Lower bound on the extragalactic magnetic field

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1 Lower bound on the extragalactic magnetic field Michael Kachelrieß NTNU, Trondheim [] Dolag, MK, Ostapchenko, Tomàs 10 Neronov, Semikoz, MK, Ostapchenko, Elyiv 10

2 Introduction Mean free path of photons 22 radio log10(e/ev) 16 photon horizon γγ e + e CMB 14 IR kpc 10kpc 100kpc Mpc Virgo 10Mpc 100Mpc Gpc Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

3 Introduction Electromagnetic cascades on EBL Development of the elmag. cascade: Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

4 Introduction Electromagnetic cascades on EBL Development of the elmag. cascade: analytical estimate: [Berezinsky, Smirnov 75 ] K(E/ε X ) 3/2 at E ε X J γ (E) = K(E/ε X ) 2 at ε X E ε a 0 at E > ε a three regimes: Thomson cooling: E γ = 4 ε bb Ee 2 3 m 2 e 100 MeV ( ) 2 Ee 1TeV plateau region: ICS Eγ E e above pair-creation threshold smin = 4E γ ε bb = 4m 2 e: flux exponentially suppressed Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

5 Upper limit Gamma-rays and extragalactic magnetic fields (EGMF) Origin of seed for EGMF is unknown Seed required as input for EGMF simulations Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

6 Upper limit Gamma-rays and extragalactic magnetic fields (EGMF) Origin of seed for EGMF is unknown Seed required as input for EGMF simulations Observations only in clusters, synchrotron halo: B (0.1 1)µG Faraday rotation: B (1 10)µG Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

7 Upper limit Gamma-rays and extragalactic magnetic fields (EGMF) Origin of seed for EGMF is unknown Seed required as input for EGMF simulations Observations only in clusters, synchrotron halo: B (0.1 1)µG Faraday rotation: B (1 10)µG Aharonian, Coppi, Völk 94: Pair halos around AGNs Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

8 Upper limit Gamma-rays and extragalactic magnetic fields (EGMF) Origin of seed for EGMF is unknown Seed required as input for EGMF simulations Observations only in clusters, synchrotron halo: B (0.1 1)µG Faraday rotation: B (1 10)µG Aharonian, Coppi, Völk 94: Pair halos around AGNs Plaga 95: EGMFs deflect and delay cascade electrons search for delayed echoes of multi-tev AGN flares/grbs Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

9 Upper limit Influence of EGMF on flux from single source: deflections Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

10 Upper limit GeV jets : B dependence G G G G 1 Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

11 Upper limit Lower limit on EGMF: [A. Neronov, I. Vovk 10, F. Tavecchio et al. 10 ] choose blazar: large z, stationary, low GeV, high multi-tev emission Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

12 Upper limit Lower limit on EGMF: [A. Neronov, I. Vovk 10, F. Tavecchio et al. 10 ] choose blazar: large z, stationary, low GeV, high multi-tev emission TeV photons cascade down: small EGMF: fill up GeV range large EGMF: deflected outside, isotropized Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

13 Upper limit Lower limit on EGMF: uniform field [Dolag et al. 10 ] log 10 (E 2 F/erg cm -2 s -1 ) G G G Fermi G direct G G E max =100 TeV HESS log 10 (E/eV) Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

14 Upper limit Lower limit on EGMF: uniform field [Dolag et al. 10 ] log 10 (E 2 F/erg cm -2 s -1 ) G G G Fermi G direct G for coherence lengths λ < l int 50kpc: G E max =100 TeV HESS log 10 (E/eV) bound improves as λ 1/2 Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

15 Upper limit Lower limit on filling factor: [Dolag et al. 10 ] model filaments by a top-hat: B = G B = 0 10 Mpc Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

16 Upper limit Lower limit on filling factor: [Dolag et al. 10 ] log 10 (E 2 F/erg cm -2 s -1 ) Fermi f=0.10 f=0.50 f=0.70 f=0.80 f=0.90 f=0.60,e max =100 TeV HESS log 10 (E/eV) Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

17 Upper limit Lower limit on filling factor: [Dolag et al. 10 ] log 10 (E 2 F/erg cm -2 s -1 ) Linear filling factor > 50% Fermi HESS f=0.10 mainly f= step cascade: γ e ± γ f=0.70 photon mean free path D γ (E) f= Mpc electron mean free path D e (E) f=0.90 few kpc f=0.60,e max =100 TeV log 10 (E/eV) Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

18 Upper limit Lower limit on filling factor: [Dolag et al. 10 ] log 10 (E 2 F/erg cm -2 s -1 ) Linear filling factor > 50% Fermi HESS f=0.10 mainly f= step cascade: γ e ± γ f=0.70 photon mean free path D γ (E) f= Mpc electron mean free path D e (E) f=0.90 few kpc f=0.60,e max =100 TeV electrons are created everywhere and feel B only close to -14 interaction point log 10 (E/eV) Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

19 Primordial fields How to create EGMFs in voids? primordial fields: inflation phase transitions (QCD, electroweak) reionization astrophysical (require seed fields): + outflows from AGNs, dwarf galaxies Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

20 Primordial fields How to create EGMFs in voids? primordial fields: inflation phase transitions (QCD, electroweak) reionization too weak astrophysical (require seed fields): + outflows from AGNs, dwarf galaxies outflows colliminated B > 0 and B = 0 plasma does not mix contamination with heavy elements Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

21 Primordial fields Expectation for causally generated fields: [Caprini, Durer,... ] 10 4 Phase transitions, n compression BΛ nanogauss QCD helical EWnon hel EW helical QCDnon hel dynamo Λ Mpc Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

22 Primordial fields Primordial magnetic fields: for a Gaussian field B i (k)b j (k ) = δ(k k ) [ (δ ij ˆk ) ] iˆkj S(k) + iε ijl k l H(k) energy density ρ = 4π 0 k 2 S(k) helicity density h = 4π 0 kh(k) characterized by B λ and coherence length L c Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

23 Primordial fields Primordial magnetic fields: for a Gaussian field B i (k)b j (k ) = δ(k k ) [ (δ ij ˆk ) ] iˆkj S(k) + iε ijl k l H(k) characterized by B λ and coherence length L c inflation: acausal, L c H 1 0 possible phase transitions: require 1./2.order transition causal, Lc (t ) < H(t ) 1 Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

24 Primordial fields Primordial magnetic fields: for a Gaussian field B i (k)b j (k ) = δ(k k ) [ (δ ij ˆk ) ] iˆkj S(k) + iε ijl k l H(k) characterized by B λ and coherence length L c inflation: acausal, L c H 1 0 possible phase transitions: require 1./2.order transition causal, Lc (t ) < H(t ) 1 B i (x)b j (y) has compact support [ ] is analytic function analyticity & finite ρ Bλ B 0 (L c /λ) 5/2 Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

25 Primordial fields Primordial magnetic fields: for a Gaussian field B i (k)b j (k ) = δ(k k ) [ (δ ij ˆk ) ] iˆkj S(k) + iε ijl k l H(k) characterized by B λ and coherence length L c inflation: acausal, L c H 1 0 possible phase transitions: require 1./2.order transition causal, Lc (t ) < H(t ) 1 B i (x)b j (y) has compact support [ ] is analytic function analyticity & finite ρ Bλ B 0 (L c /λ) 5/2 how are fields evolving after creation? Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

26 Primordial fields Evolution of primordial magnetic fields: non-helical fields: damped above k D, below B 1/a π/L(η) 0.01 E B = const K k D (η) Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

27 Primordial fields Evolution of primordial magnetic fields: helical fields: fluctuations are transferred to larger scales 1/k 0.1 D(η) 0.01 E B = const K Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

28 Primordial fields Evolution of primordial magnetic fields: helical fields: fluctuations are transferred to larger scales 1/k 0.1 D(η) 0.01 E B Picture assumes 4 static large scale tail B λ λ 5/2 : interaction with turbulent fluid generates Bλ λ 3/ = const fields from phase transitions could be strong enough K Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

29 Summary Summary Fermi non-observation of TeV blazars requires EGMF quantitative conclusions: sure: large filling factor f > 0.5 bound on EGMF: depends on assumed t, B > G can be improved by more/longer simultanous observations limit detection: CTA? suggests primordial origin: phase transition or inflation? Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

30 Summary Time dependence for flaring source: B > G log 10 (E 2 F/erg cm -2 s -1 ) Fermi t < 10 yr t < 10 2 yr t < 10 3 yr t < 10 4 yr t < 10 5 yr t < 10 6 yr HESS log 10 (E/eV) Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

31 Summary EGMF in voids already observed? [Ando, Kusenko 10 ] stack 170 brightest AGN Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

32 Summary EGMF in voids already observed? [Ando, Kusenko 10 ] stack 170 brightest AGN search for excess over PSF Rel. DEC (deg) Counts Map (3-10 GeV) Rel DEC (deg) Model Map (3-10 GeV) Rel. RA (deg) Rel RA (deg) (counts) (counts) Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

33 Summary EGMF in voids already observed? [Ando, Kusenko 10 ] stack 170 brightest AGN search for excess over PSF Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

34 Summary EGMF in voids already observed? [Ando, Kusenko 10 ] stack 170 brightest AGN search for excess over PSF Rel. DEC (deg) Counts Map (3-10 GeV) Rel DEC (deg) Model Map (3-10 GeV) Rel. RA (deg) Rel RA (deg) (counts) (counts) explained by B G (λ B /1 kpc) 1/2 and λ B < kpc Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

35 Summary EGMF in voids already observed? [Ando, Kusenko 10 ] stack 170 brightest AGN search for excess over PSF Rel. DEC (deg) Counts Map (3-10 GeV) Rel DEC (deg) Model Map (3-10 GeV) Rel. RA (deg) Rel RA (deg) (counts) (counts) lower limit B > G requires λ B < 0.1 kpc Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

36 Summary EGMF already observed? Probably not... [Neronov et al. 10 ] point source Crab shows the same halo as stacked AGN: Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

37 Summary EGMF already observed? Probably not... [Neronov et al. 10 ] point source Crab shows the same halo as stacked AGN: tail of PSF wrong (?), difference between front and back photons Michael Kachelrieß (NTNU, Trondheim) Lower bound on the EGMF Moriond EW, / 16

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