THE TIME-DEPENDENT HADRONIC MODEL OF ACTIVE GALACTIC NUCLEI A. Mastichiadis University of Athens

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

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

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

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

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

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

Protons: injection Electrons: Photons: Neutrinos: Neutrons: Bethe-Heitler proton triplet ssa γγ annihilationphotopion synchrotron pair production injectionlossesescape

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

PROTON ENERGY LOSSES photopair photomeson

APPLICATION: ONE ZONE MODELS Source of radius R containing magnetic field B. Monoenergetic proton injection at Lorentz factor γ p with luminosity L p and characteristic escape time from the source t p,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 t p,loss >>t cr =R/c  injected protons accumulate at the source  energy density u p =(L p /V) t p,esc. The system is characterized by a critical energy density u p,cr (γ p,B,R): –If u p <u p,cr (γ p,B,R)  system in linear (subcritical) regime. –If u p >u p,cr (γ p,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.

LINEAR REGIME: SECONDARY ELECTRONS AND PHOTON SPECTRA R = 3e16 cm B = 1 G γ p = 2e6 l p = 0.4 t p,esc =t cr Bethe-Heitler electrons photopion electrons γγ electrons electrons photons S. Dimitrakoudis et al., orders of magnitude X-rays to TeV

VARIABILITY I - QUADRATIC For certain γ p -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 Dimitrakoudis et al quadratic In linear regime Lorentzian variation in proton luminosity p-syn photo- meson

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

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

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

A ZOO OF PROTON SUPERCRITICALITIES quenching- πγ induced cascade PPS Loop quenching- BH induced cascade SUBCRITICAL REGIME B=10 GR=3e16 cm SUPERCRITICAL REGIME When u p >u p,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 γ p >>  u p,cr ~ u B

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

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

courtesy of M. Petropoulou

AN APPLICATION: THE CASE OF 3C 279 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. Petropoulou & AM 2012b See Maria’s poster P2-10 log δ min log B δ~20

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 proton input photon output

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

THE HADRONIC MODEL: PHYSICAL PROCESSES Courtesy of R.J. Protheroe leptonic hadronic

PHOTON AND NEUTRINO SPECTRA Power law proton injection injected protons photons neutrinos neutrons p=1.5 Neutrino spectra --different proton indices p p=2.5 Photon spectra --different proton indices p p=1.5 p=2.5 S. Dimitrakoudis et al., in preparation

INCREASING THE PROTON INJECTED ENERGY R = 3e16 cm B = 1 G l p = 0.4 γ p = 3e5γ p = 3e6γ p = 3e7

PROTONS  GAMMA-RAYS – escape | | | quenching | | (self-generated) | SOFT PHOTONS |_____________| Soft photons from γ-ray quenching pump proton energy  proton losses  more secondaries  more γ-rays Exponentiation starts when γ-rays enter the quenching regime. PHOTON QUENCHING AND PROTON SUPERCRITICALITY γ-ray quenching regime γ-ray quenching regime Photon spectra for various monoenergetic proton injection energies just before supercriticality

PAIR PRODUCTION – SYNCHROTRON LOOP PROTONS  BETHE-HEITLER PAIRS | | | SYNCHROTRON PHOTONS |_______________|________ | escape Loop operational if two criteria, feedback and marginal stability, are simultaneously satisfied  protons supercritical  Pairs/photons exponentiate in the source n γ ~ n e ~ exp(st) supercritical regime Kirk & AM 1992 s=1 s=0 Feedback criterion Marginal stability criterion

AUTOMATIC PHOTON QUENCHING Stawarz & Kirk 2007 Petropoulou & AM 2011 Injected gamma-ray luminosity Escaping luminosity gamma-rays soft photons Gamma-rays can be self-quenched: Non-linear network of photon-photon annihilation electron synchrotron radiation Operates independently of soft photons Poses a strong limit on the gamma-ray luminosity of a source quenched gamma-rays ‘reprocessed’ gamma-rays l γ,crit