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 protoninduced radiationmechanisms

… 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 processTextbook approach

Disadvantages:It does not take particle losses into account Can be (very) misleading

e.g. ‘Compton catastrophe’ of leptonic plasmas: if UB<Usyn and losses are not taken into account photon population exponentiates in the source

Particle distribution

Log γ

Log

Ν

γmin γmax

γ-p

…AND A WAY OUT

Fast radiative losses:Output Luminosity ~ Input LuminosityHigh efficiencyInjected particles ‘burned’ Low particle energy density

LEPTONIC PLASMASLEPTONIC PLASMAS

Slow radiative losses:Output Luminosity << Input LuminosityLow efficiencyInjected particles not ‘burned’ Accumulation + high particle energy density

HADRONIC PLASMASHADRONIC PLASMAS

In: Particle Luminosity

Out: Photon Luminosity

Particle losses + radiation

Particle distribution function

PROTON INJECTION

PROTON DISTRIBUTION

FUNCTION

PROTON LOSSESPROTON ESCAPE

ELECTRONS-POSITRONS

PHOTONS

OBSERVED SPECTRUM

Leptonic processes

Protons:

injection

Electrons:

Photons:

Neutrinos:

Neutrons:

Bethe-Heitler

proton

triplet

ssa

γγ

annihilationphotopion

synchrotron

synchrotron

pair production

injectionlosses escape

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 lossesIn Dimitrakoudis et al 2012

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.

LINEAR REGIME: SECONDARY ELECTRONS AND PHOTON SPECTRA

R = 3e16 cmB = 1 G

γp = 2e6lp = 0.4tp,esc=tcr

Bethe-Heitler electrons

photopion electrons

γγ electrons

electrons photons

S. Dimitrakoudis et al., 2012

8 orders of magnitude X-rays to TeV

VARIABILITY I - QUADRATIC

For certain γp -B choices p-synchrotron serve as targetsfor both photopair and photopion quadratic behavior between p-syn and photopair + photopion synchrotron analogous to syn – SSC of lepto- nic plasmas

Dimitrakoudis et al. 2012quadratic

In linear regime

Lorentzian variation in proton luminosity

p-syn photo-meson

VARIABILITY II - CUBIC

For other γp- 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 P6-06S. Dimitrakoudis

In linear regime

PROTON SUPERCRITICALITIES

Proton injected luminosity is increased by a factor 3

linearquadratic

onset of supercriticality

If up>up,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

Pho

ton

Lum

inos

ity subcritical supercritical

SEARCHING FOR THE CRITICAL DENSITY

SUPERCRITICALREGIME

B=10 G R=3e16 cm

In all cases the proton injectionluminosity is increased by 1.25 corresponding photons increase by several orders of magnitude

SUBRCRITICALREGIME

I

Time-dependent transition of photon spectra from the subcritical to the supercritical regime

A ZOO OF PROTON SUPERCRITICALITIES

quenching-πγ inducedcascade

PPS Loop

quenching-BH inducedcascade

SUBCRITICAL REGIME

B=10 G R=3e16 cm

SUPERCRITICAL REGIME

When up>up,cr various feedback loops start operating Spontaneous soft-photon outgrowth leading tosubstantial 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 modelingFor γp>> up,cr ~ uB

DYNAMICAL BEHAVIOUR IN THE SUPERCRITICAL REGIME

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 cyclesor damped oscillations.

-- see also numerical work of Stern, Svensson, Sikora (90s) and Kirk & AM (90s -00s)

photons

protons

time

Ph

oto

n d

ensi

ty

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 MAGICobservations of 3C 279.• If the proton luminosity is high System becomes supercritical spontaneously producedsoft photons violate the X-ray limits.

• Fit only possible for low proton luminosity

high Doppler factor δ>20.

Petropoulou & AM 2012b

See Maria’s posterP2-10

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