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

M_\text{Pl} \newline \sim10^{-5}\ \rm g

M_\text{Pl} \newline \sim10^{-5}\ \rm g

M_\text{evp} \newline \sim10^{15}\ \rm g

M_\text{evp} \newline \sim10^{15}\ \rm g

M_\odot \newline \sim10^{33}\ \rm g

M_\odot \newline \sim10^{33}\ \rm g

M_\text{PBH}

M_\text{PBH}

LIGO BH

Supermassive black holes

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

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

SMBH

...

Primordial black holes (PBHs)

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

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

Astrophysical BHs

M_\text{Pl} \newline \sim10^{-5}\ \rm g

M_\text{Pl} \newline \sim10^{-5}\ \rm g

M_\text{evp} \newline \sim10^{15}\ \rm g

M_\text{evp} \newline \sim10^{15}\ \rm g

M_\odot \newline \sim10^{33}\ \rm g

M_\odot \newline \sim10^{33}\ \rm g

M_\text{PBH}

M_\text{PBH}

LIGO BH

Supermassive black holes

LIGO black holes

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

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

SMBH

...

Primordial black holes (PBHs)

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

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

Astrophysical BHs

M_\text{Pl} \newline \sim10^{-5}\ \rm g

M_\text{Pl} \newline \sim10^{-5}\ \rm g

M_\text{evp} \newline \sim10^{15}\ \rm g

M_\text{evp} \newline \sim10^{15}\ \rm g

M_\odot \newline \sim10^{33}\ \rm g

M_\odot \newline \sim10^{33}\ \rm g

M_\text{PBH}

M_\text{PBH}

LIGO BH

Supermassive black holes

LIGO black holes

Dark matter

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

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

SMBH

...

Primordial black holes (PBHs)

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

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

Astrophysical BHs

Outline

Primordial black holes

Fitting LIGO black holes

LIGO BHs from bubbles?

PBHs from bubbles

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

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

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

PBH mass density

\rho_t(m)=mn_t(m)

\rho_t(m)=mn_t(m)

Number density of bubbles (BHs)

n_t(R)\to n_t(m)

n_t(R)\to n_t(m)

const over time

m^{0},\ \ \ m< m_*

m^{0},\ \ \ m< m_*

m^{-1/2},\ \ \ m> m_*

m^{-1/2},\ \ \ m> m_*

f(m)\propto

f(m)\propto

\{

\{

Broken power law

BH mass distribution from bubbles

\log(m)

\log(m)

\log(f)

\log(f)

m^{0}

m^{0}

m^{-1/2}

m^{-1/2}

m_*

m_*

subcritical

supercritical

m^{\alpha_1},\ \ \ m< m_*

m^{\alpha_1},\ \ \ m< m_*

m^{\alpha_2},\ \ \ m> m_*

m^{\alpha_2},\ \ \ m> m_*

f(m)\propto

f(m)\propto

\{

\{

A simple mass function

\log(m)

\log(m)

\log(f)

\log(f)

m^{\alpha_1}

m^{\alpha_1}

m^{\alpha_2}

m^{\alpha_2}

m_*

m_*

f_{PBH}

f_{PBH}

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

\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}

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

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

\alpha_2 = -4

\alpha_2 = -4

\alpha_1 = 1.2

\alpha_1 = 1.2

m_*=35M_\odot

m_*=35M_\odot

\log(m)

\log(m)

\log(f)

\log(f)

m^{1.2}

m^{1.2}

m^{-4}

m^{-4}

35M_\odot

35M_\odot

10^{-3}

10^{-3}

PBH mass function

Merger rate

Detection probability

Expected number of observable events

Probability of each detected event

p_i

p_i

p_{Poisson}\propto N_e^{N_o}e^{-N_e}

p_{Poisson}\propto N_e^{N_o}e^{-N_e}

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

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

N_e

N_e

+

Likelihood of all LIGO events

Intrinsic PBH merger rate

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

\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)

\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

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