THE ASTROPHYSICAL JOURNAL,

 501:397-407, 1998 July 1

DETAILED EVIDENCE FOR FLARE-TO-FLARE VARIATIONS OF THE CORONAL CALCIUM ABUNDANCE

J. SYLWESTER
Space Research Centre, Polish Academy of Sciences, ul. Kopernika 11, 51-622, Wroclaw, Poland
J. R. LEMEN
Lockheed Martin Solar and Astrophysics Laboratory, H1-12 B/252, 3251 Hanover Street, Palo Alto, CA 94304; lemen=sag.space.lockheed.com
AND
R. D. A. AND M.-C. BENTLEY, FLUDRA,1 ZOLCINSKI
Mullard Space Science Laboratory, Holmbury Saint Mary, Dorking, Surrey, RH5 6NT, United Kingdom
Received 1997 September 2; accepted 1998 February 9
 

ABSTRACT

 The analysis of X-ray solar flare spectra obtained by the Bent Crystal Spectrometer on board the Solar Maximum Mission satellite is presented. The ratio of the Ca XIX resonance line intensity to the nearby continuum is used to measure the calcium abundance relative to hydrogen (A_Ca). A description of  the spectroscopic method of determining the absolute calcium abundance is given. Possible instrumental and solar effects that might in fluence the abundance estimates are evaluated. Over 5000 spectra from more than 100 flares are analyzed. We find a flare-to-flare variation for that is not correlated with A_Ca flare size, importance, or with several other flare characteristics. For flares observed from two active regions, the observed value of increases as a function of time. The average for all flares is <A_Ca>= (5.77 ± 1.41) x 10^-6. A discussion of investigated correlations of derived values with several flare A_Ca characteristics is presented.

Subject headings : Sun: abundances - Sun: corona - Sun: flares - Sun: X-rays, gamma-rays

1. INTRODUCTION

 The determination of absolute elemental abundances is one of the fundamental problems of astrophysics. The composition of the solar plasma is one of the primary sources of information for the cosmic elemental abundances. Several spectroscopic methods, covering a wide range of the electromagnetic spectrum, are available for determination of solar abundances. At optical wavelengths, photospheric abundances can be determined from the "equivalent widths" of the Fraunhofer absorption lines of neutral, singly, and doubly ionized atoms (Athay 1986). Chromospheric and  low corona abundances may be determined from observations of permitted UV emission lines from various ionization stages  (Pottash 1964; Mariska 1980; Widing & Feldman 1989). Coronal abundances have been derived  from the analyses of the solar X-ray and EUV spectra (Parkinson 1977;  Veck&Parkinson  1981; Feldman 1992) or from optically forbidden emission lines of highly ionized species (Mason 1975; Arnaud 1984). In situ studies using  spacecraft measurements have been made for the elemental composition of the solar wind (Geiss 1982; Geiss& Bochsler 1986) and solar energetic particles (Meyer 1985a, 1985b; McGuire, von Rosevinge, & McDonald  1985; Stone 1989). Spectroscopic X-ray and EUV research over the past 10 years strongly indicates that the elemental abundances in the solar corona differ from photospheric values (Feldman 1992; Meyer 1993). The compositional differences may be  organized in terms of the first ionization potential (FIP). Elements with FIP less than 10 eV were observed to be more abundant in the corona (by up to an order of magnitude), with the abundance varying from time to time and from coronal structure to structure.

 For investigations that are made in the X-ray or EUV, there are several considerations : (1) the line intensities must be accurately determined, (2) the atomic data must be accurately known in order to calculate the synthetic spectra which are fitted to the observations, and (3) the conditions of the emitting solar plasma with regard to various assumptions such as thermal equilibrium must be evaluated. It is relatively easy to accommodate for these considerations in the analysis of X-ray or EUV spectra, contrary to the analysis of spectra from the visible range. In an earlier analysis on a limited set of data from the NASA Solar Maximum Mission (SMM) (Sylwester,  Lemen, &Mewe 1984; Lemen, Sylwester, & Bentley 1986; Fludra et. al.1991),  we were the first to point out the presence of  flare-to-flare variations of A_Ca from spectroscopic studies. More recent analyses of calcium data were done by  Fludra et al. (1993) and Bentley, Slywester, & Lemen (1998), who derived A_Ca using data from the crystal spectrometer on the Japanese Yohkoh satellite, and   Sterling, Doschek, & Feldman (1993), who studied data obtained with the  SOLFLEX instrument on P78-1. In order to obtain absolute abundances, the latter authors normalized their results to the SMM-Bent Crystal Spectrometer continuum observations.

 In this work, observations of the line and continuum obtained with the same spectrometer are analyzed. In this paper, we present a method of determining the absolute calcium abundance relative to hydrogen using the data acquired from flare plasmas observed with the Bent Crystal Spectrometer (BCS) on board SMM. The SMM-BCS was one of two spectrometers constituting the X-Ray Polychromator experiment  (Acton et al. 1980). We  investigate the flare-to-flare variations of the Ca XIX resonance line (w) intensity, ¹S₀-¹P₁ at 3.178 relative to the nearby continuum (Veck & Parkinson et al.  1981; Sylwester et al.1984). The values of A_Ca are determined for 146 flares during the decay phase. Contrary to the case for photospheric abundance studies, coronal abundances are generally not measured relative to hydrogen; only ratios of heavy elemental abundances are normally obtained. The only way to measure the ratio of heavy elemental abundances relative to H is to make use of the line-to-continuum ratio. The Ca XIX w line is a particularly good choice for abundance determinations because the intensity ratio of this line relative to the nearby continuum varies only weakly with temperature ; thus, estimates of abundance may be reliably obtained within the isothermal approximation. The Ca XIX line is very bright in solar flare spectra, and so its intensity can be easily measured. Theoretical calculations are available for the complex of Ca XVIII-XIX  The spectral fitting makes use of a semiempirical determination of the Ca XIX fractional ionization as derived by et Lemen al. (1998).

2. THE BENT CRYSTAL SPECTROMETER

The BCS is one of two X-ray spectrometers that make up the X-Ray Polychromator (XRP) instrument. The SMM-BCS consists of a collimator, eight curved germanium crystals, eight one-dimensional position-sensitive sealed proportional counters, detector amplifiers, and processing and control electronics. The multigrid collimator had a 6' x 6' FWHM triangular response in two directions, parallel and perpendicular to the dispersion axis; the dispersion axis was parallel to the east-west direction on the Sun. The collimator resolution is sufficient to isolate the field of view to an individual active region on the Sun. The observing target was selected by pointing the SMM spacecraft using ground control commands. The SMM-BCS observed the helium-like Ca XVIII-XIX lines near 3.2Ǻ in one channel and various highly ionized A? iron transitions near λ=1.9Ǻ in the other seven channels. A typical calcium flare spectrum is shown in The Figure 1. principal lines are labeled : the resonance line (1s²1S₀-1s2p¹P₁) as w, the intercombination lines as  (1s^{2 1}S₀-1s2p³P_1,2) as y and x, and the forbidden line (1s^{2 1}S₀-1s2p³S₁) as z.

FIG. 1. - Example of a Ca XVIII-XIX spectrum recorded by SMM-BCS from the decay phase of the FLare on 1980 June 29 at 10:48 UT; the integration time was 23 s. The minimum threshold for detection with this spectrometer is T >7 MK, EM>5 x 10⁴⁷ cm^-3. The principal line features are labeled and explained in the text. The thermal continuum is seen at the short wavelength side of the resonance line and longward of the j, z line complex. The insert shows the time history of the count rate integrated over all wavelengths for this flare, and the arrow marks the time of the displayed spectrum.

Besides these main spectral features, numerous blended satellite lines [e.g., k, 1s²2p²P_1/2-1s2p^{2 2}D_3/2; q, 1s²2s²S_1/2-1s2p(¹P)2s ²P_3/2] contribute to the observed spectrum. Low background count rates together with high spectral resolution permit the accurate determination of the line and continuum fluxes. The solar X-rays that enter the SMM-BCS through the multigrid collimator are dispersed by eight curved, germanium crystals (each approximately 15 cm long and 2.5 cm wide) into position-sensitive sealed proportional counters. The Ca XIX channel (channel 1) made use of the Ge 220 crystal plane. Because the crystals are curved, there are no moving parts in the spectrometer, but rather X-rays are dispersed along the position-sensitive proportional counters according to the Bragg diffraction condition :

where 2d is the crystal spacing and λ is the wavelength of the radiation refracted at the angle . Because the crystal is curved, the Bragg condition is satisfied for different wavelengths along the length of the crystal. The position at which a photon is detected in the proportional counter is related to its incident energy.

 This type of spectrometer provides an advantage over spectrometers that scan a flat crystal if the spectra evolve rapidly, as during a solar flare. The SMM-BCS observes at all wavelengths simultaneously, and so there are no uncertainties about spectral evolution during the acquisition of a spectrum as there might be if the crystal is scanned over a range of wavelengths. The SMM-BCS has high sensitivity (effective area=0.024 cm²), and relatively short integration periods, of the order of tens of seconds, are required to obtain statistically acceptable spectra. The Ca XIX channel proportional counter had a 75 µm thick beryllium window and was filled with a mixture of noble gases. The average background level due to energetic particles was low, always less than 0.03 counts per wavelength bin per second, normally less than 1% of the observed continuum. During flight, Fe⁵⁵ X-ray calibration sources were routinely exposed to the SMM-BCS detectors to monitor detector gain, and additional functional tests were carried out on a routine basis to monitor the linearity of the signal processing chain. All standard corrections resulting from the calibration data acquired in orbit have been applied to the SMM-BCS spectra in the course of our analyses.

 In the other SMM-BCS wavelength channels, an enhanced background is observed, contaminating the continuum, especially during the rise phase of flares. This is caused by the fluorescence of the germanium crystals by solar X-rays whose energies exceed the 11.1 keV ionization threshold of germanium (Parmar et al1981). Fortunately, . the calcium spectrometer channel is free from this problem, since the pulse height discrimination of the processing electronics rejected all high-energy, nonsolar flux.

 The SMM-BCS instrument operated during 1980 February-November in the first year of SMM operations and then again for several more years (1984-1989) following the in-orbit repair of the spacecraft.

3. THE LINE-TO-CONTINUUM RATIO

 The spectrum in the vicinity of Ca XIX, He-like X-ray triplet lines (resonance w, intercombination x, y, and forbidden z) includes blends of hundreds of satellite lines in Ca XVIII (see Fig. 1). The upper states of the triplets are largely populated by direct excitation with some contributions from radiative recombination. The satellites are formed by inner shell excitation and dielectronic recombination.

 The photon flux for the calcium resonance emission can be shown to be optically thin for the case of the corona (see §6.2). The flux at the Earth (photon cm^-2 s^-1) in the emission line   can be expressed as (Sylwester, & Mewe 1980b)

where is the distribution of the emission measure over the temperature (differential emission measure) in the source. A_Ca is the abundance (relative to hydrogen) of  calcium. The abundance is assumed to be uniform in the emitting region. The emission functions can be  expressed as

where N_e and N_H are the electron and hydrogen number densities, respectively; Ne/N_H=0.85 is assumed, which is  appropriate for a fully ionized solar plasma. The effective excitation rates are taken from the calculations of Bely-Dubau et al.(1982),  who take into account contributions from higher n satellite transitions. The ionization fraction is given by N_i/N_Ca. We use values for N_CaXIX/N_Ca derived by Lemen et al. (1998)  from semiempirical fits to  SMM-BCS flare spectra.

 The photon flux per unit wavelength interval in the continuum can be expressed as

where the emission function for the continuum has been taken from Mewe et al. (1986), who assume standard cosmic abundances of Allen (1973).Values of the continuum  emission function depend only weakly on the plasma composition (see discussion in §6.4).

 The ratio of the w resonance line flux to the continuum at the wavelength of this line, can be calculated from equations (2) and (4), assuming an isothermal plasma, as

 where is the continuum flux at the wavelength of the Ca XIX w line. The ratios of F_w/F_c are shown as dashed  curves in Figure 2, where the value of A_Ca has been adjusted to fit the observations. One can see from the plot that F_w/F_c varies by about a factor of 3 over the range of typical flare temperatures (8-20 MK). The relatively weak temperature dependence of this ratio means that errors in the temperature estimates of the spectra will introduce only a small uncertainty in the estimates for the calcium abundance. Furthermore, a weak dependence on temperature means that the introduction of an isothermal assumption will result in only a small error for the abundance determination (see § 6.5).

4. OBSERVATIONS

This study includes bright flares that were observed with the SMM-BCS in 1980, the first year of SMM operations, and during 1984-1987, the years following the in-orbit repair of the spacecraft. Flares in 1980 were selected from events whose integrated Ca XIX light curves had maximum count rates at the peak of the flare that were greater than 80 counts s^-1. During the postrepair mission period (1984-1987), flares listed in the XRP Team Final Report (Strong 1988) were selected that had greater than 100 counts s^-1 at flare maximum. This criterion resulted in the identification of more than 250 flares. Some flares were subsequently eliminated because of data gaps.

 The present paper concentrates on flare decay phase data. There are several reasons for this. Generally, most flares as observed in hard and soft X-rays are seen to have a prompt energy release, sometimes accompanied by the acceleration of fast particles. In hard X-rays, the emission often appears to be nonthermal and intensity increases are often impulsive. During the decay phase, there is usually no hard X-ray emission, indicating that flare heating has ceased or is greatly reduced. As a result, the ionization state of the plasma is quasi-stationary (§ 6.3) and plasma densities  are higher, so one may neglect effects of transiently ionizing plasma. An isothermal approximation is also better during the decay phase. The absence of intense hard X-ray emission with energies greater than 11.1 keV lessens the danger of contamination of the thermal continuum from fluorescence of the germanium crystals. The continuum is assumed to be thermal and not a mixture of thermal and nonthermal emission.
As the intrinsic line widths of the considered calcium transitions under low plasma density conditions are very small, the observed line widths are mainly determined by four factors : Doppler broadening, the instrument response function, the physical source size within the BCS field of view, and nonthermal plasma motions. The Doppler broadening is assumed to be Gaussian and is treated as a free parameter during the fitting procedure. The instrument spectral response function is characterized as a Voigt profile with corresponding Gaussian (FWHM-0.527 mǺ) and Lorentzian (FWHM-0.612mǺ) components. The source size is limited by the actual flare size, which is generally much less than the size of the BCS collimator (FWHM=6' x 6'). During the decay phase, the nonthermal widths are small and directed flows are small (Fludra et al.1989), which simplifies the line fitting. The observed line widths during the flare decay are dominated by Doppler broadening convolved with the instrumental response. Broadening due to other effects are less significant, but their possible presence has been accommodated by including an additional symmetric Gaussian component in the fitting process.

From the original set of over 250 flares, 146 flares with good data during the decay phase were fitted to measure the line-to-continuum values. Included in our sample are 28 flares that were analyzed by Lemen et al. (1998)  in order to  determine a semiempirical value for the ionization fraction of More than 5000 spectra were fitted in total. N_CaXIX/N_Ca. Each spectral fit was examined visually, and unsatisfactory cases were eliminated from the analysis.

5. CALCIUM ABUNDANCE RESULTS

The calcium abundance was determined by fitting the theoretical value of the line-to-continuum ratio, to F_w/F_c, the line-to-continuum observed during the decay phases of our set of flares. The value of the resonance line intensity, and the continuum flux at line w are obtained in the F_w, following manner. First, the spectrum is fitted with a complete spectral model, including all line blends and nearby satellites, in order to determine the best value of the electron temperature T and the isothermal emission measure. Under the assumption of an isothermal plasma, the emission measure becomes where is the volume of the emitting plasma. Values of were F_w/F_c computed (eq. [5]) from the fitted T and EM results,  assuming for consistency the same A_Ca that was used in the  fit. By these means, the intensity of F_w  itself can be estimated  without the contribution of the nearby dielectronic satellites. Systematic uncertainties in our derived theoretical values for F_w/F_c will lead at most to 20% errors in the  estimated values of A_Ca  (Lemen et al. 1998). In our synthetic  model, the theoretical spectra were convolved through the SMM-BCS instrument response function. The fitting code fits the resonance line (w) and wavelength region near the dielectronic satellite line (k). Further discussions about the fitting approach are given in  Lemen et al.(1998), Fludra et.al.(1989), and Lemenet et. al.(1984). The results of our fitting program have been compared with  Antonucci et al. (1982), who use the same atomic data and are shown to be in relatively good agreement, except that the temperature values obtained by Antonucci et al. (1982) appear to be  systematically lower by ~1 MK. This is probably caused by the different method of fitting spectra used by Antonucci et al. and their assumption that the thermal continuum is approximated as a constant in wavelength over the limited range of the SMM-BCS calcium spectrometer. In our fitting algorithm, the continuum spectrum is explicitly computed and a least-squares fitting method is used to chose the bestfit parameters. However, the small difference in the estimated temperatures from the two fitting methods is not significant in terms of the present analysis, and the use of the Antonucci et al.'s results would have resulted in substantially the same estimates for the A_Ca. The derived F_w/F_c values are shown for four flares in Figure 2 as data points. The values of F_w/F_c are plotted as a  function of electron temperature T , and thus the time order of the measurements generally proceeds from right to left in the plot. The error bars represent 1 p uncertainties that are derived from the estimates of the goodness of fit by the spectral fitting code. The F_w/F_c curves for the two flares in the upper panel, observed on 1980 June 29 at about 10:44 UT and 1980 November 6 at about 17:28 UT, differ by a factor of about 2, although their shapes as a function of temperature follow a similar trend. From one equation (5), interpretation for this behavior is that the calcium abundance relative to hydrogen is different for the two cases. The values of A_Ca are estimated by fitting the predicted F_w/F_c to the observed  F_w/F_c. The dashed curves are the best-fit values of F_w/F_c, where the value of A_Ca has been allowed to vary. The fits result in A_Ca = (7.30 ± 0.16) x 10^-6 for 1980  June 29 at 10:44 UT and  A_Ca =(3.40 ± 0.09) x 10^-6 the flare on 1980 November 6 at 17:28 UT. The uncertainties in the measurements of the abundances come from the fits of the observed values of F_w/F_c to the theoretical  values. These errors take into account both the uncertainties of temperature and continuum level determinations (see Lemen et al.1998). The lower panel in Figure 2  gives   two more examples of flares with significantly different lineto-continuum values. The upper set of data was also taken from 1980 June 29 but from a flare that occurred later in the day at 18:26 UT, and the lower data set is for the flare that occurred on 1985 January 20 at 20:51 UT. The derived values of A_Ca for these two flares are (8.06 ± 0.17) x 10^-6  and (5.15 ± 0.08) x 10^-6, respectively. Note that the uncertainties in the individual abundance measurements are much smaller than the flare-to-flare variations for these cases.

 In this analysis, it has been assumed that the calcium abundance remains constant during the decay phase of each flare. This assumption appears to be justified by the fact that a comparison of many flares shows that most flares have approximately the same shape of observed F_w/F_c as a  function of temperature (see Lemen et al.1998 for more   details). In some cases, one or more additional heating episodes are observed during the decay phase; these cases are treated as separate flares.

 When comparing flares with widely different abundances, it is possible to visually identify the difference in the spectra. Figure 3 shows two spectra taken from the flares shown in Figure 2, plotted as histograms. The solid curves superposed on the observed spectra are the best-fit synthetic

FIG. 3. - Comparison of two spectra observed for flares with significantly different F_w/F_c ratios. The solid curves superposed on the observed spectra are the best-fit synthetic spectra. The spectral fitting routine adjusts the electron temperature to match the temperature-sensitive intensity ratio of the dielectronic satellite line k to the resonance line w to the observed spectrum. These two spectra have nearly the same fitted electron temperatures and line widths. Note the different values of the w line-to-continuum ratio that are seen for these two spectra. The inset is as in Fig. 1.

spectra. These two spectra were chosen because their fits resulted in nearly the same electron temperatures and line widths. The plot shows the different resonance line-to-continuum ratios for these two flares.

Table 1 summarizes the results for 146 flare decay phases. Included in the table is the NOAA active region number, the location on the solar disk of the flare, and GOES X-ray flare classifications, and number of spectra included in the determination of each abundance estimate. The values of have been multiplied by 10⁶ to facilitate the A_Ca display in the table. The values labeled ±1 σ are the uncertainties that were described above. The times given represent the approximate peak of the flares as observed in the SMM-BCS. The average abundance for all 146 flare decay

FIG. 4. - Distribution of calcium abundance estimates for the studied flares. The width of a histogram bin corresponds approximately to the mean rms uncertainty for an individual abundance estimate. The width of the A_Ca distribution is over 6 times greater than the average uncertainty for  a single abundance estimate and indicates a substantial variation in the calcium composition-by over a factor of 3.5-between flares. A systematic uncertainty of up to 20% may be assigned to the abundance scale. Differently hatched areas correspond to distributions of A_Ca for flares from active regions AR 2779 (at lower values) and AR 4474 (at higher values), phases is (5.77 ± 1.41) x 10^-6. This is greater than the typically quoted photospheric value of A_Ca = (2.6 ± 0.4)  x 10^-6 or the coronal value determined by Veck & Parkin (1981) of A_Ca = (3.2 ± 1.2) x 10^-6 but is similar to the  value of 5 x 10^-6 of Sterling et al. (1993).

 The variation in the values of A_Ca is much larger than the typical errors of the abundance determination, which supports the hypothesis that the SMM-BCS observations demonstrate flare-to-flare variations in the coronal calcium abundance. Figure 4 shows a histogram distribution of the  results organized according to abundance value. The width of each bin is chosen to be approximately equal to the average root mean square (rms) uncertainty for determination of the A_Ca. The differently hatched areas correspond to subsets of flares from two active regions: Active Region 2779 and Active Region 4474. The width of the distribution for entire sample is much larger than the rms error for determining the abundance for a given flare. In case of the flares observed from AR 2779 and AR 4474, the distribution of A_Ca is narrower than for the entire sample and their centroids differ substantially.

6. DISCUSSION

A major result of this analysis is the finding of a systematic flare-to-flare variation in the Ca XIX line-to-continuum ratio during the decay phases of flares, which we interpret as a variation in the coronal calcium abundance. Meyer (1985a, 1985b) pointed out that the abundances of low-FIP elements (less than 10 eV, such as calcium) are larger in the corona compared to the photosphere. As mentioned by Sterling et al.(1993), this suggests that the composition of  the solar corona depends upon some mechanism that is acting on the ionized plasma, although there is no generally accepted mechanism to explain this phenomenon. The present results suggest that the situation is even more complicated and that the mechanism responsible for the variation of A_Ca for different flares is time- and active region-dependent.

 Solar cycle effects were investigated by comparing the average abundances recorded from flares observed in a single active region. Only active regions with four or more flares observed were considered. Table2 shows the average

calcium abundance, A_Ca, for 10 different active regions observed in 1980 and during 1984-1987. The standard deviation to the mean value of A_Ca is labeled as 1 rms. The  number of flares averaged in each active region is given in the last column. These flares represent approximately 70% of our total sample. There does not appear to be a strong dependence on the average of A_Ca with activity cycle.

 The time-dependence of A_Ca for flares observed from an individual active region was examined in detail for the 10 active regions listed in Table 2. The column P₀ gives the probability that a trend is not observed for the flares in a particular region. A trend is not likely to be present in most of the cases except for AR 2779 and possibly AR 4474. For these two cases, a slight increase is seen in the estimated A_Ca as a function of time at the rate of 1.52 x 10^-7 day^-1 and 1.48 x 10^-7 day^-1 for AR 2779 and AR 4474, respectively. Figure 5 illustrates the trend for the abundance to increase  for flares observed from AR 2779.

 Statistical tests were performed to check for signifcant differences in the average A_Ca between different active  regions. Table3 presents the results of a null hypothesis test

FIG. 5. - Values of A_Ca plotted for 36 flares observed from AR 2779 as a function of time. The trend for the abundance to increase with time, for this active region, may be seen. The slope of a fitted line gives d(A_Ca)/dt=1.52 x 10^-7 day^-1.

using a standard statistical analysis. The values represent the probabilities that two active regions are not distinguishable. Thus, low values indicate that the average abundances for the paired active regions are signifcantly different. The table shows that there is a low probability of a chance occurrence of similar values of average A_Ca between the paired active regions in most cases. The active region that has the largest difference from any other is AR 2779, and the flares with the smallest abundance estimates are all from this active region (also see Fig. 4). We note that this longitude was active for the preceding two solar rotations. Also examined was the possibility that the value of A_Ca for an individual flare is correlated with other physical flare characteristics. In particular, the correlation between A_Ca and various flare and active region characteristics were studied :

1. The importance and the GOES soft X-ray classification ;
2. Area of the sunspots in the related active region ;
3. The duration, maximum, and total count rates recorded by the SMM Hard X-Ray Burst Spectrometer et (Dennis al. 1991) ;
4. Position of the flare in latitude and Carrington longitude;
5. Center-to-limb dependence;
6. Time and phase of the solar cycle ;
7. Peak calcium temperature and emission measure;
8. Rise and decay characteristic times for calcium count rates, and calcium temperature and emission measure;
9. Ratio of decay to rise times (asymmetry) for the above mentioned parameters.

In no case was there a significant correlation detected. Figure 6 shows the values of A_Ca plotted against peak GOES   X-ray flux for those flares where the GOES classification is known. The mean value of the entire sample (5.77 x 10^-6) is indicated as well the photospheric value. Large flares have small scatter in values of A_Ca and are closer to the average for the entire sample.
 The differences in the line-to-continuum measurements have been interpreted in this work as evidence for a variation in the absolute calcium abundance on a flare-to-flare basis. Other possible causes for the variation in the observed ratio of F_w/F_c have been explored and are discussed below.

FIG. 6. - Values of A_Ca plotted against peak GOES X-ray flux for those  flares for which the GOES classification is known. The upper horizontal line indicates the mean value of A_Ca of the entire sample of this analysis,  and the lower horizontal line indicates the photospheric value.

6.2. Plasma Opacity

This present analysis is based on the intensity of the bright Ca XIX resonance line under the assumption that the thermal flare plasma is optically thin. If the plasma is not optically thin, then the intensity of the resonance line might be decreased relative to the continuum. The opacity at line center of a Doppler-broadened spectral line is given by (Sylwester et al. 1986b)

where is the oscillator strength for the w resonance line, m and e are the electron mass and charge, respectively, l is the length, R is the ideal gas constant, and µ is the atomic weight of calcium. For average flare conditions, if we assume T  = 15 MK, N_{Ca XIX}/N_Ca = 0.86, A_Ca = 7 x 1 0^-6 and for the other quantities we take N_H/N_e = 0.85,  λ = 3.178 Ǻ = 0.79, and µ = 40.08, then

 A typical flaring loop has a length of 2 x 10⁹ cm and a diameter that is 10 times smaller. Thus, if the line of sight is across the loop (perpendicular to the long axis of the loop), then for a density of N_e = 5 = 10¹¹cm^-3, we have  =  0.024. The longest possible distance is one-half the loop length, which results in = 0.12. This is an extreme case,  since flare loops normally have a temperature distribution with the hottest material at the loop top, and the peak in the Ca XIX emissivity function, _i(T ) (see eq. [3]), around 35 MK. Observations of line w will preferentially be weighted toward the hot material near the loop top. There fore, it can be concluded that opacity effects will be much less than 10%, and thus, this cannot be the reason for the observed variation in the line-to-continuum intensity ratio.

6.3. Nonequilibrium Ionization

 The effects of transient ionization in solar flare plasma have been studied in a number of papers (Mewe & Schrijver 1980;  Sylwester, Mewe & Schrijver1980a;  Meweet. et al.1985). If the plasma is not in thermal equilibrium, it is more difficult to interpret the observed X-ray spectrum. A detailed interpretation requires solving a coupled set of differential equations with time-dependent coefficients that vary with temperature and density. Under certain conditions, this can be simplified. For example, for the time during which a plasma is being heated, the characteristic time for ionization becomes important, whereas when the plasma is cooling, the recombination time should be considered Mewe (1984) considered the ionization and recombination times as a function of temperature. These results are given in Table 4 for Ca XIX.

 The temperature decay times for flares in this study were 5 minutes or more. For densities 10¹¹ cm^-3<N_e<10¹² cm^-3, which are typical for flare plasmas after the maximum (Wolfson et al.1983; Sylwester et al.1986a) is of order 30 s or less, i.e., several times less than observed. Thus, the flare plasma can be considered in quasiequilibrium during flare decay, and transient ionization effects can be considered unimportant for the purposes of this study. Spectra acquired during the flare rise phase were not included in this study.

6.4. Abundance Depletion of All Elements Except Calcium

 The calculated continuum (eq. [4] at 3.178Ǻ depends weakly on the heavy elemental composition of the emitting plasma. The main effect from heavy elements comes from recombination of oxygen, neon, magnesium, and silicon. In order to test the e†ect of abundances on the solar thermal continuum, a computation was made assuming that all elements other than Ca and H had zero abundances. The effect on the computed F_w/F_c intensity ratio was less than 60%,  and this can be ruled out as an explanation for the observed line-to-continuum variations. We can not rule out the possibility that the continuum has been affected by increases in non-Ca elemental abundances, such as helium, but this would not account for the observation of enhanced values of A_Ca relative to photospheric values.

6.5. Multithermal Plasma

Typical flare plasmas are multithermal, with temperature ranges extending to over 25 MK (see, e.g.,  Fludra & Schmelz 1995). The effect of multithermal plasma on the  line-to-continuum analysis has been investigated by assuming the following form for the differential emission measure distribution to be  . for 6 MK< T < 25 MK. The Ca XIX line and continuum fluxes were calculated for this broad differential emission measure distribution. The resulting line fluxes were used to derive temperature and the calcium abundance of the simulated spectrum assuming an isothermal approximation. Checking this result shows that the isothermal approximation introduces an error in the abundance determination that is less than 5%. Furthermore,  Fludra et al.(1991) have  calculated A_Ca for 12 flares from Table 1 using a method of multithermal analysis to obtain calcium abundances. Their results were the same, to within 3%, as those obtained from an isothermal analysis, which addresses the concern raised in Phillips & Feldman  (1991).

7. SUMMARY

 This paper presents final, detailed results of the study of variations in the line-to-continuum ratio in vicinity of the w line of Ca XIX ion using soft X-ray spectra from the BCS aboard the SMM satellite.

 The analysis of thousands of spectra obtained during decay phases of more than 100 stronger flares revealed the presence of systematic differences in the line-to-continuum ratio between flares. This difference has been interpreted in terms of the varying Ca abundance hypothesis. Detailed considerations have ruled out other possible interpretations of the observed flare-to-flare variations of this ratio. The results obtained fully confirm the discovery of variations of coronal plasma composition from spectroscopic measurements (Sylwester et al 1984). This discovery led to what is  now one of the fastest growing areas of interest in solar physics-spectroscopic X-ray and EUV determinations of coronal plasma composition.

 In this paper, absolute (relative to hydrogen) estimates of Ca abundance are given for flares observed during the period 1980È1987 by the BCS on the SMM spacecraft. The following conclusions may be drawn from this study:

1. Average flare calcium abundance (5.77 x 10^-6) is more than twice the photospheric value.
2. Flare-to-flare differences may amount to factor of ~3.5 ; the lowest flare abundance determined corresponds to the photospheric value (2.6 x 10^-6).
3. For most of flares, Ca abundance does not change during decay phase evolution.
4. Observed A_Ca variations do not correlate with any of  the many commonly used flare and/or active region characteristics, except for the time trend seen for AR 2779.
5. For a particular active region, flare calcium abundances are similar ; however, they may differ substantially from the abundances of flares for other active regions-the active region effect is clearly pronounced.

The observed pattern of flare abundance variations does not contradict the FIP-biased mechanism of coronal enrichment. As expected, the absolute abundance of Ca (a low-FIP element) in the corona is higher than in the photosphere. However, the time trend and active region effect of the present results impose substantial new limitations on the theoretical models of physical processes responsible for buildup of differences of the coronal plasma composition.

 Recently, we (Bentley et al. 1998) have performed  analyses of the flares observed with the BCS on the Yohkoh spacecraft. In this study, we considered more than 170 flares and have determined that for this group A_Ca = 3.64  x 10^-6, which is closer to the photospheric value. A comparison of the SMM and Yohkoh data is in progress in order to evaluate the significance of these results.

 The X-Ray Polychromator experiment was a collaborative program between Lockheed Palo Alto Research Laboratory, USA, the Mullard Space Science Laboratory,

UK, and the Rutherford Appleton Laboratory, UK. The authors thank Professor J. L. Culhane for useful discussions. J. S. acknowledges support for a part of this investigation from the British Council. J. R. L. acknowledges support from the Lockheed Martin Independent Research

Program. R. D. B., A. F., and M.-C. Z. acknowledge support from the UK Science and Engineering Research Council and the Particle Physics and Astrophysics Research Council.

REFERENCES

BACK