Magnetic Accretion on Neutron Stars

1. Magnetic Accretionon Neutron Stars Sudeep Das October 26, 2007

2. The Theme Rotating Neutron Stars in binary systems Disruption of disk by B-field High mass companions Matter channeled onto star Mass capture from winds/disks Transfer of angular momentum High B-fields Pulsed X-ray Emission >1 sec period HMXBs Accretion powered pulsars For review of accretion powered pulsars see, Psaltis 2006, in "Compact Stellar X-ray Sources", eds. W.H.G. Lewin, M. van der Klis Sudeep Das - Princeton University

3. Discovery Uhuru • Cen X-3(Giacconi et al., 1971) 4.8 sec pulses • Binary nature • (Schreier et al. 1972) • BeppoSAX, RXTE, Chandra, • XMM-Newton • ~ a few hundred known Sudeep Das - Princeton University

4. The Basic Picture • The qualitative picture was immediately understood. • (Pringle and Rees 1972; Davidson and Ostriker 1973; Lamb, Pethick and Pines 1973) Rotating NS High magnetic field channeling the flow onto hot spots Companion providing matter Various details of the scenario are still hot research topics! Sudeep Das - Princeton University

5. Bildsten et al. 1997 SPIN PERIOD (sec) ORBITAL PERIOD (days) The Zoo of high mass binaries Sudeep Das - Princeton University

6. Bildsten et al. 1997 SPIN PERIOD (sec) ORBITAL PERIOD (days) The Zoo of high mass binaries Be Transients Pulsar activity at periastron Sudeep Das - Princeton University

7. Bildsten et al. 1997 SPIN PERIOD (sec) ORBITAL PERIOD (days) The Zoo of high mass binaries Persistent Disk-fed Systems Sudeep Das - Princeton University

8. Bildsten et al. 1997 SPIN PERIOD (sec) ORBITAL PERIOD (days) The Zoo of high mass binaries Persistent Wind-fed Systems Sudeep Das - Princeton University

9. Spin-period EvolutionUnique behavior of transient and persistent sources Wind-fed Systems Persistent Disk-fed Systems Be Transients • Spin-up rate during outburst positively correlated with increase in accretion luminosity. • Explained by simple models like Ghosh and Lamb 1979 Bildsten et al. 1997 Sudeep Das - Princeton University

10. Spin-period EvolutionUnique behavior of transient and persistent sources Wind-fed Systems Persistent Disk-fed Systems Be Transients • Bimodal behavior with episodes of spin-up and spin-down; timescales ~ 10 days to 10 years. Transition ~ few days. • Modulation in: • mass transfer rate? • orientation of disk? • orbital velocity of gas? Cen X-3 Bildsten et al. 1997 Sudeep Das - Princeton University

11. Spin-period EvolutionUnique behavior of transient and persistent sources Wind-fed Systems Persistent Disk-fed Systems Be Transients • Similar to disk-fed in their rapid variations, but shows no secular increase /decrease in spin-period • Consistent with a random walk in spin/ white niose torque. Vela X-1 Bildsten et al. 1997 Sudeep Das - Princeton University

12. Quasi-periodic Oscillations • In several systems there are quasi-periodic oscillations in addition to the main pulsar period. • 1 mHz - 40 Hz. • Beating of orbital frequency and the stellar spin? (Finger et al. 1998) • Precessing disk warp? Power Spectral Density Fequency (Hz) Sudeep Das - Princeton University

13. Making sense of it all… Many Questions • How can the star spin-down while accreting? • There are large number of systems with long spin periods with very short spin-up time scales - Is this a paradox? • What explains the erratic behavior of the disk and wind-fed systems? • What is structure of the disk near the magnetized star? • What is force lifting the matter off the disc into the flow on the NS? • and so on … Two Main Approaches Analytical e.g. Ghosh and Lamb 1979 (More Recently) Numerical Simulations e.g. Romanova et al. 2002 Sudeep Das - Princeton University

14. Making sense of it all…The Analytical Approach Ghosh, P. and Lamb F. K., ApJ, 234, 206 (1979a, b) See also, Shapiro & Teukolsky, Chapter 15. Sudeep Das - Princeton University

15. Useful length scalesSpherical Infall -The Alfvén Radius Where does the magnetic field become dynamically important? A reasonable estimate is where Sudeep Das - Princeton University

16. Useful length scalesThe Alfvén Radius Relate to Luminosity Note: For a disk the calculation is a little more involved, but the characteristic radius comes out to be of the same order. • Far outside the Alfvén radius, magnetic field has almost no effect - Keplerian flow. • In a region near the Alfvén Radius, magnetic fields penetrate the disk via instabilities. • Inside the Alfvén Radius, the plasma is channeled by the field lines onto the stellar surface. Sudeep Das - Princeton University

17. Useful length scalesThe Alfvén Radius These spots of intense radiation appear as hot spots and for an oblique rotator gives rise to the pulsar effect. Sudeep Das - Princeton University

18. Useful length scalesThe Co-rotation Radius Another important radius is where the spin angular velocity of the star equals the Keplarian angular velocity, Angular velocity Distance from Star Sudeep Das - Princeton University

19. Spin-up/Spin-downAlfvén vs Co-rotation Radius Scenario 1: Most common scenario “ Slow Rotator” The plasma is sweeping the magnetic field lines fasters than the stellar spin in the transition region. Transfer of angular momentum via magnetic torques to the star - enhancesspin-up. Angular velocity Distance from Star Sudeep Das - Princeton University

20. Spin-up/Spin-downAlfvén vs Co-rotation Radius “ Fast Rotator” The plasma is sweeping the magnetic field lines slower than the stellar spin. Transfer of angular momentum from the star via magnetic torques - sets up spiral waves in the plasma Decreases spin-up May even spin-down. Scenario 2: Angular velocity Distance from Star Sudeep Das - Princeton University

21. Spin-up/Spin-downAlfvén vs Co-rotation Radius Scenario 3: “ The Propeller Regime” Steady accretion not possible due to the centrifugal barrier. Mass gets ejected. Angular velocity Distance from Star Sudeep Das - Princeton University

22. Period -Luminosity Relation The most powerful prediction of the Ghosh and Lamb theory is a stringent relation between the spin-up rate, the period and luminosity, having the form, Log(-dP/dt) Most observed systems seem to obey this tight relationship. Wind accretor Log(P L3/7) (See Shapiro Teukolsky, Chap 15) Sudeep Das - Princeton University

23. Making sense of it all…Summary - The Analytical Approach • The notion of disk magnetosphere interaction to explain X-ray pulsars is basically correct. • Predicts a spin-up rate - period - luminosity relation that is roughly obeyed by observed systems. • Provides a mechanism for spin braking or spin-down even when accreting. • Seemingly paradoxical systems with long spins periods but extremely short spin-up times can be explained by assuming that they underwent periods of large spin-down torques. • Provides a quantitative picture for the expectation that stellar spin will eventually settle down to the Keplerian spin at the co-rotation radius, where the net torque would be zero. • Explains why stable accretion is not possible for rapidly spinning systems. • If modulation of accretion rate is assumed, this picture naturally explains the erratic beahvior in disk-fed persistent systems. Sudeep Das - Princeton University

24. Making sense of it all…The Simulation Approach Romanova et al. ApJ, 578,1,420 (2002) Interpretation of spin-up/ spin-down mechanisms. Forces responsible for channeling matter into funnel flow. Sudeep Das - Princeton University

25. Setting upGrid and Initial conditions Minimize initial B-braking. Higher resolution at center. Sudeep Das - Princeton University

26. Funnel FlowWhere? For a wide range of parameters, the FF forms near the Alfvén radius, where magnetic pressure is comparable to thermal and kinetic pressure of the disk matter. (as predicted in GL 79a, b) Sudeep Das - Princeton University

27. Funnel FlowA Closer Look Temperature Density Pressure Distance from Star Study variation of physical quantities along this line. Gas compression near the star Sudeep Das - Princeton University

28. Funnel FlowA Closer Look Alfvén Mach Number Study variation of physical quantities along this line. Poloidal velocity strongly sub-Aflvénic Sudeep Das - Princeton University

29. Funnel FlowA Closer Look Angular velocity and twist. Twisting small (wang 1997) Slightly -ve angular velocities due to small inclination of B field in the direction of rotation. (Ghosh et al 1977) Study variation of physical quantities along this line. Sudeep Das - Princeton University

30. Funnel FlowWhat gets matter into the FF? Forces parallel to flow centrifugal Magnetic Pressure Gravity No B-Levitation Pressure Gradient Lifts matter into flow Gravity provides acceleration Study variation of physical quantities along this line. Sudeep Das - Princeton University

31. Star-Disk interactionSpin up - Spin down Angular velocity Angular velocity profile In the FF, B-field lines rotate with star In the braking region, B- lines are dragged along by matter Smaller than Keplerian Sudeep Das - Princeton University

32. Star-Disk interactionSpin up - Spin down Spin-Up Most of the L is carried by the Field lines(twist) Matter carries only 1% of the L flux For a slow rotator flux is positive and the star spins up Sudeep Das - Princeton University

33. Star-Disk interactionSpin up - Spin down Spin-Down As predicted by GL79b, For a fast rotator, these simulations show And the angular momentum flux is negative. <0 Mass gets accreted Star spins down! Sudeep Das - Princeton University

34. Star-Disk interactionTorquelss accretion? According to GL79b, at some angular velocity of the star Ωcrit, positive magnetic torque associated with the region r < rco cancels the negative magnetic torque associated with the region r > rco and the star can accrete without changing its angular momentum. This is also achieved in the simulations! ~ 0 Sudeep Das - Princeton University

35. Making sense of it all… Summary - The Simulation Approach • Detailed investigation of the disk-magnetosphere interaction. • Funnel flows (FF) are powered by pressure gradients and gravity. • Spin-up spin-down scenarios as expected from analytical calculations. • Torqueless accretion possible. • Most angular momentum is transferred via twisted fields in the FF. • Detailed studies of numerous other situations not amanable to analytical calculations have been done. See other Romanova et al, Kulkarni et al papers. Sudeep Das - Princeton University