We examine the rise and sudden demise of comet C/2010 X1 (Elenin) on its approach to perihelion. Discovered inbound at 4.2 AU, this long-period comet was predicted to become very bright when near perihelion, at 0.48 AU on 2011 September 10. Observations starting 2011 February (heliocentric distance ~3.5 AU) indeed show the comet to brighten by about 11 mag, with most of the increase occurring inside 1 AU from the Sun. The peak brightness reached mR = 6 on UT 2011 August 12.95 ± 0.50, when at ~0.83 AU from the Sun. Thereafter, the comet faded even as the heliocentric distance continued to decrease. We find that most of the surge in brightness in mid-August resulted from dust-particle forward scattering, not from a sudden increase in the activity. A much smaller (~3 mag) brightening began on UT 2011 August 18 ± 1 (heliocentric distance 0.74 AU), reached a maximum on UT 2011 August 30 ± 1 (at 0.56 AU), and reflects the true breakup of the nucleus. This second peak was matched by a change in the morphology from centrally condensed to diffuse. The estimated cross section of the nucleus when at 1 AU inbound was ~1 km2, corresponding to an equal-area circle of radius 0.6 km. Observations were taken after the second peak using the Canada–France–Hawaii 3.6 m telescope to search for surviving fragments of the nucleus. None were found to a limiting red magnitude r' = 24.4, corresponding to radii 40 m (red geometric albedo = 0.04 assumed). The brightening, the progressive elongation of the debris cloud, and the absence of a central condensation in data taken after UT 2011 August 30 are consistent with disintegration of the nucleus into a power law size distribution of fragments with index q = 3.3 ± 0.2 combined with the action of radiation pressure. In such a distribution, the largest particles contain most of the mass while the smallest particles dominate the scattering cross section and apparent brightness. We speculate about physical processes that might cause nucleus disruption in a comet when still 0.7 AU from the Sun. Tidal stresses and devolatilization of the nucleus by sublimation are both negligible at this distance. However, the torque caused by mass loss, even at the very low rates measured in comet Elenin, is potentially large enough to be responsible by driving the nucleus to rotational instability.
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