M Dwarf Cosmic Shoreline: Atmospheric Retention Boundaries

• M dwarf cosmic shoreline is a boundary defined by cumulative XUV fluence versus planetary escape velocity that predicts atmospheric retention or loss.
• It links prolonged high-energy emissions from fully convective M dwarfs with enhanced atmospheric stripping, emphasizing the roles of gravity and irradiation history.
• Revised fluence models show that only rocky worlds with high escape velocities, such as super-Earths, are prime candidates for retaining substantial atmospheres.

The M dwarf cosmic shoreline is the extension of the cosmic shoreline concept to rocky planets orbiting M stars, especially mid-to-late, fully convective M dwarfs. It is usually formulated in the plane of cumulative stellar X-ray plus extreme-ultraviolet fluence, $I_{\rm XUV}$, versus planetary escape velocity, $v_{\rm esc}$, where planets below the boundary are more likely to retain substantial atmospheres and planets above it are more likely to be stripped. Around M dwarfs, the boundary is inferred to shift because these stars sustain elevated high-energy emission for long intervals, so atmospheric survival depends more stringently on a planet’s gravity and irradiation history than in Solar-System-based calibrations (Pass et al., 1 Apr 2025, Zahnle et al., 2017).

1. Classical shoreline and physical interpretation

In its classical form, the shoreline is an empirical relation between irradiation and escape speed. Zahnle and Catling found that the Solar System dividing line follows

$I \propto v_{\rm esc}^4,$

or, in logarithmic form,

$$\log_{10} I = 4\,\log_{10} v_{\rm esc} + \mathrm{const}.$$

Bodies with atmospheres lie to the lower right of this relation and air-free worlds to the upper left. In the M-dwarf context, the same diagram is commonly recast using cumulative XUV fluence rather than bolometric instellation, because X-ray and EUV photons are the proximate drivers of upper-atmosphere escape (Zahnle et al., 2017).

The physical meaning of the shoreline is not unique. In the simple energy-limited picture, atmospheric escape scales with the incident high-energy flux relative to gravitational binding, yielding a characteristic scaling

$I_{\rm xuv}\propto v_{\rm esc}^3\sqrt{\rho},$

which differs from the empirical $v_{\rm esc}^4$ law. Zahnle and Catling also emphasized diffusion-limited escape and impact erosion as additional channels: diffusion-limited escape bounds H$_2$ loss to $\sim0.5\%$ of planetary mass over 5 Gyr for $T\sim1000$ K, while impact erosion empirically corresponds to $v_{\rm imp}\simeq4\mbox{–}5\,v_{\rm esc}$ (Zahnle et al., 2017).

Recent analytic work on secondary atmospheres has added another layer. For N$v_{\rm esc}$0- and CO$v_{\rm esc}$1-dominated atmospheres, hydrodynamic loss is described as an onset problem: a critical XUV flux must first be exceeded before transonic outflow begins. In this framework, escape rates remain approximately linear in $v_{\rm esc}$2 in a weakly ionized, energy-limited regime, but flatten to $v_{\rm esc}$3 once forbidden-line cooling produces a collisional-radiative thermostat. This places the M-dwarf shoreline in a regime where high molecular weight, ionization state, and line cooling are intrinsic to the boundary rather than secondary corrections (Chatterjee et al., 2024).

2. Why the shoreline shifts around mid-to-late M dwarfs

Earlier M-dwarf shoreline estimates often extrapolated from more massive stars using a canonical XUV scaling,

$v_{\rm esc}$4

together with the historical XUV instellation relation

$v_{\rm esc}$5

Pass et al. argued that this prescription is inadequate for mid-to-late M dwarfs because fully convective stars exhibit rotation and activity histories that differ from Sun-like stars and early M dwarfs (Pass et al., 1 Apr 2025).

For $v_{\rm esc}$6, the revised treatment adopts a saturated fractional X-ray luminosity

$v_{\rm esc}$7

and a stellar-mass-dependent saturation lifetime

$v_{\rm esc}$8

Neglecting pre-main-sequence and flaring corrections, the historical XUV fluence is written as

$v_{\rm esc}$9

Including the pre-main-sequence luminosity correction $I \propto v_{\rm esc}^4,$0 and the energetic-flare factor $I \propto v_{\rm esc}^4,$1 gives

$I \propto v_{\rm esc}^4,$2

These prescriptions formalize the statement that the M-dwarf shoreline “recedes”: the same orbital location corresponds to a much larger time-integrated high-energy dose than canonical scaling would imply (Pass et al., 1 Apr 2025).

3. Revised fluence histories and the receding shoreline

Using the revised activity-lifetime synthesis, the base mid-to-late M-dwarf model yields historical $I \propto v_{\rm esc}^4,$3 values that are on average $I \propto v_{\rm esc}^4,$4 the Zahnle et al. prescription. When pre-main-sequence evolution and energetic flares are included, the enhancement rises to $I \propto v_{\rm esc}^4,$5 on average. The largest discrepancy, $I \propto v_{\rm esc}^4,$6, occurs near $I \propto v_{\rm esc}^4,$7, where a canonical $I \propto v_{\rm esc}^4,$8 Gyr is a poor match to the revised $I \propto v_{\rm esc}^4,$9 Gyr saturation lifetime (Pass et al., 1 Apr 2025).

Within the cosmic shoreline paradigm, this shift is consequential for known rocky planets. Pass et al. found that almost all small planets with $$\log_{10} I = 4\,\log_{10} v_{\rm esc} + \mathrm{const}.$$0 around inactive mid-to-late M dwarfs fall above the updated shoreline, implying likely atmospheric loss. The best atmosphere-retention candidates are the largest terrestrial worlds, with $$\log_{10} I = 4\,\log_{10} v_{\rm esc} + \mathrm{const}.$$1. In the same interpretation, small Earth-mass planets around mid-to-late M dwarfs are generally predicted to be airless, while super-Earths with $$\log_{10} I = 4\,\log_{10} v_{\rm esc} + \mathrm{const}.$$2 and $$\log_{10} I = 4\,\log_{10} v_{\rm esc} + \mathrm{const}.$$3 are the principal candidate class for retained atmospheres (Pass et al., 1 Apr 2025).

This conclusion is consistent with analytic secondary-atmosphere escape models. In those models, planets with $$\log_{10} I = 4\,\log_{10} v_{\rm esc} + \mathrm{const}.$$4 are expected to exceed the critical XUV threshold during the long saturated phases of active M dwarfs, whereas more massive super-Earths can remain below that threshold. The examples explicitly discussed are TRAPPIST-1 b, placed well into the rapid-loss regime; LHS 1140 c, placed near the boundary; and LHS 1140 b, placed safely in the retention regime (Chatterjee et al., 2024).

4. Quantitative descriptors and probabilistic generalizations

To rank individual planets, Pass et al. introduced the Atmosphere Retention Metric (ARM), defined as the log-space distance from the shoreline: $$\log_{10} I = 4\,\log_{10} v_{\rm esc} + \mathrm{const}.$$5 with $$\log_{10} I = 4\,\log_{10} v_{\rm esc} + \mathrm{const}.$$6 in $$\log_{10} I = 4\,\log_{10} v_{\rm esc} + \mathrm{const}.$$7 and $$\log_{10} I = 4\,\log_{10} v_{\rm esc} + \mathrm{const}.$$8 in Earth units. By construction, $$\log_{10} I = 4\,\log_{10} v_{\rm esc} + \mathrm{const}.$$9 places a planet above the shoreline and implies likely complete atmospheric loss, while $I_{\rm xuv}\propto v_{\rm esc}^3\sqrt{\rho},$0 places it below the shoreline and makes retention more probable (Pass et al., 1 Apr 2025).

A separate strand of the literature replaces reconstructed XUV histories with a three-dimensional boundary in escape velocity, bolometric flux, and host luminosity: $I_{\rm xuv}\propto v_{\rm esc}^3\sqrt{\rho},$1 Under the restrictive assumption that one planar boundary applies across a wide parameter space, the inferred indices are

$I_{\rm xuv}\propto v_{\rm esc}^3\sqrt{\rho},$2

The condition $I_{\rm xuv}\propto v_{\rm esc}^3\sqrt{\rho},$3 intersects at

$I_{\rm xuv}\propto v_{\rm esc}^3\sqrt{\rho},$4

roughly spectral type M4.5V, below which Earth-sized planets at nominal habitable-zone instellation are inferred to be more likely to have lost atmospheres (Berta-Thompson et al., 2 Jul 2025).

This three-dimensional framework is explicitly probabilistic rather than deterministic. The atmosphere probability is written as

$I_{\rm xuv}\propto v_{\rm esc}^3\sqrt{\rho},$5

where $I_{\rm xuv}\propto v_{\rm esc}^3\sqrt{\rho},$6 is the intrinsic width or “fuzziness” of the boundary. The fit was performed with NUTS in numpyro, using uninformative priors on the slopes and latent true parameters for $I_{\rm xuv}\propto v_{\rm esc}^3\sqrt{\rho},$7, $I_{\rm xuv}\propto v_{\rm esc}^3\sqrt{\rho},$8, and $I_{\rm xuv}\propto v_{\rm esc}^3\sqrt{\rho},$9. In this formulation, luminosity serves as an ensemble-level proxy for integrated XUV history, partially avoiding star-by-star historical reconstruction (Berta-Thompson et al., 2 Jul 2025).

5. Known planets, boundary cases, and survey design

Applying the revised mid-to-late M-dwarf fluence history to nearby terrestrial planets leaves only a small set of strong retention candidates. Pass et al. reported that the planets with $v_{\rm esc}^4$0 are the largest known terrestrial worlds around mid-to-late M dwarfs, and that all other known $v_{\rm esc}^4$1 mid-to-late M-dwarf planets within 50 pc have $v_{\rm esc}^4$2 (Pass et al., 1 Apr 2025).

Planet	$v_{\rm esc}^4$3 (km s$v_{\rm esc}^4$4)	ARM
TOI-715 b	20.2	+0.28
TOI-6002 b	22.2	+0.12
TOI-1452 b	22.7	+0.21
LHS 1140 b	23.9	+0.72

For these same planets, the corrected fluences tabulated by Pass et al. are $v_{\rm esc}^4$5, $v_{\rm esc}^4$6, $v_{\rm esc}^4$7, and $v_{\rm esc}^4$8 in Earth XUV units, respectively (Pass et al., 1 Apr 2025).

A temperate example near the boundary is GJ 3378 b. The revised orbital solution gives $v_{\rm esc}^4$9 d, $_2$0, $_2$1 AU, $_2$2, an estimated $_2$3, and $_2$4. Its integrated XUV exposure is $_2$5 Earth’s, and its best-estimate metric, $_2$6, places it essentially on the dividing line, making it a literal case of a planet “straddling the cosmic shoreline” (Robertson et al., 15 May 2026).

At survey scale, the shoreline has also been framed as a population-level hypothesis test for the JWST Rocky Worlds DDT program. Ih et al. compared Pessimist, Random, Bolometric Shoreline, and XUV Shoreline models using secondary-eclipse depths, endmember bare-rock and shallow-CO$_2$7-atmosphere templates, and Bayesian Information Criterion model comparison. In that framework, a $_2$8 h MIRI/F1500W campaign can either place a 95% upper limit of $_2$9 on the atmosphere occurrence rate if all planets are bare, or recover strong evidence $\sim0.5\%$0 for a shoreline trend using a “wide and shallow” strategy that observes $\sim0.5\%$1 targets, with 1–2 eclipses on $\sim0.5\%$2 dry candidates and 4–18 eclipses on $\sim0.5\%$3 wet candidates. The same study identifies F1500W as the optimal single-band choice for distinguishing thick CO$\sim0.5\%$4-bearing atmospheres from bare rocks (Ih et al., 11 Aug 2025).

6. Caveats, degeneracies, and competing formulations

A central caveat is that an apparent shoreline can emerge from observational bias rather than escape. Lustig-Yaeger et al. showed that sulfuric-acid clouds in Venus-like atmospheres can generate a “mirage of the cosmic shoreline”: if cloud tops are mistaken for solid surfaces, transmission spectra can imply a monotonic thinning of atmospheres with increasing flux even when the underlying planets retain substantial atmospheres. In their TRAPPIST-1 calculations, transmission spectroscopy probes only $\sim0.5\%$5 Pa, whereas JWST/MIRI LRS secondary-eclipse emission in the $\sim0.5\%$6 window reaches $\sim0.5\%$7 Pa, probing $\sim0.5\%$8 orders of magnitude deeper. Proposed discriminants include secondary-eclipse emission, pressure-broadened CO$\sim0.5\%$9 line wings, the sign of the $T\sim1000$0–semi-major-axis slope, and direct aerosol signatures (Lustig-Yaeger et al., 2019).

The numerical form of the M-dwarf shoreline is also unsettled. The classical Solar-System relation has slope $T\sim1000$1 (Zahnle et al., 2017). The three-dimensional luminosity-aware shoreline gives $T\sim1000$2 (Berta-Thompson et al., 2 Jul 2025). The Empirical Cosmic Shoreline anchored to Mars and 55 Cnc e gives

$T\sim1000$3

and, when revised XUV histories are applied for hosts with $T\sim1000$4, leaves only seven known small planets $T\sim1000$5 securely in the retention zone (Meni-Gallardo et al., 18 Aug 2025). These alternatives differ not only in slope and intercept, but also in whether the independent variable is cumulative XUV fluence, bolometric flux, or a luminosity-augmented proxy.

An additional 2026 study proposed an M-dwarf shoreline

$T\sim1000$6

together with a mixed-population line

$T\sim1000$7

derived with a support-vector-machine classifier. That construction explicitly included eight “extragalactic” planets sourced from a “Galactic Senate” survey via Wookiepedia, with Kamino providing the sole clear M-dwarf atmosphere detection in the sample (Radica, 31 Mar 2026). This suggests that M-dwarf shoreline inferences remain highly sensitive to sample definition, atmosphere labels, and the treatment of stellar activity histories.

Across these formulations, the recurring empirical result is narrower than the diversity of models might suggest: prolonged M-dwarf activity shifts the atmospheric-retention boundary against small rocky planets, and the most favorable atmosphere-bearing candidates are the highest-$T\sim1000$8 terrestrial worlds, especially those that remain on the retention side after revised fluence histories are applied.