RM due to magnetic fields in the cosmic web and SKA observations Takuya Akahori A KRCF KASI ( ) A JSPS Sydney U. ( ) T. Akahori, 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

Magnetic Fields in the Cosmic Web (Inter-Galactic Magnetic Field, IGMF) T. Akahori, 3oo Mpc ©4D2U, NAOJ 2/16 IGMF Faraday Rotation

 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 T. Akahori, 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

 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 T. Akahori, Cho+ (09) Cho & Ryu (09) μG |B| 10μG 100 h -1 Mpc RM IGMF ~O(1) [rad/m 2 ] in a filament? Ryu+ (08) 4/16

 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 T. Akahori, n e [cm -3 ], B || [μG], l [kpc] 5/16

 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) T. Akahori, Log 10 |RM| [rad m -2 ] [Mpc/h] TA, Ryu (2010), ApJ, 723, 476 6/16

 Statistics of RMs for LoSs with Tx = 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) T. Akahori, TA, Ryu (2010), ApJ, 723, 476 ↓L crl ↓L B 48 runs average of them best-fit lognormal 7/16

 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 T. Akahori, path length (dashed) and column density (solid) across the WHIM RM IGMF ~several-10 [rad/m 2 ] through filaments? 8/16

Result: Cosmological Contribution (1/2) T. Akahori, ※ 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*> 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, run average 9/16

 Statistics of RMs for LoSs through filaments  SF 2 is flat at >0.2° with [rad 2 /m 4 ] Result: Cosmological Contribution (2/2) T. Akahori,  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, run average 10/16

 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 T. Akahori, 11/16

 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 T. Akahori, TA, Ryu, Kim, Gaensler, submitted 12/16

 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!! T. Akahori, PreviousPathfindersSKA Observational uncertainty [rad m -2 ] Average separation of sources [deg] Θ [degree] S [rad 2 m -4 ] ASKAP 30 deg Θ [degree] SKA 30 deg 2 TA+ in prep. previous 13/16 IGMF + GMF

 Faraday Tomography (RM Synthesis)  What is the best target, and what is the necessary dataset for the IGMF study? Furure (2/3): Faraday Tomography T. Akahori, λ 2 [m 2 ] P[mJy] =Q+iU Polarized intensity IGMF GMF Intrinsic F[mJy] φ [rad/m 2 ] Model Faraday Disp. Func. TA, Kumazaki, Takahashi, Ryu, submitted Reconstructed Faraday Disp. Func φ [rad/m 2 ] Faraday Tomography F[mJy] LOFAR+GMRT+ ASKAP ~ F[mJy] SKA ~ 14/16

 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 T. Akahori, 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

Summary T. Akahori,  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 º scale & flat SF at Θ>0.2º  Future  Precise modeling of Milky Way  RM Synthesis & Image processing  Tests with SKA & its pathfinders! 16/16