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- Herausgeber: Wiley-VCH
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
This timely book presents new research results on high-energy particle physics related to solar flares, covering the theory and applications of the reconnection process in a clear and comprehensible way. It investigates particle kinetics and dynamics in flaring atmospheres and their diagnostics from spectral observations, while providing an analysis of the observation data and techniques and comparing various models.
Written by an internationally acclaimed expert, this is vital reading for all solar, astro-, and plasma physicists working in the field.
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Seitenzahl: 739
Veröffentlichungsjahr: 2012
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Contents
Cover
Half Title page
Title page
Copyright page
Preface
Chapter 1: Observational Phenomena of Solar Flares
1.1 Observational Constraints
1.2 Hard X-Ray Light Curves and Spectra
1.3 Light Curves and Energy Spectra of Gamma-Rays
1.4 Geometry of Hard X-Ray and Gamma-Ray Sources
1.5 Pre- and Postflare Hard X-Ray and Radio Emission
1.6 Magnetic Field Changes Associated with Flares
1.7 UV and Optical Emission
1.8 Seismic Responses
1.9 Critical Issues
Chapter 2: Particle Acceleration in Flares
2.1 Models of Particle Acceleration
2.2 Recent Theoretical Developments
2.3 Limitations of the Test-Particle Approach
2.4 Particle-in-Cell Simulation of Acceleration in a 3-D RCS
2.5 Particle Acceleration in Collapsing Magnetic Islands
2.6 Limitations of the PIC Approach
2.7 Probing Theories versus Observations
Chapter 3: Electron-Beam Precipitation – Continuity Equation Approach
3.1 Introduction
3.2 Particle Energy Losses
3.3 Continuity Equation Approach for Electrons: Pure Collisions
3.4 Continuity Equation Approach for Electrons – Pure Electric Field
Chapter 4: Electron Beam Precipitation – Fokker–Planck Approach
4.1 General Comments on Particle and Energy Transport
4.2 Problem Formulation
4.3 Simulation Method
4.5 Time-Dependent Fokker–Planck Equation
4.6 Regime of a Stationary Injection
4.7 Impulsive Injection
4.8 Conclusions
Chapter 5: Proton Beam Kinetics
5.1 Proton Beam Distribution Function
5.2 Precipitation of Proton Beam: Numerical Simulations
5.3 General Discussion of Proton and Electron Precipitation
Chapter 6: Hydrodynamic Response to Particle Injection
6.1 Hydrodynamic Equations
6.2 Hydrodynamic Responses to Heating by Electron Beams
6.3 Case Study of a Hydrodynamics of the 25 July 2004 Flare
6.4 Conclusions
Chapter 7: Hard X-Ray Bremsstrahlung Emission and Polarization
7.1 Introduction
7.2 Stokes Parameters for HXR Emission
7.3 Simulation Results
7.4 Comparison with Observations
Chapter 8: Microwave Emission and Polarization
8.1 General Comments
8.2 Evaluation of Models for Electron Precipitation
8.3 Gyrosynchrotron Plasma Emissivity and Absorption Coefficient
8.4 Gyrosynchrotron Emission from a Homogeneous Source
8.5 Comparison with Observations
8.6 Conclusion
Chapter 9: Langmuir Wave Generation by Electron Beams
9.1 Electron Beams and Their Stability
9.2 Basic Equations
9.3 Results and Discussion
9.4 Conclusions
Chapter 10: Nonthermal Hydrogen Emission Caused by Electron Beams
10.1 Introduction
10.2 Nonthermal Excitation and Ionization Rates
10.3 Hydrogen Emission Produced by Impacts with Beam Electrons
10.4 Hydrogen Excitation and Ionization
10.5 Interpretation of Hα Emission in 25 July 2004 Flare
Chapter 11: Hα-Line Impact Polarization
11.1 Introduction
11.2 Basic Models
11.3 Density Matrix Approach
11.4 Results and Discussion
11.5 Interpretation of Polarimetric Hα Observations
11.6 Conclusions
Chapter 12: Sunquakes Associated with Solar Flares
12.1 First Sunquake of 9 July 1996 Flare
12.2 Observations of Other Sunquakes
12.3 Sunquakes Associated with the Flare of 28 October 2003
12.4 Seismic Sources Observed by GONG in 14 December 2006 Flare
12.5 Observations of Solar Interior
12.6 Theoretical Implications of Particle Kinetics and Dynamics Leading to Sunquakes
12.7 Nonthermal Ionization and Backwarming Heating
12.8 Conclusion
Reference
Index
Valentina Zharkova
Electron and Proton Kinetics and Dynamics in Flaring Atmospheres
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The Author
Prof. Valentina Zharkova Bradford University Computing and Mathematics Horton Building D1.10 UK – Bradford BD7 1DPv.v.zharkova@Bradford.ac.uk
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Preface
Charged particles, electrons, protons, ions and neutral atoms are invisible but very powerful participants in all processes in plasmas of the Sun, stars, magnetospheres, interplanetary space and laboratory experiments. Their presence in theoretical research is very often masked behind macro descriptions of the plasma status by means of temperature, density, electric and magnetic fields and so on.
All of these are defined by some sort of ensembles of particles whose various properties (e.g. velocities, charges, masses, numbers or excitation-state status) define the macro parameters which are good descriptors of a plasma’s status in equilibrium. However, in many events on the Sun or stars or in interplanetary space, the atmospheres are well beyond equilibrium. The subject of this book is the investigation of processes of non-equilibrium in flaring atmospheres with a consideration of particle kinetics, dynamics and radiative processes.
The author’s PhD thesis, titled “Radiative transfer in solar quiescent prominences with filamentary structure”, investigated non-equilibrium radiative processes in cool, steady atmospheres and their effects on hydrogen lines and continuous emission. The research was done under the supervision of the late Prof. Nina Morozhenko (Solar Division, Main Astronomical Observatory, Ukraine), a researcher of the highest caliber, who taught well how to properly conduct research and test hypotheses with theoretical predictions. After completing her PhD, the author applied the approach used and knowledge gained during the writing of her thesis to the development of physical concepts in such dynamic events as solar flares.
The research in particle kinetics was initiated at the Astronomy Unit, State Kiev University, by the prominent plasma physicist Prof. Nikolaj Kotsarenko (1941–1993), former head of the Space Physics and Astronomy division in the Physics Department, National University of Kiev, Ukraine. This work was also kindly supported by the theoretical group Theory and Diagnostics of Physical Processes in Solar Flares, led by Prof. Boris Somov of Moscow Sternberg Astronomical Institution, Moscow State University, Russia, and the researchers comprising the group who now carry out their research at various institutions around the world. During annual gatherings of this group, the researchers had many fruitful talks and discussions, which helped the author to make significant progress in her knowledge and understanding of the complex physical processes of particle acceleration and precipitation in solar flares.
My acquaintance with Prof. John Brown, Astronomer Royal for Scotland, University of Glasgow, Scotland, and his famous group, which consisted of Prof. Gordon Emslie, Drs. D. Alexander, A. MacKinnon and other researchers, gave the present author a better understanding of particle kinetics and dynamics developed by various groups in Russia, the United Kingdom and the United States. Very frequently our research seminars and talks sparked extensive debates which motivated further research to clarify the argued points. Such discussions helped the author to build, brick by brick, her knowledge and understanding of such complex phenomena as the physical processes in solar flares, for which the author is enormously grateful.
The idea of this book was conceived at one of the RHESSI workshops frequently devoted to particle acceleration and precipitation in flaring atmospheres on the Sun and their diagnostics from multi-wavelength observations. Particle kinetics is a rather complex topic which needs to be taught to younger scientists so that they may continue the research begun four decades ago with the pioneering works of Prof. Sergey Syrovatsky (Moscow Physical-Technical Institution, Russia), Prof. John Brown (Glasgow University, UK) and Dr. Olga Shmeleva (IZMIRAN, Russia).
The author is also very grateful to her PhD students, who were engaged in the study of various aspects of particle kinetics: Dr. Victor Kobylinskij V.A. (funded by Kiev University, 1989–1993), Dr. Dmitry Syniavskij (Kiev University, Ukraine) (funded by Kiev University, Ukraine, 1990–1994) and Dr. Mykola Gordovskyy (Bradford University, UK), whose study was funded by the Engineering and Physical Sciences Research Council (2002–2005). The students’ dedication to and thorough knowledge of their topics significantly advanced the subject to new levels of understanding, and their knowledge of the topic is reflected in the current book.
The research carried out with her students helped the author to produce a strong synergy between research in kinetics and the dynamics of solar flares and the helioseismology of the solar interior behind these events. The author wishes to acknowledge a very fruitful collaboration with Dr. Alexander Kosovichev (Stanford University, USA), which led to the discovery of sunquakes. These are seismic responses of the solar interior to processes occurring in solar flares. They were reported in a paper in Nature on 27 May 1998 and gained worldwide media coverage on 28 May 1998 by all major TV and radio stations and newspapers.
The author is very grateful to her younger collaborators: Dr. Taras Siversky, my former post-doctoral research assistant employed on a research grant funded by the Science, Technology and Facilities Council (2007–2009); Dr. Sergey Zharkov (son), employed on the European Framework 5 Grant EGSO (2002–2005), currently a Research Fellow at Mullard Space Science Laboratory (MSSL), University College London (UCL), UK; and Dr. Sarah Matthews, a Reader at MSSL, UCL, who helped the author to significantly advance the topics of particle acceleration and precipitation in flaring atmospheres, the generation of seismic responses (sunquakes) associated with solar flares, and the determination of the connection of these processes with the phenomenon of solar flares covering atmospheric heights from the corona to the solar interior.
The author also wishes to acknowledge the Russian collaborators from the Institute of Solar-Terrestrial Physics, Irkutsk, Russia (Prof. A. Altyntsev, Drs. L. Kashapova and N. Meshalkina), whose contribution to our joint research within the Royal Society Joint International Grant (2009–2011) made a reality of recent papers comparing our kinetic and dynamic simulations with multi-wavelength observations, which ultimately became an important part of this book.
And last but not least, the author appreciates the support of her family and partner which allowed her to stay focused on this project and complete the book.
The author hopes that this book will help researchers who are just beginning their study of the physical phenomena of flaring atmospheres on the Sun.
Bradford, January 2012 Valentina Zharkova
Chapter 1
Observational Phenomena of Solar Flares
1.1 Observational Constraints
Recent progress in hard X-ray (HXR) observations with RHESSI of light curves in numerous energy bands (Lin et al., 2002), in combination with advanced imaging (Hurford et al., 2002) and inversion techniques (Kontar et al., 2011), allows us to reconsider the current models of particle acceleration and the effect of their transport on observational characteristics.
1.2 Hard X-Ray Light Curves and Spectra
1.2.1 Light Curves
Spatially integrated HXR light curves obtained by RHESSI confirm many of the temporal features established by previous observations: sharp increases (bursts) of HXR intensity over a relatively short (~ 0.5–5 s) time scale accompanied by a more slowly varying component with a time scale of up to a few tens of minutes (Holman et al., 2011).
The appearance of both sharp HXR bursts and steady increases in HXR intensity suggests that electrons are accelerated on two fundamentally distinct time scales: a rapid acceleration to high, bremsstrahlung-emitting energies and a more stationary process that maintains the high-energy electron flux to produce steady HXR emission for a substantial fraction of an hour or even longer.
At lower photon energies , where thermal bremsstrahlung dominates the total emission, emission at higher photon energies is weighted more heavily by plasma at high temperatures T. As a result, the decrease in conductive cooling time with temperature (τ ~ T−5/2) leads to emissions at higher energies peaking sooner (Aschwanden, 2007), and hence the light curve’s peaking progressively earlier with an increase in photon energy. At higher energies, where nonthermal bremsstrahlung dominates, the relative timing of the emission at different energies depends on both the reduced “time of flight” for higher-energy electrons before they impact upon the thick target of the lower atmosphere (which tends to advance high-energy emissions relative to low-energy ones; Aschwanden and Schwartz, 1996; Brown et al., 1998) and upon the decrease in collision frequency with energy (which tends to delay high-energy emissions relative to low-energy ones – Aschwanden et al., 1997).
1.2.2 Photon and Electron Energy Spectra
HXR emission during flares typically shows a very steep spectrum at lower energies ~ 10 keV, indicative of a thermal process. It must be noted, however, that the frequent assumption (Hurford et al., 2003a) of an isothermal plasma is neither expected on the basis of simple physics nor required by observations (e.g., Brown, 1974). Indeed, Aschwanden (2007) has shown that the assumption of an isothermal source is inconsistent with the observations of temporal variations of the HXR spectrum in flares observed by RHESSI.
At higher energies, the spectrum tends to flatten to a roughly power-law form, with a spectral index γ typically in the range ~ 3–5. There is evidence for spectral flattening at higher energies ~ 500–1000 keV, likely due to the increasing contribution of electron–electron bremsstrahlung (Kontar et al., 2007). Sometimes, for the most energetic flares, there is noticeable emission up to a few hundred megaelectronvolts (Hurford et al., 2006; Kuznetsov et al., 2006). In most powerful flares the photon spectra reveal double power laws with the spectral indices below ~ 30–60 keV being smaller (flatter) than those above this energy by 2–4 units (Grigis and Benz, 2006; Krucker et al., 2008a).
Nonthermal emission in the corona is identified in the impulsive phase by its softer spectrum (Mariska and McTiernan, 1999; Petrosian et al., 2002), consistent with the small column depth of the coronal part of the source. The absence of a significant amount of (energy-dependent) collisional losses in this relatively thin target should result in a spectrum two powers steeper than the target-averaged spectrum (Brown, 1971; Datlowe and Lin, 1973; Hudson, 1972).
It should be noted that even if the accelerated electrons have a power-law energy spectrum , characteristic energies associated with either the electron transport or the radiation physics may produce deviations from the power-law behavior in the observed spatially integrated photon spectrum. Further, as elaborated upon by Kontar et al. (2011), anisotropy in the mean electron distribution, combined with the intrinsic directivity of the bremsstrahlung emission process, produces an anisotropic distribution of primary photons. Compton backscattering of photons from the photosphere (“X-ray albedo”, Bai and Ramaty, 1978; Langer and Petrosian, 1977) not only influences the observed photon spectrum but also has a diagnostic potential for determining the electron angular distribution (Kontar and Brown, 2006).
1.2.3 Electron Numbers
As pointed out by, for example, Tandberg-Hanssen and Emslie (1988), the total injected electron flux depends critically on the value of the low-energy cutoff Ec. A brief discussion of this issue is in order. Historically, a low-energy cutoff Ec was assumed simply in order to keep the injected power finite (e.g., Brown, 1971; Holman et al., 2003). To determine whether or not such a cutoff is actually required by observations, it is essential to adopt a nonparametric approach to interpreting the photon spectrum I() – that is, to infer from I() what range of mean electron source functions (E) (Brown et al., 2003) allow a statistically acceptable fit to I(). Kašparová et al. (2005a), in their analysis of the 20 August 2002 flare, have shown that a low-energy cutoff, or even a gap, in the mean source electron spectrum exists if the observed spectrum is considered as primary bremsstrahlung only; however, such cutoffs or gaps disappear if an albedo correction (for an isotropic primary source) is applied to the observed photon spectrum. Finally, Emslie et al. (2003) has shown that, when allowance is made for warm target effects in the electron energy loss rate, the injected electron energy corresponding to a pure power-law photon spectrum can be finite even if no low-energy cutoff exists.
It appears, therefore, that the actual value of Ec, if one exists at all, should be below 10 keV. In view of the steep spectra commonly observed during flares, extending the spectrum to lower and lower energies requires an ever-increasing number of accelerated electrons, thus imposing even more significant constraints on the electron-acceleration mechanism in flares.
Figure 1.2 RHESSI HXR photon spectrum for solar event on 28 October 2003 (11:06:20–11:06:40 UT). The photon flux (plus signs) is fitted with a thermal bremsstrahlung contribution from an isothermal plasma (dashed curve) plus a double power-law nonthermal electron flux component with a low-energy cutoff (dashed–dotted curve). The best-fit parameters are shown in the plot.
The total electric current corresponding to such a particle acceleration rate, if the acceleration is unidirectional, is I ~ 3 × 1017 A, with a current density of j ~ 1 A cm −2. Such high current densities, especially since they are introduced over a time scale of seconds, produce unacceptably large inductive electric and magnetic fields, unless the acceleration is near-isotropic, as in stochastic acceleration models (Miller et al., 1996; Petrosian and Liu, 2004), the source has a very fine structure (Holman, 1985), or the beam current is effectively neutralized by a cospatial return current (see Brown and Bingham, 1984; Emslie, 1980; Knight and Sturrock, 1977; Larosa and Emslie, 1989; Zharkova and Gordovskyy, 2006; van den Oord, 1990).
Finally, it must be noted that replenishment within a short time scale of flares of the particles in an acceleration region (Emslie and Hénoux, 1995) has to be accounted for by any acceleration or transport mechanisms.
1.3 Light Curves and Energy Spectra of Gamma-Rays
1.3.1 γ-Ray Light Curves
Due to the limited sensitivities of GR detectors, information regarding short times scales for ion acceleration is less stringent than for the time scales of energetic electrons described in Section 2.1. Before the RHESSI launch, no detailed analysis had been performed systematically of the temporal profiles of prompt γ-ray line (GRL) emissions, although simultaneous peaking within ±1 s of the emission in the GRL domain and of HXR emission has been reported for a few events (e.g., Kane et al., 1986). This indicates that ion acceleration to a few megaelectronvolts must happen within a very short time scale of less than 1 s. It also indicates that in most cases the ions must interact with the ambient plasma in a dense region in order to produce nuclear lines (Vilmer et al., 2011). These indications can be a reflection of either pure acceleration or acceleration and transport processes that need to be further investigated.
Recent analysis of RHESSI observations have provided the first information about the temporal evolution of prompt γ-ray lines (derived from spectral analysis) (Lin et al., 2003; Share et al., 2003; and Figure 4.7 in Chapter 4). When compared with the temporal evolution of the X-ray flux at 150 keV, it shows that the HXRs and γ-ray evolutions are roughly similar, indicating a common origin of the accelerated electrons and ions, but that there is for this event a small delay of around 10 s in the maximum of the X-ray and γ-ray flux. This has been interpreted by Dauphin and Vilmer (2007) and discussed by Vilmer et al. (2011) in terms of transport of energetic electrons and ions.
1.3.2 Energy Spectra and Abundances of Ions in Flares
As reviewed by Vilmer et al. (2011), the interactions of energetic ions in the 1 to 100 MeV/nuc range produce a complete γ-ray line spectrum. While narrow γ-ray lines result from the bombardment of ambient nuclei by accelerated protons and α particles, broad lines occur from the inverse reactions, in which accelerated carbon (C) or even heavier nuclei collide with ambient hydrogen (H) or helium (He) nuclei. Deexcitation GRLs provide information on flare ions of energies above 2 MeV/nuc. The shape of the ion distribution below this energy is unknown, but it is of particular interest for the total ion content.
Quantitative results on γ-ray line observations were obtained for more than 20 GRL events. The accelerated ion spectra were found to extend as unbroken power laws down to at least 2 MeV/nuc, if a reasonable ambient Ne/O abundance ratio was used (for details see Chapter 4 in this volume). While for the 19 solar maximum missions (SMM) flares measured prior to the launch of RHESSI the average spectral index was around −4.3, events observed with RHESSI tend to have much harder slopes (Lin et al., 2003; Share and Murphy, 2006).
Even though most of the energy contained in ions resides in protons and α-particles, the crucial constraints for acceleration processes also arise from the estimations of the abundances of heavier accelerated ions. Information on the abundances of flare-accelerated ions was deduced for the SMM/GRS (γ-ray spectrometer) flares as well as for a few flares observed by RHESSI. Noticeable enhancements are generally deduced for the numbers of alpha particles as well as of accelerated 3He isotopes compared to the standard coronal ratios of element abundances including 4He. Furthermore, accelerated heavy ions, such as Ne, Mg, and Fe, are also generally found to be overabundant with respect to their coronal composition.
1.3.3 Ion Numbers
Since the first detection of γ-ray lines in 1972, information on energy content in ions has been obtained for more than 20 events. The analysis carried out from 19 events observed by SMM/GRS and a few events observed with RHESSI show that the energy contained in > 1 MeV ions ranges from 1029 to 1032 ergs for GRL flares. This showed that the energy contained in > 1 MeV ions may be comparable to the energy contained in subrelativistic electrons. There are still large uncertainties in the determination of these quantities and a large dispersion of the relative electron (20 keV) and ion (1 MeV/nuc) energy contents from one flare to another.
The question of relative ion and electron acceleration in solar flares can also be addressed by comparing the ratios of ion production to relativistic electron production with energies of > 300 keV. This has been done using both SMM/GRS observations and recent RHESSI observations (see, e.g., Chupp and Benz, 1994; Shih et al., 2009). A good correlation has been found between the total energy content in protons above 30 MeV and the total energy content in electrons above 300 keV, suggesting that high-energy electrons and ions are directly linked by acceleration processes. This link can be even more direct than for the production ratio of subrelativistic electrons and ions due to a larger difference between electron energy contents above 20 keV and ion energy contents above 1 MeV/nuc. These differences need to be accounted for in the proton- and ion-acceleration models.
1.4 Geometry of Hard X-Ray and Gamma-Ray Sources
The imaging capabilities of RHESSI, combined with its high spectral resolution, allow us to resolve in detail coronal sources (e.g., Masuda et al., 1994) and footpoints occurring in the same flare (Figure 1.3) and hence to study the acceleration processes that give rise to such sources.
Figure 1.3 RHESSI HXR images of flare of 23 July 2003 (thin white contours) taken at 00:28 UT, overlaid on MDI (Michelson Doppler Imager) neutral-line magnetograms (thick white contours) and Hα images (negatives) taken at 00:28:45 UT. One extended (coronal A) and three compact (footpoints B, C, and D) HXR sources are evident.
From Zharkova et al. (2005a).
The coronal source often appears before the main flare HXR increase and the appearance of footpoints. In the impulsive phase, the coronal HXR emission is, generally, well correlated in both time and spectrum with the footpoints (Battaglia and Benz, 2006; Emslie et al., 2003). These observations suggest a strong coupling between the corona and chromosphere during flares, a coupling that is presumably related to transport of accelerated particles from one region to another.
1.4.1 Differences in Footpoint Spectral Indices
An interesting RHESSI observation is the approximate equality of the spectral indices in different footpoints of the same loop. Emslie et al. (2003) reported differences Δγ ~ 0.3–0.4 between the spectral indices of the two dominant footpoints in the 23 July 2002 event. In a few smaller events analyzed by Battaglia and Benz (2006), Δγ is even smaller and indeed is significant in only one out of five cases. However, other observations of X-class flares reveal a much stronger difference (up to 5) between the spectral indices of footpoints of the same loop (Battaglia and Benz, 2006; Krucker et al., 2007; Takakura et al., 1995).
Figure 1.4 Comparison of spectra of footpoint and coronal sources in flare of 13 July 2005: (a,b) footpoint spectra. A power law has been fitted between the dotted vertical lines; (c) spectrum of coronal source. A power law plus an isothermal spectrum has been fitted between the dotted lines.
From Battaglia and Benz (2006).
1.4.2 Hard X-Ray and Gamma-Ray Source Locations
Gamma-ray imaging is a unique capability of RHESSI. Gamma-ray images were first observed by RHESSI for the flare of 23 July 2002. These observations (Hurford et al., 2003a) established that the HXR sources in this flare were spatially separated by several arcseconds from the 2.223 MeV neutron-capture γ-ray source. A similar, but smaller, separation was also detected for the “Halloween” flare on 28 October 2003 (Hurford et al., 2006). This separation of HXR and γ-ray sources must be accounted for by acceleration models.
1.5 Pre- and Postflare Hard X-Ray and Radio Emission
Providing additional information to complement that provided by HXRs, radio emission is another channel of information on nonthermal electrons in flares; coherent radio emission and HXRs are often observed simultaneously. Radio emission is caused by gyrosynchrotron radiation of mildly relativistic electrons; it correlates well in time with HXRs, but, in general, not in space (Krucker et al., 2008b; White et al., 2011). Moreover, the most intense radio emission in flares at meter and decimeter wavelengths originates not from single particles, but from various plasma waves, that is, from coherent radiation processes.
An association of RHESSI HXRs with coherent radio emission in the meter and decimeter band, for 201 flares with flare classes larger than C5, has been surveyed by Benz et al. (2005). They found that coherent radio emission occurred before the onset of HXR emission in 9% of the flares studied. Most of the radio emission was type III radiation at the plasma frequency and its first harmonic, emitted by a beam of electrons moving upward in the solar atmosphere into regions of progressively lower density. In a few cases, the researchers also found a pulsating continuum, possibly caused by cyclotron maser emission. Both types of emission indicate the presence of electron acceleration in the preflare phase, which is often accompanied by X-ray emission from a thermal source in the corona.
Coronal sources can be observed to emit HXRs even before HXR footpoints appear. Nonthermal emission at centimeter wavelengths, suggesting the presence of relativistic electrons, has also been reported in such coronal sources (Asai et al., 2006). One can conclude from these observations that although the energization process that operates in the preflare phase involves mostly heating of coronal plasma, its contribution to particle acceleration cannot be excluded. Comparison of radio and HXR emissions by Benz et al. (2006) also revealed, in some events, coherent radio emission after the HXR emission had stopped. This phenomenon was reported in only 5% of the flares studied.
The kinds of emission that occur at higher frequencies, such as decimetric narrowband spikes, pulsations, and stationary type IV events, correlate more frequently with the HXR flux and thus appear to be more directly related to the acceleration process (Arzner and Benz, 2005). While there is a good association between coherent radio emission and HXRs, a strong correlation in the details of the time profile is less frequent, so that coherent emission is not a reliable proxy for the main flare energy release. This can be accounted for by invoking multiple reconnection sites connected by common field lines along which accelerated particles propagate and serve as a trigger for distant accelerations (see Figure 1.5 in Benz et al., 2005).
Figure 1.5 Schematic drawings illustrating the presence of two simultaneous reconnection sites (labeled 1 and 2) in a flare. Loop system A is the main driver, and reconnection 1 is the main energy release site. Reconnected field lines are indicated by dashed curves.
From Benz et al. (2005).
1.6 Magnetic Field Changes Associated with Flares
Sharp temporal increases of HXR emissions are often closely correlated in time with variations of the magnetic field measured in the photosphere (Kosovichev and Zharkova, 2001; Sudol and Harvey, 2005; Zharkova et al., 2005a). For the flare of 23 July 2002, the magnetic flux change over the flare duration was about 1.2 × 1021 Mx; note that the magnetic flux in the areas not spanned by the magnetic inversion line do not show significant variations above the noise level (Figure 1.6). Magnetic field changes occurring around an apparent magnetic neutral line (AMNL), in general (Figure 1.6), and in the locations of three HXR footpoint sources of the flare of 23 July 2002 (see Figure 9 in Zharkova et al., 2005a) are irreversible, or steplike, for example the magnetic field reaches a new level of the steady state and does not return to a preflare value (Kosovichev and Zharkova, 2001; Sudol and Harvey, 2005; Zharkova et al., 2005a).
Figure 1.6 Total magnetic flux variations (in Mx) from 23 July 2002 flare: (a) mask locations on magnetograms: mask 1 (left) – negative polarity only, mask 2 (middle) – including magnetic inversion (neutral line); mask 3 (right) – positive magnetic polarity only; (b) corresponding total magnetic flux variations (dashed: left mask, solid: middle mask, dashed–dotted: right mask).
The magnetic flux in the other areas of either positive or negative polarities, not including the magnetic inversion lines, does not show noticeable variations above the noise level. A cross-correlation analysis with a time lag between the temporal magnetic variations covering AMNL and the HXR light curves for the flare of 23 July 2002 reveals a noticeable positive correlation of 05–06 with a time lag no larger than 1–2 min for for all energy bands (Figure 1.7). This observation strengthens the belief, on theoretical grounds, that irreversible changes in the magnetic field are responsible for the initiation and development of flare phenomena.
Figure 1.7 Temporal variations of HXR photon intensity in 12–50 keV (a) and 300–2000 keV (b) bands of magnetic field flux in a rectangle including the magnetic inversion line and their relevant correlation coefficients.
Adapted from Zharkova et al. (2005a).
1.6.1 Local Magnetic Field Variations
In order to detect magnetic field variations in the locations of HXR emission, the precise RHESSI HXR images in the 40–80 keV band with the four HXR sources appearing during the course of the flare similar to the locations in the paper by Krucker et al. (2003) were overlaid onto MDI magnetograms (Zharkova et al., 2005a). The magnetic flux variations were extracted from the maximum areas covered by this HXR emission for each minute before and after the flare onset for four HXR sources (A, B, C, D) detected in this flare.
Source A is found not to be associated with any magnetic field changes, despite its appearance in the 12–25 keV band 1 min earlier than the other footpoint sources B, C, and D, but still 1 min later after a start of the magnetic changes. Source A is likely a projection of the top of the loop (see the TRACE image overlaid onto the Hα image, Figure 1.3, bottom); the loop is embedded into the photosphere at the locations close to the footpoints (sources B, C, and D). Source A could be a good candidate for the site of primary electron acceleration in this flare because of the HXR emission timing and energy and its relation to the radio emission discussed by Krucker et al. (2003). However, it does not show any direct connection with the magnetic field locations, possibly because of its occurrence on the loop’s top and the tilt of the loop toward the limb.
The temporal magnetic field variations in footpoint sources B, C, and D are presented in Figure 1.8 (bottom to top, respectively).
Figure 1.8 Magnetic flux variations in the locations of HXR sources D (a), B (b), and C (c). Sources A, B, C, and D are defined in Figure 1.3.
Sources B, C, and D are clearly the footpoint locations, and hence their connection with the magnetic field changes are much more pronounced. The changes in footpoints B and D are fully irreversible; the magnetic field in them decreases from −300 to −420 G. Source D has these changes from 00:26:00 UT for 2 min; they are then followed at 00:29:00 UT by the magnetic changes in sources B and C lasting for 2 and 4 min, respectively.
In source C the magnetic changes are mostly reversible, and the magnetic field first desreases from 400 to 100 G and returns to about 300 G after the flare (Figure 1.8c). Since in source C the difference between the new level of magnetic field, achieved after all changes were stopped, and the preflare level is close to the magnitude of irreversible changes measured in footpoints B and D, we can conclude that these changes are partially irreversible. The major part of these magnetic variations in source C are reversible and of the transient type, similar to those found by Paterson and Zirin (1981) that are not real magnetic field changes but caused by a short-term increase of the line intensity resulting from the nonthermal excitation of the upper level of the Ni atom in the transition 6768 A by the precipitation of high-energy electrons (see for details Zharkova and Kosovichev, 2002).
1.7 UV and Optical Emission
Often there is a close (up to 1 s) temporal correlation in spectral observations of HXR, UV, and optical emissions appearing from a flare (Asai et al., 2002; Bianda et al., 2005; Cheng et al., 1987; Hiei, 1987; Kurokawa et al., 1988). These fast temporal fluctuations in HXR and optical emissions are usually attributed to the propagation of beams of accelerated particles (electrons or protons) and to the dissipation of their energy in lower layers of the solar atmosphere via nonthermal hydrogen excitation and ionization processes and the heating of ambient plasma (Allred et al., 2005; Hénoux, 1991b; Hudson, 1972; Metcalf et al., 2003; Ricchiazzi and Canfield, 1983; Zharkova and Kobylinskii, 1993; Zharkova et al., 2007). This investigation of nonthermal hydrogen emission uncovers some details of particle precipitation into deeper atmospheric levels. However, it raises many other questions related to the exact scenario of the interaction of particles with neutral ambient atoms and the physical condition of the ambient plasma, that is, how these spectral changes are related to the magnetic structures leading to flares.
Special attention has been paid by many authors to the investigation of rapid variations of the Hα line intensity and its correlation with HXR flux during the impulsive phase of chromospheric flares, for example, Trottet et al. (2000) and references therein. This often includes a comparison of the spatial distribution of HXR sources and Hα flare kernels (Asai et al., 2002; Kashapova et al., 2006; Kashapova et al., 2007) and white light emission (Kosovichev, 2007c) showing that many Hα kernels can brighten in succession during the evolution of flare ribbons. These brightenings, frequently accompanied by white light flare (Kosovichev, 2007c), allow one to follow the process of consequent energy release in a very complicated magnetic structure of a flare and to establish that some Hα kernels coincide with HXR sources while many others do not.
In a recent multiwavelength investigation of a few solar flares (Kashapova et al., 2007; Kašparová et al., 2005a; Kašparová et al., 2005b; Zharkova et al., 2007) considerable attention was paid to the locations of fast changes of Hα intensity. In agreement with the predictions of some solar flare models, the HXR sources were located on the external edges of the Hα emission and found to be connected with chromospheric plasma heated by nonthermal electrons. But the fast changes of Hα intensity are normally placed not only inside HXR sources, as expected, if they are the signatures of the chromospheric response to the electron bombardment, but also outside of them. This fact may indicate that the response of the lower atmosphere to flare energy release is not restricted to sites of propagation of accelerated electrons only but can be associated with some other agents (Kašparová et al., 2005a; Zharkova et al., 2007).
1.8 Seismic Responses
The detection of significant seismic emissions from solar flares, or sunquakes (Donea et al., 1999; Kosovichev and Zharkova, 1998), is one of the main discoveries in solar physics in the past decade. Helioseismology of sunquakes, circular or dipole/quadruple waves propagating along the solar surface outward from an impulsive flare for ~ 30–90 min after the impulsive phase, offers us the opportunity to explore various physical processes in the lower solar atmosphere and its interior associated with flare phenomena.
However, a comparison of the observed ripples with a theoretical model of seismic ripples (Kosovichev and Zharkova, 1995; Kosovichev and Zharkova, 1998) revealed that the momentum required to produce the observed seismic response (~ 2 × 1022 g cm s−1) was one order of magnitude higher than those of ~ 1021 g cm s−1 observed from the plasma downflows in MDI dopplergrams. Also, the travel time of this shock to the photosphere was more than 2 min, while the start time, at which the helioseismic response first seen in the time-distance diagrams (where the ridge crosses the Y-axis), coincides closely (within a minute) with the time of the HXR impulse. This raises a question about some additional sources that can deliver within a very short time scale, coinciding with the start of HXR impulse, a required momentum to the solar photosphere.
Later, another method, computational seismic holography, was applied to the MDI observations of this flare to image its seismic source (Donea et al., 1999) centered on the composite umbra of the βγδ-configuration sunspot at the heart of the active region AR7978. The source was clearly visible in the 2.5–4.5 mHz spectrum and even more pronounced in the 5–7 mHz spectrum. These results indicated that the sunquakes, or ripples, could also be accompanied by seismic emission in the mHz range whose intensity varies significantly with depth in a flaring atmosphere, suggesting that different physical processes take place at different atmospheric levels.
The next four quakes were observed nearly 8 years later during the descending phase of solar cycle 23 for the X17 flare of 28 October 2003 and the X10-class flare of 29 October 2003 using a holographic analysis (Donea and Lindsey, 2005). The acoustic signatures of the 28 October 2003 flare were found to be less energetic than that of the X2.6 flare of 9 July 1996, but still detectable. Similar to the first sunquake, in all four seismic sources the emission from lower frequencies (2 mHz) occupies smaller areas.
These holographic observations were also confirmed by the time-distance approach (Kosovichev, 2006; Zharkova and Zharkov, 2007; Zharkova et al., 2005b). For the 28 October flare only 3 out of 11 seismic sources had detectable ripples with wave propagation times within the datacube of a 120 Mm flare and, thus, different horizontal velocities varying from source to source (Zharkova and Zharkov, 2007). Two seismic sources (S3 and S3) were close to the HXR and γ-ray sources observed by RHESSI, while the third largest one was cospatial with the location of the strongest HXR emission up to energies of 100 MeV. The seismic ripples in these sources are found to be anisotropic, as reported by Kosovichev (2006), manifested by the noncircular shaped (elliptical) ripples possibly caused by nonvertical initial impacts. The seismic waves, or ripples, observed in flares can be produced by the hydrodynamic shocks caused by mixed high-energy proton beams, quasithermal proton flows, or electron beams (Zharkova and Zharkov, 2007).
Donea and Lindsey (2005) anticipated that a significant seismic activity could also be excited by relatively small flares (either C- or a M-class flares) and provide enough energy to be measured as seismic sources in relatively localized footpoints. This was recently confirmed by numerous observations using the holographic method (Beliu-Ionescu et al., 2006a; Beliu-Ionescu et al., 2006b; Moradi et al., 2007). These sources of seismic emission associated with medium-sized flares were visible in the 2.5–3.5 mHz range and even more pronounced in the 5–7 mHz range and often found to be cospatial with white-light flares (Beliu-Ionescu et al., 2006b; Donea et al., 2006). In all cases the seismic sources were close to the locations of HXR emission, although they revealed a delay of up to 3 min from the start of the HXR emission for the flares of 6 and 10 April 2001 (Beliu-Ionescu et al., 2006b; Martínez-Oliveros et al., 2008b).
The time-distance diagram technique was further applied to some X-class flares, allowing us to add another three flares (16 July 2004, 15 January 2005, and 23 July 2002) to the list of observed seismic ripples associated with flares (Kosovichev, 2006; Kosovichev, 2007a). Kosovichev reported multiple sunquakes produced by each of these flares, which originated simultaneously in different spatial positions coinciding with the locations of strong downward motions detected by MDI dopplergrams and occurring within 1 min of the initiation of the HXR emission. This supports the suggestion that these sunquakes are somehow related to the precipitation of high-energy particles and their energy deposition into a flaring atmosphere and the solar interior beneath.
1.9 Critical Issues
Particle acceleration during solar flares has two stages: an impulsive one lasting from a few to tens of seconds and a gradual one lasting for tens of minutes. Accelerated particles (electrons and ions) are observed in situ in the interplanetary space at the same time as their radiative signatures in the solar atmosphere. The latter are comprised of multiwavelength observations in HXR bremsstrahlung continuous emission produced by high-energy electron scattering by ambient plasma particles, γ-ray continuous emission produced by proton and ion scattering, and gyrosynchrotron emission in a microwave range produced by the motion of high-energy electrons in the magnetic field (Benz et al., 2005; Miller et al., 1996; Miller et al., 1997).
Continuous γ-ray emission is sometimes accompanied by γ-ray line emission caused by interactions of accelerated ions with energies ≥ 1 MeV nuc−1 and ambient nuclei producing nuclei, neutrons, and positrons for nonrelativistic energies and pions and high-energy nuclei for relativistic energies of accelerated particles (Vilmer et al., 2011). These kinds of high-energy emission are accompanied by soft X-rays and lower-frequency radio emission reflecting thermal radiation, EUV, UV, and optical emission appearing in close temporal correlation to high-energy emission (Fletcher et al., 2011).
While it is well accepted that the gradual phase is a result of ambient plasma heating by processes associated with solar flares (particles, waves, or shocks), the impulsive phase is considered to be a reflection of particle acceleration processes. Some flares are considered to be electron-dominated, others proton-dominated, depending on the emission they produce. Moreover, emission observations allow us to establish a time scale within which this emission is to be produced and at what rate, for example, how many particles per second must be accelerated to account for observed intensities. This emission also allows us to deduce minimal and maximal energies of accelerated particles, their energy spectra evolution for the duration of a flare, and their associations with appearances in lower-energy emission in lines and continua occurring in deeper flaring atmospheres. These points are summarized below (Zharkova et al., 2011a).
Chapter 2
Particle Acceleration in Flares
2.1 Models of Particle Acceleration
In this section we first review some basic concepts, such as acceleration by a direct electric field in a plasma environment (Section 2.1.1) and magnetic reconnection (Section 2.1.2), in which magnetic energy is released into various forms, including the acceleration of charged particles, both electrons and ions. Recognizing the strong observational evidence for the formation of current sheets (localized regions in which a strong magnetic shear is present) in solar flares, our initial discussion relates to traditional two-dimensional (2-D) current sheets, with subsequent elaboration to the three-dimensional (3-D) case (Section 2.1.3). Two likely products of the fundamental reconnection process are magnetohydrodynamic (MHD) shocks and stochastic MHD turbulence, and particle acceleration by these agents is discussed in Section 2.1.4.
2.1.1 Basic Physics
The physics of particle acceleration is in principle rather simple – a charged particle gains energy when moving in an electric field in its rest frame. Thus the electric field E may be a large-scale externally imposed field, a V × B field associated with particles crossing magnetic field lines, or a collective field associated with the environment in which the particle finds itself (e.g., a collisional Coulomb field or a field associated with a level of plasma wave energy). The richness of these various means of creating local electric fields is evident in the richness of particle acceleration models in magnetized plasmas.
One of the most basic concepts is that of the Dreicer field (Chen, 1974). Consider an electron subject to an externally imposed large-scale electric field E, plus the frictional force due to collisions with stationary ambient particles. The equation of motion for such a particle is (in one dimension)
(2.1)
where m and e are the electron mass and (absolute value of) charge and fc is the collision frequency. Since for Coulomb collisions (e.g., Chen, 1974), one can write
(2.2)
where vth is the electron thermal speed and we have defined the Dreicer field by
(2.3)
numerically, .
2.1.2 Magnetic Reconnection Models Associated with Flares
It is generally accepted that the energy release in solar flares occurs through reconstruction of a magnetic field, caused by the change of connectivity of magnetic field lines during a magnetic reconnection. The electric field associated with this changing magnetic field or with the associated driven currents leads to particle acceleration.
Reconnection is a fundamental process defined by the magnetohydrodynamics of a magnetized plasma (Priest and Forbes, 2000; Somov, 2000). The magnetic diffusion equation (see, e.g., Eq. (3.91) of Tandberg-Hanssen and Emslie, 1988) is
(2.4)
where c is the speed of light, B the magnetic field, v the fluid velocity, and η the resistivity. The order-of-magnitude ratio of the terms on the right side of this equation defines the magnetic Reynolds number
(2.5)
it measures the ratio of the advective to diffusive contributions to the change in the magnetic field. For typical solar coronal values of η and with ~ 109 cm, Rm ~ 1014; for such high magnetic Reynolds numbers, the plasma is effectively “frozen in” to the field and negligible change in the field topology, with its concomitant release of magnetic energy, can occur. A topological change in the magnetic field requires a breakdown in this ideal “frozen-in” flux condition; by Eq. (2.5) this can occur either in small-scale regions (high values of 2B) or in regions where the resistivity η is anomalously enhanced. As a result, magnetic reconnection fundamentally occurs in narrow boundary layers called diffusion regions.
2.1.2.1 Basic 2-D MHD Theory of Magnetic Reconnection
In the simple neutral sheet geometry originally proposed by Sweet and Parker (Sweet, 1969), oppositely directed magnetic field lines B in close proximity follow a plasma inflowVi oriented in the x-direction perpendicular to the field lines – see for example Figure 2.1 where the x-direction is vertical and the y-direction is horizontal. (Note that there does exist evidence for such reconnection geometries in flares – Aulanier et al., 2000; Des Jardins et al., 2009; Fletcher et al., 2001; Sui and Holman, 2003). The increasing magnetic pressure in the localized region of field reversal is alleviated by reconnection in a small region of high 2B near the origin (dimensions 2 a in the y-direction × 2 d in the d-direction), which allows plasma outflows with velocityVo toward the sides of the diffusion region.
By mass continuity, the equation can be written as follows:
(2.6)
Integrating the steady state momentum equation gives , the Alfvén speed. Finally, conservation of energy demands that the rate of influx of magnetic energy be balanced by ohmic dissipation in the diffusion region:
(2.7)
(from Ampère’s law) gives
(2.8)
Finally, solving Eqs. (2.6) and
