RHESSI/GOES Xray Analysis using Multitemeprature plus Power law Spectra. J.McTiernan (SSL/UCB)

ABSTRACT: We present spectral fits for RHESSI and GOES solar flare data that include both a Differential Emission Measure for the thermal component and a power law fit to the nonthermal component. This is an improvement over the traditional isothermal approximation, but it results in ambiguity in the range where the thermal and nonthermal components may have similar photon fluxes. This "crossover" range can be anywhere from 10 to 30 keV for medium to large solar flares. In this work we will demonstrate the fitting process using simulated data, and then apply it to a small sample of solar flare observations. Our preliminary results indicate that it is extremely diffcult to distinguish between thermal and nonthermal emission in a single spectrum, more so than in the isothermal approximation. This, in turn, creates large uncertainties on the calculation of quantities such as the energy in the thermal plasma, the low energy cutoff of the nonthermal spectrum and the energy in nonthermal electrons. This research is supported by NASA contract NAS

INTRODUCTION: This presentation has two goals: 1) to demonstrate the ability to obtain a differential emission measure (DEM) for solar flares in the temperature range above 3 MK using RHESSI and GOES data, and 2) to use the DEM to help in quantitative estimates for the low-energy cutoff of nonthermal emission. RHESSI and GOES are used because of the availability of the data for a large number of flares. In previous work, we have used this combination of instruments to get reliable DEM estimates for solar active region emission (McTiernan, 2007, in preparation). Solar flare emission is different in that there is often a substantial nonthermal component to the emission, which can extend out to Gamma-ray energies. If this emission is included in a DEM calculation, a large fraction of the DEM piles up at the highest temperature allowed in the calculation. Here we estimate the nonthermal emission from the hard Xray spectrum and allow for the presence of nonthermal emission at lower energy when obtaining the DEM. For this calculation, the nonthermal electron spectrum is modeled by a power law with a low energy break which corresponds to a cutoff in the electron spectrum. The DEM is estimated by an arbitrary N-element power law in temperature. The fitting procedure for the DEM is as follows: First a single power law is fit to the whole temperature range. Next, this range is split into two bands and the fit is done. The reduced χ 2 is calculated. Next the range is split into 3 bands and fit again. If the value of reduced χ 2 decreases, then this fit is retained and a 4 element power law is tried. This process of adding power law components is repeated until a minimum χ 2 is found.

TEMPERATURE RESPONSES: Fig. 1 shows temperature responses for the two GOES channels and selected RHESSI energies. The inclusion of GOES in the calculation helps to obtain the low energy part of the DEM estimate; RHESSI does not have much response to temperatures less than about 10 MK. For an Xray spectrometer, the response is a monotonically increasing function of temperature. This can cause difficulties in DEM calculations. Fig. 1:

TEMPERATURE RESPONSES: Fig. 1 shows temperature responses for the two GOES channels and selected RHESSI energies. GOES is included in the calculation to help to obtain the low energy part of the DEM estimate; RHESSI does not have much response to temperatures less than about 10 MK. For an Xray spectrometer, the response is a monotonically increasing function of temperature. This can cause difficulties in DEM calculations. Fig. 1:

TEST DEM CALCULATIONS: In order to test the method of fitting the DEM, we create a trial DEM function and integrate over the response function. The resulting data is input into the DEM calculation and the output is compared to the initial function. Fig. 2

Some of these tests are shown in Fig. 2. In the figures, the red line is the test DEM, and the black line is the calculated DEM. For these calculations, χ 2 is minimized using an Amoeba function. The error bars are calculated using a Monte Carlo process. The first test, (a), is a sanity check, a simple power law in T. The second test, (b), is a half-gaussian, with a width of 3 MK. The fit is good below about 15 MK, but the error bars get large when the DEM is small. The third test, (c), adds a strong gaussian component at 20 MK. Here the fit is better for the high T part. The fourth test, (d), combines a power law with a narrow spike at 20 MK, for a test of the temperature resolution. From these tests, it looks at if the temperature resolution is a few MK at 20 MK. Test (e) combines the narrow spike with the half-gaussian function. The final test, (f), only has the source at 20 MK. The fitting procedure fits this well, but puts some emission measure at low T (albeit with very large error bars). From the tests we conclude that: 1) Power Laws are easy 2) Gaussians are harder, but fittable. 3) Narrow spikes will have finite width. 4) High T features are fit better.

Fig. 3 USING REAL DATA: Fig.3 is a plot of a typical RHESSI spectrum as seen in a large solar flare. The emission above 50 keV is fit to a power law spectrum. Below 50 keV the emission is assumed to be a sum of thermal and nonthermal components. The nonthermal spectrum is extended down to a cutoff energy; below this the spectral index is set to -1.4, which would be the spectrum for a sharp cutoff in the electron spectrum. The photon counts expected from the nonthermal component are subtracted from the total observed photon counts at low energy and the remainder is fit to a DEM.

Fig jul :30:00 to 00:30:20, X4.8 flare

RESULTS: The top panel of Fig. 4 shows the DEM for an X-flare on 23-jul-2002, for a 20 second interval near the HXR peak time. The bottom panel shows the value of the reduced χ 2 as a function of cutoff energy. This process used a simulated annealing routine to obtain the DEM – the Amoeba program used for the simulations did not work well for real data. The simulated annealing program is more robust. The low energy cutoff for is often not well constrained when the thermal and nonthermal spectra overlap. Using a DEM fit for the thermal spectrum results in a large range of possible cutoff energies, as can be seen from the plot. For low cutoff energies there is no difference in the goodness of fit. Above approximately 37 keV the data is not fit well, and this gives us an upper limit to the cutoff energy. For flares in which the thermal component is not as large, this may not be the case. Fig. 5 shows the same calculation for a flare which occurred on 26-feb This flare had less thermal emission than the 23-jul-2003 flare; it was a C9.6 in GOES class, but had a substantial nonthermal component including gamma- ray emission. For this flare, the DEM plus nonthermal model only fits well between 22 and 26 keV; giving a relatively narrow range of possible cutoff energies. We expect that most flares will lie between the two extremes, resulting in a high uncertainty (10 keV) in the cutoff energy, and a correspondingly large uncertainty (and often only a lower limit) in the energy of nonthermal electrons.

Fig Feb :26:00 to 10:28:00, C9.6 flare

CONCLUSIONS: 1)It is possible to obtain a DEM using RHESSI and GOES data while taking the nonthermal emission into account. 2)It is difficult to constrain the low energy cutoff of the nonthermal component – but an upper limit to that quantity can be obtained. 3)Imaging spectroscopy for spatially distinct thermal and nonthermal sources will help. NOTES: The T responses for the GOES channels were obtained using the results of White, Thomas and Schwartz, (Solar Physics, 227, 231.) The T response for RHESSI was calculated using the SSW program CHIANTI_KEV, which was created using the CHIANTI software package (Young, etal. 2003, Ap.J Supp. 144, 135.) The default values for abundances (coronal) ware used.