Solar cycle effects on the escape of planetary ions from Mars are investigated using Mars Express Analyzer of Space Plasmas and Energetic Atoms 3 data from June 2007 to January 2013. Average and median tail fluxes of low-energy (<300 eV) heavy ions (O+, O2+), derived from the full data set covering 7900 orbits, are highly correlated with the solar activity proxies F10.7 and the sunspot number, Ri. The average heavy ion escape rate increased by a factor of ≈ 10, from ≈ 1 · 1024 s−1 (solar minimum) to ≈ 1 · 1025 s−1 (solar maximum). Combining data from this, and other studies, an empiric model/expression is derived for the Martian escape rate versus solar activity F10.7 and Ri. The model is a useful tool to derive the accumulated ion escape rate from Mars based on historical records of solar activity, with potentials back to the young Sun époque.
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 The sunspot cycle, i.e., the cyclic occurrences of dark spots on the Sun and its influence on a planetary environment has been, and still, remains a matter of interesting discussions. With the development of in situ experiments came a deeper understanding of the Sun and its interaction with the planetary environment. An important lesson learned was that solar-driven processes in the planetary environment were not necessarily related with the total solar irradiative power. Instead, short wavelength radiation, EUV and soft X-ray, and the solar wind drive a number of processes, such as those involved in atmospheric escape.
 Solar forcing by EUV radiation and the solar wind results in a transfer of energy and momentum to the upper atmospheres and ionospheres of weakly magnetized planets [e.g., Luhmann and Bauer, 1992]. Specifically, the EUV radiation provides heating and ionization, i.e., affects the atmospheric scale height and composition of the atmosphere and ionosphere, and the subsequent energy transfer process drives the acceleration, outflow, and escape of planetary ions. The ion escape rate is related to the amount of solar forcing by the solar wind and the solar EUV.
 Solar forcing has short-term as well as long-term consequences for the atmospheres and ionospheres of terrestrial planets, including Earth, Mars, and Venus. Over the lifetime of a planet, the combined radiation and solar wind slowly drive the erosion of the upper atmosphere.
 Several studies have been made on planetary ion escape rates from Mars, based on experimental data [Lundin et al., 1990; Verigin et al., 1991; Barabash et al., 2007; Lundin et al., 2008a; Nilsson et al., 2011; Ramstad et al., 2013], as well as on simulations [e.g., Kallio and Janhunen, 2002; Ma and Nagy, 2007; Valeille et al., 2009; Curry et al., 2013]. In some cases [Lundin et al., 2008a; Edberg et al., 2010] the escape rates were derived for different solar and interplanetary conditions. However, until now, experimental studies addressing specific solar cycle effects have not been made for Mars.
2 Experimental Results
 Analyzer of Space Plasmas and Energetic Atoms 3 (ASPERA-3) on Mars Express, MEX, [Barabash et al., 2006] comprises four sensor systems measuring electron, ion, and energetic neutral particles. In this study we analyze the Martian ion outflow and escape from June 2007 to January 2013 (7900 orbits). During 2007–2013, the rising phase of solar cycle 24, solar activity rose from an unusually deep minimum to the lowest solar maximum in 100 years. We use monthly averages of F10.7 and sunspot number, Ri, both recorded at the Earth, as proxies for solar activity. By using monthly averages of the proxies, i.e., close to the Sun's spin period, we can minimize solar hemispheric activity differences related with the planetary orbital motion.
 The monthly average Ri increased from ~2 in 2008/2009 to ~65 mid-2012, while the monthly average solar activity index F10.7 increased from ~67 to ~125 during the same period of time. The monthly Ri and F10.7 proxies of solar activity display many similarities. A linear regression analysis gives the following relation between F10.7 and Ri: F10.7 = 0.86 · Ri + 67, with correlation coefficient r2 = 0.89. To get a common baseline, it is therefore useful to normalize F10.7 and Ri, i.e., to use F10.7* = F10.7 − 64, and Ri* = Ri + 1 in the regression analysis.
 The planetary ion escape from Mars near the planet is dominated by low-energy (<300 eV) H+, O+, and O2+ ions, which become energized as they move further down into the Martian-induced magnetotail tail [Lundin et al., 2008b; Nilsson et al., 2011]. A careful analysis of individual mass spectra [Lundin et al., 2009] shows that the CO2+ contribution to the low-energy (<300 eV) heavy ion outflow is ≤10%. A low CO2+ contribution to the outflow is also consistent with the ionosphere ion composition [e.g., Fox and Hac, 2009]. Figure 1 displays an overview plot of low-energy (<300 eV) O2+ fluxes and unit flow vectors projected onto the Mars Solar Oriented (MSO) XZ plane, each data point representing the average flux and flow respectively within a 500 × 500 km (XZ) quadratic column along Y. BS and IMB in the diagram indicate model positions of the bow shock and induced magnetosphere boundary near Mars [see, e.g., Lundin et al., 2008b]. To emphasize the north-south asymmetry and the general flux and flow morphology in the XZ plane, data projections over the planet (along Y) are removed. In the following discussion, we analyze how escape fluxes of O+, O2+, as well as the sum of both (∑O) vary with solar activity.
 Figure 2 displays a time series plot of the monthly averaged solar activity, F10.7* and Ri*, and the tail ∑O fluxes at Mars for the time period 2007–2013. Median (circles) and average (squares) tail ∑O ion fluxes are determined from seven time intervals when MEX accessed the induced magnetotail of Mars. (bottom) The number of consecutive data points in each time interval. Error bars, marking 25 and 75 percentiles of tail fluxes, demonstrate the high flux variability. The highest variability is found during solar minimum (2007–2009), the difference between average and median flux reaching a factor of ≈ 10. The four time interval histogram curves in the panel give the average tailward fluxes derived from the entire data set (about 0.4 million data formats).
 Based on the data displayed in Figure 1 a regression analysis is performed on the variability of median tail fluxes (for O+ O2+, ∑O) versus solar activity. In the corresponding regression analysis of average fluxes, we combine the histogram average fluxes with the four independently derived escape fluxes/escape rates derived by Lundin et al. [1990, 2008b], Nilsson et al. , and Ramstad et al. .
 The scatterplots in Figure 3 illustrate results from the regression analysis: Figure 3a showing data from seven median tail ∑O fluxes versus F10.7* and Ri*, Figure 3b showing the average escape fluxes from the histogram curve in Figure 2, plus the four independently derived values, versus F10.7*. The least square fitted power law curves are marked in both figures. Table 1 summarizes the power law expressions and correlation coefficients derived for median ion escape fluxes and escape rates of O+, O2+, and ∑O. Table 2 summarizes the corresponding ∑O power law expressions for the average escape flux and escape rates derived from the data set displayed in Figure 3b.
Table 1. Power Law Model for the Median Ion Escape Flux (Φ) and Ion Escape Rate (Θ) Versus F10.7* and Ri*a
 To determine escape rates we have for the sake of simplicity assumed a cylindrically symmetric outflow, the ions traversing a cross-section tail area AT = πRT2. A cylindrically symmetric outflow applies to the low-energy (<200 eV) ion outflow [Lundin et al., 2008b] but not for energetic ions picked up by the motional electric field [Barabash et al., 2007]. Regardless of that, average escape rates over long time periods should only depend on preset energy ranges and tail cross section.
 The escape rate (ions/s), e.g., ∑O can now be obtained from Θ∑O= Φ∑O · AT. Because the MEX orbital changes with time, orbits after 2011 were unable to access the deep tail regions; an inner tail the cross section marked out in Figure 1 has to be used. With a tail radius RT = 1.75 RM (Martian radii) we obtain AT = 1.1 · 1014 (m2). From this the following two expressions for the median (1) and average (2) ∑O ion escape rate versus F10.7* were derived.
 Expression (1) for the escape rate of the median ∑O escape rate versus the normal value of F10.7 is given by the solid curve in Figure 4a. Dashed curve gives the corresponding average escape rate (expression (2)) in Figure 4b. Notice that ions with energies >300 eV, not included in this analysis, mean that the above escape rates are underestimated. However, only marginally considering the predominance of <200 eV, heavy ions in the tail outflow near Mars [Lundin et al., 2008b].
3 Discussions and Conclusions
 We have derived an empiric model describing the monthly ion escape rate from Mars versus the monthly average of Ri and F10.7. The model does not account for other relevant ion outflow drivers, such as upstream solar wind conditions (e.g., solar wind dynamic pressure and IMF). Nevertheless, because the model scales the escape rate versus solar activity, it may serve as an input to theories and models of nonthermal escape processes and the long-term evolution of the planetary volatile inventory [Luhmann and Bauer, 1992; Lammer et al., 1996; Kulikov et al., 2007]. We note that O+, O2+, and H+ dominate the ion escape from Mars. Conversely, ionized products of the main atmospheric constituent CO2 (e.g., CO2+) represent a small fraction (≈6%) of the planetary ion escape [Lundin et al., 2009].
 Under the assumption that the derived model expressions (1) and (2) apply for F10.7 and Ri at all times, the model may be used to estimate the ∑O escape rates backward in time from the aforementioned proxy data. Figure 5 shows a time series plot of monthly F10.7 (top) and the corresponding monthly ∑O escape rates (bottom) for the time interval 1900–2012. The monthly F10.7 is derived from Ri using the linear relation between F10.7 and Ri, i.e., F10.7 = 0.86 · Ri + 67. Using the monthly variability of the escape flux during the twentieth century in Figure 5, the average centennial escape rate of ΣO corresponds to ~9.7 · 1024 s−1.
 While the model suggests minor implications on the Martian volatile inventory during the last century, major losses are expected on longer time scales. Studies of solar-like stars at different stages of their evolution [Wood et al., 2002; Ribas et al., 2005; Güdel, 2007] indicate that the activity of the early Sun (0.1 Billion year (By)) may have reached F10.7 values in the range 104 to 105. If so, the model expressions (1) and (2) suggest ∑O escape rates in the range 1027 (average)–1029 ions/s (median), disregarding source limitations from the present atmosphere. A correct source analysis requires models of the atmospheric photochemistry and the correspondingly larger obstacle size of an early dense atmosphere at Mars [Lammer et al., 2003; Terada et al., 2009; Tian et al., 2009; Fox, 2009; Lammer et al., 2013].
 ASPERA-3 on ESA Mars Express is a joint effort between 15 laboratories in 10 countries. We are indebted to the national agencies, e.g., the Swedish National Space Board, CNRS in France, and NASA (contract # NASW00003) for supporting ASPERA-3 and to the European Space Agency for making MEX a great success. Finally, we want to express our deep appreciation to Jan Karlsson, Pär-Ola Nilsson, Leif Kalla, and Emmanuel Penou for providing software support and excellent data analysis tools.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.