Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes

Solar Mass Black Holes and Dark Matter

BH fromcompactstars and DM
Summary

P. Tinyakov (ULB)

June 3, 2019, ICRR

Solar Mass
Black Holesand Dark
Matter

OutlineP. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM

1 Motivation
2 Primordial black holes

Summary

3 BH from compact stars and DM

Bosonic DM
Fermionic DM
4 SummarySolar Mass
Black Holesand Dark
MatterMOTIVATION

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Summary• GW detectors progress very fast; the number ofdetected merger events grows quickly.
• These observations will soon map out the mass
spectrum of stellar-size BH with good accuracy,
including the low-mass region ∼ M .

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Summary

MOTIVATION
LIGO & VIRGO, arXiv:1811.12907

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)

MOTIVATION
LIGO & VIRGO, arXiv:1811.12907

Motivation
Primordial
black holes
BH fromcompactstars and DM
Summaryno astrophysical BH here

Solar Mass
Black Holesand Dark
MatterMOTIVATION

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Summary• The low mass (∼ M ) region is of a particular interest,
because stellar evolution predicts NO black holes with
masses below or about 2 M .
=⇒ Searching for such light BH is a zero-backgroundsearch for new physics.
• What could be the origin of light BH with masses<∼M ?

(I) Such BH may be primordial(II) They can also be formed from compact stars – neutronstars (NS) and white dwarfs – with the help of DM[the main focus of this talk]Solar Mass
Black Holesand Dark
MatterMOTIVATION

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Summary• The low mass (∼ M ) region is of a particular interest,
because stellar evolution predicts NO black holes with
masses below or about 2 M .
=⇒ Searching for such light BH is a zero-backgroundsearch for new physics.
• What could be the origin of light BH with masses<∼M ?

(I) Such BH may be primordial(II) They can also be formed from compact stars – neutronstars (NS) and white dwarfs – with the help of DM[the main focus of this talk]Solar Mass
Black Holesand Dark
MatterMOTIVATION

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Summary• The low mass (∼ M ) region is of a particular interest,
because stellar evolution predicts NO black holes with
masses below or about 2 M .
=⇒ Searching for such light BH is a zero-backgroundsearch for new physics.
• What could be the origin of light BH with masses<∼M ?

(I) Such BH may be primordial(II) They can also be formed from compact stars – neutronstars (NS) and white dwarfs – with the help of DM[the main focus of this talk]Solar Mass
Black Holesand Dark
MatterMOTIVATION

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Summary• The low mass (∼ M ) region is of a particular interest,
because stellar evolution predicts NO black holes with
masses below or about 2 M .
=⇒ Searching for such light BH is a zero-backgroundsearch for new physics.
• What could be the origin of light BH with masses<∼M ?

(I) Such BH may be primordial(II) They can also be formed from compact stars – neutronstars (NS) and white dwarfs – with the help of DM[the main focus of this talk]Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Summary

PRIMORDIAL BLACK HOLES

Solar Mass
Black Holesand Dark
MatterPRIMORDIAL BLACK HOLES

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM

Hawking, MNRAS 152 (1971) 75• BH may be produced in the early Universe in collapseof large matter overdensities.
• For causality, their mass is limited by the total mass
within horizon at the time of production:

Summary

3

MPl
MBH <
∼ MH ' 0.02 T 2
T
MH

MeV
3 × 104 M
6 × 1037 g

100 MeV
3M
6 × 1033 g

100 GeV3 × 10−6 M
6 × 1027 g

108 GeV3 × 10−18 M
6 × 1015 g• BH relative contribution into energy density grows
linearly with the scale factor a =⇒ easy to produce
enough or even overproduce.

Solar Mass
Black Holesand Dark
MatterPlenty of production
mechanisms:

P. Tinyakov(ULB)
Motivation• Primordial density perturbations

Primordial
black holes• Soft equation of state at some period of evolution

BH fromcompactstars and DM• Bubble collisions during phase transitions

Carr, ApJ 201(1975)1
Carr, ApJ 201 (1975) 1
Khlopov, Malomed, Zel’dovich, MNRAS 215 (1985) 575
Hall, Hsu, PRL64 (1990) 2848
Jedamzik, PRD55 (1997) 5871
Jedamzik, Niemeyer, PRD59 (1999) 124014

Summary• Collapse of cosmic strings

Hawking, Phys.Lett. B231 (1989) 237
Polnarev, Zembowicz, PRD 61 (1991) 1106
• Collapse of closed domain walls

Rubin, Khlopov, Sakharov, Grav.Cosmol. 6 (2001)
Dokuchaev, Eroshenko, Rubin, Grav.Cosmol. 11 (2005) 99• At reheating

Suyama et al, PRD71 (2005) 063507• At preheating

Green, Malik, PRD64 (2001) 021301• During inflation

Garsia-Bellido, Linde, Wands PRD54 (1996) 6040

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)

Experimental constraints

Numerous constraints from various arguments:

Carr, talk at “Dark side of BH”, 2019

Motivation
Primordial
black holes
BH fromcompactstars and DM
Summary

Colored regions
are excluded

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Summary

BH FROM COMPACT STARS AND DM

Solar Mass
Black Holesand Dark
MatterBASIC PICTURE

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Summary• Stars do not collapse into BH if lighter than ∼ 20M
because the collapse is halted by the Fermi pressure ofelectrons and nucleons. Instead, they form neutronstars (NS) or white dwarfs if lighter that ∼ 9M .
• However, stars may accumulate DM and concentrate itenough to make a small seed BH inside the star thatwould then grow by accretion and convert the star intoa O(M ) BH.
• This can only work for compact stars, for two reasons:• They concentrate DM much better• They are dense enough to be eaten up in a short time

• This can only work for non-annihilating (e.g.
asymmetric) DM

Solar Mass
Black Holesand Dark
MatterDM IN COMPACT STARS

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Summary

How does DM get into stars? Basically, two ways:• Acquired at the formation of the progenitor• Captured during the evolution of the progenitor andlifetime of the compact starSolar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Capture at star formation
Capela, Pshirkov, PT, PRD87.023507, PRD90.083507• The stars are formed in the collapse of baryonic matter ingiant molecular clouds. These clouds have some DM density
gravitationally bound to them.
• Collapsing baryons gravitationally drag the DM along by
adiabatic contraction, so some DM ends up inside the star

Summary• When the star evolves into a compact remnant (NS or WD),
this DM is inherited by the latter.

Solar Mass
Black Holesand Dark
MatterCapture at star formation

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Capela, Pshirkov, PT, PRD87.023507, PRD90.083507• The stars are formed in the collapse of baryonic matter ingiant molecular clouds. These clouds have some DM density
gravitationally bound to them.
• Collapsing baryons gravitationally drag the DM along by
adiabatic contraction, so some DM ends up inside the star

Summary
prestellar corestarbound DM after
adiabatic contraction

total DM
bound DM

φ0

Rgravitational potential• When the star evolves into a compact remnant (NS or WD),
this DM is inherited by the latter.

Solar Mass
Black Holesand Dark
MatterCapture at star formation

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Capela, Pshirkov, PT, PRD87.023507, PRD90.083507• The stars are formed in the collapse of baryonic matter ingiant molecular clouds. These clouds have some DM density
gravitationally bound to them.
• Collapsing baryons gravitationally drag the DM along by
adiabatic contraction, so some DM ends up inside the star

Summary
prestellar corestarbound DM after
adiabatic contraction

total DM
bound DM

φ0

Rgravitational potential• When the star evolves into a compact remnant (NS or WD),
this DM is inherited by the latter.

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM• The density of bound DM, assuming Maxwellian parent
distribution with v̄ :
 3/2φ0ρ̄ρbound ∼ ρ̄DM
= const · DM
2
v̄
v̄ 3
• DM after the adiabatic contraction:

Fermionic DM

fraction of particles

10

Summary• Number of particles within r ,100

Bosonic DM

−1

10−2

n(r) ∝ r1.5

ν(r) ∝ rradial distribution
periastron distributionn(r ) ∝ r 3/2

10−3• Number of particles withperiastron < r ,

10−4
10−5
10−6

ν(r ) ∝ r

10−7
10−8

R /R̄ 10−5

10−4

10−3

r/R̄

10−2

10−1

1

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Summary• How much gets captured? Depends on the progenitor
mass and ambient DM density and velocity. For
numbers typical of dwarf galaxies, ρDM = 200 GeV/cm3
and v = 7 km/s, one has
M∗ /M
1
5
10
15

Mdm
9.9 × 1044 GeV
5.8 × 1046 GeV
3.6 × 1047 GeV
9.6 × 1047 GeV

Mdm /M
8.8 × 10−13
5.2 × 10−11
3.2 × 10−10
8.6 × 10−10• In the MW halo with ρDM = 0.3 GeV/cm3 andv = 220 km/s they should be rescaled by a factor
5 × 10−8 (∝ ρDM /v 3 ).

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Summary

CAPTURE DURING LIFETIME
Press, Spergel, Astrophys.J. 296(1985)679• Start with cross section of the star crossinghi2
πR∗2 1 + Rg /(R∗ v∞)• Average with Maxwell distribution



√ ρ
Rg R∗
3Elossσ1 − exp −F = 6π DM
2v∞ m 1 − Rg /R∗
σcr
mv∞
=

√

ρ Rg R∗
6π DM
× (possible suppression)v∞ m• Critical cross section σcr = R∗2 /N (= star becomes
opaque):Sun: 5×10−36 cm2 ,WD: 3×10−40 cm2 ,NS: 10−45 cm2

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Summary

CAPTURE DURING LIFETIME
Press, Spergel, Astrophys.J. 296(1985)679• Start with cross section of the star crossinghi2
πR∗2 1 + Rg /(R∗ v∞)• Average with Maxwell distribution



√ ρ
Rg R∗
3Elossσ1 − exp −F = 6π DM
2v∞ m 1 − Rg /R∗
σcr
mv∞
=

√

ρ Rg R∗
6π DM
× (possible suppression)v∞ m• Critical cross section σcr = R∗2 /N (= star becomes
opaque):Sun: 5×10−36 cm2 ,WD: 3×10−40 cm2 ,NS: 10−45 cm2

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Summary

CAPTURE DURING LIFETIME
Press, Spergel, Astrophys.J. 296(1985)679• Start with cross section of the star crossinghi2
πR∗2 1 + Rg /(R∗ v∞)• Average with Maxwell distribution



√ ρ
Rg R∗
3Elossσ1 − exp −F = 6π DM
2v∞ m 1 − Rg /R∗
σcr
mv∞
=

√

ρ Rg R∗
6π DM
× (possible suppression)v∞ m• Critical cross section σcr = R∗2 /N (= star becomes
opaque):Sun: 5×10−36 cm2 ,WD: 3×10−40 cm2 ,NS: 10−45 cm2

Solar Mass
Black Holesand Dark
MatterNumbers

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM• Assume best case (no suppression), take lifetime
10 Gyr and calculate total DM mass accumulated byNSMW

2.2 × 1044 GeV = 2 × 10−13 M

dwarf galaxies

1.5 × 1047 GeV = 1.3 × 10−10 M

Fermionic DM

Summary• Note: DM-to-nucleon cross section is strongly
constrained by direct detection, so for Sun and WD
there is typically strong suppression as compared thothese numbers.

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

WHAT HAPPENS TO
CAPTURED DM?
• Once gravitationally bound, DM
thermalizes and settles in a cloudof the size

1/2
T∗
∼ 10 cm
rth =
Gρ∗ m

NS

DM cloud

Summary• When (and if) DM mass density exceeds that of the star
it decouples from the star potential and start shrinking
under its own gravity.
• This self-gravitation condition reads:
M > 2 × 10−14 M (m/100 GeV)−3/2

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

WHAT HAPPENS TO
CAPTURED DM?
• Once gravitationally bound, DM
thermalizes and settles in a cloudof the size

1/2
T∗
∼ 10 cm
rth =
Gρ∗ m

NS

DM cloud

Summary• When (and if) DM mass density exceeds that of the star
it decouples from the star potential and start shrinking
under its own gravity.
• This self-gravitation condition reads:
M > 2 × 10−14 M (m/100 GeV)−3/2

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

WHAT HAPPENS TO
CAPTURED DM?
• Once gravitationally bound, DM
thermalizes and settles in a cloudof the size

1/2
T∗
∼ 10 cm
rth =
Gρ∗ m

NS

DM cloud

Summary• When (and if) DM mass density exceeds that of the star
it decouples from the star potential and start shrinking
under its own gravity.
• This self-gravitation condition reads:
M > 2 × 10−14 M (m/100 GeV)−3/2

Solar Mass
Black Holesand Dark
Matter

BOSONIC DM

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Summary

Kouvaris, PT, PRL 107(2011)091301• In case of bosons this constraint should bereconsidered because bosons may form Bose-Einsteincondensate which is much more compact and may
self-gravitate at smaller total accumulated mass.
• For a NS, the size of BEC state is−1/4
rBEC = Gρ∗ m2∼ 2 × 10−4 cm (GeV/m)1/2• For a given temperature, there is a critical density ofparticles above which BEC is formed:
28−3n>∼ 5 × 10 cm

mTc
GeV · 105 K

3/2

Solar Mass
Black Holesand Dark
Matter

BOSONIC DM

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Summary• For BEC the self-gravitation condition reads
MBEC > 7 × 10−30 M (m/GeV)−3/2=⇒ much easier to satisfy than for the whole cloud• Once self gravitating, BEC collapses provided theuncertainty principle does not stop the collapse
NBEC >
∼



MPl
m

2

∼ 1038 m −2
GeV

Note: this condition is more restrictive thanself-gravitation of BEC.

Solar Mass
Black Holesand Dark
Matter

BOSONIC DM• Thus one gets constraints on bosonic DM together withparameter range where some NS can be converted into
light BH:

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Summary

reg

ion

of i
n

tere
st

fi

re

g

o
ion

t
es

r
nte

Solar Mass
Black Holesand Dark
MatterFERMIONIC DM

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Summary

Kouvaris, PT, Tytgat, PRL 121(2018)221102• For fermions Pauli principle prevents collapse unlessthe number of particles is big enough (Chandrasekhar
limit),
MPl 3>∼ 1057 (GeV/m)3N∼m• =⇒ Accumulated DM mass must satisfy
M>∼m• Two ways out:



MPl
m

3

∼ 1057 GeV (GeV/m)2• Assume very high masses m >∼ 1000 TeV — not very
attractive• Add attractive self-interactions — obviously, more
attractive

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes

ATTRACTIVE FERMIONIC DM• Self-interactions modify both the self-gravitation andChandrasekhar conditions• Assume scalar exchange =⇒ 2 parameters: coupling
α and mediator mass µ

BH fromcompactstars and DM

V (r ) = αe−µr /rBosonic DM
Fermionic DM

Summary• Self-gravitation condition: assume uniform sphere ofradius r and use the virial theorem. In the limit when
the range of the potential 1/µ is larger than interparticle
distance r0 but smaller than the size of DM sphere R
this gives
2hEk i = Gρ∗ mR 2 +GNm2 Nαe−µr0+(3 + 3µr0 + µ2 r02 )Rµ2 R 3• In thermal equilibrium 2hEk i = 3T .

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)• At small N the solution for R always exists, but at somecritical value Ncr it disappears.

Motivation
Primordial
black holes
BH fromcompactstars and DM

unstablesolution

Bosonic DM
Fermionic DM

Summary

stablesolution

3T

star potential

self−attractionR• This critical N is calculated numerically.

Solar Mass
Black Holesand Dark
Matter• Chandrasekhar limit: consider E(R)P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

E(R) =

Nα
N 2/3 GNm2
− 2 3
−
2
R
mR
µ R

and look for extrema ∂E/∂R = 0. At small N there are
two; at some large N = NCh they merge and disappear.

0

Summary

1_
R2
−1
_
R3

−1
_
R
stable solution

RSolar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Summary• Parametrically

NCh =

µ
√

3 

MPl
m

3

m α
√
• Note: the parameter (µ/m α) also controls
non-relativistic approximation.
• Examples when this picture works:
µ
m
α
Ncr
NCh
#
MeV TeV
−3
35
1 10
10
1
5 · 102 · 1037
2 10−42
0.2 2 · 1035 7 · 1040
−4
3 10
1
1
3 · 1033 6 · 1035
4 10−33
0.2 2 · 1035 7 · 1039

MCh
M
10−17
10−14
10−18
10−15

Solar Mass
Black Holesand Dark
MatterPOTENTIAL CAVEAT

P. Tinyakov(ULB)

Gresham, Zurek, arXiv:1809.08254
Motivation
Primordial
black holes
BH fromcompactstars and DM
Bosonic DM
Fermionic DM

Summary• When the DM cloud collapses under gravity andself-interaction, the non-relativistic approximation
breaks• For relativistic fermions, the source of scalar field ψ̄ψ is
no longer equal to the number of fermions ψ † ψ, so theself-attraction may be dumped• =⇒ there might exist another stable phase before the
Schwarzschild radius is reached• However, the situation is far from clear as in this regime
many condensates may develop. The question is understudy.

Solar Mass
Black Holesand Dark
Matter
P. Tinyakov(ULB)
Motivation

DETECTION PROSPECTS• Can light BH mergers be detected and distinguishedfrom NS mergers?

Primordial
black holes
BH fromcompactstars and DM

LIGO2017
2M
atBosonic DM
Fermionic DM

Summary

1.
5M

40

at
4

Mp
c

0M

pc

1.
5M
at

LIGO
upgrade
ET

40
0

Mp
c

Solar Mass
Black Holesand Dark
MatterSummary

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM• If light . 2M BH are found, it would mean physics
beyond SM

Summary• But it would not necessarily mean that these BH are
primordial. Instead, it may point towards existence of aparticular type of DM.

Solar Mass
Black Holesand Dark
MatterSummary

P. Tinyakov(ULB)
Motivation
Primordial
black holes
BH fromcompactstars and DM• If light . 2M BH are found, it would mean physics
beyond SM

Summary• But it would not necessarily mean that these BH are
primordial. Instead, it may point towards existence of aparticular type of DM.