HOW IMPORTANT ARE ELECTRON BEAMS IN DRIVING CHROMOSPHERIC EVAPORATION IN THE 2014 MARCH 29 FLARE?

RHESSI full-Sun spectra were fitted during the time of the main peak, using 8 s time intervals coinciding with the start and end times of the IRIS exposures at each slit position. The spectra were fitted with a thermal component at low energies and a thick-target power-law component at energies above ∼20 keV. RHESSI CLEAN (Hurford et al. 2002) images at 6–12 keV (using grids 3–6, natural weighting with a clean beam width factor of 1.4, resulting in an effective CLEAN beam of 128) and at 30–70 keV (using grids 1–6, natural weighting with a clean beam width factor 1.4, resulting in an effective resolution of 34) were made for an overview of the flare morphology. We integrated over 75 s from the start time of each IRIS raster to be consistent with the time it takes to complete one raster (except for the first raster where the RHESSI attenuator came in during the period hence the start time of the image was 17:46:02 UT). For the more detailed analysis of the time evolution, additional RHESSI images were made with the same start times as the IRIS exposures at each slit position and an 8 s time-integration. To ensure as close a representation of the true source size as possible, only grids 1–4 were used for these images with an effective resolution of 3 arcsec FWHM. These images were used in the further analysis. The RHESSI X-ray images show a SXR source near the top of a loop system that connects the two flare ribbons. The HXR footpoints coincide with the location of the flare ribbons as seen in the IRIS 2796 Å slit-jaw images (SJI) but are less extended than the flare ribbon along the east–west direction and do not cover its entire length. Figure 1 shows IRIS 2796 Å SJI at selected times overlaid with the RHESSI contours at 6–12 keV and 30–70 keV. We found a ∼3'' offset between the RHESSI sources and SDO images of the flare ribbons, to which IRIS was aligned. Thus we applied an empirical roll correction of 015 (clockwise about Sun center) to the RHESSI images, so that the HXR emission matches emission from both flare ribbons in SDO (see also Kleint et al. 2015). This correction is justified for several reasons. In addition to the pointing uncertainty of SDO, the star-field that is used by the PMTRAS (Photo-Multiplier Tube Roll Aspect System, Hurford & Curtis 2002) to determine the RHESSI roll-angle was sparse at the time of the observations, resulting in a potential error of the RHESSI roll-angle. Moreover, the correction is justified because of physical reasons. With no correction applied, the HXR footpoints would not be co-spatial with the flare ribbons as seen in IRIS SJI and they would be trailing the motion of the ribbon. In addition, the HXR sources would be located in the same magnetic polarity. All these points would be in contradiction of our understanding of flares and flare energy input.

IRIS observations of Fe xxi λ1354.1 allow for studying flows of hot (∼10 MK) plasma near the loop footpoints. IRIS observations of Fe xxi were recently reported in selected events (Tian et al. 2014; Graham & Cauzzi 2015; Polito et al. 2015), including the 2014 March 29 flare observed by Young et al. (2015), who observed blueshifts from the flare ribbons "as expected from models of chromospheric evaporation" without going into quantitative detail. To find the center location of the Fe xxi line, we fitted two Gaussians, one to the Fe xxi line and the other to account for the intense C i λ1354.29 line. The fits were done automatically over time and along the slit. A rest-wavelength of 1354.064 Å, following Feldman et al. (2000), was used to calculate the Doppler-velocities. Fits that resulted in a line-width smaller than the theoretical thermal line-width, with too large ${\chi }^{2},$ as well as with negative or unphysically high intensities were omitted from further analysis. As validation of the fits we also fitted a single Gaussian to the Fe xxi line, omitting contributions from C i and other, weaker lines as well as multi-Gaussian fits for selected pixels. All methods give largely consistent results (to within a few km s⁻¹), indicating that the weaker lines (originating from cool, singly ionized Fe and Si) are not important for the fit and the two-component Gaussian fit, which we use for inferring the Doppler-velocity, is justified. An example is shown in Figure 2. It shows the broad, blueshifted Fe xxi line centered 1353.6 Å, the intense, narrow C i line at 1354.35 Å, and the weaker Fe ii and Si ii lines (see Tian et al. 2015, for a more detailed discussion of the whole spectrum).

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An example for this case is shown in panel one of Figure 5 for slit position 5 of raster 174. The blueshifts were observed at 17:47:28 UT. The HXR source at the same location was observed ∼56 s earlier, at 17:46:32 UT. Near the time of the IRIS observation, the HXR footpoint was ∼5 arcsec away to the south-west. For other slit positions, HXR footpoints preceded the appearance of blueshifts at a given slit-position by 30–60 s on average. The velocities in all such regions were between −30 and −100 km s⁻¹. Corrected for line of sight, this gives a maximum velocity of ∼−120 km s⁻¹. The location of the most pronounced upflows is co-spatial with the location of the ribbons in SJI at 2796 Å supporting the notion that the observed blueshifts are indeed due to chromospheric evaporation of 10 MK plasma.

During raster 173, the slit crossed the HXR footpoint at positions 4 and 5. An example is given in the second panel of Figure 5. The HXR footpoint is located at ∼[519, 262.5] arcsec. In a beam-driven evaporation model, blueshifts are expected from that same location. However upflows are observed 2–3 arcsec further north but not from the location of the HXR footpoint.

There are regions that display blueshifts in Fe xxi but no corresponding RHESSI HXR source at any time, namely, at slit-positions 7 and 8, and the northern ribbon (compare with Figure 4). An example is given in the third panel of Figure 5. The velocities are similar to the velocities at the other locations with a maximum upflow velocity of −110 km s⁻¹ (−132 km s⁻¹ line of sight corrected) in the northern ribbon and up to −200 km s⁻¹ in the southern ribbon.

The total non-thermal power in a beam of accelerated electrons with flux distribution F(E) is given as

$$\begin{eqnarray}&&{P}_{\mathrm{tot}}=\int {EF}(E){dE}.\end{eqnarray} \tag{ 1 }$$

For a power-law spectrum $F(E)={{AE}}^{-\delta }$ above a cut-off energy E_c this gives

$$\begin{eqnarray}&&{P}_{\mathrm{tot}}=\displaystyle \frac{A}{\delta -2}\;{E}_{c}^{-(\delta -2)}\;\mathrm{erg}\;{{\rm{s}}}^{-1}\end{eqnarray} \tag{ 2 }$$

or, expressed through the total electron flux per second F_tot found from a thick-target model fit:

$$\begin{eqnarray}&&{P}_{\mathrm{tot}}=\displaystyle \frac{\delta -1}{\delta -2}\;{F}_{\mathrm{tot}}{E}_{c}\;\mathrm{erg}\;{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 3 }$$

For the time-step starting at 17:46:04 UT, the total electron flux from the thick-target fit was $2.3\times {10}^{35}\;{{\rm{s}}}^{-1},$ electron spectral index $\delta =3.9,$ and cut-off energy ${E}_{c}=20\;{\rm{keV}}.$ This gives a total non-thermal power of ${P}_{\mathrm{tot}}=1.1\times {10}^{28}$ erg s⁻¹. At 17:47:10 UT, the non-thermal power had dropped to ${P}_{\mathrm{tot}}=5.5\times {10}^{27}$ erg s⁻¹. Since the fits were made on full-Sun spectra, these values include emission from both footpoints. RHESSI images suggest that the southern footpoint was more intense than the northern footpoint during most of the flare. Assuming that they were of roughly equal intensity gives a lower limit on the electron flux into the southern footpoint of ${P}_{\mathrm{tot}}=5.5\times {10}^{27}$ erg s⁻¹ and ${P}_{\mathrm{tot}}=2.8\times {10}^{27}$ erg s⁻¹, respectively. The footpoint area, estimated from IRIS 2796 Å images is $\approx {10}^{17}$ cm². A similar value is found from the 50% contour in RHESSI CLEAN images. This is an upper limit, since the IRIS images were partially saturated and source sizes with RHESSI tend to be over-estimated (e.g., Dennis & Pernak 2009; Warmuth & Mann 2013). However, this estimate is sufficient here, since we are interested in a lower limit of the energy input. The total energy flux amounts are $5.5\times {10}^{10}$ erg s⁻¹cm⁻² initially and $2.8\times {10}^{10}$ erg s⁻¹cm⁻² by 17:47:10 UT.

According to the above calculation, the non-thermal power input is big enough to trigger explosive evaporation. According to Fisher (1987), explosive evaporation ceases and becomes gradual once the conductive flux out of the evaporated plasma becomes comparable to the beam flux. The change occurs at temperatures around ∼10 MK over timescales of a few seconds to a few tens of seconds. In the presented event, the timescale would be of the order of 10 s. This scenario could explain blueshifts that are still observed long after the HXR source since gentle evaporation will continue as long as there is a temperature gradient. Gentle evaporation is further supported by the observed velocities of less than 200 km s⁻¹. Thus the observations described in Section 3.1 can be explained with energy input by a non-thermal electron beam resulting in explosive evaporation followed by a transition to gentle evaporation whose signatures are observed once the IRIS slit covers the respective area.

If energy input by electron beams is indeed the initial cause of the evaporation, as assumed in the scenario discussed above, a question immediately arises. Why are no blueshifts observed when the IRIS slit is co-spatial with the location of the HXR footpoint? In other words, why is there no high temperature signature of evaporation for the case described in Section 3.2? One potential explanation could be the delayed onset of EUV emission due to the ion equilibration time. Heating by beam-energy input is almost instantaneous. However, when neutral Fe is heated quickly from 10,000 K to 10 MK it takes a certain time to reach ionization equilibrium, depending on the ambient density. Bradshaw (2009) showed that for densities $\gt {10}^{12}$ cm⁻³, this timescale is shorter than one second. For densities of 10¹⁰ cm⁻³ equilibration takes of the order of 100 s. In a standard thick target, assuming an exponential density, the bulk of 20 keV electrons will reach heights between 1000 and 1400 km, corresponding to densities between 10¹² and 5 × 10¹³ cm⁻³ (Brown et al. 2002; Battaglia & Kontar 2011), and thus this effect can be ignored and one should expect signatures of evaporation in an 8 s integrated spectrum. However, it is likely that the Fe xxi emission is obscured by chromospheric lines in the spectral window. As shown by Graham & Cauzzi (2015), the earliest, and most shifted, instances of the Fe xxi line can be extremely weak at the footpoints. Due to the small spatial scales investigated here, accurate co-alignment between instruments is crucial. For the reasons explained in Section 2.1, we are confident that the alignment adopting a minimum 015 rotation is correct. If no such corrections were applied, the HXR footpoint would cover the southern edge of the blueshifted area in Figure 5 (middle) but would still not cover it fully. Thus an error in co-alignment alone cannot account for the observed offset.

Chromospheric evaporation in the absence of HXR emission can most readily be attributed to energy input by thermal conduction from a hot coronal source. The conductive energy input from classical Spitzer conductivity (Spitzer 1965) is given as

$$\begin{eqnarray}&&{L}_{\mathrm{cond}}={10}^{-6}{T}^{5/2}{\rm{\nabla }}T\;\mathrm{erg}\;{{\rm{s}}}^{-1}\;{\mathrm{cm}}^{-2}.\end{eqnarray} \tag{ 4 }$$

This is usually approximated to

$$\begin{eqnarray}&&{L}_{\mathrm{cond}}={10}^{-6}\;\displaystyle \frac{{T}^{7/2}}{{L}_{T}}\end{eqnarray} \tag{ 5 }$$

with L_T the temperature scale-length. The RHESSI spectra indicate a hot (∼25 MK) coronal source that persists during much of the decay phase. The temperature scale-length is the loop-half length which is approximated from the footpoint separation, assuming a semi-circular loop. For a footpoint separation of 21.4 arcsec this gives ${L}_{T}\approx 1.2\times {10}^{9}\;{\rm{cm}}.$ The resulting conductive flux is then ${L}_{\mathrm{cond}}\approx 2.9\times {10}^{9}\;{\text{erg cm}}^{-2}\;{{\rm{s}}}^{-1}.$ In typical flare conditions, the heat flux is expected to saturate (Battaglia et al. 2009). Campbell (1984) showed that this can be accounted for by a reduction factor that only depends on the electron mean free path and the temperature scale length. In the present case, this factor amounts to $\approx 0.85$ resulting in a reduced conductive flux of $\approx 2.2\times {10}^{9}\;\mathrm{erg}\;{\mathrm{cm}}^{-2}{{\rm{s}}}^{-1}$ as a lower limit. Such a conductive energy input would be sufficient to drive the observed evaporation. Another possibility is electron beams whose signatures are not observed due to RHESSI dynamic range (about 10:1). A source whose intensity at a given energy is less than one tenth of the peak intensity cannot be imaged. Assuming an electron beam with the same low-energy cutoff and spectral index as used above but ten times less flux would result in a total power input reduced by about one order of magnitude, enough to lead to gentle evaporation.

An unambiguous distinction between gentle and explosive evaporation is not possible based on the observation of the velocities at one temperature alone, but could be made via Doppler analysis of, in particular, the O iv line which forms at T ∼ 0.16 MK. For gentle evaporation one would expect to see blueshifts in the O iv line (Brosius & Phillips 2004), while redshifts are expected for explosive evaporation. However, the data from IRIS are inconclusive showing very low velocities (10 km s⁻¹) in the O iv line, as well as mixed up- and downflows at locations where evaporation is seen in Fe xxi. Figure 6 shows a selection of five spectral windows taken by IRIS at 17:46:32 UT (solar X ≈  524 arcsec). The third panel shows the rather broad Fe xxi emission with its rest wavelength 1354.06 Å indicated by the dashed line. The central part (Y ≈  265–270 arcsec) does not show significant Fe xxi velocities, only a small redshift. Northward of Y ≈ 270 and southward of Y ≈ 265 Fe xxi shows a clear blueshift on the order of 0.5 Å, corresponding to ≈110 km s⁻¹. The other spectral lines do not show clear shifts at these locations, rather some line-broadening. However, Si iv, Mg ii, and C ii show prominent downflows just north and south of these locations, which correspond to leading edges of flare ribbons. It is possible that Fe xxi has not formed yet there, which would indicate densities of the order of 10¹⁰ cm⁻³ according to the equilibration time (see Section 4.3). Or, Fe xxi could simply be too faint to be visible at these locations. The flare was also observed by Hinode/EIS and twice (∼17:46:28 UT and ∼17:48:52 UT) the EIS slit was at the same location as the IRIS slit. The line selection was rather sparse and does not provide full temperature coverage. As expected, the upflow velocities in EIS Fe xxiii (12.5 MK) are higher than those seen in Fe xxi in IRIS. However, analysis of the other available data suggests redshifts in Fe xvi (2.8 MK) and potentially in Fe xvii (5.6 MK) at both observed times. It is interesting that there should be down-flows at temperatures much higher than found by Milligan & Dennis (2009). For the time at 17:48:52 UT this would indicate that evaporation is explosive even long after particle acceleration has ceased but no definite statement can be made from the available data.

In summary, for parts of the presented flare, the timing, location, and velocities of the observed signatures of chromospheric evaporation with IRIS and RHESSI can be explained with conductive energy input due to the temperature gradient between the chromosphere and evaporated, 10 MK plasma in the loop, as well as the hot coronal SXR source. It is intriguing however, that upflows are not observed from the same location as the HXR sources where the IRIS slit was co-spatial with the HXR source. On the other hand, the EIS data could be interpreted as showing explosive evaporation even at times when no HXR emission was observed.

Future combined high-spatial resolution flare observations, including lower temperature lines such as O iv and Si iv and in combination with Hinode/EIS, should help shed some light on the matter.