Planetary Magnetic Field Control of Ion Escape from Weakly Magnetized Planets

David Brain; Hilary Egan; Riku Jarvinen; Yingjuan Ma

arxiv: 1907.02978 · v1 · pith:Q36YXK5Enew · submitted 2019-07-05 · 🌌 astro-ph.EP

Planetary Magnetic Field Control of Ion Escape from Weakly Magnetized Planets

Hilary Egan , Riku Jarvinen , Yingjuan Ma , David Brain This is my paper

Pith reviewed 2026-05-25 01:43 UTC · model grok-4.3

classification 🌌 astro-ph.EP

keywords planetary magnetic fieldsion escapeatmospheric erosionMars-sized planetstellar windhybrid simulationmagnetosphere boundaryplasma environment

0 comments

The pith

A weak planetary magnetic field first boosts then reduces ion escape from a Mars-sized world.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Global hybrid simulations of a Mars-sized planet reveal that ion escape into space rises with increasing dipolar field strength until the dipole standoff distance equals the induced magnetosphere boundary. Past that point stronger fields reduce escape through a competition between shielding one hemisphere from pickup forces and trapping ions in an equatorial plasmasphere. The field value that produces peak escape therefore depends on the pressure of the incoming stellar wind. Power-law fits describe how escape rate, escape power, polar cap angle and interaction area change with field strength, together with their upper and lower bounds. This challenges the long-held assumption that stronger magnetic fields always protect atmospheres from stellar-wind erosion.

Core claim

Increasing the strength of a planet's magnetic field enhances ion escape until the magnetic dipole's standoff distance reaches the induced magnetosphere boundary. After this point increasing the planetary magnetic field begins to inhibit ion escape. This reflects a balance between shielding of the southern hemisphere from misaligned ion pickup forces and trapping of escaping ions by an equatorial plasmasphere. The planetary magnetic field associated with the peak ion escape rate is critically dependent on the stellar wind pressure.

What carries the argument

The transition where the magnetic dipole standoff distance equals the induced magnetosphere boundary, marking the shift from net enhancement to net suppression of ion escape via competing shielding and trapping effects.

If this is right

Escape rate, escape power, polar cap opening angle and effective interaction area vary with magnetic field strength according to fitted power laws up to the transition point.
Upper and lower limits on these power-law relationships are provided by the simulation results.
The magnetic field strength that maximizes ion escape scales directly with stellar wind pressure.
Beyond the transition the shielding and trapping effects reverse the trend and lower the net escape rate.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Planets whose magnetic fields place them near the transition may lose atmosphere faster than either unmagnetized or strongly magnetized neighbors under the same wind conditions.
The same non-monotonic dependence could apply to other solar-system bodies if their size and wind environment place the standoff near the induced boundary.
Habitability assessments for exoplanets must consider not only the presence of a field but its strength relative to local stellar wind pressure.

Load-bearing premise

The induced magnetosphere boundary position remains unchanged when an intrinsic dipolar field is added.

What would settle it

A simulation or observation in which the induced boundary position is allowed to move with the added dipole field, checking whether the escape-rate peak still occurs exactly when standoff distance matches the new boundary location.

Figures

Figures reproduced from arXiv: 1907.02978 by David Brain, Hilary Egan, Riku Jarvinen, Yingjuan Ma.

**Figure 1.** Figure 1: Slices through the tail at X = −2 for each simulation (0, 10, 25, 50, 75, 100, 150 nT from left to right). Top row shows O + 2 number density while the bottom row shows the x-component of the magnetic field. The gradual twisting of the tail represents a shift from being IMF draping dominated (symmetric about Y) to dipole dominated (symmetric about Z). ues. This occurs because the analytic estimate must be … view at source ↗

**Figure 2.** Figure 2: Magnetic field line traces for three representative simulations with planetary magnetic fields of 10 nT (left), 50 nT (center), and 100 nT (right). Top row shows the planet as viewed from the star and middle row shows planet as viewed within the orbital plane; in both cases the motional electric field points upwards. Bottom row is a latitude-longitude map of the field line tracings, with white dashed lines… view at source ↗

**Figure 4.** Figure 4: Schematic depiction of the relationship of the induced (pink dashed) and intrinsic (blue solid) magnetospheric boundaries. The different regimes are responsible for different patterns of ion escape, as discussed in Section 5. 10 2 10 1 10 0 Escape Rate [1 0 2 5 / s] Earth Magnetized Strongly Magnetized Weakly Magnetized BP 0.67 0 10 0 10 1 10 2 10 3 10 4 10 5 Planetary Magnetic Field Strength [nT] 10 1 10… view at source ↗

**Figure 3.** Figure 3: Polar cap solid angle (top) and standoff altitude and proxies thereof along the sub-stellar line (bottom) plotted over planetary magnetic field. Dotted lines indicate analytic approximations while solid lines with points are calculated from the simulations. Horizontal lines indicate empirical boundaries measured for Mars (Trotignon et al. 2006) and the peak ionosphere production location in the simulati… view at source ↗

**Figure 5.** Figure 5: Ion escape rates (top), escape power (middle), and average ion escape energies (bottom) over planetary magnetic field strength for O + 2 ,O+, and the sum of both ions. Relative escape rates are normalized to the escape rate of the unmagnetized case. Power law fits to the sum are shown in with a dashed line for the escape rate and escape power for Bp ≥ 50 nT. power have clear lower limits at Bp = 50 nT, a p… view at source ↗

**Figure 6.** Figure 6: Three example particle trajectory tracings for 10, 50, and 100 nT simulations. Particle tracings are shown in red (trapped) or dark blue (escaping), and magnetic field lines are shown in light blue (open) and orange (closed). While this location was picked primarily as an illustrative example for these three simulations, it is representative of overall ion escape trends discussed in Sections 5.2 and 5.3. w… view at source ↗

**Figure 7.** Figure 7: Velocity distribution of escaping O + 2 (top) and O+ (bottom) ions weighted by number density and velocity, such that integrating over the distribution is equivalent to the escape power. Each color shows a different magnetic field. The dashed lines indicate the weighted average of each distribution (equivalent to the average reduced escape energy plotted in [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

**Figure 8.** Figure 8: Slices in the y = 0 plane of motional electric field magnitude (top), electron velocity magnitude (center), and ratio of the O + 2 velocity to the electron velocity (bottom) for the 10 nT (left), 50 nT (center), and 100 nT (right) simulations, showing the effectiveness of the 50 and 100 nT fields in standing off the stellar wind preventing strong planet-oriented electric fields. White arrows indicate direc… view at source ↗

**Figure 9.** Figure 9: Slices in the y = 0 plane showing the development of the plasmasphere. O + 2 number density (top) and motional electric field magnitude (bottom) for the 50, 75, 100, and 150 nT simulations are shown from left to right, with black arrows over-plotted indicating the direction of the magnetic field [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗

**Figure 10.** Figure 10: Coupling of the inflow and outflow mass fluxes (center) and power (right). Outflow properties are calculated over a spherical shell far from the planet, while inflow properties are calculated assuming a constant inflow from the stellar wind over an interaction region determined by the cross-sectional area at the terminator (left). Dashed lines indicate a coupling of the form M˙ out = (M˙ in) k (or Pout =… view at source ↗

read the original abstract

Intrinsic magnetic fields have long been thought to shield planets from atmospheric erosion via stellar winds; however, the influence of the plasma environment on atmospheric escape is complex. Here we study the influence of a weak intrinsic dipolar planetary magnetic field on the plasma environment and subsequent ion escape from a Mars sized planet in a global three-dimensional hybrid simulation. We find that increasing the strength of a planet's magnetic field enhances ion escape until the magnetic dipole's standoff distance reaches the induced magnetosphere boundary. After this point increasing the planetary magnetic field begins to inhibit ion escape. This reflects a balance between shielding of the southern hemisphere from ``misaligned" ion pickup forces and trapping of escaping ions by an equatorial plasmasphere. Thus, the planetary magnetic field associated with the peak ion escape rate is critically dependent on the stellar wind pressure. Where possible we have fit power laws for the variation of fundamental parameters (escape rate, escape power, polar cap opening angle and effective interaction area) with magnetic field, and assessed upper and lower limits for the relationships.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Simulations find non-monotonic ion escape with magnetic field strength peaking at standoff-boundary match, but boundary may shift with dipole.

read the letter

The simulations in this paper find that ion escape from a Mars-sized planet rises as the intrinsic magnetic field gets stronger, but only until the dipole's standoff distance matches the induced magnetosphere boundary. After that, stronger fields reduce escape. The transition point moves with stellar wind pressure, and they attribute it to shielding in one hemisphere versus trapping in an equatorial region. They also fit power laws to escape rate, escape power, polar cap opening angle, and interaction area across the runs. This is the main new quantitative result from the hybrid code parameter study. The work does well by varying the dipole moment directly in 3D simulations and producing concrete scaling relations from the output rather than from fitted assumptions. The approach is straightforward plasma simulation without circular definitions. The main soft spot is the assumption that the induced magnetosphere boundary location stays independent of the added dipole. Adding the dipole changes the global field draping and plasma flow, which can move the boundary. If that occurs, the reported peak and the physical balance tied to the matching point may not map cleanly, and the non-monotonic curve could partly reflect how the boundary is identified in each run. The abstract mentions upper and lower limits, but without explicit checks on boundary position across the sweep the central claim carries some uncertainty. This paper is for modelers of atmospheric escape and habitability on weakly magnetized planets. Readers who need updated escape prescriptions would get value from the power-law fits and the dependence on stellar wind pressure. I would bring it to a reading group to discuss the simulation outputs. I would not cite it yet. It deserves peer review because the methods are standard and the claims are quantitative enough for referees to evaluate.

Referee Report

2 major / 2 minor

Summary. The manuscript presents global 3D hybrid plasma simulations of ion escape from a Mars-sized planet with varying weak intrinsic dipolar magnetic field strengths. The central claim is that escape rate increases with field strength until the dipole standoff distance equals the induced magnetosphere boundary, after which escape decreases; this non-monotonic behavior arises from a balance between southern-hemisphere shielding from misaligned pickup forces and equatorial plasmasphere trapping. Power-law fits are reported for escape rate, escape power, polar cap opening angle, and effective interaction area as functions of magnetic field, with the peak escape rate depending on stellar wind pressure.

Significance. If the reported non-monotonic dependence and its physical mechanism hold under scrutiny, the result would meaningfully revise the standard picture that stronger intrinsic fields monotonically suppress atmospheric loss. It would imply an optimal field strength (set by stellar wind pressure) that maximizes escape for weakly magnetized bodies, with direct consequences for models of Mars' atmospheric history and for interpreting escape rates at other solar-system and exoplanet targets.

major comments (2)

[Abstract / simulation description] The identification of a clear transition point (and the subsequent decline) requires that the induced magnetosphere boundary location remain independent of the added dipole moment. The hybrid simulation necessarily modifies global field draping, compression, and plasma flow when a dipole is introduced; without explicit demonstration that the boundary position is unchanged across the dipole-moment scan, the reported peak and the shielding-vs-trapping interpretation could be an artifact of how the boundary is located or measured in each run.
[Methods / results] No information is supplied on grid resolution, particle-per-cell counts, numerical convergence tests, or direct comparison against observed Mars escape rates or MHD/hybrid benchmarks. These details are load-bearing for any quantitative claim about the location of the escape-rate maximum and the fitted power-law exponents.

minor comments (2)

[Abstract] The abstract states that power laws were fitted 'where possible'; the manuscript should explicitly state for which quantities fits were not possible and why, and report the actual exponents, uncertainties, and goodness-of-fit metrics rather than only the existence of fits.
[Abstract] Notation for the standoff distance, induced boundary, and polar-cap angle should be defined once with symbols and used consistently; the current abstract mixes descriptive phrases with quoted terms such as 'misaligned'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments. We respond to each major comment below and will revise the manuscript accordingly.

read point-by-point responses

Referee: [Abstract / simulation description] The identification of a clear transition point (and the subsequent decline) requires that the induced magnetosphere boundary location remain independent of the added dipole moment. The hybrid simulation necessarily modifies global field draping, compression, and plasma flow when a dipole is introduced; without explicit demonstration that the boundary position is unchanged across the dipole-moment scan, the reported peak and the shielding-vs-trapping interpretation could be an artifact of how the boundary is located or measured in each run.

Authors: We agree that explicit demonstration of the independence of the induced magnetosphere boundary (IMB) location is required to substantiate the non-monotonic escape behavior. We will revise the manuscript to include a dedicated analysis and figure showing the measured IMB standoff distance across the dipole-moment scan, using the same identification criteria in all runs, to confirm that the boundary position remains unchanged for the weak dipole strengths examined. revision: yes
Referee: [Methods / results] No information is supplied on grid resolution, particle-per-cell counts, numerical convergence tests, or direct comparison against observed Mars escape rates or MHD/hybrid benchmarks. These details are load-bearing for any quantitative claim about the location of the escape-rate maximum and the fitted power-law exponents.

Authors: We agree that these numerical and validation details must be provided. The revised manuscript will include a methods subsection specifying the grid resolution, particle-per-cell counts, results from convergence tests, and direct comparisons of the simulated escape rates to Mars observations as well as other MHD and hybrid benchmarks. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from direct hybrid plasma simulations.

full rationale

The paper reports ion escape trends from a series of global 3D hybrid simulations in which planetary dipole strength is varied as an input parameter while holding other conditions fixed. The non-monotonic escape behavior is an observed output of those runs rather than a quantity derived by algebraic reduction, parameter fitting to a target, or self-citation. Post-hoc power-law fits to the simulation data are explicitly labeled as such and do not feed back into the primary claim. No equations, boundary definitions, or uniqueness arguments are shown to collapse to the inputs by construction. The work is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are detailed beyond standard simulation assumptions.

free parameters (2)

magnetic dipole moment
Varied across simulation runs to identify the peak escape rate
power-law exponents for escape rate and related quantities
Fitted to simulation output as described in abstract

axioms (2)

domain assumption Hybrid plasma approximation (kinetic ions, fluid electrons) is sufficient to capture the relevant dynamics
Invoked by choice of simulation method
domain assumption Stellar wind pressure controls the location of the induced magnetosphere boundary independently of the intrinsic dipole in the weak-field regime
Required for the described transition point to exist

pith-pipeline@v0.9.0 · 5712 in / 1440 out tokens · 31733 ms · 2026-05-25T01:43:58.481079+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We find that increasing the strength of a planet's magnetic field enhances ion escape until the magnetic dipole's standoff distance reaches the induced magnetosphere boundary. After this point increasing the planetary magnetic field begins to inhibit ion escape.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Rs = RP (2 Bp² / μ0 ρsw usw²)^{1/6}

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages

[1]

doi:10.1002/2016JA022548. L. Chai, W. Wan, Y. Wei, T. Zhang, W. Exner, M. Fraenz, E. Du- binin, M. Feyerabend, U. Motschmann, Y. Ma, J. S. Halekas, Y. Li, Z. Rong, and J. Zhong. The Induced Global Loop- ing Magnetic Field on Mars. ApJ, 871:L27, February 2019. doi:10.3847/2041-8213/aaﬀ6e. J. W. Chamberlain. Charge exchange in a planetary corona - Its eﬀect...

work page doi:10.1002/2016ja022548 2019
[2]

URL http://www.sciencedirect.com/science/article/ pii/0032063374901664. T. E. Cravens. Physics of Solar System Plasmas. November 2004. T. E. Cravens, E. Howell, J. H. Waite, and G. R. Glad- stone. Auroral oxygen precipitation at Jupiter. Jour- nal of Geophysical Research , 100:17153–17162, Sep 1995. doi:10.1029/95JA00970. Margaret O. Dayhoﬀ, Richard V. Ec...

work page doi:10.1029/95ja00970 2004
[3]

URL https://agupubs

doi:10.1002/2016JA023488. URL https://agupubs. onlinelibrary.wiley.com/doi/abs/10.1002/2016JA023488. C. Dival, E. Kallio, S. Barabash, G. Stenberg, H. Nilsson, Y. Fu- taana, M. Holmstrm, A. Fedorov, R. A. Frahm, R. Jarvinen, and D. A. Brain. A case study of proton precipitation at mars: Mars express observations and hybrid simulations. Journal of Geophysi...

work page doi:10.1002/2016ja023488
[4]

doi:10.1029/2012JA017537

ISSN 2156-2202. doi:10.1029/2012JA017537. URL http://dx.doi.org/10.1029/2012JA017537. A06222. J.-D. do Nascimento, Jr., A. A. Vidotto, P. Petit, C. Folsom, M. Castro, S. C. Marsden, J. Morin, G. F. Porto de Mello, S. Meibom, S. V. Jeﬀers, E. Guinan, and I. Ribas. Magnetic Field and Wind of Kappa Ceti: Toward the Planetary Hab- itability of the Young Sun W...

work page doi:10.1029/2012ja017537 2016
[5]

URL https://agupubs

doi:10.1002/2015GL065346. URL https://agupubs. onlinelibrary.wiley.com/doi/abs/10.1002/2015GL065346. P. Driscoll and D. Bercovici. Divergent evolution of earth and venus: Inﬂuence of degassing, tectonics, and magnetic ﬁelds. Icarus, 226(2):1447 – 1464, 2013. ISSN 0019-1035. doi:https://doi.org/10.1016/j.icarus.2013.07.025. URL http://www.sciencedirect.com...

work page doi:10.1002/2015gl065346 2013
[6]

E Engwall, A I

doi:10.1093/mnras/stz788. E Engwall, A I. Eriksson, C M. Cully, M Andr, Roy Torbert, and H Vaith. Earth’s ionospheric outﬂow dominated by hidden cold plasma. Nature Geoscience, 2:24–27, 01 2009. doi:10.1038/ngeo387. M. Frnz, E. Dubinin, D. Andrews, S. Barabash, H. Nilsson, and A. Fedorov. Cold ion escape from the martian ionosphere. Planetary and Space Sc...

work page doi:10.1093/mnras/stz788 2009
[7]

doi:10.1029/JA092iA07p07606. E. Gaidos, C. P. Conrad, M. Manga, and J. Hernlund. Ther- modynamic Limits on Magnetodynamos in Rocky Exoplan- ets. ApJ, 718:596–609, August 2010. doi:10.1088/0004- 637X/718/2/596. K. Garcia-Sage, A. Glocer, J. J. Drake, G. Gronoﬀ, and O. Co- hen. On the Magnetic Protection of the Atmosphere of Prox- ima Centauri b. ApJ, 844:L...

work page doi:10.1029/ja092ia07p07606 2010
[8]

doi:10.3847/2041-8213/aa79ed. M. Gillon, A. H. M. J. Triaud, B.-O. Demory, E. Jehin, E. Agol, K. M. Deck, S. M. Lederer, J. de Wit, A. Burdanov, J. G. Ingalls, E. Bolmont, J. Leconte, S. N. Raymond, F. Selsis, M. Turbet, K. Barkaoui, A. Burgasser, M. R. Burleigh, S. J. Carey, A. Chaushev, C. M. Copperwheat, L. Delrez, C. S. Fernandes, D. L. Holdsworth, E....

work page doi:10.3847/2041-8213/aa79ed 2041
[9]

doi:10.1038/nature21360. S. Ginzburg, H. E. Schlichting, and R. Sari. Super-Earth Atmo- spheres: Self-consistent Gas Accretion and Retention. ApJ, 825:29, July 2016. doi:10.3847/0004-637X/825/1/29. S. Ginzburg, H. E. Schlichting, and R. Sari. Core-powered mass- loss and the radius distribution of small exoplanets. MNRAS, 476:759–765, May 2018. doi:10.1093...

work page doi:10.1038/nature21360 2016
[10]

doi:10.1016/0032-0633(82)90110-6. B. M. Jakosky and R. J. Phillips. Mars’ volatile and climate history. Nature, 412:237–244, July 2001. B. M. Jakosky, D. Brain, M. Chaﬃn, S. Curry, J. Deighan, J. Gre- bowsky, J. Halekas, F. Leblanc, R. Lillis, J. G. Luhmann, L. Andersson, N. Andre, D. Andrews, D. Baird, D. Baker, J. Bell, M. Benna, D. Bhattacharyya, S. Bo...

work page doi:10.1016/0032-0633(82)90110-6 2001
[11]

doi:10.1002/2017JA024324. R. Jarvinen, E. Kallio, P. Janhunen, S. Barabash, T. L. Zhang, V. Pohjola, and I. Sillanp¨ a¨ a. Oxygen ion escape from Venus in a global hybrid simulation: role of the ionospheric O + ions. Annales Geophysicae, 27:4333–4348, November 2009. doi:10.5194/angeo-27-4333-2009. R. Jarvinen, E. Kallio, and S. Dyadechkin. Hemispheric asy...

work page doi:10.1002/2017ja024324 2009
[12]

URL https://agupubs

doi:10.1029/97GL02201. URL https://agupubs. onlinelibrary.wiley.com/doi/abs/10.1029/97GL02201. R. K. Kopparapu. A Revised Estimate of the Occurrence Rate of Terrestrial Planets in the Habitable Zones around Ke- pler M-dwarfs. ApJ, 767:L8, April 2013. doi:10.1088/2041- 8205/767/1/L8. Yu.N. Kulikov, H. Lammer, H.I.M. Lichtenegger, N. Ter- ada, I. Ribas, C. ...

work page doi:10.1029/97gl02201 2013
[13]

URL https://agupubs

doi:10.1029/97JA03667. URL https://agupubs. onlinelibrary.wiley.com/doi/abs/10.1029/97JA03667. J. G. Luhmann, C. Dong, Y. Ma, S. M. Curry, D. Mitchell, J. Esp- ley, J. Connerney, J. Halekas, D. A. Brain, B. M. Jakosky, and C. Mazelle. Implications of MAVEN Mars near-wake mea- surements and models. Geophys. Res. Lett. , 42:9087–9094, November 2015. doi:10....

work page doi:10.1029/97ja03667 2015
[14]

doi:10.1089/ast.2016.1589. V. G. Merkin and C. C. Goodrich. Does the polar cap area saturate? Geophysical Research Letters , 34(9),

work page doi:10.1089/ast.2016.1589 2016
[15]

URL https://agupubs

doi:10.1029/2007GL029357. URL https://agupubs. onlinelibrary.wiley.com/doi/abs/10.1029/2007GL029357. R. Modolo, S. Hess, M. Mancini, F. Leblanc, J.-Y. Chaufray, D. Brain, L. Leclercq, R. Esteban-Hern´ andez, G. Chanteur, P. Weill, F. Gonz´ alez-Galindo, F. Forget, M. Yagi, and C. Mazelle. Mars-solar wind interaction: LatHyS, an im- proved parallel 3-D mul...

work page doi:10.1029/2007gl029357
[16]

doi:10.1002/2015JA022324. A. F. Nagy, D. Winterhalter, K. Sauer, T. E. Cravens, S. Brecht, C. Mazelle, D. Crider, E. Kallio, A. Za- kharov, E. Dubinin, M. Verigin, G. Kotova, W. I. Axford, C. Bertucci, and J. G. Trotignon. The plasma Environ- ment of Mars. Space Sci. Rev. , 111:33–114, March 2004. doi:10.1023/B:SPAC.0000032718.47512.92. R. Nakamura, W. Ba...

work page doi:10.1002/2015ja022324 2004
[17]

Shotaro Sakai, Kanako Seki, Naoki Terada, Hiroyuki Shina- gawa, Takashi Tanaka, and Yusuke Ebihara

doi:10.1029/JA087iA03p01599. Shotaro Sakai, Kanako Seki, Naoki Terada, Hiroyuki Shina- gawa, Takashi Tanaka, and Yusuke Ebihara. Eﬀects of a weak intrinsic magnetic ﬁeld on atmospheric escape from mars. Geophysical Research Letters , 45(18):9336–9343,

work page doi:10.1029/ja087ia03p01599
[18]

URL https://agupubs

doi:10.1029/2018GL079972. URL https://agupubs. onlinelibrary.wiley.com/doi/abs/10.1029/2018GL079972. A. L. Shields, S. Ballard, and J. A. Johnson. The habitability of planets orbiting M-dwarf stars. Phys. Rep., 663:1, December

work page doi:10.1029/2018gl079972
[19]

doi:10.1016/j.physrep.2016.10.003. J.A. Slavin. Mercury’s magnetosphere. Advances in Space Research, 33(11):1859 – 1874, 2004. ISSN 0273-1177. doi:https://doi.org/10.1016/j.asr.2003.02.019. URL http://www.sciencedirect.com/science/article/pii/ S0273117704000092. Comparative Magnetospheres. T. W. Speiser and N. F. Ness. The neutral sheet in the ge- omagnet...

work page doi:10.1016/j.physrep.2016.10.003 2016

[1] [1]

doi:10.1002/2016JA022548. L. Chai, W. Wan, Y. Wei, T. Zhang, W. Exner, M. Fraenz, E. Du- binin, M. Feyerabend, U. Motschmann, Y. Ma, J. S. Halekas, Y. Li, Z. Rong, and J. Zhong. The Induced Global Loop- ing Magnetic Field on Mars. ApJ, 871:L27, February 2019. doi:10.3847/2041-8213/aaﬀ6e. J. W. Chamberlain. Charge exchange in a planetary corona - Its eﬀect...

work page doi:10.1002/2016ja022548 2019

[2] [2]

URL http://www.sciencedirect.com/science/article/ pii/0032063374901664. T. E. Cravens. Physics of Solar System Plasmas. November 2004. T. E. Cravens, E. Howell, J. H. Waite, and G. R. Glad- stone. Auroral oxygen precipitation at Jupiter. Jour- nal of Geophysical Research , 100:17153–17162, Sep 1995. doi:10.1029/95JA00970. Margaret O. Dayhoﬀ, Richard V. Ec...

work page doi:10.1029/95ja00970 2004

[3] [3]

URL https://agupubs

doi:10.1002/2016JA023488. URL https://agupubs. onlinelibrary.wiley.com/doi/abs/10.1002/2016JA023488. C. Dival, E. Kallio, S. Barabash, G. Stenberg, H. Nilsson, Y. Fu- taana, M. Holmstrm, A. Fedorov, R. A. Frahm, R. Jarvinen, and D. A. Brain. A case study of proton precipitation at mars: Mars express observations and hybrid simulations. Journal of Geophysi...

work page doi:10.1002/2016ja023488

[4] [4]

doi:10.1029/2012JA017537

ISSN 2156-2202. doi:10.1029/2012JA017537. URL http://dx.doi.org/10.1029/2012JA017537. A06222. J.-D. do Nascimento, Jr., A. A. Vidotto, P. Petit, C. Folsom, M. Castro, S. C. Marsden, J. Morin, G. F. Porto de Mello, S. Meibom, S. V. Jeﬀers, E. Guinan, and I. Ribas. Magnetic Field and Wind of Kappa Ceti: Toward the Planetary Hab- itability of the Young Sun W...

work page doi:10.1029/2012ja017537 2016

[5] [5]

URL https://agupubs

doi:10.1002/2015GL065346. URL https://agupubs. onlinelibrary.wiley.com/doi/abs/10.1002/2015GL065346. P. Driscoll and D. Bercovici. Divergent evolution of earth and venus: Inﬂuence of degassing, tectonics, and magnetic ﬁelds. Icarus, 226(2):1447 – 1464, 2013. ISSN 0019-1035. doi:https://doi.org/10.1016/j.icarus.2013.07.025. URL http://www.sciencedirect.com...

work page doi:10.1002/2015gl065346 2013

[6] [6]

E Engwall, A I

doi:10.1093/mnras/stz788. E Engwall, A I. Eriksson, C M. Cully, M Andr, Roy Torbert, and H Vaith. Earth’s ionospheric outﬂow dominated by hidden cold plasma. Nature Geoscience, 2:24–27, 01 2009. doi:10.1038/ngeo387. M. Frnz, E. Dubinin, D. Andrews, S. Barabash, H. Nilsson, and A. Fedorov. Cold ion escape from the martian ionosphere. Planetary and Space Sc...

work page doi:10.1093/mnras/stz788 2009

[7] [7]

doi:10.1029/JA092iA07p07606. E. Gaidos, C. P. Conrad, M. Manga, and J. Hernlund. Ther- modynamic Limits on Magnetodynamos in Rocky Exoplan- ets. ApJ, 718:596–609, August 2010. doi:10.1088/0004- 637X/718/2/596. K. Garcia-Sage, A. Glocer, J. J. Drake, G. Gronoﬀ, and O. Co- hen. On the Magnetic Protection of the Atmosphere of Prox- ima Centauri b. ApJ, 844:L...

work page doi:10.1029/ja092ia07p07606 2010

[8] [8]

doi:10.3847/2041-8213/aa79ed. M. Gillon, A. H. M. J. Triaud, B.-O. Demory, E. Jehin, E. Agol, K. M. Deck, S. M. Lederer, J. de Wit, A. Burdanov, J. G. Ingalls, E. Bolmont, J. Leconte, S. N. Raymond, F. Selsis, M. Turbet, K. Barkaoui, A. Burgasser, M. R. Burleigh, S. J. Carey, A. Chaushev, C. M. Copperwheat, L. Delrez, C. S. Fernandes, D. L. Holdsworth, E....

work page doi:10.3847/2041-8213/aa79ed 2041

[9] [9]

doi:10.1038/nature21360. S. Ginzburg, H. E. Schlichting, and R. Sari. Super-Earth Atmo- spheres: Self-consistent Gas Accretion and Retention. ApJ, 825:29, July 2016. doi:10.3847/0004-637X/825/1/29. S. Ginzburg, H. E. Schlichting, and R. Sari. Core-powered mass- loss and the radius distribution of small exoplanets. MNRAS, 476:759–765, May 2018. doi:10.1093...

work page doi:10.1038/nature21360 2016

[10] [10]

doi:10.1016/0032-0633(82)90110-6. B. M. Jakosky and R. J. Phillips. Mars’ volatile and climate history. Nature, 412:237–244, July 2001. B. M. Jakosky, D. Brain, M. Chaﬃn, S. Curry, J. Deighan, J. Gre- bowsky, J. Halekas, F. Leblanc, R. Lillis, J. G. Luhmann, L. Andersson, N. Andre, D. Andrews, D. Baird, D. Baker, J. Bell, M. Benna, D. Bhattacharyya, S. Bo...

work page doi:10.1016/0032-0633(82)90110-6 2001

[11] [11]

doi:10.1002/2017JA024324. R. Jarvinen, E. Kallio, P. Janhunen, S. Barabash, T. L. Zhang, V. Pohjola, and I. Sillanp¨ a¨ a. Oxygen ion escape from Venus in a global hybrid simulation: role of the ionospheric O + ions. Annales Geophysicae, 27:4333–4348, November 2009. doi:10.5194/angeo-27-4333-2009. R. Jarvinen, E. Kallio, and S. Dyadechkin. Hemispheric asy...

work page doi:10.1002/2017ja024324 2009

[12] [12]

URL https://agupubs

doi:10.1029/97GL02201. URL https://agupubs. onlinelibrary.wiley.com/doi/abs/10.1029/97GL02201. R. K. Kopparapu. A Revised Estimate of the Occurrence Rate of Terrestrial Planets in the Habitable Zones around Ke- pler M-dwarfs. ApJ, 767:L8, April 2013. doi:10.1088/2041- 8205/767/1/L8. Yu.N. Kulikov, H. Lammer, H.I.M. Lichtenegger, N. Ter- ada, I. Ribas, C. ...

work page doi:10.1029/97gl02201 2013

[13] [13]

URL https://agupubs

doi:10.1029/97JA03667. URL https://agupubs. onlinelibrary.wiley.com/doi/abs/10.1029/97JA03667. J. G. Luhmann, C. Dong, Y. Ma, S. M. Curry, D. Mitchell, J. Esp- ley, J. Connerney, J. Halekas, D. A. Brain, B. M. Jakosky, and C. Mazelle. Implications of MAVEN Mars near-wake mea- surements and models. Geophys. Res. Lett. , 42:9087–9094, November 2015. doi:10....

work page doi:10.1029/97ja03667 2015

[14] [14]

doi:10.1089/ast.2016.1589. V. G. Merkin and C. C. Goodrich. Does the polar cap area saturate? Geophysical Research Letters , 34(9),

work page doi:10.1089/ast.2016.1589 2016

[15] [15]

URL https://agupubs

doi:10.1029/2007GL029357. URL https://agupubs. onlinelibrary.wiley.com/doi/abs/10.1029/2007GL029357. R. Modolo, S. Hess, M. Mancini, F. Leblanc, J.-Y. Chaufray, D. Brain, L. Leclercq, R. Esteban-Hern´ andez, G. Chanteur, P. Weill, F. Gonz´ alez-Galindo, F. Forget, M. Yagi, and C. Mazelle. Mars-solar wind interaction: LatHyS, an im- proved parallel 3-D mul...

work page doi:10.1029/2007gl029357

[16] [16]

doi:10.1002/2015JA022324. A. F. Nagy, D. Winterhalter, K. Sauer, T. E. Cravens, S. Brecht, C. Mazelle, D. Crider, E. Kallio, A. Za- kharov, E. Dubinin, M. Verigin, G. Kotova, W. I. Axford, C. Bertucci, and J. G. Trotignon. The plasma Environ- ment of Mars. Space Sci. Rev. , 111:33–114, March 2004. doi:10.1023/B:SPAC.0000032718.47512.92. R. Nakamura, W. Ba...

work page doi:10.1002/2015ja022324 2004

[17] [17]

Shotaro Sakai, Kanako Seki, Naoki Terada, Hiroyuki Shina- gawa, Takashi Tanaka, and Yusuke Ebihara

doi:10.1029/JA087iA03p01599. Shotaro Sakai, Kanako Seki, Naoki Terada, Hiroyuki Shina- gawa, Takashi Tanaka, and Yusuke Ebihara. Eﬀects of a weak intrinsic magnetic ﬁeld on atmospheric escape from mars. Geophysical Research Letters , 45(18):9336–9343,

work page doi:10.1029/ja087ia03p01599

[18] [18]

URL https://agupubs

doi:10.1029/2018GL079972. URL https://agupubs. onlinelibrary.wiley.com/doi/abs/10.1029/2018GL079972. A. L. Shields, S. Ballard, and J. A. Johnson. The habitability of planets orbiting M-dwarf stars. Phys. Rep., 663:1, December

work page doi:10.1029/2018gl079972

[19] [19]

doi:10.1016/j.physrep.2016.10.003. J.A. Slavin. Mercury’s magnetosphere. Advances in Space Research, 33(11):1859 – 1874, 2004. ISSN 0273-1177. doi:https://doi.org/10.1016/j.asr.2003.02.019. URL http://www.sciencedirect.com/science/article/pii/ S0273117704000092. Comparative Magnetospheres. T. W. Speiser and N. F. Ness. The neutral sheet in the ge- omagnet...

work page doi:10.1016/j.physrep.2016.10.003 2016