Application of the Tianwen-1 DOR Signals Observed by Very Long Baseline Interferometry Radio Telescopes in the Study of Solar Wind Plasma and a Coronal Mass Ejection

The DOR signals transmitted by TW1 consist of multiple single-frequency signals. After 2020 July 26, the x-band DOR signals are transmitted by a 2.5 m high-gain directional antenna instead of the low-gain omnidirectional antenna (Sun et al. 2021; Liu et al. 2022). Figure 1 shows the distribution of the DOR signals that consist of the carrier frequency and two groups of sidetones. The maximal frequency span between the sidetones is 38.4 MHz (CCSDS 2019).

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Furthermore, the signals of the TW1 are divided into two modes, coherent and incoherent signals. In the coherent mode, the transponder on board receives the uplink signals generated by a high stability ground-based hydrogen clock, then retransmits them to the Earth. In contrast, the downlink signals generated by the onboard crystal oscillator is the incoherent signals. The stability of the ground hydrogen clock is 10⁻¹⁵ s s⁻¹, superior to the onboard crystal oscillator of 10⁻¹² s s⁻¹ (Ma et al. 2022; Wang et al. 2022).

In ΔDOR observations, the radio telescopes of the CVN stations observe the extragalactic radio source and spacecraft alternately (detector–radio source–detector) (James et al. 2009; CCSDS 2019; Shu et al. 2017; Liu et al. 2022). The purpose of observing the radio source is to correct the common errors in ΔDOR group delay from internal instruments and the Earth's ionosphere and atmosphere. So far, CVN has conducted more than 200 observations of TW1. During the first solar conjunction observation of TW1, we select 10 days of data as symmetrically as possible according to the variations of heliocentric distance around the solar conjunction (Table 1). Every observation consists of 8–27 scans, and the duration of each scan is 3–10 minutes. The interval between scans is 7 min. The heliocentric distance of the selected data range from 129.4 to 33.5 Rs is in the ingress phase, and 13.5–102.1 Rs is in the egress phase. It should be noted that TW1 switched off the downlinked DOR signals and entered into safe mode during the solar conjunction phase from 2021 September 15 to October 18. Therefore, the CVN did not carry out the ΔDOR observation during this period. In addition, time throughout the paper is in coordinated universal time (UTC).

Figure 2 represents the differential VLBI observation and data-processing flow chart by CVN. The radio frequency signals received by each CVN station are converted into baseband signals and recorded by the Chinese VLBI Data Acquisition System terminal (Zhu et al. 2021). The record format is as follows: four channels, 8 MHz bandwidth, 16 MHz sampling rate, and 2-bit quantization. The raw observation data are transferred to the VLBI center for processing. The solid box represents the existing VLBI correlator process to obtain the ΔDOR group delay and delay rate used for the orbit and position determination of the spacecraft (Zheng et al. 2020). In this paper, we mainly focus on the Doppler process to study the application of DOR signals in solar plasma. The third-order phase locked loop (PLL) is used to obtain the frequency and phase of DOR signals (Deng et al. 2021). Then the frequency and phase used to calculate the solar wind velocity, DPD, and TEC variations.

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The sampling time of the frequency and phase of the PLL output is 0.01 s. It takes a few seconds for the PLL algorithm to start relocking from unlocking. Hence, we actively delete the first 10 s of data as it contains invalid information in each scan. In addition, when the working mode of the onboard transponder is switched, a sudden change in the transmitting frequency of the probe will cause the PLL to unlock. We delete these scans containing transponder mode switching.

After obtaining the phases and frequencies of DOR sidetones, we calculate the DPD as

$$\begin{eqnarray}&&{\rm{\Delta }}{\tau }_{12}=\displaystyle \frac{{\phi }_{1}}{2\pi {f}_{1}}-\displaystyle \frac{{\phi }_{2}}{2\pi {f}_{2}},\end{eqnarray} \tag{ 1 }$$

where Δτ₁₂ is the DPD, and f₁ and f₂ are the lowest and highest frequencies of DOR sidetones, respectively. ϕ₁ and ϕ₂ are the corresponding phases. The influences from the orbit, the Earth's atmosphere, and ground instruments can be removed. Therefore, large DPD variations are proportional to TEC changes in the ray path (Bird 1982; He et al. 2022)

$$\begin{eqnarray}&&D=-\displaystyle \frac{c}{40.31}\displaystyle \frac{{{f}_{1}}^{2}{{f}_{2}}^{2}}{{{f}_{2}}^{2}-{{f}_{1}}^{2}}{\rm{\Delta }}{\tau }_{12},\end{eqnarray} \tag{ 2 }$$

where D is the TEC variations and c is the light speed. Equation (2) demonstrates that the DPD is inversely proportional to the change in TEC. It is important to note that the absolute value of the TEC within a single scan cannot be calculated due to the cycle ambiguities between scans, but only the relative variations of the TEC (Bird 1982). In practice, simultaneously applying dual-band radio ranging measurements with the Doppler measurements can eliminate the ambiguity (Jensen et al. 2016, 2018). However, due to the absence of range data, we can only study relative TEC values.

To analyze the effect of the solar plasma on DOR signals, we first perform a 1 s integral on the data in the time domain. Second, a seventh-order polynomial fit is applied to the frequency or phase time series to determine the tendency of variations, then it is subtracted from the time series to generate the frequency and phase fluctuation time series about zero. The standard deviations (STDs) of the fluctuations are obtained. Third, according to the signals mode, the data are divided into coherent and incoherent scans. We average the STDs of scans for each mode. Finally, the STDs of all observation stations are averaged to obtain the final results.

To study the change of TEC with different heliocentric distances, we calculate the STDs of the D directly using TEC data with an integration time of 1 s without fitting. Data are then classified again into two categories: coherent and incoherent. We also average the STDs of scans with the same mode and then average the STDs across all observation stations.

To study the effect on ΔDOR group delay and the delay rate from solar wind plasma, we first perform quadratic polynomial fitting on the delay data of the probe with an integration time of 30 s for each scan of each baseline. Then, we calculate the STDs of the fitting residuals. Finally, the STDs of all scans from all baselines are averaged. It should be noted that during the ΔDOR group delay determination process, we utilize observational data from a calibrator source. As a result, ΔDOR group delay fluctuations are primarily influenced by plasma and also contain a minor amount of radio source phase error. Note that the heliocentric distance of the calibrator source is within the range of 10–122 Rs. When the heliocentric distance of the calibrator source decreases, it will introduce more phase errors into the ΔDOR group delay (CCSDS 2019). The impact of the calibrator source on the delay rate is subtracted during the differencing step. In addition, the phase, frequency of signals, and TEC are not affected by the calibrator source since we process only the detector's raw data with Doppler directly but without involving a calibrator source. All data-processing results are shown in Table 2.

We compare the radio observation data of TW1 and the Large Angle and Spectromeric Coronagraph Experiment (LASCO) data of the Solar and Heliospheric Observatory (SOHO) to study the effects of CMEs on spacecraft signals. The changing trends of the STDs of the fluctuations of frequency, phase, and TEC variations for the four stations are consistent in Figure 5, which excludes the possibility of the anomaly on a single station. The TEC variations induced by Earth's ionosphere are calculated using global navigation satellite system data. To eliminate the influence of the ionosphere, we subtract this component from the TEC measurements (Zhou et al. 2020). It can be seen that the frequency, phase, and TEC change increases gradually after 03:00 (Figure 5). The frequency fluctuation is ±0.15 Hz before the outbreak of the CME, with a maximum up to ±1 Hz after the eruption. Meanwhile, the variations of phase fluctuations and TEC range from 5 to 71 rad, and 40 to 265 TECU, respectively. In Figure 5(c), the variation of TEC has exceeded 250 TECU between UTC 05:00 and 05:30.

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Figures 6(a) and (b) show LASCO C3 images on 2021 October 26 and 2021 November 2. The position of Mars on 2021 October 26 is marked with a black arrow in Figure 6(a). Mars's position on 2021 November 2 is outside of the frame in Figure 6(b). The effective imaging range of the C3 is 32 Rs. However, the CCD detector in LASCO C3 is a square with a side length of 21 mm, and its imaging range is a square circumscribed by a circle with a radius of 30 Rs. On 2021 November 2, the apparent heliocentric distance to the line of sight to Mars is 30.6 Rs, and Mars is located in an area outside the CCD's imaging range (Brueckner et al. 1995). Therefore, Figure 6(c) presents a schematic representation of Mars's position in the LASCO C3 field of view on 2021 November 2. Mars is in the direction of the CME eruption.

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DPD is obtained by using two DOR sidetones with a frequency span width of 38.4 MHz for TW1 (1 ps = 5.8 TECU). In general, people study the trend of TEC variations by continuously observing the detector's signals over several hours. However, due to the alternate observations (detector–radio source–detector), the detector's data is discontinuous. In order to obtain a better understanding of the overall trend in TEC variations, we use the method of linear fitting and extrapolation in the literature (He et al. 2022) to connect the DPD data between the scans. Before connecting, we use the continuous 2 hr observation data of TW1 on 2021 October 23 (18.4 Rs) to verify this method. After obtaining a continuous series of DPD values, we simulate the ΔDOR observing mode by intermittently removing some of the DPD data and then connecting the remaining DPD (He et al. 2022). It should be noted that after connecting the DPD data between the scans, to better illustrate the overall trend of DPD variations, we have taken the approach of subtracting the initial value from the entire data set and set the initial value to zero. Finally, we compare the connection trend of the simulated data with the actual values. In the Appendix, the result shows that the trend of changes in DPD obtained by this connection method is similar to the actual trend of changes.

To compare the variations of TEC caused by CME, we select 3 days of data with similar heliocentric distances for further study. We subtract the effect of the Earth's ionosphere. Figure 7 shows the changing trend of connected DPD on 2021 October 26, November 2, and November 9 respectively. It is found that the DPD variations are within 30 ps on both October 26 (22.1 Rs) and November 9 (39.1 Rs). On November 2 (30.6 Rs), the variation from a single scan is greater than 50 ps (290 TECU), and the overall changing trend of the TEC reaches 170 ps (986 TECU). Meanwhile, the decline of the connected DPD indicates that the TEC is increased (He et al. 2022). The DPD technique is useful to describe the CME, as demonstrated here.

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A frequency spike refers to a sudden and significant increase in signal frequency that exceeds the ambient data. Ma et al. (2022) shows that CMEs can cause frequency spikes that can be applied to estimate the propagation velocity of CMEs. We also find two distinctive spikes with the time lag between the arrival time at different radio telescopes in Figure 8. At both 03:02:35 and 05:12:22, the fluctuations of frequency spikes and phase spikes of all stations exceed 1 Hz and 5 rad, respectively. At 03:02:35, Figures 8(a) and (c) show that frequency spikes and phase spikes associated with the CME arrive at KM, SH, BJ, and UR successively. At 05:12:22, it can be seen from Figures 8(b) and (d) that they arrive successively at SH, KM, BJ, and UR.

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To better analyze the velocity and the directionality of the CME, we first analyze the radial and tangential projections of each baseline in the heliocentric coordinate system, as seen in Figure 9. To facilitate understanding, the projected positions of CVN stations on the ecliptic plane in heliographic coordinates are presented in Figure 10. Along the radial projection direction, SH is the closest to the Sun, followed by BJ, KM, and UR is the farthest. SH–UR is suitable for studying CME radial velocity because it has the largest radial component, greater than 1600 km, and the smallest tangential component, within 220 km. On the other hand, the radial projection distance of the BJ–KM baseline is less than 540 km, but their tangential projection distance is the largest among the six baselines, with a distance greater than 875 km, making BJ–KM suitable for studying the CME tangential velocity. Therefore, we study the direction of CME propagation by calculating the velocity of the CME on these two baselines.

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Typically, if the solar wind propagates radially in the ecliptic plane, the spike first reaches the SH projection point closest to the Sun, then followed by the BJ, KM, and UR projection points. However, in Figure 8(a), the spike first reaches the KM point, and in Figure 8(b), between BJ and KM, the spike also first reaches the KM point. This suggests that, in addition to radial velocity, CME has tangential velocity when propagating toward the solar north pole.

As shown in Table 3, the radial and tangential propagation velocities of the solar wind are estimated separately using the SH–UR and BJ–KM baselines. We use the output of PLL with an integration time of 10 ms to calculate the velocity of the CME. As a comparison, we also use cross correlation method to calculate CME velocity (Ma et al. 2021, 2022). The correlation coefficients between the two stations are greater than 0.9. The error bars are determined as half of the difference between the velocities obtained from the two calculation methods.

Table 3. The Velocity of Solar Wind Measured by the Visual Frequency Spikes and Cross Correlation

Time	Spikes	Lag	vrad1 a	${v}_{\tan 1}$ b	vrad2 c	${v}_{\tan 2}$ d
	(Hz)	(s)	(km s−1)	(km s−1)	(km s−1)	(km s−1)
SH 03:02:35.925	1.15	−1.72	950 ± 37.0	...	1024 ± 37.0	...
UR 03:02:37.645	1.09
BJ 03:02:36.915	1.16	1.16	...	945 ± 9.5	...	926 ± 9.5
KM 03:02:35.755	1.10
SH 05:12:22.725	−1.66	−2.87	697 ± 22.5	...	742 ± 22.5	...
UR 05:12:25.595	−1.75
BJ 05:12:23.855	−1.80	0.63	...	1393 ± 58.5	...	1510 ± 58.5
KM 05:12:23.225	−1.97

Notes.

^a v_rad1 means the radial velocity of the CME obtained by visual frequency spikes. ^b ${v}_{\tan 1}$ means the tangential velocity of the CME obtained by visual frequency spikes. ^c v_rad2 means the radial velocity of the CME obtained by cross correlation. ^d ${v}_{\tan 2}$ means the tangential velocity of the CME obtained by cross correlation.

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The CME observed in our study is CME 7 in Li et al. (2022). The time when the CME first occurred in the SOHO/LASCO C2 images is at 21:36 on 2021 November 1. After 5.5 hr of propagation, this CME reached the signal transmission path at 30 Rs and was observed by us. From the above two spikes, at SH 03:02:35, the radial velocity v_rad on the SH–UR baseline and tangential velocity v_tan on the BJ–KM baseline of CME are 987 ± 37.0 and 935.5 ± 9.5 km s⁻¹, respectively, which is consistent with the velocity of 1014 ± 15 km s⁻¹ reported by Li et al. (2022). At SH 05:12:22, v_tan on the BJ–KM baseline is twice as fast as v_rad on the SH–UR baseline, with values of 1451.5 ± 22.5 and 720 ± 22.5 km s⁻¹, respectively. These two velocities are inconsistent with the results in Li et al. (2022). This difference in time lag and velocity can be attributed to the instantaneous velocity variations of the CME. Figure 10 shows that the CME is propagating in a direction approximately 45° offset from the radial projection from SH–UR toward the north pole in the heliocentric coordinate system. Meanwhile, we also observe a similar directional expansion of the CME in the LASCO C3 observation images, which is consistent with the analysis of velocity in this work.

It should be noted that this study employs a different method to measure CME velocities compared to Li et al. (2022). Li et al. (2022) utilized the graduated cylindrical shell modeling technique and analyzed several hours of STEREO-A COR2 and LASCO C2 coronagraph images to perform three-dimensional modeling of the CME. Due to the limited field of view of the coronagraph, the average velocity of the CME front they obtained is within 6 Rs. As a supplementary point, we use the multiground VLBI radio telescopes to detect the instantaneous velocities and density structure of the same CME at 30 Rs in the interplanetary space. From Figures 5 and 8, we can see that the frequency and phase of the spacecraft are very sensitive to the density variations of the CME, and the frequency spikes appeared because of the density contrast between the transient inhomogeneities and the ambient flow. The different appearance time of spikes at different telescopes indicates the dynamic propagation of the solar wind density structures along the spatial projection baselines. The projections along radial and latitudinal directions give the two-dimensional velocity of the CME. This method is also effective at detecting the oscillation and propagation of the nascent dynamic solar wind structure near the Sun, e.g., at 2.6 Rs (Ma et al. 2022). As a matter of fact, the density disturbance of the CME is the integration effects along the direction of the signal transmission path. However, when using spikes to calculate the velocity of the CME, we assume that the spikes are only caused by the density disturbance at the solar proximate point on the ray path. Therefore, this simplified model results in certain estimation errors. Nevertheless, comparison with Li et al. (2022) and SOHO/LASCO shows our method can be used to estimate the propagation direction and velocity of a CME with reasonable accuracy.