A Turbulent Local Environment of an FRB Siyao Xu Peking University Bing Zhang University of Nevada Las Vegas / Peking University

…… Turbulence is inevitable. Protoplanetary disks Galaxy clusters Supernova remnants Turbulence is inevitable.

Turbulence in astrophysics GRB Core-collapse supernovae Zhang & Yan 11, ICMART model Mosta et al. 2015 Turbulence in astrophysics Interstellar clouds Cosmic rays Supernova shocks First stars Xu et al. 15, 16 Xu & Yan 13 Xu et al. in prep Xu & Lazarian 16, 17

A turbulent local environment of an FRB synchrotron polarization P Faraday rotation RM B|| B^ ρ Turbulent FRB model, may also applicable to e.g., blazars RM is intrinsic to the source itself. scatter broadening τsc

A turbulent local environment of an FRB Faraday rotation RM B|| ρ Turbulent FRB model, may also applicable to e.g., blazars scatter broadening τsc

Turbulent magnetic field and density field

Turbulent magnetic field and density field Do they have the same distribution in turbulence?

Flux-freezing breakdown Magnetic field diffusion Supersonic turbulence Microscopic diffusion e.g., resistive diffusion, ambipolar diffusion Reconnection-driven turbulent diffusion (Lazarian & Vishniac 1999) e.g., the cold ISM is highly turbulent and highly supersonic, Re ~ 108, Ms>10 he shockpump thus produces density structure without the necessity of any sort of instability. We argue that the shockpump should lead to nested shock-induced structures, providing a cascade mechanism for supersonic "turbulence" and a physical explanation for the fractal-like structure of the cool interstellar medium. Over the scales where turbulence exists Eyink et al. 2013 Molecular clouds

Supersonic magnetic turbulence Spectra of magnetic and density fluctuations in Subsonic turbulence Supersonic turbulence Ms~0.35 Ms~2.5 Density Magnetic field Magnetic field Spectra Density Cho & Lazarian 2003

RM in supersonic magnetic turbulence RM density fluctuations Thermal energy < turbulent kinetic energy < magnetic energy In supersonic and sub-Alfvenic turbulence, ≈ RM fluctuations are dominated by density fluctuations.

RM in supersonic ISM β=2.64 Density spectra RM spectra Spectral slope vs. length scale Structure function of RM fluctuations dust HI absorption 12CO 13CO Data: Minter & Spangler 1996 β=2.64 Hennebelle & Falgarone 2012 Xu & Zhang 2016a, (ApJ, 824, 113)

Density distribution in supersonic turbulence Ms=0.6 A shallow density spectrum β<3 Ms~10 Kolmogorov Ms=8.3 Velocity Beresnyak et al. 2005 Kowal et al. 2007

Density distribution in supersonic turbulence

Scatter broadening in turbulence Scattering time ~ Small-scale density enhancement leads to enhanced scattering Shallower Xu & Zhang 2017 (ApJ, 835, 2) Supersonic Subsonic

Scattering time vs. DM for Galactic pulsars Data: Krishnakumar et al. 2015

Supersonic ISM β=2.6 Scattering time vs. DM for Galactic pulsars Data: Krishnakumar et al. 2015 Supersonic ISM β=2.6 Density Magnetic field Small-scale density excess enhances scattering. Xu & Zhang 2017 (ApJ, 835, 2) Cho & Lazarian 2003

Scattering time induced by supersonic turbulence (β<3) Scatter broadening of FRBs Scattering time induced by supersonic turbulence (β<3) Xu & Zhang 2016b (ApJ, 832, 199) Using parameters similar to the supersonic turbulence in the Galactic ISM (inferred from pulsars) ν= 1 GHz, β~ 2.6, δne ~ 0.3 cm-3, ne ~ 0.01 cm-3, l0 ~ 107 cm, f ~ 10-6

A turbulent local environment of an FRB synchrotron polarization P Faraday rotation RM B|| B^ ρ Turbulent FRB model, may also applicable to e.g., blazars

Simultaneous multi-wavelength observations of an FRB Faraday depolarization scale Uniform RM Stochastic RM Beck & Wielebinski 2013 Depolarization from radio sources, where the degree of polarization decreases with increasing wavelength, Lazarian & Pogosyan 2016 (ApJ, 818, 178) Emitting region scale L = Faraday depolarization scale

Simultaneous multi-wavelength observations of an FRB 1 103 106 Intrinsic polarized intensity Depolarization Pi = Q + iU λ(p-1)/2 λ< λc λ> λc

τsc RM RM λ> λc Depolarization ρ Turbulence uniform stochastic B ρ Both Turbulence sub-S & sub-A sub-S & super-A super-S & sub-A super-S & super-A RM large small large small τsc small small large small correlation of polarization at different wavelengths along a fixed line of sight. Detailed structures of …. Probable but not definite Also mention PSA ri > ri > ri > ri < Polarization Frequency Analysis (PFA) Lazarian & Pogosyan 2016 (ApJ, 818, 178)

Take-Away Soup Due to the flux-freezing breakdown, the distribution of magnetic field and density fluctuations can be different in turbulence. In supersonic and sub-Alfvenic turbulence, RM fluctuations are dominated by density fluctuations. In supersonic turbulence, At long wavelengths, at sufficiently short wavelengths small-scale density excess enhances scattering. Multi-wavelength observations of FRBs, GRBs, …., can provide a useful tool for probing magnetic field and density structure, particle acceleration and radiation mechanism at the source.