- Email: [email protected]
Analysis of a coronal loop on the limb
Available
Pergamon
online
at wwwsciencedirectxom
SCIENCE
www.elsevier.com/locate/asr
DIRECT-
doi: lO.l016/SO273-1177(03)00315-6
ANALYSIS
OF A CORONAL
iOOP ON THE LIMB
J.W. Cirtain, P.C.H Martens, H.D. Winter
Montana State University, P.O. Box 173840, Bozeman, MT 59717, USA
ABSTRACT
The ability to accurately meastire the temperature and density of the solar atmosphere is essential to understanding the physical nature of coronal loops. After (datahas been corrected to account for cosmic ray incidents on the CCD ahd instrumental effects,.there are additional sources of error that must also be addressed.We applied a correction to the intensities for spectral lines to account for line of sight effects. Having performed these procedures, the corrected intensities from the Coronal Diagnostic Spectrometer are then used to produce differential emission measure curves with much improved error estimates. 0 2003 COSPAR. Published by Elsevier Ltd. All rights reserved. INTRODUCTION
The measure of the actual intensity for a structure like the coronal loop requires application of a method that first determines the baseline value for intensity. This baseline is necessary because the corona, as ‘seen’ by Coronal Diagnostic Spectrometer (CDS) (H:arrison et al, 1995), has an appreciable emission along the line of sight that is not produced by the loop. This emission, often referred to as the coronal background, inflates the value recorded for intensity and must be subtracted before an analysis of the physical characteristics of the loop can proceed. Having established an accurate vaLluefor the intensity of spectral lines emitted from a coronal loop, the temperature and emission measure value thien obtained will provide insight into the possible heating mechanisms for loops. As loops are one of the dominant features of the corona, this evaluation of temperature and emission measure also provide information about the coronal heating mechanism in general. It is therefore the intention of the authors to implement a diagnostic analysis method that corrects for the coronal background in an effort to determine the best possible DEM curve for a loop. Currently there exists dispute among many noted solar scientists as to the temperature and temperature gradient of coronal loops, see for example Testa et al., 2002, Schmelz et al., 2001 and Aschwanden et al., 2002(b). We believe application of an analysis method that combines data from TRACE and CDS will help resolve these disputes. Consequently, this article presents the first step in our analysis method. Background
CDS on the Solar and Heliospheric Observatory (SoHO) was designed with the primary objective of determining the temperature, density and ion abundances for plasma within the solar atmosphere. CDS observes spectral lines in the Extreme Ultra Violet (EUV) range. This provides a temperature diagnostic capability that ranges from tens of thousands Kelvin to millions Kelvin. There are some complicating factors associated with the use of the Normal Incidence Spectrometer that are worth noting. The profiles for data collected after the 1998 SoHO loss of signal are now somewhat broadened from the Gaussian curves typical before the incident. This is not a serious defect in the data but it must be factored into any careful data analysis.method. Additionally, .thereis no list of Solar calibrated wavelengths for CDS, which requires a baseline determination for each observed spectral line. Also, the corona has a EUV background. As such, there is a background in the CDS data that must be subtracted from the values of intensity used for the structure under scrutiny. Lastly, time is a very important component of the CDS data. As the instrument builds a raster composed Vol. 32, No. 6, pp. 1117-1121,2003 0 2003 COSPAR. Published by Elsevier Ltd. All rights reserved Printed in Great Britain 0273-1177/$30.00 + 0.00
Adv. Space Res.
1118
J. W. Cirtain
et al.
of multiple exposures, an appreciable amount of time passesfrom the initial position of the slit to its final position. The inability of CDS to make an instantaneous measure of the intensity of multiple spectral lines for a region of the corona introduces the probability that the structure under investigation has changed from the start of the raster to its conclusion. The Transition Region and Active Coronal Explorer (TRACE Handy et al, 1999) is a multi-layer imaging telescope. Although not specific to observations in the EUV; it does have three EUV channels. Intrinsic in the design of this imaging device are several instrumental effects. Each channel has an appreciable contribution to its measured flux from several emitting species. The 171A filter, for example, has spectral lines from three ions (0 VI, Fe IX/X and Fe XXIV) within its bandwidth. Each of these ions is formed within a temperature range, and for the three ions mentioned here, the formation temperature ranges do not overlap. Accordingly, as was demonstrated in a recent letter to the Astrophysical Journal (Martens et al, 2002), careful constraints must be used to determine the plasma temperature for a structure in a TRACE image. Winebarger et al, 2002 showed that joint observations of loops with a spectrometer such as CDS or SUMER and the imager TRACE could accurately determine the temperature of the plasma imaged in any of the filters. The filter images can also be used to make an estimate of emission measure, and therefore density, and temporal evolution. OBSERVATIONS A Joint Observation Program (JOP 146) was developed and submitted to the planning teams for TRACE and CDS. The goal was to combine the exceptional spatial and temporal resolution of TRACE with the temperature diagnostic capabilities of the spectrometer. CDS was used to collect intensities for multiple spectral lines, with care taken to select less problematic lines that allowed for the greatest range of temperature coverage. The 171A filter of TRACE was used for the same region. The data for this article was collected on 18 September 2001. CDS observed a loop that was later co-aligned with a loop in the TRACE 171 filter. One of the TRACE images is shown in Figure 1 with the CDS field of view represented by a box in this figure. Analysis The data was calibrated using the standard Solarsoft routines. After the data from CDS were properly corrected for all known instrumental and systematic errors, a cosmic ray detection routine was applied to the data and any pixel found to be within the criteria imposed for a cosmic ray hit was eliminated from the study. Intensities for the thirteen CDS wavelength pass-bands were determined manually for over one hundred CDS pixels using a Gaussian curve fitting routine. The wavelengths used in this study are listed in Table 1. The limb for the CDS data was fitted to within one CDS pixel, and then a value for the background intensity was calculated. In order to determine a value for the background a segment normal to the solar disk was established. The intensities for every spectral line in the pixels along the segment, but not including the loop, were evaluated and used as the background. This method was used on ten different segments to produce the average value for background as a function of distance from the solar surface. Then, the value of this background intensity was subtracted from the loop intensities making certain that the value for background intensity was co-temporal and co-spatial to the each pixel selected along the loop. The corrected intensities were then used to determine the differential emission measure curves. The TRACE data collected during JOP 146 was used to guarantee that the structure analyzed by CDS did not change appreciably during the time to complete one raster. In a future paper, the TRACE data will be calibrated to the spectral line intensities from CDS. Having performed this calibration, the combined data will be used to calculate differential emission measure curves as a function of space and time. In a future work, these curves and the measures of temperature and density will be used to evaluate several models for the heating function of coronal loops. Differential Emission Measure Analysis The calculation of differential emission measure (DEM) curves as described by Schmelz, et al. (2001) is not a straightforward endeavor. Inadequate knowledge of the coronal plasma parameters, such as mean electron density, elemental abundance ratios, and local thermal equilibrium, compound errors made by our incomplete knowledge of the atomic physics governing the complicated electron transitions that release the measured photons. It is due to these limitations that DEM curves of Schmelz et al have a smoothing parameter added to them in order to compensate for our current lack of knowledge. However, this smoothing is often an arbitrary function and over
Analysis
of a Coronal
Loop
on the Limb
1119
smoothing rules out the possibility of finding isothermal plasma even if the observed plasma is isothermal (Aschwanden, 2002). The atomic physics errors in the CHIANTI database may be as high as 25% and this has led researchers to limit the gradient of emission measure with respect to temperature to log 0.3 (Mason, 2002). However, it is felt by this group that if the atomic physics data is not good enough to conclusively prove DEM curves have such a steep gradient then it also cannot disprove DEM curves with such a steep gradient. A DEM curve composed of superimposed Gaussian curves would resolve the apparent dispute between isothermal loops found in narrow band filter analysis, such as TRACE (Aschwanden, 2002) and multi-thermal loops observed in spectral data (Schmelz, et al., 2001). To date our research efforts have focused on modeling DEM curves with Fourier components. The DEM curves are folded through the atomic physics parameters of each observed line as calculated by the CHIANTI database (Dere, 2001). The Fourier colefficients are then iteratively adjusted by a minimization program, such as AMOEBA (Press, 1986) until the best agreement between predicted and intensities is reached. The only smoothing constraint is the number of coefficients used to describe the DEM curve, which is defined as the number of lines observed minus one. The initial DEM curves are calculated using only photon statistics for an estimation of the error. They are then folded through again using an error of 10% for the atomic physics data. The abundances of Meyer (Meyer, 1985) and a mean electron density of 5E+9 were selected using the method of Schmelz and Winter (1999). The results of our DEM analysis are shown in figures 2 and 3. Figure 2 shows the DEM analysis of the data before background subtraction. Figure 3 shows the DEM curve after the background subtraction has been applied to the data. The background subtracted DEM curve is sharply peaked and has a drastically lower reduced chisquare value than the DEM curve without the background subtraction.
CONCLUSIONS Having properly calibrated the data1and corrected the intensities to account for the coronal background, pixels along a coronal loop were selected and the intensities determined. Using these intensities, a DEM curve was calculated. The resulting DEM, as shown in Figure 2, has a much improved error estimate compared to the curve prior to the correction for the background. Additionally, this DEM shape suggeststhat the loop observed in CDS is actually composed of three strands, wi1.h Log (T) 5.15, 6.15 and 6.5 respectively. The authors realize that there exists a family of curves that represent this distribution of intensities and are currently working to analyze the data with this fact in mind. We expect to complete such an analysis in the near future. Table
1. Lines
used in loop analysis
Ion
A
0 III OIV
599.597 554.513
ov
1
FeX
1 345.723
629.732
1120
J. W. Cirtain
et al.
Figure 1. TRACE 171A image taken on September 18, 2001. The box represents the CDS field of view. The image exposure time was 32 seconds. 24 t
(al
x2=2.4X x I O4
i 22-
20-
18
5.5
6.0 Log Temperature
6.5 K
7.0
16 I 5.0
5.5
6.0 Log Temperature
6.5 K
7.0
Figure 2.a Fig. 2. Log differential emission measure in units of cm -5 K-’ plotted against log temperature. shows the DEM curve computed without the application of background subtraction. The reduced chisquare value was calculated from the photon statistics plus 10 percent of the line intensity as an estimate of atomic physics errors. The curve is similar to the broad DEMs found by Schmelz et al. (2001). Figure 2.b shows the DEM curve computed after background subtraction with much reduced chi-squared fit.
Analysis of a Coronal Loop on the Limb
1121
REFERENCES Aschwanden, M. J., The differential emission measure distribution in the multi-loop corona, Astrophysical Journal Letters, 580, pp. L79-L83,2002. Aschwanden, M., C.J. Scbrijver, Analytical Approximations to Hydrostatic Solutions and Scaling Laws of Coronal Loops, Astrophysical Journal Supplement Series, 142, pp. 269-283., 2002(b). Dere, K. P., E. Landi, P. R.Young, et al., CHIANTI-An atomic database for emission lines. IV. Extension to x-ray wavelengths, Astrophysical Journal! Supplement Series, 134, pp. 33 l-354,2001. Handy, B. N., L. W. Acton, C. C. Kankelborg, et al., The Transition Region and Coronal Explorer, Sotar Physics, 187, pp. 229-260, 1999. Harrison, R. A., E. C. Sawyer, M. K. Carter, et al., The Coronal Diagnostic Spectrometer for the Solar and Heliospheric Observatory, Solar Physics, 162, pp. 233-290, 1995. Martens, P. C. H., J. W. Cirtain, J. T. Schmelz, The inadequacy of temperature measurements in the solar corona through narrowband filter and line ratios, Astrophysical Journal Letters, 577, pp. L115-L117,2002. Mason, H., Private communication, 20021. Myers, J.P., Solar-stellar outer atmospheres and energetic particles, and galactic cosmic rays, Astrophysical Journal Supplement Series, 57, pp. 173-204, 1985. Press,'W. M., Numerical Recipes in C, Cambridge Univ. Press,New York, New York, USA, 1986. Schmelz, J.T. and H.D. Winter, Estimating electron densities of coronal plasma using forward-folding, 8th SOHO Workshop: Plasma Dynamics and Diagnostics in the Solar Transition Region and Corona, Edited by J-C. Vial and B. Kaldeich-Schumann, ESA Special Publications No. 446 p.593, 1999. Schmelz, J. T., R. T. Scopes, J. W. Qrtain, et al., Observational constraints on coronal heating models using Coronal Diagnostics Spectrometer and Soft X-Ray Telescope data, Astrophysical Journal, 556, pp. 896-904, 2001. Testa, P., G. Peres, F. Reale, S. Orlando, Temperature and Density Structure of Hot and Cool Loops Derived from the Analysis of TRACE Data, Astrophysical Journal, 580, pp. 1159-l 171,2002. Winebarger, A. R., H. Warren, A. van Ballegooijen, et al., Steady flows detected in Extreme-Ultraviolet loops, Astrophysical Journal, 557, L 89,2002. E-mail address of J.W. Cirtain [email protected] Manus#cript received 6 December 2002; revised 6 January 2003; accepted 7 March 2003.
Pergamon
online
at wwwsciencedirectxom
SCIENCE
www.elsevier.com/locate/asr
DIRECT-
doi: lO.l016/SO273-1177(03)00315-6
ANALYSIS
OF A CORONAL
iOOP ON THE LIMB
J.W. Cirtain, P.C.H Martens, H.D. Winter
Montana State University, P.O. Box 173840, Bozeman, MT 59717, USA
ABSTRACT
The ability to accurately meastire the temperature and density of the solar atmosphere is essential to understanding the physical nature of coronal loops. After (datahas been corrected to account for cosmic ray incidents on the CCD ahd instrumental effects,.there are additional sources of error that must also be addressed.We applied a correction to the intensities for spectral lines to account for line of sight effects. Having performed these procedures, the corrected intensities from the Coronal Diagnostic Spectrometer are then used to produce differential emission measure curves with much improved error estimates. 0 2003 COSPAR. Published by Elsevier Ltd. All rights reserved. INTRODUCTION
The measure of the actual intensity for a structure like the coronal loop requires application of a method that first determines the baseline value for intensity. This baseline is necessary because the corona, as ‘seen’ by Coronal Diagnostic Spectrometer (CDS) (H:arrison et al, 1995), has an appreciable emission along the line of sight that is not produced by the loop. This emission, often referred to as the coronal background, inflates the value recorded for intensity and must be subtracted before an analysis of the physical characteristics of the loop can proceed. Having established an accurate vaLluefor the intensity of spectral lines emitted from a coronal loop, the temperature and emission measure value thien obtained will provide insight into the possible heating mechanisms for loops. As loops are one of the dominant features of the corona, this evaluation of temperature and emission measure also provide information about the coronal heating mechanism in general. It is therefore the intention of the authors to implement a diagnostic analysis method that corrects for the coronal background in an effort to determine the best possible DEM curve for a loop. Currently there exists dispute among many noted solar scientists as to the temperature and temperature gradient of coronal loops, see for example Testa et al., 2002, Schmelz et al., 2001 and Aschwanden et al., 2002(b). We believe application of an analysis method that combines data from TRACE and CDS will help resolve these disputes. Consequently, this article presents the first step in our analysis method. Background
CDS on the Solar and Heliospheric Observatory (SoHO) was designed with the primary objective of determining the temperature, density and ion abundances for plasma within the solar atmosphere. CDS observes spectral lines in the Extreme Ultra Violet (EUV) range. This provides a temperature diagnostic capability that ranges from tens of thousands Kelvin to millions Kelvin. There are some complicating factors associated with the use of the Normal Incidence Spectrometer that are worth noting. The profiles for data collected after the 1998 SoHO loss of signal are now somewhat broadened from the Gaussian curves typical before the incident. This is not a serious defect in the data but it must be factored into any careful data analysis.method. Additionally, .thereis no list of Solar calibrated wavelengths for CDS, which requires a baseline determination for each observed spectral line. Also, the corona has a EUV background. As such, there is a background in the CDS data that must be subtracted from the values of intensity used for the structure under scrutiny. Lastly, time is a very important component of the CDS data. As the instrument builds a raster composed Vol. 32, No. 6, pp. 1117-1121,2003 0 2003 COSPAR. Published by Elsevier Ltd. All rights reserved Printed in Great Britain 0273-1177/$30.00 + 0.00
Adv. Space Res.
1118
J. W. Cirtain
et al.
of multiple exposures, an appreciable amount of time passesfrom the initial position of the slit to its final position. The inability of CDS to make an instantaneous measure of the intensity of multiple spectral lines for a region of the corona introduces the probability that the structure under investigation has changed from the start of the raster to its conclusion. The Transition Region and Active Coronal Explorer (TRACE Handy et al, 1999) is a multi-layer imaging telescope. Although not specific to observations in the EUV; it does have three EUV channels. Intrinsic in the design of this imaging device are several instrumental effects. Each channel has an appreciable contribution to its measured flux from several emitting species. The 171A filter, for example, has spectral lines from three ions (0 VI, Fe IX/X and Fe XXIV) within its bandwidth. Each of these ions is formed within a temperature range, and for the three ions mentioned here, the formation temperature ranges do not overlap. Accordingly, as was demonstrated in a recent letter to the Astrophysical Journal (Martens et al, 2002), careful constraints must be used to determine the plasma temperature for a structure in a TRACE image. Winebarger et al, 2002 showed that joint observations of loops with a spectrometer such as CDS or SUMER and the imager TRACE could accurately determine the temperature of the plasma imaged in any of the filters. The filter images can also be used to make an estimate of emission measure, and therefore density, and temporal evolution. OBSERVATIONS A Joint Observation Program (JOP 146) was developed and submitted to the planning teams for TRACE and CDS. The goal was to combine the exceptional spatial and temporal resolution of TRACE with the temperature diagnostic capabilities of the spectrometer. CDS was used to collect intensities for multiple spectral lines, with care taken to select less problematic lines that allowed for the greatest range of temperature coverage. The 171A filter of TRACE was used for the same region. The data for this article was collected on 18 September 2001. CDS observed a loop that was later co-aligned with a loop in the TRACE 171 filter. One of the TRACE images is shown in Figure 1 with the CDS field of view represented by a box in this figure. Analysis The data was calibrated using the standard Solarsoft routines. After the data from CDS were properly corrected for all known instrumental and systematic errors, a cosmic ray detection routine was applied to the data and any pixel found to be within the criteria imposed for a cosmic ray hit was eliminated from the study. Intensities for the thirteen CDS wavelength pass-bands were determined manually for over one hundred CDS pixels using a Gaussian curve fitting routine. The wavelengths used in this study are listed in Table 1. The limb for the CDS data was fitted to within one CDS pixel, and then a value for the background intensity was calculated. In order to determine a value for the background a segment normal to the solar disk was established. The intensities for every spectral line in the pixels along the segment, but not including the loop, were evaluated and used as the background. This method was used on ten different segments to produce the average value for background as a function of distance from the solar surface. Then, the value of this background intensity was subtracted from the loop intensities making certain that the value for background intensity was co-temporal and co-spatial to the each pixel selected along the loop. The corrected intensities were then used to determine the differential emission measure curves. The TRACE data collected during JOP 146 was used to guarantee that the structure analyzed by CDS did not change appreciably during the time to complete one raster. In a future paper, the TRACE data will be calibrated to the spectral line intensities from CDS. Having performed this calibration, the combined data will be used to calculate differential emission measure curves as a function of space and time. In a future work, these curves and the measures of temperature and density will be used to evaluate several models for the heating function of coronal loops. Differential Emission Measure Analysis The calculation of differential emission measure (DEM) curves as described by Schmelz, et al. (2001) is not a straightforward endeavor. Inadequate knowledge of the coronal plasma parameters, such as mean electron density, elemental abundance ratios, and local thermal equilibrium, compound errors made by our incomplete knowledge of the atomic physics governing the complicated electron transitions that release the measured photons. It is due to these limitations that DEM curves of Schmelz et al have a smoothing parameter added to them in order to compensate for our current lack of knowledge. However, this smoothing is often an arbitrary function and over
Analysis
of a Coronal
Loop
on the Limb
1119
smoothing rules out the possibility of finding isothermal plasma even if the observed plasma is isothermal (Aschwanden, 2002). The atomic physics errors in the CHIANTI database may be as high as 25% and this has led researchers to limit the gradient of emission measure with respect to temperature to log 0.3 (Mason, 2002). However, it is felt by this group that if the atomic physics data is not good enough to conclusively prove DEM curves have such a steep gradient then it also cannot disprove DEM curves with such a steep gradient. A DEM curve composed of superimposed Gaussian curves would resolve the apparent dispute between isothermal loops found in narrow band filter analysis, such as TRACE (Aschwanden, 2002) and multi-thermal loops observed in spectral data (Schmelz, et al., 2001). To date our research efforts have focused on modeling DEM curves with Fourier components. The DEM curves are folded through the atomic physics parameters of each observed line as calculated by the CHIANTI database (Dere, 2001). The Fourier colefficients are then iteratively adjusted by a minimization program, such as AMOEBA (Press, 1986) until the best agreement between predicted and intensities is reached. The only smoothing constraint is the number of coefficients used to describe the DEM curve, which is defined as the number of lines observed minus one. The initial DEM curves are calculated using only photon statistics for an estimation of the error. They are then folded through again using an error of 10% for the atomic physics data. The abundances of Meyer (Meyer, 1985) and a mean electron density of 5E+9 were selected using the method of Schmelz and Winter (1999). The results of our DEM analysis are shown in figures 2 and 3. Figure 2 shows the DEM analysis of the data before background subtraction. Figure 3 shows the DEM curve after the background subtraction has been applied to the data. The background subtracted DEM curve is sharply peaked and has a drastically lower reduced chisquare value than the DEM curve without the background subtraction.
CONCLUSIONS Having properly calibrated the data1and corrected the intensities to account for the coronal background, pixels along a coronal loop were selected and the intensities determined. Using these intensities, a DEM curve was calculated. The resulting DEM, as shown in Figure 2, has a much improved error estimate compared to the curve prior to the correction for the background. Additionally, this DEM shape suggeststhat the loop observed in CDS is actually composed of three strands, wi1.h Log (T) 5.15, 6.15 and 6.5 respectively. The authors realize that there exists a family of curves that represent this distribution of intensities and are currently working to analyze the data with this fact in mind. We expect to complete such an analysis in the near future. Table
1. Lines
used in loop analysis
Ion
A
0 III OIV
599.597 554.513
ov
1
FeX
1 345.723
629.732
1120
J. W. Cirtain
et al.
Figure 1. TRACE 171A image taken on September 18, 2001. The box represents the CDS field of view. The image exposure time was 32 seconds. 24 t
(al
x2=2.4X x I O4
i 22-
20-
18
5.5
6.0 Log Temperature
6.5 K
7.0
16 I 5.0
5.5
6.0 Log Temperature
6.5 K
7.0
Figure 2.a Fig. 2. Log differential emission measure in units of cm -5 K-’ plotted against log temperature. shows the DEM curve computed without the application of background subtraction. The reduced chisquare value was calculated from the photon statistics plus 10 percent of the line intensity as an estimate of atomic physics errors. The curve is similar to the broad DEMs found by Schmelz et al. (2001). Figure 2.b shows the DEM curve computed after background subtraction with much reduced chi-squared fit.
Analysis of a Coronal Loop on the Limb
1121
REFERENCES Aschwanden, M. J., The differential emission measure distribution in the multi-loop corona, Astrophysical Journal Letters, 580, pp. L79-L83,2002. Aschwanden, M., C.J. Scbrijver, Analytical Approximations to Hydrostatic Solutions and Scaling Laws of Coronal Loops, Astrophysical Journal Supplement Series, 142, pp. 269-283., 2002(b). Dere, K. P., E. Landi, P. R.Young, et al., CHIANTI-An atomic database for emission lines. IV. Extension to x-ray wavelengths, Astrophysical Journal! Supplement Series, 134, pp. 33 l-354,2001. Handy, B. N., L. W. Acton, C. C. Kankelborg, et al., The Transition Region and Coronal Explorer, Sotar Physics, 187, pp. 229-260, 1999. Harrison, R. A., E. C. Sawyer, M. K. Carter, et al., The Coronal Diagnostic Spectrometer for the Solar and Heliospheric Observatory, Solar Physics, 162, pp. 233-290, 1995. Martens, P. C. H., J. W. Cirtain, J. T. Schmelz, The inadequacy of temperature measurements in the solar corona through narrowband filter and line ratios, Astrophysical Journal Letters, 577, pp. L115-L117,2002. Mason, H., Private communication, 20021. Myers, J.P., Solar-stellar outer atmospheres and energetic particles, and galactic cosmic rays, Astrophysical Journal Supplement Series, 57, pp. 173-204, 1985. Press,'W. M., Numerical Recipes in C, Cambridge Univ. Press,New York, New York, USA, 1986. Schmelz, J.T. and H.D. Winter, Estimating electron densities of coronal plasma using forward-folding, 8th SOHO Workshop: Plasma Dynamics and Diagnostics in the Solar Transition Region and Corona, Edited by J-C. Vial and B. Kaldeich-Schumann, ESA Special Publications No. 446 p.593, 1999. Schmelz, J. T., R. T. Scopes, J. W. Qrtain, et al., Observational constraints on coronal heating models using Coronal Diagnostics Spectrometer and Soft X-Ray Telescope data, Astrophysical Journal, 556, pp. 896-904, 2001. Testa, P., G. Peres, F. Reale, S. Orlando, Temperature and Density Structure of Hot and Cool Loops Derived from the Analysis of TRACE Data, Astrophysical Journal, 580, pp. 1159-l 171,2002. Winebarger, A. R., H. Warren, A. van Ballegooijen, et al., Steady flows detected in Extreme-Ultraviolet loops, Astrophysical Journal, 557, L 89,2002. E-mail address of J.W. Cirtain [email protected] Manus#cript received 6 December 2002; revised 6 January 2003; accepted 7 March 2003.