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

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

3. 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

4. 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

5. 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

6. Turbulent magnetic field and density field

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

8. 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

9. 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

10. 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.

11. 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)

12. 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

13. Density distribution in supersonic turbulence

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

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

16. 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

17. 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

18. 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

19. 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

20. Simultaneous multi-wavelength observations of an FRB1
103
106
Intrinsic polarized intensity
Depolarization
Pi = Q + iU λ(p-1)/2
λ< λc
λ> λc

21. 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)

22. 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.