Radiative processes from energetic particles II: Gyromagnetic radiation

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1 Hale COLLAGE 2017 Lecture 21 Radiative processes from energetic particles II: Gyromagnetic radiation Bin Chen (New Jersey Institute of Technology)

2 e - Shibata et al e - magnetic reconnection Previous lectures 1) Magnetic reconnection and energy release 2) Particle acceleration and heating 3) Chromospheric evaporation, loop heating and cooling Following lectures: How to diagnose the accelerated particles and the environment? What? Where? How? When?

3 Outline Radiation from energetic particles Bremsstrahlung à Previous lecture Gyromagnetic radiation ( magnetobremsstrahlung ) à This lecture Other radiative processes à Briefly in the next lecture Coherent radiation, inverse Compton, nuclear processes Suggested reading: Synchrotron radiation: Chapter 5 of Essential Radio Astronomy by Condon & Ransom 2016 Gyroresonance radiation: Chapter 5 of Gary & Keller 2004 Gyrosynchrotron radiation: Dulk & Marsh 1982 Next two lectures: Diagnosing flare energetic particles using radio and hard X-ray imaging spectroscopy

4 Radiation from an accelerated charge Larmor formula: dp dω = q2 4πc 3 a 2 sin 2 θ P = 2q2 3c 3 a 2 Relativistic Larmor formula: θ" Radio and HXR/gammy-ray emission in flares: Acceleration experienced in the Coulomb field: bremsstrahlung Acceleration experienced in a magnetic field: gyromagnetic radiation

5 Gyromagnetic radiation Gyromagnetic radiation (sometimes called gyroemission ) is due to the acceleration experienced by an electron as it gyrates in a B field due to the Lorentz force. Acceleration is perpendicular to v "

6 Gyroemission from a single electron Let s start from Larmor s formula: dp dω = q2 4πc 3 a 2 sin 2 θ Perpendicular acceleration: a $ = ω '" v $, where ω '" is the (angular) electron gyrofrequency ω '" = 2πν '" = "+ 2π / 2.8B MHz, - ' (Direction integrated) Larmor s equation becomes: P = 2e5 3c 8 ω '" 5 5 v $ P = 2q2 3c 3 a 2 Relativistic case: P = 5"9 8' : γ< ω 5 + v 5 $, with ω + = "+ = >?- =, - ' =

7 Radiation pattern: non-relativistic Larmor s Equation dp dω = q2 4πc 3 a 2 sin 2 θ Null at θ = 0 θ Dipole pattern Observer

8 Radiation pattern: relativistic Relativistic case (γ 1) In the rest frame of the electron dp E dω E = q5 4πc 8 a5 sin 5 θ E In the observer s frame, radiation pattern found from Lorentz transform from the electron rest frame Null occurs at θ = ± arccos 1/γ Observer Strongly beamed forward along the direction of the electron!

9 Relativistic gyroemission: sharply pulsed radiation f t U W = : > X = W = 9 >?- t U W => X? t U = t end of pulse t start of pulse = x x x + x v c c = x v 1 v c x v = t

10 Power spectrum P(ν) For a nonrelativistic electron, radiation field E t is a sinusoid with frequency ω '" Power spectrum is a single tone at the electron gyrofrequency

11 Power spectrum P(ν) As the electron speed picks up, mild beaming effect takes place, E t is non-sinusoidal Low harmonics of electron gyrofrequency show up in the power spectrum Can you identify two effects in the E t plot?

12 Power spectrum P(ν) When the electron is relativistic E t is highly pulsed t..(r) + bj The power spectrum shows contribution from many harmonics

13 Types of gyromagnetic radiation Gyromagnetic radiation behaves very differently with different electron distributions A precise general expression valid for all electron energies is not available. Instead, we use approximate expressions for various electron energy regimes v Non-relativistic or thermal (γ 1 1): Gyroresonance or cyclotron radiation v Mildly relativistic (γ 1~1 5): Gyrosynchrotron radiation v Ultra-relativistic (γ 1 1): Synchrotron radiation Thermal Non-thermal

14 Thermal gyroresonance radiation At a given B, thermal gyroresonance radiation is essentially a spectral line centered at sν '", where s = 1, 2, 3 is the harmonic number Particularly relevant above active regions at microwave frequencies Why? Spectral width of a given resonance line ν/sν '" m Xn, - ' 9 Very narrow in the corona (~1/3000) High opacity only at these resonance layers

Thermal gyroresonance opacity Two different wave modes: ordinary (o mode) and extraordinary (x mode, gyrates with the same sense of rotation as an electron),,, q,,m,,, B',, v µ,,, r,, g, Opacity for

15 Thermal gyroresonance opacity Two different wave modes: ordinary (o mode) and extraordinary (x mode, gyrates with the same sense of rotation as an electron),,, q,,m,,, B',, v µ,,, r,, g, Opacity for two different wave modes ø x,o (s,, µ) =.0133 n e L B (µ) Where,,, s 2 s! F x,o (µ) º 1 æ cos µ 2 µ s 2 sin 2 µ s 1 F x,o(µ) and 2 µ μ = m " c 5 /k + T σ = 1 for x mode and 1 for o mode, L + is the scale length of B Which mode has a larger opacity? Why?

16 Thermal gyroresonance opacity 10 4 X O s = 3 B = 595 G n = cm -3 s = 4 B = 446 G n = cm -3 ν = 5 GHz T = 3 MK L + = 10 Mm Gyroresonance optical depth X O X Typically, optically thick at S=2 (o-mode) and 3 (x-mode) O 10-2 s = 2 B = 892 G n = cm Angle (degrees) Angle (degrees) Angle (degrees) From White 2004

17 Gyroresonance emission of a sunspot Height (km) x,o thin x thick, o thin x,o thick x mode o mode 2.0 T B (10 6 K) Radius (km) From White 2004

18 Actual observation from the VLA RCP LCP Q: Which polarization is the x-mode? Made by B. Chen for AR (unpublished)

19 from J. Lee

20 Nonthermal synchrotron radiation Ultra-relativistic (γ 1 1) From a single electron, adjacent spikes are separated in frequency by only ν = v?- = Fluctuations in electron energy, B strength, or pitch angle cause broadening of the spikes Spectrum is virtually continuous t..(r) + bj

21 Synchrotron spectrum P(ν) from a single electron x = ν/ν ' Most of the energy is emitted at ν ν ', where ν ' = 8 5 γ5 ν '" sin α is the critical frequency (α is the pitch angle)

22 Synchrotron spectrum of an optically thin source One electron of electron E nearly emits all energy at a single frequency ν γ 5 ν '" Optically thin source à to get emissivity j v in (ν, ν + dν), just add P ν = de/dt up from all electrons within (E, E + de): j v dν = de f E de dt Assume a power law electron energy distribution: f E = Cn " E }~ The emissivity j v ν }(~}W)/5

23 Synchrotron spectrum: optically thick regime Synchrotron brightness cannot be arbitrarily high à self-absorption becomes important at low frequencies The spectrum has a power law of slope 5/2 for optically thick source 12 ν /5 ν }(~}W)/5 log v

24 Gyrosynchrotron radiation From mildly relativistic electrons (~1 to several MeV) Expressions for the emission and absorption coefficient are much more complicated than the nonrelativistic (thermal gyroresonance) and ultrarelativistic (synchrotron) case exact Ramaty 1969 Benka & Holman 1992 approximate Petrosian 1981 Dulk & Marsh 1982, 1985 Klein 1987

25 Spectrum is also more complicated Klein (1987)

26 ν Um ~B 8/< B=1000 G B=500 G B=200 G B=100 G

27 n pk ~ n rel 1/4 n rel =1 x 10 7 cm -3 n rel =5 x 10 6 cm -3 n rel =2 x 10 6 cm -3 n rel =1 x 10 6 cm -3

28 n pk ~ q 1/2 q=80 o q=60 o q=40 o q=20 o

29 (Gyro)synchrotron spectrum Schematic diagram from Dulk & Marsh 1982

30 Gyrosynchrotron in flares Flare observed by SOHO, GOES, and Nobeyama Radioheliograph at 17 and 34 GHz Microwave: gyrosynchotron EUV/SXR: hot thermal plasma From T. Bastian

31 A schematic model of a flare loop Bastian et al 1998

32 Summary Gyromagnetic radiation results from electrons accelerated in the magnetic field Three different regimes based on energy of the source electrons: gyroresonance, gyrosynchrotron, and synchrotron Gyroresonance can be used to diagnose B fields in active regions Gyrosynchrotron can be used to probe flare-accelerated electrons and diagnose B field in flare loops Synchrotron is more relevant to cosmic sources, but still possible on the Sun (e.g., the mysterious sub-thz flare component)

Radiative Processes in Flares I: Bremsstrahlung

Hale COLLAGE 2017 Lecture 20 Radiative Processes in Flares I: Bremsstrahlung Bin Chen (New Jersey Institute of Technology) The standard flare model e - magnetic reconnection 1) Magnetic reconnection and