Solar Flares and particle acceleration
Transcription
Solar Flares and particle acceleration
Solar Flares and particle acceleration Eduard Kontar School of Physics and Astronomy University of Glasgow, UK STFC Summer School, Armagh, 2012 radio waves More prominent in X-rays, UV/EUV and radio . but can be seen from radio to 100 MeV Particles 1AU Solar flares are rapid localised brightening in the lower atmosphere. X-rays Solar flares: basics Figure from Krucker et al, 2007 Solar flares and accelerated particles Solar flares and accelerated particles From Emslie et al., 2004, 2005 Free magnetic energy ~2 1032 ergs “Standard” model of a solar flare/CME Energy release/acceleration Solar corona T ~ 106 K => 0.1 keV per particle Flaring region T ~ 4x107 K => 3 keV per particle Flare volume 1027 cm3 => (104 km)3 Plasma density 1010 cm-3 Photons up to > 100 MeV Number of energetic electrons 1036 per second Electron energies >10 MeV Proton energies >100 MeV Figure from Temmer et al, 2009 Large solar flare releases about 1032 ergs (about half energy in energetic electrons) 1 megaton of TNT is equal to about 4 x 1022 ergs. X-rays and flare accelerated electrons Observed X-rays Unknown electron distribution Emission cross-sections Thin-target case: For the electron spectrum F(E)~E-δ , bremsstrahlung (free-free emission) X-ray spectrum of solar flares Thermal X-rays Gamma-ray lines Non-thermal X-rays July 23, 2002 flare Ramaty High Energy Solar Spectroscopic Imager (RHESSI) spectrum Compton scattering in pictures Observed flux Primary Reflected flux Direct flux Reflected Observed How can we image X-rays? How can we image X-rays? Grazing Incidence optics: XMM Newton mirrors (up to ~10 keV) Works OK but only up to < a few tens of keV ! RHESSI spacecraft and imaging Ramaty High Energy Solar Spectroscopic Imager RHESSI is designed to investigate particle acceleration and energy release in solar flares through imaging and spectroscopy of hard X-ray and gamma-rays in the range from 3 keV up to 17 MeV (Lin et al 2002). Spectroscopy: 9 Ge detectors with energy resolution around 1 keV; Imaging: rotating modulating collimators allowing angular resolution down to 2.3 arcsec; Imaging spectroscopy: simultaneous images in various energy ranges Rotating Modulating Collimators RHESSI detectors look at the source through a pair of grids called Rotating Modulating Collimator (RMC) Spacecraft spins about once every ~4 sec => artificial modulation of incoming X-ray flux Amplitude Point source Time spin period Sun SUN RHESSI imaging RHESSI has 9 RMCs for 9 detectors Slats/Slits spacing growing with detector (RMC) number ⇒ angular resolution from ~2.3’’ (RMC #1) to 180’’ (RMC #9) RHESSI: ideal modulated lightcurves Modulation profiles for various ideal sources for a grid of pitch P with equal slits and slats Point source Half flux from the point source => note half amplitude 45 degrees angle => note change of phase Source further from the axis => note change of modulation frequency Source size=P/2 => note change of the amplitude Source size=P => note change of modulation depth (no modulation for source size >> P) spin period Modulation encodes spatial source information: Phase of the modulation => position angle Distance from the centre => modulation frequency Amplitude => source size Modulated lightcurves Sun Incoming photon flux from pixel m of the source Time interval = observation time – dead time Point source Modulated Lightcurve Detector area Probability to find a photon from m-th pixel in i-th time To find an image is to find the solution: bin (basically the response of the instrument) Photons (counts) in i-th time bin RHESSI imaging Who is this person ? X-ray visibilities Fourier, Joseph, Baron (From Britannica.com) Stacking (sum one roll bin over a few periods in ) RHESSI Modulation profile over three periods from (Schmahl and Hurford) (http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=39) Each period is split into roll bins (here it is 16) Stacking increasing signal-to-noise ratio and helps to calculate mean amplitude and phase => X-ray Visibilities! X-ray visibilities Visibilities amplitude X-ray Visibilities are two dimensional spatial Fourier components of X-ray source Visibilities amplitude Visibilities phase Visibilities phase Note 9 circles (nine RMCs) in U,V (spatial frequencies) plane Prato et al, 2008 RHESSI imaging The fundamental problem of RHESSI imaging is to find the spatial photon distribution knowing the modulated time profile or visibilities (solve an inverse problem! ;( ): To accomplish this task various imaging algorithms to solve this inverse problem exist: Back Projection CLEAN Maximum Entropy Method MEM based (e.g. MEM NJIT) PIXON Forward Fit Interpolated (smooth) FFT < You method could be here! Comparing imaging algorithms 06 - January, 2004 flare useful URLs Imaging lecture notes and example IDL scripts: http://www.astro.gla.ac.uk/users/eduard/sodas RHESSI imaging overview (good collection): http://hesperia.gsfc.nasa.gov/hessi/instrumentation.htm RHESSI imaging tutorials (from first steps to advanced level ): http://hesperia.gsfc.nasa.gov/rhessidatacenter/imaging/overview.html Description of all RHESSI imaging software parameters: http://hesperia.gsfc.nasa.gov/ssw/hessi/doc/hsi_params_all.htm X-ray observations What do we know from X-ray and gamma-ray observations about energetic particles? X-rays and flare accelerated electrons Observed X-rays Unknown electron distribution Emission cross-sections Thin-target case: For the electron spectrum F(E)~E-δ , Electron-ion bremsstrahlung (free-free emission) Dominant process for energies ~10 – 400 keV the photon spectrum is I(ε)~ ε-δ-1 X-ray emission processes For spatially integrated spectrum: Thin-target case: For the electron spectrum F(E)~E-δ , a) Electron-ion bremsstrahlung (free-free emission) Dominant process for energies ~10 – 400 keV the photon spectrum is I(ε)~ ε-δ-1 In the simplest form Kramers’ approximation: b) Electron-electron bremsstrahlung (free-free emission) Dominant process for energies above 400 keV the photon spectrum is I(ε)~ ε-δ c) Recombination emission (free-bound emission) Could be dominant process for energies up to 20 keV the photon spectrum is shifted by ionisation potential and I(ε)~ ε-δ-2 (The process requires high temperatures and detailed ionisation calculations) Solar flares X-ray emission from typical flares Soft X-ray coronal source HXR chromospheric footpoints Footpoints Coronal Source Standard fare geometry Soft X-ray emission up to ~10 - 20 keV Hard X-ray sources above ~20 keV RHESSI spectrum (see Hannah Lecture) ‘Standard’ flare model picture in 2D (Shibata, 1996) What do we see in RHESSI? Standard flare model picture (Shibata, 1996) Krucker et al, 2007 Mean electron spectra 1 3 5 2 4 3 12 4 5 Kontar et al, 2005 Typical spectra = thermal + non thermal components Nonthermal is often a broken power-law Break energy ~50 keV (lower-energy part is harder) Electron spectral indices 2-4 Sometimes spectral flattening at 300-500 keV Energy release inside the loop? (Xu et al, 2008, Kontar etal, 2011,Guo et al,2012) Energetic particles If the fastest process in the system is collisions we can write: The flux of the electrons (electrons s-1 cm-2 keV-1) follow: Thick target model: (Brown, 1971) Kinetic electron energy as a function of column depth E ( E0 , N ) = ( E − 2 KN ) 2 0 1/ 2 K = 2π e Λ 4 Energetic particles:transport The local electron flux as a function of column depth (Brown,71): F0 ([ E 2 + 2 KN ]1/ 2 ) F (E, N ) = E 2 1/ 2 ( E + 2 KN ) where K = 2π e 4 Λ Bremsstrahlung: The photon flux per unit source height range at Earth: ∞ A I (ε , z ) = n( z ) ∫ F ( E , N )Q(ε , E )dE 2 4π D ε The role of magnetic reconnection 6-10 keV 14-16 keV Sui et al, 2004 Local re-acceleration scenario Are particles accelerated within the loop? Vlahos et al 1998, Turkmani et al, 2005, Hood et al, 2008, Browning et al 2008 Simulations by Gordovskyy & Browning, 2011 Gamma-lines and accelerated ions October 28, 2003 Xclass flare (Share et al, 2004) spectrum Alpha-alpha lines favours forward isotropic distribution Proton & Alpha power law index is 3.75 2.2MeV line shows ~100 s delay Gamma ray emission Imaging of the 2.223 MeV neutroncapture line (blue contours) and the HXR electron bremsstrahlung (red contours) of the flare on October 28, 2003. The underlying image is from TRACE at 195 Å. The X-ray and γ-ray imaging shown here used exactly the same selection of detector arrays and imaging procedure. Note the apparent loop-top source in the hard X-ray contours Hurford et al 2006. Note shift Energetic particles at 1AU Flare particles X-rays RHESSI Energetic particles at 1AU γ δ But the spectral indices correlate well but do not match a simple scenario! From X-rays to electrons From the analysis of 16 “scatter-free” events Flare (Lin, 1985; Krucker et al, 2007) : Although there is correlation between the electrons total number of electrons at the Sun (thicktarget model estimate) the spectral indices do not match either thick-target or thintarget models. X-rays X-rays WIND RHESSI Acceleration or transport effects? Acceleration How are energetic particles produced? Electric field acceleration Let us consider electron in collisional plasma. For simplicity, we consider fields parallel to electron velocity: where is a collisional frequency. There is a critical velocity that sets right hand side to zero. Electrons with the velocities larger than the critical are accelerated. The process is called electron runaway. Assuming thermal distribution of electrons, there is critical electric field, called Dreicer field (Dreicer, 1959): Acceleration: electric field Putting the constants, one finds: where number density is measured in particles per cubic meter and temperature in K. Typical values of Dreicer field in the solar corona ~0.01 V/m Figure: Dreicer field as a function of temperature and density (Dreicer, 1959) DC electric field models can be categorized according to the electric field: a) weak sub-Driecer b) strong super-Driecer Electric field acceleration: sub-Dreicer field Runaway acceleration in sub-Dreicer fields has been applied to solar flares by a number of authors (Kuijpers (1981), Heyvaerts (1981), Holman (1985), etc) In principle, such models can explain observations, e.g. Benka and Holman (1994) demonstrate good spectral fits. Open questions: 1) Stability of the involved DC currents 2) Large scale fields e.g., the size of a loop 1010cm 3) Issues with return current Electric field acceleration: Super-Dreicer field Models with super-Dreicer require smaller spatial scales (Martens (1998), Litvinenko (1996, 2003) etc) The energy spectrum of particles near an X-point is found to have a power-law functions N(E)~E-a,a in the range 1.3-2.0 (e.g.Fletcher & Petkaki, 1997, Mori et al, 1998 ) Sub-Dreicer fields might be responsible for bulk acceleration and super-Dreicer field from superthermal seed (Aschwanden, 2006). Figures from Hannah et al, 2002 Open questions: 1) Supply of electrons 2) Consistency of the description Acceleration Fermi acceleration Observation of cosmic energetic particles The story started in 1936. Austrian physicist V. Hess measured radiation level in 1912 balloon experiment. Interesting enough, C.T.R. Wilson observed radiation with cloud chamber experiment (1902) in a railway tunnel near Peebles, Scotland. However, concluded that the radiation cannot be cosmic. Fermi acceleration Fermi (1949) explained the acceleration of cosmic-ray particles by reflection on moving magnetic clouds. Naturally explains inverse power-law distributions. Acceleration V Vs V’ V’ = V + 2Vs(t) Vs(t) > 0 => energy gain Vs(t) < 0 => energy loss Let Vs(t) =Acos(ωt) Net energy gain: <V’ >2– <V>2 = 2A2 No energy change in the frame of the racket! 1) Exchange of energy per collision is small 2) Head-on collisions are more frequent 3) Isotropic distribution of particles Shock acceleration If csh is the velocity of the shock structure (e.g. magnetic field acting as a mirror) then the change in particle energy for one collision is The probability of head-on collision is proportional to v+csh while the probability of overtaking collision is proportional to v-csh Taking into account the probabilities the average gain per collision is The energy change proportional to the velocity of the shock is first order Fermi acceleration; proportional to the square is called second order of Fermi acceleration (original Fermi model). Power-law distribution The average rate of energy gain can be written => where we introduced “collisional” time. Let E=bE0 be the average energy of the particle after one collision and P be the probability that the particle remains within the acceleration region after one collision. Then after k collisions, there are N=N0Pk particles with energies above E=bkE0. Eliminating k one finds ln P / ln b N E = N0 E0 Therefore we find N ( E )dE ∝ E −(1+(ln P / ln b))dE It can be shown that that the spectral index should be >=2. Acceleration in flares and CMEs In solar physics, first-order Fermi acceleration is often called shock-drift acceleration (Priest, 1982; Aschwanden, 2006 etc) Figure: Diffusive shock acceleration (second-order Fermi acceleration) First-order acceleration is viable for 10-100 keV electrons under Open questions: certain conditions and the energy 1) Large areas required gain is sufficiently fast 2) Number of accelerated electrons (Tsuneta & Naito, 1980) Acceleration Resonant acceleration Resonant condition The resonant condition is when the wave has zero frequency in the rest frame of particle: Cherenkov resonance (unmagnetised plasma): Cyclotron resonance (magnetised plasma): Resonance condition in unmagnetised plasma kc kvTe kvS Acceleration Figure: Electron energy spectrum and the spectral density of fast mode waves (Miller et al., 1996) Various models have been developed to model acceleration of electrons by whistler waves (e.g., Hamilton & Petrosian, 1992; Miller, 1996, 1997) Doppler resonance: Solar flare acceleration Figure: Proton distribution function and Alfven waves (Miller & Roberts, 1995) Stochastic acceleration naturally explains enhancement of heavy ions. Open questions: relatively strong turbulence and its origin Energetic particles Instead of conclusions… Energetic particles at various cosmic scales Energetic particles Scheme of possible emission mechanism: Positron beam generating waves => radio emission via coherent emission. Figure: Composite Optical/X-ray image of the Crab Nebula, showing synchrotron emission in the surrounding pulsar wind nebula, powered by injection of magnetic fields and particles from the central pulsar. Energetic particles : Earth ionosphere RHESSI Terrestrial Gamma-ray Flashes Positions Visible Lightning Positions Terrestrial gamma-ray flashes (TGFs) are very brief bursts of gamma radiation (typically around 1 millisecond long) coming upwards from the Earth's atmosphere from somewhere in the vicinity of a thunderstorm (Smith et al, 2005)