Primordial black holes from vacuum bubbles

 

邓鹤凌

Arizona State University

Outline

  • Primordial black holes
  • Fitting LIGO black holes
  • LIGO BHs from bubbles?
  • PBHs from bubbles

Outline

  • Primordial black holes
  • Fitting LIGO black holes
  • LIGO BHs from bubbles?
  • PBHs from bubbles
M_\text{Pl} \newline \sim10^{-5}\ \rm g
M_\text{evp} \newline \sim10^{15}\ \rm g
M_\odot \newline \sim10^{33}\ \rm g
M_\text{PBH}

LIGO BH

Supermassive black holes

\mathcal O (10\text{-} 100) \ M_\odot

SMBH

...

...

Primordial black holes (PBHs)

\mathcal{O}(10^6 \text{-} 10^{10})M_\odot

Astrophysical BHs

M_\text{Pl} \newline \sim10^{-5}\ \rm g
M_\text{evp} \newline \sim10^{15}\ \rm g
M_\odot \newline \sim10^{33}\ \rm g
M_\text{PBH}

LIGO BH

Supermassive black holes

LIGO black holes

\mathcal O (10\text{-} 100) \ M_\odot

SMBH

...

...

Primordial black holes (PBHs)

\mathcal{O}(10^6 \text{-} 10^{10})M_\odot

Astrophysical BHs

LIGO BHs

M_\text{Pl} \newline \sim10^{-5}\ \rm g
M_\text{evp} \newline \sim10^{15}\ \rm g
M_\odot \newline \sim10^{33}\ \rm g
M_\text{PBH}

LIGO BH

Supermassive black holes

LIGO black holes

Dark matter

\mathcal O (10\text{-} 100) \ M_\odot

SMBH

...

...

Primordial black holes (PBHs)

\mathcal{O}(10^6 \text{-} 10^{10})M_\odot

Astrophysical BHs

Observational constraints of PBHs as DM

Outline

  • Primordial black holes
  • Fitting LIGO black holes
  • LIGO BHs from bubbles?
  • PBHs from bubbles
\rho_i
\rho_i
\rho_b

Inflation \(\rho_i \to\) radiation fluid \(\rho_i\)

\rho_b

Bubble interior \(\rho_b<\rho_i\)

\rho_i
H_b^{-1}

Subcritical

Supercritical

Wormhole \(\to\) BH

H_b^{-1}

Used numerical simulations of full GR to find relation between BH mass and bubble size \(m(R)\)

subcritical

m\propto R^3

supercritical

m\propto R^2

PBH mass function (fraction of DM in PBHs with mass \(\sim m\))

f(m)\equiv \frac{\rho_t(m)}{\rho_\text{CDM}}

PBH mass density 

\rho_t(m)=mn_t(m)

Number density of bubbles (BHs) 

n_t(R)\to n_t(m)

const over time

m^{0},\ \ \ m< m_*
m^{-1/2},\ \ \ m> m_*
f(m)\propto
\{

Broken power law

BH mass distribution from bubbles

\log(m)
\log(f)
m^{0}
m^{-1/2}
m_*

subcritical

supercritical

Outline

  • Primordial black holes
  • Fitting LIGO black holes
  • LIGO BHs from bubbles?
  • PBHs from bubbles

Mass distribution of LIGO BHs

m^{\alpha_1},\ \ \ m< m_*
m^{\alpha_2},\ \ \ m> m_*
f(m)\propto
\{

A simple mass function

\log(m)
\log(f)
m^{\alpha_1}
m^{\alpha_2}
m_*
f_{PBH}
f_{PBH}

PBH mass function

Merger rate

Detection probability

Probability of each event \(p_i(m_1,m_2,z)\)

+

Likelihood of all LIGO events

\mathcal{L}\propto \prod_{i=1}^{N_o} p_i

Mergers reaching earth today

\(f(m)\) characterized by \(f_{PBH}, \alpha_1, \alpha_2, m_*\) 

f_{PBH}\approx 10^{-3}

Maximizing \(\mathcal{L}\) in a 4-parameter space

\alpha_2 = -4
\alpha_1 = 1.2
m_*=35M_\odot
\log(m)
\log(f)
m^{1.2}
m^{-4}
35M_\odot
10^{-3}

Is there a mechanism that can generate such a mass function?

Outline

  • Primordial black holes
  • Fitting LIGO black holes
  • LIGO BHs from bubbles?
  • PBHs from bubbles
\log(m)
\log(f)
m^{0}
m^{-1/2}
m_*
\log(f)
m^{1.2}
m^{-4}
35M_\odot
\log(m)
\log(m)
\log(f)
m^{0}
m^{-1/2}
m_*

Fluid not get into bubble

Fluid gets into bubble

f\propto m^{1.2}

Observational constraints of PBHs as DM

m^{1.2}
m^{-4}

Conclusions

m^{1.2}
m^{-4}

PBH mass function

Merger rate

Detection probability

Expected number of observable events

Probability of each detected event

p_i
p_{Poisson}\propto N_e^{N_o}e^{-N_e}
\mathcal{L}\propto p_{Poisson}\prod_{i=1}^{N_o} p_i
N_e

+

+

Likelihood of all LIGO events

\rho_b

Empty layer

Intrinsic PBH merger rate

\text{d}R(m_1,m_2,z)\propto f(m_1) f(m_2)

(Number of event  \((m_1,m_2,z)\) per unit volume per unit time)

Signals reaching earth 

\text{d}N(m_1,m_2,z)\propto \text{d}R(m_1,m_2,z)

(Number of event  \((m_1,m_2,z)\) reaching the earth per unit time)

Detection probability \(p_{det}(m_1,m_2,z)\)

\text{d}N_e(m_1,m_2,z)=p_{det}(m_1,m_2,z)\text{d}N\times T_o
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