The Orbit and Size of (87) Sylvia￢ﾀﾙs Romulus from the 2015 Apparition

Icarus 276 (2016) 107–115 Contents lists available at ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus The orbit and size of (87) Sylvia’s Romulus from the 2015 apparition ∗ Jack D. Drummond , Odell R. Reynolds, Miles D. Buckman Starfire Optical Range, Directed Energy Directorate, Air Force Research Laboratory, Kirtland AFB, NM 87117-5771, USA a r t i c l e i n f o a b s t r a c t Article history: Using the US Air Force’s Starfire Optical Range 3.5 meter telescope with adaptive optics and a laser Received 11 December 2015 guidestar, we obtained 68 images of asteroid (87) Sylvia and its satellite Romulus over 6 nights in March Revised 23 March 2016 and May of 2015. Adding an additional 3 images from earlier observations on one night in November Accepted 20 April 2016 2012, we are able to derive a circular (but not an eccentric) orbit for Romulus, leading to a density for Available online 3 May 2016 Sylvia of 1.37 ± 0.04 gm/cm 3. Extending the time base to 14 years by combining our data with previ- Keywords: ous observations from Keck, HST, and the VLT reported in the literature, we can fit for a new circular Satellites of asteroids orbit and change the density estimate slightly to 1.35 ± 0.04 gm/cm 3. By fitting a ratio of two Fourier Adaptive optics series to the measured magnitude difference between Sylvia (V = 12.5) and Romulus, which ranged from Image processing 4.1 to 5.0 in the J-band ( λ = 1 . 2 μm), and modeling both as triaxial ellipsoids, we are able to derive prolate spheroid equatorial diameters for Romulus of 41( ±27) × 30( ±16) km. This assumes that Romulus is rotating synchronously with its 3.64 d orbital period. However, decomposing the differential lightcurve between Sylvia and Romulus reveals a much shorter 7.96 hr rotational period, leading to more elongated prolate spheroid diameters of 82( ±7) × 21( ±2) km. As far as we know, our 3.5 m telescope is the smallest ground-based telescope to ever image any asteroid’s moon. Published by Elsevier Inc. 1. Introduction we can derive the mass and bulk density of the asteroid. Once we have found a satellite, without the pressure of competing ob- At the Starfire Optical Range 1 , the cradle if not the birth place serving time, we are able to devote a considerable amount of time of adaptive optics ( Duffner, 2009; Fugate, 1991a; Fugate et al., to orbit coverage. After several failed attempts to detect satellites 1991b ), our observatory is in a continuous state of research and around other asteroids, we finally succeeded in finding Romulus, development. One of our recent goals has been to detect close dim discovered in 2001 at the 10 m Keck II telescope by Brown et al. companions around bright objects with adaptive optics (AO) using (2001) , around asteroid (87) Sylvia on 2015 March 23, and then at- a laser guide star (LGS) on our 3.5 m telescope. In order to test tempted to image it several more times in the spring of 2015. (We our ability to discern such objects, we initially chose to observe were never able to detect Sylvia’s other smaller satellite, Remus). binary stars ( Drummond, 2014a ). However, they seldom lived up In the end we obtained some 68 measurable images over 6 nights to their reported high magnitude difference since inevitably the in March and May 2015, with several other non-detection nights. fainter partner turns out to be redder, resulting in a lower mag- The reason for so many negative observations is that the orbit of nitude difference at longer wavelengths. Therefore, we turned to Romulus was inclined only 4 ° to our line of sight during this 2015 asteroids with satellites for our targets, since they are presumed to apparition, continually moving into and out of the point spread show the same spectral signatures, chips off a block. In fact, many function (PSF) of Sylvia, rather than moving around the asteroid large Main-Belt asteroids, themselves, are in the brightness regime over the 3.6 day orbital period; this materially helped us set our of particular interest to us (magnitudes 12–15), as are those with detection limits. Nevertheless, the observations we gathered allow satellites with large magnitude differences. us to find the mass and density of Sylvia from this one opposition Moreover, by following a satellite around its parent asteroid, that is comparable to the values obtained from observations made we have the possibility to determine its orbit, and by combining over ten years with the 8–10 m telescopes at the VLT and at Keck the period and size of the orbit with the volume of the asteroid, ( Berthier et al., 2014; Fang et al., 2012 ). In addition, from measurements of the brightness difference between Sylvia and Romulus, since both Romulus’ orbital period ∗ Corresponding author. Tel.: +1 505 846 5854. E-mail address: [email protected] (J.D. Drummond). and Sylvia’s rotational period are so well known, we attempt to 1 Owned and operated by the Air Force Research Laboratory, Directed Energy Di- derive the size of Romulus from a Fourier decomposition of the rectorate, on Kirtland AFB near Albuquerque, New Mexico. relative lightcurve. The fact that we observed so close to Romulus’ http://dx.doi.org/10.1016/j.icarus.2016.04.033 0019-1035/Published by Elsevier Inc. 108 J.D. Drummond et al. / Icarus 276 (2016) 107–115 6000 6000 6000 6000 6000 6000 4000 4000 4000 4000 4000 4000 Km Km Km E Km Km Km N 2000 2000 2000 N 2000 2000 2000 E 0 0 0 0 0 0 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 Arc Sec Arc Sec Arc Sec Arc Sec Arc Sec Arc Sec 6000 6000 6000 6000 6000 6000 4000 4000 4000 4000 4000 4000 Km Km Km Km E Km Km N 2000 E N 2000 2000 N 2000 2000 2000 E 0 0 0 0 0 0 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 Arc Sec Arc Sec Arc Sec Arc Sec Arc Sec Arc Sec Fig. 1. Least squares fit of Lorentzian to Sylvia for the first detection of Romulus on Fig. 2. Same as Fig. 1 , but for the closest detection of Romulus on 2015 May 8 7.03 2015 March 23 7.95 UT. At upper left is the mean of five 10 s exposures of Sylvia UT. At upper left is the mean of two 120 s exposures of Sylvia, which overexposes and at bottom left is the log of the same image. At top center is the Lorentzian fit the asteroid. Even though the Lorentzian is a poorer fit for a saturated image, at to the image and at bottom center is the log of this Lorentzian. At upper right is lower right Romulus can be seen on the western side of Sylvia, opposite to Fig. 1 . the image minus model and at lower right is the log of the image divided by the model. Although Romulus can be seen in the lower left and upper right subplots, it is more distinct in the lower right subplot, to the east of Sylvia. were several nights when Romulus was not seen because it was too close to Sylvia, but as far as we know, our 3.5 m telescope is orbital plane and Sylvia’s equatorial plane considerably reduces the the smallest ground-based telescope to ever image a moon of an complexity of the analysis, although we still have to make a biax- asteroid. ial, not a triaxial, ellipsoid assumption for the shape of Romulus. After the asteroid’s moon is detected there still remains the We deliberately did not calculate the predicted positions of problem of measuring the moon’s position and brightness with re- satellites so that we could make true blind tests for detections. spect to the asteroid. We have used several methods, ordered here Since predicting satellite positions is not straightforward, we in- by our preference: clude an Appendix that gives a few equations to convert a satellite’s orbital elements into plane of sky orbital elements for the time of each observation, making the problem the same as calcu- 1. Simultaneously fit both components as either independent lating positions for binary stars. Lorentzians or Lorentzians having the same shape –the isopla- natic assumption. 2. Fit each component separately, cutting out a subsection cen- 2. Observations and reductions tered on the moon even if the much brighter asteroid intrudes. 3. Fit the asteroid as a Lorentzian, subtract the model, and then fit For all of our observations, a sodium laser with 40 W out of a subsection of the residuals for the moon. the top of the launch telescope produced an LGS for higher or- 4. Click on the peak of the asteroid and the moon and record their der AO correction, while the light from the V = 12 . 5 asteroid it- positions and peak pixel values. self provided tip-tilt correction. The system uses a 24 × 24 Shack– Hartmann wave front sensor (WFS), and in this case, I-band light (0.9 μm) is diverted to the track-focus sensor, while imaging in the In the case of Sylvia and Romulus, not one of the images al- J-band (1.2 μm), where the image resolution is 0.0328 /pix.

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