Using Tianwen-1 Differential One-way Range Signals to Probe Corotating Interaction Regions: Case Studies

The study reports the first detection of corotating interaction regions (CIRs) in the solar wind by the differential one-way range (DOR) signals transmitted by Tianwen-1. Differential phase delay is calculated for the DOR signals. Variations of the total electron content (TEC) along the signal path between Tianwen-1 and the ground stations are then derived from changes in the differential phase delay. Large TEC variations are found for 2021 February 11, 18, and 19 even after the influence from the Earth’s ionosphere has been removed. In situ solar wind measurements and the corresponding simulation results further show that the TEC variations are caused by the CIRs that passed through the signal path on these days. The study demonstrates that CIR structures can be probed using deep-space spacecraft range signals. Such measurements can be used to constrain global solar wind forecast models.


Introduction
Tianwen-1 is the first Chinese Mars spacecraft.It was launched on 2020 July 23 and reached Mars on 2021 February 10.Since then, the orbiter has been orbiting Mars (Zou et al. 2021;Zhang et al. 2022).A high gain antenna on board the orbiter kept transmitting differential one-way range (DOR) signals, which contain five spectral lines in the X band (∼ 8.4 GHz) and span a frequency range of 38.4 MHz (He et al. 2022).The DOR signals are received by the Chinese very long baseline interferometry (VLBI) network for improving the accuracy of Tianwen-1ʼs orbit determination (Liu et al. 2022;Yang et al. 2022).The Chinese VLBI network includes four radio telescopes, which are Tianma (TM; 65 m), Beijing (BJ; 50 m), Kunming (KM; 40 m), and Urumqi (UR; 25 m) (Liu et al. 2014;He et al. 2017).
When the DOR signals propagate from the spacecraft to the Earth, the interplanetary solar wind plasma causes extra time delays that vary with the signal frequency.Differential phase delay of the DOR signals can be used to deduce variations of the total electron content (TEC) along the signal path and thus provides information on the interplanetary solar wind plasma structures.Recently, He et al. (2022) demonstrated that the DOR signals can detect corona mass ejections (CMEs) passing through the signal path in the interplanetary space.Besides CMEs, corotating interaction regions (CIRs) are also typical large-scale structures in the interplanetary solar wind.This paper presents the first detection of CIRs by the DOR signals transmitted by Tianwen-1.
CIR is a compressed region with relatively high plasma density and magnetic field.It is formed between a slow solar wind and a fast solar wind originating from a corona hole (Belcher & Davis 1971;Smith & Wolfe 1976;Pizzo 1978;Hajra & Sunny 2022).Associated with the rotation of the Sun, a CIR often appears multiple times at a given interplanetary location after each solar rotation period (Snyder et al. 1963;Shelley et al. 1972;Perez et al. 2012).The TEC along the signal path will considerably increase and then decrease if a CIR passes through the Tianwen-1 DOR signal path.Indeed, it is found that the TEC deduced from the Tianwen-1 DOR signals has large variations for 2021 February 11, 18, and 19.The influence of the Earth's ionosphere has been removed using the Global Navigation Satellite System (GNSS) data.The Tianwen-1 orbit information confirms that the signal path did not pass the Martian ionosphere and was over 0.95 Astronomical Units (au) from the Sun on these days.Furthermore, the space weather forecast shows that there was no CME propagating in the hemisphere toward the Earth from 2021 February 1 to 20.Thus, the large TEC changes on 2021 February 11, 18, and 19 are likely caused by CIRs passing through the DOR signal path.In situ solar wind measurements and the corresponding simulation results further confirm that this is the case.
The rest of the paper is organized as follows.Section 2 presents the large differential phase delay changes of the Tianwen-1 DOR signals and the corresponding TEC variations on 2021 February 11, 18, and 19.Section 3 provides evidence to show that the large TEC variations are caused by CIRs passing through the DOR signal path.Section 4 concludes the paper.Note that time is in Coordinated Universal Time (UTC) throughout the paper.

Observation Results
The Tianwen-1 Mars orbiter transmits DOR signals at five frequencies: 8411.8,8427.2, 8431.0 (carrier), 8434.8, and 8450.2MHz (He et al. 2022;Liu et al. 2022).In the present study, the differential phase delay between the DOR signals at 8411.8 MHz (the lowest frequency) and 8450.2MHz (the highest frequency) is calculated.The details of calculating the differential phase delay and the corresponding TEC change have been described in He et al. (2021) and He et al. (2022).
It should be noted that VLBI observation was not continuously performed every day, but every 2 or 3 days and often with an observation duration of about 4 hr or less.However, VLBI observation was performed more frequently and with longer durations from 2021 February 10 to 28, with the purpose of accurately determining Tianwen-1ʼs orbit around Mars shortly after its insertion.Thus, we have scrutinized the observation data during this period to search for possible CIR influence on the DOR signals, because it takes rather long (tens of hours) for CIRs to pass the DOR signal path.Furthermore, the space weather forecast shows that there were CMEs propagating in the hemisphere toward the Earth after 2021 February 20.This leaves only the data from 2021 February 10 to 20 suitable for studying pure CIR influence on the DOR signals.And we found clear CIR influence on the DOR signals on 2021 February 11, 18, and 19.
Figure 1 shows considerable differential phase delay changes on 2021 February 11, 18, and 19.Note that the differential phase delay might further vary beyond the three intervals shown, but the DOR signals were only recorded during these intervals on the three days.The corresponding TEC change is displayed by the vertical axis on the right in each panel (in units of TECU, 1 TECU = 10 16 electrons m −2 ).Here, the influence of the Earth's ionosphere has been removed using the GNSS data.The curves of different colors represent the results from the different Chinese VLBI ground stations as indicated by the legends.On 2021 February 18, only three stations participated in the observation.
In all three panels of Figure 1, the differential phase delays from different stations vary similarly, and the corresponding TEC changes are over 60 TECU.The minor differences between the different curves in Figure 1 are caused mainly by two reasons.First, the DOR signals received by different stations suffer different local ionosphere influences that cannot be removed completely.Second, during the Tianwen-1 mission, the Chinese VLBI stations alternately observed the spacecraft and reference quasars for calibration.This leads to temporal gaps in the differential phase delay calculated.The various scans of the differential phase delay (the thick line segments in Figure 1) have been connected by a linear fitting method as in He et al. (2022).Thus, they may be slightly different from the true variation trends.
The orbit information of Tianwen-1 shows that the minimum distance of the DOR signal path to Mars was more than 80,000 km during the intervals shown.Clearly, the signal path did not pass the Martian ionosphere.On the other hand, even if there are some charged particles that are blown away from Mars and happen to get into the signal path, their spatial scale is too small to cause any significant TEC changes.Note that a density variation of 200 cm −3 along a spatial length of 50,000 km (∼15 Mars radii) produces a TEC variation of only 1 TECU.Moreover, the minimum distance of the signal path to the Sun was more than 0.95 au in the three days.Thus, some plasma structures in the interplanetary solar wind, rather than in the solar corona region, should have traversed the DOR signal path and caused the differential phase delay variations.Evidence is presented in the next section to demonstrate that the large TEC changes displayed in Figure 1 correspond to two CIRs traversing the DOR signal path.The variation in Figure 1(a) is caused by one CIR moving out of the signal path, causing the TEC to decrease.Unfortunately, due to the limited VLBI observation time, no data were recorded before the interval shown when the CIR moved into the signal path.The variations in Figures 1(b) and (c) are caused by another CIR moving into and out of the signal path, causing the TEC to first increase and then decrease.

Analysis
Figure 2 displays the solar wind structures at 09:00 on 2021 February 11 and 18, which are obtained from the Wang-Sheeley-Arge (WSA)-Enlil online archive system.WSA-Enlil is a large-scale, physics-based prediction model of the heliosphere (Space Weather Prediction Center 2023).Here, the Earth, Mars, and STEREO-A positions are also marked and the white arrows indicate the corresponding DOR signal path in the two days.Figure 2 shows that a CIR is passing through the DOR signal path on both days.Furthermore, the WSA-Enlil online archive system confirms that there is no CME propagating in the hemisphere toward the Earth from 2021 February 1 to 20.
Given the positions of the Earth, Mars, and STEREO-A shown in Figure 2, when a CIR passes through the DOR signal path, it should have already passed STEREO-A and will pass the Earth shortly.Since the solar longitude angle between the Earth and STEREO-A is about 54°from 2021 February 11 to 18, and considering that the solar rotation period is 26 days, the time lag between when the CIR passes the Earth and STEREO-A should be about 4 days.Subsequently, the in situ solar wind parameter measurements by STEREO-A and near the Earth are examined during the 5 ∼ 8 days before and after the intervals of interest, respectively.
Figure 3  From top to bottom, the different rows of Figure 3 display the solar wind density, speed, temperature, and total magnetic field, respectively.The red dashed line in each column indicates the solar wind structure of interest and is at the time of the solar wind speed maximum within the structure.In the left column, the solar wind parameters shown have obvious increases on 2021 February 9.The solar wind speed and temperature increases lag a few hours behind the solar wind density and magnetic field increases, indicating a CIR structure passing STEREO-A on 2021 February 9. Similarly, the right column of Figure 3 indicates a CIR structure passing the Earth on 2021 February 13.The time lag between when the structures passed STEREO-A and the Earth is about 4 days, consistent with the estimate above.Furthermore, the CIR could be observed more than once by STEREO-A and spacecraft near the Earth.We checked the OMNI data of solar wind parameters in 2021 March, and similar CIR structures were observed on 2021 March 9 by STEREO-A and on 2021 March 13 near the Earth.So the CIR reappeared at the spacecraft locations at an interval of about 28 days.After removing the influence of the spacecraft's motion, the interval is around 26 days and very close to the solar differential rotation period at the solar equator to mid-latitude regions.This further proves that the large solar wind density increases on 2021 February 9 (Figure 3  To quantitatively examine the effect of the CIRs passing through the DOR signal path, the CIR structures are constructed based on the in situ solar wind plasma measurements of STEREO-A.The subsequent changes in the differential phase delay and the TEC are calculated.The    determined by setting the solar rotation period as 26 days and the solar wind speed as 350 km s −1 (see Figure 3(b)).In addition, it is assumed that the solar plasma density decreases as 1/r 2 due to the radial expansion of the solar wind, where r is the radial distance from the Sun.The time in Figure 5(a) is at 00:00 on 2021 February 11, but the corresponding solar wind density near the Earth was measured by STEREO-A at 00:00 on 2021 February 7 (since the Parker spiral lines rotate with the Sun).The solar wind background density is 5 r 2 N/cm 3 .As Figure 5(a) shows, the condensed density region is very close to the DOR signal path (white arrow).The differential phase delay and TEC changes associated with the CIR passing through the DOR signal path are then calculated and presented in Figure 5 Simulations based on the solar wind density predicted by the WSA-Enlil model (as shown in Figure 2) are also carried out.The differential phase delay and TEC calculated show similar variation patterns as in Figure 1, but the variation amplitudes are smaller, and the variation time windows do not match (either earlier (Figure 2 3 and 4).Hence, just like the in situ measurements, the differential phase delay calculated from the DOR signals can be used to not only probe the solar wind plasma structures but also constrain their propagation speeds and densities.At the present time, the solar wind forecast models often compare their results only with in situ measurements.A good agreement between the model results and in situ measurements at limited locations cannot guarantee the reliability of the model results globally.In contrast, the TEC variations derived from the differential phase delay are measurements along the signal paths and provide a reference on a much larger scale.

Conclusion
The differential phase delay of Tianwen-1 DOR signals is calculated, and the corresponding TEC variations are obtained.Large variations in TEC were noticed on 2021 February 11, 18, and 19 even after the influence of the Earth's ionosphere had been removed.The signal path did not go through the Martian ionosphere and was over 0.95 au from the Sun on these days.Further evidence, including the solar wind structures predicted by the WSA-Enlil model, in situ solar wind measurements, and the subsequent simulation results, shows that the TEC variations are caused by the CIRs passing through the DOR signal path.The study represents the first observation of CIR structures using DOR signals.CIRs traversing deep-space spacecraft range signal paths can cause significant time delays of the range signals.In comparison with in situ measurements, the TEC variations derived from the differential phase delay are measurements along the signal paths and provide a reference on a much larger scale.Thus, the deep-space spacecraft range signals not only can be used to probe solar wind structures but also help to constrain global solar wind forecast models.

ORCID iDs
Qingbao He https:/ /orcid.org/0000-0003-2605-7083Zhichao Wang https:/ /orcid.org/0000-0001-9234-3921Kaijun Liu https://orcid.org/0000-0001-5882-1328 Figure2displays the solar wind structures at 09:00 on 2021 February 11 and 18, which are obtained from the Wang-Sheeley-Arge (WSA)-Enlil online archive system.WSA-Enlil is a large-scale, physics-based prediction model of the heliosphere (Space Weather Prediction Center 2023).Here, the Earth, Mars, and STEREO-A positions are also marked and the white arrows indicate the corresponding DOR signal path in the two days.Figure2shows that a CIR is passing through the DOR signal path on both days.Furthermore, the WSA-Enlil online archive system confirms that there is no CME propagating in the hemisphere toward the Earth from 2021 February 1 to 20.Given the positions of the Earth, Mars, and STEREO-A shown in Figure2, when a CIR passes through the DOR signal path, it should have already passed STEREO-A and will pass the Earth shortly.Since the solar longitude angle between the Earth and STEREO-A is about 54°from 2021 February 11 to 18, and considering that the solar rotation period is 26 days, the time lag between when the CIR passes the Earth and STEREO-A should be about 4 days.Subsequently, the in situ solar wind parameter measurements by STEREO-A and near the Earth are examined during the 5 ∼ 8 days before and after the intervals of interest, respectively.Figure3shows the solar wind parameters measured by STEREO-A (Bemporad 2011) from 2021 February 7 to 11 (panels (a)-(d)) and by spacecraft near the Earth from 2021 February 11 to 15 (panels (e)-(h)).Those measurements are obtained from the OMNI website (Papitashvili & King 2020).From top to bottom, the different rows of Figure3display the solar wind density, speed, temperature, and total magnetic field, respectively.The red dashed line in each column indicates the solar wind structure of interest and is at the time of the solar wind speed maximum within the structure.In the left column, the solar wind parameters shown have obvious increases on 2021 February 9.The solar wind speed and temperature increases lag a few hours behind the solar wind density and magnetic field increases, indicating a CIR structure passing STEREO-A on 2021 February 9. Similarly, the right column of Figure3indicates a CIR structure passing the Earth on 2021 February 13.The time lag between when the structures passed STEREO-A and the Earth is about 4 days, consistent with the estimate above.Furthermore, the CIR could be observed more than once by STEREO-A and spacecraft near the Earth.We checked the OMNI data of solar wind parameters in 2021 March, and similar CIR structures were observed on 2021 March 9 by STEREO-A and on 2021 March 13 near the Earth.So the CIR reappeared at the spacecraft locations at an interval of about 28 days.After removing the influence of the spacecraft's motion, the interval is around 26 days and very close to the solar differential rotation period at the solar equator to mid-latitude regions.This further proves that the large solar wind density increases on 2021 February 9 (Figure3(a)) and 13 (Figure 3(e)) are related to a CIR passing STEREO-A and the Earth in succession, although the speed increase in Figure 3(b) Figure2displays the solar wind structures at 09:00 on 2021 February 11 and 18, which are obtained from the Wang-Sheeley-Arge (WSA)-Enlil online archive system.WSA-Enlil is a large-scale, physics-based prediction model of the heliosphere (Space Weather Prediction Center 2023).Here, the Earth, Mars, and STEREO-A positions are also marked and the white arrows indicate the corresponding DOR signal path in the two days.Figure2shows that a CIR is passing through the DOR signal path on both days.Furthermore, the WSA-Enlil online archive system confirms that there is no CME propagating in the hemisphere toward the Earth from 2021 February 1 to 20.Given the positions of the Earth, Mars, and STEREO-A shown in Figure2, when a CIR passes through the DOR signal path, it should have already passed STEREO-A and will pass the Earth shortly.Since the solar longitude angle between the Earth and STEREO-A is about 54°from 2021 February 11 to 18, and considering that the solar rotation period is 26 days, the time lag between when the CIR passes the Earth and STEREO-A should be about 4 days.Subsequently, the in situ solar wind parameter measurements by STEREO-A and near the Earth are examined during the 5 ∼ 8 days before and after the intervals of interest, respectively.Figure3shows the solar wind parameters measured by STEREO-A (Bemporad 2011) from 2021 February 7 to 11 (panels (a)-(d)) and by spacecraft near the Earth from 2021 February 11 to 15 (panels (e)-(h)).Those measurements are obtained from the OMNI website (Papitashvili & King 2020).From top to bottom, the different rows of Figure3display the solar wind density, speed, temperature, and total magnetic field, respectively.The red dashed line in each column indicates the solar wind structure of interest and is at the time of the solar wind speed maximum within the structure.In the left column, the solar wind parameters shown have obvious increases on 2021 February 9.The solar wind speed and temperature increases lag a few hours behind the solar wind density and magnetic field increases, indicating a CIR structure passing STEREO-A on 2021 February 9. Similarly, the right column of Figure3indicates a CIR structure passing the Earth on 2021 February 13.The time lag between when the structures passed STEREO-A and the Earth is about 4 days, consistent with the estimate above.Furthermore, the CIR could be observed more than once by STEREO-A and spacecraft near the Earth.We checked the OMNI data of solar wind parameters in 2021 March, and similar CIR structures were observed on 2021 March 9 by STEREO-A and on 2021 March 13 near the Earth.So the CIR reappeared at the spacecraft locations at an interval of about 28 days.After removing the influence of the spacecraft's motion, the interval is around 26 days and very close to the solar differential rotation period at the solar equator to mid-latitude regions.This further proves that the large solar wind density increases on 2021 February 9 (Figure3(a)) and 13 (Figure 3(e)) are related to a CIR passing STEREO-A and the Earth in succession, although the speed increase in Figure 3(b)

Figure 4
presents the solar wind parameters measured by STEREO-A from 2021 February 13 to 20 (panels (a)-(d)) and by spacecraft near the Earth from 2021 February 17 to 24 (panels (e)-(h)) in the same format as Figure 3.Following the analysis of Figure 3, the large solar wind density increases on 2021 February 15 and 16 (Figure 4(a)) and on 2021 February 19 and 20 (Figure 4(e)) are caused by a CIR passing STEREO-A and the Earth in succession.The time lag is again about 4 days.In addition, the OMNI data of solar wind parameters on 2021 March 14 and 15 (observed by STEREO-A) and on 2021 March 19 and 20 (observed near the Earth) also demonstrate similar increases, confirming a CIR structure corotating with the Sun.Obviously, the CIR shown in Figure 4 has a much larger size than the one shown in Figure 3. Therefore, it would take a longer time for the CIR in Figure 4 to traverse the DOR signal path.The TEC variations shown in both Figures 1(b) and (c) indeed correspond to this larger-size CIR.The TEC reached its maximum at 12:00 on 2021 February 18 and started to decrease afterward (Figure 1(b)), while the TEC decrease continued on February 19 (Figure 1(c)).

Figure 1 .
Figure 1.Differential phase delays and their corresponding TEC changes (right axes) on 2021 February 11 (a), February 18 (b), and February 19 (c), respectively.The contribution of the Earth's ionosphere has been removed.

Figure 5
Figure 5(a) displays the CIR structure constructed using the solar wind density data from 2021 February 7 to 11 measured by STEREO-A.Here the Parker spiral lines have been

Figure 2 .
Figure 2. Solar wind structures on 2021 February 11 (a) and 2021 February 18 (b) predicted by the WSA-Enlil model.The Earth, Mars, and STEREO-A positions and the corresponding DOR signal path are also marked.

Figure 3 .
Figure 3.In situ measurements of solar wind plasma by STEREO-A from 2021 February 7 to 11 (a)-(d) and near the Earth from 2021 February 11 to 15 (e)-(h).From top to bottom, the plots show the solar wind density, speed, temperature, and total magnetic field, respectively.The red dashed lines indicate the times of the solar wind speed maxima within the CIRs of interest.
(b).The TEC indeed has a large variation.The change enclosed by the red circle in Figure 5(b) is like the observed one shown in Figure 1(a), in terms of both time and amplitude ranges.Similarly, Figure 5(c) shows the CIR structure constructed using the solar wind density data from 2021 February 13 to 18 measured by STEREO-A.The time in Figure 5(c) is at 00:00 on 2021 February 17, and the solar wind density near the Earth was measured by STEREO-A at 00:00 on 2021 February 13.Other solar wind parameters are set the same as the ones in Figure 5(a).Since the CIR size is large, the changes in the differential phase delay and TEC are calculated for 2021 February 17, 18, and 19 (Figure 5(d)).As Figure 5(d) demonstrates, the TEC first increases and then decreases; the overall change pattern is similar to what is shown in Figures 1(b) and (c), and the amplitude variation range is also comparable with the ones in Figures 1(b) and (c).
(a)) or later (Figure 2(b)) than the ones shown in Figure 1.This is because the predicted CIR densities in Figure 2 are significantly smaller than the in situ

Figure 4 .
Figure 4.In situ measurements of solar wind plasma by STEREO-A from 2021 February 13 to 20 (a)-(d) and near the Earth from 2021 February 17 to 24 (e)-(h).From top to bottom, the plots show the solar wind density, speed, temperature, and total magnetic field, respectively.The red dashed lines indicate the times of the solar wind speed maxima within the CIRs of interest.

Figure 5 .
Figure 5. Simulation results of the CIRs passing through the DOR signal path.(a) Constructed CIR structure on 2021 February 11 using the solar wind density data measured by STEREO-A.(b) The relative changes in the differential phase delay and TEC on 2021 February 11.(c) Constructed CIR structure on 2021 February 17 using the solar wind density data measured by STEREO-A.(d) The relative changes in the differential phase delay and TEC on 2021 February 17, 18, and 19.