Icy Exomoons Evidenced by Spallogenic Nuclides in Polluted White Dwarfs
DDraft version February 4, 2021
Typeset using L A TEX twocolumn style in AASTeX63
ICY EXOMOONS EVIDENCED BY SPALLOGENIC NUCLIDES IN POLLUTED WHITEDWARFS
Alexandra E. Doyle, Steven J. Desch, and Edward D. Young Earth, Planetary, and Space SciencesUniversity of California, Los AngelesLos Angeles, CA 90095, USA School of Earth and Space ExplorationArizona State UniversityTempe, AZ 85287, USA (Accepted to ApJL, January 6, 2021)
ABSTRACTWe present evidence that excesses in Be in polluted white dwarfs (WDs) are the result of accretionof icy exomoons that formed in the radiation belts of giant exoplanets. Here we use excess Be inthe white dwarf GALEX J2339-0424 as an example. We constrain the parent body abundances ofrock-forming elements in GALEX J2339-0424 and show that the over abundance of beryllium in thisWD cannot be accounted for by differences in diffusive fluxes through the WD outer envelope norby chemical fractionations during typical rock-forming processes. We argue instead that the Be wasproduced by energetic proton irradiation of ice mixed with rock. We demonstrate that the MeV protonfluence required to form the high Be/O ratio in the accreted parent body is consistent with irradiationof ice in the rings of a giant planet within its radiation belt, followed by accretion of the ices to forma moon that is later accreted by the WD. The icy moons of Saturn serve as useful analogs. Ourresults provide an estimate of spallogenic nuclide excesses in icy moons formed by rings around giantplanets in general, including those in the solar system. While excesses in Be have been detected intwo polluted WDs to date, including the WD described here, we predict that excesses in the otherspallogenic elements Li and B, although more difficult to detect, should also be observed, and that suchdetections would also indicate pollution by icy exomoons formed in the ring systems of giant planets.
Keywords: white dwarfs: exoplanets INTRODUCTIONWhite dwarfs represent the last stage of stellar evo-lution. These stellar remnants are extremely dense andhave extraordinary gravity such that elements heavierthan helium sink rapidly below their surfaces. Onewould expect to observe only H and He at the sur-faces of WDs. However, 25 - 50% of WDs exhibit ele-ments heavier than helium (Zuckerman et al. 2003, 2010;Koester et al. 2014). These white dwarfs are ‘polluted’
Corresponding author: Alexandra E. [email protected] author: Edward D. [email protected] by heavy elements resulting from accretion of asteroid-like or comet-like bodies (Jura 2003). Many WDs haveobservable debris disks from shredded rocky remnants,and a few WDs possess evidence of transiting rocky bod-ies (Vanderburg et al. 2015; Manser et al. 2019; Vander-bosch et al. 2019). The geochemical compositions of ex-trasolar rocky bodies accreting onto WDs is a burgeon-ing field unto itself (e.g., Klein et al. 2010; Zuckermanet al. 2010; Jura et al. 2012; Dufour et al. 2012; Venneset al. 2010; Melis et al. 2011; Farihi et al. 2011; Gaen-sicke et al. 2012; Jura & Young 2014; Xu et al. 2017;Harrison et al. 2018; Hollands et al. 2018; Doyle et al.2019; Swan et al. 2019; Bonsor et al. 2020).Recently, exceptionally high and robust over-abundances of Be relative to other rock-forming ele- a r X i v : . [ a s t r o - ph . E P ] F e b Doyle et al.
Table 1.
Abundances by number for GALEX J2339-0424 (GALEX 2667197548689621056) from Klein et al. (2021).GALEX J2339-0424 z n ( z )/ n (He) σ spread n ( z )/ n (Fe) σ spread (10 − ) (10 − )Be 0.0041 0.0010 3 . × − . × − O 298.9 25.7 29.02 7.74Mg 26.42 4.0 2.56 0.75Si 25.6 4.3 2.49 0.75Ca 0.94 0.28 9 . × − . × − Ti 0.027 0.007 2 . × − . × − V < < . × − Cr 0.19 0.03 1 . × − . × − Mn 0.094 0.006 9 . × − . × − Fe 10.3 2.6 1.00 0.36 ments (e.g., Fe, Mg, and O) were discovered in two pol-luted WDs, GALEX J2339-0424 and GD 378 (Klein etal., 2021), and by inference in the planetary materialspolluting them. Lithium (Li), boron (B) and Be sharethe characteristic of being the products of spallation re-actions; all three elements are under-abundant in termsof cosmic abundances but enriched by cosmic rays (CRs)as the result of spallation reactions involving collisionsbetween protons and carbon and oxygen atoms in theinterstellar medium (ISM). Rather than being producedby stellar nucleosynthesis, Li is destroyed, or astrated,in stellar interiors at temperatures > . × K, and Beand B are destroyed at temperatures > . × K and > . × K (Vangioni-Flam et al. 2000). Lithium iseasily ionized and thus is more difficult to observe in theoptical regime for stars with higher T eff , such as GALEXJ2339-0424 and GD 378. However, the first detection ofLi in polluted WDs was just recently reported for twoultra-cool white dwarfs with T eff < Li is producedin significant amounts by stellar nucleosynthesis and asa Big-Bang relic (e.g., Clayton 2003). The stable iso-tope of Be is Be and it is produced by the reaction O(p,X) Be where X, the ejected particles, in this caserefers to 3p α n. We emphasize again that no Be is pro-duced in stars. Beryllium is a rare element in the Earth’scrust, as well as in the universe, but concentrations ofthe rare radionuclide Be ( t / = 1 . Be, that precipitate onto Earth’ssurface are often used to date deep-sea sediments (e.gArnold 1956; Lal & Peters 1967) and the recycling of sed-iments through volcanoes (Morris et al. 1990). An anal-ogous means of using radio-isotope spallation products(collectively referred to as cosmogenic nuclides) has beencontemplated for dating the surfaces of icy moons in thesolar system (Nordheim et al. 2019; Hedman 2019).In this paper we consider the possible mechanisms forenriching a rocky or icy body in spallogenic nuclides. Weconsider various sources of MeV protons and evaluatethe likelihood that these sources could have producedthe high Be/O observed in bodies accreted by pollutedWDs.Using Saturn as a model, we find that rings composedmainly of water ice within the magnetosphere of a gi-ant planet satisfy the constraints imposed by the ex-cess Be concentrations exhibited by the polluted WDs.Mid-sized icy moons of Saturn evidently formed fromrings (Charnoz et al. 2009), and indeed accretion of ex-omoons by WDs was anticipated. Moons stripped fromtheir host planets were predicted to be a likely sourceof rocky/icy material for pollution of WDs based on ananalysis of post-main-sequence scattering in WD plane-tary systems (Payne et al. 2016, 2017). It is worth re-marking that the study of Li and Be as markers of stellarpollution by planets has a rich history (e.g., Tucci Maiaet al. 2019; Deliyannis et al. 1997). We suggest thatBe, and perhaps Li and B, excesses in WDs polluted byrocky and icy bodies are signatures of accretion of icyexomoons. cy exomoons evidenced by spallogenic nuclides in polluted white dwarfs THE PARENT BODY ACCRETED BY WDGALEX J2339-04242.1.
The Effects of Settling on Element Ratios
As reported by Klein et al. (2021), GALEX J2339-0424 exhibits significant pollution by the major andsome minor and trace rock-forming elements (Table 1).The uncertainties reported in Table 1 represent thespread in values obtained from different transition linesfor the same element (see Klein et al., 2021, for a moredetailed analysis). At face value, the composition ofthe rocky and icy material comprising the pollutants forGALEX J2339-0424 include an excess of oxygen rela-tive to the other rock-forming elements suggestive of alarge volume fraction of water ice and an excess in Berelative to chondritic abundances by a factor of morethan ∼ × (in CI chondrites in the solar system, theBe/Fe atomic ratio is 7 . × − ; Lodders 2019). Indetail, elemental concentrations for the accreted parentbody material are extrapolated from the WD photo-spheric abundances by taking into account changes inelement ratios produced by diffusion out of the stellaratmosphere together with the flux of material accretingonto the surface of the WD. In general, three differentphases of accretion/diffusion are recognized for pollu-tion of WDs: a build-up phase, a steady-state phase,and a declining phase (e.g., Dupuis et al. 1992; Dupuiset al. 1993; Koester 2009). Differences in diffusive ve-locities will modify abundance ratios in the second twophases, imparting disparities between the relative ele-mental abundances in the accreted body and those inthe atmosphere of the WD. Generally, heavier elementssink faster than lighter elements, but there are some ex-ceptions.Here we use the model from Jura et al. (2009) for thetime-dependent mass of element z in the WD convectivelayer ( M CV , z ( t )) assuming that the mass of the debrisdisk feeding the surface of the star decays exponentiallyas settling through the convective layer proceeds. Thismodel simulates all three phases of accretion with time.The solution for the time-dependent mass of element z in the convective layer is M CV , z ( t ) = M oPB , z τ z τ disk − τ z (cid:104) e − t/τ disk − e − t/τ z (cid:105) , (1)where M oPB , z is the initial mass of z in the parent bodythat forms the circumstellar disk, τ disk is the e-foldingtime for the depleting disk mass of parent body mate-rial, and τ z is the e-folding time for diffusive settling ofelement z through the WD’s convective zone. We usethis model to explore the effects of elemental settlingthrough the WD envelope on calculated element ratiosas a function of time.Differential settling through the WD envelope maycause lighter elements to appear in excess, altering thegeochemical interpretation (e.g., Doyle et al. 2020). Inparticular, because Be is among the lightest metals dis-covered in a polluted WD, we require an evaluation ofwhether a high beryllium concentration in the atmo-sphere of the WD could be due simply to the higher ratesof gravity-driven settling for heavier elements, comparedto Be. In practice, we calculate element abundances rel-ative to Fe in the WD atmosphere, as a function of time.We assume a CI chondrite composition for the parentbody on a water-free basis, only including the oxygenthat was available to pair with the other rock-formingelements, including Be, in the parent body. As an ex-ample, if a CI chondrite accreted onto a WD similar toGALEX J2339-0424, we would expect to see Be/Fe ra-tios elevated to 500 times chondritic by ∼ ∼ ∼ ∼
80 times chondritic, respectively. The abundanceof Al is not constrained, but Mg and Si are observed notto be supra-chondritic in GALEX J2339-0424, showingthat preferential settling of heavier elements cannot ex-plain the high Be/Fe ratio in this WD, and that thedebris disk material feeding the WD must itself have el-evated Be abundances. Another possibility is that Beaccumulated over time from multiple accretion events.However, it is straightforward to show that if excess Bewas a residue of preferential settling of heavier elementsleft over from a parent body from an earlier accretionepisode, one should expect excesses in Al, Mg and Sirelative to Fe as well.One can calculate the composition of the accreted par-ent body as a function of the duration of the accretionevent, T acc , assuming a value for τ disk and an expo-nentially decaying debris disk. Solving Equation 1 for M oPB , z where t = T acc , yields M oPB , z ( T acc ) = M CV , z [ τ disk − τ z ] τ z (cid:2) e − T acc /τ disk − e − T acc /τ z (cid:3) . (2) Doyle et al. T acc (yr) ( z / F e ) PB / ( z / F e ) C I -3 ( z / F e ) PB / ( z / F e ) BSE ( z / F e ) PB / ( z / F e ) C r u s t -1 -3 -1 -3 -1 BeMgSiCrCaTiMnO abc
Figure 1.
Element/iron atomic ratios, z /Fe, for the parentbody accreted by GALEX 2339-0424, relative to z /Fe in CIchondrite, bulk silicate Earth and the Earth’s average con-tinental crust, as a function of the duration of the accretionevent, T acc , calculated using Equation 2 assuming τ disk =10 yr. We compare the calculated parent body elementalabundances accreted by GALEX 2339-0424 to CI chondrite(a, Lodders 2019), bulk silicate Earth (BSE) (b, McDonough2003), and the Earth’s continental crust (c, Rudnick & Gao2014), each having distinctive Be abundances relative to theother major elements. Note that the curves for Mg and Sioverlap in panel a. The best-fit composition for the parentbody accreting onto GALEX 2339-0424 is CI chondrite, withBe being anomalously high by two orders of magnitude. We calculate the mass of each element in the convectivezone, M CV , z , by using the mass of the convective layer,obtained from log( M CV /M WD ) in Klein et al. (2021),and converting number ratios, z/ He, to mass ratios. Forthe purposes of this work, in the first instance we assumethat τ disk = 10 yr. These inferred abundances can thenbe compared to hypothetical starting compositions.Figure 1 shows an example calculation for the par-ent body compositions assuming different durations, T acc , for the accretion event. We compare inferredabundances of z /Fe in GALEX J2339-0424, to z /Fe inCI chondrite, bulk silicate Earth and continental crust(Lodders 2019; McDonough 2003; Rudnick & Gao 2014).In these calculations we again calculate the parent bodyaccreted by GALEX J2339-0424 and the comparisonrocks on a water-free basis, excluding the excess oxy-gen in the WD that would have existed as water ice inthe parent body. Values of unity for the ordinate in Fig-ure 1 indicate a match between the calculated composi-tion of the parent body and the reference rock materialfor the accretion duration indicated on the abscissa ifuncertainties are well characterized. We conclude thatthe composition of the planetary materials are like CIchondrite, and that the Be abundance is simply anoma-lously high in GALEX J2339-0424. All the other ele-ments’ predicted abundances match those in the whitedwarf’s atmosphere to within a factor of 2 or less, espe-cially if the accretion has been ongoing for about 2 to3 Myr. This strongly suggests that the accreted bodywas a chondrite-like body similar to those in our solarsystem. This composition is consistent with the calcu-lated oxygen fugacity for the accreted body. Based onthe mole fraction of FeO we calculate an oxygen fugacityexpressed as the difference in log f O from that of theiron-w¨ustite reference, ∆IW, of − .
35, similar to thatof carbonaceous chondrites in general. The high con-centration of Be stands out as the anomaly in being ∼ cy exomoons evidenced by spallogenic nuclides in polluted white dwarfs T acc (yr)10 -2 χ ν -1 τ disk = 10 yrs τ disk = 10 yrs τ disk = yrs CrustBSECI Figure 2.
Reduced chi-squared, χ ν , for fits of the parentbody composition to average continental crust, bulk silicateEarth, and CI chondrite, as functions of the duration of theaccretion to WD GALEX 2339-0424, T acc . Variations in con-centrations in the atmosphere of the WD as functions of ac-cretion duration are obtained using Equation 2. Various diske-folding timescales, τ disk , are shown for comparison. Thefits at each timescale for accretion are obtained for the ma-jor rock-forming elements Mg, Si, Fe, and Ca and the minorelements Ti and Mn. The best fit is obtained for a CI chon-drite composition and timescales for accretion of between 2.4and 4.0 Myr, as indicated by the minima in the reduced chi-squared value relative to CI chondrite for different values forthe lifetime of the debris disk. The fits for both bulk silicateEarth and continental crust are sufficiently poor that thesecompositions can be excluded. although a reasonable match to the Be/Fe ratio can bemade, the other ratios fail to match to even the orderof magnitude level. Although unlikely to be major con-taminants, we also performed similar calculations usingaccretion of the Be-rich mineral beryl (Be Al Si O ,e.g., aquamarine or emeralds) and other Be-rich min-erals or rocks (e.g., pegmatites). These also failed tomatch the composition of the white dwarf atmospherenearly as well as CI chondrite material.This chondrite-like parent body was water ice-rich.Three-quarters of the oxygen comprising the parentbody accreted by GALEX J2339-0424 was in excess ofthat required to form the oxides of the rock-forming el-ements. The excess oxygen was presumably accretedas water ice. Therefore, the parent body that accretedonto GALEX J2339-0424 was approximately 85% waterby volume.2.2. Duration of Accretion and Mass of the ParentBody
Under the hypothesis that the composition of the par-ent body is like that of a CI chondrite, except for theconcentration of Be, we can estimate the timescale for accretion and settling onto GALEX J2339-0424. We dothis by searching for the best fit between the parentbody element ratios and CI chondrite element ratios, asa function of the duration of accretion and settling. Wesearch for the value of T acc that yields a minimum inthe reduced chi-squared statistic, χ ν , to assess the mostlikely timescale for accretion and settling for the parentbody accreting onto GALEX J2339-0424. In our anal-ysis we make use of the random errors, σ spread , listedin Table 1, and exclude the correlated systematic errorsassociated with the effective temperature and gravity ofthe host WD; a more detailed error analysis is outlinedin Klein et al. (2021). In general, shorter timescales arebetter fits than much longer timescales, and we find theminimum in the reduced chi-squared statistic occurs foran accretion time of ≈ . τ disk = 10 yr isassumed and the debris disk decays exponentially (Fig-ure 2). Adopting this timescale, T acc , the inferred massfor the parent body accreted by GALEX J2339-0424 is4 × g, or ∼ ∼ × . If we instead assume τ disk = 10 or 10 yr, theminimum value of χ ν occurs for accretion durations of ≈ . . χ ν valueis <
1, suggesting an over-estimation of uncertainties inthe elemental ratios, but also indicating the goodness ofthe fit to a CI chondrite composition. For comparison,we also show χ ν for bulk silicate Earth and continentalcrust (Figure 2). The high χ ν values underscore thatthese compositions are not adequate matches to the par-ent body accreted by GALEX J2339-0424. The volumefraction of water obtained for the parent body from thebest-fit is approximately 85%, similar to the value ob-tained from the uncorrected data.The dependence of the derived accretion duration onthe assumed value of τ disk is shown in Figure 3. Assum-ing that 10 to 10 years spans the likely values for thee-folding time for the debris disk, we conclude that theaccretion event that added the rock-forming elementsto GALEX J2339-0424 lasted for 2 to 4 Myr, and sothe mass of the accreted parent body was 3 × to1 × g. Assumed durations for accretion less than 2.5Myr would decrease the estimated mass of the parentbody. SOURCE OF BERYLLIUM EXCESS3.1.
Constraints on the Radiation Environment
The excess Be observed in this polluted WD is al-most certainly due to spallation of heavier nuclei (inparticular, O) in rock or ice since it cannot be explainedby differential settling in the atmosphere of the WDnor by geochemical processes. Additionally, winds from
Doyle et al. τ disk (yr) T a cc ( M y r) Figure 3.
Relationship between the optimal accretion du-ration, T acc , as indicated by the minima in χ ν versus T acc in Figure 2, and the assumed debris disk e-folding timescale, τ disk . the WD itself would only be efficacious if the star wererapidly rotating, or another mechanism such as a mag-netic field were available to capture protons. GALEXJ2339-0424 is neither magnetic nor rapidly rotating. Inorder to determine the radiation environment in whichthe accreted parent body formed, we require an environ-ment that can produce the observed Be/O number ratioof approximately 10 − . This ratio is relatively insensi-tive to the details of the settling history (e.g., Figure1).In order to estimate the proton fluence required to ex-plain the observed Be/O ratio, we consider a first orderrate equation for the spallation production of Be: dn Be dt = kn p n O (3)= σf p n O , where the product of the proton number density ( n p )and rate constant ( k ) is replaced by the cross-sectionfor the spallation reaction ( σ ) and the proton flux ( f p ).Assuming no initial Be at time zero, a reasonable ap-proximation given the magnitude of the excess in Beobserved, integration yields n Be n O = σf p ∆ t (4)= σF p . Here the proton fluence ( F p ) indicated by the Be/Onumber density ratio provides the constraint on theradiation environment. The cross section for Be pro-duction by the reaction O(p,X) Be is ∼ − cm (Moskalenko & Mashnik 2003) with a minimum requiredenergy of about 10 MeV. The proton fluence required toobtain the observed Be/O atomic ratio in the accretedmaterial is therefore F p ∼ − − cm ∼ cm − . (5)The cross sections for Li and B production are compara-ble to the cross section for production of Be, and wouldyield similar Li/O and B/O ratios.Endeavors to explain the origin of the short-livedradioisotope Be in calcium-aluminum-rich inclusions(CAIs) formed in the early solar system (e.g., McKee-gan et al. 2000) have given rise to a significant litera-ture on Be production by spallation. The findings ofthese studies provide useful constraints on various as-trophysical environments for the formation of not only Be, but also as a corollary, for the formation of theisotopes of Li, Be, and B in general. These findings canbe summarized as referring to three distinctive environ-ments and/or processes for the formation of spallogeniclight nuclides. These include production of Be atomsin star-forming molecular clouds by spallation by GCRsaccelerated by core-collapse supernovae (CCSNe) (De-sch et al. 2004; Tatischeff et al. 2014), enrichment froma single low-mass CCSN adjacent a region of star for-mation (Banerjee et al. 2016), or irradiation of the inneredge of the protoplanetary disk by stellar energetic par-ticles (SEPs) from the young star (Gounelle et al. 2001,2006; Jacquet 2019). In the case of CAIs in the early so-lar system, precise isotopic ratios, including Be/ Be,are brought to bear in order to evaluate the efficacy andplausibility of these various suggested environments forthe spallation reactions. In the case of a polluted WD,we do not have access to isotope-specific data. There-fore, we make use of the fluence indicated by Equation 5as the primary arbiter for the environment that formedthe observed excess in Be (and by inference, Li and Bas well).The flux of ambient Galactic cosmic rays (GCRs) withsufficient energy ( ∼
10 MeV/nucleon) to induce spalla-tion reactions to form Be in the solar neighborhood is ∼ − s − (e.g., Tatischeff et al. 2014).To reach a fluence of 10 cm − that flux would have toact for 10 to 10 years, an impossibly long timescale.A larger flux of protons is required. Core-collapse su-pernovae are one exogenous source of high proton flux.The energy fluence ( F E ) required for Be production rel-ative to oxygen is obtained from the product of the 10MeV minimum energy per particle and the proton flu-ence, yielding 10 erg cm − . Based on the typical non- cy exomoons evidenced by spallogenic nuclides in polluted white dwarfs erg, we can write theenergy fluence due to all particles, and light, as F E = 3 × (cid:16) η . (cid:17) (cid:18) E SN erg (cid:19) (cid:18) r1 pc (cid:19) − erg cm − , (6)where η is the fraction of the SN energy carried by pro-tons that produce Be, which we have arbitrarily scaledto 0.1. Therefore, if 10% of the total energy of the SNremnant went towards the production of Be (similar tothe fraction of kinetic energy converted to escaping ac-celerated particles, Tatischeff et al. 2014), the energyfluence necessary to produce the observed Be/O ratiowould require the SN source to be 0.025 pc from theplanetary system. Besides being exceptionally improba-ble, at these distances, the system is unlikely to survivethe CCSN event (Portegies Zwart et al. 2018).A similar argument applies for the potential produc-tion of spallogenic nuclides as a result of winds fromWolf-Rayet stars (WR) in massive star-forming regionslike Orion (e.g. Ramaty & Kozlovsky 1998; Majmudar1999; Kozlovsky et al. 1997). In this case, energetic Cand O comprising the WR winds experience spallationupon striking protons in the ISM or the protoplanetarydisk (Kozlovsky et al. 1997; Prantzos 2012). We canassess the likelihood that this reverse process is impor-tant for the formation of Be by examining the averageenergy per O and C emitted. This energy is obtained us-ing E winds ( m avg /M C+O ) where E winds is the total energyreleased by the WR winds integrated over the lifetimeof the WR phase, m avg is the weighted mean mass of C and O nuclides (g/atom), and M C+O is the massof C and O released (g). For a typical WR lifespan(through the WC or WO phase) of ∼ × yr, anda maximum wind power of 10 erg s − (e.g. Prajapatiet al. 2019), one obtains E winds ∼ × erg, com-parable to E SN . Mass loss rates for WR stars are 10 − M (cid:12) yr − (Crowther 2007) and with the total fraction of C + O being on the order of 0 .
65 (e.g. Sander et al.2020; Tramper et al. 2013), the mass of C and O re-leased is about 3 . M (cid:12) . Since C/O is (cid:29) m avg ∼
12. Using these values we find that the energyper C and O nuclei for the WR winds is ∼ × yr, weobtain ∼
10 MeV per C and O nuclide. As no additionalefficiency or dilution factors have been included, this re-sult is something of a maximum, and we take this asindication that WR winds are only marginally capable,at best, of producing the fluence of >
10 MeV C and Onuclei required to generate significant excesses in Li, Beand B by spallation reactions. Accumulations of Li, Be, and B produced bylow-mass CCSNe by neutrino-driven reactions like C( ν, ν (cid:48) pp) Be are also feasible. However, the Be/ O production ratio for the low-mass (12 M (cid:12) )CCSN progenitor advocated by Banerjee et al. (2016) is4 × − . Because the Be/O ratio is lower for larger CC-SNe (Banerjee et al. 2016), this Be/O low-mass CCSNproduction ratio represents a maximum. This is alreadyorders of magnitude lower than the Be/O ∼ × − observed in GALEX J2339-0424. Furthermore, this in-jected supernova material would be diluted with oxygenin the planetary system. The abundances of short-livedradionuclides like Al in the solar nebula suggest dilu-tion factors of 4 to 5 orders of magnitude. The massof Be produced by this mechanism is far too small incomparison to oxygen to account for the observation inGALEX J2339-0424.In contrast to these exogenous sources, the fluenceof energetic protons emanating from a protostar in itsfirst ∼
10 Myr, during the lifetime of its surroundingprotoplanetary disk, far exceeds those of normal GCRsintegrated over the 10 Gyr age of the Galaxy; energeticproton fluxes from young stars at 1 au are about 10 times the GCR fluxes. From Gounelle et al. (2001) wecan estimate the fluence of SEPs with energies > F p = L p L X L X L star L star π r ∆ t, (7)where L p /L X is the proton luminosity ( L p ) scaled toX-ray values ( L X ), which at the peak of a G-star spec-trum ( ∼
10 MeV) is 0.09 (Lee et al. 1998). For G stars, L X ∼ × erg s − in the first 10 Myr of the stel-lar lifetime (Feigelson 1982). Therefore, a young solar-mass star would have a proton luminosity at 10 MeVof L p = 5 × erg s − . The progenitor main se-quence star for GALEX J2339-0424 was likely ∼ (cid:12) (Cummings et al. 2018), such that L star ∼ L (cid:12) (1 L (cid:12) = 3 . × erg s − ). Using 10 MeV as the ki-netic energy of the protons (1 . × − erg), scaling fora 1.5 M (cid:12) star, and adjusting the flux of protons for aspherical geometry at a distance from the central star of r ≈ f p , is ∼ × protonscm − s − . Assuming irradiation of the protoplanetarydisk lasts approximately 5 Myr, the fluence, F p , is then ∼ × protons cm − . Therefore, stellar winds earlyin the history of the planetary system are in principle afeasible source of high-energy protons with the fluencerequired by the Be/O ratio observed in this pollutedWD.However, the energy loss of protons due to ionizationof hydrogen severely limits Be production in the pres- Doyle et al.
Radiation belt
Energetic protons
Moon
Stellar wind
Moonlet O (p,X) Be Figure 4.
Schematic diagram depicting the proposed environment for formation of ices enriched in spallogenic nuclides. Thesource of the trapped magnetospheric particles is external, mainly from stellar winds. Once trapped, high-energy protons mirroralong magnetic field lines until they interact with icy material in the ring by the reaction O(p,X) Be. The mass of the ringsis transferred back and forth from fine particles to moonlets, until eventually icy ring material accretes around a rocky core anda moon is formed at the outer edge of the disk that includes the product Be (Cuzzi et al. 2009; Charnoz et al. 2009, 2011). ence of a protoplanetary gas. The stopping density for10 MeV protons in hydrogen gas is on the order of 70 gcm − (Clayton & Jin 1995). For typical inner-disk mid-plane mass densities of 10 − g cm − the stopping dis-tance for the relevant incident protons is approximately70 g cm − / − g cm − = 7 × cm, or 0.05 au. Thislimits the region of sufficient irradiation to within 0.05au into the inner edge of the disk. Such a localized envi-ronment for rock formation makes this scenario unlikely,especially in view of multiple instances of accretion ofBe-rich rocky bodies.3.2. Spallation in the Radiation Belts of Giant Planetsand Brown Dwarfs
Based on the discussion above, the observed excess Befound in GALEX J2339-0424 appears to require that theaccreted parent body formed in a local region of unusu-ally high proton flux that was largely free of hydrogengas. Radiation belts around giant planets satisfy theseconditions.Charged particles (mostly protons and electrons) fromthe solar wind can become trapped and forced to gyratearound the magnetic field lines of a giant planet, even- tually mirroring back and forth between the magneticpoles and filling the planet’s magnetosphere with ener-getic particles (e.g., Van Allen et al. 1980). On Earth,the magnetosphere traps solar wind particles, preventingthem from reaching the atmosphere, except when a con-traction of the magnetic field lines causes the particles toprecipitate in the atmosphere and form aurorae. Simi-larly, Jupiter and Saturn have radiation belts of trappedenergetic particles mirroring from pole to pole that havebeen recorded by spacecraft (e.g., Bolton et al. 2007;Cooper et al. 2018), as well as aurorae (e.g., Nichols et al.2014, 2017). In general, the rings of the giant planets,including Saturn, lie within the magnetospheres of thehost planet and are subject to irradiation by energeticparticles in these radiation belts. The irradiation of iceparticles in a giant planet’s rings is depicted in Figure 4.In order to assess the plausibility of this environmentfor explaining the Be excess observed in GALEX J2339-0424, we evaluate irradiation timescales required by thedata using Equation 4, but modified to include the frac-tion of oxygen present as ice in the rings that will besubject to irradiation. The stopping power of waterice is ≈
40 to 10 MeV / (g cm − ) for energetic protons cy exomoons evidenced by spallogenic nuclides in polluted white dwarfs stop of 0 .
25 g cm − to10 g cm − , respectively. The corresponding stoppinglengths, based on the density of water ice, are 0.27 cmand 11 cm, respectively.The mass of Saturn’s rings of ≈ . × g (Iesset al. 2019) and the area of the rings of ≈ × cm (Charnoz et al. 2009) suggest that the water ice columndensity in the rings, Σ rings , is of order ∼
30 g cm − .This is about 3 times the maximum stopping distancefor the energetic protons, suggesting that protons areefficiently stopped by the ring ices. Before these parti-cles are stopped, they have the opportunity to spall Oand create Be nuclei. The ratio Σ stop / Σ rings is a dilutionfactor for the production of Be relative to oxygen whereΣ stop / Σ rings ≤
1. We modify Equation 4 to include thisdilution factor: n Be n O = σf p ∆ t Σ stop Σ rings , Σ stop / Σ rings ≤ . (8)We note that the fraction of energetic protons by reac-tions that form Be nuclei is (Σ stop / m p ) σ where m p is the mass of a nucleon. This fractional factor ξ is ≈ × − to 3 × − for protons with energies of 10MeV and 100 MeV, respectively. We assume this frac-tion ξ of protons that spall ices to form Be in the ringsis a robust property of the system; even the smaller par-ticles in Saturn’s rings are cm to meters in size (Cuzziet al. 2009), comparable to, or a few times larger than,the 0.25 to 10 cm stopping distances of 10 MeV to 100MeV protons in water ice.The present-day flux of MeV protons in Saturn’s mag-netosphere is measured to be 6 × cm − s − (Koll-mann et al. 2015). For Σ stop / Σ rings = 1 /
3, Equation 8shows that the energetic proton flux in the Saturnianradiation field, f p , corresponds to an implausibly longtimescale of 2 × yr in order to produce the observedatomic Be/O ratio of 10 − in the parent body accretedby GALEX J2339-0424. The MeV proton flux in theradiation belt of Jupiter is higher, with a value of about10 cm − s − (Sawyer & Vette 1976). This flux corre-sponds to a radiation timescale of 1 × years. Esti-mates for the residence time of ices in Saturn’s rings areon the order of 10 to 10 years (Charnoz et al. 2009),suggesting that a Jovian-like radiation flux is a plausiblesource for the irradiation of ices comprising the parentbody accreted by GALEX J2339-0424.The energetic proton flux in Equation 8 depends onthe stellar wind intensity of the host star at the locationof the planet, the efficiency with which the planet trapsthe particles, and the sink terms for protons. Trapping efficiency depends foremost on the magnetic field, whichin turn depends on the mass of the planet, its rotationrate, and the conductivity of its interior. The rings area significant sink for the protons, but not the principaldetermining factor for f p . The mass of Saturn’s ringsis ∼ times that of Jupiter’s rings while the Satur-nian radiation belt MeV proton flux is about 10 − thatof Jupiter. The latter scales more closely with the ∼ < yr) protostar could easily developthe Be/O ratio of 10 − in ∼
10 Myr if they were ir-radiated for ∼ yr within the planet’s magneto-sphere. According to parameterizations by Sterenborget al. (2011), the X-ray luminosity of the Sun scales as t − . , and the mass flux in the solar wind scales as t − . , where t is the time since the Sun formed. In itsfirst tens of Myr, the solar wind easily could have been ∼ times stronger than today, and the X-ray luminos-ity and flux of energetic protons could have been ∼ times greater than today. A youthful system enhancesthe likelihood for the proton fluence indicated by theobserved excess in Be, although it is not required.Given that ices in the ring system within a giantplanet’s magnetosphere can develop a high Be/O ratio,we next address whether these ices could coalesce intoa moon comparable in mass to the roughly 4 × gparent body accreted by GALEX J2339-0424. Such abody would be greater in mass than the Saturnian icymoons Mimas and Enceladus by factors of 10 and 4, re-spectively, but lower in mass than Tethys, Dione, andRhea, by factors of 1.5, 3, and 6, respectively; the parentbody accreted by the WD is comparable in mass to theicy Saturnian satellites. Moreover, the density of the ac-creted body was ≈ . − based on the fractions ofCI-like rock and water ice indicated by the oxygen bud-get. This density is comparable to the average densi-ties of these icy moons (Mimas, 1 .
15 g cm − ; Enceladus,1 .
61 g cm − ; Tethys, 0 .
98 g cm − ; Dione, 1 .
48 g cm − ;Rhea, 1 .
24 g cm − ).The origins of the Saturnian satellites are unclear, andmany may be primordial, but the innermost satellitesare commonly hypothesized to have formed from therings themselves. Previous models have suggested that0 Doyle et al.
Saturn’s innermost, icy, moons formed as the rings vis-cously spread beyond the Roche limit, allowing the oth-erwise small (cm- to m-sized: Cuzzi et al. (2009)) par-ticles to coalesce into a medium-sized moon (Charnozet al. 2009; Canup 2010; Charnoz et al. 2010, 2011). In-deed, modeling of the coupled tidal effects on orbital pa-rameters and geophysical properties, by Neveu & Rho-den (2019), demonstrates that Mimas is almost certainlyformed in the last 0.1 - 1 Gyr, presumably from the rings.These authors constrain the ages of the other moons tobe much older, but given their common ice-rich composi-tions, it seems plausible that the other inner moons alsoformed from the rings, but much earlier. The model ofCharnoz et al. (2011) predicts that moons form steadilyover timescales from ∼ yr to ∼ yr, and formationtimescales of ∼ years is reasonable.We conclude that a mid-sized Saturnian-like icy moonhas the right mass and composition to match the par-ent body accreted by GALEX J2339-0424, and that thisbody very plausibly could have formed with a high Be/Oratio due to the irradiation of the ices that comprisedthe moon’s progenitor ring material by magnetosphericMeV protons (Figure 4). This result is consistent withthe prediction that icy exomoons liberated from theirhost planets are a likely source of WD pollution (Payneet al. 2016).Saturn provides a useful analog for the environment inwhich the body accreted by GALEX J2339-0424 formed.There are other analogs, however. As described by Ken-worthy & Mamajek (2015), the 16 Myr-old, 0 . M (cid:12) star1SWASP J1407.93-394542.6 (“J1407”) is orbited by abrown dwarf (BD) companion with an immense ringsystem, with a mass of ∼ M ⊕ and extending out toa radius of 0.6 au. The surface density of the rings istherefore ≈
25 g cm − , remarkably similar to that of Sat-urn’s rings.The presence of a large gap in the rings strongly sug-gests that a moon has already formed within these rings.The most probable mass of the BD companion, J1407b,is 13 to 26 Jupiter masses. It is unknown whetherJ1407b has an extensive magnetic field, but many BDsare magnetically active, with radio flares and aurorae(Berger et al. 2001; Hallinan et al. 2007). If J1407b hasa magnetosphere like Jupiter’s, it would extend out to ∼ × km, irradiating icy particles within it. Alter-natively, the ices outside the magnetosphere would bedirectly irradiated by energetic particles emitted by thecentral star. Given the age of J1407, the flux of ener-getic protons would be about 2 × times that fromthe Sun. Since J1407b orbits at about 3.9 au from itshost star, the proton flux would be ∼ cm − s − , andBe/O ratios ∼ . × − would be possible after irra- diation for ∼ yr. We predict that rock or ices inthe rings of J1407b have already acquired considerableamounts of spallogenic Li, Be, and B. CONCLUSIONSGALEX J2339-0424 is a WD polluted by accretion of aparent body with inferred abundances of most elementsconforming closely to a CI chondrite-like composition,but with a remarkable excess of Be (2 orders of mag-nitude more abundant than in a CI chondrite) and aconsiderable complement of water ice. We consider andrule out chemical fractionation processes as the causeof this enhancement. Based on an analysis of this WDas an archetypal example, we find that excesses in thespallation products Li, Be, and B in the parent bodyof rocky/icy debris accreted by a polluted white dwarfare most likely a signature of accretion of an icy exo-moon formed around a giant planet. Other potentialsites of spallation lack the fluence required to producethe observed excesses.The degree of enhancement of spallation products inan icy exomoon will depend on the flux of stellar ener-getic particles and the trapping efficiency of the planet’smagnetosphere. The mid-sized moons of Saturn areclose analogs to the inferred properties of the parentbody polluting GALEX J2339-0424. The masses anddensities of the Saturnian mid-sized icy moons are com-parable to those determined for the icy parent body ac-creted by the WD. A corollary of this study is that wepredict that at least some of the mid-sized icy moonsof Saturn (e.g., Mimas) should be enriched in Li, Be,and B. Additionally, the rings around the brown dwarfJ1407b also would experience intense irradiation, andthis system may also serve as an analog for how exo-moons could form with elevated Be/O ratios.Ejection of icy exomoons (like Saturn’s mid-sizedmoons) from giant exoplanets is considered a likelymeans of polluting WDs (Payne et al. 2016) after thecentral star evolves to a white dwarf. In the absence ofviable alternative explanations, supra-chondritic Be/Oratios in polluted WDs may be a signpost of this pro-cess.We focus on Be in this work, but we also expect to seeWDs with overabundances of Li and/or B produced bythe same processes. The detection of each of these ele-ments depends on factors related to the effective temper-ature of the WD, T eff , and the resolution and wavelengthrange of the observations. 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