Implications for the collisional strength of Jupiter Trojans from the Eurybates family
Authors: Marschall Raphael , Nesvorný David , Deienno Rogerio , Wong Ian , Levison Harold F. , Bottke William F. 
Published: July 2021

The Lucy mission [1] will be the first mission to study the Jupiter Trojans (JT) population up close. During flybys of six Jupiter Trojans between 2027 and 2033, it will sample the diversity of Trojans. The targets include a C-type Trojan, and the largest member of a collisional family (3548) Eurybates [2], the two D-type Trojans (11351) Leucus, and (21900) Orus, as well as the three P-type Trojans (15094) Polymele, and the almost equal mass binary pair (617) Patroclus and Menoetius.Trojans are thought to be outer solar system planetesimals. They orbit Sun in a 1:1 resonance with Jupiter in two swarms around the L4 and L5 Lagrangian points of the Sun-Jupiter system where they lead/trail Jupiter by 60&#176; respectively. Jupiter Trojans are known to be quite stable over the age of the solar system with only &#8764;25% having escaped the resonance since they were captured [5, 6, 7]. There are &#8764;3,000 Jupiter Trojans larger than 10 km [8] making the population smaller than e.g. the main-belt asteroid population (&#8764;10,000 larger than 10 km, [9]). The Trojans show a bimodal colour distribution [10, 8, 11]. While the &#8220;red" Trojans overlap with &#8220;red" Kuiper belt objects (KBOs) and Centaurs, the &#8220;less-red" Trojan population does not have a clear analogue in the KBO population [11]. On the other hand, there is no analogue for the "very red" KBOs in the Trojans. The Eurybates family members not only stand out due to their orbital elements (i.e. their inclinations are tightly confided to 7.5&#176; &#177; 0.5&#176; ) but also because they are bluer than even the &#8220;less-red" Trojans. This might imply that KBOs and Jupiter Trojans have a common origin but then evolved differently e.g. due to the different collisional environment [11]. The strong excitation in inclinations (up to 30&#176;) is an important constraint on the capture mechanism and thus the origin of Jupiter Trojans.Jupiter Trojans are unlikely to have formed at their current location. Different models have been developed to describe their origin and capture into the Lagrange regions. First, in the &#8220;jumping Jupiter" model [12] the primordial planetesimal disk gets scattered by the giant planet instability outwards into the TNO region and inwards where they are captured by Jupiter that jumps in semi-major axis. The advantage of this model lies in the fact that it accurately predicts the size of the Jupiter Trojans and their orbital distribution. In the second model proposed by [13] Jupiter forms at &#8764; 20 au and subsequently migrated to its current location sweeping up planetesimals in the process and capturing them in the resonance. This model accounts for the asymmetry in the size of the two Trojan swarms but does not capture the inclinations unless the primordial disc is already excited. The forthcoming Lucy mission will be instrumental in differentiating between these models and provide crucial information on the formation and evolution of Jupter Trojans.In this work we study the collisional evolution of the Jupiter Trojans and the Eurybates family to understand their implications for i) their material strength, and ii) the age of the Eurybates family and newly discovered satellite Queta [15] because its survival has implications for the family forming event. By modelling the collisional evolution of the L4 swarm using the Boulder collisional code [16, 17] we find that to a degree the age and strength of the Eurybates family and Queta are correlated and depend on the size-frequency distribution of the Jupiter Trojans at small sizes (< 1 km).This is illustrated in Fig. 1 showing the survival probability of the Eurybates-Queta system (green) for different ages of the Eurybates family and different disruption strengths, Q&#8727;D. We have varied the material strength over two orders of magnitude, ranging from Q&#8727;D = Q0 which corresponds to slightly weaker material than the &#8221;weak ice" of [18] and Q&#8727;D = 100 Q0 which is slightly stronger than the basalt targets in [19]. The &#8221;weak ice" material can be ruled out for any of the suggested ages of the family. Should the family be as young as 1 Gy, a material strength as low as &#8764; 4 Q0 is possible. A 4.5 Gy age of the family would require strong material for the Eurybates-Queta system to have survived to this day.Figure 1: The fraction of cases where Queta survives (green), or is destroyed or an impact dissolves the sytem (pink) is shown for simulations over 1 Gy and 4.5 Gy.The size-frequency distribution (SFD) of the Eurybates family shows a significantly steeper slope between 10 and 20 km than the L4 swarm (Fig. 2). This is indicative of a collisional family and we will show that the family SFD most closely resembles outcomes of collisions of rubble piles [20] thus implying weak material strength. In combination with the survival probability (Fig. 1) this suggests that the age of the Eurybates family is towards the lower end of the estimated age.Figure 2: The L4 (blue) and Eurybates family (red) size distribution are shown using the NEOWISE sizes.&#160;References[1] Levison et al. (2017), LPSC, 2025.[2] Bro&#382; &amp; Rozehnal (2011), MNRAS, 414, 565.[3] Buie et al. 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