Rotational Disruption of Comets with Parabolic Orbits

One of the most fundamental problems in planetary science is the natural lifetime of comets, which is limited by several processes, most notably by spontaneous disruption of the nucleus. While the underlying mechanism is uncertain, rapid rotation is often suspected. To address this problem, I derived the probability of rotational disruption, and investigated it for comets with parabolic orbits as a function of perihelion distance and nucleus size for a range of input parameters. The disruption probability is defined as the ratio of expected change in the rotation rate to the allowable span of the rotation rate, the latter being limited by the critical rotation rate (prograde and retrograde), which I adopted from Davidsson (2001, Icarus 149, 375). The expected change in the rotation rate, resulting from the action of torques generated by mass loss, is calculated following the standard approach (e.g. Drahus et al. 2011, ApJL 734, L4, and ref. therein), but taking into account the suspected decrease of the net torque with an increasing active fraction of the nucleus (Jewitt 1997, EM&P 79, 35; Samarasinha & Mueller 2013, ApJL 775, L10). The sublimation flux is obtained from the standard energy balance equation (e.g. Cowan & A’Hearn 1979, M&P 21, 155), but I also take into account extinction of sunlight in the dust coma. I find that close to the Sun coma transmission steeply decreases with a decreasing heliocentric distance, resulting in the sublimation flux at a remarkably constant level, and also that coma transmission decreases with an increasing nucleus size, both properties being critically important in the calculation of sublimation flux for large sungrazers. The obtained rotational-disruption probability features several interesting properties. It has a well-defined regime occupied by smaller comets closely approaching the Sun, for which rotational disruption is unavoidable regardless of the original rotation state. Moreover, the probability function offers a very close match to the empirical survival cutoff for long-period comets with perihelia of less than 0.5 AU (Bortle 1991, ICQ 13, 89), independently suggesting that rotational disruption is the primary mechanism responsible for the destruction of comets.