Spectral Signatures of Transient Heating in the Solar Corona

Hinode/EIS observations of an active region are presented. Intensity and Doppler velocity maps for different emission lines are constructed. Consistent with previous results, the Doppler velocities near the footpoints of coronal loops appear to be blue shifted for emission lines with temperatures above 1 MK. The gradual transition from blue shifts at temperatures above 1 MK to red shifts at temperatures below 1 MK is addressed through numerical modeling of loop dynamics. The simulation results are converted into synthetic EIS observations and compared with the actual measurements. Persistent blue shifts, blue wing enhancements, and red shifts observed in EUV lines are interpreted as a signature of repetitive heating occurring near the loop footpoints on a time scale of several minutes.


Observations
The EUV imaging-spectrometer (EIS) aboard Hinode has two CCDs covering the wavelength ranges 171 − 212Å and 245 − 291Å. EIS has both narrow (1 ′′ and 2 ′′ wide) slits, and wider (40 ′′ and 266 ′′ ) imaging slots, all with up to 512 ′′ in the solar Y direction. Spectroscopic observations can be carried out either in sit-and-stare or in scanning modes. Further details of Hinode/EIS characteristics are given by Culhane et al. (2007), Kosugi et al. (2007).
For this study, we concentrated on an active region visible on 20th February 2007. Hinode/EIS observations of the active region were carried out using the 1 ′′ wide slit in scanning mode. Spectral data for a number of wavelengths were produced. The data have been studied by Warren et al. (2011), Martinez-Sykora et al. (2011).
In the following analysis, we select the Fe viii 185.21Å, Fe x 184.54Å and Fe xii 195.12Å spectral lines with formation temperatures of log T ≈ 5.8, 6.0 and 6.2. EIS level zero data files are processed with the eis prep software, using the default options. The eis wave corr procedure and the level one data are used to calculate the wavelength corrections for each spectral line. We fit a single Gaussian profile to each line spectrum, using the eis auto fit software. The reference wavelength of each line profile has been updated to match the rest wavelength found in a laboratory, and is taken from Brown et al. (2008) relative to the final wavelength of this line. Doppler velocity measurements require the slit tilt and thermal drift of the instrument to be calculated accurately. This is achieved using the eis update fitdata procedure, which updates these parameters, based on the fitted line profile and the first approximations from eis wave corr. Finally we output intensity and Doppler velocity maps for the spectral lines. The intensity maps in Figure 1 show loops that become bright in the higher temperature line of Fe xii 195Å. The loops are connected to the footpoints which can be seen near the center of the intensity image in Fe viii 185Å. The Doppler velocity maps in the lower panel reveal the presence of blue shifts in Fe xii near the footpoints. The blue shifts fade out in Fe x and turn into red shifts in the lower temperature Fe viii line. The blue shifts at high temperatures are a persistent feature of EIS observations and may last for prolonged periods of time (e.g., Hara et al. 2008). The footpoints areas of the cool loops in Fe viii are red shifted whereas the footpoint areas of the hot loops in Fe xii are blue shifted. The velocities for the intermediate Fe x line are close to zero. This gradual transition from red to blue will be addressed in the forthcoming analysis which is based on numerical forward modeling.
In addition to loop like structures, Figure

Numerical Forward Modeling
In order to explain the features seen in Figure 2, in particular, the gradual transition from red in Fe viii to blue in Fe xii near the loop footpoints, we carry out numerical forward modeling. A single loop with a typical length of 40 Mm is initially in a cooling state due to the combined action of thermal conduction and radiation. The loop is gravitationally stratified and remains in the vertical plain. Cooling leads to downflows along the loop legs. Only longitudinal motions are considered. Motions in other directions are ignored. This is a valid approximation as long as the ratio of the thermal pressure to magnetic pressure is small. The initial peak temperature at the apex is about 0.6 MK and the dense chromospheric footpoints are kept at a constant temperature of 20 000 K. The governing equations of continuity, momentum and energy are integrated numerically to investigate the loop response to transient heating. The one dimensional treatment and the adaptive mesh refinement technique allows us to accurately model the dynamics in the steep transition region and the emission in EUV lines. The details of the HYDRAD code used in our modeling are described by Bradshaw & Mason (2003).
A phenomenological heating term is included in the energy equation. The heating is located 3 Mm inside the chromospheric boundary and it has an exponential scale height of 4 Mm. Localizing the heating near the footpoints has the effect of driving strong upflows. For simplicity, a symmetric profile about the apex is chosen. The heating occurs on a time scale of a few minutes. It smoothly increases from t = 0 s, reaches its peak rate at t = 150 s and vanishes at t = 300 s. The subsequent dynamics is determined by thermal conduction and radiation. The amount of energy input is proportional to the cross sectional area of the loop. For a cross sectional diameter of 1 Mm the total energy input near each footpoint is about 10 26 erg. The selected heating parameters are best suited for reproducing the observed temporal evolution. The velocities projected onto the line of sight are shown in the third panel of Figure 2. For simplicity, it is assumed that the loop is located in the center of the solar disc. Note the shift of the peak velocities towards the footpoints due to the semicircular geometry of the loop. Downflows correspond to positive red-shifts, and upflows correspond to negative blue shifts. The heating pulse leads to blue shifts of up to 97 km s −1 . The bottom panel of Figure 2 displays the evolution of density: heating and upflows are followed by enhanced density whereas cooling and downflows reduce the amount of material in the loop. Figure 2 suggests that the evolution of the loop proceeds in three main stages: there are blue shifts near the footpoints at high temperatures and red shifts at low temperatures. The velocities are small at intermediate temperatures when there is a transition from heating to cooling or viceversa. However, the blue shifts observed in high temperature lines are usually quite persistent and last much longer than the flows in our simulations (Hara et al. 2008). Another important difference is that Figure 1 shows an entire active region, whereas our simulations are carried out for a single loop. It is therefore not possible to directly reproduce the observed behavior from the simulations. According to the observations presented in Figure 1, there might be several loops along the line of sight. In general, the loops have different densities, temperatures, lengths, widths, inclinations, etc, and are in different stages of evolution as shown in Figure 3. All these loops converege at the footpoints where the blue shifts are mainly seen. In the absence of detailed knowledge of the involved parameters, we assume that there are four loops along the line of sight which are almost identical if their length is large compared to the cross sectional radius. Each loop follows the cycle shown in Figure 2 which is repeated upon completion and there is a lag time of 250 s between the loops.

Discussion
The simulation results are converted into synthetic spectral observations using the EIS response function. The full details of this procedure are described by Taroyan et al. (2006). The emission from the three loops shown in Figure 3 is integrated along a segment near the footpoints. The length of the segment corresponds to a 1 ′′ EIS slit. The instrumental width of the EIS instrument is added to the thermal width of the line profile. We have performed a sample simulation of heating with a similar total energy input but with a duration of 60 s: strong red shifts appear during the heating stage and blue shifts appear during the cooling stage as the rapid pressure pulse bounces back and forth along the loop. It is therefore no longer possible to reproduce the observations shown in Figures 1. A significant increase in the total heat input leads to higher maximum temperatures but results in red shifts at temperatures above 1 MK. We have therefore found important constraints on models of loop heating. Below we explain the absence of significant net shifts in the case of rapid heating. The initial heating event drives evaporation from the chromosphere which lasts for a short period of time. The emission is expected to peak during the cooling phase when the densities are high. However, these brief upflows propagate away from the footpoint segment of the loop by the time it cools to the Fe xii passband and no significant upflows are seen. Subsequently the pulse is propagating and bouncing back and forth along the loop as the loop cools to Fe x and Fe viii passbands. This may result in blue, red or no shifts. Therefore a superposition of rapidly heated loops leads to a situation whereby no significant net flows are detected. Therefore, no significant net flows will be detected if the heating time is short compared with the pulse travel time. The travel time is roughly determined as the ratio of the loop length and the sound speed. When the loops are longer than about 20 Mm, the reflection effects become small and therefore blue shifts and red shifts are seen at high and low temperatures, respectively.

Conclusions
The coexistence of blue shifts in coronal lines and red shifts in transition region lines has been known for many years. These persistent features have mainly been interpreted as a manifestation of a bi-directional flow of material from the reconnection site or nanoflares (Teriaca et al. 1999;Hansteen et al. 2010;Patsourakos & Klimchuk 2006). Hinode/EIS observations have revealed new features near the footpoints of active region loops. Figures 1 and 4 show red shifts at low temperatures (Fe viii line), blue shifts and enhanced blue wings at high temperatures (Fe xii and Fe xv lines). All these features are reproduced from numerical simulations of transient loop heating if the convergence of several loops at the footpoints is taken into account. The heating occurs on a time scale of a few minutes. The nature of the heating process remains unknown. However, the obtained results provide important constraints on models of loop heating.