Primordial Black Holes in Cosmology Lectures 1 & 2 : What are - - PowerPoint PPT Presentation

Primordial Black Holes in Cosmology Lectures 1 & 2 : What are PBHs? Do they exist?

Massimo Ricotti (University of Maryland, USA)

Institute of Cosmos Sciences, University of Barcelona 23/10/2017

What are Primordial Black Holes?

• May have masses from the Planck mass ~10-5 g to ~108 Msun.

Masses and formation quite different from standard astrophysical BHs.

• Collapsed relativistic matter (radiation).
• Mass comparable to the Horizon mass at the epoch of their

formation

• Form in quasi-linear regime (δ ~ 20%-40%)
• Tiny collapsed fraction during the radiation era may produce all the

dark matter !

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Do PBHs exist?

PBHs with mass < 1015 g evaporate in t < tH (Hawking 1975) Abundance of PBHs with mass 1 g < M < 1015 g is β < 10−20 − 10−22 (e.g., Carr 2003) More massive PBHs are poorly constrained: They may constitute the bulk of the dark matter MACHO collaboration: 20% of Milky-Way halo is in compact objects with M ∼ 0.1 − 1 M (but 2000 result, non confirmed by later data)

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Why do we care?

• 1. Physics on scale otherwise unaccessible by
• bservations

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Why do we care?

• 1. Physics on scale otherwise unaccessible by
• bservations
• 2. The dark matter can be made of PBHs
• 3. Produce MACHOS, IMBH and ULXs ?
• 4. Seeds for supermassive Black Holes?

Physics Coll. Virginia Tech, 02-08-2008 – p.11/37

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Basic Analytical Calculations

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Redshift: z=dλ/λ Scale parameter: a(t)=1/(1+z) Trad=2.7 K /a(t) Early times: a(t)=(t/2.389x1019 s)1/2 Matter domination: a(t) ~t2/3

Institute of Cosmos Sciences, University of Barcelona

Institute of Cosmos Sciences, University of Barcelona

1.1 PBHs formation mechanism:

PBH Masses=Horizon mass at formation

• What is the Jeans Mass?
• What is the Particle Horizon Mass?
• Relationship between BH radius and its mean density.

(show derivations on the blackboard)

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M ∼ c3t G ∼ 1015

• t

10−23 s

• g:

1.2 Results of GR simulations and critical collapse

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M ¼ kMHðδ − δcÞγ

where:

γ ≃ 0.36 [50,52–54,159] δc ≃ 0.45 [52–54] k = 3.3 Ref. [42]

see Carr, Kühnel, Sandstad 2016 for references

2.1 PBHs Thermodynamics and Evaporation

• PBHs with masses < 1015 g evaporate in a time <

age of universe

• It is unknown whether evaporating PBHs

disintegrate completely or leave behind stable Planck-mass relics

• (show derivations on the blackboard)

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3.1 Collapsed fraction and relics

• A very small value of β (collapsed fraction) may produce all the dark

matter in PBHs

• (show derivations on the blackboard)

Ωpbh = β(1 + zf)/(1 + zeq)

fpbh = Ωpbh Ωdm ∼ Mpbh 1 M −1/2 β 10−9

• Institute of Cosmos Sciences, University of Barcelona

M ∼ c3t G ∼ 1015

• t

10−23 s

• g:

~ βt-1/2

Anisotropies measured by Planck (contrast increased by 106)

Ref: Tegmark et al 2002

Gravitational lensing and microlensing

4.1 Mass function: Press- Schechter formalism

• (show derivations of PS on the blackboard)

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Halo mass function: analytical formalism and simulations Ref: Klypin et al 2011

4.1 Mass function: Press- Schechter formalism

• (show derivations on the blackboard)

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∼ β(M, z) ∝ exp[−(δcr/2σ(M, z))2] (as fluctuations)

δcr ∼ w where P = wρ is the cosmic EOS Any linear perturbation ∼ − collap PBH with mass Mpbh = fHorMh where fHor < 1

4.2 Effects of critical collapse on PBHs mass function

β ¼ Z ∞

δc

dδ kðδ − δcÞγPðδÞ ≈ kσ2γerfc δc ffiffiffi 2 p σ

• ;

PðδÞ ≡ 1 ffiffiffiffiffiffiffiffiffiffi 2πσ2 p exp

• − δ2

2σ2

• ;

M ¼ kMHðδ − δcÞγ

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4.2 Effects of critical collapse

10 20 50 100 0.001 0.005 0.010 0.050 0.100 0.500 1 M M

11

f f

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Ref: Carr, Kühnel, Sandstad 2016

100 10 20 50 100 0.001 0.005 0.010 0.050 M M

11

f

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Ref: Carr, Kühnel, Sandstad 2016

4.3 Caveats

• Non-sphericity: for galaxy formation (triaxiality)

this leads to small modifications of the Press- Schechter formalism (Sheth-Tormen)

• Non-Gaussianity: peak formalism instead of Press-

Schechter is probably more precise

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5.1 Evolution of PBHs in an expanding universe

• 1. Primordial binaries (Nakamura et al., 1997)
• 2. Poisson halos (Afshordi, McDonald, Spergel 2003)
• 3. Clothing halos (Mack, Ostriker, Ricotti 2007), from

theory of secondary infall (Bertshinger 1985)

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Clothing Halos (secondary infall)

Mh(z) ¼ iMPBH z þ 1 1000

• 1

; rh ¼ 0:019 pc Mh 1 M

• 1=3

1 þ z 1000

• 1

;

file / r halo radius

α = -2.25

φi=3

• Mack, Ostriker, Ricotti 2007

6.1 Sub-critical perturbations and ultra-compact minihalos (UCMHs)

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time sequence of the growth of the mass profile of a spherical halo

Lensing from PBHs differs from point mass due to the clothing halo UCMHs can exist without central PBHs and should be much more common than PBHs.

Ricotti & Gould 2009

Microlensing signal from clothed PBHs and UCMHs

Clothed PBH UCMH, without PBH

Ricotti & Gould 2009

Ultra-compact minihalos (UCMHs)

• UCMHs are a new probe of the high-z universe (Ricotti & Gould 2009): they

differ from normal small mass halos produced by DM candidates and inflationary perturbations (low angular momentum of halos).

• Observable trough:
• 1. Microlensing
• 2. DM annihilation
• For gamma-ray limits see:
• Scott & Silvertsson 2009
• Laki & Beacom 2010 (conclude: either all DM is in PBHs or a small fraction
• therwise overproduce UCMHs)

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Some models for PBH formation

• 1. Softening of the EOS during phase transitions: QCD (1

M) or e+ − e− annihilation (105 M)(Kholopov & Polnarev

80; Jedamzik 97)

• 2. Collapse of rare density peaks: depend on the shape
• f inflaton potential (e.g., potential as in Kawasaki et al 06

produces 100 M PBHs)

• 3. Collapse of cosmic string loops (e.g., Polnarev & Zemboricz

88; Hawking 89; Brandenberger & Wichoski 98)

• 4. Bubble collisions (e.g., Crawford & Schramm 82; La &

Steinhardt 89)

• 5. Collapse of domain walls (Berezin et al 83; Ipser & Sikivie

84; Rubin et al. 00)

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Newtonian limit easy to understand: During radiation era cs → c/ √ 3 hence RJ → RSch ∼ Rh Any linear perturbation δ > δcr ∼ 0.1 − 0.7 collapses into PBH with mass Mpbh = fHorMh where fHor < 1 Collapsed fraction depends on the power spectrum of initial density fluctuations and the cosmic equation of state: δcr ∼ w where P = wρ is the cosmic EOS β(M, z) ∝ exp[−(δcr/2σ(M, z))2] (assuming Gaussian fluctuations)

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Summary (I):

Radiation is redshifted away, PBHs are not: Ωpbh = β(1 + zf)/(1 + zeq) fpbh = Ωpbh Ωdm ∼ Mpbh 1 M −1/2 β 10−9

• Example:

During QCD phase transition at t = 10−5 sec Mpbh ∼ Mh = 1 M if β = 10−9 → fpbh ∼ 1: all the dark matter is made

• f PBHs

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Summary (II):

• Next: astrophysical constraints on PBHs (part I).

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