Photometry and Polarimetry of 2010 XC₁₅: Observational Confirmation of E-type Near-Earth Asteroid Pair

We performed multicolor photometry of 2010 XC₁₅ using the TriColor CMOS Camera and Spectrograph (TriCCS) on the Seimei 3.8 m telescope (Kurita et al. 2020) at the Kyoto University Okayama Observatory (133.5967° E, 34.5769° N, and 355 m in altitude). The details of the photometry are presented in Table 1. The single-exposure time was set to 5.0 s, and the telescope was operated in the nonsidereal tracking mode. The data simultaneously obtained with the g, r, and i or z bands in the Pan-STARRS system (Chambers et al. 2016) were analyzed using the same procedure described in Beniyama et al. (2023).

After bias subtraction, dark subtraction, and flat-fielding, astrometry of all the reduced images was performed using the astrometry.net software (Lang et al. 2010). Cosmic ray related signals were removed using the Python package Astro-SCRAPPY (McCully et al. 2018) based on Pieter van Dokkum's L.A.Cosmic algorithm (van Dokkum 2001). Circular aperture photometry was performed on 2010 XC₁₅ and reference stars in each frame with the SExtractor-based Python package SEP (Bertin & Arnouts 1996; Barbary et al. 2015). The aperture radii were set to twice the size of the FWHMs of the point-spread functions of the reference stars. The light-travel time of the target asteroid was corrected to obtain the time-series colors and magnitudes (Harris & Lupishko 1989).

Reference stars meeting any of the criteria below were not used in the determination of colors and magnitudes: uncertainties in the g-, r-, i-, or z-band magnitudes in Pan-STARRS Data Release 2 (DR2; Flewelling et al. 2020) are larger than 0.05, (g − r)_PS > 1.1, (g − r)_PS < 0.0, (r − i)_PS > 0.8, or (r − i)_PS < 0.0, where (g − r)_PS and (r − i)_PS are colors in the Pan-STARRS system. We discarded sources close to the edges of the image frame (100 pixels from the edge) or those with any other sources within the aperture. Objects categorized as extended sources, possible quasars, and variable stars were removed with objinfoflag and objfilterflag in Pan-STARRS DR2. After deriving the colors and magnitudes of 2010 XC₁₅ in the Pan-STARRS system for each frame, we used a binning of 60 s for all magnitudes and colors.

We conducted polarimetric observations at three sites in Japan: Nayoro Observatory (142.4830° E, 44.3736° N, and 151 m in altitude; Minor Planet Center code Q33; hereinafter referred to as NO), Nishi-Harima Astronomical Observatory (134.3356° E, 35.0253° N, and 449 m in altitude; hereinafter referred to as NHAO), and Higashi-Hiroshima Observatory (132.7767° E, 34.3775° N, and 511.2 m in altitude; hereinafter referred to as HHO). The observing specifications of the polarimetry are summarized in Table 2. We used the Multi-Spectral Imager (MSI; Watanabe et al. 2012) mounted on the 1.6 m Pirka Telescope at NO, the Wide Field Grism Spectrograph 2 (WFGS2; Uehara et al. 2004; Kawakami et al. 2021) mounted on the 2.0 m Nayuta Telescope at NHAO, and the Hiroshima Optical and Near-InfraRed Camera (HONIR; Akitaya et al. 2014) mounted on the 1.5 m Kanata telescope at HHO. Wollaston prisms and rotatable half-wave plates are installed in all three instruments; thus, data obtained at the three sites were analyzed in the same standard reduction procedure (e.g., Kawabata et al. 1999; Ishiguro et al. 2017). We used the SExtractor-based Python package SEP for the circular aperture photometry. We derived linear polarization degrees relative to the direction perpendicular to the scattering plane, P_r, and the position angles of polarization, θ_r. Additionally, we observed a polarimetric standard star HD 19820 (Schmidt et al. 1992) to verify the consistency of our measurements (Appendix). We considered deviations between the polarimetric parameters in the literature and those derived here as systematic uncertainties in the measurements of the polarimetric parameters of 2010 XC₁₅.

The orbits of 2010 XC₁₅ and the well-characterized E-type NEA 1998 WT₂₄ resemble each other with a small D_SH of 0.04. The geometric albedos of these two NEAs derived in previous studies are in agreement (Kiselev et al. 2002). This suggests that the two NEAs could be of common origin and it makes sense to investigate their orbital history.

To investigate the dynamical link and origins of 2010 XC₁₅ and 1998 WT₂₄, we performed backward orbital integrations using Mercury 6, a general-purpose software package for problems in solar system dynamics (Chambers & Migliorini 1997). We computed close encounters accurately with the general Bulirsch–Stoer algorithm available in Mercury 6. We also performed orbital integrations with the hybrid symplectic and Bulirsch–Stoer integrator in Mercury 6 and confirmed the results of our integrations do not significantly change.

The nominal orbital elements of the asteroids, their uncertainties, and the covariance data were retrieved from the NASA JPL Small-Body DataBase (SBDB). ²² The coordinates and velocities of the Sun and eight planets were obtained from NASA JPL HORIZONS. The nongravitational transverse acceleration parameters, A₂ (Farnocchia et al. 2013), are given for both 2010 XC₁₅ and 1998 WT₂₄ in NASA JPL SBDB. The semimajor axes of these two asteroids have shrunk, possibly due to the Yarkovsky effect (e.g., Vokrouhlický 1998; Vokrouhlický et al. 2000; Bottke et al. 2006). Thus, we also considered the nongravitational transverse acceleration by setting A₂ parameters in the integrations. We investigated the time evolutions of the asteroids under the gravity of the Sun and eight planets in the solar system. The first time step was set to 0.1 days in all integrations. The coordinates and velocities of the asteroids were output every 300 days. We converted the coordinates and velocities to orbital elements using element6, a program in Mercury 6.

The orbital evolution of NEAs often turns chaotic after a short period (∼100 yr) of integration due to frequent close encounters with planets (Yoshikawa et al. 2000). We generated clones utilizing the classical Monte Carlo using the covariance matrix (MCCM; Avdyushev & Banshchikova 2007; de la Fuente Marcos & de la Fuente Marcos 2015) approach to check this chaotic behavior. Each clone had initial orbital elements slightly different from the nominal ones. In total, we generated 1000 clones considering uncertainties of the eccentricity (e), perihelion distance (q), time of perihelion passage (τ), longitude of ascending node (Ω), argument of perihelion (ω), and inclination (i). The 1000 clones were generated with random numbers made with the np.random.randn function in the Python package NumPy (Oliphant 2015; Harris et al. 2020). We set the seed of the random number to 0. The semimajor axis (a) was calculated as a = q/(1 − e) after the orbital integrations. The epochs of the orbital elements of 2010 XC₁₅ and 1998 WT₂₄ were 2018 January 1 UT, JD 2458119.5, and 2016 April 16 UT, JD 2457494.5, respectively.

To discuss whether the asteroids are of common origin, we used the following three integrals of motion of the asteroids in the circular restricted three-body problem (Lidov 1962) in von Zeipel–Lidov–Kozai (vZLK) oscillation (Kozai 1962; Lidov 1962; Ito & Ohtsuka 2019):

$\begin{eqnarray}&&{C}_{0}=\displaystyle \frac{1}{a}\equiv \mathrm{const},\end{eqnarray} \tag{ 1 }$

$\begin{eqnarray}&&{C}_{1}=(1-{e}^{2}){\cos }^{2}i\equiv \mathrm{const},\end{eqnarray} \tag{ 2 }$

$\begin{eqnarray}&&{C}_{2}={e}^{2}(0.4-{\sin }^{2}i{\sin }^{2}\omega )\equiv \mathrm{const}.\end{eqnarray} \tag{ 3 }$

When an asteroid breaks up into multiple bodies by catastrophic impacts or rotational fission, the fragments have slightly different orbital elements at that time. In the orbital evolutions of NEAs, the orbital parameters could be drastically changed due to close encounters with planets. On the other hand, the integrals of C₀, C₁, and C₂ are kept constant for a longer time. Thus, these integrals should be good indicators of whether the asteroids are an NEA pair (Ohtsuka et al. 2006, 2007).

For periodic analysis, we calculated reduced magnitudes from the observed magnitudes as

$\begin{eqnarray}&&{m}_{\mathrm{red},n}(\alpha )={m}_{\mathrm{obs},n}(\alpha )-5{\mathrm{log}}_{10}({\rm{\Delta }}{r}_{{\rm{h}}}),\end{eqnarray} \tag{ 4 }$

where n is the index of the band, m_red,n (α) is a reduced magnitude in the n band, m_obs,n (α) is an observed magnitude in the n band, Δ is the distance between 2010 XC₁₅ and the Earth, and r_h is the distance between 2010 XC₁₅ and the Sun. We performed phase angle correction since the phase angle of 2010 XC₁₅ changed significantly during our observations, by ∼65 (Table 1). In general, an empirical relation, such as the H–G model (Bowell et al. 1989), which was originally applied for photometric data taken at phase angles smaller than ∼30°, is used for phase correction. The phase angles of 2010 XC₁₅ in our observations are as large as 60°, where the brightness dependence on the solar phase angle, the phase curve, is still poorly understood. We assumed a phase curve in linear form as follows:

$\begin{eqnarray}&&{m}_{\mathrm{red},n}(\alpha )={H}_{n}+b\alpha ,\end{eqnarray} \tag{ 5 }$

where H_n is an absolute magnitude in the n band, and b is the linear slope of the phase curve. We converted the reduced magnitudes to absolute magnitudes using Equation (5). Carefully checking the corrected lightcurves while setting b = 0.010, 0.015, 0.020, 0.025, 0.030, and 0.035 mag deg⁻¹, we finally adopted b = 0.030 mag deg⁻¹ for the corrected lightcurves, as shown in Figure 1. Clear variations with amplitudes of approximately 0.1 mag are seen in the corrected lightcurves.

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The rotation period of 2010 XC₁₅ has been reported in the Asteroid Lightcurve Database (LCDB; Warner et al. 2009). The period derived as 2.673 ± 0.001 hr with 2 days of optical photometry in 2022 December by Petr Pravec ²³ is a possible solution with a quality code U in the LCDB of 2-. Another period has been derived from radar observations using the Goldstone Radar at DSS-14. ²⁴ Assuming that the effective diameter of 2010 XC₁₅ is approximately 150 m, the conclusion was that the Doppler broadening of approximately 1.3 Hz at a wavelength of 3.5 cm corresponds to a rotation period of approximately 11.5 hr. The rotation period was constrained using the relation given by $B=(4\pi D)/(\lambda {P}_{\mathrm{rot}})\sin \beta$, where B is the measured bandwidth, D is the diameter, λ is the transmitted wavelength, P_rot is the rotation period, and β is the angle between the line of sight and the spin vector of the object (Ostro et al. 1988). The 11.5 hr value can be derived assuming a $\sin \beta$ of 1. Thus, 11.5 hr is an upper limit of the rotation period since the pole orientation of 2010 XC₁₅ is unknown.

We performed a periodic analysis with the g-band lightcurves using the Lomb–Scargle method limiting the period range to between 0.16 and 11.5 hr, as shown in Figure 2. We found no significant peak in the Lomb–Scargle periodogram. Figure 3 shows the phased lightcurves folded by a rotation period of 2.673 hr reported in the LCDB. We checked other phased lightcurves but it is difficult to conclude which peak to prefer over others as our lightcurve coverage is insufficient and the lightcurve amplitude of 2010 XC₁₅ is small at approximately 0.1 mag. The small lightcurve amplitude implies that 2010 XC₁₅ has a nearly spherical shape or its rotational axis is parallel to the line of sight. Lightcurves with small amplitudes sometimes show more than two maxima in a single rotation (Harris et al. 2014). For example, (5404) Uemura shows six maxima (Harris et al. 2014), and (101955) Bennu shows three maxima (Hergenrother et al. 2013) in a single rotation. Additional observations are necessary for more constraints on the rotation state of 2010 XC₁₅. Furthermore, we cannot rule out the possibility that 2010 XC₁₅ is a non–principal axis rotator (i.e., a tumbler; Paolicchi et al. 2002; Pravec et al. 2005).

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We present the colors of 2010 XC₁₅ in Figure 4. We estimated the systematic uncertainties of the g − r, r − i, and r − z colors in our observations, δ_g−r , δ_r−i , and δ_r−z , on the basis of the photometric measurements of the reference stars (Beniyama et al. 2023): δ_g−r = 0.03 and δ_r−i = 0.03 in the observations with the g-, r-, and i-band filters on December 23; δ_g−r = 0.02 and δ_r−z = 0.02 in the observations with the g-, r-, and z-band filters on December 23; δ_g−r = 0.02 and δ_r−i = 0.02 in the observations with the g-, r-, and i-band filters on December 24; and δ_g−r = 0.01 and δ_r−z = 0.01 for the observations with the g-, r-, and z-band filters on December 25. The weighted average colors of 2010 XC₁₅, except for the first night, when the conditions of the sky were not ideal, were derived as g − r = 0.435 ± 0.008, r − i = 0.158 ±0.017, and r − z = 0.186 ± 0.009. The colors correspond to V − R = 0.41 ± 0.02 and R − I = 0.39 ± 0.03 in the Johnson system (Tonry et al. 2012). We could not find notable rotational spectral variations when assuming rotation periods of 2.673 hr.

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In Figure 5, we show the observed reflectance spectrum of 2010 XC₁₅. The reflectances at the central wavelength of the g, i, and z bands, R_g , R_i , and R_z , were calculated as follows (e.g., DeMeo & Carry 2013):

$\begin{eqnarray}&&{R}_{g}={10}^{-0.4[{(g-r)}_{{\mathrm{XC}}_{15}}-{(g-r)}_{\odot }]},\end{eqnarray} \tag{ 6 }$

$\begin{eqnarray}&&{R}_{i}={10}^{-0.4[{(i-r)}_{{\mathrm{XC}}_{15}}-{(i-r)}_{\odot }]},\end{eqnarray} \tag{ 7 }$

$\begin{eqnarray}&&{R}_{z}={10}^{-0.4[{(z-r)}_{{\mathrm{XC}}_{15}}-{(z-r)}_{\odot }]},\end{eqnarray} \tag{ 8 }$

where ${(g-r)}_{{\mathrm{XC}}_{15}}$, ${(i-r)}_{{\mathrm{XC}}_{15}}$, and ${(z-r)}_{{\mathrm{XC}}_{15}}$ are the colors of 2010 XC₁₅, whereas (g − r)_⊙, (i − r)_⊙, and (z − r)_⊙ are the colors of the Sun in the Pan-STARRS system. We referred to the absolute magnitude of the Sun in the Pan-STARRS system: g = 5.03, r = 4.64, i = 4.52, and z = 4.51 (Willmer 2018). We set the uncertainties of the magnitude of the Sun to 0.02.

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The reflectance spectra in Figure 5 are normalized at the band center of the r band in the Pan-STARRS system, 0.617 μm (Tonry et al. 2012). Horizontal bars in 2010 XC₁₅'s spectrum indicate filter bandwidths (Tonry et al. 2012). The reflectance spectra other than those of 2010 XC₁₅ were originally normalized at 0.55 μm. We renormalized the spectra at 0.617 μm as follows:

$\begin{eqnarray}&&R(\lambda )^{\prime} =\displaystyle \frac{R(\lambda )}{R(0.617\,\mu {\rm{m}})},\end{eqnarray} \tag{ 9 }$

where $R(\lambda )^{\prime}$ is the renormalized reflectance at wavelength of λ, R(λ) is the original reflectance at wavelength of λ, and R(0.617 μm) is the original reflectance at wavelength of 0.617 μm. We normalized the spectra after smoothing every 0.03 μm.

The derived linear polarization degrees and position angles of 2010 XC₁₅ are listed in Table 2. Figure 6 shows the observed phase angle dependence of the linear polarization degrees of 2010 XC₁₅. The derived polarization degrees are a few percent at the phase angle range of 58°–114°. The small linear polarization degrees combined with the spectrum imply that 2010 XC₁₅ is an E-type asteroid with a high geometric albedo. This is consistent with the p_V of ${0.350}_{-0.151}^{+0.176}$ derived from thermal observations using the IRAC on SST.

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We fit the linear polarization degrees of 2010 XC₁₅ using an empirical model curve as follows:

$\begin{eqnarray}&&{P}_{{\rm{r}}}(\alpha )=b{\sin }^{{c}_{1}}(\alpha ){\cos }^{{c}_{2}}\left(\displaystyle \frac{\alpha }{2}\right)\sin (\alpha -{\alpha }_{0}),\end{eqnarray} \tag{ 10 }$

where b, c₁, c₂, and α₀ are free parameters (Lumme & Muinonen 1993; Penttilä et al. 2005). We used the curve_fit function in the Python package SciPy (Virtanen et al. 2020). The curve_fit routine determines the best-fit parameters using the Levenberg–Marquardt algorithm. Our polarimetric measurements were obtained at the phase angle range of 58°–114°. The free parameters were not constrained well with only our measurements since our phase angle coverage was insufficient. It is known that asteroids that belong to the same spectral class show a similar phase angle dependence of linear polarization (Belskaya et al. 2017). As for E-types, polarimetric measurements at phase angles larger than 50° have been reported for two NEAs: 1998 WT₂₄ (Kiselev et al. 2002) and (144898) 2004 VD₁₇ (De Luise et al. 2007). In Figure 6, we plot the polarization degrees of these two asteroids. These two asteroids were also not observed at small phase angles. We plotted the polarization degrees of the prototype E-type MBA (44) Nysa (Zellner & Gradie 1976). We adopted the polarization degrees determined using the R-band or 678 nm filter for 1998 WT₂₄, and those determined using the R-band filter for Nysa as our observations of 2010 XC₁₅ were conducted in the R band. We note that 2004 VD₁₇ was observed with the V filter. A good match was found between the phase angle dependences of the linear polarization degrees of 2010 XC₁₅ and 1998 WT₂₄, whereas the linear polarization degrees of 2004 VD₁₇ indicated a different trend. Therefore, we combined and fit the linear polarization degrees of 2010 XC₁₅ and 1998 WT₂₄ with the empirical model curve above. There is a good match between the model curve and the linear polarization degrees of Nysa.

We generated 3000 polarization data sets by randomly resampling the measured data assuming each polarization degree follows a normal distribution with a standard deviation of its uncertainty. We obtained 3000 sets of fitting parameters from the generated data sets. The maximum polarization degree of 2010 XC₁₅ was derived as approximately 2% at α of approximately 100°.

The time evolutions of the orbital elements of 2010 XC₁₅ and 1998 WT₂₄ during the last 1000 yr are presented in Figure 7. The orbital elements of 2010 XC₁₅ and 1998 WT₂₄ can be successfully traced for approximately 200 and 250 yr, respectively. The orbital elements of clones become scattered, and chaotic behaviors can be seen.

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We checked the distance between the inner planets and both 2010 XC₁₅ and 1998 WT₂₄, outputting the coordinates and velocities of the asteroids every 0.1 days. Close approaches at a few lunar distances from the Earth–Moon system had strong influences on the orbital evolution of both 1998 WT₂₄ and 2010 XC₁₅. The three integrals of motion, C₀ (= 1/a), C₁, and C₂, have been stable for 1000 yr. The C₀ of 2010 XC₁₅ and 1998 WT₂₄ are within the ranges of 1.350–1.361 and 1.391–1.398, respectively; their C₁ are within the ranges of 0.809–0.813 and 0.809–0.812, respectively; and their C₂ are within the ranges of 0.067–0.069 and 0.069–0.071, respectively.

In Figure 5, we show the template spectra of S-, Xe-, and Xc-types (Bus–DeMeo taxonomy; Bus & Binzel 2002; DeMeo & Carry 2013), ²⁵ and the spectra of the E-type (Tholen taxonomy) and Xc-type (Bus–DeMeo taxonomy) MBA Nysa (Bus & Binzel 2002) and the E-type NEA 1998 WT₂₄ (Lazzarin et al. 2004). The latter two were obtained via the M4AST online tool (Modeling for Asteroids; Popescu et al. 2012). We confirm the similarity between the spectra of 2010 XC₁₅ and 1998 WT₂₄.

We checked the difference of the phase angles at the observations as it is known that the slope of the visible spectrum changes depending on the solar phase angles, also known as the phase reddening effect (Sanchez et al. 2012). Phase angles and specific dates and times of observations of 1998 WT₂₄ are not described in Lazzarin et al. (2004). We carefully combined the available information in Lazzarin et al. (2004): their observations were performed on 2000 October 26–28 or on 2001 November 17–20 and the V-band magnitude of 1998 WT₂₄ was 16.0 mag at the observations. According to the ephemerides provided by NASA JPL HORIZONS, the V-band magnitudes are approximately 20 mag and 16 mag on 2000 October 26–28 and 2001 November 17–20, respectively. The V-band magnitudes indicate that the observations were conducted in the latter period. The phase angles of 1998 WT₂₄ on 2001 November 17–20 were 73°–77°, which are not far from those of our 2010 XC₁₅ observations, 58°–65°. Therefore, we ignored the phase reddening effect.

We found that the linear polarization degrees of 2010 XC₁₅ are a few percent at the phase angles across wide ranges. The linear polarization degrees of 2010 XC₁₅ and 1998 WT₂₄ at phase angles around 60° match well. The P_max of 2010 XC₁₅ is about 2%. This is almost equivalent to the P_max of 1998 WT₂₄, 1.6–1.8, derived in Kiselev et al. (2002), although it must be noted that the P_max of 2010 XC₁₅ was derived with the polarization degrees of 1998 WT₂₄. We further note that the P_max of 1998 WT₂₄ in Kiselev et al. (2002) was derived with the polarization degrees of other E-types, Nysa and (64) Angelina.

The physical properties and orbital elements of 2010 XC₁₅ and 1998 WT₂₄ are summarized in Table 3. Based on the photometric and polarimetric properties described above, the surface properties of the two E-type asteroids 2010 XC₁₅ and 1998 WT₂₄ resemble each other. A recent spectroscopic survey of NEAs shows E-types comprise only a few percent of the total NEA population (Marsset et al. 2022). Taking the similarity of not only physical properties but also dynamical integrals and the rarity of E-types in the near-Earth region into account, we suppose that 2010 XC₁₅ and 1998 WT₂₄ are fragments from the same parent body (i.e., an asteroid pair). They are the sixth NEA pair and the first E-type NEA pair ever confirmed. The next close approaches of 2010 XC₁₅ and 1998 WT₂₄ will take place in 2027 December with V ≤ 17 mag and in 2029 December with V ≤ 14 mag, respectively. Additional spectroscopic observations in wide wavelength coverage are encouraged to investigate the common origin of the two NEAs.

Table 3. Comparison of Physical Properties and Orbital Elements of 2010 XC₁₅ and 1998 WT₂₄

	2010 XC15	1998 WT24	References
Absolute magnitude, H (mag)	21.70	18.69 ± 0.3	1, 2
Geometric albedo, pV	${0.350}_{-0.151}^{+0.176}$	0.34 ± 0.20, 0.56 ± 0.2	1, 2, 3
Rotation period (hr)	a few to several dozen	3.6970 ± 0.0002	This study, 2
Volume-equivalent diameter (m)	${102}_{-17}^{+30}$	415 ± 40	1, 2
Maximum polarization degree, Pmax (%)	∼2	1.6–1.8	This study, 4
Shape	nearly spherical	nearly spherical	This study, 2
Semimajor axis, a (au)	0.732375383 (0.000000015)	0.7187740919 (0.0000000027)	5
Eccentricity, e	0.419862999 (0.000000040)	0.4176018439 (0.0000000098)	5
Inclination, i (deg)	8.2392588 (0.0000060)	7.3675902 (0.0000019)	5
Longitude of ascending node, Ω (deg)	94.4069555 (0.0000035)	81.6663922 (0.0000021)	5
Argument of perihelion, ω (deg)	158.1007878 (0.0000069)	167.5262827 (0.0000028)	5
Mean anomaly, M (deg)	323.063632 (0.000012)	136.978426 (0.000022)	5

Notes. References column: (1) NEOLegacy, (2) Busch et al. (2008), (3) best-fit values from thermal-infrared observations in Harris et al. (2007), (4) Kiselev et al. (2002), (5) NASA JPL SBDB. The orbital elements of 2010 XC₁₅ are from epoch JD 2460000.5 (2023 February 25.0) TDB (Barycentric Dynamical Time, J2000.0 ecliptic and equinox). They are based on 279 observations with a data-arc span of 4406 days (solution date, 2023 February 14 15:10:21). The orbital elements of 1998 WT₂₄ are from epoch JD 2460000.5 (2023 February 25.0) TDB. They are based on 1842 observations with a data-arc span of 8489 days (solution date, 2023 March 1 06:14:53). The values in parentheses are the 1σ uncertainties of the orbital elements.

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The six confirmed NEA pairs are presented on an a–e_min or 1/C₀–e_min plane in Figure 8: Phaethon–2005 UD (Ohtsuka et al. 2006), Icarus–2007 MK₆ (Ohtsuka et al. 2007), 2017 SN₁₆–2018 RY₇ (de la Fuente Marcos & de la Fuente Marcos 2019; Moskovitz et al. 2019), 2015 EE₇–2015 FP₁₂₄ (Moskovitz et al. 2019), 2019 PR₂–2019 QR₆ (Fatka et al. 2022), and 1998 WT₂₄–2010 XC₁₅. The e_min is the minimum value of the orbital eccentricity over one period of ω (Gronchi & Milani 2001). The orbital elements were extracted from the NEA element catalogs of NEODyS-2 ²⁶ as of 2023 May 1. The C₁ and C₂ of 2010 XC₁₅, 1998 WT₂₄, and the other NEA pairs are plotted on the Lidov diagram in Figure 9 (Lidov 1962; Ito & Ohtsuka 2019). The Lidov diagram helps us understand the dynamical characteristics of the system. The orbital elements used to calculate C₁ and C₂ were extracted from the Minor Planet Center Orbit Database file ²⁷ as of 2023 May 1. The separations of 2010 XC₁₅ and 1998 WT₂₄ in Figures 8 and 9 are as small as those of the other NEA pairs as summarized in Table 4. This supports the idea that the two asteroids are of common origin as these integrals are useful indicators for confirming NEA pairs (Ohtsuka et al. 2006, 2007). As shown in Figure 7, the orbital elements of 2010 XC₁₅ and 1998 WT₂₄ become scattered after backward integrations of 200 and 250 yr, respectively. Thus, we could not determine the exact time of the breaking-up event.

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It is worth mentioning that the mass ratio of 1998 WT₂₄–2010 XC₁₅ as well as those of Phaethon–2005 UD and Icarus–2007 MK₆ is close to 0.25. The rotation period of the primary 1998 WT₂₄ is 3.6970 hr (Busch et al. 2008), which is also close to that of another primary Phaethon. Busch et al. (2008) revealed that the shape of 1998 WT₂₄ looks like a spherical body with three basins. They suggested that the basins may be impact craters or a relic of past dynamical disruption. The overall shape of 1998 WT₂₄ resembles top-shaped asteroids such as 2008 EV₅ and 2000 DP₁₀₇, on which rotational fissions may have occurred (Tardivel et al. 2018). The mass ratio and rotation period are consistent with the theory of rotation fission (Scheeres 2007; Pravec et al. 2010). This is also the case for the Phaethon–2005 UD pair (Hanuš 2016). Therefore, rotational fission is favored as the formation mechanism of the 1998 WT₂₄–2010 XC₁₅ pair. Considering the diameter of the parent body of 1998 WT₂₄–2010 XC₁₅ is almost equivalent to that of 1998 WT₂₄ at approximately 400 m, YORP spin-up might play an important role in rotational fission since it strongly changes the rotation state of such small bodies (Rubincam 2000). In terms of the spherical shape of the primary 1998 WT₂₄, rotational fission is preferred over tidal disruption, which typically expects elongated primaries (Walsh & Richardson 2006).

There are some escape regions from MBAs to NEAs (Granvik et al. 2018). One is the ν₆ resonance at the inner edge of the main belt with a semimajor axis of approximately 2.1 au. Nysa is located at the inner main belt with a semimajor axis of approximately 2.4 au. Reddy et al. (2016) characterized a tiny (D ∼ 2 m) E-type NEA 2015 TC₂₅ in radar, optical lightcurves, and near-infrared spectroscopic observations. They combined the spectral and dynamical properties of 2015 TC₂₅ and concluded that it is a fragment possibly ejected from Nysa. Another representative escape region for E-types is the Hungaria region with a semimajor axis of approximately 1.9 au and an inclination of about 20°. It is known that the fraction of NEAs from the Hungaria region is smaller than that from the inner main belt through the ν₆ resonance (Granvik et al. 2018). On the other hand, considering the relative fractions of E-types in different regions of the main belt, the probability of their originating from the Hungaria region is higher than that from the ν₆ resonance or is comparable within uncertainties (Binzel et al. 2019). Thus, the source region of 2010 XC₁₅, 1998 WT₂₄, and their parent body cannot be clearly determined.