STATISTICAL ACCELERATION and SPECTRAL ENERGY DISTRIBUTION in BLAZARS

1

• STATISTICAL ACCELERATION and SPECTRAL ENERGY
  DISTRIBUTION in BLAZARS
• Enrico Massaro
• Physics Department, Spienza Univ. of Roma
• and
• Andrea Tramacere
• ISOC, SLAC
• Challenges in Particle Astrophysics
• Château de Blois May 2008

2
Blazar Properties

• Strong non-thermal emission over the entire e.m.
  spectrum (g-ray sources in the EGRET catalog and
  at TeV energies)
• Featureless optical spectrum (BL Lac objects)
• Variability on all time scales from minutes to
  about one century ......
• High (and variable) linear polarisation

3
Blazar Model Paradigma

• Relativistic beaming d1 / G(1 b cos q)
• in a jet aligned along the line of sight (q
  small)
• Synchrotron radiation (SR) and Inverse Compton
  (IC) components (one, two?) from electrons
  accelerated at relativistic energies (SSC
  Synchro Self-Compton)

4
Spectral Energy Distribution (SED)

• The typical SED of a BL Lac object shows two
  broad peaks
• the peak at LOW frequencies is explained by SR,
  that at HIGH frequencies by IC emission.

5
BL Lac classification

• Padovani Giommi (1995) introduced two BL Lac
  classes
• based on the frequency np of the Synchrotron
  peak
• LBL or Low energy peaked BL
• HBL or High energy peaked BL.
• More classes have been defined
• VLBL Very LBL
• IBL Intermediate BL
• EHBL Extreme HBL
• np changes with the source brightness

6
Spectral Energy Distribution

• Broad band observations have shown that the SED
  has a rugular mild curvature (not a sharp
  cut-off) well described by a parabola in a
  log-log plot (i.e. a log-normal law), or by a
  power-law changing in a log-parabola
• 2 main parameters
• peak frequency (or energy)
• curvature

7
Log-Parabolic Law
A log-parabolic spectral distribution is a
distribution that is a parabola in the
logarithm, and corresponds to a log-normal
distribution.

• S(E)Sp 10-(b Log(n/np?)2)
• b curvature at peak
• np peak energy
• Sp SED height _at_ Eph np

• F(E)F0(E/E?)-(a b Log(v/v0))
• b curvature at peak
• a spectral index _at_ n0

8
BeppoSAX observations of Mrk 421MASSARO et al.
2004
9
A VLBL object (OJ 425)
10
VLBL vs HBL (Mkn 421 and S4 180378)flux,frequenc
y scaling ? similar spectral changes
11
Origin of log-parabolic spectra

• LP Synchrotron spectra are originated by a
  population of relativistic electron having an
  energy distribution described by a LP function.
• A simple d-approximation gives
• b r/4

N (g) No (g/g0) -(s r Log (g / g0)) r
curvature at peak s spectral index _at_ E1
12
Relation between the observed S curvature (b) and
that of the emitting electrons (r)

F(?)F0(?/??)-(abLog(????))
N(?)N0(?/??)-(srLog(?/??))
(r)
(b)
Massaro E.,Tramacere A. et al. AA 2006
numerical computations show b r/5 _at_ 10
13
Origin of log-parabolic energy distribution of
electrons

• What information one can derive from curvature?
• Can be spectral curvature curvature to be
  considered a signature of statistical
  acceleration?

14
Origin of log-parabolic energy distribution of
electrons

• LP energy distributions are produced by
  statistical acceleration mechanisms when the
  fluctuations are taken into account.
• Fluctuations of
• 1. energy gain
• 2. number of accelerated particles

15
1st order Fermi diffusive shock acceleration
1 Gas Staz
V
U1V
U21/4U1
Shock R.F. RU1/U2
2 Shocked Gas
1 Gas Staz
Fermi 1 ?p/p (4/3)(U2 U1)/c only gain,
syst. acc. POWER LAW s log (Pacc )/log(1
Dp/p )
16
Fluctuations in the acceleration gain

The curvature r is inversely proportional to the
number of steps ns and to (sD/e)2
17
Fluctuations in the step number
(Poisson distribution)

The curvature r is inversely proportional to time
(number of steps) and to (log e)2
18

The curvature r is inversely proportional to
time (number of steps) Log of energy gain,
(log e)2

Important parameters are -- the acceleration
probability Pacc Pacc close to
unity ? LP distribution results energy
Pacc lt 1 a power law tail is developed
but, ..... Pacc can depend on
energy -- the injection spectrum N0(g)
monoenergetic ? LP distribution results
energy broad distribution ?
power law tail -- impulsive or
continuous injection

19
Monte Carlo numerical results on Electron
Distributions
Pacc1

Pacclt1

20
Fermi 2 ?p/p(VA/c)2 ( MHD Turb.
Alfven waves ecc..) gainlossbroad
Analytical solution Kardashev (1962) (Hard
spheres approximation)
FP D(p)p2/t2 acc
A2(p)syst2Ddiff(p)/p
Fermi 12

• Curvature is inversely proportional to diffusion
  term D
• Curvature decrease with acceleration time
• The peak of distribution depends on the
  quantity?A-D

21
Impulsive injection vs Continuous
injection
22
An open problemOne or two emission components ?
23
2 component flaring Optical X-ray flare
Broad band flare
24
Curvature at TeV energies

• An electron spectrum having a LP energy
  distribution (curvature parameter r) implies that
  also IC radiation has a curved spectrum.
• Curvature in SSC spectra depends on IC scattering
  occurr in the Thomson or KN regimes.

25
SSC spectra
26
HBL Mrk 501 1997 large Flare - 1 zone SSC model
Massaro ,et al. 2006
1 zone SSC model Up Low EBL realization from
Dwek and Krennrich (2005) used to evaluate the
pair production opacity. Low no EBL
opacity

• Flare dell'Aprile 1997
• Dati simultanei Sax CAT

Simultaneous broad band X-ray and g-ray/TeV
observations are very useful to constrain
curvature
27
HBL Mrk 501 SSC 2 zone model
Massaro ,et al. 2006

• 2 zone SSC model
• Black slowly variable
• component
• Red-blue flaring
• component
• The discovery at TeV energies of Blazars with
  higher z (3C 279 z 0.536, S5 0716714 z?) should
  be in contrast with high EBL densities

• Flare dell'Aprile 1997
• Dati simultanei Sax CAT

28
g-g opacity
Dwek Krennrich 2005
Franceschini et al. 2008
29
Corrected SED show significant curvatures
Dwek Krennrich 2005
30
Conclusions

1. LP spectra are expected from statistical
   acceleration when stochastic effects are taken
   into account
2. The measure of the curvature and its relation
   with the peak frequency is important to study the
   acceleration mechanisms
3. Curvatures in the X-ray and TeV bands test the
   SSC model and can be used to obtain information
   on EBL
4. Simultaneous X and TeV spectral fits indicate a
   low/very low EBL. New interactions cannot be
   necessary needs for more broad band data on EBL
   (next satellites Planck, Herschel, GLAST, ...
   very useful) .