The First Flare Observation with a New Solar Microwave Spectrometer Working in 35–40 GHz

The CBS consists of three modules. The receiving module has a Cassegrainian antenna with a diameter of 80 cm. The analog front end unit down-converts the receiving signal (35–40 GHz) to 687.5–1187.5 MHz into 10 channels. Each channel has a bandwidth of 500 MHz. The digital receiver generates the real-time dynamic spectra in two channels, with a dual-core analog-to-digital-converter and a compatible processor of the field programmable gate array. For details see Yan et al. (2020, 2021) and Shang et al. (2022). To increase the signal-to-noise ratio and reduce the data volume, we integrated the spectra over ∼134 ms that represents the time resolution of the data. The spectral resolution is ∼153 kHz.

The CBS data are calibrated with the CBS measurement of the new moon on the basis of known brightness temperature (T_NM(ν)) as follows

$$\begin{eqnarray}\begin{array}{rcl}{T}_{{\rm{S}}}(\nu ) & = & \displaystyle \frac{{R}_{{\rm{S}}}^{F}-{R}_{\mathrm{BG}}^{F}}{{R}_{\mathrm{QS}}^{F}-{R}_{\mathrm{BG}}^{F}}\beta {T}_{\mathrm{NM}}(\nu ),\\ \beta & = & \displaystyle \frac{{R}_{\mathrm{QS}}^{\mathrm{NM}}-{R}_{\mathrm{BG}}^{\mathrm{NM}}}{{R}_{{\rm{M}}}^{\mathrm{NM}}-{R}_{\mathrm{BG}}^{\mathrm{NM}}},\end{array}\end{eqnarray} \tag{ 1 }$$

where F (NM) denotes the flare (new moon) observation, R is the reading value of the receiver, T_S(ν) is the mean brightness temperature of the Sun, and BG, M, and QS denote the sky background, the moon, and the quiet Sun, respectively. Given the weak polarization at 35 GHz (<3%; see the blue line in Figure 3(e)), we assume equal T_S(ν) for the left- and right-handed circular polarizations. The total flux density I(ν) is then given by (Dulk & Marsh 1982)

$$\begin{eqnarray}&&I(\nu )=\displaystyle \frac{2{k}_{{\rm{B}}}{\nu }^{2}\int {T}_{{\rm{S}}}(\nu )d{\rm{\Omega }}}{{c}^{2}},\end{eqnarray} \tag{ 2 }$$

where dΩ is the differential solid angle of the Sun from the Earth's perspective, k_B is the Boltzmann constant, and c is the speed of light.

In line with previous reports (Linsky 1973; Krotikov & Pelyushenko 1987; Hafez et al. 2014; Kallunki & Tornikoski 2018), T_NM(ν) is set to increase linearly from ∼243.97 to 248.43 K when the frequency increases from 35 to 40 GHz. Five new moon observations were carried out by CBS dated on 2020 September 18, 2020 October 17, 2021 August 9, 2021 September 7, and 2022 May 2. According to these data, the ratio β is always in the range of 43–50, being consistent with that derived by Kuseski & Swanson (1976). Note that according to the long-term monitoring observations of NoRP (see footnote 4), the variation of the quiet Sun flux density hardly exceeds 5% at 35 GHz during a solar cycle, indicating β does not change considerably during the above periods. Therefore the average of the new moon data can be used for calibration. The daily average flux densities of the quiet Sun have been subtracted in our data analysis.

Figure 1 presents the AIA images at 131 and 171 Å during the flare on 2022 April 20 at the southwest limb. The event is partially occulted by the solar disk, and starts at 03:41 UT. At ∼03:45 UT, two sets of arcade loops emerge and ascend rapidly according to the 131 Å data (marked by black arrows in Figures 1(a) and (c)). They are not observed at 171 Å, indicating they are high-temperature structures. Around 03:53 UT, the structures expand and brighten. After ∼03:54 UT, the AIA data get saturated, and around 03:57 UT the flare reaches its peak. At ∼04:00 UT, the large-scale loop system erupts (see the red arrow in Figure 1(f)).

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The GOES SXR fluxes (solid lines in Figure 2(a)) and their corresponding time derivatives (dashed lines) reach their maxima at 03:57:25 UT and 03:55:04 UT, respectively, with the latter being earlier by about 2 minutes. Before their peak, the temporal profiles manifest a first-gradual-then-rapid increase during the impulsive phase, with the turning points at ∼03:54:24 UT. The microwave flux densities observed by NoRP (Figure 2(b)) and CBS (Figure 2(c)) show profiles similar to the SXR time derivatives.

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In Figure 3, we show other data sets around the flare peak (03:52 UT–03:58 UT). From top to bottom, the panels show (a) the CBS dynamic spectrum, the CBS (b) and the NoRP (c) microwave flux densities, (d) the GOES SXR time derivatives and the Konus-Wind HXR flux, and (e) the microwave polarization degree and the ratio of the NoRP to CBS data around 35 GHz. The dynamic spectrum presents continuum emission from 35 to 40 GHz (see Figure 3(a)). Two enhancements appear around 03:53 and 03:55 UT. The event can be split into the preimpulsive (03:52:00–03:54:24 UT), impulsive (03:54:24–03:55:29 UT), and decay (03:55:29–03:58:00 UT) stages.

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During the preimpulsive stage, the flux density from 35 to 40 GHz reaches ∼50  solar flux unit (SFU), along with the eruption of the hot arcade (Figures 1(a) and (c)), while no enhancement of HXR appears. The amplitude of the data fluctuation is ∼20–30 SFU, and this can be taken as the effective error of measurements of CBS. It is much smaller than the flux density during the impulsive stage. During this stage, the microwave flux densities above 35 GHz reach up to thousands of SFU (see Figures 3(b) and (c)). Three distinct local peaks can be identified. The HXR flux of 80–328 keV (orange line in Figure 3(d)) shows a similar profile to the microwave data, with the same local peaks. The low-energy lightcurve of HXR (18–80 keV, red line in Figure 3(d)) is similar to those of the SXR, while the high-energy lightcurve (328–1300 keV, green line in Figure 3(d)) manifests only one significant peak around the flare peak. In the decay stage, all emissions decline rapidly in intensity, and the microwave and high-energy HXR (>80 keV) intensities decrease faster than other sets of data.

As seen from Figure 3(c), during the impulsive stage the flux densities at 35 GHz (red) are larger than those at 17 GHz (blue), suggesting that the turnover frequency is above 17 GHz. The flux density ratio of the NoRP data at 35 GHz to the CBS data at 35.25 GHZ (black line in Figure 3(e)) lies between ∼0.7 and 1.15 for flux densities above 100 SFU. The relative difference of data magnitudes of CBS and NoRP is ≤15% during the impulsive stage.

The nonthermal microwave spectra can be fitted with the following function (see, e.g., Asai et al. 2013)

$$\begin{eqnarray}&&I(\nu )={I}_{t0}{\left(\displaystyle \frac{\nu }{{\nu }_{t0}}\right)}^{{\alpha }_{\mathrm{tk}}}\left(1-\exp \left(-{\left(\displaystyle \frac{\nu }{{\nu }_{t0}}\right)}^{{\alpha }_{\mathrm{tn}}-{\alpha }_{\mathrm{tk}}}\right)\right),\end{eqnarray} \tag{ 3 }$$

where ν_t0, I_t0, α_tk, α_tn, and I(ν) are the fitting parameters representative of the turnover frequency, the flux density at the turnover frequency, the optically thick and thin spectral indices, and the flux density at ν, respectively. The "real" value of ν_t (I_t ) given by the fitted spectra is slightly different from the above fitting parameter ν_t0 (I_t0).

To eliminate the systematic error between the two instruments, we cross-calibrate the CBS data by multiplying their values with the flux density ratio as shown in Figure 3(e). Figure 4 presents the fitted spectra and the corresponding parameters for 13 selected moments (T₁ − T₁₃). During the preimpulsive stage, the fitted spectra manifest a typical gyrosynchrotron spectrum (see the green line in Figure 4(a)), with a turnover frequency of 11.1 GHz. The turnover frequency ν_t goes above ∼15 GHz, and the corresponding intensity I_t goes above 1000 SFU during most of the impulsive stage extending from T₂ to T₁₀ (Figures 4(a)–(c)). The maximum flux density is ∼9300 SFU, obtained with the middle and major peak around T₆. During the decay stage (Figure 4(d)), both ν_t and I_t decrease with the declining flux density, for instance, the paired values of ν_t (GHz) and I_t (SFU) are equal to (25.2, 709) at 03:55:36 UT (T₁₁), (23.9, 464) at 03:55:46 UT (T₁₂), and (23.0, 282) at 03:55:56 UT (T₁₃).

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Figures 5(a) and (b) present the evolution of spectral parameters (α_tk, α_tn, ν_t , and I_t ). The spectral index α_C according to the CBS data within 35–40 GHz has been overplotted in Figures 5(a). Large uncertainties exist for spectral fitting with ν_t ≥ 35 GHz, and therefore at such moments the values of α_tn, ν_t , and I_t given by the fittings are not shown in the figure. No evident variation of the optically thick index α_tk is observed from 03:54 UT to 03:56 UT, while the optically thin index α_tn changes significantly. Note that α_tn changes similar to α_C. Both data reveal that ν_t is above 20 GHz for most of the first (yellow shadow) and third (orange shadow) peaks of the impulsive stage. At the start of the middle peak, the CBS index α_C increases sharply from negative (∼−2) to positive (∼1), and remains to be positive for ∼15 s. This means that the turnover frequency ν_t is larger than ∼35–40 GHz during this period.

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During the decay stage of this peak, the CBS index ν_C returns to be negative (∼−2 to −1). As seen from Figure 5, the CBS spectra present a rapid-softening-then-rapid-hardening profile in between two neighboring peaks, likely due to the rapid and intermittent energy release associated with the peaks.

In the decay stage, gradual hardening is observed from the temporal profiles of both α_C and α_tn. The difference between two sets of spectral indices is close to 1. This difference is due to the fact that α_tn represents the fitted slope at the high-frequency limit, while ν_C is given by the CBS measurement within 35–40 GHz.

Figure 5(b) presents a nice correlation between I_t and ν_t during the whole impulsive stage. The correlation can also be seen from Figure 5(c), which shows that I_t (ν_t ) can be well fitted with a power-law relation (${I}_{t}\propto {\nu }_{t}^{4.8}$). The correlation coefficient is about 0.82.