Measuring magnetic free energy in the solar atmosphere

Transcription

1 Measuring magnetic free energy in the solar atmosphere Philip G Judge, High Altitude Observatory, National Center for Atmospheric Research. judge@ucar.edu Abstract: The purpose of this white paper is to draw attention to techniques that have become available which hold promise for the measurement of the free energy in the Sun's corona. These techniques avoid problems associated with extrapolations of photospheric vector magnetic fields by making measurements directly at the coronal base. If this problem were easy, it would have been done decades ago. Nevertheless, the time appears right to pursue new spectropolarimetric capabilities offered by Fabry-Perot instruments operating at near infrared wavelengths, at existing telescopes as well as the upcoming ATST. Success is not guaranteed, but the relatively low risks might be worth the modest investment which would enhance the value of missions such as SDO and also place the problem of the origins of space weather on a firm observational basis. The problem The interplanetary and terrestrial environments are governed by the variable solar wind, solar energetic particles and UV/X-ray radiation, coronal mass ejections and flares. All of these phenomena are caused by the release of free energy contained in solar magnetic fields. It is accepted that the interplanetary and terrestrial perturbations originate from magnetic energy stored largely in the corona. This is because it is hard to store significant amounts of energy below the corona, and because the release of energy in the denser solar atmosphere is too slow to account for flares and other dynamic events. Thus in the 1960s it was recognized already that flare energy release required storage and release in the coronal plasma (see the papers in The Physics of Solar Flares, NASA-SP50, 1964). In 1973, coronagraphs on the Skylab mission allowed scientists to identify for the first time coronal mass ejections as major perturbers of the heliosphere. Later spacecraft such as OSO-8, SMM, Yohkoh, SOHO, RHESSI, STEREO, Hinode and now SDO have all carried instruments to study the dynamic release of magnetic energy by the Sun as it evolves through its magnetic activity cycle. These experiments have provided the observational basis for the huge community efforts to try to understand the magnetic energy storage and release. It is well-known that information on the free component of the magnetic energy associated with electrical currents flowing through the corona and cooler atmospheric components - can only be measured by the vector magnetic field, not just the line of sight component that has been measured since the pioneering work of Hale. However, it was not until the 1980s that the first credible measurements of the vector field were obtained, even in magnetic elements in the very bright solar photosphere where the fields are strong (> 1 kg). This is because the transverse components of the magnetic field make themselves known spectrally only as a second order term in the (usually small) Zeeman parameter (=Zeeman splitting/doppler width), whereas the line of sight component is a first order term. The transverse fields make their presence known through the linearly polarized components ( Q and U ) in spectral lines, the line of sight fields are reflected in the circularly polarized ( V ) components of the Stokes vector (IQUV, I=intensity). In principle, measurements of the magnetic field in the photosphere can be extrapolated outwards into

2 the corona, and these extrapolations should be able to yield the free energy and its evolution and release in the corona. Indeed, one of the goals of the HMI instrument on SDO is to provide global photospheric magnetic field vectors every few seconds for the lifetime of the mission. However, there are fundamental difficulties in using photospheric measurements for studying magnetic free energy. Most notably, the photospheric magnetic field is not close to a force free state, meaning that the magnetic field there is forced by the dynamics of the turbulent convection. Thus, to obtain meaningful extrapolations, a full magneto-hydrodynamic calculation is in principle required. Such calculations are possible, but the physics of the intervening layers between the photosphere and corona, namely the chromosphere and transition region, is poorly understood and can significantly effect the extrapolations. A recent example of a difficulty is evident in the very different states of the magnetic field found by Arber and colleagues (2007) when they simulated magnetic flux emergence through the chromosphere using different assumptions of the microphysics of ion-neutral collisions in the chromosphere. These and other difficulties have led researchers to adopt a simpler approach, in which observations and models are combined judiciously to try to make photospheric data consistent with a simpler (though still challenging) non-linear force-free calculation. A notable example is the wellknown nonlinear force free field project (NLFFF, Schrijver et al. 2008; Wiegelman et al. 2008). Unfortunately this approach has essentially failed despite the attempts of several groups to produce credible, reproducible results (de Rosa et al., 2009). A fundamental problem with the approach is that the measured boundary conditions at the photosphere must be altered to be consistent with the calculations themselves. This is, alas, tantamount to changing the data to match the physical conditions assumed in the model. Measuring magnetic fields at the coronal base To circumvent difficulties with using photospheric measurements, the obvious solution is to make measurements at the top of the chromosphere- the base of the corona. Here, the plasma is both close to a force-free state and yet dense enough to contribute to spectral features sensitive to the magnetic fields there. The problem is that these are not easy measurements to make or interpret. Spectral features formed in these layers are limited to vacuum UV, radio, and isolated spectral lines in the visible and IR regions. Significant progress has been made at radio wavelengths, but the heights of formation ( t=1 ) surfaces are not easily determined, the angular resolution is limited by the long wavelengths, and there are physical limitations imposed by Bremmstrahlung opacity, for example. Vacuum UV measurements are insensitive to the Zeeman effect (small Zeeman parameter). The Hanle effect has been proposed for both UV and visible chromospheric lines, a technique which should be pursued but which is not yet a proven method for chromospheric work. More direct constraints on the free energy in the solar atmosphere are however beginning to be made using chromospheric observations (e.g. Socas Navarro 2005, Solanki et al 2003, Judge et al 2009). Here I suggest that the community consider building instruments devoted to imaging spectropolarimetry of infrared lines which already have a demonstrated capability based upon slit spectropolarimetry. Imaging capability is critical to provide information on plasma velocity vectors, as discussed below. Such instruments may yield the needed measurements to measure the free energy in the corona, because: 1. In and around active regions, where the effects of magnetic free energy release are most obvious, the magnetic fields are strong enough to control the upper chromosphere's morphology and dynamics. The field there is thus in a low-b state (close to force-free), and the plasma dynamics is essentially a passive tracer of the magnetic field. 2. Such magnetic fields are not only compatible with force-free extrapolations, but also one can

3 apply Chandrasekhar's virial theorem to derive the free energy in the overlying coronal volume from measurements only at the chromospheric surface, subject to some reasonable assumptions discussed below. But difficulties naturally arise. The prospect of inferring magnetic fields in the presence of obviously complex thermal structure and dynamics in the chromosphere (e.g. Judge 2010) is indeed daunting, and it is generally believed that vector polarimetry in the chromosphere must be difficult in the extreme. These perceived difficulties have led, in part, to the situation we are in today, in which we are reduced essentially to looking at the effects of the free energy release through instruments on the historic fleet of spacecraft launched by NASA and in ground-based observatories. Thus in spite of these efforts, we are not really getting to the root of the problem. However the time appears right for a concerted effort to measure chromospheric magnetic fields, because of recent advances. Firstly, imaging spectropolarimeters based upon Fabry-Perot interferometers ( FPIs ), e.g. IBIS (Cavallini, 2006), TESOS (Tritschler et al. 2002), CRISP (Scharmer et al. 2008), and GFPI (Bello Gonzalez & Kneer 2008), have the demonstrated capability to perform the chromospheric measurements of close to the required sensitivity. Secondly, tools are now available for the reliable interpretation of a valuable line of neutral helium at 1083 nm. A way forward By good fortune, the He I 1083 nm multiplet (actually a triplet) forms in the uppermost chromospheric features (be they spicules, canopy-like fibrils, or the uppermost scale height of the stratified chromosphere). This is because the lines belong to the excited triplet system of helium. Populating this system requires photons or particles of relatively high energy, hence the triplet states are excited in a narrow region between the source of high energy photons and/or particles (the corona) and the denser layers of the chromosphere. While the formation of the intensity I of the multiplet is not fully known, for magnetic field measurements using the Stokes IQUV vectors, it need only be recognized that the line picks out certain magnetic field lines in a hydromagnetic structure at the coronal base. Of course this layer is not plane-parallel or simply structured, but observations at the solar limb show that the line is formed over a region of thickness of order 1Mm. Such 1Mm fluctuations in the geometric heights of the formation of this line will translate to errors in the free energy estimated using a planar geometry. However, given that we are interested in the magnetic structure on scales of active regions, i.e. of > 20 Mm, it can be hoped that on such large scales, some important components of the free energy will be reliably measured. General purpose inversion programs (from IQUV measurements to vector magnetic fields) have been developed including scattering polarization and the Zeeman and Hanle effects (e.g., Asensio Ramos & Trujillo Bueno 2009). A key assumption being that the maximum optical depth in the multiplet does not significantly exceed unity in the chromospheric formation region. This assumption is certainly valid for essentially all cases of interest, based upon decades of observations. The interpretation of IQUV data of the 1030nm multiplet in terms of vector magnetic field parameters is, practically speaking, now about as simple as any line in the solar spectrum. A potentially serious issue remains the relative weakness of the polarization (in plages for example, I >> V >> QU). Only with stable, mature instruments has the sensitivity been achieved to derive full Stokes vectors of the He I line (Solanki et al. 2003). When QU measurements are noisy, poor information on the full vector field is recovered. In this situation, which will generally be encountered, the data must be augmented in some way. Judge et al. (2009) have proposed to augment polarimetry

4 with measurements of the fibril morphologies and velocity vectors of plasma inhomogeneities, which have been seen clearly in high resolution (< 1, l/dl > 200,000) FPI images in other chromospheric lines (e.g. Ca II nm). Time series of chromospheric images allow one to track the plane-of-sky components of velocity vectors, Doppler shifts permit measurement of the line-of-sight component. In the low-b, highly conducting environment, the velocities are parallel to the magnetic field. Then, combining the Stokes V and I profiles yields B cos q, the derived plasma kinematics yields both q and j, which are the field inclination to the line of sight, and azimuth in the plane of the sky, respectively. This analysis can be checked for consistency with the morphology of the fibrils. Another issue is that the He I 1083 nm line forms strongly only in active regions, and there are sometimes active regions which show little He I. In such cases the data can be augmented with Ca~II infrared data (e.g., nm), routinely observed using current instruments, even though the diagnosis of magnetic fields from these lines is considerably more complex (Socas-Navarro 2005). The requirement of high spectral and spatial resolution images, at fast cadence (a 30s cadence suffices, Judge et al. 2009) indicates that, with current technology, FPIs present a promising solution. At present no infrared FPI system has been implemented for solar applications, but there is no practical problem in the development of such FPIs working near 1 micron. I suggest that the US community consider development of new infrared FPI instruments to enable the science studies outlined here, for implementation at the best solar observatories in the US. While success is not guaranteed, the potential pay-offs might be considered by some to outweigh the risks. Such risks appear to be small. A detailed study by the Arcetri group, which developed the IBIS FPI instrument (Cavallini 2006) operating below 860nm, a work-horse of the National Solar Observatory at the Dunn Solar Telescope, found that such an instrument could be delivered for operation at the Dunn Telescope for $800K with existing technology (unpublished, unfunded proposal to the NSF, 2009). The technological risks are minimal. A bigger risk is that some of the needed magnetic signatures lie close to or below the sensitivity limits achieved to date (some 3 parts in 10,000, Solanki et al 2003)- these are not easy measurements to make. It may also be difficult to apply the Chandrasekhar virial theorem in practice, since it is valid when the magnetic field is force-free at all boundaries enclosing a volume. Thus assumptions concerning the magnetic field outside of the active regions observed will have to be made. However, perhaps the biggest risk is that the community misses the opportunity to build such an instrument when NASA has invested so much on the space missions, past and present, at a time when the ATST will come on line in This endeavor is very much at the research forefront and will require the attention from individual researchers to make the measurements and to obtain the first credible measurements of the free magnetic energy (Judge et al., paper presented at the 2010 SHINE meeting). Given the known risks, it is hoped that this approach will mature to the point where it will be possible to routinely estimate the total magnetic free energy of the corona over active regions. This technique will also illuminate the problems of NLFFF extrapolations from photospheric data, which may allow us to make some ad hoc corrections to the calculations based on photospheric measurements, greatly enhancing the value of synoptic datasets such as that from the HMI instrument on SDO. If successful, such work will not only help to place coronal dynamics, flare physics and space weather origins on a firm observational footing, but also enhance the returns of huge investments by NASA and other agencies in observing the effects of the release of free energy in the Sun, and the subsequent effects on the Earth.

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