Particle Acceleration in Compact Objects

1. Particle Acceleration in Compact Objects Demosthenes Kazanas NASA Goddard Space Flight Center

2. There is plenty of evidence for the presence of particle acceleration in compact objects: • High (and low) energy emission from pulsars. • High (and low) energy emission from plerionic SN remnants. • Emission from 109 – 1027 Hz in Active Galactic Nuclei.

3. Outline Direct particle acceleration by electric fields (in EM gaps). Bulk acceleration of particles in MHD flows. Stochastic Acceleration (shocks, turbulence). Dynamic Effects of accelerated particles (effects on accretion disks, outflows).

4. The Seven Highest-Confidence Gamma-ray Pulsars

5. Broad-band spectra • Power peaked in g-rays • No pulsed emission above 20 GeV • Increase in hardness with age • High-energy turnover Increase in hardness with age • Thermal component appears in older pulsars

8. Must distinguish between acceleration of individual particles and acceleration in bulk. • These two are generally distinct processes, however, there are cases in which they are intimately related. • The most obvious evidence of the presence of acceleration of particles is that of pulsars.

9. Rotating Magnetic Field

11. Formation of an outflow • The rotation of the highly conducting neutron star crust generates enormous potential differences over the surface • above the surface => very large outward-acting unbalanced electric stresses • A charged magnetosphere is spontaneously built up in order to short-out the parallel component of the electric field (Goldreich-Julian 1969):

12. The density of charge carriers can be easily estimated: This density co-rotates with the pulsar out to the light cylinder. Beyond that the magnetic stresses cannot confine the plasma and must open-up, i.e. the dipole is not a valid magnetospheric solution

13. The flux of the open field lines at thelight cylinder defines the polar cap of thepulsar, as the region of the last open field line

14. The pulsar slow down can then be worked out in a simple way. It does not require the pulsar to be misaligned; the same slow down works out for a purely aligned magnetosphere.

15. Surface Fields and Currents

16. The presence of a sufficiently dense plasma cancels all parallel E. Discrepancy between the actual charge density from that of GJ leads to gaps (Polar Cap; Outer Gap models). Particles can be accelerated at gaps and lead to the creation of photons. The resulting spectra depend on the ensuing interactions (A. Harding) The EM potentials available are of order of 1018 (P/ms) B15eV. As such they could produce galactic cosmic rays up to the energy of ankle (Arons 02).

17. The problem of pulsar magnetospheric emission, as is the case with all problems that involve magnetic fields (which cannot be shorted out) is a global one. One has to solve for the currents and the resulting magnetic fields over all space before we can decide the dynamics and radiation emission from a pulsar.

18. The magnetosphere is determined by the balance between the current and electro- static forces in the magnetosphere. These are given by the “Pulsar Equation”

19. The parameters involved are • Poloidal electric current: • Magnetic flux: • Force-free: • Space charge density:

20. Contopoulos, Kazanas & Fendt 1999; Gruzinov 2005

21. The solution is smooth, contains a return Current, it contains a zero charge line and it provides the wind asymptotic structure. Emission is expected at places where MHD is violated (polar cap, zero charge line, return current boundary, but not the Light Cylinder).

22. For the geometry of the magnetic lines beyond the Light Cylinder (split monopole) for which Bp= 1/R2, Bf= 1/ R , r = 1/R2. Therefore their ratio, s ~106 near the LC should be independent of the radius R . However, the spectra of the Crab nebula need a value s ~3 10-3 to fit the observed spectrum and for Vela one needs s ~1. Pulsar Winds/The s-Problem

23. The asymptotic (split) monopole geometry of CKF allows a crack at this problem: The energy conservation equation along a field line has the form: While the flux freezing condition reads

24. Under force-free conditions the energy equation reads Leading eventually to: (Contopoulos & DK 2002)

25. Under conditions of a monopole geometry the Lorentz factor of the flow increases linearly with distance. This happens as long as the effects of inertia are negligible. Beyond this point the field geometry should deviate From monopolar and possibly part of it collimate and part form an equatorial wind. The wind terminates at a shock which is responsible for the nebular emission. (The extent of monopole geometry is debatable. It may extend only up to the fast magnetosonic point; then the maximum g will be only ~s1/3 ).

26. Plerion Components

27. Linearly increase in Lorentz factor is a property of general MHD flows of geometries different from monopolar (Vlahakis&Konigl 2001) Vlahakis & Konigl 2001

28. First axisymmetric wind solutions by Blandford & Payne; extended to Relativistic case by Li, Chieuh, Begelman (92) and Contopoulos (94). Solutions known only for self-similar geometry. The MHD outflow acceleration and the s-Problem are related issues. They demand the simultaneous solution of the conservation equations along with the transverse force balanc.e

29. Flow acceleration depends on assumptions used. LCB find logarithmic acceleration with height. Contopoulos (94) finds final velocity similar to that at the accretion disk at the base of the flow (Vlahakis & Konigl 04 for a more recent study).

30. The apparently thin photon spectra indicate emission from large distances and suggests association with jet flows (Mastichiadis & Kirk 1997). The relativistic outflows produce shocks, which accelerate particles and lead to radiation emission. Blazaremission is thought to be derived this way.

31. Particle acceleration (in shocks, converging flows, turbulence) is the result of an interplay between particle energy gains in scattering and particle transport. The exponentially small probability of undergoing N interactions with the plasma before escape, coupled with exponentially increasing energy with the number of scatterings lead to power law distributions.

32. The geometry of particle transport across a plane shock. The upstream velocity is u1 and the downstream u2=u. The particle velocity is v. The shaded region shows the fraction of particles that make it upstream and have a chance to accelerate.

33. Generic description of the acceleration process. Application to plane parallel shocks (r is the compres- sion ratio, P(p) is the integral spectrum).

34. The presence of relativistic particles can affect the dynamics of the flow: Relativistic particles reduce the fluid adiabatic index and increase the shock compression ratio r. This hardens the spectra; most kinetic energy is converted to relativistic particles that dominate the pressure. Particle (relativistic) escape from the system also increases the compression ratio of the shock with similar effect. (Ellison et al 2000) Effects of acceleration on dynamics

35. In the vicinity of a compact object, the strong gravitational field could separate the relativistic and the non-relativistic populations, provided that cooling does not ; this can cause outflows similar to those inferred in compact objects (DK & Ellison 86); Subramanian et al (99), provided that the accelerated particles do not lose energy on time scales shorter than free-fall. Separation can also take place through the production of neutral particles (neutrons) that can increase the power of relativistic outflows (Contopoulos & DK 94).

36. Plasma production outside an Acc. Disk from n -> p e. For a large black hole, most neutron produced protons are relativistic while for a small one most are non-relativistic. The critical value is M~108 M_o

37. The Radio Jets of GRS 1915+105

38. The Radio Jets of GRS 1915+105

39. The Radio Jets of GRS 1915+105

40. Acceleration in Accretion Disks can result from particle-wave interactions (e.g. Dermer, Miller, Li ’96). Acceler. Time scales are quite short and should Produce accelerated populations. Accretion Disks could accelerate particles by their shearing motion (Subramanian et al. ’99). This leads to 2nd order acceleration.

41. The slope of accelerated population depends on the interplay between energy gain per interaction and escape probability (e.g. the Comptonization parameter t kT/mc2). For shocks this is 3/(r-1) (integral slope). The acceleration rate is hap-pening on the gyro-period at the given field ~ E(eV)/B(G) Maximum energy is given by the balance between accele-ration and losses or escape from the system. For electrons this energy is ~TeV (blazars), while for protons it gets close to 1020 eV. Eventually, the max.energy is roughly ~R (v/c) B, where R is the size of the system, v the velocity and B the magnetic field. Slope and Maximum Energies

42. Conclusions - Questions • Particle Acceleration is a ubiquitous process in compact objects (spectra, superluminal motions). • Particles can get accelerated in EM gaps (deviations from MHD conditions). Energy/particle ~ Potential drop across gap. • MHD acceleration in rotating magnetospheres. Conversion of magnetic to kinetic energy of high efficiency (depends on current distribution). Lorentz factors of ~10 – 106 possible. • Particle acceleration possible in turbulent, shocked plasmas. Conversion of KE to relativistic particles with high efficiency. Max. energy depends on particulars of system. • Why don’t we see prominent non-thermal emission in the spectra of accreting binary sources? Why are most AGN radio quiet? • Does acceleration take place in the Acc. Disks of AGN, GBHC? If yes, do the accelerated particles play any role in the dynamics of these disks? Are observational tests to distinguish between these possibilities?

46. The geometry of particle transport across a shock. The upstream velocity is u1 and the downstream u2=u. The particle velocity is v. The shaded region shows the fraction of particles that make it upstream and have a chance to accelerate.