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.. HEA 07


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HESS ­ High Energy Stereoscopic System in Namibia E ­from 100GeV to several 10TeV 0.1gradё/E<15% I10^(­8)­10^(­16)cm^(­2)s^(­1)TeV^(­1) M87 - 3·10^(40)erg/s Power law spectrum - ­2В4


Motivation of the study
M87 · TeV variability of M87, PKS2155-304 and Mrk501 requires very small emitting zones, of the order of a few rg (even for high ) · 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 PKS2155-304


· · · · · · ·

m(vv)v=q{E+[vB]/c}+F­vP/n f(,z) ­ flux of the poloidal magnetic field B_=­f/z/,B_z=f//,f=B_zd E_=­//0 v_(mv_+qf/c)/=0,p_+qf/c=const() ^2_--^2_c(B_z) MHD: E=­[vB]/c,E_=v_B_z,B_z0


Light cylinder at RL

U = electric voltage created by rotating BH I = large scale current I U > LK


Centrifugal acceleration in BH magnetosphere
Assume `reasonable' B and E fields, from current I : Bz = 0

= v/v << 1


Motion of a test particle
P ( )

Light cylinder

Pz()

P() z()

Here = 0.01 and = rc,i/RL = 0.01


Growth of particle Lorentz factor
( )

log k

At light cylinder : = Here

with
initial value

is the absolute maximal reachable by this process (ie no losses)


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 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

correlation time

energy losses

Evolution of the distribution function :

For electrons (synchrotron losses) : with ~ 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 typically 1017 ­ 1019 eV )

This can be used as initial particle distribution for further centrifugal acceleration process ...


Proposal : a two-step mechanism for particle acceleration
· First step : stochastic acceleration in low-luminosity disk. Efficient for protons (up to 1017-1019 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 10-100 TeV and protons about 1020 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 rg, inside RL needs BH with intermediate rotation values