List Of Figures

View Image Figure 1:
A full disk magnetogram from the Kitt Peak Solar Observatory showing the line of sight magnetic flux density on the photosphere of the Sun on May 11, 2000. White (Black) color indicates a field of positive (negative) polarity.
View Image Figure 2:
A continuum intensity image of the Sun taken by the MDI instrument on board the SOHO satellite on the same day as Figure 1. It shows the sunspots that are in some of the active regions in Figure 1.
View Image Figure 3:
A full disk soft X-ray image of the solar coronal taken on the same day as Figure 1 from the soft X-ray telescope on board the Yohkoh satellite. Active regions appear as sites of bright X-ray emitting loops.
View Image Figure 4:
A soft X-ray image of the solar coronal on May 27, 1999, taken by the Yohkoh soft X-ray telescope. The arrows point to two “sigmoids” at similar longitudes north and south of the equator showing an inverse-S and a forward-S shape respectively.
View Image Figure 5:
Schematic illustrations based on Schüssler and Rempel (2002) of the various forces involved with the mechanical equilibria of an isolated toroidal flux ring (a) and a magnetic layer (b) at the base of the solar convection zone. In the case of an isolated toroidal ring (see the black dot in (a) indicating the location of the tube cross-section), the buoyancy force has a component parallel to the rotation axis, which cannot be balanced by any other forces. Thus mechanical equilibrium requires that the buoyancy force vanishes and the magnetic curvature force is balanced by the Coriolis force resulting from a prograde toroidal flow in the flux ring. For a magnetic layer (as indicated by the shaded region in (b)), on the other hand, a latitudinal pressure gradient can be built up, so that an equilibrium may also exist where a non-vanishing buoyancy force, the magnetic curvature force and the pressure gradient are in balance with vanishing Coriolis force (vanishing longitudinal flow).
View Image Figure 6:
From Caligari et al. (1995). Upper panel: Regions of unstable toroidal flux tubes in the (B0, λ0)-plane (with B0 being the magnetic field strength of the flux tubes and λ0 being the equilibrium latitude). The subadiabaticity at the location of the toroidal flux tubes is assumed to be δ ≡ ∇ − ∇ad = − 2.6 × 10− 6. The white area corresponds to a stable region while the shaded regions indicate instability. The degree of shading signifies the azimuthal wavenumber of the most unstable mode. The contours correspond to lines of constant growth time of the instability. Thicker lines are drawn for growth times of 100 days and 300 days. Lower panel: Same as the upper panel except that the subadiabaticity at the location of the toroidal tubes is δ ≡ ∇ − ∇ad = − 1.9 × 10− 7.
Watch/download Movie Figure 7: (mpg-Movie; 250 KB)
Movie The formation of arched flux tubes as a result of the non-linear growth of the undulatory buoyancy instability of a neutrally buoyant equilibrium magnetic layer perturbed by a localized velocity field. From Fan (2001a). The images show the volume rendering of the absolute magnetic field strength |B |. Only one half of the wave length of the undulating flux tubes is shown, and the left and right columns of images show, respectively, the 3D evolution as viewed from two different angles.
View Image Figure 8:
From Fan and Fisher (1996). Latitude of loop emergence as a function of the initial latitude at the base of the solar convection zone, for tubes with initial field strengths B = 30, 60, and 100kG and fluxes Φ = 1021 and 1022 Mx.
View Image Figure 9:
From Caligari et al. (1995). Tilt angles at the apex of the emerging flux loops as a function of the emergence latitudes. The squares and the asterisks denote loops originating from initial toroidal tubes located at different depths with different local subadiabaticity (squares: δ ≡ ∇ − ∇ad = − 2.6 × 10− 6 and field strength ranges between 105 G and 1.5 × 105 G; asterisks: δ ≡ ∇ − ∇ = − 1.9 × 10− 7 ad and field strength ranges between 4 × 104G and 4 6 × 10 G). The shaded region indicates the range of the observed tilt angles of sunspot groups measured by Howard (1991b).
View Image Figure 10:
Tilt angles at the apex of the emerging loops versus emerging latitudes resulting from thin flux tube simulations of Fan and Fisher (1996). The numbers used as data points indicate the corresponding initial field strength values in units of 10 kG (’X’s represent 100 kG). Also plotted (solid line) is the least squares fit: tilt angle = 15.7∘ × sin(latitude ), obtained in Fisher et al. (1995) by fitting to the measured tilt angles of 24701 sunspot groups observed at Mt. Wilson, same data set studied in Howard (1991b).
View Image Figure 11:
Plots of the magnetic field strength as a function of depth along the emerging loops calculated from the thin flux tube model of Fan and Fisher (1996) showing the asymmetry in field strength between the leading leg (solid curve) and the following leg (dash-dotted curve) of each loop. Panels (a), (b), and (c) correspond to the cases with initial toroidal field strengths of 3 × 104 G, 6 × 104 G, and 105G respectively. The flux Φ = 1022Mx and the initial latitude θ = 5∘ are the same for the three cases shown.
View Image Figure 12:
From Caligari et al. (1995). A view from the north pole of the configuration of an emerging loop obtained from a thin flux tube simulation of a buoyantly unstable initial toroidal flux tube. The initial field strength is 1.2 × 105 G, and the initial latitude is 15∘. Note the strong asymmetry in the east-west inclination of the two sides of the emerging loop.
View Image Figure 13:
From Pevtsov et al. (2001). The figure shows the latitudinal profile of αbest (see Pevtsov et al., 1995, for the exact way of determining αbest) for (a) 203 active regions in cycle 22 (Longcope et al., 1998), and (b) 263 active regions in cycle 23. Error bars (when present) correspond to 1 standard deviation of the mean αbest from multiple magnetograms of the same active region. Points without error bars correspond to active regions represented by a single magnetogram. The solid line shows a least-squares best-fit linear function.
View Image Figure 14:
From Choudhuri (2003). This figure illustrates that in the northern hemisphere, when a toroidal flux tube (whose cross-section is the hashed area with a magnetic field going into the paper) rising into a region of poloidal magnetic field (in the clockwise direction) generated by the Babcock–Leighton type α-effect of earlier emerging flux tubes of the same type, the poloidal field gets wrapped around the cross-section of the toroidal tube and reconnects behind it, creating an emerging flux tube with left-handed twist. In this figure, the north-pole is to the left, equator to the right, and the dashed line indicating the solar surface. Note the α-effect for the Babcock–Leighton type solar dynamo model mentioned above is not to be confused with the α value measured in solar active region discussed in this section.
View Image Figure 15:
From Choudhuri et al. (2004). Simulated butterfly diagram of active region emergence based on a circulation-dominated mean-field dynamo model with Babcock–Leighton α-effect. The sign of the twist of the emerging active region flux tube is determined by considering poloidal flux accretion during its rise through the convection zone. Right handed twist (left handed twist) is indicated by plus signs (circles).
View Image Figure 16:
From Fan et al. (1998a). Upper panel: Evolution of a buoyant horizontal flux tube with purely longitudinal magnetic field. Lower panel: Buoyant rise of a twisted horizontal flux tube with twist that is just above the minimum value given by Equation (26View Equation). The color indicates the longitudinal field strength and the arrows describe the velocity field. (For a corresponding movie showing the evolution of the tube for the untwisted and the twisted cases refer to Figure 17.)
Watch/download Movie Figure 17: (mpg-Movie; 196 KB)
Movie The evolution of a flux tube. From Fan et al. (1998a) For a detailed description see Figure 16.
View Image Figure 18:
The rise of a buoyant Ω-loop with an initial field strength 5 B = 10 G in a rotating model solar convection zone at a local latitude of 15∘ (from Abbett et al. (2001)). The Ω-loop rises cohesively even though it is untwisted. The loop develops an asymmetric shape with the leading side (leading in the direction of rotation) having a shallower angle relative to the horizontal direction compared to the following side.
Watch/download Movie Figure 19: (mpg-Movie; 314 KB)
Movie The rise of a kink unstable magnetic flux tube through an adiabatically stratified model solar convection zone (result from a simulation in Fan et al. (1999) with an initial right-handed twist that is 4 times the critical level for the onset of the kink instability). In this case, the initial twist of the tube is significantly supercritical so that the e-folding growth time of the most unstable kink mode is smaller than the rise time scale. The flux tube is perturbed with multiple unstable modes. The flux tube becomes kinked and arches upward at the center where the kink concentrates, with a rotation of the tube orientation at the apex that exceeds ∘ 90.
View Image Figure 20:
A horizontal cross-section near the top of the upward arching kinked loop shown in the last panel of Figure 19. The contours denote the vertical magnetic field Bz with solid (dotted) contours representing positive (negative) B z. The arrows show the horizontal magnetic field. One finds a compact bipolar region with sheared transverse field at the polarity inversion line. The apparent polarity orientation (i.e. the direction of the line drawn from the peak of the positive pole to the peak of the negative pole) is rotated clockwise by about 145 ∘ from the +x direction (the east-west direction) of the initial horizontal flux tube.
View Image Figure 21:
The evolution of a uniformly buoyant magnetic flux tube in a stratified convective velocity field from the simulations of Fan et al. (2003). Top-left image: A snapshot of the vertical velocity of the 3D convective velocity field in a superadiabatically stratified fluid. The density ratio between the bottom and the top of the domain is 20. Top-right image: The velocity field (arrows) and the tube axial field strength (color image) in the vertical plane that contains the axis of the uniformly buoyant horizontal flux tube inserted into the convecting box. Lower panel: The evolution of the buoyant flux tube with B = Beq (left column) and with B = 10Beq (right column). The color indicates the absolute field strength of the flux tube scaled to the initial tube field strength at the axis. (For a corresponding movie see Figure 22.)
Watch/download Movie Figure 22: (mpg-Movie; 328 KB)
Movie The evolution of a uniformly buoyant magnetic flux tube. From Fan et al. (2003). For a detailed description see Figure 21.
View Image Figure 23:
Depth from the surface where the apex of an emerging flux loop with varying initial field strength rising from the bottom of the convection zone looses pressure confinement or “explodes” as a result of tube plasma establishing hydrostatic equilibrium along the tube. The explosion height is computed by considering an isentropic thin flux loop with hydrostatic equilibrium along the field lines (see Moreno-Insertis et al., 1995) in a model solar convection zone of Christensen-Dalsgaard (Christensen-Dalsgaard et al., 1993).
View Image Figure 24:
From Rempel and Schüssler (2001). Evolution of magnetic field strength (gray scale: darker gray denotes stronger field) and velocity field (arrows) during the flux loop explosion. The horizontal part of the field is amplified by a factor of 3.
View Image Figure 25:
Emerging magnetic field in the solar atmosphere resulting from the 3D simulation of the emergence of a left-hand-twisted magnetic flux tube by Magara (2004). The colors of the field lines represent the square value of the current density at their footpoints on a chromospheric plane located at z = 5. top left: Top view of the magnetic field lines. Note the inverse-S shape of the brighter field lines, which is consistent with the X-ray sigmoid morphology preferentially seen in the northern hemisphere. top right: The square of the current density (color image) and vertical magnetic flux (contours) at the chromospheric plane. bottom left: Side view of the magnetic field lines. bottom right: Another perspective view of the magnetic field.