A possible mass distribution of primordial black holes implied by LIGO-Virgo
Outline
- LIGO BHs
- Primordial?
- A simple model "fitting" LIGO
- A possible mechanism
Outline
- LIGO BHs
- Primordial?
- A simple model "fitting" LIGO
- A possible mechanism
Mass distribution of LIGO BHs
BH mass
(BH number)
Outline
- LIGO BHs
- Primordial?
- A simple model "fitting" LIGO
- A possible mechanism
MPl10−5 g
M_\text{Pl} \newline
10^{-5}\ \rm g
M⊙1033 g
M_\odot \newline 10^{33}\ \rm g
MPBH
M_\text{PBH}
LIGO BHs
- Supermassive black holes
- LIGO black holes
- Dark matter
O(10-100)M⊙
\mathcal O (10\text{-} 100)M_\odot
SMBH
O(106-1010)M⊙
\mathcal{O}(10^6 \text{-} 10^{10})M_\odot
...
Primordial black holes (PBHs)
...
BHs formed during radiation era
Motivations
Observational constraints of PBHs as DM
PBH binary
PBH mass function
fPBH≡ρCDMρPBH=∫ψ(m)dm
f_{PBH}\equiv\frac{\rho_{PBH}}{\rho_{CDM}} = \int \psi(m)\text{d}m
f(m)=mψ(m)
f(m)=m\psi(m)
ψ(m)dm=ρCDMmdn
\psi(m)\text{d}m=\frac{m}{\rho_{CDM}}\text{d}n
(Fraction of CDM in PBHs with ∼m)
(Fraction of CDM in PBHs within (m,m+dm))
(Fraction of CDM in PBHs)
For example, f(30M⊙)=10−3 means PBHs of 30M⊙ constitute 0.1% DM
PBH mass function f(m)
Merger rate R(m1,m2,z)
Detection probability pdet(m1,m2,z)
Probability of each event p(m1,m2,z)
+
Likelihood of all LIGO events
L∝∏i=144pi
\mathcal{L}\propto \prod_{i=1}^{44} p_i
Merger signals reaching the earth today
Outline
- LIGO BHs
- Primordial?
- A simple model "fitting" LIGO
- A possible mechanism
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}
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}
orange: broken power law (our model)
green: log-normal
blue: LIGO
Outline
- LIGO BHs
- Primordial?
- A simple model "fitting" LIGO
- A possible mechanism
A possible mechanism
subcritical
supercritical
r
m∝r3
m\propto r^3
m∝r2
m\propto r^2
BH mass distribution f(m)
Parameters: λ, γi, ρi, ρb, σ
"initial speed"
"force"
"mass"
orange: broken power law
green: log-normal
black: our PBH model
Conclusions
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
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
Size distribution of bubbles after inflation
Constant bubble nucleation rate λ during inflation
Evolution of bubbles in radiation background r(γi, ρi, ρb, σ)
BH mass distribution f(m)
Parameters: λ, γi, ρi, ρb, σ
"initial speed"
"force"
"mass"
PBH mass function f(m)
Merger rate R(m1,m2,z)∝f(m1)f(m2)
Detection probability pdet(m1,m2,z)
Probability of each event pi(m1,m2,z)
+
Likelihood of all LIGO events
+
Expected number of detection Ne
L∝∏i=1Nopi
\mathcal{L}\propto \prod_{i=1}^{N_o} p_i
Mergers reaching earth today
N(m1,m2,z)∝R(m1,m2,z)
A possible mass distribution of primordial black holes implied by LIGO-Virgo Heling Deng Arizona State University 2101.11098
DPF21: A possible mass distribution of primordial black holes implied by LIGO-Virgo
By Heling Deng
DPF21: A possible mass distribution of primordial black holes implied by LIGO-Virgo
- 330
