stellar mass primordial black holes
Post on 31-Jul-2022
3 Views
Preview:
TRANSCRIPT
Fluctuations The threshold δc β(tk) Conclusions
Seminar of Department of Astronomy - University of Belgrade
Stellar mass Primordial Black Holes
Laurindo Sobrinho
Faculdade de Ciências Exatas e da Engenharia da Universidade da MadeiraDepartamento de Matemática
Grupo de Astronomia da Universidade da Madeira (GAUMa)Instituto de Astrofísica e Ciências do Espaço (IA)
March 2, 2021
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Table of contents
1 PBHs from density uctuations
2 The threshold for PBH formation
3 The fraction of the Universe going into PBHs
4 Conclusions and future work
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
1 - PBHs from density uctuations
Black Holes may have formed in the Early Universe as a
consequence of the gravitational collapse of density
uctuations (Hawking 1971, Hawking & Carr 1974, Novikov et
al. 1979).
These Primordial Black Holes (PBHs) could have masses
ranging from the Planck mass up to ∼ 1011M. Here we will
consider the (extended) stellar mass range
[0.05M − 500M].
During ination, uctuations of quantum origin are stretched
to scales much larger than the cosmological horizon becoming
causally disconnected from physical processes.
The inationary era is followed, respectively, by
radiation-dominated and matter-dominated epochs during
which these uctuations can re-enter the cosmological horizon.
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
For a given physical scale k, the horizon crossing time tk (i.e. the
instant when that scale re-enters the cosmological horizon) is given
by (Blais et al. 2003):
ck = a(tk)H(tk)
where a(tk) is the scale factor and H(tk) the Hubble parameter.
The collapse that gives rise to the formation of a PBH is now
possible but only if the amplitude of the density uctuation:
δ =∆m
m
is larger than a specic threshold value δc.
δk ≥ δc the expansion of the overdense region will,
eventually, come to a halt, followed by its collapse leading to
the formation of a PBH
δk < δc the uctuation dissipates without forming a PBH
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
The majority of the PBHs formed at a particular epoch have
masses within the order of the horizon mass, MH , at that epoch
(Carr et al. 2003):
MH(t) ∼ 1015(
t
10−23 s
)g.
In the case of perturbations with δ only slightly larger than δc thePBH masses rather obey the scaling law (Niemeyer &
Jedamzik 1999):
MPBH ∝MH (δ − δc)γ
where γ ≈ 0.36 in the case of a radiation-dominated Universe. This
scaling law has been found to hold down to (δ − δc) ∼ 10−10
(Musco & Miller 2013).
Here we assume: MPBH(tk) = MH(tk).
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
The probability that a uctuation crossing the horizon at some
instant tk has of collapsing and forming a PBH can be written as
(e.g. Green 2015):
β(tk) =1√
2πσ(tk)
∫ ∞δc
exp
(− δ2
2σ2(tk)
)dδ
σ2(tk) mass variance at horizon crossing
δc the threshold for PBH formation
The value of β(tk) can also be regarded as the fraction of the
Universe going into PBHs.
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
2 - The threshold for PBH formation
δc = 1/3 simplied model of an overdense collapsing region
for a radiation-dominated Universe (Carr 1975)
δc ' 0.43− 0.47 numerically solving the relativistic
hydrodynamical equations for a radiation-dominated Universe
(Musco & Miller 2013, Harada et al. 2013)
The exact value of δc depends on the perturbation prole. We
consider δc = 0.43 (Mexican-Hat perturbation, a very
representative one).
δc is constant through the radiation-dominated epoch, the
exception occurring during cosmological phase transitions, when
the value of δc decreases (as a consequence of the decrease of the
sound speed). This is relevant, since a lower value of δc favoursPBH formation (Carr 2003).
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
The Standard Model of Particle Physics (SMPP) predicts:
Electroweak (EW) phase transition at temperatures of
∼ 100 GeV (when the age of the Universe was ∼ 10−10 s),responsible for the spontaneous breaking of the EW symmetry.
PBHs formed during the epoch of the EW phase transition
would have ∼ 10−6M.
Quantum Chromodynamics (QCD) phase transition at
Tc = 170 MeV when quarks and gluons become conned in
hadrons. The QCD phase transition occurred when the
universe was ∼ 10−5 s and that corresponds to MH ∼ 0.5M.
If we want to study the formation of stellar mass PBHs we cannot
neglect the eect of the QCD phase transition. In particular we
need to know how the variation of the sound speed during theQCD phase transition will aect the value of δc.
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
During the radiation-dominated epoch the Universe can be
regarded as a diluted gas with its Equation of State (EoS) written
as (Carr 2003):
p = wρ
where p is pressure, ρ is the cosmological density, and the
dimensionless quantity w (the EoS parameter) is equal to 13 , since
the sound speed is (Schmid et al. 1999):
c2s =
(∂p
∂ρ
)S
= w =1
3
If during the QCD phase transition the Universe becomes
matter-dominated (pressureless gas), then we get w = 0 and
c2s = 0.
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
The evolution of the scale factor for the perturbed region (s(τ)) is(Sobrinho 2011; Sobrinho, Augusto & Gonçalves 2016):
(ds
dτ
)2
=8πG
3
Ks
1 + δk
(1 + δks(τ)1+3w
− Kk
Ks
δk
a1+3wkk
)
where:
Ks and Kk are constants to be determined
ak is the scale factor value at the horizon crossing time
wk is the EoS parameter at the horizon crossing time
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
The turnaround point (tc) is reached when the perturbed region
stops expanding, i.e., when ds/dτ = 0. Thus, we get:
s1+3wcc =
Ks
Kka1+3wkk
(1 + δkδk
)
which relates the size of the perturbed region at the horizon
crossing time with the respective size at the turnaround point. The
calculation of the relation Ks/Kk is detailed in Sobrinho, Augusto
& Gonçalves (2016).
We assume that whentc is reached a PBH will form. Hence, we are
not taking into account the dynamics between the turnaround point
and the instant when the PHB actually arises with the formation of
an event horizon (which would require to numerically solve the
Hernandez-Misner equations).
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
If we want to consider the formation of stellar mass PBHs we need
to take into account the QCD phase transition.
More exactly we need to know how the sound speed behaves during
the QCD phase transition.
Unfortunately we don't know exactly which model ts the QCD
phase transition. We have considered three dierent models:
Bag Model (BM)
Lattice Fit Model (LFM)
Crossover Model (CM)
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
2.1 - Bag Model (BM)
a high temperature region (T > Tc, t < t−) where we have a QuarkGluon Plasma (QGP)
T = Tc = 170 MeV ([t−, t+]): dust-like phase where quarks,gluons, and hadrons coexist in equilibrium at constant pressure andtemperature and c2s = 0
a low temperature region (T < Tc, t > t+) where we have anHadron Gas (HG).
-4.4 -4.2 -4 -3.8 -3.6Log10Ht1sL
0
0.1
0.2
0.3
0.4
cs2
t-
t+
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Classes of uctuations
Class Horizon crossing Turnaround
A quarkgluon quarkgluon
B quarkgluon mixed
C quarkgluon hadron
D mixed mixed
E mixed hadron
F hadron hadron
Idea: replace δc by δc(1− f)
f (0 ≤ f < 1) fraction of the overdense region spent in the
dust-like phase of the transition (Sobrinho, Augusto & Gonçalves
2016).
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Figure 1a in New thresholds for primordial black hole formation during the QCD phase transition",Sobrinho, J. L. G.; Augusto, P.; Gonçalves, A. L., 2016, Monthly Notices of the Royal AstronomicalSociety, Volume 463, Issue 3.
0 0.2 0.4 0.6 0.8 1∆k
0
0.2
0.4
0.6
0.8
1
∆k
HaL
ABC
∆AB∆BC
d
∆c1
solid line −→ (1− f)δc [red PBH formation allowed: δk ≥ (1− f)δc]
dashed line −→ δk
tk = 4.0× 10−5 s
δc1 = 0.28 new threshold for PBH formation (< 0.43)
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Figure 1b in New thresholds for primordial black hole formation during the QCD phase transition",Sobrinho, J. L. G.; Augusto, P.; Gonçalves, A. L., 2016, Monthly Notices of the Royal AstronomicalSociety, Volume 463, Issue 3.
0 0.1 0.2 0.3 0.4 0.5∆k
0
0.1
0.2
0.3
0.4
0.5
∆k
HbL
ABC∆AB∆BC
d
∆c1
∆c2
solid line −→ (1− f)δc [red PBH formation allowed: δk ≥ (1− f)δc]
dashed line −→ δk
tk = 1.1× 10−5 s
[δc1, δc2] = [0.15, 0.23] new thresholds (new window) for PBHformation (< 0.43)
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
δc for a QCD BM
Figure 2 in New thresholds for primordial black hole formation during the QCD phase transition",Sobrinho, J. L. G.; Augusto, P.; Gonçalves, A. L., 2016, Monthly Notices of the Royal AstronomicalSociety, Volume 463, Issue 3.
-6 -5.5 -5 -4.5 -4Log10Htk1sL
0.1
0.2
0.3
0.4
0.5
0.6
∆k
t- t+BH formation
No BH formation
∆c1
∆c2
∆c=0.43
Minimum value of δc: 0.097
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
2.2 - Crossover Model (CM)
The sound speed during a QCD Crossover (Schwarz 1998):
c2s(t) =
3 +∆gT (t)sech
(T (t)−Tc
∆T
)2
∆T(gHG + gQGP + ∆gtanh
(T (t)−Tc
∆T
))−1
T (t) = T0
[exp
(c
√Λ
3(tSN − t0)
)(teqtSN
)2/3(t
teq
)1/2]−1
∆T = 0.1Tc with Tc = 170 MeV; T0 = 2.72548 K
gQGP number of degrees of freedom for the QGP (61.75).
gHG number of degrees of freedom for the HG (17.25).
∆g = gQGP − gHG (see Sobrinho 2011 for details)
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Figure 3 in New thresholds for primordial black hole formation during the QCD phase transition",Sobrinho, J. L. G.; Augusto, P.; Gonçalves, A. L., 2016, Monthly Notices of the Royal AstronomicalSociety, Volume 463, Issue 3.
-4.4 -4.2 -4 -3.8 -3.6 -3.4 -3.2Log Ht1sL
0.1
0.15
0.2
0.25
0.3
0.35
0.4
cs2
t1 t2
f =3
2
(tk
1 + δkδk
)−3/2 ∫ tk1+δkδk
t1
(1− cs(t)
cs0
)√tdt
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Figure 4 in New thresholds for primordial black hole formation during the QCD phase transition",Sobrinho, J. L. G.; Augusto, P.; Gonçalves, A. L., 2016, Monthly Notices of the Royal AstronomicalSociety, Volume 463, Issue 3.
0.2 0.4 0.6 0.8 1∆k
0.32
0.34
0.36
0.38
0.4
0.42
0.44
∆k
∆c1
solid line −→ (1− f)δc [red PBH formation allowed: δk ≥ (1− f)δc]
dashed line −→ δk
tk = 4.2× 10−5 s
δc1 = 0.345 new threshold for PBH formation (< 0.43)
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
δc for a QCD Crossover
Figure 5 in New thresholds for primordial black hole formation during the QCD phase transition",Sobrinho, J. L. G.; Augusto, P.; Gonçalves, A. L., 2016, Monthly Notices of the Royal AstronomicalSociety, Volume 463, Issue 3.
-5 -4.5 -4 -3.5 -3Log10Htk1sL
0.34
0.36
0.38
0.4
0.42
0.44
0.46
∆k
BH formation
No BH formation
t1 t2
∆c1
∆c=0.43
Minimum value of δc: 0.345
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
2.3 - Lattice Fit Model
Figure 4 in New thresholds for primordial black hole formation during the QCD phase transition",Sobrinho, J. L. G.; Augusto, P.; Gonçalves, A. L., 2016, Monthly Notices of the Royal AstronomicalSociety, Volume 463, Issue 3.
-7 -6.5 -6 -5.5 -5 -4.5 -4 -3.5
Log10Ht1sL
0
0.1
0.2
0.3
cs2
t-
t+
t1
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
δc for a QCD LFM
Figure 4 in New thresholds for primordial black hole formation during the QCD phase transition",Sobrinho, J. L. G.; Augusto, P.; Gonçalves, A. L., 2016, Monthly Notices of the Royal AstronomicalSociety, Volume 463, Issue 3.
-9 -8 -7 -6 -5 -4 -3
Log10Htk1sL
0.1
0.2
0.3
0.4
0.5
0.6
∆k
∆c1∆c2
∆cA
∆c=0.43
t1 t- t+
BH formation
No BH formation
Minimum value of δc: 0.15
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
3 - Mass variance
(Sobrinho & Augusto 2020)
σ2(k) =
∫ kek
0x3δ2H(kx)W 2
TH(x)W 2TH(
x√3
)dx
δ2H(k) =
(10
9
)2
δ2H(kc)
(k
kc
)n(k)−1
WTH Top-hat window function
kc = 0.05Mpc−1 ≈ 1.6× 10−24m−1 → pivot scale (Planck mission)
ke ≈ 0.01m−1 → smallest slace generated by ination
δ2H(kc) ≈ 2.198× 10−9 → Planck Collaboration et al. 2016
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Spectral index:
n(k) = n0 +∑i≥1
ni(i+ 1)!
(lnk
kc
)i
n0 = 0.9476n1 = 0.001n2 = 0.022
Planck (e.g. Erfani 2014)
n3n4
work on the plane (n3, n4)
We are assuming ni = 0 when i ≥ 5
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
PBHs in signicant numbers =⇒ n(k) > 1(blue spectrum)
-10 -5 0 5 10 15
log10Htk
1 sL
0.25
0.5
0.75
1
1.25
1.5
1.75
2
nHtkLnmax=1.803, log10Htkmax1sL=-3
n3 = 0.0099, n4 = −0.0033.
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
We are interested in situations for which n(k) shows a local maximumat some point k = k+ with n+ = n(k+) > 1.
n+ = n0 +n1
2ln
k+kc
+n2
6
(ln
k+kc
)2
+n3
24
(ln
k+kc
)3
+n4
120
(ln
k+kc
)4
dn(k)
dk
∣∣k=k+ = 0⇔ n1
2+
n2
3ln
k+kc
+n3
8
(ln
k+kc
)2
+n4
30
(ln
k+kc
)3
= 0
Given a pair of values (n+, k+), or equivalently (n+, t+), we candetermine the corresponding pair of values (n3, n4):
n3 =
−4(24n0 − 24n+ + 9n1 ln
k+kc
+ 2n2
(ln
k+kc
)2)
(ln
k+kc
)3
n4 =
20
(18n0 − 18n+ + 6n1 ln
k+kc
+ n2
(ln
k+kc
)2)
(ln
k+kc
)4
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
The path for the calculus of β
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Constraints on PBHs for a variety of evaporation, dynamical, lensing,large-scale structure and accretion eects (Carr et al. 2016)
f(M) ≈ 4.11× 108β(M)
(M
M
)−1/2
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Figure 2a in Stellar mass Primordial Black Holes as Cold Dark Matter", Sobrinho, J. L. G.; Augusto, P.,2020, Monthly Notices of the Royal Astronomical Society, Volume 496, Issue 1.
1.5 1.6 1.7 1.8 1.9 2
nmax
-9
-7
-5
-3
-1
logHtkmax1sL
HaL Crossover Model
No PBH formation
Forbidden region
Below the solid curve, PBH formation is not allowed since it wouldviolate the observational constraints. Above the dashed line, PBHformation is allowed although in negligible numbers (less than one PBHwithin the observable Universe).
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Figure 2b in Stellar mass Primordial Black Holes as Cold Dark Matter", Sobrinho, J. L. G.; Augusto, P.,2020, Monthly Notices of the Royal Astronomical Society, Volume 496, Issue 1.
1.5 1.6 1.7 1.8 1.9 2
nmax
-9
-7
-5
-3
-1
logHtkmax1sL
HbL Bag Model
No PBH formation
Forbidden region
For a given value of tkmaxthe fraction of the Universe going into PBHs,
β(tk), will be maximum if the corresponding value of nmax is the onelocated over the solid curve
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Figure 2c in Stellar mass Primordial Black Holes as Cold Dark Matter", Sobrinho, J. L. G.; Augusto, P.,2020, Monthly Notices of the Royal Astronomical Society, Volume 496, Issue 1.
1.5 1.6 1.7 1.8 1.9 2
nmax
-9
-7
-5
-3
-1
logHtkmax1sL
HcL Lattice Fit Model
No PBH formation
Forbidden region
Selected cases: (a) tkmax= 10−9 s; (b) tkmax
= 10−7 s;(c) tkmax
= 10−5 s; (d) tkmax= 10−3 s, and (e) tkmax
= 10−1 s.
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Figure 3e in Stellar mass Primordial Black Holes as Cold Dark Matter", Sobrinho, J. L. G.; Augusto, P.,2020, Monthly Notices of the Royal Astronomical Society, Volume 496, Issue 1.
-2.5 -2 -1.5 -1 -0.5 0 0.5 1
log10Htk1sL
-40
-30
-20
-10
0
log10ΒHtkL
BM
LFM
CM
oc
HeL log10Htkmax1sL=-1.0
The uctuations crossed the horizon suciently after the QCD epoch.All the three QCD models share the same curve (with nmax = 1.920),characterized by a radiation peak.
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
The present day value of the PBH density parameter:
ΩPBH(t0) = a(teq)
∫ t′
t∗
β(tk)
a(tk)dtk
where
ΩPBH(t0, tk) = β(tk)a(teq)
a(tk)
The present day value of the PBH number density for PBHs
formed between two given instants t1 and t2:
nPBH(t0) = ρc(t0)
∫ t2
t1
ΩPBH(t0, tk)
MH(tk)dtk
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
1 2 3 4 5
log10HMPBH
5 ML
0
2
4
6
8
10
12
log10HNGpc3L
log10Htkmax1sL=-1.0
Intermediate mass PBHs (5× 102 − 5× 104M) with a radiation peaklocated at 5× 103M, giving ∼ 1011 PBHs/Gpc3.
Contribution to CDM: ≈ 0.001%.
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Figure 3a in Stellar mass Primordial Black Holes as Cold Dark Matter", Sobrinho, J. L. G.; Augusto, P.,2020, Monthly Notices of the Royal Astronomical Society, Volume 496, Issue 1.
-12 -10 -8 -6 -4
log10Htk1sL
-40
-30
-20
-10
0
log10ΒHtkL
BMLFM
CM
BM
ocHaL log10Htkmax1sL=-9.0
For both the CM and LFM we have the same β(tk) curve (left), whichcorresponds to a radiation peak. These uctuations crossed the horizonsuciently before the QCD epoch. If we consider a BM instead, then wecannot neglect the contribution from the QCD and we have, in addition,a QCD peak.
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
log10HMPBH
5 ML
024681012141618202224
log10HNGpc3L
log10Htkmax1sL=-9.0
BM
PBHs with sub-stellar masses (5× 10−10 − 5× 10−4M)Peak: ∼ 5× 10−7M (∼ 1026 PBHs/Gpc3).Total: ∼ 1026 PBHs/Gpc3
QCD peak (BM only): ∼ 1012Gpc3 PBHs with 0.5M.
Contribution to CDM: ≈ 29%.
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Figure 3b in Stellar mass Primordial Black Holes as Cold Dark Matter", Sobrinho, J. L. G.; Augusto, P.,2020, Monthly Notices of the Royal Astronomical Society, Volume 496, Issue 1.
-10 -8 -6 -4
log10Htk1sL
-40
-30
-20
-10
0
log10ΒHtkL
BM
LFM
CM
ocHbL log10Htkmax1sL=-7.0
CM - radiation peak
LFM - radiation peak + QCD peak
BM - dominated by a QCD peak
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
-7 -6 -5 -4 -3 -2 -1 0
log10HMPBH
5 ML
0
2
4
6
8
10
12
14
16
18
20
22
log10HNGpc3L
log10Htkmax1sL=-7.0
HaL LFM
-7 -6 -5 -4 -3 -2 -1 0
log10HMPBH
5 ML
0
2
4
6
8
10
12
14
16
18
20
22
log10HNGpc3L
log10Htkmax1sL=-7.0
HbL CM
LFM Radiation peak: 5× 10−4M, ∼ 1022 PBHs/Gpc3
QCD peak: 0.5M, ∼ 1018 PBHs/Gpc3
Contribution to CDM: ≈ 2.3%
CM Radiation peak: 5× 10−4M, ∼ 1023 PBHs/Gpc3
Contribution to CDM: ≈ 31%
BM QCD peak: 0.5M, ∼ 1020 PBHs/Gpc3
Contribution to CDM: ≈ 0.4%
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Figure 3c in Stellar mass Primordial Black Holes as Cold Dark Matter", Sobrinho, J. L. G.; Augusto, P.,2020, Monthly Notices of the Royal Astronomical Society, Volume 496, Issue 1.
-7 -6 -5 -4 -3 -2
log10Htk1sL
-40
-30
-20
-10
0log10ΒHtkL
BM
LFM CM
ocHcL log10Htkmax1sL=-5.0
-4 -3 -2 -1 0 1
log10HMPBH
5 ML
0
2
4
6
8
10
12
14
16
18
20
log10HNGpc3L
log10Htkmax1sL=-5.0
CM Radiation peak: 0.05M, ∼ 1020 PBHs/Gpc3
QCD peak somehow hidden on the 0.5M bar
Contribution to CDM: ≈ 12%
BM & LFM QCD peak: 0.5M, ∼ 1018 PBHs/Gpc3
Contribution to CDM: ≈ 0.6%
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
-5 -4 -3 -2 -1
log10Htk1sL
-40
-30
-20
-10
0
log10ΒHtkL
BM LFM
CM
oc
HdL log10Htkmax1sL=-3.0
-2 -1 0 1 2 3
log10HMPBH
5 ML
0
2
4
6
8
10
12
14
16
18
log10HNGpc3L
log10Htkmax1sL=-3.0
HaL BM
-2 -1 0 1 2 3
log10HMPBH
5 ML
0
2
4
6
8
10
12
14
16
18
log10HNGpc3L
log10Htkmax1sL=-3.0
HbL LFM
-2 -1 0 1 2 3
log10HMPBH
5 ML
0
2
4
6
8
10
12
14
16
18
log10HNGpc3L
log10Htkmax1sL=-3.0
HcL CM
BM QCD peak: 0.5M, ∼ 1019 PBHs/Gpc3, CDM: ≈ 2%
LFM QCD peak: 0.5M, ∼ 1018 PBHs/Gpc3, CDM: ≈ 2%
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Figure 4 in Stellar mass Primordial Black Holes as Cold Dark Matter", Sobrinho, J. L. G.; Augusto, P.,2020, Monthly Notices of the Royal Astronomical Society, Volume 496, Issue 1.
-2 -1 0 1 2 3
log10HMPBH
5 ML
0
2
4
6
8
10
log10HNMpc3L
log10Htkmax1sL=-3.0
10-6%
44% 32%
10-3%
CM extended mass spectrum (plateau formed by the radiation andQCD peaks):
∼ 1012 PBHs/Gpc3 (0.5M)
∼ 1019 PBHs/Gpc3 (5M)
∼ 1018 PBHs/Gpc3 (50M)
∼ 1013 PBHs/Gpc3 (500M)Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Conclusions
Stellar mass PBHs might have formed in the Early Universe
Stellar mass PBHs could be an important fraction of CDM
At least some of the BHs mergers observed (gravitational
waves) could be of primordial origin
A monochromatic peak at ∼ 0.5 M will favour a BM or LFM
model, while a broader mass spectrum (550M) will suggesta CM for the QCD.
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Some ideas for future work
Formation of PBH binaries (at the formation epoch)
Formation of PBH binaries (during the evolution of the
Universe)
Concentration of PBHs around galactic haloes
Formation of clusters of PBHs
Find out scenarios that t with the observed mergers
Consider other mass ranges (sub-stellar and supermassive)
.....
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Some (other) ideas for future work
Some ideas that can help to rene the results obtained in the
previous topics:
Consider the scaling law for the PBH masses
Consider non-gaussian distributions for the uctuations
Consider other kinds of spcetra for the uctuations
Consider other PBH formation mechanisms
.....
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
References
Sobrinho, J. L. G. (2011), The Possibility of Primordial Black Hole DirectDetection, Sobrinho, L.; Tese de Doutoramento em Matemática (especialidadede Física-Matemática), Universidade da Madeira, pp. 319.
Sobrinho, J. L. G.; Augusto, P.; Gonçalves, A. L. (2016), New thresholds forprimordial black hole formation during the QCD phase transition, MonthlyNotices of the Royal Astronomical Society (MNRAS), 463, 2348.
Sobrinho, J. L. G.; Augusto, P.; Gonçalves, A. L. (2020), Stellar massPrimordial Black Holes as Cold Dark Matter, Monthly Notices of the RoyalAstronomical Society (MNRAS), 496, 60.
Hawking S., 1971, MNRAS, 152, 75
Carr B. J., Hawking S. W., 1974, MNRAS, 168, 399
Carr B. J., 1975, ApJ, 201, 1
Novikov I. D., Polnarev A. G., Starobinskii A. A., Zeldovich I. B., 1979, A&A, 80, 104
Blais D., Bringmann T., Kiefer C., Polarski D., 2003, Phys. Rev. D, 67, 024024
Carr B. J., 2003, in D. Giulini, C. Kiefer and C. Lämmerzahl, eds, Lecture Notes in Physics, Vol.631, Quantum Gravity: From Theory to Experimental Search. Springer, Berlin, p. 301
Niemeyer J. C., Jedamzik K., 1999, Phys. Rev. D, 59, 124013
green2015 Green A. M., 2015, in Calmet X., ed., Quantum Aspects of Black Holes. Springer,London, p. 129
Musco I., Miller J. C., 2013, Class. Quantum Grav., 30, 145009
Harada T., Yoo C.-M., Kohri K., 2013, Phys. Rev. D, 88, 084051
Schmid C., Schwarz D. J., Widerin P., 1999, Phys. Rev. D, 59, 043517
Carr B., Kühnel F., Sandstad M., 2016, PhRvD, 94, 083504. doi:10.1103/PhysRevD.94.083504
Laurindo Sobrinho Stellar mass Primordial Black Holes
Fluctuations The threshold δc β(tk) Conclusions
Hvala na panºji!
(c) Grupo de Astronomia da Universidade da Madeira 2021
Laurindo Sobrinho Stellar mass Primordial Black Holes
top related