The activity pattern of distant long period comets

Modern sky surveys now regularly discover comets at distances between 5 and 10 au, or even further, from the Sun. This is expected to become more common when the Vera C Rubin observatorys Legacy Survey of Space and Time (LSST) begins in around a year. Yet the distant activity of comets is still poorly understood at such distances the equilibrium temperature is too low for water ice sublimation to be the driving mechanism, as is thought to be the case at distances closer than 3-5 au. Sublimation of more volatile ices, such as CO or CO2, is a likely activity driver at larger distance, but the relative importance of these is unknown, and other mechanisms (such as phase change between amorphous and crystalline water ice) cannot be ruled out.Observationally, we can constrain distant comet activity mainly through measurement of the total brightness of the comet. This will increase as it approaches the Sun, due to decreasing distance from the observer, and an intrinsic increase in the amount of material (and therefore reflecting area) in the coma. We typically describe the latter using the total heliocentric brightness of a comet, in magnitudes, as m = H(1,1,0) + 2.5n log(r), where H(1,1,0) is the absolute magnitude of the comet (its brightness at 1 au distance), r is the distance from the Sun, and n is a slope parameter (the activity index) that describes how quickly a comet brightens as it approaches. Historically, returning long period comets have been observed to have a larger n (i.e. a steeper slope, and more rapid brightening) than dynamically new comets (DNCs) entering the inner Solar System for the first time.We will present results on long period comets observed over a wide range of distances as part of the LCO Outbursting Objects Key project (LOOK), what this means for comet detection with LSST, and ultimately how this will influence target selection for the ESA Comet Interceptor mission. The LOOK data gives us well calibrated photometry over a much larger range of heliocentric distances than has typically been possible (Holt et al. 2024; PSJ, submitted). This shows that a single slope parameter cannot be fit over the full range for most comets. Instead, a trend is seen of steeper slopes at larger distances (Fig. 1). The shallower slopes seen for DNCs are shown to be only an effect of older observations being limited to small distances: DNCs brighten rapidly at larger distances, and their activity plateaus as they reach the water ice sublimation region.We suggest a new empirical model for comet brightening, where we replace the constant slope parameter n with a function that changes linearly with distance (r), n = ar + b, where a and b are fit coefficients. This model gives reasonable fits to the LOOK dataset (e.g., Fig. 2), and allows better prediction of future brightness of comets based on initial observations at large distance, relevant for Comet Interceptor. We will present the range of a and b parameters that we find, how these correlate with other comet parameters (such as absolute magnitude or dynamical type), and what this means for LSST predictions.Fig 1: Change of activity index n with distance for LOOK sample (from Holt et al. 2024).Fig 2: Example brightness measurement for comet C/2021 S3 (PANSTARRS), showing the change in slope with decreasing heliocentric distance, and the empirical fit, given by n = 0.31r -1.19 in this case.