2010.11.4-5 SKA-JP Workshop 2010@NAOJ Akahori 1/14

Exploring Faraday Rotation Measure due to the Intergalactic Magnetic Field w

ith the Square Kilometer Array

Takuya AkahoriChungnam National University

2010.11.4-5 SKA-JP Workshop 2010@NAOJ Akahori 2/14

Contents

• Introduction

• Faraday Rotation Measure (RM) due to the Intergalactic Magnetic Field (IGMF)– Part 1. present-day local universe– Part 2. cosmological effect– Part 3. galactic foreground

• Summary and Future

References:Akahori, Ryu (2010), ApJ, 723, 476ー (2010) to be submittedAkahori, SKA-Japan sub-SWG “Cosmic Magnetism”, Chap. 4

References:Akahori, Ryu (2010), ApJ, 723, 476ー (2010) to be submittedAkahori, SKA-Japan sub-SWG “Cosmic Magnetism”, Chap. 4

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Introduction: Baryon in our Universe

Baryon PhaseBaryon Phase

• ICM (>10ICM (>1077K)K)

• WHIM (10WHIM (105-75-7K)K)

• OthersOthersBaryon Phase Diagram from cosmo. simulation (Piro+ 07)

Intra-Cluster Medium

Warm-Hot Intergalactic Medium

Ionized MediumICM/WHIM

Magnetized?Inter-Galactic Magnetic Field

IGMF

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Introduction: IGMF and RM

Evidences of MagnetizationEvidences of Magnetization• ICM: ICM: RM ~100 [rad mRM ~100 [rad m-2-2] ] IGMF ~1-10 [μG]IGMF ~1-10 [μG]

– Kolmogorov? (Vogt & Ensslin 05; Guidetti+ 08; Bonafede+ 10)

• WHIM: WHIM: RM < 10 [rad mRM < 10 [rad m-2-2] ?] ? IGMF ~ ? IGMF ~ ?

RM through the ICMGovoni+ (10) All sky RM map

Taylor, Stil, Sunstrum (09)

IGMF remains largely unknown

Where is the large-scale structure?

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Model: Our Model for the IGMF

• Goal: Predict RM of WHIMPredict RM of WHIM & test it by future obs. • Method: Simulation of the cosmological structure fo

rmation + turbulence dynamo model (Ryu+ 08)turbulence dynamo model (Ryu+ 08)– MHD…still hard to treat evolution of turbulence and amplification of the IGMF correctly

time [teddy]

En

erg

y d

en

sity

WHIM

ICM Ryu+ (08)10-4μG |B| 10μG

100 h-1 Mpc

Ryu+ (08)

Cho & Ryu (09)

turbulence dynturbulence dynamo modelamo model

1. vorticity energy εw

2. regard εw as εturb

3. εεBB/ε/εturbturb==f(t/tf(t/teddyeddy)) 4. B=(8πεB)1/2

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1 Present-day Local universe: Profiles

• RM: ~100 (GCs), ~10 (Groups), ~0.01-1 (filaments)• RM: a random walk process, peaked at the center

Log10 |RM| [rad m-2]

-50 -25 0 25 50[h-1Mpc]

2.0

1.0

0.0

-

1.0

-2.0

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1 Present-day Local Universe: Statistics

・ Lognormal profile of PDF・ rms ~ 1.4 [rad m-2] for WHIM

PDF of |RM| for WHIM (105 K<Tx<107 K)Tx: emissivity weighted temperature. Black: 3×16 runs, Red: average, Blue: best-fit

・ Peaked at ~Mpc scale・ PRM(k) traces PB||,proj(k)

2D power spectra of RM and the projected IGMFBlack: 3×16 runs, Red: average

100 h-1 10 h-1 1 h-1Mpc 10 h-1 1 h-1Mpc

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2 Cosmological Effects: RM Stacking

• |RM| increases with integrating RM along LOS

Simulation boxes are stacked up to z=5Redshift distribution of radio sources are considered

Willman+ (08)

z=0.1 0.3 0.5 1.0 3.0 5.0

Log |RM|[rad m-2]

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2 Cosmological Effecs: rms Value

[rad m-2]

RM of WHIM (in) 7-10RM of WHIM (after) 6-7

Subtl. of ICM after the integration

temperature

107K

Subtl. of ICM in the integration

Tx=4keVTx=1.5keV

ALL

CLS1Mpc

TM7

TS8ALLMap

Pixcels w Tx>107K& Sx>10-8 e/s/cm2/sr

TS0ALLMap

Pixcels w Tx>107K& Sx>10-10e/s/cm2/sr

Line of sight

Average of 200 runs

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2 Cosmological Effects: Statistics

• PDF of |RM| follows the log-normal distribution

• Power spectrum peaks at ~0.2º scale

1.4º 0.14º

~0.2º

z<0.05

z<0.3

z<5TM7Average of 200 runs

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2nd order SF (Mao+ 10)

2 Cosmological Effect: Structure Function

• Flat SF profile in ~0.1º-10º

2nd order SFALLTS8TS0

Galactic

10º-100º10º-100º

Intergalactic?

0.2º0.2º

0.1º 1º 10º

Average of 200 runs

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• Galactic foreground RM of order ~10 [rad m-2] is a serious contamination

3 Galactic Foreground: Concept of Analysis

Intrinsic + Galactic

Intrinsic RM

Galactic RM

High-pass filter

GalacticContamination?

10º-100º10º-100º0.2º0.2º

Remove the large scale componentRemove the large scale component

Filtered RM

FFT FWTFFT FWT

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Summary

RM in filaments is discussed using a model IGMF• Present-day local universe

– rms ~ 1 [rad m-2], lognormal, peak at ~Mpc • Cosmological effects

– rms ~ several [rad m-2], lognormal, peak at ~0.2º

• Galactic Foreground– High-pass filters (FFT/FWT) may work well

A concept design for SKA Phase 1 (Garrett+ 10)

Our estimated RM could be tested with the SKAOur estimated RM could be tested with the SKA

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Future

• Wide-band observation– RM ranges from ~0.1 to ~100 rad m-2

• Collaboration with galaxy community– Modeling of galactic foreground– Development of RM analysis

• Participation in projects – ASKAP/POSSUM– Japan SKA consortium SWG– Korea SKA consortium? Sofue, Machida, Kudo (10)