Magnetic Field in Galaxies and clusters

Transcription

1 Magnetic Field in Galaxies and clusters Kandaswamy Subramanian Inter-University Centre for Astronomy and Astrophysics, Pune , India. The Magnetic Universe, February 16, 2015 p.0/27

2 Plan Observing galactic and cluster B: Radio crucial The fluctuation dynamo, Young galaxies/old clusters The large scale galactic dynamo K. Subramanian, Magnetizing the Universe, PoS proceedings, arxiv: The Magnetic Universe, February 16, 2015 p.1/27

3 Measuring B fields:synchrotorn Radiation B Electron trajectory Electron acceleration Electron's instantaneous velocity k H E Faraday Rotation gives B φ = λ 2 RM = λ 2 K n e B dl K = 0.81 rad m 2 (µg) 1 (pc) 1 cm 3 Synchrotron polarization gives B E ˆn [(ˆn β) d β/dt] d β/dt The Magnetic Universe, February 16, 2015 p.2/27

4 Galactic Magnetic Fields: Observations Synchrotron polarization and Faraday rotation probe B fields. M51 at 6 cm (Fletcher and Beck) Few µg mean Fields coherent on 10 kpc scales Correlated with optical spiral The Magnetic Universe, February 16, 2015 p.3/27

5 Magnetic Spirals: NGC6946 NGC6946 6cm Polarized Intensity + B-Vectors (VLA+Effelsberg) + H-Alpha DECLINATION (J2000) RIGHT ASCENSION (J2000) Why are optical and magnetic spirals correlated? The Magnetic Universe, February 16, 2015 p.4/27

6 Edge on Galaxies: NGC4631 Halo magnetic fields The Magnetic Universe, February 16, 2015 p.5/27

7 B in high z galaxies? The Magnetic Universe, February 16, 2015 p.6/27

8 Cluster Radio halos Chandra (X-Ray)-GMRT (235 Mhz): Giant radio halo in RXC J Giacintucci et al. A & A, 505, 45, 2009 The Magnetic Universe, February 16, 2015 p.7/27

9 Cluster Magnetism: Observations Radio halos and Faraday Rotation probe cluster B fields Vogt & Ensslin, A&A, 434, 67, e 11 k E B(k) 3 [erg/cm ] 1e 12 Magnetic Power Spectrum of Hydra A Cluster Kolmogoroff spectrum 1e 13 B = ( ) µ G l = ( ) kpc B 1e k [kpc ] Hydra Cluster B 7µG coherent on 3 kpc scale The Magnetic Universe, February 16, 2015 p.8/27

10 Cluster Magnetism: Observations Clarke et al., ApJ, 547, L111, 2001 Statistical RM study B 5(l/10kpc) 1/2 µg embedded sources background sources How are cluster fields generated/maintained against turbulent decay? The Magnetic Universe, February 16, 2015 p.9/27

11 Fluctation/Small scale turbulent dynamo Turbulence common: Stars, galaxies, galaxy clusters: leads to Random Stretching + Flux freezing Growth of B Cancellation (Eyink, 2011) and Resistance limits growth. Random B grows if R M = vl/η > R crit (Kazantsev 1967) Eigenmode solutions of form: Ψ(r)exp(2Γt) = r 2 ηt M L ΓΨ = η T d 2 Ψ dr 2 +U 0(r)Ψ Growing modes if there are bound states in potential U 0 (r). Growth rate fast ǫ v/l (10 7 yr: Galaxies; 10 8 yr clusters). Field intermittent: Eddy scale L, to resistive scale L/R 1/2 m L How does it saturate? Important for young galaxy/cluster/igm Faraday RM and mean field dynamos? The Magnetic Universe, February 16, 2015 p.10/27

12 The fluctuation dynamo Simulations Simulations by Pallavi Bhat, 2012, P m = ν/η = k -5/ M(k) K(k) k 3/ k The Magnetic Universe, February 16, 2015 p.11/27

13 The fluctuation dynamo Generated B intermittent (Pallavi Bhat, 2012) The Magnetic Universe, February 16, 2015 p.12/27

14 Faraday RM from Fluctuation dynamo (Pallavi Bhat, KS, MNRAS, 429, 6429, 2013) RMS Faraday RM σ RM by shooting lines of sight through the simulation box. Normalize by σ 0 = Kn e (B rms / 3) Ll σ RM σ 0 for various R m and P m explored. Rare structures contribute < 20% to σ RM 0.6 Rotation Measure : σ RM nocutoff 2B rms cutoff 1B rms cutoff 512 3, Pm= Eddy turn over time The Magnetic Universe, February 16, 2015 p.13/27

15 Kazantsev with Helicity: Tunneling? Fluctuation dynamo bound state problem (Kazantsev, 1967) Helicity of turbulence allows tunneling to larger scales than L (Subramanian, PRL, 1999; Brandenburg, Subramanian, A&A Lett, 2000) For M L 0, Ḣ 0 η T (d 2 Ψ/dr 2 )+Ψ [ U 0 (α 2 (r)/η T (r)) ] = 0, r L, M L (r) = M L (r) r 3/2 J ±3/2 (µr), U(r) 2 η / r 2 0 Γ = E = 0 r 2η T / r 2 α2 0 / η T L r > L The Magnetic Universe, February 16, 2015 p.14/27

16 Helically forced turbulent dynamos Axel Brandenburg, ; k f = 15 Rapid growth in kinematic stage conserving magnetic helicity. Further Slow Growth on resistive timescale (dissipating small-scale helicity) Can be understood in terms of magnetic helicity conservation; (Field and Blackman, 2002). The Magnetic Universe, February 16, 2015 p.15/27

17 Supernovae Drive Helical turbulence The Magnetic Universe, February 16, 2015 p.16/27

18 Galactic Shear and α effect Kinematic Limit? Helicity (links) conservation? Competing Fluctuation dynamo? The Magnetic Universe, February 16, 2015 p.17/27

19 Turbulent Mean-Field Dynamo Consider flow with large-scale velocity V and a turbulent stochastic velocity v V = V+v, B = B+b: Mean + Stochastic fields Average can be volume average over intermediate scales or ensemble average Averages satisfy Reynolds rules V 1 +V 2 = V 1 +V 2, V = V, V v = 0, V 1 V 2 = V 1 V 2, V / t = V / t, V / x i = V / x i. Average now the induction equation The Magnetic Universe, February 16, 2015 p.18/27

20 Turbulent Mean-Field Dynamo V = V+v, B = B+b: Mean + Stochastic fields Mean satisfies DYNAMO equation, with E = v b: B t = ( V B+E η( B) ) ; The stochastic small-scale field satisfies: b t = (V b+v B η b)+g Here G is the pain in neck nonlinear term in v and b. G = (v b) = [v b v b] Finding E = v b is a closure problem: E = αb η turb ( B) The Magnetic Universe, February 16, 2015 p.19/27

21 The kinematic limit of E For short correlation times (τ cor ), neglect G, also assume statistical isotropy of the random v : E = v t dt ( b/ τ) = v(t) t dt [ v(t ) B +B v(t )] E i = t 0 [ ] ǫ ijk v j (t)v k,p (t )B p (t )+ǫ ijp v j (t)v l (t )B p,l (t ) dt, So: E = αb η t B, where α = 1 3 t 0 v(t) ω(t ) dt 1 3 τ corv ω, η t = 1 3 t 0 v(t) v(t ) dt 1 3 τ corv 2, B/ t = ( V B+αB (η t +η)( B) ) ; The Magnetic Universe, February 16, 2015 p.20/27

22 Mean-Field Dynamo: Galactic Galactic Shear generates B φ from B r Supernovae drive HELICAL turbulence (Due to Rotation + Stratification) Helical motions generate B r from B φ α-effect (Parker, 55) Mean field satisfies dynamo equation B t = ( U B+E η( B) ) ; E = u b = αb η turb ( B) α = τ corr 3 u ω η turb = τ corr 3 u2 RSS, 1988 Exponential growth of B, t growth 10 9 yr The Magnetic Universe, February 16, 2015 p.21/27

23 A revised picture for α-effect Anvar and Natasha Shukurov 2009 E transfers helicity: Oppositely signed WRITHE AND TWIST Helicities Lorentz force of small-scale twist Helicity grows to cancel kinetic α The Magnetic Universe, February 16, 2015 p.22/27

24 Nonlinear saturation of helical dynamos E transfers helicity between small-large scales Small scale current helicity grows to cancel kinetic α Nonlinear α = (τ/3) v ω +(τ/3ρ)(4π/c) j b 0? CATASTROPHIC QUENCHING OF DYNAMO? Need to get rid of small scale helicity, by Helicity fluxes? (Blackman & Field; Kleeorin et al). But what is gauge invariant helicity density and flux? Small scale helicity density h is density of correlated b field links (Subramanian & Brandenburg, ApJ Lett., 2006) h/ t+ F = 2E B 2η(4π/c)j b Large scale dynamos need helicity fluxes The Magnetic Universe, February 16, 2015 p.23/27

25 Effect of α-quenching in galaxy Luke Chamandy, Subramanian, Shukurov, MNRAS, 428, 3569 (2013) The Magnetic Universe, February 16, 2015 p.24/27

26 Effect of advective flux in galaxy Luke Chamandy, Subramanian, Shukurov, MNRAS, 428, 3569 (2013) The Magnetic Universe, February 16, 2015 p.25/27

27 Galactic outflows and magnetic spiral Winding up Spiral with enhanced outflow along spiral (Chamandy, Shukurov, KS, 2014) The Magnetic Universe, February 16, 2015 p.26/27

28 Questions When do the first fields arise? How do they evolve with redshift in galaxies and the IGM? Dynamos required to amplify/maintain fields. Fluctuation dynamo saturation? Galaxy cluster plasma nearly collisionless...how to treat? For mean field dynamos: α, η t at large R m? How do MFD s saturate; helicity fluxes? Is an Early universe field needed? Is it inevitable? SKA will be crucial to probe the Magnetic Universe. The Magnetic Universe, February 16, 2015 p.27/27