Characteristic Timescales for the Dayside Martian Ionosphere: Chemistry, Diffusion, and Magnetization

Different boundaries could be defined in a planetary ionosphere where the dominant process in function switches from one to the other. Identifying these boundaries and understanding their variations are hence crucial for disentangling the complexity of the ionosphere. Focusing on Mars, we perform a data-driven analysis of various boundaries and the associated time constants based on the multi-instrument measurements made by the Mars Atmosphere and Volatile Evolution mission during six campaigns that sample broadly different internal and external conditions. The boundaries we investigate include the photochemical equilibrium (PCE) boundary, the magnetic frozen boundary, the ion collision boundary, and the ion gyration boundary. Our analysis reveals systematic solar cycle and diurnal variations in that all boundaries tend to be elevated at enhanced solar activity and on the dayside and duskside of Mars. The variations with the magnetic environment are not observed for all boundaries except for the PCE boundary that exhibits an obvious elevation in strongly magnetized regions. Finally, our analysis suggests interesting species-dependent variations of different boundaries. In particularly, the PCE boundary shows the largest variability among all, with reduced boundary locations for all terminal species (NO+, HCO+, O2+ , and H3O+) and one extra nonterminal species (CO2 +) owing to different chemical properties rendered by different ions.


Introduction
Any solar system body with a permanent atmosphere also possesses an ionosphere (Witasse et al. 2008, and references therein).For Mars, the ionosphere is a crucial region controlling both neutral and plasma escape (e.g., Barabash et al. 2007;Lillis et al. 2017) and thus of paramount importance to the long-term evolution of the planet (e.g., Lillis et al. 2015;Jakosky et al. 2018).In particular, the transition of Mars from the early warm and wet state to the current cold and arid state is thought to be driven, at least partially, by atomic O escape via dissociative recombination (DR) of ionospheric + O 2 (Fox & Hać 2009) and atomic H escape via a complicated network of ionospheric chemistry following CO 2 photoionization involving either H 2 in the quiet atmosphere (Krasnopolsky 2019) or H 2 O in the dusty atmosphere (Stone et al. 2020).Several studies propose that plasma escape via electromagnetic forcing, though much weaker than neutral escape via ionospheric chemical forcing at the current epoch, likely dominated the Martian climate's evolution in ancient times when subjected to a more intense solar extreme-ultraviolet (EUV) and soft X-ray (SXR) irradiance (Dong et al. 2018).In addition, understanding the ionosphere of Mars is of practical use to radio communication between the Mars rovers/landers and orbiters, as well as between the Earth and Mars (Collinson et al. 2020).
Accompanying the extensive information accumulated over the past several decades, sophisticated numerical models have been developed to characterize the plasma distribution in the Martian ionosphere (e.g., Chen et al. 1978;Shinagawa & Cravens 1989;Fox 1997Fox , 2003Fox , 2009;;Krasnopolsky 2002;Fox & Yeager 2006;González-Galindo et al. 2013;Matta et al. 2013;Chaufray et al. 2014;Bougher et al. 2015;Fox et al. 2015;Krasnopolsky 2019;Lo et al. 2021;Wu et al. 2021).It has now been generally accepted that on the dayside, the Martian ionosphere contains a well-defined primary layer and a low-altitude secondary layer produced by solar EUV and SXR ionization along with impact ionization by photoelectrons and their secondaries (Martinis et al. 2003;Fox & Yeager 2006, 2009;Fox & Weber 2012).Near the primary peak, the Martian ionosphere is reasonably described by the idealistic Chapman theory under photochemical equilibrium (PCE; Mendillo et al. 2013Mendillo et al. , 2015Mendillo et al. , 2017)).Well above this peak, transport surpasses ionospheric chemistry and becomes the dominant controlling process (Mendillo et al. 2011).As a consequence, these regions are magnetically modulated, forming stable upwelling features preferentially near vertical field lines manifest as hyperbola-shaped traces in the echogram and dual traces in the ionogram frequently revealed by the Mars Advanced Radar for Subsurface and Ionospheric Sounding measurements gathered by the Mars Express (Gurnett et al. 2005;Duru et al. 2006;Andrews et al. 2014;Diéval et al. 2018).
Existing models of the dayside Martian ionosphere are not compatible because of the various model assumptions implemented.First, several authors assumed PCE (e.g., Martinis et al. 2003;Xu et al. 2018;Mukundan et al. 2021;Wu et al. 2021).Their model results are thus not applicable to the Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
high-altitude regions well above the primary peak.The boundary between the photochemistry-and transport-dominated ionospheric regions, hereafter denoted as the PCE boundary, has not been well characterized and may vary substantially depending on the internal and external conditions on Mars.Second, most studies included ion-neutral collisions only when accounting for plasma diffusion, but it has been suggested that ion-ion Coulomb collisions are likely more important at high altitudes (Matta et al. 2013).Such an effect tends to slow down diffusion and significantly enhance the topside plasma density.Third, the effect of field-aligned plasma diffusion, which is necessary to explain the observed ionospheric upwelling on Mars, has only been considered by a few modeling studies (Matta et al. 2015).Accordingly, existing model results mostly apply to the nonmagnetized regions or magnetized regions with nearly vertical field lines.Since all of the above features are more pronounced at high altitudes, it is not surprising that the topside Martian ionosphere is less well understood than regions near the primary peak (Withers 2009, and references therein).
The situation for the nightside Martian ionosphere is different with photoionization switched off and energetic electron precipitation of solar wind origin becoming a viable ionization source (Verigin et al. 1991;Fowler et al. 2015;Girazian et al. 2017;Cui et al. 2019).Day-to-night transport is also suggested to contribute substantially to the ionospheric plasma content in the darkness, especially in regions not too far from the terminator (Němec et al. 2011;Withers et al. 2012;Cui et al. 2015;Girazian et al. 2017;Cao et al. 2019).Due to the scarcity of available measurements for comparison, the nightside Martian ionosphere has historically not been well explored by numerical modelings.The sequence of studies by S. Haider and colleagues assumed chemical equilibrium (Haider et al. 1992;Haider 1997;Haider et al. 2007Haider et al. , 2013)), whereas the early investigation by Fox et al. (1993) and the more recent one by Wu et al. (2023) included both chemistry and vertical diffusion for the ideal nonmagnetized situation (featured by unhindered external electron precipitation).Although all studies predict the existence of a clear nightside ionospheric layer, available radio occultation or radar sounding measurements instead suggest that the Martian ionosphere in the darkness is usually patchy and sporadic, showing no signature of a distinctive layer structure under most circumstances (Gurnett et al. 2008, and references therein).The frequent occurrence of energetic electron depletion in the deep nightside of Mars is a notable manifestation of the above complexity, with the highly variable and diversified magnetic field configuration either facilitating or hindering external electron precipitation (Steckiewicz et al. 2015(Steckiewicz et al. , 2017;;Niu et al. 2020).
Existing studies have revealed that the magnetic field configuration exerts a more profound influence on the structure and dynamics of the Martian ionosphere than described above, which makes the red planet an ideal laboratory for investigating the magnetic control of the space plasma environment in the vicinity of a planetary body.On the one hand, the absence of a global dynamo on Mars allows the interplanetary magnetic fields carried by the solar wind to directly interact with the Martian ionosphere, leading to the formation of a notable induced magnetosphere (e.g., Brain et al. 2006;Brain 2006;Akalin et al. 2010;Huang et al. 2023).The induced magnetic fields govern the motion of the ionospheric plasma, which can either suppress or enhance the Martian ion outflow, depending on the orientation of the ambient magnetic field lines (Liemohn et al. 2006;Safaeinili et al. 2007).On the other hand, the surface of Mars is well known to be characterized by the distribution of strong crustal magnetic anomalies, which tend to cluster over the southern hemisphere of the planet (Acuna et al. 1998(Acuna et al. , 1999)).The modulation of the Martian ionosphere by such anomalies brings further complication to the magnetic control of the ionosphere on both the dayside and nightside of Mars.The closed crustal field loops, which are preferentially associated with strong crustal anomalies, can sequester ionospheric plasma, shielding it from loss to interplanetary space and resulting in localized enhancement in ionospheric cold electron density and a decrease in electron temperature on the dayside (e.g., Flynn et al. 2017;Fan et al. 2019).Meanwhile, the closed crustal fields also prevent the precipitation of solar wind electrons into the atmosphere, which is responsible for the energetic electron depletion or cold electron density depression events well observed in the nightside Martian ionosphere (e.g., Steckiewicz et al. 2015Steckiewicz et al. , 2017;;Niu et al. 2020;Cao et al. 2023).In contrast to the shielding effect, the crustal magnetic fields are sometimes reconnected to the interplanetary magnetic fields, offering direct access for the solar wind plasma to the ionosphere in certain regions, serving as pathways for both energy influx and particle escape (e.g., Harada et al. 2018;Wu et al. 2019;Weber et al. 2020).
How the morphology of the Martian ionosphere is controlled by the known fundamental processes (chemistry, diffusion, and magnetization) is best elucidated by a data-driven evaluation, which only becomes possible with the arrival of the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft at the red planet (Jakosky et al. 2015).Equipped with a variety of particle and field instruments, unprecedented details of the Martian upper atmosphere and ionosphere have been provided, forming the complete set of physical parameters required to rigorously assess the roles of different processes.This study is intended for a systematic evaluation of how chemistry, diffusion, and magnetization shape the structure and variability of the Martian ionosphere with the aid of a data-driven comparison of different time constants related to these processes.The analysis to be presented is crucial for deciding what approximations could be reasonably implemented in future ionospheric modelings or to what extent previous modeling results could be trusted.

Data Description and Definition of Various Time Constants
Since the beginning of the mission, the MAVEN spacecraft has probed atmospheric regions down to 120-130 km during the Deep Dip (DD) campaigns, much deeper than during nominal orbits with a periapsis at 150-180 km.For the purpose of this study, we include six DDs in our analysis and estimate a variety of time constants over the altitude range of 130-300 km, above which the neutral density data are generally unavailable.The ephemeris data for each DD are listed in Table 1, providing mean values at the periapsis.In particular, each tabulated solar ionizing flux refers to the mean daily spectral irradiance at Mars integrated over the wavelength range below 90 nm (approximately the CO 2 and O ionization thresholds) based on the Flare Irradiance Spectral Model-Mars (Thiemann et al. 2017).With the aid of the measurements during these campaigns, we can analyze the variations of each time constant with respect to the solar ionizing flux, the Martian local time, and the magnetic field intensity.
To estimate various time constants during each campaign, the multi-instrument MAVEN data set is used, including the neutral and ion densities measured by the Neutral Gas and Ion Mass Spectrometer (NGIMS; Mahaffy et al. 2015), the electron temperatures measured by the Langmuir Probe and Waves (Andersson et al. 2015), the ion temperatures measured by the SupraThermal And Thermal Ion Composition (McFadden et al. 2015), and the magnetic field intensities measured by the MAGnetometer (Connerney et al. 2015).We caution that the NGIMS densities were proposed to be underestimated by a factor of ∼1.5 for O (Fox et al. 2021) and overestimated by a factor of ∼6.5 for CO (Wu et al. 2020).These multiplicative factors are used throughout our calculations (see also Wu et al. 2023).The vertical profiles for the neutral and ion densities; the neutral, ion, and electron temperatures; and the magnetic field intensity averaged over all orbits during each DD campaign can be found in the Appendix.
To evaluate the roles of chemistry, diffusion, and magnetization, we compute for each ion species (denoted as i) several time constants as described below.First, the chemical loss time constant, t i c ( ) , is given by

/
where N e is the electron number density, α i is the DR coefficient or radiative recombination coefficient (depending on whether i denotes a molecular or atomic ion species), N n is the number density of a neutral species (denoted as n) reacting with i, and k in is the corresponding reaction rate coefficient.All rate coefficients are adapted from our previous compilation in Wu et al. (2021).
Second, we compute the ion-neutral and ion-ion collision time constants, t i in summed over all neutral species, and summed over all ion species different than i, where M i , M j , and M n are the molecular masses of the relevant ion and neutral species; N n and N j are the neutral and ion number densities; γ n is the neutral polarizability; and T i is the ion temperature taken to be common to all ion species.
Third, the ion diffusion time constant, t i d ( ) , is related to the aforementioned collision time constants via where H i is the characteristic length scale for species i.In practice, the density profiles of different ion species are featured by a common scale height in the topside ionosphere (Wu et al. 2019).Hence, for simplicity, we adopt a fixed length scale, H i , for all species during each DD campaign, which is taken to be the mean + O 2 density scale height at 130-300 km.Fourth, the ion gyroperiod, t i g where B is the total magnetic field intensity, and we implicitly assume that the ion species under consideration is singly charged.Finally, analogous to Cravens et al. (2010), the magnetic diffusion time constant, τ ( m) , is estimated from where H B is the characteristic length scale over which B varies vertically, and ν e is the sum of the electron-neutral and electron-ion collision frequencies.To facilitate comparison between different time constants, here we use the mean + O 2 density scale height, H i , described above as a proxy for H B for each DD.Such a scale height is also found to properly characterize the mean variation of the draped magnetic field intensity (e.g., Akalin et al. 2010).
In the above equations, M i , M j , and M n are in units of Da; T i is in units of K; H i and H B are in units of km; B is in units of nT; and the remaining parameters (number density, neutral polarizability, and time constant) are all in Gaussian units.
For completeness, we consider a broad range of ion species, of which the dominant chemical loss pathways were discussed thoroughly in Wu et al. (2021) Mahaffy et al. (2015).All collision frequencies are computed based on the conventional kinetic theory, as outlined in Schunk & Nagy (1980).

Variations with the Solar Ionizing Flux
We start with Figure 1, where we compare the time constants estimated during DD2 and DD8.These two campaigns are ideally suited for investigating the solar cycle variations, as they both sample the near subsolar and weakly magnetized regions of Mars, but the incident solar ionizing flux differs by almost a factor of 2. In each panel, the red solid and dasheddotted lines represent the chemical loss and diffusion time constants for + O 2 , while the blue lines represent the same time constants for O + .
The left panel of Figure 1 clearly demonstrates that during DD2 with a relatively high solar ionizing flux, the chemical time constant for + O 2 , which is mainly lost via DR, increases rapidly from 20 s at 130 km to 7 × 10 3 s at 300 km, whereas that for O + , lost mainly via its reaction with CO 2 , increases from 6 ms to 6 × 10 3 s over the same altitude range.In contrast, the diffusion time constants for the two species decline rapidly from 2 × 10 6 s at 130 km to 60 s at 300 km.Both trends are the natural outcomes of reduced ambient neutral and plasma densities at high altitudes.Of particular interest is that the diffusion time constants for + O 2 and O + become comparable to their respective chemical time constants at 220 and 260 km, respectively.This transition altitude marks the so-called PCE boundary, below which ions are created and destroyed locally, and the effect of ion diffusion could be neglected in ionospheric modeling.The PCE boundaries are marked as stars in Figure 1.
By inspecting the right panel of the same figure, we observe that the PCE boundary drops appreciably to around 180 km for + O 2 and 210 km for O + during DD8 when subjected to a reduced level of solar ionizing flux.Such a distinction between the two campaigns is a natural outcome of the known solar cycle variations of the Martian upper atmosphere and ionosphere.In particular, enhanced solar activity triggers enhanced photoionization (along with concomitant photochemistry) and neutral heating, elevating both the neutral and plasma densities.As a consequence, the ion chemical time constant is shortened.Similarly, for any ion species, more frequent collisions with ambient particles are expected at enhanced solar activity, hence increasing the ion diffusion time constant.The combination of the above two effects is naturally responsible for the elevation of the PCE boundary when subjected to a higher solar ionizing flux.
In addition, we show with the black solid line in each panel of Figure 1 the magnetic diffusion time constant, featuring a less pronounced altitude variation from 3 × 10 3 to 2 × 10 5 s during DD2 and from 6 × 10 3 to 3 × 10 4 s during DD8, both over the altitude range of 130-300 km.This time constant is comparable to the ion diffusion time constants for both + O 2 and O + near 190 km during DD2 and 160 km during DD8.At higher altitudes, the magnetic field lines tend to be frozen into the bulk plasma flow.Throughout the rest of the paper, such a transition altitude is referred to as the magnetic frozen boundary, marked as squares in Figure 1.The difference in magnetic diffusion between the two campaigns is comparatively small, especially at low altitudes where the time constant differs by a factor of 2 only.This means that the solar cycle variation of the magnetic frozen boundary is mainly driven by the variation of ion diffusion.The weak solar cycle variation of magnetic diffusion is due to the fact that both the neutral and plasma concentrations are positively correlated with the solar activity; hence, their variations are partially counterbalanced according to Equation (6).
In Figure 2, we compare the ion-neutral and ion-ion collision time constants, along with the respective ion gyroperiods, between DD2 and DD8.Both collision time constants tend to increase rapidly with increasing altitude in response to the variation of the ambient neutral and plasma densities.The ion-neutral collision time constant varies more steeply than the ion-ion collision time constant because the neutral scale height is smaller than the plasma scale height due to the temperature difference between the two gases and the development of the ambipolar electric field.In particular, the former increases by as much as 5 orders of magnitude over the altitude range of 130-300 km, whereas the latter increases by only 2 orders of magnitude.In contrast, the altitude variation of the magnetic field intensity is much weaker, and as a consequence, the ion gyroperiod typically varies by no more than a factor of 5.All time constants are positively correlated with the ion mass, as indicated by Equations (2), (3), and (5).The species difference in ion-ion collisions is particularly large because it also relies on the total number of available ions being different than the species under consideration (see also Section 6), meaning that the ion-ion collision felt by + O 2 is significantly less frequent than that felt by O + .
According to Figure 2, ion-neutral collision is always more important than ion-ion collision at low altitudes, but the latter starts to dominate near 220 km for + O 2 and 180 km for O + , both during DD2.These results indicate that the Martian ionosphere switches from a weakly ionized state to a strongly ionized state in the collisional sense.Hereafter, the above transition altitude is referred to as the ion collision boundary for short, marked as triangles in Figure 2. As suggested by Matta et al. (2013), the effect of Coulomb collisions is to slow down diffusion and significantly enhance the topside distribution of all ions, as compared to the ideal situation with ion-neutral collisions only.This also highlights the necessity of including Coulomb collisions in a rigorous modeling of the topside Martian ionosphere.The situation is similar during DD8 with a reduced solar ionizing flux, but now the ion collision boundary moves downward to 190 km for + O 2 and 160 km for O + , which is driven by an increase in the ion-ion collision time and an even larger increase in the ion-neutral collision time at low solar activity.Note that in view of the solar cycle variation of ionion collision, the solar control of the ion density is partially counteracted by that of the ion temperature according to Equation (3).
During DD2, the + O 2 gyroperiod above 160 km is nearly constant at 40 s for + O 2 and 20 s for O + due to the ion mass difference.Such a time constant is longer than both collision time constants over the bulk of the altitude range considered in our analysis but becomes comparable with the ion-ion collision time constant (which is the shorter of the two collision time constants at relevant altitudes) above 260 km for both species.
For convenience, the corresponding transition altitude is referred to as the ion gyration boundary throughout the rest of the paper.The ion gyration boundaries are marked as circles in Figure 2. Below this boundary, the ion bulk flow is predominantly driven by the plasma pressure gradient and local gravity, but above it, magnetic pressure comes into effect, and a full magnetohydrodynamic approach is required for a proper characterization of the system, where the ions start to make helical motions and their trajectories are tightly bound by the magnetic fields.While a similar situation is observed during DD8, the ion gyration boundary is found to lower significantly, to 190 km for + O 2 and 230 km for O + .This is in part owing to the small difference in the ambient magnetic field intensity between the two campaigns but mostly contributed by the significant solar cycle variations of both collision time constants.

Variations with the Martian Local Time
To further explore the variability in the Martian ionosphere, we consider the full range of local time conditions sampled during four DD campaigns: DD8 for the dayside, DD7 for the duskside, DD6 for the nightside, and DD5 for the dawnside.All four campaigns sample the weakly magnetized regions of Mars and are subjected to a similar level of solar ionizing flux with a small variability of 30% or so.The chemical and diffusion time constants for + O 2 and O + , as well as the magnetic diffusion time constant, are presented in Figure 3 for each DD in the same format as in Figure 1.The day-night difference is prominent.On the dayside, the diffusion of + O 2 and O + is more effective than photochemistry above 180 and 210 km, respectively (see above).The PCE boundary is lowered to 150 km for + O 2 and 180 km for O + at midnight.These results are analogous to the solar cycle variations reported in Section 3 and are favorably interpreted by the day-night difference in the structure of the Martian upper atmosphere and ionosphere.In particular, the nightside Martian ionosphere is well known to be patchy and sporadic and is substantially thinner than the dayside ionosphere (e.g., Gurnett et al. 2008;Fowler et al. 2015;Girazian et al. 2017;Wu et al. 2023).The neutral atmosphere also tends to be more tenuous on the nightside, partially in response to the day-night temperature difference (Stone et al. 2018).These features act to slow down ion chemistry but speed up ion diffusion, which are combined to account for a reduced level of the PCE boundary on the nightside.
Not surprisingly, the day-night difference could be readily extended to the full diurnal cycle.According to Figure 3, the situation for the duskside is close to that for the dayside, whereas the situation for the dawnside is close to that for the nightside, both featuring similar locations of the PCE boundary for the two displayed species.The above difference between the dawnside and duskside could be viewed as one aspect of the well-established dawn-dusk asymmetry of the Martian ionosphere (e.g., Cao et al. 2019;Cui et al. 2020;Felici et al. 2022).For instance, it is consistent with the observation that the ion distribution on the duskside extends further into the darkness as compared to the dawnside, especially at low altitudes (Cao et al. 2019).The enhanced duskside plasma concentration accelerates ion destruction via DR and also hinders ion transport due to more frequent collisions with ambient particles.
Figure 3 further shows that the magnetic frozen boundary is located near 160 km on both the dayside and duskside but is slightly lowered to 150 km on the nightside and dawnside.Such a diurnal variation is mainly driven by the variation of ion diffusion and could be interpreted following the line of reasoning outlined in Section 3.
The diurnal variations of the ion-neutral and ion-ion collision time constants, along with the ion gyroperiods, are presented in Figure 4.As described in Section 3, the ion collision boundary is located near 190 km for + O 2 and 160 km for O + , whereas the situation for the duskside is comparable, with ion collision boundaries slightly lower by 10 km or so for both species.For the nightside and dawnside, it is interesting to note that the ion-ion collision time constants are longer than the respective ion-neutral collision time constants at almost all altitudes except for a restricted region near the top boundary.This is driven by the combination of a weak diurnal variation of ion-neutral collisions and a strong diurnal variation of ion-ion collisions.Hence, we may conclude that unlike the dayside and duskside, Coulomb collisions do not have an appreciable impact on the ion force balance on both the nightside and dawnside.Such a feature, along with the fact that all ion-ion collision time constants on these two sides appear to wiggle strongly around their mean trends, is consistent with the established observation that the Martian ionosphere in the darkness is tenuous and highly variable (Gurnett et al. 2005(Gurnett et al. , 2008;;Wu et al. 2023).For the reasons addressed above, the ion collision boundaries are not marked in Figure 4 for both the nightside and dawnside.
As mentioned in Section 3, the ion gyration boundary is estimated to be near 190 km for + O 2 and 230 km for O + on the dayside.The same boundary drops to near 180 km for both species on the nightside, as indicated in Figure 4.Such a daynight difference is mainly driven by the variation of the collision time constant rather than the variation of the gyroperiod, the latter of which is within a factor of 2, as the two campaigns sample weakly magnetized regions of comparable magnetic field intensity.The reported day-night difference is indicative of the extension of magnetically bound ion helical motion toward lower altitudes in the darkness.Similarly, the ion gyration boundary on the duskside is substantially higher than that on the dawnside, again supporting a strong dawndusk asymmetry of the Martian ionosphere.

Variations with the Ambient Magnetic Field Intensity
In addition to the solar ionizing flux and local time, the structure of the Martian ionosphere is modulated by the ambient magnetic fields, which are highly inhomogeneous and generally stronger over the southern hemisphere of the planet (Acuna et al. 1998(Acuna et al. , 1999;;Connerney et al. 1999).We compare in Figure 5 the ion chemical and diffusion time constants, as well as the magnetic diffusion time constants estimated during DD8 and DD9, which sample similar local time conditions and are subjected to a similar level of solar EUV and SXR irradiance.However, the magnetic field configurations during the two campaigns are remarkably different.In particular, the DD9 campaign covers a strongly magnetized region in the southern hemisphere.
During DD9, the PCE boundary is located near 190 and 230 km for + O 2 and O + , about 20 km higher than the boundary during DD8.A scrutinization of Figure 5 further demonstrates that the magnetic control of the PCE boundary is mainly caused by the difference in ion diffusion between the two cases.Extensive observations have revealed that the plasma concentration in strongly magnetized regions is enhanced, particularly in the topside ionosphere, as a consequence of efficient plasma outflow along nearly vertical field lines (Matta et al. 2015).This is opposed to the weakly magnetized regions, where nearly horizontal field lines are more common and tend to hinder plasma outflow (Wu et al. 2019).These features are entirely consistent with the observed magnetic control of the PCE boundary.
Furthermore, Figure 5 reveals an insignificant difference in the magnetic frozen boundary between the two campaigns, both near 160 km, a fairly low altitude just above the main ionospheric peak but below the PCE boundary.In fact, both ion and magnetic diffusion are insensitive to the magnetic field environment near this altitude.The crucial point here is that near this altitude, the ion diffusion time constant is proportional to the neutral density, which is independent of the magnetic field, and that the magnetic diffusion time constant is proportional to the electron density, which is also independent of the magnetic field (Wu et al. 2019).A similar line of reasoning helps to interpret the observation that the ion collision boundary during both campaigns is near 190 km for + O 2 and 160 km for O + , irrespective of the magnetic field environment.Such an observation could be easily seen in Figure 6, where we compare the ion-neutral and ion-ion collision time constants between DD8 and DD9.
Finally, according to Figure 6, the gyroperiod during DD9 is shorter than that during DD8 for each species, as this period is inversely proportional to the magnetic field intensity.Such a variation largely counterbalances the variation of the collision time constant, which also presents an inverse correlation with the magnetic field intensity (at relatively high altitudes) as discussed above.As a consequence, the location of the ion gyration boundary also appears to be irrespective of the magnetic field environment, near 190 km for + O 2 and 230 km for O + during both campaigns.

Species Dependence of Various Time Constants
So far, we have focused on various time constants estimated for two representative species in the Martian ionosphere, + O 2 and O + .These are the two most abundant ion species on both the dayside and nightside of Mars (e.g., Benna et al. 2015;Wu et al. 2019).It is instructive to extend our discussion to more  ion species, thanks to the excellent mass coverage and resolution of the MAVEN NGIMS instrument that allows the densities of various species over a broad mass range from as light as + H 2 to as heavy as HCO 2 + to be accurately measured (Mahaffy et al. 2015).Here, to avoid unnecessary complexity, we focus on DD8, but the analyses performed on the other campaigns render similar results.
Before further discussion, we must note that among all the time constants involved in our analysis, the ion chemical time constants exhibit the largest difference among various species due to their potentially immense difference in chemical properties.This has already been observationally demonstrated by the species-dependent depletion in ion density once the ionospheric plasma flows into the shadow across the dusk terminator (e.g., Girazian et al. 2017;Cao et al. 2019).Another instance is the ion-ion collision time constant for + O 2 , which should be much longer than those for the rest of the ion species, owing to the predominance of + O 2 in a typical NGIMS ion mass spectrum (Benna et al. 2015).For each of the remaining time constants, the mass sequence should exhibit a gradual and smooth variation, with the detailed behavior relying on the exact mass dependence of each, being a perfect linear dependence for the ion gyroperiod (see Equation (5)) or a more complicated dependence for the collision or diffusion time constant (see Equations (2)-( 4)).The above discussion essentially lays the foundation for understanding the speciesdependent locations of each boundary discussed so far, which we elaborate below.
The species-dependent variation of each boundary altitude is displayed in Figure 7, showing that the location of the magnetic frozen boundary, where the ion diffusion and magnetic diffusion time constants are intersected, is indeed smooth.For the ion collision boundary, + O 2 stands out as a remarkable distinction from the remaining species, as the location of this boundary relies on how the ion-ion collision time constant varies with the altitude.A similar argument also holds for the ion gyration boundary, for which all species display gradual and smooth variations, except for + O 2 .Finally, the variation of the PCE boundary among different species is indeed the largest of all.In particular, several species act as terminal species in the Martian ionosphere that are mainly lost via the slow DR process, including NO + , HCO + , + O 2 , and H 3 O + in Figure 7 (e.g., Wu et al. 2021).Each of these species displays a relatively low PCE boundary as compared to the remaining ones because its chemical loss time constant is relatively long, thus lowering the altitude where the chemical time constant intersects with the respective diffusion time constant.Interestingly, CO 2 + also displays a low PCE boundary, though it is a nonterminal species lost mainly via fast ion-neutral reactions.In practice, most of the nonterminal species in the Martian ionosphere tend to be lost via its reactions with the two dominant constituents of the background atmosphere, CO 2 and O (Mahaffy et al. 2015), but for CO 2 + , the former reaction is a null one.As a consequence, the chemical loss of CO 2 + is retarded due to the limited number of available reactants.The above reasoning naturally explains the low PCE boundary obtained for CO 2 + .We also caution that, to estimate the CO 2 + chemical time constant, the old reaction rate coefficients from Fehsenfeld et al. (1970)    producing + O 2 of about an order of magnitude lower than the old Fehsenfeld et al. (1970) value.Here we use the old Fehsenfeld et al. (1970) results, as they were found to better reproduce the MAVEN NGIMS measurements of the Martian ionosphere (Fox et al. 2021).But if the new measurements are proven to be reliable, the PCE boundary for CO 2 + would be even lower.The above discussion highlights that the conventional PCE modeling of the dayside Martian ionosphere up to an altitude of 200 km (e.g., Mendillo et al. 2011;Xu et al. 2018;Mukundan et al. 2021;Wu et al. 2021) may not be valid for some ionospheric species on Mars, such as the terminal ones in general and nonterminal CO 2 + in particular.

Concluding Remarks
The ionosphere of Mars, as the interface between its atmosphere and external magnetized plasma environment, is an extremely complicated region where a variety of processes coexist and jointly function.A useful way to explore different regions where any given process dominates is to estimate the relevant time constants, from which a properly defined boundary location could be determined.In this study, we estimate a range of time constants for each ion species in the Martian ionosphere (Benna et al. 2015), including the chemical loss time constant, the diffusion time constant, the ion-neutral and ion-ion collision time constants, and the gyroperiod.By comparing these time constants, we identify the locations of a set of boundaries: (1) the PCE boundary, below which ions tend to be created and destroyed locally; (2) the magnetic frozen boundary, above which the magnetic field lines tend to be frozen into the bulk plasma flow; (3) the ion collision boundary, above which ion-ion Coulomb collisions become more important than ion-neutral collisions in maintaining the ion force balance; and (4) the ion gyration boundary, below which the ion bulk flow is predominantly driven by the plasma pressure and local gravity, with magnetic pressure playing an insignificant role.For the purpose of this study, we perform a thorough data-driven analysis, with all parameters required for computing the time constants adapted from a multi-instrument MAVEN data set (Jakosky et al. 2015).
Six MAVEN DD campaigns with broadly different internal and external conditions are considered, allowing us to examine the variations of the aforementioned boundaries with the solar ionizing flux, Martian local time, and ambient magnetic field intensity.Our analysis suggests a range of interesting features, as summarized in Table 2 for easy reference.First, all boundaries tend to be higher at high solar activity than at low solar activity, in response to the solar cycle variations of the Martian upper atmosphere and ionosphere, with enhanced solar EUV and SXR irradiance causing stronger ionization, higher neutral and plasma concentrations, more frequent ionneutral and ion-ion collisions, and slower diffusion.Second, all boundaries show similarly elevated locations on the dayside and duskside as compared to the nightside and dawnside, a feature that is naturally driven by the diurnal cycle of the ambient atmosphere and ionosphere and is also an important aspect of the dawn-dusk asymmetry of the Martian ionosphere (e.g., Cao et al. 2019;Cui et al. 2020;Felici et al. 2022).Third, no boundaries show significant variations with the magnetic field environment, except for the PCE boundary, which tends to be elevated in strongly magnetized regions.The former could be interpreted by the fact that, despite the magnetic modulation of relevant time constants, their effects on the location of the respective boundary tend to cancel out, whereas the latter is mainly driven by the known magnetic control of the plasma distribution in the Martian ionosphere, which slows down ion diffusion (e.g., Gurnett et al. 2005;Duru et al. 2006;Andrews et al. 2014;Diéval et al. 2018;Wu et al. 2019).
Finally, we examine the species dependence of each boundary location.The most prominent feature is a significant variability in the PCE boundary.In general, this boundary is found to be lower for all terminal species (NO + , HCO + , + O 2 , and H 3 O + ) and one nonterminal species (CO 2 + ), as compared to the remaining (nonterminal) species, which could be readily interpreted by the large difference in chemical properties between the two categories of ions (e.g., Fox 2015;Wu et al. 2021).Another phenomenon worth emphasizing is that + O 2 stands out as a remarkable distinction in its ion-ion collision time constant due to the predominance of this species in a typical MAVEN NGIMS ion mass spectrum over the rest (Benna et al. 2015).This accounts for the observation of elevated ion collision and gyration boundaries for + O 2 .All in all, the analysis presented here is useful for deciding what approximations could be reasonably implemented in future ionospheric modelings or to what extent previous modeling results could be trusted.

Figure 1 .
Figure 1.The time constants estimated during DD2 and DD8 subjected to different solar ionizing fluxes.The red solid and dashed-dotted lines represent the chemical and diffusion time constants for +O 2 , whereas the blue lines represent the same time constants for O + .The black solid line in each panel shows the magnetic diffusion time constant for comparison.The stars and squares indicate the PCE boundaries (the diffusion time constant becoming comparable to the chemical time constant) and the magnetic frozen boundaries (the magnetic diffusion time constant becoming comparable to the ion diffusion time constant), respectively.

Figure 2 .
Figure 2. The time constants estimated during DD2 and DD8 subjected to different solar ionizing fluxes.The red solid and dashed-dotted lines represent the ionneutral and ion-ion collision time constants for +O 2 , whereas the blue lines represent the same time constants for O + .The dashed lines show the ion gyroperiods for comparison.The triangles and circles indicate the ion collision boundaries (the ion-ion collision time constant becoming comparable to the ion-neutral collision time constant) and the ion gyration boundaries (the gyroperiod becoming comparable to the ion-ion collision time constant), respectively.

Figure 3 .
Figure 3. Similar to Figure 1 but for the local time variations of different time constants (ion chemical and diffusion time constants, magnetic diffusion time constants) based on the estimates made during four DD campaigns: DD8 for the dayside, DD7 for the duskside, DD6 for the nightside, and DD5 for the dawnside.The upper left panel is identical to the right panel of Figure 1.

Figure 4 .
Figure 4. Similar to Figure 2 but for the local time variations of different time constants (ion-neutral and ion-ion collision time constants, ion gyroperiods) based on the estimates made during four DD campaigns: DD8 for the dayside, DD7 for the duskside, DD6 for the nightside, and DD5 for the dawnside.The upper left panel is identical to the right panel of Figure 2.

Figure 5 .
Figure 5. Similar to Figure 1 but for the magnetic control of different time constants (ion chemical and diffusion time constants, magnetic diffusion time constants) based on the estimates made for DD8 and DD9, respectively, characterizing the weakly and strongly magnetized regions of Mars.The left panel is identical to the right panel of Figure 1.

Figure 6 .
Figure 6.Similar to Figure 2 but for the magnetic control of different time constants (ion-neutral and ion-ion collision time constants, ion gyroperiods) based on the estimates made for DD8 and DD9, respectively, characterizing the weakly and strongly magnetized regions of Mars.The left panel is identical to the right panel of Figure 2.

Figure 7 .
Figure7.The species-dependent variations of different boundary altitudes discussed in this study, including the PCE boundary (red), the magnetic frozen boundary (blue), the ion collision boundary (green), and the ion gyration boundary (black).The displayed variations are specific for the DD8 campaign, but the variations obtained for the remaining campaigns are comparable.

Figure 9 .
Figure9.The neutral, ion, and electron temperature profiles averaged over each campaign.

Table 2 A
Summary of the Variations of Different Ionospheric Boundaries with the Solar Ionizing Flux, Martian Local Time, and Magnetic Field Intensity Notes.Not including the variations among different species; see text.