1. Diffusive Particle Acceleration in Shocked, Viscous Accretion Disks Peter A. Becker (GMU) Santabrata Das (IIT) Truong Le (STScI)

2. Diffusive Particle Acceleration in Shocked, Viscous Disks Talk Outline o o Why do we frequently see outflows from radio-loud AGNs and galactic black-hole candidates? o o How are these outflows produced, powered, and collimated? o o Can shock acceleration in the accretion disk play a role?

3. Diffusive Particle Acceleration in Shocked, Viscous Disks Talk Outline o o How would the presence of a shock affect the dynamical structure and stability of the disk? o o How is particle acceleration in the disk related to supernova- driven cosmic ray acceleration? o o Conclusions and plans for future work

4. o o Advection-dominated inflows are frequently used to model underfed black-hole accretion o o The stability of these models is called into question by large Bernoulli parameters o o The Bernoulli parameter is always positive in ADAF models without outflows – hence these are not self-consistent o o Can shock-powered outflows carry away excess binding energy, and stabilize the disk? Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Background Narayan, et al., ApJ, 476, 49, 1997

5. o o Shocks in luminous X-ray disks will heat the gas, but not accelerate particles – the gas is too dense o o Previous work obtained shock solutions in inviscid ADAF disks o o Hot, tenuous ADAF disks are ideal sites for particle acceleration o o When dynamically possible, shocks should be the preferred solutions according to the Second Law of Thermodynamics Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Background Le & Becker, ApJ, 632, 476, 2005

6. o o Narayan et al. (1997) modeled viscous ADAF disks without shocks Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Background sonic point sub-Keplerian Narayan, et al., ApJ, 476, 49, 1997

7. Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Background o o Using the Narayan equations, we showed that shocks can occur in viscous disks Das, Becker, & Le, ApJ, 702, 649, 2009

8. o o Using the Narayan equations, we showed that shocks can occur in viscous disks Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Background Das, Becker, & Le, ApJ, 702, 649, 2009

9. o o But are shocks really present in disks?? o o General relativistic hydrodynamical models confirm the presence of shocks – but these models do not consider the consequences for nonthermal particle acceleration Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Background De Villiers & Hawley, ApJ, 599, 1238, 2003 Shock forms at funnel wall – centrifugal barrier

10. Diffusive Particle Acceleration in Shocked, Viscous Disks o ADAF disks contain hot, tenuous gas o Collisionless plasma allows Fermi acceleration of relativistic particles o Small fraction of particles get boosted via multiple scatterings with MHD waves Theory: Background

11. Diffusive Particle Acceleration in Shocked, Viscous Disks o Most efficient acceleration mechanism is first-order Fermi at a discontinuous shock o Shock-driven acceleration is augmented by additional acceleration due to bulk compression of the background gas Theory: Background Don Ellison, NCSU

12. Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Background

13. Diffusive Particle Acceleration in Shocked, Viscous Disks n Mass and Angular Momentum Transport n Radial momentum conservation n Torque and viscosity Theory: Conservation Equations

14. Diffusive Particle Acceleration in Shocked, Viscous Disks n Keplerian angular velocity in Pseudo-Newtonian potential n Disk half-thickness and sound speed n Angular momentum gradient Theory: Conservation Equations

15. Diffusive Particle Acceleration in Shocked, Viscous Disks n Total energy transport n Thermal energy density n Entropy variation Theory: Conservation Equations Jumps at shock

16. Diffusive Particle Acceleration in Shocked, Viscous Disks n Combining energy and angular momentum transport equations yields n Combining torque and angular momentum transport equations yields n These are supplemented by the wind equation Theory: Differential Equations Jumps at shock

17. Theory: Critical Behavior Diffusive Particle Acceleration in Shocked, Viscous Disks n The Wind Equation can be written in the form n The Numerator and Denominator functions are

18. Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Critical Conditions n Setting N=0 and D=0 yields the critical conditions n These must be satisfied simultaneously so that the flows passes smoothly through the critical point (or points)

19. Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Transport Equation n Transport equation n Specific Flux n Convection-Diffusion Equation Fermi acceleration Spatial diffusion Source term Comoving time derivative Escape term Localized to shock High-energy tail of Maxwellian... or pre-accel due to reconnection at shock?

20. Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Transport Equation n Eigenfunction expansion n ODE for Separation Functions n Eigenfunction Orthogonality n Expansion Coefficients gives high- energy slope

21. Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Results n Energy jump condition n Velocity jump condition n Injected energy E 0 = 0.002 ergs n Injection from Maxwellian tail? Or via pre-acceleration due to reconnection at shock? Injected proton Lorentz factor 1.3 Injected proton Lorentz factor 1.3

22. Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Results o M87 parameters: o Sgr A * parameters: x sun sun /year L jet = x ergs/sec x sun x sun /year L jet = x ergs/sec

23. Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Results gives high- energy slope shock (smooth) (shock), (smooth) o Eigenvalues

24. Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Results o Greens function inside the disk

25. Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Results o We can compute the number and energy densities by integrating the Greens function, or by solving independent equations o Solution accuracy is confirmed

26. Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Results o Outflowing particle spectrum from shock location L=5.5 x 10 43 ergs/sec L=5.0 x 10 38 ergs/sec =6.3 (proton) =10 4 (electron) =5.9 (proton) =10 4 (electron)

27. o Interesting to compare with equivalent cosmic-ray case o Supernova-driven plane-parallel shock with compression ratio R has spectral index o Mean energy of SN-driven shock is Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Results R=2.04, CR =5.90 R=2.04, CR

28. o Disk Stability: Bernoulli parameter o Shock-driven outflow carries away energy, allowing the remaining gas to accrete Diffusive Particle Acceleration in Shocked, Viscous Disks Theory: Results

29. Diffusive Particle Acceleration in Shocked, Viscous Disks o Compare particle pressure with background pressure: Particle pressure is significant near shock Theory: Results

30. Diffusive Particle Acceleration in Shocked, Viscous Disks o Examine vertical momentum flux: Diffusive vertical momentum flux drives escape

31. Diffusive Particle Acceleration in Shocked, Viscous Disks Conclusions o Diffusive shock acceleration in the disk can power the energetic outflows in M87 and Sgr A* o Green's function for the accelerated particles is obtained using eigenfunction expansion – and verified o Accretion-driven shock acceleration is similar to the standard model of supernova-driven cosmic-ray acceleration o Both processes efficiently channel energy into a small population of relativistic particles o The spectrum is a relatively flat power-law, much harder than would be expected for a SN-driven shock with the same compression ratio o The disk environment plays a key role in enhancing the efficiency of the acceleration process

32. Diffusive Particle Acceleration in Shocked, Viscous Disks o In two-fluid model, multiple dynamical modes may occur o Possible occurrence of sharp sub-shocks, with state transitions? o May be relevant for Sgr A* X-ray flares – 10 fold increase in X-rays for a few hours...possible state transition? Conclusions

33. Diffusive Particle Acceleration in Shocked, Viscous Disks o In two-fluid model, multiple dynamical modes may occur o Possible occurrence of sharp sub-shocks, with state transitions? Conclusions One shock solution 3 shock solutions 2 shock, 1 smooth solutions One smooth solution Becker & Kazanas, ApJ, 546, 429, 2001

34. Diffusive Particle Acceleration in Shocked, Viscous Disks o In two-fluid model, multiple dynamical modes may occur o Possible occurrence of sharp sub-shocks, with state transitions? Conclusions 1 smooth solution Becker & Kazanas, ApJ, 546, 429, 2001

35. Diffusive Particle Acceleration in Shocked, Viscous Disks o In two-fluid model, multiple dynamical modes may occur o Possible occurrence of sharp sub-shocks, with state transitions? Conclusions 1 shock solution Becker & Kazanas, ApJ, 546, 429, 2001

36. Diffusive Particle Acceleration in Shocked, Viscous Disks o In two-fluid model, multiple dynamical modes may occur o Possible occurrence of sharp sub-shocks, with state transitions? Conclusions 2 shock solutions, plus 1 smooth solution Becker & Kazanas, ApJ, 546, 429, 2001

37. Diffusive Particle Acceleration in Shocked, Viscous Disks o In two-fluid model, multiple dynamical modes may occur o Possible occurrence of sharp sub-shocks, with state transitions? Conclusions 3 shock solutions Becker & Kazanas, ApJ, 546, 429, 2001

38. Diffusive Particle Acceleration in Shocked, Viscous Disks o The shock stabilizes the disk by reducing the Bernoulli parameter (are flows convectively stable??) o Excess binding energy is channeled into outflows o Particle pressure exceeds background pressure near the shock o Particle source at shock (local reconnection? Pickup from Maxwellian? We need a trans-relativistic model.) o Relax test-particle approximation and include dynamical effect of particles (two-fluid model) o Allow the outflow to carry away angular momentum o Compute primary and secondary radiation o Include the effect of stochastic wave scattering Could be important in CR shocks too, especially for trans-relativistic model Future Work Conclusions