## Abstract

Quantifying the atmospheric mass loss during planet formation is crucial for understanding the origin and evolution of planetary atmospheres. We examine the contributions to atmospheric loss from both giant impacts and planetesimal accretion. Giant impacts cause global motion of the ground. Using analytic self-similar solutions and full numerical integrations we find (for isothermal atmospheres with adiabatic index γ=5/3) that the local atmospheric mass loss fraction for ground velocities vg≲0.25vesc is given by χloss=(1.71vg/vesc)4.9, where vesc is the escape velocity from the target. Yet, the global atmospheric mass loss is a weaker function of the impactor velocity vImp and mass m_{Imp} and given by X_{loss}≲0.4x+1.4x^{2}-0.8x^{3} (isothermal atmosphere) and X_{loss}≃0.4x+1.8x^{2}-1.2x^{3} (adiabatic atmosphere), where x=(vImpm/vescM). Atmospheric mass loss due to planetesimal impacts proceeds in two different regimes: (1) large enough impactors m≳√2ρ0(πhR)3/2 (25km for the current Earth), are able to eject all the atmosphere above the tangent plane of the impact site, which ish/2R of the whole atmosphere, where h, R and ρ_{0} are the atmospheric scale height, radius of the target, and its atmospheric density at the ground. (2) Smaller impactors, but above m>4πρ_{0}h^{3} (1km for the current Earth) are only able to eject a fraction of the atmospheric mass above the tangent plane. We find that the most efficient impactors (per unit impactor mass) for atmospheric loss are planetesimals just above that lower limit (2km for the current Earth). For impactor flux size distributions parametrized by a single power law, N(>r)∝r^{-q+1}, with differential power law index q, we find that for 1<q<3 the atmospheric mass loss proceeds in regime (1) whereas for q>3 the mass loss is dominated by regime (2). Impactors with m≲4πρ_{0}h^{3} are not able to eject any atmosphere. Despite being bombarded by the same planetesimal population, we find that the current differences in Earth's and Venus' atmospheric masses can be explained by modest differences in their initial atmospheric masses and that the current atmosphere of the Earth could have resulted from an equilibrium between atmospheric erosion and volatile delivery to the atmosphere from planetesimal impacts. We conclude that planetesimal impacts are likely to have played a major role in atmospheric mass loss over the formation history of the terrestrial planets.

Original language | American English |
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Pages (from-to) | 81-94 |

Number of pages | 14 |

Journal | Icarus |

Volume | 247 |

DOIs | |

State | Published - 1 Feb 2015 |

### Bibliographical note

Publisher Copyright:© 2014 Elsevier Inc.

## Keywords

- Atmospheres, evolution
- Collisional physics
- Planetary formation
- Planetesimals
- Terrestrial planets