Tidally locked rotation and spin phase dependent J - H color of the dwarf planet (136199) Eris
Authors: Szakáts Róbert , Kiss Csaba , Ortiz José Luis , Morales Nicolas , Pál András , Müller Thomas , Greiner Jochen , Santos-Sanz Pablo , Marton Gábor , Duffard Rene , Sági Petra , Forgács-Dajka Emese 
Published: July 2024

The spin of dwarf planets and their satellites in the outer solar system is governed by their formation history and the tidal forces acting between them. By studying the rotation of these objects, we can track their evolution over time. In the case of the dwarf planet (136199) Eris the previously obtained rotation periods were not consistent in the literature. The values ranged from a few hours to ~15 days.&#160;We used new data from ground based ~1-2m telescopes and light curves from Gaia and TESS space telescopes to determine the rotation period of Eris. The data from TESS wasn&#8217;t conclusive, but the combined ground based and Gaia data showed a period almost identical to the orbital period of Eris&#8217;s moon, Dysnomia with a &#916;m &#8776; 0.03 mag amplitude. We concluded that the rotation of Eris should be tidally locked.Figure 1.: C(P, &#8710;m) (period cost function) contour map; The most prominent minima is identified at a period of &#8764;16 d, very close to the orbital period of Dysnomia, 15.78 d.&#160;We used a simple tidal evolution model, assuming that Dysnomia has a collisional origin, and we found that Dysnomia must be relatively massive (mass ratio of q = 0.01-0.03) and large (radius of Rs &#8805; 300 km) or Eris must have a low Q tidal parameter similar to that of terrestrial planets to have the potential to slow Eris down to a synchronised rotation. In the first scenario assuming usual tidal parameters for trans-Neptunian objects the calculations indicate that the density of Dysnomia should be 1.8-2.4 g cm&#8722;3. This density considered very high among similarly sized objects and could set important constraints on their formation conditions.&#160;The size (R&#8776;1100 km) suggests that Eris should be spherical and the observed light curve probably comes from some surface variegations. This is not unusual among large trans-Neptunian objects because they can be characterized by bright surfaces and variable volatile compositions.&#160;We compared the visible range and J - H colors of Eris from the literature and while the visible range colors showed consistent values the J - H colors varied in a large range. To clarify whether the J - H color changes we used the GuideDog camera of the Infrared Telescope Facility to observe Eris for a two week period to cover a full rotation. We found that the J - H color of Eris indeed changes with the rotational phase. This suggests notable surface heterogenity in chemical composition and/or other material properties. With a simple calculation we tested that the grain size of the dominant CH4 may in general be responsible for notable changes in the J - H color, but in the current observing geometry of the system it can only partially explain the observed J - H variation.Figure 2.: &#160;Top: (J &#8722; H) colors of Eris converted to the 2MASS system, as a function of rotational phase (phase zero epoch is 2457357.8929 JD, as obtained fromBernstein et al. 2023). The dark blue markers represent the J &#8722; H colors from this work, labeled as I1...I4. The colored markers represent the J &#8722; Hvalues from the literature. Bottom: An approximate representation of the Eris visible range light curve using a properly phased sinusoidal curve. The phasesof IRTF, XShooter (X1 and X2) and JWST/NIRSpec (JWST) measurements are marked by vertical dashed lines.