TY - JOUR
AU - Kereszturi,, Ákos
AB - Abstract This work gives an overview on the general consequences of serpentinization occurring in the planetesimals of any planetary system. These processes were studied by numerical simulations and the model used – based on earlier works – was developed by implementing the effect of interfacial water. As liquid water is fundamentally required for serpentinization, previous simulations considered only such cases when the initial temperature inside the planetesimal was above the melting point of ice thus neglecting the effect of microscopic water layer completely. However, our results show that it must be taken into account and since it facilitates the reaction to occur at temperatures even as low as 200 K – at which bulk liquid water is completely absent – it substantially broadens the initiation of this alteration regarding the range of possible objects. Investigating the effect of changing the initial parameters helps examine the serpentinization in more general terms. Consequently, the findings described here are ubiquitous and can be applied to any exoplanetary system, even if the initial conditions differ considerably from those that were characteristic to our early Solar system. As a first step towards the generalization of such heating processes, we evaluate the role of composition, starting temperature, porosity and planetesimal size on this heating effect. Besides heat generated by decay of radioactive nuclei, serpentinization should be considered as a ‘universal process’ in the thermal evolution of planetesimals, and variations of parameters considered in this model might provide an insight into differences between objects in various protoplanetary discs. astrochemistry, methods: numerical, protoplanetary discs 1 INTRODUCTION 1.1 Astrophysical importance of serpentinization The hydration of various silicates is an exothermic reaction, which may play a role in the heating of planetesimals. The models of this process in the Solar system are discussed in the literature extensively, but it is poorly explored what role such exothermic chemical reactions may play in other planetary systems. In the early Solar system, the 26/27Al-related radiogenic heat was important for the heating and differentiation of planetesimals, and hydration reactions could also serve as heat source, occasionally releasing large amount of heat during a short period of time. Although it is still unknown how abundant the isotopes with short lifetime are in different planetary systems, silicates and ices need to be abundant – with the exception of very early periods of nucleosynthesis – thus silicate hydration could be a possible general heat source in exoplanetary systems. However, substantial differences may exist in the ratio of these two groups of material, in the requirements for the heat generation and in other various factors. Here, we evaluate the possible thermal consequences of silicate hydration on young planetary systems in order to get insight into what differences between various systems could be, and what consequences they can have on the later planetary evolution. In this work, we analyse serpentinization as a model approach to get some general insight into the role of such exothermic hydration based processes in the evolution of planetesimals. Although several exothermic hydration-related reaction may occur in the early phase of planet formation, here we used serpentinization since it is a relatively simple reaction and could probably happen inside young planetesimals, however, there is an ongoing debate on the possible early existence of this reaction. On one hand there are observations suggesting that the process may take place inside meteorites and on a few occasions serpentine was found in meteorites such as Kaidun (Brandstätter, Ivanov & Kurat 1998), in fine grained rims (Buseck & Hua 1993), and recent findings on the small-scale structures of matrices of Mighei-type (CM) carbonaceous chondrites suggests that they contain serpentine-group minerals in Mighei and Murchinson meteorites (Trigo-Rodriguez, Rubin & Wasson 2006). Recent high-resolution Focused Ion Beam (FIB), Scanning Tunneling Microscopy (STM) and Transmission Electron Microscopy (TEM) analyses also provided information on the existence of small and often amorphous hydrated phases including intermediate minerals between serpentine and saponite (Zega, Garvic & Buseck 2003). On the other hand there are different views, which suggest that serpentinization is a rare process and large part of the hydrated components inside meteorites might be of ‘primordial’ origin, e.g. formed by hydration in the solar nebula before or during the accretion of parent bodies (Lunine 2006). To give an exact answer to this question is difficult, partly as such changes may have also happened that eventually overwrote the result of serpentinization. For instance, because of the runaway exothermic heating effect (happened not in carbonaceous chondrites but in more evolved parent bodies of meteorites), the components produced by serpentinization may have been dehydrated and/or altered in a later phase, thus it is not surprising if no well-crystallized serpentine minerals were observed. The large amount of serpentinization might produce such amount of heat that could easily decompose this mineral. Nevertheless, amorphous serpentine-like minerals are expected at least occasionally and have been identified in several meteorites recently. Thus, we use serpentinization as a model approach to estimate the thermal evolution of planetesimals by a relatively simple way, as this or similar exothermic processes could play a role in their evolution. Olivine minerals are abundant (in many cases the most abundant) in meteorites occurring as a solid solution of the two end members: (Mg2SiO4) and fayalite (Fe2SiO4), usually even within the same meteorite (McSween 1977; Scott & Krot 2005). Because of the higher condensation temperature of forsterite compared to fayalite, the former one is more abundant in primitive planetesimals. It should also be noted that forsterite has also been found in asteroids (Cruikshank & Hartmann 1984) and comets (Zolensky et al. 2006; Wooden et al. 1999; Campins & Ryan 1989). It was also spectrally identified in several extrasolar discs (Malfait et al. 1998; Messenger et al. 2003; McClure et al. 2013), as it probably was abundant in the forming planetary systems (Hashimoto 1990) as well. The results of olivine and pyroxene hydration could also be analysed in meteorites in the form of phyllosilicates, often in their matrix – especially in CM chondrites (Tomeoka & Buseck 1985). Serpentine minerals may be present in the matrix of meteorites (McSween 1987; Tomeoka & Buseck 1988) with occasionally elevated Mg (Tomeoka & Buseck 1985) and K with simultaneously reduced Ca and Cl (Bunch & Chang 1980) concentrations as assemblages in Renazzo-type (CR) carbonaceous chondrites (Weisberg et al. 1993). Serpentine is also present in fine-grained rims of several chondrites (Zolensky, Barrett & Browning 1993). According to the various serpentinization reactions other products might also form during the chemical changes such as brucite (Mg(OH)2, see reaction R1) and talc composition minerals (Mg3Si4O10(OH)2). The former one was found to be rare in meteorites, but it can be present in poorly characterized phases of CM2 meteorites (MacKinnon & Zolensky 1984), in layers of Murchison CM2 meteorites (MacKinnon & Buseck 1979), in the matrix of Mighei (MacKinnon 1982) and some observations suggest its presence on Ceres (Milliken & Rivkin 2009); its general lack can be related to the extensive heating effect of runaway exothermic reactions in parent bodies. Minerals with talc-like composition (OH layers in tochilinite and serpentine, Zolensky 1984) is also rare therefore its existence is uncertain, but may have been found in Allende (Brearley 1997), in Tagish lake (Izawa et al. 2010) and possibly on the asteroid 434 Hungaria (Kelley & Gaffey 1999). The other main components of the analysed reactions, i.e. the H2O in the solid phase might be more frequent by adsorption (Drake 2005) than previously thought. The hydration and serpentine formation may be the result of post-accretional H2O-related alteration (Zolensky, Barrett & Browning 1993) supported by certain physical conditions inside the parent body. By analysing the characteristics of these minerals their formation conditions could be roughly estimated. In the case of Ornans-type (CO) carbonaceous chondrites low f(O2) (oxygen fugacity), low water:rock ratio and temperatures below +50|$^\circ$|C are assumed (Zolensky et al. 1993). CR chondrites probably experienced higher water:rock ratio, temperature between 50 and 150|$^\circ$|C and wide range of f(O2). In Vigarano-type (CV) carbonaceous chondrites water:rock ratio is at the high end of CR chondrites, whereas Ivuna-type (CI) carbonaceous chondrites experienced 50 and 150|$^\circ$|C temperature, high water:rock ratio and variable f(O2) (Zolensky, Barrett & Browning 1993). It is important to note that duration of the hydrating aqueous phase could be longer than 1000 yr in some meteorites (Dufresne & Anders 1962). However, serpentinization may have happened (or even could be exhaustive) in the early period of more evolved parent bodies. As it has been previously mentioned, the possible lack or rarity of well-crystallized serpentine in primitive meteorites does not necessarily mean that serpentinization did not happen there. The widespread lack of well-crystallized serpentine may have been caused by the heating effect itself. During the temperature increase serpentine starts to lose water and its decomposition happens along with the increasing temperature. Thus in a meteorite that experienced runaway heating by serpentinization, serpentine is not necessarily expected to be present whereas other mineral alterations may have happened. Furthermore, if the original body melts through, it will not belong to the carbonaceous chondrites any more, since it becomes structurally and geochemically evolved. Despite the heat produced by serpentinization may have contributed to the lack of signature of the process itself, it is worth analysing it as there is a good chance that this (or similar exothermic chemical reactions) could take place. Model-based analysis is a straightforward step towards the understanding of the thermal evolution of planetesimals accounting for this heating effect, including the extrapolation to exoplanetary systems – exactly what this work aims. The main astrophysical importance of serpentinization is the released reaction heat influencing the primitive planetesimals in the following ways: the heat melts water ice and the percolating fluid can cause weathering, OH uptake, and oxidation of reduced minerals. At the same time, new minerals are formed including phyllosilicates (e.g. serpentines) that are able to catalyse several chemical processes on their surface including the polymerization of prebiotic molecules. Impact fragmentation of such planetesimals can cause the widespread occurrence of these phyllosilicates throughout the exoplanetary system. Heat produced by serpentinization can also melt minerals with low melting points and contribute to the differentiation and separation of different components of planetesimals. As a summary, serpentinization increases the mineral diversity and heterogeneity of planetesimals, processes their interior and can contribute to the mineral and chemical diversity of exoplanetary systems. Hence, substantial difference can exist between planetary systems with or without serpentinization in their planetesimals; their larger chemical diversity are more favourable for the emergence of life – although the exact connection is complex and poorly known. The main contributions of this work to the field of astrophysics are (1) to highlight the main parameters influencing the serpentinization-based heat production, (2) to determine the range of temperatures where microscopic liquid water may initiate and support the chemical alteration and (3) to point out to specific examples where serpentinization might be applied to exoplanetary systems. Although it is highly difficult to draw general conclusions in this third topic yet, it is of primary importance to consider further possibilities to support more sophisticated model developments in the future. 1.2 Physicochemical background of serpentinization and earlier models Two important serpentinization reactions of the Mg-rich olivine (forsterite) occur as follows: \begin{equation} {\rm 2Mg_2SiO_4 + 3H_2O \rightarrow Mg_3Si_2O_5(OH)_4 + Mg(OH)_2 } \end{equation} (R1) i.e. reaction of forsterite with water produces serpentine and brucite (Martin & Fyfe 1970). Although not much brucite has been found in meteorites so far (see Section 1.1) this reaction might still be taken into account in our first, rough approach. For the second serpentinization process pyroxene is required as well and in this reaction serpentinite is the only product (Fyfe & Lonsdale 1981): \begin{eqnarray} {\rm Mg_2SiO_4 + MgSiO_3 (pyroxene) + 2H_2O \rightarrow Mg_3Si_2O_5(OH)_4 } \nonumber\\ \end{eqnarray} (R2) The enthalpies at 298 K are 367 kJ mol–1 (Wegner & Ernst 1983) for reaction R1 and 69 kJ mol–1 for reaction R2 (Robie & Waldbaum 1968), respectively. These values may change with temperature but this difference can be neglected in most of the cases (Fyfe 1974). The rate of serpentinization has been previously determined by various groups for many different systems. Velbel and his co-workers extrapolated the rate of serpentinization of Nogoya (CM2) meteorite to room temperature from high-temperature experiments (Velbel, Tonui & Zolensky 2012). They used two different activation energies taken from previous papers regarding forsterite samples: Ea = 15 kJ mol–1 (Martin & Fyfe 1970) and 30 kJ mol–1 (Wegner & Ernst 1983). In these investigations particle sizes were in the range of several tens of µm s, temperature varied from 80 to 560|$^\circ$|C; the serpentinite production required from 4 h to 56 d, the conversion rates were roughly between 40 and 90 per cent, respectively. The basic assumption that the rate of reaction may be extrapolated over this temperature range can be justified by the fact that the calculated serpentinization time-scales were in accordance with estimations using experimental data (Velbel, Tonui & Zolensky 2012; Jones & Brearley 2006). When constructing a serpentinization model there are at least three heat-related phenomenons that have to be considered: Heat release by serpentinization: several models have been introduced so far to estimate the heat formed upon serpentinization. The most simple is the so-called heat balance model (Lowell & Rona 2002), which assumes that rock:water system is in stationary state and reaction heat is absorbed by the species in the environment (more or less, depending on their mass and heat capacity) or carried away by a hydrothermal flow. Both diffusion and thermal conductivity are completely neglected. A universal enthalpy of reaction was assumed (ΔHr = 225 kJ kg–1) based on the serpentinization reactions that can be found in the book chapter of Fyfe & Lonsdale (1981). The model was improved further (Allen & Seyfried 2004) and this so-called extended heat balance model took also into consideration the temperature dependence of reaction enthalpies and heat capacities. Although these methods were primarily developed to simulate the serpentinization processes at seafloor level on Earth, they can still be implemented for reactions taking place in meteorites and/or planetesimals as well. Nevertheless, using these methods allow only the estimation of the temperature increase of surrounding material compared to an initial reaction temperature if stationary state is assumed. Due to these limitations, dynamical models may be used taking into account many other parameters such as grain porosity as well (Cohen & Coker 2000; Iyer, Rüpke & Morgan 2010). Heat consumption of melting ice: one source of the heat loss is the latent heat of ice, which requires 6 kJ mol–1 of ice from the heat budget, and is considered by dynamical models only (Cohen & Coker 2000). Heat transport away: three modes of heat transport are important for the analysis: (1) convection as circulation by liquid water, (2) conduction in solid state ingredients and (3) diffusion of molecules, especially liquid water and vapour. While heat balance models assume the first to be the primary one, dynamical models regard the latter two ones as the main driving forces of heat transport. Thermal conductivity strongly affects the heat budget, especially the occurrence of warming/cooling inside planetesimals. However, it is also well known that several other parameters influence the heat conduction in a solid body including porosity. Therefore, porosity is also an important factor and appears as micro-cracks in the meteorites and as voids between the accreted primordial materials. Its value in carbonaceous chondrites is around 20 per cent (Consolmagno, Britt & Macke 2008), and does not vary with increasing petrographic grade, likely due to the formation of minerals during metamorphism. Porosity influences the melting and heat transport via the following effects: Decreases heat conductivity with its non-continuous structure of the solid material, e.g. via impact-induced micro-cracks causing microporosity (Henke, Gail & Trieloff 2016). This differs from the primordial porosity coming from the loosely packed chondrules and matrix material that did not experience much compaction, sintering and thermal metamorphism (Gail, Henke & Trieloff 2015). As a consequence, early differentiation by certain iron meteorites might have been supported by poor heat conduction of radiogenic heat by porous material in relatively small planetesimals (Gail et al. 2014). Increases heat transport by convection in the case of interconnected porosity, since it allows the migration of fluids inside the parent bodies of meteorites. Increases surface relevant to catalytic reactions, i.e. higher porosity results in a larger effective surface thus increased reaction rates. Namely, specific area determines the extent of physical contact H2O molecules and olivine minerals can make and also fundamentally influences the amount of interfacial liquid water below freezing point of bulk water. The larger this area, the greater the possibility for reactions and greater the amount of microscopic liquid water layer is. Besides these effects the increased interconnected (or communicating) porosity facilitates the percolation of melted liquid to locations where the serpentinization has already used up all H2O in the excess of silicates therefore supports the continuation of chemical reactions. The planetesimals are expected to be porous if they are below some hundred km in diameter as their self-gravity is not strong enough to induce compaction. The porosity also changes (increases) during serpentinization and ice melting via decrease in volume, thus porosity should be present even in melted meteorites, although it is also partly produced by impact fracturing. Because the silicate hydration in planetesimals is a complex problem, we use simplified approaches in this work to see the main ‘trend lines’ and to identify critical factors and scale of processes, which can help develop more focused models for exoplanetary systems in the future. These current models use mostly olivine and simple reaction pathways with restricted conditions. Then – partly based on these simulations – results can eventually be extrapolated to other exoplanetary systems with different conditions. 2 METHODS Two different models were used; the first one is based on the heat balance model (Lowell & Rona 2002; Allen & Seyfried 2004) using a kinetic approach similar to the one used in one of our earlier investigations (Kereszturi & Góbi 2014) to estimate the rate of serpentinization. The other one uses the model developed by Cohen & Coker (2000) utilizing some simplifications and implementing the role of interfacial water, both models are described in Sections 3.1 and 3.2 in details. Our goal is to demonstrate that these serpentinization reactions may occur in icy meteorites at very low temperatures and to estimate what changes can be caused by varying the initial values of different parameters (such as initial temperature, porosity, etc.). Many other possible parameters may play a role, which need further discussion. One of them is the role of heat originating from radioactive decays, which may be important in young exoplanetary systems. In this work, we focused solely on olivine hydration and neglected one of the main heat sources in the early Solar system, i.e. the decay of 26Al that probably produced melting of 80–100 km diameter asteroids for 2–5 Myr. This allows us making more general conclusions as the effect of radioactive decays may vary extensively depending on the system. The heat released by chemical reactions were calculated by assuming reaction R2 to be the dominant process in planetesimals accounting for serpentinite production therefore only this one was taken into consideration. To calculate the serpentinization rate temperatures and activation energies relevant to these environments were estimated after theoretical considerations. Many different olivine:water ratios have been used to study the process under different conditions and in order to be able to make general conclusions on exoplanetary systems with different olivine:water contents. Although the increasing interconnected porosity might increase the convection its effect was neglected as the thermal gradient is small between the neighbouring zones in the planetesimal (Cohen & Coker 2000). Thermal conduction and diffusion may play an important role in heat transport and is included in dynamic models (Cohen & Coker 2000), and heat transport in serpentinites was also examined by Seipold & Schilling (2003) in general. Nevertheless, our aim was to study the effects of serpentinization only locally hence this present simulation does not consider it, however, our future plan is to improve the model and implement heat transport into it. Specific area of minerals was considered in our dynamic model to take into account its role in the formation of microscopic liquid water layer at low temperatures. Porosity was also included although it primarily affects the heat transport processes with a smaller contribution to heterogeneous catalytic reactions, which are out of the scope of our work. To simplify our approach we used spherical olivine grains in our heat balance model, while in reality the structure may also influence the reactions to some extent. There are several other factors beyond the above-mentioned ones that may influence the heat budget. Although they may play some role in the processes, one needs to evaluate the effect of a few selected parameters at first to see the role of hydration. However, more parameters could be evaluated in the future using findings from this restricted case. Furthermore, our aim is to give a general overview on the thermal behaviour of planetesimals in any system focusing on the hydration driven heat to see the basic roles of the hydration process. Most importantly, this work tries to extrapolate to exoplanetary system conditions, i.e. how common and important such serpentinization-related heating effects may be in other planetary systems. This estimation can only be done roughly, primarily because of our limited current knowledge on the forming planetary systems, and also since the result from these models depends on many factors with several of them being uncertain. Therefore we used the following approach: estimated the interval of the otherwise poorly known physical parameters, checked them by test runs after determining the most critical ones by theoretical argumentation. By knowing this, possible effects of the most relevant ones can be evaluated to gather more information and to improve the current models. 3 RESULTS 3.1 Heat budget calculations – heat balance model Before calculating the heat released during serpentinization, reaction rates have to be estimated. Temperature was assumed to be 200 K, this may be prevalent inside several bodies in certain parts of the protoplanetary discs. There were not detailed calculations made to estimate this initial temperature; it was rather a basic assumption taken from various sources including accretion, impact (and radioactive heat). In other words we use this temperature value as an example to see the processes and develop the methods of the computation. For this the equation of Velbel (1990) can be used: \begin{equation} \frac{t({T}_{\text{alt}})}{t({T}_{\text{exp}})} = \exp \left(-\frac{{E}_{\text{a}} {T}_{\text{alt}} - {T}_{\text{exp}}}{R {T}_{\text{alt}} {T}_{\text{exp}}}\right). \end{equation} (1) t(T) is the reaction time at temperature T (typically in days or years), Talt is the temperature in K at which the aqueous alteration occurs, Texp is the temperature in K at which experimental rates were determined, Ea is the apparent activation energy in J mol–1 determined from the measured temperature dependence of t(T) and R is the ideal gas constant and has a value of 8.314 J mol–1 K–1. Based on the work of Martin & Fyfe (1970), the physical parameters have the following values: Texp = 523 K (= 250|$^\circ$|C), Ea = 15 kJ mol–1 and kMF(texp) = 8 d, respectively. Using equation (1) to extrapolate to Talt = 200 K, we can conclude that \begin{equation} \frac{{t}_{\text{MF}}(200\,\text{K})}{{t}_{\text{MF}}(523\,\text{K})} = 3.81 \times 10^{-3}, \end{equation} (2) this means that tMF(200 K) = 6 yr, i.e. the serpentinization reaction takes several years at 200 K to occur in the kbar pressure range. If the results of Wegner & Ernst (1983) are taken into consideration [Texp = 461 K (= 188|$^\circ$|C), Ea = 30 kJ mol1 and tWE(Texp) = 56 d, respectively] then \begin{equation} \frac{{t}_{\text{WE}}(200\,\text{K})}{{t}_{\text{WE}}(461\,\text{K})} = 3.66 \times 10^{-5}, \end{equation} (3) so tWE(200 K) = 4200 yr. Even though these activation energies are those of reaction R1, that of the primary serpentinization reaction R2 can be assumed to be similar, therefore its reaction time does not differ significantly from these values. It is worth noting that all these studies were conducted in excess of water (olivine:water ratio was higher than the stoichiometric value of 2 for reaction R2). Although these studies were carried out at high pressure (between 1000 and 2000 bars), if one assumes that reaction rate depends on the pressure linearly (Cohen & Coker 2000), these results are in good agreement with the ones of other experiments performed on Allende meteorite at lower pressures (at around 10 bars; Jones & Brearley 2006). As the lithospheric pressure inside a planetesimal with a radius of 15 km should be at around this latter value one should adjust the reaction rates calculated above to pressures relevant to the inside of a planetesimal. If linear pressure dependence is assumed one can conclude that at 10 bar these reactions happen approximately 200 times slower, and serpentinization would take place at 200 K between 1200 and 840 000 yr at lower pressures depending on which high-pressure value is used (i.e. tMF(200 K) = 6 yr or tWE(200 K) = 4200 yr), respectively. This result shows that the serpentinization reaction can take place on a reasonable time-scale even at this low temperature; the actual rate of reaction at 200 K may presumably lie somewhere between these two values. In order to calculate the rise in temperature caused by serpentinization, we can use the heat balance model of Lowell & Rona (2002), as a first approach. This neglects heat transport and furthermore it assumes that only the heat capacities of water and silicates account for the increasing temperature: \begin{equation} \Delta T = \frac{\Delta H k}{(Q \cdot {c}_{\text{f}} + k \cdot {c}_{\text{r}})} + \frac{F}{(Q \cdot {c}_{\text{f}})}, \end{equation} (4) where ΔH is the enthalpy of reaction in (4.50 × 105 J kg–1 for reaction R2), k is the estimated rate of serpentinization in kg s–1, Q is the total mass inflow rate of water in kg s–1 (i.e. amount of water per time unit that is necessary for serpentinization, which is proportional to the rate of serpentinization), whereas cf and cr denote the heat capacities of water (4200 J kg–1 K–1) and forsterite (1000 J kg–1 K–1), respectively. There is an additional term in equation (4), and let us assume F (i.e. the heat flux coming from the environment, e.g. heat production of radioactive decays) to be zero. It should be pointed out that in planetesimals where the temperature is lower than the freezing point of water, ice is present instead of liquid water, which would prohibit the occurrence of serpentinization completely. However, there must be some interfacial water on the surface of olivine grains even at low temperatures (Kereszturi & Góbi 2014), hence serpentinization may occur and due to its highly exothermic nature it gradually melts the ice surrounding the silicate grain. This leads to the eventual formation of even more liquid water under certain conditions. We also assume high excess of water replenished instantly after the reaction takes place (i.e. diffusion rate is higher than the rate of reaction). This latter can be justified by the results of our aforementioned work on the decomposition rate of H2O2 in the presence of interfacial water at similar temperatures (Kereszturi & Góbi 2014). When applying these assumptions the rate of reaction is constrained by the olivine serpentinization rate (k) only, calculated below. Based on these considerations, let us assume the serpentinization time of reaction to be t = 5 × 105 yr = 1.6 × 1013 s and particle radius r = 100 µm = 10–4 m. As it could be seen earlier, similar grains sizes were used during the experiments carried out by previous works (Martin & Fyfe 1970; Wegner & Ernst 1983; Jones & Brearley 2006). From the time needed for serpentinization to occur (t) its rate (k) can be also estimated for 200 K. Thus, \begin{eqnarray} k &=& \frac{{m}_{{\rm olivine}}}{t} = \frac{{\rho }_{{\rm olivine}} {V}_{{\rm olivine}}}{t} \nonumber\\ &=&\frac{3270\ \mbox{kg m}^{-3} \times 4.19\,\times \,10^{-12}\ {\mbox{m}}^{3}}{1.6 \times 10^{13}\ \mbox{s}} = 8.6 \times 10^{-12}\ \mbox{kg s}^{-1}. \end{eqnarray} (5) For this (based on reaction R2) two water molecules are need-ed to serpentinize every silicate unit therefore Q = 2k/7.82 = 2.2 × 10–12 kg –1 (as their mass ratio is equal to 7.82). Substituting these to equation (4) gives that ΔT ≃ 48 K showing the temperature rise of the material, regardless of its amount and how long it takes for the alteration to happen eventually. In contrast to the extended heat balance model (Allen & Seyfried 2004), it does not take into consideration the temperature dependence of reaction enthalpies nor heat capacities, which might alter this result when temperature changes. More importantly, this rise in temperature obviously induces the increase in reaction rate therefore the heat production as a consequence of the temperature dependence of reactions. Nevertheless, with this static model our intention was only to show whether there is a chance of a significant heat production (ΔT ≫ 0) and to point out to the possibility of the positive feedback in serpentinization rate under these circumstances. 3.2 Heat budget calculations – dynamic model The method described in the previous subsection is incapable to simulate olivine serpentinization dynamically. In order to determine how this reaction evolves with time and what the optimal olivine:water ratio is, which facilitates the reaction rate the most, the use of a more complex model is necessary. This one is based on the work of Cohen & Coker (2000) with some alterations described in details below to examine the effect of time, temperature, initial olivine:water ratio and porosity on the reaction rate inside a planetesimal. This model examines a segment of the planetesimal rather than investigate the whole celestial body, deep under the surface where the lithospheric pressure is high enough for the reaction to take place. The deepest 100 m thick zone of a body with a diameter of 15 km was examined, where heat and matter flow with the upper layers were neglected, as it was assumed that the layers are in thermal equilibrium and the resultant material transport is zero between these rock layers. These assumptions can be justified since differences in the physical conditions (i.e. in reaction, diffusion and convection rates, etc.) between these layers can be regarded as negligible, especially at the beginning of the serpentinization; Cohen & Coker (2000) also concluded that the thermal gradient between the layers are minor. Furthermore, the time-scale used here is relatively short (in the order of thousand or ten thousand years), which may also lower the amount of heat exchanged with other parts of the planetesimal. It was presumed that the planetesimal consists of variable amount of olivine, enstatite and water (depending on the initial olivine:water ratio), 14 per cent non-reactive material and 16 per cent porosity (ηvoid, which is supposed to be filled with water vapour completely) by volume at the beginning of the simulation. The latter two values and the starting olivine:enstatite = 1.3 ratio was taken from the work of Cohen & Coker (2000). Although ice should melt at around 273 K at the pressure relevant to the simulation, it was assumed that water exists in liquid form above 268 K due to the likely presence of salts. Therefore, water was initially in the form of ice if starting temperature was set below 268 K, otherwise only the presence of liquid water was assumed. However, it is worth noting that liquid water is needed for the serpentinization reactions, hence below the melting point of ice one has to assume the presence of a microscopic liquid water layer even at temperatures as low as 200 K (Kereszturi & Góbi 2014) to help the reaction take place. To estimate the heat released during serpentinization, enthalpy of reaction R2 is used. Although its rate of reaction is unknown, that of reaction R1 (Wegner & Ernst 1983) can be used and assumed that it is linearly dependent on pressure and exponentially on temperature: \begin{equation} {k}_{\mbox{r}} = 4383 p\,\exp \left(-\frac{3463}{T}\right), \end{equation} (6) being kr the observable serpentinization rate (in mol yr–1), T the actual temperature in K and p the total pressure (in Pa), which is the sum of the lithospheric (plith = ρR g, where ρ is the average planetesimal density, R its radius in m and g is the gravitational acceleration on the surface of the body, and equals to 9.28 × 10–3 m s–2 in the case of this body with a radius of 15 km) and vapour pressures [pvap = p0 exp(–T0/T), where p0 and T0 are constants varying on the ratio of ice and liquid water (Grimm & McSween 1989), respectively]. By knowing kr, the number of serpentine produced [Δnserp(t)] can then be calculated in moles: \begin{equation} \Delta {n}_{{\rm serp}}(t + \Delta t) = {n}_{{\rm serp}}(t) (1 - \exp ({k}_{{\rm r}} \Delta t), \end{equation} (7) where t denotes time and Δt the time step (in years) used during the simulation. When olivine is in excess, then nwater(t)/2 is used in equation (7) as being the limiting reagent. It is important to point out to the role of the time step applied. On one hand, they have to be small enough to represent the modelled system with a proper accuracy. However, on the other hand if they are chosen to be too small, the simulation takes much longer therefore a delicate compromise is needed giving adequate results quickly enough. The use of gradually increasing time steps results in improving results in a sense that they become closer to the exact solution of the model, i.e. that one could get if infinite number of points were used. These slight differences are the following if more time steps for the same timespan are used for the canonical case: the calculated initial temperatures required for the same serpentinization level become lower, the final temperatures will be higher when using smaller time steps therefore resulting in bigger overall heat production in our simulations. We took three different time steps when the whole timespan/serpentinization reaction were covered with 1000, 10 000 and 100 000 points representing equal time intervals. For instance the 10 000 yr in the canonical case described in Section 3.3 were divided into equal incremental time steps of 10 (= 1000 points), 1 (10 000 points) and 0.1 yr (100 000 points). As the improvement in the outcome of 10 000 and 100 000 time points was a few per cent only on average (<6 per cent in extreme cases but usually <1 per cent, see Supplementary Material) thus being much lower than the relative difference in the results when using 1000 and 10 000 points for the simulation (<50 per cent, usually in the order of a few per cent), the one with the most points was assumed to be close enough to the exact solution of our model. This assumption can also be justified by the fact that other important physical parameters were neglected (such as heat transport processes) and/or estimated (e.g. reaction enthalpy, activation energy) making up the majority of the uncertainty of this model; compared to these the contribution of not using infinite points is minor to the uncertainty. The rise in temperature due to serpentinization (ΔTserp) can be estimated as follows: \begin{equation} \Delta {T}_{{\rm serp}} = \Delta {H}_{{\rm r}}\frac{\Delta {n}_{{\rm serp}}(t + \Delta t)}{{c}_{p} {m}_{{\rm zone}}}, \end{equation} (8) where ΔHr is the reaction enthalpy of the reaction (69 kJ mol–1, Robie & Waldbaum 1968), cp is the average specific heat and mzone is the mass of the examined zone in the planetesimal. Part of the released heat is used up by the phase transitions occurring within the investigated zone of the planetesimal. Some water vapour always forms filling up the void space, which increases by 3 cm3 per every mole serpentine produced on average (Cohen & Coker 2000). The amount of water vapour (mvap, in kg) was estimated based on the following equation: \begin{equation} {m}_{{\rm vap}} = {M}_{{\rm water}} \frac{{P}_{{\rm vap}} {V}_{{\rm void}}}{R T}, \end{equation} (9) where Mwater is the molar mass of water in kg mol–1, Vvoid is the volume of void space in m3 and R is the gas constant (8.314 J mol–1 K–1). The evaporation of water also needs some heat, decreasing the temperature (ΔTevap) thus reducing the rise in temperature caused by the serpentinization reaction: \begin{equation} \Delta {T}_{{\rm evap}} = \frac{\Delta {m}_{{\rm vap}} \Delta {H}_{{\rm v}}}{{M}_{{\rm zone}} {c}_{p}} \end{equation} (10) being ΔHv the latent heat of vapourization of water (in J kg–1). Furthermore, if the initial temperature is below 268 K, part of the water ice transforms into interfacial water (Anderson, Tice & McKim 1973) \begin{equation} {\ln {{w}_{{\rm i.f.}}} = 0.2618 + 0.5519 \ln {S} - 1.449 {S} - 0.264\ln {\theta }} \end{equation} (11) being wi.f. the content of microscopic liquid water (in g/100 g soil), S the specific surface area (100 m2 g–1 based on the values of Anderson, Tice & McKim 1973) and Θ the temperature below 268 K. This amount of microscopic liquid water is presumed to help the serpentinization reaction occur at low temperatures (below 268 K), the amount of reacting interfacial water is replenished continuously from the water ice source, while this requires some heat released upon serpentinization. If the temperature reaches 268 K, the heat formed during serpentinization melts water. As a consequence the temperature does not rise and the heat of serpentinization is used for melting until the ice fully transforms into water or all the olivine transforms into serpentine. The energy needed for melting a certain mass of ice (Δmice) in a given timestep can be calculated if we deduct the heat necessary for the vapour formation from the serpentinization heat formed during that timestep and divide it by the latent heat of fusion of ice (330 kJ kg–1). All physical parameters and constants not specified here (specific heats and densities of the constituents of the planetesimal, ΔHv values) were determined by using the equations described in the work of Cohen & Coker (2000). Table 1 summarizes all the initial values of parameters for the canonical case. Table 1. Initial parameters used for canonical simulation. Initial oli-vine:water ratio (no/nw) was set to the stoichiometric value of 1:2 = 0.5. Name . Initial value . Remarks . Radius of planetesimal, R (m) 15 000 Inner radius of planetesimal layer examined, ri (m) 15 000 Outer radius of planetesimal layer examined, ro (m) 14 900 Total volume of planetesimal, V (m3) 1.41×1013 Total mass of planetesimal, m (kg) 1.86×1016 Total volume of planetesimal layer, Vl (m3) 2.81×1011 Total mass of planetesimal layer, ml (kg) 3.69×1014 Volume of non-reactive rocks, Vnr (m3) 3.93×1010 Initial value: 14 per cent of Vl Mass of non-reactive rocks, mnr (kg) 1.43×1014 Volume of void space, Vvoid (m3) 4.49×1010 Initial value: 16 per cent of Vl Volume of olivine, Vo (m3) 7.37×1010 Mass of olivine, mo (kg) 2.37×1014 Volume of enstatite, Ve (m3) 5.71×1010 Initial Vo/Ve = 1.3 Mass of enstatite, mo (kg) 1.82×1014 Volume of water, Vw (m3) 6.58×1010 Phase and volume are determined by the actual temperature Mass of water, mo (kg) 6.05×1013 Initial value depends on no/nw Time interval between steps, Δt (yr) 0.1 Temperature, T (K) 253.6 Name . Initial value . Remarks . Radius of planetesimal, R (m) 15 000 Inner radius of planetesimal layer examined, ri (m) 15 000 Outer radius of planetesimal layer examined, ro (m) 14 900 Total volume of planetesimal, V (m3) 1.41×1013 Total mass of planetesimal, m (kg) 1.86×1016 Total volume of planetesimal layer, Vl (m3) 2.81×1011 Total mass of planetesimal layer, ml (kg) 3.69×1014 Volume of non-reactive rocks, Vnr (m3) 3.93×1010 Initial value: 14 per cent of Vl Mass of non-reactive rocks, mnr (kg) 1.43×1014 Volume of void space, Vvoid (m3) 4.49×1010 Initial value: 16 per cent of Vl Volume of olivine, Vo (m3) 7.37×1010 Mass of olivine, mo (kg) 2.37×1014 Volume of enstatite, Ve (m3) 5.71×1010 Initial Vo/Ve = 1.3 Mass of enstatite, mo (kg) 1.82×1014 Volume of water, Vw (m3) 6.58×1010 Phase and volume are determined by the actual temperature Mass of water, mo (kg) 6.05×1013 Initial value depends on no/nw Time interval between steps, Δt (yr) 0.1 Temperature, T (K) 253.6 Open in new tab Table 1. Initial parameters used for canonical simulation. Initial oli-vine:water ratio (no/nw) was set to the stoichiometric value of 1:2 = 0.5. Name . Initial value . Remarks . Radius of planetesimal, R (m) 15 000 Inner radius of planetesimal layer examined, ri (m) 15 000 Outer radius of planetesimal layer examined, ro (m) 14 900 Total volume of planetesimal, V (m3) 1.41×1013 Total mass of planetesimal, m (kg) 1.86×1016 Total volume of planetesimal layer, Vl (m3) 2.81×1011 Total mass of planetesimal layer, ml (kg) 3.69×1014 Volume of non-reactive rocks, Vnr (m3) 3.93×1010 Initial value: 14 per cent of Vl Mass of non-reactive rocks, mnr (kg) 1.43×1014 Volume of void space, Vvoid (m3) 4.49×1010 Initial value: 16 per cent of Vl Volume of olivine, Vo (m3) 7.37×1010 Mass of olivine, mo (kg) 2.37×1014 Volume of enstatite, Ve (m3) 5.71×1010 Initial Vo/Ve = 1.3 Mass of enstatite, mo (kg) 1.82×1014 Volume of water, Vw (m3) 6.58×1010 Phase and volume are determined by the actual temperature Mass of water, mo (kg) 6.05×1013 Initial value depends on no/nw Time interval between steps, Δt (yr) 0.1 Temperature, T (K) 253.6 Name . Initial value . Remarks . Radius of planetesimal, R (m) 15 000 Inner radius of planetesimal layer examined, ri (m) 15 000 Outer radius of planetesimal layer examined, ro (m) 14 900 Total volume of planetesimal, V (m3) 1.41×1013 Total mass of planetesimal, m (kg) 1.86×1016 Total volume of planetesimal layer, Vl (m3) 2.81×1011 Total mass of planetesimal layer, ml (kg) 3.69×1014 Volume of non-reactive rocks, Vnr (m3) 3.93×1010 Initial value: 14 per cent of Vl Mass of non-reactive rocks, mnr (kg) 1.43×1014 Volume of void space, Vvoid (m3) 4.49×1010 Initial value: 16 per cent of Vl Volume of olivine, Vo (m3) 7.37×1010 Mass of olivine, mo (kg) 2.37×1014 Volume of enstatite, Ve (m3) 5.71×1010 Initial Vo/Ve = 1.3 Mass of enstatite, mo (kg) 1.82×1014 Volume of water, Vw (m3) 6.58×1010 Phase and volume are determined by the actual temperature Mass of water, mo (kg) 6.05×1013 Initial value depends on no/nw Time interval between steps, Δt (yr) 0.1 Temperature, T (K) 253.6 Open in new tab 3.3 Results of the dynamic model – canonical case In this section, the simulated results for the planetesimal described in Section 3.2 are discussed; only the role of initial olivine:water ratio and presence of interfacial water is regarded in this canonical case. There are several other factors that may influence the serpentinization process, which are also discussed later in Section 4.1. Fig. 1(a) shows the initial temperatures necessary for the serpentinization reaction to occur (>90 per cent of either olivine or water reacted) in 10 000 yr plotted against the initial olivine:water ratio (Tinit, black squares) using 100 000 time steps (meaning time resolution of 0.1 yr). This is also related to the reaction speed, as the lower the temperature required for the realization of 90 per cent the faster the reaction is. The temperature increase due to the reaction is also shown in Fig. 1(a) (ΔT, red circles), and the heat production reaches the maximum value at the ideal stoichiometric ratio, and it gradually decreases with ratios differing from this value. This can be explained by the fact that the maximum amount of reactant is available at the stoichiometric point. Interestingly, the rate of reaction increases (the initial temperature for the same reaction rate is lower) with increasing olivine amount. When it is in great excess (>25:1) the reaction happens at even very low temperatures as well (at around 200 K); this is allowed by the presence of interfacial water (Kereszturi & Góbi 2014), which provides the liquid water being essential for the serpentinization to occur and continuously replenished by the melting of water ice present in various concentrations in different planetesimals. The heat needed to melt the water ice is covered by the serpentinization heat itself. Figure 1. Open in new tabDownload slide Initial temperature (Tinit in K, black square, a) needed for serpentinization to take place with a 90 per cent yield in 10 000 yr and change in porosity (Δη in percentage, blue triangle, b) after the end of serpentinization reaction (initial porosity was set to 16 per cent) for different initial olivine:water ratios, respectively. Rise in temperature due to reaction (ΔT in K, red circle) is also shown in both panels and stoichiometric olivine:water = 1:2 ratio is marked with a solid black vertical line. Figure 1. Open in new tabDownload slide Initial temperature (Tinit in K, black square, a) needed for serpentinization to take place with a 90 per cent yield in 10 000 yr and change in porosity (Δη in percentage, blue triangle, b) after the end of serpentinization reaction (initial porosity was set to 16 per cent) for different initial olivine:water ratios, respectively. Rise in temperature due to reaction (ΔT in K, red circle) is also shown in both panels and stoichiometric olivine:water = 1:2 ratio is marked with a solid black vertical line. In Fig. 1(b), the calculated change in porosities (Δη, blue triangles) after the end of the serpentinization are plotted against the initial olivine:water ratios. The increase in temperature is plotted in this figure again as well, for the sake of comparison. As can be clearly seen it reaches its maximum (+1.6 per cent compared to the initial value of 16 per cent) in the ideal case when the most serpentinite forms, i.e. when the olivine and water is in stoichiometric ratio. This is a direct consequence of the fact that the production of 1 mol serpentinite increases the void volume by approximately 3 cm3 (Cohen & Coker 2000). It should also be noted that the divergence of the results obtained for the different time steps were the highest in cases close to the ideal (stoichiometric) one, where even slight differences in the simulated olivine:water ratios lead to the large perturbations in the parameters derived from it (e.g. in the temperature increase caused by serpentinization, also see Supplementary Material). 4 DISCUSSION In this section we overview the general consequences of the serpentinization first, then have an outlook on the possible consequences for various exoplanetary systems. For the latter we analyse to what extent the different parameters play a role in the process influencing the final outcome and how different conditions in various forming planetary systems can cause a difference between their thermal evolution and related consequences. Since serpentinization can potentially play an important role in the building blocks of planets, there might be important general ‘rules’ as connections between the conditions inside the disc and the planets produced. Here, we exclude the possible role of various types and concentration of short-lived radionuclides and search for such processes that are related purely to heat produced via serpentinization. Although the current knowledge is insufficient to firmly identify possible outcomes on planet formation during serpentinization, we can still point out to the main directions where further research could provide useful results. 4.1 General consequences of serpentinization The main contributions in this work to the topic are outlined below: the estimation of the role of composition and the role of microscopic liquid water. The consequences caused by them and other possible influencing factors such as starting temperature, size of the body, porosity is discussed as well to have a general view on the role of different conditions in various protoplanetary discs and planetesimals inside them. Olivine:water ratio is a highly important parameter determining the fate of serpentinization fundamentally (Section 3.3), which is influenced by several factors. Assuming the improbable theoretical ‘steady state’ case (radially monotonic decrease in temperature inside the disc), substantial mixing of high-temperature condensates like olivine and low-temperature condensates like H2O is not expected. However, there are several processes in reality that can produce substantial radial migration of materials condensed at different locations, like radial FU Ori-type outbursts that generate mixing and planetesimal migration (for more detailed discussion see Section 4.2). To examine the occurrence of H2O the location of the snow-line does matter in the disc. In a thin disc it should be located at around 3 au stellar distances, but its exact location depends on the stellar mass and ranges between 2 and 5 au for solar mass stars (Mulders et al. 2015). However, in the first 1–5 Myr of a protoplanetary disc evolution the nebula may be optically thick, thus the snow-line might be found at a smaller distance as a consequence of shielding or inversely, at larger distances because of viscous heating.  Another effect related to the ratio of components besides the initial temperature and its change with space and time is the porosity produced. During the reactions pore voids emerge because the total volume changes, which latter is bigger if the olivine:water ratio is closer to the stoichiometric value. The bigger increase in porosity might help the liquid migrate farther thus the propagation of the reactions further – although we do not take into account the effects of fluid migration. Beyond these issues, Fig. 1 shows that substantial differences in the required initial temperature exist, suggesting that higher olivine:water ratio supports the serpentinization at lower temperatures. In this aspect locations/conditions with lower water content favours the initiation of serpentinization at lower temperatures (e.g. protoplanetary discs with less heat originating from radioactive decay or accretion). Microscopic liquid water: by looking at the results of the canonical case (Section 3.3) the importance of interfacial liquid water can be clearly seen. For most of the initial olivine:water ratios the temperature needed for the serpentinization reaction to take place in a reasonable time-scale is under the freezing point of water even if the presence of dissolved salts lowering it is taken into account. Since the serpentinization process needs liquid water to occur, one has to assume the presence of microscopic water phase. Our results clearly show that interfacial water might help the reaction to advance in its early stages, when the temperature is too low for the presence of bulk liquid water. Starting temperature is a critical point. The temperature of these objects is influenced mainly at their surface by insolation of the central star (i.e. the distance between them) or by the temperature of the gas in the disc, but their formation temperature also does matter. Here comes to the picture the heat generated by short-lived radiogenic isotopes altogether with the above-mentioned accretional heating determined by its speed, and also the existence of impact fragmented, porous surface regolith layer acting as an insulator.  Fig. 2 shows the time (tserp. in years, black squares), which is needed for the serpentinization process to take place with a 90 per cent yield as well as the temperature rises due to the reaction (ΔT in K, red circles) at different initial temperature values (Tinit in K) for a planetesimals having canonical initial parameters (Table 1) otherwise. Surprisingly, both of them are temperature-dependent, and while the former one can easily be explained by the inherent temperature dependence of chemical reactions (the higher initial temperature the faster the process is) the second one needs some more consideration. It gradually decreases with increasing initial temperature, caused by the fact that the heat capacities of the constituent minerals are temperature-dependent. Namely, some of them increase with increasing temperature especially those of the silicates olivine, enstatite and the non-reactive rock (the equations for calculating the heat capacities can be found in the work of Cohen & Coker 2000). According to Fig. 2, faster accretion rates produce higher starting temperatures therefore also cause faster and more exhaustive serpentinization – thus discs with faster accretion helps serpentinization and related alteration more than discs with slower growing planetesimals. It is worth noting that the increase in porosity compared to the initial value of 16 per cent of the canonical model can have two values depending on the initial temperature: if the latter is lower than 268 K (melting point of water ice in presence of dissolved salts) than the former one is 1.5 per cent, otherwise it is equal to 1.3 per cent. This can be explained by the fact that although the absolute volume of the void space (i.e. porosity) changed to the same extent as the same amount of serpentinite formed in both cases, their volume relative to the total volume of the examined section of the planetesimal is different. The main cause is the different mechanism at below and above this limit: at colder temperatures the predominant water phase is ice and the reaction is promoted by the presence of microscopic water layers, if the initial temperature is higher than 268 K then the presence of liquid water is exclusive. Since the densities of liquid water and ice are different, this results in a different total volume.  From the temperature dependence of the reaction rate one can also determine its activation energies: Fig. 3 depicts the Arrhenius plot of the system, i.e. ln k (k is the rate constant determined from tserp. in s) is plotted against 1/Tinit (for more detailed discussion see also Kereszturi & Góbi 2014). The slope of the fitted linear is –Eact/R = –2967 K, from this Eact can be determined and equals to roughly 24.7 kJ mol–1, which is comparable to the activation energies determined by earlier works (Section 3.1; Martin & Fyfe 1970; Wegner & Ernst 1983). It is important to note, however, that the plot is not entirely linear: at lower temperatures it differs (is higher) slightly from the fitted linear having higher ln k values implying somewhat higher activation energies at lower temperatures (Eact usually shows a slight temperature dependence). Size of planetesimals, pressure: besides temperature, there is also a pressure requirement for the reaction to occur; hence protoplanetary embryos with a minimal size are needed. The rate of reaction is influenced by the pressure inside the planetesimals made up by lithospheric and vapour pressures, thus larger bodies require lower temperature for the process to begin. Most of the studies on serpentinization have been done for pressure range around 1–200 MPa (Martin & Fyfe 1970; Wegner & Ernst 1983; Jones & Brearley 2006); they found that the rate of reaction depends on pressure almost linearly (Cohen & Coker 2000).  In brief, planetesimal size does matter: Fig. 4 displays both the rate of reaction (via the Tinit needed for the serpentinization to take place, black square) and the temperature change (ΔT, red circle) plotted against the size of the planetesimal. It shows that they both depend strongly on the size (mass) and the reaction rate can be easily explained by the aforementioned linear dependence. In brief, higher planet radius (mass) results in higher pressures, at which the serpentinization can occur faster. Therefore, lower initial temperatures are needed for it to take place, and the heat capacities become lower, i.e. the temperature change during serpentinization increases with increasing planetesimals size. For instance in large planetesimals much lower initial temperature can produce exhaustive serpentinization. Comparing a 10 and a 100 km bodies in diameter, a temperature of 80–100 K higher is needed for the smaller object to produce the ‘same level’ of alteration. This underlines the importance of size, thus larger mass of serpentine is expected in such discs where the oligarchic growth could reach larger sizes – both inside planetesimals and as fragmentation-ejected small grains spread in the given planetary system. Although the cause of the mass dependence of the change in temperature may seem unambiguous, it is also caused by the temperature dependence of the heat capacities as we have already concluded previously. The change in porosity shows the same attributes like that we have discussed at the initial temperature dependence of serpentinization already (Fig. 2), i.e. it depends on whether the reaction involves bulk liquid water or microscopic water layer and the difference in total volume due to the different densities of liquid water and ice results in different change in relative porosity values (cf. 1.5 and 1.3 per cent). Initial porosity: calculating with extreme values we analyse the effect of changing porosity between 0 and 32 per cent. It is reasonable to assume that different porosities might prevail in different planetesimals, and even inside the same body. It may also change with time by compaction, melting–recrystallization, impact fracturing, etc. Zero porosity is expected in the case of recrystallized structure, moderate porosity (e.g. 16 per cent used in the canonical case) in the case of impact fracturing and certain level or alteration, while the highest 32 per cent is an experiment-based value and is probably characteristic for the primary, accretion-produced ‘loose’ planetesimals (Teiser, Engelhardt & Wurm 2011). The increasing porosity during the serpentinization has two main consequences. The increased voids might support the spatial spreading of the process with providing pathways for H2O migration to more distant locations inside the planetary body if interconnected pores (or so-called communicating porosity) are present, whose formation is a difficult and poorly resolved issue. Another effect is related to heat transport, i.e. that is accelerated by fluid migration via interconnected pores. However, with separated pores an opposite effect emerges: heat insulation that may enhance the local alterations by conserving the heat produced.  In Fig. 5, one can see the effect of porosity: the initial temperatures required for the reaction (Tinit., Fig. 5a), the temperature rise during the serpentinization (ΔT, Fig. 5b) and change in porosity (Δη, Fig. 5c), respectively; the different symbols show the different initial porosity values. What one can clearly conclude is that the higher the initial porosity the slower the reaction and lower the heat production is, which also implies the smaller change in porosity. This can be simply explained by the lower concentration of the reactants (as the void space takes up bigger part of the planetesimal) resulting in the formation of less serpentinite and therefore less heat. Figure 2. Open in new tabDownload slide Time (tserp in years, black square) needed for serpentinization to take place with a 90 per cent yield and rise in temperature due to reaction (ΔT in K, red circles) for different initial temperature values (Tinit in K), respectively; their canonical values are encircled. Note the logarithmic scale of tserp. Figure 2. Open in new tabDownload slide Time (tserp in years, black square) needed for serpentinization to take place with a 90 per cent yield and rise in temperature due to reaction (ΔT in K, red circles) for different initial temperature values (Tinit in K), respectively; their canonical values are encircled. Note the logarithmic scale of tserp. Figure 3. Open in new tabDownload slide Arrhenius plot (ln k versus 1/Tinit in K–1) of the serpentinization reaction for a planetesimal with a diameter of 15 000 m. Figure 3. Open in new tabDownload slide Arrhenius plot (ln k versus 1/Tinit in K–1) of the serpentinization reaction for a planetesimal with a diameter of 15 000 m. Figure 4. Open in new tabDownload slide Initial temperature (Tinit in K, black square) needed for serpentinization to take place with a 90 per cent yield and rise in temperature due to reaction (ΔT in K, red circles) for different planetesimals sizes (rplanet. in m, note the logarithmic scale), respectively; their canonical values are encircled. Figure 4. Open in new tabDownload slide Initial temperature (Tinit in K, black square) needed for serpentinization to take place with a 90 per cent yield and rise in temperature due to reaction (ΔT in K, red circles) for different planetesimals sizes (rplanet. in m, note the logarithmic scale), respectively; their canonical values are encircled. Figure 5. Open in new tabDownload slide Initial temperature (Tinit in K, a) needed for serpentinization to take place with a 90 per cent yield in 10 000 yr, rise in temperature due to reaction (ΔT in K, b) and change in porosity (Δη, c) after the end of serpentinization reaction for three different initial porosity values (0 per cent: blue triangle, 16 per cent: black square, 32 per cent: red circle), respectively. Stoichiometric olivine:water = 1:2 ratio is marked with a solid black vertical line, i.e. black squares at this line represent the canonical values. Figure 5. Open in new tabDownload slide Initial temperature (Tinit in K, a) needed for serpentinization to take place with a 90 per cent yield in 10 000 yr, rise in temperature due to reaction (ΔT in K, b) and change in porosity (Δη, c) after the end of serpentinization reaction for three different initial porosity values (0 per cent: blue triangle, 16 per cent: black square, 32 per cent: red circle), respectively. Stoichiometric olivine:water = 1:2 ratio is marked with a solid black vertical line, i.e. black squares at this line represent the canonical values. 4.2 Implications to extrasolar protoplanetary discs To extrapolate the consequences for forming planetary systems we compared some end cases and the scale of processes. The first step in connecting serpentinization-related processes to disc observations could be the identification of examples where certain observed features can have relevant aspects in the serpentinization process – such systems are listed in Table 2 below. Based on the topics listed there the observations and modelling of protoplanetary discs mainly focus on the temperature (and related snow-line distance), accretion history (and influenced composition) and radial mixing of the materials there. Table 2. Some observations and model computations of protoplanetary discs relevant to processes, which may influence serpentinization in exoplanetary systems. Observable disc properties . Examples . Connection to serpentinization-related processes . Internal cavities of discs Many transition discs (Andrews et al. 2011) Clearing effect probably by gravitational scattering of grains to the outer disc Decreasing grain size with distance TW Hydrae (Menu et al. 2014) Spatial characteristics of grain growth and snow-line location Radial and azimuthal asymmetries HD 142527 (Rameau et al. 2012) Mass migration in the disc, inhomogeneous mass distribution Spatially homogeneous particle size distribution in the circumbinary ring GGTau (Andrews et al. 2014) Mapping the spatial homogeneity or heterogeneity of the accretion process Inhomogeneity and signs of particle settling-migration HH30 (Madlener et al. 2012) Accretion history of grains → olivine:water ratio Snow-line migration by stellar radiation intensity change Model calculations (Martin & Livio 2012) Possible condensation of different materials at the same location Shadowing effects at the snow-line Model calculations (Jang-Condell & Sasselov 2004) Spatial temperature distribution → condensation sequence Temporal heating of the disc FU Orionis stars (Ábrahám et al. 2009; Sirono 2013) Temporal changes of condensation and structure of crystalized solids Observable disc properties . Examples . Connection to serpentinization-related processes . Internal cavities of discs Many transition discs (Andrews et al. 2011) Clearing effect probably by gravitational scattering of grains to the outer disc Decreasing grain size with distance TW Hydrae (Menu et al. 2014) Spatial characteristics of grain growth and snow-line location Radial and azimuthal asymmetries HD 142527 (Rameau et al. 2012) Mass migration in the disc, inhomogeneous mass distribution Spatially homogeneous particle size distribution in the circumbinary ring GGTau (Andrews et al. 2014) Mapping the spatial homogeneity or heterogeneity of the accretion process Inhomogeneity and signs of particle settling-migration HH30 (Madlener et al. 2012) Accretion history of grains → olivine:water ratio Snow-line migration by stellar radiation intensity change Model calculations (Martin & Livio 2012) Possible condensation of different materials at the same location Shadowing effects at the snow-line Model calculations (Jang-Condell & Sasselov 2004) Spatial temperature distribution → condensation sequence Temporal heating of the disc FU Orionis stars (Ábrahám et al. 2009; Sirono 2013) Temporal changes of condensation and structure of crystalized solids Open in new tab Table 2. Some observations and model computations of protoplanetary discs relevant to processes, which may influence serpentinization in exoplanetary systems. Observable disc properties . Examples . Connection to serpentinization-related processes . Internal cavities of discs Many transition discs (Andrews et al. 2011) Clearing effect probably by gravitational scattering of grains to the outer disc Decreasing grain size with distance TW Hydrae (Menu et al. 2014) Spatial characteristics of grain growth and snow-line location Radial and azimuthal asymmetries HD 142527 (Rameau et al. 2012) Mass migration in the disc, inhomogeneous mass distribution Spatially homogeneous particle size distribution in the circumbinary ring GGTau (Andrews et al. 2014) Mapping the spatial homogeneity or heterogeneity of the accretion process Inhomogeneity and signs of particle settling-migration HH30 (Madlener et al. 2012) Accretion history of grains → olivine:water ratio Snow-line migration by stellar radiation intensity change Model calculations (Martin & Livio 2012) Possible condensation of different materials at the same location Shadowing effects at the snow-line Model calculations (Jang-Condell & Sasselov 2004) Spatial temperature distribution → condensation sequence Temporal heating of the disc FU Orionis stars (Ábrahám et al. 2009; Sirono 2013) Temporal changes of condensation and structure of crystalized solids Observable disc properties . Examples . Connection to serpentinization-related processes . Internal cavities of discs Many transition discs (Andrews et al. 2011) Clearing effect probably by gravitational scattering of grains to the outer disc Decreasing grain size with distance TW Hydrae (Menu et al. 2014) Spatial characteristics of grain growth and snow-line location Radial and azimuthal asymmetries HD 142527 (Rameau et al. 2012) Mass migration in the disc, inhomogeneous mass distribution Spatially homogeneous particle size distribution in the circumbinary ring GGTau (Andrews et al. 2014) Mapping the spatial homogeneity or heterogeneity of the accretion process Inhomogeneity and signs of particle settling-migration HH30 (Madlener et al. 2012) Accretion history of grains → olivine:water ratio Snow-line migration by stellar radiation intensity change Model calculations (Martin & Livio 2012) Possible condensation of different materials at the same location Shadowing effects at the snow-line Model calculations (Jang-Condell & Sasselov 2004) Spatial temperature distribution → condensation sequence Temporal heating of the disc FU Orionis stars (Ábrahám et al. 2009; Sirono 2013) Temporal changes of condensation and structure of crystalized solids Open in new tab High-temperature condensate olivine and low-temperature (180–140 K) water ice condensate form at different locations in a protoplanetary disc with static structure, or could be present together by temporal heating effect of by radial mixing. There are various candidate processes proposed that work in protoplanetary discs and might be related to radial mixing, including the consequences of X-ray heating, disc structure modulation by forming giant planets. Condensation and crystallization may change with time at a given location in the disc, for example hot ionized bubbles ejected from young, accreting protostars could process dust from amorphous to crystalline phase (Watson et al. 2009; Ábrahám et al. 2009). Spatial changes, e.g. radial and inward (Pringle 1981; Lin & Papaloizou 1985; Wehrstedt & Gail 2004), or outward migration (Urpin 1984) support radial mixing, potentially mixing olivine and water. Radial transport of olivine grains is demonstrated by the composition of cometary materials (IDPs and Wild-2 samples), which is also expected in forming planetary systems (van Boekel et al. 2004; Juhász et al. 2012). The occurrence of radial mixing can probably increase the radial extension of regions where olivine:water ratio converges towards the stoichiometric ideal for heat production by serpentinization. The differences in the ratio of olivine and water may also support or inhibit substantial heat release inside planetesimals with different sizes, which can differ between certain exoplanetary systems largely enough. When reviewing the current results from protoplanetary disc observations (examples can be read in Table 2), it is evident that some radial mixing should exist; spatial inhomogeneities in density, particle size and temperature are obviously present as well. The evolution of such disc properties could be partly implemented into future models when knowledge on this topic further improves in order to differentiate between systems at different levels of serpentinization. The better understanding of the differences in intensity of (and the mass affected within) radial mixing or complete lack of it is imperative, as in certain systems it may produce planetesimals with highly different olivine:water ratios. The estimation on the growing speed of planetesimals (deduced from disc age and estimated grain size distribution) might point out to the scale of differences in accretion speed and related initial temperature of planetesimals. The temperature changes at the same radial distance in discs could also have an impact on the condensation sequence, and models should be improved from static towards complex and dynamic approaches, which take into account temperature change with time on condensation sequence, especially for the possible mixing of silicates and water ice. 5 CONCLUSION In this work, we overviewed the general effects of serpentinization on the thermal evolution of planetesimals. The model developed by Cohen & Coker (2000) was improved by implementing the effect of microscopic water layers, which latter may help the occurrence of reaction at temperatures even below the freezing point of bulk water. As liquid water is fundamentally needed for the serpentinization reaction, previous works considered cases only when the initial temperature inside the planetesimal was high enough and neglected the effect of interfacial water completely. The results show that it must be taken into consideration and facilitates the reaction to take place even at 200 K, where bulk liquid water is not expected to be present – substantially broadening the initiation of this alteration regarding the range of possible objects. By studying the effect of changing the starting parameters on the canonical result our primary goal was to investigate the serpentinization in general terms. Consequently, these findings are ubiquitous and can be applied to any exoplanetary system, where the prevailing conditions (such as heat from radioactive decay and accretion, initial silicate/water ratio, porosity) might be even completely different than those were prevalent in our early Solar system. Although the effect of heat transport was neglected in our simulations, it will be the in the focus of interest in a future paper after further development of this model enabling the modelling of multiple layers of the planetesimals and the heat transport between them. A canonical case and the effect of changing some initial parameters (such as initial olivine:water ratio, temperature, body size and porosity) on the results have been studied and the following basic conclusions can be formulated: In all simulations serpentinization happens until all olivine – or water, whichever is in the smaller concentration – is used up. Thus the main limiting factor for the process is the ratio of these two species provided that the initial temperature is high enough. The originally accreted olivine:water ratio fundamentally influences the thermal evolution afterwards by determining the starting temperature at which serpentinization can occur in a reasonable time-scale. Its second effect is on the different heat production from the same mass of accreted material therefore on the internal differentiation and chemical diversification of the planetesimal. It has been concluded that the serpentinization reaction becomes gradually faster with increasing olivine:water ratio but the stoichiometric ratio produces the most heat since the most reactant is available in this case. The different compositional ratios have other consequences as well – besides the required initial temperature and heat produced – like changing the porosity of the planetesimal to a different extent. Similarly to the heat produced the change in porosity has a maximum (roughly 2 per cent) at the stoichiometric ratio. Although this porosity can have diverse effects, only the decreasing reactant concentration with increasing porosity was considered here. Serpentinization reactions can take place at initial temperatures as low as 200 K. Since the presence of liquid water is needed one has to assume the primary role of the microscopic water layers (interfacial water) at low temperatures. Its consideration expands the possible range of compositions at which reactions might start and progress – although detailed calculations require more known parameters that those are available today (i.e. there are still many parameters to ‘play with’). Initial temperature of the planetesimal is influenced by numerous factors – such as its distance from the central star, heat produced by radioactive decay and/or accretion speed and related heating effect, its age, etc. – and it also strongly affects the serpentinization rate and the rise in temperature. The former one can be easily explained by the inherent temperature dependence of chemical reactions, whereas the second one is caused by the increasing heat capacities with increasing temperature. Size of the planetesimal determines the pressure inside the body via lithospheric pressures and it has been previously shown that serpentinization depends on the prevailing pressure nearly linearly. As a rule of thumb one can state that the bigger the planetesimal the faster the serpentinization can take place or consequently, lower initial temperature is needed for the reaction to progress at the same rate. Different initial porosity values have been considered modelling planetesimals at different levels of evolution and/or located in different exoplanetary systems. Porosity gradually increases with progressing serpentinization, and higher starting porosities lower the rate of serpentinization by simply decreasing the available reactants in the planetesimal. Besides this explicit effect, porosity also implicitly affects the serpentinization by affecting the heat transport, which was out of the scope of this work. Focusing on the possible consequences and aspects on planetesimal evolution beyond the Solar system in general, serpentinization might provide a ‘universal’ heating effect, regardless of the local isotopic composition of the given contracting cloud. Although the data on the structure and composition of protoplanetary discs is not known enough to make specific model runs for embryos in forming planetary systems, some general conclusions could be drawn. Several candidate processes exist for the mixing of high-temperature olivine and low-temperature water ice condensates (radial mixing, temperature changes in discs) that must be better understood to classify forming planetary systems with different amount of heat originating from the serpentinization reaction. Besides all these issues, serpentinization might be only one example reaction type, and as being a relatively simple one, it provides a useful model to analyse the role of exothermic reactions on the evolution of planetesimals even without considering substantial radioactive heating. This work was supported by the ‘Főigazgatói Intézkedési Tervezet’ SZ-002/2014 project, the European Cooperation in Science and Technology (COST) TD1308 action, and the ‘Gazdaságfejlesztési és Innovációs Operatív Program’ (GINOP) 2.3.2-15-2016-00003 grant. † " Present address: Department of Chemistry, University of Hawaii at Mānoa, 2545 McCarthy Mall, Honolulu, HI 96822, USA. 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TI - Role of serpentinization in the thermal and connected mineral evolution of planetesimals – evaluating possible consequences for exoplanetary systems
JF - Monthly Notices of the Royal Astronomical Society
DO - 10.1093/mnras/stw3223
DA - 2017-04-11
UR - https://www.deepdyve.com/lp/oxford-university-press/role-of-serpentinization-in-the-thermal-and-connected-mineral-TI0Vtms9Ib
SP - 2099
VL - 466
IS - 2
DP - DeepDyve
ER -