Future evolution of 12P and other Halley-type comets in near-polar orbits

ABSTRACT We investigate the future 100 kyr evolution of six selected Halley-type comets (HTCs) to show their basic commonalities and differences in dynamical behaviour. This includes estimating the probability of sungrazing and flipping. We combined three complementary numerical methods to study the dynamical features: the numerical integrations forwards in time, the Lyapunov time estimations, and the mean exponential growth factor of nearby orbits (MEGNO). For each comet, we obtain the osculation orbits from the available observations. We then construct swarms of virtual comets as the basis for all dynamical studies. We show that two comets with $q<1.3$ au achieve the sungrazing state in the future with high probability: 161P with the likelihood of $\sim$80 per cent will be a sungrazing object with $q<0.005$ au in the next 13 kyr, and 122P with 50 per cent in the next 100 kyr. We found that both these HTCs reach the sungrazing states due to Kozai resonances with other planets than Jupiter; for example, Uranus acts as the agent of Kozai resonance for 161P. We indicate that the high sungrazing probability for both comets is connected with a high likelihood of orbit flipping. The other four HTCs have a slight chance to be sungrazers after 100 kyr ($< 2.2$ per cent); however, three of them can achieve a high flipping probability. We show that the Lyapunov time and MEGNO indicator give a complementary picture of the orbital stability after 104 yr. Results allow us to rank comets from the most to least chaotic, where 161P is a particular case with its high probability to disintegrate due to the Kozai mechanism.