primordial black holes as dark matter
TRANSCRIPT
Primordial black holes as dark matter
Francesc Ferrer, Washington University in St. LouisB [email protected]
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+.