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INAF, Osservatorio Astronomico di Roma
XI Advanced School of Astrophysics, Brazil, 1-6 September 2002
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
Timescales relevant to evolution
• Nuclear tn
• Thermal tKH
~GM2/RL
• Dynamical td
~(2R3/GM)1/2
For stars it is generally
t d << t KH << t n
Binary evolution depends on the relation of these
quantities with the mass loss timescale
t mdot ~M/Mdot
The Eddington limit to mass accretion
The limiting
luminosity which can
be produced by
accretion is selflimited by a feedback
mechanism: namly by
the pressure exerted
from the radiation
produced by accretion
against the gravity of
the falling matter
Roche lobe
geometry
CM
[-GM1/(r1+RL1)2 ]
+[GM2/(r2-RL1)
2]+W R =0
2 L1
(reference frame with
origin in the mass
center, corotating
with the system at
velocity W=2 p /Porb).
RL1 is the distance of
L1 from the CM
Roche lobe: The
smallest closed
equipotential surface
containing both objects
Approximate expressions
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 q=M2/M1<0.8
(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
Total mass and angular
momentum evolution
If M2/M1<1, 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)
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 tKH~tmdot . Finally the
degenerate sequence is reached and the period
increases again. Pmin~80m if GR operates
Porb- Mdot evolution in CVs
Secular evolution: from
long to short periods
M1=1.4Mo
M2=0.8Mo
f_VZ=0.7
JMB=0 when M2
becomes fully
convective: M2
recovers thermal
equilibrium and
a Period Gap is
established
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!
Evolution with mass
transfer
If R2<R 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
Non stationary mass transfer
formulation
depends on the donor star parameters,
mass, radius Teff, photospheric density
Hp ~ 10 –4 R2 for low mass stars: thus the
Mdot is a sensitive function of R2R- R2 :
R2 must be computed with care
Stability of mass transfer
.
For a general discussion on M see Ritter 1995,
in Evolutionary Processes in Binary Stars
(CUP)
Stationary mass
transfer if:
z ad
zR
2 dln J/ dt
Tells which are the system angular
momentum primary losses
The denominator terms
can enhance Mdot by
destabilizing it
Includes all the terms: nuclear expansion,
thermal relaxation, illumination
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 < RRL
Lirr=Lx in Xray binaries
Lirr=L(pulsar) in MSPs
“heating” luminosity:
Fraction of Lirr impinging
The secondary star
f = possible screening factor
The reaction of convective stars to
mass loss
If Lh>Lnuc 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
The onset of mass transfer in Xray
binaries
Mass transfer due to AML
begins, with a given Mdot
Mdot increases
.
Lx= GMM/RNS
Lh~0.03Lx shields the
secondary star,
causing a radius increase
Runaway? Limitation in Mdot comes from the
thermal relaxation of the star
Effect of
irradiation
on the onset
of mass
transfer
M2=0.8Mo in
main
sequence
Full line:
with
irradiation
Dotted:
standard
evolution
Acceleration of mass transfer
when illumination is present
Onset of mass
transfer with
irradiation
Stationary phase due to
balance between thermal
relaxation and expansion
due to irradiation
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
Standard
Evolution
compared to
irradiation
Green:
CV type
evolution
Yellow:
irradiated
evolution
Porb
increases;
Mdot is 10100 times
larger
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)
Disc – Magnetic Field
Interaction
Disc Pressure .
proportional to M
Magnetic Pressure
Proportional to B2
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
The energy lost in
electromagnetic radiation and
in the relastivistic particle
beam comes from the
rotational energy of the
pulsar, which slows down
Pulsar power
.
Measuring P and P
allows to derive m
B~108Gauss for MSPs
.
M
Accretion conditions: 1
(Illarionov & Sunyaev 1975)
Accretion regime
R(m) < R(cor)
• accretion onto NS surface (magnetic poles)
• energy release L=GMM(dot)/R*
R(m) ~ f RA,
f ~1
Accretion conditions: 2
Propeller regime
R(cor) < R(m) < 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
Accretion conditions: 3
Radio Pulsar regime
R(m) > R(lc)
.
M
• no accretion
• disk matter swept away
by pulsar wind and pressure
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