MNRAS 445, 3669–3673 (2014) doi:10.1093/mnras/stu1993 On the dynamics of volatile meteorites S. G. Coulson,1‹ M. K. Wallis1 and N. C. Wickramasinghe1,2 1Buckingham Centre for Astrobiology, The University of Buckingham, Buckingham MK18 1EG, UK 2International Research Centre, University of Peradeniya, Peradeniya 20400, Sri Lanka Accepted 2014 September 22. Received 2014 September 18; in original form 2014 July 22 ABSTRACT Canonical models for bolides in the atmosphere predict that fragile bolides break up at much higher altitudes than those actually observed. Here, we investigate the hypothesis that such fragile bolides may survive to low altitudes by a protective outgassing sheath of volatile ices and organics that shields the meteoroid from direct atmospheric heating. Downloaded from Key words: Astrobiology – methods: analytical – comets: general – meteorites, meteors, meteoroids. http://mnras.oxfordjournals.org/ Investigation of the tracks in aerogel formed by particles collected 1 INTRODUCTION from the comet 81P/Wild 2 indicated that the cometary dust con- Observational data of meteoroids show inconsistencies with the sisted of a mixture of cohesive, relatively strong particles as well models used to predict their behaviour. For millimetre to tens of as particles with a more volatile matrix containing smaller stronger metre-sized bolides, canonical models are unable to account for grains (Burchell et al. 2008). Similarly, modelling a Leonid mete- the survival of very fragile bolides to the lower altitudes as has oroid, Coulson (2003) predicted ∼90 per cent of the initial mass of been observed. The Maribo meteorite that fell in Denmark on 2009 cometary fragments are a composite of low-density material with January 17 had an entry velocity of 28.5 km s−1 and has been the remainder made up of denser carbonaceous material in order to linked to the Taurids meteor stream, which itself is thought to be correctly describe its trajectory. by guest on November 6, 2014 associated with comet Encke (Haack et al. 2011). When recovered, Here, we consider a meteoroid consisting of a coherent carbona- the weak 25 g fragment appeared intact but fell apart when touched ceous matrix with pores filled with water ice and volatile organics. (Haack et al. 2012). The fragment has now been classified as a CM2 In the next section, we model the meteoroid in free-space at a solar carbonaceous chrondite. This is evidence for the ability of weak and distance of 1 au and calculate the rate of sublimation of volatile friable material to survive atmospheric entry and fall as recoverable material prior to collision with the Earth’s atmosphere. meteorites. Disintegration of meteoroids descending through the atmosphere 2 A COMPOSITE BOLIDE IN FREE SPACE is usually described by a process of continual ablation where the energy used to heat the bolide is proportional to the cube of its speed We assume that the bolide was a typical cometary fragment, com- (u3) (Bronshten 1983); or by catastrophic fragmentation when the posed of volatile ices and organics held within as well as surround- ram pressure (∼u2) exceeds the tensile strength of the body (Hills & ing a denser core of either a stone or chronditic-type material. For Goda 1993). Both these models predict that ∼1 m radii, low-density simplicity, we suppose that the initial bolide was spherical with a meteoroids must reach a minimum altitude of 80–60 km. radius a ∼ 1 m with an average density of 0.9gcm−3. Frequently, fireballs are observed at altitudes between 90 and 50 In free-space within the Solar System, such a cometary body is km above the Earth; however, other fireballs, such as the Tunguska heated by the Sun. At a solar distance R andanangleθ between bolide, appear to survive to much lower altitudes, exploding at ∼10 the Sun and a normal to the surface of the body, the energy balance km or less (Chyba, Thomas & Zahnle 1993). Here, we hypothesize equation is that meteoroids which survive to lower than expected altitudes are − Fe τT (1 − A (υ)) cos θ Z (θ) L (T ) ∂T composed of volatile ices and organics held within and surrounding = εσT 4 + B + K B , 2 B a denser core. The gases from outgassing, volatile material form R N0 ∂r r=a a sheath around the body thus protecting it from direct interaction (1) with the atmosphere as it decelerates. where F is the energy flux from the Sun, A(υ) is the effective Studies of cometary meteoroids suggest that rather than being albedo at a given frequency υ and τT is the total optical depth be- composed of a homogeneous material such as stone or chrondite, tween the Sun and the body. The energy from the Sun is dissipated they possess both volatile and high-density refractory components. through thermal radiation, sublimation of volatile particles from the body and conduction of heat throughout the body – the successive terms on the right-hand side of equation (1). Here, TB is the equi- E-mail: [email protected] librium temperature of the body, Z (θ) is the sublimation rate of C 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society 3670 S. G. Coulson, M. K. Wallis & N. C. Wickramasinghe the volatile material with a latent heat of sublimation L (usually a 3 MODELLING THE BOLIDE IN THE function of temperature) and thermal conductivity K. N0,εand σ EARTH’S ATMOSPHERE are Avogadro’s constant, the emissivity and the Stefan–Boltzmann On its fall through the low-density atmosphere, the bolide is heated constant, respectively. by direct impact from incoming gas molecules from the Earth’s At a distance of 1 au, a 1 m radius body has a temperature approx- atmosphere. These impacting gas molecules deposit energy in the imately equal the blackbody temperature of ∼260–270 K (Coulson surface as well as sputtering ice molecules (Coulson & Wickramas- & Wickramasinghe 2003) depending on the effective albedo. Sub- inghe 2003). If the bolide is travelling through the atmosphere with limation cooling and the subsequent increase in optical depth from a speed u, the sublimation rate is increased by ∼ 0.5ρ u3L−1, dust production through the release of volatiles lowers typical tem- atm where ρ is the density of the atmosphere (Coulson & Wickra- peratures of cometary bodies to ∼200 K at 1 au (Keller 1990). At atm masinghe 2003). such values of temperatures, energy losses from the body occur For a body entering the Earth’s atmosphere with the minimum principally by sublimation (radiation losses are lower by a factor initial speed of 12 km s−1, the increased sublimation from col- ∼50). lisions with incoming air molecules at an altitude of 100 km is The saturation pressure of the sublimating grains is given by the 1.5 × 1023 m−2 s−1, approximately three times greater than the sub- Clausius–Clapeyron equation limation rate from thermally sublimating grains. For a body enter- ing the atmosphere with the maximum initial speed of 72 km s−1, = H 1 − 1 Psat Pref exp , (2) the sublimation rate is increased by two orders of magnitude to Rgas Tref T 3.1 × 1025 m−2 s−1. Downloaded from where Rgas is the universal gas constant and H is the enthalpy As the bolide descends, the increasing densities of the atmosphere change of sublimation increased by the enthalpy of vaporization and the outflowing gas lead to a transition from free molecular flow at temperatures above the melting point of the volatile material to hydrodynamic flow. This transition occurs when the total mean ≡ + (Coulson & Wickramasinghe 2003). free-path of atmospheric and sublimated molecules (λ λatm λg) Assuming that the volatile material can be treated as an ideal gas, is less than the bolide radius (λ<a). In the absence of sublimation, the number density n of the sublimating gas particles is related to for a bolide with a radius of 1 m, the hydrodynamic region corre- http://mnras.oxfordjournals.org/ ∼ ∼ the saturation pressure by sponds to an altitude of 80 km, where λatm 1 cm (Allen 2000). In the case of a sublimating bolide, the ‘outgas’ density increases ≈ Psat nkBTB, (3) the altitude at which the transition to hydrodynamic flow occurs. For a water-ice-dominated bolide, this occurs at an altitude ∼100 where k is Boltzmann’s constant. B km. In the case of thermodynamic equilibrium, the speed v of the Within the hydrodynamic flow region, the aerodynamic drag is sublimating molecules can be calculated using 2 proportional to u (Coulson 2003). We calculate that the total mass lost through sublimation is < 1 per cent of the original mass of the k T v = B B , (4) bolide. Hence, the equation of motion for the deceleration of the 2πm M by guest on November 6, 2014 u body can be greatly simplified by assuming that the mass remains essentially constant during deceleration. Solving the equations of where mu is the atomic mass of the sublimating molecules and M the molecular weight. motion for a bolide entering the Earth’s atmosphere under the influ- From equations (2)–(4), the rate of sublimation can be found ence of atmospheric drag, the velocity profile for the body can be written as a function of its altitude h using 3CD ρ0 −h/H u (h) = u0 exp − H e , (7) kBTB a ρ Z (θ) = n (θ) . (5) m 2πmuM −h/H where ρ0e is the variation in atmospheric density at a scale- For water ice at a temperature of 200 K, the sublimation rate is ∼ 5 × height H (Allen 2000)andCD is the atmospheric drag coefficient. − − 1022m 2 s 1 and the saturation pressure is ∼1 torr.