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Pluto and Charon limb profile topography

Citation

Conrad, Jack (2020), Pluto and Charon limb profile topography, Dryad, Dataset, https://doi.org/10.7291/D16H3S

Abstract

We derived updated and expanded topography datasets for Pluto and Charon. This is done through finding the body edge (i.e. the limb) in images, and with those body edge locations we can apply simple geographical techniques to produce limb profiles. The process involves some human intervention, but is primarily automation based. Our limb profile topography is useful for geologic and geophysical studies of Pluto and Charon. Additionally, we provide processed data of how we used the limb profile data in our study. The first set of additional data is the result of the processing required to determine the Fourier transformation that breaks down the data into its wavelength based components. This is done by interpolating the raw data onto a evenly spaced grid, then detrending the data by setting the end-points to equal elevations. Our second addition has the base 10 logarithm of our variance spectra results for Pluto and Charon, which is the primary result of the scientific portion of the study. We found that Charon has a statistically significant break in slope, while Pluto does not. This is likely a signal of their crust's structures.

Methods

We achieve this by determining the edge of the planetary body from images (“limb picks”). Using map projections and the known observing geometry, we can transform the pixel locations of the limb picks into a list of elevations at specific latitude and longitude locations. While our methodology mostly matches that of Nimmo et al. (2017), we will reiterate some aspects of their methods to detail updates and changes.

We began our process with a survey of New Horizons images from the Long-Range Reconnaissance Imager (LORRI; Cheng et al., 2008) and the Ralph instrument’s Multispectral Visible Imaging Camera (MVIC; Reuter et al., 2008) sub-instrument. Data from both instruments have been used extensively to study Pluto, Charon, and most recently Arrokoth (Spencer et al., 2020). Starting with the Planetary Data System, we surveyed the images to create a list of images containing body edges starting when Pluto was ~100 pixels in diameter. In addition, we removed redundant images from the list. This list contained both day-side and night-side images from both LORRI and MVIC as the starting point for further analysis.

While we initially performed limb picks and fits for both LORRI and MVIC images, we found large-amplitude, long-wavelength undulations for MVIC limb profiles. This occurs in MVIC images due to the line-scan exposure method combined with spacecraft motion (Weaver et al., 2009). Due to the relatively small number of MVIC images, we instead focus on the LORRI images in this analysis.

For limb picks of day-side (i.e. front-lit) images, we use Method A as presented in Nimmo et al. (2017). This method scans each row and column in the image, using a threshold approach similar to the method described in Dermott and Thomas (1988). We generally use the same brightness threshold (50%) and calculate the average brightness over the same distance range (0.5d to 0.9d, where d is the on-body profile length from center to body edge) as used in Nimmo et al. (2017).

Once the list of limb pixel locations is determined, we visually verify the algorithmically chosen limb picks and manually remove picks that are obviously not on the limb. These false limb points are often the result of either albedo variations or the terminator. Large albedo variations are only an issue with Pluto images that contain Cthulhu Regio (CR), a region south-west of Sputnik Planitia (SP). Limb picks of images that contain areas of CR that border regions of high albedo (e.g. SP) tend to place the limb location in CR inward of the actual limb. This happens because the average disk brightness is incorporated into the algorithm, and if the brightest area of Pluto is near the middle while the darkest is at the edge, the 50% cutoff will occur before the actual limb location. However, we note that the local albedo at the limb does not show a systematic correlation with topography (see section 3.1), suggesting that this effect is minor. The algorithm also does not discriminate between the limb and terminator of the body, and we only use locations where the edge of the lighted hemisphere is caused by the edge of the body (limb) rather than the edge of the illuminated hemisphere (terminator). While some terminator picks can be accidentally incorporated into a set of limb picks, we apply additional geometric checks in the fitting method described below to remove points not located on the illuminated limb.

After determining the limb location in terms of pixels (x,y), we project these points onto a spherical body to convert to an equivalent latitude, longitude position (φ, θ) on a spherical body given the image coordinates of the body’s center (x0, y0), the latitude and longitude of the sub-spacecraft location (φ0, θ0), the body’s radius R and the orientation of the rotation pole relative to the image (ϕ). The spacecraft parameters are calculated using the most consistent SPICE information based on the smithed kernels from Schenk et al. (2018a&b). We report these values for all used images in supplementary Tables 1 and 2 of the study, and the results of the pixel locations for x0, y0 and R (in pixels) in supplementary Tables 3 and 4. We utilize a general vertical perspective (GVP) projection for determining the latitude, longitude positions (φ, θ) of limb pick locations (Snyder, 1987). Near closest approach, we account for the effect that can lead to a shifting of the limb to an angle less than 900 away from the sub-spacecraft point. At distances d far from the body center (d >> R), the GVP projection reduces to the orthographic projection, which is commonly used in limb profile fitting studies (Nimmo et al., 2017). In our projections we assume that both Pluto and Charon are spherical, based on the results of Nimmo et al. (2017). This simplifies the map projection calculations and determination of the radii from the (x,y) pixel locations. Elevation is reported as relative to the mean radius of Pluto (1188.3 km) and Charon (606 km) also determined in Nimmo et al. (2017).

After we obtain raw limb profile topography, the data are processed to remove a few different possible problems as described below. Generally, we use the raw data for most of our analysis, while the processed data is used with presentation of limb profiles and some aspects of our analysis. When we apply the line-scan method, the algorithm scans both vertically and horizontally. This can introduce noise when the scan brightness curves to pick the limb near the same coordinate are different in the horizontal and vertical, and usually occurs in areas of varying brightness around the limb. To remove the shorter wavelength noise, as well as prepare our limb profiles for further analysis, we interpolate the limb topography onto a grid with constant spacing at a slightly worse ground sampling distance (half the total number of original data points). We use a gaussian weighted interpolation technique (equation 1 in the study). We then detrend the profiles by removing the linear trend through the end-points of the profile.

Topography generated from limb profiles can be used to analyze the long-wavelength properties of worlds. Limb topography variance spectra are a useful way of quantifying roughness as a function of wavelength (Araki et al., 2009; Shepard et al., 2001; Nimmo et al., 2011; Ermakov et al., 2018). To obtain the average variance spectrum, we calculate the discrete Fourier transform for each limb profile and then find the mean variance in a sequence of bins (Press, 1992; see equation 2 in the study).


Usage Notes

The data is contained within comma separated values files with the .llk extension, treat them as text files with loading them into your mapping software or programs.

A read me file is contained within the zip file, but the information contained is repeated here:


This data repository contains Limb profile topography data of Pluto and Charon from New Horizons images of the two worlds, this in addition to 2 derivative products. The first is the processed data from the initial processing we do in order to perform Fourier transformations on the data. Second is the binned Variance Spectra results.

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Limb profile topography files are in a comma separated values format with the file type llk. "llk" refers to latitude, longitude, radius (kilometers).

Each line of values includes:
latitude, longitude, radius (kilometers), x pixel, y pixel, radius (pixels)

Latitude is between +/- 90 degrees.
Longitude is sometimes above 360 degrees if the limb profile wraps around the "prime" meridian.
Radius is from the body center. The Nimmo et al. (2017) mean values for Pluto and Charon are 1188.6 km and 606.0 km respectively.
x pixel/y pixel are based on the source image.

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Processed limb profile topography files are in a comma separated values format with the file type dlle. "dlle" refers to distance, latitude, longitude, elevation (kilometers, with mean body radius removed). The limb profiles were processes by interpolating onto an even grid spacing and detrended by setting the end points to equal elevations.

Each line of values includes:
distance, latitude, longitude, elevation

Latitude is between +/- 90 degrees.
Longitude is sometimes above 360 degrees if the limb profile wraps around the "prime" meridian.

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Variance spectra files are in a comma separated values format with the standard file type .csv.

There are column headers with labels of the contained information.
Each line contains the base 10 logarithm of the Wavenumber (km**-1), Variance (km**2), and Standard Deviation


 

Funding

Planetary Data Archiving, Restoration, and Tools Program, Award: 80NSSC18K0549