A NEW LARGE SUPER-FAST ROTATOR: (335433) 2005 UW163

Asteroids, with the dwarf planet Ceres as the largest member, have sizes ranging from a few meters to a few hundred kilometers. They were subject to strong collisional interaction, as indicated by the formation of many asteroid families composed of breakup fragments from disruptive impact events. A fundamental discovery made by Harris (1996) concerning the internal structures of asteroids has to do with the statistical result that objects with sizes larger than 150 m have rotation periods longer than 2.2 hr. This spin cutoff can be explained by the rubble-pile structure in which the asteroids are made up of collisional breakup fragments bound together by mutual gravitational force. Faster rotation will lead to centrifugal disruption. Only one object, 2001 OE84, which is a near-Earth asteroid with a diameter of 0.65 km (Warner et al. 2009) and has a rotation period of 29.19 minutes, has been found to be exception to this rule (Pravec et al. 2002). Holsapple (2007) subsequently proposed that the binding of such fast rotating asteroids could be the result of size-dependent material strength and predicted the presence of kilometer-/sub-kilometer-sized super-fast rotators (hereafter SFRs). It is noteworthy to point out that several SFR candidates of this size range were reported by Masiero et al. (2009) and Dermawan et al. (2011), but none of them had reliably determined periods (Harris et al. 2012). This is because their low brightness and fast rotation make such SFRs difficult to be detected and confirmed by follow-up observations. A comprehensive program is required to produce quantitative measurements.

Within the framework of the PTF/iPTF project⁶ and the TANGO project,⁷ a systematic survey of asteroid light curves has been carried out by data mining of the archived data (see Polishook et al. 2012 for the pilot study) and dedicated observational campaigns (see Chang et al. 2014 for the result for the first campaign) using the 48 inch Oschin Schmidt telescope (P48). In our second (2014 January 6–9) and third (2014 February 20–23) dedicated observational campaigns, a number of SFR candidates have been identified in the analysis of these data sets (the result including asteroid rotation periods and SFR candidates will be published in the near future). One of them is (335433) 2005 UW163. In this work, we report on the P48 discovery observation during 2014 February 20–23, and the follow-up observations conducted on the 200 inch Hale Telescope at the Palomar Observatory on 2014 March 25 to confirm the identity of this interesting object. In Section 2, we describe our observations and data reduction. The rotation period analysis is given in Section 3. The results and discussion are presented in Section 4. A summary and conclusion can be found in Section 5.

2.1. PTF Photometry

The PTF is a synoptic survey designed to explore the transient and variable sky (Law et al. 2009; Rau et al. 2009). It employs the 48 inch Oschin Schmidt Telescope equipped with an 11 chip mosaic CCD camera that has a field of view of ∼7.26 deg² and a pixel scale of 101. The available filters include Mould R, Gunn g', and H_α, and its 5σ median limiting magnitude of an exposure of 60 s in the R band is ∼21 mag (Law et al. 2010). Each PTF exposure was processed by the IPAC-PTF photometric pipeline including image splitting, de-biasing, flat-fielding, source extraction, astrometric calibration, and photometric calibration (Grillmair et al. 2010; Laher et al. 2014). Its final products include reduced images, mask images, and source catalogs. The PTF absolute photometric calibration was done by fitting to catalog data in Sloan Digital Sky Survey (SDSS) fields (York et al. 2000), which routinely reached a precision of ∼0.02 mag (Ofek et al. 2012a, 2012b). Since the calibration was done on a per-night, per-field, per-filter, per-chip basis, small photometric zero-point variations are possible from night to night, the accuracy of which depends on the degree to which a night is affected by mist and cloud cover, and transient variations in atmospheric conditions.

As part of the TANGO project, we conducted an asteroid rotation-period survey during 2014 February 20–23, which continuously scanned 12 consecutive PTF fields on the ecliptic plane in R band with a cadence of ∼20 min and an exposure time of 60 s for each frame. The total sky area was ∼87 deg². Table 1 lists the observational metadata and Figure 1 shows the field configuration. To extract known asteroid light curves, the source catalogs were purged of all stationary sources and then matched against the ephemerides obtained from the JPL/HORIZONS system with a radius of 2''. In this campaign, we extracted ∼2500 light curves suitable for rotation period analysis. The preliminary result showed ∼910 objects had good rotation period determinations, and 11 of them were identified as SFR candidates. The result will be published in a separate paper soon. Follow-up observations for the SFR candidates are also planned. Our main-belt asteroid of interest, (335433) 2005 UW163, was close to its opposition and located on chips 7, 6, and 6 of field 3161 on 2014 February 20, 21, and 22, and on chip 11 of field 3160 on 2014 February 23. Therefore, we were able to obtain its light curve over a four-night time span to identify it as a highly probable SFR and conducted a follow-up observation to confirm its short rotation period.

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Table 1. The PTF Observation

Field ID	R.A.	Decl.	Feb 20	Feb 21	Feb 22	Feb 23
	(°)	(°)	Δt, Nexp	Δt, Nexp	Δt, Nexp	Δt, Nexp
3158	143.65	10.12	7.9, 19	7.6, 22	7.9, 22	7.2, 20
3159	147.12	10.12	8.0, 17	7.3, 20	7.9, 21	7.7, 22
3160	150.58	10.12	7.6, 18	7.7, 21	7.7, 22	7.7, 22
3161	154.04	10.12	8.0, 20	8.0, 22	7.9, 23	7.9, 23
3162	157.50	10.12	8.3, 20	7.9, 22	8.0, 24	7.9, 23
3163	160.96	10.12	8.0, 19	7.8, 22	8.0, 24	8.0, 24
3261	141.55	12.38	7.7, 20	7.6, 21	8.2, 23	7.1, 20
3262	145.05	12.38	8.1, 20	7.9, 23	8.2, 23	7.5, 20
3263	148.54	12.38	8.2, 20	7.6, 22	8.1, 23	7.7, 21
3264	152.04	12.38	7.9, 20	8.0, 23	8.2, 24	8.2, 24
3265	155.53	12.38	8.7, 19	8.0, 22	8.1, 24	8.2, 23
3266	159.03	12.38	8.0, 21	8.2, 23	8.1, 25	8.2, 24

Notes. Δt is the time duration spanned by each observing set in hours and N_exp is the total number of exposures for each night and field.

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2.2. The Follow-up Observation

To measure the synodic rotation period of (335433) 2005 UW163, all data points were corrected for light-travel time (i.e., the time interval of a photon traveling from the object to Earth) and the magnitudes were reduced to both heliocentric (r) and geocentric ▵ distances at 1 AU by

$$\begin{equation} M(r=1,\triangle =1) = m + 5\log (r\triangle), \end{equation} \tag{ 1 }$$

where M and m are the reduced and apparent magnitudes, respectively. The r and ▵ were calculated using PyEphem⁸ using the orbital elements obtained from the Minor Planet Center.⁹

We applied a second-order Fourier series, which was developed by Harris et al. (1989) and has since become the standard for asteroid light-curve fitting (e.g., Pravec et al. 2005), to the PTF R-band light curve and the P200 r'-band light curve separately, in order to search for their rotation periods:

$$\begin{eqnarray} M_{i,j} &=& \sum _{k=1,2}^{N_k} B_k\sin \left[\frac{2\pi k}{P} (t_j-t_0)\right] \nonumber\\ && + C_k\cos \left[\frac{2\pi k}{P} (t_j-t_0)\right] + Z_i, \end{eqnarray} \tag{ 2 }$$

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, and t₀ is an arbitrary epoch. Following Polishook et al. (2012), we also fitted a constant value Z_i in Equation (2) to correct the small systematic offsets between different PTF data sets, where a data set was defined as all the measurements taken on the same night, field, filter, and CCD. Then, Equation (2) was solved by least-squares minimization for each given P to obtain the other free parameters. We tried a frequency range of 0.25–25 revolutions per day with a step of 0.0025 revolutions per day to cover the majority of asteroid rotation periods (Pravec & Harris 2000). The uncertainty of the derived rotation period was calculated from the range of periods with χ² smaller than $\chi _{{\rm best}}^2+\triangle \chi ^2$, where $\chi _{{\rm best}}^2$ is the χ² of the picked-out period and ▵χ² is calculated from the inverse χ² distribution, assuming 1 + 2N_k + N_i degrees of freedom.

The rotation periods of (335433) 2005 UW163 derived from the PTF and the P200 observations, which are 1.290 ± 0.034 and 1.290 ± 0.058 hr, respectively, are very compatible with each other. The super-fast rotating nature of this asteroid is very convincingly demonstrated in both folded light curves (see Figure 2). The peak-to-peak variation of the PTF light curve is R ∼ 0.6 mag and that of the P200 light curve is r' ∼ 0.8 mag. Although the P200 folded light curve does not cover two full cycles of the derived period, we do not see any particular offset in the overlap between the first (red filled circles) and second (black filled circles) cycles. Moreover, the light curve shows a large amplitude. Therefore, it is very unlikely that (335433) 2005 UW163 would be the case as discussed in Harris et al. (2014), where the authors pointed out that some asteroids might have ambiguous rotation period determinations due to their small light curve amplitudes (i.e., the half rotation period was misidentified as a "real" rotation period). One special case reported by Polishook (2010) that (40701) 1999 RG235 showed a possible three-peaked light curve with a large amplitude. This could be a possibility for (335433) 2005 UW163. If the light curve of our target has four peaks, then it must have identical odd maxima, even maxima, and even minima as seen in our case. Such a chance seems to be very small, and we thus believe our derived rotation period is highly probable to be the true rotation period of (335433) 2005 UW163.

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In order to improve the P200 light-curve fitting, we used a sixth-order Fourier series to analyze its rotation period again. The result is shown in Figure 2 as well. We see the best-fit rotation period still remains at 1.29 hr and the fine features on the P200 folded light curve are reproduced relatively well as pointed out by Harris et al. (2014). This means (335433) 2005 UW163 has a more complex shape.

Since the g' and i' data points show similar variation to the P200 r'-band light curve, we use Equation (2) with the derived rotation period, 1.290 hr, to obtain the offsets, Z_i, between the measurements for the g', r', and i' bands, where a data set was then defined as the measurements taken with the same filter. The best-fitting results were g' − r' = 0.68 ± 0.03 mag and r' − i' = 0.19 ± 0.02 mag, which indicates an S- or V-type asteroid for (335433) 2005 UW163 (Ivezi'c et al. 2001). Incorporating i − z = −0.45 obtained from the SDSS moving object catalog (Ivezi'c et al. 2002), we believe (335433) 2005 UW163 is most likely a V-type asteroid (Parker et al. 2008).

Since the PTF and P200 light curves were observed in different bands and the phase angles (α) had a small change in both observations, we only applied, instead of fitting, the H–G system (Equation (3) Bowell et al. 1989) with a fixed G slope of 0.43  ±  0.08 (i.e., a typical G value for a V-type asteroid; Warner et al. 2009) to the P200 r'-band light curve to estimate the absolute magnitude H of (335433) 2005 UW163.

$$\begin{equation} H = \langle M(r=1,\triangle =1)\rangle +2.5\log [(1-G)\phi _1+G\phi _2], \end{equation} \tag{ 3 }$$

where

$$\begin{equation} \phi _1 = \exp [-3.33 \tan (0.5\langle \alpha \rangle)^{0.63}], \end{equation} \tag{ 4 }$$

$$\begin{equation} \phi _2 = \exp [-1.87 \tan (0.5\langle \alpha \rangle)^{1.22}]. \end{equation} \tag{ 5 }$$

This gives a mean value of $H_{r^{\prime }} = 17.69 \pm 0.27$ mag. Moreover, its diameter is estimated using

$$\begin{equation} D = {1130 \over \sqrt{p_{r^{\prime }}}} 10^{-H_{r^{\prime }}/5}, \end{equation} \tag{ 6 }$$

where $p_{r^{\prime }}$ is the r'-band albedo and the conversion constant, 1130, adopted from Jewitt et al. (2013). We assumed an albedo of $p_{r^{\prime }} = 0.297 \pm 0.131$, which was adopted from the geometric albedo in visible wavelengths (p_v) appropriate for a V-type asteroid (Usui et al. 2013). Although there is a small difference between $p_{r^{\prime }}$ and p_v, we treat this difference as part of the uncertainty in our assumed albedo. Therefore, we have a derived diameter of D = 0.6 + 0.3/ − 0.2 km, where the diameter range is estimated from the uncertainties introduced by $p_{r^{\prime }}$, G and $H_{r^{\prime }}$.

Combining the data taken from Warner et al. (2009) and Chang et al. (2014), we plot the asteroid spin rate versus diameter in Figure 3. We see both (335433) 2005 UW163 and 2001 OE84 located above the "spin barrier" of the "rubble-pile" asteroids and away from the small monolithic SFRs. This result indicates (335433) 2005 UW163 is an SFR. To keep (335433) 2005 UW163 from breaking apart under such fast rotation by its own gravity only, it requires a bulk density as high as ρ ∼ 11 g cm⁻³ when assuming a critical rotation period of $P \sim 3.3 \sqrt{(1+\Delta m)/\rho }$ hr for an object with a light curve variation of r' ∼ 0.8 mag (Pravec & Harris 2000). Such high bulk density is very unusual for the "rubble-pile" asteroids. This is because as shown in the plot of the spin rate versus light curve amplitude in Figure 4, the "rubble-pile" asteroids cannot have a bulk density >3 g cm⁻³ (Pravec & Harris 2000). To explain the presence of kilometer-/sub-kilometer-sized SFRs, Holsapple (2007) used a size-dependent strength for asteroids, which included tensile strength and cohesiveness, in addition to gravity. This additional size-dependent effect could produce a transition from the small monolithic object region to the large gravitationally bound aggregation region. Therefore, a comprehensive survey of the population of kilometer-/sub-kilometer-sized SFRs would help us understand this question.

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The sub-kilometer-sized SFR (335433) 2005 UW163, which is a main-belt asteroid with a rotation period of 1.290 hr (i.e., a frequency of 18.6 revolutions per day), was discovered in the asteroid rotation period survey conducted on the PTF during 2014 February 20–23 as part of the TANGO project. It was confirmed by the follow-up observation carried out on 2014 March 25 using the P200. Its multi-band colors (i.e., g' − r' = 0.68  ±  0.03 mag, r' − i' = 0.19 ± 0.02 mag, and the SDSS i − z = −0.45) indicate that (335433) 2005 UW163 is a V-type asteroid. With an assumed albedo of 0.297 ± 0.131, the SFR asteroid's $H_{r^{\prime }} = 17.69 \pm 0.27$ mag allows us to infer a diameter of D = 0.6  +  0.3/ − 0.2 km. This shows that if (335433) 2005 UW163 is a "rubble-pile" asteroid, it would require a bulk density as high as 11 g cm⁻³ to keep itself from breaking apart under such fast rotation. Therefore, other mechanisms, such as a combination of tensile strength and cohesiveness, should be taken into account (Holsapple 2007). To search for a larger sample of kilometer-/sub-kilometer-sized SFRs through comprehensive asteroid rotation surveys, as is being planned, would be very helpful to the investigation of the origin and internal structures of asteroids.

This work is supported in part by the National Science Council of Taiwan under the grants NSC 101-2119-M-008-007-MY3. We are greateful for the indispensable support provided by the staff of the Palomar Observatory. We also thank the referee, Alan Harris, for useful comments that helped to improve the content of the paper.