Astrophysics 2: Stellar and Circumstellar Physics

1
Astrophysics 2Stellar and Circumstellar Physics
6. Stellar Evolution in Binaries
http//www.arc.hokkai-s-u.ac.jp/
okazaki/astrophys-2/
2
Outline of Part 3

• Stellar Evolution in Binaries
• X-ray Binaries (1)
• X-ray Binaries (2)
• X-ray Binaries (3)

3
6.1 Complexities in binary evolution
Stellar evolution in binaries is much more
complicated than the evolution of single stars,
mainly because of the presence of mass exchange
between stars (via the Roche lobe overflow).
Other processes, e.g., the common envelope
phase and supernova kicks, cause extra
complications in binary evolution.
4
6.2 Roche lobe overflow
6.2.1 The Roche potential
The effective potential (Roche potential) in a
frame comoving with binary rotation
5
Roche potential
The Roche lobe (the region of space around a star
in a binary within which orbiting material is
gravitationally bound to that star)
6
Roche potential (2)
Roche lobe

• Mass ejection from the binary through

7
Roche-lobe overflow
If the initially more massive star (the donor)
evolves to fill its Roche-lobe, either because of
expansion of its envelope or because the binary
shrinks sufficiently as a result of orbital
angular momentum losses, the unbalanced pressure
at will initiate mass transfer (Roche-lobe
overflow, RLO) onto its companion star (the
accretor).
8
Classification of RLO
Case A The system is so close that the donor
star begins to fill its Roche-lobe during
core-hydrogen burning. Case B Overflow begins
after the end of core-hydrogen burning but before
helium ignition. Case C Overflow begins during
helium shell burning or beyond.
9
Evolutionary tracks of single stars
3
4
1
2
10
Evolutionary change of the radius of a 5
star
AGB
Case C
4
RGB
Case B
2
MS
1
Case A
3
11
6.2.2 Loss of Orbital Angular Momentum
For simplicity, consider a circular binary. Then,
the orbital angular momentum of the binary is
given by
12
is governed by

• gravitational wave radiation
• magnetic breaking
• spin-orbit coupling
• mass loss from the system

i.e.,
13
Accretion efficiency of the accreting star
14
6.2.3 Stability of Roche-lobe overflow
The stability and nature of the mass transfer
depends on the response of the mass-losing donor
star and of the Roche-lobe, and is determined by
a comparison of the changes in radii of the donor
star and the Roche-lobe.
15
Response of the Roche-lobe
accretion efficiency
16
(No Transcript)
17
Accretor more massive than donor
Donor star shrinks, Roche-lobe expands
RLO stable
Donor more massive than accretor
Donor star shrinks, Roche-lobe shrinks
RLO can be unstable
18
6.3 Common Envelope Evolution
There is strong evidence of orbital shrinkage
Likely scenario
Formation of a common envelope
Large froctional torques
Large ang. mom. loss
Spiral-in
19
Estimation of the orbital shrinkage
binding energy of donors envelope
Change in orbital energy

20
Envelope easily ejected
(RGB)
(AGB)


Stars coalesce
(Dewi Tauris 2000 Tauris Dewi 2001)
21
6.4 Supernova kicks
Observations

• Runaway pulsars

• Large eccentricities in high-mass X-ray binaries

Asymmetric supernova explosion
Many binaries were destructed. Survived binaries
got large eccentricities.
22
6.5 Examples of binary evolution
Evolutionary model of Type Ia supernovae
23
(No Transcript)
24
Evolutionary model of low mass X-ray binaries
(Tauris van den Heuvel 2003)
ZAMS
RLO
CE spiral-in
25
He star
SN
NS
LMXB
WD
ms PSR
26
Evolutionary model of high mass X-ray binaries
(Tauris van den Heuvel 2003)
ZAMS
RLO
He star
SN
NS
27
HMXB
CE spiral-in
He star RLO
2nd SN
young PSR
recycled PSR