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

TL;DR

This paper confirms that asteroid 2005 EC127 is a large super-fast rotator with a rotation period of 1.65 hours, challenging the typical rubble-pile structure assumption for its size and suggesting internal cohesion or high density.

Contribution

First confirmation of a large super-fast rotator among inner-main-belt asteroids, providing insights into its internal structure and cohesion properties.

Findings

2005 EC127 completes a rotation in 1.65 hours

It likely has internal cohesion or high bulk density

Only six large super-fast rotators are known to date

Abstract

(144977) 2005 EC127 is an V-/A-type inner-main-belt asteroid with a diameter of 0.6 +- 0.1 km. Asteroids of this size are believed to have rubble-pile structure, and, therefore, cannot have a rotation period shorter than 2.2 hours. However, our measurements show that asteroid 2005 EC127 completes one rotation in 1.65 +- 0.01 hours with a peak-to-peak light-curve variation of ~0.5 mag. Therefore, this asteroid is identified as a large super-fast rotator. Either a rubble-pile asteroid with a bulk density of ~6 g cm^-3 or an asteroid with an internal cohesion of 47 +- 30 Pa can explain 2005 EC127. However, the scenario of high bulk density is very unlikely for asteroids. To date, only six large super-fast rotators, including 2005 EC127, have been reported, and this number is very small when compared with the much more numerous fast rotators. We also note that none of the six reported large SFRs are classified as C-type asteroids.

Tables

Table 1. Table 1: Observational details.

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

Table 2. Table 2: Confirmed large SFRs to date.

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

Equations

$$M_{i,j}=\sum _{k=1,2}^{N_k}{B}_k\sin \left[\frac{2\pi k}{P}(t_j-t_0)\right]+C_k\cos \left[\frac{2\pi k}{P}(t_j-t_0)\right]+Z_i,$$

$$D=\frac{1329}{\sqrt{p_v}}10^{-H/5}$$

Full text

surveys - minor planets, asteroids: individual (144977) 2005 EC127

1 Introduction

The large (i.e., a diameter of a few hundreds of meters) super-fast rotators (hereafter, 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 hours (Harris, 1996)111The 2.2-hour spin barrier was calculated for an asteroid with a bulk density of $\rho=3$ g cm*-3*.. However, the first large SFR, 2001 OE84, a near-Earth asteroid of $\sim 0.7$ 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 0.5–10 km and rotation periods between 2-3 hours) in the up-to-date Asteroid Light Curve Database (hereafter, LCDB222http://www.minorplanet.info/lightcurvedatabase.html; 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 ZTF333Zwicky Transient Facility; http://ptf.caltech.edu/ztf, 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 project444Taiwan New Generation OIR Astronomy has been conducting asteroid rotation-period surveys since 2013 using the iPTF555intermediate Palomar Transient Factory; http://ptf.caltech.edu/iptf (for details, see Chang et al., 2014a, 2015, 2016). From these surveys, two 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 Feb 2015 (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 article 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.

2 Observations

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.

2.1 iPTF Observations

The iPTF is a follow-on project of the PTF, a project whose aim is to explore the transient and variable sky synoptically. The iPTF/PTF employ the Palomar 48-inch Oschin Schmidt Telescope and an 11-chip mosaic CCD camera with a field of view of $\sim 7.26$ deg2 (Law et al., 2009; Rau et al., 2009). This wide field of view is extremely useful in collecting a large number of asteroid light curves within a short period of time. Four filters are currently available, including a Mould-R, Gunn-g’, and two different $H\alpha$ bands. The exposure time of the PTF is fixed at 60 seconds, which routinely reaches a limiting magnitude of $R\sim$21 mag at the $5\sigma$ level (Law et al., 2010). All iPTF exposures are processed by the IPAC-PTF photometric pipeline (Grillmair et al., 2010; Laher et al., 2014), and the Sloan Digital Sky Survey fields (SDSS; York et al., 2000) are used in the magnitude calibration. Typically, an accuracy of $\sim 0.02$ mag can be reached for photometric nights (Ofek et al., 2012a, b). Since the magnitude calibration is done on a per-night, per-filter, per-chip basis, small photometric zero-point variations are present in PTF catalogs for different nights, fields, filters and chips.

In the asteroid rotation-period survey conducted on Feb 25–26, 2015, we repeatedly observed six consecutive PTF fields near the ecliptic plane, in the $R$-band with a cadence of $\sim 10$ minutes. Asteroid 2005 EC127 was observed in the PTF field centered at $R.A.=154.04^{\circ}$ and $Dec.=10.12^{\circ}$ when it was approaching its opposition at a low phase angle of $\alpha\sim 1.3^{\circ}$. After all stationary sources were removed from the source catalogs, the light curves for known asteroids were extracted using a radius of 2″ to match with the ephemerides obtained from the JPL/HORIZONS system. The light curve of 2005 EC127 contains 42 clean detections from this observation run (i.e., the detections flagged as defective by the IPAC-PTF photometric pipeline were not included in the light curve).

2.2 LOT Observations

The follow-up observations to confirm the rotation period of 2005 EC127 were carried out on Sept 24, 2016 using the LOT when 2005 EC127 had a magnitude of $r^{\prime}\sim 19.2$ at its low phase angle of $\alpha\sim 2.6^{\circ}$. The average seeing during the observations was $\sim 1.3$″. All images were taken in the $r^{\prime}$-band with a fixed exposure time of 300 seconds using the Apogee U42 camera, a 2K$\times$2K charge-coupled device with a pixel scale of 0.35″. We acquired a total of 84 exposures over a time span of $\sim 440$ minutes, and the time difference between consecutive exposures was $\sim 5$ minutes. The image processing and reduction included standard procedures of bias and flat-field corrections, astrometric calibration using $astrometry.net$666http://astrometry.net, and aperture photometry using SExtractor (Bertin & Arnouts, 1996). The photometric calibration was done against Pan-STARRS1 point sources of $r^{\prime}\sim 14$ to 22 mag (Magnier et al., 2016) using linear least-squares fitting, which typically achieved a fitting residual $\sim 0.01$ mag. We improved the photometric accuracy by employing the trail-fitting method (Vereš et al., 2012; Lin et al., 2015) to accommodate the streaked image of 2005 EC127 as a result of asteroid motion over the 300-second exposure time.

2.3 Spectroscopic Observations

To determine the taxonomic type for 2005 EC127, its optical spectra were obtained using the Palomar 200-inch Hale Telescope (hereafter, P200) and the Double-Beam Spectrograph (DBSP; Oke & Gunn, 1982) in low-resolution mode ($R\sim 1500$). Three consecutive exposures were taken on Oct 4, 2016 with an exposure time of 300 seconds each. An average bias frame was made out of 10 individual bias frames and a normalized flat-field frame was constructed out of 10 individual lamp flat-field exposures. For the blue and red arms, respectively, FeAr and HeNeAr arc exposures were taken at the beginning of the night. Both arms of the spectrograph were reduced using a custom PyRAF-based pipeline777https://github.com/ebellm/pyraf-dbsp (Bellm & Sesar, 2016). The pipeline performs standard image processing and spectral reduction procedures, including bias subtraction, flat-field correction, wavelength calibration, optimal spectral extraction, and flux calibration. The average spectrum of 2005 EC127 was constructed by combining all individual exposures, and then it was divided by the solar spectrum888The solar spectrum was obtained from Kurucz et al. (1984), and was then convolved with a Gaussian function to match the resolution of the spectrum of 2005 EC127. to obtain the reflectance spectrum of 2005 EC127 (Fig. 2). The trend of the reflectance spectrum suggests an V-/A-type asteroid for 2005 EC127, according to the Bus-DeMeo classification scheme (DeMeo et al., 2009).

3 Rotation-Period Analysis

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 ($\Delta$) distances at 1 AU by $M=m+5\log(r\Delta)$, 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:

[TABLE]

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; $t_{0}$ 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 Eq. (1). The frequency range was explored between 0.25–50 rev/day with a step of 0.001 rev/day. To estimate the uncertainty of the derived rotation periods, we calculated the range of periods with $\chi^{2}$ smaller than $\chi_{best}^{2}+\triangle\chi^{2}$, where $\chi_{best}^{2}$ is the chi-squared value of the picked-out period and $\triangle\chi^{2}$ is obtained from the inverse chi-squared distribution, assuming $1+2N_{k}+N_{i}$ degrees of freedom.

The rotation period of $1.64\pm 0.01$ hours (i.e., 14.6 rev/day) of 2005 EC127 was first identified using the PTF light curve (Chang et al., 2016). Although the derived frequency of 14.6 rev/day is significant in the periodogram calculated from the PTF light curve, the corresponding folded light curve is relatively scattered (see upper panels of Fig. 1). Therefore, we triggered the follow-up observations using the LOT. The rotation periods of 2005 EC127 derived from the LOT light curve is $1.65\pm 0.01$ hours (i.e., 14.52 rev/day), which is in good agreement with the PTF result (see lower panels of Fig. 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 $\sim 0.6$ and $\sim 0.5$ 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 $\Delta m<0.4$ 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 hours is the true rotation period for 2005 EC127.

4 Results and Discussion

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

[TABLE]

(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, respectively999A $G$ slope of 0.24 for S-type asteroids (Pravec et al., 2012) would make the $H$ magnitude $\sim 0.03$ mag fainter, which is equivalent to a $\sim 0.01$ km diameter difference, and within the uncertainty of our estimation.. 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 Fig. 4, 2005 EC127 lies in the rubble-pile asteroid region and has a rotation period shorter than 2 hours. 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 Fig. 3). This would suggest that 2005 EC127 is a very compact object, i.e., comprised mostly of metal. However, such high bulk density is very unusual among asteroids. Moreover, 2005 EC127 is probably an V-type asteroid. Therefore, this is a very unlikely scenario indeed.

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 criterion101010The detailed calculation is given in Chang et al. (2016). This method has been widely used, e.g., in Holsapple (2007); Rozitis et al. (2014); Polishook et al. (2016)., we can estimate the internal cohesion for asteroids. Assuming an average $\rho=1.93$ g/cm3 for V-type asteroids (Carry, 2012), a cohesion of $47\pm 20$ Pa results for 2005 EC127111111For an A-type asteroid with average density $\rho=3.73$ g/cm3 (Carry, 2012), the cohesion would be 52 Pa.. This modest value is comparable with that of the other large SFRs (see Table 2), and also nearly in the cohesion range of lunar regolith, i.e., 100-1000 Pa (Mitchell, 1974).

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 Fig. 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.

We also note that none of the six reported large SFRs are 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 SFR diameter is also important for understanding asteroid interior structure, since this can constrain the upper limit of internal cohesion of asteroids.

5 Summary and Conclusions

(144977) 2005 EC127 is consistent with an V-/A-type inner-main-belt asteroid, based on our follow-up spectroscopic observations, with a diameter estimated to be $0.6\pm 0.1$ km from the standard brightness/albedo relation. Its rotation period was first determined to be $1.64\pm 0.01$ hours from our iPTF asteroid rotation-period survey, and then confirmed as $1.65\pm 0.01$ hours 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-hour 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 $47\pm 20$ Pa or an unusually high bulk density of $\rho\sim 6$ g/cm3 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 super-fast rotators have been classified as C-type asteroids, and the discovery of a large super-fast rotator 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 his useful suggestions and comments.