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Limitations

ZEPHYRUS implements the energy-limited (EL) approximation to hydrodynamic atmospheric escape, given by Eq. (1) of the model overview. This is a deliberate simplification of a much richer physical problem. The most important regimes and processes the model does not cover are summarised below.

What ZEPHYRUS does model

A single regime: bulk hydrodynamic escape driven by stellar XUV irradiation, in the energy-limited approximation, with an optional tidal correction (Eq. 2 of the model overview). The mass-loss rate is partitioned across atmospheric species in proportion to their elemental mass mixing ratios.

Everything below is not modelled.

Other hydrodynamic regimes

The EL approximation assumes a fixed fraction \(\epsilon\) of absorbed XUV energy goes into driving the outflow. This breaks down in several ways:

  • Radiative cooling is ignored. Atomic line cooling, molecular emission, and ionisation losses can divert XUV energy away from heating the bulk gas, reducing the effective \(\epsilon\). ZEPHYRUS treats \(\epsilon\) as a constant input rather than computing it self-consistently. Setting \(\epsilon = 1\) in particular is a non-physical upper limit on the mass-loss rate.
  • Fractionation in the outflow is not captured. When the particle flux drops below the critical value required to drag heavy species along, the outflow becomes compositionally fractionated: hydrogen escapes preferentially and the residual atmosphere is enriched in heavy species. ZEPHYRUS removes everything in bulk. Fractionation will be implemented in the future.
  • \(\epsilon\) is held constant in time. In reality the efficiency evolves with planet mass, radius, and incident flux. Fixed-\(\epsilon\) models can overestimate mass loss at late times.

Non-hydrodynamic escape

These processes operate on a different physical basis (kinetic rather than fluid) and are neglected because they are subdominant in the high-XUV regime that ZEPHYRUS targets:

  • Jeans escape
  • Ion pickup
  • Charge exchange
  • Photochemical escape
  • Sputtering
  • Polar wind / unmagnetised ion outflow

For present-day Earth and Venus these mechanisms dominate over hydrodynamic escape, with total non-thermal rates around \(\sim 10^3\) g s\(^{-1}\); many orders of magnitude below the EL rates ZEPHYRUS produces during the early evolution phase.

Other escape drivers

Core-powered mass loss is not implemented. This mechanism is driven by the planet's own internal heat and dominates for low-gravity planets at high equilibrium temperatures (~500–2000 K) over \(\sim 10^9\) yr timescales. It is complementary to XUV-driven escape rather than competing with it.

Stellar XUV uncertainties

The XUV flux \(F_\mathrm{XUV}\) that enters Eq. (1) of the model overview carries large intrinsic uncertainties from the underlying stellar evolution model:

  • Saturation timescales for the stellar XUV phase can vary from ~10 to ~300 Myr for G stars and up to ~1 Gyr for fully convective M dwarfs, depending on initial rotation.
  • The integrated XUV flux, and therefore the integrated mass loss, can vary by factors of \(\sim 2–10\) between standard stellar evolution prescriptions.
  • The ISM absorbs stellar XUV emission, so observational anchors on young-star XUV luminosities are themselves uncertain.

Because of these uncertainties, the mass-loss rates computed by ZEPHYRUS should generally be treated as an upper bound.

Atmospheric chemistry

  • No photochemistry. Hazes, aerosols, and photochemically-produced species are not tracked in the coupled framework.
  • \(R_\mathrm{XUV}\) is set by a single reference pressure \(P_\mathrm{XUV}\) specified in the config.

Practical implications

For users:

  • Avoid \(\epsilon > 0.3\) for rocky planets unless you have a specific reason. \(\epsilon \approx 0.15\) is the conservative baseline.
  • For close-in M-dwarf planets where elemental fractionation is expected to matter, ZEPHYRUS bulk rates are a lower bound on the change in atmospheric mean molecular weight. The actual atmosphere should become heavier faster than the model predicts.