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
MPl∼10−5 g
M_\text{Pl} \newline
\sim10^{-5}\ \rm g
Mevp∼1015 g
M_\text{evp} \newline \sim10^{15}\ \rm g
M⊙∼1033 g
M_\odot \newline \sim10^{33}\ \rm g
MPBH
M_\text{PBH}
LIGO BH
Supermassive black holes
O(10-100) M⊙
\mathcal O (10\text{-} 100) \ M_\odot
SMBH
...
...
Primordial black holes (PBHs)
O(106-1010)M⊙
\mathcal{O}(10^6 \text{-} 10^{10})M_\odot
Astrophysical BHs
MPl∼10−5 g
M_\text{Pl} \newline
\sim10^{-5}\ \rm g
Mevp∼1015 g
M_\text{evp} \newline \sim10^{15}\ \rm g
M⊙∼1033 g
M_\odot \newline \sim10^{33}\ \rm g
MPBH
M_\text{PBH}
LIGO BH
Supermassive black holes
LIGO black holes
O(10-100) M⊙
\mathcal O (10\text{-} 100) \ M_\odot
SMBH
...
...
Primordial black holes (PBHs)
O(106-1010)M⊙
\mathcal{O}(10^6 \text{-} 10^{10})M_\odot
Astrophysical BHs
LIGO BHs
MPl∼10−5 g
M_\text{Pl} \newline
\sim10^{-5}\ \rm g
Mevp∼1015 g
M_\text{evp} \newline \sim10^{15}\ \rm g
M⊙∼1033 g
M_\odot \newline \sim10^{33}\ \rm g
MPBH
M_\text{PBH}
LIGO BH
Supermassive black holes
LIGO black holes
Dark matter
O(10-100) M⊙
\mathcal O (10\text{-} 100) \ M_\odot
SMBH
...
...
Primordial black holes (PBHs)
O(106-1010)M⊙
\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
ρi
\rho_i
ρi
\rho_i
ρb
\rho_b
Inflation ρi→ radiation fluid ρi
ρb
\rho_b
Bubble interior ρb<ρi
ρi
\rho_i
Hb−1
H_b^{-1}
Subcritical
Supercritical
Wormhole → BH
Hb−1
H_b^{-1}
Used numerical simulations of full GR to find relation between BH mass and bubble size m(R)
subcritical
m∝R3
m\propto R^3
supercritical
m∝R2
m\propto R^2
PBH mass function (fraction of DM in PBHs with mass ∼m)
f(m)≡ρCDMρt(m)
f(m)\equiv \frac{\rho_t(m)}{\rho_\text{CDM}}
PBH mass density
ρt(m)=mnt(m)
\rho_t(m)=mn_t(m)
Number density of bubbles (BHs)
nt(R)→nt(m)
n_t(R)\to n_t(m)
const over time
m0, m<m∗
m^{0},\ \ \ m< m_*
m−1/2, m>m∗
m^{-1/2},\ \ \ m> m_*
f(m)∝
f(m)\propto
{
\{
Broken power law
BH mass distribution from bubbles
log(m)
\log(m)
log(f)
\log(f)
m0
m^{0}
m−1/2
m^{-1/2}
m∗
m_*
subcritical
supercritical
Outline
- Primordial black holes
- Fitting LIGO black holes
- LIGO BHs from bubbles?
- PBHs from bubbles
Mass distribution of LIGO BHs
mα1, m<m∗
m^{\alpha_1},\ \ \ m< m_*
mα2, m>m∗
m^{\alpha_2},\ \ \ m> m_*
f(m)∝
f(m)\propto
{
\{
A simple mass function
log(m)
\log(m)
log(f)
\log(f)
mα1
m^{\alpha_1}
mα2
m^{\alpha_2}
m∗
m_*
fPBH
f_{PBH}
fPBH
f_{PBH}
PBH mass function
Merger rate
Detection probability
Probability of each event pi(m1,m2,z)
+
Likelihood of all LIGO events
L∝∏i=1Nopi
\mathcal{L}\propto \prod_{i=1}^{N_o} p_i
Mergers reaching earth today
f(m) characterized by fPBH,α1,α2,m∗
fPBH≈10−3
f_{PBH}\approx 10^{-3}
Maximizing L in a 4-parameter space
α2=−4
\alpha_2 = -4
α1=1.2
\alpha_1 = 1.2
m∗=35M⊙
m_*=35M_\odot
log(m)
\log(m)
log(f)
\log(f)
m1.2
m^{1.2}
m−4
m^{-4}
35M⊙
35M_\odot
10−3
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(m)
log(f)
\log(f)
m0
m^{0}
m−1/2
m^{-1/2}
m∗
m_*
log(f)
\log(f)
m1.2
m^{1.2}
m−4
m^{-4}
35M⊙
35M_\odot
log(m)
\log(m)
log(m)
\log(m)
log(f)
\log(f)
m0
m^{0}
m−1/2
m^{-1/2}
m∗
m_*
Fluid not get into bubble
Fluid gets into bubble
f∝m1.2
f\propto m^{1.2}
Observational constraints of PBHs as DM
m1.2
m^{1.2}
m−4
m^{-4}
Conclusions
m1.2
m^{1.2}
m−4
m^{-4}
PBH mass function
Merger rate
Detection probability
Expected number of observable events
Probability of each detected event
pi
p_i
pPoisson∝NeNoe−Ne
p_{Poisson}\propto N_e^{N_o}e^{-N_e}
L∝pPoisson∏i=1Nopi
\mathcal{L}\propto p_{Poisson}\prod_{i=1}^{N_o} p_i
Ne
N_e
+
+
Likelihood of all LIGO events
ρb
\rho_b
Empty layer
Intrinsic PBH merger rate
dR(m1,m2,z)∝f(m1)f(m2)
\text{d}R(m_1,m_2,z)\propto f(m_1) f(m_2)
(Number of event (m1,m2,z) per unit volume per unit time)
Signals reaching earth
dN(m1,m2,z)∝dR(m1,m2,z)
\text{d}N(m_1,m_2,z)\propto \text{d}R(m_1,m_2,z)
(Number of event (m1,m2,z) reaching the earth per unit time)
Detection probability pdet(m1,m2,z)
dNe(m1,m2,z)=pdet(m1,m2,z)dN×To
\text{d}N_e(m_1,m_2,z)=p_{det}(m_1,m_2,z)\text{d}N\times T_o
Primordial black holes from vacuum bubbles 邓鹤凌 Arizona State University
A possible mass distribution of primordial black holes implied by LIGO-Virgo
By Heling Deng
A possible mass distribution of primordial black holes implied by LIGO-Virgo
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