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Radiative Processes in Flares I: Bremsstrahlung

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Radiative Processes in Flares I: Bremsstrahlung Hale COLLAGE 2017 Lecture 20 Radiative Processes in Flares I: Bremsstrahlung Bin Chen (New Jersey Institute of Technology) 8/3/10 The standard flare model No. 2, 1997 ELECTRON DENSITIES IN SOLAR FLARES 837 Escaping particles Upward Beams III n acc=3 109 cm-3 e !III=500 MHz Acceleration Site FREQUENCY RS Downward Beams !dm,1=1 GHz Trapped particles MW dm,1 10 -3 ne =10 cm DCIM Chromospheric SXR Evaporation Front SXT 11 -3 dm,2 10 -3 n =10 cm ne =5 10 cm dm,2 e ! =2 GHz Precipitating TIME particles HXR HXR FIG. 10.ÈDiagram of a Ñare model envisioning magnetic reconnectionAschwandenand chromospheric& Benz 1997 evaporation processes in the context of our electron density measurements. The panel on the right illustrates a dynamic radio spectrum with radio bursts indicated in the frequency-time plane. The acceleration site is located in a low-density region (in the cusp) with a density of neacc B 109 cm~3 from where electron beams are accelerated in upward (type III) and downward (RS bursts) directions. Downward-precipitating electron beams that intercept the chromospheric evaporation front with density jumps over neupflow \ (1È5) ] 1010 cm~3 can be traced as decimetric bursts with almost inÐnite drift rate in the 1È2 GHz range. The SXR-bright Ñare loops completely Ðlled up by evaporated plasma have somewhat higher densities of neSXR B 1011 cm~3. The chromospheric upÑow Ðlls loops subsequently with wider footpoint separation while the reconnection point rises higher. 6 region. The type III and RS bursts identiÐed here occur This result has dramatic consequences for the location of during the main impulsive Ñare phase, and their detailed the acceleration site. The extremely low density ratio in the correlation with HXRs was established in several recent acceleration site found in all Ñares, without exception, studies (e.g., Aschwanden et al. 1993, 1995). It was not leaves no room to place the acceleration site inside the known in earlier studies whether the start frequency of SXR-bright Ñare loop (assuming a Ðlling factor near unity). metric type III bursts would be signiÐcantly displaced to If we were to allow for harmonic plasma emission or for lower frequencies than the plasma frequency of the acceler- nonunity Ðlling factors of the SXR loop, the density ratio ation region, because a minimal propagation distance is between the acceleration site and the SXR loop would be needed for electron beams to become unstable (Kane, Benz, even more extreme. Therefore we see no other possibility & Treumann 1982). However, recent studies of the starting than to conclude that the acceleration site is located outside point of combined upward- and downward-propagating the SXR-bright Ñare loop. The next question is the magnetic beam signatures (see bidirectional type III ] RS burst pairs topology that can accommodate such large density gra- in Aschwanden et al. 1995, 1993; Klassen 1996) demon- dients (D2È5 density scale heights). A possible topology is a strated that the centroid position of the acceleration region cusp-shaped magnetic Ðeld geometry above the SXR-bright is close to the start frequency of strong type III bursts. The Ñare loop, where acceleration is assumed to take place only major difficulty with this scenario is the observed beneath the X- or Y-type magnetic reconnection point (see asymmetry of electron numbers accelerated in the upward/ diagram in Fig. 10; for a detailed physical model, see downward direction, which was inferred to be as low as Tsuneta 1996). The magnetic Ðeld lines that connect the 10~2 to 10~3, comparing the electrons detected in inter- cusp with the footpoints can have arbitrarily lower densities planetary space with those required to satisfy the chromo- than the encompassed closed Ðeld lines that have been Ðlled spheric thick-target HXR emission (Lin 1974). It is not clear by evaporated plasma. Of course, the high density gradient whether this asymmetry can be explained by the dominance between the acceleration site and the Ðlled SXR-bright Ñare of closed magnetic Ðeld lines above acceleration regions. In loops can only be maintained in a dynamical process in the following discussion, we associate the start frequency lIII which the reconnection point proceeds to higher altitudes of type III bursts with the electron density neacc in the accel- (Kopp & Pneuman 1976) before chromospheric evapo- eration region. The range of type III start frequencies (220È ration has Ðlled up the cusp volume. This race of the recon- 910 MHz) measured here is found to be nearly identical nection point with the evaporation front in the upward with that (270È950 MHz) of 30 bidirectional III ] RS burst direction may come to a halt in long-duration Ñares, where pairs analyzed in Aschwanden et al. (1995). Comparing the cusp volume becomes clearly Ðlled up (Tsuneta et al. these densities in the acceleration region with those in the 1992; Forbes & Acton 1995). SXR-bright Ñare loop, we Ðnd very low ratios of This Ñare scenario, in which acceleration takes place in a neacc/neSXR \ 0.007È0.127 (with a median of 0.027), i.e., the low-density region above the much denser SXR-bright Ñare density in the acceleration region is 1È2 orders of magnitude loop, would predict a physical separation between non- lower than in the SXR-bright Ñare loop. thermal and thermal electrons. While the SXR-bright Ñare 1) Magnetic reconnection and energy release 2) Particle acceleration and heating 3) Chromospheric evaporation and e- magnetic loop heating reconnection Previous lectures Following lectures: e- How to diagnose the accelerated particles? • What? • Where? How? Shibata et al. 1995 • When? Outline • Introduction • Radiation from energetic particles • Bremsstrahlung à this lecture • Gyrosynchrotron • Other radiative processes (time permitting) • Coherent emission • Inverse Compton • Nuclear processes • Suggested reading: Ch. 5 of Tandberg- Hanssen & Emslie Thermal and non-thermal radiation • Refer to the distribution function of source particles �(�) (# of particles per unit energy per unit volume) • Radiation from a Maxwellian particle distribution is referred to as thermal radiation • Radiation from a non-Maxwellian particle distribution is referred to as nonthermal radiation • In flare physics, the nonthermal population we consider usually has much larger energies than that of the thermal “background” • Example of a nonthermal distribution function: � � �� = �� �*+��, where � is the normalization ) - factor to make ∫. � � �� = �) à “power law” *See Lecture 17 (by Prof. Longcope) for details on the distribution function 8/3/10 8/3/10 Radio'Emission' Radio'Emission' .'Thermal' bremsstrahlung'(eAp)' .' Gyrosynchrotron'radia5on'(eAB)' .'Thermal' bremsstrahlung'(eAp)' .'Plasma'radia5on'( wAw)' .' Gyrosynchrotron'radia5on'(eAB)' .'Plasma'radia5on'( wAw)' Radiation from an accelerated charge LarmorLarmor'formulae:'radia5on'from'an'accelerated'charge'''formulae:'radia5on'from'an'accelerated'charge'' dP q2 2q2 dP = q2 a 2 sin2 θ P = a22q2 Larmor formula: dΩ =4πc 3 a 2 sin2 θ P3c=3 a 2 dΩ 4πc 3 3c 3 Rela5vis5c'Larmor'formulae'' Rela5vis5c'Larmor'formulae'' Relativistic Larmor€ formula: € € € θ" θ" Cases'relevant'to'radio'and'HXR/gammaAray'emission:'' Accelera2on#experienced#in#the#Coulomb#field:'bremsstrahlung' Cases'relevant'to'radio'and'HXR/gammaAray'emission:'' Radio and HXR/gammyAccelera2on#experience#in#a#magne2c#field:#-ray emission in flares: gyromagne5c'radia5on' • Acceleration experienced in the Coulomb field: Accelera2on#experienced#in#the#Coulomb#fieldbremsstrahlung:'bremsstrahlung' • Acceleration experienced in a magnetic field: Accelera2on#experience#in#a#magne2c#field:#gyromagnetic radiationgyromagne5c'radia5on' 10 10 8/3/10 ElectronAion'Bremsstrahlung'' e- ν" +Ze Electron-ion bremsstrahlung .'At'radio'wavelengths,' thermal'bremsstrahlung'or'thermal'freeAfree' radia5on'is'relevant'to'the'quiet'Sun,'flares,'and'CMEs' .'Nonthermal'bremsstrahlung' is'relevant'to'HXR/gammaAray'bursts' • e-i bremsstrahlung is relevant to quiet Sun, flares, and CMEs 11 Bremsstrahlung • Each electron-ion interaction generates a single pulse of radiation -e Ze Strong interaction Weak interaction 4/2/2017 4 Free–Free Radiation‣ Essential Radio Astronomy Figure 4.4: The actual power spectrum of the electromagnetic pulse generated by one electron–ion interaction is nearly flat up to frequency , where is the electron speed and is the impact parameter, and declines at higher frequencies. The approximation for all and at higher frequencies (dashed line) is quite good at radio frequencies . Power spectrum of a single interaction The typical electron speed in a K HII region is and the minimum impact parameter is cm, so Hz, much higher than radio frequencies. In the approximation that the power spectrum is flat out to and zero at higher frequencies (dashed line in Figure 4.4), the average energy per unit frequency emitted during a single interaction is approximately Weak interaction (4.25) which simplifies to Single pulse duration �~�/� Emitted energy (4.26) 4.3.2 Radio Radiation From an HII Region http://www.cv.nrao.edu/~sransom/web/Ch4.html 11/23 A note on the impact parameter • Maximum value �456 9: @/A v Debye Length �8 = ? = �BC/�E), Where �BC is the thermal ;<=>) ? F ;<=>) speed and �E) = is the plasma frequency 4> Why this length scale sets �456? H v � ≈ , where � is the observing frequency 456 I • Minimum value �4J= K)? v �4J= ≈ ?, given by maximum possible momentum change of the 4>H electron ∆�) = 2�). ℏ v�4J= = , from uncertainty principle 4>H 4/2/20174/2/2017 4 4Free–Free
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