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List of Figures

View Image Figure 1:
Observation of a small-scale emerging flux event within an active region. The left two panels show the G-band intensity and Stokes V signal from the photosphere. The right two panels show the chromospheric intensity in Hα and Ca ii H. Image reproduced with permission from Guglielmino et al. (2010), copyright by AAS.
View Image Figure 2:
Observations of an emerging flux region by SDO/HMI and SDO/AIA. Images from AIA show the response of the corona to the birth of an active region at the solar surface. Image reproduced with permission from Centeno (2012), copyright by AAS.
View Image Figure 3:
Hinode/SOT Ca ii H observation of NOAA AR 11158, which produced a series of M and X-class flares as it emerged into the solar atmosphere. This particular image shows the flare ribbons and post-flare loops after the X-class flare on Feb. 15, 2011 (Image credit: Joten Okamoto).
View Image Figure 4:
SDO/AIA observations of NOAA AR 11112 in UV and EUV channels. Tarr et al. (2014) estimate that, over the course of two days, the quantity of (steadily) reconnected flux between the emerging flux region and preexisting field is comparable to a large M- or a small X-class flare.
View Image Figure 5:
Models of magnetic flux emergence can be roughly divided into three categories, though there are large areas of overlap between them. So-called ‘realistic’ models attempt to include all the known important physical ingredients, while idealize models generally focus on studying a more limited set of effects. For case studies of certain observed emerging flux studies, data-driven models are used.
View Image Figure 6:
Synthetic Hinode/SOT Ca ii H image from the flux emergence simulation by Martínez-Sykora et al. (2009). The line-of-sight is taken to be parallel to the solar surface to mimic observations of such regions at the solar limb. Image reproduced with permission, copyright by AAS.
View Image Figure 7:
Figure from Spruit et al. (1987) illustrating the conjectured behavior of a buoyant flux tube as it approaches the photospheric base (indicated by the flat horizontal line) from below. The arrows indicate the direction of plasma motion. The severe change in aspect ratio of the tube’s cross-section is due to the diminishing pressure scale height at the top of the convection zone. This predicted behavior is a robust result in numerical MHD simulations of emerging flux. Image reproduced with permission, copyright by Springer.
View Image Figure 8:
Sequence of snapshots from a 2D MHD simulation of the buoyant of a twisted buoyant flux tube through a polytropic model of the convection zone. The left and right panels show the magnetic field strength and out-of-plane component of vorticity, respectively. The top of the convection zone in this model is at z = 0. Image reproduced with permission from Toriumi and Yokoyama (2011), copyright by AAS.
View Image Figure 9:
The top panel shows the photospheric distribution of the vertical component of the magnetic field resulting the simulated rise of a semi-toroidal flux tube from at depth of 7.5 Mm to the surface. The bottom panel shows a vertical cross-section (at y = 0) of the magnetic field strength in the photosphere and in the subsurface layers captured by the simulation. Due to the density and pressure drop over this height range, the emerged flux is dispersed and covers a much larger area that the subsurface roots of the torus. Image reproduced with permission from Cheung et al. (2010), copyright by AAS.
View Image Figure 10:
Two different scenarios considered for deriving the scaling relation between density and magnetic field strength in Section 3.2.1. Panel (a) illustrates the case where a horizontal flux tube rises uniformly and expands only in the directions perpendicular to the tube axis. Panel (b) shows a scenario where a localized segment of a flux tube rises and expands (‘magnetic bubble’ case). Due to the diminishing scale heights near the surface, it has a flattened structure (cf. Figures 7 and 8).
View Image Figure 11:
Horizontally-averaged logarithmic temperature gradients in a radiative hydrodynamic simulation of the near-surface layers of the convection zone and overlying photosphere. The solid line shows ∇ ad, the dotted line shows ∇, and the dashed line shows δ = ∇ − ∇ ad. The photosphere has δ < 0 and is convectively stable. Image reproduced with permission from Cheung et al. (2007b), copyright by ESO.
View Image Figure 12:
A typical example of a model stratification used for numerical simulations of flux emergence from the convection zone into the corona. In this figure the height scale z is expressed in units of 170 km. The solid line (labeled P0) indicates the height profile of gas pressure in the initial plane-parallel stratification in units of p0 = 1.4 × 105 dyn cm −2. The dashed line indicates the mass density profile in units of ϱ0 = 3 × 10− 7 g cm −3. The dash-dotted line indicates the temperature profile in units of T0 = 5600 K. The solid line labeled Pm indicates the magnetic pressure (in units of p0) associated with a vertical cut through the mid-plane of the initially horizontal tube. Image reproduced with permission from Archontis et al. (2004), copyright by AAS.
View Image Figure 13:
The solar atmosphere is strongly stratified: the mass contained in a single granule (left, Hinode SOT image of a sunspot surrounded by granulation) is comparable to the mass content of the largest CMEs (right, composite of running difference images from the SOHO/LASCO C2 and SDO/AIA instruments. Both quantities are of order 16 10 g. (Credit for right image: NASA CDAW Data Center.)
View Image Figure 14:
Schematic illustration of the different modes of the magnetic buoyancy instability of a horizontal flux sheet. Image reproduced with permission from Matsumoto et al. (1993), copyright by AAS.
View Image Figure 15:
Growth rates of different modes for the magnetic buoyancy instability of an isolated flux sheet. Here kx and ky are the wavenumbers parallel and perpendicular to the magnetic field. The case ky∕kx = 0 represents the pure undular mode while ky∕kx → ∞ represents the interchange mode. The left panel shows the growth rates for the case without magnetic shear (in the vertical direction) while the right panel shows the corresponding growth rates with magnetic shear. Image reproduced with permission from Nozawa (2005), copyright by PASJ.
View Image Figure 16:
The eigenfunction of the undular mode. Image reproduced with permission from Horiuchi et al. (1988), copyright by PASJ.
View Image Figure 17:
2D MHD simulation of undular mode instability of a flux sheet in the photosphere. Image reproduced with permission from Shibata et al. (1989b), copyright by AAS.
View Image Figure 18:
Magnetic field lines in the 3D MHD simulation of emerging flux. Image reproduced with permission from Matsumoto et al. (1993), copyright by AAS.
View Image Figure 19:
Surface of constant magnetic field strength from the result of 3D simulation of the rise of isolated flux tubes. Image reproduced with permission from Matsumoto et al. (1993), copyright by AAS.
View Image Figure 20:
Result of 3D simulation of the emergence of a twisted flux tube. Panels (a) and (b) show magnetic field lines at different times. In both panels, the red line indicates locus of the tube axis, which is seen to be trapped in the photosphere while the peripheral field lines are able to reach the corona. Image reproduced with permission from Fan (2001b), copyright by AAS.
View Image Figure 21:
2.5D simulation of the cross section of an emerging twisted flux tube by Magara (2001). In all panels the color coding indicates the density stratification and the arrows indicate the flow velocity in the plane of the simulation domain. The development of a magnetic buoyancy instability at the top of the tube (see panels d to f) leads to the dramatic expansion of the emerging flux into the coronal layers. Image reproduced with permission, copyright by AAS.
View Image Figure 22:
Isosurface of the magnitude of the magnetic field in the 3D simulation of the emergence of twisted and toloidal flux tube. The times are t = 0 (top left), 40 (top right), 60 (bottom left), and 80 (bottom right). Image reproduced with permission from Hood et al. (2012), copyright by Springer.
View Image Figure 23:
Traces of magnetic field lines in three separate numerical experiments of twisted flux tube emergence. Panels (a)–(c) show simulations with an initial twist parameters of q = 0.3, q = 0.2, and q = 0.1, respectively. The radius initial radius of the tube in these experiments is a = 2.5 (see Eqs. (40*) and (41*)). Image reproduced with permission from Murray et al. (2006), copyright by ESO.
View Image Figure 24:
From the parameter study of twisted flux tube emergence, a plot showing the height of the tube apex as functions of time and magnetic twist (q). With sufficiently weak twist (q = 0.05), the tube is trapped in the photosphere. For twist q = 0.1 and higher, the magnetic field is launched into the corona due to magnetic buoyancy instabilities. The time delay between arrival at photosphere and passage into the corona decreases with increasing twist. Image reproduced with permission from Toriumi et al. (2011), copyright by PASJ.
View Image Figure 25:
Magnetic Rayleigh–Taylor instability. The color shows mass density distribution in panels (a)–(c) and current density distribution in panel (d). Image reproduced with permission from Isobe et al. (2007a).
View Image Figure 26:
Vertical distribution of the buoyancy force (i.e., relative density perturbation) in a simulation of buoyant flux tubes interacting with ambient convective flows. Dark regions show antibuoyant downflows. The white horizontal structure in the top panel shows the initially horizontal flux tube. In a later snapshot (lower panel), two portions of the tube are seen to be pinned down by downflows. Image reproduced with permission from Fan et al. (2003), copyright by AAS.
View Image Figure 27:
Continuum intensity images (top, at 5000 Å) and (bottom) synthetic magnetograms of a simulated emerging flux region. The snapshot at t = 66 min shows the appearance of anomalously large granules and intergranular bright points in the emerging flux region. The magnetogram shows mixed polarity structures down to the granulation scale. Image reproduced with permission from Cheung et al. (2008), copyright by AAS.
View Image Figure 28:
3D visualization of the interaction of emerging horizontal magnetic field with granular convection (from Tortosa-Andreu and Moreno-Insertis, 2009). The grey scale maps show the distribution of vertical velocity at constant geometrical height in the photosphere. This sequence of magnetic field line visualizations shows how the convective flows undulate emerging field lines at the scale of granulation and leads to the formation of submerging U-loops aligned with downflows. Image reproduced with permission, copyright by ESO.
View Image Figure 29:
3D visualization of the creation of small-scale twisted magnetic flux tube at an intergranular lane immediately below the photosphere (from Tortosa-Andreu and Moreno-Insertis, 2009). Images with yellow color-coding show the distribution of vertical velocity at constant geometrical height in the photosphere. Image reproduced with permission, copyright by ESO.
View Image Figure 30:
Schematic illustration of serpentine field lines in an emerging flux region. In this picture, development of the undular (Parker) magnetic buoyancy instability leads to loops with a characteristic separation of a few Mm. Magnetic dips occur between adjacent opposite polarities and reconnection between field lines from the polarities lead to plasma heating, which show up as Ellerman bombs in Hα observations. Image reproduced with permission from Pariat et al. (2004), copyright by AAS.
View Image Figure 31:
Hinode Spectropolarimeter (SP) observations of an emerging flux in NOAA AR 10978. The upper and lower right panels show the continuum intensity and line-of-sight magnetic flux densities, respectively. The left panels show the Stokes V signal at ± 260 mÅ from the center of the Fe i 6302.5 Å line. The mixed polarity pattern in the simulated magnetograms of Figure 27 shows some resemblance the observed pattern. Image reproduced with permission from Lites (2009), copyright by Springer.
View Image Figure 32:
Field line rendering from a magnetoconvection simulation by Abbett (2007). The rendering shows collections of field lines that poke through the surface as granular-scale Ω-loops as well as some U-loops that are trapped by downflow lanes. Image reproduced with permission, copyright by AAS.
View Image Figure 33:
In the simulation of Isobe et al. (2008), the convectively-driven emergence of a granular-scale flux loop reconnects with ambient vertical field. Such reconnection events eject mass into the height atmosphere and provides an in-situ source of magneto-acoustic power (as opposed to waves propagating from photospheric base). The central and left panels show an example of such an event in a 3D magnetoconvection simulation. The right panel shows a 2D counterpart. Image reproduced with permission, copyright by AAS.
View Image Figure 34:
The passage of a magnetic loop from the photosphere to chromosphere as revealed by Hinode/SOT observations. Image reproduced with permission from Martínez González et al. (2010), copyright by AAS.
View Image Figure 35:
Vertical velocity patterns from a solar-like model of convection. Blue and green indicate upflows whereas yellow and red indicate downflows. The different panels show the velocity distribution at various depths of the model. The horizontal extent of the computation domain is 48 × 48 Mm2 and the bottom boundary is at 20 Mm below optical depth unity. Image reproduced with permission from Stein et al. (2011), copyright the authors.
View Image Figure 36:
Synthetic brightness images of a simulated emerging flux region. Overlaid are traces along horizontal magnetic field vectors at the surface. Image reproduced with permission from Stein and Nordlund (2012), copyright by AAS.
View Image Figure 37:
Schematic drawing illustrating the effect of granular flows on magnetic polarities from a serpentine field line. Image reproduced with permission from Cheung et al. (2010), copyright by AAS.
View Image Figure 38:
Evidence for twisted flux tube emergence. The top row shows three SoHO/MDI magnetograms of NOAA AR 10808. The positive and negative polarities have ‘magnetic tongue’ morphology. The bottom row shows three synthetic magnetograms from the simulation of the emergence of a twist flux tube. The striking resemblance in morphology suggests a twisted flux rope structure for NOAA AR 10808. Image reproduced with permission from Archontis and Hood (2010), copyright by ESO.
View Image Figure 39:
3D rendering of a simulation of a twisted magnetic flux rope undergoing the helical kink instability. While the helical instability is developing, the crests of the flux tube are emerging into the idealized (initially plane-parallel) model atmosphere. Image reproduced with permission from Matsumoto et al. (1998), copyright by AAS.
Watch/download Movie Figure 40: (gif-Movie; 736 KB)
Movie: Volumetric rendering of a rising flux tube experiencing the developing of the helical kink instability (Fan et al., 1998).
View Image Figure 41:
Distribution of the vertical component of vorticity (ωz) at the photospheric level at two different times in a numerical model of twisted flux tube emergence. In both panels, the two yellow patches are co-incident with the central portions of the twisted tube. Through they have opposite polarity, they have the same sign and amplitude of ωz. Image reproduced with permission from Fan (2009a), copyright by AAS.
View Image Figure 42:
Numerical simulation of the evolution of magnetic field from twisted flux rope emergence. Panels (a)–(f) show a vertical plane normal to the axis of the initial submerged tube. The direction of the magnetic field in the plane is depicted with solid white lines. Panels (a)–(c) show the velocity Ux (out of the plane), while panels (d)–(f) show color images of the shear angle measured in degrees. Panels (g)–(i) show 3D visualizations of magnetic field lines and the vertical field strength Bz at the photosphere. Panel (h) shows Ux at the photospheric level along with arrows indicating the flow velocity. Isosurfaces of Ux are shown colored in blue (–19 km s–1) and red (+19 km s–1). Image adapted from Manchester IV et al. (2004), courtesy of W. Manchester.
View Image Figure 43:
Time profiles of the magnetic energies and relative magnetic helicity as well as their fluxes as computed at the photospheric surface from a 3D numerical simulation of the emergence of a twisted flux tube. Image reproduced with permission from Magara and Longcope (2003), copyright by AAS.
View Image Figure 44:
Magnetic fields in the simulations of the emergence of toroidal flux tube from MacTaggart and Hood (2009b), with weaker field (left) and stronger field (right). The red line in each panel indicates the axial field line. The grey horizontal slice shows the distribution of vertical magnetic field in the photosphere. In the stronger field case (right), twisted field lines above the photospheric layer yield a flux rope-like structure. Images reproduced with permission, copyright by ESO.
View Image Figure 45:
Temporal evolution of current density (color) and magnetic field lines of 2D simulation of emerging flux with uniform (left) and anomalous (right) resistivity models. Image adapted from Yokoyama and Shibata (1994), courtesy of T. Yokoyama.
View Image Figure 46:
The left and right panels respectively show field line contours from 2.5D flux emergence simulations through the chromosphere excluding and including Cowling resistivity. Image reproduced with permission from Leake and Arber (2006), copyright by ESO.
View Image Figure 47:
A model of solar flares produced by magnetic reconnection between the emerging flux and the pre-existing field. Image reproduced with permission from Heyvaerts et al. (1977), copyright by AAS.
View Image Figure 48:
Time evolution of the magnetic field lines in the simulation by Archontis et al. (2004). The grey isosurfaces show the location of strong fields corresponding to the part of flux tube that remains below the photosphere. The red field lines are traced from the isosurfaces, while the other field lines are traced from the side boundaries. Image reproduced with permission, copyright by AAS.
View Image Figure 49:
Temporal evolution of temperature (color), velocity (arrows), and magnetic field lines of 2D simulation of emerging flux with pre-existing oblique fields. Image adapted from Yokoyama and Shibata (1996), courtesy of T. Yokoyama.
View Image Figure 50:
3D visualization of the MHD simulation of an emerging twisted flux tube and pre-existing oblique field by Moreno-Insertis et al. (2008). The orange, blue, and green lines indicate the field lines in the emerging flux, the pre-existing field, and the reconnected field, respectively. The red and blue isosurfaces are that of temperature (T = 6.5 MK) and J ∕B (blue), respectively. Image reproduced with permission, copyright by AAS.
View Image Figure 51:
Gas pressure (a–c) and magnetic pressure (d–f) and magnetic field lines in 2D MHD simulation of emerging flux and oscillatory reconnection. Image reproduced with permission from Murray et al. (2009), copyright by ESO.
View Image Figure 52:
2D simulation of hierarchical evolution of multiple emerging loops. Image reproduced with permission from Isobe et al. (2007b), copyright by AAS.
View Image Figure 53:
Left: Schematic illustration of jets associated with emerging flux observed in different scales. Image reproduced with permission from Shibata et al. (2007), copyright by AAAS. Right: example of observed jets in different scales. From top to bottom, an X-ray jet observed by the X-ray Telescope of Hinode, an EUV jets observed in Fe xii 195 Å filter by TRACE (Nishizuka et al., 2008), and a chromospheric jet observed by the Solar Optical Telescope of Hinode (Singh et al., 2012).
View Image Figure 54:
Left: 2D simulations of emerging flux with pre-existing horizontal coronal field including the anisotropic thermal conduction. Top and middle panels show density distribution (color), magnetic field lines, and velocity field. The color in the bottom panes shows temperature distribution. Two evaporation jets are seen in the both side of the emerging loop as dense ejecting structure with coronal temperature. Right: same simulation but without thermal conduction. Image reproduced with permission from Miyagoshi and Yokoyama (2003), copyright by AAS.
View Image Figure 55:
Schematic illustration of the acceleration mechanisms of chromospheric jets. Image reproduced with permission from Takasao et al. (2013), copyright by PASJ.
View Image Figure 56:
Schematic illustration of the trigger of flux rope eruption by reconnection-favorable emerging flux. Image reproduced with permission from Chen (2008), copyright by the Indian Academy of Sciences.
View Image Figure 57:
Three-dimensional visualization of the case of a successful eruption by Kusano et al. (2012). Each subset represent a birds eye view (a, c, e–h), top view (b), and enlarged side view (d) of the magnetic field at different times. Green tubes represent magnetic field lines with connectivity that differs from the initial state. Selected magnetic fields in the initial state and those retaining the initial connectivity are plotted by blue tubes in (a) and (d), respectively. Red isosurfaces correspond to intensive current layers, and ray scales (white, position) on the bottom plane indicate the distribution of the z component of magnetic field Bz. Image reproduced with permission, copyright by AAS.
View Image Figure 58:
Diagram showing the parameter study of Kusano et al. (2012) with various shear angles 𝜃0 and the emerging flux orientation ϕe. The orientations of the coronal and emerging fields for different 𝜃0 and ϕe are also shown. Image reproduced with permission, copyright by AAS.
View Image Figure 59:
Snapshots of the field lines of the 3D simulation by Fan and Gibson (2004) as viewed from the side (left panels) and the top (right panels). Image reproduced with permission, copyright by AAS.
View Image Figure 60:
Temporal profile of the height of the emerging (erupting) flux and its vertical velocity for different orientations of the ambient field. Φ = 0, 90, 180 corresponds to the ambient field parallel, perpendicular, and anti-parallel to the axis of the initial flux tube. Image reproduced with permission from Archontis and Hood (2012), copyright by ESO.
View Image Figure 61:
3D rendering illustrating the one-way coupled model of flux emergence by Abbett and Fisher (2003). MHD quantities from anelastic simulations of the rise of Ω-loops in the convection zone are used to drive the bottom boundary of a compressible MHD code. Image reproduced with permission, copyright by AAS.
View Image Figure 62:
This model of the formation of AR corona by Chen et al. (2014) is driven at the bottom boundary (z = 0) by a radiative MHD simulation of AR-scale flux emergence (Rempel and Cheung, 2014). The greyscale in panels (a) and (b) shows synthetic magnetograms at the photospheric layer. The yellow shading in all four panels shows EUV images of AR coronal loops synthesized for the 193 Å channel of SDO/AIA. Image reproduced with permission from Chen et al. (2014), copyright by ESO.
Watch/download Movie Figure 63: (mpeg-Movie; 8155 KB)
Movie: 3D rendering from a simulation of an eruption following emergence of a twisted flux tube into a pre-existing sunspot. This is an idealized scenario to mimic the evolution of NOAA AR 10930, which produced an X3.4 flare with an Earth-directed CME. Observations of AR 10930 showed the formation of a delta spot following emergence of a parasitic bipolar region. Reproduced with permission from Fan (2011), copyright by AAS.
Watch/download Movie Figure 64: (mov-Movie; 21784 KB)
Movie: Left: Distribution of normalized current density (j/B, green) and magnetic field orientation (arrows) at a vertical cut along the dashed line shown in the right panel. Right: Magnetogram sequence (remapped from SDO/HMI data) used for the data-driven simulation of NOAA AR 11158 by Cheung and DeRosa (2012). Image reproduced with permission, copyright by AAS.