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Accretion in Binaries II • Classes of X-ray binaries – – – – Low-mass (BH and NS) High-mass (BH and NS) X-ray pulsars (NS) Be/X-ray binaries (NS) • Distinguishing NS versus BH binaries X-Ray Binaries • Low mass: companion star mass less than one solar mass • High mass: companion star mass greater than one solar mass. Wind Fed Accretion racc bow shock matter collects in wake Wind Fed Accretion Matter in wind will accrete if its speed is less than the escape speed from the compact object at the radius of closest approach Vw = wind velocity Vx = velocity of compact object Rc = capture radius 2GM X Rc 2 2 VX VW Luminosity 2 m&w racc m& 4 Dorb L m&c 2 m&wc 2GM 2 4 2 vw 4 , if vw v X Dorb If a neutron star binary has the following parameters, Dorb=1012 cm, vw= 1000 km/s, 1 R 2 c 4 2 4 2 s & & L mwc 4 10 (mwc ) 4 Dorb vw Accreting Pulsars High mass X-ray binary Accretion in magnetic field Magnetosphere boundary Magnetopheric boundary, rM, is where the magnetic pressure balances the ram pressure of accreted matter pmag B2 pram v 2 8 Assuming spherical accretion and a dipole field with the dipole moment m = BSRS3, where RS and BS are the radius of the star and the field strength at the surface. m& rM 5.110 cm 16 10 g/s 8 2 / 7 M M 1 / 7 m 30 3 10 G cm 4/7 Accretion Torque Angular momentum transport m&v r & m&v rm Torque on star I GMm& 2 & & 2 P Note L and rM P P& 6/7 Find PL P Accretion Torque Pulse Period Variations What happens if the spin rate of the pulsar is faster than Keplerian rotation rate at the magnetospheric boundary? Corotation radius lies outside magnetopheric boundary Equilibrium Period The accreted matter ceases to transfer angular momentum to the neutron star when K (rM ) 1/ 2 r Peq 2 GM 3 M 2 R 1/ 2 (GM ) 8GMm& 12 3 / 14 BS6 / 7 For a maximum (Eddington) luminosity and typical neutron star mass and radius, we have Pmin B 9 0.002s 10 G 6/7 Emission Geometry Accreted plasma Shock front Hot spot Settling matter Pulse Profiles Landau Levels Quantization of energy due to magnetic field: Landau levels where p|| is the momentum of the electron parallel to the field, n is the quantum number, and Bcrit is the critical field, Bcrit me2c 3 4.4 1013 G eh For B << Bcrit, the spacing between adjacent levels is Ecyc En1 En B he B 11.6 keV 12 me c 10 G Cyclotron Lines X-Ray Pulsar Cen X-3 Pulses are modulated at orbital period of 2.09 days Distinguishing BH vs NS Mass function 3 3 P K sin i M 0 0 f0 2 (M X M 0 ) 2G 3 X f0 M X Compact object masses