a new enthalpy-based approach to the transition region ... - IOPscience

The Astrophysical Journal Letters, 710:L39–L43, 2010 February 10  C 2010.

doi:10.1088/2041-8205/710/1/L39

The American Astronomical Society. All rights reserved. Printed in the U.S.A.

A NEW ENTHALPY-BASED APPROACH TO THE TRANSITION REGION IN AN IMPULSIVELY HEATED CORONA S. J. Bradshaw1,2 and P. J. Cargill3,4 1

NASA Goddard Space Flight Center, Solar Physics Lab., Code 671, 8800 Greenbelt Road, Greenbelt, MD 20771, USA; [email protected] 2 Department of Computational and Data Sciences, George Mason University, 4400 University Drive, MSN 6A2, Fairfax, VA 22030, USA 3 Space and Atmospheric Physics, The Blackett Laboratory, Imperial College, London, SW7 2BW, UK; [email protected] 4 School of Mathematics and Statistics, University of St. Andrews, St. Andrews, Scotland, KY16 9SS, UK Received 2009 October 5; accepted 2009 December 21; published 2010 January 20

ABSTRACT Observations of the solar corona reveal persistent and ubiquitous redshifts, which correspond to bulk downflows. For an impulsively heated corona (e.g., by nanoflares), this indicates that a majority of the component loop structures are in the radiatively cooling phase of their lifecycle, and these motions should not be used to verify the predictions of any proposed theory of heating. However, the nature of the bulk downflows raises the possibility that enthalpy may play a key role in the energy balance of the loops and in particular that it powers the transition region radiation. In this Letter, we use one-dimensional hydrodynamic simulations of loop cooling to show that enthalpy losses from the corona are easily sufficient to power the transition region radiation. This contrasts with the long-held view that downward thermal conduction powers the transition region. The traditional distinction between the transition region and the corona in terms of temperature alone is then a grossly unphysical simplification, and a proper definition of the interface between these atmospheric layers requires a detailed knowledge of their energy balance. To this end, we propose a robust new definition of the transition region. Key words: Sun: corona – Sun: transition region an important, perhaps dominant, role in the transition region energy balance. This is in contrast with “traditional” models, such as those of a steady corona, where the transition region radiative losses are supported by thermal conduction from the corona (Vesecky et al. 1979). Such enthalpy-dominated transition regions were explored in the context of the fall of spicular material in quiet-Sun network regions by Pneuman & Kopp (1977, 1978) and Athay & Holzer (1982) who found that the energy in downflowing material greatly exceeded the contribution from thermal conduction. Athay (1981, 1982) also showed that enthalpy-dominated models provide the best fit to observed emission measure distributions at temperatures greater than 0.25 MK, though fail to reproduce the EM ∝ T −2 property at lower temperatures. Bradshaw (2008) provided an initial assessment of the importance of such downflows in active regions, suggesting that enthalpy can indeed play an important role in the transition region. Through simple energy balance arguments, the critical downflow speed (v critical , Equation (11) in that work) required for enthalpy to prevent the transition region from undergoing radiative collapse was obtained. It was shown that v critical depends strongly on the local density and weakly on the loop apex temperature, yielding downflow speeds in good agreement with the measured Doppler shifts of Del Zanna (2008). This result is very significant for how we understand the corona and transition region, and this Letter uses onedimensional hydrodynamic simulations of a coronal strand or loop to place the “enthalpy-driven transition region” on a firm footing (Section 2). The consequences are that, in an impulsively heated corona, the old conductively driven transition region paradigm must be discarded for much of the time (Section 3).

1. INTRODUCTION The mechanism by which the solar corona is heated to million degree temperatures is the subject of much debate. One likely possibility is in situ heating by impulsive energy releases on relatively small spatial and temporal scales, often referred to as nanoflares (Parker 1988; Cargill 1993, 1994; Cargill & Klimchuk 1997). Evidence for these is gradually accumulating, especially from the detection of extremely hot but weakly emitting plasma (Schmelz et al. 2009; Reale et al. 2009; Patsourakos & Klimchuk 2009). In the nanoflare scenario, small strands of the corona are heated rapidly but the subsequent cooling plasma contributes most of the observed emission. The cooling is initially due to thermal conduction at high temperatures and low densities, followed by optically thin radiative emission at lower temperatures and higher densities (Cargill 1993; Cargill et al. 1995). Both cooling phases have characteristic mass motions. In the conductive phase, material moves into the corona when the chromosphere is conductively heated (Antiochos & Sturrock 1978). During radiative cooling material drains from the corona when the pressure gradient can no longer support it against gravity (Bradshaw & Cargill 2005). In this phase, the loop is overdense compared with one at the same temperature in static equilibrium. Bulk downflows have been measured in the quiet Sun and active regions by Doschek et al. (1976), Athay et al. (1983), Klimchuk (1987), Athay & Dere (1989), Achour et al. (1995), Brekke et al. (1997), Chae et al. (1998), Peter (1999), Del Zanna (2008), Warren et al. (2008), Doschek et al. (2008), and Tripathi et al. (2009) from Doppler shifts in emission lines of C, N, O, Ne, Mg, Si, S, and Fe, covering the temperature range 104  T  106.4 . The pervasive nature of the bulk downflows suggests that the majority of the quiet-Sun and active region component loop structures are in the radiative cooling phase of their lifecycle (Bradshaw & Cargill 2005), raising the possibility that the enthalpy flux associated with the downflows plays

2. RESULTS We address the transition region structure by looking at the cooling of a loop (or strand) using a numerical hydrodynamic code (HYDRAD: Bradshaw & Mason 2003; Bradshaw & L39

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Figure 1. Average coronal temperature and density during the cooling and draining phase (upper panel: the upper line is the density; and the lower line the temperature) and average coronal temperature vs. density phase space plot (lower panel).

Cargill 2006; Bradshaw & Erd´elyi 2008). The classical, Spitzer– Harm formulation is assumed for conductive cooling, and radiative cooling is described by a loss function of the form χ T α , where χ = 10−18.66 and α = − 12 (valid for T > 0.1 MK), in order to facilitate an analytical study to be described in forthcoming work. A high temperature hydrostatic equilibrium is first established and then the external heating required to maintain it is switched off. The equilibrium loop has a cool (T = 0.02 MK), dense chromosphere at each foot-point, self-consistent chromosphere–corona transition regions, and an overlying hot corona. In the present work, the transition region foot-point to foot-point length is 6.74×109 cm (∼67 Mm), with an apex temperature and density of 3.6 MK and 3.31×109 cm−3 obtained for a uniform heating rate of 5.31×10−3 erg cm−3 s−1 . The loop is judged to have reached hydrostatic equilibrium when residual flows associated with the equilibration process drop to background values of O(104 ) cm s−1 (or M ∼ 10−3 , where M is the Mach number). This was found to take  3600 s (a few tens of sound wave crossing times). Initiating the cooling from hydrostatic equilibrium ensures that, once the external heating is turned off, all subsequent dynamical behavior is due only to the cooling process, and allows the key physics to be more easily identified. In reality, even the initial period of cooling that follows an impulsive heating event is likely to be influenced by significant dynamical activity because the loop is unlikely to reach hydrostatic equilibrium first. Figure 1 (upper panel) shows the evolution of the average coronal temperature T and density n when the external heating is switched off at t = 0 s. The corona gradually cools and drains for a period of 1600 s (∼27 min) before transitioning into a catastrophic phase during which it cools to chromospheric temperatures significantly more rapidly than it drains. The lower panel of Figure 1 shows a phase space plot describing the evolution of the loop in terms of its average coronal temperature and density. The region of ≈ constant gradient between log10 n = 9.5 and log10 n = 9.0 corresponds to the radiative cooling phase, where τR < τC (the radiative and conductive cooling timescales); hence there is a relationship T ∝ nδ and a linear fit yields δ = 1.79 with coefficient of determination R 2 = 0.9996. The existence of such a relationship has previously been established and studied by Serio et al. (1991), Jakimiec et al. (1992), Reale et al. (1993),

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Figure 2. Bulk flow velocity plotted as a function of spatial location (upper panel) and temperature (lower panel) at 400 s (solid), 800 s (dot), 1200 s (dash), and 1600 s (dot–dash) during the cooling and draining phase.

Sylwester et al. (1993), Cargill et al. (1995), and Bradshaw & Cargill (2005). Figure 2 shows four snapshots of the bulk velocity profile plotted as a function of spatial coordinate (upper panel) and temperature (lower panel) between the foot-point (located deep in the chromosphere) and the apex of the loop. The expansion of the chromosphere in response to decreasing coronal pressure slightly displaces the peak downflow toward the apex as the loop cools. Such a slight displacement, approximately 2 Mm, indicates that the transition region foot-point to foot-point length of the loop does not change significantly during cooling. The peak downflow speed accelerates from 8 km s−1 at t = 400 s to 45 km s−1 at t = 1600 s and shifts to lower temperatures as cooling proceeds. In the multi-stranded scenario (Klimchuk 2006, and references therein) monolithic loops are interpreted as “bundles” of unresolved strands that are rapidly heated and then cool relatively slowly. Figure 2 shows that stronger redshifts are predicted in cooler strands and the apparent velocity structure of the bundle would then have redshifts increasing with decreasing temperature (Spadaro et al. 2006), which is consistent with observations (see the list of references in Section 1). Indeed, to take one particular example, Figure 2 shows remarkable agreement with the pattern of redshifts measured by Del Zanna (2008). For example: Figure 2 shows a peak downflow of 45 km s−1 at T = 105.35 K; Del Zanna (2008) measured a redshift of 20–30 km s−1 at T = 105.60 K (Fe viii); peak downflows of 20 km s−1 and 15 km s−1 are shown at T = 105.85 K and T = 106.10 K; a downflow of 8 km s−1 is shown at T = 106.20 K where Del Zanna (2008) measured a redshift of 5–10 km s−1 (Fe xii), and finally a downflow of