Magnetic interaction in ultra-compact binary systems

1. Magnetic interaction in ultra-compact binary systems 报告人：徐 倩 Astron.Astrophys.2009 Vol.9 No.7,725-744

2. Outline • 1. Introduction • 2. Orbital dynamics in compact bianries • 3. Unipolar induction in compact binaries • 4. Orbital evolution of unipolar-inductor compact binaries • 5. Further

3. Introduction • binary : double-star,star-planet,planet-moon system (under gravity) a—seperation of the two components P0—orbital period “0”,”1”,”2”—the orbit,the primary star and the secondary star,respectively

4. Introduction P0<600s Binaries: degenerate stars or black holes • short-period systems,ultra-compact double-degenerate systems(UCDs) • UCDs: combination of white dwarfs,neutron stars or black holes • UCDs short-period systems,two white dwarfs

5. Orbital dynamics in compact binaries • AM CVn binaries,direct-impact mass-transfer double degenerates(Algol binaries) orbital dynamics,orbital evolution:mass transfer • Magnetic interacting UCDs angular momentum redistribution orbital dynamics,orbital evolution: internal energy dissipation

6. Orbital dynamics in compact binaries • UCDs:strong sources of gravitational waves compact orbits • The power of their gravitaional radiation(assuming an orbital eccentricity e=0):

7. Fig.1 Power of gravitional waves from white-dwarf pairs,normalized to the solar bolometric luminosity,as a function of the primary white-dwarf mass M1,for orbital periods of 600s(solid lines) and 300s(dotted lines).Each curve corresponds to a value of the secondary white-dwarf mass,labeled in solar-mass unit.

8. The evolution of the binary orbit: redistribution of angular momentum within the system,loss of angular momentum from the system • The processes: assume

9. Orbital angular momentum is extracted from the binary only through the emission of gravitational waves. Rate of orbital angular-momentum loss:

10. If the stellar spins are decoupled from the orbital rotation: It is clear that: the binary orbit is always spun up.return

11. If the stellar spins are coupled with the orbital rotation: angular momenta can be injected from the orbit into the stars ‘ideal’ case,synchronous rotation return

12. In reality,perfect synchronism,hard to achieve for any binary system Spin-orbit asynchronism,despite tidal forces,magnetic interaction • Mass exchange,mass loss of system,complicated dynamics • Next: slightly asynchronous UCDs,magnetic interaction,mediates angular momentum exchange,stars and orbit

13. Unipolar induction in compact binaries • Basic principle: a non-magnetic conducting body ,linear size R,traverse a magnetic field B,velocity v,e.m.f.Φ~R|E|, • The e.m.f. across the non-magnetic WD in orbit with a magnetic WD:18 (anti-clockwise direction is positive)

14. Fig.2 Schematic illustration of the unipolar-inductor model for white-dwarf pairs.As the system revolves,a large e.m.f. is induced across the non-magnetic white dwarf and currents are driven between the two stars.The resistance in the atmospheric layers of the white dwarfs causes energy dissipation.Electromagnetic waves are emitted from the heated white-dwarf atmosphere.

15. f is the fractional effective area of the magnetic poles(hot spots) on the surface of the magnetic white dwarf • f<<1, • electrical circuit model: • non-magnetic white dwarf electric generator or a battery(with a small internal resistance) • plasmas conducting circuit wires • magnetic white dwarf resistive load

16. What actually drives the electric currents? The energy reservoir is in fact the binary orbit. • Similar to accretion,the ultimate energy source in a unipolar-inductor white-dwarf pair is still the gravitational potential

17. Orbital evolution of unipolar-inductor compact bianries • Unipolar inductor model,asynchronous,orbital evolution,neither by equations in page 10,11 • Additional energy dissipation needs to be taken into account • consider: non-magnetic white dwarf,tidally locked to synchronous rotation with the orbit

18. Further 13 Synchronizaton(unipolar-induction) time scale: η depends on the density distribution and shape of the white dwarf Merging time scale: WD coalescence, gravitational radiation losses

19. Further • Unipolar induction phase,X-ray pulses,over system lifetime before coalescence occur,even • Compact white-dwarf pairs,strong sources of gravitational radiation • Without taking into account contribution of unipolar induction,gravitational signal,de-coherent,short timescale,posing problem in UCD detection

20. Thank you!