THE TIME-DEPENDENT HADRONIC MODEL OF ACTIVE GALACTIC NUCLEI

1. THE TIME-DEPENDENT HADRONIC MODELOF ACTIVE GALACTIC NUCLEI A. Mastichiadis University of Athens

2. ...in collaboration with • Stavros Dimitrakoudis – UoA • Maria Petropoulou – UoA • Ray Protheroe – University of Adelaide • Anita Reimer – University of Innsbruck

3. THE LEPTONIC MODEL FOR H.E. EMISSION… Log Ν Active Region aka The Blob: Relativistic Electrons Log γ B-field soft photons synchrotron inverse compton

4. … THE HADRONIC MODEL… Proton distribution Log Ν Active Region aka The Blob: Relativistic Electrons and Protons Gamma-rays from proton induced radiation mechanisms Log γ synchrotron

5. … A RELATED PROBLEM… Particle distribution Usual approach: Fit MW spectrum using particle distribution function N(γ) (parti-cles/volume/energy) Log Ν γ-p γmin γmax Define energy limits, power law slopes, breaks  use emissivities to calculate radiated spectrum. Log γ Advantages: Simple – One-step process Textbook approach e.g. ‘Compton catastrophe’ of leptonic plasmas: if UB<Usyn and losses are not taken into account  photon population exponentiates in the source Disadvantages: It does not take particle losses into account  Can be (very) misleading

6. …AND A WAY OUT Particle losses + radiation In: Particle Luminosity Out: Photon Luminosity Particle distribution function Slow radiative losses: Output Luminosity << Input Luminosity Low efficiency Injected particles not ‘burned’  Accumulation + high particle energy density Fast radiative losses: Output Luminosity ~ Input Luminosity High efficiency Injected particles ‘burned’  Low particle energy density LEPTONIC PLASMAS HADRONIC PLASMAS

7. PROTON INJECTION PROTON DISTRIBUTION FUNCTION PROTON LOSSES PROTON ESCAPE ELECTRONS- POSITRONS PHOTONS Leptonic processes OBSERVED SPECTRUM

8. Protons: Electrons: losses escape injection Photons: Neutrinos: injection Bethe-Heitler proton ssa Neutrons: synchrotron γγ synchrotron photopion annihilation triplet pair production

9. INTERACTIONS OF PROTONS WITH PHOTON FIELDS photopair production (Bethe-Heitler) • Secondary distribution functions Protheroe & Johnson 1996 • Modeling of proton energy losses in AM et al 2005 photomeson production • Secondary distribution functions SOPHIA code (Muecke et al 2000) • Modeling of proton energy losses In Dimitrakoudis et al 2012

10. APPLICATION: ONE ZONE MODELS • Source of radius R containing magnetic field B. • Monoenergetic proton injection at Lorentz factor γp with luminosity Lp and characteristic escape time from the source tp,esc • System of four coupled P.I.D.E.  Study its properties. • Keep free parameters at minimum: No external photons/no electron injection. Simplest case solution: • If tp,loss>>tcr=R/c  injected protons accumulate at the source  energy density up =(Lp /V) tp,esc. • The system is characterized by a critical energy density up,cr(γp,B,R): • If up <up,cr(γp,B,R)  system in linear (subcritical) regime. • If up >up,cr(γp,B,R)  system in non-linear (supercritical) regime. If system in linear regime: model fits with ‘ready’ distribution function is o.k. Problem: this is not known a priori.

11. LINEAR REGIME: SECONDARYELECTRONS AND PHOTON SPECTRA photons electrons photopion electrons 8 orders of magnitude X-rays to TeV Bethe-Heitler electrons γγ electrons R=3e16cm B = 1 G γp =2e6 lp= 0.4 tp,esc=tcr S. Dimitrakoudis et al., 2012

12. VARIABILITY I - QUADRATIC In linear regime quadratic • For certain γp -B choices •  p-synchrotron serve as targets • for both photopair and photopion • quadratic behavior between p-syn and photopair + photopion synchrotron  analogous to syn – SSC of lepto- nic plasmas p-syn photo- meson Dimitrakoudis et al. 2012 Lorentzian variation in proton luminosity

13. VARIABILITY II - CUBIC In linear regime see poster P6-06 S. Dimitrakoudis cubic p-syn photo- meson For other γp- B choices  p-synchrotron serve as targets only for photopair (photomeson below threshold) cubic behavior between p-syn and photomeson. Lorentzian variation in proton luminosity

14. PROTON SUPERCRITICALITIES If up>up,cr  system undergoes a phase transition and becomes supercritical Log Photon Luminosity subcritical supercritical ~3.5 orders of magnitude onset of supercriticality r ~0.01 orders of magnitude linear quadratic quadratic Proton injected luminosity is increased by a factor 3 log lp Log Proton Luminosity

15. SEARCHING FOR THE CRITICAL DENSITY B=10 G R=3e16 cm SUPERCRITICAL REGIME I SUBRCRITICAL REGIME In all casesthe proton injection luminosity is increased by 1.25  corresponding photons increase by several orders of magnitude Time-dependent transition of photon spectra from the subcritical to the supercritical regime

16. A ZOO OF PROTON SUPERCRITICALITIES • When up>up,cr various feedback • loops start operating • Spontaneous soft-photon • outgrowth leading to • substantial proton losses. • Feedback Loops • Pair Production – Synchrotron Loop (Kirk & AM 1992) • Automatic Photon Quenching (Stawarz & Kirk 2007; Petropoulou & AM 2011). Probably there are more. Each loop has its own modus operandi. Parameters similar to the ones used for blazar modeling For γp>>  up,cr ~ uB B=10 G R=3e16 cm SUPERCRITICAL REGIME PPS Loop quenching- πγ induced cascade quenching- BH induced cascade SUBCRITICALREGIME

17. DYNAMICAL BEHAVIOUR IN THE SUPERCRITICAL REGIME protons • If up>up,cr exponential growth of soft photons. • Subsequent behavior: • If tp,esc<Tc system reaches quickly a steady state characterized by high efficiency. • If tp,esc>Tc  system exhibits limit cycles or damped oscillations. -- see also numerical work of Stern, Svensson, Sikora (90s) and Kirk & AM (90s -00s) photons time Photon density Proton density

18. ANALYTIC APPROACH TO A SIMPLIFIED HADRONIC SYSTEM • 2 (in subcritical) or 3 (in supercritical) populations: • Relativistic protons • ‘Hard’ photons (from π-interactions) • ‘Soft’ photons (from quenching) Retains the dynamical behavior of the full system Limit cycles or damped oscillations as it enters the supercritical regime M. Petropoulou & AM 2012

19. courtesy of M. Petropoulou

20. AN APPLICATION: THE CASE OF 3C 279 Petropoulou & AM 2012b • Hadronic fitting to the TeV MAGIC observations of 3C 279. • If the proton luminosity is high  • System becomes supercritical  • spontaneously produced soft photons violate the X-ray limits. • Fit only possible for low proton luminosity  high Doppler factor δ>20. log δmin See Maria’s poster P2-10 δ~20 log B

21. TIME-DEPENDENT EXCURSIONS INTO THE SUPERCRITICAL REGIME • Perturb system from steady-state in the linear regime  Lorentzian in proton injection. •  Proton energy is burned into flaring episodes of varying amplitude. PRELIMINARY photon output proton input

22. CONCLUSIONS • One-zone hadronic model • Accurate secondary injection (photopion + Bethe Heitler) • Time dependent - energy conserving PIDE scheme • Four non-linear PIDE – c.f. leptonic models have only two First results of pure hadronic injection • In subcritical regime: - Low efficiencies - Quadratic and cubic time-behavior of radiation from secondaries • In supercritical regime: - High efficiencies / Burst type of behavior - Parameters relevant to AGNs and GRBs - Warning to modelers: The supercriticalities exclude sections of parameter-space used for modeling these sources