LIGHTCURVE ANALYSIS OF L5 TROJAN ASTERIODS AT THE CENTER FOR SOLAR SYSTEM STUDIES: 2019 ARPIL TO JUNE

Abstract

Lightcurves for five L₅ Jovian Trojan asteroids were obtained at the Center for Solar System Studies (CS3) from 2019 April to June.

CCD Photometric observations of five Trojan asteroids from the L₅ (Trojan) Lagrange point were obtained at the Center for Solar System Studies (CS3, MPC U81). For several years, CS3 has been conducting a study of Jovian Trojan asteroids. This is another in a series of papers reporting data analysis being accumulated for family pole and shape model studies. It is anticipated that for most Jovian Trojans, two to five dense lightcurves per target at oppositions well distributed in ecliptic longitudes will be needed and can be supplemented with reliable sparse data for the brighter Trojan asteroids. For most of these targets we were able to get preliminary pole positions and create shape models from sparse data and the dense lightcurves obtained to date. These preliminary models will be improved as more data are acquired at future oppositions and will be published at a later date.

Table I lists the telescopes and CCD cameras that were used to make the observations. Images were unbinned with no filter and had master flats and darks applied. The exposures depended upon various factors including magnitude of the target, sky motion, and Moon illumination.

Table I.

List of telescopes and CCD cameras used at CS3.

Telescope	Camera
0.40-m f/10 Schmidt-Cass	FLI Proline 1001E
0.40-m f/10 Schmidt-Cass	Fli Microline 1001E
0.35-m f/10 Schmidt-Cass	Fli Microline 1001E

Image processing, measurement, and period analysis were done using MPO Canopus (Bdw Publishing), which incorporates the Fourier analysis algorithm (FALC) developed by Harris (Harris et al., 1989). The Comp Star Selector feature in MPO Canopus was used to limit the comparison stars to near solar color. Night-tonight calibration was done using field stars from the CMC-15 or the ATLAS catalog (Tonry et al., 2018), which has Sloan griz magnitudes that were derived from the GAIA and Pan-STARRS catalogs, among others. The authors state that systematic errors are generally no larger than 0.005 mag, although they can reach 0.02 mag in small areas near the Galactic plane. BVRI magnitudes were derived by Warner using formulae from Kostov and Bonev (2017). The overall errors for the BVRI magnitudes, when combining those in the ATLAS catalog and the conversion formulae, are on the order of 0.04–0.05 mag.

Even so, we found in most cases that nightly zero point adjustments for the ATLAS catalog to be on the order of only 0.02–0.03 mag were required during period analysis. There were occasional exceptions that required up to 0.10 mag. These may have been related in part to using unfiltered observations, poor centroiding of the reference stars, and not correcting for second-order extinction terms. Regardless, the systematic errors seem to be considerably less than other catalogs, which reduces the uncertainty in the results when analysis involves data from extended periods or the asteroid is tumbling.

In the lightcurve plots, the “Reduced Magnitude” is Johnson V corrected to a unity distance by applying −5*log (r*) to the measured sky magnitudes with r and * being, respectively, the Sun-asteroid and the Earth-asteroid distances in AU. The magnitudes were normalized to the phase angle given in parentheses using G = 0.15. The X-axis rotational phase ranges from −0.05 to 1.05. The amplitude indicated in the plots (e.g. Amp. 0.23) is the amplitude of the Fourier model curve and not necessarily the adopted amplitude of the lightcurve. Targets were selected for this L₅ observing campaign based upon the availability of dense lightcurves acquired in previous years. We obtained two to four lightcurves for most of these Trojans at previous oppositions. For brevity, only some of the previously reported rotational periods may be referenced. A complete list is available at the lightcurve database (LCDB; Warner et al., 2009).

To evaluate the quality of the data obtained to determine how much more data might be needed, preliminary pole and shape models were created for all of these targets. Sparse data observations were obtained from the Catalina Sky Survey and USNO-Flagstaff survey using the AstDyS-3 site (http://hamilton.dm.unipi.it/asdys2/). These sparse data were combined with our dense data as well as any other dense data found in the ALCDEF asteroid photometry database (http://www.alcdef.org/) using MPO LCInvert, (Bdw Publishing). This Windows-based program incorporates the algorithms developed by Kassalainen et al (2001a, 2001b) and converted by Josef Durech from the original FORTRAN to C. A period search was made over a sufficiently wide range to assure finding a global minimum in χ² values.

2357 Phereclos.

The synodic period found this year produced a low amplitude, lightcurve with three extrema consistent with rotational periods found in previous years (Mottola et al., 2011; Stephens et al., 2016b; 2017; 2018). These data were combined with our data from the last three years and available sparse data to create a preliminary shape model with a sidereal period of 14.36221 ± 0.00001 h.

2363 Cebriones.

Reliable rotational rates for this Trojan were obtained three times in the past (Galad et al., 2008; Mottola et al., 2011; Skiff et al., 2019), each time finding a period near 20.1 h. The 2019 results are in good agreement.

Using sparse data from the Asteroids – Dynamic Site and the Skiff data from the Asteroid Lightcurve Photometry Database, a preliminary shape model with a sidereal rotational period of 20.09748 ± 0.00001 h was created.

3451 Mentor.

Judging by the number entries in the LCDB, this is one of the better-studied Trojans. All the results have been consistently near 7.7 h. Among those rated U ≥ 2+ are Melita et al. (2010; 7.68 h), French et al. (2011b; 7.730 h), Mottola et al. (2011; 7.675 h), and Stephens et al. (2014; 7.68 h). Our result of 7.6922 h is in good agreement.

This Trojan is obliging when it comes to trying to model its shape and spin axis. It has shown lightcurves amplitudes ranging from 0.13 mag (L_PAB = 59°) to 0.63 mag (L_PAB = 167°). From this, the spin axis should have an ecliptic longitude near 60° or 240°. This is confirmed by our preliminary model with ecliptic coordinates of λ, β = (255°, +60°) and sidereal period of 7.6966420 ± 0.000002 h.

(12929) 1999 TZ1.

This L₅ Jovian Trojan has been observed several times in the past. Moullet et al. (2008) observed it in 2007 reporting a rotational period of 10.4 h from sparse data over 12 nights. The resulting lightcurve was a poor fit. Over seven nights in 2009, Mottola et al. (2011) used sparse data and found a rotational period of 9.2749 h with a single extremum. Thirourin et al. (2010) used sparse data over six nights in 2007 to find two ambiguous periods, a bimodal 5.211 h period and a 10.422 h period with four extrema. Both lightcurves show scatter equal to the 0.07 mag. amplitude.

The results in 2019 are from a much denser dataset but still result in an ambiguous solution. Our preferred solution and the one adopted for this paper is 13.73 h which is a 3:4 alias of the previously reported 10.4 h period. A 19.26 h rotational period also produces a bimodal solution. Both solutions are low amplitude. 1999 TZ1 is yet another example of the problems involved in trying to use sparse observational data to determine low amplitude lightcurves.

17492 Hippasos.

We observed this Trojan once before (Stephens and Warner, 2014) and found a synodic rotational period of 17.75 h. This 2019 result is in good agreement. Using sparse data from the Asteroids – Dynamic Site, we were able to create a preliminary shape model with a sidereal rotational period of 17.71126 ± 0.00001 h.

Table II.

Observing circumstances and results. The phase angle is given for the first and last date. If preceded by an asterisk, the phase angle reached a minimum or maximum during the period. L_PAB and B_PAB are the approximate phase angle bisector longitude/latitude at mid-date range (see Harris et al., 1984).

Number	Name	2019 mm/dd	Phase	LPAB	BPAB	Period(h)	P.E.	Amp	A.E.
2357	Phereclos	03/31–04/15	*2.5,0.9	201	1	14.449	0.003	0.15	0.02
2363	Cebriones	05/29–06/04	6.9,7.8	214	4	20.099	0.003	0.34	0.02
3451	Mentor	12/31–12/31	*6.9,7.8	0	0	7.6922	0.0004	0.31	0.02
12929	1999 TZ1	05/26–06/02	7.3,8.3	208	11	13.73	0.02	0.08	0.02
17492	Hippasos	05/12–05/21	5.7,6.5	219	25	17.699	0.006	0.40	0.03