New Evidence that Magnetoconvection Drives Solar–Stellar Coronal Heating

Active regions have the strongest magnetic field on the Sun and contain the brightest extreme-ultraviolet (EUV) and X-ray coronal loops (Withbroe & Noyes 1977; Vaiana & Rosner 1978; Golub et al. 1980; Reale 2014), heated to 2–6 MK (Zirker 1993; Reale 2014) by unknown magnetic processes (Fisher et al. 1998; Schrijver et al. 1998; Moore et al. 1999; Katsukawa & Tsuneta 2005; Klimchuk 2006; De Pontieu et al. 2007). As a rule, the stronger the photospheric magnetic flux, the brighter the corona—the EUV/X-ray corona in active regions is 10–100 times more luminous and 2–4 times hotter than that in quiet regions and coronal holes, which are heated to only about 1.5 MK (Withbroe & Noyes 1977; Vaiana & Rosner 1978; Zirker 1993; Reale 2014) and have fields that are 10–100 times weaker than active regions (Wiegelmann et al. 2014). The two most widely argued mechanisms for coronal heating are (i) magnetic-wave heating (e.g., De Pontieu et al. 2007; van Ballegooijen et al. 2011), which is possibly dominant for heating the coronal plasma in the quiet-Sun and coronal holes, and (ii) nanoflare heating (Parker 1983, 1988), which is possibly dominant in active region coronal loops (Cirtain et al. 2013). For (ii), the continuous shuffling of the field in the feet of coronal loops by the (sub-)photospheric convection supposedly braids the field in the coronal loops. This results in the corona being heated to EUV and X-ray temperatures by Ohmic dissipation of magnetic energy via reconnection in these braided loops, impulsively at many small-scale current sheets, at a rate of 10⁷ erg cm⁻² s⁻¹ (Parker 1983, 1988). Recent observations and coronal magnetic field modeling have provided evidence for the presence of braided loop structures and nanoflaring in the active region corona (Cirtain et al. 2013; Winebarger et al. 2013; Brosius et al. 2014; Thalmann et al. 2014; Tiwari et al. 2014).

Active regions with stronger magnetic fields (often having sunspots) have brighter coronal emission than active regions with weaker magnetic fields (Withbroe & Noyes 1977; Vaiana & Rosner 1978; Golub et al. 1980; Reale 2014). Most coronal loop feet in sunspots are rooted in the umbra or in penumbral spines in the inner penumbra (these penumbral spines are intrusions of steeply inclined strong umbral field into the inner penumbra; Tiwari et al. 2015). Sunspots host one foot of some of an active region's brightest coronal loops observed in EUV and X-ray wavelengths, and some of these have that foot in umbra (e.g., Foukal 1975; Alissandrakis & Patsourakos 2013), consistent with sunspot umbrae having the strongest field in an active region. Even so, umbrae often have the darkest areas of an active region in coronal EUV and X-ray images (Pallavicini et al. 1979; Webb & Zirin 1981; Sams et al. 1992; Golub et al. 1994). Here, we resolve this paradox (of why some active region coronal loops rooted in an umbra are the brightest but others are the dimmest) by showing that the coronal EUV brightness of active region coronal loops depends on the convective freedom in both photospheric feet of the loops, and that considering only the loop ends rooted in an umbra and not knowing the rooting of the opposite ends, as was the case in previous studies (e.g., Foukal 1975; Pallavicini et al. 1979; Webb & Zirin 1981; Sams et al. 1992; Golub et al. 1994; Alissandrakis & Patsourakos 2013), resulted in this paradox.

2.1. Instrumentation and Data

2.2. Nonlinear Force-free Field Modeling

In Figure 1, we show an example active region (NOAA 12108) in UV, EUV, continuum-intensity images, and a line-of-sight magnetogram. This active region has a simple bipolar field configuration and contains sunspots of opposite magnetic polarity. The active region was flare-quiet—it produced no C-class or larger flares within 24 hr before and after our observations. We selected a non-flaring active region because we are interested in quasi-steady heating and not in the large bursts of heating by flares. During the 26 hr of our observations, the active region passed the central meridian 8° south of disk center, and thus was always close to disk center, thus avoiding projection errors. Coronal loops of different temperatures can be identified in the coronal EUV images of SDO/AIA. Noticeably, the sunspots of the active region appear dark in continuum-intensity (Figure 1(b)) and UV images (Figure 1(a)). The sunspots are surrounded by weaker-field plage regions, which are bright in the AIA 1600 Å image (Figure 1(a)). The loops are rooted in different photospheric magnetic features such as sunspots, unipolar plage, and mixed-polarity plage (compare Figures 1(c)–(e)). The temperature map (Figure 1(f)), derived from taking into account the emission across the temperature regime ∼0.6–6 MK (corresponding to AIA 171–94 Å channels) through DEM, following Aschwanden et al. (2013), shows the approximate temperatures of coronal loops. The temperature map shows that the brightest coronal loops in the 94 Å image are the hottest ones. We emphasize that, although the DEM analysis indicates that the brightest AIA 94 Å loops are the hottest, our main results of the paper do not depend on the DEM calculations.

We use sequences of AIA 193 and 94 Å images, such as those shown in Figure 1, to study the evolution of bright active region coronal loops (Movie 1). In these sequences (i) bright EUV coronal loops are episodic, with lifetimes of 1–2 hr; (ii) many of the brightest EUV loops are apparently rooted within or at the edge of a sunspot umbra at one foot, with their other foot located in opposite-polarity plage or penumbra; (iii) some of the other brightest loops have one foot rooted in umbra or penumbra, and the other foot in mixed-polarity flux; (iv) the bright coronal loops connecting opposite unipolar plage regions are never as bright as those with one foot rooted in a sunspot or in mixed-polarity plage; (v) coronal loops with each foot in a sunspot umbra of opposite polarity ("umbra-to-umbra" loops) are never visible, neither in the wavelength bands presented here, nor in any of the other AIA passbands.

To examine whether umbra-to-umbra coronal magnetic loops are present, we use a NLFF field model of the active region coronal magnetic field, based on a SDO/HMI photospheric vector magnetogram. In Figure 2(a), selected model field lines are shown overlaid on the nearest-in-time AIA 94 Å image. Each of these model field lines traces an observed loop closely, validating the model field. Despite the absence of any discernible connection between the two sunspot umbrae in EUV coronal images, the three-dimensional model magnetic field shows that there are field lines connecting the opposite-polarity umbrae of the active region (Movie 2). In Figures 2(b)–(c), we plot two sets of the model field lines that link the two opposite-polarity umbrae. Since the length of a coronal loop is an important factor in determining the loop's coronal brightness—shorter loops require a smaller amount of heating than longer ones for the same brightness (Mandrini et al. 2000; Klimchuk 2006; Kano et al. 2014; Reale 2014)—we display umbra-to-umbra loops of different apex heights (and therefore of different lengths). The two sets of umbra-to-umbra loops displayed in Figures 2(b) and (c) have apex heights of ∼90–100 mega-meters (hereafter Mm), "low-apex" fields, and ∼150–175 Mm, "high-apex" fields, respectively. Neither low-apex (short) nor high-apex (long) loops that connect the sunspot umbrae are visible in the AIA 94 and 193 Å images. We also verified the invisibility of these loops in the movies from all other AIA channels. This indicates that the coronal loops connecting opposite-polarity umbrae have the lowest coronal-temperature plasma density (and thus the lowest coronal brightness), and hence are the least heated (Vaiana & Rosner 1978). It is worth mentioning here that a dim umbra-to-umbra loop seen in AIA 171 Å images of the active region (NOAA 12108) two days after our observations (Chitta et al. 2016), is reasonable because a light bridge, which is a signature of magnetoconvection in the umbra, was present then in the leading-polarity sunspot, and was at the foot of that loop.

In Figure 3, we show images and the temperature map of another flare-quiet active region (NOAA 12021), the model field lines of which are shown in Figure 4. We find the same pattern for the EUV brightness of coronal loops with respect to their magnetic rooting within the active region. Again, the modeled umbra-to-umbra field lines do not match any discernible EUV coronal loops within an extended 24 hr time span (Movie 3). Although here we show ∼24–26 hr of data for only two examples, we have used JHelioviewer Software to find  similar active regions characterized by a large sunspot for each polarity with no light bridges in the umbrae. These active regions show no exception to our results, e.g., we do not find any visible umbra-to-umbra coronal loops.

We interpret our observational and modeling results as follows. The convective freedom at both photospheric feet is the primary determinant of the brightness of active region coronal loops. Umbra-to-umbra loops are the dimmest (invisible) because the convection in each foot of these loops is so strongly suppressed by the strong umbral fields that the magnetic energy input to those loops is quenched. That is, field braiding for powering heating by magnetic reconnection is quenched in these coronal loops. On the one hand, the EUV invisibility of umbra-to-umbra loops and the observed magnetic rooting of the bright EUV loops are consistent with Parker's idea (Parker 1983) that convection shuffles field lines and the subsequent small-scale reconnection (nanoflares; Parker 1988) in the resulting braided coronal loops (Cirtain et al. 2013; Winebarger et al. 2013; Brosius et al. 2014; Tiwari et al. 2014; Thalmann et al. 2014; Pontin et al. 2017) releases magnetic energy to heat the corona, which implies that the strong suppression of convection by the strong field in umbrae should quench coronal heating in umbra-to-umbra loops. On the other hand, any appreciable heating from magnetic waves generated by convection-churning of the loop feet is evidently also suppressed in umbra-to-umbra coronal loops.

Because the brightest coronal loops are the ones linking an umbra or inner penumbra to unipolar plage, mixed-polarity plage, or penumbra, we infer that they are the brightest because they have one foot rooted in umbra or inner penumbral spines and therefore have stronger magnetic field in the loop body than do plage-to-plage loops of the same length (which never become as bright as the brightest loops). Plausibly, because of that and because the other foot has vigorous convection, these loops with only one end in umbra have a higher rate of magnetic energy injection (higher Poynting flux), and a higher dissipation rate via reconnection, and thus brighter coronal emission than the plage-to-plage loops. All previous studies of the brightness of coronal loops stemming from an umbra considered only the loop feet in that umbra and did not know the magnetic settings of the other ends of the loops. Thus, they did not discern why some active region coronal loops rooted in umbra are the brightest (Foukal 1975; Alissandrakis & Patsourakos 2013) and others are the dimmest (Pallavicini et al. 1979; Webb & Zirin 1981; Sams et al. 1992; Golub et al. 1994). The sketch in Figure 5 depicts what we infer to be the dependence of the brightness of coronal loops on their magnetic rooting in an active region. Our observations imply that as long as the field can be braided by convection in a loop foot, the stronger the field in the loop, the stronger the coronal heating. Our results qualitatively support the models of Hurlburt et al. (2002) and Chen et al. (2014).

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Thus, magnetoconvective driving at both feet of a loop is the key. Whether the subsequent transport and dissipation mechanism is braiding/nanoflare or wave heating is beyond this investigation. Irrespective of whether the active-region corona is heated more by dissipation of magnetic waves or more by nanoflares, our results indicate that, depending on the field strength in both feet, the photospheric feet of any coronal loop on the Sun—or on any star with a convective envelope—can either engender or quench coronal heating in the loop's body. Our results are new evidence for the widely held view that the quasi-steady coronal heating in active regions is driven by magnetoconvection in the feet of the loops (Parker 1983, 1988). The alternative possibility, that the heating mostly comes from dissipation of free magnetic energy already in the loop field when it emerged from inside the Sun (Fisher et al. 1998), is unlikely in view of the EUV invisibility of umbra-to-umbra loops.

We observed, as have a few other researchers (Falconer et al. 1997; Chitta et al. 2017), that the active region coronal loops that are most persistently the brightest are rooted in regions of mixed-polarity magnetic flux at one end or at both ends. This indicates that the evolutionary interaction of the opposite-polarity flux, which is driven by magnetoconvection in and below the photosphere, somehow enhances the rate of injection of free magnetic energy into the accessed coronal loops, in excess of what the rate would be were the magnetic flux unipolar at both ends.

We thank Allen Gary, Alphonse Sterling, David McKenzie, Davina Innes, and P. Venkatakrishnan for useful comments on the manuscript. S.K.T., R.L.M., and A.R.W. were supported by funding from the LWS-TRT program and the HGI Program of the Heliophysics Division of NASA's SMD. N.K.P.'s research was supported by an appointment to the NASA Postdoctoral Program at the NASA/MSFC, administered by USRA under a contract with NASA. J.K.T. acknowledges support from the Austrian Science Fund (FWF): P25383-N27. We acknowledge using NASA/SDO-AIA-HMI data and the software JHelioviewer.