Volume 126, Issue 3 e2020JA028485
Research Article
Free Access

Effects of the IMF Direction on Atmospheric Escape From a Mars-like Planet Under Weak Intrinsic Magnetic Field Conditions

Shotaro Sakai

Corresponding Author

Shotaro Sakai

Department of Geophysics, Graduate School of Science, Tohoku University, Sendai, Japan

Planetary Plasma and Atmospheric Research Center, Graduate School of Science, Tohoku University, Sendai, Japan

Correspondence to:

S. Sakai,

[email protected]

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Kanako Seki

Kanako Seki

Department of Earth and Planetary Science, Graduate School of Science, University of Tokyo, Tokyo, Japan

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Naoki Terada

Naoki Terada

Department of Geophysics, Graduate School of Science, Tohoku University, Sendai, Japan

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Hiroyuki Shinagawa

Hiroyuki Shinagawa

National Institute of Information and Communications Technology, Koganei, Tokyo, Japan

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Ryoya Sakata

Ryoya Sakata

Department of Earth and Planetary Science, Graduate School of Science, University of Tokyo, Tokyo, Japan

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Takashi Tanaka

Takashi Tanaka

National Institute of Information and Communications Technology, Koganei, Tokyo, Japan

International Center for Space Weather Science and Education, Kyushu University, Fukuoka, Japan

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Yusuke Ebihara

Yusuke Ebihara

Research Institute for Sustainable Humanosphere, Kyoto University, Uji, Kyoto, Japan

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First published: 23 February 2021
Citations: 8

Abstract

Direction of the upstream interplanetary magnetic field (IMF) significantly changes the magnetospheric configuration, influencing the atmospheric escape mechanism. This paper investigates effects of IMF on the ion escape mechanism from a Mars-like planet that has a weak dipole magnetic field directing northward on the equatorial surface. The northward (parallel to the dipole at subsolar), southward (antiparallel), and Parker-spiral IMFs under present solar wind conditions are compared based on multispecies magnetohydrodynamics simulations. In the northward IMF case, molecular ions escape from the high-latitude lobe reconnection region, where ionospheric ions are transported upward along open field lines. Atomic oxygen ions originating either in the ionosphere or oxygen corona escape through a broader ring-shaped region. In the southward IMF case, the escape flux of heavy ions increases significantly and has peaks around the equatorial dawn and dusk flanks. The draped IMF can penetrate into the subsolar ionosphere by erosion, and the IMF becomes mass-loaded as it is transported through the dayside ionosphere. The mass-loaded draped IMF is carried to the tail, contributing to ion escape. The escape channels in the northward and southward IMF cases are different from those in the Parker-spiral IMF case. The escape rate is the lowest in the northward IMF case and comparable in the Parker-spiral and southward IMF cases. In the northward IMF case, a weak intrinsic dipole forms a magnetosphere configuration similar to that of Earth, quenching the escape rate, while the Parker-spiral and southward IMFs cause reconnection and erosion, promoting ion escape from the upper atmosphere.

Key Points

  • The ion escape rate is the lowest in northward (parallel) interplanetary magnetic field (IMF) case and comparable in Parker-spiral and southward (antiparallel) IMF cases

  • In the northward IMF case, ionospheric ions escape from limited regions of the high-latitude lobe reconnection with a draped IMF

  • In the southward IMF case, IMF penetration into the dayside ionosphere and its subsequent transport to tail flanks cause efficient ion loss

1 Introduction

The planetary intrinsic magnetic field is critical when considering the atmospheric escape from planets. The strength of the intrinsic magnetic field particularly affects the interaction between solar wind and terrestrial-type planets (e.g., Chassefière & Leblanc, 2004; Seki et al., 2001), and it changes the escape mechanism. The terrestrial global magnetic field has also experienced strength changes (e.g., Guyodo & Valet, 1999) and recurring reversals over 4.6 billion years (Gyr) that could have affected the atmospheric composition of planets. It is believed that ancient Mars had a global intrinsic magnetic field of interior origin and the magnetic field decayed by ∼3.9 Gyr ago (Acuña et al., 1999). One of the pieces of evidence that ancient Mars had an intrinsic field is the existence of a “crustal magnetic field” (Acuña et al., 1999). Present-day Mars has a remanent magnetism in the crust mainly in the southern hemisphere, which is called the crustal magnetic field.

The relationship between planetary climate change and the existence of intrinsic magnetic fields is an interesting research topic. It is considered that Mars had maintained a warm and wet climate until ∼4 Gyr ago (e.g., Goldspiel & Squyres, 1991; Jakosky et al., 1994; Malin & Edgett, 2003). However, the atmosphere and water were lost, resulting in only a thin Martian atmosphere. A recent model study suggests that Mars lost a large portion of the atmosphere within 500 million years of its origin (Lammer et al., 2013). The atmospheric escape can be separated into the neutral and ion escape. The neutral escape channels include the Jeans escape and hydrodynamical escape associated with the escape of relatively light species such as hydrogen, and photochemical escape associated with the dissociative recombination of molecular ions, while the ion escape channels include the ion outflows and pickup ions. One of the important processes of atmospheric escape is ion outflow from the Martian upper atmosphere, which is useful for the escape of heavy species such as ionospheric ions. The escape mechanism due to ion outflow strongly depends on the solar wind parameters, solar X-ray and extreme ultraviolet (XUV) irradiances, and magnetic field conditions. Previous observations and modeling suggested that the ion escape rate increases under the high XUV radiation (e.g., Dong et al., 2017; Ramstad et al., 2015; Terada, Kulikov, et al., 2009). Terada, Kulikov et al. (2009) showed by the simulations that the ion escape rate under 100 times the current XUV irradiances was up to five orders of magnitude greater (∼1028–1029 s−1) than the current rate.

Sakai et al. (2018) investigated the effect of a weak intrinsic magnetic field of 100 nT at the Martian equatorial surface on the escape rate and mechanism on the basis of magnetohydrodynamic (MHD) modeling. It was revealed that the escape channels are associated with regions of open field lines such as in the cusp and reconnection of the intrinsic magnetic field and Parker-spiral interplanetary magnetic field (IMF), and the escape rate increases by ∼25% under a weak intrinsic magnetic field than when considering only the IMF. Moreover, they showed that the intrinsic magnetic field promotes the escape of heavy ions such as O2+ and CO2+ present in the deep ionosphere. This study was also a breakthrough in terms of the fact that the role the intrinsic magnetic field plays in atmospheric escape is investigated by adding an intrinsic magnetic field to present-day (unmagnetized) Mars. Note that the escape rate of present-day unmagnetized Mars (1023–1025 s−1) is broadly known from many studies (e.g., Brain et al., 2015; Inui et al., 2019; Jakosky et al., 2018; Nilsson et al., 2011; Ramstad et al., 2013) based on observation missions such as Phobos 2 (Sagdeev et al., 1988), Mars Express (Chicarro et al., 2004), and Mars Atmosphere and Volatile EvolutioN (MAVEN) (Jakosky et al., 2015) and modeling.

The dependence of the ion escape rate on magnetic field strength under extreme XUV conditions was investigated by Sakata et al. (2020). The O+ escape rate is 1027–1028 s-1, while the rates of molecular ions (O2+ and CO2+) are 1023–1026 s−1. The highest escape rate of molecular ions is at an intrinsic magnetic field strength of ∼1000 nT. The escape rate of molecular ions decreases when the intrinsic magnetic field strength reaches ∼3000 nT, at which the magnetic pressure is mostly comparable to the solar dynamic pressure. The O+ escape rate does not decrease much even if the magnetic field strength increases because the oxygen corona is extended around the planet under extreme XUV conditions.

The IMF direction generally affects the shape of the magnetosphere (e.g., Ogino et al., 1994). In the paper by Sakai et al. (2018) and Sakata et al. (2020), a change of IMF direction was not considered because the Parker-spiral IMF, namely, Bz = 0, was used as the solar wind condition. On Earth, a southward orientation of the IMF can cause reconnection with the intrinsic magnetic field in the subsolar region (e.g., Dungey, 1961). A long-lasting southward IMF often occurs in conjunction with interplanetary coronal mass ejection. Winglee (2000) studied the IMF dependence on the O+ outflow from the terrestrial ionosphere using global multifluid simulations. The southward IMF enhances the O+ outflow from the ionosphere, but O+ is confined to the inner part of the magnetosphere by a strong convective electric field. With the northward turning of the IMF, ionospheric plasma is ejected tailward and leads to oxygen concentrations in the deep tail (Winglee, 2000). Lennartsson et al. (2004) showed that the total rate of ion outflow is enhanced with the southward IMF by factors of 2.5–3 for O+ and 1.5–2 for H+ compared to the northward IMF with observations from the Toroidal Imaging Mass-Angle Spectrograph instrument (Shelley et al., 1995) onboard the Polar satellite. As described above, the IMF direction significantly affects the ion escape rate and magnetospheric form factor of Earth, and thus, the IMF direction is one of the key parameters to understand the atmospheric escape mechanism of Mars.

We investigate the effect of the IMF direction on the ion escape rates and mechanisms of a Mars-like planet under a weak intrinsic magnetic field and current typical solar wind conditions based on multispecies single-fluid MHD numerical simulations. Note that in a Mars-like planet background parameters of present-day Mars at solar minimum are used except for the assumption of an intrinsic magnetic field. A CO2-rich atmosphere such as that of Mars is common and could also be applicable for exoplanets. In the current paper, we assume a Mars-like planet with a CO2-rich atmosphere and weak intrinsic field as a first step for future exoplanet studies. This research is also useful for understanding how the IMF direction and intrinsic magnetic field affect the escape mechanism in the upper atmosphere because the escape rate and mechanisms of present-day Mars, namely, an unmagnetized planet, is starting to be apparent from recent studies (e.g., Brain et al., 2010; Dubinin et al., 2016, 2017; Jakosky et al., 2018; Nilsson et al., 2011; Ramstad et al., 2013). In Section 2, the numerical simulation model used in this study is explained briefly. The results of three simulation runs under new simulation settings, namely, the northward IMF case, Parker-spiral IMF case and southward IMF case, are shown in Section 3 and 4. The discussion, including a comparison of the results in each case, is presented in Section 5, and the main results of the paper are summarized in Section 6.

2 Numerical Model

2.1 Model Description

A three-dimensional multispecies single-fluid magnetohydrodynamic approximation is applied to the simulation, which was introduced in early papers (Sakai et al., 2018; Terada, Kulikov, et al., 2009; Terada, Shinagawa, et al., 2009). The model was originally constructed for the modeling of an unmagnetized object (Tanaka, 1993) and afterward was improved for the Earth's magnetosphere and planetary ionosphere (Tanaka, 1998; Terada, Kulikov, et al., 2009; Terada, Shinagawa, et al., 2009). This model reproduced the data observed by the Viking lander well (Terada, Kulikov, et al., 2009). The model solves a set of MHD equations for eight variables (ρ, ρV , B, and U), where ρ and U are the mass and energy densities, respectively, and V and B are the velocity and magnetic field vectors, respectively. The continuity equation for the total ion mass density ρ is given by
urn:x-wiley:21699380:media:jgra56340:jgra56340-math-0001(1)
where mi is the ion mass, qi is the total production rate of the ith ion, and Li is the loss rate of the ith ion. The equation of the ion mass flux vector ρV is
urn:x-wiley:21699380:media:jgra56340:jgra56340-math-0002(2)
where P is the gas pressure, g is the gravitational acceleration vector, μ0 is the vacuum permeability, and νit is the total effective momentum transfer collision frequency of the ions given by Terada, Shinagawa et al. (2009). The equation of the magnetic field vector is urn:x-wiley:21699380:media:jgra56340:jgra56340-math-0003, where E is the electric field vector. The conserved equation for the energy density urn:x-wiley:21699380:media:jgra56340:jgra56340-math-0004 is given by
urn:x-wiley:21699380:media:jgra56340:jgra56340-math-0005(3)

where kB is the Boltzmann constant, γ is the ratio of specific heat, K is the thermal conductivity, Tq is the plasma temperature in the ion production reaction, TL = P/nek is the plasma temperature in the ion loss reaction, TEII is the temperature corresponding to the plasma energy loss due to electron-impact ionization, and ne is the electron number density. In this MHD model, Tq in Equation 3 is approximated as Tq = Te input + Ti input where Te input and Ti input are the electron and ion temperatures derived from spacecraft observations or empirical models. This approximation has been often used for a present-day Mars and Venus simulations (Ma et al., 2004; Terada et al., 2002; Terada, Kulikov et al., 2009). Te input and Ti input are taken from Figure 2 of Shinagawa and Cravens (1989) based on the Viking observations and theoretical studies (Chen et al., 1978; Hanson et al., 1977).

The electric field E is given from Ohm's law and is defined by
urn:x-wiley:21699380:media:jgra56340:jgra56340-math-0006(4)
where σe = nee2/meνet is the electric conductivity and νet is the total effective momentum transfer collision frequency of electrons given by Terada, Shinagawa et al. (2009), and thus the electron collision frequency is important in determining the magnetic diffusion associated with magnetic reconnection or annihilation. The total electron collision frequency is expressed as the sum of the electron-neutral collision frequency (νen) and the electron-ion collision frequency (νei), which are given by Schunk and Nagy (1980)
urn:x-wiley:21699380:media:jgra56340:jgra56340-math-0007(5)
and
urn:x-wiley:21699380:media:jgra56340:jgra56340-math-0008(6)

where bracket symbol denotes the number density of neutrals, Te (= Te input) is the electron temperature and ni is the total ion number density.

This model also solves the continuity equation for 14 ion species, namely, CO2+, O2+, NO+, CO+, N2+, O+, N+, C+, He+, H2+, H+, Ar+, Ne+, and Na+, which are the major ion species present in the ionosphere of terrestrial-type planets. The continuity equation for ionospheric ion densities is
urn:x-wiley:21699380:media:jgra56340:jgra56340-math-0009(7)

where ρi is the mass density of the ith ion. In this study, we use a steady neutral atmosphere model consisting of 10 species (CO2, O2, NO, CO, N2, O, N, C, He, and H) as inputs, and as a result, our simulations include major ion species in the Martian upper atmosphere (CO2+, O2+, NO+, CO+, N2+, O+, N+, C+, He+, and H+). The neutral-density profile is shown in Figure 2a of the study by Terada, Kulikov et al. (2009), which was also used in the paper by Sakai et al. (2018); this profile is based on measurements by the Viking spacecraft (e.g., Fox & Dalgarno, 1979; Nier & McElroy, 1977) in a period when solar activity was low. The rates for ion-neutral reactions, dissociative recombination, photoionization, electron-impact ionization, ion-neutral and electron-neutral collision frequencies, energy loss by electron-impact ionization, and thermal conductivity were taken from Terada, Kulikov et al. (2009 and the references therein). The ion-neutral reaction and dissociative recombination rate constants are shown in Table B1 of the study by Terada, Shinagawa et al. (2009). The EUVAC solar flux model is used for the photoionization rates (Richards et al., 1994). The model includes neither the viscosity term nor the anomalous resistivity.

2.2 Parameter Settings

The solar wind or IMF parameters are set to standard values for present-day Mars. A solar wind density of 3 cm−3, a velocity of 400 km/s, a magnetic intensity of 2.5 nT and a temperature of 105 K are used as input values. These solar wind parameters are changed from those used by Sakai et al. (2018), following the MAVEN observations over several years. A global intrinsic dipole field of 100 nT and a northward direction at 100 km altitude on the equator are assumed for this simulation. The magnetic field distribution is described by the far-field solution of a point-like dipole at the center of the planet and the dipole moment is set to 4.3 × 1019 A m2. The crustal magnetic field is not included in this model and the magnetic axis is aligned with the z-axis of the Mars-centered Solar Orbital (MSO) coordinate system (x is the Sun direction, y is the dusk direction, and z is the x × y direction). The parameters are also summarized in Table 1.

Table 1. Simulation Settings
Solar wind parameters Northward IMF case Parker-spiral IMF case Southward IMF case
Solar wind density 3 cm−3
Solar wind velocity 400 km/s
Solar wind temperature 105 K
Intrinsic magnetic field 100 nT at 100 km altitude on the equatorial surface
IMF intensity 2.5 nT
IMF direction North Parker-spiral South
  • IMF, interplanetary magnetic field.

Simulations are conducted for three different IMF conditions. The purely northward IMF parallel to the intrinsic dipole field is considered in Case 1, which is called the “northward IMF case,” the Parker-spiral IMF is given in Case 2, which is called the “Parker-spiral IMF case,” and Case 3 is the case involving the purely southward IMF antiparallel to the dipole field, which is called the “southward IMF case.” The calculations are performed until a quasi-steady state, which is determined by a variation of the escape rate in the tail region within ∼1%. The outer boundary is fixed at r = 32 Martian radii (RM) upstream and r = 40 RM downstream, where r is the radial distance. The number of grid points is 1922 for the longitudinal and latitudinal components and 336 for the radial component. The spatial resolution is ∼3° for the latitudinal direction, ∼4° for the longitudinal direction. The distance between radial grid points is 4 km near the lower boundary and increases exponentially as altitude increases. The time interval of the simulation is determined by the Courant-Friedrichs-Lewy conditions.

The inner radial boundary is located 100 km above the surface, which corresponds to the bottom of the ionosphere. At this location, the plasma velocity is set to zero, while the ion densities and gas pressure are fixed by assuming that the ions achieve photochemical equilibrium in which the ion loss rate is mostly comparable to the ion production rate.

3 Magnetosphere

The magnetosphere configuration is first compared among the three cases: the northward IMF case, Parker-spiral IMF case, and southward IMF case. Figure 1 shows the plasma thermal pressure (panels a, b, and c for the three cases, respectively) and the magnetic field strength (panels d, e, and f for the three cases, respectively), and Figure 2 shows the magnetic field configuration for three different cases. For all three cases, a magnetic field of 100 nT at the equatorial surface increases to 200 nT at the polar surface. In the northward IMF case, there exists a region of high plasma pressure, which is known as the magnetosheath, between ∼1.5 and 2 RM on the dayside, where the pressure increases to ∼0.7 Pa (Figure 1a). The reconnection between the intrinsic magnetic field and IMF does not occur in the subsolar region because the intrinsic magnetic field and IMF are parallel, resulting in the formation of a magnetosphere configuration similar to that of Earth (Figures 1d and 2a). The cusp is also seen at the latitude of ∼45° (Figures 1d and 2a). The magnetosheath or high-pressure region is extended to a width of ∼1 RM in the Parker-spiral IMF case (Figure 1b), and the value is almost 0.7 nPa, as is that of the northward IMF case. The magnetosphere shape seems to be a hybrid between that of the magnetosphere for a strong dipole magnetic field and the induced magnetosphere (Figures 1e and 2b). In the southward IMF case, the magnetosheath spreads out to the vicinity of the planet (Figure 1c) because the reconnection between the intrinsic magnetic field and IMF occurs in the subsolar region by the antiparallel field of the intrinsic field and IMF, which makes the IMF erode into the Martian ionosphere (Figures 1f and 2c), resulting in the formation of an “opened magnetosphere” in this case. Note that the reconnection (annihilation) occurs in the collisional region at low altitudes. The wave-like features on the wings of the magnetosheath are likely artifacts from numerical simulations and might appear far from the planet due to low spatial resolution, which do not affect the escape mechanism from the ionosphere because of their location far from the planet.

Details are in the caption following the image

The plasma thermal pressure (a, b, and c) and the strength of the magnetic field (d, e, and f) in the x-y (upper half) and x-z (lower half) planes obtained by the MHD simulation for (a and d) the northward, (b and e) Parker-spiral, and (c and f) southward IMF cases. The thermal pressure and magnetic field strength are almost symmetric between the north-south and dawn-dusk hemispheres. MHD, magnetohydrodynamic.

Details are in the caption following the image

The magnetic field configuration for (a) the northward (parallel) IMF case, (b) the Parker-spiral IMF case, and (c) the southward (antiparallel) IMF case. IMF, interplanetary magnetic field.

4 Heavy Ion Escape Under a Weak Intrinsic Magnetic Field

The influence of the IMF direction on the heavy ion escape channels is described in this section. Figure 3 shows the total tailward (or negative x-directional) flux of O+, O2+ and CO2+ for the northward IMF case (panel a), Parker-spiral IMF case (panel b), and southward IMF case (panel c) at x = −28 RM in the southern hemisphere on the y-z plane.

Details are in the caption following the image

Total tailward flux of O+, O2+ and CO2+ on the y-z plane at x = −28 RM of the MSO coordinate system for the (a) northward, (b) Parker-spiral, and (c) southward IMF cases. IMF, interplanetary magnetic field. MSO, Mars-centered Solar Orbital.

In the northward IMF case, the tailward flux has each peak in both the northern and southern hemispheres along the meridian (Figure 3a), and it is almost 3 × 108 m−2 s−1. In the Parker-spiral IMF case, the tailward flux peaks are seen in the tail-flank region (Figure 3b), called the tail-flank channel on the neutral sheet of Bx = 0, and the peak value is ∼5 × 109 m−2 s−1. The tailward flux increases to ∼1010 m−2 s−1 in the southward IMF case. The two flux peaks are located in the equatorial tail flanks on the dawn and dusk sides (Figure 3c). Figure 3 also suggests that the escape channels significantly depend on the IMF direction. In the following subsection, we investigate in detail the escape mechanism and channels in each case.

4.1 Northward IMF Case

In the northward IMF case, the two tailward flux peaks are seen in the high-latitude region at x = −28 RM. Figure 4 shows the tailward fluxes of the (a) O2+, (b) O+, and (c) CO2+ ions on the y-z plane at x = −2 RM. All ion fluxes still have each peak in the northern and southern hemispheres (Figures 4a–4c), which is called the “high-latitude peak.” The maximum values of the tailward O2+, O+, and CO2+ fluxes are ∼2 × 1010 m−2 s−1, ∼1 × 109 m−2 s−1 and ∼6 × 108 m−2 s−1, respectively, at x = −2 RM. In addition to the high-latitude peaks in the magnetotail, the O+ ions escape from a broader ring-shaped region (Figure 4b), which is called the “ring-shaped peak.” The value of the ring-shaped O+ flux is ∼3 × 108 m−2 s−1, which is smaller than that of the O2+ flux but comparable to the CO2+ peak flux.

Details are in the caption following the image

Tailward fluxes of (a) O2+, (b) O+, and (c) CO2+ ions at x = −2 RM for the northward IMF case. The white region denotes the sunward flow, and the black line denotes the neutral sheet of Bx = 0. (d) The magnetic configurations are shown in squares for the draped field line, circles for the open field line and crosses for the closed field line. The warm and cool colors denote the field lines at Bx > 0 and Bx < 0, respectively. The gray dashed lines are O2+ flux contour lines of 109 m–2 s–1. IMF, interplanetary magnetic field.

The magnetic field lines are mostly closed for the northward IMF case. Figure 4d shows the magnetic field configuration at x = −2 RM. Closed field lines dominate the region of |y, z| < 3 RM (the cross symbols in Figure 4d), which means that the field lines form a “closed magnetosphere.” Draped field lines are dominant outside of the magnetosphere (the square symbols in Figure 4d), and they originate in the IMF. A bow shock generates the fluctuations in the magnetic field, resulting in a change in the sign of Bx along the circle.

There exist two escape channels, namely, high-latitude channel for all ions and ring-shaped channel for O+ ions, in the northward IMF case, but each channel might have a different escape mechanism. Figure 5 shows the magnetic field lines associated with ion escape through the high-latitude channel. Note that those field lines are drawn by tracing the real field lines through the model. In this case, the reconnections of the intrinsic closed field line and draped IMF are important for ion escape. Once the closed field line (white) and the draped IMF (cyan) are reconnected in the magnetospheric lobe region of one hemisphere, the field line open at one end and attached to the planet at the other end (magenta) is generated (#1 in Figure 5). The draped field line (red) is newly generated as with substantial ionospheric ions when the open field line (magenta) reconnects with the draped field lines in the other hemisphere (#2 in Figure 5). Note that on Earth, the lobe reconnections such as #1 and #2 is not likely to occur simultaneously in a purely northward IMF due to instability around the magnetopause (Tanaka et al., 2019). The field line is carried to the tail region (green), and the ions escape to the space (#3 in Figure 5). It is suggested that double lobe reconnections make heavy ions escape through high-latitude channels. A large amount of molecular ions are included in the flux tube of the closed intrinsic magnetic field. This closed intrinsic field line is reconnected twice with the draped solar wind field line, resulting in the mass-loaded draped field lines connected to the solar wind contributing to the escape. The solar wind originally has a tailward velocity of 400 km/s, and moreover, the magnetic tension force generated by reconnection helps the escape to the tail. The ring-shaped O+ flux is related to both the oxygen corona. The hot oxygen atoms created by the recombination of O2+ collide with the neutral atmosphere and lose energy. Nevertheless, some hot oxygen atoms escape from Mars and comprise the extended Martian hot oxygen corona (e.g., Feldman et al., 2011). Once the hot oxygen corona is photoionized by EUV radiation, newly created O+ is carried to the tail after the lobe reconnections. The other channel of O+ escape is the high-latitude channel the same as the escape channel of molecular ions. That is, O+ escape possibly occurs by both the photoionization of the oxygen corona and transportation from the ionosphere to the tail after lobe reconnections.

Details are in the caption following the image

The selected field lines for the northward IMF case attached to the planet at both ends (white), those open at both ends or the IMF (cyan), those attached to the planet of the northern hemisphere at one end and open to the tail at the other end (magenta), those that are open at both ends after reconnections (red), and those transported to the tail region (green). The numbers in the figure show the trace of the time evolution of the magnetic field line. The arrows denote the direction of the magnetic field. IMF, interplanetary magnetic field.

4.2 Parker-Spiral IMF Case

In the Parker-spiral IMF case, heavy ions escape from the flank region on the neutral sheet in dawn and dusk of the magnetosphere at x = −2 RM, called the “tail-flank peak.” Figure 6 shows the tailward flux of (a) O2+, (b) O+, and (c) CO2+ on the y-z plane at x = −2 RM. The O2+ flux is the largest among the three ion species, but the shape of the flux is mostly the same among them. The maximum O2+ flux value is ∼2 × 1011 m−2 s−1. This flux value is an order of magnitude greater than that in the northward IMF case.

Details are in the caption following the image

Same format as Figure 4, but for the Parker-spiral IMF case. The gray dashed lines in (d) are O2+ flux contour lines of 1010 m–2 s–1. IMF, interplanetary magnetic field.

The interaction between the Parker-spiral IMF and intrinsic magnetic field forms a hybrid magnetosphere between that for a strong dipole magnetic field such as that of Earth and the induced magnetosphere such as that of present-day Mars. Figure 6d shows the magnetic configuration at x = −2 RM in the Parker-spiral IMF case. The magnetosphere is formed by closed field lines in the inner region rather than |y| ≲ 2 RM (cross symbols in Figure 6d), while in the outer region, it is formed by open field lines (square symbols in Figure 6d).

The escape mechanism from the tail-flank channel is associated with the reconnection between the intrinsic field line and IMF in a magnetospheric flank region, as explained by Sakai et al. (2018). In this case, the reconnection occurs in a region where open field lines encounter the antiparallel IMF, e.g., on the dawn side surrounded by gray dashed lines in Figure 6d where blue circles make contact with orange squares, resulting in escape from the ionosphere. Figure 7a shows the magnetic field lines colored according to the tailward flux on a streamline (white arrows) defined by the ion velocity vector (yellow), and one can follow the time evolution of a field line on the streamline. A field line close to the planet is open, and this field line finally becomes draped in the tail region, where escape occurs. Figure 7b illustrates an example of the process of generating a looped field line by reconnections. Once cyan and orange open field lines are reconnected, the green and magenta field lines are generated. The green field line corresponds to the looped open field line shown in Figure 7a, which eventually contributes to the escape. In the flank region in this case, magnetic reconnection is more likely to occur in the extended region of anti-parallel field lines, resulting in multiple reconnections. The orange open field line originally had a loop structure, and it is expected that the closed field line and draped IMF were reconnected in the flank region before the series of reconnection processes shown in Figure 7b. The largest tailward flux at (x, y) ∼ (±2 RM, 0) is seen in the region where closed field lines are dominant (Figure 6d), but this flux does not contribute to the escape because it eventually returns as a sunward flow.

Details are in the caption following the image

(a) The magnetic field lines on a streamline (yellow) penetrate into the flux peak in the tail region for the Parker-spiral IMF case. The color of the field lines shows the magnitude of tailward flux. The sphere represents the planet, and the black line shows the meridian. The white arrows indicate the crossing point of the streamline and field lines. (b) The reconnection process for the Parker-spiral IMF case is represented. Each color line denotes the magnetic field line before and after reconnection. IMF, interplanetary magnetic field.

In the study by Sakai et al. (2018), the escape was generated by the reconnection between the closed field line and antiparallel IMF. It is expected that this difference appears to be due to the variation in the plasma beta of the solar wind. A solar wind temperature of 105 K is used for this study, but 106 K was used by Sakai et al. (2018) to compare the results with those from Terada, Kulikov et al. (2009). A temperature drop of one order of magnitude changes the magnetosheath properties due to the change in the shock condition at the bow shock. It leads to change the meridional convection in the magnetosphere and consequently affects the reconnection rate in the flank region. Such changes in meridional convection leads to an increase in escape flux from low latitudes. Moreover, it is expected that the variation in plasma beta results in the disappearance of the high-latitude peak seen by Sakai et al. (2018) (Figure 3a in the study by Sakai et al., 2018).

4.3 Southward IMF Case

In the southward IMF case, ions escape from the two regions around the equatorial tail flanks on the dawn and dusk sides, called the “equatorial channel.” Figure 8 shows the tailward flux of (a) O2+, (b) O+, and (c) CO2+ on the y-z plane at x = −2 RM. The shape of the flux peaks does not change among the three ion species, but the maximum value of O2+ (∼2 × 1011 m−2 s−1) is larger than that of O+ and CO2+ (Figures 8a and 8c, respectively). This flux is an order of magnitude greater than that in the northward IMF case and comparable to that in the Parker-spiral IMF case.

Details are in the caption following the image

Same format as Figure 4, but for the southward IMF case. The gray dashed lines in (d) are O2+ flux contour lines of 1010 m–2 s–1. IMF, interplanetary magnetic field.

The magnetosphere is dominated by the open field lines in the southward IMF case (Figure 8d). Most of the field lines are open, as shown by the circle symbols in Figure 8d, although a part of the magnetosphere near the equator is formed by closed field lines. The draped field lines originating in the IMF contribute to the flux peak region on the dawn and dusk sides (surrounded by gray dashed lines).

The escape mechanism in the southward IMF case is significantly different from that in the northward IMF case. Figure 9 shows the magnetic field lines colored according to the tailward flux on a streamline (yellow), and one can follow the time evolution of a field line on the streamline. In this case, ion escape is driven by the mass-loading of ionospheric ions to the IMF. The IMF is draped around the planet. The draped IMF can easily penetrate into the lower ionosphere once the reconnection between the southward IMF and intrinsic magnetic field occurs in the subsolar region (i.e., IMF erosion). Afterward, the draped IMF is mass-loaded by ions as it is transported through the dayside ionosphere. The mass-loaded draped IMF, which holds a large amount of ionospheric ions, is carried directly to the tail, resulting in ion escape. It is suggested that ion escape is promoted by the mass-loading in the ionosphere of the IMF for the southward IMF case.

Details are in the caption following the image

Same format as Figure 7a, but for the southward IMF case. The white arrows denote the direction of the magnetic field. IMF, interplanetary magnetic field.

4.4 Ion Escape Rate in the Tail

We evaluated the total O+, O2+, and CO2+ ion escape rate by integrating over the flux in the tail region. The integral for the ion escape rate is calculated on the hemisphere of x < 0 at r = 28 RM, and the spatial resolution is ∼3° for the latitudinal direction and ∼4° for the longitudinal direction. The ion escape rates are also calculated for snapshots of time shown in the figures after the model has achieved the quasi-steady state. Figure 10 shows the escape rate of each ion species for the four cases. In the northward IMF case, the total ion escape rate is ∼5.1 × 1023 s−1. The ratio of the escape rates is O2+: O+: CO2+ ≈ 69 : 28: 3. The total escape rates of O+, O2+, and CO2+ are ∼1.0 × 1025 s-1 in both the Parker-spiral and southward IMF cases, and they are approximately two orders of magnitude greater than those in the northward IMF case. These results suggest that the northward IMF significantly decreases the ion escape rate. The ratio of the ion escape rates is O2+: O+: CO2+ ≈ 79.4 : 20.2: 0.4 in the Parker-spiral IMF case, and 81.6: 17.9: 0.5 in the southward IMF case. The ion escape rate in the Parker-spiral IMF without a dipole magnetic field is also recalculated under the new solar wind conditions. The total ion escape rate is 5.9 × 1024 m−2 s−1 and increases by a factor of ∼2 from the results of Sakai et al. (2018), but it is still smaller than the escape rate in the Parker-spiral IMF with a dipole field. The decrease in solar wind temperature alters the magnetosheath properties in the case of the Parker-spiral IMF without a dipole magnetic field as well as in the dipole case. It changes the convection in the induced magnetosphere and thus increases the ion density on the nightside. That generates a difference of escape rate by a factor of 2. Note that the escape mechanism does not change much compared to the results of Sakai et al. (2018) in the Parker-spiral IMF without a dipole field (see Appendix A). The escape rate of CO2+ is the lowest in the Parker-spiral IMF without a dipole magnetic field because the field lines that contribute to escape do not penetrate to low altitudes where CO2+ is abundant. The uncertainty is approximately ±20% for each of the total escape rates, which is estimated from fluctuations of the calculated escape rate. The escape rates could vary by ∼20% even after quasi-steady state is achieved due to the timing of reconnection and ionospheric flow.

Details are in the caption following the image

The total escape rate (black) and the O2+ (blue), O+ (red), and CO2+ (green) escape rates are described for the cases of a northward IMF, a Parker-spiral IMF with a dipole field, a southward IMF, and a Parker-spiral IMF without a dipole field. IMF, interplanetary magnetic field.

5 Discussion

The current study focuses on the effect of the IMF direction under a weak global magnetic field on the ion escape mechanisms for a Mars-like planet. In the northward IMF case, the ions created near the planet are transported to the tail along the draped field lines after double lobe reconnections between an intrinsic magnetic field and the IMF, and the oxygen corona also contributes to ion escape. In the southward IMF case, the mass-loading of the IMF in the ionosphere contributes to ion escape. These processes are different from the escape mechanism in the Parker-spiral case. In the Parker-spiral IMF case, ions escape through the tail-flank channel by the reconnection between the intrinsic field and IMF occurring in the flank region of the magnetosphere (Figure 6d and also see Figure 3 in the study by Sakai et al., 2018). However, the locations of the escape channel change if a purely northward or southward IMF is assumed. It is suggested that the IMF direction is critical for the escape mechanism and channels.

The total ion escape rate is approximately two orders of magnitude greater in the Parker-spiral and southward IMF cases than in the northward IMF case (Figure 10). The reconnection in the flank region of the magnetosphere regularly occurs in the Parker-spiral IMF, promoting escape from the ionosphere. In the southward IMF, the ions are stripped out on the dayside by IMF erosion into the ionosphere, and the ions can easily escape to the space along the field lines from the deep ionosphere. The escape rate is lower in the case of the Parker-spiral IMF without a dipole field than in the southward IMF case because molecular ions cannot escape from the deep ionosphere below 300 km, where the plasma pressure dominates the dynamic pressure and the IMF cannot penetrate. On the other hand, the ion escape rate in the northward IMF case is lower than that in any other cases, including even the Parker-spiral IMF case without a dipole field (Figure 10). A magnetosphere similar to that of Earth is formed around the planet because a reconnection unlikely occurs in the dayside ionosphere due to the parallel magnetic field between a dipole field and the IMF in the northward IMF case and the IMF does not erode the ionosphere. It is suggested that the atmosphere tends to be protected by the magnetosphere in the northward IMF case. The escape rate is the lowest in the northward IMF case, the second lowest in the case of the Parker-spiral IMF without a dipole magnetic field, and the highest in the case of the Parker-spiral IMF with a dipole field and in the southward IMF case.

In the southward IMF case, the erosion of the IMF to the ionosphere is important to the escape process. The eroded altitude of the IMF, which means the minimum altitude on the dayside to which the IMF can penetrate into the ionosphere, could vary by certain factors. The Hall term is one of the candidates, and it could change the eroded altitude; therefore, the effects on escape rate and mechanism should be verified in the future. In contrast, once the erosion of the IMF occurs in the dayside, the draped IMF moves from the dayside to the dawn or dusk side by the magnetic tension force while passing the ionosphere after the erosion of the ionosphere, contributing to ion escape in the tail.

We have discussed the molecular ion escape rate, and oxygen escape is also important in understanding climate change in the Martian system. The integrated escape rates of ionized oxygen by O+, O2+, and CO2+ estimated from the MHD simulation in each case are ∼8.8 × 1023 s−1 in the northward IMF case and ∼1.9 × 1025 s−1 in the case of the Parker-spiral IMF with a dipole field and in the southward IMF case. The oxygen ion escape rate in the case of the Parker-spiral IMF without a dipole field is ∼9.6 × 1024 s−1, which is mostly consistent with the present-day loss rate from the MAVEN statistical observations (Inui et al., 2019). The oxygen escape rate is higher in the Parker-spiral IMF with a dipole field than in the Parker-spiral IMF without a dipole field, which is consistent with previous studies (Egan et al., 2019; Sakata et al., 2020). The increase in the escape rate suggests the average influence of the intrinsic magnetic field on the escape rate because the Parker-spiral IMF is probably the average upstream condition. In contrast, the northward IMF makes the escape rate of oxygen ions an order of magnitude lower than in the Parker-spiral and the southward IMF cases. The ancient solar activity was higher than that in the present (e.g., Tu et al., 2015), and thus, the IMF was also variable (Vidotto et al., 2014). This finding suggests that the IMF direction and the intrinsic magnetic field varying the escape rate are also important factors in revealing climate change on Mars from the past to the present.

The magnetic diffusion term associated with magnetic reconnection (annihilation) depends on the electron collision frequency, namely, the electron temperature and the ion and neutral densities. The electron temperature used in this model by Shinagawa and Cravens (1989) is 2000–3000 K above 300 km altitude, corresponding to the temperature observed by MAVEN (Sakai et al., 2019). In contrast, in the MHD model, it is difficult to treat the plasma temperature precisely because the temperatures are determined by the suprathermal electron profile (e.g., Sakai et al., 2016), which is not included in the MHD model, resulting in the possibility that the suprathermal electrons modify the magnetic diffusion term. Variations in ion and neutral densities induced by coronal mass ejections or solar flares also affect the magnetic diffusion, leading to changes in magnetic reconnection or annihilation rate.

The ion finite Larmor radius effects might be important above the induced magnetosphere boundary of unmagnetized Mars. In the current paper, the escape mechanisms are discussed under the intrinsic magnetic field, and therefore the kinetic effects due to gyro motion are mostly negligible.

The ambipolar electric field could affect the ion escape rate. Ma et al. (2019) compared the ion escape rate of a multifluid model including the electron pressure gradient (MFpe) with that of a multispecies model as well as our model (MS) and normal multifluid model (MF) in present-day unmagnetized Mars. They showed that the escape rate for the MFpe model is greater by a factor of 2–3 than that for the MS model, which is associated with the ambipolar electric field, and thus our loss rate is somewhat underestimated compared to other sophisticated models. However, the variation in the IMF direction does not change the escape mechanism due to the ambipolar electric field such as a polar plume, while it changes the escape mechanism occurring in the tail, namely, lobe reconnections for the northward IMF case and mass-loading for the southward IMF case.

6 Conclusion

The ion escape rate and mechanisms for a hypothetical Mars-like planet with a weak (100 nT) dipole intrinsic magnetic field in the northward, southward, and Parker-spiral IMF were investigated from studies based on three-dimensional multispecies single-fluid MHD simulations. In the northward IMF case, the magnetosphere along with the cusp at the latitude of ∼45° is formed rigidly around the planet, while in the southward IMF case, the IMF erodes the Martian ionosphere, resulting in the formation of an opened magnetosphere.

In the northward IMF case, the tailward flux peak is seen in two regions, namely, the “high-latitude channel” and “ring-shaped channel.” All ions escape through the high-latitude channel. This escape channel is generated by the reconnections between the closed intrinsic magnetic field and draped IMF in the lobe region. The ions present in the lower ionosphere were originally included in the flux tube of closed field lines and carried to the tail after double lobe reconnections. O+ ions also escape through the ring-shaped channel that appears to originate in the oxygen corona in addition to the high-latitude channel. In the Parker-spiral IMF case, the tailward flux is enlarged in the tail-flank magnetosphere, namely, the “tail-flank channel.” This escape channel is associated with the reconnection between the draped IMF and intrinsic magnetic field in the flank region of the magnetosphere. Ion escape is promoted when reconnection in the flank occurs. The main escape mechanism in both the northward and Parker-spiral IMF cases is that the intrinsic magnetic field, including the ionospheric ions, reconnects with the draped IMF and connects with solar wind, resulting in ionospheric ions escaping to the space. In the southward IMF case, the tailward flux has two peaks on the dawn and dusk sides of the equatorial tail region, namely, the “equatorial channel.” The IMF can penetrate into the ionosphere due to erosion by the reconnection of the antiparallel IMF and intrinsic magnetic field in the subsolar region. The draped IMF is mass-loaded by the molecular ions in the dayside ionosphere, and the mass-loaded draped IMF is directly transported to the tail, contributing to ion escape.

The ion escape rate is the lowest in the northward IMF, the second lowest in the case of the Parker-spiral IMF without a dipole magnetic field, the highest in the case of the Parker-spiral IMF with dipole field, and in the southward IMF case. The total ion escape rate is approximately two orders of magnitude lower in the northward IMF case than in both the Parker-spiral and southward IMF cases. The northward IMF forms a firm magnetosphere similar to that of Earth, resulting in the tendency of the magnetosphere to protect the atmosphere. The ion escape rate in the southward IMF case is comparable to that in the Parker-spiral IMF case. The Parker-spiral and southward IMFs cause magnetic reconnection and erosion into the ionosphere, leading to more ion escape from the upper atmosphere than in the northward IMF. The escape rate of molecular ions is much greater when the weak intrinsic magnetic field is assumed, which is consistent with the results of Sakai et al. (2018).

Oxygen escape is important to understand H2O and/or CO2 escape, and these processes are related to Martian climate change. Our simulation showed that the IMF direction greatly affects the escape rate of oxygen ions and that the intrinsic magnetic field enhances the ion escape rate in the Parker-spiral IMF case, which is the average upstream condition. The ancient Sun was more active than the present-day Sun such that the IMF was more variable. These results suggest that ancient solar wind parameters, such as the IMF direction and the planetary magnetic field, should be studied to understand oxygen escape. It would lead to revealing how Mars changed from a warm and wet climate in the past to a cold and dry climate in the present day.

Acknowledgments

This work was supported by Grant-in-Aid for Scientific Research (A) 19H00707 and 20H00192, Fostering Joint International Research (B) 18KK0093, and Scientific Research on Innovative Areas 18H05439 from the JSPS. This work is related to MACH DRIVE Center supported by the NASA Heliophysics Program. The computer simulation was partly performed on the KDK computer system at the Research Institute for Sustainable Humanosphere (RISH), Kyoto University.

    Appendix A: Brief of a Case of the Parker-Spiral IMF Without a Dipole Field

    The case of the Parker-spiral IMF without a dipole field as investigated by Sakai et al. (2018) was revisited for the solar conditions as shown in Table 1. The magnetosheath in the high pressure region is located near the planet on the dayside, at ∼1–1.5 RM at the subsolar point, and the pressure increases to ∼0.7 nPa (Figure A1a). Unmagnetized planets form an induced magnetosphere due to the interaction between the obstacle and the IMF, and the magnetism builds up in the dayside ionosphere with an intensity of 30 nT (Figure A1b). These results are quite consistent with the results of Sakai et al. (2018) (see also Figure 1 of Sakai et al., 2018). Figure A1c shows the total tailward flux of heavy ions (O2+, O+, and CO2+) at x = −2 RM. The tailward flux has a peak near the center of the magnetotail with some elongation on the neutral sheet along the z axis, which is also consistent with the results of Sakai et al. (2018), but the structure of Bx = 0 is more complex near the center (black dashed line of Figure A1c). Figure A1d shows the magnetic configuration at x = −2 RM. The change in the draped field from to sunward to tailward appears around the center where magnetic structures such as flux rope are formed, in agreement with observations (e.g., Hara et al., 2017).

    Details are in the caption following the image

    MHD simulations for the Parker-spiral IMF without a dipole field, showing (a) plasma thermal pressure, (b) strength of the magnetic field in the x-y (upper half) and x-z (lower half) planes, (c) total tailward flux of heavy ions (O2+, O+, and CO2+) with magnetic neutral lines of Bx = 0 (dashed lines), and (d) magnetic configurations indicated by the squares for the draped field line. The gray dashed lines in (d) are flux contour lines of 1010 m–2 s–1. IMF, interplanetary magnetic field.

    Data Availability Statement

    The data used in this study are available at the UTokyo Repository (https://doi.org/10.15083/00080061).