44th Lunar and Planetary Science Conference (2013)
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CHRONOLOGICAL CONSTRAINTS ON COMET ACCRETION. M. Monnereau1, O. Mousis1,2, M. J. Toplis1, D. Baratoux1, J. Lasue1, J.-M. Petit2. 1Université de Toulouse/CNRS, IRAP, 14 avenue E. Belin, 31400 Toulouse, France (
[email protected]), 2Institut UTINAM, CNRS/INSU, UMR 6213, Université de Franche-Comté, 25030, Besançon Cedex, France. Introduction: The only existing estimates of comet accretion timescales derive from dynamical models aiming at simulating planetesimal accretion in protoplanetary disks [1,2]. These formation models are poorly related to the composition of comets whose comae appear depleted in N2 compared to the atmospheres of Pluto and Triton, and are usually dominated by H2O and CO [3]. It has been recently proposed that the noticeable N2 deficiency of comets results from postformation internal heating fueled by the decay of short-lived radiogenic nuclides [4, 5]. Because the composition of comets strongly depends on the evolution of their interior’s temperature, we use models similar to [4, 5] in order to explore the influence of their accretion timescales on this thermal heating. We show that a range of plausible accretion timescales can be derived from exploration of the parameter space representing the thermodynamic properties and the content in radiogenic nuclides of comets. Accretion timescales consistent with internal temperature profiles allowing the devolatilization of N2 and the preservation of CO will be compared to those derived from dynamical simulations in a near future. Temperature dependence of comet compositions: In our model, the volatile phase incorporated in cometesimals is composed of a mixture of pure ices, stoichiometric hydrates and multiple guest clathrates that crystallized in the form of microscopic grains at various temperatures in the outer part of the disk. Our model is based on the assumption that cometesimals have grown from the agglomeration of these icy grains due to collisional coagulation, implying no loss of volatiles during their growth phase [1]. Here, the clathration process stops in the nebula when no more crystalline water ice is available to trap the volatile species after which only pure condensates form at lower temperature in the disk. The process of volatile trapping in icy grains is calculated using the equilibrium curves of hydrates and pure condensates, our model determining the equilibrium curves and compositions of multiple guest clathrates, and the thermodynamic paths detailing the evolution of temperature and pressure in the outer part of the protoplanetary disk. Figure 1 represents the composition of the volatile phase incorporated in cometesimals as a function of their formation temperature in the disk. As a first approximation, this figure can also be used to
investigate the volatile content present in comets as a function of their internal temperature. The figure shows that the N2/H2O and CO/H2O ratios match the observed values [3] for internal temperatures in the 2247 K range. This implies that, at any stage of their accretion and subsequent evolution, comets that experienced internal heating reaching this temperature range would present compositions matching the observations.
Figure 1. Composition of the volatile phase incorporated in cometesimals as a function of their formation temperature in the outer solar nebula.
Thermal modelling of cometary nuclei: Assuming that no material transport is associated with heating in the range of interest, numerical simulations have been performed using a spherical 1-D conduction equation including a heat-source term. Progressive accretion has been modeled using the method of [6] that considers non-dimensional radius r' (defined as r/R) of a body of time dependent total radius R(t). This operation transforms the moving boundary problem of a growing body into a fixed boundary problem. The comet was considered as a ternary mixture of silicate dust, water ice and pore space, in relative proportions of 1/4:1/4:1/2 respectively. Both 26Al and 60Fe were considered as heat sources, assuming an 26Al/27Al ratio of 5x10-5 at the time of condensation of the solar nebula [7], an 60Fe/56Fe ratio of 1x10-8 at that time [8], and a dust component of CV composition [9]. Heat capacity was assumed to be the simple weighted mean of those of water ice and silicate dust, including the temperature dependence (see [5]). Thermal conductivity was assessed taking into account the roles of solid materials and pores. A range of potential thermal conductivities was tested, from the lower
44th Lunar and Planetary Science Conference (2013)
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Results: For a thermal conductivity of 0.09W/mK, it is found that bodies do not experience a temperature greater than 47 K anywhere at any time (dark grey region in Fig. 2), if their accretion starts 6 Myr after condensation of CAI's. This time after condensation of the solar nebular is shortened to 4.7 Myr when the accretion process is spread-out over 5 Myr. In this particular case of slow accretion, we note that the major part of the body remains below the 47 K threshold, i.e. deacreasing to 3.3 Myr after condensation if accretion lasts 5 Myr (light grey region in Fig 2). In this case, 47 K is reached at mid-depth, preserving N2 in more than 85% of the body. Models run with a larger thermal conductivity show that these curves are shifted toward smaller accretion delay, because the thermal boundary layer affects a deeper part of the body.
5 Myr is shown in the top panels. The left-hand panels are simulations for which the maximum temperature at the centre of the body is 47 K, while the right-hand panels are simulations for which the maximum temperature at mid-depth is 47 K. These simulations demonstrate that fast accretion leads to a temperature gradient restricted to the upper part of the body. This feature is amplified when thermal conductivity is smaller. Thus, the condition that the temperature must be in the 22-47 K range is satisfied in a larger part of the body when thermal conductivity is smaller and accretion length shorter. This conclusion is consistent with formation scenarios advocating that comets accreted during the solar nebula phase, and not later. 1.0
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bound employed by [4,5] to an upper bound corresponding to that of pure silicate+ice. For each set of thermal properties a series of simulations was performed for a body of final radius 35 km for which accretion initiated at times in the range from 0 to 6 Myr after condensation of the solar nebula, and for accretion durations from instantaneous to 5 million years. The surface temperature has been fixed to 20K.
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1 0 3.0 3.5 4.0 4.5 5.0 5.5 6.0 Accretion delay after CAI formation (Myr)
Figure 2. Temperature reached at the center (thick line) and at mid-depth (thin line) of a 35 km radius body as a function of the delay and duration of accretion. Dark grey region corresponds to bodies that never reached a temperature greater than 47 K; light grey region is for bodies that reached 47 K at the center, but not at middepth; white region indicates parameters for which at least half the body has been heated to more than 47 K.
In detail, later onset of rapid accretion is not equivalent to earlier onset of slow accretion, as may be appreciated by consideration of Figure 3. In this plot, simulations assuming instaneous accretion are shown in the bottom panels and accretion spread out over
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Figure 3. Evolution of the temperature within a 35 km radius body heated by 26Al and 60Fe. In the top panels, the accretion is spread over 5 Myr, whereas it is instantaneous in the bottom panels. The delay of accretion after condensation of CAI’s has been adjusted so that the maximum temperature is 47 K at the center of the body (left-hand panels) or at mid-depth (right-hand panels).
References: [1] Weidenschilling S. (1997) Icarus, 127, 290-306. [2] Morbidelli A. et al. (2007) LPI Contribution 1374, 120-121. [3] Bockelée-Morvan D. et al. (2004) In Comets II, M. C. Festou, H. U. Keller, and H. A. Weaver (eds.), University of Arizona Press, Tucson, 745 pp., p.391-423. [4] Mousis O. et al. (2012) The Astrophysical Journal 757, 146. [5] Guilbert-Lepoutre A. et al. (2011) Astron. Astrophys. 529, A71. [6] Merk R. et al. (2002) Icarus 159, 183191. [7] MacPherson G. J. et al. (1995) Meteoritics, 30, 365-386. [8] Spivak-Birndorf L. J., et al. (2011) Meteorit. Planet. Sci. Suppl., 74, 5442. [9] Wasson J.T. and Kallemeyn G.W. (1988) Philos. Trans. R. Soc. Lond. A, 325, 535–544.
