Coronal Seismology E-Book

Alexander V. Stepanov

• Herausgeber: Wiley-VCH
• Kategorie: Lebensstil
• Sprache: Englisch
• Veröffentlichungsjahr: 2012

Seitenzahl: 441

Beschreibung

This concise and systematic account of the current state of this new branch of astrophysics presents the theoretical foundations of plasma astrophysics, magneto-hydrodynamics and coronal magnetic structures, taking into account the full range of available observation techniques -- from radio to gamma. The book discusses stellar loops during flare energy releases, MHD waves and oscillations, plasma instabilities and heating and charged particle acceleration. Current trends and developments in MHD seismology of solar and stellar coronal plasma systems are also covered, while recent progress is presented in the observational study of quasi-periodic pulsations in solar and stellar flares with radio, optical, X and gamma rays. In addition, the authors investigate the origin of coherent radio emission from stellar loops, paying special attention to their fine structure. For advanced students and specialists in astronomy, as well as theoretical and plasma physics.

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The Authors

Prof. Alexander V. Stepanov

Russian Academy of Sciences

Pulkovo Observatory St. Petersburg

Russia Federation

[email protected]

Prof. Valery V. Zaitsev

Russian Academy of Sciences

Institute of Applied Physics

Nizhny Novgorod

Russia Federation

Prof. Valery M. Nakariakov

University of Warwick

Department of Physics

Coventry, United Kingdom

Cover picture

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Table of Contents

Cover

Title

Copyright

Preface

Chapter 1: Introduction

1.1 Magnetic Loops and Open Flux Tubes as Basic Structural Elements in Solar and Stellar Coronae

1.2 Data of Observations and Types of Coronal Loops

1.3 The MHD Approach for Coronal Plasma

References

Chapter 2: Coronal Magnetic Loop as an Equivalent Electric Circuit

2.1 A Physical Model of an Isolated Loop

2.2 The Formation of Magnetic Tubes by Photospheric Convection

2.3 The Structure of the Coronal Part of a Flux Tube

2.4 Diagnostics of Electric Currents

2.5 The Equivalent Electric Circuit

2.6 Inductive Interaction of Magnetic Loops

2.7 Waves of Electric Current in Arcades of Coronal Magnetic Loops

2.8 Magnetic Loops above Spots

References

Chapter 3: Resonators for MHD Oscillations in Stellar Coronae

3.1 Eigenmodes of Coronal Loops: The Plasma Cylinder Approach and the Dispersion Equation

3.2 MHD Resonator at ∼1RO in the Solar Corona

3.3 Excitation Mechanisms for Loop Oscillations

References

Further Heading

Chapter 4: Propagating MHD Waves in Coronal Plasma Waveguides

4.1 MHD Waves in Vertical Coronal Magnetic Flux Tubes

4.2 Propagating Waves in Coronal Loops

4.3 Waves in Coronal Jets

4.4 Evolution of Short-Wavelength, Fast Magnetoacoustic Waves

4.5 Alfvén Wave Phase Mixing

References

Chapter 5: Prominence Seismology

5.1 Prominence Models

5.2 Prominence Oscillations

5.3 The Heating Effect

5.4 Nonlinear Oscillations: Dynamical Modes

5.5 Flare Processes in Prominences

5.6 Stellar and Interstellar Prominences

References

Chapter 6: The Coronal Loop as a Magnetic Mirror Trap

6.1 Particle Distribution in a Coronal Loop

6.2 Kinetic Instabilities in a Loop

6.3 The Fine Structure of Radio Emission from Coronal Loops

References

Chapter 7: Flaring Events in Stellar Coronal Loops

7.1 Particle Acceleration and Explosive Joule Heating in Current-Carrying Loops

7.2 The Kinematics of Energetic Particles in a Loop and the Consequent Radiation

References

Further Reading

Chapter 8: Stellar Coronal Seismology as a Diagnostic Tool for Flare Plasma

8.1 Modulation of Flaring Emission by MHD Oscillations

8.2 Global Sausage Mode and Diagnostics of the Solar Event of 12 January 2000

8.3 Dissipative Processes in Coronal Loop for MHD Modes

8.4 The Stellar Flare Plasma Diagnostics from Multiwavelength Observations Stellar Flares

8.5 Diagnostics of Electric Currents in Stellar Atmospheres

References

Chapter 9: Heating Mechanisms in Stellar Coronae

9.1 Wave Heating

9.2 Ohmic Dissipation of Electric Currents

9.3 Heating by Microflares

References

Chapter 10: Loops and QPOs in Neutron Stars and Accretion Disk Coronae

10.1 The Origin of Fast QPOs from Magnetars and Diagnostics of Magnetar Corona

10.2 Coronae of Accretion Disks

References

Chapter 11: Conclusions

References

Index

Preface

Wave and oscillatory phenomena, which are intrinsically inherent in the activity of solar and stellar coronae, present the subject of coronal seismology – a new rapidly developing branch of astrophysics. The philosophy of this novel method of remote diagnostics of plasma parameters is analogous to the study of the Earth's interior by surface and body waves, geoseismology. In solar and stellar physics, a similar technique for probing of the interiors, helio- and asteroseismology, is successfully applied. Moreover, the observational detection of waves and oscillations in accretion disks recently gave rise to the topic of diskoseismology. Likewise, magnetoseismology, the diagnostics of the Earth's (and, potentially, planetary) magnetospheres with magnetohydrodynamic waves and oscillations, is another successful manifestation of this technique.

Hundreds of papers and reviews as well as national and international meetings are devoted now to the current problems in the field of the coronal seismology. Flares, charged particle acceleration and emission, plasma heating, prominence dynamics, and coronal mass ejections are related to the magnetic structures of active regions of the stars. Numerous ground- and space-borne observations provide evidence that magnetic flux tubes and loops, being a typical structure of solar and stellar coronae, act as waveguides and resonators for magnetohydrodynamical (MHD) waves and oscillations. Moreover, modern view suggests that coronae of accretion disks and neutron stars also consist of magnetic loops. Waves and oscillations in open and closed magnetic structures modulate solar and stellar emission in various wave bands. Hence, coronal seismology can provide a good diagnostic tool for flare plasma as well as for energy transfer and energy transformation in solar and stellar atmospheres. More opportunities in the coronal seismology were made more than a decade ago with the use of space missions: the Solar and Heliospheric Observatory and Transition Region and Coronal Explorer. New good chances for coronal plasma diagnostics open now with the Solar Dynamic Observatory and Solar Terrestrial Relations Observatory.

This book is devoted to the successive exposition of the main problems of the coronal seismology. Two approaches are mainly used for the interpretation of the wave and oscillatory phenomena in solar and stellar coronae. The first approach represents the coronal magnetic loops and flux tubes as resonators and waveguides for MHD oscillations and waves. The second one describes the coronal loop in terms of an equivalent electric circuit with the effective resistance, inductance, and capacitance. Both these approaches complement one another effectively in the process of diagnostics of coronal plasma. Because waves and oscillations cause quasi-periodic modulations of plasma parameters of coronal magnetic structures, the emission mechanisms from coronal structures of both thermal and nonthermal origins should be studied in this context. Most pronounced phase of quasi-periodic pulsations is in the course of flaring event. Hence, the flare plasma heating and charged particle acceleration are also the subjects of this book.

It should be noted that the author's views are biased by their own preferences and interests. However, they tried to address wider problems of the coronal seismology. Sometimes the main formulas and notations are repeated in various chapters for the reader's convenience.

December 2011

A. V. Stepanov

V. V. Zaitsev

V. M. Nakariakov

Chapter 1

Introduction

Uchida [1], who suggested the idea of plasma and magnetic field diagnostics in the solar corona on the basis of waves and oscillations in 1970, and Rosenberg [2], who first explained the pulsations in type IV solar radio bursts in terms of the loop magnetohydrodynamic (MHD) oscillations, can be considered to be pioneers of coronal seismology.

Various approaches have been used to describe physical processes in stellar coronal structures: kinetic, MHD, and electric circuit models are among them. Two main models are presently very popular in coronal seismology. The first considers magnetic flux tubes and loops as wave guides and resonators for MHD waves and oscillations, whereas the second describes a loop in terms of an equivalent electric (RLC) circuit. Several detailed reviews are devoted to problems of coronal seismology (see, i.e., [3–7]). Recent achievements in the solar coronal seismology are also referred in Space Sci. Rev. vol. 149, No. 1–4 (2009). Nevertheless, some important issues related to diagnostics of physical processes and plasma parameters in solar and stellar flares are still insufficiently presented in the literature. The main goal of the book is the successive description and analysis of the main achievements and problems of coronal seismology.

There is much in common between flares on the Sun and on late-type stars, especially red dwarfs [8]. Indeed, the timescales, the Neupert effect, the fine structure of the optical, radio, and X-ray emission, and the pulsations are similar for both solar and stellar flares. Studies of many hundreds of stellar flares have indicated that the latter display a power–law radiation energy distribution, similar to that found for solar flares. Thus, we can use the solar–stellar analogy to study flaring stars.

The next goal of this book is to illustrate the efficiency of coronal seismology as a diagnostic tool for the analysis of stellar flares.

1.1 Magnetic Loops and Open Flux Tubes as Basic Structural Elements in Solar and Stellar Coronae

Magnetic loops constitute the basic structural element in the coronae of the Sun and late-type stars [9–11]. They play an important role in solar activity. Observations made with Skylab, Solar and Heliospheric Observatory (SOHO), Yohkoh, Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI), Transition Region and Coronal Explorer (TRACE), Complex Orbital Near-Earth Observations of Activity of the Sun – Photon (CORONAS–F), Hinode, Solar Dynamic Observatory (SDO) space missions, as well as with large optical telescopes Vacuum Tower Telescope (VTT), and radio telescopes (Very Large Array (VLA), Siberian Solar Radio Telescope (SSRT), NoRH (Nobeyama Radioheliograph)) have shown that solar flares originate in coronal loops [3, 12]. Eruptive prominences and coronal transients result in giant coronal mass ejections (CMEs) and also frequently display the loop shape [13]. The flaring activity of dMe-stars and close binaries is also spawned by the energy release in magnetic loops [9, 14, 15]. In some late-type stars, magnetic spots cover up to 70–80% of the surface, whereas solar spots occupy ∼0.04% of the photosphere. This implies that, in fact, loops form the magnetic structure of stellar coronae. In addition, loops are typical for the magnetic structure of the atmospheres of accretion disks, young stellar objects, and neutron stars [16–19]. Owing to space-borne observations and advances in the physics of the loops, some progress has been recently made in finding a solution for the problem of the origin of coronal loops. Alfvén and Carlqvist [20] have suggested that a flaring loop can be considered to be an equivalent electric circuit. This phenomenological approach was nevertheless very productive in understanding the energy pattern of flare processes. The description of the loops in terms of resonators and wave guides for MHD waves explains various kinds of modulations of stellar flare emissions and serves as a diagnostic tool for the flare plasma. The concept of a coronal loop as a magnetic mirror trap for energetic particles makes it possible to efficiently describe particle dynamics and peculiarities of emission generated by energetic particles.

Open magnetic structures – the flux tubes – are wave guides for MHD waves, which make them important channels of energy transfer from one part of the stellar atmosphere to another, from the photosphere and chromosphere to the corona, and further to the solar and stellar wind. Similar to magnetic loops, the flux tubes provide a necessary link in the mechanism of coronal heating. Flux tubes are exemplified by solar spicules, which are energy/mass bridges between the dense and dynamic photosphere and the tenuous hot solar corona [21].

Prominence dynamics and oscillations also present important subjects for coronal seismology [22, 23] since prominences play a crucial role both in triggering flares [24, 25] and in CME’s origin [26]. Therefore, the study of ballooning instability presents a very important point in the context of flaring and CME’s activity.

1.2 Data of Observations and Types of Coronal Loops

The corona of the Sun (a main-sequence G2 star) in its active phase consists predominantly of magnetic loops filled with comparatively dense and hot plasma, which is observed in soft X rays and constitutes an essential part of the total mass of the corona. The presence of magnetic loops indicates the complexity of the subphotospheric magnetic field, which is most likely linked to convective motions of the photosphere matter. Observations indicate that there are at least five morphologically distinct types of loops present in the solar atmosphere (see, i.e., [27, 28]):

1) Loops connecting different active regions. Their lengths reach 700 000 km, the plasma temperature in such loops is (2–3) × 106 K, and the density is about 109 cm−3. The loop footpoints are located in islands of the strong magnetic field on the periphery of active regions. The characteristic lifetime of such loops is about one day.

2) Loops in quiescent regions. They do not connect active regions; their lengths are the same as those of the previous types of loops. Their temperature, however, is somewhat lower, within the interval (1.5–2.1) × 106 K, while the density is in the range (2–10) × 108 cm−3.

3) Loops in active regions. Their lengths span from 10 000 to 100 000 km and temperature and density are within the intervals 104 − 2.5 × 106 K and (0.5–5.0) × 109 cm−3, respectively.

4) Post-flare loops. They commonly connect footpoints of two-ribbon flares, and display lengths of 10 000–100 000 km, temperature 104 − 4 × 106 K, and density up to 1011 cm−3.

5) Single-flare loops. These are separate loops, in which flare energy is released. Hard X-ray bursts last for about a minute and are the most pertinent feature of such flares. In soft X rays, these loops are characterized by small volumes and low heights. The loops are 5000–50 000 km in length, their temperature is less than 4 × 107 K, and their plasma density reaches 1012 cm−3 [12].

Closed magnetic structures resembling coronal loops also exist in stars of other types. Data obtained with Einstein, ROSAT (Röntgensatellit), and XMM-Newton (XMM stands for X-ray multimirror mission) space missions indicate that virtually all stars on the Hertzsprung–Russel diagram possess hot coronae with temperatures ranging between 107 and 108 K [29–31]. They are not confined gravitationally, which implies the presence of magnetic fields. Of special interest are late-type stars, particularly dMe red dwarfs, which display high flare activity and represent nearly 80% of the total number of stars in the Galaxy and in its close neighborhood. Although red dwarfs are morphologically similar to the Sun, especially in their radio-wavelength radiation (the slowly varying component, rapidly drifting bursts, sudden reductions, spike bursts, and quasi-periodical pulsations [15, 32]), these objects present some peculiarities, which stem from the high activity of their coronae.

First, note the high brightness temperature of the “quiescent” radio emission of dMe-stars (up to 1010 K), which cannot be described in terms of thermal coronal plasma with the temperature 107 − 108K. This radiation is commonly interpreted as gyrosynchrotron emission of nonthermal electrons abundant in the coronae of red dwarfs. The coexistence of the hot plasma and subrelativistic particles is also suggested by the correlation between the radio and soft X-ray emission over six orders of magnitude in intensity [33]. This phenomenon is not observed in the solar corona. In the quiescent state, the corona of the Sun does not host a sufficient number of high-energy particles, and the brightness temperature of solar radio emission does not exceed 106 K.

Second, the difference is manifested in the extremely high brightness temperature of flare radio emission of red dwarves, sometimes exceeding 1016 K, which is three to four orders of magnitude higher than that of the most powerful radio bursts in the Sun. This suggests the presence of an efficient coherent (maser) mechanism of emission from stellar coronae. Moreover, in red dwarfs, radio flares can frequently occur independently of optical flares.

Third, the sizes of loops on the Sun and red dwarves are different [9, 10]. As a rule, the length of the solar loops, with the exception of trans-equatorial ones, is substantially smaller than that of the solar radius (Figure 1.1a). On red dwarves, the size of magnetic loops can be comparable to the stellar radii or can exceed them by a few factors (Figure 1.1b). The magnetic field in stellar loops can exceed that in solar loops by an order of magnitude.

Table 1.1 presents parameters of flare loops on the Sun and late-type stars derived from multiwavelength (optical, radio, and X-ray) observations and various diagnostic methods.

Table 1.1 Parameters of Coronal Flare Loops

1.3 The MHD Approach for Coronal Plasma

In our study of magnetic structures in coronal plasma and their evolution, we frequently use MHD approximation. It includes Maxwell equations, generalized Ohm’s law, and also equations of motion and continuity of mass, the energy equation, and the gas equation of state. In MHD approximation, it is common to take the simplified Maxwell equations, without taking into account the bias current, and also the simplified form of the Ohm’s law in the approximation of isotropic conductivity of plasma. For a number of problems of coronal seismology, such approximations appear to be insufficient, and more general equations are used. In addition to that, when the dynamics and radiation of fast particles in coronal magnetic loops are analyzed, the kinetic equation for the velocity distribution of particles should be used (see, for example, Chapters 6 and 7). Below, we present the basic equations of magnetic hydrodynamics in their generalized form, which is applied further on. For the sake of convenience, we repeatedly reproduce these equations along with the explanation for the previously used notation in different sections.

The Maxwell equations in the Gaussian system of units (cgs) may be written in the form

(1.1)

(1.2)

(1.3)

(1.4)

The generalized Ohm’s law follows the “three-fluid” model for electrons, ions, and neutral atoms; it connects the electric current with the velocity of the center of mass, and also with the electric and magnetic fields. When the inertia of electrons is neglected, the generalized Ohm’s law is written as follows:

(1.5)

The induction equation. Excluding the electric field from Eq. (1.5) with the use of Eq. (1.2), we obtain the following equation for magnetic induction:

(1.6)

(1.5a)

This form of Ohm’s law may be applied, for instance, in the case of totally ionized plasma , provided the Ampere force becomes zero (, the so-called force-free approximation). In a more general case, for example, in the lower chromosphere or in the prominence, plasma is partly ionized, and the anisotropy of conductivity becomes essential. Therefore, the more general induction Eq. (1.6) should be used.

Equations of plasma. The induction Eq. (1.6) indicates that the behavior of the magnetic field is related to the motion of plasma, since in this equation some summands contain the matter velocity. In turn, the motion of plasma is specified by the continuity equation, the equation of motion, and the energy equation:

(1.7)

(1.8)

(1.9)

(1.10)

(1.11)

The connection between the pressure and the density is specified by the equation of state; for ideal gas,

(1.12)

References

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2. Rosenberg, H. (1970) Astron. Astrophys., 9, 159.

3. Aschwanden, M.J., Poland, A.I., and Rabin, D. (2001) Ann. Rev. Astron. Astrophys., 39, 175.

4. Aschwanden, M.J. (2003) NATO Advances Research Workshop, NATO Science Series II, p. 22.

5. Nakariakov, V.M. and Verwichte, E. (2005) Living Rev. Sol. Phys. Coronal waves and oscillations, 2, No 3, pp. 3–65

6. Nakariakov, V.M. and Stepanov, A.V. (2007) Lect. Notes Phys., 725, 221.

7. Zaitsev, V.V. and Stepanov, A.V. (2008) Phys. Usp., 51, 1123.

8. Gershberg, R.E. (2005) Solar-Type Activity in Main-Sequence Stars, Springer, Berlin, Heidelberg.

9. Bray, R.J., Cram, L.E., Durrant, C.J., and Loughhead, R.E. (1991) Plasma Loops in the Solar Corona, Cambridge University Press.

10. Benz, A., Conway, J., and Güdel, M. (1998) Astron. Astrophys., 331, 596.

11. Schrijver, C.J., Title, A.M., Berger, T.E., Fletcher, L. et al. (1999) Sol. Phys., 187, 261.

12. Sakai, J.-I. and de Jager, C. (1996) Space Sci. Rev., 77, 1.

13. Plunkett, S.P., Vourlidas, A., Šimberová, S., Karlický, M. et al. (2000) Sol. Phys., 194, 371.

14. Lestrade, J.F. (1988) Astrophys. J., 328, 232.

15. Bastian, T.S., Bookbinder, J.A., Dulk, G.A., and Davis, M. (1990) Astrophys. J., 353, 265.

16. Galeev, A.A., Rosner, R., Serio, S., and Vaiana, G.S. (1981) Astrophys. J., 243, 301.

17. Kuijpers, J. (1995) Lect. Notes Phys., 444, 135.

18. Feigelson, E.D. and Montmerle, T. (1999) Ann. Rev. Astron. Astrophys., 37, 363.

19. Beloborodov, A.M. and Thompson, C. (2007) Astrophys. J., 657, 967.

20. Alfvén, H. and Carlqvist, P. (1967) Sol. Phys., 1, 220.

21. Zaqarashvili, T.V. and Erdelyi, R. (2009) Space Sci. Rev., 149, 355.

22. Oliver, R. (2009) Space Sci. Rev., 149, 175.

23. Tripathi, D., Isobe, H., and Jain, R. (2009) Space Sci. Rev., 149, 283.

24. Pustyl–nik, L.A. (1974) Sov. Astron., 17, 763.

25. Zaitsev, V.V., Urpo, S., and Stepanov, A.V. (2000) Astron. Astrophys., 357, 1105.

26. Gopalswamy, N. (2006) Space Sci. Rev., 124, 145.

27. Priest, E.R. (1982) Solar Magnetohydrodynamics, D. Reidel Publishing Company, Dordrecht.

28. Aschwanden, M.J. (2005) Physics of the Solar Corona. An Introduction with Problems and Solutions, Springer.

29. Haisch, B.M. (1983) in Activity in Red-Dwarf Stars X-ray Oscillations of Stellar Flares (eds P.B. Birne and M. Rodono), Reidel, p. 255–268.

30. Schmitt, J.H.M.M., Collura, A., Sciortino, S., Vaiana, G.S. et al. (1990) Astrophys. J., 365, 704.

31. Mullan, D.J., Mathioudakis, M., Bloomfield, D.S., and Christian, D.J. (2006) Astrophys. J. Suppl., 164, 173.

32. Stepanov, A.V., Kliem, B., Zaitsev, V.V. et al. (2001) Astron. Astrophys., 374, 1072.

33. Güdel, M. and Benz, A.O. (1993) Astrophys. J., 405, L63.

34. Rosner, R., Tucker, G.S., and Vaiana, R. (1978) Astrophys. J., 220, 643.

Chapter 2

Coronal Magnetic Loop as an Equivalent Electric Circuit

In Chapter 1, we presented numerous evidences for the fact that the solar and stellar coronae are structured and consist of magnetic loops and open flux tubes filled with plasma. Therewith the parameters of the loops vary within a broad range [1, 2]. For example, hot X-ray loops with a temperature of up to 10 MK, observed with the Yohkoh mission, may be located at quite a large distance from the spots. In contrast, “warm” loops with a temperature of (1.0–1.5) MK, observed with the Transition Region and Coronal Explorer (TRACE) mission, are, as a rule, situated in the vicinity of the spots; the footpoints of these loops are located in the penumbral regions. This fact, as well as the difference in the density and size of these types of loops, may provide evidence of different mechanisms of formation and heating of hot X-ray and “warm” loops [3].

Essentially, two different types of magnetic flux tubes are possible. The first type originates in the course of “raking” the background magnetic field up by convective flows of photospheric plasma. Footpoints of these tubes are commonly located either in the nodes of several supergranulation cells, where horizontal convective flows converge, or close to the boundary of two adjacent supergranules. In the latter case, arcades of coronal magnetic loops may be formed along the boundary of the supergranules. Such loops may be located in the distance from sunspots; inside them, a large (up to 10A) electric current may occur due to the interaction between the convective plasma flow and the intrinsic magnetic field of the tubes. Magnetic flux tubes with parallel currents may contain large nonpotential energy and may therefore be a source of powerful flares.