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
A possible mass distribution of primordial black holes implied by LIGO-Virgo
By Heling Deng
