Magnetic flux emergence in the solar photosphere [Elektronische Ressource] / vorgelegt von Chun Ming Mark Cheung
135
pages
Documents
2006
Le téléchargement nécessite un accès à la bibliothèque YouScribe Tout savoir sur nos offres
135
pages
Ebook
2006
Le téléchargement nécessite un accès à la bibliothèque YouScribe Tout savoir sur nos offres
Publié par
Publié le
01 janvier 2006
Nombre de lectures
38
Poids de l'ouvrage
10 Mo
Publié par
Publié le
01 janvier 2006
Nombre de lectures
38
Poids de l'ouvrage
10 Mo
Magnetic flux emergence in the solar
photosphere
Dissertation
zur Erlangung des Doktorgrades
der Mathematisch Naturwissenschaftlichen Fakultäten
der Georg August Universität zu Göttingen
vorgelegt von
Chun Ming Mark Cheung
aus Hong Kong
Göttingen 2006Bibliografische Information Der Deutschen Bibliothek
Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen
Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über
http://dnb.ddb.de abrufbar.
D7
Referent: Prof. Dr. F. Kneer
Korreferent: Prof. Dr. M. Schüssler
Tag der mündlichen Prüfung: 27 Februar 2006
Copyright?c Copernicus GmbH 2006
ISBN 3 936586 51 9
Copernicus GmbH, Katlenburg Lindau
Druck: Schaltungsdienst Lange, Berlin
Printed in GermanyContents
Contents 3
Summary 7
1 Introduction 9
1.1 Global properties of magnetic flux emergence . . . . . . . . . . . . . . . 9
1.2 Small scale properties of magnetic flux emergence . . . . . . . . . . . . 12
1.3 The buoyant rise of magnetic flux tubes . . . . . . . . . . . . . . . . . . 14
1.4 Research program of the present thesis . . . . . . . . . . . . . . . . . . . 15
2 Moving magnetic flux tubes: fragmentation, vortex streets and the limit of
the approximation of thin flux tubes 17
2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Equations, numerical method and initial conditions . . . . . . . . . . . . 17
2.2.1 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 Initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2.1 Background stratification . . . . . . . . . . . . . . . . 18
2.2.2.2 Initial magnetic profile of the flux tube . . . . . . . . . 19
2.2.3 Numerical method . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.4 Tracking the flux tube . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 Dependence on Reynolds number . . . . . . . . . . . . . . . . . 21
2.3.1.1 Structure of the wake . . . . . . . . . . . . . . . . . . 22
2.3.1.2 Flux retention and field diffusion . . . . . . . . . . . . 23
2.3.2 Dependence of flux retention on twist . . . . . . . . . . . . . . . 26
2.3.3 Evolution of twist in the flux tube . . . . . . . . . . . . . . . . . 27
2.4 Comparison with a thin flux tube model . . . . . . . . . . . . . . . . . . 28
2.4.1 Thin flux tube model . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.2 Modelling the motion of the main tube . . . . . . . . . . . . . . 32
2.4.3 The asymmetric rise of magnetic flux tubes and their trailing vor-
tex streets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.5 Exploring the limits of the thin flux tube approximation . . . . . . . . . . 35
2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3Contents
3 Simulation of near surface convection and the photosphere 41
3.1 The radiative MHD equations . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.1 The equations of magnetohydrodynamics . . . . . . . . . . . . . 43
3.1.2 Equation of state . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.1.3 Numerical treatment of the MHD equations . . . . . . . . . . . . 44
3.1.4 Radiative Transfer Equation . . . . . . . . . . . . . . . . . . . . 45
3.1.5 Numerical treatment of the RTE . . . . . . . . . . . . . . . . . . 47
3.2 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 Properties of near surface convection and the photosphere . . . . . . . . . 49
3.3.1 Topology of near surface convection . . . . . . . . . . . . . . . . 50
3.3.2 Logarithmic temperature and density gradients . . . . . . . . . . 51
3.3.3 Specific entropy distribution . . . . . . . . . . . . . . . . . . . . 53
3.4 The structure of the reversed granulation in the photosphere . . . . . . . . 55
4 Photospheric flux emergence: 2 dimensional simulations 63
4.1 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.1.1 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . 63
4.1.2 Initial . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2.1 Dependence of emergence morphology on twist . . . . . . . . . . 66
4.2.2 Intensification of emerging magnetic fields by radiative cooling . 69
4.2.3 of emerged flux on twist . . . . . . . . . . . . . . . 72
5 Photospheric flux emergence: 3 dimensional simulations 75
5.1 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1.1 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1.2 Initial . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2 Influence of convection on flux emergence . . . . . . . . . . . . . . . . . 77
5.3 Observational signatures . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.3.1 Quiescent flux emergence . . . . . . . . . . . . . . . . . . . . . 81
5.3.1.1 Surface evolution of emerged field: cancellation, coa
lescence and secondary emergence . . . . . . . . . . . 88
5.3.2 Emergence of strong magnetic field . . . . . . . . . . . . . . . . 93
5.3.2.1 The relation between field strength and zenith angle . . 94
5.3.2.2 Anomalous transient dark lane . . . . . . . . . . . . . 98
5.4 Emergence of an arched magnetic flux tube . . . . . . . . . . . . . . . . 100
5.4.1 Appearance of bright grains at the footpoints of the loop . . . . . 102
5.4.2 Detection of an ephemeral region . . . . . . . . . . . . . . . . . 107
6 Concluding remarks 113
Bibliography 115
A Calculation of important thermodynamic quantities 121
A.1 Specific entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
A.2 The Jacobian matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
A.3 Specific heatsc andc . . . . . . . . . . . . . . . . . . . . . . . . . . . 122v p
4Contents
A.4 Adiabatic temperature gradient . . . . . . . . . . . . . . . . . . . . . . . 123
A.5 Chandrasekhar’s adiabatic exponents . . . . . . . . . . . . . . . . . . . . 123
B Diffusion of a magnetic structure with a Gaussian profile 125
C Magnetic field extrapolation 127
C.1 Potential field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
C.2 Linear force free field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Publications 131
Acknowledgements 133
Lebenslauf 135
5Summary
Observations indicate that magnetic fields emerge into the photosphere of the Sun as
bundles of magnetic flux, also referred to as magnetic flux tubes. In this dissertation, this
phenomenon is studied by means of numerical simulations.
† Idealized two dimensional magnetohydrodynamics (MHD) simulations of the rise
of individual horizontal magnetic flux tubes through an initially static, stratified
medium were carried out. The buoyant rise, fragmentation, and vortex shedding of
magnetic flux tubes were studied.
† Three dimensional radiative hydrodynamics simulations were carried out to study
the properties and dynamics of near surface convection and the photosphere in the
quiet Sun. The convection zone and the photosphere are, respectively, super- and
sub adiabatically stratified. The granulation pattern of the quiet Sun consists of
relatively hot and bright cells (granules) separated by cool and dark intercellular
boundaries at optical depth unity. With increasing geometrical height and decreas
ing optical depth, the pattern of temperature fluctuations reverses, so that the inter-
cellular boundaries become hotter than the cellular regions. This reversed granu
lation pattern results from the radiative heating and cooling of convecting plasma
overturning in the stably stratified photosphere.
† To model magnetic flux emergence, we carried out radiative MHD simulations of
buoyant flux tubes, initially embedded in the near surface layers of the
convection zone. The results from the simulations highlight the important of radia
tive energy exchange and magneto convection on the properties of emerging mag
netic flux.
† The observational signatures of magnetic flux emergence in our simulations agree
qualitatively and quantitatively with observations of emerging flux regions. Flux
18tubes with a longitudinal flux of about 10 Mx evolve passively with the convec
tive flow and magnetic flux preferentially emerges in the form of horizontal fields
through the interior of granules. Within a granulation time scale (» 5 min), the
emerged flux is expelled to the intergranular downflow network.
19† The emergence of an arched flux tube carrying a longitudinal flux of about 10
Mx can lead to the transient appearance of an anomalous dark lane, which has a
life time of about10 min and is spatially coincident with upflows at the emergence
site. The appearance of bright grains flanking the ends of the transient darkening is
associated with the development of downflows at the photospheric footpoints of the
arched flux tube.
7Summary
† Synthetic magnetograms for the previous emergence event were produced. The
appearance of the surface field depends on the spatial resolution and effective noise
level in the magnetograms. At a resolution of about 1 Mm, the evolution of the
surface flux in the synthetic magnetograms is akin to that of an
