Ускорение частиц вблизи массивных черных дыр Я.Н. Истомин ФИАН HEA 07

HESS – High Energy Stereoscopic System in Namibia E –from 100GeV to several 10TeV Δθ≤0.1grad¸ΔΕ/E<15% I­10^(–8)–10^(–16)cm^(–2)s^(–1)TeV^(–1) M87 - 3·10^(40)erg/s Power law spectrum - α–2÷4

Motivation of the study TeV variability of M87, PKS and Mrk501 requires very small emitting zones, of the order of a few r g (even for high δ) Challenge : how to efficiently accelerate particles in such small zones ? Tentative : try from the most compact and potentially energetic region, the close surroundings of the BH M87 PKS

m(vv)v=q{E+[vB]/c}+F–vP/n f(ρ,z) – flux of the poloidal magnetic field B_ρ=–∂f/∂z/ρ,B_z=∂f/∂ρ/ρ,f=∫B_zρdρ E_φ=–∂Φ/∂φ/ρ≡0 v_ρ∂(mρv_φ+qf/c)/∂ρ=0,ρp_φ+qf/c=const(ρ) ρ^2ω_φ—ρ^2ω_c(B_z) MHD: E=–[vB]/c,E_φ=v_ρB_z,B_z≡0

U = electric voltage created by rotating BH I = large scale current I U > L K Light cylinder at R L

Centrifugal acceleration in BH magnetosphere Assume ‘reasonable’ B and E fields, from current I : B z = 0 α = v ρ /v φ << 1

Motion of a test particle Pρ(ρ)Pρ(ρ) Pφ(ρ)Pφ(ρ) Pz(ρ)Pz(ρ) z(ρ) Here α = 0.01 and κ = r c,i /R L = 0.01 Light cylinder

γ(ρ)γ(ρ) Growth of particle Lorentz factor At light cylinder :with log k Here is the absolute maximal γ reachable by this process (ie no losses) initial value =

Maximal energies for e - and p + For an initial power law the output is also a power law Balance between radiative losses and acceleration rate gives a γ max For electrons : For protons : for M87 values

Stochastic acceleration in disk How to generate initial power law ? Analyze a 2D turbulent velocity field u in (low luminosity) disk laminar turbulent It induces a turbulent E, E = - u x B/c for high conductivity : Then, energy growth rate of a charged particle :

Integrating, and then averaging (for strong acceleration), we get : What about Related to drift velocities, ie here to the polarization drift, which has a non-zero component along z : ? 

Then coefficient of diffusion≠ 0 Evolution of the distribution function : energy losses For electrons (synchrotron losses) : with correlation time ~ 100 (typical for M87) No efficient e - acceleration due to too strong synchrotron losses

For protons (main losses from collisions with p+ from disk) : with The distribution function is a power law with index possibly ~ 1 (Here This can be used as initial particle distribution for further centrifugal acceleration process …  typically – eV )

Proposal : a two-step mechanism for particle acceleration First step : stochastic acceleration in low-luminosity disk. Efficient for protons (up to eV), not for electrons. Provide power law particle distribution. Likely a slower varying process  related to ‘stationary’ TeV components ? Second step : centrifugal acceleration in BH magnetosphere. Electrons can reach TeV and protons about eV. Both can radiate in VHE range. Direct acceleration, a faster process  related to highly variable events ? A mixture of hadronic and leptonic scenarios Such mechanism well occurs in a few r g, inside R L  needs BH with intermediate rotation values