Studying turbulence from polarized synchrotron emission with multifrequency

Studying turbulence from polarized synchrotron emission with multifrequency measurement Hyeseung Lee 1 with Jungyeon Cho 1, A. Lazarian 2 1 Chungnam Nation University, South Korea 2 University of Wisconsin-Madison, USA EANAM 2016, Beijing, China

1 Motivation MHD Turbulence BK workshop 2016

1 Motivation ic t e n g Ma ion t c e n recon Cosm ic ra Magnetohydrodynamic Turbulence Dens ity Faraday rotation star formation ity c o l Ve Magnetic Field Magnetic Synchrotron emission ys PDF Power spectrum Structure function BK workshop 2016

2 -1 Method –Data Synthetic Data B 0 = 0 where kmax= N/2 (N=resolution) N 3=5123 In Fourier space 2 |A(k)|2 k-m m=11/3 for Kolmogorov (Cho&Lazarian 2010) Spectrum of magnetic field follows a Kolmogorov spectrum EANAM 2016, Beijing, China

2 -2 Method –Data Synthetic Data B 0 = 0 where kmax= N/2 (N=resolution) N 3=5123 Turbulence Data : based on a 3 rd order accurate hybrid non- osciallatory (ENO) scheme in a periodic box of size 2π (Cho & Lazarian 2002) MA = v/VA ~ 0. 7 MS = v/a ~ 0. 7 EANAM 2016, Beijing, China

2 -3 Method : Polarization from synchrotron rad. § Polarized intensity observed at a 2 D position X on the plane of the sky at wavelength λ z Intrinsic polarization defined by the Stokes parameters Q and U : Pj = Qj + i. Uj Faraday rotation measure EANAM 2016, Beijing, China

2 -4 Statistics – Power spectrum shell-integrated 1 D spectrum for a 3 D variable Ring-integrated 1 D spectrum for a 2 D variable ky Ky Kx k k+1 kx kz EANAM 2016, Beijing, China

3 -1 Result 1 – spectral index of EED ( ) The variations of the spectral index of relativistic electron energy distribution change the amplitude of the fluctuations, but not the spectral slope of the synchrotron power spectrum. (Lazarian&Pogosyan 2012) = 1. 5 ~ 4. 0 = 2. 0 EED (Electron Energy Distribution) : N(E)d. E=N 0 E-γd. E EANAM 2016, Beijing, China

3 -3 Result 2 - synchrotron radiation & Faraday rotation in code unit fluctuations in F. R. measure Faraday depolarization effect synchrotron emission F. R. effect (Lazarian&Pogosyan 2016) d. P/dλ 2 is also useful to recover the statistics of MHD turbulence! EANAM 2016, Beijing, China

4 -1 Interferometric method ★ number of baselines NBASE=30 noise Telescope resolution S/N=1/5 θFWHM=3’ KNAG 2016

4 -2 Results 3 – using MHD turbulence data θFWHM=3’ , NBASE = 30 , S/N = 1/5 EANAM 2016, Beijing, China

5 Summary Our numerical results show that we can study MHD turbulence through polarized synchrotron emission. This study can be performed • in the presence of Faraday rotation and depolarization caused by turbulent magnetic field, • in the settings when only Faraday rotation is responsible for the polarization fluctuations, • in the presence of effects of finite beamsize, noise, and a few baselines Our present study paves the way for the successful use of spectrum with observational data. EANAM 2016, Beijing, China

In progress statistical description : anisotropy Quadrupole moment Structure function 2 -nd order structure function Ii(X)-Ii (X+R) R⊥ R|| Quadrupole ratio y <Bx> ~ 1. 0 z B 0 x EANAM 2016, Beijing, China

In progress Mode decoupling : Alfven, fast, slow EANAM 2016, Beijing, China

In progress Mode decoupling : Alfven, fast, slow Alfven Fast Slow B 0 EANAM 2016, Beijing, China

Polarization from spatially separated In progress medium y y z LOS <Bx> ~ 1. 0 x <By> ~ 1. 0 x B 0 EANAM 2016, Beijing, China B 0

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2 -0 statistical description : power spectrum real-space distribution of v(r), b(r), ρ(r), … Fourier transform Amplitude (S) || + + + E(k) wave number (k ∝ 1/λ) || Power spectrum : E(k) e. g) E(k) ~ k 5/3 (Kolmogorov spectrum) EANAM 2016, Beijing, China k [Hz]

2 -1 Method –Data Synthetic Data B 0 = 0 where kmax= N/2 (N=resolution) N 3=5123 k-5/3 for magnetic field k-1 for density EANAM 2016, Beijing, China

3 -2 Result 2 - synchrotron radiation or Faraday rotation Effect of Faraday rotation Fixed intrinsic synchrotron emission (Q/I=1, U/I=0) P 4 P 3 P 2 Pj = Qj + i. Uj P 1 λ~1 xn-4 xn-2 xn-1 xn P 1= P 2= P 3= P 4 P 1 Φ 2 Φ 3 Φ 2 P 2 Φ 3 Φ 1≠ Φ 2≠ Φ 3 EANAM 2016, Beijing, China

3 -2 Result 2 - synchrotron radiation or Faraday rotation Effect of synchrotron emission Uniform Faraday roatation (ne(z)=1, Bz(z)=1) P 4 P 3 P 2 P 1 xn-4 xn-2 xn-1 xn small λ P 1≠ P 2≠ P 3≠ P 4 Φ 3 small-K Faraday depolarization effect Φ 3 large-K Φ 2 negligible EANAM 2016, Beijing, China Φ 1 P 2 Φ 1= Φ 2= Φ 3

4 -0 Interferometric method ★ noise Telescope resolution number of baselines We can obtain spectrum in Fourier space for certain wavevectors through interferometric observations! Ky Kx KNAG 2016