=">AAACAnicbVBNS8NAEN34WetX1JN4WSyCBymJCHoRih70WMF+QBPKZjtpl+4mYXcjlBC8+Fe8eFDEq7/Cm//GbZuDtj4YeLw3w8y8IOFMacf5thYWl5ZXVktr5fWNza1te2e3qeJUUmjQmMeyHRAFnEXQ0ExzaCcSiAg4tILh9dhvPYBULI7u9SgBX5B+xEJGiTZS194X3cyjA5bjS+xi7wRnnhT4Bpp51644VWcCPE/cglRQgXrX/vJ6MU0FRJpyolTHdRLtZ0RqRjnkZS9VkBA6JH3oGBoRAcrPJi/k+MgoPRzG0lSk8UT9PZERodRIBKZTED1Qs95Y/M/rpDq88DMWJamGiE4XhSnHOsbjPHCPSaCajwwhVDJzK6YDIgnVJrWyCcGdfXmeNE+rrlN1784qtasijhI6QIfoGLnoHNXQLaqjBqLoET2jV/RmPVkv1rv1MW1dsIqZPfQH1ucP1HSVxA==</latexit><latexit sha1_base64="qTUE/dFm+xen54htTwnSw3FJKaQ=">AAACAnicbVBNS8NAEN34WetX1JN4WSyCBymJCHoRih70WMF+QBPKZjtpl+4mYXcjlBC8+Fe8eFDEq7/Cm//GbZuDtj4YeLw3w8y8IOFMacf5thYWl5ZXVktr5fWNza1te2e3qeJUUmjQmMeyHRAFnEXQ0ExzaCcSiAg4tILh9dhvPYBULI7u9SgBX5B+xEJGiTZS194X3cyjA5bjS+xi7wRnnhT4Bpp51644VWcCPE/cglRQgXrX/vJ6MU0FRJpyolTHdRLtZ0RqRjnkZS9VkBA6JH3oGBoRAcrPJi/k+MgoPRzG0lSk8UT9PZERodRIBKZTED1Qs95Y/M/rpDq88DMWJamGiE4XhSnHOsbjPHCPSaCajwwhVDJzK6YDIgnVJrWyCcGdfXmeNE+rrlN1784qtasijhI6QIfoGLnoHNXQLaqjBqLoET2jV/RmPVkv1rv1MW1dsIqZPfQH1ucP1HSVxA==</latexit>

m� = 10GeV<latexit sha1_base64="5bJh45hM61mJMnG7aU+EvSf20jM=">AAACA3icbVBNS8NAEN34WetX1JteFovgQUoigl6Eogc9VrAf0ISy2U7apbtJ2N0IJQS8+Fe8eFDEq3/Cm//GbZuDtj4YeLw3w8y8IOFMacf5thYWl5ZXVktr5fWNza1te2e3qeJUUmjQmMeyHRAFnEXQ0ExzaCcSiAg4tILh9dhvPYBULI7u9SgBX5B+xEJGiTZS194X3cyjA5bjS+w62DvBmScFvoFm3rUrTtWZAM8TtyAVVKDetb+8XkxTAZGmnCjVcZ1E+xmRmlEOedlLFSSEDkkfOoZGRIDys8kPOT4ySg+HsTQVaTxRf09kRCg1EoHpFEQP1Kw3Fv/zOqkOL/yMRUmqIaLTRWHKsY7xOBDcYxKo5iNDCJXM3IrpgEhCtYmtbEJwZ1+eJ83TqutU3buzSu2qiKOEDtAhOkYuOkc1dIvqqIEoekTP6BW9WU/Wi/VufUxbF6xiZg/9gfX5A0jolf4=</latexit><latexit sha1_base64="5bJh45hM61mJMnG7aU+EvSf20jM=">AAACA3icbVBNS8NAEN34WetX1JteFovgQUoigl6Eogc9VrAf0ISy2U7apbtJ2N0IJQS8+Fe8eFDEq3/Cm//GbZuDtj4YeLw3w8y8IOFMacf5thYWl5ZXVktr5fWNza1te2e3qeJUUmjQmMeyHRAFnEXQ0ExzaCcSiAg4tILh9dhvPYBULI7u9SgBX5B+xEJGiTZS194X3cyjA5bjS+w62DvBmScFvoFm3rUrTtWZAM8TtyAVVKDetb+8XkxTAZGmnCjVcZ1E+xmRmlEOedlLFSSEDkkfOoZGRIDys8kPOT4ySg+HsTQVaTxRf09kRCg1EoHpFEQP1Kw3Fv/zOqkOL/yMRUmqIaLTRWHKsY7xOBDcYxKo5iNDCJXM3IrpgEhCtYmtbEJwZ1+eJ83TqutU3buzSu2qiKOEDtAhOkYuOkc1dIvqqIEoekTP6BW9WU/Wi/VufUxbF6xiZg/9gfX5A0jolf4=</latexit><latexit sha1_base64="5bJh45hM61mJMnG7aU+EvSf20jM=">AAACA3icbVBNS8NAEN34WetX1JteFovgQUoigl6Eogc9VrAf0ISy2U7apbtJ2N0IJQS8+Fe8eFDEq3/Cm//GbZuDtj4YeLw3w8y8IOFMacf5thYWl5ZXVktr5fWNza1te2e3qeJUUmjQmMeyHRAFnEXQ0ExzaCcSiAg4tILh9dhvPYBULI7u9SgBX5B+xEJGiTZS194X3cyjA5bjS+w62DvBmScFvoFm3rUrTtWZAM8TtyAVVKDetb+8XkxTAZGmnCjVcZ1E+xmRmlEOedlLFSSEDkkfOoZGRIDys8kPOT4ySg+HsTQVaTxRf09kRCg1EoHpFEQP1Kw3Fv/zOqkOL/yMRUmqIaLTRWHKsY7xOBDcYxKo5iNDCJXM3IrpgEhCtYmtbEJwZ1+eJ83TqutU3buzSu2qiKOEDtAhOkYuOkc1dIvqqIEoekTP6BW9WU/Wi/VufUxbF6xiZg/9gfX5A0jolf4=</latexit><latexit sha1_base64="5bJh45hM61mJMnG7aU+EvSf20jM=">AAACA3icbVBNS8NAEN34WetX1JteFovgQUoigl6Eogc9VrAf0ISy2U7apbtJ2N0IJQS8+Fe8eFDEq3/Cm//GbZuDtj4YeLw3w8y8IOFMacf5thYWl5ZXVktr5fWNza1te2e3qeJUUmjQmMeyHRAFnEXQ0ExzaCcSiAg4tILh9dhvPYBULI7u9SgBX5B+xEJGiTZS194X3cyjA5bjS+w62DvBmScFvoFm3rUrTtWZAM8TtyAVVKDetb+8XkxTAZGmnCjVcZ1E+xmRmlEOedlLFSSEDkkfOoZGRIDys8kPOT4ySg+HsTQVaTxRf09kRCg1EoHpFEQP1Kw3Fv/zOqkOL/yMRUmqIaLTRWHKsY7xOBDcYxKo5iNDCJXM3IrpgEhCtYmtbEJwZ1+eJ83TqutU3buzSu2qiKOEDtAhOkYuOkc1dIvqqIEoekTP6BW9WU/Wi/VufUxbF6xiZg/9gfX5A0jolf4=</latexit>

Linear matter power spectrumAK, Kim, and Kim, PRD, 2018

Self-heating ceases when self-scattering becomes inefficient

mwdm

5.3 keV≃ 3 ( mχ

1 GeV )3/8

max 1,Tself

Teq

3/4

(Tχ

T )−3/8

asy

Tself

Warmness (WDM) is related with self-scattering (SIDM)

25

Summary

Self-heating (or generically exothermic) dark matter

- sharply increasing impact on a smaller-size halo

Velocity-dependent (pure) SIDM is an interesting possibility- at galaxy clustersσself /m ∼ 0.1 cm2/g

- at dwarf/LSB galaxiesσself /m ∼ 1 cm2/g M ∼ 1010-11 M⊙

M ∼ 1014-15 M⊙ v ∼ 103 km/s

v ∼ 102 km/s

-⚠ (or ❌) MW satellites-⭕ galaxy clusters, dwarf/LSB galaxies σself /m ∼ 0.1 cm2/g

m ∼ O(1) MeV

⟨σsemivrel⟩ = 6 × 10−26 cm3/s

- suppress the linear matter power spectrum- worth studying in more detail

- velocity dependent cross section + heating

Structure formation of the Universe provides a good (although indirect) bottom-up test on the nature of DM

M ∼ 109 M⊙

Thank you for your attention

26

(maximum) circular velocity:

27

maximal circular velocity of subhalo

cum

ulat

ive

num

ber o

f sub

halo

s

Kratsov, Advances in Astronomy, 2010

N-body (DM-only) simulations in the ΛCDM model → a MW-size halo hosts a times larger number of subhalos than that of observed dwarf spheroidal galaxies

Missing satellite problem

V2circ =

GM( < r)r

Vmax = maxr

(Vcirc(r))

Vmax = 160 km/s

208 km/s

𝒪(10)

28

SIDM reduces the central mass density


Cusp vs core problem w/ SIDM

Mhalo ∼ 1010M⊙

Boylan-Kolchin et al., MNRAS, 2011

29

N-body (DM-only) simulations in the ΛCDM model → missing galaxies are the biggest subhalos in simulations (to big to fail to be detected)

circ

ular

vel

ocity

of s

ubha

los

radius

- MW-like halos

Too-big-to-fail problem

∼ 10

30


circ

ular

vel

ocity

Diversity of inner rotation curvesCollisionless dark matter prediction: inner circular velocity is almost uniquely determined by outer circular velocity↔ observations show diversity

✴ unique prediction is related with the concentration-mass relation

- overpredict the circular velocity by a factor of

( in mass)∼ 2 ∼ 4

Vmax = 80-100 km/s

31

SIDM-only simulation


tem

pera

ture

↔

Iso-thermal haloSelf-scattering leads to thermalization of DM halos at where self-scattering happens at least one time until now

r < r1

σ/m ρ(r1)v(r1) tage = 1

Mhalo ∼ 1010M⊙

32

Key observation

⇢DM(~x) = ⇢0DM exp(��(~x)/�2)

�� = 4⇡G(⇢DM + ⇢baryon)- inner profile is exponentially

sensitive to baryon distribution

Baryons form complex objects, which show a large diversity→ SIDM particles, redistributed according to formed baryonic objects, can show a diversity

✴ do not rely on unconstrained subgrid astrophysical processes take into account observed baryon distribution

Iso-thermal → Boltzmann distribution

**********

**************

***********************

NGC 6503, c200:median, M200:2.5×1011M⊙

StarsGas

Halo

0 5 10 15 200

50

100

150

200

250

Radius (kpc)

Vcir(km/s)

*******************************

*******************

UGC 128, c200:median, M200:3.8×1011M⊙

Stars

Gas

Halo

0 10 20 30 40

Radius (kpc)

**********

************

*********************

NGC 2903, c200:median, M200:1.2×1012M⊙

StarsGasBulge

Halo

0 5 10 15 20 25 30

Radius (kpc)

circ

ular

vel

ocity

(km

/s)

CDM

SIDM-only

redistributed SIDM

50

100

150

200

250

0

33

Impacts in observed galaxies

- Observed stellar disk makes SIDM inner circular velocity times higher

∼ 3

→ reproducing flat circular velocity at


✴ Hereafter σ/m = 3 cm2/g

10-20 kpc

M* = 5.5 × 1010 M⊙

**********

**************

***********************

NGC 6503, c200:median, M200:2.5×1011M⊙

StarsGas

Halo

0 5 10 15 200

50

100

150

200

250

Radius (kpc)

Vcir(km/s)

*******************************

*******************

UGC 128, c200:median, M200:3.8×1011M⊙

Stars

Gas

Halo

0 10 20 30 40

Radius (kpc)

**********

************

*********************

NGC 2903, c200:median, M200:1.2×1012M⊙

StarsGasBulge

Halo

0 5 10 15 20 25 30

Radius (kpc)

34

compact stellar disk extended stellar disk

Diversity in stellar distribution

Similar outer circular velocity and stellar mass, but different stellar distribution

- compact → redistribute SIDM significantly- extended → unchange SIDM distribution


M* = 0.83 × 1010 M⊙ M* = 0.57 × 1010 M⊙

IC 2574, c200:-1.5σ, M200:9×1010M⊙

*******************

******

*******

***********

********

0 2 4 6 8 10 12 140

20

40

60

80

100

Radius (kpc)

Vcir(km/s)

IC 2574, c200:-2.5σ, M200:1.5×1011M⊙

*******************

******

*******

*********

**********

*******************

******

*******

*********

**********

0 2 4 6 8 10 12 140

20

40

60

80

100

Radius (kpc)

Vcir(km/s)


circ

ular

vel

ocity

circ

ular

vel

ocity

Radius Radius

35

Intrinsic scatter

Intrinsic diversity of DM halos should be taken into account to explain the observed diversity


36

Lagrangian vs Eulerian

10-2

10-1

100

101

10-3

10-2

10-1

100

101

102

103

10-2

10-1

100

101

5

6

7

8

9

10t/t0 = 10�2

t/t0 = 10�1

t/t0 = 1t/t0 = 10

2 4 6 8 10-1

0

1

2

3

4

2 4 6 8 10-1

0

1

2

3

4

2 4 6 8 10-1

0

1

2

3

4

2 4 6 8 10-1

0

1

2

3

4

EulerianLagrangian

t/t0 = 10�2

t/t0 = 10�1

t/t0 = 1t/t0 = 10

2 4 6 8 10-1

0

1

2

3

4

2 4 6 8 10-1

0

1

2

3

4

2 4 6 8 10-1

0

1

2

3

4

2 4 6 8 10-1

0

1

2

3

4

EulerianLagrangianh�semivreli = 6⇥ 10�26 cm3/s


b = 1, m = 2MeV

∂ρ∂t

+1r2

∂∂r (r2ρVr) = 0

∂Vr

∂t+ Vr

∂Vr

∂r= −

∂Φ∂r

−1ρ

∂ (ρν2)∂r

DM fluid: Eulerian picture

1r2

∂∂r (r2 ∂Φ

∂r ) = 4πGρ1r2

∂∂r (r2Vr) +

3ν [ ∂ν

∂t+ Vr

∂ν∂r ] =

1ν2

δuδt

- equation of continuity - Euler equation

- Poisson equation - energy conservation

37

Initial condition dependence

\

10-1

100

101

10-2

10-1

0.1

0.2

0.3

0.5

0.9

1.3

10-2

10-1

10-27

10-26

10-25

10-24

m = 10MeV

m = 1MeV

m = 0.1MeV

m = 100MeV

\⇢s = 0.011M�/pc

3

rs = 3.43 kpc , b = 1



2 4 6 8 10-1

0

1

2

3

4

2 4 6 8 10-1

0

1

2

3

4

2 4 6 8 10-1

0

1

2

3

4

2 4 6 8 10-1

0

1

2

3

4

rc/rs = 0.003

rc/rs = 0.01

rc/rs = 0.03

rc/rs = 0.1

�self/m = 0.1 cm2/g, m = 2MeV

rc/rs

Different initial profiles converge into the attractor solution

rc ≪ rcore

- initial core sizeas long asrcore(t) ≃ rs ⋅ (t/t𝒥)

0.57

38Hidden sector in an ALP-extended SIMP model

Lagrangian density w/ and :

Lhid = L0 + LCP + LCPV + LWZW

L0 =1

2(@µ⇡

a)2 +1

2(@µ�)

2 � 1

2m2

⇡ (⇡a)2 � 1

2m2

��2

LCP =m2

⇡

4N2f f

2(⇡a)2 �2 � 1

6f2⇡

rabcd (@µ⇡a)

�@µ⇡b

�⇡c⇡d

+m2

⇡

6Nff⇡fdabc⇡

a⇡b⇡c�+m2

⇡

12f2⇡

cabcd⇡a⇡b⇡c⇡d

G = SU(Nf )L ⇥ SU(Nf )R H = SU(Nf )V

LCPV = tan (✓H/Nf )

m2

⇡

2Nff�(⇡a)2

+m2

⇡

6f⇡dabc⇡

a⇡b⇡c � m2⇡

30f3⇡

⇡a⇡b⇡c⇡d⇡ecabcde

�

39

Co-evolution equations·nχ + 3Hnχ = − nχ⟨σsemiv⟩TχTχ[nχ − 𝒥(Tχ, Tϕ)neq

χ (Tχ)]·Tχ + 3HTχ (

Tχ

σE )2

= − (Tχ

σE )2 neq

ϕ (Tχ)

neqχ (Tχ)


× [nχ − neqχ (Tχ)𝒦(Tχ, Tϕ)]

𝒥(Tχ, Tϕ) =neq

ϕ (Tϕ)

neqϕ (Tχ)

⟨σinvv⟩Tχ,Tϕ

⟨σinvv⟩Tχ,Tϕ=Tχ

𝒦(Tχ, Tϕ) =neq

ϕ (Tϕ)

neqϕ (Tχ)

⟨ΔEσinvv⟩Tχ,Tϕ


σ2E = 3Tχ

non-relativistic: σ2E = 3/2Tχ

relativistic:

ΔE = Eϕ − ⟨Eχ⟩Tχ

σ2E = ⟨E2

χ ⟩ − ⟨Eχ⟩2

𝒥(Tχ = Tϕ, Tϕ) = 1

𝒦(Tχ = Tϕ, Tϕ) = 1

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