RADIO IMAGING OF A TYPE IVM RADIO BURST ON THE 14TH OF AUGUST 2010

Radio images for this event are available from NRH. Throughout the event, there is a type I noise storm (NS) present that is observed at all NRH observing frequencies. The left panel of Figure 3 shows a pre flare image from AIA 304 Å at 09:20 UT, highlighting the AR and filament material prior to eruption. Radio contours are overplotted for 173 MHz, 228 MHz, 270 MHz, 298 MHz, 327 MHz and 360 MHz, outlining the NS. Contours are shown for 50%, 70% and 90% of the maximum T_b in the full radio map for 173 MHz to 327 MHz, and at 70% and 90% for 360 MHz. Noise storms are typically located in the corona above active regions and are commonly observed below ∼400 MHz. They exhibit two components: slowly varying, broadband emission that can last for several tens of minutes to several days and; numerous short duration, narrowband bursts lasting <1 s, which are superimposed on the slowly varying component. Type I noise storms are evidence for small-scale energy release and electron acceleration events and are often observed prior to a solar flare.

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The right panel of Figure 3 utilizes the extended field of view of a SWAP 171 Å image to show the erupting plasmoid that becomes the CME core at 10:04 UT, when it is beyond the field of view of AIA. NRH 298 MHz T_b contours (white) are overplotted from a "standard" 10 s NRH map at 4%, 8%, 16%, 32%, 64% and 96% of the maximum T_b. While the NS storm is the dominant source throughout the event, an additional source associated with the CME can be seen propagating away from the sun in a south-west direction. In order to isolate this CME radio source (CME-RS) the radio images were first integrated over 30 s time intervals to improve the signal to noise ratio of the CME-RS. This was achieved by integrating three standard 10 s NRH back projected images and then applying the CLEAN algorithm using beam parameters for the middle time interval. The NS was then fitted with a 2D Gaussian and the contribution removed from the NRH images. It is important to note that the CME-RS feature is already clearly observed in the standard 10 s NRH radio maps, as is shown in the right plot of Figure 3 (NRH images shown in the rest of the paper are made using the 30 s time integrated images). Green contours in Figure 3 (right) show an example of the resulting isolated CME-RS source at 298 MHz, after the NS contribution was subtracted. The plotted contours are for 50%, 70% and 90% of the maximum T_b of the CME-RS alone. This process was carried out for all images at each of the NRH observation frequencies. Since the beam parameters and hence the spatial resolution varies with frequency (292'' FWHM at 150 MHz to 122'' at 360 MHz) the height at which we can isolate the CME source from the NS varies for each frequency. This corresponds to times from around 09:58 UT onward, when it was possible to recover the CME source at all frequencies. The radio analysis presented in the following sections occurs for time intervals after those in the top left and middle panels shown in Figure 2.

Figure 4 shows the temporal evolution of the CME-RS with respect to its EUV and WL counterparts, within the AIA, SWAP and LASCO fields of view, respectively. For all panels, NRH radio T_b contours for the isolated CME-RS are plotted at 50%, 70% and 90% of the maximum T_b. For clarity, Figures 2 and 4 use matching image times (to within the EUV/WL image cadence while highlighting changes observed by NRH) for cross-checking sources where NRH image contours may obscure details in the EUV/WL images. The top row of Figure 4 shows AIA 171 Å (left) and SWAP 171 Å (middle and right) difference images corresponding to NRH images at 09:58 UT, 10:04 UT and 10:07 UT. In general the radio source is well aligned with the erupting filament that forms the core. At the time of the first image (top left at 09:58 UT), the separation of the core into two components (pointed out earlier in the AIA images shown in Figure 2) has already occurred. By 10:04 UT and 10:07 UT (top middle and right) the CME-RS has broken into two clear sources, labeled I and II. The separation is seen first at the highest frequencies and then at subsequently lower frequencies. This is probably the result of the finer spatial resolution for higher observing channels, especially since the 228 MHz, 173 MHz and 150 MHz contours at 10:04 UT stretch across both source I and II. In addition to the radio source associated with the core, another source is observed along the northern flank of the CME as it erupts. This source first appears at 09:55 UT at frequencies between 270 MHz and 150 MHz. It is most predominant at 173 MHz between 10:01 UT and 10:14 UT and at 150 MHz between 10:01:00 UT and 10:16:30 UT.

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The bottom row of Figure 4 shows LASCO C2 WL difference images corresponding to NRH images at 10:09 UT, 10:12 UT and 10:25 UT as the CME enters the LASCO FOV. Images of the disk are from SWAP 171 Å. Plotted stars indicate the locations of the CME front (blue), cavity (red) and core (green) obtained by performing stereoscopic reconstruction using images from the Inner Coronagraph (Cor1) onboard STEREO A and B (Thompson 2008, 2009). This was only possible once the CME reached heights great enough to be viewed from both spacecraft. The positions are corrected for projection effects for an observer with the same line of sight as LASCO. From images at 10:09 UT and 10:12 UT we find that sources I and II have separated further. After 10:18 UT the radio source is visible only at 173 MHz and 150 MHz. By 10:25 UT, source I is no longer visible and source II has divided into two sources, where the new outer source is labeled source III. From the bottom right panel of Figure 4, source III is observed to be cospatial with the core of the CME as it enters the LASCO C2 FOV. By around 10:30 UT the radio source is at the background noise level and is no longer visible at the time of the next available LASCO image.

Figure 5 shows the direction of propagation for the CME-RS. Contours outline the NS source at 09:41 UT for each frequency and the flare site is indicated by a black triangle. Colored crosses indicate the CME-RS centroid position as a function of time (from blue to yellow), taken at 10 s time intervals for each of the NRH observing frequencies between 150 MHz and 327 MHz (the propagation at 360 MHz is very similar to that at 327 MHz and therefore is not plotted). When the source fragments, the path of the secondary and tertiary sources continues to follow the temporal color gradient. The initial radio source, labeled I, fragments to I and II at 10:04:21 UT, 10:10:11 UT and 10:14:01 UT for 228 MHz, 173 MHz, and 150 MHz respectively (see labels on Figure 5). Source II then fragments again into sources II and III in the time ranges 10:19:21–10:20:11 UT and 10:20:51–10:22:31 UT for 173 MHz and 150 MHz respectively. Labels S1 and S2 indicate times when the sources fragments. From the plotted crosses, the track of the main radio source appears to split suddenly. In reality the splitting process occurs more smoothly since the centroid position of the combined source was situated between the two separating sources. Figure 6 shows plots of T_b for the NS (top) and the CME-RS (middle). Colored vertical lines and hashed regions show times S1 and S2 at each frequency.

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Fitting the propagation paths with a constant acceleration model we determine a propagation velocity in range 250–500 km s⁻¹ for the different NRH frequencies. The CORonal Image Processing (CORIMP) CME catalog (Byrne et al. 2012; Morgan et al. 2012), which automatically detects and tracks CMEs in the LASCO field of view, finds a top speed of 1000–1200 km s⁻¹ for the CME front at an angle of 220° counter clockwise from solar north during the acceleration phase around 11:00 UT. This is similar to the value of 1205 km s⁻¹ quoted in the CDAW CME catalog. However, for the period of 10:00 UT–10:30 UT used for the type IV velocity estimate, CORIMP gives a bulk velocity in the range 200–600 km s⁻¹, which is similar to the range found for the type IVM and also to quotes from the SEEDS and CACTus CME catalogs.

From the plots of T_b shown in Figure 6, we find that T_b of the NS is around an order of magnitude greater than that of the CME-RS. The peak T_b for the NS and CME-RS at each frequency are stated in Table 1, along with their flux values in S.F.U. We note that these values are on a par with those expected for a type IVM (Robinson 1978). The bottom panel of Figure 6 shows $T_{b_{{\rm CME\hbox{-}RS}}} / T_{b_{{\rm NS}}}$. The profiles are plotted only for times when the CME-RS is visible above the off-limb background. The bottom panel of Figure 6 shows the CME-RS is observed when T_b of the source is no less that 5% of the NS T_b, most likely as a result of the NRH dynamic range. This corresponds to times from 10:00 UT to 10:20 UT for observing channels between 360 MHz and 228 MHz, and until 10:30 UT at 173 and 150 MHz.

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Table 1. Noise Storm (NS) and CME Radio Source (CME-RS) Properties

ν	Peak $T_{b_{{\rm NS}}}$	Peak $T_{b_{{\rm CME-RS}}}$	Peak SNS	Peak SCME-RS
(MHz)	(K)	(K)	(S.F.U.)	(S.F.U.)
150	5.76 × 108	1.07 × 107	368.36	14.05
173	3.99 × 108	8.67 × 106	291.14	15.80
228	1.38 × 108	4.82 × 106	103.58	4.32
270	9.47 × 107	3.25 × 106	66.52	6.66
298	7.57 × 107	1.97 × 106	52.83	6.47
327	6.02 × 107	2.29 × 106	52.21	2.36
360	1.01 × 108	2.16 × 106	116.45	3.62

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Since the observed T_b varies in the range 10⁶–10⁷ K, it is unlikely that plasma emission is the source of the emission, as we would typically expect T_b in excess of 10⁹K for such processes. Plasma emission resulting from, e.g., type II and type III radio bursts, usually results in an enhanced brightness over a narrow band of frequencies over a short timescale, on the order of seconds to minutes. Instead, the CME-RS appears consistently at a number of frequencies spanning the NRH observing range for a sustained period of time. Source II shows very little spatial dispersion across all frequencies which is consistent with gyrosynchrotron emission. Source III is observed only at 150 and 173 MHz, but also appears cospatial across these two frequencies. However, source I does show some degree of spatial separation.

For further diagnosis of the emission mechanism we refer to the radio spectral shape. Figure 7 (left) shows an example of the CME-RS at 10:09:41 UT and the region chosen for spectral analysis is indicated by a black circle. Figure 7 (right) shows the corresponding fitted spectra for source II. Error bars represent the standard deviation of the expected source flux density for the region of interest based on the standard deviation of the noise in a quiet Sun region. The value of which varies for each frequency (0.03 S.F.U at 150 MHz to 0.49 S.F.U. at 360 MHz). For this time interval, the spectrum was well fitted by a power law with a spectral index (α) of 3.3. Such a power law is consistent with what we would expect from optically thin gyrosynchrotron emission where the flux density, F(ν)∝ν^α. Figure 8 shows the evolution of α throughout the duration of the burst. The spectral index for source II hardens slightly over the duration of the burst, with α in the range 3 to 5.

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Assuming gyrosynchrotron emission we can determine the spectral index, δ, of the underlying nonthermal electron distribution using the approximation

$$\begin{equation} \delta = -1.1 (\alpha - 1.2) \end{equation} \tag{ 1 }$$

from Dulk (1985). This approximate relation between α and δ assumes that the radio spectra are described by a power law distribution with a constant value of α. In the full gyrosynchrotron expressions defined in Ramaty (1969), α is frequency dependent. The Dulk (1985) approximation gives δ = 4.9 for source II, as selected in Figure 7, at 10:09:41 UT.

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Figure 9 shows the degree of polarization, i.e., stokes V/I, for four snapshots during the burst at 228 MHz. White contours indicate the 4%, 8%, 16%, 32%, 64% and 96% levels of the maximum intensity in each radio map to delineate the noise storm and the propagating radio sources. We show only polarization data within the selected contours to avoid noise from low flux regions. Figure 10 shows the polarization as a function of time throughout the burst for source II at 150 MHz, 173 MHz and 228 MHz. At other frequencies the polarization data was unreliable. From Figure 10 we find that in general all three of the lowest NRH frequencies were around 40% polarized until around 10:12 UT, after which the degree of polarization at 150 MHz steadily increased to around 70%, while at 173 MHz and 228 MHz the degree of polarization slowly decreased over time.

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Using the relation

$$\begin{equation} r_{c} \approx 1.26\; 10^{0.035\delta } 10^{-0.071\cos \theta } \bigg (\frac{\nu }{\nu _{B}}\bigg)^{-0.782+0.545\cos \theta } \end{equation} \tag{ 2 }$$

from Dulk (1985), where r_c is the degree of circular polarization, θ is the viewing angle of the observer with respect to the magnetic field and ν_B is the electron gyrofrequency (ν_B = eB/2πm_ec ≈ 2.8B MHz, where B is the magnetic field strength in units of Gauss), we can determine an estimate of B. Assuming θ ≈ 80° (since the CME-RS appears over the limb) and using δ = 4.9, ν = 150 MHz and r_c ≈ 40% for source II at 10:09:41 UT, we find B ≈ 5.9 G. Furthermore, Razin-Tsytovich suppression can occur in a magnetized plasma when the effects of the medium become important and the refractive index is greater than 1 (Ginzburg & Syrovatskii 1965). When this occurs the emitted radiation becomes suppressed below the critical frequency ν_R

$$\begin{equation} \nu _{R}\approx \frac{2\nu _{p}^{2}}{3\nu _{B}^2}\approx \frac{20n_{e}}{B} \end{equation} \tag{ 3 }$$

where ν_p is the local plasma frequency and n_e is the ambient thermal electron density. Since no suppression is observed in the radio spectrum for source II, ν_R ≪ 150 MHz. From the LASCO WL CME observations we can determine the CME mass and in turn, estimate the electron density, n_e in the CME core to be in the range 10⁵–10⁶ cm⁻³. This provides us with a lower limit on B of 0.01 G.

Using the relation

$$\begin{equation} T_{b} = \tau T_{{\rm eff}} = c^2\eta L/k_{B}\nu ^2 \end{equation} \tag{ 4 }$$

for optically thin plasma, where τ is the optical depth, T_eff is the effective temperature, L the line of sight distance through the source and k_B is Boltzmann's constant, with the Dulk (1985) relation for emissivity, η, expressed in terms of η/BN

$$\begin{equation} \frac{\eta }{BN} = 3.3\times 10^{-24}10^{-0.52\delta }(\sin \theta)^{-0.43+0.65\delta }\frac{\nu }{\nu _{B}}^{1.22-0.90\delta } \end{equation} \tag{ 5 }$$

where N is the non thermal electron density, and rearranging, we can determine N for electrons greater than E₀ = 10 keV. Here E₀ is the low electron energy cut off, with 10 keV being the value used in the determination of the semi-empirical formulae of Dulk (1985).

$$\begin{equation} N = 2.8\times 10^{6}T_{b}\bigg (\frac{k_{B}\nu }{c^{2}L}\bigg)\frac{\nu }{\nu _{B}}\bigg (\frac{\eta }{BN}\bigg)^{-1}. \end{equation} \tag{ 6 }$$

From radio imaging we estimate L ≈ 300'' ≈ 2 × 10¹⁰ cm, assuming the extent of source II along the line of sight is similar to its diameter in the plane of sky. Using B = 5.9 G, we find a nonthermal electron density, N, above 10 keV to be roughly 10⁴ cm⁻³ (the lower limit of 0.01 G requires an unrealistically high nonthermal electron density, when compared to the thermal electron density).

It is known that parameters derived using the semi-empirical relations of Dulk (1985) can contain inaccuracies. We have therefore compared our observations with simulated spectra generated using fast gyrosynchrotron codes (see Fleishman & Kuznetsov (2010) for details) covering a large parameter space. Spectra were generated for a number of instances with varying values of B, N, θ, E_min and δ, and maps of the reduced χ² produced. Figure 11 shows χ² maps in the plane of B and N, for varying values of E_min (plots left to right) and θ (top to bottom). For all plots in Figure 11, we have imposed δ = 5, as determined from the fitted source II spectrum. Colored pixels are only shown for reduced χ² values of less than 100 (shown to high values to highlight the mapping of χ²), while the remaining white space contains χ² greater than 100. The colored pixels are normalized across the parameter space shown in the complete figure, not just to the values in each plot. Reasonable comparisons between the simulated spectra and the observed data start with χ² < 7, corresponding to green pixels, however for our discussion we refer to only the lowest χ² values corresponding to the red/orange pixels.

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Without a turnover in the gyrosynchrotron spectrum, there exists a number of local minima that can provide a good fit to the observed spectrum, as is seen by the spatial variance of the red/orange pixels in each plot of Figure 11. We choose to show only a subset of the explored parameter space, limited to plots with typical values of E_min between 10 keV and 316 keV. This chosen range contains the lowest χ² pixels for δ = 5, and the ranges of B and N examined. Each plot shows B in the range 1 to 20 G, based loosely on the expected value of B calculated above. A lower limit of 1 G is used as, below this value, the required nonthermal electron density to match the data approaches the estimated thermal electron density. Such a scenario is unlikely as this would require a very efficient acceleration mechanism.

Focusing on the top row of Figure 11 where θ = 80°, and assuming E_min = 10 keV, the best fit to the data requires N = 3.98 × 10⁴ cm⁻³ with B = 3.7 G. For a source volume of 4.2 × 10³⁰ cm⁻³, the total number of nonthermal electrons (above 10 keV) present in the source is then around 1.67 × 10³⁵. This corresponds to a nonthermal electron energy content of 2.68 × 10²⁷ erg. Applied similarly to E_min = 31.62 keV and 100 keV, Table 2 shows the resulting number of electrons within the source and the corresponding nonthermal energy content. For comparison, the thermal contribution to the source, with n_e = 10⁶ cm⁻³, contains around 10³⁷ ambient electrons. Assuming a rough temperature estimate of 0.7 MK, i.e., the peak temperature response at 171 Å (O'Dwyer et al. 2010; Boerner et al. 2012) where the source was last observed in EUV a few minutes prior (we note that the source may have cooled during this period), gives a thermal energy of 10²⁷ erg. It is therefore likely that the values in the first row of Table 2 are an upper limit to the number of nonthermal electrons and nonthermal energy content within source II. We also point out that the minimum χ² in the bottom left plot for θ = 10° also requires an unrealistic nonthermal electron density of 10⁶cm⁻³ to match the observed spectrum (Table 2, bottom row). In reality, θ is most likely varying throughout the source. This is evidenced in the AIA images which show the field to be highly twisted and change in orientation as the CME erupts, see Figure 2. While we cannot distinguish between several parameter combinations that match the data equally well, previous studies of gyrosynchrotron emission from CMEs have shown that the emission typically results from electrons in the range 100 keV to 1 MeV (Bastian et al. 2001). If we therefore assume a low energy cut off of several tens to 100 keV, the nonthermal energy content of source II is between 0.001% and 0.1% of the thermal energy content of the source.

Table 2. Input Parameters for the Simulated Gyrosynchrotron Spectra and the Resulting Nonthermal Energy Content

δ	θ	Emin	B	N	No. of e−	$\mathrm{E_{{\rm nontherm}}}$
	(°)	(keV)	(G)	(cm−3)		(erg)
5	80	10.0	3.7	3.98 × 104	1.67 × 1035	2.68 × 1027
5	80	31.6	3.7	3.98 × 102	1.67 × 1033	8.47 × 1025
5	80	100.0	3.7	3.98	1.67 × 1031	2.68 × 1024
5	10	10.0	5.2	3.98 × 106	1.67 × 1037	2.68 × 1029

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For 10 keV electrons, the energy loss timescale by Coulomb collisions for a source with the value for n_e estimated above is 4 hr (longer if you consider synchrotron energy loss alone) and over 49 hr at 100 keV to 1 MeV. Therefore a population of trapped accelerated electrons have the ability to explain the observed emission throughout the duration of the burst without needing to be replenished. However assuming the electrons are able to escape, the crossing time through the source is <1 s, which would require there to be a continued injection of accelerated electrons into the source.

The parameters recovered from this study are somewhat different to those found in a recent study by Tun & Vourlidas (2013). Firstly, the spectra presented in the Tun & Vourlidas (2013) paper shows a turnover at low frequencies which they attribute to gyrosynchrotron self-absorption. Our analysis shows no evidence of a turnover. Tun & Vourlidas (2013) finds B in the (slightly higher) range of 5–15 G and N = 2 × 10⁶ cm⁻³. However, the Tun & Vourlidas (2013) study assumes an electron energy range of 1–100 keV and fitting the data, finds δ = 3. Alternatively, for the simulated spectra shown here, we set an upper limit for the electron energy to 10 MeV and varied the lower energy cutoff. We also impose the value δ = 5, which was found by fitting the radio spectrum with a power law to determine α, and using the Dulk (1985) approximation to determine δ. The choice of high energy cutoff can change the spectral slope of the fitted spectrum (Holman 2003) and may explain the discrepancy. Although not show in Figure 11, our parameter survey was extended to E_min = 1 keV, but this parameter range did not contain the minimum χ² for the parameter space.