The Astronomical Journal, 144:97 (7pp), 2012 October doi:10.1088/0004-6256/144/4/97 C 2012. The American Astronomical Society. All rights reserved. Printed in the U.S.A. SURVIVAL OF AMORPHOUS WATER ICE ON CENTAURS Aurelie´ Guilbert-Lepoutre Department of Earth and Space Sciences, UCLA, Los Angeles, CA 90095, USA; [email protected] Received 2012 March 12; accepted 2012 July 24; published 2012 August 30 ABSTRACT Centaurs are believed to be Kuiper Belt objects in transition between Jupiter and Neptune before possibly becoming Jupiter family comets. Some indirect observational evidence is consistent with the presence of amorphous water ice in Centaurs. Some of them also display a cometary activity, probably triggered by the crystallization of the amorphous water ice, as suggested by Jewitt and this work. Indeed, we investigate the survival of amorphous water ice against crystallization, using a fully three-dimensional thermal evolution model. Simulations are performed for varying heliocentric distances and obliquities. They suggest that crystallization can be triggered as far as 16 AU, though amorphous ice can survive beyond 10 AU. The phase transition is an efficient source of outgassing up to 10–12 AU, which is broadly consistent with the observations of the active Centaurs. The most extreme case is 167P/CINEOS, which barely crystallizes in our simulations. However, amorphous ice can be preserved inside Centaurs in many heliocentric distance–obliquity combinations, below a ∼5–10 m crystallized crust. We also find that outgassing due to crystallization cannot be sustained for a time longer than 104–104 years, leading to the hypothesis that active Centaurs might have recently suffered from orbital changes. This could be supported by both observations (although limited) and dynamical studies. Key words: comets: general – Kuiper Belt: general – methods: numerical Online-only material: color figures 1. INTRODUCTION fore interesting to understand whether amorphous water ice can survive on Centaurs. Amorphous water ice can persist for Centaurs are a population of small bodies in the outer solar timescales comparable to the age of the solar system because system, orbiting in the giant planets region. In this work, we the rate of phase transition λ(T ) depends on the temperature, de- define Centaurs as objects orbiting between Jupiter and Nep- termined by an activation law found experimentally by Schmitt tune, with the following constraints on their perihelion distance et al. (1989): q and semimajor axis a: q <q<q and a <a<a .They J N J N = × 13 −5370/T −1 experience repeated close encounters with giant planets, result- λ(T ) 1.05 10 e s . (1) ing in short-lived chaotic orbits. Centaur orbits are typically sta- Amorphous water ice also has the ability to trap large ble on timescales ranging from a few million years to a hundred amounts of volatiles that can be expelled upon crystallization million years (Levison & Duncan 1997; Tiscareno & Malhotra (Bar-Nun et al. 1985; Laufer et al. 1987; Hudson & Donn 1991; 2003; Horner et al. 2004; di Sisto & Brunini 2007). They are Jenniskens & Blake 1994; Notesco & Bar-Nun 1996; Bar-Nun therefore a transient population of recent escapees from a source & Owen 1998; Notesco et al. 2003). The phase transition is an region possibly further out in the solar system, like the Kuiper exothermic and irreversible process, which could be the source Belt or the Scattered Disk (Levison & Duncan 1997;Volk& of activity in the giant planet regions, where the equilibrium Malhotra 2008), or possibly from the Trojan clouds (Horner temperature is too low for water ice to sublimate. & Lykawka 2010). The fate of Centaurs could be to impact In this paper, we use a fully three-dimensional model of a giant planet or being broken apart by gravitational stresses. small bodies thermal evolution to study the occurrence of More than two-thirds can escape the solar system (Tiscareno & crystallization at the surface and in the interior of Centaurs. We Malhotra 2003), and the rest could become Jupiter family comets follow the idea developed by Jewitt (2009) that crystallization (JFCs). Centaurs offer the possibility to study some of the most is the driver for Centaur activity, and investigate the effect of primordial material in the solar system. They are more accessi- orbital parameters on the process to understand how amorphous ble than Kuiper Belt objects, and more stable from a physical water ice can survive in this region of the solar system. Section 2 point of view than JFCs, whose lifetime is limited by different briefly presents the model, Sections 3 and 4 give results from the dynamical and physical processes. modeling compared to observations concerning the presence of Some observational evidence, albeit indirect, are consistent crystalline and amorphous water at the surface of Centaurs and with the presence of amorphous water ice in both comets (Meech crystallization as a source of cometary activity among them. et al. 2009) and Centaurs (Jewitt 2009). Some Centaurs display comet-like activity, even though they are orbiting beyond the 2. THERMAL EVOLUTION MODEL snowline, the limit beyond which water ice is thermodynami- cally stable. Their mass loss is therefore not driven by water-ice We use a model of Centaurs in which the parameters are sublimation. A recent study on active Centaurs showed that their idealized in order to make the problem tractable. We consider activity could be thermally driven, meaning that the trigger for that the objects—50 km bodies with a 10 hr rotation period—are mass loss is a temperature-related process (Jewitt 2009). The initially spheres made of a porous mixture of water ice and dust results suggest that crystallization of amorphous water ice is a grains. We assume the ice to be initially amorphous, which also plausible explanation for the activity of Centaurs. It is there- assumes a cold accretion and no previous thermal alteration due 1 The Astronomical Journal, 144:97 (7pp), 2012 October Guilbert-Lepoutre Table 1 conduction equation: Heat Capacities and Thermal Conductivities ∂T Parameters Value Unit References ρ c + ∇(−κ∇T ) = Q , (5) bulk ∂t cryst −1 −1 cH2O 7.49 T +90 J kg K G&S36 −1 −1 cd 1200 J kg K E&S83 where T [K] is the temperature distribution to be determined, −3 −2 −1 −1 −3 −1 −1 κa 2.34 × 10 T +2.8 × 10 Wm K Kl80 ρbulk [kg m ] is the object’s bulk density, c [J kg K ] −1 −1 −1 −1 κcr 567/T Wm K Kl80 is the material heat capacity, κ [W m K ] is its effective −1 −1 −3 κd 4.2 W m K E&S83 thermal conductivity, and Qcryst [W m ] is the internal power −1 −1 cinit 830 J kg K production per unit volume due to the amorphous-crystalline −2 −1 −1 κinit 6.4 × 10 Wm K phase transition. We investigate the effects of heliocentric distance and obliq- Θ Θ = ◦ Notes. T: temperature [K]. cH2O, cd: heat capacity for water ice and for dust, uity ( 0 corresponds to the case where the spin axis is respectively. κa, κcr, κd : thermal conductivities of amorphous and crystalline normal to the orbital plane, other angles correspond to a tilt of water ice, and dust, respectively. cinit and κinit: initial values of the heat capacity the spin axis toward the Sun at perihelion), on the temperature and thermal conductivity. distribution at the surface and inside of Centaurs. We consider a References. G&S36: Giauque & Stout (1936); E&S83: Ellsworth & Schubert Bond albedo of 6% (Stansberry et al. 2008), and an initial tem- (1983); Kl80: Klinger (1980). perature of 50 K, which is about the equilibrium temperature in the Kuiper Belt. The time 0 in our simulations corresponds to the to radioactive decay. The bulk material can be described with moment when the objects are placed in the Centaur orbits. We = = a dust to water ice mass ratio Xd /XH2O 1, a porosity ψ compute the evolution of temperatures for 10 Myr, the average −3 30%, and a bulk density ρbulk = 1gcm . The heat capacity of time a Centaur can spend on its orbit before either leaving the the mixture is obtained by averaging the values weighted by the solar system or becoming a JFC, due to gravitational interactions mass fraction of each component: with giant planets (Tiscareno & Malhotra 2003; Horner et al. 2004). Our main orbital assumption is that we consider circular = c XH2OcH2O + Xd cd , (2) orbits. This is justified by the fact that the thermal evolution under insolation is linked to the amount of energy received per with XH2O and Xd the mass fraction of water ice and dust, orbit (see also Section 4.2). For each eccentric orbit, it is thus −1 −1 and cH2O and cd [J kg K ] the heat capacities of each possible to computed an equivalent circular orbit with a radius 2 component. The numerical values used in this work can be found ac = a(1 − e ), which receives the same amount of energy per in Table 1. The thermal conductivity is obtained by considering orbit (Prialnik & Rosenberg 2009). Considering circular orbits the material as made of two phases, the empty pores with a will therefore allow us to decrease the number of free param- 3 thermal conductivity κp = 4rpεσT (Huebner et al. 2006), eters to investigate, and dress a framework in which any real with rp = 1 μm the average pore radius, ε = 0.9 the medium Centaur, with an eccentric orbit, can be placed through ac. emissivity, σ the Stefan–Boltzmann constant and T [K] the temperature, and the solid matrix with a thermal conductivity 3. CRYSTALLIZATION AT THE SURFACE κ . The latter is computed as follows: s 3.1.