Distribution of Europium in The Milky Way Disk; Its Connection to Planetary Habitability and The Source of The R-Process

The metallicity dependence is representative of an astrophysical bias consequence of stellar evolution. Colloquially, metallicity refers to [Fe/H], a well established stellar evolutionary probe. However, in this study we have elected to use an $\alpha$ element based metallicity: [$\alpha$/H]. This is motivated by chemical differentiation within the stellar neighborhood in the high-$\alpha$ and low-$\alpha$ groups (correlated with the thick and thin disk of the MW). High-$\alpha$ population stars have systematically larger [Eu/H] abundances than the low-$\alpha$ population stars, making the correlation between [Fe/H] and [Eu/H] distinct for each group. Instead of conducting analysis on each population separately we fit metallicity as [$\alpha$/H]. [Fe/H] and [$\alpha$/H] are both well connected to stellar evolution; however, in this context [$\alpha$/H] serves the distinct advantage of coupling metallicity to the galactic $\alpha$ population while still being a robust probe for stellar evolution.

Our $\alpha$ metallicity term is defined as the average of silicon (Si), magnesium (Mg), titanium (Ti), and calcium (Ca). Si and Mg are the typical elements used to describe $\alpha$ element abundance, while Ti and Ca are incorporated to reduce the measurement uncertainty through averaging of all four elements which track each other closely in the stellar neighborhood.

The bias in effective temperature ($T_{\rm eff}$) is not reflective of any astrophysical process; in principle $T_{\rm eff}$ should not chemically have an effect on [Eu/H] abundance. However, we find in the sample from DM that cool stars have systematically lower [Eu/H] than hot stars, while in the sample from BB there is an anti-correlation between $T_{\rm eff}$ and [Eu/H]. This bias is likely representative of a methodological bias introduced in elemental parameters for abundance measurement in each study.

The identified biases inflate the star-to-star dispersion in [Eu/H] and are removed via regression of a linear contour fit simultaneously to [$\alpha$/H] and $T_{\rm eff}$. This is done using the IRAF task Surfit, under a reduced $\chi$-squared test. The best fit coefficients are shown in Table 1.

An expression for detrended [Eu/H] as a function of metallicity and temperature is created by subtracting the contour fit from [Eu/H] for each sample, this function represents the [Eu/H] independent of metallicity and $T_{\rm eff}$. The standard deviation about detrended [Eu/H], is 0.071 dex and 0.081 dex in samples by DM, and BB, respectively.

While the two samples from DM, and BB represent some of the highest quality chemical measurements available on the stellar neighborhood, there are still inconsistencies in measured [Eu/H] between stars in each sample. In an attempt to reduce these inconsistencies, we create a cross-matched sample of the 68 stars that appear in common between these surveys and average their detrended [Eu/H] expressions. Under the cross matched sample the standard deviation about detrended [Eu/H] is reduced to 0.057 dex and 0.065 dex for DM, and BB, respectively.

Cross matching our samples provides an opportunity to reduce the uncertainty associated with detrended [Eu/H] even further. If the detrended [Eu/H] dispersion is contributed entirely by Poisson noise, we would expect the dispersion about the averaged detredned [Eu/H] to reduce by a factor of $1/\sqrt{2}$. However we find this is not the case; The average detrended [Eu/H] scatter is only 0.047 dex. This would imply there is a secondary factor dominating the detrended [Eu/H] spread. We refer to this term as the intrinsic dispersion, which can be solved for:

To begin, the total error budget is assumed to be the sum of three terms: uncertainty contributed by Poisson noise, uncertainty contributed by systematic biases in the data, and the independent intrinsic term. Thus the error budget on detrended [Eu/H] for both sample from DM and BB can be written as Equation 1:

In the creation of the detrended [Eu/H] expression, all significant systematic biases (metallicity and temperature) have been removed. Therefore we assume the uncertainty contributed by symmetric biases is effectively removed. The total error budget is then written as the sum of only the Possion and intrinsic terms. When combining data samples, the resulting uncertainty associated with the average detrended [Eu/H] can be represented as the average of the two total error budgets from each sample. The intrinsic term should be constant across both samples and thus can be combined.

Which is then rearranged to solve for the constant intrinsic uncertainty in equation 3:

This results in an intrinsic uncertainly of $\sigma_{\rm Intrinsic}$ = 0.025 dex. We believe this to be the intrinsic star-to-star variation in [Eu/H] in the stellar neighborhood of F, G and K type stars in the MW disk independent of metallicity and temperature biases. The identified dispersion is corroborated by the solar twins analysis by Bedell et al. (2018) and Spina et al. (2018) discussed in Section 7.1. outliers in the samples are discussed in Appendix  7.2.

Decay of radioactive elements in the mantles of rocky planets moderates geodynamic processes, such as a protective planetary magnetic dynamo - an excessive amount of radioactive heating can disrupt core convection responsible for maintaining a magnetic dynamo (Nimmo et al., 2020). While the effect of magnetic dynamo failure on atmospheric loss is still debated (e.g., Gunell et al., 2018), it is generally thought that its persistence is important for preventing loss of ozone, water and protecting planetary surfaces from energetic charged particle bombardment (e.g., Lundin et al., 2007).

Sustained periods of dynamo failure for just tens of Myr could lead to significant atmospheric loss (particularly if the stellar EUV flux is enhanced) (Lichtenegger et al., 2010). Once the mantle cools, magnetic dynamos can resume after failure as core convection reinstates (Nimmo et al., 2020). However atmospheric re-establishment of a planets $H_{2}O$ and nitrogen inventory may be more difficult.

As we have discussed, Th and U are the primary contributors to radiogenic heating at late times. The abundance of these elements is commonly estimated using the surrogate element Eu. The Si content can be estimated by $\alpha$ element abundance being a part of the $\alpha$ group elements described in Section 2.1 but with the advantage of reducing the Poisson noise in the associated uncertainties of Si, Mg, Ti, and Ca through averaging.

The 1D convective model described in Nimmo et al. (2020) is adopted to predict at what [Eu/$\alpha$] ratio a dyanmo failure occurs. For an Earth-like planet, of similar composition, metallicity, and size as Earth, this model exhibits a dynamo failure of $100$ Myr at [Eu/$\alpha$]=0.08 (see Figure 1). This is a conservative estimate for a critical period of dynamo collapse in which significant time has passed so that substantial atmospheric loss may occur - preventing or delaying the emergence of a hospitable surface environment.

The scatter of [Eu/$\alpha$] independent of temperature bias as a function of [$\alpha$/H] is presented in Figure 2. Also shown is the critical value of [Eu/$\alpha$]=0.08, highlighted by the red dashed line, where an extended dynamo failure of $\geq 100$ Myr occurs. Assuming that Eu and $\alpha$ element abundances correspond between stars and attendant planets, stars with sub-solar $\alpha$-metallicity [$\alpha$/H]$<-0.4$ are most likely to host Earth-like planets that experience some degree of extended dynamo failure. This should be contrasted with the range of planet-forming metallicities, which is estimated to be between -1.5 $<[\alpha/H]<$0.6 in the MW disk (e.g., Johnson & Li, 2012; Ercolano & Clarke, 2010; Behroozi & Peeples, 2015; Boley et al., 2024). It is thus only near-solar metallicity stars that have terrestrial planet compositions supportive of a sustained magnetic dynamo.

It is important to note that this 1D model has only been configured for Earth-like planets, with the same radii, mass, and composition as the terrestrial value (e.g., Seager et al., 2007; Mordasini et al., 2012; Alibert, 2014). The mass-radius scaling relation for rocky planets has recently been revised in Otegi et al. (2020) and Müller et al. (2024). Furthermore, heat production is expected to decrease at a fixed radius with increasing [Fe/H] due to a larger core-to-mantle ratio O’Neill et al. (2020). It would be worth exploring in future work where a prospective “habitable metallicity zone” maps out in the radii and composition parameter space based on changing radiogenic fraction and [Fe/H] (e.g., Howard et al., 2012) using a more comprehensive model including a 2D or 3D assessment of core convection.

Understanding how Eu is distributed throughout the local stellar population may shed light on the source of r-process element production. The nucleosynthetic pathways and conditions for the production of r-process elements have been understood since Burbidge et al. (1957) and Cameron (1957), but the specific site(s) responsible for the modern day galactic disk enrichment of r-process elements is an area of active study (Arcones & Thielemann, 2023). The primary formation sites of r-process elements are believed to be either core collapse supernovae (e.g., Woosley et al., 1994) or by NS-NS mergers (e.g., Lattimer & Schramm, 1974). On the other hand, $\alpha$ elements (including O, Mg, Si, Ca, and Ti) are primarily produced in CC-SNe (Woosley & Weaver, 1995). Thus by studying the distribution of r-process elements with respect to $\alpha$ elements the production of r-process elements can be correlated with rate of CC-SNe.

Here we focus on $\alpha$, Fe, and Eu production at higher metallicities in the MW in order to derive meaningful constraints on the r-process production sites. If galactic r-process injection is dominated by CC-SNe, Eu and $\alpha$ will be co-produced. This predicts [Eu/$\alpha$] to remain relatively constant with increasing [$\alpha$/H] metallicity; in this case, the constant ratio should be representative of the IMF-weighted yield of the ejecta (Macias & Ramirez-Ruiz, 2018; Kolborg et al., 2023). However, as shown in Figure 2, we find a robust anti-correlation between [Eu/$\alpha$] and [$\alpha$/H]. The anti-correlation is consistent with a metallicity dependent r-process in CC-SNe.

Alternatively, The gravitational wave discovery of GW170817 (Abbott et al., 2017) and ensuing kilonova SSS17a/AT2017gfo (e.g., Coulter et al., 2017), provided definitive evidence of NS-NS mergers being a viable source of r-process elements but the current galactic distribution of r-process cannot be explained assuming NS-NS mergers are the only significant source of the r-process throughout cosmic time (see e.g. Siegel, 2019; Chen et al., 2024, for a summary of relevant issues).

If the r-process occurs mainly in NS-NS mergers, the production of Eu is decoupled from $\alpha$ and Fe production (Sneden et al., 2008). The anti-correlation between [Eu/$\alpha$] and [$\alpha$/H] thus suggests that r-process injection from NS-NS mergers increases with time compared with $\alpha$-element production. This is expected with NS-NS mergers, as they naturally experience a time delay from neutron-star pair formation to merger, which combined with the star formation history, yields a sizable increase in the number of NS-NS mergers at high metallicities (e.g., Shen et al., 2015). Due to the restricted metallicities used in this sample, the relative rate is subject to change at earlier periods, but for [$\alpha$/H] between -0.7 and 0.5. The negative slope (Figure 2) suggests r-process injection by NS-NS mergers with a time delay consistent with models (e.g., Siegel, 2019).

A delay-time distribution $t^{-1}$ of NS-NS mergers predicts a flat [Eu/Fe] trend with [Fe/H] (e.g., Côté et al., 2019). However, this is not observed in the data (Figure 3(c)) and suggests that the delay-time distribution of NS-NS mergers differs from the $t^{-1}$ of type Ia supernovae (e.g., Simonetti et al., 2019), which controls Fe production and is thought to be set by the merger of white dwarf binaries (e.g., Toonen et al., 2012). As such, this naturally explains the [Eu/Fe] knee seen around [Fe/H]=-1 (e.g., Côté et al., 2019).

A caveat is noted when including Si, Ti and Ca in our $\alpha$ metallicity term. Si, Ti and Ca are fractionally produced by type Ia supernovae while Mg is exclusively produced in CC-SNe (Woosley & Weaver, 1995). A more “pure” $\alpha$ metallicity was tested using just [Mg/H], which we found to produce similar results but with a noisier dispersion.

The determined dispersion in detrended [Eu/H] of $\pm$ 0.025 dex is further corroborated by data from a solar twins analysis by Spina et al. (2018) and Bedell et al. (2018). This sample of 79 stars uses near solar parameters with temperature within $\pm$ 100 K in $T_{\rm eff}$, [Fe/H] within $\pm$ 0.1 dex and surface gravity within $\pm$ 0.1 dex in Log $g$ of the solar value. These restricted parameters combined with high S/N and high resolution contribute to exceptionally low quoted uncertainties on abundance measurements.

We repeat the same simultaneous contour-fit methodology described in Section 2.3 to create an expression for detrended [Eu/H] as a function of metalicity and temperature under the solar twins sample. We fit these two terms to [Eu/H] simultaneously in a linear surface-fit polynomial with an intercept of -1.534 $\pm$ 0.112 dex, metallicity slope of 0.789 $\pm$ 0.018, and temperature slope of 2.7434$\times 10^{-4}$ $\pm$ 1.944$\times 10^{-5}$ dex, with a reduced $\chi^{2}$=10.22 and standard deviation of 0.031. The reduced $\chi^{2}$ is notably high, consequence of exceptionally low quoted uncertainties in elemental abundance measurements.

In our earlier analysis we were able to cross match detrended [Eu/H] measurements in an effort to further reduce the dispersion. However, the sample from Spina et al. (2018) and Bedell et al. (2018) shares no stars in common with either DM or BB. Instead, tweaking the formalism described in Section 3.2 we can reduce the dispersion in detrended [Eu/H] further. Due to the exceptionally low uncertainty in [Eu/H], we claim that the error on [Eu/H] is solely the uncertainty contributed by Poisson noise. In this way, the dispersion of detrended [Eu/H] is given as:

Re-arranging this equation and assuming the error on [Eu/H] is entirely the Possion noise $\sigma_{\rm Possion}$ = 0.012 dex (using the mean of the error on [Eu/H]), the intrinsic dispersion is determined as $\sigma_{\rm intrinsic}$ = 0.029 dex.

Without a secondary analysis to compare against, we cannot reduce the dispersion any further. The intrinsic dispersion determined here is supportive of the dispersion calculated in Section 3.1. This suggests we are indeed approaching a star-to-star dispersion reflective of the actual stellar chemical environment in the local stellar neighborhood.

Within the samples used, a handful of outliers in [Eu/H] abundance have been identified. We consider an outlier as any star whose detrended [Eu/H] value is greater than 3 standard deviations (SD) from the mean. These stars are worth particular attention for two reasons, their unusual [Eu/H] abundance contributes to the inflation of the intrinsic dispersion significantly and secondly these stars may have unique chemical-evolutionary histories worth investigating.

Under the cross-matched sample as described in Section 3.1 there is one outlier. The cross-matched sample has a significantly smaller SD than in the full samples due to reduced uncertainties from averaging, stars that appear as outliers in the full samples do not reappear in the cross matched sample.

In the sample from DM, containing 570 stars with [Eu/H] abundance measurements, the standard deviation was found to be 0.071 (methodology described in 2.3). Under this standard deviation, 9 stars are measured with detrended [Eu/H] greater than 3 SD from the mean. These stars are listed in Table 2. Assuming the sample follows a normal Gaussian distribution, we would only expect 1-2 stars above 3 SD in a sample size of 577, this suggests the existence of at most 7 statistical outliers in detrended [Eu/H].

Using a similar analysis, in the sample from BB, containing 377 stars with valid [Eu/H] and [$\alpha$/H] abundance measurements, the standard deviation is found to be 0.081. Under this standard deviation, 3 stars are measured with detrended [Eu/H] of greater than 3 SD. These stars are listed in Table 2. Following a normal Gaussian distribution, we only expect 1 star above 3 SD in a sample size of 377, this suggests the existence of at most 2 statistical outliers in detrended [Eu/H].

In the cross-matched sample, HD11397 has a detrended [Eu/H] abundance of 0.150 dex pushing it out to 3.192 SDs from the mean trend; see Table 2 in bold. This star is likely to be real outlier as its unusual detrended [Eu/H] measurement is corroborated by both data sets.

No outliers were found in the sample from Spina et al. (2018) and Bedell et al. (2018). This may be owed to the small sample size and/or the exceptionally small quoted uncertainties.

These stars’ odd compositions may be a result of a particularly r-process rich birth cloud or another heavy element doping mechanism such as a binary-supernova pair. Further analysis is needed to determine the unique properties of the stars listed.