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The author has declared that no competing interests exist.

Conceived and designed the experiments: DET. Performed the experiments: DET. Analyzed the data: DET. Wrote the paper: DET.

Data from the New Horizons mission to Pluto show no craters on Sputnik Planum down to the detection limit (2 km for low resolution data, 625 m for high resolution data). The number of small Kuiper Belt Objects that should be impacting Pluto is known to some degree from various astronomical surveys. We combine these geological and telescopic observations to make an order of magnitude estimate that the surface age of Sputnik Planum must be less than 10 million years. This maximum surface age is surprisingly young and implies that this area of Pluto must be undergoing active resurfacing, presumably through some cryo-geophysical process. We discuss three possible resurfacing mechanisms and the implications of each one for Pluto’s physical properties.

Recent images of Pluto from the New Horizons spacecraft [

A number of observatories on the ground and in space have been used to measure the size distribution of KBOs, which is usually expressed as ^{1.7} for ^{4} KBOs per square degree [^{5.8} KBOs larger than

The ecliptic plane is something like 10 degrees in height, so the total area of the ecliptic is 360 degrees times 10 degrees, or 3600 deg^{2}.

Pluto sweeps out a torus around the Sun as it orbits; the volume of this torus is _{Pl} ^{2}, where _{Pl} is the circumference of Pluto’s orbit (to first order, 40 AU) and _{KB} ^{2}, where _{KB} is approximately 40 AU, and ^{2}, which is around 1.5 × 10^{−11}. This fraction must be reduced by the ratio of the mean impact velocity (estimated to be around 2 km/sec by [

The number of impacts onto Pluto per Pluto year as a function of size (that is,

One over this number is therefore the mean impact interval, in Pluto years; this number times 250 gives the impact interval in Earth years.

The entirety of SP, which covers some 2.5% of the surface of Pluto, has been imaged at the relatively low resolution of 400 m/pixel. No craters are evident in this data set, giving a conservative result that no craters larger than 2 km exist in SP (using 5 pixels conservatively as the detection limit). A small fraction of SP, amounting to around 0.13% of the surface of Pluto, has been imaged at the relatively high resolution of 125 m/pixel. No craters are evident in this data set either, giving a conservative result that no craters larger than ∼625 m exist in this small region of SP. We correct the impact interval above by this surface coverage fraction (1/2.5% and 1/0.13%, respectively).

Recent detailed work on the cratering behavior on Pluto [^{0.783}, where

The imagery requires that no craters caused by 400 m (low resolution) or 90 m (high resolution) impactors exist in SP. Given the known impact interval as a function of size (from above), we can estimate the maximum surface age of SP. The results are shown in

The black line shows the constraint from the low resolution imaging (400 m/pixel), which has greater areal coverage; the red line shows the constraint from the small amount of high resolution (125 m/pixel) imaging available at the time of writing. The size distribution of KBOs larger than 10 km is taken from [

This maximum surface age is surprisingly young and implies that this area of Pluto must be undergoing active resurfacing, presumably through some cryo-geophysical process. There are at least three potential mechanisms by which craters could be erased from SP. The following discussion is largely adapted from [

It is possible that craters in SP undergo _{R}—the time it takes for the height of a surface feature to diminish by a factor of 1/^{3}[^{2}. To cause a 625 meter crater (the smallest size detectable in the data) to relax over 10^{7} years therefore requires an effective viscosity of the SP surface layer material, which is largely nitrogen ice, of around 4 × 10^{19} Pa-s. Because the relaxation timescale is an upper limit (the surface must be younger than 10^{7} years), the actual effective viscosity must be equal to or less than this value. This is a relatively loose constraint on viscosity; a tighter constraint arises from the next interpretation.

A second possibility is that craters in SP are erased and the surface reset through _{overturn} is therefore approximately ^{17} Pa-s. We have not taken into account the stress dependence of the effective viscosity, which would lower our estimate somewhat. Nevertheless, this result is consistent with the viscosity of nitrogen ice at 45 K derived by [^{8} Pa-s, and indicates that convective overturn is a plausible mechanism for removing craters of this size on SP.

A third possible mechanism to erase craters on SP is through ^{7} years must equal the volume of the crater that is erased, which is roughly ^{3}/80, where the factor of 10 in the denominator arises from the typical depth/diameter ratio of 1:10. The melt production rate must therefore be around 1 m^{3}/year or 10^{7} m^{3} (0.01 km^{3}) in ten million years in order to erase a single crater of order 625 meters in diameter.

A last uncertainty in the above constraints is that the size distribution of KBOs at 100 meters is not well known. In our estimate here we have used a reasonable extrapolation from [

We have used knowledge of the Kuiper Belt from telescopic observations to constrain the age of Sputnik Planum, Pluto. In the future, additional high-resolution imaging of SP as well as well-characterized crater counting on Pluto’s surface could be used to constrain the small size end of the KBO population. In particular, a better understanding of the crater detection limit in SP will help constrain the number of KBOs smaller than 100 meters. Alternately, very deep and well-characterized surveys for small KBOs might place interesting constraints on the cryo-geophysics of Pluto.

I thank Will Grundy for many helpful conversations and John Compton for suggestions about geophysical possibilities. Two anonymous referees provided helpful comments.