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

Blazar Properties: Strong non-thermal emission over the entire e.m. spectrum (  -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

Blazar Model Paradigma: Relativistic beaming:  =1 /  (1 –  cos  ) in a jet aligned along the line of sight (  small) Synchrotron radiation (SR) and Inverse Compton (IC) components (one, two?) from electrons accelerated at relativistic energies (SSC: Synchro Self-Compton)

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.

BL Lac classification Padovani & Giommi (1995) introduced two BL Lac classes based on the frequency  p 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  p changes with the source brightness

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

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)=S p 10 -(b Log( / p  ) 2 ) b: curvature at peak p : peak energy S p: SED E p =h  p F(E)=F 0 (E/E  ) -(a +b Log(v/v 0 )) b: curvature at peak a: spectral 0

BeppoSAX observations of Mrk 421 MASSARO et al. 2004

A VLBL object (OJ 425)

VLBL vs HBL (Mkn 421 and S ) flux,frequency scaling  similar spectral changes

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  -approximation gives b = r/4 N (  ) = No (   )  (s + r Log (   )) r: curvature at peak s: spectral E 1

Relation between the observed S curvature (b) and that of the emitting electrons (r) numerical computations show b ~ 10 % Massaro E.,Tramacere A. et al. A&A 2006 (r) (b)(b) F( )=F 0 ( /  ) -(a+b*Log(   )) N(  )=N 0 (  /   ) -(s+r*Log(  /   ))

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?

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

1st order Fermi diffusive shock acceleration U 1 =|V| U 2 =1/4U 1 Fermi 1:  p/p =(4/3)(U 2 – U 1 )/c only gain, syst. acc.: POWER LAW s =log (P acc )/log(1+  p/p ) 1 Gas Staz V Shock R.F. R=U1/U2 2 Shocked Gas 1 Gas Staz

Fluctuations in the acceleration gain The curvature r is inversely proportional to the number of steps n s and to (   /  ) 2

Fluctuations in the step number (Poisson distribution) The curvature r is inversely proportional to time (number of steps) and to (log  ) 2

The curvature r is inversely proportional to time (number of steps) Log of energy gain, (log  ) 2 Important parameters are -- the acceleration probability P acc : P acc close to unity  LP distribution results energy P acc < 1 a power law tail is developed but,..... P acc can depend on energy -- the injection spectrum N 0 (  ): monoenergetic  LP distribution results energy broad distribution  power law tail -- impulsive or continuous injection

Monte Carlo numerical results on Electron Distributions P acc ~1 P acc <1

Analytical solution Kardashev (1962) (Hard spheres approximation) ●Curvature is inversely proportional to diffusion term D ●Curvature decrease with acceleration time ●The peak of distribution depends on the quantity  A-D Fermi 2:  p/p~(V A /c) 2 ( MHD Turb. Alfven waves ecc..) gain+loss=broad FP: D(p)~p 2 /t 2 acc A 2 (p) syst =2D diff (p)/p Fermi 1+2

Impulsive injection vs Continuous injection

An open problem: One or two emission components ?

2 component flaring Optical X-ray flare Broad band flare

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.

SSC spectra

HBL Mrk large Flare - 1 zone SSC model ●Flare dell'Aprile 1997 ●Dati simultanei Sax CAT 1 zone SSC model Up: Low EBL realization from Dwek and Krennrich (2005) used to evaluate the pair production opacity. Low: no EBL opacity Massaro,et al Simultaneous broad band X-ray and  -ray/TeV observations are very useful to constrain curvature

HBL Mrk 501 – SSC 2 zone model ●Flare dell'Aprile 1997 ●Dati simultanei Sax CAT ● 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, S z?) should be in contrast with high EBL densities Massaro,et al. 2006

 opacity Dwek & Krennrich 2005Franceschini et al. 2008

Corrected SED show significant curvatures Dwek & Krennrich 2005

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).