Turbulence Particle Acceleration and UHECR Katsuaki Asano ICRR

Turbulence Particle Acceleration and UHECR Katsuaki Asano (ICRR, U. Tokyo) Yuto Teraki, Masaaki Hayashida, and Peter Meszaros

Shock Acceleration Non-relativistic Shock: Supernova Remnant SN 1006 Electron energy distribution: Single power-law with the index of 2. 1, cut off at 10 Te. V and B=30μG. Main Mechanism for Cosmic-Ray Production?

Shock Acceleration Relativistic Shock: GRB afterglow Talk by K. Noda on Thursday. SSC emission @ Te. V Fukushima+ 2017 Consistent with SSC by accelerated electrons at a relativistic shock! All non-thermal phenomena are due to shocks?

But in Blazars… Lower maximum energy Mrk 421： The acceleration mechanism seems different. Magnetic Reconnection Inoue & Takahara 2002 Sironi+ 2015 Equipartition Disagree with the leptonic model.

Alternative: stochastic acceleration by turbulece Energy=const. Diffusion Acceleration Cooling Injection

Excitation of Turbulence Rayleigh-Taylor (Toma+ 2017) Kelvin-Helmholtz (Beckwith+ 2011) Kink (Bromberg & Tchekhovskoy) 2016

Instability 2 Centrifugal Instability Gourgouliatos & Komissarov 2018 Star-jet interaction Perucho+ 2017

Wave-Particle Interaction High-energy particles interact with macroscopic E-M waves. Hereafter, we consider waves in MHD approximation. The gyroresonance with Alfven waves has been discussed. The kinetic energy and magnetic energy in perturbation are comparable.

Mrk 421+Kolmogorov The spectrum becomes too hard. Asano+ 14

＋Escape Effect? Kakuwa+ 2015 Possible but Even in the comoving frame

Mrk 421+Hard Sphere

MHD: Fast mode. Simulation （Inoue+ 2011） As for the magnetic field fluctuation, In the gas pressure dominant case,

Transit Time Damping Accelerate

Test particle simulation in pure linear Waves Fast High-beta plasma Projection Teraki & Asano 2019

Energy Diffusion Significant fraction of particles diffuses in the energy space.

Hard Sphere-like diffusion

Blazars with hard-sphere model Mrk 421 Asano & Hayashida 2018 1 ES 1959+650 3 C 279 The required acceleration efficiency is possible within the fast-wave TTD picture.

Ultra High-Energy Cosmic-Rays (UHECRs) Aab+ 2015 Transient Phenomena, such as GRBs, are still candidate. A significant correlation between AGNs and UHECRs has not been found.

UHECR production at the onset of GRB afterglow Duffell and Mac. Fadyen 2013 Injection energy Injection rate Diffusion coefficient Elapsed time

Average UHECR spectrum for a GRB Magnetic Field is normalized by the prompt emission. Shock acc. model

Total UHECR Flux Calculating the propagation of UHECRs Asano & Meszaros 2016 Seems possible as UHECR sources

Diffusion Coefficient

Summary • A significant fraction of particles can resonate with fast waves via TTD. • When the cut-off scale is larger than the Larmor radius, the hard-sphere acceleration realizes. • Most of blazar spectra can be explained by the hardsphere acceleration model. • UHECRs can be accelerated by turbulence at the onset of GRB afterglow. • Since the acceleration timescale is long, electrons cool before accelerating. • The required diffusion coefficient for UHECR production is not extreme one compared to our test particle simulation.

Fraction of particles in resonant Resonance broadening by Mirror Force

Pitch angle diffusion Due to Mirror Force No Gyroresonance

Enrgy diffusion Energy gain by the TTD resonance

Dependence on Parameters Those agree with theoretical expect.

3 C 279 Representative FSRQ z=0. 538 Ackerman+ 2016

Applications 1 -D time-dependent. Steady outflow. The acceleration timescale is comparable to the dynamical timescale. The time-dependent treatment is essential.

2013 flare with the stochastic acceleration model Asano & Hayashida 2015 Spectrum Lightcurve

2015 flare Bright and short variability Ackerman+ 2016

Synchrotron model for 2015 flare: Prompt injection Power-law injection (Reconnection-like) Asano & Hayashida submitted Secondary synch. The Poynting flux is comparable to electron luminosity.

Stochastic Acceleration Model for 2015 Flare A B C

Model A (EIC model neglecting the X-ray data) Particle dominant. The X-ray component has a different origin in this scenario.

Model B (EIC+SSC model with the X-ray data) Synchrotron cooling effect Too bright synchrotron? Larger B-field and Diffusion coefficient. The maximum energy of electrons is suppressed due to cooling. Magnetic field dominant. The X-ray component is SSC. Too bright synchrotron component.

Model C (Syn model with the secondary pair injection) Secondary pairs dominate the number of particles! Neglecting the secondary pair. Particle dominant, though synchrotron model! Large Diffusion coefficient+Weka B-field. Electromagnetic cascade+Re-acceleration+cooling. Secondary pairs dominate. Resultant electron spectrum: roughly E-2

Parameters in Mrk 421 The simulations of wave-particle interaction suggests Acceleration timescale