Confirmation of Large Super-fast Rotator (144977) 2005 EC₁₂₇

The large (i.e., a diameter of a few hundreds of meters) super-fast rotators (SFRs) are of interest for understanding asteroid interior structure. Because asteroids of sub-kilometer size are believed to have rubble-pile structure (i.e., gravitationally bounded aggregations) and cannot have super-fast rotation, defined as a rotation period shorter than 2.2 hr (Harris 1996).⁷ However, the first large SFR, 2001 OE84, a near-Earth asteroid of ∼0.7 km in size and completing one rotation in 29.19 minutes (Pravec et al. 2002), cannot be explained by rubble-pile structure, and consequently, internal cohesion was proposed to be a possible solution (Holsapple 2007). Although several attempts were made to discover large SFRs with extensive-sky surveys (Masiero et al. 2009; Dermawan et al. 2011), this asteroid group was not confirmed until another large SFR, 2005 UW163, was found by Chang et al. (2014b). Up to now, five large SFRs have been reported, additionally including 1950 DA (Rozitis et al. 2014), 2000 GD65 (Polishook et al. 2016), and 1999 RE88 (Chang et al. 2016). However, the population size of large SFRs is still not clear. Compared with the 738 large fast rotators (i.e., diameters between 0.5 and 10 km and rotation periods between 2–3 hr) in the up-to-date Asteroid Light Curve Database (LCDB⁸ ; Warner et al. 2009), large SFRs are rare. Either the difficulty of discovering them due to their sub-kilometer sizes (i.e., relatively faint) or the intrinsically small population size of this group could lead to this rarity in detection. Therefore, a more comprehensive survey of asteroid rotation period with a wider sky coverage and a deeper limiting magnitude, such as the ZTF,⁹ could help in finding more large SFRs. With more SFR samples, a thorough study of their physical properties could be conducted, and therefore further insights about asteroid interior structure are possible. To this objective, the TANGO project¹⁰ has been conducting asteroid rotation-period surveys since 2013 using the iPTF¹¹ (for details, see Chang et al. 2014a, 2015, 2016). From these surveys, 2 large SFRs and 27 candidates were discovered. Here, we report the confirmation of asteroid (144977) 2005 EC₁₂₇ as a new large SFR. The super-fast rotation of (144977) 2005 EC₁₂₇ was initially and tentatively identified in the asteroid rotation-period survey using the iPTF in 2015 February (Chang et al. 2016), and then later confirmed in this work by follow-up observations using the Lulin One-meter Telescope in Taiwan (LOT; Kinoshita et al. 2005).

This Letter is organized as follows. The observations and measurements are given in Section 2, the rotation period analysis is described in Section 3, the results and discussion are presented in Section 4, and a summary and conclusions can be found in Section 5.

The iPTF, LOT, and spectroscopic observations that support the findings in this work are described in this section. The details of each of these observation runs are summarized in Table 1.

Table 1.  Observational Details

Telescope	Date	Filter	R.A. (°)	Decl. (°)	${N}_{\exp }$	${\rm{\Delta }}t$ (hr)	α (°)	r (au)	Δ (au)	m (mag)	H (mag)
PTF	2015 Feb 25–26	$R^{\prime}$	154.04	10.12	43	28.3	1.3	2.45	1.46	20.3	17.3
LOT	2016 Sept 24	$r^{\prime}$	23.81	2.81	84	7.3	2.5	2.03	1.03	19.2	17.3
P200	2016 Oct 4	Spec.: $0.4-0.9\,\mu {\rm{m}}$	23.65	2.21	3	0.5	7.7	2.05	1.07	19.5

Note. ${\rm{\Delta }}t$ is observation time span and ${N}_{\exp }$ is the total number of exposures.

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2.1. iPTF Observations

2.2. LOT Observations

2.3. Spectroscopic Observations

Before measuring the synodic rotation period for 2005 EC₁₂₇, the light-curve data points were corrected for light-travel time and were reduced to both heliocentric (r) and geocentric (Δ) distances at 1 au by $M=m+5\mathrm{log}(r{\rm{\Delta }})$, where M and m are reduced and apparent magnitudes, respectively. A second-order Fourier series (Harris et al. 1989) was then applied to search for the rotation periods:

$$\begin{eqnarray}{M}_{i,j} & = & \displaystyle \sum _{k=1,2}^{{N}_{k}}{B}_{k}\sin \left[\displaystyle \frac{2\pi k}{P}({t}_{j}-{t}_{0})\right]\\ & & +{C}_{k}\cos \left[\displaystyle \frac{2\pi k}{P}({t}_{j}-{t}_{0})\right]+{Z}_{i},\end{eqnarray} \tag{ 1 }$$

where ${M}_{i,j}$ is the reduced magnitude measured at the light-travel-time-corrected epoch, t_j; B_k and C_k are the Fourier coefficients; P is the rotation period; t₀ is an arbitrary epoch; and Z_i is the zero point. For the PTF light curve, the fitting of Z_i also includes a correction for the small photometric zero-point variations mentioned in Section 2.1 (for details, see Polishook et al. 2012). To obtain the other free parameters for a given P, we used least-squares minimization to solve Equation (1). The frequency range was explored between 0.25 and 50 rev day⁻¹ with a step of 0.001 rev day⁻¹. To estimate the uncertainty of the derived rotation periods, we calculated the range of periods with ${\chi }^{2}$ smaller than ${\chi }_{\mathrm{best}}^{2}+\bigtriangleup {\chi }^{2}$, where ${\chi }_{\mathrm{best}}^{2}$ is the chi-squared value of the picked-out period and $\bigtriangleup {\chi }^{2}$ is obtained from the inverse chi-squared distribution, assuming $1+2{N}_{k}+{N}_{i}$ degrees of freedom.

The rotation period of 1.64 ± 0.01 hr (i.e., 14.6 rev day⁻¹) of 2005 EC₁₂₇ was first identified using the PTF light curve (Chang et al. 2016). Although the derived frequency of 14.6 rev day⁻¹ is significant in the periodogram calculated from the PTF light curve, the corresponding folded light curve is relatively scattered (see the upper panels of Figure 2). Therefore, we triggered the follow-up observations using the LOT. The rotation periods of 2005 EC₁₂₇ derived from the LOT light curve is 1.65 ± 0.01 hr (i.e., 14.52 rev day⁻¹), which is in good agreement with the PTF result (see the lower panels of Figure 1). Both folded light curves show a clear double-peak/valley feature for asteroid rotation (i.e., two periodic cycles). The peak-to-peak variations of the PTF and LOT light curves are ∼0.6 and ∼0.5 mag, respectively. This indicates that 2005 EC₁₂₇ is a moderately elongated asteroid and rules out the possibility of an octahedronal shape for 2005 EC₁₂₇, which would lead to a light curve with four peaks and an amplitude of ${\rm{\Delta }}m\lt 0.4$ mag (Harris et al. 2014). Moreover, we cannot morphologically distinguish between the even and odd cycles in the LOT light curve. Therefore, we believe that 1.65 hr is the true rotation period for 2005 EC₁₂₇.

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To estimate the diameter, D, of 2005 EC₁₂₇, we use

$$\begin{eqnarray}&&D=\displaystyle \frac{1329}{\sqrt{{p}_{v}}}{10}^{-H/5}\end{eqnarray} \tag{ 2 }$$

(see Harris & Lagerros 2002, and references therein). Since the phase angle of the asteroid had a small change during our relatively short observation time span, the absolute magnitude of 2005 EC₁₂₇ is simply calculated using a fixed G slope of 0.15 in the H–G system (Bowell et al. 1989). We obtain ${H}_{R^{\prime} }=17.27\pm 0.22$ and ${H}_{r^{\prime} }17.30\pm 0.02$ mag from the PTF and LOT observations, respectively.¹⁵ Because the absolute magnitude derived from the LOT observation has a smaller dispersion, we finally adopt ${H}_{r^{\prime} }=17.30$ mag for 2005 EC₁₂₇. We use $(V-R)=0.516$ in the conversion of ${H}_{r^{\prime} }$ to H_V (DeMeo et al. 2009; Pravec et al. 2012) and then obtain H_V = 17.82 for 2005 EC₁₂₇. Assuming an albedo value of ${p}_{v}=0.36\pm 0.10$ for V-type and ${p}_{v}=0.19\pm 0.03$ for A-type asteroids (Masiero et al. 2011; DeMeo & Carry 2013), diameters of $D\sim 0.6\pm 0.1$ and $\sim 0.8\pm 0.1$ km, respectively, are estimated for 2005 EC₁₂₇, where the uncertainty includes the residuals in light-curve fitting and the range of assumed albedos. Even when an extreme albedo value of p_v = 1.0 is applied, a diameter of 0.4 km is still obtained for 2005 EC₁₂₇. Since A-type asteroids are relatively uncommon in the inner main belt, we therefore assume an V-type asteroid for 2005 EC₁₂₇ in the following discussion. As shown in Figure 4, 2005 EC₁₂₇ lies in the rubble-pile asteroid region and has a rotation period shorter than 2 hr. Therefore, we conclude that 2005 EC₁₂₇ is a large SFR.

If 2005 EC₁₂₇ is a rubble-pile asteroid, a bulk density of $\rho \sim 6$ g cm⁻³ would be required to withstand its super-fast rotation (see Figure 3). This would suggest that 2005 EC₁₂₇ is a very compact object, i.e., composed mostly of metal. However, such high bulk density is very unusual among asteroids. Moreover, 2005 EC₁₂₇ is probably a V-type asteroid. Therefore, this is a very unlikely scenario indeed.

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Another possible explanation for the super-fast rotation of 2005 EC₁₂₇ is that it has substantial internal cohesion (Holsapple 2007; Sánchez & Scheeres 2014). Using the Drucker–Prager yield criterion,¹⁶ we can estimate the internal cohesion for asteroids. Assuming an average $\rho =1.93$ g cm⁻³ for V-type asteroids (Carry 2012), a cohesion of 47 ± 20 Pa results for 2005 EC₁₂₇.¹⁷ This modest value is comparable with that of the other large SFRs (see Table 2) and is also nearly in the cohesion range of lunar regolith, i.e., 100–1000 Pa (Mitchell et al. 1974).

Table 2.  Confirmed Large SFRs to Date

	Asteroid	Tax.	Per.	${\rm{\Delta }}m$	Dia.	H	Coh.	a	e	i	Ω	ω	Reference
			(hr)	(mag)	(km)	(mag)	(Pa)	(au)		(°)	(°)	(°)
(144977)	2005 EC127	V/A	1.65 ± 0.01	0.5	0.6 ± 0.1	17.8 ± 0.1	47 ± 30	2.21	0.17	4.75	336.9	312.8	This work
(455213)	2001 OE84	S	0.49 ± 0.00	0.5	0.7 ± 0.1	18.3 ± 0.2	∼1500a	2.28	0.47	9.34	32.2	2.8	Pravec et al. (2002)
(335433)	2005 UW163	V	1.29 ± 0.01	0.8	0.6 ± 0.3	17.7 ± 0.3	∼200a	2.39	0.15	1.62	224.6	183.6	Chang et al. (2014b)
(29075)	1950 DA	M	2.12 ± 0.00	0.2b	1.3 ± 0.1	16.8 ± 0.2	64 ± 20	1.70	0.51	12.17	356.7	312.8	Rozitis et al. (2014)
(60716)	2000 GD65	S	1.95 ± 0.00	0.3	2.0 ± 0.6	15.6 ± 0.5	150–450	2.42	0.10	3.17	42.1	162.4	Polishook et al. (2016)
(40511)	1999 RE88	S	1.96 ± 0.01	1.0	1.9 ± 0.3	16.4 ± 0.3	780 ± 500	2.38	0.17	2.04	341.6	279.8	Chang et al. (2016)

Notes. The orbital elements were obtained from the MPC website, http://www.minorplanetcenter.net/iau/mpc.html.

^aThe cohesion is adopted from Chang et al. (2016). ^b ${\rm{\Delta }}m$ is adopted from Busch et al. (2007).

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As shown by Holsapple (2007), the size-dependent cohesion would allow large SFRs to be present in the transition zone between monolithic and rubble-pile asteroids. However, only six large SFRs have been reported to date (including this work). This number is very small when compared with the number of large fast rotators (i.e., 738 objects in the LCDB). The reason for the rarity in detecting large SFRs from previous studies (i.e., the sparse number of large SFRs in the transition zone in Figure 4) could be that (a) the rotation periods are difficult to obtain for large SFRs due to their small diameters (i.e., faint brightness) or (b) the population size of large SFRs is intrinsically small. Therefore, a survey of asteroid rotation period with a larger sky coverage and deeper limiting magnitude can help to resolve the aforementioned question. If it is the latter case, these large SFRs might be monoliths, which have relatively large diameters and unusual collision histories.

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We also note that none of the six reported large SFRs is classified as C-type asteroids. Therefore, any discovery of a large C-type SFR would fill out this taxonomic vacancy and help to understand the formation of large SFRs. In addition, the determination of the upper limit of the SFR diameter is also important for understanding asteroid interior structure since this can constrain the upper limit of the internal cohesion of asteroids.

(144977) 2005 EC₁₂₇ is consistent with a V-/A-type inner-main-belt asteroid, based on our follow-up spectroscopic observations, with a diameter estimated to be 0.6 ± 0.1 km from the standard brightness/albedo relation. Its rotation period was first determined to be 1.64 ± 0.01 hr from our iPTF asteroid rotation-period survey and then was confirmed as 1.65 ± 0.01 hr by the follow-up observations reported here using the LOT. We categorize 2005 EC₁₂₇ as a large SFR, given its size and since its rotation period is less than the 2.2 hr spin barrier.

Considering its 0.6 km diameter, 2005 EC₁₂₇ is most likely a rubble-pile asteroid. For 2005 EC₁₂₇ to survive under its super-fast rotation, either an internal cohesion of 47 ± 20 Pa or an unusually high bulk density of $\rho \sim 6$ g cm⁻³ is required. However, the latter case is very unlikely for large asteroids, and more so for V-/A-type asteroids, as 2005 EC₁₂₇ has been classified. Only six large SFRs have been reported in the literature, including 2005 EC₁₂₇, the subject of this work. This number is very small compared with the number of existing large fast rotators. Therefore, future surveys will help to reveal whether this rarity in detection is due to the intrinsically small population size of large SFRs. Moreover, none of the known SFRs have been classified as C-type asteroids, and the discovery of a large SFR of this type in future work would be an interesting development to further our understanding of the formation of large super-fast rotators.

This work is supported in part by the Ministry of Science and Technology of Taiwan under grants MOST 104-2112-M-008-014-MY3, MOST 104-2119-M-008-024, and MOST 105-2112-M-008-002-MY3, and also by Macau Science and Technology Fund No. 017/2014/A1 of MSAR. We are thankful for the indispensable support provided by the staff of the Lulin Observatory and the staff of the Palomar Observatory. We thank the anonymous referee for useful suggestions and comments.