RM Synthesis. & magnetic field statistics. Max-Planck-Institut für Astrophysik

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2 A8 RM Synthesis & magnetic field statistics Torsten Enßlin, Rainer Beck, Marcus Brüggen Michael Bell, Thomas Riller, Henrik Junklewitz [Andre Waelkens, Petr Kuchar, Niels Oppermann,...] Max-Planck-Institut für Astrophysik

3 Galactic Magnetic Fields 1.4 GHz: Reich & Wolleben 22 GHz: WMAP team

4 Galactic Magnetic Fields 1.4 GHz: Reich & Wolleben 22 GHz: WMAP team

5 22 GHz Hammurabi-Simulation

6 2.4 GHz Hammurabi-Simulation

7 1.4 GHz Hammurabi-Simulation

8 0.8 GHz Hammurabi-Simulation

9 0.4 GHz Hammurabi-Simulation

10 Hammurabi simulation of galactic magnetic field observables Total Intensity Waelkens et al. (2009) Sun et al. (2008) Janson et al. (2008) Polarized Intensity Ha pu m bli mu c a ra lly b i a v co ail de ab le Polarization Angle Rotation Measure

11 model fitting i.e. data space Ha mm ur ab i realities cod e model space

12 Magnetic power spectrum in Hydra A cool core cluster Kuchar & Enßlin (2009)

13 Observational Setup Hydra A cluster

14 Observational Setup Hydra A cluster

15 Magnetic power spectrum in Hydra A cool core cluster Kuchar & Enßlin (2009) REALMAF code publically available

16 inference i.e. data space RE AL MA F realities cod e model space

17 RM Synthesis de Bruyn & Brentjens (2005)

18 RM Synthesis de Bruyn & Brentjens (2005)

19 RM Synthesis de Bruyn & Brentjens (2005)

20 RM Synthesis

21 3d RM Synthesis

22 3d RM Synthesis

23 3d RM Synthesis

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29 What is information theory?

30 How to obtain information? physical signal s 1) prior knowledge: P(s) 2) measurement: d = R(s) + n, P(d s) 3) inference: P(s d) = P(d s) P(s) / P(d), d s

31 Wiener filter physical signal s 1) prior knowledge: P(s) = G(s,S) Gaussian 2) linear measurement: d = R s + n, P(n) = G(n,N) 3) inference: P(s d) = G(s-m,D) m = (S +R N R) R N d D = (S-1+R N-1 R)-1

32 Prior information? physical signal s 1) prior knowledge: optimal algorithm: s sparse in pixel space s sparse in wavelet space s Gaussian random field s non-gaussian random field CLEAN Compressed Sensing Wiener Filtering Information Field Theory chicken & egg problem: signal statistics & signal reconstruction are interdependent

33 The RM Sky Taylor,Stil,Sunstrum ,534 RM extragalactic RM-sources in the northern sky

34 The RM Sky Taylor,Stil,Sunstrum 2009 Image of the median value of RM

35 The RM Sky Oppermann, Junklewitz, Robbers, Enßlin, 2010 arxiv: Wiener filtered RM-map with inferred power spectrum

36 The RM Sky Oppermann, Junklewitz, Robbers, Enßlin, 2010 arxiv: Wiener filtered RM-map with latitude profile removed

37 The RM Sky Oppermann, Junklewitz, Robbers, Enßlin, 2010 arxiv: RM uncertainty map with latitude profile removed

38 The RM Sky RM uncertainty map Oppermann, Junklewitz, Robbers, Enßlin, 2010 arxiv:

39 The RM Sky Oppermann, Junklewitz, Robbers, Enßlin, 2010 arxiv: Wiener filtered RM-map with inferred power spectrum

40 Summary A8: research tools for the research unit magnetic field statistics: Hammurabi simulation of galactic observables REALMAF magnetic power spectrum inference Litmus Test magnetic helicity detection Faraday tomography: 1d & 3d RM Synthesis in development [implementing CLEAN, Wiener Filter,...]

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44 Why Information Field Theory? inverse problem => Information Theory spatially distributed quantity => Field Theory

45 Information Field Theory Translation: inference problem Enßlin et al.(2009) Enßlin & Frommert Enßlin & Weig statistical field theory Wiener filter Dictionary: log-posterior Evidence Wiener variance noise weighted data inference algorithms maximum a Posteriori uncertainty correct. Shannon information = = = = = = negative Hamiltonian partition function Z information propagator information source Feynman diagrams classical solution loop corrections negative entropy non-linear correction uncertainty loop correction