²⁶Al IN THE EARLY SOLAR SYSTEM: NOT SO UNUSUAL AFTER ALL

Concentrations of excess ²⁶Mg, the decay product of the short-lived radionuclide ²⁶Al (mean life = 1.03 Myr; Castillo-Rogez et al. 2009), show that the solar system formed with n(²⁶Al)/n(²⁷Al) = 5.2 × 10⁻⁵ (Jacobsen et al. 2008). Although there is evidence that there may have been deviations from this "canonical" ratio across the solar protoplanetary disk by as much as a factor of two (Larsen et al. 2011; Liu et al. 2012), the overall concentration of ²⁶Al in the solar disk was more than a factor of 10 greater than the current average value in the interstellar medium of 3.0 × 10⁻⁶ (Tang & Dauphas 2012). While some ²⁶Al may have been produced within the early solar system, most of it was not (Duprat & Tatischeff 2007; Desch et al. 2010); there must have been a significant external source of this short-lived nuclide. Commonly, the natal ²⁶Al is taken as a signature of a nearby supernova that may have triggered the collapse of the molecular cloud from which the Sun formed (Meyer & Clayton 2000; Gritschneder et al. 2012). Alternatively, winds from massive stars may have supplied the bulk of the ²⁶Al (Prantzos 2004; Gaidos et al. 2009; Gounelle & Meynet 2012).

A major consequence of large amounts of ²⁶Al in the early solar system was substantial internal heating of young planetesimals which therefore melted and subsequently experienced igneous differentiation. Iron meteorites are thought to be modern fragments of iron-rich cores formed during this era (McSween & Huss 2010). If other planetary systems formed with considerably less ²⁶Al, then their asteroids may not be differentiated. We can test this scenario by examining the elemental compositions of extrasolar minor planets.

Evidence is now compelling that some white dwarfs have accreted some of their own asteroids (Debes & Sigurdsson 2002; Jura 2003; Jura & Young 2014). In some instances, we have detected excess infrared emission from circumstellar disks composed of dust (Farihi et al. 2009; Xu & Jura 2012) where gas also is sometimes evident (Gaensicke et al. 2006). These disks lie within the tidal radius of the white dwarf and are understood to be the consequence of an asteroid having been shredded after its orbit was perturbed so it passed very close to the star (Debes & Sigurdsson 2002; Bonsor et al. 2011; Debes et al. 2012). Accretion from these disks supplies the orbited white dwarf's atmosphere with elements heavier than helium where they are normally not found because the gravitationally settling times are very short compared to the cooling age of the star. Estimates of the amount of accreted mass argue that we are witnessing the long-lived evolution of ancient asteroid belts (Zuckerman et al. 2010; Jura & Young 2014). In the most extreme case, the accreted parent body may have been as massive as Ceres (Dufour et al. 2012) which has a radius near 500 km. However, the required mass more typically implies parent bodies with radii near 200 km (Xu et al. 2013). Externally polluted white dwarfs provide a means for placing the solar concentration of ²⁶Al in context.

As a first approximation, extrasolar asteroids resemble bulk Earth being largely composed of oxygen, magnesium, silicon, and iron, and deficient in volatiles such as carbon and water (Klein et al. 2010; Jura 2006; Jura & Xu 2012) as expected in simple models for planet formation from a nebular disk. When eight or more polluting elements are detected, it is possible to tightly constrain the history and evolution of the parent body (Zuckerman et al. 2007; Xu et al. 2013). Recent studies of such richly polluted stars have shown abundance patterns that can be best explained if the accreted planetesimal evolved beyond simple condensation from the nebula where it formed. For example, NLTT 43806 is aluminum-rich as would be expected if the accreted planetesimal largely was composed of a crust (Zuckerman et al. 2011) while PG 0843+516 is iron rich which can be explained by the accretion of a core (Gaensicke et al. 2012). Xu et al. (2013) found that the abundance pattern of the object accreted onto GD 362 resembles that of a mesosiderite—a rare kind of meteorite that is best understood as a blend of core and crustal material (Scott et al. 2001).

Here, we first revisit the current sample of extrasolar planetesimals with well-measured abundances and reconfirm that igneous differentiation is widespread (Jura & Young 2014). We then present a model to explain this result. Finally, we consider our solar system from the perspective of extrasolar environments.

The evidence for igneous differentiation among extrasolar planetesimals can be presented in a variety of ways (Jura & Young 2014). Here, we display in Figure 1 the abundance ratios by number, n(Fe)/n(Al) versus n(Si)/n(Al), for all seven externally polluted white dwarf atmospheres where these three elements have been reported.³ We see that n(Fe)/n(Al) varies by more than a factor of 100, a much greater range than shown among main-sequence planet-hosting stars, solar system chondrites, and even n(Si)/n(Al) among these same polluted stars.

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The large range in n(Fe)/n(Al) among extrasolar planetesimals must be the result of some powerful cosmochemical process. One possibility is that unlike in the solar system, some extrasolar planetesimals were formed largely of refractory elements (Bond et al. 2010) resulting in low values of n(Fe)/n(Al) because Al is highly refractory. However, this scenario is not supported by available observations (Jura & Xu 2013), and cannot explain why some systems have relatively high values of n(Fe)/n(Al). Because there is no viable nebular model to explain the observed range in n(Fe)/n(Al), the abundance variations must have been produced within the planetesimals themselves.

Abundance patterns in extrasolar planetesimals reproduce those in familiar rocks. The lowest value of n(Fe)/n(Al) is comparable to the ratio in MORB (Mid Ocean Ridge Basalt), a characteristic crustal rock (Presnall & Hoover 1987). The highest value of n(Fe)/n(Al) exceeds that of dunite, a mantle rock, implying sampling of iron-rich core material (Hanghoj et al. 2010). Figure 1 shows that the range of n(Fe)/n(Al) among extrasolar asteroids is even greater than the difference found between bulk Moon (Warren 2005) and bulk Mercury (Brown & Elkins-Tanton 2009), two solar system objects which are understood as having a small and large iron core, respectively.

We understand the variety of elemental compositions among extrasolar planetesimals as the consequence of a familiar three-step process. First, planetesimals form within the disk; in this environment, volatiles such as water may be excluded. Second, differentiation results in iron being concentrated in the core and aluminum being concentrated in the crust. Third, collisions lead to stripping and blending of cores and crusts with a consequent dramatic variation in n(Fe)/n(Al) in the end-product planetesimals, blends of different portions of core, mantle, and crustal material.

As with solar system asteroids, the heat source for igneous differentiation of extrasolar planetesimals most likely was from radioactive decay of ²⁶Al (Ghosh & McSween 1998). Other possibilities do not seem viable. The gravitational potential energy released by forming a body of radius, R₀, and mass, M, can raise the temperature an amount, ΔT, given by

$$\begin{equation} {CM{\Delta }T}\;=\;\frac{3}{5}\,\frac{{GM}^{2}}{R_{0}}, \end{equation} \tag{ 1 }$$

where C is the specific heat (J kg⁻¹ K⁻¹) and G is the gravitational constant. For a typical object with R₀ ≈ 200 km and M ≈ 1.0 × 10²⁰ kg (Jura & Young 2014) and with C ≈ 1000 J kg⁻¹ s⁻¹ (Turcotte & Schubert 2002), then ΔT ≈ 20 K, much too small to be of importance. Although mutual collisions can produce local heating, it seems unlikely that most of the material is melted during the period of planetesimal growth by collisions (Davison et al. 2010). Within the average interstellar medium, ⁶⁰Fe/⁵⁶Fe = 2.8 × 10⁻⁷ (Tang & Dauphas 2012), and if this ratio prevails within star-forming regions, then heating from the radioactive decay of ⁶⁰Fe cannot be an important heating source within extrasolar planetesimals. It is possible that some stars form near supernovae that produce large amounts of ⁶⁰Fe (Vasileiadis et al. 2013), and in these environments newly formed planetesimals could be significantly heated by radioactive decay of this radionuclide. However, because by number there is more ²⁶Al than ⁶⁰Fe within the entire Galaxy (Tang & Dauphas 2012) and because ²⁶Al is readily produced within massive stars and then injected into the local molecular interstellar medium where new stars form (Gounelle & Meynet 2012), it is probable that the majority of young stellar disks are similar to our own solar system where radioactive decay of ²⁶Al was the dominant source of planetesimal heating.

The usual expression (Turcotte & Schubert 2002) governing the time (t) variation of internal temperature, T, as a function of radius, r, of a spherical rocky body is

$$\begin{equation} \frac{{\partial }T}{{\partial }t}\;\;=\;\frac{1}{r^{2}}\frac{{\partial }}{{\partial }r}\,\left(r^{2}\,{\kappa }\,\frac{{\partial }T}{{\partial }r}\right)\;+\;\frac{{\dot{Q}}(t)}{C(T)}, \end{equation} \tag{ 2 }$$

where κ (m² s⁻¹) is the thermal diffusivity and ${\dot{Q}}(t)$ (J kg⁻¹ s⁻¹) is the heating energy per unit mass per unit time. The typical timescale for the loss of internal heat is $R_{0}^{2}\,{\kappa }^{-1}$. For a 200 km radius object with a thermal diffusivity of 10⁻⁶ m² s⁻¹ (Turcotte & Schubert 2002), the outward diffusion of heat represented by the first term on the right-hand side of Equation (2) typically requires more than 1 Gyr and has a negligible effect on the body's central temperature during the era of heating from ²⁶Al. To compute the maximum internal temperature, T_Max, we integrate over a timescale much longer than the average decay time, t_R, and consider the total released energy, Q₀, defined as

$$\begin{equation} Q_{0}\;=\;{\int }_{0}^{\infty }{\dot{Q}}(t)\,dt \end{equation} \tag{ 3 }$$

from the decay of ²⁶Al. Consequently, if the planetesimal originates at temperature, T₀ (K), then

$$\begin{equation} {\int }^{T_{{\rm max}}}_{T_{0}}C(T)\,dT\;{\approx }\;f_{26}\,Q_{0}, \end{equation} \tag{ 4 }$$

where f₂₆ is the initial fraction of the mass of the planetesimal that is ²⁶Al.

We assume that igneous differentiation is only possible if the internal temperature exceeds the solidus temperature, T_solidus, (Turcotte & Schubert 2002) and then derive the minimum aluminum isotope ratio by number, n(²⁶Al)/n(²⁷Al), required to achieve this temperature. We assume that the extrasolar planetesimal will have formed at some time, t_form, after inheritance of ²⁶Al from the molecular cloud. Subsequently, no fresh ²⁶Al enters the star-forming cloud; instead, there is only radioactive decay with mean life, t_R. Validated by our detailed calculations not shown here, we take C to be constant and independent of temperature. If f_Al is the fraction of mass of the planetesimal which is aluminum, and if T₀ ≪ T_solidus, then

$$\begin{equation} \left(\frac{n(^{26}{\rm Al})}{n(^{27}{\rm Al})}\right)\;{\ge }\;\;\left(\frac{27}{26}\right)\,\left(\frac{T_{{\rm solidus}}\,C}{Q_{0}\,f_{{\rm Al}}}\right)\,e^{t_{{\rm form}}/t_{R}}. \end{equation} \tag{ 5 }$$

Using CV chondrites with their relatively high Al abundance, thus providing a minimum for Equation (5), we take f_Al = 0.0175 (Wasson & Kallemeyn 1988). We adopt T_solidus = 1500 K (Turcotte & Schubert 2002), and, for ²⁶Al, we take Q₀ = 1.2 × 10¹² J kg⁻¹ (Castillo-Rogez et al. 2009). We assume two contributions to t_form. First, there is free-fall gravitational collapse of a cloud core with an initial radius of 0.1 pc that requires ≈0.5 Myr (Hartmann 2009). Second, planetesimals must assemble within the disk which, by analogy with the solar system, probably takes ∼1 Myr (Zhou et al. 2013). Adding both terms, t_form = 1.5 Myr. Consequently, we compute from Equation (5) that in extrasolar environments where planetesimals internally melted, n(²⁶Al)/n(²⁷Al) ⩾ 3 × 10⁻⁵, approximately its value in the early solar system. This result is inexact. If, for example, we take f_Al = 0.0086 as found in CI chondrites (Wasson & Kallemeyn 1988), then the minimum values of n(²⁶Al)/n(²⁷Al) should be doubled.

As has been previously suggested qualitatively, a general enrichment of ²⁶Al in protoplanetary disks might occur if this radionuclide is not distributed evenly throughout the Milky Way but, instead, is confined to regions of star formation (Draine 2011). A plausible model to explain why ²⁶Al would be so concentrated is that this species is largely injected into the interstellar medium from rotating massive stars (Gaidos et al. 2009; Gounelle & Meynet 2012). These massive stars are so short-lived that they all reside near their birth sites within molecular clouds. Such a model can also explain why the solar system has a relatively high concentration of ²⁶Al and a relatively low concentration of ⁶⁰Fe (Tang & Dauphas 2012). However, winds from Wolf–Rayet stars might shred cloud cores and prevent the formation of planets (Boss & Keiser 2013). While some recent models for supernova ejecta into molecular clouds also predict that solar mass stars commonly form with elevated amounts of ²⁶Al (Pan et al. 2012; Vasileiadis et al. 2013), they do not naturally explain the solar system's simultaneously depressed value of ⁶⁰Fe/⁵⁶Fe.

In the entire Milky Way, the mass of hydrogen in H₂ is 8.4 × 10⁸ M_☉ (Draine 2011). The amount of interstellar ²⁶Al is measured from the intensity of the γ-ray line at 1.8 MeV that results from its radioactive decay. Including foreground emission, there is somewhere between 1.5 and 2.2 M_☉ of ²⁶Al within the Galaxy (Martin et al. 2009). If we assume the solar aluminum abundance of n(²⁷Al)/n(H) = 3.5 × 10⁻⁶ (Lodders 2003), and if all measured interstellar ²⁶Al is confined only to molecular clouds, then in these locations n(²⁶Al)/n(²⁷Al) ≈ 2.0–3.0 × 10⁻⁵, nearly the same as the minimum ratio we infer for the birth environment of extrasolar planetesimals. Consider not only the entire Milky Way but also observations of the Orion region, the nearest molecular cloud where large numbers of high-mass stars currently are being formed. Orion's γ-ray line emission is explained with 5.8 × 10⁻⁴ M_☉ of ²⁶Al (Voss et al. 2010) from a region where the total mass of H₂ is approximately 2 × 10⁵ M_☉ (Genzel & Stutzki 1989). The implied value of n(²⁶Al)/n(²⁷Al) in the Orion star-forming region is therefore 3 × 10⁻⁵, again substantially elevated over the average interstellar value. Remarkably, the apparent fraction of ²⁶Al within star-forming molecular clouds agrees with the value required to explain the widespread occurrence of differentiated extrasolar planetesimals. It follows that the solar system's initial complement of ²⁶Al was essentially normal.

We thank L. Yeung for suggesting a title for this manuscript. This work has been partly supported by the NSF.