Implications for the Formation of (155140) 2005 UD from a New Convex Shape Model

We present photometric observations of 2005 UD obtained using the following telescopes: the Ondřejov Observatory 0.65 m telescope, the Danish 1.54 m Telescope, North 0.6 m TRAnsiting Planets and PlanetesImals Small Telescopes (TRAPPIST-N), the 4.3 m Lowell Discovery Telescope (LDT), and the 2.6 m Nordic Optical Telescope (NOT). Our analysis also includes sparse data sets from various surveys (discussed below). Tables B1, B2, and B3  B provide details about the observing circumstances.

We used the 4.3 m Lowell Discovery Telescope (LDT, located in Happy Jack, Arizona, USA) on the nights of UT 2019 October 19, 2019 November 18, and 2021 November 3. Images were captured using a broadband VR filter (approximately encompassing the Johnson–Cousins V and R bands) and the Large Monolithic Imager, which features 6144 × 6160 pixels and a square $12\buildrel{\,\prime}\over{.} 5$ field of view. This instrument samples at a pixel scale of 012 pixel⁻¹ but was used in 3 × 3 binning mode. Exposure times ranged from 60 to 120 s for the first night, from 14 to 20 s for the second, and from 30 to 35 s for the last. Seeing conditions were very stable for the first and last night and stable at the 25% level for the second night. We recorded median FWHM values of on-chip point sources of about 27, 15, and 23 for the first, middle, and last night, respectively.

The 2.6 m NOT is located at the Spanish Observatorio del Roque de los Muchachos, La Palma, Canarias, Spain. For these data the NOT imaged with the Alhambra Faint Object Spectrograph and Camera (ALFOSC), which equips a nearly square 2048 × 2064 pixel detector sampled at 021 pixel⁻¹. Observations were carried out on the nights of UT 4 November 2019 and 18 November 2019 in the Sloan Digital Sky Survey (SDSS) r filter and with a SDSS g-r-i sequence, respectively. The images were subject to 2 × 2 binning and exposure times set at 30 s across both nights. Seeing varied typically from 1'' to 25 across both nights, with conditions improving during the later half of the night for both runs.

Additional observations were collected by the robotic 0.6 m TRAPPIST-North (Jehin et al. 2011) on the nights of UT 2019 November 24–26. TRAPPIST-N is located at the Oukaïmeden Observatory in the Atlas Mountains in Morocco. This telescope features an Andor iKON-L BEX2-DD CCD camera imaging through a Cousins R filter. Additional instrument specifications include a 060 pixel⁻¹ scale and a 22' square field of view. The images were binned 2 × 2 with exposure times set at 120 s. Seeing for the first night was variable with median on-chip values ranging from ∼3'' to 42, with conditions improving on the second night, where values were in the range of ∼27–4''. The final night unfortunately presented poor observing conditions, so we refrained from using data from this night in our analysis.

Observations in 2021 corresponding to nights UT October 27–30, as well as one night in 2018 on UT November 04, were carried out at La Silla Observatory using the Danish 1.54 m telescope (labeled "Danish" in Table B3). The DFOSC instrument on this telescope has a deep depleted BI 2k × 2k sensor with 13.5 μm square pixels, and we used it unbinned. Integration times were between 60 and 140 s, and the telescope was tracked at half the apparent rate of the asteroid, providing star and asteroid source profiles in one frame.

For the remaining observations from the 2018 apparition we used the Ondřejov Observatory 0.65 m telescope (labeled "Ondřejov" in Appendix B). The 0.65 m is a reflecting telescope operated jointly by the Astronomical Institute of ASCR and the Astronomical Institute of the Charles University of Prague, Czech Republic. It uses a Moravian Instruments G2-3200 MkII CCD camera (with a Kodak KAF-3200ME sensor and standard BVRI photometric filters) mounted at the prime focus. The CCD sensor has 2184 × 1472 square pixels (6.8 μm pitch) with microlenses, and we imaged in 2 × 2 binning mode, providing 105 pixel⁻¹ and a 19' × 128 field of view. Integration times were between 30 and 100 s, and we set the tracking at half-apparent rate of the asteroid.

We sourced the sparse data from the following:

• 1.  
  observations from the Catalina Sky Survey (CSS; Larson et al. 2003);
• 2.  
  observations from the Pan-STARRS project (Chambers et al. 2016);
• 3.  
  images from the ZTF project (Bellm et al. 2019) downloaded from the IRSA server (https://irsa.ipac.caltech.edu/applications/ztf/); and
• 4.  
  observations from the ATLAS project (Tonry et al. 2018).

For all but the ZTF sparse data we utilized the calibrated chip-stage photometry (unpublished) and associated Julian dates reported on the Minor Planet Center (MPC). ²¹ Processing of the ZTF images is described in the following paragraph.

We bias- and flat-field-corrected data from our new observations using standard techniques. We used the Python-based PhotometryPipeline (Mommert 2017) to measure the photometry of these new data, as well as the ZTF sparse data. We note that neither the field stars nor 2005 UD were trailed, and thus irregular photometry was not required for these new observations. A high-level overview of the pipeline workflow is as follows: astrometry using SCAMP (Bertin 2006), which utilizes the VizieR catalog service (Ochsenbein et al. 2000) to perform image registration via the Gaia Data Release 2 catalog (Gaia Collaboration et al. 2018); point-source extraction using Source Extractor (Bertin & Arnouts 1996); photometric zero-point calibration using the Pan-STARRS DR1 catalog (Flewelling et al. 2020); and distilling the calibrated photometry by using the object's position in the frame as returned through a query to the JPL Horizons system (Giorgini et al. 1996). Additionally, the pipeline executed photometric calibration using stars with solar-like colors in the same frame from the SDSS DR9 catalog (Ahn et al. 2012), where the color thresholds were set at (g − r) = 0.44 ± 0.2 and (r − i) = 0.11 ± 0.2. Using the curve-of-growth procedure outlined in Mommert (2017), the pipeline determined a best-fit aperture radius of 2.84–4.53 binned pixels (122''–194) for the NOT data and 3.26–5.37 binned pixels (117–193) for the LDT data. The TRAPPIST data were the only exception to this, where we manually set apertures of 5-pixel radius (3'').

Data from the 2018 and 2021 apparition that were taken with the Ondřejov Observatory 0.65 m and Danish 1.54 m telescopes were subject to a custom aperture photometry program Aphot + Redlink developed by Petr Pravec and Miroslav Velen. In short, the software performs a semiautomated routine to select optimal apertures for the photometry. Star-like sources in the science frames are calibrated in the Johnson–Cousins V–R system with standard stars from Landolt (1992) facilitating 0.01 mag precision in photometric conditions.

Appendix B includes further details of all light curves used in our analysis. Figure 1 shows ecliptic coordinates corresponding to our new observations, as well as future apparitions.

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To get a reliable shape solution, it is imperative to constrain the rotational period of the object. The parameter space is riddled with local minima due to the rotational period, which, since convexinv is a gradient-based algorithm, will cause the optimizer to get trapped and converge to an ill-fitting solution. The spacing of these local minima ΔP (in hours) in the period-space χ² spectrum is given roughly by ΔP ≈ P²/(2T), where P is the rotational period of the object and T is the time span of the entire data set (Kaasalainen et al. 2001). We ensured that the step size of the period search did not increase significantly above this value to prevent missing the correct period. We define a unique period or spin solution if its χ² (see Section 3.1 in Kaasalainen & Torppa 2001 for how this test statistic is calculated) is lower than that of all other candidate solutions by at least 10% (also used in Hanuš et al. 2011). Note that while the criterion employed in Hanuš et al. (2018) suggests that a χ² threshold of ∼5% above the minimum is valid for our data set, we opt for the more rigorous 10% threshold to make the global minimum more distinct.

Prior to running period_scan, we specified a narrow period search window centered on the literature value and assigned weights to each light curve to improve the goodness of fit; noisy and sparse light curves were assigned lower weights. We optimized the individual weights W_LC for each remaining dense light curve quantitatively using W_LC = 1/rms², where the rms error is obtained by fitting a Fourier series to each light curve. Next, all nonzero weights for dense light curves were then multiplied by a scale factor to bring the sum of the dense light curve weights equal to the number of nonrejected dense light curves (in our case 78). For the 2005, 2019, and 2021 apparitions we fit a Fourier series up to the seventh order to each light curve. For the 2018 apparition, we limited the fitted Fourier series to second order as a form of regularization since these 2018 data compose ∼80% of our dense light curves. Performing various shape modeling trials showed that fully optimizing the weights for all dense light curves biased the model heavily to the 2018 apparition by suppressing the weights of the light curves from the other apparitions. This is likely because data from the other apparitions, particularly from 2005 and 2021, are quite limited in both quantity and quality. Further, because of 2005 UD's relatively smooth and invariant sinusoidal light curve (see Figure 5 for an example), we determined that a second-order Fourier series was sufficient in penalizing lower-quality light curves without significantly underestimating the weights of the high-quality ones. For the sparse light curves, we assign weights at the 10% or 20% level (see Section 3.2) by taking the average of the lowest 10% or 20% of weights of the dense light curves.

The period_scan results within a search range of 5.225 and 5.245 hr produced a unique sidereal rotational period value of P_sid = 5.234246 ± 0.000097 hr (Figure 2). A comparison of our period solution with those from previous studies is presented in Table 1. A previous period search for 2005 UD conducted in Devogèle et al. (2020) suggested the possibility of a three-peaked light curve corresponding to a rotation period around 7.85 hr. With the addition of our new data, we note significant reduction in the goodness of fit for periods in this vicinity. As such, we can now exclude sidereal period solutions in this range and surmise that this is an alias.

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Table 1. Comparison of Previous Rotational Period Estimates for 2005 UD with This Work

Period	Uncertainty	Source
(hr)	(hr)
5.23		Jewitt & Hsieh (2006)
5.2492		Kinoshita et al. (2007)
5.231	±0.034	Sonka et al. (2019)
5.235	±0.005	Devogèle et al. (2020)
5.2340	${}_{-0.00001}^{+0.00004}$	Huang et al. (2021)
5.234246	±0.000097	This work

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Using our period solution, we followed the standard convexinv recipe to derive a shape model. We specified 48 initial pole orientations isotropically distributed on the celestial sphere at 30° spacing, which is later optimized during the inversion procedure. The uncertainties for the sparse data from the MPC (all but the ZTF data) are not reported. Thus, the contribution of each sparse data set toward convergence was assessed by performing a coarse grid search across all sparse data combinations, where each individual sparse light curve was assigned a 0%, 10%, or 20% weight. By scanning through these weights, we aimed to minimize the relative χ² value for the dense light curves only. Following this test, we assigned a weight of 10% to all but the ZTF data (assigned 20%), as this specific combination produced the lowest χ². This combination is not surprising since we reduced the ZTF sparse data ourselves and thus had the knowledge to reject individual data points based on error, source blending, etc. The ZTF data also had the largest phase-angle coverage (i.e., more viewing geometries) of the sparse data sets, covering ∼100° in phase over a 3 yr span.

Following this, we were left with four probable spin solutions, which are listed in Table 2. All four shape models had a small dark facet area (below 1% of the total facet area), which is needed to preserve convexity, so we were not able to eliminate any of these candidate solutions using this metric. Further, this suggests that nonconvex features (e.g., concavities) do not occupy a significant area on 2005 UD's surface. Following this, we computed the inertia tensors (see Dobrovolskis 1996 for a full description) of the shape models to discover that Solution 1 and Solution 4 had an inertial axis significantly misaligned from the z-axis, so we rejected these solutions on the basis of being nonphysical (i.e., there is no evidence that 2005 UD is in nonprincipal axis rotation). However, one caveat is that if 2005 UD is not uniform in color (see Section 4.1) or density, then our convex approximation may contain systematic errors that could manifest as the aforementioned inertial axis misalignment.

This left us with Solution 2, (λ₂, β₂) = (1166 ± 22, − 536 ± 47), and Solution 3, (λ₃, β₃) = (3003 ± 25 − 554 ± 22) (1σ errors), which are equally well fitting. Errors were estimated by agitating various parameters during dozens of trial runs and investigating the effects on χ² values. Solution 3 is interesting because constraints on the pole orientation of (3200) Phaethon place it in the range of 308° ≲ λ ≲ 322° and −40° ≲ β ≲ − 52° (Kim et al. 2018 and Hanuš et al. 2018), which is within our 3σ error. Further discussion on the implications of these pole solutions for the formation of 2005 UD is given in Section 5.

Recent shape modeling efforts using the Lommel–Seeliger ellipsoid method by Huang et al. (2021) yielded two candidate pole solutions for 2005 UD: (1) $(72\buildrel{\circ}\over{.} {6}_{-7.3}^{+4.2},-84\buildrel{\circ}\over{.} {6}_{-2.1}^{+6.2})$ and (2) $(285\buildrel{\circ}\over{.} {8}_{-5.3}^{+1.1},-25\buildrel{\circ}\over{.} {8}_{-12.5}^{+5.3})$. Pole 2 is favored as their preferred solution and is both comparable to Phaethon's and largely in agreement with our Solution 3 with overlap in longitude within 3σ errors.

Thermal data of 2005 UD from two different epochs were obtained during the Near-Earth Object Wide Infrared Explorer (NEOWISE) reactivation mission (Mainzer et al. 2014) using the two shortwave filters (W1: 3.1 μm; W2: 4.6 μm). Thermophysical modeling of these data was presented in Devogèle et al. (2020). The best-fit solution from the thermophysical model (λ_TPM = 102° ± 20° and β_TPM = −35° ± 30°) is consistent with Solution 2. Given that the other pole solution candidates (Solutions 1, 3, and 4) were inconsistent with the predicted longitude from the thermophysical analysis and Solution 2 consistently attained the lower χ² among numerous trial runs, we adopt λ_p = 1166 ± 23, β_p = −536 ± 54 as our preferred solution. A comparison between our pole solutions from light curve inversion, solutions from the above thermophysical modeling, and Phaethon's pole is illustrated in Figure 3.

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The convex shape (Figure 4) from our preferred pole solution (λ_p , β_p ) = (1166, − 536) is nearly identical to our other candidate solution (λ, β) = (3003, − 554). This is expected because there remains a 180° ambiguity in ecliptic longitude for the two solutions for roughly the same pole latitude. We thus expect features to be mirrored across the x-z plane. As an additional test in the validity of these two solutions, we computed light curve predictions of these two shapes and analyzed them by eye to find equally good agreement with all of our light curves. A suite of 12 plots illustrating the fits between synthetic and real light curves from epochs in 2005, 2018, 2019, and 2021 using our preferred solution is shown in Figure 5.

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Thermal emission observations, coupled with photometry, are of particular value for albedo and size determination. A thermophysical study of 2005 UD by Masiero et al. (2019) presented a value of 0.14 ± 0.09 for the geometric albedo and 1.2 ± 0.4 km for the effective diameter. However, Masiero et al. (2019) note that the modeling was only based on data from two observational epochs from the NEOWISE survey.

The most recent values to be reported come from Devogèle et al. (2020), with an effective diameter of 1.3 ± 0.2 km and geometric albedo of 0.10 ± 0.02 based on photometry and an albedo−polarimetry relation (Cellino et al. 2015). Devogèle et al. (2020) also included thermophysical modeling (using a different technique from that used in Masiero et al. 2019) to derive a geometric albedo of 0.14 ± 0.07 and effective diameter of ${1.12}_{-0.21}^{+0.49}$ from the same limited NEOWISE data set. Despite the slight differences in these nominal values, they are all consistent and suggest that the albedo and diameter of 2005 UD are well constrained.

Our shape models of 2005 UD reveal that the general shape can be inferred as a triaxial ellipsoid with a/b = 1.41 axis ratio that produces symmetric sinusoidal light curves with amplitude of about 0.4 mag. We notice prominent flat areas at the north and south poles on our convex shape approximation, which is expected, as these areas are the least constrained with unresolved disk-integrated photometry. Devogèle et al. (2020) is the only other work to have attempted shape modeling of 2005 UD using our methods (as presented in Kaasalainen et al. 2001), and they showed that their light curve data alone could not eliminate the possibility of a sidereal period of ∼7.85 hr. With the addition of our new data, the possibility of a three-peaked light curve and consequently a shape more akin to a tetrahedron is nonviable.

We analyzed a time series of photometric colors of 2005 UD derived from 341 × 30 s exposures taken in a g-r-i sequence at the NOT (Section 2.1) to investigate previously reported variations in surface color (Kinoshita et al. 2007). These multifilter light curves span one complete rotation of the body. Calibrated photometry using the Aperture Photometry Tool (APT; Laher et al. 2012) shows the following apparent magnitudes: g = 19.34 ± 0.01, r = 18.87 ± 0.01, and i = 18.80 ± 0.01. We thus report colors as (g − r) = 0.47 ± 0.01 and (r − i) = 0.07 ± 0.01. To compare with Johnson−Cousins colors of 2005 UD from prior analyses, we performed color transformations using (B − g), (V − g), (R − r), and (R − I) equations from Jordi et al. (2006). Our results are consistent with previous works and are displayed in Table 3.

To check for rotational color variability, we computed color as a function of rotation by linearly interpolating between adjacent points, e.g., measured g minus interpolated r (Figure 6). Within the signal-to-noise ratio of our data we did not detect any systematic color variations that are more significant than 1σ away from the mean across the region of the body visible during this observation period. This null detection is consistent with the results of (1) Devogèle et al. (2020), who used separate spectroscopic and polarimetric methods to probe for surface heterogeneity, and (2) Kareta et al. (2021), who saw no color variations in the near-infrared.

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Our above-mentioned results are in contrast to Kinoshita et al. (2007), who reported ∼0.2 mag R − I color variation. One explanation for this discrepancy is that 2005 UD's surface color differs as a function of latitude, as there was a ∼52° difference in the subobserver ecliptic latitudes accessed by these two color data sets. This modest difference in subobserver latitude suggests that any color heterogeneity on the surface would have to be confined to small (<50° in latitude) yet highly contrasting spots in order to have an influence on the hemispherical averages represented by unresolved, ground-based photometry. Photometric modeling of such a spotted surface could provide insight on whether this interpretation is physically plausible, but this is beyond the scope of this work. Notably, a recent study by MacLennan et al. (2022) found evidence that Phaethon's surface is heterogeneous as a function of latitude, which adds merit to the above hypothesis. Future multicolor photometric observations could provide further insight into 2005 UD's surface properties.

Given the detection of activity associated with Phaethon, we conducted a search for indications of a faint coma or dust tail around 2005 UD. We utilized the image processing tool Siril ²² to stack LDT images from the night of 2019 November 18 using an average combination procedure with no rejection (Figure 7). The stacked image corresponds to 10,910 s (about 3 hr) of integration time with a calculated depth of 26.8 mag arcsec⁻² within an annulus extending θ = 18–36 from the object center; this is the deepest existing stacked image of 2005 UD at the time of writing. We used the APT (Laher et al. 2012) to measure a radial surface brightness profile to compare this stacked image of 2005 UD with a close field star to search for indications of a faint coma. We then fit the model

$$\begin{eqnarray*}&&S(r)=A+{Br}+{{Cr}}^{2}+{{Dr}}^{3}+{{Er}}^{4}+{{Fe}}^{-\tfrac{{r}^{2}}{2\sigma }},\end{eqnarray*}$$

which is explained in Laher et al. (2012). Next, we subtracted the background levels from the profiles and associated models before normalizing the field star radial profile to the peak flux of the stacked 2005 UD profile. The results of these efforts are showcased in Figure 7 alongside a similar analysis performed on the active Centaur 2014 OG392 from Chandler et al. (2020) for comparison.

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An additional quantitative search for a faint dust stream or tail was performed by analyzing summed pixel values in annular slices around the stacked asteroid (as demonstrated in Chandler et al. 2021) to search for excess flux in the anti-solar and anti-motion direction. Along with visual scrutiny, no indications of activity from 2005 UD were detected. Importantly, if 2005 UD exhibits activity via thermal fracturing of the surface regolith (akin to Phaethon), we would expect difficult detection circumstances (Ye et al. 2021) because 2005 UD was close to aphelion (heliocentric distance of 1.7 au) at the time these data were gathered. Targeted observations of 2005 UD near perihelion might offer a better chance at detecting activity.

One way to place an upper limit on mass loss is by using a simple model with knowledge of the limiting magnitude within a projected annulus. We again used the stacked image from the LDT for this procedure using an annulus of size θ = 18–36. Using the procedure outlined in Section 3.2 of Jewitt (2013), we derive an upper limit of either 0.37 kg s⁻¹ or 0.04 kg s⁻¹ based on assumed grain radii of 10 mm (the upper limit of surface grain size from Devogèle et al. 2020) and 1 μm, respectively. Additionally, we assume a material density of 1500 kg m⁻³. Following Jewitt (2013), we use particle ejection velocities of 1 m s⁻¹ for millimeter-sized grains and 1 km s⁻¹ for micron-sized grains. These upper limit results are largely consistent with the ≲0.1 kg s⁻¹ estimate derived by Kasuga & Masiero (2022) using NEOWISE observations.

An intriguing result to come out of our analysis is a well-fitting pole solution that is consistent with Phaethon's in both longitude and latitude (see Section 3.2). This encourages a formation scenario where 2005 UD separates from parent body Phaethon under a mechanism that does not disturb the spin vector. Formation via Yarkovsky–O'Keefe–Radzievskii–Paddack (YORP) spin-up (Rubincam 2000) is one such possible formation mechanism for the Phaethon–2005 UD pair. Certainly this is a common mechanism for the formation of most known asteroid pair systems (Pravec et al. 2010), and interestingly, both the convex approximation of Phaethon from Hanuš et al. (2018) and the radar shape model from MacLennan et al. (2022) suggest the existence of an equatorial ridge and top-like shape, characteristic of YORPoids (Ostro et al. 2006; Busch et al. 2011; Naidu et al. 2015). Under a YORP-induced, post-fission scenario, 2005 UD and Phaethon would have engaged in a protobinary state before disruption, eventually evolving into the unbound asteroid pair seen today (Jacobson & Scheeres 2011). Due to the complexity of this process and uncertainties regarding the mass distribution and morphology of both Phaethon and 2005 UD, it remains unclear whether aligned poles are expected and/or consistent with a YORP spin-up scenario. Conversely, Pravec et al. (2019) found that current pole orientations of asteroids in a paired system generally do not reflect the original orientations at the time of separation, possibly due to solar torques (Breiter et al. 2005), YORP effects, and/or planetary encounters. For Phaethon (and possibly 2005 UD), the added dynamical effects of de-volatilization add more uncertainty on how pole orientations would be affected (discussed more below). In the case of our preferred solution, which only shares a common ecliptic latitude with Phaethon, we do not consider pole realignment due to planetary flybys a likely scenario because the minimum orbital intersection distance (MOID) value for both bodies is too high for all planets. YORP ultimately may also be invalid here due to the proposed recent separation of less than 100 kyr (Hanuš et al. 2016; MacLennan et al. 2021), which is much shorter than the tens of millions of years required for significant changes due to YORP (Rubincam 2000). To probe the extent to which current-day spin poles for 2005 UD and Phaethon line up or differ as a result of any of these physical process would require detailed modeling beyond the scope of this paper.

Due to Phaethon's rare status as an active asteroid, volatile-driven separation is another possible formation mechanism for this pair. This conjecture, however, does not rule out rotational fission entirely since induced torques due to outgassing cause spin changes in comets (Steckloff & Jacobson 2016). Akin to similar processes responsible for cometary splitting (see Jewitt 2021 and references therein), episodes of activity in an ancestor body could have worked, perhaps in concert with YORP, to accelerate the body to its critical spin rate, resulting in fission. However, the fact that 2005 UD is clearly in a principal axis rotation state (i.e., it is not tumbling) may speak to a more ordered scenario of formation that did not involve processes, like volatile-driven outgassing, that can produce nonprincipal axis rotation. Damping time estimates using Equation (11) in Pravec et al. (2014) of a nonprincipal axis rotator of 2005 UD's size and rotation exceed the proposed age of this system by millions of years, further suggesting that a chaotic, purely volatile-driven splitting event was unlikely.

Based on our results and arguments presented above, we lean toward a common origin due to a YORP fission scenario being the most likely progenitor for the 2005 UD–Phaethon cluster. This interpretation is consistent with that made by Huang et al. (2021), who also presented a Phaethon-like pole solution for 2005 UD using a different method. We encourage modeling of this specific sequence of events to probe the effects on spin pole in such a scenario.

The Yarkovsky effect (Bottke et al. 2006) is relevant when considering nongravitational perturbations for small (generally less than ∼10 km diameter) bodies. In general, a secular decrease in semimajor axis is expected for retrograde rotators (as opposed to outward drift for prograde rotators) such as Phaethon and 2005 UD. 2005 UD is approximately one-fifth the size of Phaethon, which would subject it to more rapid inward drift in semimajor axis. However, the semimajor axis of 2005 UD is currently greater by ∼3.5 × 10⁻³ au than that of Phaethon, and dynamical integrations (Ohtsuka et al. 2006) suggest that that has been the case for thousands of years. Furthermore, the presumed recent (<100 kyr ago) separation of this pair means that the Yarkovsky effect has not had enough time to significantly alter these objects' orbits. Typical Yarkovsky drift rates of 10⁻⁴ au Myr⁻¹ for kilometer-scale bodies suggest that ∼10 Myr would be needed to explain their current difference in semimajor axis, and that does not account for any time associated with a necessary change in pole orientation (e.g., by the YORP effect) that would allow for Yarkovsky drift to be in the right direction. It is additionally unlikely that the current low levels of activity seen for Phaethon play any significant role in the orbital dynamics of the system, though prior epochs with higher levels of activity may have contributed to the present-day separation.

If Phaethon and 2005 UD did in fact separate recently, it is suggested (MacLennan et al. 2021) that orbital dynamics governed by interactions with the terrestrial planets remain the most plausible dynamical pathway to produce the configuration of orbital elements we see today. However, a definitive time line associated with a separation event between Phaethon and 2005 UD has yet to come to fruition. We hope that improved orbit solutions and physical evidence of a fission-type disruption event following the DESTINY+ flyby could provide more insight into this issue.

Lastly, it is worth mentioning that (225416) 1999 YC is a putative third component in the 2005 UD–Phaethon system (Kasuga & Jewitt 2008; Ohtsuka et al. 2008). The addition of this body to the system supports a rotational fission formation scenario (Hanuš et al. 2018), but a spectral type inconsistent with the other two bodies (Kasuga & Jewitt 2008) and a significantly larger semimajor axis are hard to reconcile with any common origin theory.

Given these considerations, it seems unlikely that nongravitational forces would have played an important role in any evolution of 2005 UD relative to Phaethon. This does not necessarily influence arguments in favor of or against these two objects sharing a common origin.