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Constraining Ongoing Volcanic Outgassing Rates and Interior Compositions of Extrasolar Planets with Mass Measurements of Plasma Tori

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A circumstellar plasma torus, if detected around a close-in rocky exoplanet, would be direct evidence of ongoing volcanism and would bound each species' outgassing rate to an order of magnitude.

desk verdict Useful forward model for exoplanet plasma tori, but the scale-height temperature choice inflates feasibility by ~10^3; fixable, worth refereeing. read the letter →

arxiv 2506.08177 v1 pith:DXRNDDIY submitted 2025-06-09 astro-ph.EP physics.space-ph

V. Abby Boehm , Darryl Z. Seligman , Nikole K. Lewis This is my paper
classification astro-ph.EPphysics.space-ph
keywords plasmatorusexoplanetvolcanismtidalheatingmagnetosphericconvectionAlfvénradiusultravioletspectroscopyGJ367brockyexoplanets
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims that volcanically active rocky exoplanets on short, eccentric orbits can build circumstellar plasma tori, the same kind of structure Io maintains inside Jupiter's magnetosphere, and that these tori would be observable as atomic absorption features in the host star's ultraviolet spectrum. Because the torus is dispersed by magnetospheric convection in weeks to months, its mere presence implies recent and ongoing volcanic replenishment, making it a direct probe of active volcanism rather than a fossil signature. The paper's central inequality, Eq. 16, converts the measured absorption strength of any atomic species into an order-of-magnitude upper limit on the volcanic outgassing rate of that species, and the pattern of detected and missing species constrains the planet's interior composition. Applying this to known terrestrial exoplanets, the paper identifies GJ 367 b as the most promising target, where Io-like outgassing of about one ton per second could already produce detectable absorption. If correct, the method would give the first quantitative access to the internal heating and volatile content of an intact exoplanet, information currently available only after a planet is torn apart by tides.

What carries the argument

The central object is the hypothetical circumstellar plasma torus, a quasi-steady ring of ionized volcanic material confined by the host star's magnetic field and forced to corotate with it, modeled directly on Jupiter's Io plasma torus. The argument runs on the mass balance between injection and the flux-tube interchange of magnetospheric convection, with the Alfvén radius $R_A$ marking the boundary where magnetic confinement loses to the stellar wind. The torus is approximated as a uniform-density warm torus occupying three scale heights $H_i = \sqrt{2k_B T/(3m_i\Omega^2)}$ beyond the planet's orbit, so a line-of-sight column $3H_i n_i$ produces absorption $f_{\mathrm{abs},i}\simeq 3H_i n_i\sigma_i$. Equation 16 ties these ingredients together, with $R_A$ and $\Omega$ carrying the star's influence and $H_i$, $\sigma_i$, and $m_i$ carrying the species dependence.

What would settle it

Observe GJ 367 A with a UV spectrograph at the C-II 134 nm and O-I 130 nm lines over multiple epochs spaced months apart, reaching sensitivity to 10% absorption. If the star shows no variable, species-selective absorption even though the planet outgasses above the Table 2 thresholds, the torus model underlying Eq. 16 is falsified for that system; conversely, variable absorption that tracks stellar rotation phase would confirm the torus and its magnetospheric confinement.

Watch

Extended reading notes

Core claim

The central claim is that the quasi-steady mass of a circumstellar plasma torus is set by the balance between volcanic injection and removal by corotating magnetospheric convection, and that this mass can be read off from atomic absorption lines. Combining the convection timescale $\tau\gtrsim \sqrt{2/3}(R_A/a)^2 \Omega^{-1}$ with a warm-torus geometry of thickness three scale heights $H_i$ yields $f_{\mathrm{esc},i}\dot{M}_{\mathrm{volc},i}\lesssim (3/2)^{5/2}\pi^2 f_{\mathrm{abs},i}(H_i^2/\sigma_i)(a/R_A)^2 (1+2a/(3H_i)) m_i\Omega$, where $f_{\mathrm{abs},i}$ is the measured line absorption strength, $\sigma_i$ the absorbing cross section, $m_i$ the ion mass, $a$ the orbit radius, $R_A$ the stellar Alfvén radius, and $\Omega$ the stellar spin rate. This inequality is the load-bearing result: it turns a spectrum into an upper limit on volcanic outgassing per species, and it makes the detection itself a proof of ongoing volcanism because the torus cannot survive without continuous replenishment.

Load-bearing premise

The load-bearing premise is that each host star's magnetosphere can be treated as a symmetric dipole whose Alfvén radius is set by log-normal priors on field strength (mean 200 G, width 0.5 dex) and wind mass-loss rate (mean $10^{-14}\,M_\odot$/yr, width 0.5 dex); if the true Alfvén surface is smaller, more time-variable, or shredded by flares and coronal mass ejections, the predicted torus masses and detectability fall by orders of magnitude.

Editorial extensions

If this is right

  • A detected plasma torus is a timestamp: since the torus disperses in weeks to months, its observation proves that the planet is volcanically active now, not merely that it was active sometime in the past.
  • Measured absorption strengths give order-of-magnitude upper limits on each detected species' outgassing rate, so the ratio of detected to absent species (e.g., sulfur-rich, carbon-poor like Io) constrains the mantle's volatile inventory.
  • Because the quasi-steady torus mass scales as $\sim R_A^2$, torus measurements also constrain the host star's magnetic field strength and wind mass-loss rate, turning the torus into a stellar magnetosphere probe.
  • For GJ 367 b, total outgassing near 50 tons per second would produce 10% absorption in multiple carbon, oxygen, sodium, sulfur, and potassium lines, within reach of current UV-optical instruments; Io-like and Earth-like rates of 1-10 tons per second suffice for a few species.
  • Torus observations are not phase-constrained like transits, so they can be scheduled at any time, which removes a major practical barrier to follow-up with space observatories.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's formalism could be applied to archival ultraviolet spectra of M dwarfs already known to host close-in rocky planets, searching for torus absorption without new observations.
  • If torus mass tracks stellar magnetic activity, long-term monitoring would reveal stellar magnetic cycles from the waxing and waning of absorption strength, a diagnostic the paper mentions but does not develop.
  • Non-detections will be ambiguous: because the predicted mass scales as $R_A^2$ and $R_A$ is uncertain by roughly an order of magnitude, a null detection could mean either no volcanism or a smaller Alfvén surface, so the strongest scientific return comes from positive detections.
  • The same mass-balance argument should apply to volcanically active exomoons orbiting giant exoplanets inside their host magnetospheres, extending the method to a population the paper does not target.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript proposes a method for detecting ongoing volcanic outgassing from exoplanets via circumstellar plasma tori. It scales the Io plasma torus physics to star-planet systems: volcanic mass loss is ionized and confined by the stellar magnetosphere, the quasi-steady torus mass is set by the injection rate times a magnetospheric convection timescale (Eq. 13), and torus absorption against the stellar disc is related to the species-specific injected mass rate (Eq. 16). The authors identify 13 high-priority targets, estimate Alfvén radii from log-normal priors on B* and Mdot_wind, and tabulate the outgassing rates needed to produce 10% absorption features, highlighting GJ 367 b as the most promising candidate. The paper is candid about several caveats, including the Hill et al. convection-timescale underestimation, the unmeasured escape fraction fesc, and ISM/stellar contamination.

Significance. If the method is correct, it offers a genuinely new observable for ongoing exoplanetary volcanism and interior composition, with a clear external anchor in the Io torus and a measurement that is not phase-constrained like transits. The analytic derivation in Section 3 is transparent and algebraically sound, the software is made available on Zenodo/GitHub, and the caveat section is unusually thorough for a proposal paper. The principal value is as a feasibility framework for future UV missions. The quantitative claims in Tables 1 and 2 should, however, be read as illustrative scalings rather than robust predictions, because the required rates depend strongly on several unmeasured or order-of-magnitude-uncertain inputs, notably the torus plasma temperature, the stellar magnetosphere priors, and the treatment of neutral species.

major comments (3)
  1. [Section 2.5, Eq. (11), Table 2] The torus scale height H in Eq. (11) is evaluated with T = Teq (1000–2000 K), but the relevant temperature for magnetically confined torus plasma is the post-pickup plasma temperature, not the planet's equilibrium temperature. The pickup energies quoted in Section 2.1 are tens of keV per ion for GJ 367 b, and the Io warm torus—the benchmark for this model—has T ~ 10^5 K rather than 10^3 K. Because Eq. (16) scales as (H_i^2/σ_i)(1 + 2a/(3H_i)), increasing T to 10^5 K raises the required injection rates in Table 2 by roughly two to three orders of magnitude (the scaling transitions from ~T to ~T^{3/2} once H_i becomes comparable to a). For several targets, 3H would then exceed R_A, violating the confinement geometry used to derive Eqs. (12)–(16). I recommend recomputing Table 2 with a physical torus temperature, or explicitly presenting the rates as functions of T over a wide range.
  2. [Sections 3.2.1 and 4, Table 2] Section 3.2.1 explicitly states that Eq. (16) cannot be used as-is for neutral clouds because the volume and removal timescale differ for neutral material, yet Table 2 and Section 4 quote required rates for C-I, O-I, Na-I, S-I, and K-I (and totals that include these species) using Eq. (16). This inconsistency directly affects the headline claim that Io-like rates of order 1 t/s of carbon and sodium would produce detectable absorption around GJ 367 b. The neutral-species rates should either be derived from an explicit neutral-cloud model or removed from Table 2, leaving the quantitative method to the ionic lines (C-II, S-II, S-III).
  3. [Tables 1 and 2, Eq. (16)] Table 2 reports single-valued required outgassing rates with no propagated uncertainties, even though the inputs R_A (log-normal priors of width 0.5 dex on B* and Mdot_wind), fesc, and T each carry factors of a few to orders of magnitude. Since Eq. (16) depends on (a/R_A)^2, the ~50% R_A uncertainties in Table 1 alone change the quoted rates by factors of roughly 2–4, and the prior widths imply larger excursions. Because the central comparison is whether required rates are 'realistic' (1–10 t/s) or exceptional (>100 t/s), the conclusions are sensitive to these unpropagated inputs. I recommend reporting the rates as ranges, or at least stating the dominant error terms and their effect on the Table 2 values.
minor comments (5)
  1. [Section 2.2, paragraph after Eq. (5)] The statement that changes in B* by a factor of ~2 can yield order-of-magnitude changes in the quasi-steady torus mass is not supported by Eq. (5): for large η*, R_A ∝ η*^{1/4}, so M_torus ∝ R_A^2 ∝ B*, i.e., a factor of 2 in B* changes the mass by a factor of ~2, not ~10.
  2. [Abstract] The abstract's phrase 'with minimal assumptions' overstates the method's current status: the calculation requires priors on B* and Mdot_wind, an assumed torus geometry and temperature, and the unmeasured escape fraction fesc. I suggest rewording to 'with a small number of stated assumptions' or similar.
  3. [Section 5.6] The text says 'HST STIS/FUV-MAMA low-resolution gratings can recover near-UV emission lines'; since FUV-MAMA is the far-UV channel, this should likely read NUV-MAMA for near-UV, or the wavelength range should be corrected.
  4. [Section 5.1.3] The target name 'HD 63443 d' appears twice; it should be 'HD 63433 d', matching Table 1 and the rest of the text.
  5. [Section 5.3] The sentence about the Hill et al. (1981) timescale being underestimated by ~100 and outgassing rates being overestimated is correct but could be clarified: because Eq. (16) is an upper limit, a larger true τ makes the inferred upper bound more stringent, not less.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; the derivation is a self-contained forward model and the self-citations are not load-bearing.

full rationale

The paper's central derivation chain (Eqs. 10-16) is an analytic forward model: it combines the Hill et al. (1981) magnetospheric convection timescale, a dipolar Alfvén radius estimate with explicitly stated log-normal priors, and the Bagenal (1994) scale height to relate an assumed absorption strength fabs to the required volcanic injection rate fesc Mdot_volc. No parameter is fitted to the output it is used to predict; Table 2 is a detectability-threshold calculation for hypothetical 10% absorption features, not an inversion of measured data. The paper explicitly labels Eq. 10 as a lower bound and Eq. 16 as an upper limit, and Section 5.3 acknowledges that the convection timescale may be underestimated, which only strengthens the conservative direction of the bounds. The self-citations (Seligman et al. 2022, 2024; Feinstein et al. 2022) are used for tidal-heating scaling and flare statistics, which are ancillary to the main derivation and rest on standard results (Beuthe 2013; Peale & Cassen 1978). The temperature assumption for the torus scale height (Teq versus pickup-heated plasma) is a physical modeling choice, not a circular step; it affects numerical predictions but does not reduce Eq. 16 to its own inputs by definition. Therefore no circular step can be exhibited, and the paper is not circular in any load-bearing sense.

Assumptions & free parameters 5 free parameters · 6 assumptions · 1 invented entities

The central calculation rests on roughly five hand-chosen inputs or unvalidated analogies: the stellar B* and Mdot_wind priors (which set RA and hence Mtorus), the escape fraction fesc, the 3H torus thickness, and the torus pressure/temperature. The physics of the Io torus supplies the geometric and dynamical template; the extrapolation to star-planet systems is the paper's core assumption. No new fundamental entities are introduced beyond the hypothetical torus itself, which is a falsifiable prediction rather than an ad hoc contrivance.

free parameters (5)
  • Stellar surface magnetic field prior B* = log-normal mean 200 G, width 0.5 dex
    Central input for RA via Eq. 4-5; not measured per target, chosen from GKM star literature (Section 2.2).
  • Stellar wind mass-loss prior Mdot_wind = log-normal mean log10(Mdot_wind[Msun/yr]) = -14, width 0.5 dex
    Also sets RA through Eq. 4-5; has order-of-magnitude uncertainty (Section 2.2).
  • Atmospheric escape fraction fesc = assumed 1
    Only the product fesc * Mdot_volc is observable (Eq. 16); paper argues fesc~1 from photoevaporation but cannot rule out smaller values (Section 5.4).
  • Torus thickness factor = 3 scale heights (H from Eq. 11)
    Warm-torus analog containing ~90% of mass; directly sets column density 3Hn in Eq. 14 and volume in Eq. 12.
  • Torus plasma temperature/pressure for line profiles = T=1000 K, p=1 nbar
    Controls thermal/pressure broadening in Cthulhu cross-section calculation; affects required rates in Table 2 (Section 4, Section 5.1.2).
assumptions (6)
  • standard math Plasma behaves as an ideal MHD fluid and is confined to stellar magnetic field lines.
    Invoked at start of Section 2, referenced to Priest (2014), underpins all torus confinement.
  • domain assumption Stellar magnetosphere is azimuthally symmetric, dipolar, and corotates with the star; orbital angular momentum aligned.
    Eq. 1 and assumptions (i)-(iii) in Section 2; used for RA, tau, and torus geometry.
  • domain assumption Magnetospheric convection timescale from Hill et al. (1981), Eq. 10, scales to star-planet systems despite known ~100x underestimate at Io.
    Used to convert torus mass to outgassing rate; authors acknowledge it is a lower bound and likely overestimates rates (Section 5.3).
  • domain assumption Outgassed material is substantially ionized and picked up by the stellar magnetosphere with fesc ~ 1.
    Required for torus formation; supported by photoevaporation arguments and GJ 367 b's airless eclipse observation, but not directly measured (Sections 2.1, 5.4).
  • domain assumption Torus density is uniform within a torus of thickness 3H; number density follows isotropic exponential diffusion with scale height H.
    Underlies Eq. 11, 12, 14, 15; Io torus has significant radial/vertical variations, so this is an order-of-magnitude simplification (Sections 2.5, 5.3).
  • domain assumption Atomic absorption cross-sections from Cthulhu/VALD are accurate at torus conditions.
    Used to compute fabs and required rates in Table 2; uncertainty in line-list data is not propagated.
invented entities (1)
  • Circumstellar plasma torus (hypothetical) independent evidence
    purpose: Observable tracer of ongoing exoplanet volcanic outgassing; mass and absorption lines encode outgassing rate and composition.
    No torus has been detected. The paper supplies falsifiable handles: predicted atomic absorption-line strengths at specified wavelengths for specific target stars (Table 2, Figure 6), observable with HST and future UV missions. No independent evidence outside this paper yet, but the handle is falsifiable.

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Cite this review

Pith. "Pith review of Constraining Ongoing Volcanic Outgassing Rates and Interior Compositions of Extrasolar Planets with Mass Measurements of Plasma Tori." pith.science (2026). https://pith.science/paper/DXRNDDIY

@misc{pith2026250608177,
  author       = {Pith},
  title        = {Pith review of: Constraining Ongoing Volcanic Outgassing Rates and Interior Compositions of Extrasolar Planets with Mass Measurements of Plasma Tori},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DXRNDDIY}},
  note         = {Machine review of arXiv:2506.08177}
}
abstract

We present a novel method of constraining volcanic activity on extrasolar terrestrial worlds via characterization of circumstellar plasma tori. Our work generalizes the physics of the Io plasma torus to propose a hypothetical circumstellar plasma torus generated by exoplanetary volcanism. The quasi-steady torus mass is determined by a balance between material injection and ejection rates from volcanic activity and corotating magnetospheric convection, respectively. By estimating the Alfv\'en surfaces of planet-hosting stars, we calculate the torus mass-removal timescale for a number of exoplanets with properties amenable to plasma torus construction. Assuming a uniform toroidal geometry comparable to Io's "warm" torus, we calculate quasi-steady torus masses inferable from the optical depth of atomic spectral features in torus-contaminated stellar spectra. The calculated quasi-steady masses can be used to constrain the volcanic outgassing rates of each species detected in the torus, providing quantitative estimates of bulk volcanic activity and interior composition with minimal assumptions. Such insight into the interior state of an exoplanet is otherwise accessible only after destruction via tidal forces. We demonstrate the feasibility of our method by showcasing known exoplanets which are susceptible to tidal heating and could generate readily-detectable tori with realistic outgassing rates of order 1 ton s$^{-1}$, comparable to the Io plasma torus mass injection rate. This methodology may be applied to stellar spectra measured with ultraviolet instruments with sufficient resolution to detect atomic lines and sensitivity to recover the ultraviolet continuum of GKM dwarf stars. This further motivates the need for ultraviolet instrumentation above Earth's atmosphere.

Figures

Figures reproduced from arXiv: 2506.08177 by the authors.

Figure 1
Figure 1. Stellar Alfv´en radii of stars with measured masses, radii, and spin periods which are also known to host terrestrial exoplanets. For the 33 exoplanets which orbit at a < RA, magnetic confinement is strong enough to permit construction of plasma tori. Io is plotted in terms of Jupiter radii RJ; the Jovian Alfv´en radius is sourced from McNutt et al. (1979) and Hill (1980). Targets in the grey region or￾bit outside o… view at source ↗
Figure 2
Figure 2. Radiation magnetic confinement parameter ζ for the 33 exoplanets which orbit at a < RA identified in [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Magnetospheric convection timescale τ over which mass injected into a plasma torus by an exoplanet at distance a/RA would be removed. Less time is required to remove mass when the injection occurs closer to the Alfv´en radius. We calculate τ with Equation 10 using the same as￾sumptions and exoplanets as in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Schematic illustration of the plasma torus (grey) built by a volcanically-active exoplanet (red shaded circle) in orbit around a star (yellow circle), with a neutral cloud extending a few planetary radii ahead and behind the source exoplanet (dotted grey). a. The torus…
Figure 5
Figure 5. Figure 5: Magnetospheric convection timescale shows a positive correlation with the tidal heating rate. This sug￾gests that exoplanets which are well-positioned for plasma torus construction will generally also receive the necessary tidal power to drive volcanism. This plot incl…
Figure 6
Figure 6. Figure 6: Measurable contamination by a hypothetical plasma torus in the GJ 367 system. Top: Model spectrum (S. Peacock, private communication) of the M dwarf star GJ 367 A (solid black), using stellar parameters Teff = 3560 K, log g = 4.78 in cgs units, M = 0.44 M⊙, and [Fe/H] …
Figure 7
Figure 7. Figure 7: The 13 high-priority exoplanets highlighted in this study as they appear on the thermal cosmic shoreline. With increasing vertical distance above the shoreline, the likelihood of substantial volatile depletion rises. Many of our target exoplanets lie above or near the …
Figure 8
Figure 8. Figure 8: The 13 high-priority exoplanets highlighted in this study as they appear on the XUV-driven cosmic shoreline. With increasing vertical distance above the shoreline, the likelihood of substantial volatile depletion rises. All but one of our targets lie above the XUV-driv…
Figure 9
Figure 9. Figure 9: B∗ and M˙ wind priors and resultant RA posterior for GJ 367 A (R∗ = 0.458 R⊕, v∞ ≃ 616 km s−1 ; from Goffo et al. 2023). Left: Log-normal prior for B∗. As an M dwarf star with P∗ = 51.3 days, the most probable value of magnetic field strength for GJ 367 A is B∗ = 200+2…

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Pith tools

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