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RM due to magnetic fields in the cosmic web and SKA observations Takuya Akahori A KRCF fellow @ KASI (-2012.9) A JSPS fellow @ Sydney U. (2012.10-) 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing References: TA, Ryu (2010), ApJ, 723, 476 TA, Ryu (2011), ApJ, 738, 134 TA, et al. submitted x2 1/16 Collaborators: D. Ryu, J. Kim, B. G. Gaensler, K. Takahashi, K. Kumazaki Special thanks: J. Stil, S. A. Mao, X. Sun, M. Machida
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Magnetic Fields in the Cosmic Web (Inter-Galactic Magnetic Field, IGMF) 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing 3oo Mpc ©4D2U, NAOJ 2/16 IGMF Faraday Rotation
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Residual RM, RRM (observed RM-Galactic RM) 7-15 [rad/m 2 ] RRM deviation tends to be larger for higher redshift extragalactic sources (e.g., Kronberg+ 08; Hammond 11) RMs through superclusters in nearby universe 9-60 [rad/m 2 ] RM enhancements in Hercules and Perseus-Pisces (but very tentative, see Xu+ 06) Cluster outskirts observations <50 [rad/m 2 ] RM deviation at cluster outskirts (e.g., Govoni+ 10) Observational Implications of RM IGMF 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing Govoni+ (10) RM IGMF ~O(1-10) [rad/m 2 ] in filaments? 3Mpc 4Mpc 5Mpc … RM~O(100) [rad/m 2 ] in GCs |B|~O(1) µG 3/16
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Estimations from LSS formation simulations HD and MHD (e.g., Ryu+ 98; Dubois & Teyssier 08; Cho & Ryu 09; Dolag & Stasyszyn 09; Stasyszyn+ 10) IGMF based on MHD turbulence 1/2 / 1/2 ∼ a few × 100 nG (note: ∼ 10 nG) Coherent length, L int /L 0 ~1/15 Theoretical Estimations of RM IGMF 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing Cho+ (09) Cho & Ryu (09) 10 -4 μG |B| 10μG 100 h -1 Mpc RM IGMF ~O(1) [rad/m 2 ] in a filament? Ryu+ (08) 4/16
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Questions: What’s the nature of RM due to turbulent-amplified IGMF? Can we discover (and test) them with latest/future observations such as SKA and its pathfinders? To answer these questions, we calculate RM maps using a model of the IGMF by Ryu+ (08) Calculations of RM IGMF 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing n e [cm -3 ], B || [μG], l [kpc] 5/16
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2D RM map & 1D RM profile 100 (GCs), ~10 (GGs), ~1 (filaments) [rad/m 2 ] RM behaves like a random walk with the scale ~ several x 100 [kpc] RM at the density peak mostly contributes to the accumulated RM Result: Local Universe (1/2) 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing 2.0 1.0 0.0 -1.0 -2.0 Log 10 |RM| [rad m -2 ] -10 -5 0 5 10 [Mpc/h] TA, Ryu (2010), ApJ, 723, 476 6/16
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Statistics of RMs for LoSs with Tx = 10 5-7 K Probability Distribution Function (PDF) Log-normal Root mean square value rms ~1.4 [rad/m 2 ] P RM (k)~P B||,proj (k), L B ~1 Mpc ~L crl /4 in the linear growth stage Result: Local Universe (2/2) 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing TA, Ryu (2010), ApJ, 723, 476 ↓L crl ↓L B 48 runs average of them best-fit lognormal 7/16
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Simple estimation of RM IGMF RM~1 [rad/m 2 ] for a filament in a local universe RM ∝ √N since an accumulation of RM is a random walk process If N from the path length N~100 [Mpc] / 10 [Mpc] ~10 1×√10 ~3.2 [rad/m 2 ] If N from the column density N~2×10 -3 [Mpc/cm 3 ] / 5×10 -5 [Mpc/cm 3 ] ~40 1×√40 ~6.3 [rad/m 2 ] IGMF in the WHIM range increases with z by a factor of ~2 (Ryu+ 08) Calculation 2: Cosmological Contribution 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing path length (dashed) and column density (solid) across the WHIM RM IGMF ~several-10 [rad/m 2 ] through filaments? 8/16
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Result: Cosmological Contribution (1/2) 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing ※ Galaxy Cluster Subtraction CLS:ALL – grids (1 Mpc around Tx > 2 keV) TM7:ALL – grids (T > 10 7 K) TS8:ALL – pixels (Tx* > 10 7 K & Sx*>10 -8 erg/s/cm 2 /sr) TS0:ALL – pixels (Tx* > 10 7 K & Sx*>10 -10 erg/s/cm 2 /sr) Integration of RM IGMF RM behaves like a random walk rms ~7-10 [rad/m 2 ] through filaments TA, Ryu (2011), ApJ, 738, 134 200 run average 9/16
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Statistics of RMs for LoSs through filaments SF 2 is flat at >0.2° with 100-200 [rad 2 /m 4 ] Result: Cosmological Contribution (2/2) 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing South Pole ● : Mao+ (10) WSRT+ACTA ー: Stil+ (11) NVSS(VLA) North Pole ◯: Mao+ (10) WSRT+ACTA ー: Stil+ (11) NVSS(VLA) Our Predictions Color : Akahori, Ryu (2011) TA, Ryu (2011), ApJ, 738, 134 200 run average 10/16
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RM IGMF in filaments would be 1-10 [rad/m 2 ] RM rms ~1.4 [rad/m 2 ] in the local universe RM rms ~7-10 [rad/m 2 ] up to z=5 It would have characteristic structures A peak scale of 1 Mpc for RMs in the local universe A flat SF at Θ>0.2º for RMs up to z=5 Next questions: How much is the Galactic Foreground? How can we find (and test) the RM IGMF ? Summary of the points so far 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing 11/16
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Toward the poles, turbulent magnetic field is predominant. Its precise modeling is important Amplitudes of regular and turbulent fields should be related each other, depending on rms Mach number of turbulence and plasma β Analytic + MHD turbulence model (Akahori+) SF is <100 [rad 2 /m 4 ] at 10° scale toward the poles The slope is much steeper that the observed ones at Θ<~1º Observed RMs would contain significant contributions at small angular scales from local structure, intrinsic RM, and/or the IGMF! Furure (1/3): Galactic Foreground 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing TA, Ryu, Kim, Gaensler, submitted 12/16
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The Square Kilometer Array Ultra-wide band & ultra-dense RM grid “Cosmic Magnetism” is one of the five key science projects Furure (1/3): Dense RM Grid!! 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing PreviousPathfindersSKA Observational uncertainty [rad m -2 ]1010.1 Average separation of sources [deg]10.10.01 0.1 1 10 Θ [degree] S [rad 2 m -4 ] 10 100 ASKAP 30 deg 2 0.1 1 10 Θ [degree] SKA 30 deg 2 TA+ in prep. previous 13/16 IGMF + GMF
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Faraday Tomography (RM Synthesis) What is the best target, and what is the necessary dataset for the IGMF study? Furure (2/3): Faraday Tomography 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing 0.01 0.1 1 10 λ 2 [m 2 ] P[mJy] =Q+iU Polarized intensity IGMF GMF Intrinsic F[mJy] 0 20 40 φ [rad/m 2 ] Model Faraday Disp. Func. TA, Kumazaki, Takahashi, Ryu, submitted Reconstructed Faraday Disp. Func. 0 20 40 φ [rad/m 2 ] Faraday Tomography F[mJy] LOFAR+GMRT+ ASKAP ~ F[mJy] SKA ~ 14/16
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RRM or high-pass filter in Fourier-space How can we treat unevenly sampled data? What is the necessary dataset for IGMF studies? Furure (3/3): Image Processing 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing TA+ in prep. Fourier transformation of RM map Chop the large-scale power in Fourier space Inverse Fourier transformation IGMF + GMFIGMF onlyHigh-pass filtered 15/16
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Summary 2012.8.20-23 T. Akahori, IAU-GA2012-SpS4@Beijing RM due to turbulent-driven IGMF in filaments Local universe RM rms ~1.4 [rad/m 2 ], lognormal 1 Mpc scale Cosmological contribution RM rms ~7-10 [rad/m 2 ], lognormal 0.1-0.2º scale & flat SF at Θ>0.2º Future Precise modeling of Milky Way RM Synthesis & Image processing Tests with SKA & its pathfinders! 16/16
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