First Report of a Solar Energetic Particle Event Observed by China's Tianwen-1 Mission in Transit to Mars

We collected proton flux measurements from two sources: one from the TW-1/MEPA instrument, and the other one from three near-Earth spacecraft, including ACE, SOHO, and Wind. These near-Earth spacecraft are stationed at the Sun–Earth first Lagrange (L1) point, which is about 1.5 million kilometers from Earth (∼0.01 au), along the Sun–Earth connection line.

The TW-1/MEPA data were acquired from the Planet Exploration Program Scientific Data Release System (http://202.106.152.98:8081/marsdata/web/datainfo/main.action#). The level-2 ACE/EPAM/LEMS120 data were available from the ACE Science Center (http://www.srl.caltech.edu/ACE/ASC/level2/). The level-2 SOHO/ERNE data were available for download at https://srl.utu.fi/erne_data/. The level-3 SOHO/COSTEP/EPHIN data were available from http://ulysses.physik.uni-kiel.de/costep/level3/l3i/. The Wind/EPACT/STEP data were downloaded from https://spdf.gsfc.nasa.gov/pub/data/wind/epact/step/differential-ion-flux-1hr/. All data were acquired from 2020 November 28 to December 5 and were collated to a 1 hr resolution.

Considering the measured SEP proton spectra show a clear double-power-law feature, we fit them using a Band-function form, given by Band et al. (1993),

$$\begin{eqnarray}F(E)=\left\{\begin{array}{ll}{{CE}}^{-{\gamma }_{a}}\exp \left(-E/{E}_{0}\right) & \mathrm{for}\ E\lt \left({\gamma }_{b}-{\gamma }_{a}\right){E}_{0},\\ {{CE}}^{-{\gamma }_{b}}{\left[\left({\gamma }_{b}-{\gamma }_{a}\right){E}_{0}\right]}^{\left({\gamma }_{b}-{\gamma }_{a}\right)}\exp \left({\gamma }_{a}-{\gamma }_{b}\right) & \mathrm{for}\ E\gt \left({\gamma }_{b}-{\gamma }_{a}\right){E}_{0},\end{array}\right.\end{eqnarray} \tag{ 1 }$$

where F(E) is the particle fluence, C is a normalization constant, E₀ is the spectral break energy in units of MeV/nuc, and γ_a and γ_b are the spectral indexes in the low- and high-energy ends, respectively.

We use Equation (2) to calculate the index of the peak intensity radial dependence (α) and Equation (3) to calculate the index of the peak intensity IMF path-length dependence (β):

$$\begin{eqnarray}&&J{\left(E\right)}_{\max }\propto {R}^{\alpha (E)},\quad \alpha (E)={\mathrm{log}}_{\tfrac{{R}_{1}}{{R}_{2}}}\displaystyle \frac{J{\left(E\right)}_{\max ,1}}{J{\left(E\right)}_{\max ,2}},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&J{\left(E\right)}_{\max }\propto {L}^{\beta (E)},\quad \beta (E)={\mathrm{log}}_{\tfrac{{L}_{1}}{{L}_{2}}}\displaystyle \frac{J{\left(E\right)}_{\max ,1}}{J{\left(E\right)}_{\max ,2}},\end{eqnarray} \tag{ 3 }$$

where $J{\left(E\right)}_{\max }$ is the measured proton peak intensity in the energy interval E, R(L) is the radial distance (IMF path length) of a spacecraft from the Sun, with the subscript "1" for near-Earth spacecraft (R₁ = 1.0 au, L₁ = 1.152 au), and the subscript "2" for at TW-1 (R₂ = 1.39 au, L₂ = 1.818 au).

The 2020 November 29 SEP event originated from a fast and relatively wide CME, associated with an M4.4-class X-ray flare from active region (AR) 12790. Figure 1(a) illustrates the relative locations of multiple spacecraft with large radial and longitudinal separations in heliocentric Earth ecliptic (HEE) coordinate at 12:00 UT (universal time, same as below) on 2020 November 29. The TW-1 spacecraft was located at 20° east of Earth and about 1.39 au from the Sun, and some other locations, including Earth, Mars, PSP, SolO, and STEREO-Ahead (STA) are also shown. The AR (solar flare) was located at E98 seen from Earth (Kollhoff et al. 2021; Kouloumvakos et al. 2022), as indicated by the black arrow. The nominal Parker spiral IMF lines connecting each location are shown by solid colored curves. The spacecraft locations and the magnetic field footpoints within 1 au are taken from Kollhoff et al. (2021). The longitudinal separation between the AR and PSP is ∼2° and between the AR and STA is ∼51°. From in situ magnetic field measurements, the CME-driven shock reached PSP (at 0.81 au from the Sun) at 18:35 UT on 30 November 2020 and reached STA at 07:23 UT on 2020 December 1. Moreover, this event was also observed by SolO, TW-1, and near-Earth spacecraft. Of note here is that the magnetic field line connected to Earth is calculated by using the 12 hr solar wind speed (∼391 km s⁻¹) measured before the onset of the flare. Because TW-1/MINPA (Mars Ion and Neutral Particle Analyzer) was not operating during that period, there were no direct solar wind observations at TW-1. However, assuming that the solar wind stream observed at Earth does not vary significantly within two days prior to arriving at Earth, then it is easy to see that the observations at Earth and at the TW-1/MINPA correspond to plasma from the same footpoint. This is because the travel time of a solar wind parcel with a speed of 391 km s⁻¹ over 0.39 au is 1.73 days. For a solar rotation of 142 per day, this translates to 2445. Because Mars is 20° east of Earth, Mars and Earth are in very good magnetic connection (assuming a Parker field geometry) in this event. This conclusion is also supported by the recent works of Zhang et al. (2022) and Fan et al. (2022) in which the TW-1/MINPA data were available a few days before this event (between 2020 November 20 and 27). With this solar wind speed, the longitudinal angle between the flare and the magnetic footpoint of Earth is ∼157°, and it is ∼162° for TW-1. In the work of Moradi & Li (2019) and Bian & Li (2021), it was shown that the angular spreading of magnetic field lines at 1 au due to footpoint random walk on the source surface can be as large as 10°. Other relevant work on magnetic field line spreading and lengthening from turbulence has also been done by Ragot (2006) and Laitinen & Dalla (2019). Furthermore, as discussed in Li et al. (2021b), the intrinsic uncertainty associated with a CME-driven shock implies observers separated longitudinally within ∼10° at 1 au can be effectively regarded as connected to the same part of the shock. In this work, we therefore assume that Earth and TW-1 are on the same Parker magnetic field line and are connected to the same area at the shock front. This assumption is well supported by Posner et al. (2013), who found that a spacecraft traveling to Mars would first maintain good magnetic connectivity to Earth and then to Mars, the so-called Hohmann–Parker effect.

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Figures 1(b) and (c) plot the time–intensity profiles as observed by near-Earth spacecraft and TW-1 from day 334 (November 29) to 340 (December 5) of the year 2020, respectively. The vertical dashed line indicates the onset of the flare at 12:34 UT on November 29. Figure 1(b) shows the ensemble measurements from ACE/EPAM (0.59–4.8 MeV), SOHO/EPHIN (4.3–53.0 MeV), and SOHO/ERNE (13.8–53.5 MeV), suggesting that the event is a midsized SEP event with a maximum proton energy around 60 MeV. Earth was located west of the source and therefore observed a gradual increase of low-energy (e.g., <5 MeV) proton intensities. In comparison, high-energy protons (e.g., >30 MeV) show a delayed enhancement (several hours after the onset of flare) and peaked around day 335.8. The peak is followed by a long-duration decay. The onset time for the highest-energy bin of 40–53 MeV is about 6.6 hr after the onset of the flare. This can be explained by an extended shock acceleration process and a varying magnetic connection to the CME-driven shock (or the lack of it) for an observer (Ding et al. 2020; Li et al. 2021b; Ding et al. 2022). High-energy protons are only accelerated when the CME-driven shock is still close to the Sun (e.g., Li et al. 2003, 2005; Hu et al. 2017; Ding et al. 2020; Li et al. 2021b; Li & Lugaz 2022), while low-energy protons can be accelerated at shock front over a wide range of longitudes and at large distances from the Sun. Note that Earth's magnetic footpoint is approximately 157° west of the flare. Since the flare was located at E98°, even if we assume a half-width of the shock to be ∼98°, Earth cannot connect to the shock until the shock arrives at and passes 1 au. However, there is no measurable plasma signature of shock arrival from near-Earth spacecraft. Therefore, particles observed at Earth early on must propagate to the Earth-connected field lines by cross-field diffusion. Because the earliest high-energy particles take at least 6 hr to reach Earth, this can be used to put an upper limit on the strength of cross-field diffusion as protons propagate from the Sun to Earth. Comprehensive modeling studies as done in Li et al. (2021b) are needed to understand the role of perpendicular diffusion in this event. Figure 1(c) plots the proton time–intensity profiles at energies of 2–100 MeV measured by TW-1/MEPA. Obviously, the observed profiles show similar enhancements and decay phases compared to the measurements near Earth, which further supports the assumption that Earth and TW-1 have similar magnetic connections to the shock. Therefore, in the following analysis, we assume Earth and TW-1 are tied on the same field line, enabling us to investigate the physics of particle transport along a magnetic field line with different path lengths and ignore the first-order effect of an inhomogeneous particle source at the shock front.

In Figure 2, we compare the proton time–intensity profiles in similar energy bins from near-Earth measurements and TW-1/MEPA. The upper (lower) row represents the comparison between SOHO/EPHIN (SOHO/ERNE) and TW-1/MEPA. The corresponding energy channels are labeled in each panel, ranging from ∼4 to ∼50 MeV. It is worth noting that within 48 hr after the onset of the associated flare, the proton intensities of TW-1 are always lower than those around Earth. Under the assumption that the parallel diffusion coefficient is significantly larger than the cross-field diffusion coefficient, we can envision the following scenario: at the beginning of this event, some accelerated protons first propagate to the Earth-connected field line via cross-field diffusion and these particles then propagate to Earth and TW-1 along the same field line. Comparing observations at Earth and TW-1/MEPA requires a good understanding of several transport processes, including convection, pitch-angle scattering, and adiabatic deceleration. These processes combine to yield the observed radial dependence of the SEP peak intensities, which will be discussed in more detail below. After day 337 (December 2), the decay phase of SEPs from the TW-1 observation is similar to that of Earth for multiple energy bins. This can be explained by the so-called "reservoir phenomenon" (Roelof et al. 1992; Reames et al. 1997), which argues that in the late phase of large SEP events, the SEPs are nearly uniformly distributed throughout the inner heliosphere. Recent studies suggested that magnetic mirroring and the effect of perpendicular diffusion are important in the reservoir phenomenon (Wang et al. 2021).

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Although the cross-field diffusion coefficient is significantly smaller than the parallel diffusion coefficient, given enough time, energetic particles can still occupy a broad range of longitudes through cross-field diffusion. In fact, in this event, because Earth and TW-1 are not magnetically connected to the shock front, cross-field diffusion is necessary to understand these observations. We speculate that cross-field diffusion plays a key role in forming the reservoir of SEPs in this event. We note that the SEP event of 2020 November 29 bears an interesting resemblance to the 2006 December 5 event: Both events have a fast CME accompanying a large east limb flare and the onset of SEPs in both events is delayed hours after the flare. In the 2006 SEP event, the onset of SEPs was preceded by a small energetic neutral atom (ENA) event (Mewaldt et al. 2009) in the energy range of a few MeV. Because for the eastern event an earlier signal due to ENA can be clearly discerned from the SEPs, we were curious to examine if there were also ENA precursors in this event. Assuming a 2 (4) MeV ENA particle, the travel time from the Sun to Mars is ∼3.25 (2.3) hr. Upon further examination, however, we do not find ENA precursors in this event.

Figure 3 plots the temporal evolution of proton fluence spectra with a 12 hr interval increase, with the starting time of 2020-11-30 00:03:20 UT and the ending time marked on the top right of each panel. To match the energy range of TW-1/MEPA, the spectra at Earth use data from the measurements of ACE/EPAM, Wind/EPACT, SOHO/EPHIN, and SOHO/ERNE. Figure 3(a) shows that the low-energy fluence of TW-1 is clearly lower than that of the near-Earth spacecraft in the first 24 hr, reflecting that the larger the IMF path length, the more significant the transport effect. As time increases, however, the two time-integrated proton spectra gradually approach each other (Figures 3(b) and (c)), and they almost overlap after 60 hr and onward after the solar flare erupted (Figures 3(d)–(h)).

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The event-integrated spectra show a clear double-power-law feature, prompting us to utilize a commonly used Band-function form (Band et al. 1993) to fit the spectrum in Figure 3(h), which is integrated for 108 hr after the onset of the flare. Based on Equation (1), the spectrum near Earth has a spectral index (γ_a ) ∼1.34 for the low-energy end, ∼6.36 (γ_b ) for the high-energy end, and a break energy (E₀) of ∼8.1 MeV. The corresponding values of TW-1 are ∼0.67, ∼6.92, and ∼5.5 MeV, respectively. The smaller spectral index at the low-energy end of TW-1 can be understood in terms of transport effects where pitch-angle scattering and adiabatic deceleration are dominant factors for the propagation of low-energy particles. A radial-dependent low-energy spectral index is an important feature in understanding the mean free path of low-energy particles. At high energies, the spectral indexes for both Earth and TW-1 are similar and they are softer than those from most large SEP events, which are typically in the range of 2–5 (Mewaldt et al. 2012). Furthermore, the break energies at Earth and at TW-1 are very close, suggesting that this break and the spectrum above the break show no clear radial dependence. Some earlier work suggested that a double power law or a power law with an exponential decay at high energies is the consequence of a finite lifetime and a finite size of shock (Forman & Drury 1983; Ellison & Ramaty 1985). Mason et al. (2012) studied the interplanetary transport effects in some large SEP events using a transport model that includes magnetic focusing, convection, adiabatic deceleration, and pitch-angle scattering. They found that the spectral break location differs slightly through the transport, and the particle spectrum at high energy shows a small radial dependence. They suggested that the spectral break must be a consequence of the acceleration process in the source region. In contrast, by fine-tuning solar wind turbulence levels, Li & Lee (2015) and Zhao et al. (2017) have argued that a double-power-law spectrum can result from a single power-law spectrum at the source, but gradually develop as particles propagate out from the Sun. In this scenario, the break location, as well as the spectral shape above the break location, depends on the radial distance of the observer. In this work, the similarity of the spectra between Earth and TW-1 indicates that transport effects play a minor role in causing the spectral break. The observations at Earth and Mars suggest that the double-power-law spectrum is likely generated at the acceleration site. Furthermore, the very soft high-energy spectral index may suggest that the shock acceleration efficiency is not strong in this event. This is consistent with the maximum proton energy of around 60 MeV in this event.

The dependence of SEP peak intensities on radial distance and longitude has been examined in many previous works, such as Lario et al. (2006, 2013), He et al. (2017), and references therein. In these phenomenological studies, the radial dependence of peak intensities of SEPs is often fitted by R^α in Equation (2). As discussed above, in this event, Earth and TW-1 are connected in the same field line, and the effects of the inhomogeneous source distribution along the shock can be ignored. Therefore, this is an ideal case for studying how the peak intensity varies along a Parker field line and/or the radial dependence. Figure 4(a) plots the peak intensities of SEPs observed by SOHO/ERNE and TW-1/MEPA, respectively. Due to the differences in effective energies between the two instruments, we use a Band-function form in Equation (1) to fit the observation data from 13.8 to 67.3 MeV. We then calculate the index α as a function of proton energies from the two fitted curves as shown in Figure 4(a) (colored blue and red) using Equation (2). Further, to study the IMF path-length (L) dependence, we assume an L^β relation for the SEP peak intensities and obtain the index β from Equation (3). We plot the calculated indexes α and β as a function of energies (13.8–67.3 MeV) in Figure 4(b). Because the particles propagate along magnetic field lines, the IMF length dependence (L^β ) is more physical and proper than the radial dependence.

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From Figure 4(b), we can see that although the values of α and β are very different, they both have similar variation trends and significant energy dependence. As expected, the magnitude of β is smaller than that of α due to the winding nature of the Parker spiral, which means that the path length increases much faster than linearly with radial distance. Given that previous works, including both observations and numerical simulations, focused mainly on the study of α, we will also discuss it in the following. As shown by the solid line in Figure 4(b), the radial dependence index, α, has a clear two-stage energy dependence—specifically, it increases with increasing energy below ∼20 MeV and varies between −2.5 and −2.0, whereas it decreases with increasing energy for energies above ∼20 MeV. In some early works (e.g., Smart & Shea 2003; Lario et al. 2006, and references therein), proton fluxes from 1 au to radial distances >1 au were recommended to use the functional form of R^−3.3, with variations ranging from R⁻⁴ to R⁻³, based on both the results from a numerical model of diffusive energetic particle transport in the heliosphere and the spacecraft measurements at energies of 10 to 70 MeV from 1 to 5 au. Using the 1D Particle Acceleration and Transport in the Heliosphere (PATH) model (Zank et al. 2000; Li et al. 2003; Rice et al. 2003), Ruzmaikin et al. (2005) found α in the range of −2.3 (low energy) to −2.9 (high energy). In the work of Lario et al. (2006), they reported that α varies from −2.7 to −1.9 for 4–13 and 27–37 MeV proton peak intensities in a statistical study of 72 SEP events. However, this statistical work ignored the longitudinal separation of the spacecraft from the source location and the influence of the inhomogeneous source on the shock. In the modeling work of He et al. (2017), they suggested that α ∼ −1.7 is the lower limit of SEP peak intensities in the case of observers at different radial distances but connected to an impulsive source along the same field line. He et al. (2017) further suggested that this index does not strongly depend on the particle energies and the ratio of perpendicular diffusion to parallel diffusion, in contrast to the work of Lario et al. (2007), who suggested that α highly depends on the mean free path of the protons, which can have a strong dependence on particle energy. Lario et al. (2007) suggested that (1) a smaller mean free path leads to a larger decrease of peak intensity with radial distance, and (2) the higher the particle energy, the smaller the decrease of peak intensity with radial distance. In contrast, our results show that the higher the energy of protons, the larger the decrease of peak intensity with larger radial distances. Interestingly, such an energy dependence was predicted in the work of Ruzmaikin et al. (2005) and was also confirmed in subsequent event modeling by Verkhoglyadova et al. (2009, 2010) using the PATH model. Although it was a 1D model, the work of Ruzmaikin et al. (2005) correctly captured the radial dependence of the peak intensity for this event. Note that in this event, the source of the accelerated protons is located east of the magnetic footpoints of Earth and TW-1, and the particles propagate to the field lines that connect to Earth and TW-1 in a longer duration, which amplifies the effects of the transport process, including both parallel diffusion and perpendicular diffusion, as well as adiabatic cooling. A better understanding of the radial dependence calls for a 2D/3D modeling effort, which can be achieved by the improved PATH (iPATH-2D) model (Hu et al. 2017, 2018).