ダークマター候補
Primordial Black Hole, axion, WIMPの問題点

Kazunori Kohri
郡 和範

KEK and SOKENDAI, Tsukuba
U of Tokyo, Kavli IPMU

Candidate of Dark Ma/er
My favorite DMs (推しダークマター)• WIMP• Axion• Primordial Black Hole• ...
19/07/06

Kaz Kohri (KEK)Why PBHs?
• We need 30 M◉ BHs to explain LIGO/VIRGO GW events•

We do not know the origin of 30 M◉ BHs to be astrophysical or
cosmological.

• PBHs should be a good candidate for Cold Dark Matter (CDM)• Some inflation modes predict PBHs formed at small scales inthe early Universe (much before 1 sec)
• Scenarios have been constrained by BBN, CMB, lensing、gammaray, and so on.
• In future, scenarios can be investigated further by PIXIE-likesatellite (CMB µ-distortion), SKA/Ominiscope (21cm), CTA(gamma-ray), DECIGO (Gravitational Wave), …

How to produce the binary black holewith masses of O(10) M◉?
• Have binaries originated from Pop III or Pop II
stars collided within cosmic Jme?
[astrophysically model-dependent]• Primordial black holes (PBHs) formed throughcollapses of perturbaJons produced byInﬂaJon[Cosmologically model-dependent]
19/07/06

Kaz Kohri

CondiJons for a PBH formaJon in RadiaJon
dominated (RD) Universe
Zel’dovich and Novikov (1967), Hawking (1971), Carr (1975)
Harada,Yoo and KK (2013)• Gravity could be stronger than pressure

δ > δc ~ p / ρ ~ c s = w = 1 / 32δBlack HoleA fluctuation with the wave number k

A closed universe immediately
Horizon size = H-1 = (k/a)-1

collapsing into a BH

Primordial Black Hole (PBH)• Large perturbaJon at small scales
was produced by InﬂaJon at around> 10-36 second

19/07/06

Kazunori Kohri (KEK/Sokendai)Pζ (k) and PBH abundance β(M)ΩPBH = ρPBH / ρtot

• FracJon of PBH to the total at its formaJon epoch withGaussian ﬂuctuaJon.

~ 0.3 − 0.4• Finally we have a relaJon between β and ﬂuctuaJon σ (or βand Ω)

β ( M) ~⎛m ⎞−18= 1.5 × 10 ⎜ PBH⎟⎜⎝ 1015 g ⎟⎠1/2⎛ Ω h2 ⎞⎜ PBH ⎟⎜⎝ 0.13 ⎟⎠~ PζTypical quanJJes of PBHs in RD• Mass (horizon mass =ρ(tform) H(tform)-3 )⎛ T⎞−13215form
M PBH ~ ρ(H form ) ~ M plt from ~ 2 ~ 10 g ⎜⎟8⎜
T form⎝ 3 × 10 GeV ⎟⎠M3pl• LifeJme−2⎛ T⎞
form~ 30M⊙ ⎜⎟⎜⎝ 40MeV ⎟⎠3⎛ M⎞
⎛M
⎞
M PBH
1768
PBHPBHτ PBH ~~ 4 × 10 sec ⎜ 15 ⎟ ~ 3 × 10 yrs ⎜⎟
4⎜
⎟
⎜
M pl
⎝ 10 g ⎠⎝ 30M ⊙ ⎟⎠3• Hawking Temperature
M

⎛M
⎞
pl
PBHT PBH ~~ 0.1MeV ⎜ 15 ⎟⎜⎝ 10 g ⎟⎠MPBH2−1⎛ M⎞−11PBH~ 3 × 10 K ⎜⎟⎜⎝ 30M ⎟⎠⊙• Wave number of horizon
length⎛⎞Mk = aH ~ 105 Mpc −1 ⎜ 4 PBH ⎟⎜⎝ 10 M ⎟⎠⊙• FracJon to CDM⎛ β ⎞ffraction ≡~ ⎜ −18 ⎟ΩCDM ⎝ 10 ⎠
ΩPBH

⎛M
⎞
PBH
⎜ 15 ⎟⎜⎝ 10 g ⎟⎠−1/2−1/2⎛ β ⎞~ ⎜ −8 ⎟⎝ 10 ⎠⎛T⎞
5−1form~ 10 Mpc ⎜⎟⎜⎝ MeV ⎟⎠

⎛ M⎞
PBH⎜⎟
⎜⎝ 30M ⎟⎠⊙−1/2−23−1+1⎛ M⎞
8PBH~ 10 ⎜⎟⎜⎝ 30M ⎟⎠
⊙

−1/2⎡
1 ⎤⎥
Pδ exp ⎢ −⎢⎣ 18Pδ ⎥⎦Rate of GW140914

GW150914
anditsmergerrate
M. Sasaki, T. Suyama, T. Tanaka and S. Yokoyama (2016).
3-body is important for theBBH formations
See also, Ali-Haimound, Kovetz and Kamionkowski (2017)

f=10-3

f=10-2

fraction to CDM (ffraction)

CMB bound on PBHs by disk-accreJon inthe late MD epoch
Poulin, Serpico, Calore, Clesse, KK (2017)• A non-spherical accreJon disk (ADAF(slim) +Standard disk) around a PBH caused by anangular momentum emits radiaJon• CMB anisotropies are aﬀected• From observaJons, we can constrain thenumber density of PBHs.

Ionization fraction

Luminosity

Modiﬁed CMB
anisotropy
Poulin, Serpico, Calore, Clesse, Kohri (2017)

disk
disk
disk

disk
spherical

standard

spherical
redshift z

redshift z

Luminosity

Ionization fraction

standard
spherical
disk

multipole ℓ

EE polarization correlation CEEℓ

TT corrrelation CTTℓ

Modiﬁed CMB
anisotropy
Poulin, Serpico, Calore, Clesse, Kohri (2017)

disk
spherical
standard

multipole ℓCMB bound by disk-accreJon in thelatest MD epoch

Fraction to CDM

Poulin, Serpico, Calore, Clesse, KK (2017)

EvaporaJng PBHs due to Hawking
ProcessCarr, Kohri, Sendouda and Yokoyama (2010)

CTA will give stronger
bounds!

GravitaJonal lensing constrains on PBHs
Hiroko Niikura, Masahiro Takada, Shuichiro Yokoyama, Takahiro Sumi, Shogo Masaki,arXiv:1901.07120 [astro-ph.CO]

2622 microlensing in Galactic bulge byOGLE

19/07/06

Kaz Kohri (KEK)fPBH=ΩPBH/ΩCDM

Upper bounds on the fracJon to CDM

19/07/06

CMB y-distortion

30M⊙ ~ 1035 g

MPBH

Kaz Kohri

Carr, Kohri, Sendouda and Yokoyama (2010)

100 % Dark Ma/er by PBHs

KK and T.Terada, 2018

AxionorAxion-LikeParJcle (ALP)
19/07/06

Kaz Kohri (KEK)OscillaJon probability• Probability

2⎤⎡
⎛
⎞
gBr
Ε
1aγ
⎥2⎢
*Pa↔γ =sin ⎢1+ ⎜ ⎟ ⎥22Εγ ⎠⎝
⎛Ε ⎞⎢
⎥
*⎣
⎦
1+ ⎜ ⎟⎝ Εγ ⎠• For eﬃcient oscillaJon,
2am
Eγ > E* =2g aγ B
19/07/06

andKaz Kohri (KEK)r ≥ rHa ≡2g aγ B

Cosmic Infrared Background (CIB) by CIBER
2016, IRTS 2013, Akari 2013

Gamma-ray horizon

ＴｅＶ

Kohri and Kodama, arXiv:2017.05189

γ (AGN) →axion (IGM)→γ (Milky-Way)

γTeV + γIR ! e+ + e-

19/07/06

Kaz Kohri (KEK)Spectrum reduction by axion mixing
Shimet, Hooper, Serpico (08)H 2356-309

z=0.165
r=610Mpc

1ES1101-232

z=0.186
r=680Mpc
19/07/06

Kaz Kohri (KEK)We need axion or ALPs
z=0.186
r=680Mpc

z=0.165
r=610Mpc

Kohri and Kodama, arXiv:2017.05189

An axion solution

Kohri and Kodama, arXiv:2017.05189

Photon-axion mixing through gammaray emission from 6 galacJc pulsars
Jhilik Majumdar, Francesca Calore, Dieter Horns, arXiv:1801.08813 [hep-ph]CTAshouldgive us
stronger
bound

CIBER : Femi+HESS+CIBER, Kohri and Kodama (2017)19/07/06

Kaz Kohri (KEK)WIMP
19/07/06

Kaz Kohri (KEK)Future TeV-gamma observaJon
Cherenkov Telescope Array (CTA)
One order of magnitude be/er sensiJvity at TeV← Uncertainties
at galactic center?
19/07/06

Kaz Kohri (KEK)Fermi bounds on annihilaJon into WW
M. L. Ahnen et al., MAGIC and Fermi-LAT Collaborations, arXiv:1601.06590[astro-ph.HE]

19/07/06

Kaz Kohri (KEK)Point source or Diﬀusive source?
• However, Fermi observed each dwarf
Spheroidal galaxy to be a point source inO(0.1°) x O(0.1°)• CTA can resolve the spaJal structure muchbe/er in future, e.g., in 0.03° x 0.03°• The limit should have been stronger bymeasuring it to be a point source
19/07/06

Kaz Kohri (KEK)Future limits on cross secJon by
Draco dwarf spheroidal with some density proﬁlesN.Hiroshima, M.Hayashida, and KK, arXiv:1905.12940 [astro-ph.HE]
NFW
BurkertCore (flat)

winoFermi+ MagicBBNCMB↑ canonical cross section
19/07/06
Kaz Kohri (KEK)Big
uncertainties due toa variety of density profiles

Should we sJck to canonical σ?
σ > σ canonical• Such a smaller relic density can bereplaced by non-thermally-produced DMe.g, by massive-decaying parJcles(moduli, graviJno, ...)σ < σ canonical• Such a larger relic density can be dilutedby entropy producJon e.g, by massivedecaying parJcles (moduli, graviJno, ...)
We may allow even a decaying DM with lifetime of > 1026 sec throughanother interactions or a parity violation (e.g., R-parity violation in SUSY)
19/07/06

Kaz Kohri (KEK)Summary• PBHs can be dark ma/er, which is related withinﬂaJon• We need axion-like parJcle with its mass of O(1) –O(102) neV and a coupling with photon to be gaγγ=O(10-11) GeV-1 to agree with both IR (CIBER) andgamma-ray (HESS &Fermi) observaJons• CTA can resolve the spaJal structure of dwarf
spheroidal to constrain WIMP dark ma/er for theﬁrst Jme. Then, we deﬁnitely need informaJon for
density proﬁles of dSphs
19/07/06

Kaz Kohri (KEK)