The Astrophysical Journal, 832:59 (7pp), 2016 November 20 doi:10.3847/0004-637X/832/1/59
© 2016. The American Astronomical Society. All rights reserved.
CONSTRAINING THE SOLAR CORONAL MAGNETIC FIELD STRENGTH USING
SPLIT-BAND TYPE II RADIO BURST OBSERVATIONS
P. Kishore1, R. Ramesh1, K. Hariharan1, C. Kathiravan1, and N. Gopalswamy2
1 Indian Institute of Astrophysics, 2nd Block, Koramangala, Bangalore—560034, India; kishore@iiap.res.in
2 Code 671, Solar Physics Laboratory, NASA/GSFC, Greenbelt, MD 20771 USA
Received 2016 April 13; revised 2016 September 14; accepted 2016 September 16; published 2016 November 17
ABSTRACT
We report on low-frequency radio (85–35MHz) spectral observations of four different type II radio bursts, which
exhibited fundamental-harmonic emission and split-band structure. Each of the bursts was found to be closely
associated with a whitelight coronal mass ejection (CME) close to the Sun. We estimated the coronal magnetic
field strength from the split-band characteristics of the bursts, by assuming a model for the coronal electron density
distribution. The choice of the model was constrained, based on the following criteria: (1) when the radio burst is
observed simultaneously in the upper and lower bands of the fundamental component, the location of the plasma
level corresponding to the frequency of the burst in the lower band should be consistent with the deprojected
location of the leading edge (LE) of the associated CME; (2) the drift speed of the type II bursts derived from such
a model should agree closely with the deprojected speed of the LE of the corresponding CMEs. With the above
conditions, we find that: (1) the estimated field strengths are unique to each type II burst, and (2) the radial variation
of the field strength in the different events indicate a pattern. It is steepest for the case where the heliocentric
distance range over which the associated burst is observed is closest to the Sun, and vice versa.
Key words: solar–terrestrial relations – Sun: activity – Sun: corona – Sun: coronal mass ejections (CMEs) –
Sun: magnetic fields – Sun: radio radiation
1. INTRODUCTION (Schatten et al. 1969; Schrijver & Derosa 2003). Although
Type II radio bursts from the Sun are caused by Langmuir estimates of coronal magnetic field strength (B(r)) from
waves generated by nonthermal electrons in magnetohydro- observations in infrared, microwave, and EUV wavelength
dynamic (MHD) shocks propagating outward in the solar bands (Lin et al. 2000; Lee 2007; West et al. 2011) are
atmosphere. The characteristics and description of the solar possible, they are limited mostly to the “inner” corona
type II bursts can be found in the review by Nelson & Melrose (r1.2Re). But phenomena like the acceleration of energetic
(1985). The bursts are observed as narrow-band emission particles by coronal mass ejection (CME) driven shocks,
features drifting from higher to lower frequencies in spectral acceleration of fast solar wind, etc., occur typically in the
observations. They occur frequently as two relatively slow “middle” corona, i.e., 1.2 R  r  3.0 R (Gopalswamy
drifting emission bands (fundamental (F ) and harmonic (H)) et al. 2012b; Mancuso & Garzelli 2013). There are estimates of
with a frequency ratio of ≈1:2. The frequency drift (typically B(r) in the above heliocentric distance range from the spectral
∼0.1 MHz s−1, see Mann et al. 1996; Gopalswamy et al. 2009) observations of split-band type II solar radio bursts (Smerd
results from the decrease of the coronal electron density (N ) et al. 1974, 1975; Vršnak et al. 2002; Cho et al. 2007; Zimovetse
and hence the plasma frequency, with increasing distance (r) et al. 2012; Mancuso & Garzelli 2013; Hariharan et al. 2014,
from the Sun. The observed drift rate can be converted into the 2015; Vasant et al. 2014). But the locations of the bursts at
speed of the associated MHD shock if the N (r) is known. At different frequencies, and hence the B at the correspondinge
times, type II bursts exhibit split-band structure: either or both values of r, were derived without referring to the deprojected
the F and H components of the burst are split into two sub- height-time details of the associated shock driver. Considering
bands (the upper band U and the lower band L) with a that there is close spatio-temporal association between the
separation in frequency, which is usually small compared to the type II bursts and the CMEs (Stewart et al. 1974a, 1974b;
frequency separation between the F and H components Gopalswamy & Kundu 1992; Mancuso & Raymond 2004;
themselves. The L and U bands in a split-band type II burst Gopalswamy et al. 2005, 2009; Lin et al. 2006; Cho et al. 2008,
are considered to be due to emission generated ahead of and 2013; Liu et al. 2009; Ramesh et al. 2010, 2012; Ma
behind the associated MHD shock front, i.e., at the upstream et al. 2011; Hariharan et al. 2014, 2015; Kouloumvakos et al.
and downstream regions or the pre-shock and post-shock 2014), we have attempted to derive B(r) by constraining the
regions or the “undisturbed” and “disturbed” corona, respec- choice of Ne(r) and consequently the locations of the bursts
tively (Tidman et al. 1966; Vršnak et al. 2001; Hariharan based on the observed parameters of the type II bursts and the
et al. 2014). accompanying CMEs together. There is considerable evidence
It was first shown by Smerd et al. (1974, 1975) that type II for this method, because the starting frequency of the type II
solar radio bursts that exhibit split-band structure can be used to bursts has a power-law relationship with the leading edge (LE)
determine the magnetic field strength (B(r)) along the paths of of the associated CMEs, as was shown by Gopalswamy et al.
the propagating MHD shocks. Note that magnetic field strength (2013). Note that the most important requirement for the
is routinely measured only in the photosphere at present. The estimation of B(r) from a type II burst, which exhibits a band-
magnetic field strength of the “undisturbed” corona is obtained splitting phenomenon is the identification of the appropriate
from such measurements using extrapolation techniques Ne(r) model, which can satisfactorily explain the observed
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The Astrophysical Journal, 832:59 (7pp), 2016 November 20 Kishore et al.
Figure 1. Dynamic spectrum (85–35 MHz) of the type II radio burst from the solar corona obtained with the GLOSS on 2013 November 8 during 04:27–04:42 UT.
The F and H components of the type II burst with band splitting (in the F component) are clearly noticeable. The labels FL and FU represent the lower and upper bands
in the F component of the type II burst. The white horizontal line close to 35 MHz is due to local radio frequency interference (RFI).
characteristics of the burst since B(r) is more sensitive to it (see (SOHO) for information on the associated CMEs. For flare
for example Cho et al. 2007). information, we used soft X-ray data obtained with the
Geostationary Operational Environmental Satellite (GOES).
2. OBSERVATIONS Figure 1 shows the dynamic spectrum of a typical split-band
type II burst observed with the GLOSS on 2013 November 8
The radio spectral data were obtained during the period 2013 during the interval 04:27–04:42 UT in the frequency range
October–2014 February with the Gauribidanur LOw frequency
3 85–35MHz. The splitting of the F component into lower (L)Solar Spectrograph (GLOSS) in the Gauribidanur observatory , and upper (U) bands, i.e., FL and F , can be clearly seen. In thelocated about 100 km north of Bangalore in India (Ramesh UH component, only the HL band could be seen. The HU band is2011). It is a total power instrument operating in the frequency close to the detection limit of GLOSS and hence, unnoticeable
range 85–35MHz. The primary receiving element used is a
( in the dynamic spectrum (see Figure 2). The onset times of thelog-periodic dipole antenna LPDA, Ebenezer et al. 2001,
2007; Kishore et al. 2014). The primary receiving element used FL and FU bands at a typical frequency such as 80MHz are
is a log-periodic dipole antenna (LPDA, Carrel 1961). Eight ≈04:28 UT and ≈04:30 UT, respectively. They are last
such LPDAs, arranged in the north–south direction with a observed at ≈40MHz at ≈04:34 UT and ≈04:35 UT,
spacing of ≈5 m between the adjacent antennae, have been respectively. The duration of the FL, FU, HL and HU bands
combined in a branched feeder system to generate a single estimated from their temporal profile at 80MHz are tfl: tfu ≈ 1:2
output (see for example Ramesh et al. 1998). The half-power and thl: thu ≈ 1:1.7 (see Figure 2). The frequency ratio of the FL
width of the response pattern (“beam”) of the GLOSS at a and HL bands estimated from the respective maximum
typical frequency such as 80MHz is ≈90°×6° (R.A. × amplitudes ( fl and hl) in the spectral profile at ≈04:33 UT
decl.). The integration time is ≈100 ms and the observing are fl : hl≈1:2 (see Figure 3). The ratio of the corresponding
bandwidth is ≈300 kHz at each frequency. The width of the instantaneous bandwidths FL: HL is ≈1:1. These values are
beam of the GLOSS in R.A. (i.e., hour angle) is nearly consistent with those reported in the literature for split-band
independent of frequency. The beam can be steered in type II radio bursts (see for example Hariharan et al. 2014). An
declination by including switchable cable delay lines in the inspection of the e-CALLISTO solar radio spectrometer
aforementioned branched feeder system. The minimum detect- (Monstein et al. 2007; Benz et al. 2009) observations at the
able flux density (1σ level) with the GLOSS is ≈3000 Jy Gauribidanur Observatory in the frequency range 45–440MHz
(1 Jy = 10-26 Wm-2 Hz-1). We specifically chose the above revealed that the above type II burst was limited to frequencies
period for the present work, since the Sun was closer to 150MHz. The STEREO-B COR1 coronagraph observed a
the Galactic Center (GC) in both R.A. and decl., and it CME in close temporal association with the burst. The first
facilitated the calibration of the antennae in the GLOSS array appearance of the CME in the field of view (FOV) of STEREO-
(Ramesh et al. 2013; Kishore et al. 2015). Even here, we have B COR1 was at ≈04:45 UT. The angular width of the CME
considered only those type II bursts, which showed both split- was ≈24°, and its LE was at ≈1.8Re. There was also a X1.1
band and F–H structure, and there was simultaneous class GOES soft X-ray flare from the NOAA active region
availability of CME observations in white light near the Sun AR118904 located at S13E13. The above active region had 15
(<2Re). We used images obtained with the COR1 spots and β−δ configuration. Its total area was ≈480
coronagraph of the Sun–Earth Connection Coronal and millionths of the solar disk.5 Note that STEREO-B was behind
Heliospheric Investigation (Howard et al. 2008) on board the the Earth at ≈E144 in the above epoch.6 This implies that
Solar TErrestrial RElations Observatory (STEREO), and the AR11890 was at ≈W131 (i.e., ≈41° behind the limb) for the
Large Angle and Spectrometric Coronagraph (Brueckner
et al. 1995) on board the Solar and Heliospheric Observatory 4 ftp://ftp.swpc.noaa.gov/pub/warehouse
5 http://www.lmsal.com/solarsoft/latest_events/
3 http://www.iiap.res.in/centers/radio 6 http://stereo-ssc.nascom.nasa.gov/cgi-bin/make_where_gif
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The Astrophysical Journal, 832:59 (7pp), 2016 November 20 Kishore et al.
Figure 2. Temporal profile of the type II burst in Figure 1 at 80 MHz showing emission corresponding to the FL, FU, HL, and HU bands.
Figure 3. Spectral profile of the type II burst in Figure 1 at ≈04:33 UT. The emission corresponding to the FL, FU, and HL bands can be seen. The HU was not
observable during the above time (see Figure 1).
STEREO-B view. Assuming that the projection effects vary as An extrapolation of the h–t locations of the associated CME
1/cos(f), where f is the angle from the plane of the sky (POS), mentioned in Section 2 indicates that rCME » 1.65 R at
we calculated the deprojected location of the CME LE (rCME) ≈04:30 UT. We adopted different coronal electron density
at ≈04:45 UT to be »2.33 R. The corresponding location at models (Baumbach 1937; Allen 1947; Newkirk 1961; Saito
≈04:50 UT is »2.64 R. The speed of the CME LE (vCME) et al. 1977; Vršnak et al. 2004) in order to identify the
calculated from the above values is ≈719 km s−1. Although the particular model(s) that satisfies the following criteria for the
above values of rCME and vCME correspond to the LE of the type II bursts caused by CME-driven shock: (1) the location of
CME, in the present case they can also be considered to be the plasma level (rradio) corresponding to fs should be consistent
nearly the same for the flank of the CME, since the angular with rCME at the same time as the occurrence of fs; (2) the drift
width of the CME is small (≈24°) in the STEREO-B COR1 speed (vtypeII) of the type II bursts based on such a model for
FOV. Note that the type II burst in Figure 1 was observed Ne (r) should agree closely with the vCME of the corresponding
before the CME appeared in the STEREO-B COR1 FOV at CMEs. Note that all the above density models are applicable in
≈04:45 UT. This implies that the angular width of the CME the “middle” corona, where the density falls off typically as r-6
could have been 24° during the type II burst period. So the (Leblanc et al. 1998). After various trials, finally we found that
above assumption regarding rCME and vCME is reasonable. The both the aforementioned criteria were satisfied for all the four
details related to the type II bursts, flares, CMEs, and the type II bursts and the associated CMEs by adopting the Saito
coronal electron density distribution reported in the present model with suitable density enhancement factor (D) for each
work are listed in Table 1. burst. For example, in the case of the type II burst of 2013
November 8 (Figure 1), we find that 6× Saito model gives the
best results. The estimated r
3. RESULTS AND ANALYSIS typeII
≈1.61Re corresponding to
fs = 68MHz at ≈04:40 UT (see columns 3, 4 and 11 in
An inspection of Figure 1 indicates that the earliest time at Table 1) agrees closely with the rCME » 1.67 R at the above
which the type II burst can be noticed simultaneously in both epoch. The estimated v −1typeII≈843 km s , obtained after
the FL and FU bands is ≈04:30 UT. The burst was present at satisfactorily addressing the first criteria mentioned above, is
frequency ( fs)≈60MHz in the FL band at the above epoch. reasonably close to v
−1
CME≈719 km s . The drift rate of the
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The Astrophysical Journal, 832:59 (7pp), 2016 November 20 Kishore et al.
Table 1
Details Related to Type II Bursts, Flares, CMEs, Ne (r), and B (r)
c
S.No. Date Type II Burst X-ray Spacecraftb/ CME LE CME Ne (r) rtypeII vtypeII B (r)
Freq. Onset Flare Location Proj./ Proj./ Widthc Modelf Range (km s−1) Range
Rangea Time Class/ de-proj. de-proj. (deg.) (R) (G)
(MHz) (UT) Location r dCME vCME
(R) (km s
−1)
1 2013 68–51 04:50 B6.9/ S-B/E140 1.58/1.67 411/435 29 6S 1.61–1.77 555 1.73–1.32
Oct 08 S13E63
2G 1.63–1.76 431 1.34–01.02
2 2013 60–37 04:30 X1.1/ S-B/E144 1.25/1.65 549/719 24 6S 1.67–1.97 843 1.80-1.30
Nov 08 S13E13
2G 1.68–1.91 635 1.35-0.97
3 2013 61–36 10:29 X1.0/ S-A/W149 1.96/2.00 878/894 40e 17S 2.00–2.40 711 1.50–1.11
Nov 19 S13W69
8G 2.01–2.30 503 1.00–0.80
4 2014 43-38 05:16 C3.0/ S-B/E158 1.56/2.02 696/900 14 9S 2.01–2.12 847 1.17–1.04
Feb 10 S12E29
4G 2.01–2.09 620 0.86–0.76
Notes.
a Corresponds to the FL band.
b S-A and S-B stand for STEREO-A and STEREO-B, respectively.
c STEREO-COR1 measurements during/close to the type II burst period.
d At the onset time of the type II burst (see column 4).
e Evolved into a “halo” CME in the SOHO-LASCO C2 FOV.
f S and G indicate Saito and Gopalswamy model, respectively. The prefixed numbers specify the density enhancement factor D.
Table 2
Shock Parameters Estimated from the Band-split of the Type II Bursts Listed in Table 1
S.No. Date Freq. ( b c d e fNe r) rtypeII BDW X MA vA B (r)
Range Modela (R) (km s
−1) (G)
(MHz)
1 2013 Oct 08 68–51 2G 1.63–1.76 0.06 1.13 1.10 508–498 1.34–1.02
2 2013 Nov 08 60–37 2G 1.68–1.91 0.21 1.45 1.36 681–585 1.35–0.97
3 2013 Nov 19 61–36 17S 2.00–2.40 0.22 1.50 1.40 598–495 1.50–1.11
4 2014 Feb 10 43–38 9S 2.01–2.12 0.30 1.69 1.56 638–631 1.17–1.04
Notes.
a G and S indicate the Saito and Gopalswamy coronal electron density model, respectively. The prefixed numbers specify the density enhancement factor.
b Instantaneous bandwidth BDW = ( fu - fl ) fl , where fl and fu are the corresponding mid-frequencies in the FL and FU bands of the type II burst, respectively.
c Density jump across the shock X = (BDW + 1)2.
d Alfvénic Mach number MA = X (X + 5) 2(4 - X ) .
e Alfvén speed vA = vcme MA.
f B (r) = 5.1 ´ 10-5 fl vA.
above type II burst is ≈0.1 MHz s−1. The density scale height burst association in the case of the 2013 November 8 event.
in the 6× Saito model is ≈2.3×105 km. This is nearly the The estimated vtypeII≈635km s
−1 agrees closely with the
same as the typical density scale height for the coronal aforementioned vCME.
streamers at r  1.5Re (Aschwanden & Acton 2001). We calculated the associated coronal magnetic field strength
Considering that the CMEs are also density enhancements like (B(r)) from the split-band characteristics of the type II burst of
the streamers, the similarity is possible. We also used the 2013 November 8, following the methodology described
correspondence between the starting frequency ( f ) of the type in Vršnak et al. (2002), Cho et al. (2007). The results indicate
II bursts and the distance (r) of the associated CME LE, i.e., that B(r)≈1.8–1.3 G in the range r » 1.67–1.97 R in
f (r) = 307.87r-3.78 - 0.14, to estimate v (Gopalswamy the case of 6× Saito model. For 2× Gopalswamy model,typeII
et al. 2013). Note that the above power-law relationship should B(r) ≈ 1.35–0.97 G in the range r » 1.68–1.91 R. Note that
the above distance ranges correspond to the frequency interval
be converted to a “model” (hereinafter referred to as the of 60-37 MHz over which both the F and F bands in the
Gopalswamy model) for Ne (r) to calculate v L UtypeII. We used the 2013 November 8 type II burst were observed with the GLOSS
equality f (r) = 9 ´ 10-3 Ne (r) , where f (r) and Ne(r) are in (see Figure 1). Based on similar CME-associated type II burst
units of MHz and cm−3, respectively, for this purpose. The observations and independent electron density estimates, Zucca
density was enhanced by a factor of two (i.e., 2× Gopalswamy et al. (2014) recently reported B≈1 G at r≈1.6Re. The
model) to meet criteria 1 and 2 listed above for the CME-type II corresponding plasma frequency was 70MHz. These numbers
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The Astrophysical Journal, 832:59 (7pp), 2016 November 20 Kishore et al.
Figure 4. B (r) estimates from the split-band type II bursts reported in the present work (see Table 1). The “circle” and “square” symbols correspond to the Saito (S)
and Gopalswamy (G) models, respectively. The “solid” and “dashed” lines are the power-law fit to the estimates using the above two models. The error bars are due to
the spectral width of the FL and FU bands.
are in good agreement with our above results. We carried out levels corresponding to ≈60–30MHz as in the present case
similar analysis for the other type II bursts reported in the (see column 3 in Table 1) can occur at heliocentric distances as
present work, by using both the Saito and Gopalswamy large as r≈2.5–4.0Re when there is a CME. We found that
models. The results are listed in columns 11–13 of Table 1. The for this to happen, the value of D as per the Saito model used in
associated shock parameters are listed in Table 2. The rtypeII the present work should be 35; (3) whitelight
(corresponding to the start frequency of the type II bursts in our coronagraph observations of CME-associated MHD shock
observations) and rCME (at the epoch corresponding to rtypeII) indicate that even the POS density ahead of the propagating
agree closely for all the events in both the models. This CME front is enhanced by 10× for “halo” CMEs at r≈6Re
indicates that we are using the appropriate distribution of Ne(r) (Vourlidas et al. 2003; Ontiveros & Vourlidas 2009). This
for each event. Note that the CME associated with one of the implies that the enhancement could be larger when the CMEs
split-band type II bursts (2013 November 19) evolved into a are located comparatively closer to the Sun, since the size of
“halo” CME in the SOHO-LASCO C2 FOV (see column 9 in the CMEs increase as they propagate (Gopalswamy et al.
Table 1). This probably could be the reason for the higher value 2012a). This probably could be the reason for the compara-
of D in both the Saito and Gopalswamy models for the above tively larger density enhancement factor for the event of 2013
event. We would like to add here that the D values used in the November 19, in both the Saito and Gopalswamy models (see
Ne(r) model for each event (see column 10 of Table 1) are column 10 in Table 1).
consistent with: (1) those reported earlier for radio observations Figure 4 shows the estimates of B from each split-band type
associated with large-scale density enhancements like the II burst reported in the present work using D× Saito and D×
CMEs and coronal streamers in the solar atmosphere (Sastry Gopalswamy models. They are in the range of B values
et al. 1981, 1983; Lantos et al. 1987; Schmahl et al. 1994; reported in the literature from some of the other CME-
Ramesh et al. 2001; Kathiravan et al. 2002; Kathiravan & associated phenomena like moving type IV bursts and quasi-
Ramesh 2004, 2005; Subramanian 2004); (2) recent observa- periodic type III bursts in the “middle” corona (Bastian
tions by Morosan et al. (2014) which indicate that plasma et al. 2001; Ramesh et al. 2003a, 2003b; Sasikumar Raja
5
The Astrophysical Journal, 832:59 (7pp), 2016 November 20 Kishore et al.
et al. 2014; Hariharan et al. 2016). A comparison with the non- type II bursts indicates that they follow a pattern. The closer the
flaring corona case indicates that the present estimates are ≈2× heliocentric distance range of the type II burst to the Sun, the
larger (Gopalswamy et al. 1986; Ramesh et al. 2011). Our steeper is the variation. Since, currently, it is difficult to
interest is to obtain B(r). Since the number of events is limited, measure B in the “middle” corona at other spectral bands in the
we treated them separately and used an independent power-law electromagnetic spectrum, it is hoped that more “radio”
fit of the type B (r) = Cr-a for each of them (see Figure 4). An estimates of B(r) with tight constraints, as in the present work,
inspection of the B(r) profiles indicates that they are different will be useful particularly for the shock acceleration theories.
for the above two models. The B values estimated using the
D× Saito model are ≈1.2 times larger in each event. Since We thank the staff of the Gauribidanur Observatory for their
B µ Ne , this is primarily due to the differences between the help with observations, and maintenance of the antenna and
two density models and the use of comparatively larger values receiver systems there. We are grateful to the referee for his/
of D in the Saito model (see column 10 in Table 1) to satisfy her kind comments, which helped us to present the results more
the criteria mentioned earlier to select the coronal electron clearly. The SOHO data are produced by a consortium of the
density model. Note that one of the main criteria used in the Naval Research Laboratory (USA), Max-Planck-Institut fuer
present work to constrain B is that vtypeII should be close to Aeronomie (Germany), Laboratoire d’Astronomie (France),
vCME for each event. We note from columns 8 and 12 in and the University of Birmingham (UK). SOHO is a project of
Table 1 that for the 1st and 2nd events in the list, the above two international cooperation between ESA and NASA. The
quantities agree closely if we use the Gopalswamy model. The SOHO-LASCO CME catalog and STEREO movies are
differences are ≈4 km s−1 (2013 October 8) and ≈84 km s−1 generated and maintained at the CDAW Data Center by
(2013 November 8). For the 3rd and 4th events, the use of the NASA and the Catholic University of America in cooperation
Saito model gives better agreement between vtypeII and vCME. with the Naval Research Laboratory. NG was supported by
The differences are ≈183 km s−1 (2013 November 19) and NASAʼs LWS TR&T program.
≈53 km s−1 (2014 February 10). There is excellent agreement
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