Heliophysics White Paper

Coronal Magnetic Fields

Stephen White, Carl Henney (AFRL Space Vehicles Directorate) Tim Bastian (NRAO) Marc DeRosa (LMSAL) Dale Gary (NJIT) Phil Judge, Scott McIntosh (HAO) Haosheng Lin (IfA, University of Hawaii)

Summary. After a long period in which we have recognized the overriding importance of coronal magnetic fields for many phenomena in the atmosphere of the Sun but have been powerless to make suitable detailed measurements, recent developments are now making it possible to address this topic in a more programmatic fashion. This paper outlines the difficulties we face in making advances in this field, and describes the directions in and means by which we can expect to make progress in the period to be addressed by the Heliophysics decade report. A combination of algorithmic development in extrapolation techniques, improved observations of vector magnetic fields in the chromosphere and corona, radio measurements of absolute magnetic field strengths in the corona, and continued EUV and X–ray observations of field line topology are needed together for further progress. Introduction

It is universally recognized that magnetic fields in general, and coronal magnetic fields in particular, are of crucial importance in understanding the major phenomena currently at the forefront of solar physics research. Magnetic fields

• are the only plausible source for the energy released during solar flares;

• are almost certainly a key component in the heating of the solar chromosphere and corona, a process that we still do not understand and that has broad implications in the rest of astro- physics;

• probably control the acceleration mechanism that results in the nonthermal energetic electrons that produce solar hard X–rays, as well as the energetic protons that can affect space assets;

• and are clearly involved in the eruption of coronal mass ejections.

The interaction between magnetic fields and the dynamic plasma in the solar atmosphere is complex and multi–faceted. The mechanism for conversion of the free (i.e., non–potential) magnetic energy to other forms has not been identified and remains a topic of intense study. Magnetic fields alone cannot do work on a particle since they only exert forces orthogonal to particle motion, so electric fields (which can be produced by changing magnetic fields) must also be involved. Classic ohmic resistivity is much too slow to explain the dissipation of energy in flares. Reconnection of magnetic fields is the main contender for energy conversion in the corona: oppositely–directed fields can be driven towards each other, reconnect and release energy in the form of heating, plasma flows out of the reconnection region, and turbulence. Dissipation of currents that are an intrinsic part of the non–potential fields can also release magnetic energy in the form of heat. All conversion mechanisms share a common property: due to the low resistivity of the corona, the spatial scale in which energy conversion takes place must be small for non–ideal–MHD behavior to permit energy conversion. In the solar corona this scale is of order tens of meters, much too small for the spatial resolution of current instruments. Once magnetic energy has been converted to particle energy, other mechanisms can take over to produce the nonthermal energy distributions that we measure via X–ray, γ–ray and radio observations. In the solar paradigm, these nonthermal particles transport energy from the corona to the chromosphere where it heats plasma to soft X–ray temperatures. The resulting hot plasma is responsible for the X–ray flares that we observe on the Sun with the GOES satellites, and presumably those on active stars that we observe with satellites such as Chandra and XMM. Detailed understanding of the role of the coronal magnetic field in these physical processes requires better observations than we presently have. The magnetic field distribution at the solar surface has been well studied, since we have long been able to measure line–of–sight magnetic field components at the photosphere using circular polarization induced in spectral lines by the Zeeman effect. We are now even able to sense the presence of magnetic fields below the photosphere using helioseismic techniques (e.g., Gonzalez´ Hernandez´ et al., 2007; Komm et al., 2009), and incorporate flow patterns in studying the evolution and emergence of magnetic flux at the surface (e.g., Wang et al., 2009; Arge et al., 2010). However, we are only too well aware that the surface line–of–sight magnetic fields measured by conventional magnetographs are not sufficient to tell us what is happening in the Sun’s atmosphere above the surface where, e.g., energy release by conversion of free magnetic energy into particle energy must be taking place since particle acceleration to nonthermal energies cannot happen in the collision–dominated photosphere. To make further progress a quantitative understanding of coronal and chromospheric magnetic fields, and the ways in which the atmospheric fields are coupled to the dynamic and turbulent motions below the surface, is needed. However, it is crucial to recognize the fundamental difference between studying the two–dimensional magnetic field at the (relatively) well–defined photospheric surface, and the intrinsically three–dimensional field of the corona. The amount of information needed to describe a three–dimensional field is obviously much greater, and the complications imposed by having to take into account line–of–sight depths (i.e., the fact that material at any point along a given line of sight can contribute to an optically thin diagnostic, which is not an issue for photospheric measurements) pose a major headache in deconvolving raw data into magnetic field models. This simple consideration makes it clear that we cannot expect a quick resolution of this issue and need to be realistic in the problems that we tackle in the near term. In this paper we describe the current state of studies of coronal magnetic fields, starting with the topic of extrapolation of surface field measurements that has been the primary source of coronal magnetic field models for research purposes, and then go on to describe examples of new instru- mentation that will contribute important results to this field and can be constructed over the next decade.

Extrapolations of Photospheric Magnetic Field Measurements

Extrapolation of photospheric magnetic fields into the corona can be carried out as a boundary value problem, but in order to do more than a potential–field extrapolation (which has no free energy avail- able for conversion, and therefore is not very useful for any of the physical problems listed earlier) we require, at least, a complete measurement of the vector magnetic field B. Recognition of the im- portance of coronal magnetic fields has led to major investments in two directions: (i) instruments capable of measuring the full vector magnetic field at the photosphere, and (ii) efforts to develop algorithms for solving the magnetic boundary–value problem in the solar atmosphere under the con- straint of nonlinear force–free (J B) conditions applicable to the quasi–static (i.e., slowly varying) corona. Determination of the full magnetic vector at the photosphere requires spectropolarimetric measurements and sophisticated modelling of the lower atmosphere, including motions, and is in it- self a difficult problem even with suitable data. Once we have suitable magnetic data, the system of Maxwell’s equations plus a boundary measurement set then constitutes a mixed elliptic-hyperbolic boundary value problem that has proven remarkably difficult to solve (Gary, 1989; McClymont & Mikic,´ 1994; Amari et al., 1999). There has been a concerted effort to develop robust nonlinear force–free–field extrapolation techniques, summarized initially by Schrijver et al. (2006) and more recently by Schrijver et al. (2008) and DeRosa et al. (2009). One of the problems with these extrap- olations is that the photospheric magnetograms are not force–free and further the results are very sensitive to errors in the input magnetograms, and to imbalance in positive and negative flux. This has led to the need to “precondition” the magnetograms, i.e., to alter them in order to force them to match the conditions required for successful extrapolations (for a description of this process see Wiegelmann et al., 2006; DeRosa et al., 2009). Thus in parallel with the extrapolation efforts, a series of workshops is underway to compare vector magnetograms from different instruments and to reconcile differences between the measurements. In the long run global extrapolations are desirable, but these are not really feasible unless we are able to measure the vector magnetic field over the entire photosphere, not just the hemisphere visible from Earth, and there is no prospect for this in the next decade. A major issue for extrapolations is that the magnetic field in the photosphere and lower chro- mosphere carries less energy than the plasma and therefore is not force–free: the plasma can sustain forces and currents orthogonal to the magnetic field. This complication leads to the desire to use measurements of the vector field in the force–free upper chromosphere instead: this topic is ad- dressed in more detail in a White Paper by Judge (2010). As Judge’s discussion stresses, the surface in which any particular magnetically–sensitive line will form varies in time and space, and in partic- ular the height will be different along different lines of sight. The practical use of the chromospheric magnetograms as boundary conditions for extrapolations is currently being explored. One advan- tage of the chromospheric measurements is that Chandrasekhar’s virial theorem can in principle be applied, with no need for ill-posed extrapolations, to derive the total free magnetic energy in the overlying coronal volume. Yet another major problem for developing reliable extrapolation algorithms is the lack of suit- able measurements to compare with. Idealized models with exact solutions provide a test, but they cannot incorporate all the complications of the real solar atmosphere (Barnes et al., 2006). A stan- dard approach is to compare field lines derived from extrapolations with field lines observed in EUV and/or X–ray observations of the corona. However, the mathematical rigor of this test appears never to have been established: the field lines visible in EUV images are a measure–zero subset of all the field lines in the volume (those that happen to carry excess density). Given the limited spatial resolu- tion of the observations and the uncertainty in exact footpoint locations of field lines, the modeller is free to choose extrapolated field lines in the vicinity that best match those observed. Unfortunately, in the absence of better data, this is the only observational test that is routinely available. Never- theless, more stringent and bias-free tests of extrapolations using actual measurements of magnetic fields in the corona have been demonstrated, for example, by dedicated programs using Very Large Array radio measurements of coronal magnetic field strengths at the base of the corona (e.g., Lee et al., 1998a) and using IR spectropolarimetric measurements of near-IR coronal emission line (e.g., Liu & Lin, 2008). With the establishment of the suite of facilities that we advocate in this paper these observations will become routinely available for vigorous observational tests of competing coronal magnetic field extrapolation tools and models. Another approach to testing of extrapolations that avoids the issues of field–line selection is to generate synthetic images in EUV or X–ray bands, for comparison with observations, based on self– consistent determination of extrapolated coronal fields and emission measure distributions using a heating model, as in the calculations of Mok et al. (2005). However, robust coronal heating models have yet to be identified and this makes comparisons more a test of the heating mechanism than of the magnetic field model, but this approach may prove valuable in the future.

Resources

As noted earlier, the challenge of characterizing the magnetic field in the chromosphere and corona is being addressed by a combination of observational advances and improved numerical techniques. Observations of photospheric fields are not very useful for further progress unless they measure the full three–dimensional vector field, and even then they suffer from not being force–free. The position endorsed by this paper is that a combination of a number of techniques is required in order to measure properties of magnetic fields in the corona that will help to address the questions raised in the Introduction. Results from the following methods are needed:

• Extrapolations of surface measurements are discussed in detail above. Chromospheric mag- netic fields measured in a force–free region of the atmosphere are preferred over the non– force–free photospheric fields as the boundary condition. Testing and validating the extrapo- lation algorithms requires the actual measurements described in the following items as con- straints.

• Polarization measurements of optically-thin magnetically-sensitive coronal lines such as for- bidden Fe XIII near 10750 A.˚ Such lines cannot be observed polarimetrically in the presence of the bright continuum from the solar disk and therefore magnetic field measurements are limited to regions above the solar limb in projection, with the attendant line–of–sight issues. Nevertheless, the full polarization state can be measured and a two-dimensional image of the vector field in the corona in the plane of the sky containing sun center can be approximated from the data. The power of these measurements is demonstrated by the direct detection of Alfvenic´ waves in the corona (Tomczyk et al., 2007).

• Radio measurements are currently the only means by which magnetic field strengths in the corona can be measured against the solar disk. For this reason they have a unique role to play in constraining extrapolations, which invariably use disk regions where we can measure the surface fields, in addition to the science derived from coronal field strength measurements. An example of such science is searching for changes in coronal field strength produced by flares: changes associated with flares are seen in photospheric magnetic patterns, but the coronal changes should be more dramatic, if only because of the motion of field lines seen in eruptive events. Magnetograms of the absolute field strength at the base of the corona above active re- gions, in the range 200–2000 G, are straightforwardly obtained using the radio gyroresonance technique (White & Kundu, 1997). The gyroresonance data also contain information on the three–dimensional field but significant algorithm development is required to exploit this fully: the radio data at each frequency sample a narrow optically-thick constant-field-strength layer, but the height of each layer is not independently measured. Magnetic field measurements at lower field strengths (< 200 G) can also be made using the polarization of bremsstrahlung (Gelfreikh, 2004) and mode coupling observations of polarization reversals (Lee et al., 1998b).

• EUV and soft X–ray images are now available at very high spatial resolution and show those magnetic field lines that carry significant density, but due to the density–squared dependence of the emissivity at these wavelengths, which enhances contrast in density, we cannot “see” the bulk of the field lines since they do not carry sufficient density.

These four techniques complement each other. We argue that all four are needed simultaneously if we are to make significant progress in understanding coronal magnetic fields. Finding: spectropolarimetric measurements of optically thin coronal and chromospheric lines, broadband radio measurements of optically thick isogauss layers, and field–line images are all needed in combination to constrain and lead to improved extrapolation techniques. Existing and near–term facilities Measurements of the vector magnetic field are now being carried out by numerous instruments, including the following:

• Ground–based telescopes that can make routine photospheric and chromospheric vector mag- netogram observations with arcsecond resolution include the Facility Infrared Spectropo- larimeter (FIRS) and the Spectro-Polarimeter for Infrared and Optical Regions (SPINOR) at Sacramento Peak, the Imaging Vector Magnetograph at Mees Solar Observatory, the MSFC Magnetograph now at the University of Alabama/Huntsville, and the Vector SpectroMagne- tograph of the SOLIS project, together with other facilities overseas. An increasing number of instruments are able to measure the vector magnetic field on the solar disk in the preferred chromospheric lines (Judge, 2010; McIntosh et al., 2010).

• The Solar Optical Telescope on the Japan–U.S. satellite Hinode carries a Stokes Polarimeter that can make vector magnetograms over a field of 300′′ with a pixel size of 0.16′′ (110 km at the Sun) every 90 minutes.

• The Helioseismic and Magnetic Imager on the Solar Dynamics Observatory takes data full– disk vector magnetograms at high cadence with 1′′ resolution. However, as with all spec- tropolarimetric data, conversion of these observations to vector magnetograms is not a simple procedure and is still being developed for HMI.

• The HAO Coronal Multi-channel Polarimeter (CoMP), now deployed at Mauna Loa, com- bines a polarimeter and tunable filter to measure the complete polarization state of the Fe XIII and He I lines near 10800 A˚ in the solar atmosphere above the limb. CoMP has demonstrated the presence of Alfvenic´ waves in the corona (Tomczyk et al., 2007).

• The University of Hawaii SOLARC instrument is an 0.5m off–axis coronagraph equipped with a fiber-optic imaging spectropolarimeter located at Haleakala. SOLARC produced the first “Coronal Vector Magnetogram” from spectropolarimetric observations of the Fe XIII line (Lin et al., 2004).

• The 1m Sunrise telescope (operated by a large international consortium led by the Max Planck Institute for Solar System Research) carries a spectropolarimeter that can achieve very high spatial resolution measurements of the vector magnetic field during balloon flights.

Future facilities needed Proposed facilities that will be important for advancing this field include:

• The Advanced Technology Solar Telescope (ATST) has now been approved for funding in the NSF Major Research Equipment and Facilities Construction line. It is a 4–meter optical/IR telescope optimized for low-scattering coronagraph observations with resolution of order 0.2′′ and field–of–view 300′′, and will be able to acquire high–resolution vector magnetograph observations above the limb in coronal lines. • The COronal Solar Magnetism Observatory (COSMO) facility consists of a 1.5 m aperture coronagraph and a 20 cm aperture telescope to take regular synoptic spectropolarimetric mea- surements in chromospheric lines (He I, Hα) on the disk and coronal lines (Fe XIII 1074.7A˚ and 1079.8A,˚ He I 1083.0A)˚ above the limb with a cadence of order 10 minutes. COSMO will observe a one–degree field of view with a resolution of 5 arcseconds and a sensitivity of a few Gauss. In order to minimize scattered light from the solar disk, the COSMO coronagraph will use a fused–silica lens rather than a mirror. COSMO’s wide–field synoptic measurements of chromospheric and coronal magnetic fields will complement user-designed observations with the narrower but higher-resolution field of ATST. More details are given in the White Paper by Tomczyk et al. (2010).

• The Frequency Agile Solar Radiotelescope (FASR) will exploit radio techniques to measure magnetic field strengths in the corona above active regions. FASR will be a full–disk solar– dedicated instrument with spatial resolution scaling with frequency, and hence measured mag- netic field strength, continuously from 1′′ at 2000 G to 10′′ at 200 G. Routine measurement of coronal magnetic fields is a prime scientific goal of FASR, which is described in more detail in a White Paper by Gary et al. (2010). The solar radio array at Owens Valley operated by NJIT is currently undergoing an expansion that will prototype some technical aspects of FASR.

• The Expanded Very Large Array (EVLA) is currently being instrumented and, when complete, will be a valuable tool combining a wide frequency range (equivalent to sensitivity to a wide range of magnetic field strengths) with excellent spatial resolution and sensitivity. However, it is not solar–dedicated and suitable coronal magnetic field measurements are only likely to be obtained on a few days per year, at most.

Finding: These facilities in combination with the ongoing algorithm development and vector mag- netogram reconciliation efforts described earlier will provide a wealth of detail on coronal magnetic fields and permit us to move forward in understanding the detailed role of magnetic fields in atmo- spheric phenomena.

The importance of coronal magnetic fields in solar phenomena that have relevance well beyond the Sun itself, in addition to their impact on the Earth, demands that research in this field should continue to be a high priority over the next decade. References

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