MGS electron density profiles: Analysis and modeling of peak altitudes

Icarus 221 (2012) 1002–1019

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MGS electron density profiles: Analysis and modeling of peak altitudes Jane L. Fox ⇑, Andrew J. Weber Department of Physics, Wright State University, Dayton, OH 45435, United States

a r t i c l e

i n f o

Article history: Received 17 July 2012 Revised 2 October 2012 Accepted 3 October 2012 Available online 23 October 2012 Keywords: Mars Ionospheres Aeronomy Terrestrial planets

a b s t r a c t We have analyzed most of the electron density profiles returned from the Mars Global Surveyor Radio Science Experiment, with a view toward investigating the shapes of the profiles and the altitudes of the upper (F1) and lower (E) peaks as a function of solar zenith angle and solar activity. We first categorize the shapes of the profiles according to the morphology of the F1 and E peaks, and find that there is an expected variation with solar activity of the two major types of shapes, those in which the E-peak appears as a shoulder on the bottomside of the F1 peak, and those in which the E peak is separated by a small minimum from the F1 peak. Since the peak altitudes have been shown to vary with planetocentric longitude, we divide the data into 36 10°E. longitude bins. We have plotted the peak altitudes of both the upper and lower peaks as a function of ln(effective secant v), where v is the solar zenith angle. The ‘‘effective secant’’ is derived by integrating the densities along the line of sight to the Sun and dividing the result by the vertically integrated densities. We then fit the peak altitudes in each longitude bin with linear least squared regressions, and report the slopes and intercepts of the lines, which, in Chapman theory, correspond to the scale heights and the subsolar peak altitudes, respectively. We find that both parameters are highly variable, and the median slopes for the F1 and E peaks are about 7 and 4 km, respectively. If interpreted as a scale height, the latter value implies a temperature in the unrealistic range of 70–75 K. In Chapman theory, there is no solar activity variation of the peak heights. When we plot the peak altitudes versus F10.7 for each longitude bin, however, and fit them to a trendline, we find that the mean slopes are negative for both the F1 and E peaks, although the slopes are in general smaller for the F1 peaks. We conclude that the E peak heights are inversely correlated with solar activity, but the evidence is not as strong for the F1 peaks. We compare electron density profiles from a numerical model to Chapman profiles, and show that the fit is poor for one Chapman profile, but is improved with a superposition of two Chapman profiles, although there are still large deviations, especially on the topside. Finally, we plot the peaks of the near-terminator numerical models for low and high solar activities as a function of ln(effective secant v), and find that the linear fits appear to be good, but the slopes are not indicative of the scale heights in our models, nor are the intercepts the same as the peak heights of our 0° models. We conclude from these various studies that there is considerable evidence for non-Chapman behavior in the ionosphere of Mars. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction 1.1. General background The Mars Global Surveyor (MGS) spacecraft was launched in November, 1996 and arrived at Mars in September, 1997. After several months of aerobraking, it achieved its final near polar, circular orbit (e.g., Albee et al., 1998). Among the suite of instruments that was carried to Mars was the Radio Science Subsystem (RSS), which provided profiles of the pressure and temperature in the lower atmosphere, and of electron densities in the ionosphere (e.g., Hinson et al., 1999, Tyler et al., 2001).

⇑ Corresponding author. E-mail address: [email protected] (J.L. Fox). 0019-1035/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.icarus.2012.10.002

The MGS RSS electron density profiles are available on a CD from the Planetary Data System (Hinson and Simpson, 2008). A total of 5600 ionospheric radio occultation (RO) profiles were returned by the instrument in seven seasons between 1998 December and 2005 June. Six of the seven seasons were in the northern hemisphere in the latitude range 60.6–85.5°. The solar zenith angle (SZA) range for these occultations is about 71–89.2°. The 220 occultations in season 3 were in the southern hemisphere, where the latitude ranged from 60.6° to 69.9°, and the SZA ranged from 78.5° to 86.9°. Although the lack of data for smaller SZAs imposes some limitations, the MGS RO profiles have provided an unprecedented opportunity to investigate the dayside near-terminator martian ionosphere. Most of the electron density profiles in the ionosphere of Mars are characterized by an upper F1 peak, and a lower E-region peak. For SZAs in the range of the MGS RSS electron

J.L. Fox, A.J. Weber / Icarus 221 (2012) 1002–1019

density profiles, the F1 peak usually appears between about 130 and 140 km, with a median altitude of 135.5 km, and the E-region peak appears between about 108 and 120 km, with a median altitude of 114.1 km. The E-region peak is usually seen as a shoulder on the lower side of the F1 peak or as a more-or-less distinct peak below a small minimum in the electron density profile. This is also true for most of the RO electron density profiles returned from earlier spacecraft, such as the Mariner 6 and 7 flybys (e.g., Fjeldbo and Eshleman, 1968, Fjeldbo et al., 1970, Hogan et al., 1972); the Soviet Mars-2 orbiter, and the Mars-4 and Mars-6 flybys (e.g., Kolosov et al., 1973, 1975, Vasil’ev et al., 1975); the Mariner 9 orbiter (e.g., Kliore et al., 1972a, 1973; Kliore, 1974); and the Viking 1 and 2 orbiters (e.g., Lindal et al., 1979; Kliore, 1992; Zhang et al., 1990). These early missions returned fewer RO profiles, but in general, they covered a greater range of SZA, for which the geometrical minimum is near 45°. The only in situ data available for individual ion densities are those measured by the retarding potential analyzers (RPAs) on the Viking 1 and 2 landers near 44° SZA (Hanson et al., 1977). The Viking RPA data show only a single Oþ 2 peak near 130 km, but no lower peak. Hanson et al. (1977) advised that, although the RPA attempted to detect ions near 112 km, problems related to the short mean free path at low altitudes limited the accuracy of the density profiles to altitudes above 120 km. Therefore, a lower peak or shoulder could easily have escaped detection. The two-peaked structure of the ionosphere has been modeled by, for example, Fox and Dalgarno (1979), Fox et al. (1995), Bougher et al. (2001), Krasnopolsky (2002), Martinis et al. (2003), Fox (2004), and Fox and Yeager (2006). Our nomenclature for the two peaks is based on the nature of their production mechanisms, and is consistent with those of, for example, Bauer (1973), Banks and Kockarts (1973), Stewart and Hanson (1982), and Bauer and Lammer (2004). The F1 or upper peak is produced mostly by ionization by solar photons in the main region of the solar EUV (200–1000 Å). Ionization by the more energetic EUV solar photons produces photoelectrons that also contribute to ionization; the peak of the electron-impact ionization profile appears on the lower side of the F1 photoionization peak, which acts to broaden and lower the peak. Ionization in the region of the E peak is produced initially by photoionization by soft X-rays (10–150 Å), and subsequently by the concomitant very energetic photoelectrons, secondary, Auger, and further ionizing electrons. In fact, electron impact ionization is the major source of the E layer. Other investigators have used different nomenclature for the two main peaks, calling the lower or E-region peak ‘‘M1’’ and the upper or F1 peak ‘‘M2’’ (e.g., Martinis et al., 2003; Mendillo et al., 2003, 2006; Rishbeth and Mendillo, 2004; Withers and Mendillo, 2005; Withers, 2009). Rishbeth and Mendillo (2004) showed, however, that the terrestrial F1 shoulders and the E region peaks appeared at the same pressure levels as the Mars ‘‘M2’’ and ‘‘M1’’ peaks, respectively, and that they responded similarly to changing solar fluxes. Mendillo et al. (2003) showed that the ‘‘M1’’ peak on Mars responds to solar flares in much the same way as the E region on Earth. In their study of the Mars Express (MEX) radio occultation profiles, Pätzold et al. (2005) named the upper peak ‘‘M1’’, the lower peak ‘‘M2’’, and a sporadic peak that appears below 110 km ‘‘M3’’. The latter peak has been suggested to arise from meteoric ions, such as Fe+, Mg+, Si+ and their oxides, which are formed either directly from ablation of meteors, or indirectly by photoionization and charge transfer to the ablated meteoric neutrals. On the inner planets, the latter two sources are the most important (e.g., Grebowsky et al., 2002). Withers et al. (2008) have investigated the occurrence of these lower layers in the MGS RSS profiles, and they have called the peaks ‘‘MM’’.

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1.2. Essentials of Chapman theory Several attempts have been made to explain the behavior of the martian ionosphere within the framework of Chapman (1931a,b) theory or somewhat modified Chapman theory, including, for example, Lindal et al. (1979), Bauer and Hantsch (1989), Hantsch and Bauer (1990), Zhang et al. (1990), Kliore (1992), Breus et al. (1998), Rishbeth and Mendillo (2004), Martinis et al. (2003), Zou et al. (2005, 2006), Withers and Mendillo (2005), Nielsen et al. (2006), Morgan et al. (2008), and Withers (2009). Most of these studies are based on radio occultation profiles from various previous and current Mars missions, but recently there have been investigations that employ data from the MEX MARSIS (Mars Advanced Radar for Subsurface and Ionospheric Sounding) instrument, which is a low frequency radar that operates by vertical sounding (e.g., Picardi et al., 1999; Gurnett et al., 2005, 2008). The ionograms produced by this instrument can be used to infer the altitude and magnitude of the F1 electron peak and the shape of the topside electron density profile. Most of the investigations of both types have focused on the variation of the peak densities and altitudes as a function of SZA and/or solar activity. Some have used the shape of a narrow region around the main peak profiles to derive the neutral scale heights of the thermosphere (e.g., Bauer and Hantsch, 1989; Breus et al., 2004; Zou et al., 2005; Withers and Mendillo, 2005). A full exposition of Chapman layer theory as it relates to ionospheres can be found in many standard text books including, for example, Bauer (1973), Banks and Kockarts (1973), Rishbeth and Garriott (1969), Chamberlain and Hunten (1987), Bauer and Lammer (2004), Prölss (2004), and Schunk and Nagy (2009). Here we present only a few key equations. In Chapman theory, ionization of a single molecular species XY is produced by monochromatic solar photons in an isothermal atmosphere, and a single positive ion is formed. The ion production rate at altitude z is given by the general expression qi(z) = F(z)rinXY(z), where F(z) is the local monochromatic solar photon flux, ri is the photoionization cross section of the single species at a single wavelength, and nXY(z) is the number density of the single neutral constituent. The altitude dependence of the ion production rate as a function of SZA v and altitude z can be expressed as

h i z qiv ðzÞ ¼ qimax;0 exp 1   sec vez=H ; H

ð1Þ

where qimax;0 is the ionization rate for overhead Sun (v = 0), H = kT/ mg is the (assumed constant) scale height of the neutral atmosphere, m is the mass of the species XY, T is the (assumed constant) neutral temperature, and g is the (assumed constant) acceleration of gravity. We have simplified Eq. (1) by defining z = 0 as the altitude of the subsolar maximum ionization rate, which is found at unit optical depth; z is defined relative to this altitude. Other authors have replaced z with equivalent expressions, such as (h  h0) where h is the altitude, and h0 is the altitude of the peak for v = 0. Since photochemical equilibrium prevails in a Chapman layer, the altitude of ion production is assumed to be equal to the altitude of ion loss. It is not widely recognized that dissociative recombination (DR) was not a part of original Chapman theory. Chapman (1931a) assumed that the single ion could be atomic or molecular, and that the recombining negative particles could be either negative ions or electrons, or some combination thereof. A generic recombination rate coefficient of 2  1010 cm3 s1 was assumed for the unknown recombination process or processes. During the following 15 years, investigators gradually realized that the measured ionospheric electron densities were not consistent with several of the possible recombination

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mechanisms, including either radiative or three-body recombination of the positive ions with electrons or negative ions, or mutual neutralization of positive ions with negative ions. It was almost two decades before the DR process þ

XY þ e ! X þ Y;

ð2Þ

which had been suggested by a few laboratory experiments, was put on a firm theoretical foundation in the seminal paper by Bates (1950), and it was finally recognized as the major recombination mechanism for both the E and F1 regions. Bates (1988) has described in detail the circuitous and interesting process by which this conclusion was reached. We now know that the photoionization rate qi(z) in the photochemical equilibrium region is balanced largely by DR, which proceeds with a rate aDRne(z)ni(z), where aDR is the DR coefficient. Charge balance dictates that the ion number density, ni(z), and the electron number density, ne(z), must be equal. Thus the ion or electron density is given by

ne ¼ ni ¼

 i 1=2 F r nXY

aDR

ð3Þ

where the dependence on z has been suppressed for clarity and compactness. The maximum electron density occurs at unit optical depth, and is given as a function of SZA v by

nemax;v ¼



1=2 F 1 ri cos v ¼ nemax;0 ðcos vÞ0:5 era Hadr

ð4Þ

where F1 is the solar photon flux outside the atmosphere, and ra is the photoabsorption cross section at the same wavelength as the photoionization cross section, ri. From this equation we see that in Chapman theory, the maximum density varies as the square root of cos(v) and as the square root of the solar photon flux F1. In a previous paper, we investigated the behavior of the magnitudes of the F1 and E peaks of the electron density profiles of the martian ionosphere in the northern hemisphere as measured by the MGS RSS (Fox and Yeager, 2009). We analyzed the behavior of the peak densities as a function of solar zenith angle and solar flux, including in our analysis one radio occultation profile per Earth day: that which exhibited the median F1 peak density for that day. We then divided the F1 and E peak magnitudes into six F10.7 bins, where F10.7 is the usual EUV solar flux proxy, the 10.7 cm radio flux in units of 1022 W m2 Hz1; we fitted the peak magnitudes to the formula

nemax ðv; F 10:7 Þ ¼ AF10:7 ðcos vÞa ;

ð5Þ

where AF10.7 can be interpreted as the predicted subsolar (v = 0) peak density, and a is equal to 0.5 in Chapman theory. The values of a that we derived, however, ranged from 0.41 to 0.51, with a median of 0.46 for the F1 peak, and from 0.33 to 0.54, with a median of 0.48, for the E-region peak. We also divided peak densities into eight solar zenith angle bins, and fitted each set of peak magnitudes to the formula

nemax ðv; F 10:7 Þ ¼ Bv ðF 10:7 Þb ;

ð6Þ

where Bv is a constant with dimensions of cm3 for each SZA; b is equal to 0.5 in Chapman theory. The values of b that we found, however, ranged from 0.063 to 0.33 for the F1 peaks, with a median value of 0.20, and from 0.095 to 0.61 for the E peaks, with a median value of 0.395. We also carried out a three-parameter fit to the peak magnitudes, which reflects their behavior as a function of both SZA and F10.7. We found that the magnitude of the F1 peaks (in cm3) could be expressed by

 nemax ðv; F 10:7 Þ ¼ 8:90  104 ðþ151; 150Þ  

F 10:7 128

0:2630:0075

0:4510:0049 cos v  cosð76:9 Þ ð7Þ

;

and that the E peak densities could be expressed as

nemax ðv; F 10:7 Þ ¼ 3:93  104 ðþ157; 156Þ  

F 10:7 128

0:4620:012 :



0:3900:018 cos v cosð76:9 Þ ð8Þ

Eqs. (7) and (8) are expected to be most accurate in the region of the average cosine (cos 76.9°) and the average F10.7 (128) for the dataset. These two equations show that, in determining the magnitude of the F1 peak, the SZA is more important than solar activity, and the reverse is true for the E peak. The exponent of F10.7 for the E peak in Eq. (8), 0.46, is much larger than that of the F1 peak in Eq. (7), 0.26. This implies that the magnitude of the E peak varies more strongly with solar activity than does the F1 peak. Neither peak, however, showed classical Chapman behavior. We note that Chapman (1931a) stated in the introduction to his seminal paper, ‘‘the problem is an ideal one which will scarcely represent adequately all the factors of importance in any actual case. It is thought likely, however, to be of value as an approximation, and as a starting point for further investigation into the influence of factors here neglected.’’ 1.3. Overview of this study In this study we focus on the shapes and peak altitudes of the electron density profiles recorded by the RSS on MGS. We categorize the shapes of the profiles, and we investigate the variability of the altitudes of the F1 and E peaks with SZA and with solar activity. In Chapman theory, the altitude of the peak zmax;v can be derived from Eq. (1) by taking the logarithm of both sides, and differentiating with respect to z. The derivative is zero if zmax;v ¼ H lnðsec vÞ. Recalling that we defined z as the altitude relative to that of the subsolar peak, zmax,0, for simplicity, we now substitute (z  zmax,0) for z. The expression for the peak altitude as a function of SZA v in Chapman theory is then

zmax;v ¼ zmax;0 þ H lnðsec vÞ;

ð9Þ

where H is the neutral scale height, and zmax,0 is the predicted peak altitude for v = 0. In this expression, there is no explicit dependence of the electron density peak altitude upon solar photon flux F1. The electron density peak occurs at a constant column density along the line of sight to the Sun, which is equal to (ra)1. Since the underlying thermospheric neutral number density and temperature profiles are assumed to be independent of SZA and solar activity, the altitude of the electron density peak is independent of solar activity in Chapman theory. The MGS electron density profiles are all characterized by SZAs P 71°. The plane parallel approximation breaks down in this SZA range. Chapman (1931b) described a function, Ch (x, v), now known as the Chapman function, where x = R/H, R is the radial distance from the center of the planet and H is the scale height. This function is to be substituted for sec (v) for grazing incidence radiation in Eq. (9). Various investigators have computed more accurate, or more user-friendly Chapman functions (e.g., Rishbeth and Garriott, 1969; Smith and Smith, 1972; Bauer, 1973; Huestis, 2001). In this investigation, we do not use Chapman functions; we substitute ‘‘effective secants’’ for the actual secants. The effective secant for a given SZA is obtained in the following way. First, we integrate numerically the total number densities of the neutral

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species in a model thermosphere along the line of sight to the Sun in spherical geometry using the method outlined by Rees (1989). The altitude range of the integrated densities is 100–700 km. We have adopted the neutral density profiles of a 12-species 60° SZA martian thermospheric model; we did not change the neutral density profiles or temperatures as the SZA was changed. The total column density for each SZA determined in this way was then divided by the corresponding vertically integrated column density. We define this ratio as the effective secant, and we have computed it for SZAs from 70° to 87° on a 1° grid, and from 87° to 90° on a 0.5° grid. In Fig. 1, we present the effective secants compared to the actual secants from 70° to 90° SZA. It appears that for Mars, the effective secants deviate significantly from the actual secants for SZAs greater than about 80°. Therefore, in analyzing the MGS data, we replace the values of sec v in Eq. (9) with effective secants obtained by interpolating the SZA of the occultation between the computed grid values, and we then fit the RSS electron density profile peak heights to the linear equation

zmax;v ¼ A þ B lnðeffective secant vÞ;

ð10Þ

using the Numerical Recipes algorithms (Press et al., 1987). Here A is the intercept and B is the slope of the fitted line. Use of the ‘‘effective secants’’ mitigates the effects of deviations from plane-parallel geometry, but it does not account for the effects of changes in the underlying neutral atmosphere as the SZA increases. We expect this change to be small for SZAs less than 60°, but it is undoubtedly larger for SZAs greater than 60°, and to be especially large close to and beyond 90° SZA, as the thermosphere is changing from sunlit to non-sunlit conditions beyond 100° SZA. One complication in analyzing any set of electron density profiles is that the altitudes of the electron density peaks respond to variability in the dust loading of the lower atmosphere (e.g., Pollack et al., 1977; Kahn et al., 1992). Suspended dust particles are normally found in the lower atmosphere up to about 30 km, but with variable optical depths. Dust absorbs solar energy, which causes the atmosphere to heat and expand, thus raising the altitude of the base of the thermosphere, and that of the ionospheric

Fig. 1. Effective secants computed for a low solar activity Mars model compared to the actual secants, from 70° to 90° SZA. The effective secants are shown as squares, and appear to deviate significantly from the actual secant, which is shown as a solid curve, beyond 80° SZA.

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peak as well. (e.g., Kliore et al., 1972a,b, 1973; McElroy et al., 1977; Stewart and Hanson, 1982; Stewart, 1987; Zhang et al., 1990; Keating et al., 1998; Forbes and Hagan, 2000; Wang and Nielsen, 2003; Moudden and Forbes, 2008a). The Mariner 9 primary mission occurred as the great planetwide dust storm of 1971 was subsiding, and the RO profiles showed F1 peak maxima that were higher by 20–30 km than those at similar SZAs at other times, including those from the Mariner 9 extended mission, and the Viking 1 and 2 missions. The Viking 1 and 2 landers recorded two more modest global dust storms (e.g., Pollack et al., 1977; Kahn et al., 1992; Keating et al., 1998; Stewart, 1987; Zhang et al., 1990; Wang and Nielsen, 2003; Forbes and Miyahara, 2006). The altitudes of the electron density peaks in the RSS dataset have been found to vary with planetocentric longitude (e.g., Bougher et al., 2001, 2004), due presumably to wave activity in the lower atmosphere that propagates up to the thermosphere, causing the atmosphere above to expand and contract. Bougher et al. (2001) analyzed the altitudes of the MGS RSS F1 and E peaks from the MGS RSS season 1 profiles. Even with this small dataset, they showed that the peak heights as a function of longitude could be fitted using harmonics up to wave number 3. This behavior is strongly correlated with mass densities at 130 km as measured by the MGS Accelerometer (e.g., Keating et al., 1998, 2001), appears to be fixed in planetocentric longitude, and to persist on an interannual basis. Fig. 2, reproduced from Bougher et al. (2004), shows the variability of the main peak altitudes as a function of longitude, from 134 MGS RSS occultations between 2000 December 9 and 2000 December 21. These occultations cover a fairly narrow SZA range of 80.5–82.2°. The solid curve is a least squares wavenumber 1–3 spectral fit, and the dotted curves are the standard deviations, which are of the order of 4 km. The variability of the ionospheric peaks with planetocentric longitude has been explained as due to vertically propagating migrating and nonmigrating thermal tides forced by interactions with solar heating near the surface; some investigators have suggested that the differential heating is due to effects such as topography or dust loading (e.g., Forbes and Hagan, 2000; Wilson, 2002; Forbes et al., 2002; Wang and Nielsen, 2003, 2004a; Withers et al., 2003, Angelats i Coll et al., 2004, Forbes and Miyahara, 2006; Moudden and Forbes, 2008a). Moudden and Forbes (2010) used the MGS and MRO aerobraking data in conjunction with a general circulation model to argue that planetary wave-tide interactions provide

Fig. 2. Altitudes of F1 peak densities for 134 MGS RSS profiles in the ‘‘EDS3’’ dataset. This dataset covers the period 2000 December 9–2000 December 21, northern summer for a narrow solar zenith angle range of 80.5–82.2°, and a narrow latitude range 67.5–69.6°N. The solid curve shows a least squares wave number 1–3 spectral fit, with 1-r errors shown by the dashed curves. Reproduced from Bougher et al. (2004) with permission.

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an alternative explanation for driving density variability in the aerobraking region in the lower thermosphere. In Section 2, we examine most of the 5380 MGS RSS electron density profiles in the northern hemisphere, and determine the F1 and E peak altitudes. Since the peak height varies quite substantially with planetocentric longitude, in order to obtain good longitudinal coverage, many more profiles were required than those of our previous study of the peak magnitudes (Fox and Yeager, 2009). We have divided the east longitude range from 0° to 360° into 36 bins, and we have assigned each occultation profile to the appropriate 10° longitude bin. We then analyze the peaks in each longitude bin separately. For the purpose of determining the longitudinal effect on the peak profiles, we do not include the 220 season 3 RSS profiles. Because the occultations of season 3 were in the southern hemisphere, the underlying topography, and other sources of wave activity are expected to be different from those of the high latitude northern hemisphere (e.g., Bougher et al., 2004). In addition, the electron density profiles in the southern hemisphere appear to be modified due to the presence of remanent crustal magnetic fields (e.g., Withers et al., 2005). We have fitted the peak altitudes in each of the longitudinal bins to Eq. (10), and report the values of the slopes and intercepts of the linear fits. In Chapman theory, the altitudes of the peaks are independent of solar activity. We test this theory by examining the behavior of the peak altitudes as a function of F10.7. In Fig. 3, we present the altitudes of optical depth unity as a function of wavelength from 3 Å to 1700 Å for a low solar activity model of the martian thermosphere for 4 SZAs: 0°, 60°, 75°, and 90°. The shorter wavelength photons can be seen to penetrate much more deeply than those of the main part of the EUV. In addition, the variability of the photon fluxes from low to high solar activity ranges from a factor of 3 in the main part of the EUV to factors of 10  100 for the shorter wavelength soft X-rays (e.g., Woods et al., 2008). We therefore expect that, at high solar activity, the more penetrating higher energy photons will be more important in producing very energetic photoelectrons, along with the accompanying ionizing electrons. This effect, by itself, would tend to lower the peaks, especially that of the E region. We do not expect the dependence, if any, to be linear, but we fit the peak altitudes in each longitude bin as a function of

Fig. 3. Altitude of optical depth unity for wavelengths from 3 to 1700 Å for four SZA models: 0°, 60°, 75°, and 90°. The variation in depth of penetration for ionizing wavelengths below 150 Å is substantial.

F10.7 to a ‘‘trendline’’, in order to determine the possible extent of this effect for the dataset. In Section 3, we compare the near-terminator numerical models of the martian ionosphere of Fox and Yeager (2006) to Chapman models. We first present electron density profiles of the low solar activity 60° numerical model, and show that it differs substantially from a profile that is formed by a single Chapman layer, and less so from that formed by a superposition of two Chapman layers. We then apply data analysis techniques to peak densities in the near terminator region for both the high and low solar activity numerical models for seven solar zenith angles, including 60°, 65°, 70°, 75°, 80°, 85°, and 90° SZA. We fit the electron density peak altitudes from our models to the linear Eq. (10), and compare the resulting slopes and intercepts to those of classical Chapman layers, and to the peak altitudes of the 0° SZA numerical models. We show that the electron density profiles from the numerical models deviate substantially from Chapman behavior. 2. Analysis of peak altitudes The characteristics of the MGS RSS occultation seasons 1–7 are shown in Table 1. In addition to the total number of occultations for each season, the start and end dates of the seasons are presented, along with the start and end values for the martian year (Clancy et al., 2000), and the areocentric longitude, Ls. Ls ranges from 0° to 360°, is 0° at the northern vernal equinox, and can be computed according to a formula provided by Allison and McEwan (2000). We have combined the last two seasons, which are separated by three days, (the apparent Christmas gap), from 2004 December 23 to 2004 December 25, and called the entire subset of data season 7 in this investigation. In general, several RO profiles were obtained each day during the seven occultation seasons, at 2– 4 h intervals. 2.1. Profile types First, we have classified each electron density profile as one of four types. Two examples of each of the four types are shown in Fig. 4. The first profile type is one in which the E region appears only as a change in the slope of the bottomside of the profile, and the altitude of the lower peak is virtually impossible to infer. In the second type of profile, the E peak occurs as a recognizable shoulder on the lower side of the F1 peak. For this type of profile, identifying the altitude and magnitude of the E peak required visual inspection. In numerical models, a peak that is partially hidden as a shoulder is assumed to be located at the altitude where the derivative of the density with respect to altitude is a minimum. With inherently noisy data, this criterion could not be applied to identify the altitude of the lower peak. Nevertheless, the estimated E peak altitude was deemed to be accurate to ±(2  3) km or so. In the type 3 profiles, the lower peak is separated from the upper peak by a small minimum, which we call ‘‘the notch’’, and the altitude and magnitude of both peaks are more easily identifiable. Type 4 profiles exhibit a large minimum between the two peaks, and the E peak is clearly separate from the F1 peak. The second example of a type 4 profile shown in Fig. 3 appears to be disturbed, possibly by wave activity, magnetization, or as a result of the interaction of the ionosphere with the solar wind. This is not uncommon in the RSS profiles. In addition, this profile exhibits a peak below 100 km that we have assumed to be evidence of a meteoric ion layer. Such layers have been investigated by Withers et al. (2008). Withers et al. identified a peak as due to meteoric ions by the presence of a negative density gradient below 100 km, which was interpreted as the topside of a layer. Out of the 5600 radio occultation profiles of the

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J.L. Fox, A.J. Weber / Icarus 221 (2012) 1002–1019 Table 1 Characteristics of MGS radio occultation seasons used in this study.

a b

Season

Start date yyyy-mm-dd

End date yyyy-mm-dd

Start MYa/Lsb

End MY/Ls

Total number of occultations

1 2 3 4 5 6 7 7

1998-12-24 1999-03-09 1999-05-06 2000-11-01 2002-11-01 2003-06-22 2004-11-23 2004-12-26

1998-12-31 1999-03-27 1999-05-29 2001-06-06 2003-06-04 2003-07-02 2004-12-22 2005-06-09

24/074 24/108 24/134 25/070 26/089 26/208 27/119 27/135

24/077 24/116 24/146 25/174 26/197 26/214 27/133 27/227

32 43 220 1572 1806 76 270 1581

Martian year as defined by Clancy et al. (2000). MY 1 began at Ls = 0, 11 April 1955. Areocentric Longitude (in degrees) relative the northern vernal equinox, for which Ls = 0.

Fig. 4. Examples of electron density profile types 1–4. Two examples of each type are illustrated. The profiles are labeled with their MGS identifiers. The second example of type 2 and the second example of type 4 profiles appear to be disturbed by wave activity.

MGS RSS, they found 71 meteoric ion peaks. The mean altitude of the meteoric ion peak was found to be 91.7 ± 4.8 km, with a

width of 10.3 ± 5.2 km. Pätzold et al. (2005) found a third peak in the MEX RO profiles that appeared between 65 and 110 km

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in nearly 10% of the first 120 electron density profiles returned from the RO experiment on MEX. We have found, however, that, for the SZA range of the MGS RSS dataset, the E peak often appears below 110 km. The difference in the method of identification may account for greater frequency of meteoric peaks in the MEX data than in the MGS data. We have eliminated these third peaks from this study by assuming that any peak below 100 km is a meteoric ion peak. Peaks that appeared between 100 and 103 km were also assumed to be meteoric in nature if visual inspection of the profile showed an E peak or shoulder at higher altitudes. We also note that the transitions between the various peak types are really a continuum, that the classification of a given profile is by visual inspection, and is therefore somewhat arbitrary. We will show, however, that classification of the profiles as one of four types is a useful and illuminating exercise. The very few RO profiles that we do not categorize here are characterized by irregularities that make the identification of the maximum electron densities and altitudes extremely difficult, such as bifurcated F1 peaks, or large oscillations that appear to reflect extensive wave activity. There are only 19 such profiles in the dataset, which we have classified as type 5. Two examples of type 5 profiles are shown in Fig. 5. We had intended to include the season 3 dataset, which is confined to the southern hemisphere, in identifying the types of the profiles. Season 3, however, contains many profiles that appear to be extremely disturbed, possibly due to the effects of the remanent magnetic fields on the ionosphere. In fact, we found that type 5 profiles appear with so much greater frequency in the southern hemisphere than in the northern hemisphere, that we have excluded the entire season 3 dataset from our profile type analysis. We had expected the relative occurrence of the profile types to be correlated with solar activity. In particular, at very low solar activity, the E peak may be small, and perhaps barely perceptible in the electron density profiles; the overall profile could be expected to be classified as type 1. For low to moderate solar activity, the E peak is expected to be slightly larger and to appear as a shoulder on the bottom-side of the F1 peak; it could therefore be classified as type 2. It has been pointed out that in such profiles, identification of the E peak magnitude and altitude is not repeatable (Withers, 2009). Identifying the height of the F1 peak as that of the absolute maximum of the profile is certainly repeatable, but due to noise in the data, the identified peak altitude may also be subject to a similar uncertainty as well. Although in Chapman theory, the F1 peak is narrow and drops off rapidly below the peak, we find that in realistic RO profiles, as well as our model profiles, the electron density peaks are broader than those of a simple Chapman layer.

For type 3 profiles, the E peak is low enough and large enough to be separated from the F1 peak by a small minimum, which we called a ‘‘notch’’, and the identification of the altitude and magnitude of the peak is likely to be more accurate. We surmised that this may be an indicator of higher solar activity. Finally, type 4 profiles might be expected at times of very high solar activity, or as a result of solar flares, when the X-ray fluxes are large. Because both the penetration depth of solar X-rays and their enhancement with solar activity increase with decreasing wavelength, the E peak may then be expected to appear at lower altitudes where it is clearly separated from the F1 peak by a large minimum. In Table 2, we present the fractions and numbers of each type of profile for the 5380 occultations in the northern hemisphere divided into seven ranges of F10.7. The daily values of F10.7 adjusted to 1 AU at local noon were taken from the National Geophysical Data Center website (ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SOLAR_ RADIO/FLUX). We have shifted the value of F10.7 to account for the relative orbital position, that is, the angular lead or lag, of Mars with respect to Earth. For Earth–Sun–Mars angles greater than 120° we have averaged the angular lead and lag values of the F10.7. We have also adjusted the F10.7 to account for the actual distance r of Mars from the Sun compared to the average distance ravg = 1.5237 AU, by the factor (ravg/r)2. We have retained the values of F10.7 in Earth-like units, rather than scaling them by (1/r)2, in order to make the level of solar activity more readily apparent. We note that shifting the F10.7 measured at Earth to the orbit of Mars is problematic, and is a source of uncertainty in the data analysis. In particular, solar flares, which greatly enhance the solar soft and hard X-ray fluxes, may last only minutes to hours and therefore may be seen at Earth and not at Mars and vice versa. The seven ranges of F10.7 presented in Table 2 include <96, 96– 116, 116–136, 136–156, 156–176, 176–196, and >196. In total, we see that 17.4%, 34.7%, 38.4% and 9.2% of the profiles are classified as types 1, 2, 3, and 4, respectively. Thus for the bulk of the profiles, the E-region peak appears as a shoulder on the lower side of the F1 peak, or with a small minimum between it and the F1 peak. For low solar activities, that is, for F10.7 < 116, the fraction of type 1 profiles is about 17%, and is representative of the frequency of type 1 profiles in the entire dataset; about 12% of the profiles are classified as type 1 for F10.7 > 196. Thus our prediction of decreasing frequency of type 1 profiles with increasing solar activity did not hold up. The fraction of type 2 profiles is 43.1% for F10.7 < 96; for F10.7 P 96 it decreases almost monotonically from 42.3% to 13% for F10.7 > 196. For F10.7 over the range from 96  116 to >196, the fraction of profiles classified as type 3 increases almost monotonically from about 30% to 63%. Clearly, solar activity seems to be

Fig. 5. Examples of electron density profiles of type 5 and their MGS identifiers. For these profiles, assigning F1 and E peak altitudes was deemed to be virtually impossible.

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F10.7 range <96

96–116

A. Fractions of each profile type (%) for F10.7 ranges 1 16.4 18.4 2 43.1 42.3 3 30.8 30.1 4 8.7 8.7 5 0.96 0.44 B. Numbers of each profile type for F10.7 ranges 1 154 211 2 405 486 3 290 346 4 82 101 5 9 5 Total

940

1149

116–136 17.0 34.7 38.6 9.6 0.14

136–156 18.4 26.9 45.7 8.9 0.17

156–176 17.4 26.5 45.4 10.7 0.0

176–196

>196

17.5 21.9 52.6 8.03 0.0

12.0 13.0 63.0 12.0 0.0

Total 17.4 34.7 38.4 9.2 0.33

241 492 548 137 2

216 316 536 104 2

80 122 209 46 0

24 30 72 11 0

12 13 63 12 0

938 1864 2064 496 18

1420

1174

460

137

100

5380

important in determining whether a profile is of type 2 or type 3, with the former occurring more often at low solar activity and the latter occurring more often at high solar activity, as predicted. The number of profiles classified as type 4 varies from 8% to 12% over the F10.7 bins, and accounts for only a small number of profiles. The occurrence of type 4 profiles appears not to be correlated with solar activity. Clearly there are other effects for these profiles that have not been taken into account. For example, the lower peaks in some type 4 occultations may actually be meteoric ion peaks that appear slightly above 100 km. Type 5 profiles tend to be concentrated at low solar activity, suggesting that perhaps, under those conditions the ionospheric plasma pressure is not strong enough to stand off the solar wind, and the disturbances may be due to the interaction of the ionosphere with the solar wind. Further study, which is beyond the scope of this work, would be required to understand these phenomena.

2.2. Peak altitudes We now turn to the altitudes of the F1 and E peaks, which we have recorded for most of the 5380 occultation profiles in the northern hemisphere. Since no E peaks were recorded for type 1 profiles, the number of data points for the E peaks is smaller than that for the F1 peaks. Here we analyze only the altitudes of the peaks. The magnitudes of the peaks were analyzed previously by Fox and Yeager (2006, 2009). As described in the introduction, to mitigate the observed variation of the peak altitudes with planetocentric longitude, we have divided the data into 36 10°E. longitude bins, and we have analyzed the data in each bin separately. We have computed the average peak heights and their standard deviations for both the F1 and E peaks in each longitude bin, and we have carried out linear least squares fits to Eq. (10) to obtain the intercepts A and the slopes B. In Fig. 6, we present the peak electron densities and the linear fits to Eq. (10) for a sample of eight of the 36 longitude bins. Plots of the peak altitudes and linear fits for all 36 longitude bins can be found in the Supplemental material for this paper. The fits to Eq. (10) appear to be acceptable, but there is a great deal of scatter in the data. The derived values of the intercepts A and the slopes B are shown in Tables 3 and 4 for the F1 and E peaks, respectively, for all 36 longitude bins. Also shown in these tables are the mean peak altitude along with its standard deviation, the average SZA, and the number of data points in each bin. The latter numbers show that the distribution of the dataset with planetocentric longitude is fairly uniform. The standard deviations around the mean for the average peak altitudes are about 5 km, and are similar for the

F1 and E peaks despite the uncertainty in identifying the E peak altitude for some of the profiles. In Figs. 7a and 8a, we show the average altitudes (zavg) of the F1 and E peaks, respectively, at the midpoints of each of the 36 10° longitude bins. The longitudinal variations of zavg show quite good agreement with the variation of peak altitudes reported by Bougher et al. (2001, 2004), some of which are reproduced here as Fig. 2. The intercepts A from our linear fits to Eq. (10) for each longitude bin for the F1 and E peaks are shown in Figs. 7b and 8b, respectively. In Chapman theory the intercept A in Eq. (10) is interpreted as zmax,0, the subsolar value for the altitude of the peak (cf., Eq. (9)). For the F1 peak, A ranges from 122 to 131 km, with a median of 125 km. For the E peak, A ranges from 103 to 111 km, with a median of about 109 km. For Chapman behavior, we would expect the variability of A = zmax,0, the predicted altitude of the subsolar peak, to be correlated with that of zavg as a function of longitude. Comparing Fig. 7a and b for the F1 peak, and Fig. 8a and b for the E peak, we see that the intercepts A as a function of longitude appear not to be correlated with the median altitudes. In Chapman theory, the slope B in Eq. (10) corresponds to the scale height H = kT/mg of the thermosphere, and has been used to derive the neutral temperature T. The slopes B from our linear fits to Eq. (10) for each longitude bin for the F1 peak are shown in Fig. 7c. They range from 2.8 km to 9.5 km, with a median of 7.2 km, an average of 6.8 km and a standard deviation 1.7 km. The median is consistent with the number density scale heights at the base of the thermosphere in the low solar activity model of Fox and Yeager (2006) of 7.4 km at 100 km, but there is considerable scatter in the data. The derived values of B for the E peak are shown in Fig. 8c. They range from 1.4 to 7.3 km, with a median of 4.0 km, an average of 4.2 km, and a standard deviation of 1.6 km. Clearly, the values of B do not represent the scale heights. The neutral temperature at the bottom boundary of the low solar activity model is about 139 K at 100 km and increases to 144.7 K at 135 km, the altitude of the F1 peak. If we were to assume that the median value of B that we derive for the E peak, 4.0 km, is indicative of the thermospheric temperatures, unrealistic values of about 70–75 K would be derived. Thus the values of B that we obtain for the E region are clearly indicative of non-Chapman behavior. Further study is required to determine the source of this interesting phenomenon. The variability of the derived value of B for both the F1 and E peaks is of uncertain origin, and may arise partly from the small number of data points, and the small SZA range of the dataset, combined with the uncertainty in determining the altitudes of the peaks to ±(2  3) km. We suggest, however, that some of the variability around the medians for both the F1 and E region peak altitudes reflects changes in the temperatures at the peak altitudes,

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Fig. 6. F1 and E peak altitudes from the RSS electron density profiles versus ln(effective secant v) (see text), and the corresponding linear fits to Eq. (10), for a random selection of eight 10° longitude bins. The complete set of 36 plots and linear fits is included in the Supplemental material for this paper.

solar activity variations, changes in the underlying thermospheric neutral densities, and other deviations from Chapman behavior. As discussed previously, the longitudinal variations are usually assumed to arise from the expansion of the atmosphere due to differential heating near the surface, and the increase in the altitude of the base of the thermosphere, rather than changes in the thermospheric temperatures. Application of Chapman theory would then imply that the scale height at the electron density peaks H in Eq. (9), or the slope B in Eq. (10), should be constant. There have been suggestions, however, that the thermospheric temperatures are affected by these waves, which break at thermospheric altitudes (e.g., Moudden and Forbes, 2008b). For example, Forbes and Miyahara (2006) have suggested that dissipation of the semidiurnal tide above 100 km will heat the thermosphere above 150 km by 50 K, while heating the atmosphere at 50 km by 10– 20 K. Parish et al. (2009) have argued that gravity waves observed by the MGS Mars Orbiter Laser Altimeter are capable of propagating upward, where they can cause heating and cooling at different altitudes in the thermosphere. Thermospheric heating and cooling could therefore account for some variability in the slopes B. There are many reasons, however, that we do not expect Chapman theory to describe either the ion production rates, the

electron density profiles, their peak densities, or peak altitudes. The thermosphere of Mars is not isothermal; the temperatures in the thermosphere increases from the mesopause, where T  140 K to a constant exospheric temperature which varies with solar activity between 170 K and 380 K (e.g., Nier and McElroy, 1977; Bougher et al., 2000, 2009). The solar ionizing flux is not monochromatic, and the photoionization and photoabsorption cross sections vary among species and as a function of wavelength across the ionizing spectrum from X-rays to the EUV. Ionization is also produced by interactions of neutral species with photoelectrons, which are not extinguished, as are photons in ionization. Photoelectrons may be energetic and produce further ionization, the rate of which maximizes on the bottom side of the photoionization peaks, lowering and broadening the total production rate peaks. As Fig. 3 shows, the depth of penetration of soft X-ray solar photons can be seen to be larger and more variable than that of the main part of the EUV. When Chapman (1931a) presented his simple theory, the solar flux in the ultraviolet was assumed to be characterized by the same blackbody temperature as that of the visible spectrum (6000 K). Thus ionization was expected to be dominated by photons near the ionization thresholds.

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J.L. Fox, A.J. Weber / Icarus 221 (2012) 1002–1019 Table 3 Best fit parameters in Eq. (10) for the F1 peaks, average SZA, average altitude (with standard deviations) and number of data points for each 10°E longitude bin.

a b

E longitude range (°)

Aa (km)

Bb (km)

Average SZA (°)

Average alt. (km)

Number of data points

0–10 10–20 20–30 30–40 40–50 50–60 60–70 70–80 80–90 90–100 100–110 110–120 120–130 130–140 140–150 150–160 160–170 170–180 180–190 190–200 200–210 210–220 220–230 230–240 240–250 250–260 260–270 270–280 280–290 290–300 300–310 310–320 320–330 330–340 340–350 350–360

123.1 128.3 122.0 127.7 126.3 130.3 125.0 131.0 127.8 122.2 127.3 124.9 124.2 124.6 125.1 123.0 123.9 127.8 127.6 126.1 127.4 128.7 126.7 124.0 127.4 124.1 124.1 124.3 123.9 124.9 128.5 124.2 123.7 124.5 126.8 123.4

9.23 5.09 9.52 5.10 6.09 3.03 6.96 2.82 5.24 8.94 6.28 8.07 8.60 8.30 7.86 8.91 8.11 5.45 5.24 6.29 5.47 4.50 6.07 8.22 5.69 7.58 7.87 7.41 7.56 6.82 4.59 7.82 7.85 7.88 6.41 8.67

76.9 76.5 77.0 76.8 76.8 77.0 77.0 77.0 76.7 77.7 77.0 77.4 77.1 77.4 77.1 77.2 77.4 76.5 77.4 77.1 76.8 77.2 76.9 76.9 76.7 77.2 76.6 77.2 76.9 77.2 77.2 77.1 77.0 77.4 76.9 77.2

137.0 ± 5.3 135.8 ± 4.4 136.6 ± 5.9 135.3 ± 5.0 135.4 ± 4.8 134.9 ± 5.1 135.6 ± 5.5 135.3 ± 5.1 135.6 ± 5.0 136.2 ± 5.8 136.8 ± 4.3 137.4 ± 5.0 137.4 ± 5.3 137.5 ± 5.1 137.0 ± 5.0 136.7 ± 5.5 136.5 ± 5.4 135.8 ± 4.4 135.7 ± 4.7 135.7 ± 4.9 135.7 ± 5.1 135.6 ± 4.6 135.9 ± 5.0 136.4 ± 5.7 135.8 ± 4.7 135.8 ± 5.1 135.7 ± 4.6 135.6 ± 4.9 135.3 ± 5.2 135.3 ± 5.5 135.5 ± 4.7 136.2 ± 5.1 135.6 ± 5.0 136.6 ± 4.9 136.5 ± 4.5 136.7 ± 4.9

132 150 150 148 145 149 146 148 152 151 155 153 161 156 152 155 167 151 151 162 156 143 155 156 138 161 140 147 155 158 128 148 151 131 149 129

The intercept, A, is z0, the peak altitude for 0° SZA in Chapman theory. The slope, B, is H, the scale height, in Chapman theory.

The thermosphere/ionosphere of Mars is comprised of many atomic and molecular neutral and ion species. In addition to loss by DR (Eq. (2)), the atomic and molecular ions are transformed by ion–molecule reactions. The rate coefficients for DR differ from one ion to another, and vary inversely with Te, usually as (300/ þ + Te)0.5±0.2. On Mars the major ions produced are COþ 2 and O . CO2 is transformed into other ions via ion-neutral reactions, including + reaction with O, which produces Oþ 2 . O reacts with neutral species þ þ including CO2, which forms O2 . O2 may be transformed into NO+ by reaction with N or NO before recombining dissociatively. NO+ is abundant on the lower side of the Oþ 2 peak. All of these effects tend to displace and broaden the electron density peaks. Among the most important effects that Chapman theory does not into account, in addition to variations with season (Zou et al., 2005; Bougher et al., 2006), longitude, and solar activity, are changes in the properties of the underlying thermospheres: the neutral density profiles, the decoupling between the neutral and plasma temperatures (Tn, Ti, and Te) and their gradients. All of these factors combine to produce a realistic martian ionosphere that is expected to deviate quite substantially from Chapman behavior. The F1 peak is formed mostly by solar photons in the main part of the EUV, and by photoelectrons created by the more energetic ionizing EUV photons. Electron impact ionization will tend to lower the altitude of the F1 peak, but positive gradients in Te will reduce the DR rate, and cause the peak to rise. Both effects will broaden the peak. The E region is initiated by absorption of soft X-rays, but the main ion production mechanism is impact of energetic electrons. The variability in the magnitude of the F1 peak as a function of solar activity, expressed as F10.7, has been shown to be

smaller than that of the E peak (cf., Eqs. (7) and (8); Fox and Yeager, 2009). In addition, Wang and Nielsen (2004b) have adduced evidence that the interaction of solar wind protons with the martian thermosphere increases the temperature at thermospheric altitudes, and raises the altitude of the F1 peak. The E peaks have been found to be greatly enhanced in the presence of solar flares, which occur more often at high than at low solar activity (e.g., Mendillo et al., 2006; Haider et al., 2009). Since the solar flux is more variable at the shorter wavelengths in the soft X-ray portion of the solar spectrum, the altitude of the E peak may be expected to decrease as solar activity increases. 2.3. Solar activity effects on peak altitudes In Chapman theory (Eqs. (9) and (10)) there is no dependence of the altitudes of the electron density peaks with solar photon flux F1. As stated previously, the electron density peaks are predicted to occur at a constant column density along the line of sight to the Sun, which is equal to (ra)1, where ra is the photoabsorption cross section characteristic of a single species at a single ionizing wavelength. As Fig. 3 illustrates, however, the altitudes at which ionizing solar photons deposit their energy in a model atmosphere occur over a large range from the EUV to soft X-rays, with X-rays penetrating deeper in the atmosphere. The solar activity variation of the photon fluxes generally increases with decreasing wavelength. The variation in the EUV photon fluxes is a factor of 3, whereas in the soft to hard X-ray region the variation may reach factors of 100 or more. We therefore expect that, for similar underlying

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Table 4 Best fit parameters in Eq. (10) for the E-region peaks, average SZA, average altitude (with standard deviations) and number of data points for each 10°E longitude bin.

a b

E longitude range (°)

Aa (km)

Bb (km)

Average SZA (°)

Average alt. (km)

Number of data points

0–10 10–20 20–30 30–40 40–50 50–60 60–70 70–80 80–90 90–100 100–110 110–120 120–130 130–140 140–150 150–160 160–170 170–180 180–190 190–200 200–210 210–220 220–230 230–240 240–250 250–260 260–270 270–280 280–290 290–300 300–310 310–320 320–330 330–340 340–350 350–360

109.4 109.2 107.0 109.5 107.2 108.2 106.3 109.7 109.0 105.3 104.4 107.3 109.9 109.4 111.1 111.2 111.2 109.0 111.5 103.4 111.1 109.3 108.8 104.7 109.0 105.6 103.9 107.1 105.8 106.3 106.6 108.6 108.0 108.5 109.0 109.0

3.27 3.15 3.94 2.56 4.83 3.31 5.27 3.01 3.66 6.31 7.31 5.05 3.32 3.66 2.19 2.37 2.00 3.58 1.40 7.05 1.70 3.18 4.23 6.74 4.31 6.15 7.13 4.57 5.51 5.35 5.50 3.83 5.07 4.05 4.09 3.48

77.1 76.4 77.3 77.0 77.0 76.7 76.8 77.1 76.7 77.9 76.8 77.4 77.4 77.4 77.3 77.4 77.5 76.4 77.5 77.1 76.8 77.0 76.9 76.9 76.6 77.3 76.5 76.9 76.7 76.9 77.1 76.8 77.2 77.5 77.3 77.0

114.4 ± 5.9 113.8 ± 5.1 113.1 ± 5.9 113.4 ± 4.9 114.5 ± 5.9 113.1 ± 5.2 114.3 ± 5.1 114.1 ± 4.1 115.2 ± 4.9 115.3 ± 5.1 115.4 ± 4.8 115.1 ± 5.1 115.1 ± 4.6 115.1 ± 4.5 114.5 ± 4.5 114.9 ± 5.0 114.4 ± 4.5 114.3 ± 4.8 113.7 ± 4.1 114.1 ± 6.3 113.7 ± 4.5 114.1 ± 4.5 115.2 ± 5.2 114.9 ± 5.7 115.4 ± 4.3 115.1 ± 5.0 114.5 ± 5.6 114.0 ± 4.6 114.1 ± 5.3 114.3 ± 5.3 115.0 ± 4.4 114.4 ± 4.6 115.8 ± 4.7 114.7 ± 4.3 115.3 ± 4.6 114.2 ± 5.0

116 132 125 127 116 112 113 113 116 120 123 123 135 130 119 124 144 123 123 137 133 117 127 131 113 137 115 124 128 125 108 128 126 111 129 105

The intercept A is z0, the peak altitude for 0° SZA in Chapman theory. The slope B is H, the scale height, in Chapman theory.

thermospheres, the electron density peak altitudes will decrease with solar activity. We have tested this prediction by plotting the altitudes of the F1 and E peaks in each of the 36 longitude bins as a function of F10.7. Although F10.7 is not a measure of the X-ray fluxes per se, solar flares are more frequent during periods of high solar activity. We do not expect the variation to be linear, but we have fitted the peak altitudes in each longitudinal bin with a linear trendline. A selection of 8 of the 36 plots is presented in Fig. 9. All 36 plots are shown in the Supplemental material for this paper. For the F1 peaks, 21 of the 36 slopes of the trendlines are negative; they range from 2.4  102 to 3.3  102 km per unit F10.7, with a median of 3.2  103 km per unit F10.7. For the E peaks, 30 of the 36 trendlines are negative; they range from 3.7  102 to 2.7  102 km per unit F10.7, with a median value of 1.6  102 km per unit F10.7. In general, the absolute values of the slopes of the F1 peaks appear to be smaller than those of the E peaks. Thus we have tentatively confirmed our expectation that the altitudes of the E peaks are lower at higher solar activities for otherwise similar conditions, in contrast to Chapman layer theory. The F1 peak altitudes appear to vary less with solar activity, although the median slope of the trendlines is negative. This phenomenon probably arises from the lesser contribution of energetic photoelectrons to the F1 peak and/or as a result of other compensating effects, such as increases in thermospheric temperatures. The MGS RSS datasets in the northern hemisphere are all at high latitudes and high solar zenith angles. The mean value of F10.7 and its standard deviation for the whole dataset is 126 ± 29 km. The number of profiles that are characterized by very large values of F10.7 is relatively small. Therefore,

the derived slopes are subject to some uncertainly owing to the uneven coverage in solar activity, as represented by the F10.7 proxy.

3. Model comparisons 3.1. Comparison of model electron density profiles to Chapman profiles Although the magnitudes and altitudes of the F1 peak as a function of SZA may behave somewhat like an idealized Chapman layer, that does not imply that the shape of the profile is Chapman-like. We here illustrate the difference between the Chapman profiles and a more realistic numerical Mars model. These models are similar to those of Fox (2004) and Fox and Yeager (2006), with densities and temperatures appropriate to 60° SZA. In order to construct the F1-region Chapman profile, we have adopted the temperature at the F1 peak, 144.7 K, of the low solar activity realistic model, and we have assumed that the thermosphere is isothermal. The CO2 density profile from 80 to 320 km is then fixed by the adopted temperature and the number density at 100 km, which is assumed to be equal to the total number density of all the neutral species in the numerical model. The effective cross section ra is determined by assuming optical depth unity appears at 135 km, which is the altitude of the peak electron density in the model. The effective monochromatic solar photon flux is then determined by fitting the peak ionization rate at 135 km to that of the numerical model. In Fig. 10a, we show the resulting Chapman CO2 density profile as a dotted curve; it is compared to the profile that represents the sum of the densities of the 12 neutral species in the numerical

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a

a

b

b

c

c

Fig. 7. Characteristics of the F1 peak altitudes as a function of E. longitude. (a) Average F1 peak altitude for each 10° longitude bin. Note the striking resemblance of the averages in each longitude bin to the wave (1–3) fits to the RSS data in Fig. 2 from Bougher et al. (2004). (b) Intercepts A from the linear fits to Eq. (10) for each longitude bin. (c) Slopes B from the linear fits to Eq. (10) for each longitude bin.

model, which is shown by a solid curve. The neutral scale height of the numerical model increases with altitude because the neutral temperature and the abundance of the lighter species both increase with altitude. We have included ionization by photoelectrons by using the total ionization rate in the model to compute the effective ‘‘photon flux’’; the resulting production profile is shown in Fig. 10b as a dotted curve, while that of the numerical model is shown as a solid curve. The effect of including photoelectron impact on the F1 peak altitude is small, although the model peak is broader than it would be, if we had included only photoionization. It is obvious that the single Chapman ion production profile fails to fit the more realistic model profiles either above or below the peak. In order to compute the Chapman ion/electron density profile, we have assumed a DR coefficient of 1.95  107(300/T)0.7 cm2 s1, which mimics that of Oþ 2 (e.g., Mehr and Biondi, 1969), and we have assumed photochemical equilibrium. The resulting electron density profiles are compared in Fig. 10c, where the solid curve is that for the numerical model, and the dotted curve is that for the Chapman model. Above the peak, the numerical model electron densities are clearly larger than those of a Chapman layer. Similar behavior has been observed by, for example, Nielsen et al. (2006), for a number of electron density profiles obtained from MARSIS soundings, one of which is reproduced here as Fig. 11. Nielsen

Fig. 8. Characteristics of the E peak altitudes as a function of E longitude. (a) Average E peak altitude for each 10° longitude bin. (b) Intercepts A for the linear fits to Eq. (10) for each longitude bin. (c) Slopes B for the linear fits to Eq. (10) for each longitude bin.

et al. have proposed that this deviation from Chapman behavior may be due to the presence of a third layer. Withers (2009) suggested that the origin of this feature has not been explained. It is, however, obvious, when comparing the topside numerical model electron density profile in Fig. 10c to the measured profile in Fig. 11, that this behavior is merely due to deviations of a more realistic ionosphere from classical Chapman behavior. This is illustrated in Fig. 10d, where we have presented the major ion density profiles that correspond to the electron density profile in Fig. 10c. It is clearly shown that the deviation from Chapman behavior that is seen on the topside is not due to the presence of another layer of ions; it is due, rather, to the increase in density of Oþ 2 that occurs when Te decouples from Tn and increases rapidly. Since the DR coefficient for Oþ 2 is inversely proportional to Te, the loss rate of Oþ 2 due to DR decreases with increasing altitude. When the specific loss rate decreases, the Oþ 2 density increases, producing the ‘‘bulge’’ that is seen on the topside of the ne profile. Thus even though the behavior of the peak magnitudes or altitudes as a function of SZA or solar activity may be somewhat Chapman-like, the shapes of the electron density profiles are decidedly nonChapman. Below the F1 peak, the electron densities from the model do not fall off as quickly as those of the Chapman layer. The agreement may be improved by fitting a second Chapman profile to the E region, although doing so is problematic, since the lower region is

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Fig. 9. Altitudes of peak densities as a function of shifted F10.7 (see text) for both F1 and E regions for the same 8 longitude bins shown in Fig. 6. Linear trendlines are fitted for both peaks in each bin. The full set of 36 plots and linear fits can be found in the Supplemental material for this paper.

mostly produced by energetic electron impact. We have attempted, however, to fit the E-region profile by adopting the altitude and magnitude of the maximum ionization rate from the numerical model, as well as the temperature of 139.4 K at the E peak, which is near 108 km. The Chapman CO2 density profile for the E peak is normalized to the total neutral density at 108 km, and is shown in Fig. 10a as a dashed curve. The CO2 profiles for the two Chapman layers are not the same owing to the difference in temperatures at the peaks. We have determined the effective cross section and solar flux for the lower Chapman profile in the same manner as for the upper profile. In Fig. 10b, we show total the total ionization rate profile for the lower Chapman layer as a dashed curve. The Chapman ion production profile for the E region differs significantly from the model total ionization rate profile. On the topside, the model production profiles are obviously larger than those of the Chapman profiles. On the bottomside, the Chapman production profile differs from both the model photoionization rate profile and the model total ionization rate profile. In particular, at altitudes near the bottom of the model, the Chapman profile falls off too quickly with decreasing altitude. Unlike the F1 layer, there is a large difference between the total ionization rate profile and the photoionization

profile, because electron impact is the dominant ionization process in the E-region. In Fig. 10c, we present the electron density profiles for the numerical model, and those from Chapman theory for both the F1 and E peaks. The peaks in the Chapman layers are narrower than those in the model, and the model density profiles do not follow the Chapman profiles either on the topside or the bottomside. Since it is produced mostly by electron-impact, the lower layer is closer to parabolic than is the profile that would be obtained by photoionization alone, but the inclusion of electron-impact ionization in the total production rate changes the profile drastically. The total electron content (TEC) for the upper Chapman layer is 2.74  1011 cm2, and that for the lower Chapman layer is 1.39  1011 cm2, for a total of 4.1  1011 cm2. If we were to include only photoionization in constructing the Chapman model for the E-region, the TEC of the lower layer would be only 5.2  1010 cm2. For comparison, the total electron content above 80 km for the numerical model atmosphere is 4.9  1011 cm2. In some studies, the shape of the peak of the ion density profile in a narrow altitude range of 10  20 km around the F1 maximum is analyzed to predict the scale height in Chapman layer theory (e.g., Bauer and Hantsch, 1989). Other investigators have utilized

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a

b

c

d

Fig. 10. Comparison of numerical model for 60° SZA to a single theoretical Chapman profile and to a superposition of Chapman profiles. (a) Neutral densities for the 12species numerical model compared to those in Chapman layers for a pure CO2 model. The top solid curve is the total neutral density profile for the numerical model. The dotted curve labeled ‘‘CO2’’ represents the density variation for the Chapman model of the F1 peak, for which the temperature is 144.7 K. The dashed curve is the CO2 profile for a temperature of 139.4 K, which is representative of that of the E peak. (b) Ionization rate profiles for the F1 and E peaks in Chapman layer theory and in the numerical model. The solid curve labeled ‘‘Model’’ is the total ion production rate in the numerical model, including photoionization and electron-impact ionization. The Chapman production profile for the upper (F1) peak is represented by a dotted curve. For the lower (E) peak, the Chapman production profile is represented by the dashed curve. It is clear that there are large deviations from Chapman theory in the more realistic numerical model. (c) Electron density profiles for the numerical model, shown as a solid curve, and for the classical Chapman models for the upper and lower peaks, shown as dotted and dashed curves, along with the total electron contents (TEC) for each model. (d) Individual ion density profiles for the six major ions that correspond to the electron density profile in panel (c). The non-Chapman behavior that is seen on the topside is due to the increase in the Oþ 2 densities that results from the increase of the electron temperature as it decouples from the neutral temperature above the ion peak.

a Taylor expansion of Eq. (4) in the region of the peak, keeping terms to order 2. The peak shape in this approximation is therefore assumed to be parabolic (either on a linear or a log scale), and the peak altitude hmax, the peak electron number density nmax, and the neutral scale height Hn are related to the coefficients of the expansion (e.g., Breus et al., 2004; Zou et al., 2005; Withers and Mendillo, 2005). Fig. 10b and c show that both the production rate profiles and the ion density profiles in Chapman layer theory are narrower than those of a numerical model. The Chapman profile is highly asymmetric about the peak, falling off exponentially above the peak and much more rapidly below the peak, as shown in Eq. (1). For positive values of z, that is, above the peak, the third term on the right side becomes negligible, the second term dominates, and the production rate falls off with increasing altitude as exp(z/H). As Fig. 10b shows, the topside of the Chapman production profiles fall off with altitude more rapidly than does that of the numerical model. For negative values of z, that is, altitudes below the peak, the second term in Eq. (1) becomes small relative to the third, and the production rate becomes proportional to exp[(sec v)exp(z/H)], or as a negative exponential of a positive exponential. Thus approximating the electron density peak as a parabola in Chapman theory would seem to be inappropriate, even over small distances. Ironically, the presence of peak broadening

and displacement by the sources of non-Chapman behavior mentioned above actually make the density profiles appear more parabolic near the peak. Analyses based on Chapman theory for these shapes will, however, give erroneous results. Sometimes attempts are made to fit the topside of the electron density profile by assuming diffusive equilibrium, with the scale height equal to the ion pressure scale height Hp = k Tp/mig, where Tp = Ti + Te. The ion number density scale height Hi, however, differs from the pressure scale height. For an ideal atmosphere comprised of a single ion, the two quantities are related by the equation

1 1 1 dT p ¼ þ : Hi Hp T p dz

ð11Þ

(e.g., Banks and Kockarts, 1973). Fox (2009) and Fox and Yeager (2009) presented this equation without specifying the narrow application of this formula. For a more realistic ionosphere which contains multiple ions, Eq. (11) is not valid. For each individual ion the number density scale height is given by

1 mi g T e =T i dne 1 dðT e þ T i Þ ¼ þ þ Hi kT i dz ne dz T i

ð12Þ

(e.g., Chen et al., 1978). Since there are terms in Eqs. (11) and (12) that involve Te, Ti, and their gradients, the number density scale

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Fig. 11. Electron density profile for the topside and the F1 peak derived from a MEX MARSIS sounding on 2005 October 29, and the best fit to a Chapman profile for a neutral scale height of 10 km. The characteristics of the sounding are shown on the plot. The electron density maximum is 1.48  105 cm3 at an altitude of 124 km. The difference in the topside profile and the Chapman profile can be compared to that in Fig. 10c, and is characteristic of deviations from Chapman theory. Reproduced from Fig. 6 of Nielsen et al. (2006) with kind permission of Springer Science + Business Media B. V.

height Hi is not equal to the pressure scale height, Hp. In the region below the peak, where the values of Ti and Te are equilibrated with Tn, and vary little with altitude, the difference is smaller. Since there may be large gradients in the plasma temperatures up to the ‘‘top’’ of the ionosphere, it is not appropriate to assume that the ion density scale height is equal to the ion pressure scale height on the topside of the ionosphere, even in the absence of upward flowing ions (e.g., Fox, 2009). 3.2. Model peak altitudes as a function of SZA As another illustration of the difference between numerical models and Chapman layers, we can apply data analysis tech-

a

niques to our model ‘‘data’’, specifically to the peak altitudes that we predict in the near-terminator region. Fox and Yeager (2006) computed high and low solar activity thermosphere/ionosphere models for seven SZAs in the near-terminator region of Mars: 60°, 65°, 70°, 75°, 80°, 85°, and 90°. For comparison, we also modeled the ion density profiles for 0° SZA. We used different background neutral thermospheres and temperatures for low and high solar activities. We did not, however, change the background thermospheric models for different solar zenith angles; we simply used the neutral density profiles and temperatures of the 60° SZA models, and changed the SZAs. In Fig. 12 the model F1 and E peak altitudes are plotted as a function of ln(effective secant v), and the model peak altitudes are fitted to Eq. (10). We can compare the model number density scale heights H to the slopes B, and the subsolar peak altitudes zmax,0 to the intercepts A in Eq. (10). Fig. 12a shows the results for the low solar activity models, and Fig. 12b shows the results for the high solar activity models. For high solar activity, the 90° F1 peak, which appears near 178 km, is anomalous (cf. Fox and Yeager, 2006). Further inspection shows that this peak is coincident with a slope discontinuity in the adopted electron temperature profile. We have therefore eliminated this point from our fit of the F1 peaks for the high solar activity model. The linear fits shown in Fig. 12 appear to be very good. For the low solar activity models, the fitted intercepts A in Eq. (10) are 130 km and 104 km, for the F1 and E peaks, respectively. In the 0° SZA low solar activity numerical model, the altitudes of the F1 and E peaks are 126.5 km and 105.5 km, respectively. Thus the altitude of the subsolar F1 peak predicted by Chapman theory is higher by almost 4 km than that of the 0° numerical model. For the high solar activity numerical models, the intercepts A of the linear fits to Eq. (10) for the F1 and E peaks are 127.1 km and 108.5 km, respectively, as shown in Fig. 12b. In Chapman theory, these intercepts are the peak altitudes for overhead Sun. In the 0° SZA numerical model, however, the F1 and E peak altitudes are 134 km and 110 km, respectively. Thus the altitude of the subsolar F1 peak predicted by Chapman theory again differs substantially from that of the 0° SZA numerical model; it is lower by 7 km. The altitudes of the predicted and model subsolar E peaks differ, but not significantly. This is largely because the E peaks in the numerical models fall in an altitude range where the thermospheric temperatures are nearly constant, and

b

Fig. 12. Altitudes of peaks of electron densities from the near terminator numerical models of Fox and Yeager (2006) for solar zenith angles of 60°, 65°, 70°, 75°, 80°, 85°, and 90° as a function of ln(effective secant v). The left panel is for the low solar activity model (Low SA), and the right is for the high solar activity model (High SA). The F1 peaks are shown as filled circles, and the E peaks as open circles. The peaks are fitted to Eq. (10) with linear least squares regressions. The slopes of the linear fits B (in km) are labeled. The intercepts of the linear fits A are indicated by triangles. The peak altitudes for the 0° SZA numerical models are shown for comparison.

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where the neutral mixing ratios do not change significantly with altitude. We now turn our attention to the fitted slopes B in Eq. (10). At low solar activity the derived slopes for the model F1 and E peaks are 8.2 and 8.1 km, respectively, as shown in Fig. 12a. In Chapman theory, the slopes correspond to the neutral scale heights. In the numerical models, however, the neutral scale heights at the electron density peaks increase monotonically with SZA from 60° to 90°: from 9.0 to 10.3 km for the F1 peaks, and from 7.2 to 8.7 km for the E peaks (cf., Fox and Yeager, 2006). Thus, the fitted slopes B for the F1 peaks are significantly smaller than the scale heights H at the peak altitudes in the numerical model, and the model scale heights are not constant, but increase with SZA. For the E peak, the slope B of 8.1 km falls in the range of the numerical model scale heights, which also increase with SZA. For the high solar activity models shown in Fig. 12b, the slope B obtained from fitting the model F1 peak altitudes to Eq. (10) for the SZA range 60–85° is 13.2 km. By comparison, the number density scale heights H at the model F1 peaks increase monotonically from 8.0 to 15.2 km as the SZA increases. We find that, even though the linear fit appears to be good, the ‘‘scale height’’ retrieved from the slope B does not capture the nearly doubling of the scale height in the numerical models; at best it can be interpreted as a sort of average value of the scale height over the SZA range. For the high solar activity E peak, the linear fit to Eq. (10) is characterized by a slope of 8.3 km, whereas the model scale height at the E peak altitudes increases from 7.3 to 8.0 km over the SZA range 60–90°. These values are close to, but smaller than that predicted by the slope B of the linear fits to Eq. (10). The large increase in the scale heights at the F1 peaks as a function of SZA, especially at high solar activity, reflects the increasing altitude of the peaks, where the neutral temperatures are larger and the lighter species become more abundant. This behavior partly reflects the fact that, in our numerical models, the background thermosphere is fixed to the 60° SZA model (Fox and Yeager, 2006). We also note that the slopes B that were fitted to the MGS data in the near terminator region, as shown in Table 3, do not exceed 9 km, and the average value of B is less than 7 km. We can therefore conclude that, in the thermosphere of Mars, there is evidence from the MGS RSS data that the underlying neutral densities and temperatures do change rapidly with SZA in the near-terminator region, and that the near-terminator thermosphere ‘‘collapses’’ somewhat with SZA. A larger effect of this kind has been found for the Venus near-terminator region (e.g., Cravens et al., 1983). There is also evidence from global models, such as the MTGCM of Bougher et al. (e.g., 1999, 2000; cf. Valeille et al., 2009), that the neutral thermosphere changes substantially in the region of the terminators. Chapman theory does not account for this phenomenon.

4. Conclusions We have analyzed nearly all the 5380 Mars Global Surveyor Radio Science electron density profiles that are at high northern latitudes, with a view toward investigating the behavior of the profile types and peak altitudes with SZA and solar activity. We have classified each of the electron density profiles as one of four main types of profiles, which depend on the visibility and altitude behavior of the lower or E region peak relative to that of the upper or F1 peak. In type 1 profiles, no lower peak is visible, although there may be a change in slope on the lower side of the profile. In type 2 profiles, the E peak appears as a shoulder on the lower side of the F1 peak. In type 3 profiles, the lower peak is separated from the upper peak by a small minimum, which we call a ‘‘notch’’. Type 4 profiles are characterized by a large minimum between the

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F1 and E peaks. We have investigated the variation in the occurrence of profiles of these four basic types with the F10.7 parameter. We show that the occurrence of types 2 and 3 profiles varies in the expected way with solar activity, that is, type 2 profiles are more common at lower solar activities and type 3 at higher solar activities. Clear trends for the type 1 and type 4 profiles are not evident in the dataset. We have divided the altitudes of the martian E and F1 peaks from the MGS RSS dataset into 36 10°E. longitude bins from 0° to 360°. For each longitude bin, we have fitted the peak altitudes to Eq. (10). In this equation, we have substituted ‘‘effective secants’’ for actual secants, which we have determined by integrating the neutral model densities along the line of sight to the Sun, and dividing by vertically integrated densities. In Chapman theory (Eq. (9)), the values of the intercepts A correspond to the predicted subsolar peak altitude zmax,0, and the slopes B to the scale height H. For the F1 peaks, the fitted values of the intercepts A range from 122 to 130 km, with a median value of 125 km. The fitted values of the slopes B range from 2.8 to 9.2 km, with a median of 7.2 km, an average of 6.82 km, and a standard deviation of 1.7 km. For the E peaks, the derived values of A range from 103 to 111.5 km, with a median of 108.8 km. The derived values of B range from 1.4 to 7.3 km with a median value of 4.0 km, an average value of 4.23 km, and a standard deviation of 1.6 km. The latter values, and the variability about the mean are clearly indicative of deviations from Chapman behavior. If B is interpreted as the scale height, a value of 4 km implies temperatures of 75 K, which is neither credible nor predicted for the lower martian thermosphere. The origin of this phenomenon is a subject for further investigation. We have evaluated the solar activity dependence of the peak altitude for the F1 and E-region peaks by plotting the peak altitudes in each longitude bin as a function of F10.7, and fitting trendlines to the data. We find that, for the F1 peaks, 21 of the 36 slopes of the trendlines are negative, and the median value of the slope is 3.6  103 km per F10.7 unit. For the E peaks a large majority, 30 of the 36 trendlines have negative slopes, and the median value is 1.6  102 km per F10.7 unit. We propose that this is because at high solar activity, the increases in the more penetrating solar soft X-ray fluxes are larger than those of the EUV fluxes, which vary less with solar activity, and do not penetrate to altitudes that vary strongly with wavelength. We tentatively conclude that, for similar underlying thermospheres, the altitudes of the E peaks decrease with increasing solar activity. While the median value of the trendline for the F1 peak is negative, the evidence for the negative variation of the F1 peak with solar activity is not as strong, and the absolute values of the slopes are in general smaller than those of the E peak. We propose that this is because the increases in the soft X-ray fluxes do not affect the altitude of the F1 peak as much as they do that of the E peak. Also, the neutral, electron, and ion temperatures of the thermosphere at F1 peak altitudes increase with solar activity, which may cause the F1 peaks to rise, whereas the thermosphere in the region of the E peaks is nearly isothermal. The evidence for decreasing altitude of the E-region peak as solar activity increases is fairly strong, in contrast to Chapman theory, in which there is no solar activity variation of the peak altitudes. We have compared a Chapman profile of ion production rates and electron density profiles to that of a more realistic numerical model, and find large deviations both above and below the peak. Fitting a second Chapman profile to the lower peak ameliorates the non-Chapman behavior between the peaks, but there are still deviations above and below the peaks. The topside of the electron density profile of the numerical model agrees qualitatively with that of the measured profiles obtained from the MARSIS on MEX, and clearly shows that deviations from Chapman behavior can

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account for the difference between the two. There is no need to invoke a third layer. Finally, we have used data fitting techniques with our numerical models for solar zenith angles between 60° and 90° at 5° intervals. We have plotted the altitudes of the F1 and E peaks for each model as a function of ln(effective secant v), and fitted the points to Eq. (10). Although the linear fits appear to be good, the slopes and intercepts of the fitted lines do not closely follow Chapman theory. Our investigations here show that, while the variations of the F1 and E peak magnitudes with characteristics such as the SZA or solar activity may exhibit some quasi-Chapman behavior, the measured and modeled electron density profiles are clearly not characterized by Chapman behavior. Because the RSS data do not exhibit slopes that are as large as the model values, we conclude that the underlying thermosphere in the near-terminator region changes significantly with solar zenith angle. Acknowledgments This work has been supported in part by NASA Grants NNX07AR39G and NNX09AB70G to Wright State University. We thank A. Nagy for pointing out the limited applicability of Eq. (11). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.icarus.2012. 10.002. References Albee, A.L., Palluconi, F.D., Arvidson, R.E., 1998. Mars Global Surveyor mission: Overview and status. Science 279, 1671–1672. Allison, M., McEwan, M., 2000. A post-pathfinder evaluation of areocentric solar coordinates with improved timing recipes for Mars seasonal/diurnal climate studies. Planet. Space Sci. 48, 215–235. Angelats i Coll, M., Forget, F., López-Valverde, M.A., Read, P.L., Lewis, S.R., 2004. Upper atmosphere of Mars up to 120 km: Mars Global Surveyor accelerometer data analysis with the LMD general circulation model. J. Geophys. Res. 109, E01011. http://dx.doi.org/10.1029/2003JE002163. Banks, P.M., Kockarts, G., 1973. Aeronomy. Academic Press, New York. Bates, D.R., 1950. Dissociative recombination. Phys. Rev. 78, 492–493. Bates, D.R., 1988. Recombination of the normal E and F layers of the ionosphere. Planet. Space Sci. 36, 55–63. Bauer, S.J., 1973. Physics of Planetary Ionospheres. Springer-Verlag, New York. Bauer, S.J., Hantsch, M.H., 1989. Solar cycle variation of the upper atmosphere temperature of Mars. Geophys. Res. Lett. 16, 373–376. Bauer, S.J., Lammer, H., 2004. Planetary Aeronomy. Springer-Verlag, Berlin. Bougher, S.W., Engel, S., Roble, R.G., Foster, B., 1999. Comparative terrestrial planet thermospheres 2. Solar cycle variation of global structure and winds at equinoxes.. J. Geophys. Res. 105, 16591–16611. Bougher, S.W., Engel, S., Roble, R.G., Foster, B., 2000. Comparative terrestrial planet thermospheres 3. Solar cycle variation of global structure and winds at solstices. J. Geophys. Res. 105, 17669–17692. Bougher, S.W., Engel, S., Hinson, D.P., Forbes, J.M., 2001. Mars Global Surveyor Radio Science electron density profiles: Neutral atmosphere implications. Geophys. Res. Lett. 28, 3091–3094. Bougher, S.W., Engel, S., Hinson, D.P., Murphy, J.R., 2004. MGS radio science electron density profiles: Interannual variability an implications for the martian neutral atmosphere. J. Geophys. Res. 109. http://dx.doi.org/10.1029/2003JE002154. Bougher, S.W., Bell, J.M., Murphy, J.R., Lopez-Valverde, M.A., Withers, P.G., 2006. Polar warming in the Mars thermosphere: Seasonal variations owing to changing insolation and dust distributions. Geophys. Res. Lett. 33, L02203. Bougher, S.W., McDunn, T.M., Zoldak, K.A., Forbes, J.M., 2009. Solar cycle variability of Mars dayside exospheric temperatures: Model evaluation of underlying thermal balances. Geophys. Res. Lett. 36, L05201. http://dx.doi.org/10.1029/ 2008GL0376. Breus, T.K., Pimenov, K.Yu., Izakov, M.N., Krymskii, A.M., Luhmann, J.G., Kliore, A.J., 1998. Conditions in the martian ionosphere/atmosphere from a comparison of a thermospheric model with radio occultation data. Planet. Space Sci. 46, 367– 376. Breus, T.K., Krymskii, A.M., Crider, D.H., Ness, N.F., Hinson, D., Barashyan, K.K., 2004. Effect of the solar radiation in the topside atmosphere/ionosphere at Mars: Mars Global Surveyor observations. J. Geophys. Res. 109, A09310. http:// dx.doi.org/10.1029/2004JA010431.

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