Influence of Cross-sectional Expansion on Coronal Emissions from a Radiatively Cooling Solar Flare Loop

Abstract

Loop-aligned hydrodynamic modelings help better understand the thermodynamic evolution of flaring plasma confined in solar flare loops. Conventional loop modelings typically assume a uniform loop cross section. With a variation of the cross section taken into account, in this work we carry out both analytical and numerical modelings of the radiative cooling in a solar flare loop. It is found that a cross-sectional expansion with height can efficiently suppress the draining of loop material from the corona while not significantly affecting the decrease of loop temperature. Reflected to the loop energetics, the coronal part of the loop cools more dominantly by radiation, and more importantly, the loop radiative outputs are shifted toward lower temperatures. These findings pose important physical implications for extreme-ultraviolet (EUV) late-phase emissions discovered in some solar flares. The late-phase loops in these flares are believed to bear a more notable cross-sectional expansion owing to their longer lengths. Compared with the main-phase loops, the late-phase loops would emit more effectively at middle temperatures, which could, to a certain degree, mitigate the severe heating requirement for the production of a prominent warm coronal late-phase peak. In addition, the cross-sectional expansion also affects the shape of the emission lights curves, causing a sharper decay after the emission peak. Such an emission pattern has been validated with the observations of an EUV late-phase flare, and could serve as a potential diagnostic tool to judge the degree of loop cross-sectional expansion in an extended flare dataset.

Figures (10)

• Figure 1: Analytical solutions for radiative cooling. Panel (a) plots the variations of the power exponents on $(1+\eta t)$ versus $\delta$ for both temperature (dashed curve) and density (dashed--dotted curve), where the color-filled circles highlight the results evaluated at $\delta=2$ (red), $\delta=4$ (green), and $\delta=8$ (blue), respectively. Panels (b) and (c) display the temporal profiles of the looptop temperature and density for three different values of $\delta$, which are color-coded according to panel (a). In computing the analytical solutions, the values of $\l$ and $\gamma$ are set to be 1/2 and 5/3, respectively.
• Figure 2: Temporal profiles of the total loop radiation (dashed curves) and interface enthalpy flow (dashed--dotted curves) derived from the analytical solutions (Equations (\ref{['solrl']}) and (\ref{['solfei']})) for different values of $\delta$ (discriminated with different colors).
• Figure 3: Variation of the dimensionless ratio $R$ (=$\mathcal{R}_L/\mathcal{F}_{Ei}-1$) vs. the scaling index $\delta$. The solid curve is derived from the analytical solutions in this work, where the color-filled circles highlight the results evaluated at $\delta=2$ (red), $\delta=4$ (green), and $\delta=8$ (blue), respectively, and the dashed--dotted curve is based on the approach in Bradshaw2005, which is plotted here for comparison.
• Figure 4: Light curves of the apex region of a radiatively cooling flare loop, which are synthesized with the analytical solutions for different values of $\delta$. The upper and lower panels display the synthetic light curves in two iron lines and two AIA passbands, respectively. The meaning of the color and style for each curve is detailed in the legend.
• Figure 5: Temporal profiles of loop quantities derived from the HYDRAD numerical simulations for different values of $\Gamma$ (discriminated with different colors). The left panels show the evolutions the looptop temperature (a) and density (b), and the right panels display the evolutions of the average coronal temperature (c) and density (d). The inset in panel (b) gives an enlarged view of the shaded region in a linear scale.