Expressions which give the effective color temperatures and corresponding emission measures for solar X-ray events observed with instruments onboard any of the GOES satellites are developed. Theoretical spectra were used to simulate the solar X-ray input at a variety of plasma temperatures. These spectra were folded through the wavelength dependent transfer functions for the two GOES detectors. The resulting detector responses and their ratio as a function of plasma temperature were then fit with simple analytic curves. Over the entire range between 5 and 30 million degrees, these fits reproduce the calculated color temperatures within 2% and the calculated emission measures within 5%. With the theoretical spectra, similar expressions for any pair of broadband X-ray detectors whose sensitivities are limited to wavelengths between 0.2 and 100 A are calculable

Crannell, C. J.

Starr, R.

Thomas, R. J.

English

NASA Technical Reports Server

*S4-33325
NASA
Technical Memorandum 86142
EXPRESSIONS TO DETERMINE
TEMPERATURES AND EMISSION
MEASURES FOR SOLAR X-RAY
EVENTS FROM GOES
MEASUREMENTS
R. J. Thomas, R. Starr, C. J. Crannell
AUGUST 1984
National Aeronautics and
Space Administration
Goddard Space Flight Center
Greenbelt, Maryland 20771
V \
https://ntrs.nasa.gov/search.jsp?R=19840025254 2020-03-20T20:40:00+00:00Z
EXPRESSIONS TO DETERMINE TEMPERATURES AND EMISSION MEASURES FOR
SOLAR X-RAY EVENTS FROM GOES MEASUREMENTS
R. J. Thomas
Laboratory for Astronomy and Solar Physics
NASA Goddard Space Flight Center
Greenbelt, Maryland 20771
R. Starr
Department of Physics
The Catholic University of America
Washington, DC 20064
and
C. J. Crannell
Laboratory for Astronomy and Solar Physics
NASA Goddard Space Flight Center
Greenbelt, Maryland 20771
Research Note
to be submitted to
SOLAR PHYSICS
August 1984
Abstract
We have developed expressions which give the effective color temperatures and
corresponding emission measures for solar X-ray events observed with instruments
onboard any of the GOES satellites. Since 1976, these satellites have been used
to monitor continuously the full-Sun X-ray emission in two broadband wavelength
o ointervals (approximately 0.5-4 A and 1-8 A) with a time resolution of 3 seconds.
To simulate the solar X-ray input at a variety of plasma temperatures, we used
theoretical spectra provided by D. L. McKenzie. These spectra were folded
through the wavelength dependent transfer functions for the two GOES detectors
as given by R. F. Donnelly, R. N. Grubb, and F. C. Cowley. The resulting
detector responses and their ratio as a function of plasma temperature were then
fit with simple analytic curves. Over the entire range between 5 and 30 million
degrees, these fits reproduce the calculated color temperatures within 2% and
the calculated emission measures within 5%. With the theoretical spectra
provided by McKenzie, we can determine similar expressions for any pair of
broadband X-ray detectors whose sensitivities are limited to wavelengths between
0.2 and 100 A.
Since 1976, the solar X-ray flux has been monitored continuously with
instruments on board, a series of Geostationary Operational Environmental Satellites
(GOES). The measurements are reported as the full-Sun X-ray emission in two
o o
broadband wavelength intervals (1/2 to 4 A and 1 to 8 A) with a time resolution of
3 seconds. They are routinely published in the Solar-Geophysical Data Bulletin
(Comprehensive Reports) and are widely available from the National Oceanic and
Atmospheric Administration (NOAA) by request. We have developed expressions which
give the effective color temperatures, T, and corresponding emission measures, EM,
for solar X-ray bursts from these GOES data. Here, the effective color temperature
is defined to be the temperature of an isothermal plasma which would produce the
observed ratio of responses in the two GOES detectors.
The output current, A., of detector i is related to the incident radient
flux, F(EM,T,X), by means of a wavelength dependent transfer function, G.(X), as
follows:
oc
' /*G.(%) 'A. = C. )  F(EM,T,^,) d^, (1)
where C. is a constant near unity. The measured currents are converted into the
reported X-ray flux values, B., according to the expression:
B. = A. / (C. ' G.) , (2)
where G. is the wavelength-averaged transfer function for detector i. Because the
radient flux from an isothermal plasma can be expressed as:
F(EM,T,A) = EM ' f(T,X) , (3)
- 1 -
we can combine Equations (1) through (3) to gives
90
B. = EM ' /*G.(X) ' f(T,X) d X / G. . (4)
If the temperature dependent part of the detector's response is defined as:
QC
.(T) = Tb ) o-CX) * f(TA) d l G. , (5)
o
Equation (4) can be written as:
B. = EM ' b.(T) . (6)
It is clear that, for an isothermal plasma, the ratio R of these detector
responses is independent of EM and is a function only of T, so that:
R(T) = B4 / Bg = b4(T) / bg(T) . (7)
(Here, i = 4 denotes the 1/2 to 4 A GOES detector and i = 8 the 1 to 8 A detector.)
Once the effective color temperature is determined from the ratio of detector
responses, bg(T) can be found and Equation (6) can then be inverted to give the
corresponding emission measure:
EM = Ba / bfl(T) . (8)o o
Values of G. and G.(X) for each of the GOES detectors are shown in Figure 1 as
given by Donnelly et al. (1977), who also describe the satellite instrumentation and
- 2 -
available data base in detail. The isothermal spectra, f(T, X), for plasmas with unit
emission measure were provided by McKenzie (private communication) from a variety of
sources as follows. The continuum and some line fluxes were taken from unpublished
calculations originally done by Walker and used in Walker et al. (1974a) and Walker
et al. (1974b). Satellite-line fluxes also were based on Walker's calculations, but
with scaling factors from Bhalla et al. (1975). Results for Fe XVII lines were from
Walker et al. (1974c), which used analyses of Loulergue and Nussbaumer (1975).
Additional line fluxes were derived from the data of Kato (1976) using formulas from
Tucker and Koren (1971). Finally, ionization equilibrium results were taken from
Jordan (1969) and Jordan (1970). Representative spectra at three different
temperatures are shown in Figure 2.
All of the above results were combined to calculate b.(T) and bg(T) from
fi fiEquation (5) for a number of plasma temperatures between 4 x 10 K and 30 x 10 K.
In addition, the ratio R of these responses as a function of plasma temperature was
also found. To simplify the use of this procedure, analytic fits to our calculations
were determined which can be written as follows:
T(R) = 3.15 + 77.2 R - 164 R2 + 205 R3 , (9)
and:
bg(T) ' 1055 = -3.86 + 1.17 T - 1.31 x 10"2 T2 + 1.78 x 10"4 T3 . (10)
The effective emission measure can then be found directly from these fits by writing
Equation (8) in the following form:
EM = 1055 ' B8 / ( b8(T) ' 1055 ) . (11)
- 3 -
In these expressions, each B. is the reported X-ray flux enhancement above the
_2pre-flare background in units of W m as measured with the appropriate GOES
detector, R is the ratio of the reported flux enhancements from the two detectors as
6 —3defined by Equation (7), T is in units of 10 K, and EM is in units of cm . The
calculated points and our fits to them for T(R) and for bg(T) are shown in Figure 3
and Figure 4, respectively. Over the entire range between 5 and 30 million degrees
(0.025 < R < 0.548), these fits reproduce the calculated color temperatures within 2%
and the calculated response per unit emission measure within 5%. The fits should be
relatively insensitive to details of the theoretical line-flux calculations because
the response of both detectors is dominated by continuum emission, except for the
o
response of the 1 to 8 A detector to plasma radiation at temperatures below
g
10 x 10 K. Even in the latter case, however, the sum of all line emission
contributes no more than 54% to the total, as shown in Figure 5. Therefore, our
results should not be seriously affected by simplifying assumptions such as, for
example, neglecting density sensitive effects in certain satellite lines.
Although these results were derived from parameters for the detectors on the
GOES-1 satellite, they can be applied to measurements from any in the series of GOES
satellites due to the designed similarity and stability of the instrumentation. The
wavelength dependent transfer functions used here are estimated to be accurate within
20% (Donnelly et al., 1977). All other instrumental uncertainties and sources of
error are significantly smaller.
The procedure described above is quite general. With this procedure and the
theoretical spectra provided by McKenzie, we can determine similar expressions for
any pair of broadband X-ray detectors whose sensitivities are limited to wavelengths
between 0.2 and 100 A.
- 4 -
Acknowledgements
This work was supported in part by NASA grant 5066. The authors thank
D. L. McKenzie (Aerospace Corp.) for collating all of the spectral data and for
providing the results to us in machine readable form. The assistance of M. Cleary
and P. Russell in preparing the text of this manuscript is also gratefully
acknowledged.
References
Bhalla C. P., Gabriel, A. H., and Presnyakov, L. P. 1975, Mon. Not. R.
Astr. Soe.f 172, 359.
Donnelly, R. F., Grubb, R. N., and Cowley, F. C. 1977, NOAA Tech. Memo.
ERL SEL-48.
Jordan, C. 1969, Mon. Not. R. Astr. Soe.. 142. 501.
Jordan, C. 1970, Mon. Not. R. Astr. Soc.. 148, 17.
Kato, T. 1976, Ap. J. Supp.. 30, 397.
Loulergue, M. and Nussbaumer, H. 1975, Astr on. and Astrophys., 45_, 125.
Walker, A. B. C., Jr., Rugge, H. R., and Weiss, K. 1974, Ap. J. 188, 423.
Walker, A. B. C., Jr., Rugge, H. R., and Weiss, K. 1974, Ap. J., 192, 169.
Walker, A. B. C., Jr., Rugge, H. R., and Weiss, K. 1974, Ap. JM 194, 471.
- 5 -
Figure Captions
Figure 1: The transfer functions for each of the two GOES detectors with
o o
nominal wavelength ranges of 1/2 to 4 A and 1 to 8 A.
Figure 2: Examples of the theoretical spectra provided by McKenzie for
isothermal plasmas at a variety of temperatures. Emission lines were
o
given an arbitrary width of 0.01 A in these graphs.
Figure 3: Calculated points for the effective plasma temperatures as a
function of detector response ratios, and our analytic fit to them
given by Equation (9).
Figure 4: Calculated points for the response per unit emission measure of
o
the 1 to 8 A GOES detector as a function of temperature of the emitting
plasma. Our analytic fit to these points as given by Equation (10)
is also shown.
Figure 5: The contribution of all line emission to the total response of
each GOES detector as a function of plasma temperature.
- 6 -
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BIBLIOGRAPHIC DATA SHEET
1 . Report No. 2. Government Accession No.
86142
4. Title and Subtitle
EXPRESSIONS TO DETERMINE TEMPERATURES
AND EMISSION MEASURES FOR SOLAR X-RAY
EVENTS FROM GOES MEASUREMENTS
7. Author(s)
R. J. Thomas, R. Starr, C. J. Crannell
9. Performing Organization Name and Address
Solar Physics Branch
Laboratory for Astronomy and Solar Physics
NASA/Goddard Space Flight Center
Greenbelt, Maryland 20771
12. Sponsoring Agency Name and Address
3. Recipient's Catalog No.
5. Report Date
August 1984
6. Performing Organization Code
682
8. Performing Organization Report No.
10. Work Unit No.
1 1 . Contract or Grant No.
13. Type of Report and Period Covered
14. Sponsoring Agency Code
15. Supplementary Notes
16. Abstract
We have developed expressions which give the effective color temperatures and
corresponding emission measures for solar X-ray events observed with instruments
onboard any of the GOES satellites. Since 1976, these satellites have been used
to monitor continuously the fuU-Sun X-rajj, emission in two broadband wavelength
intervals (approximately 0.5-4 A and 1-8 A) with a time resolution of 3 seconds.
To simulate the solar X-ray input at a variety of plasma temperatures, we used
theoretical spectra provided by D. L. McKenzie. These spectra were folded
through the wavelength dependent transfer functions for the two GOES detectors
as given by R. F. Donnelly, R. N. Grubb, and F. C. Cowley. The resulting
detector responses and their ratio as a function of plasma temperature were then
fit with simple analytic curves. Over the entire range between 5 and 30 million
degrees, these fits reproduce the calculated color temperatures within 2% and
the calculated emission measures within 5%. With the theoretical spectra
provided by McKenzie, we can determine similar expressions for any pair of
broadband X-ray detectors whose sensitivities are limited to wavelengths between
0.2 and 100 A.
17. Key Words (Selected by Author(s))
Solar Flares, X Rays, Line Emission
18. Distribution Statement
19. Security Classif. (of this report)
Unclassified
20. Security Classif. (of this page)
Unclassified
21. No. of Pages
7
22. Price*
•For sale by the National Technical Information Service, Springfield, Virginia 221 61 GSFC 25-44 (10/77)


Expressions to determine temperatures and emission measures for solar X-ray events from GOES measurements

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