A link between the size and composition of comets
Authors: Robinson Jamie , Malamud Uri , Opitom Cyrielle , Perets Hagai , Blum Jürgen 
Published: July 2024

INTRODUCTIONWe present the results of our recent work investigating possible correlations between cometary composition and nucleus size, as detailed in Robinson et al. 2024. This work follows on from laboratory experiments and numerical modelling of comet nuclei thermal evolution by Malamud et al. 2022, who considered a pebble pile internal structure with a low thermal conductivity for the nucleus. In this scenario heat from radionuclide decay can build up within the nucleus and form a thermal gradient. This then drives the outward migration of volatile species until they reach a region where they condense out, are entrapped in an amorphous ice, or they are depleted from the nucleus altogether. Radiogenic heating is stronger for larger comet nuclei, as such one would expect the effects of internal differentiation to be stronger for larger comets. Therefore in this work we conduct an analysis of literature data for the presence of any correlations between cometary volatile abundance and nucleus size which may be explained by the predictions of Malamud et al. 2022.&#160;METHODSFor this study we have gathered together a significant number of measurements of comet composition and nucleus size from the available literature. Comet composition can be estimated from spectroscopic and/or narrowband photometric observations which measure the strength of emission features in the coma which are associated with various volatile species. We focus on measurements in which the production rate of a given species is measured contemporaneously with that of the most abundant cometary volatile, H2O. We therefore analyse the abundance ratio of a given volatile relative to H2O, which helps to reduce the effects of changing levels of cometary activity. It is difficult to remotely measure the size of a comet nucleus, which is generally small in size (often km scale) and low albedo. Furthermore when the observing geometry is favourable the comet is generally approaching the warmer inner Solar System and so the nucleus is obscured by the coma. When the nucleus is inactive size can be estimated from photometric observations and an albedo, similar to asteroid size measurements. Likewise thermal observations can be combined with a thermal model to estimate nucleus size. The most accurate size estimates are made using radar observations and imaging from spacecraft flyby/rendezvous, but opportunities to obtain such measurements are rare and/or costly.&#160;As such we searched the literature and gathered published measurements of volatile species abundance and nucleus size from surveys, compilations and targeted observations of single objects. For both properties we often found multiple measurements from different sources. In our analysis we selected a single source for each measurement. We did this to avoid biases from the combination of measurements obtained using a variety of techniques, however, this method ignores the possible variations in the property (e.g. changes in volatile abundance as a function of time/measurement technique). Regardless, in Robinson et al. 2024 we outline our selection criteria and the full dataset is available to enable indenopendent investigations by the community.This dataset was used to search for possible correlations between the abundance of the main cometary volatiles and the size of the nucleus, as would be expected from the predictions of Malamud et al. 2022. The correlation of the data (in log-log space) was assessed using the Pearson correlation coefficient. We attempted to account for possible observational biases, such as heliocentric distance of the abundance measurement, when assessing the strength of each correlation.&#160;RESULTS AND SUMMARYIn our analysis we found a statistically significant correlation between cometary CO/H2O abundance and nucleus size. This trend remains when only compositional measurements within 2 au are considered. Furthermore, bootstrap/jack-knife statistical resampling tests indicate that this trend is not overly dominated by a particular comet. We show that the CO/H2O trend is compatible with a simple adaptation of the Malamud et al. 2022 theoretical model, whereby CO enrichment occurs via outward migration of CO gas followed by entrapment in an outer amorphous ice layer. For some volatile species we found only weak correlations that are not robust for the given data, for others there was no indication of correlation at all.&#160;This work highlights the need for more measurements of the physical properties of comets, namely composition and size. More accurate measurements for more objects, ideally obtained in a homogeneous and consistent manner, would enable future studies to probe these initial findings in greater detail. The literature data is particularly lacking measurements for larger comets. With more data one could more accurately account for biases in observation and/or comet population (regarding dynamical evolution and thermal history for example). It is hoped that continuing community effort and future state of the art facilities will greatly increase the size and quality of measurements of cometary physical properties.&#160;The full database of comet composition and nucleus size measurements compiled in this work is available online for the use of the community (see Robinson et al. 2024 and https://doi.org/10.7488/ds/7723).&#160;&#160;&#160;Figure 1: Log scale plot of cometary CO/H2O abundance against nucleus size. Only composition measurements taken within a heliocentric distance of 2 au are considered here, in an attempt to reduce observational bias. Marker colour denotes heliocentric distance of the composition measurement and marker shape indicates dynamical class (square - ecliptic comets, triangular - nearly isotropic comets). The presence of a correlation is indicated by a linear fit to the data (in log-log space) for the whole dataset (solid line).&#160;Figure 2: The CO/H2O abundance versus nucleus size from figure 1 is replotted (circular markers). The curves indicate the predictions of the adapted Malamud et al. 2022 model, where each curve indicates a different formation time. The other parameters used in this thermal model are: mineral fraction = 1, pebble radius = 0.1 cm, and permeability = 1.&#160;REFERENCESMalamud, Uri, Wolf A Landeck, et al.. &#8216;Are There Any Pristine Comets? Constraints from Pebble Structure&#8217;. MNRAS 514, no. 3 (23 June 2022): 3366&#8211;94. https://doi.org/10.1093/mnras/stac1535.&#160;Robinson, James E, Uri Malamud, et al.. &#8216;A Link between the Size and Composition of Comets&#8217;. MNRAS, 28 March 2024, stae881. https://doi.org/10.1093/mnras/stae881.