STATISTICAL ACCELERATION and SPECTRAL ENERGY DISTRIBUTION in BLAZARS Enrico Massaro

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: d=1 / 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 frequencynp 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 npchanges 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)=Sp10-(b Log(n/np)2) • b: curvature at peak • np: peak energy • Sp: SED height @ Ep=hnp F(E)=F0(E/E)-(a +b Log(v/v0)) • b: curvature at peak • a: spectral index @ n0

8. BeppoSAX observations of Mrk 421MASSARO et al. 2004

9. A VLBL object (OJ 425)

10. VLBL vs HBL (Mkn 421 and S4 1803+78)flux,frequency 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 @ E1

12. Relation between the observed S curvature (b) and that of the emitting electrons (r) F()=F0(/)-(a+b*Log()) N()=N0(/)-(s+r*Log(/)) (r) (b) Massaro E.,Tramacere A. et al. A&A 2006 numerical computations show b ~ r/5 @ 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 U1=|V| U2=1/4U1 Shock R.F. R=U1/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 < 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 Pacc~1 Pacc<1

20. Fermi 2: p/p~(VA/c)2 ( MHD Turb. Alfven waves ecc..) gain+loss=broad Analytical solution Kardashev (1962) (Hard spheres approximation) FP: D(p)~p2/t2 acc A2(p)syst=2Ddiff(p)/p Fermi 1+2 • 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 problem:One 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 0716+714 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 • LP spectra are expected from statistical acceleration when stochastic effects are taken into account • The measure of the curvature and its relation with the peak frequency is important to study the acceleration mechanisms • Curvatures in the X-ray and TeV bands test the SSC model and can be used to obtain information on EBL • 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) .