SKA-JP Workshop Akahori 1/14 Exploring Faraday Rotation Measure due to the Intergalactic Magnetic Field with the Square Kilometer Array Takuya Akahori Chungnam National University

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

SKA-JP Workshop 3/14 Introduction: Baryon in our Universe Baryon Phase ICM (>10 7 K)ICM (>10 7 K) WHIM ( K)WHIM ( K) OthersOthers Baryon Phase Diagram from cosmo. simulation (Piro+ 07) Intra-Cluster Medium Warm-Hot Intergalactic Medium Ionized Medium ICM/WHIM Magnetized? Inter-Galactic Magnetic Field IGMF

SKA-JP Workshop 4/14 Introduction: IGMF and RM Evidences of Magnetization ICM: RM ~100 [rad m -2 ] IGMF ~1-10 [μG]ICM: RM ~100 [rad m -2 ] IGMF ~1-10 [μG] –Kolmogorov? (Vogt & Ensslin 05; Guidetti+ 08; Bonafede+ 10) WHIM: RM < 10 [rad m -2 ] ? IGMF ~ ?WHIM: RM < 10 [rad m -2 ] ? IGMF ~ ? RM through the ICM Govoni+ (10) All sky RM map Taylor, Stil, Sunstrum (09) IGMF remains largely unknown Where is the large-scale structure?

SKA-JP Workshop 5/14 Model: Our Model for the IGMF Predict RM of WHIMGoal: Predict RM of WHIM & test it by future obs. turbulence dynamo model (Ryu+ 08)Method: Simulation of the cosmological structure formation + turbulence dynamo model (Ryu+ 08) –MHD…still hard to treat evolution of turbulence and amplification of the IGMF correctly time [t eddy ] Energy density WHIM ICM Ryu+ (08) μG |B| 10μG 100 h -1 Mpc Ryu+ (08) Cho & Ryu (09) turbulence dynamo model 1. vorticity energy ε w 2. regard ε w as ε turb ε B /ε turb =f(t/t eddy ) 3. ε B /ε turb =f(t/t eddy ) 4. B=(8πε B ) 1/2

SKA-JP Workshop 6/14 1 Present-day Local universe: Profiles RM: ~100 (GCs), ~10 (Groups), ~ (filaments) RM: a random walk process, peaked at the center Log 10 |RM| [rad m -2 ] [h -1 Mpc]

SKA-JP Workshop 7/14 1 Present-day Local Universe: Statistics ・ Lognormal profile of PDF ・ rms ~ 1.4 [rad m -2 ] for WHIM PDF of |RM| for WHIM (10 5 K<Tx<10 7 K) Tx: emissivity weighted temperature. Black: 3×16 runs, Red: average, Blue: best-fit ・ Peaked at ~Mpc scale ・ P RM (k) traces P B||,proj (k) 2D power spectra of RM and the projected IGMF Black: 3×16 runs, Red: average 100 h h -1 1 h -1 Mpc 10 h -1 1 h -1 Mpc

SKA-JP Workshop 8/14 2 Cosmological Effects: RM Stacking |RM| increases with integrating RM along LOS Simulation boxes are stacked up to z=5 Redshift distribution of radio sources are considered Willman+ (08) z= Log |RM| [rad m -2 ]

SKA-JP Workshop 9/14 2 Cosmological Effecs: rms Value [rad m -2 ] RM of WHIM (in) 7-10 RM of WHIM (after) Subtl. of ICM after the integration temperature 10 7 K Subtl. of ICM in the integration Tx=4keV Tx=1.5keV ALL CLS 1Mpc TM7 TS8 ALL Map Pixcels w Tx>10 7 K & Sx>10 -8 e/s/cm 2 /sr TS0 ALL Map Pixcels w Tx>10 7 K & Sx> e/s/cm 2 /sr Line of sight Average of 200 runs

SKA-JP Workshop 10/14 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<5 TM7 Average of 200 runs

SKA-JP Workshop 11/14 2nd order SF (Mao+ 10) 2 Cosmological Effect: Structure Function Flat SF profile in ~0.1º-10º 2nd order SF ALL TS8 TS0 Galactic10º-100º Intergalactic ?0.2º 0.1º 1º 10º Average of 200 runs

SKA-JP Workshop 12/14 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 Galactic Contamination? 10º-100º 0.2º Remove the large scale component Filtered RM FFT FWT

SKA-JP Workshop 13/14 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 SKA

SKA-JP Workshop 14/14 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)