Possible Activity in 468861 (2013 LU28)

Manx comets are objects on long-period comet orbits that are inactive as they approach perihelion. They are of particular interest because they may help constrain solar system formation models. 2013 LU28 was discovered as an inactive asteroidal object on 2013 June 8 at a heliocentric distance of 21.8 au. Images and photometric data were obtained of 2013 LU28 from multiple telescopes from pre-discovery data in 2010 until the present. Its spectral reflectivity is consistent with typical organic-rich comet surfaces with colors of g′−r′ = 0.97 ± 0.02, r′−i′ = 0.43 ± 0.02, and r′−z′ = 0.65 ± 0.03, corresponding to a spectral reflectivity slope of 30 ± 3%/100 nm. There is no obvious indication of dust coma in deep stacked images. We estimate the nucleus radius to be ∼55.7 ± 0.3 km assuming an albedo of 4%. This is much smaller than the 1σ upper limits on the nucleus size of 79.9 km from the NEOWISE survey assuming the same albedo, since the NEOWISE survey is not very sensitive to objects this small at this distance. The heliocentric light curve suggests possible activity between r ∼ 17 and 13 au where 2013 LU28 is brighter than expected. This is consistent with outgassing from CO or CO2. Using surface brightness profiles, we estimate an upper limit of ∼0.01 kg s−1 for micron-sized dust that can be produced without us detecting it for the inactive portion of the light curve, and upper limits of ∼1 kg s−1 for CO and ∼1.5 kg s−1 for CO2 between 20 and 14.7 au.


Introduction
Object (468861) 2013 LU28 was discovered by the Mt. Lemmon Survey on 2013 June 8. It has a long-period (LP) comet orbit (a = 184.2 au, e = 0.953, i = 125°.3 , q = 8.743 au, Q = 359.8 au, P = 2501 yr at the time of perihelion) and will reach perihelion on 2024 June 20. However, although the orbit of 2013 LU28 identified it as an LP comet, no dust coma associated with comet activity has been observed. This suggests that 2013 LU28 is a "Manx" comet-an object coming from the Oort cloud with an LP orbit that lacks the typical outgassing from near-surface ices of an LP comet (Meech et al. 2016).
In 1950, although Jan Oort (Oort 1950) did not include these inactive objects in his study that proposed the existence of the Oort cloud, his investigation suggested a source region for inactive LP objects. He proposed that the disappearances of the bright, highly active comets that were coming from the Oort cloud could be due to the loss of a layer of "volatile frosting." This highly reactive outer layer caused by interaction with space radiation is lost once these comets first approach perihelion. Later, Levison proposed that Oort's missing comets were disrupting, and that there should not be inactive objects on LP orbits (Levison et al. 2002). Alternatively, there is a more recent possibility that some of these objects coming from the Oort cloud may never have had significant volatiles. The Manx comets may represent objects that formed in the inner solar system and never had much ice. Manx comets, if they formed just inside the snowline of the early solar system before they were ejected outwards to the Oort cloud, could show evidence of this chemistry (Meech & Raymond 2020).
Several models can account for much of the formation and current architecture of our solar system, including the Nice model (Gomes et al. 2005), the Grand Tack model (Walsh et al. 2011), and the model by Raymond and Izidoro (Raymond and Izidoro 2017). In the Grand Tack model, the fully grown gas giants migrate from the location of their initial formation into the inner solar system, before moving out to their final orbital distances around the Sun. This would lead to a scattering of volatile-rich (C-type) bodies from past the snowline inwards and volatile-poor (S-type) rocky bodies within the snowline outwards toward the Kuiper Belt and Oort cloud (Walsh et al. 2012). The Nice model then describes the instability and migration of the orbits of Jupiter and Saturn that lead to a major restructuring of the orbits of the gas giants along with the smaller planetesimal bodies. This leads to further scattering of the volatile-rich (C-type) planetesimals that formed past the snowline in toward the inner solar system (Tsiganis 2015). Other models show how small planetesimals can be scattered throughout the solar system even without the massive migration of the giant planets (Raymond & Izidoro 2017).
These models make different predictions about the relative amount of inner versus outer solar system material that gets ejected to the Oort cloud. The LP comet reservoir will then reflect the surface properties of the scattered populations. The pattern and amount of inner solar system material that is found in the Oort cloud from the scattering will differentiate between the predictions of the various solar system models (Meech et al. 2016). The spectral reflectivity of inner solar system material is distinctly different from organic-rich outer solar system material, which is red. Inner solar system material has a shallow 1 μm absorption feature from the presence of anhydrous minerals that cannot form in the presence of water. Along with interest in understanding the surface composition, modeling the activity of LP comets that have had many passages through the inner solar system (often known as dynamically old) can provide insight into the distribution of volatiles in the solar system. LP comets are usually not discovered pre-perihelion at large enough distances from the Sun to watch the onset of activity (likely due to CO and CO 2 sublimation) since this occurs at such large distances (Meech & Svoren 2004). Analyzing 2013 LU28 gives us a unique opportunity to search for the onset of CO and CO 2 sublimationdriven activity.
In this paper, we use data from multiple telescopes to determine the spectral reflectivity of 2013 LU28 to see if the surface resembles inner or outer solar system taxonomies. We also use the data to construct a heliocentric light curve and use this to determine the approximate size of the nucleus and to constrain and characterize any activity using an ice sublimation model.

Observations and Data Reduction
We obtained images of 2013 LU28 using the following facilities: Canada-France-Hawai'i Telescope (CFHT) and Gemini North on Maunakea, Hawai'i; Himalayan Chandra Telescope (HCT) on Mt. Saraswati, Hanle, India; Pan-STARRS (Denneau et al. 2013;Magnier et al. 2020) and ATLAS on Haleakelā Hawai'i (Tonry et al. 2018), and NEOWISE surveys (Mainzer et al. 2011). The particulars of the facilities are shown in Table 1. Unless otherwise noted, we used our own pipeline software for flattening.
The data were obtained through different photometric systems as noted in Table 1. To photometrically calibrate the data, we calculated a photometric zero-point for each image using the Pan-STARRS and SDSS catalogs and published color corrections to translate photometric bands to the SDSS g, r, i, z system and the BVRI system using the transforms of Tonry et al. (2012). The photometry pipeline uses our computed world coordinate system information in the image headers combined with orbital elements from the Minor Planet Center to compute the object location in the image and determine which object in the frame corresponded to the target. Terapix tools (SExtractor; Bertin & Arnouts 1996) were used to produce multi-aperture and automatic-aperture target photometry and uncertainties for several of the data sets. Error bars on the photometric calibration are computed by assigning each calibration star a Gaussian error based on image photometry and catalog errors, plus a long error tail that falls off as 1/ magnitude to mitigate non-Gaussian outliers, and computing the peak likelihood and error using a nonlinear optimization. Error bars on individual points are computed either by SExtractor or by applying photon shot noise statistics to the total flux in the aperture, along with a similar error contribution from a background annulus. A full description of the pipeline is given in Meech et al. (2017a).
All of the photometry reported in this paper is in the SDSS system (Fukugita et al. 1996). The transformations between photometric systems depend on the color of the object. Gemini measurements obtained on 2017 April 4 yielded colors g¢-r¢ = 0.97 ± 0.02, r¢-i¢ = 0.43 ± 0.02, and r¢-z¢ = 0.65 ± 0.03, which were used for all the subsequent filter system transformations.
To convert the R Cousins system magnitudes to the SDSSband r¢ shown in Table 4, we used the transformations of Lupton (2005) The transformations from the PS1 filters to the SDSS-band r¢ are given by Tonry et al. (2012).
The transformations from the ATLAS filter system described are given in Tonry et al. (2018).
We obtained images using the CFHT MegaCam wide-field imager, an array of forty 2048 × 4612 pixel CCDs with a plate scale of 0″.187 pixel −1 and a 1.1 square degree field of view (e.g., Figure 1). The data were obtained through SDSS filters using queue observing and were processed to remove the instrumental signature through the Elixir pipeline (Magnier & Cuillandre 2004). We have data obtained during 22 separate nights, as shown in Table 4.

Gemini North
We obtained data for 2013 LU28 on eight dates from 2017 April to 2020 February with the Gemini North telescope using GMOS with 2 × 2 binning. Our custom observing planning tool was used to schedule observations to avoid contamination from field stars, galaxies, and nearby bright sources. All raw images were reduced with Gemini's new python-based data reduction platform, DRAGONS (Labrie et al. 2019). We cropped the images to remove traces of air bubbles and other artifacts, and extracted the central chip on nights where the outer chips were nonphotometric due to vignetting. We measured the photometry for these images using IRAF with a 2″ radius aperture. These images were also used to find the spectral reflectivity of 2013 LU28 over four different filters.

Himalayan Chandra Telescope
Images were obtained from the 2.01 m Himalayan Chandra Telescope (HCT) at Mt. Saraswati, Hanle, India. We used the Himalaya Faint Object Spectropraph and Camera (HFOSC) and the new 4k × 4k e2V CCD with the Cousins filter system to obtain data on the dates shown in Table 4.
Photometry was initially measured with an automatic 5″ radius aperture for all of the images, resulting in relatively large errors with the measurements and a wide spread of observed magnitudes within a small amount of time. Additionally, in many of the early PanSTARRS images when 2013 LU28 was beyond r ∼ 17 au, the object was near the limit of detection. Thus, in order to obtain better magnitude measurements, we used small apertures to minimize the sky noise, then used the curve of growth on a bright unsaturated star to correct for the amount of light lost. This process was done for all of the filters available for a given date. For the magnitude measurements used for the spectral reflectivity, a 1″ radius aperture was used to measure the magnitude in order to minimize errors. The same aperture size was used for all the images for the sublimation model. All the images were examined for quality, and the photometry shown in Table 4 has been averaged by night.

NEOWISE
The NEOWISE survey (Mainzer et al. 2014) observed the position of 2013 LU28 during 13 visits between 2010 March 1 and 2019 June 17 when it was between 26.33-13.23 au. Only the first visit was during the cryogenic part of the mission. Even having all four bands is insufficient for detections of small bodies beyond about 20 au. The data from 2010 March were stacked, but there was no signal, and using the techniques described in Bauer et al. (2015), a 1σ upper limit of 160 km radius for an albedo of 10% was determined. The remaining visits also showed no significant detections. The 2019 June 15-17 visit had the most data, and this was stacked to yield 1σ upper limit for a nucleus radius of 50.5 km. This assumes a 10% albedo. For a 4% albedo, the 1σ upper limit is 79.9 km. Unfortunately, for targets beyond r ∼ 10 au, the NEOWISE photometry is not very useful for small bodies without the thermal bands.

ATLAS
Images were obtained by ATLAS consisting of two 0.5 m telescopes in Hawai'i, using an STA-1600 detector with a 10.5 × 10.5k CCD array as shown in Table 1. The automatic magnitude measurements of 2013 LU28 were produced with the ATLAS image subtraction pipeline. The ATLAS filter system is specialized for asteroids, intended to be sensitive to the silicate band of stony asteroids. The filters are cyan (c) from 0.42-0.65 μm, orange (o) from 0.56-0.82 μm, and a red band from 0.56-0.97 μ. This paper uses survey data in the c and o filters, which can be transformed to the approximate SDSS bands (Tonry et al. 2018) as noted above. All of the images were examined and averaged over the same night. The photometry is shown in Table 4, and the data are plotted in Figure 3.

Spectral Reflectivity
We used IRAF to make photometric measurements of the Gemini images and develop the curve of growth to get the optimal aperture size for spectral reflectivity. Magnitudes with a 5″ radius aperture were also obtained for the sublimation modeling (see Section 3.2). Observations were bracketed with g-filter images in order to correct for any variation in the light curve over the course of the various images taken. Given that the total length of time between the first and last observation was typically less than 30 minutes, this was well below the timescale of the comet's rotation. Once the optimal aperture size was determined for each image, we used the magnitude measurements to compute the spectral reflectivity of 2013 LU28. We converted the magnitude measurements and their uncertainties to a relative spectral reflectivity using The term m λ is the magnitude in a specific filter λ, σ λ is the uncertainty on m λ , m o is the reference bandpass that we normalize to, and m e is the absolute magnitude of the Sun. In the SDSS System, the solar colors 8 are given by g e = 5.12 ± 0.02, r e = 4.68 ± 0.03, i e = 4.57 ± 0.04, and z e = 4.54 ± 0.04. 2013 LU28ʼs surface color is similar to cometary colors measured from in situ space missions (9P, 103P, and 67P) and not like TNOs as determined from BVRI photometry (see Figure 2 and Table 2 for derived colors).
The spectral reflectivity gradients for 2013 LU28 expressed in %/100 nm are calculated from S % 100 nm 20 10 1 10 1 10 where Δm is the comet color minus the solar color, and Δλ (μm) is the difference in the effective wavelengths of the bandpasses. The average for 2013 LU28 is S' = 30 ± 3%/ 100 nm.

Sublimation Models
We used a surface ice sublimation model (Meech et al. 1986) to investigate the heliocentric light curve of 2013 LU28 to search for possible activity. The model computes the amount of gas sublimating from an icy surface exposed to solar heating, as described in detail in Meech et al. (2017a). The total brightness within a fixed aperture combines radiation scattered from both the nucleus and the dust dragged from the nucleus in the escaping gas flow, assuming a dust to gas mass ratio of 1 (Marschall et al. 2020). The output of the model is the predicted brightness as a function of the comet's position along its orbit, or true anomaly. This type of model can distinguish between H 2 O, CO, and CO 2 driven activity. The model free parameters include the following: nucleus radius, albedo, emissivity, nucleus density, dust properties, and fractional active area. When there is information about some of the parameters, it is possible to constrain many of the others.
Because 2013 LU28 has not been previously studied, none of the model parameters are constrained. However, based on typical values for other comets seen in situ and from the ground (Meech et al. 2017a), we assumed the following: nucleus albedo, p v = 0.04, emissivity, ò = 0.9, nucleus phase function, β = 0.04 mag deg −1 , coma phase function, β c = 0.03 mag deg −1 , nucleus density, ρ N = 400 kg m −3 , and an average dust size of 5 μm. With an assumed steep power-law size distribution typical of comets for grains ranging in size between 0.1 μm-mm, the small particles dominate (Kolokolova et al. 2004).
We start by assuming that the initial observations of 2013 LU28 are during a period of inactivity (see Figure 3); thus the entirety of the scattered light is from the nucleus. If we do not include the MPC observations, which have the largest uncertainty because they include a variety of nonprofessional telescopes with unknown photometric aperture sizes, and some with unknown filters, there is a possible increase in brightness starting near TA = −90°. This is suggested by the fact that most of the observations lie above the curve representing the nucleus as defined by the observations from TA = −110°to −100°, and more recent data near TA = −70°to −50°. Bodies with diameters less than about 100 km tend to possess irregular shapes, and thus we expect some variation in brightness due to a rotational light curve. Because the envelope of the majority of the observations lies above the nucleus curve between TA = −90°to −70°, this could represent possible activity. The data in this region have been manually inspected to ensure that the brightness increase is not due to star or cosmic ray contamination. Individual images showed no evidence for any dust coma; however this could mean that the activity may not be spatially resolved.
Assuming that 2013 LU28 was inactive prior to TA = −95°, we fit a nucleus light curve to the Pan-STARRS data. We assumed an albedo of 0.04 and a linear phase function of 0.04 mag dec −1 and used least squares fitting to minimize the chisquared residuals for a range of nucleus sizes. We found that for a radius R N ∼ 55.7 ± 0.3 km the model brightness for the nucleus matched the photometry.
Assuming that the excess brightness for TA from −90°to −70°is due to activity, we ran sublimation models for CO and CO 2 assuming micron-sized dust (as discussed in Section 3.3). We found that a circular area of radius ∼1300 m (∼5.3 × 10 6 m 2 ) of CO 2 ice sublimation or radius ∼240 m (∼1.8 × 10 5 m 2 ) of CO ice would produce a brightening of the comet to a degree that matches the photometric data seen from −90°< TA < −70°(see Figure 3). This is too far out from the Sun for the water-ice sublimation that can lift micron-sized grains only, inside ∼5-6 au (Meech et al. 1986). Furthermore, at these distances, CO 2 is just beginning to turn on, and does not match the data as well as CO sublimation. The likely scenario is that CO was buried subsurface, which caused a delay in the onset of activity. If the data represents activity, there was a finite reservoir of accessible ice because the TA = −65°, and the photometry matched the nucleus light curve.

Image Profile Analysis and Dust Production Limits
Given that in Section 3.2 we are suggesting that 2013 LU28 might have been active, what is the limit for any dust? In order to search for dust, we made deep stacks of images, including images from 17 nights of CFHT data from 2016 September 16 to 2019 August 13. Deep sky flats were made in order to correct for any nonuniformities in the sky background by dividing all images by their exposure time and subtracting out the background counts. The images were then shifted to centroid the object on the same pixel and then median combined to remove all background objects. The resulting image shows no obvious indication of a coma around the object, as shown in Figure 4(a). To produce the normalized surface brightness profiles of both the reference stars and the object, we used the same deep sky flattening process to stack 8 CFHT Megacam images from 2018 May 16. On this night, the stars were slightly trailed (<1″) despite guiding at the sidereal rate (see Figure 1(a)). Because of this, we implement two methods to place limits on the amount of dust as discussed below.

1D Projection
To eliminate star trails, we rotate the image using imrotate in IRAF so that the trail is aligned with the x-axis. We average the counts in each row, 30 pixels in length, centered on the target to obtain the 1D projection of the star without trails (see Figure 4(B)). We do the same for 2013 LU28. When we compare their normalized intensities, we find no evidence of a dust tail in the 1D projection (Figure 4(C)).

Azimuthally Averaged Profiles
To calculate an upper limit on the dust production and activity for 2013 LU28, we compared the azimuthally averaged surface brightness profiles of the reference field stars to that of our object. The subtraction of the normalized stellar profile fluxes from those of an untrailed object with no apparent coma should yield a value of zero with an associated error. The 3σ error can be used as the limiting possible maximum flux contributed from the scattered coma light that went undetected. This flux is given by Meech & Weaver (1996): , v gr [m s −1 ] the grain velocity, and r is in au and Δ in m. If an empirical Bobrovnikoff relation for the terminal grain velocities is assumed (Bobrovnikoff 1954), v gr = v bob = 600 r −0.5 , and f = Δ f¢/206265 where f¢ is the angular size of the aperture (″), then for a given observed flux, the limiting dust production rate will vary as The most sensitive limits will be made when the object is observed at the smallest heliocentric and geocentric distance. Further, because the sky noise dominates the errors in the surface brightness at larger apertures, the most sensitive limits on the dust will be made close to the nucleus, just outside the seeing disk.
Photometric measurements through a series of 15 apertures of eight reference stars that were at least 60 pixels or 11″ from other objects were made from an image stacked on the stars. The same measurements were made of 2013 LU28 in an image stacked at non-sidereal rates. We calculated the surface brightness of the stars and object from the measured fluxes as a function of distance from the center and normalized them to the peak brightness of 2013 LU28 (see Figure 5(A)). The normalized surface brightness of the stars were averaged, then a 3σ upper limit on the possible dust production was found for each aperture size by subtracting the two profiles. This is shown in Figure 5(B).
Given that the seeing for these images was ∼1″.0, the dust production estimates just outside of this aperture places the limit of 0.01 kg s −1 for 1 μm grains coming from the surface at r = 14.7 au.
We ran sublimation models for various volatiles to see how much ice could be sublimating and removing dust at this level. For data from 2018 May 16 and earlier (representative of an inactive nucleus), the sublimation model was also consistent with  the low dust production rate of 0.01 kg s −1 . However, in order to match the brightness of 2013 LU28 between ∼TA = −90°to −80°, we needed to have a gas production rate between 1.1 kg s −1 for CO to 1.5 kg s −1 for CO 2 as shown in Table 3 and in Figure 3. This corresponds to a circular area of radius ∼130 m for CO 2 ice sublimation or radius ∼22 m for CO ice sublimation.

Discussion
Given the possible activity of 2013 LU28 from −90°< TA < −70°, corresponding to r ∼ 17.2-13.1 au (full observations in Table 4) , it is possible that there was an outburst of activity from deeply buried CO or CO 2 ice beneath the surface. With an eccentricity of 0.953, this object is not dynamically new, having been heated on many previous perihelion passages. During sublimation, gases both escape into space and migrate into the interior of the comet. The gas that migrates inwards encounters colder temperatures, and freezes in irregular layers of solid ice (Sarid et al. 2005). As heat from the Sun penetrates the surface as it approaches perihelion, ice beneath the surface can begin to sublimate, building pressure until it breaks through the solid ice above. The escaping gas will lift dust grains from the surface, increasing the brightness of the object. The Deep Impact, EPOXI, and Rosetta missions showed that, even at perihelion, there was very little ice on the comet's surface; however water ice was close to the surface and CO and CO 2 buried deeper (A' Hearn et al. 2012;Capaccioni et al. 2015).
In the regime where the temperatures are high enough that most of the the incident energy is going into sublimation, the very volatile ices will be lost from the surface and migrate to deeper layers. Because the comet nucleus is highly porous, processes that would normally be confined to the surface can occur at deeper layers, e.g., sublimation of ice condensed onto the pore walls. The gas flowing inward will result in a chemical differentiation in the nucleus with the most volatile species at lower depths. Between 17 and 13 au when 2013 LU28 may have been active, the surface is cold enough that CO 2 would be just beginning to sublimate if there were surface ice present. However, if there were significant surface CO 2 ice, then the brightness should have continued to increase to the present, but it has not (see Figure 3, and the model curve for CO 2 sublimation). Surface CO ice would have been active much farther from the Sun. It is more likely that the activity is driven by sublimation from subsurface CO ice.
In the case of 2013 LU28, the activity seen may be similar to the centaur 95P/Chiron. 95P/Chiron was found to have a long slow outburst of activity beginning near r = 14 au and decreasing until ∼11 au, lasting over 4 yr (Meech & Belton 1990;Meech et al. 1997). The cause of this activity was determined to be crystallization of amorphous water ice (Prialnik et al. 1995). Many laboratory experiments have shown that the subsurface release of  Notes. a Radius of equivalent circular patch of ice sublimating to match the dust production limits. b Model dust production rate assuming 10 μm grains. The data presented for the inactive nucleus represent limits to the true values. Active phase data are estimated based on possible photometric detection of activity; c Maximum dust grain size that can be lifted in the gas flow (Meech & Svoren 2004).    Fornasier et al. 2013), the grains were being lifted from the surface on ballistic trajectories that were then perturbed by solar radiation pressure into a bound dust atmosphere (Meech & Belton 1990). Only some small grains escaped and were imaged from the ground at very low surface brightnesses (Figure 4(B)). The bound atmosphere was imaged by the Hubble Space Telescope in Meech et al. (1997).
In a typical comet, dust is lifted off of the surface of the comet by the flow of sublimating gas (Finson & Probstein 1968;Wallis 1982). Once the dust reaches a few nuclear radii above the surface of the comet, the gas and small dust particles become dynamically decoupled and are traveling at speeds near to the gas flow velocity, which is much greater than the typical nuclear escape velocity. Thus, the visible dust coma of a typical comet is dominated by the scattering from dust particles that are on escape trajectories. It is well known that comets can eject large particles (approximately centimeter-sized, or larger) as has been seen at radio wavelengths (Harmon et al. 2004;Nolan et al. 2006), and in situ from missions (A'Hearn et al. 2011;Fulle et al. 2016). Lab experiments show that the ejection of large material typically occurs when the sublimation is occurring at some depth beneath the surface after the buildup of gas pressure (Laufer et al. 2005).
Only the dust particles that are small enough to be lifted from the surface and remain dynamically coupled to the gas will reach escape velocities. Any larger particles lifted off of the surface by the gas remain on bound-ballistic trajectories, following orbits that mostly remain within the comet's Hill lobe before they collide back down with the surface (Meech & Belton 1990). The Hill lobe is where the gravitation forces from the comet remains greater than the gravitational force from the Sun. The Hill lobe is given by where R Hill is the radius of the Hill lobe in km, r is the heliocentric distance in km, m N is the mass of the nucleus in g, and m e is the mass of the Sun. As these larger particles remain above the surface of the comet on their ballistic trajectories, they can be perturbed by radiation pressure and complete several orbits around the comet nucleus before colliding with the surface (Bishop & Chamberlain 1989). The Hill radius for 2013 LU28 was found to be ∼7″.7 between r = 17 and 13 au. In a parallel approach, Bishop (1985) introduced the concept of an "exopause" to describe the level in a planet's atmosphere where the acceleration due to radiation pressure exceeds that due to the gravitational attraction of the planet. Particles on trajectories that intersect the exopause are presumed to be so strongly affected by radiation pressure that they are effectively lost to space. The distance to the exopause is therefore a function of the heliocentric distance, and is given by where β is the ratio of the forces due to the Sun's radiation, and gravity is defined by Burns et al. (1979). For a typical comet at 1 au, R exo ∼2.4β −1/2 km. For 1 cm particles that might be gravitationally bound in a typical comet, R exo ∼ 300 km (i.e., the exopause is within a few nuclear radii of the surface for the optically important particles). In general, the exopause is found to fall within the gravitational Hill radius of the nucleus. It is this level that effectively defines the physical limits to the influence of nuclear gravity. Thomas & Bohlin (1972) also discuss this concept of the exopause with respect to the hydrogen geocorona seen about the Earth. They note that atoms whose initial velocities would have placed them in the bound population (within the Earth's Roche lobe) could actually escape under the influence of Lyα radiation pressure (i.e., particles with orbits above the exopause can escape and form a geotail). The influence of such large bound particles on the visual brightness of the coma of a typical comet at 1 au is negligible since their total effective scattering area for sunlight is an extremely small fraction of that presented by the population of optically significant particles on escape trajectories. We calculated the exopause for 2013 LU28 to be approximately 0″.11 in radius, which is well within the seeing disk of the telescope. Like Chiron, 2013 LU28 could have a bound atmosphere of larger dust particles. 2013 LU28 shows evidence of brightening beginning near 20 au and continuing until around 13 au. The brightening begins as pressure is relieved from the sublimating gasses beneath the surface, exposing ice that begins sublimating and lifting dust off of the surface. The bright trend continues as the exposed ice continues to sublimate, and larger dust grains remain close to the object nucleus within the typical seeing of ground-based telescopes. The brightening only dims back to the apparent brightness of the bare nucleus once the thermally exposed ice is gone or the activity is quenched due to fallback from a layer of insulating dust and a dust coma no longer surrounds the nucleus. Table 3 shows the critical grain size that can be lifted off the surface in the gas flow against the pull of gravity from the nucleus (Meech & Svoren 2004). When only small grains are able to be lifted off of the surface, since the optical observations are most sensitive to scattered light at micron scales, we may not see much material.
In the case of Chiron, the proposed mechanism for activity was amorphous ice crystallization, based on detailed thermal modeling (Prialnik et al. 1995). Here, we propose that for 2013 LU28 there was a period of activity caused by low-level subsurface ice sublimation of CO. Unlike Chiron, which has a neutral spectral slope, 2013 LU28 has a red spectral slope that is consistent with organic-rich comet surfaces. Wide field surveys are now discovering many objects on LP comet orbits: the Manxes, which exhibit no activity, comets active at large distances such as C/2017 K2 at ∼24 au driven by CO (Meech et al. 2017a), and others that become active closer to the Sun, such as C/2015 ER61 near 8.8 au driven by CO or CO 2 (Meech et al. 2017b). Both volatiles are abundant in the outer solar system and have been expected to be present on objects on long-period comet orbits. Objects like 2013 LU28 will help us distinguish between solar system formation models or may represent some of Oort's missing comets. We plan to continue to observe 2013 LU28 as it comes to perihelion.    (13), the difference in surface profiles is converted to a maximum dust production rate that can remain undetected.