INAF, Osservatorio Astronomico di Roma

XI Advanced School of Astrophysics, Brazil, 1-6 September 2002

* 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

* 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

Summary

• Nuclear n

• Thermal KH ~GM2/RL

• Dynamical d ~(2R3/GM)1/2

For stars it is generally

d KH n

Binary evolution depends on the relation of these quantities with the mass loss timescale

mdot ~M/Mdot

Timescales relevant to evolution

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

Roche lobe

geometry

[-GM1/(r1+RL1)2 ]+[GM2/(r2-RL1) 2]+2RL1=0

(reference frame with origin in the mass center, corotating with the system at velocity =2 /Porb). RL1 is the distance of L1 from the CM

Roche lobe: The smallest closed equipotential surface containing both objects

CM

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

M1=1.4Mo M2=0.8Mof_VZ=0.7JMB=0 when M2 becomes fully convective: M2 recovers thermal equilibrium and a Period Gap is established

Secular evolution: fromlong to short periods

Low mass X ray binaries secular evolution

WARNINGThe orbital periods and type of secondarycomponents 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:

ad

Rln J/t

Includes all the terms: nuclear expansion,thermal relaxation, illumination

Tells which are the system angular momentum primary losses

The denominator terms can enhance Mdot by destabilizing it

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

Lirr=Lx in Xray binariesLirr=L(pulsar) in MSPs

“heating” luminosity:Fraction of Lirr impinging The secondary star

f = possible screening factor

R2 is < RRL

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 AMLbegins, with a given Mdot

Lh~0.03Lx shields the secondary star,causing a radius increase

Lx= GMM/RNS

.

Mdot increases

Runaway? Limitation in Mdot comes from thethermal 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

irradiationStationary 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 detachesThe 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 10-100 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 Pressureproportional to M

. Magnetic PressureProportional to B2

Disc – Magnetic Field Interaction

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

Pulsar powerThe energy lost in electromagnetic radiation and in the relastivistic particle beam comes from the rotational energy of the pulsar, which slows down

Measuring P and P.

allows to derive B~108Gauss for MSPs

Accretion conditions: 1(Illarionov & Sunyaev 1975)

M.

Accretion regimeR(m) < R(cor)

• accretion onto NS surface (magnetic poles)• energy release L=GMM(dot)/R*

R(m) ~ RA, ~1

Accretion conditions: 2

M.

Propeller regimeR(cor) < R(m) <

R(lc)

• 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

M.

Radio Pulsar regime

R(m) > R(lc)

• 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