Upstream proton cyclotron waves at Mars during the passage of solar wind stream interaction regions

Proton cyclotron waves (PCWs) upstream from Mars are generated by ion–ion instabilities due to the interaction between the solar wind and the pickup protons that originate from the extended hydrogen (H) exosphere of Mars, indicating a loss of H to interplanetary space. Their occurrences and properties associated with nominal solar wind conditions have been widely studied, but relatively little is known about PCW activity under extreme solar wind conditions. In this work we characterize the upstream PCWs during the passage of solar wind stream interaction regions (SIRs) utilizing in situ observations by the Mars Atmosphere and Volatile EvolutioN spacecraft from October 2014 to August 2021. The 46 analyzed SIR events are a subset of the events that occurred in the perihelion season of Martian years 32–35. We find that the PCW occurrence rate is increased by a factor of about 1.8 during the SIR phase relative to the pre-SIR and post-SIR phases. Furthermore, the PCW activity tends to occur more frequently in the leading portion of the SIR. The PCWs detected during the SIR phase have more pronounced wave characteristics, namely larger wave amplitudes, smaller propagation angles with respect to the background magnetic field, and closer-to-circular polarization.


Introduction
Due to weak gravity and the lack of an internal magnetic field on Mars, the Martian hydrogen (H) exosphere extends far beyond the bow shock (BS) and directly interacts with the solar wind. The upstream neutral H atoms can be ionized through photoionization, charge exchange, and electron impact (Zhang et al. 1993). The newborn protons are immediately picked up by the solar wind electromagnetic fields. As a nonthermal component of the solar wind velocity distribution function, these so-called pickup protons provide free energies that induce several kinetic instabilities (Wu & Davidson 1972;Wu & Hartle 1974). Interaction of the beam of pickup protons with the background solar wind plasma enables wave generation through electromagnetic ion-ion instabilities. The resonant instabilities are largely dependent on the interplanetary magnetic field (IMF) cone angle, α VB , the angle between the solar wind velocity vector and the IMF (Tsurutani & Smith 1986;Tsurutani et al. 1987). Linear theories predict that the electromagnetic ion-ion right-hand (RH) instability is the dominant mode for low to moderate α VB , while the electromagnetic ion-ion left-hand (LH) instability becomes the predominant mode when α VB is large and particularly close to ∼90 • . The transition between the two types of instabilities is proposed to take place around 70 • (Gary 1991). Both resonant instabilities can excite waves observed near the local proton gyrofrequency and, with a LH polarization, in the rest frame of Mars (or a spacecraft orbiting Mars); these waves are known as proton cyclotron waves (PCWs). It should be noted here that the RH mode is perceived to be a LH polarized wave in the spacecraft frame due to the anomalous Doppler effect (Mazelle et al. 2004).
Since the first detection of PCWs at Mars by the MAGMA magnetometer on board the Phobos-2 spacecraft in 1989 (Russell et al. 1990), their specific properties, generation mechanisms, and generation conditions have received considerable attention from theoretical and experimental points of view (Brain et al. 2002;Mazelle et al. 2004;Wei & Russell 2006;Wei et al. 2011Wei et al. , 2014Bertucci et al. 2013;Romanelli et al. 2013Romanelli et al. , 2016Ruhunusiri et al. 2015Ruhunusiri et al. , 2016Romeo et al. 2021;Lin et al. 2022). It is now widely known that PCWs are LH polarized in the spacecraft frame and propagate nearly parallel to the background magnetic field direction. In addition to the IMF cone angle mentioned above, their generation is also strongly dependent on solar wind properties, for example the solar wind particle flux, as well as on the density of the newborn protons relative to the background solar wind plasma  A158, page 1 of 12 Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is published in open access under the Subscribe to Open model. Subscribe to A&A to support open access publication. Romanelli et al. 2016), roughly similar to the scenario at Venus (Delva et al. 2011a(Delva et al. ,b, 2015. For example, Lin et al. (2022) find that, around the peak of the X8.2 flare on 10 September 2017, the increased solar irradiance gave rise to higher pickup proton fluxes upstream from Mars and therefore a higher relative density, which in turn excited PCWs.
Stream interaction regions (SIRs) arise when fast solar wind streams emanating from coronal holes overtake and interact with the preceding slow stream (Richardson et al. 1996;Gosling & Pizzo 1999;Jian et al. 2006;Richardson 2018;Huang et al. 2019, and references therein). The boundaries separating what are originally the fast and slow streams are referred to as the stream interfaces (SIs). SIRs are typically characterized by enhanced plasma densities, temperatures, pressures, and magnetic field magnitudes. SIRs, one of the predominant large-scale solar wind structures, have an average duration of about 37.0 hr near Mars (1.38-1.67 AU), which is comparable to that near Earth (1 AU; Huang et al. 2019). The leading edge of an SIR is a forward pressure wave that propagates into the slow solar wind ahead, and the trailing edge is a reverse pressure wave that propagates back into the trailing high-speed stream. At large heliocentric distances, the pressure waves commonly steepen into forward and reverse shocks. Huang et al. (2019) find that the shock association rate of SIRs is about 33.3% near the Martian orbit (∼1.52 AU). The shocks associated with SIRs can accelerate solar wind particles up to a few MeV/n in energy, which often peak either in the trailing portion of the SIRs (from the SIs to the trailing edges) or in the high-speed streams beyond the SIRs (Ebert et al. 2012;Richardson 2018, and references therein). SIRassociated energetic particles have been observed upstream of Mars in several studies (Lee et al. 2017;Thampi et al. 2019). Like interplanetary coronal mass ejections (ICMEs), SIRs can give rise to enhanced solar wind plasma and field disturbances and drive major space weather impacts at Mars. The impacts typically include a significant compression and reconfiguration of the induced magnetosphere and ionosphere, enhanced ion energization and escape, and increased particle precipitation and atmospheric heating and chemistry (generally associated with incident solar energetic particles), as recorded in the past using multi-spacecraft measurements (Dubinin et al. 2009;Morgan et al. 2010;Hara et al. 2011;Nilsson et al. 2011;Wei et al. 2012;Elliott et al. 2013;Opgenoorth et al. 2013;Sánchez-Cano et al. 2017;Jakosky et al. 2018;Krishnaprasad et al. 2019). In general, the enhanced atmospheric ionization and heating can result in an enhancement of exospheric H abundance above the Martian BS (Chaufray et al. 2015). Moreover, an increase in the upstream solar wind particle flux can give rise to an increase in the photoionization frequency of the exospheric H atoms through charge exchange and electron impact during the passage of SIRs. Thus, the increased ionization of more H atoms could increase the newborn proton density in the upstream regime of the Martian BS and, therefore, the linear growth rate of PCWs. A question that naturally arises here concerns whether or not the upstream PCW properties are strongly modulated by SIRs. This issue has received little attention in previous research, largely because of limited upstream solar wind measurements.
The ongoing Mars Atmosphere and Volatile EvolutioN (MAVEN) mission was designed to investigate the Martian upper atmosphere, ionosphere, and magnetosphere response to energy and particle input from the Sun, and the resulting escape of gas to space, particularly the process of atmospheric escape associated with extreme space weather events, such as ICMEs, SIRs, and interplanetary shocks (Jakosky et al. 2015). MAVEN provides simultaneous magnetic field and solar wind measurements, which allow us to characterize low-frequency plasma waves in the medium upstream from the Martian BS (e.g., Romanelli et al. 2016Romanelli et al. , 2022Ruhunusiri et al. 2016;Andrés et al. 2020;Halekas et al. 2020;Romeo et al. 2021;Lin et al. 2022). The aim of this paper is to conduct the first comprehensive analysis of the occurrence rate and characteristics of upstream PCWs during the passage of SIRs. For this purpose, we identified and selected 46 SIR events that occurred in the perihelion season (L s = 180 • -360 • ) of Martian years (MYs) 32-35, based on the MAVEN measurements from October 2014 to August 2021; this period covers the declining phase of solar cycle 24 to the ascending phase of solar cycle 25. We note that the PCW activity in the aphelion season is not considered within this work, due to its low occurrence rate Romanelli et al. 2013Romanelli et al. , 2016. More specifically, our preliminary analysis shows that, in the aphelion seasons (L s = 0 • -180 • ), the average value of the PCW occurrence rate is around 3% for disturbed times of SIR passage, in agreement with previous results (see Fig. 3c of Romeo et al. 2021). Furthermore, it seems that SIRs do not have a statistically significant impact on the PCW activity during the aphelion period.
The rest of this paper is structured as follows. Section 2 describes the MAVEN data sets, the identification criteria for SIRs, the method and criteria used for the identification of PCWs, and the wave parameters during individual SIRs and their upstream and downstream periods. Section 3 presents the statistical properties of the detected PCWs and their association with the upstream conditions. Sections 4 and 5 are devoted to related discussions and conclusions, respectively.

MAVEN data
We mainly used data from two instruments on board the MAVEN spacecraft: the Magnetometer (MAG; Connerney et al. 2015) and the Solar Wind Ion Analyzer (SWIA; Halekas et al. 2015). MAG measures the vector magnetic field with a sampling frequency of 32 Hz and a resolution of 0.008 nT. The characteristic frequencies of PCWs upstream from the Martian BS are observed at about 0.05-0.15 Hz for the magnetic field magnitude of 3-9.5 nT, and thus the 1 Hz resolution of magnetic field data is sufficient for the spectral analysis in the present study. SWIA measures the solar wind ion flows around Mars, with an angular coverage of 360 • ×90 • , an angular resolution of 25 • ×25 • , and a broad energy range from 5 eV to 25 keV, with a cadence of 4 s. The onboard solar wind ion moments (ion density, temperature, and velocity moments) obtained from SWIA are calculated assuming all ions are protons. In addition, the energy and angular distributions of 3-4600 eV electrons from the Solar Wind Electron Analyzer (SWEA) instrument (Mitchell et al. 2016) provides complementary measurements to MAG and SWIA in the identification of the Martian BS crossings. Furthermore, the Extreme Ultraviolet (EUV) monitor (Eparvier et al. 2015) provides the measurements of the solar irradiance in the soft X-rays and EUV wavelength range at a cadence of 1 s. EUV monitor consists of three broadband radiometers, allowing us to evaluate and validate the variation of solar irradiance in three broad bands (0.1-7 nm, 17-22 nm, and 121-122 nm). The MAVEN data are utilized in Mars Solar Orbital (MSO) coordinates, where X is aligned from Mars to the Sun, Y opposes the direction of the orbital motion of Mars, and Z completes the right-handed coordinate system.

SIR identification
The SIRs were identified if they had three or more of the following features: a compression of magnetic field magnitude B, an increase in proton speed V p , an increase and then a decrease in proton density N p , a rise of proton temperature T p , an increase and then a decrease in the total perpendicular pressure P t (the sum of the magnetic pressure and proton thermal pressure perpendicular to the magnetic field), and an increase in proton specific entropy S p (defined as ln(T 3/2 p /N p ) (Neugebauer et al. 2004;Pagel et al. 2004;Jian et al. 2011Jian et al. , 2019. The SIs were distinguished as abrupt drops in proton density N p and simultaneous rises in proton temperature T p . The resulting changes in proton specific entropy S p are generally convenient SI markers (Crooker & McPherron 2012).
It is important to note that MAVEN samples upstream solar wind at times when its ∼4.5 h orbit extends outside the Martian BS, and thus it is unable to encounter the entire structure of an SIR. In cases that the leading and trailing edges are not well determined from magnetic field and plasma observations, presumably not encountered by MAVEN, the time just after (before) the outbound (inbound) BS crossings adjacent to the start (end) of P t enhancement are taken as the leading (trailing) edge passage time. In cases that SIs are not recorded, the locations of maximum pressure P t are taken as the SI passage time (Jian et al. 2006). If the maximum pressure points occur sometime between the inbound and outbound BS crossings, the middle time points are crudely taken as the SI passage time. The locations of SIs will be used to define the zero epoch in the superposed epoch analysis, as described below. For more details on the identification of SIRs using in situ measurements from MAVEN, we refer the reader to a recent article by Huang et al. (2019).
With magnetic field and plasma data measured by MAVEN from October 2014 to August 2021, we identify more than one hundred SIR events. Certainly, we might have missed some SIRs that are not effectively encountered due to the limited spacecraft coverage and that have evolved through interaction with other structures such as ICMEs. The SIR events in the perihelion season (L s = 180 • -360 • ) of MYs 32-35 are picked for the present statistical analysis. Meanwhile, the SIR events are required to meet the following criteria: (1) SIRs have effective data rates of more than 30% (here the effective data rate is defined as the ratio of the portions of an SIR encountered by MAVEN to the entire SIR interval); (2) SIRs and their upstream and downstream regions are little contaminated by other solar wind structures; and (3) The solar irradiance and Martian dust activity (Fang et al. 2020) do not show remarkable changes during the SIR intervals or their upstream and downstream intervals (on timescales of a few days). This third criterion was evaluated and validated by examining the solar irradiance in three broad wavelength bands (0.1-7 nm, 17-22 nm, and 121-122 nm) detected by the EUV monitor (Eparvier et al. 2015) on board MAVEN and the Martian dust storm activity (cf. Fig. 1 of Fang et al. 2020). Finally, we obtain a data set containing 46 SIR events that satisfied our selection criteria, as listed in Table A.1.

PCW identification
For each SIR event, we selected the corresponding upstream solar wind interval based on the outbound and inbound crossings of the Martian BS, which are identified by sudden increases in magnetic field magnitude and fluctuation level, an abrupt change in the flow direction and velocity, and a widening of the ion energy spectra and the electron energy spectra across the BS from the upstream to the downstream. Then we discarded a short time interval of 10∼15 min before and after each BS crossing, thereby avoiding the possibility of contamination from non-solar wind sources, such as magnetic structures related to the Martian BS. Due to the fact the MAVEN orbit does not extend far beyond the Martian BS, a fraction of the sampled upstream solar wind might be contaminated from the foreshock regions of the quasi-parallel BS, permeated by ultra-low frequency waves. In order to eliminate foreshock disturbances, we used a criterion of the normalized magnetic field fluctuations, σ B /B < 0.15 (σ B represents a root-sum-squared value of the 32 Hz fluctuation levels in all three components over a 4 s interval), which is proposed by Halekas et al. (2017). In a similar way, the upstream and downstream intervals with durations comparable to the SIR passage are also selected. In general, the upstream region is dominated by the slow stream prior to the SIR, and the downstream region is dominated by the high-speed stream, or the high speed together with the rarefaction region associated with the trailing edge of the high-speed stream. By comparing PCW occurrence rates and wave properties during the selected intervals, corresponding to three SIR phases -pre-SIR phase, SIR phase, and post-SIR phase -we can evaluate the potential impacts of SIRs on upstream PCW activity.
To extract wave information from the magnetic field fluctuations, the 1 Hz MAG data within the selected intervals were processed in three steps. Firstly, the magnetic field data were converted from the MSO coordinates to the mean magneticfield-aligned coordinates, in which the parallel unit vector B par is positive parallel to the 10-min running mean magnetic field vector B 0 , the azimuthal unit vector B azi is perpendicular to the plane determined by B par and the Mars-centered radial vector to the spacecraft position, and the radial unit vector B rad completes the right-handed system. Secondly, the generalized Morse wavelets (Olhede & Walden 2002) were employed on the transverse (B TRA , perpendicular to B 0 ) and compressive (B COMP , parallel to B 0 ) components to produce frequency-time spectrograms. Based on the spectrograms, the ratio of B TRA to the total (B Total ) power spectral density (PSD) and the wave amplitude (δB, the square root of the cumulative sum of the PSD(B TRA ) over a frequency interval) are derived. Lastly, the wave propagation angle θ kB and ellipticity (−1/+1 = LH/RH circular polarization) were calculated from the complex spectral matrix consisting of B azi , B rad , and B par by applying the singular value decomposition method (Santolík et al. 2003;Taubenschuss & Santolík 2019;Harada et al. 2019).
In order to diagnose the presence of PCWs near the local proton cyclotron frequency ( f H + =q|B 0 |/2πm, where q and m denote the proton charge and mass, respectively), all the frequency-time spectrograms are trimmed to a frequency range from 0.8 f H + to 1.2 f H + . According to the properties of upstream PCWs established experimentally through observational studies (Brain et al. 2002;Mazelle et al. 2004;Wei & Russell 2006;Bertucci et al. 2013;Wei et al. 2011Wei et al. , 2014Connerney et al. 2015;Ruhunusiri et al. 2015Ruhunusiri et al. , 2016Romanelli et al. 2013Romanelli et al. , 2016Romeo et al. 2021;Lin et al. 2022) and theoretical studies (Brinca 1991;Gary 1991), we propose a set of diagnostic criteria for a tentative PCW event from the trimmed spectrograms: (1) PSD (B TRA ) PSD(B Total ) > 0.75; (2) θ kB < 20 • ; (3) ellipticity <−0.7. In addition, the wave amplitude δB over the frequency interval from 0.8 f H + to 1.2 f H + is required to be larger than 0.05 nT. This constraint is to ensure that turbulent fluctuations are not inadvertently identified as PCWs. Finally, we selected wave events (i.e., PCW diagnostics) that are persistent for at least three proton cyclotron periods.

List of wave parameters during SIRs
Based on the specific diagnostic criteria for PCWs described above, we identified the PCW events during the passage of individual SIRs and their upstream and downstream regions (corresponding to the SIR phase, pre-SIR phase, and post-SIR phase, respectively) and obtained the PCW occurrence rate, main wave parameters, and the associated upstream solar wind conditions. The results for our sample of 46 events are summarized in Table A.1. The first five columns of this table indicate the event reference number, the SIR leading and trailing edge passage times, the SI passage time, and the Martian solar longitude L s corresponding to the SIR passage. The subsequent seven columns exhibit the median values together with 68.3% confidence intervals of the wave amplitude δB, wave propagation angle θ kB , absolute value of ellipticity, proton density N p , proton bulk velocity V p , proton flux per unit time N p V p , and IMF cone angle α VB . The last column presents the PCW occurrence rate, defined as the ratio of PCW events to the total number of the SIR interval (or the upstream/downstream interval). Also, all the 46 events in the perihelion season (L s = 180 • -360 • ) are grouped together to obtain the overall average properties of detected PCWs and their upstream solar wind conditions. The results for this group are given in the last row of Table A.1. To provide a more visual representation, the PCW occurrence rate and the median amplitude δB are plotted as a function of time, as shown in Fig. 1. The tendency for a solar cycle dependence can be discerned in the both wave parameters, in agreement with previous findings (e.g., Romeo et al. 2021). Since the number of SIRs in each solar cycle phase is relatively small, we do not consider the cycle phases separately. Instead, all the 46 SIRs are combined into one group to investigate the statistical properties of upstream PCW activity during the passage of SIRs.

Results
In this section, we first show a representative example of PCWs detected at Mars during the passage of an SIR and its upstream and downstream regions, and then present and compare statistical properties of PCWs during three SIR phases for the group of 46 SIR events and their association with upstream conditions.
3.1. Case study: PCWs during the 26-28 August 2016 SIR Figure 2 shows the magnetic field and plasma measurement from MAVEN from the period 26-28 August 2016, during which an SIR event encountered (event 23 in Table A.1) when Mars was at a solar longitude L s of 212 • . We note that we use only the data points outside the Martian BS. This SIR is clearly identified by the signatures including a compression of magnetic field A158, page 4 of 12 Zhao,D.,et al.: A&A proofs, (θ) and (f) azimuth angle (ϕ) of field direction, (g) proton bulk velocity (V p ), (h) proton number density (N p ), (i) proton temperature (T p ), (j) proton β (the ratio of proton thermal pressure to magnetic pressure), (k) proton total perpendicular pressure (P t ), (l) proton specific entropy (S p ), and (m) corresponding dynamic pressure (Pdy). Two vertical dashed blue lines indicate the leading and trailing boundaries of the SIR; the vertical dashed red line marks the SI. magnitude B (Fig. 2d), an overall increase in proton velocity V p (Fig. 2g), an increase and then a decrease in proton density N p (Fig. 2h), an enhancement of proton temperature T p (Fig. 2i), a pile-up of total perpendicular pressure P t (Fig. 2k), and a pronounced increase in proton specific entropy S p (Fig. 2l). The leading and trailing edges of the SIR were not encountered by MAVEN, and thus the edges plotted in this figure (vertical blue dashed lines) are approximate. The SI is characterized by relatively abrupt transitions of proton density N p and proton temperature T p , and is also verified by a relatively abrupt rise in proton specific entropy S p . It was not encountered by MAVEN, and thus its location shown in this figure (vertical red dashed lines) is approximate. Figure 3 shows the frequency-time spectrograms of magnetic field data and wave parameters including wave propagation angle θ kB , ellipticity, wave amplitude δB and the IMF cone angle α VB during the SIR interval and its upstream and downstream. The red dots shown in the solar wind intervals of Fig. 3h indicate the occurrence of PCWs that satisfy our diagnostic criteria. It is readily seen that higher PCW occurrence rates take place during the SIR interval. More precisely, the PCW occurrence rate is about 29% during the SIR phase, compared to 6% for the pre-SIR phase and 5% for the post-SIR phase. Moreover, PCWs tend to occur more frequently in the leading portion of the SIR (i.e., from the leading edge to the SI). The wave amplitudes during the SIR interval are statistically greater than those during the A158, page 5 of 12 A&A 674, A158 (2023) pre-SIR and post-SIR intervals. To quantitatively compare the main properties of identified PCWs during the three SIR phases, we plot the probability distribution P(x) of wave properties in Fig. 4. The PCW probability distribution function P(x) is created by discretizing the number of PCW events into bins of a given wave property x and normalizing by the total number of PCW events. The bin sizes for δB, θ kB , and absolute value of ellipticity are 0.1ṅT, 2 • , and 0.025, respectively. The median value of P(δB) is about 0.33 nT during the SIR interval, which is over three times the median values of 0.08 nT and 0.09 nT during the pre-SIR and post-SIR intervals, respectively. The median value of P(θ kB ) is about 9.6 • during the SIR interval, which is smaller than the median values of about 11.9 • and 11.7 • during the pre-SIR and post-SIR intervals, respectively. The median value of the probability distribution function of the |ellipticity| is about 0.811 during the SIR interval, which is slightly higher than the median values of 0.784 and 0.777 during the pre-SIR and post-SIR intervals, respectively. Overall, the properties of PCWs detected during the SIR interval are more pronounced, with larger amplitudes, smaller propagation angles with respect to the ambient magnetic field direction, and closer to circular polarization than those during the pre-SIR and post-SIR intervals. A single event may not be reasonably definitive. So we conducted a statistical analysis based on our sample of 46 SIR events.

Statistical analysis
For the group of the 46 events, all data points belonging to the same SIR phase were collected together to calculate the PCW occurrence rate, defined as the ratio of PCW events to the total number of upstream intervals. The result indicates that the occurrence rates during the pre-SIR, SIR, and post-SIR phases are ∼14%, ∼24%, and ∼13%, respectively (Fig. 5a). This means that the occurrence rate is increased by a factor of about 1.8 during the SIR phase relative to the pre-SIR and post-SIR phases.
We further explore whether the SIR passage produces more favorable conditions for the PCW generation, by comparing the distributions of solar wind parameters, including proton density N p , proton bulk velocity V p , proton flux N p V p , IMF cone angle α VB , and the PCW occurrence rates, within each bin of these solar wind parameters for the three SIR phases. The distributions are illustrated in Fig. 6, where the bin sizes of the four solar wind parameters are set to 3 cm −3 , 100 km s −1 , 1 × 10 8 cm 2 s −1 , and 15 • , respectively. We note that the PCW occurrence rates for some bins are not calculated when the number of sampled points falling within the bins is very small. The median value of the distribution of N p for the SIR phase is about 2 times as high as those for the pre-SIR and post-SIR phases (Fig. 6a1). The median value of the distribution of V p for the SIR phase is larger than that for the pre-SIR phase and smaller than that for the post-SIR phase (Fig. 6b1). The median value of the distribution of N p V p for the SIR phase is larger than those for the pre-SIR and post-SIR phases (Fig. 6c1). The distributions of α VB are roughly similar for the three SIR phases (Fig. 6d1). These distributions are consistent with the defining characteristics of the SIR structures, which can be seen more clearly in superposed-epoch averaging triggered on the SI (i.e., the zero epoch is the passage of the SI), as shown in Fig. 7. The superposed-epoch plots extend from 3 days prior to the passage of the SI to 5 days afterward. We can see that the proton velocity V p exhibits an increase associated with the passage of SIRs, and the proton density N p peaks in the vicinity of the SI, with a higher average value on the slow stream side of the SI. As a result, the peak value of proton flux N p V p occurs just ahead of the SI, primarily due to the proton density N p enhancement.
In general, the higher proton flux N p V p (and thus higher electron flux in the quasi-neutral upstream region of the Martian BS) during the SIR phase could result in an increase in the newborn proton production through charge exchange (and electron impact) ionization, which in turn gives rise to higher PCW occurrence rates. This can partly explain the higher PCW occurrence rates during the SIR phase (Fig. 5a). Moreover, we find that, as expected, PCWs tend to occur more frequently in the leading portion of the SIR. More specifically, the PCW occurrence rate is about ∼31% for the leading portion of the SIR, compared to ∼19% for the trailing portion of the SIR (Fig. 5b).
In agreement with the observations of Romeo et al. (2021), we find that the PCW occurrence rate increases with increasing of N p and N p V p (Figs. 6a2 and 6c2  increasing of V p (Fig. 6b2). However, interestingly, the PCW occurrence rates during the SIR phase are much larger than those during the pre-SIR and post-SIR phases event at the same proton flux N p V p . It implies that additional ionization of the exospheric H atoms creates more pickup H + upstream from the Martian BS in response to SIR events, as discussed later. This implication can also help explain why the PCW occurrence rates during the SIR phase are much larger for all IMF cone angles, as shown in Fig. 6d2. We further compare the probability distribution P(x) of the wave properties during the three SIR phases. The results are given in Fig. 8. The median value of P(δB) is about 0.44 nT during the SIR phase, compared to 0.27 nT and 0.29 nT during the pre-SIR and post-SIR phases, respectively. That is, the median wave amplitude is increased by a factor of about 1.6 during the SIR phase relative to the pre-SIR and post-SIR phases. The median value of P(θ kB ) is about 11.4 • during the SIR phase, which is slightly smaller than the median values of 12.5 • and 12.3 • during the pre-SIR and post-SIR phases, respectively. The median value of P(|ellipticity|) is about 0.809 during the SIR phase, which is slightly larger than the median values of 0.804 and 0.802 during the pre-SIR and post-SIR phases, respectively. These results suggest that the PCWs observed during the passage of SIRs have more pronounced wave characteristics, namely, larger wave amplitudes, smaller propagation angles with respect to the ambient magnetic field direction, and closer-to-circular polarization.

Discussion
Our statistical analysis shows that the PCW occurrence rate is increased by a factor of about 1.8 during the SIR phase, compared with the pre-SIR and post-SIR phases. Moreover, PCWs tend to occur more frequently in the leading portion of the SIR. We find that the IMF cone angle α VB exhibits a similar distribution pattern for the three SIR phases (Fig. 6d1) and moreover the PCW occurrence rates show roughly similar trends with changes in IMF cone angle α VB (Fig. 6d2), indicating no statistically significant differences in the generation mechanisms of PCWs (the PCW generation is believed to be closely related with IMF cone angle, as mentioned earlier). We accordingly believe that the increased PCW occurrence rate during the SIR phase is mainly due to the enhancement in the newborn proton production, which provides more energy to increase the abundance of PCWs. The enhancement of newborn proton production could be attributed to both solar wind and exospheric factors. First, the increased solar wind proton flux and electron flux result in an increase in newborn proton production through augmented charge exchange reactions and electron impact ionization. We examined the ion energy-time spectrograms in all 64 look directions of SWIA and STATIC (SupraThermal and Thermal Ion Composition; McFadden et al. 2015), consisting of 16 azimuth bins of 22.5 • (A00-A15) and 4 elevation bins of 22.5 • (D00-D03), and generally observed the elevated flux of pickup H + in the field of view of SWIA and/or STATIC during the SIR intervals (now shown). Second, the Martian atmosphere undergoes additional ionization and heating (coupled with the plasma heating through a series of collisions and chemical reactions, see Krasnopolsky 2002) from the SIRs and the SIR-associated energetic particles enhancement (Lee et al. 2010(Lee et al. , 2017Thampi et al. 2019), which elevate the H density in the upper exosphere (e.g., above ∼4000 km) (Chaufray et al. 2015). It is worth mentioning here that enhanced ionospheric ionization and heating from the SIR-associated energetic particles could also occur during the passage of the trailing high-speed stream (mainly corresponding to the post-SIR phase, Lee et al. 2017), but do not result in a higher PCW occurrence rate, compared to the pre-SIR phase. This indicates that the SIR-associated energetic particles are likely to be relatively minor contributors. Additionally, as a direct consequence of the enhanced solar wind dynamic pressure during the passage of SIRs (Fig. 6h), the Martian BS moves to lower altitudes, where the exospheric H density is higher. This suggests that more sample points at lower altitudes are collected to identify the PCW events during the SIR phase. This may at least partly contribute to the higher PCW occurrence rate observed during the SIR phase.
Also, we find that the median amplitude of PCWs is increased by a factor of about 1.6 (from 0.27-0.29 nT to 0.44 nT) during the SIR phase relative to the pre-SIR and post-SIR phases. Linear theories demonstrate that the wave amplitudes are closely related to the production rates of newborn protons from the neutral hydrogen exosphere, and therefore to the local exospheric density (e.g., Huddleston & Johnstone 1992), which falls off with distance from Mars. Previous spacecraft observations indicated that, consistent with theoretical expectations, the wave amplitudes generally increase as the spacecraft approached Mars (Brain et al. 2002;Wei & Russell 2006;Romanelli et al. 2013). This indicates that the wave amplitudes do reflect the production rates of newborn protons within a certain distance range, not far from the BS. This connection may offer at least a partial explanation of the larger wave amplitudes observed by MAVEN during the SIR phase, from a statistical point of view. The growth times of the waves and effects of nonuniform proton production rates across the upstream region could complicate such an interpretation (Cowee et al. 2012). Furthermore, some waves recorded by MAVEN might be generated further upstream in the solar wind. They might have evolved a lot from the linear phase as they were convected back by the solar wind, and thus do not appear as quasi-monochromatic and linearly polarized waves (e.g., Lin et al. 2022). On such occasions, the connection between the wave amplitudes and the exospheric H density could be much more complicated, requiring a nonlinear scenario (Mazelle et al. 2004).

Conclusions
In this work, we present a statistical study of the properties of upstream PCWs during three SIR phases (the pre-SIR phase, the SIR phase, and the post-SIR phase) and their association with upstream conditions using in situ magnetic field and plasma measurements by MAVEN from October 2014 to August 2021. The 46 SIR events studied are a subset of the events that occurred in the perihelion season (L s = 180 • -360 • ) of MYs 32-35. We find that the PCW occurrence rate is increased by a factor of about 1.8 (from 13-14% to 24%) during the SIR phase relative to the pre-SIR and post-SIR phases. Furthermore, PCWs tend to occur more frequently in the leading portion of the SIR. The increase is attributed mainly to the enhanced production rates of newborn protons, which is the result of two factors: (1) the elevated solar wind proton and electron fluxes and thus higher ionization rates of exospheric H atoms via charge exchange and electron impact, and (2) the increased exospheric H density above the Martian BS, a result of enhanced ionization and heating from the SIRs. In addition, the increase in the PCW occurrence rate could be partly due to a greater exposure of the A158, page 9 of 12 A&A 674, A158 (2023) hydrogen exosphere to the solar wind during the SIR intervals, when the BS moves to lower altitudes, where the exospheric H density is higher. The median wave amplitude is enhanced by a factor of about 1.6 during the SIR phase relative to the pre-SIR and post-SIR phases. The PCWs observed during the SIR phase propagate at smaller angles to the background magnetic field, and are closer to being circularly polarized.    A158, page 12 of 12