Generating magnetic fields at reionisation Generating magnetic fields at reionisation Mathieu Langer Mathieu Langer Institut d'Astrophysique d'Astrophysique Spatiale Spatiale Institut Université Paris Sud 11 Paris Sud 11 Université Orsay – France Orsay – France 1 Cosmological Reionisation – Allahabad – 18 February 2010
Measured magnetic fields in the Universe Measured magnetic fields in the Universe ● In galaxies In galaxies Zeeman splitting Zeeman splitting ● Synchrotron emission Synchrotron emission ● Faraday Rotation Measure Faraday Rotation Measure ● B ~ 1 – 10 ~ 1 – 10 µ G B µ G Note : large B B in galaxies even at high redshift in galaxies even at high redshift Note : large ( 84 µ G @ z ~ 0.7, Wolfe et al. 2008 // ~10 µ G up to z = 3, Kronberg et al. 2008) ( 84 µ G @ z ~ 0.7, Wolfe et al. 2008 // ~10 µ G up to z = 3, Kronberg et al. 2008) 2 Cosmological Reionisation – Allahabad – 18 February 2010
Measured magnetic fields in the Universe Measured magnetic fields in the Universe ● In galaxy clusters In galaxy clusters Faraday Rotation Measure Faraday Rotation Measure ● of background radio of background radio sources sources Clear excess up to 500 kpc Clear excess up to 500 kpc ● ● B B ~ 5 ~ 5 µ G at L L ~ 10 kpc ~ 10 kpc µ G at (Clarke et al. 2001) 3 Cosmological Reionisation – Allahabad – 18 February 2010
Measured magnetic fields in the Universe Measured magnetic fields in the Universe ● On larger scales On larger scales Cross-correlation of |RM| Cross-correlation of |RM| ● and galaxy density field and galaxy density field Significant excess detected Significant excess detected ● at large distances at large distances ● B B ~ 30 nG ~ 30 nG L ~ 1 Mpc ~ 1 Mpc L (Lee et al. 2009) (Lee et al. 2009) 4 Cosmological Reionisation – Allahabad – 18 February 2010
Where do those fields come from? Where do those fields come from? Most likely scenario in two steps : Most likely scenario in two steps : ● Amplification and organisation (build-up of coherence) Amplification and organisation (build-up of coherence) ● Adiabatic compression (frozen-in flux) Adiabatic compression (frozen-in flux) ● Galactic α – Ω dynamo Galactic α – Ω dynamo ● Turbulent dynamo (small scales, Intra-Cluster Medium) Turbulent dynamo (small scales, Intra-Cluster Medium) ● Ex nihilo Ex nihilo generation of non-zero fields generation of non-zero fields 5 Cosmological Reionisation – Allahabad – 18 February 2010
The need of weak seeds The need of weak seeds Linearised fluid equations 6 Cosmological Reionisation – Allahabad – 18 February 2010
The need of weak seeds The need of weak seeds Linearised fluid equations ● B B as a source of density fluctuations as a source of density fluctuations (Rees & Reinhardt 1975, (Rees & Reinhardt 1975, Wasserman 1978, Kim et al. 1996, …) Wasserman 1978, Kim et al. 1996, …) → modifies structure formation history modifies structure formation history → ● In particular, In particular, B B ~ 1 nG, on ~ 1 nG, on L L ≲ 10 ckpc, → additional additional power on power on ≲ 10 ckpc, → 6 M scales M ~ 10 6 M ⊙ → enhances Pop III star formation scales M ~ 10 ⊙ → enhances Pop III star formation → early reionisation completed by z ~ 15 early reionisation completed by z ~ 15 → (Sethi & Subramanian 2003 ; Tashiro & Sugiyama 2006) (Sethi & Subramanian 2003 ; Tashiro & Sugiyama 2006) 7 Cosmological Reionisation – Allahabad – 18 February 2010
Seed field generation mechanisms Seed field generation mechanisms ● Primordial Universe Primordial Universe Inflation Inflation ● Phase transitions Phase transitions ● ● Recombination Recombination Second order perturbations Second order perturbations ● ● Post-recombination Universe Post-recombination Universe Plasma instabilities (e.g. Weibel) Plasma instabilities (e.g. Weibel) ● Biermann Battery Biermann Battery ● Photon drag of charged particles Photon drag of charged particles ● 8 Cosmological Reionisation – Allahabad – 18 February 2010
Seed field generation mechanisms Seed field generation mechanisms ● Primordial Universe Primordial Universe Ridiculously weak seeds Ridiculously weak seeds Inflation Inflation ● Too small scales Too small scales Phase transitions Phase transitions ● ● Recombination Recombination Small fields, needs vorticity & Small fields, needs vorticity & Second order perturbations Second order perturbations ● tight coupling breaking tight coupling breaking ● Post-recombination Universe Post-recombination Universe Too small scales Too small scales Plasma instabilities (e.g. Weibel) Plasma instabilities (e.g. Weibel) ● Biermann Battery Biermann Battery ● Photon drag of charged particles Photon drag of charged particles ● 9 Cosmological Reionisation – Allahabad – 18 February 2010
Biermann battery at reionisation Biermann battery at reionisation Subramanian et al. 1994, Gnedin et al. 2000 Subramanian et al. 1994, Gnedin et al. 2000 Induction : source term ∇ T × d ∇ n e dt =− c k B B q e n e 0 8 G @ L ∼ a few kpc B ∼ 10 - 2 − 10 - 1 10 Cosmological Reionisation – Allahabad – 18 February 2010
B fields from radiation drag at reionisation B fields from radiation drag at reionisation Langer, Aghanim, Puget 2005 Langer, Aghanim, Puget 2005 ● Maxwell equations Maxwell equations ● Generalised Ohm's law Generalised Ohm's law 4 c d p 2 u × E q e j B j × B − c j dt = I m e c ● Radiation drag Radiation drag source term source term = ion Photon-electron interaction : photoionisation Photon-electron interaction : photoionisation ● Source current : momentum transferred to bound electrons Source current : momentum transferred to bound electrons ● − 0 h f mt = 8 I = f mt 2 q e n H c where where 5 m e c 11 Cosmological Reionisation – Allahabad – 18 February 2010
- - + + X Φ - + E - + + - Φ ionising source E Z (quasar) Y + - - E + + - + Φ - + - 12 Cosmological Reionisation – Allahabad – 18 February 2010
- - + + X Φ - + E - + + - Φ ionising j source v SHADOWED e SHADOWED E over- density Φ 1 << Φ Z TUBE TUBE v e (quasar) j B Y + - - E + + - + Φ - + - 13 Cosmological Reionisation – Allahabad – 18 February 2010
B fields from radiation drag at reionisation B fields from radiation drag at reionisation Langer, Aghanim, Puget 2005 Langer, Aghanim, Puget 2005 ● Ionising source : quasar Ionising source : quasar B = 4 c 2 ∇× ● Amplitude of the generated field Amplitude of the generated field I t p 8 yrs 16 1 / 3 2 / 3 n H / n e 4 1 z L 12 t S − 15 F C 10 B ~ 1.6 × 10 Gauss Gauss 4 R 2 10 10 ● Mean free path of ionising photons outside Strömgren sphere Mean free path of ionising photons outside Strömgren sphere l mfp ≈ 50 0 16 − 3 3 1 z parsecs parsecs 14 Cosmological Reionisation – Allahabad – 18 February 2010
B fields from radiation drag at reionisation B fields from radiation drag at reionisation Langer, Aghanim, Puget 2005 Langer, Aghanim, Puget 2005 6 G @ L ~ 100 pc B ~ 2 × 10 - 1 15 Cosmological Reionisation – Allahabad – 18 February 2010
B fields from radiation drag at reionisation B fields from radiation drag at reionisation Langer, Aghanim, Puget 2005 Langer, Aghanim, Puget 2005 6 G @ L ~ 100 pc B ~ 2 × 10 - 1 9 G @ L ~ 50 kpc B ~ 5 × 10 - 1 16 Cosmological Reionisation – Allahabad – 18 February 2010
B fields from radiation drag at reionisation B fields from radiation drag at reionisation Langer, Aghanim, Puget 2005 Langer, Aghanim, Puget 2005 6 G @ L ~ 100 pc B ~ 2 × 10 - 1 9 G @ L ~ 50 kpc B ~ 5 × 10 - 1 Distance between 3.9 σ sources : ⇒ Pre-magnetisation of the Universe 880 kpc @ z ~ 15 0 G B ~ 4 × 10 - 2 17 Cosmological Reionisation – Allahabad – 18 February 2010
Eventual statistics of the produced seeds? Eventual statistics of the produced seeds? Langer, Puget, Aghanim 2003 Langer, Puget, Aghanim 2003 B field power spectrum : field power spectrum : B ● 4 on cluster scales P B (k) ~ k - - 4 on cluster scales P B (k) ~ k . 7 on galactic scales P B (k) ~ k - - 4 4 . 7 on galactic scales P B (k) ~ k (k) B (k) P B P But there's not enough time : But there's not enough time : ● − 1 yrs t nl ~ 4 × 10 8 k 8 yrs t S ~ t E ~ 4 × 10 1 10 1 10 Non-linear effects Non-linear effects 1 ) - k (Mpc - 1 ) k (Mpc 3 3 (turbulence) set in! (turbulence) set in! 18 Cosmological Reionisation – Allahabad – 18 February 2010
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