Reply to: Penitente formation is unlikely on Europa

Abstract

1School of Earth & Ocean Sciences, Cardiff University, Cardiff, UK. 2NASA Ames Research Center, Moffett Field, CA, USA. 3Department of Environmental Sciences, University of Virginia, Charlottesville, VA, USA. *e-mail: [email protected] Hand and colleagues1 critique aspects of the analysis within our work2, and criticize our reference to the emergent metre-scale blade-like structures that we inferred to be ‘penitentes’. Strictly from the vantage point of nomenclature, Hand et al.1 are justified in criticizing our use of the word penitente to describe the phenomenon discussed in our study. The initial instability producing penitentes in terrestrial ices depends in part on a well-known fluid dynamical process whereby ice temperatures and sublimation rates are enhanced over troughs and lessened over peaks, although some simulations of terrestrial penitentes still do not model this fluid effect3. Under terrestrial conditions, the transport of water vapour is controlled by the ease of its diffusion through the fluid. As such, the penitente is sensitive to spatial variations of the local humidity: growth is promoted when the relative humidity is low over troughs. Theoretically speaking, the bladed appearance of an ice penitente (in its terrestrial guise) is shaped by thermal and insolation effects working in concert with vapour diffusion. Laboratory experiments in which a cold chamber was held at 200 Pa show the emergence of ‘micropenitentes’4, with characteristic length scales of less than a centimetre, are amenable to and wellexplained by the classical penitente analysis. This is because the gas in this experimental set-up4 remains sufficiently dense to be treated as a fluid (mean free paths of 0.1 mm), for which humidity effects play an important role. As noted by Hand et al.1, on the scales of interest (on the order of 10 m), Europa’s near-vacuum atmosphere certainly cannot be treated as a fluid, as the mean free paths of particles are so large (>100 km); for this reason, we made no appeal to the fluid theory of penitentes5,6. Hand et al.1 acknowledge that the emergence of bladed structures is feasible in a harsh environment in which humidity is not the controlling factor7,8, as on Europa. Moore et al.7 have previously shown that for icy worlds, the combined focusing of solar insolation into ice troughs and surface re-radiation results in enhanced regional sublimation. This effect is amplified if the troughs already have a relatively increased abundance of low-albedo refractory materials—possibly mass-wasted from the surrounding steepened slopes eroded by sublimation. The overall effect is similar to the humiditycontrolled development of penitentes, and troughs evaporate more than peaks. This process has led to the development of penitentelike crenellated surfaces on Pluto7. We expect the timescales for the emergence of metre-scale blades in near vacuum settings like Europa to be long (millions of years)2, and are frank about our extrapolation of aspects of terrestrial dynamics to Europa. Hand et al.1 also query our choice of a 2:1 ratio to describe sublimation geometry. We chose this experimental value9 because it was produced under sustained, stable illumination from a single angle, and it was not subject to the natural terrestrial weather and insolation conditions that typically produce lower field values. In the absence of markedly different literature values, and because we assume that the final form of a growing sublimation pit is controlled primarily by radiative properties and less by vapour, a 2:1 ratio seems a plausible value. Similarly, in these experiments, once the sublimation pit is stable in form, it can continue to grow deeper. As we acknowledged, our analysis provides only a first-order constraint on the possible structure size and spacing (clearly stated as a maximum limit), as these and a number of other unmodelled factors could also play a role. However, the observed circular polarization ratios (μc) discussed further below support a spacing of penitentelike depressions in excess of 13 cm, consistent with our suggestions. Hand et al.1 criticize our use of Callisto as a proof-of-concept for penitentes because Callisto and Europa radar returns do not share the same patterns. The surface geology of Callisto and Europa are very different, and it is to be expected that even with the same processes acting on the surfaces, the resulting patterns of expression would differ. We invoked Callisto as a proof-of-concept of a radiative model similar to the one we apply here. In terms of form, however, the pinnacles of Callisto are singular structures surrounded by mass-wasted refractory materials, and poor analogues in form for what we infer for Europa. Hand et al.1 suggest that particulates on Europa’s trailing hemisphere would accelerate, rather than suppress, penitente formation. However, although small quantities of implanted dirt could increase penitente formation rates, large quantities would swamp the surface and completely inhibit formation10,11. The significant quantities of particulates accumulated on Europa’s trailing hemisphere are therefore consistent with our interpretation that sublimation is smothered in many places by a surface lag. Finally, Hand et al.1 also criticize us for invoking large radar μc values around the equator of Europa as support for bladed structures on the basis that radar data for Europa12 do not resolve an equatorial low in μc. We would dispute this reading of the data. Existing μc data are not disc-resolved, and only permit the calculation of latitudinally averaged values at various phases. There are no large longitudinal variations—consistent with our suggestion that all longitudes are capable of developing penitentes if unsuppressed—but variations with latitude would not be expected to appear. We concede that perhaps we should have consistently referred to the metre-scale bladed structures predicted by our study as morphological analogues of terrestrial penitentes rather than simply penitentes. The analogy emerges from inferred form and from the decisive role of solar radiation in sculpting the structures as they develop, as our numerical analysis demonstrates. We also clarify here that a 7.5 m spacing between spikes is a theoretical maximum, with a minimum instead set by the wavelength of the polarized radar returns (that is, tens of centimetres). We stand by the analyses Reply to: Penitente formation is unlikely on Europa