Evidence for a close in satellite in the large TNO Varuna
Authors: Fernández-Valenzuela Estela , Ortiz Jose Luis , Morales Nicolás , Santos-Sanz Pablo , Duffard René , Lellouch Emmanuel 
Published: October 2020

Introduction20000 Varuna is one of the most interesting TNOs due to its peculiar physical properties. It rotates relatively fast with a period of 6.3435674 h Santos-Sanz et al. (2013), producing a double-peaked rotational light-curve with a very large amplitude, ~ 0.45 mag, dominated by the body shape (e.g., Jewitt &amp; Sheppard 2002, Lellouch et al. 2002, Hicks et al. 2005, Belskaya et al. 2006). Varuna's area-equivalent diameter is ~700 km (Lellouch et al. 2013) and its estimated density, under the assumption of hydrostatic equilibrium (Chandrasekhar et al. 1987), has a value of ~ 1000 kgm-3, which is somewhat high compared to other TNOs of similar sizes (Ortiz et al. 2012).&#160;ObservationsWe present here a collection of new rotational light-curves from 2005 to 2019, taken from three different observatories in Spain (Sierra Nevada Observatory, Calar Alto Observatory and Roque de los Muchachos Observatory), using telescopes of 1.5-m, 1.23-m and 2.2-m, and 3.6-m diameter, respectively. Additionally, we have included three rotational light-curves from the literature (Jewitt &amp; Sheppard 2002, Lellouch et al. 2002, Hicks et al. 2005) to our study. This data set provides different rotational light-curves in a time span of 19 years.&#160;Results&#160;We have detected that the amplitude of the rotational light-curve has evolved over time, producing a considerable change along these 19 years, increasing ~ 0.13 mag. We think that this change is due to a variation in Varuna's aspect angle. We model this variation assuming a simple triaxial shape for Varuna's body. The best fit to the data corresponds to a family of solutions with axial ratios b/a between 0.56 and 0.60, which constrains the pole orientation in two different ranges of solutions (see figure 1).&#160;&#160;Figure 1. &#967;2 map of possible values for the axis ratio b/a = 0.60. &#955;P and &#946;P&#160;are the ecliptic longitude and latitude of the pole orientation (Schroll et al. 1976). The best solution is given by the range &#955;P&#8712;[43, 63]&#186; and &#946;P&#8712;[-70, -58]&#186; (with its complementary direction also possible for the same values of &#967;2PDF). Figure from Fernandez-Valenzuela et al. (2019).Apart from the remarkable variation of the rotational light-curve amplitude along the 19-year time span, we have detected changes in the overall shape of the rotational light-curve in shorter time scales. After the analysis of the periodogram of the residuals to a 6.3435674 h double-peaked rotational light-curve fit, we found a clear additional periodicity (see figure 2). We propose that these changes in the rotational light-curve shape are due to a large and close-in satellite whose rotation induces the additional periodicity. The peak-to-valley amplitude of this oscillation is in the order of 0.06 mag (see figure 3). We estimate that the proposed satellite orbits Varuna with a period of 11.9897 h (or 23.9794 h), assuming that the satellite is tidally locked at a distance of 1300 km (or 2000 km) from Varuna. For more detailed information see Fernandez-Valenzuela et al. (2019).&#160;Figure 2. Lomb periodogram spectral power derived from the residuals of the Fourier function fit to Varuna's photometric data. A maximum spectral power of 45 is obtained at the frequency of 2.003 cycles/day (11.9819 h). This periodicity corresponds to the satellite's revolution period. Figure from Fernandez-Valenzuela et al. (2019).&#160;Figure 3. Residuals of Varuna's observational data folded to the 11.9819 h period detected using the Lomb periodogram technique. The blue line represents a one-order Fourier function fit to the points. Figure from Fernandez-Valenzuela et al. (2019).&#160;Acknowlegements: EFV acknowledges UCF 2017 Preeminent Postdoctoral Program&#160;(P3).&#160;Part of the research leading to these results has received funding from the European Unions Horizon 2020 Research and Innovation Programme, under Grant Agreement No. 687378 (SBNAF). P.S-S. acknowledges financial support by the Spanish grant AYA-RTI2018-098657-J-I00 "LEO-SBNAF" (MCIU/AEI/FEDER, UE). We would like to acknowledge financial support by the Spanish grant AYA-2017-84637-R and the financial support from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award for the Instituto de Astrof&#237;sica de Andaluc&#237;a (SEV- 2017-0709).