Detailed morphological and photometric characterisation of Comet 29P in the optical region is presented comprising: (a) multi-filter observations of the outburst coma in 2010–2012 with the 2.0-m Faulkes Telescopes (FT); (b) high-cadence, high-precision photometry in May–September 2014; and (c) HST observations in March 1996 (WFPC2/F702W filter). Outbursts appear to be explosive in that: the rise to maximum light is short-lived; the expanding coma fits a model in which ejecta are produced in a singular event and expand into space with uniform velocity; and the motion of condensations within the outburst coma indicate a common onset time and origin. The bright outburst of 2010 February 2 generated a dust coma exhibiting expansion speeds up to 0.257±0.013kms−1 consistent with acceleration of cometary grains close to the nucleus driven by sublimating CO ice and N2 ice at 24±6K. Material ejected ∼1d after this outburst exhibited a V–R colour gradient: redder towards the main outflow, bluer in the opposite sense; potentially arising from differences in spectral emission (from gas), light scattering (particle size), and spectral reflectance (composition). B–V, V–R and R–I colour images revealed colour/compositional differences in near-nucleus structures and the evolution of the expanding coma, which brightened by ∼30% within 5–6days of the outburst. Broadband photometry indicated a general reddening coma with time (change in B–V from +0.76 to +0.83; V–SDSS-r′ from 0.25 to +0.31 in 14d). SDSS-r′–SDSS-i′ photometry indicated gradual spectral attenuation at >700nm. Asymmetric, fan-shaped comae, characteristic of 29P, potentially form when the expanding cloud from an outburst is shielded by the nucleus. Rotational-gradient filtered HST and FT images show unusual 2-fold and 4-fold symmetry involving oppositely-directed radial outflows moving at up to 0.15kms−1: possibly an indication of material escaping from fissures along the perimeter of a crustal ‘plate’ when dislodged by pressure build-up in the subsurface. Pairs of outbursts separated in time by 52–65d took place in 2010, 2011, and 2012 exhibiting similar coma outflow patterns indicative of outbursts repeating a second time from the same source, and suggesting a nuclear rotation period of 59±4 (s.e.)d. The escape velocity of the nucleus is sufficiently high (0.013–0.023kms−1) that a significant fraction of ejecta falls back onto its surface, the action of which, we suggest, re-forms the crust and may trigger outbursts from nearby sites (e.g. triple events of February 2010, and May 2014). A short-lived (<1d) anomalous brightening of 0.36±0.12mag observed on 2014 July 21 during quiescence may have arisen from an especially weak mini-outburst in which most of the ejected material failed to reach escape velocity. During quiescence in 2014, Comet 29P fluctuated in brightness over time-scales of 2–10d by up to ±0.25mag, probably via local jet activity continuing to feed the faint persistent inner coma. 29P also exhibited weak outbursts of <1mag amplitude during quiescence and these will generally be missed by observers. Image analysis methodology tracking the locus of the coma photocentre with increasing photometric aperture size is used to quantify the directional motion of cometary haloes within 1–2d of an outburst.
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