Astrophysical Radiation Mechanisms and Polarization. Markus Böttcher North-West University Potchefstroom, South Africa

Transcription

1 Astrophysical Radiation Mechanisms and Polarization Markus Böttcher North-West University Potchefstroom, South Africa

2 Outline 1. Introduction to Radiation Transfer 2. Blackbody Spectrum Brightness Temperature 3. Introduction to Synchrotron Radiation (spectra, energy losses, polarization, Stokes parameters) 4. Introduction to Compton Scattering (spectra, energy losses, Compton polarization, X-ray/γ-ray polarimetry)

3 Radiation Transfer z I ν II νν = dddd dddd ccccccθθ dddd dddd ddω dω θ dθ dφ da y x

4 Radiation Transfer Emission j ν I ν 0 dddd νν dddd = jj νν em dddd νν dddd = jj νν κκκκ II νν Optical depth τ ν : dτ ν = κ ν ds => Absorption κ ν dddd νν dddd = κκ νν II νν abs dddd νν ddττ νν = SS νν II νν Source Function: SS νν = jj νν κκ νν Radiative Transfer Equation General solution for homogeneous S ν : I ν (τ ν ) = I ν (0) e -τ ν + S ν (1 e -τ ν)

5 Radiation Transfer (II) Special Cases I + S ν (1 e -τ ν (τ ν ) = I ν (0) e -τ ν ν) 1) Absorption spectra Bright background source behind a cold absorber (S ν 0)

6 Radiation Transfer (III) Special Cases I I ν (0) e -τ ν + S ν (1 e -τ ν (τ ν ) = ν) S ν 2) Emission spectra No significant background source (I ν (0) 0) I) Optically thick emission: (τ ν >> 1)

7 Radiation Transfer (IV) Special Cases I = I ν (0) e -τ ν + (1 e -τ ν (τ ν ) S ν τ ν j ν ν) s 2) Emission spectra No significant background source (I λ (0) 0) II) Optically thin emission: (τ λ << 1)

8 Outline 1. Introduction to Radiation Transfer 2. Blackbody Spectrum Brightness Temperature 3. Introduction to Synchrotron Radiation (spectra, energy losses, polarization, Stokes parameters) 4. Introduction to Compton Scattering (spectra, energy losses, Compton polarization, X-ray/γ-ray polarimetry)

9 Thermal Blackbody Radiation I ν (τ ν ) = I ν (0) e -τ ν + S ν (1 e -τ ν) In Thermal Equilibrium (LTE): S ν = I ν = B ν (T) = 2 h νν3 cc 2 1 (ee hνν /kk BB TT 1) = Planck Function Rayleigh-Jeans Limit: hν << k B T => B ν (T) 2 νν2 cc 2 kk BB TT

10 Thermal Blackbody Spectrum

11 Brightness Temperature Define Brightness Temperature T b by setting measured intensity I ν equal to Blackbody in Rayleigh-Jeans Limit: I ν = 2 (ν 2 /c 2 ) k B T b T b = II νν cc2 2 νν 2 kk BB Note: T b usually has nothing to do with the source s real temperature!

12 Brightness Temperature Brightness temperatures T b > K seem unphysical because of strong Compton scattering (see point 4 below) but many active galactic nuclei show T b > K (Angelakis et al. 2012)

13 Relativistic Beaming / Boosting In the co-moving frame of the emission region: In the stationary (observer s) frame: δ = (Γ[1 β Γ cosθ]) -1 : Doppler boosting factor ν Γ = (1 β Γ2 ) 1/2 Isotropic emission I ν at frequency ν Time interval t var Beamed emission: I ν = δ 3 I ν ν = δ ν For power-law F ν ν α : F ν = δ (3+α) F ν Time interval t var = t var / δ

14 Relativistic Beaming / Boosting F ν νf ν δ δ 3 ν α δ 3+α δ δ 4 νf ν pk L 4π d 2 L ν ν L ~ δ 4 L T b ~ δ 3 T b (if the size of the emitter is determined from variability)

15 Outline 1. Introduction to Radiation Transfer 2. Blackbody Spectrum Brightness Temperature 3. Introduction to Synchrotron Radiation (spectra, energy losses, polarization, Stokes parameters) 4. Introduction to Compton Scattering (spectra, energy losses, Compton polarization, X-ray/γ-ray polarimetry)

16 Cyclotron/Synchrotron Radiation Cyclotron frequency: ν cy = eb/(2πm e c) ~ 2.8*10 6 (B/G) Hz I ν Nonrelativistic electrons Harmonics: Magnetic field B Cyclotron radiation I n ~ (v/c) 2n ν cy ν

17 Synchrotron Radiation Relativistic electrons: ν sy (γ) ~ 4.2*10 6 (B/G) γ 2 Hz Power output into synchrotron radiation (single electron): Log(I ν ) ν 1/3 e ν/ν sy Single Electron ν sy Log(ν)

18 Synchrotron Emissivity

19 Synchrotron Radiation Power-law distribution of relativistic electrons: N e (γ) ~ γ -p If there are electrons with ν = ν sy (γ), then: j ν ~ ν -α κ ν ~ ν -β α = (p 1)/2 β = (p+4)/2 log(i ν ) Opt. thick ν 5/2 Opt. thin ν -(p 1)/2 Log(ν)

20 Polarization Preferred direction of E-field vectors of radiation B. β β n Obs.. E rad ~ n x [(n β) x β] E rad predominantly to projection of B

21 Synchrotron Polarization p = 2 Π = 69 % p = 3 Π = 75 %

22 Stokes Parameters +Q -U y -Q +U χ E rad x (= North) Define Stokes Parameters: χ = polarization angle (180 o ambituity!) Ι = Total intensity -> Polarized Intensity Ι pol = Π Ι Q = Ι pol cos(2β) cos(2χ) (β = phase-shift y vs. x => circ. pol.) U = Ι pol cos(2β) sin(2χ) V = Ι pol sin(2β) = circularly polarized intensity (typically, β << 1)

23 Stokes Parameters Stokes parameters are additive:

24 Outline 1. Introduction to Radiation Transfer 2. Blackbody Spectrum Brightness Temperature 3. Introduction to Synchrotron Radiation (spectra, energy losses, polarization, Stokes parameters) 4. Introduction to Compton Scattering (spectra, energy losses, Compton polarization, X-ray/γ-ray polarimetry)

25 Compton Scattering In the electron rest frame: ε = hν/(m e c 2 ) For ε' << 1 ε' s ε' (elastic scattering Thomson Regime) For ε' >> 1 ε' s ~ 1 (inelastic scattering Klein-Nishina [KN] Regime)

26 Compton Scattering Thomson

27 Compton Scattering by Relativistic Electrons Thomson Regime µ = cos(θ) θ ph in electron rest frame ( ): ε = ε γ (1 βµ) In Thomson Regime (ε << 1): ε s = ε Doppler boost into lab frame: Concentrated in forward direction (Ω e ) ε s = γ ε s = ε γ 2 (1 βµ)

28 Compton Losses and Spectra Power output into Compton radiation (single electron):

29 Compton Spectra Power-law distribution of relativistic electrons: N e (γ) ~ γ -p If there are electrons with ν = ν C (γ), then: j ν ~ ν -α α = (p 1)/2 log(i ν ) ν 2 ν -(p 1)/2 ν = ν 0 γ min 2 Log(ν)

30 Compton Scattering by Relativistic Electrons KN Regime ph in electron rest frame ( ): In the KN-Regime (ε >> 1): ε s = 1 Doppler boost into lab frame: ε = ε γ (1 βµ) ε s = γ ε s = γ Photon takes all of the electron s energy (ε s ~ εγ 2 > γ would violate energy conservation!) F ν Cut-off in the resulting Comptonscattered spectra around ε s ~ 1/ε ε 1 1/ε ε 2 ε s

31 Total Energy Loss Rate of Relativistic Electrons dγ/dt Thomson Klein-Nishina 1/ε γ Compton energy loss becomes less efficient at high energies (Klein-Nishina regime).

32 Compton Polarization Compton cross section is polarization-dependent: (e - rest frame) ε = hν/(m e c 2 ) Thomson regime: ε ε dσ/dω = 0 if e e = 0 Scattering preferentially in the plane perpendicular to e! Preferred EVPA is preserved. p p e k Scattering of polarized rad. by relativistic e - => Π reduced to ~ ½ of target-photon polarization.

33 X-ray Polarimeters INTEGRAL XIPE X-Calibur PolSTAR ASTROSAT

34 X-Ray Polarimeters B Single Compton scattering Look for angular modulation of scattered X-rays

35 X-Ray Polarimetry (POLAR: Kole et al. 2016)

36 Gamma-Ray Polarimetry with Fermi-LAT e k e - e + e + e - pair is preferentially produced in the plane of (k, e) of the γ-ray. Potentially detectable at E < 200 MeV PANGU / eastrogam

37 Thank you!

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40 Outline 1. Introduction to Radiation Transfer 2. Radiation Mechanisms: Introduction to Synchrotron Radiation (spectra, energy losses, polarization, Stokes parameters) 3. Introduction to Compton Scattering (spectra, energy losses, Compton polarization, X-ray/γ-ray polarimetry) 4. Introduction to γγ absorption / pair production, Doppler factor estimate from γγ opacity

41 γγ Absorption and Pair Production Threshold energy ε thr of a γ-ray to interact with a background photon with energy ε 1 : 2 ε thr = ε 1 (1 cosθ) e + e - θ ε pk ~ 2/ε 1 ε 1 ε γ

42 γγ Absorption Delta-Function Approximation: VHE gamma-rays interact preferentially with IR photons:

43 Spectrum of the Extrgalactic Background Light (EBL) Starlight Dust (Finke et al. 2010)

44 EBL Absorption (Finke et al. 2010)

45 γγ Absorption Intrinsic to the Source Optical depth to γγ-absorption: ττ γγγγ εε γγ ~ nn ppp 2 εε γγ RRRR TT nn ppp ~ LL 4ππ RR 2 cc εε mm ee cc 2 = 4ππ dd LL 2 FF 4ππ RR 2 cc εε mm ee cc 2 Importance of intrinsic γγ-absorption is estimated by the Compactness Parameter:

46 γγ Absorption Intrinsic to the Source Estimate R from variability time scale: RR ~ cc tt vvvvvv Optical depth to γγ-absorption: ττ γγγγ εε γγ ~ dd LL2 FF 2 εε σσ TT εε γγ tt vvvvvv ( 2 ) mm εε ee cc 4 γγ PKS VHE γ-rays (Aharonian et al. 2007) With F x and t var from PKS : τ γγ (ε TeV ) >> 1

47 Relativistic Beaming / Boosting In the co-moving frame of the emission region: In the stationary (observer s) frame: δ = (Γ[1 β Γ cosθ]) -1 : Doppler boosting factor ν Γ = (1 β Γ2 ) 1/2 Isotropic emission I ν at frequency ν Time interval t var Beamed emission: I ν = δ 3 I ν ν = δ ν For power-law F ν ν α : F ν = δ (3+α) F ν Time interval t var = t var / δ

48 Relativistic Beaming / Boosting F ν νf ν δ δ 3 ν α δ 3+α δ δ 4 νf ν pk L 4π d 2 L ν ν L ~ δ 4 L

49 γγ Absorption Intrinsic to the Source Optical depth to γγ-absorption: ττ γγγγ εε γγ ~ dd LL2 FF 2 εε σσ TT εε γγ tt vvvvvv ( 2 ) mm εε ee cc 4 γγ FF εε = δ (3+α) FF εε oooooo εε γγ = εε γγ oooooo /δδ tt vvvvvv = δδ tt vvvvvv oooooo ττ γγγγ δ (5+α)

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51 Radiation Mechanisms ε ν ~ e -(hν/kt) Bremsstrahlung log(i ν ) Opt. thick ~ ν 2 Opt. thin log(ν)

52 Blazars Class of AGN consisting of BL Lac objects and gamma-ray bright quasars Rapidly (often intra-day) variable Strong gamma-ray sources Radio jets, often with superluminal motion Radio and optical polarization

53 Blazar Spectral Energy Distributions (SEDs) 3C66A Non-thermal spectra with two broad bumps: Low-energy (probably synchrotron): radio-ir-optical(-uv-x-rays) High-energy (X-ray γ-rays)

54 (Abdo et al. 2010) Flux and Polarization Variability Multi-wavelength variability on various time scales (months minutes) Sometimes correlated, sometimes not Observed polarization fractions Π obs <~ 10 % << Π max => Not perfectly ordered magnetic fields! Both degree of polarization and polarization angles vary. Swings in polarization angle sometimes associated with high-energy flares!

55 Open Physics Questions Source of Jet Power (Blandford-Znajek / Blandford/Payne?) Physics of jet launching / collimation / acceleration role / topology of magnetic fields Composition of jets (e - -p or e + -e - plasma?) leptonic or hadronic high-energy emission? Mode of particle acceleration (shocks / shear layers / magnetic reconnection?) - role of magnetic fields Location of the energy dissipation / gamma-ray emission region

56 Blazar Models Relativistic jet outflow with Γ 10 Synchrotron emission Injection, acceleration of ultrarelativistic electrons νf ν ν Q e (γ,t) γ -q Compton emission γ 1 γ 2 Injection over finite length near the base of the jet. Additional contribution from γγ absorption along the jet γ Leptonic Models νf ν Seed photons: ν Synchrotron (SSC), Accr. Disk + BLR (EC)

57 Q e,p (γ,t) Injection, acceleration of ultrarelativistic electrons and protons γ 1 γ -q γ 2 γ Blazar Models Relativistic jet outflow with Γ 10 νf ν Protoninduced radiation mechanisms: ν Proton synchrotron pγ pπ 0 π 0 2γ νf ν Synchrotron emission of primary e - ν Hadronic Models pγ nπ + ; π + µ + ν µ µ + e + ν e ν µ secondary µ-, e-synchrotron Cascades

58 Requirements for lepto-hadronic models To exceed p-γ pion production threshold on interactions with synchrotron (optical) photons: E p > 7x10 16 E -1 ph,ev ev For proton synchrotron emission at multi-gev energies: E p up to ~ ev (=> UHECR) Require Larmor radius r L ~ 3x10 16 E 19 /B G cm a few x cm => B 10 G (Also: to suppress leptonic SSC component below synchrotron) inconsistent with radio-core-shift measurements if emission region is located at ~ pc scales (e.g., Zdziarski & Böttcher 2015). Low radiative efficiency: Requiring jet powers L jet ~ L Edd

59 SED Model Fit Degeneracy (HBL) Red = leptonic Green = lepto-hadronic In many cases, leptonic and hadronic models can produce equally good fits to the SEDs. Possible Diagnostics to distinguish: Variability Neutrinos Polarization

60 Polarization Induced by Anisotropic Compton Scattering Summerlin & Baring (2012) Thermal + Non-Thermal Electron Distributions from Diffusive Shock Acceleration

61 Bulk Compton emission (Comptonization of dust-torus IR by thermal e - in the jet) (Baring et al. 2016)

62 Expected Polarization from Bulk Compton IC by Thermal Electrons ε Γ 2 ε 0 IC by Non- Thermal (Relativistic) Electrons (Garrigoux et al., in prep.)

63 Polarization Induced by Anisotropic Scattering E Obs. (Moran 2007)

64 Calculation of X-Ray and Gamma-Ray Polarization in Leptonic and Hadronic Blazar Models Upper limits on high-energy polarization, assuming perfectly ordered magnetic field perpendicular to the line of sight (Zhang & Böttcher 2013) Synchrotron polarization: Standard Rybicki & Lightman description SSC Polarization: Bonometto & Saggion (1974) for Compton scattering in Thomson regime External-Compton emission (relativistic e - ): Unpolarized: e (γ) 1/γ

65 The Doppler Factor Crisis PKS VHE γ-rays γ γ opacity constraints, assuming isotropic emission in the co-moving frame of the emission region => Γ ~ δ > 50 (Aharonian et al. 2007) VHE γ-ray variability on time scales as short as a few minutes! Strong disagreement with observed superluminal motions!

66 Thank you