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Formation and EvolutionFormation and Evolutionofof
Compact BinariesCompact Binaries
Niels Bohr International Academy Summer School 2009Thomas Tauris
Lecture topics:Lecture topics:
HMXBs and LMXBs HMXBs and LMXBs –– a cartoon overviewa cartoon overview
RocheRoche--lobe overflow (RLO): case A, case B, case Clobe overflow (RLO): case A, case B, case C
Stability criteria for mass transfer / stellar evolutionStability criteria for mass transfer / stellar evolution
The orbital angular momentum balance equationThe orbital angular momentum balance equation
Common envelope + spiralCommon envelope + spiral--inin
NBI 2009 T. Tauris 2
Common envelope + spiralCommon envelope + spiral--inin
Formation of millisecond pulsarsFormation of millisecond pulsars
•• Detailed evolution of LMXBsDetailed evolution of LMXBs
LMXB cartoon
common
envelope
ZAM
S
Roche-lobe
overflow
+ spiral-in
15.0 1.6
1200 days
0.0 Myr
ag
e
P orb
1538 days
13.87 Myr
0.83 days 13.87 Myr
13.1 1.6
4.86
eccentricity: 0.0
NBI 2009 T. Tauris 3
LMX
B
white dwarfmillisecond
pulsar
supernov
a
helium
star
neutron
star
3.99
1.6
1.3 1.6
1.6 0.303
1.10 days 14.95 Myr
80.75 days
15 Myr
1.3 1.59558 days 2.39 Gyr
4.11 days 2.29 Gyr
eccentricity: 0.93
eccentricity: 0.0
HMXB cartoon
supernova
helium
star
ZAM
S
Roche-lobe
overflow
neutron
How to make a double pulsar
Perfect playground for:
- population synthesis
- Monte Carlo simulations
Things you need to consider:
- stellar evolution (incl. He-star evoution)
- various binary interactions
(mass transfer, accretion, CE
tidal interactions, GWR)
NBI 2009 T. Tauris 4
HMX
B
young
pulsar
recycled
pulsar
neutron
star
common
envelope+ spiral-in
supernova
tidal interactions, GWR)
- asymmetric supernovae
standard Xstandard X--ray binariesray binaries
timescale: 10 – 10 yr5 6
- wind accretion
- beginning atmospheric
Roche-lobe overflow
NBI 2009 T. Tauris 5
timescale: 10 – 10 yr8 9- Roche-lobe overflow
BeBe--star Xstar X--ray binaryray binary
neutron
star
Be-starexpelled material
NBI 2009 T. Tauris 6
star
orbP
time
X-ray flux
Aspects of Roche-lobe overflow
Accretion ?
super-Eddington ?
jet ?
B-field, spin ?
Stability ?response of donor star ?
dynamically stable ?
NBI 2009 T. Tauris 7
B-field, spin ?
Mode of mass loss ?specific orbital angular momentum ?
Equipotential surfacesEquipotential surfaces
2
2
3
2
2
2
1
1r
r
GM
r
GM Ω−−−=Φ
effective gravitationaleffective gravitationalpotential:potential:
RocheRoche--lobe radius:lobe radius:
coco--moving framemoving frame
( )3/13/2
3/2
1ln6.0
49.0
q
a
RL
++=
RocheRoche--lobe radius:lobe radius:
Stellar evolution
RLO case B
RLO case C
NBI 2009 T. Tauris 9
RLO case A
RLO case B
22
2
ln
ln
ln
ln
M
R
M
R LLdonor
∂
∂≡∧
∂
∂≡ ζζ
Stability criteria for mass transferStability criteria for mass transfer
exponents of radius to mass:exponents of radius to mass: ζMR ∝
adiabatic or thermal response of the donor star to mass lossadiabatic or thermal response of the donor star to mass loss
initial stability criteria:initial stability criteria: ζζ ≤initial stability criteria:initial stability criteria: donorL ζζ ≤
2
2
2
22
2 M
MR
t
RR donorM
&& ζ+
∂
∂=
2
2
2 M
MR
t
RR LLM
LL
&& ζ+
∂
∂=
nuclear burningnuclear burning tidal spintidal spin--orbit couplingsorbit couplingsgravitational wave radiationgravitational wave radiation
LRR && =2 yields mass loss rateyields mass loss rate!!
The Orbital Angular Momentum Balance EquationThe Orbital Angular Momentum Balance Equation
orbital angular momentum2221 1 eaM
MMJorb −Ω=
The Orbital Angular Momentum Balance EquationThe Orbital Angular Momentum Balance Equation
|| prJ ×=
⇓⇓
logarithmic differentiationlogarithmic differentiation
(e=0, tidal circularization)(e=0, tidal circularization)
MMMMJa &&&&&& +
orb
ml
orb
ls
orb
mb
orb
gwr
orb
orb
J
J
J
J
J
J
J
J
J
J &&&&&
+++=
|| prJorb ×=
M
MM
M
M
M
M
J
J
a
a
orb
orb 21
2
2
1
1 222&&&&&& +
+−−=
1
4
21
5
3
5
32 −−= sa
MMM
c
G
J
J
orb
gwr&
Gravitational wave radiation:Gravitational wave radiation:
LowLow--mass stars:mass stars: magnetic wind!magnetic wind!⇒⇒ loss of spin angular momentumloss of spin angular momentum
In tight binaries the systemIn tight binaries the system
Magnetic braking:Magnetic braking:
342GMRkJmb −∝
&
In tight binaries the systemIn tight binaries the systemis tidally locked (synchronized)is tidally locked (synchronized)and spinand spin--orbit couplings operateorbit couplings operate
⇒⇒ loss of orbital angular momentumloss of orbital angular momentum P < 2 daysP < 2 daysorborb
M < 1.5 MM < 1.5 M22 oo..
SpinSpin--orbit couplings:orbit couplings:
orb
ls
J
J&
(as a result of nuclear burning or mass loss)(as a result of nuclear burning or mass loss)
-- fx . change in stellar moment of inertiafx . change in stellar moment of inertia
21
5MMaJorb
mb −∝
(uncertain)(uncertain)
2
2
22
1
)1(
M
M
q
J
J
orb
ml&&
+
+++=
γδβα
Mass loss:Mass loss:
αα: direct fast wind: direct fast wind
-- fx. in a relativistic jetfx. in a relativistic jet
ββ: mass ejected from accretor: mass ejected from accretor
(isotropic re(isotropic re--emission)emission)
( )0,||
||max
2
2
M
MM Edd
&
&& −=β
accretion efficiency: accretion efficiency: εε = 1= 1-- αα -- ββ -- δδ ((∂∂M = M = -- εε ∂∂M ) M ) NSNS 22
coplanar toroid withcoplanar toroid with
radius: radius: γγ aa22
δδ: mass loss via circumbinary: mass loss via circumbinary
Common envelope + spiralCommon envelope + spiral--in evolutionin evolution
dynamically dynamically ununstable mass transfer:stable mass transfer:
•• deep convective envelope of donor stardeep convective envelope of donor star
(rapid expasion in response to mass loss) (rapid expasion in response to mass loss)
•• M > M M > M
(orbit shrinks in response to mass loss)(orbit shrinks in response to mass loss)
donordonor accretoraccretor
⇓⇓ RunRunRunRunRunRunRunRun--------away processaway processaway processaway processaway processaway processaway processaway process!!!!!!!!!!!!!!!!
common envelopecommon envelope
drag force drag force →→ dissipation of orb. ang. mom. + deposition of E in the envelopedissipation of orb. ang. mom. + deposition of E in the envelopeorb orb
outcome:outcome:
•• huge reduction of orbital separationhuge reduction of orbital separationrejection of stellar enveloperejection of stellar envelope
merging of NS + coremerging of NS + core(Thorne(Thorne--Zytkow object / black hole)Zytkow object / black hole)
(NS orbiting a naked helium star)(NS orbiting a naked helium star)
Needed to explain observed tight systems!!
How to define M ?core
- quite important!
NBI 2009 T. Tauris 15Tauris & Dewi (2001)
Intermediate Mass XIntermediate Mass X--ray Binariesray BinariesWhy are so few IMXBs observed ?Why are so few IMXBs observed ?
HMXB: wind accretion (beginning atmospheric RLO)HMXB: wind accretion (beginning atmospheric RLO)
RLO is dynamically RLO is dynamically unstableunstable and a CE formsand a CE forms
210M M>
IMXB: wind accretion is too weak, andIMXB: wind accretion is too weak, and
RLO is often unstable (or very short)RLO is often unstable (or very short)
LMXB: stable RLO LMXB: stable RLO
21.5M M≤
Formation of millisecond pulsars (MSPs)Formation of millisecond pulsars (MSPs)
First binary pulsar discovered in 1974: PSR 1913+16 (today ~50 systems are known)First binary pulsar discovered in 1974: PSR 1913+16 (today ~50 systems are known)
First pulsar discovered in 1967 (today ~1800 pulsars are known) First pulsar discovered in 1967 (today ~1800 pulsars are known)
First millisecond pulsar discovered in 1982: PSR 1937+21 (P=1.5 msec)First millisecond pulsar discovered in 1982: PSR 1937+21 (P=1.5 msec)
Millisecond pulsar characteristics:Millisecond pulsar characteristics:
•• high incidence of binaries among millisecond pulsarshigh incidence of binaries among millisecond pulsars
•• rapid spin (P < 20 msec)rapid spin (P < 20 msec)
P-Pdot diagram
old neutron stars which have been old neutron stars which have been ””recycledrecycled””
via accretion of mass and angular momentumvia accretion of mass and angular momentum
•• relatively weak magnetic fields (B=10 relatively weak magnetic fields (B=10 -- 10 G)10 G)88 99
Single millisecond pulsarsSingle millisecond pulsars
All single millisecond pulsars are born in a binary system.
Once a recycled millisecond pulsar turns on its emission of ultra-relativistic particles, it is often able to completely evaporate its companion and thus end up as an isolated millisecond pulsar.
Observational evidence:Observational evidence:
eclipsing MSPs with 0.02 M companionseclipsing MSPs with 0.02 M companions
the ”planetary pulsar”, PSR 1257+12 the ”planetary pulsar”, PSR 1257+12
oo........
as an isolated millisecond pulsar.
Double degenerate systems:X-ray progenitor systems
NS+WD millisecond pulsars slow binary pulsars
LMXBs
millisecond X-ray pulsars (SAX 1808.8-3658)
WD+WD super-soft X-ray sources M > M 2 WD
novae-like systems M < M 2 WD
(CO) WD + (CO) WD
(AM CVn systems, RLO)
WD+NS old WD + young pulsar
(PSR 2303+46)
?
observed systems
WD+BH (not possible)
WD
NS+NS recycled pulsar + young pulsar
(PSR 1913+16)
HMXBs
BH+NS BH + young pulsar (no detections)
HMXBs (Cyg X-1)
NS+BH semi-recycled pulsar + BH
(no detections yet)
HMXBs
BH+BH (only detectable via gwr) HMXBs
BH+WD (no detections) SXTs
Tauris & Sennels (1999)
NS
Summary:Summary: To study the formation and evolution of compact binaries To study the formation and evolution of compact binaries
one must have a detailed knowledge stellar evolution and one must have a detailed knowledge stellar evolution and binary interactionsbinary interactions
Common envelope + spiralCommon envelope + spiral--in explain very narrow orbitsin explain very narrow orbits
Millisecond pulsars are old ”rejuvenated” pulsarsMillisecond pulsars are old ”rejuvenated” pulsars
HMXBs and LMXBs are wellknown b/c they are detectedHMXBs and LMXBs are wellknown b/c they are detected
–– IMXBs are not detectedIMXBs are not detected
Common envelope + spiralCommon envelope + spiral--in explain very narrow orbitsin explain very narrow orbits
Perfect scenario for Monte Carlo simulationsPerfect scenario for Monte Carlo simulations
