Three flares observed by the Soft X-Ray Polychromator on the Solar Maximum Mission were studied. Flare light curves from the Flat Crystal Spectrometer and Bent Crystal Spectrometer were examined for rapid signal variations. Each flare was characterized by an initial fast (less than 1 min) burst, observed by the Hard X-Ray Burst Spectrometer (HXRBS), followed by softer gradual X-ray emission lasting several minutes. From an autocorrelation function analysis, evidence was found for quasi-periodic fluctuations with rise and decay times of 10 s in the Ca XIX and Fe XXV light curves. These variations were of small amplitude (less than 20%), often coincided with hard X-ray emissions, and were prominent during the onset of the gradual phase after the initial hard X-ray burst. It is speculated that these fluctuations were caused by repeated energy injections in a coronal loop that had already been heated and filled with dense plasma associated with the initial hard X-ray burst

Saba, J. L. R.

Strong, K. T.

Zarro, D. M.

English

NASA Technical Reports Server

N87-21815
RAPID SOFT X-RAY FLUCTUATIONS IN SOLAR FLARES
OBSERVED WITH THE X-RAY POLYCHROMATOR
D. M. Zarro and J. L. R. Saba
Applied Research Corporation
Landover, MD
K. T. Strong
Lockheed Palo Alto Research Laboratories
Palo Alto, CA
ABSTRACT
We have studied three flares observed by the Soft X-Ray Polychromator on the Solar
Maximum Mission. Flare light curves from the Flat Crystal Spectrometer and Bent Crystal
Spectrometer were examined for rapid signal variations. Each flare was characterized by an
initial fast (<1 min) burst, observed by the Hard X-Ray Buret Spectrometer (HXR), followed
by softer gradual X-ray erni_ion lasting several minutes. From an autocorrelation function
analysis, we have found evidence for quasi-periodic fluctuations with rise and decay times of 10
s in the Ca XIX and Fe XXV light curves. These variations were of small amplitude (<20%),
often coincided with hard X-ray emissions, and were prominent during the onset of the gradual
phase after the initial hard X-ray burst. We speculate that these fluctuations were caused by
repeated energy injections in a coronal loop that had already been heated and filled with dense
plasma associated with the initial hard X-ray burst.
1. INTRODUCTION
Soft X-ray emission from solar flares is usually characterized by timescales ranging from
several minutes to many hours. However, this impression is based on observations by instru-
ments of limited spatial, spectral, and temporal resolution and coverage. In this paper we
use Solar Maximum Mission (SMM) observations to demonstrate the existence of soft X-ray
fluctuations with faster timescales of seconds to minutes.
The X-Ray Polychromator (XRP) on board the SMM is composed of two soft X-ray in-
struments: the Bent Crystal Spectrometer (BCS) and the Flat Crystal Spectrometer (FCS)
(Acton et al. 1980). These instruments are ideal for high time resolution studies since they
have good temporal resolution (0.5-10 s for the BCS and 0.256 s for the FCS), high spectral
resolution (A/6A > 1000), and well-collimated fields of view (6 arcmin FWHM for the BCS and
14 arcsec FWHM for the FCS). Among the various techniques for analysing time series data,
the autocorrelation function (ACF) provides a direct method of extracting the mean timescale
of rapid variations that are superimposed on a slowly varying background (Jenkins and Watts
1908). The following is a brief description of the technique and its application.
Given a sequence of N observations Y(i), the ACF is calculated by the formula:
N_u
ACF(u) = E
i----1
[Y(i)- < Y >][Y(i + u)- < Y >],
289 P'RECEbg iGPAGE NOT
https://ntrs.nasa.gov/search.jsp?R=19870012382 2020-03-20T11:43:31+00:00Z
where u isthe lag time in unitsof the accumulation time and < Y > isthe data mean. For
statisticallysignificantvariationsinthe data, the characteristictimescaleisrelatedto the 1/e
width ofthe ACF (Jenkinsand Watts, 1968).This relationshipisdemonstrated inthe following
simulation.We model a fluctuatingdata stream by a firstorder autoregressiveseriesdefined
by the algorithm:
Y(i) = aY(i - 1)+ bZ + c,
where Z denotesa random noisevariableand r -- -In(a)-1 isthe characteristicfluctuation
timescale.The constantsb and c are chosen such that the mean and varianceof the autore-
gressiveseriesmatch those of the observations.For example, figurela shows an example of
fluctuationswith r = 17.5s,generatedwith a poissonnoiserandom number generator.Figure
lb illustratesthe correspondingACF with a superposed exponentialfitbased on the firsten
points.The timescaleimplied by thisfunctionisapproximately r = 20 s. The errorin this
valuemay be estimatedvia a simpleiterativeprocedure whereby a new autoregressiveseries
isgeneratedbased on the currentr. An autocorrelationfunctionisthen calculatedand a new
r derived.Thisprocedure isrepeated to yielda set oftimescalesfrom which a corresponding
mean and standard deviationcan be assigned. Thus, in the above example, fiveiterations
with differentrandom number seeds gave r : 19.5± 4 s. Note that the autocorrelationwidth
isan approximate measure of the mean temporal width of spike-likenhancements occuring
withinthe data train.Hence, forexample, an autocorrelationwidth of lessthan 20 s would
imply thatthe riseand decay timesofsignificantfluctuationsaretypicallyfasterthan 10 s (i.e.,
rria_ tACt/2). In the followingsectionwe apply thisautocorrelationtechniqueto X-ray light
curvesforthreestrongsolarflaresobserved with SMM.
r-_4
47.5
35.6
823.8
i i i i J
13.45 13.47 13.45 13 ..52 ,3.54 13 56
TIME
I
0.7
0.4
< 0.2
-0.1
-0.4 i
21 42 63 84 105
LAG
Figure la (leftpanel). Lightcurverepresentingan autoregressives rieswith a 17.5s
timescalefluctuationabove a mean backgroundof42 counts.The seriesisgeneratedusing
the algorithmdescribedinthe text.Time axisisinunitsofhours.
Figure Ib (right panel). Autocorrelationfunctionoftheabove lightcurve(normalized
to unityatzerolag).The smooth curverepresentsa fittedexponentialwith 20 s 1//ewidth.
Time-lagaxisisinunitsof3.8s accumulationbins.
290
2. OBSERVATIONS AND ANALYSIS
Flare 1 - GOES class M3 at UT 13:25 on 21 May 1984
This event was studied by Kaufmann et d. (1984), who demonstrated that hard X-ray
structures and intensity fluctuations at 90 Ghz were well-correlated during the burst phase.
Figure 2a indicates that hard X-ray fluctuations persisted with much weaker intensity for several
minutes beyond the initial hard X-ray burst and were evidently correlated with soft X-ray
features in the BCS Fe XXV (1.85 _) and Ca XIX (3.18 A) channels; with typical delays of
less than 10 s.
d
gJ
O3
tr"
w
_L
O3
I--
Z
:::)
0
r,D
Z
I,,M
l--
<l:
nr-
IOO0
I / I I I I I I I I I I I I I
- -
,_ HXRBS 24-440keY,r __=._
20
0
40
0
13:25 13:30 13:35 13:40
UNIVERSAL TIME
Figure 2a. HXRBS (1 s resolution) and BCS (3.8 s resolution) light curves are compared
for flare 1. After the initial hard X-ray burst, there appear to be quasi-periodic fluctuations
in the three light curves. Error bars denote _r variations
Figures 3a-C illustrate the HXRBS and BCS light curves in the period following the initial
hard X-ray burst. The poisson error bars indicate that rapid 2-3 _ level fluctuations are present
within the longer-term variation. Figures 4a-c show the corresponding autocorrelation functions
for the above light curves. The fluctuation timescales implied by the 1/e widths are 14.1, 17.7,
and 14.6 s for the HXRBS, Fe XXV, and Ca XIX light curves, respectively, with associated
errors of 4- 4 s. Hence, to within our measurement errors, the soft and hard X-ray emissions
following the initial burst in flare 1 fluctuate with similar timescales of 15 - 20 s. Equivalently,
the X-ray rise and decay times are typically faster than 10 s.
291
z_
273
91.1
3_ HXRBS
13.45 1347 13.49 1352 13.54 13.54
UTnmu_J
67.1
53?
|
40.3
26|
.u
13._
0
13.45 13.47 13.49 13.52 13.54 13.56
UT Ihound
1
0.?
0.4
<
o.2
-Ol
-0.4
4eIHXRBS
51.8 T04 1_ 207
BIN LAG
- 0._
04
O.2
-0.1
0
el)l Fe XXV
21 42 63 84 I0_
BIN LAG
3c)CJ xtx
70 _ _, 0
_ : .
¢z: 52.5 05
_ 35 0.2
U
17 -007
-03
13.45 1347 1349 1352 13J4 13.N
UT (hound
4_)Ca XtX
20.4 40 8 612 81.6 102
81N LAG
Figure 3a-c (left panel). Post impulsive phase light curves for flare i commencing at UT
13:27 are shown with o poisson error baxs. Intensity is in units of counts per bin resolution.
Figure 4a-c (right panel). Corresponding autocorrelation functions for the above curves
with fitted exponentials.
Flare 2 - GOES class C3/M2 at UT 12:48 on 8 August 1980
Figure 2b illustrates the double event nature of this strong flare, with the second component
(M2) exhibiting rapid fluctuations in the BCS Ca XIX light curve. As in flare 1, these soft
X-ray features corresponded to specific hard X-ray spikes. From an autocorrelation function
analysis of the second event, we inferred a characteristic spike width of 15 + 5 s in both soft
and hard X-rays. Note that this timescale is similar to the mean value obtained in flare 1.
The dynamics of flare 2 was studied by Strong et al. (1984), who found that the evolution of
the second event was influenced significantly by the thermodynamic initial conditions created
292
6000
z
82000
tJ
HXRBS
JJ
z
o
(,3
4OO
3OO
2O0
100
BCS Ca XlX RESONANCE LINE
/J .... | [ -",,,.dI
1248 1250
TIME UT
I
\
I I I
1252 1254
Figure 2b. HXRBS (top panel) and BCS Ca XIX (lower panel) light curves for the double-
event flare 2. Note the prominence of fluctuatiorm in hard and soft X-rays at approximately
UT 12:53.
by the first event. In particular, prior to the first event, coronal plasma was relatively cool
(Te _ 3 x 10 e K) and tenuous (Ne _ 4 x 109cm-S). However, at the onset of the second event,
the temperature and density had both increased (Te _ 5 x 10eK, Ne _ 3 x 101Zcm -s) due
to previously heated chromospheric material being evaporated into the corona. Accordingly,
Strong etal. (1984) suggested that a large fraction of the energy emitted subsequent to the first
event would be absorbed high in the hot dense corona, with only a small proportion reaching
the denser transition region and chromosphere. In view of this circumstance, we speculate that
the rapid soft X-ray fluctuations that characterize the second event are a consequence of local
heating by energy deposition in the upper flaring corona. This model will be examined further
in section 3.
Flare 3- GOES class M3 at UT 01:25 on 20 May 1984
This flare exhibited fast fluctuations in the high-temperature FCS channels during the
rise and decay phase of the soft component. The FCS Fe XXV channel light curve is shown in
figure 2c. We used a I rain running mean of the data to approximate the soft X-ray background
and then subtracted it to produce the residuals shown in the upper curve. Comparison with
293
the HXRBS light curve reveals a close correspondence between features, with FCS fluctuations
being most prominent in the post-impulsive phase. From an autocorrelation analysis of the
Fe XXV residuals, we derived a fluctuation timescale of 12 + 5 s, which is comparable with
timescales determined for the previous two flares.
O3
Z
0
n-
n-
rr
72
48
.,_HXRBS 24-440keY
24 / FCS Fe XXV
0 I I I I I
1.4 1.43 1.46 1.5 1.53 1.56
UT (hours)
Figure 2c. FCS Fe XXV light curve (lower) for flare 3 is plotted at 2 s resolution. The
middle curve shows the hard X-ray counterpart at equivalent resolution. The upper curve
displays the Fe XXV residuals (magnified x 10) obtained after subtraction of a 1 rain running
mean of the FCS light curve. There is good qualitative correspondence between variations
in the residuals and hard X-ray features. Note that the soft X-ray fluctuations became
prominent after the initial hard X-ray burst.
To a first approximation, we can assess the statistical significance of these fluctuations
by computing the deviation of the FCS residuals from the mean soft X-ray background. For
example, figure 5 illustrates the Fe XXV residuals during the the first 1 rain of the gradual rise
phase plotted with constant a lines (# calculated from the square root of the smoothed soft
294
X-ray background). There are two features (A and B) that rise 2 to 3 ¢ above the background.
38.2
27.7
Z
"17.1
D.
¢/)
I--
Z
0 6.5
-4.09
-14.7
1.44
S
#
3
jl
I I I I I I-1
1.445 1.45 1.454 1.459 1.464
UT (hours)
Figure 5. FCS Fe XXV residuals during the first 1 min of flare 3, plotted at 0.256 s
resolution. The curves of constant _r are computed by assuming poisson counting statistics.
Two featur_ (A and B) lie approximately 3_rabove the background.
Further analysis of this flare revealed that the prominence of fast intensity fluctuations
decreased in the cooler-temperature sensitive FCS channels. For example, in figure 6 we com-
pare the Fe XXV (Te _ 2 x 107 K) channel light curve with the less temperature sensitive S
XV (5 x 106 K) and Mg XI (3 x 106 K) channel light curves obtained simultaneously. The
lack of stong fluctuations in the cooler-ion channels is further indication that these fluctuations
are temperature-related phenomena. In particular, Peres etal. (1985) have indicated that the
Fe XXV light curve represents the shape of the heating function, with the Fe XXV emissivity
function being very steep at typical flare temperatures of 15 - 20 x 106 K. Accordingly, sudden
temperature changes produced by heating would be strongly reflected as rapid changes in Fe
XXV intensity. By contrast, the emissivity functions for the lower temperature sensitive ions
such as Mg XI are broader and, thus, less responsive to sudden temperature changes.
3. DISCUSSION
The gradual soft X-ray phase of a flare is the response of the corona to the initial energy
release - presumably characterized by the hard X-ray burst - and the thermalization of the non-
thermal energy components of the flare (Strong et al. 1984). During the flare impulsive stage,
energy is deposited deep down in the transition region and chromosphere. Whether this energy
295
zz
o
u
9O80
7264
5448
3632
1816
0
:_ ,1.42 1. 5 1.48
I z I
1.52 1.55 1.58
UT (hours)
1127 b) S XV iv-'__
A
/ \
451 / "
/
....
1.42 1.45 1.48 1.52 1.55 1.58
UT (hours)
1068
854
641
427
214
0 | I I I m
1.42 1.45 1.48 1.52 1.55 1.58
UT (hours)
Figure 6a-c. FCS light curves of Mg XI, S XV, and Fe XXV, respectively, for flare 3
flareplotted at 4 s resolution. Note the decreasing prominence of fast spikes in the cooler-
temperature sensitive channels.
296
is transported by a particle beam or by a thermal conduction front, chromospheric evaporation
should result. This phenomenon is commonly observed as a high-velocity (V _ 400krns -1)
stream of hot (Te > 10 e K) coronal plasma (Antonucci et al. 1982). The timescale to fill typical
coronal loops of about 109 cm length is of the order of 30 s, which is comparable with the
observed delay time between the hard and soft X-ray maxima.
The observations reported in this paper provide evidence for fast soft X-ray flare fluctua-
tions with timescales that are shorter than expected for simple hydrodynamic processes. For
example, an upward velocity in excess of 1000 km s -1 would be required to evaporate hot,
dense chromospheric material sufficiently fast to produce a 10 s soft X-ray enhancement. Such
a large blueshift was not observed in, for example, the BCS Ca XIX resonance line wing. Con-
sequently, the observed intensity brightenings in soft X-rays are more probably due to local
temperature enhancements that occur in the upper layers of the flaring coronal loop. This is
consistent with our observation that the rapid soft X-ray fluctuations often corresponded with
hard X-ray emissions.
The amplitudes of the soft X-ray fluctuations were typically less than 20_ in the three
flares studied. Based on the theoretical emissivity functions for Ca XIX and Fe XXV, such
intensity changes would require a temperature increase of about 5 x 10e K. A possible driver
for this increase could be magnetic reconnection occuring after the initial hard X-ray burst.
Following each local heating episode, the hot plasma is likely to cool conductively within a
timesoale given by the expression:
rc _ 2 x 10 -10 Ne L _ T_ s/2,
where L denotes the conductive lengthscale (Svestka 1976). Setting Te _ 2 x 107 K for the
enhanced temperature of the soft X-ray emitting plasma (Strong et al. 1984), assuming Ne
1011cm -s as characteristic of the peak coronal electron density (Veck et al. 1984), and adopting
the 10 s soft X-ray decay time as representative of re, we derive L _ 10s cm. Note that this
value is an order of magnitude less than typical loop lengths, indicating that the locally injected
heat energy is conducted quite rapidly into the surrounding cooler medium. This is in contrast
with the energy associated with the initial hard X-ray burst, which is dissipated over much
longer length scales (L _ 109 cm).
4. CONCLUSIONS
We have presented evidence for fast soft X-ray fluctuations during the onset of the gradual
component in three solar flares. These variations occurred in conjunction with similar features
in hard X-rays, although they were not necessarily correlated in intensity. The timescales of
these fluctuations were shorter than the typical hydrodynamic timescales expected for solar
flares.
It is generally accepted that the initial hard X-ray burst in a solar flare is responsible for
heating dense chromospheric material which subsequently evaporates into the corona. It is likely
that in the ensuing soft X-ray gradual phase, secondary heating may occur (e.g., by magnetic
reconnection). Since the coronal density is already enhanced by evaporation (Ne > 1011cm-S),
this energy is absorbed in situ rather than being transported to lower transition region layers.
We have speculated that such secondary heating may be responsible for the observed soft X-ray
intensity spikes. A more detailed study of this mechanism would demand theoretical calculations
that are beyond the scope of this exploratory investigation. However, past numerical simulations
297
of rapid heating of coronal loop plasma predict that, among the many non-equilibrium effects
to arise, burst-like enhancements in soft X-ray flux are indeed likely to be a very common
phenomenon (Shapiro and Moore 1977).
Acknowledgements
This work was performed at the Goddard Space Flight Center and supported by NASA
contract NASS-28713 and the Lockheed Independent Research Programme. We thank Allyn
F. Tennant for helpful discussions on autocorrelation techniques.
REFERENCES
Acton, L. W., et al. 1980, Solar Phys., 65, 53.
Antonucci, E., et al. 1982, Solar Phys., 78, 107.
Jenkins, G.M., and Watts, D.C. 1968, in Spectral Analysis and its Applications, ed. (San
Francisco: Holden-Day).
Kaufmann, P., Correia, E., Costa, J.E.R, Zodi Vaz, A.M., and Dennis, B.R. 1985, Nature, 313,
380.
Peres, G., Serio, S., and PaUavicini, R. 1985, submitted to Astrophys. J.
Shapiro, P.R., and Moore, R.T. 1977, Ap. J., 217, 621.
Strong, K.T., et al. 1984, Solar Phy., 91, 325.
Svestka, Z. 1976, in Solar Flares, ed. (Reideh Dordrecht).
Veck, N.J., Strong, K.T., Jordan, C., Simnett, G.M., Cargill, P.J., and Priest, E.R. 1984,
M.N.R.A.S., 210, 443.
298


Rapid soft X-ray fluctuations in solar flares observed with the X-ray polychromator

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