primordial black holes as dark matter

Primordial black holes as dark matter

Francesc Ferrer, Washington University in St. LouisB ferrer@wustl.edu

Next frontiers in the search for DM.August 29, 2019. GGI, Firenze.

Unexpected/surprising?

Most astrophysical models did not predict BHs with M & 20M.But, large BHs masses can be generated from ≥ 40Mmetal-free stars undergoing direct collapse.

Mapelli, 1809.09130

How are binaries formed?

Could work in young star clusters or in nuclear star clusterssurrounding SMBHs. Unlike isolated binaries, spins aremisaligned/isotropic. But, three body encounters (necessary toharden the binary) can eject the system.

The astrophysical picture is largely incomplete:I The formation channels of merging BH binaries are still

uncertain. Major simplifications are adopted in dynamicalsimulations, and the statistics about BHs in young starclusters is small.

I A global picture of the BH merger history as a function ofredshift is missing.

The LIGO/Virgo horizon is z ∼ 0.1− 0.2, but third-generationground-based GW detectors (e.g. Einstein Telescope) will beable to observe binary mergers up to z ∼ 10.

Another (more massive) puzzle

SMBHs reaching & 1010M are present in the centers of mostmassive galaxies, even at large redshifts.

Outline

Overview and motivation

PBHs as dark matter

Could LIGO detect axions?PBHs from QCD axion dynamics

FF, E. Massó, G. Panico, O. Pujolàs & F. Rompineve, 1807.01707

GWs from a phase transition at the PQ scaleB. Dev, FF, Y. Zhang & Y. Zhang, 1905.00891

Conclusions

Could they be primordial?

Rare Hubble scale perturbations can collapse into BHs:

β ≈ erfc(

δc√2σ

)B.J. Carr & S.W. Hawking, MNRAS 1974; S. Bird et al, 1603.00464; S. Clesse & J.

García-Bellido, 1603.05234; M. Sasaki et al. 1603.08338

HSC

EROS

OGLE

Kepler

Femtolensing

NS

WD

Accretion (CMB)

Accretion (X-ray-II)

Accretion (X-ray)

Accretion (Radio)

DF

UFDs

Eri-II

Millilensing

WB

Caustic

Accretion disk (CMB)

Accretion disk (CMB-II)

Sasaki et al. CQG 35 (2018) 063001

10-18 10-16 10-14 10-12 10-10 10-8 10-6 10-4 10-2 100 102

PBH Mass [M¯ ]

10-3

10-2

10-1

100

PHB

frac

tion

ΩPBH/Ω

DM

femto-lensing

aS = 108 cm 20 GRBs

(projection)

aS = 109 cm100 GRBs

EGγ

WD

Subaru HSC

Kepler

MACHO/EROS/OGLE

CM

B

ultra

-fain

t dw

arfs

1016 1020 1024 1028 1032 1036PBH Mass [g]

Katz et al. 1807.11495

Binary formation

PBHs are randomly distributed, but some pairs are closeenough to decouple from Hubble flow.

Nakamura, Sasaki, Tanaka & Thorne, 1997

Most of the BH pairs that merge today form in the earlyuniverse, deep in the radiation era. Pairs form due to thechance proximity of PHB pairs and merge on a time-scale:

tmerge =3c5

170G3N

a4(1− e2)7/2

M3pbh

Several processes (torques due to other BHs, encounters withother BHs, DM spikes around PBHs, . . . ) influence the mergerrate that is measured by LIGO.Clustering might substantially change the picture.

Ali-Haïmoud, Kovetz & Kamionkowski, 1709.06576

Kavanagh, Gaggero & Bertone, 1805.09034

Pair formation in present day halos

Binary BHs can also form in present day halos from GWemission. These binaries are very tight and highly eccentric sothat they coalesce within a very short timescale. In principlethis population gives a subdominant contribution to the LIGOobserved events, but:I PBHs could be clumped around SMBH spikesI Merger rates could be boostedI The cross-section is strongly velocity dependent,

σ ∝ v−18/7rel

FF & A. Medeiros, 1810.xxxx

PBHs are not exactly CDM

101 102

r [pc]

1.0

0.8

0.6

0.4

0.2

0.0

δρs/ρ

s

fDM = 0. 01 mBH = 10 M¯

fDM = 0. 01 mBH = 30 M¯

fDM = 0. 01 mBH = 50 M¯

fDM = 0. 1 mBH = 30 M¯

fDM = 0. 001 mBH = 30 M¯

T.D. Brandt, ApJ 2016; Koushiappas & Loeb, 1704.01668

0 2 4 6

log10 (r/Gm)

4

8

12

16

20

log10ρ[GeV

/cm

3]

FF, A. Medeiros & C.M. Will, 1707.06302

Outline

Overview and motivation

PBHs as dark matter

Could LIGO detect axions?PBHs from QCD axion dynamics

FF, E. Massó, G. Panico, O. Pujolàs & F. Rompineve, 1807.01707

GWs from a phase transition at the PQ scaleB. Dev, FF, Y. Zhang & Y. Zhang, 1905.00891

Conclusions

Alternative mechanisms?

Phase transitions in the early universe provide a potentialavenue: Several violent phenomena naturally occur that canassist in generating large overdensities that gravitationallycollapse into BHs: bubble collisions, topological defects, . . .

I We will consider axionic string-wall networks.

F.F., E. Massó, G. Panico, O. Pujolàs & F. Rompineve, 1807.01707, PRL 2019

Alternative mechanisms?

Phase transitions in the early universe provide a potentialavenue: Several violent phenomena naturally occur that canassist in generating large overdensities that gravitationallycollapse into BHs: bubble collisions, topological defects, . . .

I We will consider axionic string-wall networks.

F.F., E. Massó, G. Panico, O. Pujolàs & F. Rompineve, 1807.01707, PRL 2019

Cosmological evolution

Important distinction whether PQ symmetry is broken before orafter inflation:I Pre-inflationary PQ breaking→ the axion has a single

uniform initial value ai within the observable universe.I In the post-inflationary case the axion takes different

values in different regions.

In the latter case when the axion gets its mass, around the QCDphase transition, a hybrid string-domain wall network is formed.

Eventually, the network has to decay. Otherwise, the energy density would be quickly

dominated by domain walls.

Cosmological evolution

Important distinction whether PQ symmetry is broken before orafter inflation:I Pre-inflationary PQ breaking→ the axion has a single

uniform initial value ai within the observable universe.I In the post-inflationary case the axion takes different

values in different regions.

In the latter case when the axion gets its mass, around the QCDphase transition, a hybrid string-domain wall network is formed.

Eventually, the network has to decay. Otherwise, the energy density would be quickly

dominated by domain walls.

Cosmological evolution

Important distinction whether PQ symmetry is broken before orafter inflation:I Pre-inflationary PQ breaking→ the axion has a single

uniform initial value ai within the observable universe.I In the post-inflationary case the axion takes different

values in different regions.

In the latter case when the axion gets its mass, around the QCDphase transition, a hybrid string-domain wall network is formed.

Eventually, the network has to decay. Otherwise, the energy density would be quickly

dominated by domain walls.

The collapse of closed domain walls, which belong to the hybridstring-wall network can lead to the formation of PBHs.

T. Vachaspati, 1706.03868

It is crucial that the annihilation of the network proceeds slowly.

I This mechanism does not rely on (nor complicate) thephysics of inflation.

I GW astronomy can potentially probe the physics of axions.

The collapse of closed domain walls, which belong to the hybridstring-wall network can lead to the formation of PBHs.

T. Vachaspati, 1706.03868

It is crucial that the annihilation of the network proceeds slowly.

I This mechanism does not rely on (nor complicate) thephysics of inflation.

I GW astronomy can potentially probe the physics of axions.

NDW = 1Only one domain wall is attached to each string. Suchtopological configurations quickly annihilate leaving behind apopulation of barely relativistic axions.

T. Hiramatsu, et al., PRD 85, 105020 (2012)

NDW > 1

There are NDW domain walls attached to every string, each onepulling in a different direction. The network can actually bestable, and dominate the universe.

T. Hiramatsu, et al., JCAP 1301 (2013) 001

Lift the degeneracy of axionic vacua by introducing a bias term(dark QCD?). The energy difference between the differentminima acts as a pressure force on the corresponding domainwalls.

ΔV

-π πa/η

V(a/η)

I The domain walls are created at T1 ∼ TQCD.I A closed DW of size R∗ may rapidly shrink (if NDW = 1)

because of its own tension, onceR∗ ∼ H−1 ≈ geff(T∗)−1/2Mp/T 2

∗ .

I If NDW > 1, the annihilation occurs at T2 > T∗ set by∆Vσ

.There can be a significant separation between formationT1 and T2.

The addition of the bias term misaligns the axion:

θmin ≈A4

BNDW sin δ

m2NDWF 2 +A4B cos δ

. 10−10.

The phase is related to T2, i.e. the bias,

A4B ∼ T 2

2 σ/MP .

At constant δ, this corresponds to a line in the log F − log T2plane. We would like δ ∼ 1.

PBHs from string-wall defects

A closed DW of size R∗ will rapidly shrink because of its owntension, once R∗ ∼ H−1 ≈ geff(T∗)−1/2Mp/T 2

∗ .Its mass has contributions from the wall tension and from anydifference in energy density between the two regions separatedby the DW:

M∗ = 4πσR2∗ +

43π∆ρR3

∗ ≈ 4πσH−2∗ +

43π∆ρH−3

∗

⇒ Heavier black holes form from DW which collapse later incosmological history.

The Schwarzschild radius of the collapsing defect isRS,∗ = 2GNM∗, and the figure of merit for PBH formation is:

p ≡ RS,∗/R∗ ∼σH−1

∗M2

p+

∆ρH−2∗

3M2p

⇒ As the temperature decreases it becomes more likely toform a black hole.

Two regimes:I When the tension dominates, M∗ ∼ T−4

∗ an p ∼ T−2.I When the energy density dominates, M∗ ∼ T−6

∗ anp ∼ T−4.

(Deviations from spherical symmetry, radiation friction during collapse can partly

modify this picture.)

SN 1987A

Chang et al. ' 18 PDG ' 18

p = 10-8

p = 10-6

p = 10-4

δ = 0.1

δ = 1

10-8 M⊙

10-4 M⊙

1M⊙

Ωa >ΩCDM

107 108 109 1010 101110-4

10-3

10-2

10-1

100

101

F[GeV]

T2[GeV

]

Axion-QCD vs ALPs

I For the QCD axion we find an interesting region around

fa ∼ 109 GeV.

PBHs of mass 10−4M can form with p ∼ 10−6.I For generic ALPs we can reach larger probabilities

p ∼ 10−3 in scenarios where

T2 ∼ keV.

Interestingly much larger BHs, . 108M could be formed.

B. Carr & J. Silk, 1801.00672

Late collapses

Most of the axionic string-wall network disappears at T2, whichis when the vacuum contribution starts dominating, and both pand M∗ increase steeply.But, 1− 10% of the walls survive until ∼ 0.1T2, when:I p ∼ 1I M∗ ∼ 106M

⇒ A fraction f ∼ 10−6 of the DM end up forming SMBHs!

B. Carr & J. Silk, 1801.00672

Late collapses

SN 1987 A

Ωa>ΩCDM

PDG ' 18

T2 ≃ 7MeV

p = 0.01

p = 0.1

p = 1

104 M⊙

106 M⊙

108 M⊙

2×108 4×108 6×108 8×10810-4

10-3

10-2

F[GeV]

T*[GeV

]

We have not said much about the bias term . . .Planck suppressed operators are unlikely.A dark gauge sector with ΛB ∼ MeV is an interesting possibility.

A. Caputo & M. Reig, 1905.13116

Or it might not be needed after all..

Stojkovic, Freese & Starkman, hep-ph/0505026

Outline

Overview and motivation

PBHs as dark matter

Could LIGO detect axions?PBHs from QCD axion dynamics

FF, E. Massó, G. Panico, O. Pujolàs & F. Rompineve, 1807.01707

GWs from a phase transition at the PQ scaleB. Dev, FF, Y. Zhang & Y. Zhang, 1905.00891

Conclusions

Model

V0 = −µ2|H|2 + λ|H|4 + κ|Φ|2|H|2 + λa

(|Φ|2 − 1

2f 2a

)2

.

I fa, κ and λa are free parameters.I To obtain the observed Higgs mass, µ2 ≈ κf 2

a /2.

Phase transition

Fixing fa, scan the region (κ, λa) to find where a FOPT can takeplace.

Gravitational wave production

h2ΩGW ' h2Ωφ + h2ΩSW + h2ΩMHD .

C. Caprini et al. 1512.06239

Input quantities to be calculated from our model parameters:I Ratio α of vacuum energy density released in the PT to

radiation.I Rate of the PT, β/H∗.I Latent heat fractions for each of the three processes.I Bubble wall velocity.

In the phenomenologically relevant cases, the bubble wallcollision contribution dominates.

Detection prospects

Detection prospects

Detection prospects

Detection prospects

Comparison with other ALP constraints

10-8 10-5 0.01 10 104 107

10-12

10-10

10-8

10-6

ma [eV]

gaγ

γ[GeV

-1]

LSW

helioscopes

Sun

HB stars

γ-rays

haloscopes

DFSZ

KSVZ

telescopes

xion

X-rays

EBL

CMB

BBN

SN

beamdum

p

LISA

BBO

aLIGO+

Comparison with other ALP constraints

10-4 0.01 1 100 104 106 108

10-14

10-12

10-10

10-8

10-6

ma [eV]

gaee

DSFZ

KSVZ

Edelweiss

Red Giants

E137

MINOS/MINERvA

LISA

BBO

aLIGO+

Comparison with other ALP constraints

10-6 0.001 1 1000 106 109

10-9

10-7

10-5

10-3

ma [eV]

gaNN

DFSZ KSVZ

SN1987A

BBO

LISA

aLIGO+

Conclusions

I LIGO has confirmed the existence of BH binaries that areable to merge within a Hubble time.

I The observed BHs mass & 20M is somewhat surprisingfrom the astrophysics point of view. A fraction, but not all,of the DM could be made of black holes.

I Axionic topological defects with NDW > 1 lead to a newNetwork Annihilation epoch that can potentially generatePBHs of up to 106M, and can be tested by LISA.

I A FOPT at the PQ scale could take place in some ALPmodels. The GW signal strength could be as large ash2ΩGW ∼ 10−8, within reach of aLIGO+.