semi-annihilation + self-interactionDark matter Accumulated evidences from observations of the...
Transcript of semi-annihilation + self-interactionDark matter Accumulated evidences from observations of the...
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
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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⊙
*******************
******
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******
*******
*********
**********
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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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
AK and Kim, in preparation
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
h�semivreli = 6⇥ 10�26 cm3/s
�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
�self/m = 0.2 cm2/g
�self/m = 0.1 cm2/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!
AK and Kim, in preparation
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
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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
�
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�
�
→ 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
Elbert et al., MNRAS, 2015
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
Oman et al., MNRAS, 2015
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
Elbert et al., MNRAS, 2015
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
AK, Kaplinghat, Pace, and Yu, PRL, 2017
✴ 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
AK, Kaplinghat, Pace, and Yu, PRL, 2017
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)
Oman et al., MNRAS, 2015
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
AK, Kaplinghat, Pace, and Yu, PRL, 2017
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
�self/m = 0.1 cm2/g
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
�self/m = 0.1 cm2/g
h�semivreli = 6⇥ 10�26 cm3/s
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)
⟨ΔEσinvv⟩Tχ,Tϕ=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
⟨ΔEσinvv⟩Tχ,Tϕ=Tχ
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