The Neupert Effect as a Function of Temperature

Before reading this, It's a good idea to go over jimm's last poster , on SXT and BCS differential emission measures for solar flares, presented at the June, 97 SPD meeting. This is a continuation of that work, and will be presented as another poster at the Fall, 97 AGU meeting in San Fransisco.

Given the Soft X-ray DEM , we would like to see how the solar flare plasma relates to the hard X-ray burst as a function of temperature. It is well-known that soft X-ray time derivative is similar to the hard X-ray (or microwave) light curve. This is thought of as evidence for "chromosphseric evaporation"; i.e., the idea that the soft X-ray emission comes from a plasma that is heated by the nonthermal electrons which are responsible for the hard X-rays. The nonthermal electrons lose most of their energy via Coulomb collisions in the chromosphere. The temperature rises and a high pressure region forms which drives material both upward and downward ("chromospheric evaporation and condensation"). The coronal temperature and density increase as the evaporated material rises, resulting in soft X-rays. The hard X-ray light curves are proportional to the time profile of the input electrons. The soft X-rays, which come from the plasma heated by the nonthermal electrons, are proportional to the accumulated energy of the electrons up to a given time. The soft X-ray emission is thus proportional to the time integration of the profile of the input electrons, and the time derivative of the soft X-ray profile will look like the hard X-ray time profile. This is known as "derivativity" or the "Neupert Effect".

In a study of large flares observed by HXRBS, B. Dennis and D. Zarro (1993, Solar Physics, 146, 177) found that 80% of the flares showed good correlations between hard X-ray peaks and peaks in the time derivatives of the soft X-rays. They noted that gradual hard X-ray flares were less likely to show correlations. Here we will use a less restrictive definition of the Neupert effect: Instead of requiring that the peaks in the soft X-ray time derivative be correlated with the hard X-ray peaks, we simply require that the time derivative of the soft X-ray energy be positive during the hard X-ray burst.

Sometimes it works

The question here is: How does the Neupert effect manifest itself at different temperatures?

The answer is: It's different for different flares; not too surprising. Figure 1 shows typical behavior for some flares, in particular those flares that have a distinct high temperature hump in the DEM . The top plot is of the energy in the SXR plasma for the flare of 13-Jan-1992. The white dashed line shows the total energy, the red line shows the energy in high temperature plasma (T > 18 MK), the blue line shows the energy in low temperature plasma (3 MK < T < 18 MK). Note that for the energy calculation, we've assumed that the volume and filling factor are the same for all temperatures. ("Filling Factor": how much of a given volume actually has hot plasma in it.)

Figure 1. Top--The thermal energy (actually the square root of the integral over dT of T² times the DEM) as a function of time for the 13-Jan-1992 flare, total (white dashed lines), high-T (red line), low-T (Blue line). Dash-dot vertical lines indicate the peaks for the different components. Bottom--The time derivatives of the energy for each component (same colors), plotted along with the hard X-ray time profile as seen in the HXT-M2 and HI channels (arbitrarily scaled, green line), covering the energy range above 33 keV.

The bottom plot shows the time derivatives for each component, compared with the 30 keV hard X-ray time profile as seen by the HXT. The color scheme is the same, and as you can see, the total energy and high-T component look similar to the HXR burst. The high-T derivative peaks before the HXR's and goes to zero at the end of the HXR burst, consistent with the Neupert effect. The total energy derivative is positive until 2 minutes after the HXR burst. This implies that there is another heating source along with nonthermal electrons. The low-T component behaves a bit differently. Its derivative has a small peak at the same time as the HXR peak, but it remains positive for 5 minutes after the HXR burst. This late increase in low-T plasma is due to cooling of the high temperature plasma, not heating, since the total energy is decreasing by this time.

How do we interpret this in terms of chromospheric evaporation? Here's my try at it: The electrons pump up plasma to high (> 18 MK) temperature. Some of the HXR electron energy goes into low-T plasma. At the same time, there's a more gradual heating mechanism, unrelated to the hard X-rays, that is slowly heating low-T plasma; this extra heating lasts until 2 minutes after the HXR burst.

You can see the effect of how the DEM varies with time in the SXT and BCS data. The top plot of Figure 2 shows the data from the Al.1 (white) and Be119 (blue) filters of SXT, and the FeXXV channel of BCS (red). The bottom plot shows the time derivatives of the data, along with the HXT data. For this case, the curves have been arbitrarily scaled. The FeXXV channel is only sensitive to high T plasma, and its derivative closely follows the hard X-ray time profile. (You can find plots of the temperature responses in the SPD 97 poster .) The Be119 filter is sensitive to low and high T plasma; its derivative has a peak with the HXR burst, and remains positive long after the HXR burst. The Al.1 filter is sensitive to high and low T plasma, but is much more sensitive to low T plasma than the Be119 filter. Its derivative has a peak with the HXR burst, but also has a peak long after the HXR burst. Al.1 brightness increases (i.e., has a positive derivative) until 17:37 UT. The late increase in Al.1 counts isn't due to extra heating, however; the total energy decreases after 17:32 UT. Instead, it's due to cooling of the high T plasma, and the corresponding increase in low T plasma. The plasma moves into the temperature range where the Al.1 filter is more sensitive, and the Al.1 brightness increases, even though the total energy in the plasma is decreasing.

Figure 2. Top--SXT-Al.1 brightness (dashed white line), Be119 brightness (blue line), and BCS-FeXXV brightness (red line), for the 13-Jan-1992 flare, scaled arbitrarily. Dash-dot vertical lines indicate the peaks for the different curves. Bottom--The time derivatives for each curve, along with the HXT-M1 data (green line).

The lesson here is that you need to look at the DEM before you can discuss whether there is extended heating. If, for example, you only look at SXT Al.1 data, you may decide that heating lasts for a long time after the HXR burst. If you only look at the BCS FeXXV data, you decide that the heating ends with the HXR burst. In reality, the answer is somewhere in between.

Sometimes it doesn't

Figure 3. Top--The thermal energy (actually the square root of the integral over dT of T² times the DEM) as a function of time for the 19-Feb-1992 flare, total (white dashed lines), high-T (red line), low-T (Blue line). Dash-dot vertical lines indicate the peaks for the different components. Bottom--The time derivatives of the energy for each component (same colors), plotted along with the hard X-ray time profile as seen in the HXT-M2 and HI channesl (arbitrarily scaled, green line), covering the energy range above 33 keV.

Here, none of the derivatives look like the HXR time profile, and they all remain positive after the HXR emission is gone. The derivative of the high-T component and the total energy peak about 1 minute after the HXR peak, just after the end of the HXR burst. The low-T component derivative has a smaller peak at this point, and a higher peak later in the flare. The behavior of the low and high-T components relative to each other is similar to the 13-Jan-1992 flare, but their relation to the HXR time profile is different. Odd.

Figure 4 shows the time profile for all of the HXT channels for the 19-feb-1992 flare. From this we can see that there is a gradual hard X-ray component seen in the two low energy channels. Gradual HXR bursts such as the one in the 19-feb-1992 flare are typically assumed to be thermal for two reasons: (1) It's gradual, like the thermal soft X-ray flare, and (2) there's an extremely soft spectrum; no emission above 33 keV, and temperature measurements made using the HXT alone give values of about 20-30 MK (A "superhot" component). If the gradual HXRs are due to thermal emission, then there's no way that this flare is consistent with the Neupert effect.

Figure 4. HXT data, all four channels, for the 19-feb-1992 flare.

Of course, the gradual HXR burst doesn't have to be thermal. If it's nonthermal, then you could say that this flare is consistent with the Neupert effect. I personally wouldn't bet on it.

Conclusions

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16-Oct-1997, jmm