Timescales for Hypervolatile Depletion from Small Kuiper Belt Objects

Introduction: Small, ice-rich objects in and beyond the Kuiper Belt are likely to have undergone the least amount of processing in the billions of years since their formation, and can be used to form a more complete picture of the conditions and materials present in the early solar system. However, even these objects are unlikely to have remained entirely pristine. Since they would originally have contained substantial amounts of hypervolatile ice, even minor sources of heating may have resulted in significant thermal alteration.

To understand the extent to which the presence and quantity of volatile materials in a small body is indicative of when and where an object formed, we have developed a new thermophysical evolution model for small bodies, which includes all physical processes relevant to volatile loss at low temperatures.

Methods: We have developed a 1D spherically symmetric finite difference model for the thermophysical evolution of small porous bodies with volatile-rich interiors. We treat one species as a volatile material and track sublimation, deposition, and gas flow for this species. All other materials (predominantly silicates, complex organic materials, and amorphous water ice) make up the matrix, which is all treated as entirely refractory, consistent with the low range of temperatures we consider.

Our system is described by a set of coupled partial differential equations for the conservation of energy and mass through time. At each model time step, we solve the diffusion equation for volatile gas in the Knudsen flow regime, with phase change as a source term. This is done implicitly, assuming that the time step is long enough for the gas density to adjust to an equilibrium profile. We then update the temperature profile by solving an explicit form of the thermal diffusion equation, with the latent heat of phase change as an energy sink and the decay of long-lived radioisotopes as an energy source. We use a constant value for thermal conductivity but investigate the effect of varying this value, since the functional form generally has a strong dependence on both the porosity structure [1,2] and the distribution of solid components [3], neither of which are well constrained for small porous bodies.

For this study, the volatile of interest is carbon monoxide, and we use the updated vapor pressure curves from [4]. We use CI chondrite abundances of radioisotopes for the silicate portion of the body [16], and we assume a 1:1 ratio by mass of silicates to complex organic material [17]. We consider a range of temperatures between 30 K and 39 K, broadly consistent with equilibrium surface temperatures in the Kuiper Belt. We choose initial CO mass fractions between 0.05 and 0.15, generally consistent with estimates of protoplanetary disc composition at the location of the future Kuiper Belt [5]. We vary the pore size of the matrix material between 1 and 0.01 mm, and we test values of effective thermal conductivity between 1e-2 and 1e-4 W/m/K, both consistent with remote measurements of comets [6].

Results: We find that it is possible for a porous Kuiper Belt Object with a 5 km radius, such as Arrokoth, to retain CO over the lifetime of the solar system, although many plausible combinations of matrix porosity and thermal conductivity result in CO depletion even at a surface temperature of 30 K. Lower temperatures and porosities, and higher values for effective thermal conductivity result in slower rates of CO loss. Higher initial CO mass fractions also increase the volatile retention lifetime in a weakly nonlinear manner.

Discussion: It has been suggested [7,8] that the minimal amount of solar radiation received by objects in the Kuiper Belt and Oort Cloud may still have been enough to fully remove volatile ices, such as CO, on timescales much shorter than the age of the solar system. However, CO outgassing has been observed from comets sourced from these regions. This has led various workers to hypothesize that CO is trapped in less volatile materials such as amorphous water [9,10], clathrates [11], or CO₂ ice [7,12]. If such mechanisms were responsible for the release of CO vapor, one would expect CO outgassing rates to be correlated with rates of H₂O and CO₂ vapor production, but this does not seem to be the case [12,13]. Furthermore, CO outgassing has been observed in recent years at large heliocentric distances where less volatile ices should be stable [15].

If CO can be preserved for billions of years within small bodies in the outer solar system, then additional mechanisms for volatile retention are not categorically required to explain observations, and the discrepancy outlined above is resolved. We suggest that this may be the case for some portion of comets which formed cold [18] and late [19], with small pores and thermally conductive interiors.

 

References: [1] Shoshany, Y., et al. (2002) Icarus 157, 219–227. [2] Krause, M., et al. (2011) Icarus 214.1, 286-296. [3] Wang, M., et al. (2007) J. Phys. D: Appl. Phys., 40, 260. [4] Grundy, W. M., et al. (2024) Icarus 410, 115767. [5] Estrada, P. R., Cuzzi, J. N. (2022) APJ 936 (1), 40. [6] Groussin, O., et al. (2019) Space Sci Rev, 215:29. [7] Lisse, C. M., et al. (2021) Icarus 356, 114072. [8] Bouziani, N., and Jewitt, D. (2022) APJ 924:37. [9] Jewitt, D. APJ 137, 4296–4312. [10] Prialnik, D., and Rosenberg, E. D. (2009) MNRAS 399, L79–L83. [11] Marboeuf, U., et al. (2010), APJ 708, 812. [12] Davidsson, B. J. R. (2021) MNRAS 505 (4), 5654–5685. [13] Kipfer, K. A., et al. (2024) A&A 686, A102. [14] De Prá, M. N., et al. (2024) Nat. Astro. 1-10. [15] Harrington Pinto, O., et al. (2022) PSJ 3:247. [16] Robuchon, G., and Nimmo, F. (2011) Icarus 216, 426-439. [17] Bardyn, A., et al. (2017) MNRAS 469, S712–S722. [18] Marschall, R., et al. (2025) PSS. [19] Davidsson, B. J. R. (2016) A&A 592, A63.