4.3 Flows

A generalization of static models of loops (Section 4.1.1) is represented by models of loops with stationary flows, driven by a pressure imbalance between the footpoints (siphon flows). The properties of siphon flows have been studied by several authors (Cargill and Priest, 1980Priest, 1981Noci, 1981Borrini and Noci, 1982Antiochos, 1984Thomas, 1988Montesinos and Thomas, 1989Noci et al., 1989Thomas and Montesinos, 1990Spadaro et al., 1990Jump To The Next Citation PointThomas and Montesinos, 1991Peres et al., 1992Montesinos and Thomas, 1993). Orlando et al. (1995a) developed a complete detailed model of loop siphon flows and used it to explore the space of the solutions and to derive an extension of RTV scaling laws to loops containing subsonic flows.
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Figure 17: Example of solutions of a siphon flow loop model including a shock (from Orlando and Peres, 1999Jump To The Next Citation Point).

Orlando et al. (1995b) explored the conditions for the presence of stationary shocks in critical and supersonic siphon flows in coronal loops (Figure 17View Image), finding that the shock position depends on the volumetric heating rate of the loop, and devising related scaling laws. The presence of massive flows may alter the line emission with respect to static plasma, because of the delay of the moving plasma to settle to ionization equilibrium (Golub et al., 1989). Spadaro et al. (1990) modelled that, even including the effect of ionization non-equilibrium, the UV lines are predicted to be blue-shifted by loop models. So non-equilibrium emission from flows cannot explain the observed dominant redshifts (Section 3.5). The effects of non-equilibrium of ionization in UV line emission from shocked siphon flows are further discussed in Orlando and Peres (1999).

Modeling efforts were devoted in the 1990s to explain specifically the extensive evidence of redshifted UV lines on the solar disk. Hansteen (1993) used a hydrodynamic loop model including the effects of non-equilibrium of ionization to show that the redshifts might be produced by downward propagating acoustic waves, possibly stimulated by nanoflares. By means of two-dimensional hydrodynamic simulations, Reale et al. (19961997b) proposed that the UV redshifts might be due to downdrafts driven by radiatively-cooling condensations in the solar transition region. In the exploration of the parameter space, they found redshifted components at speeds of several km s–1 for ambient pressure values ranging from those typical of quiet Sun to active regions and predicted that redshifts may occur more easily in the higher pressure plasma, typical of active regions.

Teriaca et al. (1999b) explored the idea that the occurrence of nanoflares in a magnetic loop around the O vi formation temperature could explain the observed redshift of mid-low transition region lines as well as the blueshift observed in low coronal lines (T > 6 × 105 K). Observations were compared to numerical simulations of the response of the solar atmosphere to an energy perturbation of 4 × 1024 erg, including non-equilibrium of ionization. Performing an integration over the entire period of simulations, they found a redshift in C iv, and a blueshift in O vi and Ne viii, of a few km s–1, in reasonable agreement with observations. A similar idea was applied by Patsourakos and Klimchuk (2006Jump To The Next Citation Point) to make predictions about the presence or absence of nonthermal broadening in several spectral lines (e.g., Ne viii, Mg x, Fe xvii) due to nanoflare-driven chromospheric evaporation. Clearly, the occurrence of such effects in the lines depends considerably on the choice of the heat pulse parameters. Therefore, more constraints are needed to make the whole model more consistent. In other words, modeling should address specific observations to provide more conclusive results.

Theoretical reasons indicate that flows should be invariably present in coronal loop systems, although they may not be necessarily important in the global loop momentum and energy budget. For instance, it has been shown that the presence of, at least, moderate flows is necessary to explain why we actually see the loops (Lenz, 2004). The loop emission and detection is in fact due to the emission from heavy ions, like Fe. In hydrostatic equilibrium conditions, gravitational settlement should keep the emitting elements low on the solar surface, and we should not be able to see but the loop footpoints. Instead, detailed modeling shows that flows of few km s–1 are enough to drag ions high in the corona by Coulomb coupling and to enhance coronal ion abundances by orders of magnitudes. Incidentally, the same modeling shows that, for the same mechanisms, no chemical fractionation of coronal plasma with respect to photospheric composition as a function of the element First Ionization Potential (FIP) should be present in coronal loops.

Other studies point instead to the relative unimportance of flows in coronal loops. In particular, as already mentioned in Section 3.2.2, by means of steady hydrodynamic loop modeling (i.e., assuming equilibrium condition and, therefore, dropping the time-dependent terms in Equations (3View Equation), (4View Equation), and (5View Equation), Patsourakos et al. (2004) showed that flows may not be able to explain the evidence of isothermal loops, as instead proposed by Winebarger et al. (2002c). They found that a heating deposited asymmetrically in a loop is able to drive significant flows in the loop and to enhance its density to the levels typically diagnosed from TRACE observations, but it also produces an inversion of the temperature distribution and, consequently, a highly structured distribution of the relevant filter ratio along the loop, which is not observed.

Plasma cooling is a mechanism that may drive significant downflows in a loop (e.g., Bradshaw and Cargill, 20052010). As an extension of studies on modeling catastrophic cooling in loops (Müller et al., 2004Jump To The Next Citation Point), Müller et al. (2005) tried to explain the evidence of propagating intensity variations observed in the He ii 304 Å line with SoHO/EIT (De Groof et al., 2004, Section 3.5). Two possible driving mechanisms had been proposed: slow magnetoacoustic waves or blobs of cool downfalling plasma. A model of cool downfalling blob triggered in a thermally-unstable loop heated at the footpoints gave a qualitative agreement with measured speeds and predicted a significant braking in the high-pressure transition region, to be checked in future high cadence observations in cool lines.

Plasma waves have been more recently proposed to have an important role in driving flows within loops. Acoustic waves excited by heat pulses at the chromospheric loop footpoints and damped by thermal conduction in corona are possible candidates (Taroyan et al., 2005). Even more attention received the propagation of Alfvén waves in coronal loops. Hydrodynamic loop modeling O’Neill and Li (2005Jump To The Next Citation Point) showed that Alfvén waves deposit significant momentum in the plasma, and that steady state conditions with significant flows and relatively high density can be reached. Analogous results were independently obtained with a different approach: considering a wind-like model to describe a long isothermal loop, Grappin et al. (20032005) showed that the waves can drive pressure variations along the loop which trigger siphon flows. Alfvén disturbances have been recently shown to be amplified by the presence of loop flows (Taroyan, 2009).

As listed above, models predict the development of flows inside coronal loops in a wide variety of situations, namely evaporation, draining, siphon flows, waves. The challenge will be to distinguish clearly among them and to assess the appropriate weight and importance to them both in the spatial and temporal distribution.


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