Capability for Probing the Intergalactic Magnetic Field (IGMF) - PowerPoint PPT Presentation

SKA Science W orkshop in East Asia 2013 @ Nagoya Univ. 5 - 7 June 2013 Capability for Probing the Intergalactic Magnetic Field (IGMF) Shinsuke Ideguchi Kumamoto University, Japan Collaborators: K. Takahashi (Kumamoto Univ.), T. Akahori (Sydney Univ.), K. Kumazaki (Nagoya Univ.) & D. Ryu (Chungnam National Univ.)

Our Goal Find IGMF in filaments of galaxies by radio telescopes have never been observed a ff ect to many cosmic phenomena - CMB fluctuation, propagation of UHECR, etc... may have information of early universe - based on ideas : the current comic magnetisms originate from primordial MF ~100 nG, a few rad/m 2 in RM ( Akahori & Ryu 2010 ) Akahori & Ryu ( 2010 ) In this study: W e forecast the capability for proving the IGMF in filaments assuming “LOFAR, ASKAP & GMRT” observation

Polarization angle [ deg. ] 350 Observation 300 slope : RM 250 Faraday Rotation 200 χ = ( RM ) λ 2 + χ 0 150 100 � � B � � � dl � l s � n e 50 � RM � 0 . 81 rad 0 cm � 3 m 2 µ G Mpc 0 -50 0 0.2 0.4 0.6 0.8 1 Integration along a LOS avelength λ 2 [ m 2 ] W Situation needed for observing IGMF source IGMF Foreground Need to distinguish the Galaxy component, IGMF & source

[mJy] Faraday Dispersion Function ( FDF ) Distribution of MF & radio source along a LOS � ∞ F ( φ ) e 2 i φλ 2 d φ P ( λ 2 ) = Q + iU = −∞ Observed polarized intensity Intrinsic polarized intensity Relation between d “observed PI” n u o r g e r o F source & 0.1 F( � ) “FDF” IGMF 0.08 0.06 0.04 Faraday depth gap 0.02 ( ~distance measured by MF ) � here 0 n e B · d r rad m − 2 φ ( r ) = 0 . 81 0 5 10 15 20 25 30 -2 ] � [rad m there

RM IGMF Diffuse source Compact source P ( λ 2 ; p 1 , p 2 , . . . , p N ) = Q ( λ 2 ; p 1 , p 2 , . . . , p N ) + iU ( λ 2 ; p 1 , p 2 , . . . , p N ) QU - fitting � ∞ F ( φ ; p 1 , p 2 , . . . , p N ) e 2 i φλ 2 d φ = −∞ observed Q & U data parameters per each source 0.15 φ : faraday depth of source 0.1 0.05 δφ : width of source 0 Q f : peak intensity of source -0.05 -0.1 θ : intrinsic polarization angle -0.15 0.2 0.15 0.1 0.05 U QU - fitting 0 -0.05 -0.1 Model FDF -0.15 0.001 0.01 0.1 1 10 � 2 0.1 F( � ) model Q & U [mJy] 0.15 0.08 0.1 0.05 0 0.06 Q -0.05 -0.1 -0.15 0.04 parameter set 1 0.2 parameter set 2 0.15 … 0.02 0.1 0.05 U 0 -0.05 0 -0.1 0 5 10 15 20 25 30 -0.15 -2 ] � [rad m 0.001 0.01 0.1 1 10 � 2

RM IGMF Diffuse source Compact source P ( λ 2 ; p 1 , p 2 , . . . , p N ) = Q ( λ 2 ; p 1 , p 2 , . . . , p N ) + iU ( λ 2 ; p 1 , p 2 , . . . , p N ) QU - fitting � ∞ F ( φ ; p 1 , p 2 , . . . , p N ) e 2 i φλ 2 d φ = −∞ observed Q & U data parameters per each source 0.15 φ : faraday depth of source 0.1 0.05 δφ : width of source 0 Q f : peak intensity of source -0.05 -0.1 θ : intrinsic polarization angle -0.15 This Study: 0.2 0.15 0.1 Forecast the capability of ongoing telescope 0.05 U QU - fitting 0 -0.05 -0.1 Model FDF -0.15 for proving the IGMF by QU - fitting 0.001 0.01 0.1 1 10 � 2 0.1 F( � ) model Q & U through Fisher analysis [mJy] 0.15 0.08 0.1 0.05 0 0.06 Q -0.05 -0.1 -0.15 0.04 parameter set 1 0.2 parameter set 2 0.15 … 0.02 0.1 0.05 U 0 -0.05 0 -0.1 0 5 10 15 20 25 30 -0.15 -2 ] � [rad m 0.001 0.01 0.1 1 10 � 2

1σ 2σ Fiducial value 0 Fisher Analysis Observed data Fisher Matrix Model ∂ 2 χ 2 F jk = 1 N [ Y l ( p ) − Z l ] 2 ∂ p j ∂ p k χ 2 = 2 � σ 2 ~ C (Curvature) l l =1 Curvature at the fiducial value in parameter space Covariance Matrix χ 2 σ jk = ( F − 1 ) 1 / 2 jk R ~ (1/C) 1/2 = R (Curvature Radius) diagonal : 1 - σ error of parameter p non - diagonal : correlation of error

Assumption • An observation of a compact source through the Galaxy • RM of IGMF in filaments is a few rad/m 2 Quasar • One hour exposure Foreground IGMF ASKAP GMRT LOFAR 2 P( � 2 ) 0.1 F( � ) 1.5 0.08 1 0.06 0.04 0.5 0.02 0 0 0.001 0.01 0.1 1 10 0 5 10 15 20 25 30 2 ] � 2 [m -2 ] � [rad m

δφ c f c (0.1) δφ c (0.4) 1-σ confidence region (0.4) RM IGMF (3.0) RM IGMF =3.0 rad/m 2 Results Ⅰ f=0.1 mJy 40 1.2 35 long wavelength 1 (LOFAR) 30 0.8 25 RM= 0 is not short wavelength 20 excluded 0.6 (ASKAP) 15 0.4 10 0.2 5 0 0 0 10 20 30 40 50 0 2 4 6 8 10 L A AL AGL (A : ASKAP, G : GMRT, L : LOFAR)

1-σ confidence region δφ c (0.4) RM IGMF (5.0) RM IGMF (3.0) δφ c (0.4) RM IGMF =3.0 rad/m 2 Results Ⅱ f=0.1 mJy RM IGMF =5.0 rad/m 2 RM IGMF =3.0 rad/m 2 f=0.1 mJy f=0.5 mJy RM= 0 is excluded RM= 0 is excluded 9 40 8 35 7 30 6 25 5 20 4 15 3 10 2 5 1 0 0 1.5 2 2.5 3 3.5 4 4.5 2 3 4 5 6 7 8 9 10 Larger RM IGMF / Brighter source make it easier to detect the IGMF

Results Ⅲ Necessary source intensities for detecting IGMF ( 3 - σ CL ) IGMF is detected in the up - right regions of the lines RM=3.0 rad/m 2 RM=1.0 rad/m 2 The Galaxy intensity [mJy] The Galaxy intensity [mJy] 100 100 10 10 1 1 0.1 0.1 A AL 0.01 0.01 AGL 0.001 0.001 0.001 0.01 0.1 1 10 100 0.001 0.01 0.1 1 10 100 Compact source intensity [mJy] Compact source intensity [mJy] (A : ASKAP, G : GMRT, L : LOFAR)

Results Ⅲ Necessary source intensities for detecting IGMF ( 3 - σ CL ) IGMF is detected in the up - right regions of the lines Intensity of the Galaxy RM=3.0 rad/m 2 RM=1.0 rad/m 2 ( high latitude ) The Galaxy intensity [mJy] The Galaxy intensity [mJy] 100 100 10 10 1 1 0.1 0.1 A AL 0.01 0.01 AGL 0.001 0.001 0.001 0.01 0.1 1 10 100 0.001 0.01 0.1 1 10 100 ~0.03mJy ~0.09mJy Compact source intensity [mJy] Compact source intensity [mJy] [RM=3] [RM=1] (A : ASKAP, G : GMRT, L : LOFAR)

SUMMARY IGMF may a ff ect to many phenomena in the universe W e forecast the capability of ongoing telescope for proving IGMFs of filaments by QU - fitting through Fisher analysis Assuming very simple model as the Galaxy component and RM of the IGMF is a few rad/m 2 , the IGMF can be detected by observing some compact source with intensities more than 0.03mJy by LOFAR & ASKAP By using seamless data with SKA, we would be able to detail discussion for IGMFs