Evidence of scale height variations in the Martian ionosphere over the solar cycle

Solar cycle variations in solar radiation create density changes in any planetary ionosphere, which are well established in the Earth's case. At Mars, however, the ionospheric response to such changes is not well understood. We show the solar cycle impact on the topside ionosphere of Mars, using data from the Mars Advance Radar for Subsurface and Ionospheric Sounding (MARSIS) on board Mars Express. Topside ionospheric variability during the solar cycle is analyzed through neutral scale height behavior. For moderate and high solar activity phases, the topside electron density profile is reproduced with an altitude‐variable scale height. However, for the period of extremely low solar activity in 2008 and 2009, the topside was smaller in density than in the other phases of the solar cycle, and there is evidence that it could be reproduced with either a constant scale height or a height‐variable scale height with lower electron density. Moreover, the ionosphere during this time did not show any apparent dependence on the EUV flux. This singular behavior during low solar activity may respond to the presence of an induced magnetic field which can penetrate to lower ionospheric altitudes than in other phases of the solar cycle due to the reduced thermal pressure. Numerical simulations of possible scenarios for two different solar cycle phases indicate that this hypothesis is consistent with the observations.


Introduction
Solar extreme ultraviolet (EUV) and X-ray photon flux are the main sources of ionization of a planetary atmosphere, especially in the inner solar system [e.g., Witasse et al., 2008;Schunk and Nagy, 2009]. Consequently, long-term changes in solar flux due to the different phases of the solar cycle produce important changes in the dayside ionospheric structure of any solar system body.
At Mars, due to the lack of a global-scale internal magnetic field [Acuña et al., 1999], the ionosphere is the main part of the upper atmosphere that interacts directly with the solar wind. In the last 40 years, many efforts have been made in order to understand the ionospheric response to the solar cycle [e.g., Zhang and Luhmann, 1992;Luhmann et al., 1992;Fox et al., 1996;Cravens, 1997;Mendillo et al., 2006;Dubinin et al., 2008;Withers, 2009;Lillis et al., 2010;Akalin et al., 2010;Withers et al., 2014]. This resultant knowledge was limited initially to a few time intervals of data because of a lack of continuous missions, and an incomplete solar zenith angle (SZA) coverage due to planetary geometry constrains. The radio occultation experiment has been the most utilized method for deriving electron density profiles over time, but this technique only provides profiles for SZA between 45 and 127°in the so-called "occultation seasons" [Ness et al., 2000], when the Mars and Earth positions are optimal for the radio science experiment. On the other hand, measurements of the temperature and composition of the ionosphere, until the arrival of Mars Atmosphere and Volatile EvolutioN (MAVEN) mission in 2014, came from only two single profiles measured by the Viking I and II landers with the retarding potential analyzer instrument [Hanson et al., 1977]. Nevertheless, since 1997, Martian ionospheric understanding has been significantly improved because plasma measurements have been collected on a subseasonal timescale until the present date by Mars Global Surveyor (MGS) [Hinson et al., 1999] and Mars Express [Chicarro et al., 2004]. the variation of solar irradiance in the EUV and soft X-ray spectral range from 1 to 105 nm [Schunk and Nagy, 2009]. This temperature change causes an even larger density change in the upper thermosphere [Solomon et al., 2011]. The same radiation is also responsible for the main ionization of Mars' atmosphere, and, in general, the thermosphere has a solar cycle-dependent behavior similar to Earth [e.g., Bougher et al., 2015].
The response of Earth's ionosphere to periodic and nonperiodic changes of solar activity is well known and has been widely modeled. The International Reference Ionosphere (IRI) [Bilitza and Reinisch, 2008] and the NeQuick model [Nava et al., 2008] are two examples of widely used empirical models. However, during the last solar minimum (end 2007 to end 2009), deficiencies in these models became apparent. EUV and X-ray radiation were exceptionally reduced compared with the previous solar minimum. As a result, the terrestrial thermosphere at high altitude was cooler and lower in density than expected [Solomon et al., 2010[Solomon et al., , 2011[Solomon et al., , 2013, and in general, the low-density values measured either from space or from the ground were overestimated by the ionospheric models for local and global conditions [e.g., Sethi et al., 2011;Adewale et al., 2012;Klenzing et al., 2013;Yue et al., 2013].
The objective of this paper is to show the effect of the latest solar activity cycle on measured topside profiles of the ionosphere of Mars. Ionospheric variability over the solar cycle is analyzed through the neutral scale height, which gives information on the density distribution with altitude in the ionosphere, and in turn is related to thermal and transport processes. Furthermore, at Earth during the recent solar minimum the thermosphere became much colder and lower in density, although it is not clear if this was the case at Mars. For this reason, we look for evidence of similar or otherwise exceptional behavior as we analyze the response of Mars' ionosphere during this period of extreme low solar activity.

Data
The Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) [Picardi et al., 2004] on board Mars Express has been probing the topside ionosphere of Mars since June 2005, currently covering 10 years and with the best planetary coverage yet archived. When this instrument operates in the Active Ionospheric Sounding (AIS) mode, which occurs for short periods close to periapsis, the topside ionosphere is sounded [Gurnett et al., 2005] following exactly the same physical principles of ionosondes on Earth [Sánchez-Cano et al., 2012;Morgan et al., 2013]. The final product is the topside electron density profile, which gives the electron density distribution with altitude from the main ionization peak to the spacecraft position. Figure 1 shows the evolution of the 10 years of solar activity since the Mars Express spacecraft arrived at Mars. In Figure 1 (first and second rows), the sunspot number (SSN), the EUV proxy F 10.7 , and the EUV solar irradiance measured by Thermosphere, Ionosphere, Mesosphere Energetics and Dynamics (TIMED)-Solar EUV Experiment (SEE) satellite [Woods and Eparvier, 2006] at a wavelength of 30.5 nm are plotted, all of them at 1 AU. This wavelength is the closest one obtained from TIMED to the solar 30.4 nm He-line, primarily responsible for the CO 2 photoionization at Mars [Kieffer et al., 1992;Withers, 2009]. The EUV solar irradiance at 30.5 nm and the solar X-ray radiation measured by the GOES family of satellites [Grubb, 1975] have been scaled to the Mars heliocentric distance in Figure 1 (third and fourth rows, respectively). In order to analyze the ionospheric response to solar cycle changes, the AIS data set was split into four periods according to notable changes in the solar spectrum, as seen in Figure 1 by considering all the panels together. Period A corresponds to the moderate solar activity phase of the solar cycle in the declining phase of solar cycle 23, from the MARSIS radar deployment (mid-June 2005) to mid-September of 2007. As observed in Figure 1, all the parameters exhibit a lower level than the previous years (high solar activity), and a progressive reduction along the period. Period B corresponds to the low solar activity phase of the solar cycle 23/24, from mid-September 2007 to mid-September 2009. This period was characterized by a lower level of SSN, EUV, and F 10.7 index at 1 AU in comparison to Period A, being almost constant for these three parameters along the full period. The EUV at Mars, which depends on the orbit evolution, showed a general reduction in comparison to the former period, although the planetary orbit change did result in a 25% change during this interval. If Periods A and B are compared for the same heliocentric distances, e.g., the EUV minima and maxima of Periods A and B (farther and closer Mars-Sun position, respectively), the EUV flux is always smaller during the low solar activity phase. However, the most notable difference of this period is the almost permanent absence of measurable X-ray flux. Period C corresponds to the moderate solar activity in the ascending phase of the solar cycle 24, from mid-September 2009 to mid-February 2011. During this phase, every parameter showed similar levels to those in Period A, with a progressive ascending trend along the period. This phase is the shortest of the four intervals. The main difference with respect to Period B is the notable increment of the X-ray flux to levels which are similar to Period A. Finally, Period D corresponds to the high activity phase of the solar cycle 24, from mid-February 2011 to June 2012. On average, all the parameters were higher in Period D than in the other three periods. The EUV flux at Mars reached the maximum of the four periods, and the level of X-ray flux was, on average, 1 order of magnitude larger than during Period C.
We have a number of selection criteria to identify the AIS profiles. The most general of these were described before by Morgan et al. [2013] and Sánchez-Cano et al. [2012 and are summarized here.
1. MARSIS needs to be working in AIS mode instead of subsurface mode. 2. Data have to be recorded in the dayside and with the specific SZA required by the study. This may seem trivial, but we note that Mars Express periapsis is in the nightside of the planet for large periods of time. 3. The presence of local plasma harmonics [Andrews et al., 2013] is necessary to provide a measure of the local plasma density in order to derive the correct altitude of the electron density profile. This implies that Mars Express needs to be often below 500-600 km altitude. During the low solar activity phase, this altitude may even be reduced to 350-400 km (the periapsis is at~275-300 km), resulting in the absence of local plasma harmonics. 4. The whole ionospheric trace (including the lowest and the highest frequencies of the trace) has to be clearly recorded [see, e.g., Sánchez-Cano et al., 2013, Figure 2]. At the lowest-frequency part, the trace is difficult to track because of the noise and the overlap with the harmonic oscillations, and at the highest-frequency part, it is necessary to select a well-defined vertical signature of the trace in order to be sure that the values extracted are not affected by lack of definition in the ionogram, thereby minimizing the uncertainty of this parameter [Sánchez-Cano et al., 2013]. Moreover, atmospheric absorption often inhibits part of the full trace.
In addition to these four standard criteria, we have only selected profiles which occur over regions where no crustal magnetic field is present as the presence of the field makes the analysis of the ionograms more complex. Likewise, data from orbits affected by strong and/or fast solar wind, such as Coronal Mass Ejections (CMEs) are not considered because additional ionization sources (i.e., other than EUV) are enhanced at these times such as penetrating solar wind proton precipitation [Halekas et al., 2015], solar energetic particles [Lillis et al., 2012], and pickup oxygen ion precipitation [Leblanc et al., 2015]. Finally, we focus on two adjacent narrow ranges of SZA, 45-50°and 50-55°, as these provide us with the best distribution across all four periods of solar activity. These selection criteria result in 626 AIS topside electron density profiles over the two SZA ranges. These profiles are distributed in each solar cycle phase as specified in Table 1. We note that the amount of available AIS profiles that fulfill the above criteria depends on the time length of each solar phase, on the time slots that MARSIS was working in AIS mode, and on the planetary coverage described by the Mars Express orbit evolution.

Electron Density and Neutral Scale Height Variation With Solar Cycle
The atmospheric and ionospheric scale heights are two of the main parameters that define the electron density profile. The scale height measures the height range in which the plasma and neutral density change by a factor of e, such that these parameters control the shape of the vertical density profile [Belehaki et al., 2006].
For a medium in hydrostatic equilibrium and with constant temperature, the scale height, H, is defined as where m is the mean molecular mass of the medium, T is its temperature, g is the acceleration due to the gravity of the planet at ionospheric altitudes, and K B is the Boltzmann constant. The scale height can describe the altitude distribution of the neutral and plasma components of the ionosphere, depending on which mass, m, and temperature, T, are considered: that is, for the atmospheric scale height, the temperature of the neutral components and the mass of CO 2 are used, and for the ionospheric scale height, the temperature of the ions plus electrons and the mass of O 2 + for the ion mass are used. This work focuses on the neutral scale height because this is appropriate for the Chapman formulation that describes the shape of the electron density profile at Mars [Gurnett et al., 2005]. However, a similar result is expected if the plasma population is considered. Since only small changes in composition due to the solar cycle are expected in the photochemical region (hydrostatic region) [e.g., Fox et al., 1996, Figure 1], the neutral scale height differences are expected to be directly dependent on the temperature variations.
We use profiles that have the same SZA, but the heliocentric distance and therefore the incident solar flux are different for each particular case and the profiles cannot be directly compared. Therefore, we normalize the profiles using where N and h are the density and altitude along the profile, respectively; N o and h o are the density and altitude values of the electron density peak of each profile, respectively; and H o is the neutral scale height of each profile in the peak region. H o is calculated by numerically fitting each individual profile to an α-Chapman layer with a scale height which varies with height as described by equation (3) H where a is the normalization factor which reflects the degree to which H depends on h. (left column) and 4 (left column) show the normalized AIS topside profiles selected for this study for the SZA ranges 45-50°and 50-55°, respectively. Although the profiles may look similar for the four cases with this representation, there are clear differences in density that will be analyzed later. Table 1 shows the averaged H of the profiles for different altitudes and for each phase of the solar cycle in the photochemical region (up to about 170 km, i.e., below the horizontal green line in Figures 3 and 4). For both SZA intervals, all periods have a similar variation of H with altitude as indicated by the parameter, a, except the period of low solar activity (Period B) which has the smallest degree of variation. Based on a Student's t test, the mean value of the parameter a of Period B is statistically significantly different, at the 99% or above, with respect to the other three Periods in both SZA intervals.
In order to evaluate quantitatively the differences of the density profiles in altitude for each solar cycle period and, in particular, to assess the degree of variation of the ionospheric density during the low solar activity . This model is based on the Chapman formulation and describes the shape of the modeled electron density topside with a scale height H that depends linearly on altitude (similar to equation (3)) and with an exponential SZA dependence. Therefore, the model does not consider any variation of H with solar activity or with the different phases of the solar cycle and can be used as a reference for this study. In Figures 3 (middle and right columns) and 4 (middle and right columns), the relationship between the normalized densities of the observations (N data /No data ) and the normalized model reference density (N model /No model ) is plotted, where a constant scale height, H, has been used in the middle column (i.e., the altitude dependence of H in the model was removed) and an altitude-varying H in the right column (i.e., the altitude dependence of H in the model was kept). In each panel, the relation 1:1 is indicated with a black dashed line and the current linear best fit with a blue (middle column) or red (right column) solid line. The equations of these best fits are included in each subpanel. In general, Periods A, C, and D show a closer behavior to the Chapman model reference when an altitude-variable H is considered instead of a constant value. For the high solar activity period (Period D), the density is slightly larger than the reference altitude-variable H for the SZA range 50-55° (Figure 4, right column). These results are in accordance with Table 1, in particular at higher altitudes (at 0.2-0.6 normalized density). However, for periods A, C, and D the relationship between the observed and reference values when a constant H is considered is poor. This is evidence that the altitude-variable H is more appropriate for describing the ionosphere during these periods.
For Period B (low solar activity), the density behavior is closer to the reference one when a constant H is considered for both SZA intervals (Figures 3, middle column, and 4, middle column), while a clear reduction in density is observed for almost all the data points with respect to the relation 1:1 in the altitude-variable case (Figures 3, right column, and 4, right column). The lines of best fits in the altitude-variable case (Figures 3, right column, and 4, right column) do follow a simple trend but with an offset below that trend. However, the constant scale height profile provides a closer fit to the simple trend. The ionospheric density may have responded to a linear altitude-variable H with a smaller rate of variation in altitude (as the red fit indicates), or simply the scale height becomes constant (as the blue fit indicates), which is not the case in other phases of the solar cycle. We can, however, conclude that during Period B, a notable topside electron density reduction with altitude took place. As mentioned above, this period was characterized by an especially prolonged solar minimum, which was deeper than the previous solar minimum: the EUV radiation was extremely reduced from end 2007 to end 2009, and detectable X-rays were practically absent ( Figure 1). We believe that the ionosphere and thermosphere may have been cooler, and therefore, an overall reduction of the scale height is found.
We note that although changes in the neutral atmosphere inferred from electron density variability have been previously analyzed [e.g., Bougher et al., 2001], our analysis shows that solar cycle variations can be identified in neutral scale height changes in the topside ionosphere of Mars, which has never been noted before with observational data.

Possible Induced Magnetic Field in the Upper Ionosphere
The low solar activity phase resulted in a general reduction in the density of the topside ionosphere of Mars. Generally, topside reductions are associated with induced magnetic fields of solar wind origin at the top of the ionosphere. This has been extensively analyzed with different data sets and modeling. For example, Russell and Vaisberg [1983] show a combination of magnetic field and electron density profiles from the Pioneer Venus Orbiter (PVO) mission to Venus, where the stronger the magnetic field is at the top of the ionosphere, the deeper it penetrates and a more compressed ionosphere (characterized by a lower scale height) is found. In the case of Mars, Morel et al. [2004] modeled the ionospheric behavior under differing magnetic field magnitudes at the top of the ionosphere and found that the magnetic field can influence the electron density profile of the Martian ionosphere [see Morel et al., 2004, Figure 6]. Similarly, during a period of numerous coronal mass ejections a clear lower topside scale height was seen at Mars using Mars Express radio occultation data [Withers et al., 2012, Figure 2A].
It could be possible that for the minimum solar cycle condition, the Martian ionosphere was in most of the cases weak enough to allow the penetration of an induced magnetic field from the solar wind at the uppermost ionosphere. We do not mean that the magnitude of the induced magnetic field was greater during that period, but the ionosphere was smaller in extent, and therefore, an induced magnetic field could penetrate to lower altitudes, resulting in a less extended photochemical region. To evaluate this possible scenario, numerical simulations are required. The numerical/fluid model TRANSMARS has been used for this task. This model was built from the models existing for the Earth [e.g., Lilensten et al., 1989;Blelly et al., 1996;Diloy et al., 1996;Witasse et al., 1999;Culot et al., 2004;Simon et al., 2005] and adapted for Mars [Witasse, 2000;Witasse et al., 2002Witasse et al., , 2003Morel et al., 2004;Leblanc et al., 2008;Simon et al., 2009]. It is a one-dimensional kinetic-fluid coupled model covering the altitude range 100-500 km. The kinetic part is a stationary Boltzmann approach, which computes the energetic electron flux. The ionizing source may be either the incoming solar wind electrons or photoelectrons. In this latter case, a photoproduction equation is also solved. The fluid part is an eight moment time-dependent model that solves the transport equations of different charged species e À , CO 2 + , O 2 + , O + , H + , NO+, and N 2 + . The formalism allows the computation of an equation for the induced magnetic field, similarly to Shinagawa and Cravens [1989]. The main inputs of the model are the neutral atmosphere, the solar flux in the EUV range [Richards et al., 1994], and the Journal of Geophysical Research: Space Physics 10.1002/2015JA021949 energetic electron precipitation. The main outputs are, as a function of altitude, the energetic ionizing electron fluxes, the primary and secondary ion production rates, the ion and neutral excitation production rates, the ion densities, the ion and electron velocities, and the ion and electron temperatures.
A case study is presented in Figure 5, where 14 AIS profiles are analyzed from two different orbits belonging to different phases of the solar cycle, but with similar solar activity and planetary and spacecraft orbital characteristics. In black, seven profiles from Mars Express orbit 4210 (Period A) and in red, seven profiles from Mars Express orbit 6592 (Period B). Both sets of profiles have practically the same conditions: SZA between 45 and 55°; a heliocentric distance of 1.40 AU; latitudes of À40 and À63°, respectively; longitudes of 73 and 327°E, respectively; solar longitudes of 220 and 213°, respectively (spring); 69 solar flux unit of F 10.7 index as a proxy of EUV radiation; and 1.5 · 10 À4 W/m 2 /nm for the 30.5 nm wavelength of the EUV solar irradiance at Mars (see Figure 1). As in the previous figures, profiles are located over areas where the crustal magnetic field is negligible [Cain et al., 2003]. In principle, since the conditions for ionospheric formation are equivalent, both orbits should yield similar results. Indeed, the peak characteristics (altitude and electron density) are practically the same for both cases. The neutral scale height at the altitude of the peak electron density of both orbits is on average 10.5 km, which implies a temperature of the neutral population around 190 K (calculated with equation (1)). This suggests that the density of the neutral atmosphere at that height was quite similar for these cases, since the peak altitude is directly proportional to the neutral density of the atmosphere [Schunk and Nagy, 2009]. Nevertheless, the first important difference is that the electron density of the red profiles at higher altitudes is smaller, suggesting additional ionospheric cooling for this case despite having, in principle, the same level of solar radiation. The second important difference is the transition altitude (sudden change of slope) found at 180 km in the red profiles, which is interpreted as being the lowest altitude at which the induced magnetic field has a significant influence.
Although Mars Express does not have a magnetometer, the magnetic field magnitude at the spacecraft location can be derived from the MARSIS instrument under certain circumstances [Gurnett et al., 2008;Akalin et al., 2010]. For the orbit 6592 (in red, low solar activity), MARSIS recorded a clear magnetic field value of 26 nT at the spacecraft altitude in the seven profiles, during which the spacecraft altitude barely changed, while no estimates of the magnetic field were available for orbit 4210. Note that the lack of a magnetic measurement at the spacecraft position does not mean an absence of a field. This observed magnetic field allows us to set up the upper boundary condition at 500 km altitude needed in the numerical model to compute the vertical profile of the magnetic field. The lower boundary condition is set at 0 nT at 100 km altitude. The resulting profile of the magnetic field is displayed in Figure 5. The model was run for each data set for the conditions of each date (Table 2), while a magnetic field of magnitude 26 nT at 370 km of altitude was used for orbit 6592, and a value of 0 nT for orbit 4210. Figure 5a shows the simulated electron density  Although the numerical solution is not unique since the run was based on a single value of magnetic field and the behavior of the red profiles is less constant than the black ones, the electron density simulations reproduce the slope of both sets of profiles. It indicates that the induced magnetic field scenario for the low solar activity case is reasonable. Indeed, the simulated magnetic field profile is in good agreement with the magnetic field profiles measured by MGS in the previous solar cycle [Opgenoorth et al., 2010, Figure 6]. For almost the same neutral scale height at the peak, the slope of the topside profiles is smaller for orbit 6592 (Period B). This means that the plasma pressure of the ionosphere for that case was smaller, as can also be observed from the smaller electron temperature between 150 and 250 km (Figure 5b). Thus, the simulations indicate a cooler ionosphere for the low solar activity case: 16 K and 72 K lower for the neutral and electron temperatures, respectively, at 35 km above the peak (which is at 135 km); 22 K and 113 K lower at 45 km above the peak; and 32 K and 183 K lower at 65 km above the peak. This produces the observed reduction in the density, as suggested above. Indeed, the average neutral temperature difference at 40 km from the peak is about 20 K in the simulations, which is the same result found in Table 1 for Periods A and B with equation (1). There is a transition in the electron density profile which starts at about 180 km, the limit between the photochemical and diffusion region for the red profiles. As observed in the vertical ion velocity panel, for the red profiles, the photochemical region (velocity close to zero) finished at this altitude, leading to a downward ion velocity associated with the penetration of the magnetic field in the ionosphere. The electron temperature becomes higher at altitudes above 250 km due to lower thermal conductivities. On the contrary, the diffusion region starts at about 220 km for the unmagnetized case, having first a small negative incursion of the velocity, mostly due to ion thermal diffusion, and then an upward plasma velocity, which is explained by the change in which O + became the major ion (Figure 5c).

Summary
Solar cycle variations create changes in the topside ionosphere of Mars. The Mars Express MARSIS AIS data set, within the SZA interval of 45-55°, was split into four periods according to notable changes in the solar spectrum ( Figure 1). A singular behavior is observed for low and high solar activity phases, which do not respond in the same way to changes in the EUV flux at Mars (the main factor of ionization). Specifically, the low solar activity phase (Period B) differs from the other periods as the topside electron density does not show any apparent dependence on this radiation, while during the high solar activity phase, the topside density profile was larger. The absence of X-ray flux during the low solar activity period may have played a major role, although this radiation is typically associated with the formation of the ionospheric secondary layer (~110 km of altitude).
In general, the Martian topside ionosphere observations are better reproduced with a neutral scale height that increases linearly with altitude, except for the case of the low solar activity phase (Figures 3 and 4). In this latter case, there is evidence for either a constant scale height or a height-variable scale height with lower electron density. During that phase, the ionospheric temperature was cooler, and therefore, the electron density and scale height were smaller than in other phases of the solar cycle, resulting in a reduced plasma pressure.
Simulations made with the numerical/fluid model TRANSMARS ( Figure 5) indicate that most probably, the induced solar wind magnetic field penetrated more easily into the ionosphere, leading to a larger compression of the topside than in other phases of the solar cycle.
All the available evidence seems to indicate that as for Earth, the deep and long recent solar minimum created a colder thermosphere with lower density, and therefore, an exceptional behavior in the response of the Mars' ionosphere was found. Despite the substantial geophysical differences between Mars and Earth, the vertical structure of their dayside ionospheres seems to respond similarly to solar cycle variability.