Evidence for post-nebula volatilisation in an exo-planetary body
EEvidence for post-nebula volatilisation in an exo-planetary body
John H. D. Harrison a , ∗ , Oliver Shorttle a,b and Amy Bonsor a a Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK b Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EQ, UK
A R T I C L E I N F O
Keywords :planetary volatile depletionpost-nebula volatilisationpolluted white dwarf starsexo-planetary bodies
A B S T R A C T
The loss and gain of volatile elements during planet formation is key for setting their subsequentclimate, geodynamics, and habitability. Two broad regimes of volatile element transport in and outof planetary building blocks have been identified: that occurring when the nebula is still present, andthat occurring after it has dissipated. Evidence for volatile element loss in planetary bodies after thedissipation of the solar nebula is found in the high Mn to Na abundance ratio of Mars, the Moon,and many of the solar system’s minor bodies. This volatile loss is expected to occur when the bodiesare heated by planetary collisions and short-lived radionuclides, and enter a global magma oceanstage early in their history. The bulk composition of exo-planetary bodies can be determined byobserving white dwarfs which have accreted planetary material. The abundances of Na, Mn, andMg have been measured for the accreting material in four polluted white dwarf systems. Whilst theMn/Na abundances of three white dwarf systems are consistent with the fractionations expected duringnebula condensation, the high Mn/Na abundance ratio of GD362 means that it is not (>3 𝜎 ). Wefind that heating of the planetary system orbiting GD362 during the star’s giant branch evolutionis insufficient to produce such a high Mn/Na. We, therefore, propose that volatile loss occurred in amanner analogous to that of the solar system bodies, either due to impacts shortly after their formationor from heating by short-lived radionuclides. We present potential evidence for a magma ocean stageon the exo-planetary body which currently pollutes the atmosphere of GD362.
1. Introduction
Most rocky planet forming material originates in proto-planetary discs, when hot circumstellar gas condenses intosolid matter at the midplane of the disc (Williams and Cieza,2011). Through the subsequent growth of dust particles intoever larger aggregates: pebbles, planetary embryos and even-tually terrestrial planets are formed. The bulk compositionof both Earth and the chondrites are well explained usingsuch a nebula condensation model, despite Earth’s complexand ongoing differentiation history and alteration processeshaving affected chondrite parent bodies (Anders, 1964; Was-son and Kallemeyn, 1988; Lodders, 2003, 2010; Siebert et al.,2018). The refractory elemental abundances of the chon-drites match those of the Sun, whilst their volatile elementalabundances are depleted relative to the Sun in accordancewith their individual elemental condensation temperatures(McDonough and Sun, 1995; McDonough, 2003; Lodders,2003). Different thermal conditions in the solar nebula haveimparted a fundamental compositional fingerprint on plane-tary material through condensation processes. How univer-sal this process is to planet formation is a key question, onewhich can be answered through study of extra-solar rockymaterial.It is possible to probe the abundances of planetary ma-terial from outside the solar system by observing metal fea-tures in the atmospheres of white dwarfs (Jura and Young,2014). White dwarfs are the faint remnants of the cores ofstars like the Sun, and theoretically they should have atmo-spheres only composed of hydrogen and helium (Althaus [email protected] (J.H.D. Harrison)
ORCID (s): (J.H.D. Harrison) et al., 2010; Koester, 2013). The metal features observedin many white dwarfs are thought to be present due to theaccretion of rocky planetary bodies (Jura and Young, 2014;Farihi, 2016). As the properties of the metal spectral featurescan be used to constrain the relative abundances of the metalsin white dwarf atmospheres’ (Koester, 2009), polluted whitedwarfs can probe the composition of exo-planetary bodiesand test whether nebula condensation can explain the abun-dances found (Harrison et al., 2018).Nebula condensation is not the sole process which de-termines the composition of rocky planetary material. Thecomposition of bodies can also be significantly altered postformation (O’Neill and Palme, 2008). Significant meltingand the formation of a global magma ocean can occur onrocky planetary bodies due to high energy planetary impactsand the decay of short-lived radioactive isotopes (Keil, 2000;Pringle et al., 2014; Wang and Jacobsen, 2016; Hin et al.,2017; Siebert et al., 2018). This heating, referred to in thiswork as post-nebula volatilisation, causes the preferentialloss of volatile elements, especially on less massive bodieswhich do not have sufficient surface gravity to stop the ther-mal escape of the vapour (O’Neill and Palme, 2008; Pringleet al., 2014). Post-nebula volatilisation occurs at much higherpressures and in much more oxidising conditions than solarnebula condensation (Visscher and Fegley, 2013). Thus, in-dividual elemental behaviours and speciations may be sig-nificantly different between these two regimes, and conse-quently the abundance signatures created during post-nebulavolatilisation need not match those expected from nebulacondensation (Sossi and Fegley, 2018). The atmosphericcompositions of polluted white dwarfs could, therefore, po-tentially provide evidence for post-nebula volatilisation in
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Page 1 of 13 a r X i v : . [ a s t r o - ph . E P ] F e b xo-planetary post-nebula volatilisation exo-planetary bodies. In the case of white dwarf systemsthere is the added complexity that the planetary bodies mustsurvive the star’s giant branch evolution, so may experiencestrong heating processes as the host star leaves the main se-quence and increases in luminosity.As well as trends related to volatility, planetary compo-sitions can be altered by large scale melting and the segre-gation of siderophilic elements into a planetary core. Col-lisions between differentiated bodies can separate core andmantle material and can lead to the production of bodieswith bulk compositions dissimilar to those of the bodies thatcondensed out of the stellar nebula. Iron meteorites and theachondrites are examples which provide evidence for the oc-currence of this process in the solar system (Scott and Was-son, 1975; Lodders and Fegley, 1998; Scott, 2013; Michelet al., 2015). As planetary differentiation preferentially movessiderophilic elements into the core and lithophilic elementsinto the mantle and crust, planetary bodies are no longerhomogeneous, thus, disruptive collisions may produce frag-ments which are correspondingly enhanced/depleted in suchelements. The atmospheric compositions of polluted whitedwarfs have been used to provide evidence of planetary dif-ferentiation and collisional processing in exo-planetary sys-tems due to observations of siderophile/lithophile rich/pooratmospheric compositions (Jura and Young, 2014; Harrisonet al., 2018).We can trace the environment of volatilisation processesusing Mn, Na, and Mg. Figure 1 is a modified version ofFigure 1 from Siebert et al. (2018) (Data sources are O’Neilland Palme (2008); Dauphas et al. (2014); Palme and O’Neill(2014); Brewer et al. (2016); Siebert et al. (2018)). The posi-tions of the solar system bodies in log(Mn/Na) and log(Mn/Mg)space can be readily explained by three processes: conden-sation from the solar nebula (blue), planetary differentiation(green), and post-nebula volatilisation (red).Mn can behave as both a lithophile and a siderophilewhile Na and Mg dominantly behave as lithophiles, hence,the Mn/Na ratio and the Mn/Mg ratio of a body can be alteredby differentiation, collisions, and fragmentation. Evidencefor this is found in their abundances in the silicate Earthwhere Mn is depleted relative to bulk Earth (i.e., partiallylost to the core), while Na and Mg are enriched (i.e., retainedin the mantle) (McDonough, 2003; Palme and O’Neill, 2014;Siebert et al., 2018). The green vector on Figure 1 corre-sponds to the abundances expected for increasingly mantle-rich collisional fragments of differentiated bodies.Mn and Na are both volatile elements in solar nebulaconditions with 50% condensation temperatures of 1158 Kand 958 K respectively, while Mg is a non-volatile elementwith a 50% condensation temperature of 1336 K (Lodders,2003). Therefore, bodies which experienced hotter forma-tion temperatures are expected to have higher Mn/Na ratiosand lower Mn/Mg ratios. Evidence for this is found in the − . − . − . − . − . − . − . log(Mn/Mg) − . − . − . − . − . . . . . l og ( M n / N a ) Post-NebulaVolatilisation TrendCondensationVolatilisation TrendMantle-RichFragment Trend SunChondritesEPBAPBIPBMarsMoon BulkEarthSilicateEarth
Stellar & Solar Data: Brewer & Fischer (2016).Meteoritic Data: Siebert et al. (2018), Warren & Dauphas (2014), and Palme & O’Neill (2008).Terrestrial Data: Siebert et al. (2018) and Palme & O’Neill (2014).
Figure 1:
A modified version of Figure 1 from Siebert et al.(2018). The Mn/Na and Mn/Mg ratios of solar system bod-ies and fragments can be explained by three processes: con-densation from the solar nebula (blue), planetary differentia-tion (green), and post-nebula volatilisation (red). The threecoloured arrows indicate trends relating to the three processesbased on starting with initially solar abundance values. Er-rors are displayed as 1 𝜎 error ellipses to capture the correlationbetween the axes. abundances of the chondrites and bulk Earth (O’Neill andPalme, 2008; Siebert et al., 2018) which lie along the bluecondensation vector plotted on Figure 1.However, in detail the relative volatility of Mn and Na isheavily dependent on the oxygen fugacity and the pressure atwhich the condensation/volatilisation process is occurring.Impact generated silicate melting (post-nebula volatilisation)would have occurred under much more oxidising conditionsand at much higher pressures than nebula condensation (Viss-cher and Fegley, 2013; O’Neill and Palme, 2008; Siebertet al., 2018). Such conditions would cause Na to becomemuch more volatile relative to Mn and Mg, and thus, wouldcause preferential loss of Na, leading to enhanced Mn/Na ra-tios but unchanged Mn/Mg ratios (O’Neill and Palme, 2008;Pringle et al., 2014). Evidence for post-nebula volatilisationis found in the super-chondritic Mn/Na ratios of Mars, theMoon, the Angrite parent body, the Ibitira parent body, andthe Eucrite parent body. This process is described by thecomposition of objects moving along the red vector in Fig-ure 1.By finding the Mn, Mg, and Na abundances of rockybodies in exo-planetary systems we can attempt to answertwo main questions: Firstly, do the three processes of nebulacondensation, differentiation, and post-nebula volatilisationoccur regularly in other planetary systems? Secondly, are Harrison et al.:
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Page 2 of 13xo-planetary post-nebula volatilisation these three processes the major factors which determine thebulk composition of rocky exo-planetary bodies?In this work we use the Mn/Na ratio and the Mn/Mg ratioof the exo-planetary bodies which pollute white dwarfs toassess whether the three processes known to alter the Mn/Naratio and Mn/Mg ratio in the solar system can explain theabundances observed. We also investigate whether the effectof post-main sequence stellar evolution is expected to alterthe composition of the rocky bodies polluting white dwarfs.In section 2 we outline the polluted white dwarf data used, insection 3 we outline the post-main sequence heating modelused, in section 4 we discuss the caveats of our work and ourresults, and in section 5 we state our conclusions.
2. Polluted white dwarf data
Currently the most direct method for measuring the bulkcomposition of rocky bodies in exo-planetary systems is byobserving the atmospheres of externally polluted white dwarfs.Externally polluted white dwarfs are cool white dwarf starswith metal features in their spectra (Jura and Young, 2014).Metal absorption lines have been detected in more than onethousand cool white dwarfs (Kepler et al., 2016; Hollandset al., 2017; Coutu et al., 2019). The polluting metals musthave been accumulated in the upper atmospheres of the coolwhite dwarf stars relatively recently because the cooling agesof the white dwarfs (of the order tens of millions of years tobillions of years) are far longer than the time it takes for themetals to sink out of the upper atmosphere and become un-observable (of the order days to millions of years) (Koester,2009; Jura and Young, 2014). For the white dwarf starsin question the polluting metals cannot originate from theinterstellar medium, the fallback of the star’s giant branchwinds, or the radiative levitation of primordial metals (Far-ihi et al., 2010; Jura and Young, 2014; Farihi, 2016; Veras,2016; Preval et al., 2019). It is now widely accepted that forthese stars the polluting material is of an exo-planetary ori-gin, and therefore, by measuring the relative abundances ofthe metals in the polluted white dwarf atmospheres a uniqueinsight into the bulk compositions of exo-planetary rockymaterial can be found (Jura and Young, 2014; Farihi, 2016;Veras, 2016).
Table 1
The atmospheric abundances (log number fraction) for the fourpolluted white dwarf stars with Mg, Na, and Mn abundancemeasurements. The atmospheric abundances were derived inZuckerman et al. (2007); Dufour et al. (2012); Xu et al. (2013);Hollands et al. (2017); Swan et al. (2019).System log(Mg/He) log(Na/He) log(Mn/He)GD362 −5 .
98 ± 0 .
25 −7 .
79 ± 0 .
20 −7 .
47 ± 0 . J0738+1835 −4 .
68 ± 0 .
07 −6 .
36 ± 0 .
16 −7 .
11 ± 0 . WD 0446-255 −6 .
60 ± 0 .
10 −7 .
90 ± 0 .
10 −9 .
10 ± 0 . J1535+1247 −7 .
36 ± 0 .
10 −8 .
72 ± 0 .
05 −9 .
80 ± 0 . Table 1 contains the atmospheric abundances for the fourpolluted white dwarfs investigated in this work. The atmo-spheric abundances were derived in Zuckerman et al. (2007);Dufour et al. (2012); Xu et al. (2013); Hollands et al. (2017);Swan et al. (2019) (the Mn value was not published in Hol-lands et al. (2017) as that paper focused on a restricted setof elements, however, the Mn abundance was provided byMark Hollands via private communication) and they are cur-rently the only white dwarfs which have measured abun-dances of Mn, Mg, and Na in their atmospheres. Six otherwhite dwarfs are known to have two of the three elementsof interest in their atmospheres, however, with only upperlimits at best on the third elemental abundance we do not in-vestigate these white dwarfs further.The abundances in Table 1 cannot necessarily be directlycompared to the solar system bodies. This is because thedifferential sinking times of Mn, Na, and Mg through thewhite dwarf’s photosphere cause fractionation of the photo-spheric abundances away from that of the accreting mate-rial. For example, for Mn, Na, and Mg in the atmosphere ofJ0738+1835 the sinking times are 0.11, 0.17, and 0.18 Myrsrespectively (Dufour et al., 2012). The abundances tend fromthose of the accreted body (‘build-up phase’) to a steady statebetween accretion and diffusion on timescales of order thesinking timescale (Koester, 2009). Once accretion has fin-ished, abundances decrease in a ‘declining phase’ (Koester,2009). In Harrison (2020), a Bayesian model is used to as-sess the most likely state of each body. The model finds thatfor GD362, J1535+1247, and WD 0446-255 the accretingmaterial is most likely in the build-up phase while J0738+1835is likely to be in a steady state accretion phase.
Table 2
The polluted white dwarf abundances (log number fraction)adjusted from the values in Table 1 in order to account fordifferential sinking. The abundances for GD362, J1535+1247,and WD 0446-255 assume the polluting material is accreting inbuild-up phase (the abundances of the accreting material areidentical to that of the atmosphere (Table 1)) while the abun-dances for J0738+1835 assume that the polluting material isaccreting in steady state (the abundances of the accreting ma-terial have been adjusted using the sinking timescales quotedin the text).System log(Mn/Mg) log(Mn/Na)GD362 −1 .
49 ± 0 .
27 +0 .
32 ± 0 . J0738+1835 −2 .
20 ± 0 .
12 −0 .
54 ± 0 . WD 0446-255 −2 .
50 ± 0 .
14 −1 .
20 ± 0 . J1535+1247 −2 .
44 ± 0 .
22 −1 .
08 ± 0 . Table 2 outlines the expected abundance ratios of therocky material that pollutes the white dwarfs GD362, WD 0446-255, J1535+1247, and J0738+1835. These abundances cannow be directly compared to those of the solar system rockybodies.
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Page 3 of 13xo-planetary post-nebula volatilisation − . − . − . − . − . − . − . log(Mn/Mg) − . − . − . − . − . . . . . l og ( M n / N a ) CondensationVolatilisation TrendMantle-RichFragment Trend GD362WD0446J1535 J0738SunChondrites Stellar Range(1 σ , 2 σ , 3 σ )EPBAPBIPBMarsMoon BulkEarthSilicate Earth White Dwarf Data: Swan et al. (2019), Hollands et al. (2017), Dufour et al. (2012), andZuckerman et al. (2007).Stellar & Solar Data: Brewer & Fischer (2016).Meteoritic Data: Siebert et al. (2018), Warren & Dauphas (2014), and Palme & O’Neill (2008).Terrestrial Data: Siebert et al. (2018) and Palme & O’Neill (2014).
Post-NebulaVolatilisation Trend
Figure 2:
The Mn/Na and Mn/Mg ratios of the bodies whichpollute white dwarfs (Table 2) are plotted onto Figure 1. Thewhite dwarf data (black) suggests that the three processes:condensation from the stellar nebula (blue), planetary differen-tiation (green), and post-nebula volatilization (red) may haveoccurred in exo-planetary systems, as the pollutant body ratiosappear to have been moved along vectors away from the initialstellar abundance values (grey area). The errors are displayedas 1 𝜎 error ellipses to capture the correlation between the axes. The abundance ratios from Table 2 of these four pollutedwhite dwarfs are shown in Figure 2. An additional greyshaded region is added to account for the fact that in exo-planetary systems the initial composition of the stellar neb-ula may differ from that of the solar nebula. We model thispotential variation using compositions estimated for nearbystars (Brewer et al., 2016). If the stellar compositions foundin Brewer et al. (2016) represent the range of possible initialnebula abundances, then the possible nebula compositionsare not likely to be sufficiently different from the solar systemthat the elemental condensation sequences derived for thesolar system are invalidated. Crucially, there are no nearbystars with C/O ratios above the threshold at which carbidespecies preferentially condense out of the disc (C/O>0.75)and alter significantly the elemental condensation behaviour(Moriarty et al., 2014).Figure 2 highlights a diversity in the relative abundancesof Mn, Mg, and Na in rocky exo-planetary bodies. The abun-dances of WD 0446-255, J1535+1247, and J0738+1835 canbe easily explained by condensation followed by differentia-tion and finally fragmentation of the body. This conclusionholds when all the derived abundances are analysed, not justNa, Mg, and Mn (Harrison, 2020). J1535+1247 is readilyexplained by the accretion of a primitive planetesimal with acomposition identical to that of the stellar nebula from which it formed as it overlaps the grey shaded region in Figure 2,this is not only true for Mg, Mn, and Na but for all elementsobserved (Harrison, 2020). WD 0446-255 has a composi-tion which is consistent with the accreted material being amantle rich fragment of a differentiated body which did notundergo substantial volatile loss during condensation. Thisis indicated by its position below grey-shaded region, read-ily accessible by core-mantle differentiation, as indicated bythe green vector. These conclusions are reinforced in Har-rison (2020) where it is shown that the material has underabundances, relative to the stellar abundances, in all of theobserved siderophiles (Fe, Ni, Mn etc.) and likely formedbelow 1000 K. J0738+1835 is best explained by a scenariowhere the accreted material is a crust-stripped differentiatedbody which experienced limited volatile loss during conden-sation, as indicated by its high Mn/Na ratio, which lies abovethose predicted for initial nebula conditions (grey shaded re-gion). This hypothesis holds when all observed elements areexamined as there is a consistent depletion of the lithophiles(Ca, Mg, Si, Na etc.) in comparison to the stellar abundances(Harrison, 2020). A full discussion about polluted whitedwarfs as evidence for exo-planetary differentiation and col-lisional processing is given in Harrison et al. (2018) and Har-rison (2020) and no further discussion will take place here.Unlike the previously discussed objects, the Mn/Na abun-dance of GD362 is inconsistent with condensation volatili-sation (>3 𝜎 ). The abundances of the detected siderophileelements in GD362 (Fe, Ni, Cr etc.) are also inconsistentwith the material being a fragment of a larger body whichdifferentiated and was subsequently collisionally processed(Harrison, 2020). The stellar properties of GD 362 (shownin Table 3) do not indicate any obvious differences fromthe other white dwarf stars considered, except in the unusu-ally high level of trace hydrogen in its helium-rich atmo-sphere, a fact that initially made GD362 difficult to charac-terise (Kawka and Vennes, 2005). However, this should notaffect the abundance determinations used here as the modelsused in Xu et al. (2013) take this into consideration. The ele-mental abundances seen in GD362 are, therefore, difficult toexplain without invoking post-nebula volatilisation to raisethe Mn/Na ratio. Table 3
The stellar data for the four polluted white dwarfs analysedin this work. None of the major characteristics of GD362 areparticularly unique in the sample analysed. The data is takenfrom Zuckerman et al. (2007); Dufour et al. (2012); Hollandset al. (2017); Swan et al. (2019).System Type WD Mass WD T eff WD 𝜏 Mg GD362 He 0.72 𝑀 ⊙ 𝑀 ⊙ 𝑀 ⊙ 𝑀 ⊙ As the material that pollutes GD362 survived the giant
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Page 4 of 13xo-planetary post-nebula volatilisation branch evolution of the star, it is possible that devolatilisationcould have occurred during the post-main sequence, whenthe luminosity of the star increases by many orders of mag-nitude, rather than shortly after or during formation. In or-der to investigate this possibility in Section 3 we model thecompositional changes expected to occur to an asteroid inthe GD362 system during the post-main sequence evolutionof the host star.
3. Modelling volatile loss during thepost-main sequence
When the progenitor of a white dwarf (a star with ini-tial mass under 8-11 solar masses (Siess, 2007)) evolves offthe main sequence, it will go through phases where its lumi-nosity exceeds 10,000 times the luminosity of the Sun andits radius exceeds a few astronomical units. During this post-main sequence evolution the equilibrium temperatures of thebodies orbiting the star can increase dramatically. Therefore,rocky bodies could potentially experience significant heatingand volatile loss during this interval.
Our aim is to determine whether post-main sequence heat-ing during the host star’s giant branch evolution could heatan asteroid sufficiently to vaporise Na, whilst not vaporisingMn (or the whole asteroid for that matter), and produce theobserved Mn/Na ratio in the pollutant body of GD362. First,we must estimate the sublimation temperatures of the Na andMn species expected to be present in extra solar asteroids.
Table 4
The possible solid, liquid, and gaseous species that could formwhen running the HSC Chemistry v. 8.0 equilibrium chem-istry program to determine the behaviour of Na and Mn whenheated.Gaseous Species Liquid Species Solid SpeciesNa Na NaNa O Na O Na ONa NaO NaO NaO Na O Na O OO Gaseous Species Liquid Species Solid SpeciesMn Mn MnMnO MnO MnOMnO Mn O MnO O Mn O O Mn O In this work we used the software package HSC chem-istry version 8 to produce vaporisation curves for Na and Mn. For Na we inputted 100 kmol of solid Na O and 1000 kmolof gaseous O into HSC chemistry and allowed it to equlib-riate assuming the Na and O could only be in the form ofthe species listed in Table 4. We tracked the percentage ofNa in gaseous form as a function of temperature and pres-sure and the vaporisation curve was defined as the line inpressure temperature space at which over 10 percent of theNa was in the gas. For Mn we performed an analogous pro-cedure, however in this case we inputted 100 kmol of solidMnO and 1000 kmol of gaseous oxygen into HSC chemistryand allowed it to equilibriate assuming the Mn and O couldonly be in the form of the species in Table 4. We variedthe abundances of the excess gaseous O in both cases to aslow as 100 kmol and found that this only caused the subli-mation temperatures to vary by ∼
50 K and in both cases thisvariation caused the sublimation temperatures to increase.Therefore, variability in the abundance of available O willnot dramatically effect our conclusions.The vaporisation curves found are strong functions ofpressure, therefore, in order to calculate the temperature atwhich Na starts to vaporise from an externally heated aster-oid, one must know the pressure at which the potential va-porisation is occurring. Assuming that the atmosphere of theheated body is solely composed of the Na that is vaporisedfrom its surface and the major factor contributing to atmo-spheric loss is Jeans loss, we can find the steady state massof the atmosphere, and hence the surface pressure.The steady state mass of the atmosphere 𝑀 atmo is definedas 𝑀 atmo = Φ 𝜏 escape . (1)The mass of Na sublimated per second, Φ , is: Φ = 4 𝜋𝑅 ast 𝜎𝜖𝑇 𝐶 Na , (2)where 𝑅 ast is the radius of the asteroid, 𝜎 is the stefan-boltzmannconstant, 𝜖 is the emissivity of the asteroid, 𝑇 is the surfacetemperature, and 𝐶 Na is the latent heat of vaporisation of Na.The Jeans escape timescale, 𝜏 escape is given by 𝜏 escape = √√√√ 𝜋𝑘𝑅 ast 𝑇𝐺 𝑀 ast 𝜇 𝑒 𝜆 (1 + 𝜆 ) , (3)where 𝜆 = 𝐺𝑀 ast 𝜇𝑘𝑅 ast 𝑇 , (4) 𝑘 is the boltzmann constant, 𝑀 ast is the mass of the asteroid, 𝐺 is the gravitational constant, and 𝜇 is the mean molecularmass of the atmosphere.As the gravitational surface pressure is defined as 𝑃 = 𝐺𝑀 ast 𝑀 atmo 𝜋𝑅 ast , (5) Harrison et al.:
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Page 5 of 13xo-planetary post-nebula volatilisation − . − . − . − . − . − . − . − . − . Log(Surface Pressure/Bar) E q u ili b r i u m T e m p e r a t u r e / K Too Hot:Na vaporisesMn vaporisesNa vaporisesMn does not vaporiseToo Cool:Na does not vaporiseMn does not vaporise
Mn Vaporisation CurveNa Vaporisation CurveGD362 Min Mass Heated Asteroid10 GD362 Min Mass Heated Asteroid50 GD362 Min Mass Heated Asteroid100 GD362 Min Mass Heated Asteroid
Figure 3:
The solid lines show the equilibrium temperature ofan externally heated asteroid as a function of surface pressureand asteroid mass. The white region indicates the region ofinterest where Na vaporises but Mn does not. The Mn andNa vaporisation curves were found using the software packageHSC Chemistry version 8 (For further details see Section 3.1). surface pressure can be written as a function of asteroid sur-face temperature, asteroid radius and asteroid mass: 𝑃 = √ 𝜋𝑘𝜎 𝜖 𝑇 𝜇𝐶 Na 𝑒 𝐺𝑀 ast 𝜇𝑘𝑅 ast 𝑇 (1 + 𝐺𝑀 ast 𝜇𝑘𝑅 ast 𝑇 ) . (6)Figure 3 shows how for externally heated spherical blackbody asteroids, of density 3000 kg m −3 and Bond albedo 0.035,the surface pressure varies with surface temperature and as-teroid mass. The body is assumed to have no initial atmo-sphere and the steady state atmosphere produced is only com-posed of vapourised Na. The four solid lines shown corre-spond to four different asteroid masses and highlight howlarger asteroids retain larger atmospheres and, therefore, re-quire larger temperatures to cause vaporisation. We findthat in the minimum mass scenario (where we assume allof the asteroid is currently in the white dwarf’s atmosphereand none is left in a disc around the star, the value usedis .
31 × 10 kg (Xu et al., 2013)) for temperatures above1186 K, and below 2344 K, Na will vaporise from the surfacewhile Mn will not. We also find that even if the mass of theasteroid polluting GD362 is 100 times larger than the mini-mum mass scenario, the above quoted temperatures vary byless than 40 K. The evolution of the luminosity of the progenitor to GD362is calculated using the single star evolution (SSE) code (Hur- ley et al., 2013). The code was run assuming an initial stel-lar mass of 3.2 solar masses. The mass of the white dwarfGD362 is 0.72 solar masses (Xu et al., 2013). The valueof 3.2 solar masses was chosen because it is the initial stel-lar mass which, given the star is solar metallicity, results inthe formation of a white dwarf of 0.72 solar masses (Menget al., 2008). The stellar luminosity calculated can then beconverted into an equilibrium temperature which is a func-tion of radial distance from the star and can then be com-pared to the required vaporisation conditions. However, notall bodies in the planetary system will survive until the whitedwarf phase. Bodies with close-in orbits (small radial dis-tances from the star) can be either engulfed by the star as itexpands or be spun to break up as the star’s luminosity in-creases.The Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP)effect causes asteroids to become spun up by stellar radi-ation (Rubincam, 2000). On the giant branches, when thestar’s luminosity greatly increases, asteroids may be spun upto the point of break up (Veras et al., 2014). Smaller bod-ies which are closer to the star are easier to destroy due tothe YORP effect. Therefore, for GD362, the YORP effectwould be maximised for the case where the polluting aster-oid only has mass equal to that of the material in the atmo-sphere (minimum mass assumption). The code presented inVeras et al. (2014) calculates that if the body was interior to0.4 au it would be spun to break up during the giant branch,assuming the body was the minimum possible mass.During post-main sequence evolution, the radii of a starcan increase by orders of magnitude, potentially causing bod-ies which orbit too close to the star to become engulfed anddestroyed. Whilst strong stellar winds during this phase ofradial expansion cause the orbits of bodies around the starto migrate outwards as the star loses mass, this is often notenough to stop engulfment (Mustill and Villaver, 2012; Adamsand Bloch, 2013). Using the analytical expression given inAdams and Bloch (2013), for the minimum mass case forGD362, we find that the body would be engulfed inside of0.46 au. The parameter values inputted into the analyticalexpression were those given by the SSE code for a 3.2 solarmass star: An initial AGB stellar mass of 3.2 solar masses,an initial AGB stellar radius of 1.22 au, and an AGB du-ration time of 0.96 Myrs. The gamma parameter was con-servatively set to a value of 1, in order to minimise the en-gulfment radius. Larger bodies are engulfed more readily,and therefore, need to orbit further from the star in order toavoid destruction (Mustill and Villaver, 2012; Adams andBloch, 2013). Thus, for all possible masses of the pollutantof GD362, engulfment will be the dominant factor in deter-mining the closest orbit the body could have been on andsurvived to the white dwarf phase. Therefore, in order toconsider the case of maximum heating, and therefore max-imum Na loss, we assume the minimum possible mass forthe progenitor to the GD362 pollutants, as it allows the bodyto orbit closer to the star without being destroyed. We note
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Page 6 of 13xo-planetary post-nebula volatilisation here that this assumption is somewhat contradictory to theassumption that the white dwarf is currently accreting mate-rial (i.e., that the mass of the object is large enough to havesupplied all material seen in the white dwarf’s atmosphereand still provide a larger reservoir of as yet unaccreted mate-rial.). However, it is consistent with our attempt to model themaximum possible fractionation of Mn from Na that couldhave occurred during the post-main sequence life of the star,to see whether earlier post-nebula volatilisation can be ruledout.Figure 4 displays the equilibrium temperature of a spher-ical black body asteroid of Bond albedo 0.035 orbiting a 3.2solar mass star as a function of radial distance from the starand time. The luminosity as a function of time was calcu-lated using the SSE code (Hurley et al., 2013). The grey areais the region for which an asteroid of density 3000 kg m −3 and radius 170 km (the minimum mass assumption) wouldbe destroyed by stellar engulfment (Adams and Bloch, 2013).The regions where Mn and Na vaporise were taken from Fig-ure 3 assuming the minimum mass scenario. By assumingthe minimum mass scenario we minimise the size of the greyarea, thus, maximising the size of the region where Na canbe vaporised from the surface while Mn is retained.Figure 4 highlights how the surface of an asteroid of ra-dius 170 km orbiting the progenitor of the star GD362 wouldbe at temperatures such that Na vaporises while Mn wouldnot for potentially up to 4 million years. Figure 4 addition-ally displays that the vaporisation of Na could occur on allbodies interior to approximately 8 au. In order to calculate whether a sufficient fraction of theNa from the body can be vaporised and lost, thereby, alteringthe bulk composition of the asteroid, we must calculate howthe temperature of the interior of the asteroid evolves duringthe post-main sequence.Thoroughly investigating this would require a completeasteroid interior model. However, due to the uncertainty onthe mass of the asteroid and the abundances in this work, weadopt a simple heat diffusion model in order to calculate amaximum possible volume heated and, therefore, the maxi-mum fraction of Na lost.In order to calculate the temperature of the interior at agiven depth and at a given time we assume the asteroid is asphere. Therefore, the relevant heat diffusion equation is: 𝜕𝑇𝜕𝑡 = 𝜅𝜌𝐶 b 𝑟 𝜕𝜕𝑟 ( 𝑟 𝜕𝑇𝜕𝑟 ) , (7)where 𝑇 is the temperature of the asteroid at a given distancefrom the centre 𝑟 and a given time 𝑡 , 𝜅 is the thermal con- Radial Distance from Star/AU E q u ili b r i u m T e m p e r a t u r e / K Bodydoes notsurvive
Too Hot:Na vaporisesMn vaporisesNa vaporisesMn does not vaporiseToo Cool:Na does not vaporiseMn does not vaporise
Tip of Red Giant Branch1.5 Myrs into AGB2.0 Myrs into AGB2.5 Myrs into AGB3.0 Myrs into AGB3.5 Myrs into AGBTip of Asymptotic Giant Branch
Figure 4:
The solid lines show the equilibrium temperature ofa spherical black body asteroid as a function of radial distancefrom an initially 3.2 solar mass star at various epochs whichare 0.5 Myrs apart. If the equilibrium temperatures enter thewhite region Na can be vaporised from the surface while Mnis retained. The grey area is the region for which an asteroidof density 3000 kg m −3 and radius 170 km would be destroyedby stellar engulfment which in this scenario dominates over theYORP effect (Adams and Bloch, 2013; Veras et al., 2014). Forfurther details see Section 3.2. ductivity of the asteroid, 𝜌 is the density of the asteroid, and 𝐶 𝑏 is the heat capacity of the asteroid.The boundary conditions for an isothermal sphere of ra-dius a are: 𝑇 ( 𝑎, 𝑡 ) = 𝑇 𝑇 ( 𝑟,
0) = 𝑇 . (8)Assuming a steady state is reached the solution must havethe form 𝑇 = 𝐴 + 𝐵𝑟 , (9)therefore, the following substitution can be used 𝐵 ( 𝑟, 𝑡 ) = 𝑟 ( 𝑇 ( 𝑟, 𝑡 ) − 𝑇 ) . (10)Equation 7 then becomes 𝜕𝐵𝜕𝑡 = 𝜅𝜌𝐶 b 𝜕 𝐵𝜕𝑟 , (11)and the boundary conditions become 𝐵 ( 𝑎, 𝑡 ) = 0 𝐵 ( 𝑟,
0) = 𝑟 ( 𝑇 − 𝑇 ) 𝐵 (0 , 𝑡 ) = 0 . (12) Harrison et al.:
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The solution to Equation 11 is 𝐵 ( 𝑟, 𝑡 ) = 2 𝑎𝜋 ( 𝑇 − 𝑇 ) ∞ ∑ 𝑛 =1 (−1) 𝑛 𝑛 𝑠𝑖𝑛 ( 𝑛𝜋𝑟𝑎 ) 𝑒 − 𝜅𝑛 𝜋 𝑡𝜌𝐶 b 𝑎 , (13)therefore the solution to Equation 7 is 𝑇 ( 𝑟, 𝑡 ) = 𝑇 + 2 𝑎𝜋𝑟 ( 𝑇 − 𝑇 ) ∞ ∑ 𝑛 =1 (−1) 𝑛 𝑛 𝑠𝑖𝑛 ( 𝑛𝜋𝑟𝑎 ) 𝑒 − 𝜅𝑛 𝜋 𝑡𝜌𝐶 b 𝑎 . (14)This solution can then be used to calculate the tempera-ture at a given depth inside the asteroid during the post-mainsequence evolution of the star. In this work, we make thesimplistic assumption that if part of the asteroid gets to thetemperature required to vaporise Na on the surface, then itis possible for the Na to be lost to this depth. This will cer-tainly be an overestimate as, firstly, the temperature requiredto vaporise Na will actually be higher the deeper in the as-teroid due to the increased pressure and, secondly, being atdepth inside the asteroid will make it more difficult for theNa to out-gas and leave the asteroid once it does vaporise.The distribution of Na in the asteroid may not be uni-form. Hence, if we wish to find the fraction of Na it is possi-ble to heat, we need to estimate the fraction of Na at a givendepth. In this work we calculate two end member assump-tions. Firstly, a case where Na is distributed homogeneouslythroughout the whole body. This is analogous to the asteroidbeing primitive and undifferentiated. Secondly, a case whereNa is mainly sequestered in the upper layers of the asteroid.This is analogous to the asteroid being differentiated into acore, a mantle, and a crust. We assume the maximum sizecore a body of radius 170 km could differentiate into is 85 kmand the maximum thickness of the crust is 6 km. 6 km waschosen, as if we fix the composition of this crust to be thesame as the Earth’s oceanic crust (White and Klein, 2014),at 6 km thickness the interior would be depleted in an in-compatible manner. Assuming no Na is sequestered into thecore and the crust has the same composition as the Earth’soceanic crust then 17% of the body’s Na is in the first 6 kmand 83% of the body’s Na is in the next 79 km.Figure 5 shows the maximum percentage of volume heatedfor the minimum mass assumption asteroid during the post-main sequence evolution of GD362, as a function of initialradial distance from the star. We assume a heat capacity of840 J kg −1 K −1 and a thermal conductivity of 2 J s −1 m −1 K −1 .As outlined earlier, as orbital migration occurs during theevolution of the star the radial locations in Figure 5 are theinitial orbital distances and, therefore, the percentage of vol-ume heated is an upper bound. The volume required to beheated to fit the abundance observed in GD362 to within the1 𝜎 uncertainties depends on the distribution of Na in thebody. Figure 5 shows the volumes required for a homoge-neous body and a maximally differentiated one: it is very Initial Radial Distance from Star/AU M a x i m u m P e r ce n t ag e o f V o l u m e H e a t e d Volume heated to fit observationswithin 1 σ if body homogenousVolume heated to fit observationswithin 1 σ if body optimallydifferentiated B o d y d o e s n o t s u r v i v e B o d y m u s t m i g r a t e t o s u r v i v e Figure 5:
The maximum percentage of the volume of a spheri-cal 170 km radius 3000 kg m −3 density asteroid which is heatedto a given temperature as a function of initial radial distancefrom the star. The white area is the region where the asteroidis heated to a temperature such that Na on the surface wouldvaporise while Mn on the surface would not. The reason thisplot highlights the maximum possible percentage heated is be-cause the calculated percentage of the volume heated assumesa fixed radial location whereas in reality due to stellar massloss all bodies will migrate outward over time. difficult to heat a large fraction of the body on the post-mainsequence. Thus, it is not possible to produce the observedabundances to within their 1 𝜎 uncertainties. This is mainlydue to the timescales of heat diffusion being longer than thetime it takes to evolve through the post-main sequence evo-lution. In fact, Figure 5 shows that any body orbiting outsideof the first astronomical unit will only experience heating toa very small fraction of the body. Our result is consistentwith previous work that has noted the difficulty of post-mainsequence heating to drastically change the composition ofasteroidal bodies, for example Malamud and Perets (2016)and Malamud and Perets (2017) showed that even interiorice species are expected to survive the giant branch.Figure 6 is an updated version of Figure 2 now includ-ing the maximum possible change in Mn/Na estimated fromour work due to post-main sequence heating. Two additionalpurple vectors are plotted; the longer vector assumes thebody is differentiated, whereas the shorter vector assumesthe body is homogeneous. We emphasise that these vectorsare upper limits for what post-main sequence heating couldachieve in terms of Mn/Na fractionation, as we assume themass of the pollutant is the minimum possible mass, there-fore, maximising both its volume heated and the possibleproximity to the star whilst avoiding engulfment. Harrison et al.:
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Page 8 of 13xo-planetary post-nebula volatilisation − . − . − . − . − . − . − . log(Mn/Mg) − . − . − . − . − . . . . . l og ( M n / N a ) CondensationVolatilisation TrendMantle-RichFragment Trend GD362WD0446J1535 J0738SunChondrites Stellar Range(1 σ , 2 σ , 3 σ )EPBAPBIPBMarsMoon BulkEarthSilicate Earth White Dwarf Data: Swan et al. (2019), Hollands et al. (2017), Dufour et al. (2012), andZuckerman et al. (2007).Stellar & Solar Data: Brewer & Fischer (2016).Meteoritic Data: Siebert et al. (2018), Warren & Dauphas (2014), and Palme & O’Neill (2008).Terrestrial Data: Siebert et al. (2018) and Palme & O’Neill (2014).
Post-NebulaVolatilisation Trend MaximumVolatilisationfromAGB Heating
Figure 6:
An updated version of Figure 2 which includes twoadditional vectors (purple) which indicate the maximum possi-ble change in composition which could be attributed to heat-ing during the post-main sequence evolution of the star. Theshorter vector assumes the asteroid is homogeneous, whereas,the longer vector assumes a scenario where Na is easier toremove due to the fact it is mainly sequestered in the upperlayers of the asteroid. For further details see Section 3.3.
The results of Figure 6 highlight that it is not possibleto produce the abundance pattern seen in the pollutant ofGD362 to within the quoted 1 𝜎 error bars with post-mainsequence stellar heating.
4. Discussion
The main aim of this work was to investigate how volatilesare lost in exo-planetary bodies. In the solar system, Mn andNa abundances suggest that there are three key processes:nebula condensation, differentiation and fragmentation, andpost-nebula volatilisation. In order to probe these effects inexo-planetary systems we utilise the Mn, Mg, and Na abun-dances of the planetary material that has accreted onto whitedwarfs. Application of this method to exo-planetary systemsdoes come with additional assumptions and complications,most notably an extra potential phase of volatile loss whenthe star expanded on the giant branch before becoming awhite dwarf. Evidence from the four white dwarfs inves-tigated suggests that only condensation, differentiation andpost-nebula volatilisation are required, and our simple modelrules out heating on the giant branches as a likely explana-tion for the observed Mn/Na abundance of GD362. We nowdiscuss the validity of our results and justify the assumptionsmade in our simple post-main sequence heating model.
In order to discuss the validity of our results we mustfirst address the validity of white dwarfs as a ‘laboratory’ tostudy the composition of exo-planetary material. Currently,white dwarfs offer a unique insight into the bulk composi-tion of exo-planetary bodies, which can not be offered by thestudy of exo-planet masses and radii or atmospheric compo-sitions. As discussed in Section 2 the prevailing explana-tion for the presence of metals in cool white dwarf atmo-spheres is the accretion of exo-planetary material. In thiswork we assume that the metals originate from one body andthat they can be related to the elemental abundances of theexo-planetary body accreted via consideration of the relevantsinking timescales. It is possible that the white dwarfs arepolluted by multiple bodies. However, even if this was thecase the metal abundances will be dominated by the largestbody, meaning the assumption of a single accreting bodymay still effectively hold in this case. Even if multiple simi-lar mass bodies did pollute GD362, at least one of the bodieswould be required to have an enhanced Mn/Na ratio and sucha scenario would make the observed abundance an underesti-mate of the true Mn/Na fractionation that body experienced.It is also possible that GD362 is not accreting material in thebuild-up phase and the abundances in the atmosphere arerelated to the abundances of the accreting material in a man-ner dissimilar to those calculated in this work. However, asMn sinks faster than Na, if GD362 was in fact in a differentphase of accretion the true Mn/Na ratio of the original bodywould in fact be even higher. Therefore, we do not expectour assumptions regarding the link between polluted whitedwarf atmospheres and exo-planetary compositions to affectour results.Only four white dwarf systems have measurements of theelements required to probe the nature of planetary volatileloss (Mg, Mn, and Na). The lack of observations are due tothe fact that only sufficiently heavily polluted white dwarfsthat lie in a narrow temperature range produce strong enoughMn and Na absorption features for both elements to be si-multaneously detected. Therefore, in order to robustly con-clude that only condensation, differentiation and post-nebulavolatilisation are required to explain the abundances in exo-planetary material, additional observations of heavily pol-luted white dwarf systems within the relevant temperaturerange will be required.The major caveats which affect the validity of our resultsinvolve the simple model we established in order to rule outpost-main sequence heating as an alternative explanation forthe enhanced Mn/Na ratio of GD362. The major caveatsof the model can be separated into two categories. Caveatswhich have been designed specifically so that they maximisethe post-main sequence heating effect, and caveats which donot, and therefore, could potentially affect the conclusions ofthis work. The following assumptions are ones which couldpotentially alter the conclusions of this work:•
Modelling the post main-sequence : The duration of
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Page 9 of 13xo-planetary post-nebula volatilisation the giant branches, the maximum luminosity on the gi-ant branches, and the closest possible orbit for which abody can survive to the white dwarf phase are all func-tions of the initial main sequence mass of the star. Alonger duration for the AGB phase would lead to in-creased heating and could potentially explain the ob-served signature. For GD362 to spend significantlylonger on the giant branch than we have modelled,given its observed mass of .
72 ± 0 . solar masses(Xu et al., 2013), GD362 would need an initial metal-licity higher than 3 times solar or lower than one thirdsolar, in either of these cases, GD362 would have aninitial mass which was considerably less than than 3.2solar masses and therefore spend longer on the giantbranch (Meng et al., 2008). However, the majority ofnearby stars do not have metallicities which are thisextreme, therefore, it is unlikely that the metallicityof GD362 could be such that our conclusions wouldbe affected (Brewer et al., 2016). Additionally, if themodel used to calculate the progenitor mass was inac-curate this could also cause the AGB lifetime to ex-tend. However, while there is uncertainty on the pro-genitor masses predicted by each model, the massespredicted by various different methods (El-Badry et al.,2018; Cummings et al., 2018) are consistent with themass used in this work.• Modelling Na loss : In this work we assumed chemi-cal equilibrium would be reached when calculating thesublimation temperature of Na and Mn and that subli-mation would occur in an environment with plentifuloxygen. It is not obvious whether these assumptionswill hold and indeed the volatilisation of Na and Mnas a function of prevailing conditions is complex andthe basis of ongoing work (Sossi and Fegley, 2018).Additionally, the volatilisation will occur to the sub-stances when they are in a complex multi-componentsilicate melt, where the activity of the Mn and Na com-ponents will play a vital role in the volatilisation pro-cess. However, regardless of the exact temperature re-quired to vaporise Na, unless it becomes substantiallyeasier to vaporise Na, it will remain difficult to heata large enough volume of the body to create the ob-served elevated Mn/Na ratio. In any case, the activi-ties of Na and Mn in silicate liquids reported in Sossiand Fegley (2018) suggest that our simple model willin fact overestimate the ease at which Na is lost ratherthan underestimate it.•
Modelling silicate vapour escape : In order to calcu-late the surface pressure of the body it is assumed thatthe vaporised Na escapes the planetary body via Jeansescape. In reality many escape mechanisms may be atwork, for example the hydrodynamic and sputteringescape mechanisms. If these escape mechanisms areimportant, their efficiency will cause a reduction insurface pressure, which will decrease the vaporisation temperature of Na and will potentially allow it to bemore readily lost. However, this decrease is not ex-pected to be drastic enough to change our conclusionsas Na will still be difficult to vaporise from deep insidethe body’s interior.The following assumptions have been designed such thatthey maximise the potential for the abundances in GD362’satmosphere to be explained by post-main sequence heating:• The mass of the polluting body is equal to the totalmass of the metals in the atmosphere of GD362. Lessmassive bodies can survive closer in orbits and canhave more of their total volume heated in a given time,therefore, minimising the mass of a body maximisesthe potential heating it can experience.• The pollutant body has an atmosphere solely composedof material which sublimates from its surface. Thislowers the total surface pressure and therefore the sub-limation temperatures.• The chosen model parameters for the asteroid survivalmodels presented in Adams and Bloch (2013) and Ve-ras et al. (2014) have been set such that the destructiondistances for planetesimals during the evolution of thestar are minimised.• The pollutant body can survive on a stellar-surface-skimming orbit.• Any Na which reaches the sublimation criteria can es-cape from the polluting body.• The pollutant can be a differentiated body with a thickcrust and a core that has a radius of half that of thebody, allowing the majority of the Na to be sequesteredin the upper layers of the pollutant.
This work has shown that the Mg, Na, and Mn abun-dances of three of the analysed polluted white dwarf sys-tems can be well explained by condensation and differenti-ation processes. This provides evidence that the main pro-cesses which determined the bulk composition of the rockyworlds in the solar system have determined the bulk com-position of the rocky worlds in exo-planetary systems. Thisreinforces previous findings which have suggested that thegeological processes which occur in white dwarf planetarysystems do not appear to be dissimilar from the geologicalprocesses which occur in the solar system (Jura and Young,2014; Harrison et al., 2018; Doyle et al., 2019, 2020).The most significant result of this work is that one pol-luted white dwarf system, GD362, requires post-nebula volatil-isation. GD362 is a historically significant system as it was
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Page 10 of 13xo-planetary post-nebula volatilisation the first polluted white dwarf to have the abundances of themetals in its atmosphere measured in detail Zuckerman et al.(2007). Additionally, GD362 has abundance measurementsof 16 different metal elements, the most of any single systemto date (Zuckerman et al., 2007; Xu et al., 2013). The differ-ences between the depletion of volatiles due to incompletecondensation from the nebula, and the depletion of volatilesdue to post-nebula heating are well understood (O’Neill andPalme, 2008; Visscher and Fegley, 2013; Siebert et al., 2018).The enhanced Mn/Na ratio of GD362 is a signature of post-nebula volatilisation and, crucially, we find that the requiredvolatilisation cannot be easily produced during the post-mainsequence evolution of the star. This implies that the planetes-imal which pollutes GD362 underwent a period of heatingsuch that it developed a global magma ocean once the stellarnebula had dissipated.The formation of global magma oceans is predicted tohave occurred on many of the solar system’s minor bod-ies. The heat required to form global magma oceans is ex-pected to be generated by a combination of impact heat-ing from planetary collisions and short-lived radionuclides.This heating must have been able to melt the deep interiorof the planetesimal in order to remove the required fractionof Na. The feasibility of this mechanism is not calculated inthis paper, however, we note that the position of GD362 onFigure 6 is not dissimilar to that of Vesta (the Eucrite parentbody, EPB). Therefore, it seems likely that the same processpredicted to have removed volatiles from Vesta could de-volatilise the pollutant of GD362. Additionally, we note thatthe availability of short-lived radionuclides in exo-planetarysystems is not well constrained and whether or not short-lived radionuclides pollute exo-planetary systems remains asubject of debate due to their stochastic production process(e.g. Lichtenberg et al., 2016; Young, 2016). It is also pos-sible that the heating process could have been powered bycollisions alone, either way, additional white dwarf observa-tions capable of identifying post-nebula volatilisation couldpotentially provide useful insights and constraints into thisarea of research.The Mn/Mg ratio of GD362 is potentially difficult to ex-plain. As highlighted by Figure 2, it is simply possible thatthe progenitor star had an unusually low Mg abundance. How-ever, analysis of all the elements present in the atmospheregiven in Harrison (2020) found that the estimated Mg valuefor the pollutant of GD362 is potentially too low, and thatre-observation would likely yield a higher abundance mea-surement. Additional observations of polluted white dwarfsystems could yield more systems with enhanced Mn/Na ra-tios and add further weight to the conclusions presented here,and therefore, would be a worthwhile project. Additionally,further modelling to investigate whether post-main sequenceheating can contribute to smaller changes in the Mn/Na ra-tio of planetary bodies would be of great interest, especiallyonce more white dwarf systems with Mn and Na abundancesare discovered.
5. Conclusions
Volatile loss is a key process in rocky planetary bodies.Mn and Na trace the loss of volatiles and, crucially, can dis-tinguish between volatile loss occurring under two physical-chemical regimes. First, the incomplete condensation of thenebula gas, early in a system’s evolution. Second, the lossof volatiles late in a system’s evolution, after the nebula gashas dissipated.The Mn to Na ratio and Mn to Mg ratio observed inthe material accreted by polluted white dwarfs can be usedto provide evidence for condensation processes and post-nebula volatilisation occurring in exo-planetary systems. Inthis study we found that the abundances present in the ma-terial polluting J0738+1835, J1535+1247, and WD 0446-255 are consistent with a scenario in which the material con-densed out of a protoplanetary disc, before undergoing dif-ferentiation and collisional processing, and then finally ac-creting onto the white dwarf. The Mn/Na ratio of the mate-rial polluting the star GD362 cannot be explained by con-densation volatilisation processes (>3 𝜎 ). We hypothesisethat the enhanced Mn/Na ratio is a signature of post-nebulavolatilisation. We show that any alterations to the composi-tion of the material orbiting GD362, that could develop dueto heating during the giant branch evolution of the star, arenot significant enough to increase the Mn/Na ratio to matchthat observed in GD362. Even if the polluting body was suit-ably small, suitably differentiated, and orbited its host staron a surface grazing orbit we still cannot explain the abun-dances to within their 1 𝜎 error bars. Therefore, we concludeit is most likely that the volatile loss that occurred on thepollutant of GD362 after the dissipation of the nebula gaswas due to impact heating and/or short-lived radionuclides,which created a global magma ocean, allowing Na to be ef-ficiently outgassed, similar to the process experienced bysmall rocky bodies of the solar system. Therefore, GD362may provide evidence for the occurrence of global magmaoceans and post-nebula volatilisation in exo-planetary sys-tems.
6. Acknowledgements
We would like to thank Dimitri Veras for his helpful, use-ful, and insightful comments regarding post-main sequencestellar evolution. We would also like to thank Mark Hol-lands for providing additional data for the white dwarf sys-tem SDSSJ1535+1247. We also thank Mark Wyatt for hisuseful comments which improved the quality of the paper.We are also grateful to the Science & Technology FacilitiesCouncil, and the Royal Society - Dorothy Hodgkin Fellow-ship for funding the authors of this paper. We would also liketo thank the anonymous reviewers whose comments helpedimprove this manuscript.
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