Asteroid 2014 YX49: a large transient Trojan of Uranus

TL;DR

This paper reports the discovery and analysis of a second transient Uranian Trojan asteroid, 2014 YX49, highlighting its orbital characteristics, stability, and the dynamical mechanisms involved in its capture and ejection.

Contribution

It presents the identification and detailed dynamical analysis of a new transient Uranian Trojan, expanding knowledge of small body populations in the outer Solar system.

Findings

2014 YX49 is a transient L4 Trojan of Uranus with higher inclination and larger size than the first known Uranian Trojan.

It may remain co-orbital with Uranus for nearly 1 million years, with stability influenced by Jupiter and Neptune.

The capture and ejection involve ephemeral multibody mean motion resonances.

Abstract

In the outer Solar system, primordial Trojan asteroids may have remained dynamically stable for billions of years. Several thousands of them accompany Jupiter in its journey around the Sun and a similarly large population may be hosted by Neptune. In addition, recently captured or transient Jovian and Neptunian Trojans are not uncommon. In contrast, no Trojans of Saturn have been found yet and just one Uranian Trojan is known, 2011 QF99. Here, we discuss the identification of a second Trojan of Uranus: 2014 YX49. Like 2011 QF99, 2014 YX49 is a transient L4 Trojan although it orbits at higher inclination (25.55 degrees versus 10.83 degrees), is larger (absolute magnitude of 8.5 versus 9.7) and its libration period is slightly shorter (5.1 versus 5.9 kyr); contrary to 2011 QF99, its discovery was not the result of a targeted survey. It is less stable than 2011 QF99; our extensive N-body simulations show that 2014 YX49 may have been following a tadpole trajectory ahead of Uranus for about 60 kyr and it can continue doing so for another 80 kyr. Our analysis suggests that it may remain as co-orbital for nearly 1 Myr. As in the case of 2011 QF99, the long-term stability of 2014 YX49 is controlled by Jupiter and Neptune, but it is currently trapped in the 7:20 mean motion resonance with Saturn. Consistently, the dynamical mechanism leading to the capture into and the ejection from the Trojan state involves ephemeral multibody mean motion resonances.

Tables

Table 1. Table 1: Heliocentric Keplerian orbital elements of 2014 YX 49 utilized in this paper. This orbital determination is based on 70 observations spanning a data-arc of 4 876 days or 13.35 yr, from 2001 September 22 to 2015 January 28. In addition to the nominal value of each parameter, the 1 σ 𝜎 \sigma uncertainty is provided as well. The solution is computed at epoch JD 2457800.5, which corresponds to 0:00 UT on 2017 February 16 (J2000.0 ecliptic and equinox). This reference epoch coincides with the t = 0 𝑡 0 t=0 instant in the figures. Source: JPL’s Small-Body Database.

Semimajor axis, $a$ (au)	=	19.1304$\pm$0.0005
Eccentricity, $e$	=	0.276539$\pm$0.000013
Inclination, $i$ (°)	=	25.55097$\pm$0.00002
Longitude of the ascending node, $\Omega$ (°)	=	91.44425$\pm$0.00003
Argument of perihelion, $\omega$ (°)	=	280.584$\pm$0.003
Mean anomaly, $M$ (°)	=	75.587$\pm$0.005
Perihelion, $q$ (au)	=	13.84012$\pm$0.00015
Aphelion, $Q$ (au)	=	24.4207$\pm$0.0007
Absolute magnitude, $H$ (mag)	=	8.5

Full text

††pubyear: 2017††pagerange: Asteroid 2014 YX49: a large transient Trojan of Uranus–References

1 Introduction

Among the giant planets, Saturn and Uranus lack a significant present-day population of small bodies subjected to their respective 1:1 mean motion or co-orbital resonances (quasi-satellite, Trojan, horseshoe or combinations of these three elementary resonant states). This is particularly true in the case of Trojans or minor bodies librating 60° ahead (L4 Lagrangian point) or behind (L5) a host planet in its orbit.

Trojans describe a shifting path in the shape of a tadpole around the associated Lagrangian point when seen in a frame of reference centred at the Sun and rotating with the host planet (for further details, see e.g. Murray & Dermott 1999). Jupiter is accompanied by many thousands of them (see e.g. Milani 1993; Jewitt, Trujillo & Luu 2000; Morbidelli et al. 2005; Yoshida & Nakamura 2005; Robutel & Gabern 2006; Robutel & Bodossian 2009; Grav et al. 2011; Nesvorný, Vokrouhlický & Morbidelli 2013) and Neptune may have a similarly large population including both primordial or long-term stable Trojans (e.g. Kortenkamp, Malhotra & Michtchenko 2004; Nesvorný & Vokrouhlický 2009; Sheppard & Trujillo 2006, 2010) and transient or recently captured ones (e.g. de la Fuente Marcos & de la Fuente Marcos 2012b,c). In contrast to the cases of Jupiter and Neptune, any existing Trojans of Saturn still remain to be detected and the first Trojan of Uranus —a transient one, 2011 QF99— was announced in 2013 (Alexandersen et al. 2013a). This long-sought first Uranian Trojan was found within the context of a carefully planned survey (Alexandersen et al. 2013b).

Alexandersen et al. (2013b) have shown that 2011 QF99 may stay as L4 Trojan of Uranus for 100 kyr to 1 Myr; prior to and/or after leaving its current tadpole path, 2011 QF99 may have experienced other co-orbital states. Unlike 2011 QF99, Jovian or Neptunian primordial Trojans may have remained as such for the age of the Solar system or over 4.5 Gyr. In total, 2011 QF99 may spend about 3 Myr trapped in a co-orbital resonance with Uranus. Asteroid 2011 QF99 could be a former member of the Centaur population and it may return to it after being scattered away at the end of its current co-orbital episode.

The present-day dynamical status as Uranian Trojan of 2011 QF99 was further confirmed by de la Fuente Marcos & de la Fuente Marcos (2014) who showed that a three-body mean motion resonance is responsible for both its insertion into Uranus’ co-orbital region and its eventual escape from there. The critical role of three-body resonances as source of instability for Uranian Trojans was first discussed by Marzari, Tricarico & Scholl (2003). Here, we identify a second Trojan of Uranus, 2014 YX49, and explore numerically its past, current and future dynamical evolution. This paper is organized as follows. In Section 2, we show the data available on 2014 YX49 and discuss our methodology. The orbital evolution of 2014 YX49 is studied in Section 3, where its current dynamical status as Uranian Trojan is confirmed statistically. In Section 4, we discuss our results within the context of our present knowledge of the population of Uranian co-orbitals. Our conclusions are summarized in Section 5.

2 Asteroid 2014 YX49: data and methodology

Asteroid 2014 YX49 was discovered on 2014 December 26 by B. Gibson, T. Goggia, N. Primak, A. Schultz and M. Willman (Gibson et al. 2016)111http://www.minorplanetcenter.net/iau/mpec/K16/K16O10.html observing with the 1.8-m Ritchey-Chretien telescope of the Pan-STARRS Project (Kaiser et al. 2004) from Haleakala. At discovery time, its $w$-magnitude was 21.4, its right ascension was 7h 29m 22$\aas@@fstack{s}$659, and its declination was +30° 24′ 00$\aas@@fstack{\prime\prime}$37 at an heliocentric distance of 18.398 au. As the primary mission of the Pan-STARRS astronomical survey is to detect incoming near-Earth objects not minor bodies moving within the outer Solar system, the discovery of 2014 YX49 can be considered of serendipitous nature.

The discovery was made public on 2016 July 16 (Gibson et al. 2016) and during the following month a relatively large number of precovery images from other surveys were identified, which translated into a rapid improvement of its orbital determination. The solution for the orbit of 2014 YX49 currently available (as of 2017 January 9) from Jet Propulsion Laboratory’s (JPL) Small-Body Database222http://ssd.jpl.nasa.gov/sbdb.cgi is statistically robust (see Table 1) as it is based on 70 observations spanning a data-arc of 4 876 days or 13.35 yr, from 2001 September 22 to 2015 January 28. Formally classified dynamically as a Centaur, it has a value of the semimajor axis $a$ = 19.13 au, and moves in an eccentric, $e$ = 0.28, and rather inclined path, $i$ = 25$\aas@@fstack{\circ}$55. It is a comparatively large object with $H$ = 8.5 mag, which implies a diameter in the range 40–120 km for an assumed albedo of 0.50–0.05. Its period of revolution around the Sun, 83.7$\pm$1.3 yr at present, matches well that of Uranus and this fact makes it a strong candidate to moving co-orbital with this giant planet.

The value of the relative semimajor axis of 2014 YX49 with respect to Uranus, $|a-a_{\rm U}|=0.00012$ au, is lower than those of any other previously documented Uranian co-orbitals —(83982) Crantor (0.304 au), 2011 QF99 (0.079 au) and (472651) 2015 DB216 (0.087 au)— or candidates —1999 HD12 (0.210 au), 2002 VG131 (0.026 au) and 2010 EU65 (0.265 au). Uranus’ co-orbital region goes approximately from 19.0 to 19.4 au, although co-orbitals with $a$ in the range 19.1–19.2 au are far less unstable (de la Fuente Marcos & de la Fuente Marcos 2015). The orbit of 2014 YX49 in Table 1 indicates that it can only experience close encounters with Uranus because its perihelion distance is well beyond the aphelion of Saturn and its aphelion distance is far shorter than the perihelion of Neptune; this property suggests that 2014 YX49 may be as dynamically stable as 2011 QF99 or 472651.

The path currently followed by 2014 YX49 is more eccentric than that of 2011 QF99 (0.277 versus 0.178) and also more inclined (25$\aas@@fstack{\circ}$55 versus 10$\aas@@fstack{\circ}$83). Although the values of their respective arguments of perihelion are separated by just 7$\aas@@fstack{\circ}$5, their longitudes of the ascending node are over 131° apart. As for a comparison between the orbits of 2014 YX49 and 472651, the former moves in a less eccentric (0.277 versus 0.326) and also less inclined (25$\aas@@fstack{\circ}$55 versus 37$\aas@@fstack{\circ}$70) path. In terms of its present-day orbit, the dynamical behaviour of 2014 YX49 could be intermediate between those of 2011 QF99 and 472651.

The actual dynamical status of prospective co-orbital bodies is not assessed directly from their present-day orbits but from the analysis of a relevant set of numerical integrations. Such analysis focuses on the study of the behaviour of a critical angle that, in the case of Uranus’ co-orbital candidates, is the relative mean longitude $\lambda_{\rm r}=\lambda-\lambda_{\rm U}$, where $\lambda$ and $\lambda_{\rm U}$ are the mean longitudes of the object and Uranus, respectively; $\lambda$ = $M$ + $\Omega$ + $\omega$, where $M$ is the mean anomaly, $\Omega$ is the longitude of the ascending node, and $\omega$ is the argument of perihelion (see e.g. Murray & Dermott 1999).

For non-co-orbital or passing bodies $\lambda_{\rm r}\in(0,360)\degr$, with all the values being equally probable; this behaviour is known as circulation. True co-orbitals exhibit an oscillatory evolution over time of the value of $\lambda_{\rm r}$; this behaviour is known as libration. For a L4 Trojan the libration is around +60°, for a L5 Trojan the libration is around $-$60° or 300° (see e.g. Murray & Dermott 1999), although the oscillation centre could be significantly shifted from the typical equilateral location in the case of eccentric orbits (Namouni, Christou & Murray 1999; Namouni & Murray 2000). The current value of $\lambda_{\rm r}$ for 2014 YX49 is $\sim$61°, which suggests that 2014 YX49 could be indeed a present-day Uranian Trojan, but this must be confirmed using $N$-body simulations (for 2011 QF99, a Trojan, is $\sim$47° and $\sim$170° for 472651, a horseshoe librator).

As in our previous studies on the dynamics of Crantor (de la Fuente Marcos & de la Fuente Marcos 2013), 2011 QF99 (de la Fuente Marcos & de la Fuente Marcos 2014) and 472651 (de la Fuente Marcos & de la Fuente Marcos 2015), we use direct $N$-body integrations performed with a modified version of a code written by Aarseth (2003) —the standard version of this software is publicly available from the IoA website333http://www.ast.cam.ac.uk/$\sim$sverre/web/pages/nbody.htm— that implements the Hermite integration scheme described by Makino (1991). The performance of this code, when applied to Solar system numerical investigations, has been studied thoroughly (for further details, see de la Fuente Marcos & de la Fuente Marcos 2012a). The physical model is the same one used in the works on Crantor, 2011 QF99 and 472651 cited above and includes the perturbations by the eight major planets, the Moon, the barycentre of the Pluto-Charon system, and the three largest asteroids. Initial positions and velocities are based on the DE405 planetary orbital ephemerides (Standish 1998) referred to the barycentre of the Solar system and to the epoch JD TDB 2457800.5 (2017-February-16.0), which is the $t$ = 0 instant in our simulations. They have been provided by JPL’s online Solar system data service444http://ssd.jpl.nasa.gov/?planet_pos (Giorgini et al. 1996).

3 Asteroid 2014 YX49: orbital evolution

In this section, we show the results of simulations that use the nominal orbit in Table 1 and those of additional control calculations based on sets of orbital elements obtained from the nominal ones as described in de la Fuente Marcos & de la Fuente Marcos (2013, 2014, 2015). The main set of numerical integrations explores the dynamical evolution of 2014 YX49 for 0.6 Myr forward and backwards in time. Another set of shorter simulations aimed at characterizing the short-term stability of 2014 YX49 applies the implementation of the Monte Carlo using the Covariance Matrix (MCCM) method discussed by de la Fuente Marcos & de la Fuente Marcos (2015).

3.1 Current dynamical state

Fig. 1, left-hand panel, displays the motion of 2014 YX49 as characterized by the nominal orbit shown in Table 1 over the time range ($-$3 286, 1 840) yr projected on to the ecliptic plane in a coordinate system centred at the Sun and rotating with Uranus. This figure is equivalent to fig. 1 for 2011 QF99 in Alexandersen et al. (2013b) or fig. 1 in de la Fuente Marcos & de la Fuente Marcos (2014). Only one oscillation of the tadpole motion of 2014 YX49 is displayed (see the evolution of $\lambda_{\rm r}$ in Fig. 1, right-hand panel). All the control orbits (several hundreds) show virtually the same behaviour in the neighbourhood of $t$ = 0. Alexandersen et al. (2013b) have found a libration period for 2011 QF99 of 5.9 kyr. Our calculations indicate that the libration period of 2014 YX49 is slightly shorter, of about 5.1 kyr. Fig. 1 confirms 2014 YX49 as the second Trojan of Uranus; this conclusion is robust because the results of the evolution of a large set of statistically consistent short integrations (lasting $\pm 20$ kyr) are virtually identical to each other.

Fig. 2 shows the variation of the orbital elements $a$, $e$, $i$, $\Omega$, and $\omega$ of 2014 YX49 over time. This figure displays the average evolution (black curve) of 250 control orbits obtained via MCCM and its associated dispersion (red curves). These control orbits have been computed as described in section 3 of de la Fuente Marcos & de la Fuente Marcos (2015). The covariance matrix used to perform these calculations was provided by JPL’s Small-Body Database. The overall level of stability that characterizes the orbital solution currently available for 2014 YX49 can be evaluated quantitatively by computing its associated Lyapunov time or time-scale for exponential divergence of orbits that are started arbitrarily close to each other. Our calculations show that the Lyapunov time is somewhat different for forward ($\sim$20 000 yr) and backwards ($\sim$9 000 yr) integrations; this is relatively common in the case of transient co-orbitals. For instance, the Lyapunov time of 2011 QF99 is longer for backwards integrations. In the short term, 2014 YX49 is clearly more stable than (472651) 2015 DB216 (see fig. 1 in de la Fuente Marcos & de la Fuente Marcos 2015); asteroid 472651 is a Uranian asymmetric horseshoe librator.

3.2 Past and future orbital evolution

Fig. 3, central panels, shows the time evolution of various parameters for the nominal orbit of 2014 YX49 in Table 1 over an interval of $\pm$0.6 Myr. In addition to the nominal orbit, results for two other representative control orbits are also displayed (left-hand and right-hand panels); they have been computed by adding (+) or subtracting ($-$) 6-times the uncertainty from the orbital elements (the six parameters) in Table 1. The comparative evolution shows that 2014 YX49 is a transient L4 Trojan of Uranus. We have already pointed out above that close encounters of 2014 YX49 with Saturn or Neptune are not possible; Fig. 3, A-panels, indicate that no close approaches to Uranus under one Hill radius are recorded during the studied time interval. Fig. 3, B-panels, shows that the duration of the present Trojan episode of 2014 YX49 is expected to be shorter than that of 2011 QF99 (see fig. 4 in de la Fuente Marcos & de la Fuente Marcos 2014). In general, the dynamical evolution of 2014 YX49 is more complex than that of 2011 QF99 and multiple transitions between the various incarnations of the 1:1 mean motion resonance with Uranus are observed. Our calculations show that 2014 YX49 may become a transient L5 Trojan but also engage in quasi-satellite (the value of $\lambda_{\rm r}$ oscillates around 0°) or horseshoe behaviour ($\lambda_{\rm r}$ librates around the Lagrangian point L3, which is located at 180° from Uranus on its orbit); trajectories hybrid of two (or more) elementary co-orbital states are also possible (see Fig. 3, B-panels). During most of the Trojan phase, the amplitude of the oscillation of the tadpole motion is $<70\degr$.

The evolution of the value of the semimajor axis (Fig. 3, C-panels) provides insight on how much time 2014 YX49 spends within Uranus’ co-orbital zone. Our calculations indicate that this minor body may be co-orbital to Uranus for an average of 600 kyr with a minimum of about 400 kyr and a maximum close to 1 Myr. This makes it less long-term stable than both 2011 QF99 and 472651. In general, the values of $e$ (Fig. 3, D-panels) and $i$ (Fig. 3, E-panels) do not exhibit obvious signs of coupling as those characteristic of the Kozai resonance (Kozai 1962); this is consistent with the behaviour of the argument of perihelion (Fig. 3, F-panels) that mostly circulates. When compared with 2011 QF99, 2014 YX49 shows significantly less evidence of Kozai-like resonant behaviour.

Fig. 3, G-panels, shows the evolution of the distance to the nodes of 2014 YX49 over time; the separation between the Sun and the nodes has been computed by applying the expression $r=a(1-e^{2})/(1\pm e\cos\omega)$, where the ‘+’ sign is used for the ascending node and the ‘$-$’ sign for the descending node. In the case of Solar system objects that move in orbits inclined with respect to the ecliptic plane, close encounters with major planets can only take place in the vicinity of the nodes. Our calculations show that the evolution is quite regular and resembles that of 2011 QF99 (see fig. 4, G-panels, in de la Fuente Marcos & de la Fuente Marcos 2014).

The secular dynamics of known Uranian co-orbitals has been studied in de la Fuente Marcos & de la Fuente Marcos (2014) and de la Fuente Marcos & de la Fuente Marcos (2015). These studies singled out 472651 as peculiar because the precession frequency of the longitude of the perihelion, $\varpi=\Omega+\omega$, of this object is not in secular resonance with Jupiter, Saturn or Uranus, only with Neptune and for a limited amount of time. Fig. 4 shows the time evolution of the relative longitude of the perihelion, $\Delta\varpi$, of 2014 YX49 with respect to the giant planets. The precession frequency of the longitude of the perihelion of 2014 YX49 is only in secular resonance with Neptune, but for the entire simulation. The value of $\Delta\varpi=\varpi-\varpi_{\rm N}$ librates around -90° (or 270°). This type of secular behaviour is not observed for any other known Uranian co-orbital. The time evolution of the relative longitude of the perihelion with respect to Jupiter, Saturn and Uranus closely resembles that of 472651 (see fig. 5 in de la Fuente Marcos & de la Fuente Marcos 2015).

3.3 Stability analysis

The overall dynamical stability associated with the path currently followed by 2014 YX49 has been discussed in Sections 3.1 and 3.2; the orbit of 2014 YX49 is not long-term stable even if no truly close encounters with planetary bodies are observed. In absence of sufficiently close approaches to Uranus, the dynamical evolution of this minor body must be fully driven by mean motion resonances with the giant planets. Here, we investigate what sequence of resonant events placed 2014 YX49 in its present orbit and how was it temporarily stabilized. We also explore the circumstances that will surround its future ejection from the Trojan state.

As pointed out by de la Fuente Marcos & de la Fuente Marcos (2014), the Uranian Trojan 2011 QF99 is not currently engaged in resonant behaviour with Jupiter or Neptune, but it is subjected to the 7:20 mean motion resonance with Saturn. This dynamical response is characteristic of Uranian Trojans and it was first predicted by Gallardo (2006). Although the shape and orientation of the orbits of 2011 QF99 and 2014 YX49 are rather different, the perturbational scenario that drives their evolution is virtually identical and their resonant profiles must also be very similar. In addition to the 1:1 mean motion resonance with Uranus in any of its forms (elementary or composite), the three mean motion resonances of interest here are 1:7 with Jupiter, 7:20 with Saturn and 2:1 with Neptune. Their respective resonant arguments are $\sigma_{\rm J}=7\lambda-\lambda_{\rm J}-6\varpi$, $\sigma_{\rm S}=20\lambda-7\lambda_{\rm S}-13\varpi$ and $\sigma_{\rm N}=\lambda-2\lambda_{\rm N}+\varpi$, where $\lambda_{\rm J}$, $\lambda_{\rm S}$ and $\lambda_{\rm N}$ are the respective mean longitudes of Jupiter, Saturn and Neptune.

Fig. 5 shows the time evolution of the various resonant arguments pointed out above. It is fully consistent with the behaviour depicted in fig. 5 of de la Fuente Marcos & de la Fuente Marcos (2014) for 2011 QF99 and it confirms that, during its current Trojan episode, 2014 YX49 is simultaneously trapped in the 7:20 mean motion resonance with Saturn. The resonant argument $\sigma_{\rm S}$ alternates between circulation and asymmetric libration because the motion is chaotic. During the Trojan resonant episode, 2014 YX49 is subjected to a three-body resonance: the 1:1 mean motion resonance with Uranus and the 7:20 mean motion resonance with Saturn.

In de la Fuente Marcos & de la Fuente Marcos (2014), we showed that 2011 QF99 was captured into Uranus’ co-orbital zone after experiencing a three-body resonance with Jupiter and Neptune. Fig. 6 shows that the same mechanism drives the insertion of 2014 YX49 in its present resonant state (see left-hand and central panels). As Newtonian gravitation is time symmetric, the mechanism leading to a certain resonant state should also be able to take the affected minor body out of it. This was already discussed in de la Fuente Marcos & de la Fuente Marcos (2014) for the case of 2011 QF99 and Fig. 6, right-hand panels, shows that it is also certain for 2014 YX49. However, the details of the resonant events behind the transitions between co-orbital states are different although they involve ephemeral or very brief multibody mean motion resonances.

Becoming a jumping Trojan, i.e. going from L4 to L5 and (perhaps) back, also involves three-body resonances but in this case with Jupiter and Uranus. Fig. 7 shows two examples of this type of behaviour. However, Neptune may also be involved when transitioning to the horseshoe state (de la Fuente Marcos & de la Fuente Marcos 2014). Additional examples of similar transitions for the cases of 2011 QF99 and 472651 can be found in de la Fuente Marcos & de la Fuente Marcos (2014) and de la Fuente Marcos & de la Fuente Marcos (2015), respectively. As pointed out in de la Fuente Marcos & de la Fuente Marcos (2015), the outcome of these rapid transitions is unusually sensitive to the physical model used to perform the calculations. A five-body physical model including the Sun and the four outer planets such as the one used by Marzari et al. (2003) or Alexandersen et al. (2013b) may not be able to arrive to realistic conclusions regarding the resonant details associated with the transitions between co-orbital states experienced by objects like 2011 QF99, 2014 YX49 and 472651.

4 Discussion

The discovery of 2014 YX49, the second Uranian Trojan, confirms that, contrary to the conclusions reached by Horner & Evans (2006), Uranus can capture efficiently minor bodies into the 1:1 commensurability. In addition, the fact that it was originally found at a declination above +30° by Pan-STARRS strongly suggests that the number of objects moving in similar orbits may not be negligible (see the detailed discussion in section 8 of de la Fuente Marcos & de la Fuente Marcos 2014). Asteroid (472651) 2015 DB216 is another example of transient Uranian co-orbital discovered under similar circumstances, i.e. serendipitously. If the analysis in de la Fuente Marcos & de la Fuente Marcos (2015) showed that there is enough theoretical ground to assume that a population of high orbital inclination Uranian co-orbitals may exist, the identification of this Trojan shows that there are also robust observational grounds, adding more weight to the hypothesis. Both 2014 YX49 and 472651 are comparatively large and bright, making them easier to detect; finding any fainter, hypothetical bodies moving in somewhat similar orbits may require a carefully planned survey though.

Dvorak, Bazsó & Zhou (2010) investigated the stability of putative primordial Uranus’ Trojans and found stable islands at the inclination intervals (0, 7)°, (9, 13)°, (31, 36)°and (38, 50)°. Asteroid 2011 QF99, the first Uranian Trojan, inhabits one of these stable areas as its current value of the orbital inclination is nearly 11°; however, this object is not a primordial Uranus’ Trojan (Alexandersen et al. 2013b; de la Fuente Marcos & de la Fuente Marcos 2014). In contrast, 2014 YX49 currently occupies (see Fig. 3, E-panels) an unstable region between two of the stable islands described in Dvorak et al. (2010) as its current value of the inclination is nearly 26°. In addition, its inclination remains in the range 20–27° for most of the studied time. However, our analysis shows that even if 2014 YX49 is less dynamically stable than 2011 QF99, it can still remain as transient Trojan of Uranus for a relatively long period of time. The situation is similar to that of 472651, although this object moves in a higher inclination orbit.

Our results provide additional confirmation that overlapping mean motion resonances can trigger transitions between co-orbital states and also deliver minor bodies inside the co-orbital zone of a planetary body as well as evict them from there. The duration of these episodes is short, typically 10–20 kyr in the cases of captures as co-orbitals or ejections from the co-orbital zone, and about 5 kyr when inducing transitions between the various co-orbital states (see Figs 6 and 7). The dynamical effects of three-body mean motion resonances have been studied recently by Gallardo (2014).

5 Conclusions

In this paper, we provide a detailed exploration of the past, present and future orbital evolution of 2014 YX49, the second Trojan of Uranus. Our conclusions can be summarized as follows.

1. (i)

Asteroid 2014 YX49 is a transient L4 Trojan of Uranus, the second minor body to be confirmed as currently engaged in this type of resonant state. Its current libration period is over 5 100 yr. 2. (ii)

Although 2014 YX49 may have remained in its current Trojan state for about 60 kyr, it can continue doing so for another 80 kyr. Our calculations suggest that it may stay within Uranus’ co-orbital zone for nearly 1 Myr. 3. (iii)

In addition to being a Uranian Trojan, 2014 YX49 is currently trapped in the 7:20 mean motion resonance with Saturn; therefore, this minor body is currently subjected to a three-body resonance. It is also engaged in a long-term secular resonance with Neptune. 4. (iv)

The dynamical mechanism behind the insertion of 2014 YX49 in Uranus’ co-orbital zone involves a brief episode of concurrent resonant behaviour with Jupiter (1:7) and Neptune (2:1). A virtually identical mechanism is also responsible for scattering 2014 YX49 away from the 1:1 commensurability with Uranus. 5. (v)

Transitions between the various states within the 1:1 mean motion resonance with Uranus are mainly triggered by ephemeral resonant episodes with Jupiter. 6. (vi)

Our analysis shows that 2014 YX49 shares a number of dynamical characteristics with (472651) 2015 DB216, another Uranian co-orbital that follows a relatively high-inclination orbit. As these two objects are comparatively rather bright/large, the presence of fainter/smaller minor bodies following somewhat similar paths is highly probable and this plausible conjecture lends credibility to the idea that a population of temporary Uranian co-orbitals may exist at relatively high orbital inclinations.

Our investigation of the dynamics of 2011 QF99, 472651 and 2014 YX49 shows that ephemeral multibody mean motion resonance episodes are behind the events that lead to the capture and ejection of transient Uranian co-orbitals. This general mechanism may have also played some role in the loss of any putative primordial Uranus’ Trojans early in the history of the Solar system.

Acknowledgements

We thank the anonymous referee for a prompt report, S. J. Aarseth for providing the code used in this research, A. I. Gómez de Castro, I. Lizasoain and L. Hernández Yáñez of the Universidad Complutense de Madrid (UCM) for providing access to computing facilities, and S. Deen for finding precovery images of 2014 YX49 that improved the orbital solution of this object and for additional comments. This work was partially supported by the Spanish ‘Ministerio de Economía y Competitividad’ (MINECO) under grant ESP2014-54243-R. Part of the calculations and the data analysis were completed on the EOLO cluster of the UCM, and we thank S. Cano Alsúa for his help during this stage. EOLO, the HPC of Climate Change of the International Campus of Excellence of Moncloa, is funded by the MECD and MICINN. This is a contribution to the CEI Moncloa. In preparation of this paper, we made use of the NASA Astrophysics Data System, the ASTRO-PH e-print server, and the MPC data server.