A THEORETICAL STUDY OF SOLAR

CORONAL HEATING MECHANISMS BY

MICROFLARES AND NANOFLARES

A

Thesis

Submitted to

Kumaun University Nainital

for the Degree of

Doctor of philosophy

In

Physics

Supervised by Submitted by

Dr. Lalan Prasad VINOD KUMAR JOSHI

Head, Department of Physics

M. B. Govt. P. G. College, Haldwani

Department of Physics

M. B. Govt. P. G. College, Haldwani

Nainital, Uttarakhand (India)-263141

July - 2011

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“I would like to dedicate this work to my

parents, brothers, guide and friends

whose inspirations and guidance provided

me strength to complete this work”

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ACKNOWLEDGEMENTS

I am grateful to my research supervisor Dr. Lalan Prasad, Head, Department of

Physics, M. B. Govt. P. G. College, Haldwani, Nainital and Associate of Inter

University Centre for Astronomy and Astrophysics (IUCAA), Pune, for his

noble guidance and assiduous help, patience and giving me the opportunity to

go beyond perceived limitations. He has given me a gift of knowledge, which

can never be taken away. I would like to thank him for his friendly and

encouraging attitude and the support he provided. I thank him for reviewing my

work from time to time and for providing me with his constructive feedback. I

also thank him for his timely support and feedback which helped me in shaping

my career and also for keeping track of my progress during the work. I feel

indebted to him for all his help, motivation and active cooperation, without his

guidance this work would have been difficult to complete. I would like to

express my heartfelt gratitude to his wife Dr. Vimala Kumari (Govt. School,

Dhaulakhera, Haldwani), who always cooperate and inspired me to complete

the research work.

I express my deep gratitude to my beloved Parents, father Shri. Ramesh

Chandra Joshi (N. E. Railway, Nainital), and mother Smt. Pushpa Joshi to help

me financially, motivations, constant encouragements to complete this work.

I am sincerely thankful to Prof. D. S. Mahori (Principal, M. B. Govt. P. G.

College, Haldwani), Prof. M. C. Pandey (former Director Higher Education,

Uttarakhand), Prof. B. S. Bisht (former Joint Director, Higher Education,

Uttarakhand and Principal, M. B. Govt. P. G. College, Haldwani), Dr. Kamal

Pandey (Registrar, Kumaun University, Nainital), Dr. Wahab Uddin (Scientist

E, ARIES, Nainital), Dr. Udit Narain (Meerut College, Meerut), Prof. Suresh

Chandra (former Head, Department of Physics, SRTM University, Nanded),

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Prof. Ram Sagar (Director, ARIES, Nainital), Dr. N. K. Lohani (Govt. P. G.

College, Ranikhet) and Dr. P. K. Srivastava (Govt. P. G. College, Reva) for

their valuable advice and encouragements during the course of these

investigations.

I would like to thank Prof. J. V. Narlikar, Prof. Naresh Dadhich (Ex.

Director, IUCAA), Prof. Ajit Kembhavi (Director, IUCAA), and other faculty

members of IUCAA, Pune for their ever constructive suggestions, kind

cooperation, encouragement and help. The library and computer facilities of

IUCAA, Pune used by us and the major part of the research work has been

carried out at IUCAA, Pune. I also thanks to the Director of NCRA Pune, for

giving me the opportunities to used freely library and computer facilities. I also

thanks to Shri Yugal Kishore Joshi for providing me the library facilities at

Kumaun University, Nainital. I highly thanks to our host institution M. B. Govt.

P. G. College, Haldwani, for providing the place for doing the constant work.

I thank the scientists and researchers of different institution/university

who gave moral support to do this work.

Thanks to Dr. Seema Pandey, Dr. S. K. Srivastava, Dr. Tara Bhatt, Dr. M.

K. Pandey, Smt. Suman Garia (Research Scholar), Department of Physics and

other teaching and non-teaching staff of M. B. Govt. P. G. College, Haldwani.

Thanks are due to my friends and all of my current and former colleagues.

Special thanks are due to Prof. B. C. Joshi (Head & Convener, BOS/RDC

Dept. of the Physics, Kumaun University, Nainital), Dr. M. C. Durgapal, Dr. K.

L. Shah, Dr. O. P. S. Negi, Dr. P. S. Bisht, Dept. of Physics, S. S. J. Campus

Almora and Dr. Pankaj Kumar (PDF, Solar and Space Weather Research

Group, KASI, South Korea) for their ever constructive suggestions, kind

cooperation, encouragements and help.

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I find no words to express my feelings for constant encouragement and

inspiration; I received from my grandmother Smt. Basanti Joshi, Uncles Mr. S.

C. Joshi, Mr. G. D. Joshi (L. I. C., Haldwani), and Brothers Dr. Girja Shankar

Pandey (S. S. J. Campus, Almora), Er. Umesh Joshi (Manager, Bajaj Electricals

Pvt. Ltd., Mumbai), Er. Manoj Kandpal (Infosysis Pvt. Ltd., Pune, India ) Mr.

Hame pandey, Mr. Manoj Pandey (Jyotishi), Mr. Rohit Joshi (ITC Royal

Gardenia, Bangalore), Mr. Himanshu Joshi and Bhabhi Smt. Kajal Kiran Joshi

(Sr. Engineer, Chemtex Pvt. Ltd., Mumbai).

This acknowledgement would be incomplete without expressing my

whole hearted thanks to my following friends who motivated me during the

course of the work Er. Nitin Tiwari (Asst. Professor, NIT Jalandhar), Mr. Nitin

Arya (Central Excise Inspector, Vadodara), Mr. Ajay Bisht (Nainital Bank,

Rudrapur), Mr. Mohit Rawat (Asst. Branch Manager, Nainital Bank, Tehari),

Er. Mani Dev (Software Engineer, Capgemeni, Chennai), Mr. Vineet Brijwasi

(Almora Urban Co-operative Bank, Almora), Er. Vikas Gupta (Associate

System Engineer-IBM, Bangalore), Er. Vinay Ohra (ASIC Design Engineer-

Open Silicon, Bangalore), Er. Rajendra Prasad (Asst. Professor, Mewar

University, Rajasthan), Er. Krishna Murari, Er. Ashish Pathak, Er. Ankit Bapna

(Design Engineer, Sankalp Semiconductor, Hubli), Er. Ankit Aggarwal (Design

Engineer, Ericson R & D, Bangalore), Mr. Pitamber Tewari, Mr. Saurabh

Verma, Mr. Harish Chand (Indian Air Force, Nashik), Mr. Arvind Kumar (SRF,

BARC, Mumbai), Mr. Rumi Ali and Mr. Meesam Ali (Student, Pantnagar

University). It is very difficult to write the name of each friend here but there

support and help will be unforgettable for me.

VINOD KUMAR JOSHI

(Research Scholar)

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LIST OF PUBLICATION

1. “Power-Law Nanoflare Heating”

L. Prasad and V. K. Joshi; 2009, Astrophysics and Space Science

Proceedings Springer-Verlag, Heidelberg, Berlin, 452-453.

2. “Power Law and Hydrodynamical Approach of Nanoflare Heating”

L. Prasad and V. K. Joshi; 2009, Asian Journal of Physics, India, 18,

No. 1, 79-88.

3. “Study of Solar Coronal Heating by Nanoflares”

L. Prasad, V. K. Joshi and M. K. Pandey; 2009, Acta Ciencia Indica, India

XXXV No. 2, 113.

4. “Nanoflare Heating of Solar Corona by Reconnection Model”

V. K. Joshi and L. Prasad (Submitted, 2011, Spacetime & Substance,

Ukrain)

Article

1. “Solar Flares and Their Effects”

L. Prasad and V. K. Joshi; 2008, Physics Education, 25, No. 4, 267-275.

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POSTER

1. “Nanoflares as a Plausible Coronal Heating Agent”

L. Prasad and V. K. Joshi; First Uttaranchal State Science Congress held

at DIT, Dehradun during 10-11 Nov., 2006.

2. “Possibility of Coronal Loops heating by Phase Mixing”

M. K. Pandey, L. Prasad and V. K. Joshi; International conference on

Challenges for Solar Cycle-24 held at PRL-Ahemadabad, during 22-25

Jan., 2007.

3. “Dynamics of Phase-Mixing in Force-Free State”

L. Prasad, M. K. Pandey and V. K. Joshi; “ XXV Meeting of the

Astronomical Society of India” held at Department of Astronomy,

Osmania University, Hyderabad, India during 07- 09 Feb., 2007.

4. “Nanoflare Heating of Solar Corona by Reconnection Model”

V. K. Joshi, L. Prasad and M. K. Pandey; “IHY-2007” held at ARIES,

Nainital during 07-10 May, 2007.

5. “Plasma Heating by Alfven Wave Phase-Mixing Through the Nonlinear

excitation of fast Magnetosonic Waves”

M. K. Pandey, L. Prasad and V. K. Joshi; “IHY-2007” held at ARIES,

Nainital during 07-10 May, 2007.

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6. “Power Law and Hydrodynamical Approach of Nanoflare Heating”

L. Prasad and V. K. Joshi; Third Uttarakhand Sate Science and

Technology Congress held at IIT-Roorkee, during 10-11 Nov., 2008.

7. “Power Law and Hydrodynamical Approach of Nanoflare Heating”

L. Prasad and V. K. Joshi; “Evershed Meeting” held at IIA-Banglore,

during 2-5 Dec., 2008.

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VISITS/CONFRENCES/SEMINAR

1. Attended a workshop entitled in “From Atom to Galaxy” during 09-11 Oct.,

2006 in Dept. of Physics H. N. B. Garhwal University, Shrinagar.

2. Participated in a national workshop entitled in “Recent Advances in Solar

Physics” during 07-10 Nov., 2006 in Meerut College, Meerut.

3. Visited IUCAA, Pune under visiting programme during 22 Nov. to 10

Dec., 2006.

4. International Heliophysical Workshop on Solar active Regions of Solar

Cycle and their Geo-space Impact (IHY-2007) held in ARIES, Nainital

during 07-10 May, 2007.

5. Visited IUCAA, Pune under visiting programme during 19 May to 18 June,

2007.

6. Visited IUCAA, Pune under visiting programme during 25 May to 10 June,

2008.

7. Third Uttarakhand Sate Science and Technology Congress held at IIT,

Roorkee, during 10-11 Nov., 2008.

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Contents

Preface xxix

Chapter 1

1. INTRODUCTION 2

1.1 Solar System 2

1.1.1 Formation and Evolution of Solar System 3

1.2 A Brief History of the Sun 5

1.3 Characteristics and Position in H-R Diagram 8

1.3.1 Relative strength with temperature 9

1.4 Some Moments/Views of the Sun 11

1.4.1 The Unquiet Sun 11

1.4.2 Image of the Sun prominence 12

1.4.3 Comet SOHO-6 and Solar Polar Plumes 12

1.4.4 X-ray Images of the Sun 13

1.4.5 Image of Solar Disk in H-Alpha 13

1.4.6 Image of Solar Flare in H-Alpha 14

1.4.7 Image of Solar Magnetic Fields 14

1.4.8 Image of the Sun Spot 15

1.4.9 A new look at the Sun 16

1.5 Some interesting Solar Eclipses of the Sun 16

1.5.1 1991 Solar Eclipses 16

1.5.2 1994 Solar Eclipses 17

1.5.3 1999 Solar Eclipses 17

1.5.4 Eclipse from STEREO spacecraft 18

1.6 Mythological approach of Solar Physics 18

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1.6.1 Some Historical moments in History of Solar Physics 20

1.7 The Vital Statistics of the Sun 21

1.8 Internal Structure of the sun 25

1.8.1 Interior Layers of the Sun 25

1.8.1.1 The Core 26

1.8.1.1.1 Energy Production in Core 26

1.8.1.2 The Radiative Zone 28

1.8.1.3 The convective zone 29

1.8.2 The Sun’s Outer Layer and Regions 30

1.8.2.1 The Photosphere 31

1.8.2.2 The Photosphere Faculae 32

1.8.3 The Chromosphere 32

1.8.3.1 The Chromospheric Plages 33

1.8.4 The Solar Transition region 33

1.8.5 The Solar Corona 34

1.8.5.1 Classifications of the Coronal Structure 36

1.8.6 The Coronal Hole 37

1.8.7 The Coronal plumes 38

1.8.8 The Coronal Active Regions 38

1.8.9 The Coronal Quiet Regions 38

1.8.10 The Coronal Prominences 38

1.8.11 The Coronal Radio Bursts 39

1.8.12 The Heliosphere 40

1.9 The Solar Wind 40

1.10 The Coronal Mass Ejections 41

1.11 Sun Spot and their Life Cycle 43

1.11.1 Umbra and Pen umbra 44

1.11.1.1 Pores 45

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1.11.2 Life Cycle 45

1.12 Granulation 45

1.12.1 Observations of Granulation 46

1.12.2 Cause of Granulation 46

1.12.3 Super Granulation 47

1.13 Solar Prominence and their view in different perspective 47

1.14 The Solar Flares 50

1.14.1 Cause of Solar Flares 51

1.14.2 The classification of X-ray Solar Flares 52

1.14.3 Observations for Solar Flares 53

1.14.3.1 Optical Observations 54

1.14.3.2 Radio Observations 54

1.14.3.3 Space Telescopes 55

1.15 The Coronal Loops 55

1.16 The Plasma Heating 56

1.17 Introduction to the Problem 57

1.18 The Coronal Heating 58

1.19 Solar Exploration 59

1.19.1 Ulysses 60

1.19.2 Yohkoh 60

1.19.3 SOHO 60

1.19.4 Wind & Polar 62

1.19.5 ACE 62

1.19.6 TRACE 63

1.19.7 GOES/SOLAR X-ray Imager 64

1.19.8 GENESIS 65

1.19.9 CORONAS- F 65

1.19.10 RHESSI 66

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1.19.11 SOLAR-B 67

1.19.12 STEREO 68

1.19.13 SDO 68

1.19.14 SOLO 70

2. CHAPTER 2

A BRIEF OVERVIEW ON SOLAR FLARE

2.1 Solar Flares 72

2.2 History of Observations 72

2.2.1 Missions to Observe Solar Flares 75

2.3 Observations of Solar Flares in different light ranges 77

2.3.1 Observations in Visible light 77

2.3.2 Observations in extreme UV light 80

2.3.3 Sun’s Magnetograms 81

2.3.4 Doppler’s Images 82

2.4 Classification of Solar Flares 83

2.4.1 X-ray Classification 83

2.4.2 Visible Light Classification 84

2.4.2.1 Chromospheric Flare 89

2.4.2.2 Two Ribbon Flares 90

2.4.2.3 Limb Flare 91

2.5 Energy Budget 93

2.5.1 Non thermal Electron Energy 95

2.5.2 Thermal Energy 97

2.5.3 Energy in Waves 99

2.5.4 Other energies 101

2.6 How the Energy released? 103

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2.6.1 Coronal hard X-ray signatures 103

2.6.2 Soft-hard-soft behaviour in hard X-rays 106

2.6.3 Radio emissions from the Acceleration region 107

2.7 Results and Conclusions 110

3. CHAPTER 3

ROLE OF MHD AND MAGNETIC RECONNECTION

3.1 Definition of MHD 112

3.1.1 Coronal Seismology 113

3.2 Ideal MHD Equations 113

3.3 Basic MHD Equation in Resistive Medium 116

3.4 Magnetic Reconnection 117

3.4.1 The Origins of Reconnection Theory 119

3.4.2 Goals of Reconnection Theory 120

3.5 Six Reconnection Model to Explain magnetic reconnection 121

3.5.1 Sweet-Parker Reconnection Model 124

3.5.2 Petschek reconnection Model 127

3.5.3 Unsteady/Bursty 2D reconnection 128

3.5.3.1 Tearing Mode Instability 129

3.5.3.2 Coalescence Instability 130

3.6 3D Magnetic Reconnection 131

3.6.1 3D X-Type Reconnection 132

3.6.2 3D Null Points 134

3.6.3 3D Spine, Fan, and Separator Reconnection 136

3.7 Magnetic reconnection as a Heating Mechanisms 138

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3.7.1 Energy of a Current Sheet formed by steady Magnetic

Reconnection 139

3.8 Results and Conclusions 145

4. CHAPTER 4

HYDRODYNAMICAL APPROACH OF NANOFLARES

HEATING

4.1 Introduction 147

4.2 Concept of Hydrodynamic Simulations 149

4.3 Power Law and Hydrodynamical Approach 151

4.3.1 Hydrodynamical Equations 153

4.4 Low Region Plasma response of a Nanoflare 155

4.5 Results and Conclusions 159

5. CHAPTER 5

SOLAR CORONAL HEATING BY MICROFLARES AND

NANOFLARES

SECTION A

5A. 1 Introduction 162

5A.2 Observations for Microflares 163

5A2.1 HINODE is another spacecraft that observes Mysterious

Solar Microflares 165

5A.3 Solar Coronal Heating by Microflares/Transients 166

5A.4 Energy Range Distribution of Flares 169

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5A.5 Theoretical Estimation 171

5A.6 Results and Conclusions 172

SECTION B

5B.1 Introduction 174

5B.2 Theoretical Details 176

5B.2.1 Power Law Distribution 177

5B.3 The Power Law Exponent (α) 182

5B.4 Estimation of Coronal Radiation 183

5B.5 Results and Conclusions 184

SUMMARY AND CONCLUSIONS 186

APPENDIX

A.1 Particle Conservations 195

A.2 Force or Momentum Equation 197

A.3 Energy Equation 198

A.4 Maxwell’s Equations 201

A.5 Ampere’s Current Law 201

A.6 Ohm’s Law 202

BIBILOGRAPHY 204

WEBHELP 220

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LIST OF FIGURES

1.1 The Solar System 2

1.2 Formation and Evolution of the Sun 3

1.3 H-R Diagram 9

1.4 Relative strength of stars with temperature 10

1.5 Images of Sun in UV light taken by SOHO 11

1.6 Most spectacular Solar Flare 12

1.7 Image of solar corona taken by LASCO on SOHO spacecraft 13

1.8 X-ray image of the sun 13

1.9 H-alpha image of the Sun 14

1.10 Solar Flare observed in H-Alpha 14

1.11 The magnetic polarity of the Sun 15

1.12 Sun Spots 15

1.13 A new look of the sun in UV light taken by SOHO 16

1.14 Image of Solar eclipse-1991 17

1.15 Image of Solar eclipse-1994 17

1.16 Image of Solar eclipse-1999 17

1.17 Image of solar eclipse obtained by STEREO Spacecraft 18

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1.18 An illustration of the structure of the Sun in various modes to

understand the internal structure of the Sun 25

1.19 Energy Production in Core 27

1.20 Zig-Zag motion in radiative zone 29

1.21 Convection zone represents the boiling of water in a pot 30

1.22 3-D picture of sun 31

1.23 The thin chromosphere is visible in this solar eclipse picture 32

1.24 Variation of temperature in different zones with distance 34

1.25 The Solar Corona 35

(a) Solar Corona at Eclipse, 3 Nov 1994, Putre, Chile, High Altitude

Observatory, NCAR, Boulder, Colorado, USA 35

(b) Soft X-ray image of Corona 35

1.26 Solar Prominence observed by Yohkoh Satellite in 1992 in Soft

X-ray 39

1.27 Solar wind 41

1.28 Coronal Mass Ejection 42

(a) A coronal mass ejection in time-lapse imagery obtained with the

LASCO instrument. The Sun (center) is obscured by the

coronagraph's mask. (September 30 – October 1, 2001) 42

(b) Illustration of CME moving beyond the planets towards the

Heliopause. 42

1.29 Sun spot and Solar Cycle 44

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(a) The Solar disk in white light represents Sunspots 44

(b) Measurements of Solar Cycle variation during the last 30 years 44

(c) Sunspot vs Years 44

1.30 Sun Spots with Umbra and Penumbra 45

1.31 Granulation 46

(a) Granulation near sun spot group 46

(b) Granulation region 46

1.32 Solar Prominence 48

(a) Solar prominence with images of Jupiter and Earth for size

comparison 48

(b) Major eruptive prominence (Skylab 1973) 48

(c) A Limb's Flare and after-Flare Prominence. 48

1.33 Various Solar Prominences 49

(a) Solar Prominence 49

(b) Detached solar prominence 49

1.34 Solar Prominence 49

(a) Solar prominence STEREO behind 49

(b) Solar prominence STEREO ahead 49

1.35 The Sun shows a C3-class solar flare (white area on upper left), a solar

tsunami (wave-like structure, upper right) and multiple filaments of

magnetism lifting off the stellar surface. 53

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1.36 Coronal Loops 56

(a) Typical coronal loops observed by TRACE 56

(b) Diagram of the low corona and transition region, where many

scales of coronal loops can be observed 56

(c) X-ray solar coronal loops as viewed by Yohkoh observatory 56

1.37 Yohkoh spacecraft 61

1.38 Spacecraft illustration – SOHO 61

1.39 Illustration of Advance Composition Explorer (ACE) 62

1.40 TRACE Mission 63

1.41 GOES Satellite 64

1.42 GENESIS Spacecraft 65

1.43 RHESSI Satellite 66

1.44 SOLAR-B Satellite 67

1.45 STEREO Satellite 68

1.46 SDO Satellite 69

1.47 SOLO Proposed Mission 70

2.1 Images of Sun in Visible light from various Solar Observatory

(a) White light image from Big Bear Solar Observatory(California) 77

(b) White light image from Mees Solar Observatory (Hawaii) 77

(c) SOHO-MDI Intensity gram from Stanford University Solar Group 77

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(d) White light image from ISOON-NSO Sacramento Peak (New Mexico)

77

(e) H-alpha image from ISOON-NSO Sacramento Peak (New Mexico) 78

(f) H-alpha image with limb darkening removed from ISOON-NSO

Sacramento Peak (New Mexico) 78

(g) H-alpha image from Big Bear Solar Observatory (California) 78

(h) H-alpha image from Mauna Loa Solar Observatory (Hawaii) 78

(i) Solar Flare in H-Alpha 78

(j) Helium I image from Mauna Loa Solar Observatory (Hawaii) 79

(k) He I 10830 Å image from SOLIS at the National Solar Observatory,

Kitt Peak (Arizona) 79

(l) He I 10830 Å image from ISOON-NSO Sacramento Peak (New

Mexico). 79

(m) Calcium K line image from Mees Solar Observatory (Hawaii) 79

(n) Calcium K-line image from Big Bear Solar Observatory (California)

79

(o) Fe I line (5250.2 angstrom) image from Mt. Wilson Observatory

(California) 80

(p) Na I line (5895.9 angstrom) image from Mt. Wilson Observatory

(California) 80

2.2 Extreme UV light Images 80

(a) SOHO Extreme ultraviolet Imaging Telescope (EIT) Fe XII 195 Å,

image from NASA Goddard Space Flight Center SDAC 80

(b) SOHO Extreme ultraviolet Imaging Telescope (EIT) Fe IX, X 171 Å

image from NASA Goddard Space Flight Center SDAC 80

(c) SOHO Extreme ultraviolet Imaging Telescope (EIT) Fe XV 284 Å

image from NASA Goddard Space Flight Center SDAC 81

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(d) SOHO Extreme ultraviolet Imaging Telescope (EIT) He II 304 Å

image from NASA Goddard Space Flight Center SDAC, NOAA SEC

SXI latest images 81

2.3 Sun’s Magnetograms 81

(a) 6302 Å longitudinal magnetogram from SOLIS at the National Solar

Observatory, Kitt Peak (Arizona) 81

(b) 8542 Å longitudinal magnetogram from SOLIS at the National Solar

Observatory, Kitt Peak (Arizona) 81

(c) Fe I line magnetogram from Mt. Wilson Observatory (California) 82

(d) Na I line magnetogram from Mt. Wilson Solar Observatory 82

2.4 Dopplers Images 82

(a) Dopplergram from the MDI experiment on SOHO 82

(b) Fe I dopplergram from Mt. Wilson Observatory (California) 82

(c) Na I dopplergram from Mt. Wilson Observatory (California) 83

2.5 Time Profile of flare energy release at various types of radiation

extending from radio to hard X-ray. The various phases indicated at the

top vary greatly in duration. In a large event, the preflare phase typically

lasts ten minutes, the impulsive phase one minute, the flash phase five

minutes, and the decay one hour. 87

2.6 Showing Soft X-rays (red), hard X-rays (blue) and gamma-rays (purple)

observed by the RHESSI satellite is overlaid on an optical Hα image.

88

2.7 Showing flare observed in the FeXII line at 195 Å (sensitive to 1.5 MK

plasma) by the TRACE satellite 90

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2.8 Showing Left: RHESSI flare observations of soft X-rays (red, 8 – 12

keV) and hard X-rays (blue, 20 – 50 keV) overlaid on a Hα background.

Note the high-energy foot points moving on the Hα flare ribbons, which

moves apart in the very late phase. 91

2.9 Showing Thermal emission and a flare observed with the Nobeyama

interferometer at 17 GHz. 91

2.10 Left: A schematic drawing of the one-loop flare model. Right:

Observation of an apparent X-point behind a Coronal Mass Ejection

observed by LASCO/SOHO in white light. 93

2.11 Overlays of RHESSI hard X-ray (orange) and white light

difference (thick blue) image contours on a white-light image observed

by the TRACE satellite. 96

2.12 Typical X-ray spectrum of flare observed by the RHESSI satellite

99

2.13 An overview in Fe XII EUV emission observed by EIT/SOHO,

showing thermal coronal emission of plasma at about 1.5 MK. The 12 –

25 keV hard X-ray emission observed by RHESSI is shown in red and

yellow colors 101

2.14 Top: Light curves in two energy bands (upper curve, 6 – 12 keV;

lower curve, 25 – 50 keV) of the April 15, 2002 flare observed by

RHESSI. Bottom: Altitude of the loop-top centroid obtained using the

60% contour for the images in the 6 – 12 (crosses) and 12 – 25 keV

(diamonds) bands. 104

2.15 Flux density at 35 keV and power-law index as determined from

RHESSI observations of the non-thermal component of flare hard X-ray

emission 106

2.16 Radio spectrogram observed by the Phoenix-2 spectro-polarimeter

operated by ETH Zurich 108

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3.1 The image of the Sweet-Parker model. The geometry of the diffusion

region follow the condition L >> l 125

3.2 Petscheck reconnection model. The diffusion region follows the

condition 127

3.3 Magnetic island formation by tearing-mode instability in the magnetic

reconnection region. 130

3.4 Classification of X-type magnetic reconnection topologies: 134

(a) bipolar models have reconnection between two open field lines; 134

(b) tripolar models have reconnection between an open and a closed field

line; and 134

(d) quadrupolar models have reconnection between two closed field lines.

134

3.5 Topology of 3D reconnection features for a quadrupolar region 136

3.6 Classification of 3D null point reconnection topologies: 137

(a) spine reconnection (left), 137

(b) fan reconnection (middle), and 137

(c) separator reconnection (right) 137

3.7 Magnetic Reconnection 138

3.8 Basic 2D model of a magnetic reconnection process 139

3.9 A sketch representing both the opposite magnetic pressure in formation

of current sheet. 141

4.1 The successive variation of nanoflare evolution of temperature at

different time scales with positions. 156

4.2 The successive variation of nanoflare evolution of velocity at different

time scales with positions. 157

4.3 Evolution of the nanoflare apex temperature with time after a localized

energy burst. 158

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4.4 Evolution of the nanoflare apex density with time after a localized energy

burst. 159

5.1 Image of the individual bright points are circled in green. These data were

taken on March 16, 2007 165

5.2 Showing Soft X-ray images observed by Hinode on April 30, 2007 166

5.3 Thermal energy vs Spatial scale for various category of flares

(1, 3; dark grey), soft X-ray brightenings (5, 6; middle grey),

SXR jets (8; white). 170

5.4 The variation of the rate of flaring agents with flaring energy for different

values of power law index α:

(a) α = 1.5, (b) α = 2.0, (c) α = 2.5 and (d) α = 3.0 180

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LIST OF TABLES

1.1 Physical Parameters of the Sun 21

1.2 Classification of Solar Flares with emitting surface, measured in

terms of millionths of the hemisphere 53

2.1 H Flare classification 85

2.2 Flares Classification for H , Radio and Soft X-ray

class Flares 88

2.3 Energy Budgets for M and X class Flares 95

5.1 Flares Characteristics 170

5.2 Nanoflare generation rate per flux tube 181

5.3 Various values of α 182

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The Sun is the star at the center of the solar system. It is almost perfectly

spherical and consists of hot plasma interwoven with magnetic fields. It is a

main sequence star, and thus generates its energy by nuclear fusion of hydrogen

nuclei into helium. In its core, the sun fuses 620 million metric tons of hydrogen

each second. The optical surface of the sun (the photosphere) is known to have

a temperature of approximately 6,000 K. Above it lies the solar corona, rising to

a temperature of 1MK – 2 MK. The high temperature of the corona shows that it

is heated by something other than direct heat conduction from the photosphere.

Therefore, the temperature is expected to fall as we move away from this

central “core”. The temperature of the solar atmosphere, however, instead of

dropping as you move away from the sun, actually increases as we move

outward from the photosphere to the corona. Since the convection zone of the

sun is very turbulent, like a pot of boiling water, the magnetic field in the

corona is anchored in the convection zone. The gas pressure in the convection

zone dominates the magnetic field pressure. As a result, the magnetic field is

dragged around and twisted by the turbulent motions of the gas in the

convection zone. These motions can propagate up the magnetic field lines to the

corona. The extra energy is transferred to the magnetic field is presumably to

the coronal plasma. In this thesis we provide a comprehensive introduction into

the basic physics of solar coronal loops and to investigate their heating

mechanisms. It was found that the energy necessary to heat the corona is

provided by turbulent motion in the convection zone below the photosphere,

and two main mechanisms have been proposed to explain coronal heating. The

first is wave heating, in which sound, gravitational or magnetohydrodynamics

waves are produced by turbulence in the convection zone. These waves travel

upward and dissipate in the corona, depositing their energy in the ambient gas in

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the form of heat. The other is magnetic heating, in which magnetic energy is

continuously built up by photospheric motion and released through magnetic

reconnection in the form of large solar flares and myriad similar but smaller

events-nanoflares. We follow the second one, and presented each chapter

analytically and theoretically to solve the problem of solar coronal heating. This

thesis is aimed to bring up-to-date introduction into the physics of the solar

coronal loops and heating mechanisms. The work is compiled into five chapters,

the chapter wise outline of the thesis is as follows:

The chapter 1 consists of the brief explanation of the solar system,

formation and evolution of solar system, characteristics and position of sun in

H-R diagram followed by the brief history of the sun. Some interesting

views/moments of the sun, some interesting solar eclipses taken by various solar

missions are presented. It is further followed by parameters of the sun, interior

and exterior structures of the sun and different activities i.e. solar wind, coronal

mass ejection, sunspots and their cycle, solar prominence, solar flares, coronal

loops, plasma heating and solar-terrestrial interactions including problems and

the solar exploration mission to solve a lot of enigma related with sun. This

chapter provides the basics and objective of the research work.

The chapter 2 represents the standard models of the flare geometry, their

classification (in Hα, radio, soft X-ray) and various types of flare on the basis of

shape, size and position obtained by various satellites (TRACE, RHESSI,

LASCO, SOHO etc). It also explains that how the large flares influence

interplanetary space and substantially affect the earth’s lower ionosphere. The

soft X-ray flux of X-class flares increases the ionization of the upper

atmosphere. which can interfere with short radio communication, and can

increase the drag on low orbiting satellites, leading to orbital decay.

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The chapter 3 deals with the explanation of MHD as a tool for our work

to solve a lot of phenomena related with sun. A combined set of ideal MHD

equations that includes the MHD continuity equation, the momentum equation,

Maxwell’s equations, Ohm’s law, and a specialized equation of state for energy

conservation (incompressible, isothermal, or adiabatic) is presented (In

Appendix). After applying some approximations a set of resistive MHD

equations are obtained.

Magnetic reconnection is the phenomena in which magnetic energy in

plasma is rapidly converted to heat and jets of energetic particles. This chapter

deals with the origin of reconnection theory and their goal. Six reconnection

models are explained. 2D and 3D magnetic reconnections are briefly explained.

Finally the energy of a current sheet is calculated that is formed when two

magnetic fields of opposite polarity come closer. The energy calculated in 2D

reconnection of a current sheet is near to the energy of a nanoflare.

In chapter 4 the time dependent hydrodynamical equations under the

conservation of mass, momentum and energy in one special dimension “s” are

numerically solved and it coupled with ionization rate equations. We discussed

the evolution of the nanoflare apex temperature and density with time after a

localized energy burst. The successive variation of nanoflare evolution of

temperature and velocity at different time scales with positions are presented.

Here we examined a fully 1D hydrodynamic simulation of a 109 cm long loop

with cross sectional radius of ~1.1 × 10�cm. The loop consists of a number of

individual nanoflare elements. We discussed the hydrodynamic modelling for

solar flares, power law and hydrodynamic simulation, hydrodynamical

equations in low region plasma response followed by results and conclusions.

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The chapter 5 divided into two sections A and B. The section A

describes the physics of microflares which is followed by the observations taken

by RHESSI and HINODE, and tries to solve the mysteries of microflares. The

steady state heating of the solar corona by microflares and transients are

discussed in next subsection. The large flares, microflares and nanoflares are

distinguished in terms of thermal energy, temperature and electron density.

Theoretical estimation of microflares followed with the results and conclusions.

In section B the analysis of nanoflares are represented by power law

distribution as a function of their energies with the negative slope of -2 and it

may be larger. We discuss the physical characteristics of nanoflare heating

process in respect of power law distribution and formulate the coronal

luminosity. We estimate the coronal radiation energy and generation rate of

nanoflares.

In the last the results and conclusions of my work is presented.

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