Thermal Convection, Magnetic Field, and Differential Rotation in Solar-type Stars

88 Pages·2015·6.663 MB·English

by  Hideyuki Hotta

Springer Theses
Recognizing Outstanding Ph.D. Research
Hideyuki Hotta

Thermal Convection,
Magnetic Field, and
Differential Rotation
in Solar-type Stars
Springer Theses
Recognizing Outstanding Ph.D. Research
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Hideyuki Hotta
Thermal Convection,
Magnetic Field,
and Differential Rotation
in Solar-type Stars
Doctoral Thesis accepted by
The University of Tokyo, Tokyo, Japan
123
Author(Present Address) Supervisor
Dr. HideyukiHotta Assoc. Prof. TakaakiYokoyama
HAO/NCAR The Universityof Tokyo
Boulder, CO Tokyo
USA Japan
ISSN 2190-5053 ISSN 2190-5061 (electronic)
Springer Theses
ISBN 978-4-431-55398-4 ISBN 978-4-431-55399-1 (eBook)
DOI 10.1007/978-4-431-55399-1
LibraryofCongressControlNumber:2014959127
SpringerTokyoHeidelbergNewYorkDordrechtLondon
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Parts of this thesis have been published in the following journal articles:
H. Hotta, M. Rempel, and T. Yokoyama, 2014, ApJ, 786, 24
H. Hotta, M. Rempel, and T. Yokoyama, 2015, ApJ, 798, 51
’
Supervisor s Foreword
This thesis describes the studies on the solar interior where turbulent thermal
convection plays an important role. Dr. Hideyuki Hotta solved, for the first time,
one of the long-standing issues in solar physics, i.e., the maintenance mechanism
of the solar differential rotation in the near-surface shear layer. He attacked this
problemwithhisnewlydevelopedapproach,thereducedspeedofsoundtechnique,
which enabled him to study the surface and deep solar layers in a self-consistent
manner. This technique also made it possible to achieve an unprecedented
performance in the solar convection simulations for use of massively parallel
supercomputerssuchastheRIKENKsystem.Itwasfoundthattheturbulenceand
the mean flows such as the differential rotation and the meridional circulation
mutuallyinteractwitheachothertomaintaintheflowstructuresinthesun.Recent
observations by helioseismology support his proposed theoretical mechanism. He
also addressed the generation of the magnetic field in such turbulent convective
motions, which is an important step forward for the solar cyclic dynamo research.
Tokyo, Japan, December 2014 Assoc. Prof. Takaaki Yokoyama
vii
Acknowledgments
I would like to express my gratitude to my supervisor Takaaki Yokoyama for his
contributiontomyeducationinthelast6years.IwouldalsoliketothankMatthias
Rempel of the High Altitude Observatory (HAO), USA, for his assistance during
mystay inBoulder andhis insightfuladvice.Igreatlyappreciate thehelp ofHAO
scientists Mark Miesch, Nick Featherstone, and Yuhong Fan. I acknowledge the
members of the Yokoyama lab Yusuke Iida, Naomasa Kitagawa, Shin Toriumi,
YukiMatsui,HaruhisaIijima,TakafumiKaneko,ShyuoyangWang,ShunyaKono,
andTetsuyaNasuda,andthemembersintheSTPgroupattheUniversityofTokyo
forhelpfuldiscussionsintheseminarsandcolloquium.Thenumericalcalculations
in this thesis were carried out in the K-computer and FX10. My work was
supportedbyaJSPSfellowship.MystayattheHAOandtheMaxPlanckInstitute
weresupportedbytheJSPSstudyabroadprogram.Finally,Iwouldliketoexpress
my deepest thanks to my parents and other family members for their continuous
support and encouragement.
ix
Contents
1 General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Solar Structure and Mean Flow . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Solar Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Observation of Solar Mean Flow, Differential
Rotation and Meridional Flow. . . . . . . . . . . . . . . . . . . . 3
1.2 Theory and Numerical Calculation for Differential
Rotation and Meridional Flow. . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Gyroscopic Pumping and Thermal Wind Balance . . . . . . 5
1.2.2 Numerical Calculations for Differential Rotation
and Meridional Flow . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Remaining Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Reduced Speed of Sound Technique. . . . . . . . . . . . . . . . . . . . . 13
1.5 Thesis Goals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Basic Equations and Development of Numerical Code . . . . . . . . . . 19
2.1 Model Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.1 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.2 Background Stratification and Radiation. . . . . . . . . . . . . 20
2.1.3 Setting for RSST. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.4 Divergence Free Condition for Magnetic Field . . . . . . . . 22
2.1.5 Equation of State. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Numerical Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.1 Space Derivative and Time Integration. . . . . . . . . . . . . . 24
2.2.2 Artificial Viscosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.3 Peano-Hilbert Space Filling Curve
for MPI Communication. . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.4 Yin-Yang Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.5 Big Data Management . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.6 Code Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
xi
xii Contents
3 Structure of Convection and Magnetic Field Without Rotation. . . . 33
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.1 Structure of Convection and Magnetic Field . . . . . . . . . . 35
3.3.2 Integrated Energy Flux . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.3 Analysis Using Spherical Harmonics
for Hydrodynamic Cases. . . . . . . . . . . . . . . . . . . . . . . . 42
3.3.4 Analysis Using Spherical Harmonics and Probability
Density Function for Magnetohydrodynamic Cases . . . . . 44
3.3.5 Generation and Transportation of Magnetic Field. . . . . . . 48
3.4 Discussion and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 Reproduction of Near Surface Shear Layer with Rotation . . . . . . . 59
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.4 Calculation with High Rotation Rate and Solar Luminosity. . . . . 70
4.5 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1 Summary of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1.1 Achievements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1.2 Findings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2 Remaining Problems and Future Work . . . . . . . . . . . . . . . . . . . 76
5.2.1 Comparison with Helioseismology. . . . . . . . . . . . . . . . . 76
5.2.2 Proper Reproduction of Solar Differential Rotation . . . . . 77
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Curriculum Vitae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81