The Unusual Apparition of Comet 252P/2000 G1 (LINEAR) and Comparison with Comet P/2016 BA₁₄ (PanSTARRS)

The planned observations of the comet near its close encounter at <0.1 au, coupled with the small FOV of WFC3/UVIS detector (160'' × 160'' maximum, as small as 40'' × 40'' for our subarray images) posed a challenge for the accurate ephemeris predictions, especially for a comet. Reliable characterization of the comet's ephemeris prediction uncertainties was essential for the success of our HST observations.

Previous experience (Rayman 2003; Chesley & Yeomans 2006; Farnocchia et al. 2016) has shown the challenges of accurately estimating comet trajectories. The presence of a coma makes it difficult to correctly locate a comet's nucleus in optical images, and tailward (or sunward in some cases, e.g., Yeomans & Chodas 1989) biases can affect the quality of the astrometric positions used to estimate a comet's trajectory (Tholen & Chesley 2004). Moreover, non-gravitational accelerations could affect the trajectory in ways that are difficult to separate from astrometric biases. Generally, as the prediction lead times shorten and data arcs lengthen, the effects of modeling errors are significantly reduced. A further complication arises from the need for sufficient time to build and upload the HST observation sequence. This requirement places an ephemeris deadline roughly two weeks before the observations are executed. In two weeks, a comet could behave in unexpected ways, especially if close to perihelion, and we have no way to correct the trajectory accordingly.

The data arc for comet 252P is composed of three apparitions, 2000, 2011, and 2015–2016. To mitigate the effect of astrometric biases we conducted an observation campaign from MaunaKea, Las Cumbres Observatory, and the DCT to obtain high-quality imaging data. This observational effort includes the 2015 September recovery of the comet (MPEC 2015-S97). The astrometric positions were extrapolated to the limit of a zero-sized photometric aperture around the brightness peak (Tholen & Chesley 2004), and we also estimated their uncertainties when estimating the trajectory of 252P. For the 2015–2016 interval, we only used astrometry from our observation campaign.

To account for non-gravitational perturbations, we considered two models. The first one is the classical Marsden et al. (1973) model, where the radial, transverse, and normal acceleration components are A_ig(r), i = 1, 2, and 3, and g(r) is a scale factor driven by water sublimation with a peak at perihelion. An asymmetric variant of this model includes a time-offset ΔT in the non-gravitational acceleration peak with respect to perihelion (Yeomans & Chodas 1989). A second, higher fidelity model is the rotating jet model (Chesley & Yeomans 2005), which averages the thrust of a discrete number of jets over a comet rotation.

To analyze the ephemeris of 252P we computed solutions corresponding to three configurations:

• (1)  
  Data since 2000, Marsden et al. (1973) model with A₁, A₂, A₃, and ΔT.
• (2)  
  Data since 2000, rotating jet model with two jets.
• (3)  
  Data since 2011, Marsden et al. (1973) model with A₁, A₂, A₃.

These sets of solutions were helpful to compare the different non-gravitational models and to analyze the sensitivity to the length of the data arc. In particular, while a long data arc put a better formal constraint on the trajectory, non-gravitational perturbations could change behavior with time and so the corresponding ephemeris could be negatively affected.

Figure 1 shows the comparison between the different predictions for the geocentric ephemeris at closest approach. The data cutoff for this prediction is March 7, two weeks before perigee. The jet model and the short-arc solutions provide successful predictions as the reconstructed astrometric position (computed using post-encounter data) falls well within the uncertainty ellipses. Between these two solutions the jet model has smaller prediction uncertainties thanks to the longer data arc used in the fit. On the other hand the A₁, A₂, A_3, and ΔT solution over the long arc fails to accurately predict the plane-of-sky position of the comet at closest approach. This result further confirms the suitability of the rotating jet model and that it is important to exercise care when comet trajectories are fit to a long data arc.

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Another useful step to assess the consistency of an orbit solution is to track its evolution as more data become available to refine the orbit. Figure 2 shows this evolution for the jet model solution starting from a data cutoff of 2016 January 27 and updating the solution every 10 days until 2016 March 7. The prediction ellipses are nicely nested and converge toward the final reconstruction, thus increasing our confidence that the prediction was robust. For these reasons we used the jet model solution for the HST pointing.

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As will be discussed later in Sections 3.1 and 4.2, 252P experienced a significant increase in brightness and non-gravitational perturbations around perihelion. None of the solutions discussed above can fit the post-perihelion data and actually we have not yet found a way to fit the whole 2015–2016 apparition data. When planning comet observations, it is wise to have some margin to account for this stochastic behavior in non-gravitational perturbations, especially when the ephemeris delivery is a week or more before the observation execution. The experience with the ephemeris predictions of 252P for the HST observations is applicable to future comet observations using small-FOV detectors, especially near their close encounters with the observatory.

2.2.1. HST/WFC3 Data

2.2.2. DCT/LMI

We subtracted the bias and applied flat-field corrections created from twilight sky to all images. The photometric calibration was generated from observations of standard stars from the Landolt (2009), Smith et al. (2002), and Farnham et al. (2000) catalogs. Extinction across the OH filter bandpass is highly variable and critically depends on the ozone content of the atmosphere. Therefore, we followed the iterative procedure for OH calibration outlined in Farnham et al. (2000). Images were median combined in the rest frame of each target (Figures 3 and 4).

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The target brightnesses were measured with standard aperture photometry techniques using circular apertures up to 80 pixels (192) in radius. The Farnham et al. (2000) and Landolt (2009) catalogs are on the Vega magnitude system, whereas the Smith et al. (2002) catalog uses the AB magnitude system. The HB filter photometry was converted to gas flux (CN, OH) or continuum flux density (BC, RC) using the calibration constants from Farnham et al. (2000). For V , we used 3.631 × 10⁻⁸ W m⁻² μm⁻¹ for the zero-point flux density and −26.76 for the apparent magnitude of the Sun (Bessell et al. 1998). For r' we used an apparent magnitude of −26.93 for the Sun, based on the color of the Sun (V − R = 0.370; Colina et al. 1996) and the Smith et al. (2002) V to r' transformation.

We converted observed fluxes into production rates using D. Schleicher's online tool at Lowell Observatory.¹¹ The calculations use a Haser (1957) model with scale lengths from A'Hearn et al. (1995) and Cochran & Schleicher (1993). For 252P, we remove the dust continuum from the OH and CN filters by scaling the BC photometry to each respective filter using the continuum color. We measured a BC − RC color of 0.082 and 0.073 mag per 0.1 μm (centered at BC) in 40 and 80 pix apertures, respectively. For BA₁₄, we do not have a continuum color estimate, but experimented with a neutral reflectance, and a reddened color of 0.070 mag per 0.1 μm (similar to the measured values for 252P). The difference between the two colors is 6%; therefore, we incorporate an additional uncertainty of 3% in our CN fluxes. Gas production rates and coma Afρ values are presented for both comets in Table 3. Note that no dust coma for BA₁₄ was identifiable in the r'-band image, so its Afρ estimate should be treated as an upper limit.

Table 3.  DCT/LMI Photometry and Derived Parameters

Target	Time	V	r'	OH	CN	BC	RC
	(UT)	m (mag)	m (mag)	m (mag)	m (mag)	m (mag)	m (mag)
		Afρ (cm)a	Afρ (cm)a	Q (1025/s)b	Q (1023/s)b	Afρ (cm)a	Afρ (cm)a
252P/2000 G1	08:35				10.30 (0.01)	13.06 (0.01)	11.59 (0.01)
					120 (1)	24.3 (0.2)	28.9 (0.3)
252P/2000 G1	09:10	12.01 (0.02)	11.97 (0.03)
		39.5 (0.7)	34.9 (1.0)
252P/2000 G1	11:30		11.99 (0.03)	9.88 (0.02)	10.26 (0.01)	13.04 (0.01)	11.57 (0.01)
			34.6 (1.0)	581 (11)	125 (1)	24.8 (0.2)	29.7 (0.3)
P/2016 BA14	10:10		17.90 (0.04)		17.56 (0.10)
			0.19 (0.01)		0.14 (0.01)

Notes. All photometry is within a 192 radius circle. Uncertainties are empirically measured and listed in the parentheses. Calibration uncertainties for the HB filters and derived gas fluxes are 5%–10% (Farnham et al. 2000).

^aAfρ parameter of A'Hearn et al. (1984). ^bMolecule production rate.

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Since 252P was <0.1 au from Earth during our observations, the orbital motion of HST resulted in a parallax of the target of up to 500'', or >3 FOVs of UVIS full frame. While HST automatically compensated for the parallax in its pointing based on the calculated orbital position, the comet still drifted inside the FOV, causing smearing in many frames. To quantify the smearing, we used the time rate of the measured centroid locations within each HST orbit to approximate the drift and direction of the pointing at the time of each image acquisition. For the exposure time, we can calculate the corresponding amount and the direction of smearing in each image frame (Figure 5). For about half of the images, the smearing is <2 pixels, while in about 10 images the smearing is >5 pixels and up to 7 pixels.

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Smearing affects the measurement of the centroid and all quantities that rely on it, such as aperture photometry, color, and coma morphology. The various amounts of smearing in our images suggests that we should not interpret those measurements made from <5 pixel or smaller apertures or distances from the center without taking special precautions. In addition, we should check all results against the possible effects due to smearing in order not to interpret artifacts.

Five images have their peak pixel values above the 67k DN linearity limit for the detector we used (UVIS2 C-amplifier) with a maximum of 71k DN. Aperture photometry can still be preserved with great accuracy as long as all the blooming in the pixels adjacent to the saturated pixel is included in the measurement (Deustua 2016). The blooming is expected to be small for our maximum saturation level of 6% above linearity limit in a single pixel, and therefore no detectable effect in photometry is expected. For nucleus size measurements (Section 3.4), we simply avoided using those five images with saturated peak pixels.

The light curve of the comet within a 10 pixel (27 km) radius aperture on April 4 shows clear variability (Figure 6 upper) that appears to contain both a periodic component and an overall decreasing trend in a timescale much longer than the duration of our observations in this epoch. The photometric data of 252P from the Minor Planet Center (MPC) database suggest that the comet increased its total brightness significantly around the start of 2016 March with an extremely steep dependence on heliocentric distance. Given the small changes in the geometry of 252P during the April epoch (∼0.1% in heliocentric distance, 2% in the geocentric distance, and 044 in phase angle), we decided to correct the photometry for its geometry dependence using a simple linear correction with respect to time, with a factor of −0.18 mag day⁻¹ derived from trial and error. After this correction, the secular brightness change within the April epoch appears to be removed, and period-searching algorithms (see Section 3.5) suggested a 5.41 hr single-peaked periodicity (Figure 6 middle and lower). However, we note that this purely empirical correction failed to bring the light curve from the March epoch to the same magnitude level as the April light curve.

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Since the aperture photometry, at least those from apertures larger than tens of pixels in radius, is dominated by coma brightness rather than nucleus, the light-curve amplitude decreases with increasing aperture size. The light-curve amplitude vanishes at the point where the dust grain aperture crossing timescale is comparable to the time between consecutive light-curve extrema, which is somewhere between 50 and 60 pixels, or 130–160 km from the nucleus (Figure 7). Using half periodicity of 2.7 hr, the mean expansion speed of the dust in the coma is estimated to be 10–20 m s⁻¹. Given the small expansion speed of coma dust, the periodicity in cometary photometry can only be detected when the aperture size is smaller than a few hundred kilometers, which is generally achievable with HST but difficult from seeing-limited ground-based observing facilities.

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From images acquired through the V- and r'-band, we calculated the linear color slope of the comet. The azimuthally averaged color slope of the dust coma is measured in co-centric annular apertures centered at the nucleus, with the median from all images obtained in the same HST orbit plotted (Figure 8). Overall the color measurement has error bars of up to ±2%/100 nm for the March epoch measurements, and up to ±0.3%/100 nm for the April epoch measurements. Although at small distances (<20 pixels or <50 km) from the nucleus, the color measurement could be affected by the smearing, the color plots appear to be smooth and the median appears to have effectively filtered out the potential artifacts due to smearing.

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Overall the color slopes of 252P on March 14 and April 4 are consistent with each other, and have a similar cometocentric distance trend. At within 100 km from the nucleus, the color slope of 252P's dust coma is about (6 ± 1)%/100 nm for both epochs. At between 100 and ∼500 km from the nucleus, the color slope decreases (bluing) with distance. At >500–600 km, the dust coma shows a bluer color (negative slope). The decreasing trend in color slope with cometocentric distance on March 14 may be slightly steeper than that on April 4, but not statistically significant. Similarly, any possible variations in the color slope with rotation are not statistically significant in our data.

This color–distance behavior of 252P is different from previous HST observations of Comets C/2012 S1 (ISON), which showed an increase of color slope (reddening) with distance (Li et al. 2013a), and C/2013 A1 (Siding Spring) had a nearly neutral dependence (Li et al. 2014, 2016), although the trend for those comets are at a distance of 10,000 km from the comet. The factors that could affect the color of the dust coma include composition, grain size, and possible contamination from gas emission lines in the filter bandpasses. Comparisons with the typical spectrum of comets (e.g., Feldman et al. 2004) suggest that the V-band filter that we used to image the comet covers the Δν = 0, 1 bands and part of the Δν = −1 band of C₂ gas fluorescent emissions, while the bandpass of the r'-filter covers part of the Δν = −1 band and much weaker Δν = −2, −3 bands of C₂ gas emission, as well as the weak NH₂ bands. Ground-based observations suggest that 252P is extremely gas rich with strong C₂ (McKay et al. 2017). From our DCT observations (Table 3), the Afρ values derived for BC and RC filters, which are relatively clean of gas contamination compared to V and r' filters, were 24.8 and 29.7 cm, respectively, whereas the values for V and r' filters are 39.5 and 34.9 cm, respectively. The higher value from V-band suggests more gas contamination than in r'-band, consistent with being contaminated by C₂. Gas contamination is more evident further out from the nucleus due to the much slower brightness falloff of gas coma compared to the dust, consistent with the color–distance trend that we observed. Therefore, the bluing trend of the coma color that we measured for 252P is likely a result of more gas contamination in the V-band filter than in the r'-band filter.

After enhancing the HST images by dividing out the 1/ρ brightness model that represents a coma with a constant dust outflow (e.g., Samarasinha & Larson 2014), we can see an obvious jet-like feature in the sunward direction in both epochs of images (Figure 9). The jet feature appears to be narrow and well defined in most images in both epochs, and the length of its brightest core is >20 pixels (∼50 km). At 50–100 km from the nucleus, the opening angle of the feature widens to about 30°–40°, diffusing into the background coma at ∼200 km from the nucleus. In the April epoch, the projected position angle (PA) of this jet feature changed systematically from ∼60° to ∼120°, suggesting a rotation of the nucleus over the duration of our observations.

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To estimate the possible periodicity in the PAs of the sunward jet, we measured the PAs of the centerline of the jet feature by fitting a Gaussian and a fourth-order polynomial to the azimuthal brightness profile within ±50° of the centerline. The measured PAs from both techniques agree with each other within 5°. The measurements of the PAs at 5–50 pixels from the nucleus showed that the jet feature as projected in the sky plane is mostly radial from the nucleus in the March epoch (Figures 9(a), (b)). In the April epoch when the PAs are <90° (Figures 9(c)–(g)), the jet feature is also nearly radial, but slightly curved toward north when PA > 90° (Figures 9(h)–(k)). Near the maximum PA of ∼120° (Figures 9(m), (n)), the jet feature quickly becomes diffuse and non-distinguishable from the background coma. The curvature and the diffuse behavior of the jet feature at this time suggest that it was likely pointing close to and sweeping through the line-of-sight (LOS) but at ∼120° PA.

Figure 10 (upper) shows the measured PA of the jet feature at 11 pixels (30 km) from the nucleus. The scatter in the fourth orbit (cyan symbols) is during a period when the jet was sweeping through the LOS and became much more diffuse than before, resulting in higher uncertainty in the measured PAs. The PAs measured at other times are all accurate to a few degrees as suggested by the scatter in the data. Since the change in the jet feature should be due to the rotation of the nucleus, we can infer the periodicity from the PA measurements. However, when using the periodicity suggested by the light curves, 5.41 hr as discussed earlier, the PAs do not phase together (Figure 10 middle). The best periodicity that can phase the jet morphology data is 7.24 hr (Figure 10 lower). We will discuss the rotation of the nucleus in Section 3.6.

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3.4.1. Measurements

The unresolved central portion of each comet image is a combination of scattered light from the nucleus and coma dust, and resonance emission from coma gas. By measuring the inner-coma surface brightness radial profile, we can separate the coma contribution from the nucleus contribution, and estimate the nucleus brightness and size (e.g., Lamy et al. 2011). Our approach is summarized as follows, and is depicted by Figure 11.

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We start with images that have had standard calibrations applied (e.g., dark subtraction, flat-field correction), but have not had the field distortions removed, preserving the original shape of the point response function. The inner coma is divided into 30–100 azimuthal bins, and a radial power law is fit to the surface brightness profile within a 12–100 pixels annulus within each resulting wedge, except for image icvbb3f6q where we used a smaller outer radius of 33 pixels to avoid a background source. The power-law slopes and scales are used to generate a synthetic super-resolution image of a coma (0.1 pixel steps), taking care to estimate the surface brightness on subpixel scales. We then convolve the image with a synthetic point source generated with 0.1 pixel steps using the TinyTim software (Krist et al. 2011) version 7.5. Each run of TinyTim considered the filter and array position of the comet from each image, an assumed telescope focus position, and used a G2V spectral energy distribution. A scaled point-source image is then added with the same position as the center of the coma, and the image rebinned to the native pixel scale. The image is then convolved with a model of WFC3's charge diffusion, and the result compared to the original data.

The scale factor for the point source is derived from a least-squares fit to the two-dimensional image, and the result saved. We then perform a grid search over a range of subpixel positions for the comet, and over a range of telescope focus values. The final comet position and focus value is based on a by-eye examination of the image and fit residuals.

We initially examined images with the least amount of smearing (<1 pixel), but with integrations long enough for a high signal-to-noise detection of the coma (generally 30 s or more). However, the resulting data set was limited. In order to consider images from both March and April, and with both the V and r' filters, we necessarily included some smeared images. We chose frames with an apparent linear smearing of only a few pixels. The smearing was accounted for by convolving the super-resolution TinyTim point-source image with a line. We chose a smear length and PA based on our estimate of smearing (Section 2.3), but fine-tuned with by-eye examination of the image and fit residuals.

The nucleus size measurements from those six selected images are summarized in Table 4. To convert the total magnitude of the nucleus to its size, we assumed an r'-band geometric albedo of 0.04, and a slope of 0.04 mag deg⁻¹ for its phase function. The color term V − r' = 0.463 mag (∼6%/100 nm) in a three-pixel-radius aperture is also taken into account in the conversion from different bands. The smear lengths for images icvb12d4q, icvbb3f6q, and icvb12d1q were one, two, and three pixels long, respectively. Image icvbb3f6q was from April, and the other two were from March. The agreement between the nucleus size measured from variously smeared images and those not smeared in the same epoch suggests that our approach to account for smearing is robust.

Table 4.  Summary of Nucleus Fitting Results

Image	UT	Band	rha	Δb	αc	Nucleus	Coma	Residual	Mnucd	Rnuce
			(au)		(°)	(105 DN)				(km)
icvb12d1q	2016 Mar 14T06:19:23.722	V	0.996	0.0566	86.5	0.91	1.22	0.39	17.60	0.28
icvb12d4q	2016 Mar 14T06:26:40.731	r'	0.996	0.0566	86.5	1.09	1.30	0.21	16.94	0.31
icvbb1e9q	2016 Apr 04T16:28:03.789	V	1.037	0.0922	64.5	3.13	3.32	0.89	16.57	0.51
icvbb3f5q	2016 Apr 04T19:35:31.805	r'	1.037	0.0929	64.4	2.70	3.16	0.57	16.27	0.48
icvbb3f6q	2016 Apr 04T19:38:50.797	V	1.037	0.0929	64.3	3.11	3.19	0.31	16.58	0.51
icvbb4ftq	2016 Apr 04T21:01:08.797	V	1.037	0.0933	64.3	3.98	2.93	0.25	16.31	0.58

Notes.

^aHeliocentric distance. ^bGeocentric distance. ^cSolar phase angle. ^dNucleus magnitude. ^eNucleus radius.

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3.4.2. Quality Assessment

The OH production rate of 252P on 2016 April 17 is Q(OH) = 5.8 × 10²⁷ s⁻¹ from our DCT data (Table 2). This value is comparable to that measured in late March by TRAPPIST ((4.5 ± 1.0) × 10²⁷ ${{\rm{s}}}^{-1};$ E. Jehin & C. Opitom 2017, private communication), and 10× of that in late February (3.9 × 10²⁶ ${{\rm{s}}}^{-1};$ D. Schleicher 2017, private communication), consistent with each other considering the heliocentric distance trend of the sublimation activity.

Based on the sublimation model of Cowan & A'Hearn (1984), the sublimation rate of water ice at 1 au is about 1.6 × 10²² s⁻¹ m⁻² for a slow rotator model, and 3.3 × 10²¹ s⁻¹ m⁻² for an isothermal model. Assuming a branching ratio of 0.86 from water to OH by photodissociation (Huebner et al. 1992), the Q(H₂O) of 252P in late 2017 April is about 7 × 10²⁷ s⁻¹, and requires an active area of 0.4 and 1.8 km² on the nucleus for the two extreme models, respectively. For a nucleus of 0.3 km radius, the active fraction of 252P is from ∼40% to over 100%.

For typical JFCs, the active area is a few percent (A'Hearn et al. 1995; Lamy et al. 2004). Some small comets, such as 103P (Groussin et al. 2004) and 46P/Wirtanen (Lamy et al. 1999), have an active fraction of >100% near perihelion. Spacecraft images from close distances of 103P not only showed that its gas activity still appear to originate from discrete areas on the nucleus (Protopapa et al. 2014), but also resolved numerous icy chunks centimeters to decimeters in size ejected from the nucleus and sublimating as they move away (Hermalyn et al. 2013; Kelley et al. 2013), increasing the total active area of the comet as measured remotely. Thus, the large active fraction of 252P of possibly near or greater than 100% could also indicate a large amount of icy grains surrounding the nucleus, consistent with the scenario we proposed previously (Section 3.4). Considering that the dust activity level of 252P was much weaker than this current 2016 apparition, those icy grains, if indeed there, should be ejected in this current apparition rather than in the past.

We searched for periodicities in both the photometry data from 10 pixel radius apertures, and the jet PA data at 11 pixels from the nucleus with two different period-searching algorithms, the Lomb–Scargle (LS) method (Lomb 1976; Scargle 1982) with super smoother, and the Bayesian generalized Lomb–Scargle (BGLS) method (Zechmeister & Kürster 2009; Mortier et al. 2015). The LS periodogram expresses the period search results in the arbitrary power, and the periods with the highest power are considered the most likely periods in the data. The BGLS periodogram is extended from the LS method by using the Bayesian probability theory to describe the probability in frequency/period space. Figure 12 shows the probability plot of our period search with the V-band photometric data using the BGLS method as an example. We also searched the period in r'-band photometric data and the combined dataset with both r'-band and V-band (shifted by the V− r' color of 0.458 mag). All methods for all photometric datasets returned a similar periodicity of 5.41 ± 0.07 hr, and for the jet PA data returned a periodicity of 7.24 ± 0.07 hr. The uncertainties in the best-fit periods are estimated as the standard deviation of the approximate Gaussian shape of the power-frequency plots (for LS method) and the probability frequency plots (for BGLS method). The best-fit periodicities for both the light curve and the jet PA do result in good phasing of data (Figures 6 and 10).

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Comet 252P was observed from the ground before and after its Earth encounter, and the observing conditions during its encounter were unfavorable for most ground-based telescopes due to its southern declination and the full Moon. Knight & Schleicher (2016) reported observations from the ground in early 2016 April in dust, CN, and OH. They detected a short sunward dust feature that has a length and projected orientations consistent with our April epoch observations. On the other hand, the gas coma in both CN and OH displays a different morphology from the dust coma (Figure 3). In particular, what appeared to be two coma features in the gas were visible in the sunward side of the nucleus, and varied smoothly along the north–south directions. Due to their vastly different size scales, it is unclear whether the dust feature and one gas feature originate from the same sources on the nucleus. Despite this, the CN coma morphology as they observed varied smoothly during a night and showed repeatability in ∼22 hr and ∼95.5 hr, implying a period of 7.35 ± 0.05 hr. This periodicity is consistent with the value that we derived from dust morphology, but not with the value derived from our light-curve data.

In order to assess the relative contributions of the sunward jet and the ambient coma to our photometric light curve, we divided the circular aperture into two half-circles, one centered at the azimuthal direction of the jet in the sky, and the other centered at the anti-jet direction. The azimuthal profiles of the coma showed much larger azimuthal variations in the jet side than the anti-jet side (Figure 13(a)). Therefore, we use the total brightness on the anti-jet side to approximate the total brightness of the ambient coma on the jet side, and subtract it from the jet-side photometry to estimate the fractional contribution of jet in the coma light curve (Figure 13(b)). Overall, the sunward jet contributes a few percent to up to 20% of the total brightness in the 10 pixel-radius aperture photometry. In addition, the 5.41 hr periodicity keeps visible in full-circle aperture light curves for larger apertures until about a 50 pixel radius aperture (Section 3.1, Figure 7), consistent with being dominated by the overall dust coma rather than the jet. Therefore, we conclude that the jet and the ambient coma have different sources on the nucleus, and the light curve and the associated 5.41 hr periodicity (Figure 6) are dominated by the ambient coma rather than the jet.

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Details of how cometary jets hundreds to thousands of kilometers in extent form and extend to space are largely unknown. Recent spacecraft observations of comets from close distances revealed a large number of small jets that only extend a few to tens of kilometers from the nuclei, and some attempts have been made to correlate those small jets to large-scale jets observed from the ground (e.g., Farnham et al. 2007, 2013). In the case of 19P/Borrelly, the large-scale sunward jet observed from the ground directly originates from the nucleus (Soderblom et al. 2004). In other cases, at least some small jets near the nucleus probably merge together at some distance from the nucleus to form large-scale jets that are observable from the ground (e.g., Sekanina et al. 2004). On the other hand, at least for the case of 67P, the observations by Rosetta suggested that the whole sunlit areas together with multiple sources that produce enhanced dust release are the dominant source of its ambient coma (Kramer & Noack 2016). If this is the case for 252P, then the modulation of the whole sunlit area due to the rotation of the nucleus could cause the modulation of the dust release into the ambient coma, while the large-scale jet that we observed could originate from a relatively small, isolated area on the nucleus. Therefore, the rotational modulations of the light curve and that of the projected PA of the jet could be different for 252P: the light curve reflects the change in the entire sunlit area, while the jet reflects the illumination condition and the orientation of its source region.

The different periodicities derived based on the repetition of coma morphology and light curves present a dilemma. If the nucleus is in the most dynamically stable rotation around the short principal axis, under certain circumstances, periodicities in the 1:2 ratio can be understood. However, a periodicity ratio of 4:3 (7.24 hr versus 5.41 hr) cannot be explained in terms of a principal axis rotator, and we suggest that Comet 252P is likely in a non-principal-axis (NPA) rotational state. The limited amount of data on this comet makes it difficult to derive a definite rotational state. However, three additional lines of evidence support the possibility of an NPA rotator.

First, since the nucleus of 252P is relatively small, it is a likely candidate for rapid changes in its rotational state including the possibility for excitation into an NPA rotational state (cf. Samarasinha & Mueller 2013 and references therein). NPA rotational states are not rare in comets, with the best examples being comets 1P/Halley (e.g., Samarasinha & A'Hearn 1991) and 103P (Belton et al. 2013). Second, numerical studies indicate that as rotational states of comets evolve, they may spend considerable amounts of time near states having commensurable component periods (Samarasinha & Belton 1995; Neishtadt et al. 2002). This is also the case for 1P and 103P. Third, the activity of 252P in its 2016 apparition increased by a factor of nearly 100 from its 2000 apparition level (Section 4.3). If we fit the non-gravitational force to 252P's orbit before and after 2016 April 1 separately, the amplitudes of A₁ and A₂ parameters both increase by a factor of ∼10. Such a sudden and significant increase in the activity level on a small nucleus could likely change the rotational state and even put it into excited rotation during its 2016 perihelion passage.

We can propose one possible scenario for the rotational state of 252P to explain the conflicting periodicities derived from coma morphology and light curve. If the partial light-curve-based periodicity (5.41 hr) is manifesting the total outgassing from the entire sunlit side of the nucleus, it may correspond to a period P = 5.41 hr given by $\tfrac{1}{P}=\tfrac{1}{{P}_{\phi }}+\tfrac{1}{{P}_{\psi }}$ where P_ϕ is the precessional period of the long axis (7.24 hr) and P_ψ is the rotational period of the long axis around itself (∼22.0 hr). If the morphological features in the dust (and in CN) are originating from a source region near the end of the long axis, it may only be mimicking P_ϕ. One potential difficulty for this scenario, though, is that if there are two CN jets observed from the ground and both rotating about the nucleus at a period of 7.35 hr (Knight & Schleicher 2016), then they would have to both originate from close to the two ends of the long axis. More data from the ground are needed to study the phasing of the two CN jets and see how they are related to each other. While this scenario may not be the only solution, it is a possible scenario.

BA₁₄ had a close encounter to Earth at 0.0237 au on 2016 March 22.64682, one day after the close approach of 252P. The total magnitude data of BA₁₄ from the MPC can be fitted with a scaling of (r_hΔ)⁻² and the typical phase slope between 0.02 and 0.06 mag deg⁻¹ for cometary nuclei and dark asteroids (e.g., Lamy et al. 2004; Li et al. 2013b) (Figure 14). In addition, the non-gravitational force parameters A₁, A₂, and A₃ for BA₁₄ are constrained to be <10⁻¹⁰ au ${{\rm{d}}}^{-2}$ in their absolute values, which are one or two orders of magnitude lower than typical comets (Farnocchia et al. 2014) and consistent with lack of non-gravitational forces. Therefore, we assume that the total brightness of BA₁₄ throughout its perihelion passage has always been dominated by the nucleus, and derived an absolute magnitude H = 19.2 for BA₁₄ with a phase slope of 0.04 mag deg⁻¹. The corresponding diameter is ∼1 km if we further assume a geometric albedo of 4%. This estimate is consistent with the results from radar observations, which has a diameter of >1 km (Naidu et al. 2016), and the estimate from NEOWISE data (700 m, J. Bauer 2017, private communication.) and ground-based observations with IRTF (V. Reddy 2017, private communication).

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Despite having about 10× the surface area of that of 252P, BA₁₄ has much weaker activity than 252P. We observed the two comets by the DCT at similar heliocentric distances. Thus, we can use their CN production rates as a proxy for water, assuming that the CN/OH coma mixing ratio is constant. Thus, comet 252P was ∼900× more active than BA14, and the active fraction of BA₁₄ is about ${10}^{-4}$ of that of 252P at ∼0.01% level.

Radar observation also revealed BA₁₄ as a slow rotator with a period of ∼40 hr, (Naidu et al. 2016), which is much slower than that of 252P. The limited duration of radar data cannot constrain the mode of its rotation. Given the relatively large size of BA₁₄, it is probably in a relaxed rotational state with any NPA mode damped out already. On the other hand, the much smaller size of 252P compared to that of BA₁₄ and the active nature of 252P suggest that it is more likely for 252P to have changed its rotational state.

Whether 252P and BA₁₄ are a split pair is still unclear. The similarity in their orbits and that in their cometary activities (excluding the elevated activity of 252P in the 2016 apparition) suggest that they are associated. Split events are not rare among JFCs. 169P/2002 EX12 (LINEAR; hereafter 169P) and P/2003 T₁₂ (SOHO) are another example of such a pair (Sosa & Fernández 2015). Comet 289P/Blanpain (D/1819 W₁; hereafter 289P) is a small (300–400 m in diameter) and very weakly active JFC that survived from a split event (Jewitt 2006). No other asteroidal or cometary object that appears to be dynamically associated with 289P, but a meteoroid stream is confirmed to be associated with it (Jenniskens & Lyytinen 2005).

A 0.3 km nucleus makes Comet 252P one of the smallest cometary nuclei known to date (Fernández et al. 2013). Comet 252P appears to be hyperactive in its 2016 apparition with nearly 100% or even higher active fraction. However, the dust activity in its 2016 apparition is substantially stronger than that in its 2000 apparition (Figure 15), which had similar observing geometry to its 2016 apparition. The Afρ measured from the 2000 apparition of about 0.6 cm (30–90 days post-perihelion), together with the lack of evidence for a dust trail associated with this comet, suggests that its activity has remained weak since entering its current orbit a few hundred years ago (Ye et al. 2016a). Although observations during its 2005 and 2010 apparitions are unavailable due to the unfavorable geometries, the success in fitting its orbit solution using the astrometric data from both the 2000 apparition and 2016 pre-perihelion (Section 2.1) suggests that the activity level of 252P in the previous two apparitions was not unusual.

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In the 2016 apparition, the activity level of 252P remained similar to its 2000 apparition level until about two weeks pre-perihelion when its brightness increased significantly. Such an elevated dust activity gradually decreased, and returned to a level comparable to its 2000 apparition level at about 70 days post-perihelion. The sudden increase in non-gravitational force (Section 4.1) during its 2016 perihelion passage strongly suggests that the significant increase in activity level started from this apparition. The reason for the elevated dust activity is not clear. The Afρ of 50–60 cm about 20 days post-perihelion measured from our data is nearly 100× higher than its activity level in the 2000 apparition at comparable heliocentric distance, and represents the peak dust activity in this 2016 apparition. If its dust-to-gas ratio remains constant, then the active fraction of 252P in the 2000 apparition would be just <1%, putting it into the category of weakly active comets.

If the increased activity level of 252P in this apparition is unusual, and the activity level of this comet has remained weak as suggested by previous studies, then the small size of this comet could be primordial. However, the possible dynamic link between 252P and BA₁₄ means that if they are indeed split pairs, then its size will not be primordial. In this case, if we assume that these two objects are the dominant components of all fragments, then the diameter of the parent comet would be about 1–2 km, which would still be near the small end of the cometary nucleus size distribution (Fernández et al. 2013). The weak active fraction of both objects suggests that the small primordial sizes of their parents are likely, whether common or not.

The weak activity and the possible association of 252P and BA₁₄ offer some hints about the end state of JFCs. The possible end states of JFCs include dormancy, extinction, fragmentation, impact on a planet or the Sun, and removal from inner solar system due to planet encounters (mainly with Jupiter). It is not clear how the dormancy and/or extinction occur—whether it is a gradual process and the comet activity decreases slowly, or whether it is a relatively abrupt process when the (near-surface) volatiles in a cometary nucleus depletes. The existence of a number of extremely weakly active comets, including 169P (Kasuga et al. 2011), 209P/2004 CB (LINEAR; Ye et al. 2016b), 252P, 289P (Jewitt 2006), 300P/2005 JQ5 (Catalina; Ye et al. 2016b) suggest that the shutoff process is probably gradual.

On the other hand, although the causes for cometary nucleus fragmentation are not obvious and not well understood (e.g., Boehnhardt 2004), most comets that we have observed fragmentation events have moderate-to-high activity level, although observational selection effect could have played a role. The fragmentation events of those weakly active comets, including the 289P parent comet (Jenniskens & Lyytinen 2005), and the parent comets of the putative pairs of 169P and P/2003 T12, as well as 252P and BA₁₄, indicate that fragmentations also occur in weakly active comets quite frequently, whether on their way to dormancy or extinction or being weakly active ever since their formation. Therefore, fragmentation and dormancy/extinction are not necessarily exclusive of each other. A common pattern for the end state of JFCs might be a long-term, gradual decrease in cometary activity toward dormancy or extinction, accompanied by occasional fragmentation events. One could imagine that the parent of 252P and BA₁₄ might behave like 252P. Although it is weakly active during most of its lifetime, the occasional significant increase in the activity might trigger a fragmentation event, ejecting an inert section of its nucleus, and such processes just keep on going. If this is the dominant pattern for the end state of JFCs, then the implication is that most dormant/extinct comets would be fragments and have relatively small sizes, probably around a kilometer in diameter.