The long-term evolution and initial size of comets 46P/Wirtanen and 67P/Churyumov–Gerasimenko

We present a new method to study the long-term evolution of cometary nuclei in order to estimate their original size, and we consider the case of comets 46P/Wirtanen (hereafter 46P) and 67P/Churyumov–Gerasimenko (hereafter 67P). We calculate the past evolution of the orbital elements of both comets over 100 000 yr using a Bulirsch–Stoer integrator and over 450 000 yr using a Radau integrator, and we incorporate a realistic model of the erosion of their nucleus. Their long-term orbital evolution is prominently chaotic, resulting from several close encounters with planets, and this result is independent of the choice of the integrator and of the presence or not of non-gravitational forces. The dynamical lifetime of comet 46P is estimated at ∼133 000 yr and that of comet 67P at ∼105 000 yr. Our erosion model assumes a spherical nucleus composed of a macroscopic mixture of two thermally decoupled components, dust and pure water ice. Erosion strongly depends upon the active fraction and the density of the nucleus. It mainly takes place at heliocentric distances <4 au and lasts for only ∼7 per cent of the lifetime. Assuming a density of 300 kg m⁻³ and an average active fraction over time of 10 per cent, we find an initial radius of ∼1.3 km for 46P and ∼2.8 km for 67P. Upper limit are obtained assuming a density of 100 kg m⁻³ and an active fraction of 100 per cent, and amounts to 21 km for 46P and 25 km for 67P. Erosion acts as a rejuvenating process of the surface so that exposed materials on the surface may only contain very little quantities of primordial materials. However, materials located just under it (a few centimetres to metres) may still be much less evolved. We will apply this method to several other comets in the future.