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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]. 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.

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Takuya Akahori, Dongsu Ryu Chungnam National University

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  1. 2.0 1.0 0.0 -1.0 -2.0 Log10 |RM| [rad m-2] -50 -25 0 25 50 [h-1Mpc] 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 SKA-KR Workshop 2010, KASI, Daejeon, Korea

  2. 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 SKA-KR Workshop 2010, KASI, Daejeon, Korea

  3. Introduction State-of-the-Art / Unresolved Problems • 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 SKA-KR Workshop 2010, KASI, Daejeon, Korea

  4. 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? Galaxy cluster RM~ 100 [rad m-2] IGMF ~1-10 [μG] Radial RM profiles Clarke, Kronberg, Bohringer (01) Govoni+ arXiv:1007.5207 SKA-KR Workshop 2010, KASI, Daejeon, Korea

  5. Estimations of RM in Galaxy Clusters • Power-law Gaussian random IGMF model • e.g.,Murgia+ (2004) 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 Kolmogorovturbulence and turbulence amplificationof the IGMF? Govoni+ arXiv:1007.5207 Guidetti+ (08) SKA-KR Workshop 2010, KASI, Daejeon, Korea

  6. Coma Loop I Hercules supercluster Virgo North Polar Spar Perseus Orion Arm Region A Loop II 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 /arcmin2 with ~1 rad m-2 error Xu+ (06) All sky RM map, Taylor, Stil, Sunstrum (09) RM < 10 [rad m-2] ? IGMF < 1 [μG] ? SKA-KR Workshop 2010, KASI, Daejeon, Korea

  7. log |B| μG 5 Mpc 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 Dubios, Teyssier (08) Stasyszyn+ arXiv:1003.5085 Akahori, Ryu (10) ApJ submitted 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 SKA-KR Workshop 2010, KASI, Daejeon, Korea

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

  9. (z=0, L=100 h-1 Mpc) 2.0 1.0 0.0 -1.0 -2.0 10. 5.0 0.0 -5.0 -10. Log10 |RM| [rad m-2] Log10 |RM| [rad m-2] RM [rad m-2] -10 -5 0 5 10 [h-1Mpc] -50 -25 0 25 50 [h-1Mpc] 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 SKA-KR Workshop 2010, KASI, Daejeon, Korea

  10. 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 SKA-KR Workshop 2010, KASI, Daejeon, Korea

  11. 100 h-1 10 h-1 1 h-1Mpc 10 h-1 1 h-1Mpc 2D power spectra of RM and the projected IGMF Black: 3×16 runs, Red: average ・Peaked at ~Mpc scale ・PRM(k) is close to PB||,proj(k): RM traces B well 1 Present-day local universe: statistics PDF of |RM| for WHIM (105 K<Tx<107 K) Tx: emissivity weighted temperature. Black: 3×16 runs,Red: average,Blue: best-fit ・Lognormal profile of PDF ・rms ~ 1.4 [rad m-2] for WHIM ↑ in good agreement with Cho, Ryu (09) SKA-KR Workshop 2010, KASI, Daejeon, Korea

  12. z=0.1 0.3 0.5 1.0 3.0 5.0 Log |RM| [rad m-2] 2 Cosmological effects: RM stacking Willman+ (08) • |RM| increases with integrating RM along LOS Simulation boxes are stacked up to z=5 Redshift distribution of radio sources are considered SKA-KR Workshop 2010, KASI, Daejeon, Korea

  13. ★ theoretical T [K] Tx=4keV Tx=1.5keV 107 ALL 1Mpc CLS TM7 ★ observational Pixcels w Tx>107K & Sx>10-8 e/s/cm2/sr Map TS8 Pixcels w Tx>107K & Sx>10-10e/s/cm2/sr Map TS0 Map Pixcels w Tx>107K T57 2 Cosmological effects: statistics • rms of RM • PDF • lognormal rms of RM integrated up to z. ICM candidates are subtracted in the integration (theoretical) or after the integration (observational) of RM SKA-KR Workshop 2010, KASI, Daejeon, Korea

  14. 2 Cosmological effects: statistics ~0.2º • P(k): peak scale at~0.2º • S2(r): characteristic scale at ~0.1-0.2º 1.4º 0.14º 2D power spectra P(k) integrated up to z=0.05, 0.3, 5 (thin to thick) 2nd order structure function S2(r) SKA-KR Workshop 2010, KASI, Daejeon, Korea

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

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

  17. 3 Galactic foreground: What’s the Best kf? • A high-pass filter with kf ~ 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: kn= 5 (2.8º scale), <RM>rms, noise= 20 [rad m-2] SKA-KR Workshop 2010, KASI, Daejeon, Korea

  18. 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 SKA-KR Workshop 2010, KASI, Daejeon, Korea

  19. 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 SKA-KR Workshop 2010, KASI, Daejeon, Korea

  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 SKA-KR Workshop 2010, KASI, Daejeon, Korea

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