The Astrophysical Journal, 572:L109–L112, 2002 June 10
䉷 2002. The American Astronomical Society. All rights reserved. Printed in U.S.A.

SIMULTANEOUS OBSERVATION OF A MORETON WAVE ON 1997 NOVEMBER 3 IN Ha AND SOFT X-RAYS
N. Narukage,1 H. S. Hudson,2 T. Morimoto,1 S. Akiyama,1,3 R. Kitai,1 H. Kurokawa,1 and K. Shibata1
Received 2002 February 16; accepted 2002 May 6; published 2002 May 20

ABSTRACTWe report the observation of a Moreton wave in Ha (line center and Ⳳ0.8 Å) with the Flare Monitoring Telescopeat the Hida Observatory of Kyoto University at 4:36–4:41 UT on 1997 November 3. The same region (NOAA
Active Region 8100) was simultaneously observed in soft X-rays with the soft X-ray telescope on board Yohkoh,
and a wavelike disturbance (“X-ray wave”) was also found. The position of the wave front as well as the directionof propagation of the X-ray wave roughly agree with those of the Moreton wave. The propagation speeds of theMoreton wave and the X-ray wave are about 490 Ⳳ 40 and 630 Ⳳ 100 km s⫺1, respectively. Assuming that the
X-ray wave is an MHD fast-mode shock, we can estimate the propagation speed of the shock, on the basis of MHD
shock theory and the observed soft X-ray intensities ahead of and behind the X-ray wave front. The estimated fastshock speed is 400–760 km s⫺1, which is in rough agreement with the observed propagation speed of the X-ray
wave. The fast-mode Mach number of the X-ray wave is also estimated to be about 1.15–1.25. These results suggestthat the X-ray wave is a weak MHD fast-mode shock propagating through the corona and hence is the coronalcounterpart of the Moreton wave.
Subject headings: shock waves — Sun: chromosphere — Sun: corona — Sun: flares — Sun: magnetic fields
1. INTRODUCTION

2. OBSERVATIONS

Moreton waves are flare-associated waves observed to propagate across the solar disk in Ha, especially in the wing of Ha(Moreton 1960; Smith & Harvey 1971). They propagate at
speeds of 500–1500 km s⫺1 with arclike fronts in somewhat
restricted angles and are often associated with type II radio bursts(Kai 1969) and coronal EIT waves (Thompson et al. 2000; Klassen et al. 2000; Warmuth et al. 2001). The Moreton wave has
been identified as the intersection of a coronal MHD fast-mode
weak shock wave and the chromosphere (Uchida 1968, 1970;
Uchida, Altschuler, & Newkirk 1973). However, the generation
mechanism of a Moreton wave has not been made clear yet.
Recently, the soft X-ray telescope (SXT) on board Yohkoh
discovered wavelike disturbances in the solar corona associatedwith flares (Khan & Hudson 2000), which we call “X-ray
waves” in this Letter. The first simultaneous observation of aMoreton wave and an X-ray wave was reported by Khan &Aurass (2002). In this Letter, we report a second example.
Interestingly, our event and the Khan-Aurass event were observed on the same day (1997 November 3) in the same region(NOAA Active Region 8100) but at different times (04:32 and
09:04, respectively). The next day, another Moreton wave occurred in this region (Eto et al. 2002).
The purpose of this Letter is to examine the basic questionof whether the X-ray wave is the coronal counterpart of theMoreton wave, i.e., a coronal MHD fast-mode shock, basedon MHD shock theory and Yohkoh/SXT soft X-ray images.
The result shows that the observed properties of the X-ray wave
are consistent with the wave interpreted as a coronal MHD
fast-mode weak shock.
In § 2, the instrumentation and observing methods are summarized. In § 3, the results of the analysis of the Moreton wave
and the X-ray wave are described. In § 4, a summary and a
discussion are given.

In this Letter, we study two kinds of flare-associated waves:the chromospheric Moreton wave and coronal X-ray wave associated with a C-class flare in NOAA AR 8100 at S20⬚, W13⬚
on 1997 November 3. The flare started at 04:32 UT and peaked
at 04:38 (GOES times).
The Moreton wave was observed in Ha (line center andⳲ0.8 Å) with the Flare Monitoring Telescope (FMT; Kurokawa et al. 1995) at the Hida Observatory of Kyoto University.
The FMT observes four full-disk images (in the Ha line centerand Ⳳ0.8 Å and continuum) and one solar limb image (in the
Ha line center). We use the full-disk images in Ha ⫹0.8 Å,
because a Moreton wave front is best seen in the red wing of
the Ha line (Ha ⫹0.8 Å). This is because the mass motion at
the wave front is downward when the front enters the chromosphere. The time resolution of the images used in this Letteris 1 minute, although the FMT operates at a higher time resolution. The pixel size is 4⬙. 2.
The X-ray wave was observed in soft X-rays with Yohkoh/
SXT (Tsuneta et al. 1991). The SXT is sensitive to soft X-ray
photons in the energy range ∼0.28–4 keV, which corresponds
to wavelengths ∼3–45 Å. In this Letter, we use partial frame
images observed with the AlMg filter. The observing time cadence is about 50 s. The pixel sizes of the half- and quarterresolution images are 4⬙. 91 and 9⬙. 82, respectively.
The magnetic field of the photosphere was observed with
the Michelson Doppler Imager (MDI; Scherrer et al. 1995) on
board the Solar and Heliospheric Observatory (SOHO). The
time resolution and pixel sizes are about 90 minutes and 2⬙,
respectively.
3. RESULTS

Figure 1 shows the observed images on 1997 November 3
of NOAA AR 8100. Figures 1a–1f are “running difference”
images (where each image has the previous image subtracted
from it) observed in Ha ⫹0.8 Å. The running difference
method clearly shows the motion of the Moreton wave. Figures 1g–1j are the direct soft X-ray images (middle panels) andrunning difference images (bottom panels). In Figure 1k, the1
Kwasan and Hida Observatories, Kyoto University, Yamashina, Kyoto
607-8471, Japan; naru@kwasan.kyoto-u.ac.jp.
2
Solar Physics Research Corporation, Sagamihara, Kanagawa 229-8510,
Japan.
3
Present address: Naval Research Laboratory, 4555 Overlook Avenue, SW,
Washington, DC 20375-5320.

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Fig. 1.—Observed images on 1997 November 3 at NOAA AR 8100. (a–f) Ha ⫹0.8 Å running difference images of a Moreton wave (black arrows). (g–j) Soft
X-ray (middle panels) and running difference (bottom panels) images of an X-ray wave (white arrows) taken with the AlMg filter. The images inside and outside
the boxes are half-resolution (4⬙. 91) and quarter-resolution (9⬙. 82) images, respectively. (k) Wave fronts of the Moreton wave at every minute from 04:36:01 to
04:41:01 UT (black lines) and the X-ray wave at 04:35:26, 04:36:14, 04:37:00, and 04:37:48 UT (white lines) overlaid on the photospheric magnetic field observed
at 04:51:04. Gray lines show the great circles through the flare site (gray arrow). The rectangle, circle, and lines shown in (l) are the field of view of (a)–(k), the limbof the Sun, and the great circles, respectively.

apparent positions of the wave fronts are overlaid on the longitudinal magnetogram from MDI. Using the running difference images, the Moreton wave (black lines) can be identified
visually from 04:36:01 to 04:41:01 UT, and the X-ray wave
(white lines) from 04:35:26 to 04:37:48 UT. Both propagate
roughly in the same direction and agree approximately in location. The field of view is illustrated by the box in Figure 1l.
In Figure 2, the distances of the wave fronts from the flaresite along the great circles are plotted. We assume the brightest
region is the flare site. The propagation speeds of the Moreton
wave and the X-ray wave are roughly constant at 490 Ⳳ 40 and
630 Ⳳ 100 km s⫺1, respectively, using the scatter of points fromthe four great circles as a measure. In fact, the Moreton wave
seems to be somewhat decelerating. The positions refer to theleading edge of the wave front rather than to the peak.

X-ray wave is a fast shock, we can estimate its propagation
speed, based on MHD shock theory and the observed soft Xray intensities ahead of and behind the X-ray wave front. If
this estimated speed of the shock is consistent with the observed
propagation speed of the X-ray wave, we can conclude that
the X-ray wave is a fast shock.

4. DISCUSSION

In the model of Uchida (1968, 1970; Uchida et al. 1973), aMoreton wave is the sweeping skirt on the chromosphere of a
weak MHD fast-mode shock that propagates in the corona.
This model thus also explains the meter-wave type II radio
burst as a signature of the coronal propagation and predicts theexistence of a coronal counterpart of the chromospheric Moreton wave. In fact, in our event, the position of the wave front
as well as the direction of propagation of the X-ray wave
roughly agree with those of the Moreton wave (Fig. 1k).
Let us now examine whether the X-ray wave is an MHD
fast-mode shock (hereafter simply called a fast shock), i.e., thecoronal counterpart of the Moreton wave. Assuming that theFig. 2.—Propagation of the Moreton wave (filled circles) and the X-ray wave
(open circles). First-degree polynomial fits of the Moreton wave (solid line) andthe X-ray wave (dashed line) are shown. The propagation speeds of the Moreton
wave and the X-ray wave are 490 Ⳳ 40 and 630 Ⳳ 100 km s⫺1, respectively.
The dotted line shows the soft X-ray flux observed by the GOES 9 satellite.

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NARUKAGE ET AL.

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The jump condition of MHD shock theory (Priest 1982), for
X{

r2
,
r1

(1)

gives
1
2
( v21 ⫺ XvA1
) 2{Xc 2s1 ⫹ v21 cos 2 v1[X(g ⫺ 1) ⫺ (g ⫹ 1)]}2⫹

1 2 2 2v v sin v1 X
2 A1 1

2# {[g ⫹ X(2 ⫺ g)] v21 ⫺ XvA1[(g ⫹ 1) ⫺ X(g ⫺ 1)]} p 0,

(2)

v 2x
p X ⫺1,
v1x

(3)

2
v 2y
v2 ⫺ vA1
p 21
2 ,v1y v1 ⫺ XvA1

(4)

p2
(g ⫺ 1)Xv12
v22
pX⫹
1
⫺
,
p1
2c 2s1
v12

(5)

T2
p /p
p /p
p 2 1p 2 1.
T1
r 2 /r1
X

(6)

( )

Here the quantities ahead of the shock are denoted by 1 andthose behind by 2, in a frame of reference moving withthe shock. In equation (2), vA1 is the Alfvén velocity[pB1 /(m 0 r1 )1/2], c s1 the sound speed, given as (g p1 /r1 )1/2 p
˜ 1/2, where m˜ is the mean atomic weight (taken as 0.6 in(gRT1 /m)this Letter; Priest 1982), g the ratio of specific heats (p5/3 inthis Letter), and v1 the inclination of the upstream magnetic field
to the shock normal (the x-axis). The y-axis is taken to be perpendicular to the shock normal, such that the magnetic field andvelocity vectors are in the x-y plane. There are three solutions
for v1 from equation (2), among which the largest corresponds
to the fast-mode shock. In the limit of v1 r 90⬚, the shock becomes perpendicular. Using these six equations, the quantities
ahead of the shock (r1, T1, B1, v1, v1) determine those behind(r 2, T2, B2, v2, v 2).
In the simplest approximation, the soft X-ray intensity is
proportional to the square of the plasma density and an
instrument-specific function of the temperature,
IX p n 2lf (T ) ∝ r 2 f (T ),(7)

where IX is the soft X-ray intensity, n is the plasma number
density, l is the line-of-sight plasma scale, and f (T ) represents
the plasma emissivity and the filter response (Tsuneta et al. 1991).
Hence, the above can be rewritten such that (IX1, T1, B1, v1, v1)
determine (IX2, T2, B2, v2, v 2). In other words, if we know (IX1,
T1, B1, v1, IX2), we can find (v1, T2, B2, v2, v 2). (See the Appendix
and Fig. 3 for a different approach.) The physical parameters
ahead of the shock (i.e., in region 1), such as temperature (T1)

Fig. 3.—Estimated perpendicular (solid lines) and oblique (dashed lines)
shock speeds. B1 and Bp1 are the coronal and photospheric magnetic fieldstrengths, respectively. The dot-dashed and dotted lines show the observed
propagation speeds of the X-ray wave (630 km s⫺1) and the error bar (Ⳳ100
km s⫺1), respectively.

and density (r1) are obtained from the preflare images and thefilter ratio method (Tsuneta et al. 1991). The coronal magnetic
field strength (B1) is derived from the MDI images.
We have four images of the X-ray wave (Figs. 1g–1j), butthree of them are inappropriate for analysis. The wave front in
Figure 1g is too near the flare site and too greatly influenced byscattered light from the flare. The intensities of the wave fronts
in Figures 1i and 1j are too low, so we cannot distinguish thereal signal from noise. We analyze a single image, Figure 1h,observed at 04:36:14.
We measure IX1 and IX2 and obtain IX2 /IX1 p 3.27, where theintensities of the X-ray wave are measured in the area encircled
by a dashed line in Figure 1h. The value of T1 is calculated using
preflare full-frame images taken with the thin Al and AlMg filtersof SXT as T1 p 2.25 Ⳳ 0.25 MK. Substituting this T1 into the
SXT response function gives the emission measure. We calculate
the density (r1) assuming that the line-of-sight distance (l) of theobserved region is the coronal pressure scale height [(1.00–
1.26) # 10 5 km for 2.00–2.50 MK]. The photospheric magnetic
field strength (Bp1) was observed by MDI, and we assume thatthe coronal magnetic field strength (B1) is one-third or one-halfof Bp1. This assumption is justified from a different approach
discussed in the Appendix and Figure 3. When v1 p 90⬚, theshock is perpendicular, and v1 p 60⬚ corresponds to an oblique
shock. Using equations (1)–(7), these observational properties
give the propagation speed of the shock (vsh p v1x p v1 cos v1)
as shown in Table 1.
The estimated fast-shock speed, 400–760 km s⫺1, is in roughagreement with the observed propagation speed of the X-ray
wave, 630 Ⳳ 100 km s⫺1. The fast-mode Mach number of the
X-ray wave is consistent with values in the range of 1.15–1.25.
These results suggest that the X-ray wave is a fast shock propagating through the corona and hence is the coronal counterpartof the Moreton wave.
From Figure 1k, we see that the position of the wave front
as well as the direction of propagation of the X-ray wave
roughly agree with those of the Moreton wave, although theexact positions and speeds are different. We think these differences may be explained by the three-dimensional distribution of the Alfvén speed. We will study the three-dimensional

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MORETON WAVE IN Ha AND SOFT X-RAYS
TABLE 1
Estimated Fast-Shock Speed vsh
B1/Bp1 p 1/3aParameter
B1 (G) . . . . . . . . . . . .
T1 (MK) . . . . . . . . . .
EM1b (cm⫺5) . . . . . .
n1 (cm⫺3) . . . . . . . . .
vA1 (km s⫺1) . . . . . .
cs1 (km s⫺1) . . . . . . .

2.66
2.00
1027.3
108.7
274
215

T2 (MK) . . . . . . . . . .
X ..................
vsh (km s⫺1) . . . . . . .
Mfc . . . . . . . . . . . . . . . .

2.33
1.25
410
1.18

T2 (MK) . . . . . . . . . .
X ..................
vsh (km s⫺1) . . . . . . .
Mf . . . . . . . . . . . . . . . . .

2.33
1.24
397
1.14

2.66
2.25
1027.0
108.5
328
228

2.66
2.50
1026.9
108.4
369
240

B1/Bp1 p 1/2
3.99
2.00
1027.3
108.7
411
215

3.99
2.25
1027.0
108.5
492
228

3.99
2.50
1026.9
108.4
553
240

2.34
1.24
546
1.18

2.77
1.31
668
1.23

3.19
1.35
761
1.26

2.34
1.24
533
1.15

2.78
1.30
653
1.20

3.20
1.34
745
1.24

v1 p 90⬚
2.75
1.32
493
1.23

3.16
1.36
559
1.27

v1 p 60⬚
2.75
1.32
478
1.20

3.16
1.36
542
1.23

Note.—v1 p 90⬚ means perpendicular shock, and v1 p 60⬚ oblique.
Bp1 is the photospheric magnetic field strength.
b
EM1 p n21l, where l is the line-of-sight length, which is assumed
equal to the pressure scale height of the corona.
c
Mf is fast-mode Mach number.
astructure of the propagation of the coronal shock with more
observed data and will simulate the flare-associated coronal
wave in our future work.
From the above analysis, we can estimate the coronal plasma
velocity just behind the Moreton wave (fast-mode MHD
shock), v1 ⫺ v 2, to be about 100–200 km s⫺1, which would beobserved at 50–100 km s⫺1 along the line of sight with the
SOHO/Coronal Diagnostics Spectrometer or the Solar-B/EUV
Imaging Spectrometer.
Our result, Mf p 1.15–1.25, indicates that the propagation
speed of the Moreton wave is comparable to the MHD fast-

Vol. 572

mode speed and consistent with Uchida’s model of a weak
MHD fast-mode shock. On the other hand, Wang (2000)
showed that the propagation speed of an EIT wave is comparable to the coronal MHD fast-mode speed and suggested
that the Moreton wave may be associated with a highly superAlfvénic shock. This seems inconsistent with our result. But
if we assume that the Alfvén (and the fast-mode) velocity is
increasing with height in the low corona (Mann et al. 1999),
and that X-ray waves and EIT waves are propagating at two
different heights, Wang’s suggestion may not be in contradiction to our results.
The fitting lines for the Moreton wave and X-ray wave in
Figure 2 suggest that the start time of these waves may besomewhat earlier than the flare. This is curious since Moreton
waves usually occur with flares. It may be explained by thedeceleration of the Moreton wave as seen in Figure 2. This isin accordance with the results of Warmuth et al. (2001) and
implies that the initial velocities of the Moreton wave andprobably also the X-ray wave were actually higher than themean values we found; i.e., the shock may be stronger in theearly phase.
Finally, we note that an EIT wave and a type II radio burst
were also observed simultaneously with this Moreton wave.
The relationship between the EIT wave and the Moreton wave
will be studied in our future paper (N. Narukage et al. 2002,
in preparation).
The authors thank S. Eto, H. Isobe, A. Asai, H. Kozu, T. T.
Ishii, and M. Kadota for useful discussions. The Yohkoh satellite is a Japanese national project, launched and operated by
ISAS, and involving many domestic institutions, with multilateral international collaboration with the US and the UK.
SOHO is a mission of international cooperation between theEuropean Space Agency and NASA. This work was supported
in part by the JSPS Japan-US Cooperation Science Program(principal investigators: K. Shibata and K. I. Nishikawa).

APPENDIX

In this Letter, we estimated the fast-shock speed (vsh p v1x p v1 cos v1 ) by assuming the coronal magnetic field strength, B1 p
( 13 or 12 )Bp1, and found that vsh is comparable to the observed X-ray wave speed, confirming that the X-ray wave is an MHD fastmode shock. However, we can take a different approach; it is possible to estimate the coronal magnetic field strength, if we use theobserved X-ray wave propagation speed and the MHD shock theory (eqs. [1]–[7]), since (IX1 , T1 , v1 , v1 , IX2) determines (B1, T2, B2,
v2, v 2). Figure 3 shows the estimated fast shock speed as a function of B1 /Bp1 on the basis of equations (1)–(7). From this figure andthe observed propagation speed of the X-ray wave, 630 Ⳳ 100 km s⫺1, we can estimate B1 /Bp1 to be 0.3–0.7. This value seems to
be consistent with the calculated coronal magnetic field strength using source-surface field extrapolations (e.g., Dere 1996; Wang
2000). Hence, this approach also confirms that the X-ray wave is an MHD fast-mode shock.
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