Looking at a full disk magnetogram (a map showing spatially the line of sight flux density of the magnetic field) of the solar photosphere one sees that the most prominent large scale pattern of magnetic flux concentrations on the solar surface are the bipolar active regions (see Figure 1).When observed in white light (see Figure 2), an active region usually contains sunspots and is sometimes called a sunspot group. Active regions are so named because they are centers of various forms of solar activity (such as solar flares) and sites of X-ray emitting coronal loops (see Figure 3).
Besides their highly organized behavior during each solar cycle, active regions are found to possess some interesting asymmetries between their leading and following polarities. Observations show that the axis connecting the leading and the following polarities of each active region is nearly east-west oriented (or toroidal) but on average shows a small tilt relative to the east-west direction with the leading polarity of the region being slightly closer to the equator than the following (see Figure 1). This small mean tilt angle is found to increase approximately linearly with the latitude of the active region (Wang and Sheeley Jr, 1989, 1991; Howard, 1991a,b; Fisher et al., 1995). This observation of active region tilts is originally summarized in Hale et al. (1919) and is generally referred to as Joy’s law. Note that Joy’s law describes the statistical mean behavior of the active region tilts. The tilt angles of individual active regions also show a large scatter about the mean (Wang and Sheeley Jr, 1989, 1991; Howard, 1991a,b; Fisher et al., 1995). Another intriguing asymmetry is found in the morphology of the leading and the following polarities of an active region. The flux of the leading polarity tends to be concentrated in large well-formed sunspots, whereas the flux of the following polarity tends to be more dispersed and to have a fragmented appearance (see Bray and Loughhead, 1979). Observations also show that the magnetic inversion lines (the neutral lines separating the fluxes of the two opposite polarities) in bipolar active regions are statistically nearer to the main following polarity spot than to the main leading spot (van Driel-Gesztelyi and Petrovay, 1990; Petrovay et al., 1990). Furthermore for young growing active regions, there is an asymmetry in the east-west proper motions of the two polarities, with the leading polarity spots moving prograde more rapidly than the retrograde motion of the following polarity spots (see Chou and Wang, 1987; van Driel-Gesztelyi and Petrovay, 1990; Petrovay et al., 1990).
More recently, vector magnetic field observations of active regions on the photosphere have shown that active region magnetic fields have a small but statistically significant mean twist that is left-handed in the northern hemisphere and right-handed in the southern hemisphere (see Pevtsov et al., 1995, 2001). The twist is measured in terms of the quantity , the ratio of the vertical electric current over the vertical magnetic field averaged over an active region. The measured for individual solar active regions show considerable scatter, but there is clearly a statistically significant trend for negative (left-handed field line twist) in the northern hemisphere and positive (right-handed field line twist) in the southern hemisphere. In addition, soft X-ray observations of solar active regions sometimes show hot plasma of S or inverse-S shapes called “sigmoids” with the northern hemisphere preferentially showing inverse-S shapes and the southern hemisphere forward-S shapes (Rust and Kumar, 1996; Pevtsov et al., 2001, see Figure 4 for an example).This hemispheric preference of the sign of the active region field line twist and the direction of X-ray sigmoids do not change with the solar cycle (see Pevtsov et al., 2001).
The cyclic large scale magnetic field of the Sun with a period of 22 years is believed to be sustained by a dynamo mechanism. The Hale polarity law of solar active regions indicates the presence of a large scale subsurface toroidal magnetic field generated by the solar dynamo mechanism. In the past decade, the picture of how and where the large scale solar dynamo operates has undergone substantial revision due in part to new knowledge from helioseismology regarding the solar internal rotation profile (see Deluca and Gilman, 1991; Gilman, 2000). Evidence now points to the tachocline, the thin shear layer at the base of the solar convection zone, where solar rotation changes from the latitudinal differential rotation of the solar convective envelope to the nearly solid-body rotation of the radiative interior, as the site for the generation and amplification of the large scale toroidal magnetic field from a weak poloidal magnetic field (see Charbonneau and MacGregor, 1997; Dikpati and Charbonneau, 1999; Dikpati and Gilman, 2001). Furthermore, with its stable (weakly) subadiabatic stratification, the thin overshoot region in the upper part of the tachocline layer (Gilman, 2000) allows storage of strong toroidal magnetic fields against their magnetic buoyancy for time scales comparable to the solar cycle period (Parker, 1975, 1979; van Ballegooijen, 1982; Moreno-Insertis et al., 1992; Fan and Fisher, 1996; Moreno-Insertis et al., 2002; Rempel, 2003). Thus with toroidal magnetic fields being generated and stored in the tachocline layer at the base of the solar convection zone, these fields need to traverse the entire convection zone before they can emerge at the photosphere to form the observed solar active regions.
High resolution observations have shown that magnetic fields on the solar photosphere are in a fibril state, i.e. in the form of discrete flux tubes of high field strength ( in equipartition with the thermal pressure) having a hierarchy of cross-sectional sizes that range from sunspots of active regions down to below the limit of observational resolution (see Zwaan, 1987; Stenflo, 1989; Domínguez Cerdeña et al., 2003; Khomenko et al., 2003; Socas-Navarro and Sánchez Almeida, 2003). It is thus likely that the subsurface magnetic fields in the solar convection zone are also concentrated into discrete flux tubes. One mechanism that can concentrate magnetic flux in a turbulent conducting fluid, such as the solar convection zone, into high field strength flux tubes is the process known as “flux expulsion”, i.e. magnetic fields are expelled from the interior of convecting cells into the boundaries. This process has been studied by MHD simulations of the interaction between convection and magnetic fields (see Galloway and Weiss, 1981; Nordlund et al., 1992). In particular, the 3D simulations of magnetic fields in convecting flows by Nordlund et al. (1992) show the formation of strong discrete flux tubes in the vicinity of strong downdrafts. In addition, Parker (1984) put forth an interesting argument that supports the fibril form of magnetic fields in the solar convection zone. He points out that although the magnetic energy is increased by the compression from a continuum field into the fibril state, the total energy of the convection zone (thermal + gravitational + magnetic) is reduced by the fibril state of the magnetic field by avoiding the magnetic inhibition of convective overturning. Assuming an idealized polytropic atmosphere, he was able to derive the filling factor of the magnetic fields that corresponds to the minimum total energy state of the atmosphere. By applying an appropriate polytropic index for the solar convection zone, he computed the filling factor which yielded fibril magnetic fields of about , roughly in agreement with the observed fibril fields at the solar surface.
Since both observational evidence and theoretical arguments support the fibril picture of solar magnetic fields, the concept of isolated magnetic flux tubes surrounded by “field-free” plasmas has been developed and widely used in modeling magnetic fields in the solar convection zone (see Parker, 1979; Spruit, 1981; Vishniac, 1995a,b). The manner in which individual solar active regions emerge at the photosphere (see Zwaan, 1987) and the well-defined order of the active regions as described by the Hale polarity rule suggest that they correspond to coherent and discrete flux tubes rising through the solar convection zone and reaching the photosphere in a reasonably cohesive fashion, not severely distorted by convection. It is this process – the formation of buoyant flux tubes from the toroidal magnetic field stored in the overshoot region and their dynamic rise through the convection zone to form solar active regions – that is the central focus of this review.
The remainder of the review will be organized as follows.
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