1. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, Korea Akahori 1/20 Study of Faraday Rotation due to the Intergalactic Magnetic Field ~Preparing the Era of the Square Kilometer Array~ Takuya Akahori, Dongsu Ryu Chungnam National University 2.0 1.0 0.0 -1.0 -2.0 Log 10 |RM| [rad m -2 ] -50 -25 0 25 50 [h -1 Mpc]

2. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 2/20 Contents Introduction –State-of-the-Art/Unresolved Problems Faraday Rotation Measure (RM) due to the Intergalactic Magnetic Field (IGMF) –Part 1. present-day local universe Coherence length, rms value, PDF, power spectrum –Part 2. cosmological effects LSS evolution, radio source distribution, X-ray emission –Part 3. galactic foreground Scale difference, FFT/FWT filtering analyses Summary Status of SKA in Japan

3. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 3/20 Introduction RM & synchrotron observations –Simard-Normandin, Kronberg, Button (81), Kim+ (89; 90; 91), Clarke, Kronberg, Bohringer (01), Taylor, Fabian, Allen (02), Govoni+ (04), Xu+ (06), Pizzo+ (08), Taylor+ (09), Govoni+ (10) Cross correlation & structure function of RM –Brown, Farnsworth, Rudnick (09), Lee+ (09), Stasyszyu+ (10), Mao+ (10) Spectral analyses, tomography –Frick+ (01), Brentjens, Bruyn (05), Schnitzeler, Katgert, Bruyn (09) Modeling of magnetic field and its power spectrum –Feretti+ (95), Felton (96), Krause+ (09) –Vogt, Ensslin (03; 05), Murgia+ (04), Guidetti+ (08), Bonafede+ (10) Simulations and estimation of RM in the LSS –Kulsrud+ (97), Ryu, Kang, Biermann (98), Dolag+ (99; 05), Dubios. Teyssier (08), Ryu+ (08), Dolag, Stasyszyu (09), Akahori, Ryu (10) Relation with metal enrichment, effects of AGN & galaxies State-of-the-Art / Unresolved Problems

4. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 4/20 Observations of RM in Galaxy Clusters Now) profile of RM, correlation with the X-ray morphology SKA) what’s the origin? when developed? how important? Radial RM profiles Clarke, Kronberg, Bohringer (01) Govoni+ arXiv:1007.5207 Galaxy cluster RM~ 100 [rad m -2 ] IGMF ~1-10 [μG]

5. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 5/20 Estimations of RM in Galaxy Clusters Now) constrains of IGMF structure by fitting with models SKA) statistical argument using large samples n=11/3 (Kolmogorov)? (e.g. Vogt, Ensslin 05; Guidetti+08; Bonafede+10) → existence of Kolmogorov turbulence and turbulence amplification of the IGMF? - Power-law Gaussian random IGMF model e.g., Murgia+ (2004) Govoni+ arXiv:1007.5207 Guidetti+ (08)

6. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 6/20 Observations of RM in the LSS Now) RM<10 rad m -2, or it has too complicate structures to distinguish them from noise SKA) 1 source /arcmin 2 with ~1 rad m -2 error Orion Arm Region A Loop II Loop I Coma Virgo Perseus North Polar Spar Hercules supercluster All sky RM map, Taylor, Stil, Sunstrum (09) Xu+ (06) RM < 10 [rad m -2 ] ? IGMF < 1 [μG] ?

7. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 7/20 Estimations of RM in the LSS Cosmological HD/MHD simulations –MHD…still hard to treat the evolution of turbulence and amplification of the IGMF correctly log |B| μG 5 Mpc Dubios, Teyssier (08) Now) estimations of RM from HD/MHD simulations SKA) observational appearance of RM → Radio source distribution in space → Uncertainty of RM at the source, our local group, and our galaxy → Of course, a reasonable IGMF model Stasyszyn+ arXiv:1003.5085 Akahori, Ryu (10) ApJ submitted

8. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 8/20 Turbulence Dynamo Model ① Calculate curl component of flow motion & its energy ε w ② Regard ε w as the turbulence energy ε turb ③ Adopt the growth model ε B /ε turb =f(t/t eddy ) & B=(8πε B ) 1/2 Our Model for the IGMF time [t eddy ] Energy density filaments GCs Ryu+ (08) 10 -4 μG |B| 10μG 100 h -1 Mpc Ryu+ (08) Cho & Ryu (09) IGMF ~0.1 [μG] RM~ 1 [rad m -2 ]

9. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 9/20 1 Present-day local universe: 2D map RM ~100 (GCs), ~10 (Groups), ~0.01-1 (filaments) Mixture of positive and negative RM, that reflects the randomness and the coherence scale of IGMFs in the LSS 2.0 1.0 0.0 -1.0 -2.0 Log 10 |RM| [rad m -2 ] -50 -25 0 25 50 [h -1 Mpc] (z=0, L=100 h -1 Mpc) -10 -5 0 5 10 [h -1 Mpc] Log 10 |RM| [rad m -2 ] 10. 5.0 0.0 -5.0 -10. RM [rad m -2 ]

10. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 10/20 1 Present-day local universe: radial profile Inducement of RM is a random walk process with the coherence length < path length, but is dominated by the contribution from the density peak along LOS

11. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 11/20 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) is close to P B||,proj (k): RM traces B well 2D power spectra of RM and the projected IGMF Black: 3×16 runs, Red: average 100 h -1 10 h -1 1 h -1 Mpc 10 h -1 1 h -1 Mpc ↑ in good agreement with Cho, Ryu (09)

12. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 12/20 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=0.1 0.3 0.5 1.0 3.0 5.0 Log |RM| [rad m -2 ]

13. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 13/20 2 Cosmological effects: statistics rms of RM PDF –lognormal [rad m -2 ] WHIM+ICM 40 WHIM (theoretical) 7-10 WHIM (observational) 6-10 rms of RM integrated up to z. ICM candidates are subtracted in the integration (theoretical) or after the integration (observational) of RM ★ observational T [K] 10 7 ★ theoretical Tx=4keV Tx=1.5keV ALL CLS 1Mpc TM7 T57 MapPixcels w Tx>10 7 K TS8 Map Pixcels w Tx>10 7 K & Sx>10 -8 e/s/cm 2 /sr TS0 Map Pixcels w Tx>10 7 K & Sx>10 -10 e/s/cm 2 /sr

14. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 14/20 2 Cosmological effects: statistics P(k): peak scale at ~0.2º S 2 (r): characteristic scale at ~0.1-0.2º 2D power spectra P(k) integrated up to z=0.05, 0.3, 5 (thin to thick) 2nd order structure function S 2 (r) 1.4º 0.14º ~0.2º

15. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 15/20 All sky RM (Taylor+ 09) Galactic RM is a serious contamination for studying RM in filaments –galactic RM ~10-100 [rad m -2 ] 3 Galactic foreground: Concept of Analysis Spectra of observed all-sky RM (Frick+ 01) Key point: peak scales are different 10-100 degree 0.1-1 degree Chop!Use!

16. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 16/20 3 Galactic foreground: High-pass filters High-pass filters have potential to subtract galactic component Intrinsic +Noise High-pass filter Fast Fourier transformation (FFT) Fast Wavelet transformation (FWT) Transform→ low frequency cut at k f → inverse-Transform Parameter: k f Noise RM Gaussian random fluctuation Kolmogorov spectrum |Q(k)| 2 ∝ k -11/3 (k>k n ), k -1 (k<k n ) =0, rms = σ n Parameters: σ n & k n Intrinsic RM Filtered RM (FFT/FWT)

17. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 17/20 3 Galactic foreground: What’s the Best k f ? A high-pass filter with k f ~ degree would effectively reduce the galactic foreground contamination rms of RM as a function of the filter scales of FFT (left) and FWT (right) Noise model: k n = 5 (2.8º scale), rms, noise = 20 [rad m -2 ]

18. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 18/20 Summary RM in filaments is discussed using a model IGMF Present-day local universe –rms ~ 1 [rad m -2 ] for WHIM, lognormal, peak at ~Mpc Cosmological effects (stcking up to z=5) –rms ~ several-10 [rad m -2 ] for WHIM, lognormal, peak at ~0.2º Galactic Foreground –Degree-scale high-pass filters (FFT/FWT) works well SKA will highlight and reveal origin and nature of the IGMF. Our estimated RM is in detection range on SKA. The high-pass filter is quite effective to remove galactic foreground RM, which would improve statistical analyses – e.g., cross correlation and structure function

19. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 19/20 Status of SKA in Japan Japanese SKA consortium (SKA-JP) –since 2008.5, ~70 members, ~20 Institute –Science & Engineer Working Groups –Regular meeting (TV, Site) ~1/month International Workshops –SKA-JP WS 2004.11, 2008.11 –SKA-JP Workshop 2010.11.3-4@NAOJ Recommendation of Science Council of Japan –LCGT, TMT, SKA, SPICA, ASTRO-H,.. –Japan should bear 10% (~2-300M$?) of construction and use costs –But, “observer” so far

20. 2010.08.20SKA-KR Workshop 2010, KASI, Daejeon, KoreaAkahori 20/20 Status of SKA in Japan Science Working Group –8 subgroups Cosmic Magnetic Fields / AGN / Pulsars / Galaxy evolution and high-z universe / Astrometry / Star and Planet Formation / Wide-Band Spectral Line Survey / Antenna –Summary of unresolved problems To be uploaded on SKA memo http://www.skatelescope.org/pages/page_memos.htm Engineer Working Group –Ultra-wide band polarized wave measurement on >~ 10 GHz Ultra-wide feed, tapered slot antenna Digital polarized wave measurement system Collaboration with East- Asian countries