Thermal history of comets during residence in the Oort cloud - Effect of radiogenic heating in combination with the very low thermal conductivity of amorphous ice

The thermal history of long-period comets initially composed of amorphous ice is studied. It is shown that such comets with a small nucleus thermal conductivity (kappa) experience a runaway increase in the internal temperature during residence in the Oort cloud. The temperature increase is a result of rapid release of the latent heat at crystallization triggered by gradual heating due to decay of radioactive nuclides. The time of the runaway temperature increase is about ten to a hundred million years after the formation of the nucleus depending on the fraction of refractory grains which contain radioactive nuclides. Most of the amorphous ice in the nuclides except just beneath the surface transforms into crystalline ice due to the runaway temperature increase. This implies that the ice in short-period comets is crystalline from the initial time when the long-period comet becomes a short-period one. In comets with large kappa the temperature does not rise much compared to the small kappa case and the initial amorphous ice is preserved. A criterion for the crystallization of the nucleus ice is derived.