Primordial black holes as dark matter Francesc Ferrer, Washington - PowerPoint PPT Presentation

Primordial black holes as dark matter Francesc Ferrer, Washington University in St. Louis � 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 � 20 M ⊙ . But, large BHs masses can be generated from ≥ 40 M ⊙ metal-free stars undergoing direct collapse. Mapelli, 1809.09130

How are binaries formed? Could work in young star clusters or in nuclear star clusters surrounding SMBHs. Unlike isolated binaries, spins are misaligned/isotropic. But, three body encounters (necessary to harden the binary) can eject the system.

The astrophysical picture is largely incomplete: ◮ The formation channels of merging BH binaries are still uncertain. Major simplifications are adopted in dynamical simulations, and the statistics about BHs in young star clusters is small. ◮ A global picture of the BH merger history as a function of redshift is missing. The LIGO/Virgo horizon is z ∼ 0 . 1 − 0 . 2, but third-generation ground-based GW detectors (e.g. Einstein Telescope) will be able to observe binary mergers up to z ∼ 10.

Another (more massive) puzzle SMBHs reaching � 10 10 M ⊙ are present in the centers of most massive 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 scale B. Dev, FF, Y. Zhang & Y. Zhang, 1905.00891 Conclusions

Could they be primordial? Rare Hubble scale perturbations can collapse into BHs: � δ c � √ β ≈ erfc 2 σ 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

Accretion WD (X-ray) WB OGLE Kepler NS Eri-II Caustic EROS Accretion Femtolensing (Radio) UFDs HSC Millilensing Accretion (X-ray-II) DF Accretion disk (CMB) Accretion (CMB) Accretion disk (CMB-II) Sasaki et al. CQG 35 (2018) 063001

PBH Mass [ g ] 10 16 10 20 10 24 10 28 10 32 10 36 10 0 u l t femto- WD r lensing a - f a PHB fraction Ω PBH / Ω DM i a S = 10 8 cm n t a S = 10 9 cm Kepler 20 GRBs d 100 GRBs 10 -1 w a (projection) r f s γ G CMB E MACHO/ EROS/OGLE 10 -2 Subaru HSC 10 -3 10 -18 10 -16 10 -14 10 -12 10 -10 10 -8 10 -6 10 -4 10 -2 10 0 10 2 PBH Mass [ M ⊙ ] Katz et al. 1807.11495

Binary formation PBHs are randomly distributed, but some pairs are close enough to decouple from Hubble flow. Nakamura, Sasaki, Tanaka & Thorne, 1997

Most of the BH pairs that merge today form in the early universe, deep in the radiation era. Pairs form due to the chance proximity of PHB pairs and merge on a time-scale: 3 c 5 a 4 ( 1 − e 2 ) 7 / 2 t merge = 170 G 3 M 3 N pbh Several processes (torques due to other BHs, encounters with other BHs, DM spikes around PBHs, . . . ) influence the merger rate 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 GW emission. These binaries are very tight and highly eccentric so that they coalesce within a very short timescale. In principle this population gives a subdominant contribution to the LIGO observed events, but: ◮ PBHs could be clumped around SMBH spikes ◮ Merger rates could be boosted ◮ The cross-section is strongly velocity dependent, σ ∝ v − 18 / 7 rel FF & A. Medeiros, 1810.xxxx

PBHs are not exactly CDM 0.0 0.2 0.4 δρ s /ρ s 0.6 f DM = 0 . 01 m BH = 10 M ⊙ f DM = 0 . 01 m BH = 30 M ⊙ 0.8 f DM = 0 . 01 m BH = 50 M ⊙ f DM = 0 . 1 m BH = 30 M ⊙ f DM = 0 . 001 m BH = 30 M ⊙ 1.0 10 1 10 2 r [pc] T.D. Brandt, ApJ 2016; Koushiappas & Loeb, 1704.01668

✷✵ log 10 ρ ❬●❡❱✴❝♠ 3 ❪ ✶✻ ✶✷ ✽ ✹ ✵ ✷ ✹ ✻ log 10 ( r/Gm ) 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 scale B. Dev, FF, Y. Zhang & Y. Zhang, 1905.00891 Conclusions

Alternative mechanisms? Phase transitions in the early universe provide a potential avenue: Several violent phenomena naturally occur that can assist in generating large overdensities that gravitationally collapse into BHs: bubble collisions, topological defects, . . .

Alternative mechanisms? Phase transitions in the early universe provide a potential avenue: Several violent phenomena naturally occur that can assist in generating large overdensities that gravitationally collapse into BHs: bubble collisions, topological defects, . . . ◮ 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 or after inflation: ◮ Pre-inflationary PQ breaking → the axion has a single uniform initial value a i within the observable universe. ◮ In the post-inflationary case the axion takes different values in different regions.

Cosmological evolution Important distinction whether PQ symmetry is broken before or after inflation: ◮ Pre-inflationary PQ breaking → the axion has a single uniform initial value a i within the observable universe. ◮ 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 QCD phase transition, a hybrid string-domain wall network is formed.

Cosmological evolution Important distinction whether PQ symmetry is broken before or after inflation: ◮ Pre-inflationary PQ breaking → the axion has a single uniform initial value a i within the observable universe. ◮ 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 QCD phase 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 hybrid string-wall network can lead to the formation of PBHs. T. Vachaspati, 1706.03868 It is crucial that the annihilation of the network proceeds slowly.

The collapse of closed domain walls, which belong to the hybrid string-wall network can lead to the formation of PBHs. T. Vachaspati, 1706.03868 It is crucial that the annihilation of the network proceeds slowly. ◮ This mechanism does not rely on (nor complicate) the physics of inflation. ◮ GW astronomy can potentially probe the physics of axions.

N DW = 1 Only one domain wall is attached to each string. Such topological configurations quickly annihilate leaving behind a population of barely relativistic axions. T. Hiramatsu, et al. , PRD 85, 105020 (2012)

N DW > 1 There are N DW domain walls attached to every string, each one pulling in a different direction. The network can actually be stable, 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 different minima acts as a pressure force on the corresponding domain walls. V ( a / η ) Δ V π a / η - π

◮ The domain walls are created at T 1 ∼ T QCD . ◮ A closed DW of size R ∗ may rapidly shrink (if N DW = 1) because of its own tension, once R ∗ ∼ H − 1 ≈ g eff ( T ∗ ) − 1 / 2 M p / T 2 ∗ . ◮ If N DW > 1, the annihilation occurs at T 2 > T ∗ set by ∆ V σ . There can be a significant separation between formation T 1 and T 2 .

The addition of the bias term misaligns the axion: A 4 B N DW sin δ B cos δ � 10 − 10 . θ min ≈ m 2 N DW F 2 + A 4 The phase is related to T 2 , i.e. the bias, A 4 B ∼ T 2 2 σ/ M P . At constant δ , this corresponds to a line in the log F − log T 2 plane. We would like δ ∼ 1.

PBHs from string-wall defects A closed DW of size R ∗ will rapidly shrink because of its own tension, once R ∗ ∼ H − 1 ≈ g eff ( T ∗ ) − 1 / 2 M p / T 2 ∗ . Its mass has contributions from the wall tension and from any difference in energy density between the two regions separated by the DW: ∗ + 4 + 4 M ∗ = 4 πσ R 2 3 π ∆ ρ R 3 ∗ ≈ 4 πσ H − 2 3 π ∆ ρ H − 3 ∗ ∗ ⇒ Heavier black holes form from DW which collapse later in cosmological history.

The Schwarzschild radius of the collapsing defect is R S , ∗ = 2 G N M ∗ , and the figure of merit for PBH formation is: p ≡ R S , ∗ / R ∗ ∼ σ H − 1 + ∆ ρ H − 2 ∗ ∗ M 2 3 M 2 p p ⇒ As the temperature decreases it becomes more likely to form a black hole.

Two regimes: ◮ When the tension dominates, M ∗ ∼ T − 4 an p ∼ T − 2 . ∗ ◮ When the energy density dominates, M ∗ ∼ T − 6 an ∗ p ∼ T − 4 . (Deviations from spherical symmetry, radiation friction during collapse can partly modify this picture.)