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A few basic concepts of binary stellar evolution
F. D'Antona
INAF, Osservatorio Astronomico di Roma
XI Advanced School of Astrophysics, Brazil, 1-6
September 2002
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Summary

• Fundamentals of binary evolution
• Roche lobe and mass transfer
• Timescales of mass transfer
• Role of angular momentum losses
• Onset of mass transfer in the case of
  iradiation and its influence on low mass Xray
  binary secular evolution
• Pulsars and the spin-up phase
• Modalities of mass transfer towards neutron
  stars

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Timescales relevant to evolution

• Nuclear tn
• Thermal tKH GM2/RL
• Dynamical td (2R3/GM)1/2
• For stars it is generally
• t d ltlt t KH ltlt t n
• Binary evolution depends on the relation of these
  quantities with the mass loss timescale
• t mdot M/Mdot

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The Eddington limit to mass accretion
The limiting luminosity which can be produced by
accretion is self-limited by a feedback
mechanism namly by the pressure exerted from the
radiation produced by accretion against the
gravity of the falling matter
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Roche lobe geometry
-GM1/(r1RL1)2 GM2/(r2-RL1) 2W2RL10
(reference frame with origin in the mass center,
corotating with the system at velocity W2 p
/Porb). RL1 is the distance of L1 from the CM
Roche lobe The smallest closed equipotential
surface containing both objects
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Approximate expressions
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Definition of Roche lobe radius
It is the radius of the sphere which has the same
volume as the Roche lobe of the star. For the
secondary component in a binary in which
qM2/M1lt0.8 (from Paczynski 1971)
In binary computations, we use spherical stars,
so the evolution is followed by requiring a
comparison between stellar radius and Roche lobe
radius
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Total mass and angular momentum evolution
If M2/M1lt1, the orbital separation a increases
with mass transfer. In cases of unevolved mass
losing components (e.g. CVs) this implies that
the orbital angular momentum can not be constant
Gravitational radiation (Landau Lifshitz 58
Magnetic braking (Verbunt Zwaan 81)
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Standard evolution driven by AML cataclysmic
binaries
the secondary quasi-MS star evolves first down
along the MS, then its radius becomes larger than
the MS radius, when tKHtmdot . Finally the
degenerate sequence is reached and the period
increases again. Pmin80m if GR operates
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Porb- Mdot evolution in CVs
M11.4Mo M20.8Mo f_VZ0.7 JMB0 when M2 becomes
fully convective M2 recovers thermal equilibrium
and a Period Gap is established
Secular evolution from long to short periods
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Low mass X ray binaries secular evolution
WARNING The orbital periods and type of
secondary components are similar to those of CVs,
so the first idea is that they evolve similarly,
through loss or orbital angular momentum, from
long to short periods. Actually this is probably
not true!
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Evolution with mass transfer
If R2ltR 2,R, no mass transfer. Simplest
prescription R2,R2,R, enforced in the structure
computations. This allows to follow stationary
mass transfer phases. Second approximation
Lubow and Shu 1975 subsonical and isothermal
mass flow in optically thin layers, reaching
sound velocity at L1, or adiabatic in optically
thick layers
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Non stationary mass transfer formulation
Hp 10 4 R2 for low mass stars thus the Mdot
is a sensitive function of R2R- R2 R2 must be
computed with care
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Stability of mass transfer
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Tells which are the system angular momentum
primary losses
Includes all the terms nuclear
expansion, thermal relaxation, illumination
The denominator terms can enhance Mdot by
destabilizing it
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The mass transfer with irradiation
In some important cases, the secondary star is
immerged in the radiation field of the primary
and this produces an effect on its radius
derivative
R2 is lt RRL
LirrLx in Xray binaries LirrL(pulsar) in MSPs
heating luminosity Fraction of Lirr impinging
The secondary star
f possible screening factor
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The reaction of convective stars to mass loss
If LhgtLnuc the radiation field shields the star
and does not allow to the nuclearly energy
generated luminosity to freely escape from the
surface. If the star has a convective envelope,
it expands on the thermal timescale at its bottom
Although the long term effect of illumination is
not easy to be understood, the short term effect
on the onset of mass transfer is clear mass
transfer is enhanced
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The onset of mass transfer in Xray binaries
Mass transfer due to AML begins, with a given Mdot
Lh0.03Lx shields the secondary star, causing a
radius increase
Mdot increases
Runaway? Limitation in Mdot comes from
the thermal relaxation of the star
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Effect of irradiation on the onset of mass
transfer
M20.8Mo in main sequence Full line with
irradiation Dotted standard evolution
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Acceleration of mass transfer when illumination
is present
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Onset of mass transfer with irradiation
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Mass transfer with irradiation will be subject
to instability
If, for any reason, there is a shielding of Lx,
so that Lh decreases, the radius of the secondary
will tend to decrease, Mdot will decrease and,
this time, this is a runaway situation and the
system detaches
The system comes back again to a semidetached
stage, but this will occur on the timescale of
the systemic AM losses detached phases may be
much longer than mass transfer phases
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Standard Evolution compared to irradiation
Green CV type evolution
Yellow irradiated evolution
Porb increases Mdot is 10-100 times larger
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How irradiation helps in X-ray binaries

• The orbital period increases as observed
• The mass loss rate is larger
• The number ratio LMXB/MSPs is more reasonable
• The system evolves through alternated high Mdot
  phases and detached phases which may help in
  explaining why radio MSPs do not accrete too much
  mass (see later)

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Disc Magnetic Field Interaction
Magnetic Pressure Proportional to B2
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Pulsars spin up
The accreting matter transfers its specific
angular momentum (the Keplerian AM at the
magnetospheric radius) to the neutron
star L(GmRm)1/2
The process goes on until the pulsar reaches the
keplerian velocity at Rm (equilibrium period)
The conservation of AM tells us how much mass is
necesssary to reach Peq starting from a
non-rotating NS. A trivial approximation gives
0.9Msun
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Pulsar power
The energy lost in electromagnetic radiation and
in the relastivistic particle beam comes from the
rotational energy of the pulsar, which slows down
allows to derive m B108Gauss for MSPs
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Accretion conditions 1
(Illarionov Sunyaev 1975)
.
M
Accretion regime R(m) lt R(cor)

• accretion onto NS surface (magnetic poles)
• energy release LGMM(dot)/R

R(m) f RA, f 1
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Accretion conditions 2
Propeller regime R(cor) lt R(m) lt R(lc)
.
M

• centrifugal barrier closes (B-field drag
  stronger than gravity)
• matter accumulates or is ejected from R(m)
• accretion onto R(m) lower gravitational energy
  released

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Accretion conditions 3
Radio Pulsar regime R(m) gt R(lc)
.
M

• no accretion
• disk matter swept away
• by pulsar wind and pressure

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We have set the stage!
In the following, we can talk about the MSP
population of globular clusters. Then we go back
to our favourite globular cluster and show that
it harbors the most incredible pulsar, an MSP in
an interacting binary