Shock vs Stochastic Acceleration of Ultrarelativistic Particles in Active Galaxies

1
Shock vs Stochastic Acceleration of
Ultrarelativistic Particles in Active Galaxies

• Lukasz Stawarz
• KIPAC, Stanford University

2
Problems to discuss

• What are the particle (electron) spectra produced
  in relativistic jets of active galaxies?
• What are the particle acceleration and energy
  dissipation processes involved?
• Shock vs stochastic acceleration (vs magnetic
  reconnection?)

3
Jets in active galaxies (scales!)
1022-1024 cm matter dominated ?
Rj 1021-1024 cm MHD/HD (Perucho 07)
rg Ee/eB 1016 (?/108) (B/10-5G)-1 cm MC
(Niemiec 04)
?e c/?e 109 (ne/10-5cm-3)-1/2 cm PIC
(Spitkovsky 05)
1016-1017 cm magnetic dominated ?
NO LABORATORY DATA TO COMPARE WITH (magnet.
collisionless plasma). BUT THEN WE HAVE
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Sun turbulence and reconnection
Stochastic processes (interactions of charged
particles with magnetic turbulence within
reconnecting magnetic filaments in chromosphere)
may successfully explain several crucial
observations regarding the electron and ion
acceleration in solar flares (Liu, Petrosian
04/06).
Magnetic reconnection not fully understood.
Rates, efficiency, and the resulting particle
spectra still debated in the context of the
heliosphere and the Earths magnetosphere (e.g.,
Drake 06). The relativistic regime even less
understood (Zenitani Hoshino 02/08, Lyutikov
Uzdenski 03, Lyubarsky 04/06) Magnetic
reconnection may be just a source of turbulence
for the Fermi-type acceleration!
5
Sun Shock Waves
Shock waves are driven by fast Coronal Mass
Ejections (CMEs) in the inner heliosphere (10
solar radii). These are sometimes associated with
Solar Energetic Particles (SEPs), carrying up to
20 of the CME kinetic energy (very efficient
acceleration! Lin 08).
Ions up to 1-10 GeV 1031 erg 1028 erg/s in
103 s Electrons up to 0.1-1 GeV 3 ? 1031
erg 3 ? 1028 erg/s in 103 s (Mewaldt 04).
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Blazar phenomena
3C 454.3
1) Emission regions are compact, R 1016 cm . 2)
Implied highly relativistic bulk velocities of
the emitting regions, ? 10-30 , are in
agreement with the ones inferred from the
observed superluminal motions of VLBI jets on pc
(kpc?) scales. 3) Energy density of magnetic
field is comparable to energy density of
radiating ultrarelativistic electrons, UB
Ue,rel . 4) The implied magnetic fields B 0.1-1
G are consistent with the ones inferred from the
SSA features in flat spectra of compact radio
cores.
Modeling of the broad-band blazar emission (and
its variability) in a framework of the leptonic
scenario (Dermer Schlickaiser 1993, Sikora,
Begelman Rees 94, Blandford Levinson 95)
allows to put some constraints on the physical
parameters of the blazar emission region. In
particular, such modeling indicate that
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Blazar jets
?2
In addition, the power carried by
ultrarelativistic electrons cannot account for
the total radiated power of blazars, or for the
kinetic power of quasar jets deposited far away
from the active nucleus (e.g., Sikora Madejski
00, Celotti Ghisellini 08). So (1) magnetic
field is dominating dynamically, while the blazar
emission is produced in small jet sub-volumes
with magnetic intensity lower than average (?),
or (2) jets already on blazar scales are
dynamically dominated by protons and/or cold
electrons. However, lack of bulk-Compton features
in soft-X-ray spectra of blazars (Begelman
Sikora 87, Sikora 97) indicates that (3) cold
electrons cannot carry bulk of the jet power, at
least in luminous blazars.
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Powerful blazars shock spectra
Energy distribution of the radiating
electrons ne(?) ? ?-1.35 for ? lt ?br
100 ?-3.35 for ? gt ?br 100
Sikora bump?
Kataoka 08 parameters of blazar PKS
1510-089 G 20 , r 1 pc , R 1016 cm ,
Ne/Np 10 , B 0.6 G , Lp 2 ? 1046 erg/s ,
Le 0.1 ? 1046 erg/s , LB 0.6 ? 1046 erg/s
The implied physical parameters of the blazar
emission zone, as well as the spectral energy
distribution of the emitting ultrarelativistic
electrons being consistent with the shock
acceleration scenario (though not the standard
diffusive shock acceleration model!) suggest that
the extragalactic jets are matter (proton)
dominated already at sub-pc scales
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Powerful blazars shock spectra
Energy distribution of the radiating
electrons ne(?) ? ?-1.35 for ? lt ?br
100 ?-3.35 for ? gt ?br 100
Sikora bump?
Kataoka 08 parameters of blazar PKS
1510-089 G 20 , r 1 pc , R 1016 cm ,
Ne/Np 10 , B 0.6 G , Lp 2 ? 1046 erg/s ,
Le 0.1 ? 1046 erg/s , LB 0.6 ? 1046 erg/s
The implied physical parameters of the blazar
emission zone, as well as the spectral energy
distribution of the emitting ultrarelativistic
electrons being consistent with the shock
acceleration scenario (though not the standard
diffusive shock acceleration model!) suggest that
the extragalactic jets are matter (proton)
dominated already at sub-pc scales (self-cosistent
scenario!)
10
Relativistic pe- shocks
PIC simulations show that within the velocity
transition region of relativistic,
proton-mediated, transverse shocks, electrons and
positrons can absorb electromagnetic cyclotron
waves emitted at high harmonics by cold protons
reflected from the shock front. The resulting
ee- spectra are consistent with a flat (1 lt s lt
2) power-law between energies ? Gsh and ? Gsh
(mp/me) (Hoshino 92 Amato Arons 06).
energy index 1 lt s lt 2 for Ee lt Ep
MC simulations reveal variety of particles'
spectra resulting from 1st-order Fermi
acceleration at relativistic subluminal or
superluminal shocks (left and right panels).
Previous claims of the universal shock spectrum
(s2.2, first found by Bednarz Ostrowski 98)
were based on simulations or calculations
involving unphysical/unrealistic conditions
(Ostrowski 02, Niemiec Ostrowski 04,06).
energy index s gtgt 2 for Ee gt Ep
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Low-Power Blazars (BL Lacs)
Low-power BL Lacs are substantially different
from the high-power, quasar-hosted blazars. They
accrete at low rates, and lack intense
circumnuclear photon fields. The blazar emission
zone in BL Lacs seems to be located very close to
the central SMBH, as indicated by a complex and
rapid variability.
Katarzynski 01,03 The representative modeling
of broad-band spectra of well known TeV-emitting
BL Lacs Mkn 501 and Mkn 421 in the framework of
a simple one-zone SYN SYN SELF-COMPTON
scenario (quite successful prior to Fermi/LAT and
H.E.S.S. results )
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Rapid variability of BL Lacs
1 min-bin lightcurve of PKS 2155-304 during the
flare (28 July 2006) detected by H.E.S.S. Flux
changes between 0.6 And 15 Crab above 200 GeV
Aharonian 07 The shortest observed variability
timescales tvar lt 200 s imply linear sizes of the
emitting region R lt c tvar ? With the expected
mass of SMBH in PKS 2155-304, MBH 109 Msun,
this gives R (?/100) ? Rg We should expect
magnetic domination at such small scale, and
therefore no shocks!
13
Synchrotron spectra of BL Lacs
Mkn 501
1H 1100
UV-X-ray spectra of BL Lacs are smoothly curved.
They cannot be really fitted by a power-law and
an exponential cut-off form, F(E) ?
E-Gexp(-E/Ecr) . Instead, log-parabolic shape
represents the X-ray continua well, F(E) ? E- a
blog(E/Ecr) (Landau 86, Krennrich 99, Giommi
02, Perri 03, Massaro 03,08, Perlman 05,
Tramacere 07). Caution analysis of the X-ray
spectra is hampered by the unknown/hardly known
intrinsic absorbing column density. In the case
of BL Lacs, on the other hand, such absorption is
not expected to be significant. Analysis of the
optical spectra are hampered by the contribution
of the elliptical host.
14
Modified ultrarelativistic Maxwellian
As long as particle escape from the acceleration
region is inefficient, stochastic acceleration of
ultrarelativistic particles undergoing radiative
cooling trad ? Ex tends to establish modified
ultrarelativistic Maxwellian spectrum
n(E) ? E2 ? exp - (1/a) (E/Eeq)a
where W(k) ? k-q is the energy spectrum of the
turbulence, a 2-q-x, and Eeq is the maximum
particle energy defined by the balance between
the acceleration and losses timescales,
tacc(Eeq) trad(Eeq) (LS Petrosian 08,
Schlickeiser 84, Park Petrosian 95).
Tavecchio 09
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Complex spectral behavior
Ushio 09 Simultaneous plots of "variable" and
"steady" components for the highest flux period
(left panel) and the end of decay period (right
panel) of BL Lac object Mkn 421. The red and
black data sets are for the "variable" components
and the total ("steady""variable") spectra. The
blue data set corresponds to the lowest-flux
period and is common to two plots. Shocks ----
variable ---- broken power-law ??? Turbulent ----
steady ---- Maxwellian ???
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High-power large-scale jets
Chandra X-ray Observatory detected surprisingly
intense X-ray emission from large-scale (100 kpc
1 Mpc) quasar jets (LX 1044-1045 erg/s). Many
well studied cases known (e.g., Schwartz,
Cheung, Hardcatle, Harris, Jorstad, Kataoka,
Kraft, Marshall, Sambruna, Siemiginowska).
shock?
It was proposed that this X-ray emission is due
to inverse-Compton scattering of the CMB photons
by low-energy electrons (Tavecchio 00, Celotti
01).
IC/CMB model requires highly relativistic bulk
velocities (G gt 10) on Mpc scales, and
dynamically dominating protons, Lp gt Le LB with
B Beq 1-10 ?G, and the electron energy
distribution roughly ne(?) ? ?-2.2 for 10
lt ? lt 105
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X-ray jets at high redshifts

• Lic/cmb (d/G )2 (Ucmb/UB) Lsyn
• Ucmb 4 10-13 (1z)4G 2 erg/cm3
• Ucmb ? (1z)4 ?
• if the IC/CMB model is correct, then
• one should expect
• an increase in the X-ray core
• luminosity with redshift due to
• unresolved portion of the jet
• LX/LR ? (1z)4 for the resolved
• portion of the jet.

z 4.3
z 3.89
(Siemiginowska03, Cheung 04, Cheung, LS,
Siemiginowska 06, Cheung, LS et al., in prep.)
z 3.6
z 2.1
z 3.69
z 3.82
z 4.715
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Quasar 3C 273
(Jester 02/07)
Radio-to-UV emission of 100-kpc-long 3C 273 jet
is polarized, and therefore synchrotronin origin.
Spectral profiles inconsistent with the shock
scenario. UV-to-X-ray continuum seems to form an
additional synchrotron component. Does it
indicate single but non-standard electron
energy distribution? Or rather two distinct
electron populations?
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Non-standard electron spectra?
3C 353
X-ray counterjet!
polarized!
3C 273
The spectral character of the broad-band emission
of 3C 273 jet (Jester 07), as well as the
detection of the X-ray counterjet in FR II radio
galaxy 3C 353 (Kataoka, LS 08), indicates that
the X-ray emission of high-power large-scale jets
may not be due to the IC/CMB, but due to the
synchrotron radiation of 100 TeV energy electrons
with a non-standard spectrum.
20
Spectral pile-ups again?

• Relativistic large-scale jets are highly
• turbulent, and velocities of turbulent modes
  thereby may be high. As a result, stochastic (2nd
  order Fermi) acceleration processes may be
  dominant. Assuming efficient Bohm diffusion (i.e.
  turbulence spectrum d B2(k) ? k-1), one has
• tacc (rg/c) (c/vA)2 103 ? s
• tesc Rj2/? 1025 ?--1 s
• trad 6pmec / sT? B2 1019 ? -1 s
• rg ? mec2 / eB , ? rgc / 3 ,
• vA B / (4pmpn)1/2 108 cm/s ,
• B 10-5 G , Rj 1 kpc .
• tesc/trad 106
• tacc trad for Ee,eq 10-100 TeV
• Pile-up synchrotron X-ray emission expected!
• (LS 02, 04)

Relativistic 3D-HD simulations indicate presence
of highly turbulent shear boundary layers
surrounding relativistic jets (Aloy 99).
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Terminal hotspots
Kino Takahara 04
Chandra VLA
Hotspots in powerful radio sources are
understood as the terminal regions of
relativistic jets, where bulk kinetic power
transported by the outflows from the active
centers is converted at a strong shock (formed
due to the interaction of the jet with the
ambient gaseous medium) to the internal energy
of the jet plasma.
Hotspots of exceptionally bright radio
galaxy Cygnus A (dL 250 Mpc) can be resolved
at different frequencies (VLA, Spitzer, Chandra),
enabling us to understand how (mildly)
relativistic shocks work (LS 07).
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Shocks!
LS 07 analysis of the broad-band emission of
hotspots in the exceptionally bright radio galaxy
Cygnus A indicates UBUe and terminal shocks
dynamically dominated by protons.
Mildly-relativistic shock with perpendicular MF
results in a Steep particle spectrum Niemiec
Ostrowski 04
Resonant acceleration of the type discussed by
Hoshino92 Amato Arons 07
mp/me
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Extended lobes
Giant (8deg 600 kpc!) radio structure of
nearby (3.7 Mpc) radio galaxy Centaurus A, which
may be resolved by both Fermi/LAT and H.E.S.S.
Total ?-ray spectrum of Centaurus A
In extended lobes we typically have UBUe (e.g.,
Kataoka LS 05, Croston 05)
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Cen A powerful accelerator!
but also by WMAP and (?) Pierre Auger
Observatory (Hardcastle 09 and Moskalenko, LS
09, respectively)
0.1-1 TeV energy electrons
10-100 EeV energy protons (?)
quite likely stochastic acceleration! (see, the
discussion in Hardcastle 09, Fraschetti Melia
08, OSullivan 09)
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Stochastic acceleration is it really
inefficient?
The characteristic acceleration timescale for the
2nd-order Fermi process, for a given (say,
Alfven) velocity of magnetic inhomogeneities, is
tturb ? (vA/c)-2 Thus, for commonly occurring
non-relativistic turbulence and weakly magnetized
plasma, vA ltlt c, stochastic acceleration
mechanism is often deemed less efficient when
compared to acceleration by shocks where the
acceleration timescale is tshock ? (vsh/c)-1
(hence the name 1st-order Fermi process). This,
however, may not be the case in many
astrophysical plasmas. We note that in a
relativistic regime, for example, 1st-order Fermi
process encounters several difficulties in
accelerating particles to high energies, while at
the same time stochastic particle energization
may play a major role, since velocities of the
turbulent modes may be high, vA c .
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Conclusions I

• Relativistic jets in active galaxies are primary
  cosmic accelerators. They constitute the most
  numerous class of objects detected by Fermi/LAT
  and Cherenkov Telescopes (H.E.S.S., MAGIC,
  VERITAS). They are also most likely sources of
  UHECRs (as claimed by PAO).
• Extragalactic jets accelerate efficiently
  electrons up to 100 TeV energies, and also
  (possibly!) protons up to 100 EeV energies.
• Extragalactic jets are relativistic objects, and
  this hampers understanding of the particle
  acceleration processes taking place thereby (we
  cannot simply extrapolate the results obtained in
  the non-relativistic regime regarding shock,
  turbulent, or reconnection-related acceleration
  processes!).

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Conclusions II

• We do see signatures of shocks in the spectra of
  ultrarelativistic electrons accelerated within
  the regions where the jets are expected to be
  dynamically dominated by cold protons. Such
  spectra deviate significantly, however, from a
  simple power-law form n(Ee) ? Ee-s with s 2 or
  s 2.2 . In particular, typically we see a
  broken power-law with s1lt2 for Eelt Ep and s2gtgt2
  for Eegt Ep , in energy equipartition with the
  magnetic field, UeUB .
• In several cases, on the other hand, we do
  observe electron spectra characterized by a more
  complex shape, most likely involving spectral
  pile-ups/Maxwellian distributions around the
  highest electron energies Ee 10-100 TeV. These
  may indicate very efficient stochastic
  acceleration/magnetic reconnection processes
  taking place in strongly magnetized jet regions.
• Hadronic acceleration in extragalactic jets
  remains elusive. We do not observe radiative
  signatures of relativistic hadrons, although
  active galaxies may be the sources of UHECRs.
  This, together with the indications for the
  dynamical dominance of cold protons in the outer
  portions of extragalactic jets (pc-Mpc), may
  suggest a low efficiency of hadronic
  acceleration, or their inefficient confinement in
  jets.