Introduction
Inorganic carbonates play a very important role when meteor matter is considered in an astrobiological context (Fonti et al. Reference Fonti, Jurewicz, Blanco, Blecka and Orofino2001; Orofino et al. Reference Orofino, Blanco, DElia, Fonti and Licchelli2009; Blanco et al. Reference Blanco, Orofino, DElia, Fonti, Mastandrea, Guido and Russo2013, Reference Blanco, Orofino, Mancarella, Fonti, Mastandrea, Guido, Tosti, Russo and D'Elia2014; D'Elia et al. Reference D'Elia, Blanco, Galiano, Orofino, Fonti, Mancarella, Guido, Russo and Mastandrea2016) and the knowledge of their physical and compositional properties in meteorites may also provide information about the presence of organic matter in their parent bodies (comets, asteroids, interplanetary dust). Indeed, carbonates are often associated with the presence of organic matter (Flynn et al. Reference Flynn, Keller, Jacobsen, Wirick and Miller2000; Pizzarello et al. Reference Pizzarello, Cooper and Flynn2006; Matrajt et al. Reference Matrajt, Messenger, Brownlee and Joswiak2012), so, in this perspective, they could be one of the keys to understand the complex chemistry of the Solar System (Flynn et al. Reference Flynn, Keller, Feser, Wirick and Jacobsen2003). In particular, they have been found in Mars meteorites (Borg et al. Reference Borg, Connelly, Nyquist, Shih, Wiesmann and Reese1999; McKay et al. Reference McKay, Gibson, Thomas-Keprta, Vali, Romanek, Clemett, Chillier, Maechling and Zare1996), on the surface of Mars (Orofino et al. Reference Orofino, Blanco, Blecka, Fonti and Jurewicz2000; Boynton et al. Reference Boynton2009; Palomba et al. Reference Palomba, Zinzi, Cloutis, DAmore, Grassi and Maturilli2009), on the surface of Ceres and Vesta (Rivkin et al. Reference Rivkin, Volquardsen and Clark2006), as well as in cometary dust (Busemann et al. Reference Busemann, Nguyen, Cody, Hoppe, Kilcoyne, Stroud, Zega and Nittler2009). (Mg,Fe)CO3 (the carbonate analogue of the Forsterite–Fayalite series) is common among phyllosilicate-rich micrometeorites and CI chondrites and has been reported as well in micrometeorites (Noguchi et al. Reference Noguchi, Nakamura and Nozaki2002). Carbonates of II group elements (in particular aragonite and calcite) have been detected spectroscopically in cometary grain in close association to complex organic molecules (de LEUW et al. Reference De LEUW, Rubin and Wasson2010; Yabuta et al. Reference Yabuta2014). In the Martian meteorite ALH 84001, magnetite nanocrystals showing some analogies with those produced by magnetotactic Earth bacteria have been found into a carbonate matrix (McKay et al. Reference McKay, Gibson, Thomas-Keprta, Vali, Romanek, Clemett, Chillier, Maechling and Zare1996, Reference McKay, Friedmann, Frankel and Bazylinski2003; Thomas-Keprta et al. Reference Thomas-Keprta, Clemett, Mckay, Gibson and Wentworth2009) refreshing the interest in panspermia theory, according to which life forms could spread from planet to planet carried by ice or mineral matter. In a weaker version of this theory, life templates (complex biomolecules, mineral catalysts to nucleic acid polymerization) might have survived during the atmospheric entry. In (Bisceglia et al. Reference Bisceglia, Micca Longo and Longo2016), the facile decomposition of magnesium carbonate has been advocated as a possible cooling mechanism during delivery scenarios of organic matter to primordial Earth. The issue of complex organism survival during atmospheric entry has also been investigated in the STONE experiment series, where several rock materials, including sedimentary rocks, were subjected to real entry tests on the surface of the thermal protection systems of a FOTON capsule (Foucher et al. Reference Foucher, Westall, Brandstätter, Demets, Parnell, Cockell, Edwards, Bény and Brack2010; Parnell et al. Reference Parnell, Bowden, Muirhead, Blamey, Westall, Demets, Verchovsky, Brandstätter and Brack2011). These experiments, because of their nature, cannot however consider real entry speeds for comet grains (being limited to orbital speed) and microscopic particles, which need be addressed by computer simulations.
In spite of this state-of-the-art, there has been little attention to the thermal properties of carbonate minerals in the context of meteoritic studies, in particular to assess their behaviour when grains rich in carbonates enter Earth's atmosphere. It is true that the thermal decomposition of carbonates is poorly characterized from a kinetic point of view (Rao Reference Rao1996; L'vov Reference L'vov1997; Lvov Reference Lvov2002). While this difficulty is hardly overemphasized, times are mature to start a rigorous theoretical study of the behaviour of pure and mixed carbonates in atmospheric entry scenarios, in order to gather the essential information on which future evaluations will be grounded.
Therefore, in this paper a preliminary work for a specific material (pure magnesite), based on a rigorous dynamic and thermal model of the grain entry, is presented and a first-attempt model of the decomposition kinetics is proposed. The critical hypothesis, on which this first model is based, is as much as possible carefully described.
Theoretical background
Thermal effects experienced by micrometeoroids entering Earth's atmosphere have been intensively studied (Love & Brownlee Reference Love and Brownlee1991; Opik Reference Opik2004) and these results have been preliminary reproduced by the authors assuming a silicate composition. Then, in view of the presence of Mg in carbonates and the predominance of Mg in silicates, pure magnesite (MgCO3) is proposed as a mineral model. This mineral is much more sensitive to the high temperatures reached during an entry process, compared with silicates, due to facile decomposition into MgO and gaseous carbon dioxide.
Realistic entry conditions need be simulated in order to assess the contribution of chemical decomposition to the power balance of the grain. We have developed a dynamic-kinetic model, very close to that reported on (Love & Brownlee Reference Love and Brownlee1991) although improved in some minor details, and used it as a standard description of the entry process in order to evaluate the effects to carbonate evaporation kinetics. Actually we used the same set of entry parameters of the cited paper, since this allowed a benchmarking of our computer code for silicates and a clear, comprehensive comparison between carbonates and silicates.
The model has two equations for two Cartesian components of velocity in the vertical entry plane xy (parallel to initial speed and through Earth's centre; v y is assumed positive when moving towards the Earth) and includes the effect of gravity and drag forces, i.e.
$$m{\dot {\bf v}} = {\bf f}_{\rm D} + {\bf g}.$$
Assuming hundred-μm-sized dust grains, the interaction of the grain with the atmosphere is always direct, with no effect due to hydrodynamics or shocks, and the radiation power from the atmospheric and evaporated components is negligible. Therefore, considering a spherical particle moving in a hypersonic molecular flux, the drag force can be estimated as usual by
$$f_{{\rm D}x} = - \pi r^2 \rho _{{\rm atm}} (d)v_x v,$$
$$f_{{\rm D}y} = - \pi r^2 \rho _{{\rm atm}} (d)v_y v,$$
where r is the grain radius, v is velocity magnitude and ρ atm(d) is the standard atmospheric density as a function of the distance d from the ground d = (x 2 + y 2)1/2 − R Earth.
The gravitational acceleration is given by
$$g_x = - g\displaystyle{x \over {d + R_{{\rm Earth}}}}, $$
$$g_y = g\displaystyle{y \over {d + R_{{\rm Earth}}}}. $$
In this way, the Earth curvature is accounted as appropriate in the case of grazing entry. The initial values of v x and v y are given from the initial speed v and entry angle θ defined in such a way that
$$v_y (0) = v(0)\cos \theta. $$
Regarding the function ρ atm(d), this model uses an actual atmospheric density profile: a fit of the atmospheric density (from 600 to 10 km), as a function of the distance from Earth's surface, has been calculated; data have been collected from the empirical model in (Rees Reference Rees1989) [equation (2.6) and Fig. 1].
$$\eqalign{\rho _{{\rm atm}} (d) &= {\rm exp}[ - 7.39 \times 10^{ - 1} - 2.63 \times 10^{ - 5} d \cr & \quad- 3.03 \times 10^{ - 9} d^2 + 2.83 \times 10^{ - 14} d^3 \cr & \quad- 1.16 \times 10^{ - 19} d^4 + 2.44 \times 10^{ - 25} d^5 \cr & \quad- 2.62 \times 10^{ - 31} d^6 + 1.12 \times 10^{ - 37} d^7 ],} $$
where d is in metres and ρ atm(d) in kg m−3.
Fig. 1. Atmospheric density fit (kg m−3), using equation (2.6) of data from (Rees Reference Rees1989).
Concerning heating effects (Love & Brownlee Reference Love and Brownlee1991), air molecules give all their energy to the micrometeoroid entering Earth's atmosphere, so the power P in delivered as heat to the particle is the rate at which the kinetic energy is deposited into it:
$$P_{{\rm in}} = \displaystyle{1 \over 2}\rho _{{\rm atm}} \pi r^2 v^3. $$
The input power is balanced by radiation, vaporization and other mechanisms. In our case, radiative and evaporative energy losses are taken into consideration:
$$P_{{\rm in}} = 4\pi r^2 ({\rm \epsilon} \sigma T^4 + H_{\rm v} Cp_{\rm v} \sqrt {m_{{\rm mol}} /T} ),$$
where ε is the body's emissivity, σ is the Stefan–Boltzmann constant, T is the temperature, H v is the latent heat of vaporization, C is 4.377 × 10−5 (cgs units), p v is the vapour pressure, and m mol is the molecular weight.
Our numerical code is able to calculate the equilibrium temperature at which the sum of radiative and evaporative energy losses equals the input power by means of a binary algorithm: it starts from a ‘guess temperature’ of 1500 K and it adapts it with a ‘jump’ that is progressively halved until the best matching of the values of P in given by the previous two formulae is obtained.
Temperature gradients and heat conduction are not important processes for micrometer particles considered here. In addition, we assume that evaporation takes place in vacuum.
Evaporation affects both particle's temperature and mass. In particular, it is possible to evaluate mass loss rate:
$$\dot m = 4\pi r^2 Cp_{\rm v} \sqrt {\displaystyle{{m_{{\rm mol}}} \over T}}. $$
The updated radius r is calculated from the mass using the known material density.
Evaporation kinetics
Silicates
Although this paper is devoted to the new case study of carbonates, the silicate evaporation law is included to provide a full compatibility with (Love & Brownlee Reference Love and Brownlee1991) for benchmarking and to provide a comparison of the cooling channels (Section 4).
Accordingly, following (Love & Brownlee Reference Love and Brownlee1991; Opik Reference Opik2004), we assume that the vapour pressure of silicates follows the simple law:
$$\log \,p_{\rm v} = \displaystyle{A} - {{B} \over T},$$
where A and B are constants and T is the temperature. Opik (Reference Opik2004) finds the values of A and B to be respectively 10.6 and 13 500, in cgs units. Mean molecular weight of the evaporate components for condritic micrometeoroids is 45.
Carbonates
Here we present the first attempt to explore, by means of a numerical model, the phenomena associated to carbonate grain atmospheric entry. Accordingly, the largest part of the development is connected to the thermochemical aspect: how to capture the main characteristics of a carbonate grain, which, in the course of the process, changes not only its temperature, but also its mass and average chemical composition.
As it is well known, carbonates undergo facile decomposition into CO2 and oxide when heated in vacuum, due to the gain in lattice energy when the bulky carbonate ion is replaced by the small oxide ion. In the course of the entry process, the grain composition is therefore expected to be enriched in oxides at the expense of the initial carbonate content. In this respect, we have elaborated a model based on a well-mixed and ideal solid mixture, which is highly questionable, but allows a first evaluation of the grain behaviour. This model can be resumed into the following assumptions:
-
• pure MgCO3 grain enters the atmosphere;
-
• the Langmuir law is assumed to be valid, based the vapour pressure calculated using thermodynamic data for MgCO3, MgO and CO2;
-
• the grain temperature is uniform; furthermore, the temperature is, at any time instant, equal to the stationary temperature of the equation (8) balance;
-
• the vapour pressure of the solid mixture MgCO3/MgO follows Raoult's law;
-
• there is no limit for CO2 diffusion inside the grain;
-
• mass loss and evaporation can continue until complete stoichiometric conversion to MgO is reached.
In literature, carbonates in meteorites and micrometeorites account for a very small amount of the total volume, not for the entire bulk. Here we are considering a rough model for a carbonate micrometeoroid in order to assess its behaviour during the atmospheric entry. Actually, an ‘artificial’ bulk carbonate meteorite has been considered in the STONE experiment in (Brack et al. Reference Brack2002). The weakest assumption of the model is that the diffusion of CO2 is unhindered, corresponding to highly porous material. Under such hypothesis, however, the vapour pressure of the well-mixed solid based on Raoult's law is
$$p_{{\rm CO}_2} = e^{ - \textstyle{{\Delta G_0 (T)} \over {RT}}} \chi _{{\rm MgCO}_3}, $$
where
$\chi _{{\rm MgCO}_3} $
is the mole fraction of carbonate in the grain and ΔG
0 (T) is calculated using polynomial fits of ΔH
f, ΔS
0 and c
p from (Chase Reference Chase1986).
$\chi _{{\rm MgCO}_3} $
is calculated using stoichiometry. After introducing m
min, the minimum mass in which all carbonate is turned into MgO:
$$m_{{\rm min}} = \displaystyle{{M_{{\rm MgO}}} \over {M_{{\rm MgCO}_3}}} m_0, $$
where M
MgO is the molecular weight of the pure oxide,
$M_{{\rm MgCO}_3} $
is the molecular weight of the magnesite and m
0 represent the mass of the object when it is all composed by carbonate,
$\chi _{{\rm MgCO}_3} $
is given by:
$$\chi _{{\rm MgCO}_3} = \displaystyle{{m - m_{{\rm min}}} \over {m_0 - m_{min}}}. $$
Results
The mathematical model described in the previous section has been implemented as a native Fortran code. We found that a solution of the coupled differential equations based on the simple second-order Leapfrog method is accurate enough. A time step of 1 ms is used in all simulations.
All simulations begin at 190 km altitude, with velocity and entry angles as free parameters. The micrometeoroid material density is set at 3 g cm−3, both for silicates and carbonates.
Silicates
Different entry scenarios are plotted for a silicate micrometeoroid, in order to focus on the duration of the peak temperature (Fig. 2).
Fig. 2. Thermal curves for different entry scenarios (α is the entry angle, v is the entry velocity and dm is the meteoroid diameter) of a silicate micrometeoroid.
Both radiative and evaporative contributions during the atmospheric entry of a silicate micrometeroid are proposed in Fig. 3, for few entry scenarios.
Fig. 3. Radiative and evaporative contributions during the atmospheric entry of a silicate micrometeoroid (α is the entry angle, v is the entry velocity and dm is the meteoroid diameter).
Carbonates
In Fig. 4, different entry scenarios for a carbonate micrometeoroid are plotted.
Fig. 4. Thermal curves for different entry scenarios (α is the entry angle, v is the entry velocity and dm is the meteoroid diameter) of a carbonate micrometeoroid.
These results show that the thermal behaviour of a carbonate grain, at least at the early stage of the entry process, is markedly different from that of the corresponding silicate. Because of the very low evaporation enthalpy of MgCO3 in particular, the evaporation process soon becomes the most important energy dissipation process, thermal radiation being negligible in comparison (see Fig. 5).
Fig. 5. Radiative and evaporative contributions during the atmospheric entry of a carbonate micrometeoroid (α is the entry angle, v is the entry velocity and dm is the meteoroid diameter).
Figure 6 reports
$\chi _{{\rm MgCO}_3} $
as a function of the quota and shows that CO2 fully evaporates until the grain becomes pure oxide.
Fig. 6. Amount of MgCO3 during the atmospheric entry (α is the entry angle, v is the entry velocity and dm is the meteoroid diameter).
In Fig. 7, the equilibration temperature is plotted as a function of the quota d, under the assumption of unlimited gas diffusion in the grain and full decomposition.
Fig. 7. Thermal curves, as a function of the quota d, for different entry scenarios (α is the entry angle, v is the entry velocity and dm is the meteoroid diameter) of a carbonate micrometeoroid.
Discussion
Silicates
Our results, on the scale of the plots, are the same as those originally reported by Love & Brownlee (Reference Love and Brownlee1991) for the same scenarios, showing that our dynamic model is appropriate to provide a comparative study. In the case of silicates, high-peak temperatures of the order of 1500 K are preceded by a steady temperature increase already at early stages of the entry trajectories. This monotonous behaviour is due to the fact that most of the energy is dissipated via black-body radiation at any stage of the entry, as shown in Fig. 3. Evaporation of silicates requires in fact quite high temperatures even in vacuum and can play a significant role only at the temperature peak.
Carbonates
As can be seen from Figs. 4 and 5, the global composition of the original MgCO3 grain changes very fast as the carbonate grain, while entering the atmosphere, gradually release CO2 and it becomes a solid mixture of carbonate and oxide. When CO2 is completely evaporated and the grain becomes a pure oxide (Fig. 6), the grain mass does not change anymore and the temperature increases dramatically, only mitigated by black-body radiation, since MgO is actually much more refractory even than silicate.
As can be seen from Fig. 7, MgCO3 grain will be converted into oxide at altitudes between ~90 and ~130 km, depending on entry conditions and grain size.
Of course, this result can be affected by a revision of the hypotheses of the model. Nevertheless, as soon as MgCO3 is the material under consideration, the general conclusion of our simulation can hardly be modified substantially. The high volatility of magnesium carbonate produces this thermal scenario.
The approximations made in the simulation, in particular the description of the very poorly known decomposition kinetics, could be replaced by different ones in the future, leading to different results. The weakest one is probably the hypothesis of well-mixed solid, which is hardly actually fulfilled at the low temperatures envisaged by these calculations. Changing this hypothesis would shift the evaporation peak at later times and higher temperatures.
Conclusions
In this paper, we have studied, by using a comprehensive numerical method, several scenarios for the entry into Earth's atmosphere of magnesite grains, in order to evaluate the additional thermal protection offered to organic matter, to which they are frequently associated. The present study assumes microsized grains since this scenario allows a rigorous study on physical basis even without considering fluid dynamics effects, and additionally it makes possible a full validation of the dynamic and thermal part of the model by comparing results on silicate grains with literature.
At the same time, it must be recognized that this scenario is the harshest possible one for this material, since under these conditions the kinetic energy needs to be dissipated fully by the grain surface. Even so, we found that chemical decomposition of magnesite provides so much additional cooling, with respect to silicate grains, to keep very low temperatures at early stages of the entry process, compared to silicate grains. This very strong effect is actually a weakness of the specific material (MgCO3), since a lower volatility would allow thermal radiation to dissipate more energy, while this material exhaust its capability to offer additional cooling quite early, having been completely converted into oxide. Although pure magnesite provides an encouraging perspective for the study of carbonates in space, on the other hand it is not able to guarantee thermal protection throughout the whole Earth atmosphere, considering in particular microsized meteoroids in an astrobiological context.
Future studies should therefore consider less volatile carbonate, like calcite and aragonite. Different scenarios, including fragmentation of a larger body into smaller meteoroids at a lower quota, could be taken into consideration. Finally, the inclusion of a true fluid dynamic treatment will illustrate more realistic results: the air cap (Opik Reference Opik2004) provided by air fluid dynamics could be one of the key point for offering a thermal protection during the atmospheric entry.
Acknowledgements
The present research is part of the activities of the PON Apulia Space, which is acknowledged for partial financial support. Savino Longo would like to thank Dr Emiljana Krali for help in the development of the first version of the atmospheric entry code during her BS.
