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1 Introduction

The study of how magnetic flux emerges onto the Sun is motivated by a number of fundamental questions about solar magnetic activity. First of all, a complete picture of the solar dynamo requires not only an understanding of how magnetic fields are generated and amplified in the solar interior, it also requires an understanding of the transport processes that bring magnetic fields to the solar atmosphere. Observations of how active regions and smaller scale flux emergence events appear give telltale signs of the structure of magnetic fields below the surface. However, the interpretation of what the observed patterns of magnetic activity mean requires us to know how they got there in the first place. Are buoyant flux bundles that form active regions twisted, and what does that mean for the solar dynamo? How deep are sunspots anchored, and do their formation and decay influence the activity cycle?

In addition to its relation to the solar dynamo problem, the study of magnetic flux emergence helps us understand the basic physical mechanisms that are responsible for a myriad of dynamical atmospheric phenomena. For instance, emerging magnetic flux can help energize the solar atmosphere by building up free magnetic energy, or it lowers it by triggering eruptive events such as flares, coronal mass ejections (CMEs), and jets. The interaction of emerging flux with pre-existing magnetic field in the atmosphere can lead to the creation of current sheets, and magnetic reconnection in these regions can lead to impulsive releases of energy. The basic physical processes that control the rate of magnetic reconnection and the means by which magnetic energy is released into other forms of energy (kinetic, thermal, and radiative) are of interest for the larger astrophysical and plasma physics community.

Magnetic flux emergence is a vibrant and active area of research in solar physics driven forward partly by advances in observational capabilities of the solar atmosphere (and interior) and partly by the availability of supercomputers that facilitate large-scale numerical simulations. For the uninitiated, an attempt to digest the diverse range of studies (both theoretical and observational) in the flux emergence literature can be a daunting task. We hope to make this task easier. This review article aims to provide

  1. a primer on the physics that govern the behavior of emerging magnetic flux,
  2. an introduction of how magnetic flux emergence plays a key role in many aspects of solar physics, and
  3. a broad overview of both established and recent developments in this very active field of research.

The main scope of this review is to cover theoretical aspects of magnetic flux emergence. We hope that, upon exposure to the information contained in this article, the reader will be sufficiently familiar with the key physical concepts that they can become discerning readers of the flux emergence literature. Readers interested in observational studies of flux emergence will find relevant references. However, there are simply too many studies to be included in a review of this limited scope (which is focused on theory).

1.1 Structure of this review article

The article is structured as follows. Section 1.2 expands on the introduction and discusses how flux emergence fits in with a broad range of problems in solar physics.

Section 2 provides a brief discussion of magnetohydrodynamics (MHD), which is the most useful theoretical framework for studying magnetic flux emergence. Section 2.1 introduces the basic MHD equations capturing conservation principles and Faraday’s law of electromagnetic induction. Section 2.2 discusses how constitutive relations describing the material properties of the plasma are used to supplement the MHD equations. The science questions that are being addressed and the choice of constitutive relations largely determines the differences between different models.

Section 3 details how certain physical mechanisms and processes play key roles in the progression of magnetic flux emergence.

Section 4 discusses the relation between flux emergence and eruptive events such as jets and CMEs.

Section 5 discusses how data-driven models are starting to be used in the study of flux emergence.

Finally, Section 6 will give some thoughts on open questions.

1.2 Science questions and challenges in flux emergence

Emerging flux plays a key role in many aspects of solar magnetic activity. The role of theories and numerical modeling of emerging flux is to clarify the various physical processes involved in flux emergence and therefore contribute to a better understanding of the solar magnetic activity and ultimately improve our ability to forecast hazardous space weather events.

Specific science questions in the modeling of emerging flux include:

  • What is the mechanism that brings the magnetic flux from the interior to the atmosphere?
  • How does emerging flux transport the magnetic energy and helicity?
  • How much flux is trapped below the surface during flux emergence, and what is the contribution of this trapped flux to the solar dynamo?
  • What are the roles of emerging flux in the free energy accumulation and triggering of the transient events such as jets, flares, CMEs?
  • What are the physical properties of subsurface magnetic structures that rise and eventually emerge onto the surface?
  • Does flux emergence occur as the rise of coherent bundles or as smaller elementary units? (Zwaan, 1978*, 1985*)?
  • What is the difference between flare-productive sunspots and quiet sunspots?
  • How do convective flows impact the morphology and physical character of emerging flux (e.g., Fan et al., 2003*; Cheung et al., 2007a*)?
  • Is magnetic twist necessary for magnetic flux to emerge (e.g., Moreno-Insertis and Emonet, 1996*; Murray et al., 2006*)?
  • How do the individual and statistical properties (e.g., Hagenaar, 2001; Hagenaar et al., 2003; Iida et al., 2012; Otsuji et al., 2011*) of emerging flux relate to the solar activity cycle?
  • What are the observational consequences of emerging magnetic flux (Bruzek, 1967*; Zwaan, 1978*), and what are the physical mechanisms responsible?
  • Can we predict the appearance of new emerging flux region?
  • What are the physical ingredients necessary for a realistic model of emerging flux?
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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.
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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.
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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).

Figures 1*3* show a selection of observations of emerging flux regions covering the photosphere to corona. They illustrate the range in temperature, density, and plasma-β (ratio of gas to magnetic pressures) found in emerging flux regions. By definition, flux emergence consists of magnetic field reaching the atmospheric layers from the solar interior. Models that describe this evolution need to take into accounts physical effects that are important for the convection zone, the photosphere, the chromosphere, transition region, and eventually the corona. Different models attempt to include the relevant effects to varying degrees of comprehensiveness. The choice depends on the science question, but all models face the challenge of capturing the wide range of length and time scales relevant for flux emergence. Whereas active regions are born over the course of days and may spawn eruptions throughout their lifetimes (e.g., see Figure 3*), Alfvénic crossing times over active region loops can be of the order of minutes or less. While G-band bright points can be just a few tens of km across in diameter (see Figure 1*), sunspots can have diameters exceeding 10 Mm. The abrupt changes in physical regimes also pose challenges. For instance, whereas radiative cooling can be approximated by optically thin losses in the corona, the full radiative transfer equations need to be solved for the photosphere and chromosphere (in order to have thermodynamic structures that comparable to observations). The plasma-β is greater than unity in the convection zone, but tiny in the corona (where the magnetic field is dominant).

Whether during solar maximum or minimum, the Sun’s surface is pervaded by magnetic fields at all scales. High-sensitivity measurements of the photospheric magnetic field show this is true even in so-called ‘quiet-Sun’ regions (Lites et al., 1996*; Domínguez Cerdeña et al., 2003; Harvey et al., 2007; Orozco Suárez et al., 2007; Lites et al., 2008; Pietarila Graham et al., 2009; Danilovic et al., 2010b,a). Turbulent motions of the plasma from scales beyond supergranulation (L ∼ 30 Mm) down to scales below granulation (L ∼ 1 Mm) weave the magnetic field into complex configurations that lead to the formation of current sheets that facilitate magnetic reconnection. When Parker (1988*) put forth his nanoflare model of coronal heating based on the dissipation of current sheets in the corona, he considered continuous horizontal photospheric motions of line-tied magnetic fields as the source of energy build-up in the corona. This by itself is considered sufficient for the production of current sheets, which then dissipate via magnetic reconnection. When emerging flux is introduced into this picture (even if the problem of interest is not coronal heating), one can expect magnetic reconnection to be even more pervasive. This is due to the fact that magnetic fields emerging through the convection zone (a low plasma-β environment) are not constrained to emerge into the atmosphere with an orientation that is aligned with pre-existing field (e.g., see Figure 4*). As demonstrated in several models of flux emergence (see Section 4), this misalignment will create current sheets that are amenable to reconnection. So studies of flux emergence are also relevant for magnetic reconnection research, and the fact that reconnection can occur in different plasma regimes in the solar atmosphere (see Section 3.7.1) means flux emergence events are natural experiments for magnetic reconnection. One of the challenges of flux emergence research is to create models with reconnection behavior that is justified by the underlying microphysics and matches observed behavior at large (observable) scales.

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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. Image courtesy of L. A. Tarr.


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