Chemical Evolution of ²⁴⁴Pu in the Solar Vicinity and Its Implications for the Properties of r-process Production

Meteoritic abundances of short-lived radioactive r-nuclides are dominated by the nuclides ejected from the last r-process production event as long as the time interval between r-process events is much longer than the half-lives of the r-nuclides. ${}^{244}\mathrm{Pu}$, along with other r-nuclides such as ${}^{247}\mathrm{Cm}$ and ${}^{129}{\rm{I}}$, meets this condition. From this fact, we will deduce how much a single r-process event enriches the surrounding ISM with r-nuclides.

First, we deduce the mass fraction of ${}^{244}\mathrm{Pu}$ at the ESS. The number fraction of ²³⁵U relative to hydrogen at the ESS is estimated to be $6.37\times {10}^{-13}$ from meteorites, considering the radioactive decay (half-life: 4.47 Gyr) until the present over 4.56 Gyr (Lodders et al. 2009). Then, from the abundance of ²⁴⁴Pu relative to ²³⁵U (0.008) at the ESS (Turner et al. 2004, 2007) and a typical number density of hydrogen in the ISM (1 cm⁻³), the number density of ²⁴⁴Pu at the ESS is deduced to be $5.10\times {10}^{-15}$ cm⁻³ with a corresponding mass fraction of $8.90\times {10}^{-13}$.

The amount of ²⁴⁴Pu thus obtained includes small contributions from a few events before the last one. By removing these small contributions, we obtain how much a single r-process event polluted the ISM with ²⁴⁴Pu at the ESS. For this estimate, two timescales are required. One is the time interval ${t}_{\mathrm{LE}}$ between the last r-process event and solar system formation. The other is the mean time interval ${t}_{\mathrm{int}}$ between individual r-process events before the ESS epoch. ${t}_{\mathrm{LE}}$ is necessary to know the remaining fraction of ²⁴⁴Pu owing to radioactive decay from the last r-process event. This, together with ${t}_{\mathrm{int}}$, gives the contributing fraction from prior events to meteoritic ²⁴⁴Pu abundance.

${t}_{\mathrm{LE}}$ is deduced from a comparison of the ratio of unstable to stable r-process isotopes between meteoritic abundances and the theoretical production yields. Since ${t}_{\mathrm{LE}}$ critically depends on the assumed production ratio, we need several combinations of unstable/stable isotopes to make an independent estimate of ${t}_{\mathrm{LE}}$. For instance, the useful isotope combinations are ${}^{247}\mathrm{Cm}{/}^{235}{\rm{U}}$, ${}^{129}{\rm{I}}{/}^{127}{\rm{I}}$, and ${}^{244}\mathrm{Pu}{/}^{238}{\rm{U}}$, where the unstable isotopes have half-lives of $1.56\times {10}^{7}$ yr, $1.57\times {10}^{7}$ yr, and $8.1\times {10}^{7}$ yr, respectively. From ${}^{244}\mathrm{Pu}{/}^{238}{\rm{U}}$ and ${}^{129}{\rm{I}}{/}^{127}{\rm{I}}$, a relatively long interval of ${t}_{\mathrm{LE}}\approx 100$ Myr is obtained (Reynolds 1960; Wasserburg et al. 1969; Clayton 1983; Dauphas 2005). More recently, using the latest nucleosynthesis results of ${}^{129}{\rm{I}}$ and ${}^{127}{\rm{I}}$, Lugaro et al. (2014) deduced ${t}_{\mathrm{LE}}=109\,\mathrm{Myr}$ together with ${t}_{\mathrm{LE}}=123\,\mathrm{Myr}$ from ${}^{247}\mathrm{Cm}{/}^{235}{\rm{U}}$. Though the value of ${t}_{\mathrm{LE}}$ thus obtained should be revised, as will be discussed in Section 2.3, we here adopt ${t}_{\mathrm{LE}}=120\,\mathrm{Myr}$ as an initial input. In addition, we assume ${t}_{\mathrm{int}}=200$ Myr, which will yield the adopted ${t}_{\mathrm{LE}}$ as one of the plausible cases.

From ${t}_{\mathrm{LE}}=120\,\mathrm{Myr}$, the remaining fraction of ${}^{244}\mathrm{Pu}$ from the last event at the ESS is estimated to be 35.8%. Then, from both ${t}_{\mathrm{LE}}=120\,\mathrm{Myr}$ and ${t}_{\mathrm{int}}=200$ Myr, we deduce that the fraction of ${}^{244}\mathrm{Pu}$ from the last event with respect to the total ${}^{244}\mathrm{Pu}$ in meteoritic abundance is 82%, which is confirmed to be a large fraction as expected. These values, combined with the prior estimate of $8.90\times {10}^{-13}$, result in $2.03\times {10}^{-12}$ as the mass fraction of ${}^{244}\mathrm{Pu}$ in the ISM yielded from an injection by a single r-process event.

Next, we relate the above ${}^{244}\mathrm{Pu}$ mass fraction to that of stable Eu nuclei by introducing the theoretical production ratio between the two nuclei. The production of radioactive r-nuclides such as Th, U, and Pu is investigated by Goriely & Arnould (2001), and according to their latest nucleosynthesis results (Goriely & Janka 2016), the updated production ratio for ${}^{244}\mathrm{Pu}$/${}^{238}{\rm{U}}$ is 0.33. This value is identical to other estimates by Cowan et al. (1987) (=0.4) and Eichler et al. (2015) (=0.33).

On the other hand, regarding the existing r-nuclides in meteorites (or solar photosphere), we anticipate that the production pattern follows the solar r-process pattern. This hypothesis is justified by the observation that Galactic metal-poor halo stars exhibit the universality of r-process abundance distribution for heavy r-nuclides, which matches the solar r-process pattern (e.g., Montes et al. 2007; Sneden et al. 2008). Accordingly, the relative production ratio for ${}^{238}{\rm{U}}$/Eu is inferred from the solar r-process ratio corrected by the radioactive decay for ${}^{238}{\rm{U}}$ (Eu: 0.0984, ²³⁸U: 0.018 (atoms/10⁶ Si); Lodders et al. 2009), as well as by a 3% contribution to Eu from the s-process. The mass ratio is found to be 0.2955. This, together with ${}^{244}\mathrm{Pu}{/}^{238}{\rm{U}}=0.33$, results in ${}^{244}\mathrm{Pu}/\mathrm{Eu}=0.097$. Then, we finally obtain the value of the Eu mass fraction due to enrichment by a single r-process event as $2.10\times {10}^{-11}$.

The solar r-process abundance of Eu, $3.75\times {10}^{-10}$, is the end result of the accumulation of Eu by individual r-process events in the solar vicinity until the ESS. Thus, using the enrichment caused by each event, we can count the total number of events until the ESS. Dividing $3.75\times {10}^{-10}$ by $2.10\times {10}^{-11}$, we obtain the total number of r-process events until the ESS as ∼18. Here we ignore the mixing process of the ISM on the ∼100 Myr timescale, which may allow Eu atoms to move into and out of the ISM, yielding the solar system over ∼7.5 Gyr. Simulations of r-process enrichment that are combined with hydrodynamics of the ISM in the Galaxy are indeed awaited.

Since the total number N_r of r-process events determines the abundances of stable r-nuclei at the ESS, ${t}_{\mathrm{LE}}$ is largely influenced by N_r. This is understood from the abundance ratio ${R}_{\mathrm{LE}}$ of a radioactive isotope to a stable isotope after the last event within meteorites, which is given by the following equation (Lugaro et al. 2014):

$$\begin{eqnarray}&&{R}_{\mathrm{LE}}={R}_{\mathrm{yield}}\times \displaystyle \frac{1}{{N}_{r}}\times \left(1+\displaystyle \frac{{e}^{-{t}_{\mathrm{int}}/\tau }}{1-{e}^{-{t}_{\mathrm{int}}/\tau }}\right)\ ,\end{eqnarray} \tag{ 1 }$$

where ${R}_{\mathrm{yield}}$ is the production ratio of each single event and τ is the mean lifetime (=half-life/$\mathrm{ln}2$) of a radioactive isotope. Thus, ${t}_{\mathrm{LE}}$ should be updated with our result. To calculate ${t}_{\mathrm{LE}}$, we need to assume ${t}_{\mathrm{int}}$ for a period of ≲1 Gyr before the ESS, in addition to N_r. Then, incorporating N_r = 18 with ${t}_{\mathrm{int}}=200$ Myr before the ESS into calculations, we deduce ${t}_{\mathrm{LE}}=137$, 139, and 145 Myr from ${}^{129}{\rm{I}}{/}^{127}{\rm{I}}$, ${}^{247}\mathrm{Cm}{/}^{235}{\rm{U}}$, and ${}^{244}\mathrm{Pu}{/}^{238}{\rm{U}}$, respectively. Accordingly, we here adopt ${t}_{\mathrm{LE}}=140$ Myr. This revised ${t}_{\mathrm{LE}}$ modifies the prior ${}^{244}\mathrm{Pu}$ remaining fraction of the last event in meteorites from 0.358 to 0.302. Then the resultant mass fractions of ${}^{244}\mathrm{Pu}$ and Eu by one r-process event are slightly modified to $2.41\times {10}^{-12}$ and $2.49\times {10}^{-11}$, respectively. These new values result in ${N}_{r}\,\sim$ 15. Hereafter we adopt N_r = 15, though this value can be improved further, as there are still uncertainties in ${t}_{\mathrm{LE}}$ and ${t}_{\mathrm{int}}$. A further update of ${t}_{\mathrm{LE}}$ will be done with a variable ${t}_{\mathrm{int}}$ in the next section.

By comparing the deduced ²⁴⁴Pu density ejected in the ISM by a single r-process event with the ²⁴⁴Pu nucleosynthesis yield from an r-process site, we can estimate how much the ISM will be eventually mixed with the ejecta-carrying r-process elements. Considering the implied rarity of frequency as a countable number of ∼30 events over the period of 12 Gyr in the solar vicinity, together with a detailed discussion in a previous work (Hotokezaka et al. 2015), the r-process production site can be reasonably identified with an NS merger. Then, we assume a typical ejecta mass for an NS merger of 0.01 M_⊙ and individual element production obeying the solar r-process pattern. In addition, we assume that light r-process elements such as Sr, Y, and Zr ($A\approx 90$) are not synthesized in an NS merger from the implication of an elemental feature among Galactic halo stars (Tsujimoto & Shigeyama 2014b, see also Montes et al. 2007). According to the calculations claiming the production of A ≳ 130 by an NS merger (e.g., Bauswein et al. 2013), we set the lower boundary at A = 127, since the discussion based on the last r-process event (see Section 2.1) suggests that the production site of iodine is the same as that of heavier r-nuclei such as Pu.

The above hypotheses, together with the radio-decay correction, find the ²³⁸U mass fraction inside the ejecta to be $2.55\times {10}^{-3}$ M_⊙. Then, from ${}^{244}\mathrm{Pu}$/${}^{238}{\rm{U}}=0.33$, the mass fraction of ²⁴⁴Pu is estimated to be $8.42\times {10}^{-4}$, which is equivalent to a mass of $8.42\times {10}^{-6}$ M_⊙ in the ejecta with a mass of 0.01 M_⊙. Combining this ejected mass of ²⁴⁴Pu with its resultant density in the ISM, the mass of ISM mixed with the r-process ejecta is deduced to be $8.42\times {10}^{-6}$ M_⊙ /$2.41\times {10}^{-12}\approx 3.5\times {10}^{6}$ M_⊙. It turns out that the mass mixed with the ejecta of an NS merger that expands with a velocity of 10% to 30% of the speed of light is much larger than that swept-up by an SN of $5.1\times {10}^{4}$ M_⊙ (Shigeyama & Tsujimoto 1998). The corresponding radius of the cylindrical disk is found to be 370 pc, assuming a local surface density of gas (H i + H₂) of 8 M_⊙ pc⁻² (Koda et al. 2016). The timescale to pervade the ISM could be as short as on the order of Myr (Tsujimoto & Shigeyama 2014a) and is thus negligible.

Utilizing the propagation of r-process ejecta, we can deduce the event frequency of r-process production with respect to the occurrence rate of CCSNe. The current time interval between r-process production events is found to be about 400 Myr. Thus, it turns out that the total number of CCSNe inside a cylindrical disk with a 370 pc radius for a period of 400 Myr eventually yields one r-process production event. Here we assess a local CCSN rate from two approaches. For the Galaxy as a whole, the current SFR and CCSN rates are estimated to be 1.65 M_⊙ yr⁻¹ (Licquia & Newman 2015) and 2.3 CCSNe per century (Li et al. 2011), respectively; these two rates establish the correlation that an SFR of 1 M_⊙ yr⁻¹ is equal to 1.4 CCSNe per century. Then, from the present-day local SFR of 0.48–1.1 M_⊙ Gyr⁻¹ pc⁻² (Fuchs et al. 2009; Tsujimoto 2011), we obtain a CCSN rate of 1 per 2.1–4.8 Myr, within a 100 pc radius. On the other hand, the recent detection of ⁶⁰Fe in deep-sea sediments reveals that two CCSNe occurred 1.5–3.2 Myr and 6.5–8.7 Myr ago (Wallner et al. 2016), within a distance of 100 pc (Breitschwerdt et al. 2016). Then, putting the two results together, we finally adopt a CCSN rate of 1 per 4 Myr, within a 100 pc radius.

The derived CCSN rate gives 1370 CCSNe in total inside a cylindrical disk with a 370 pc radius for a period of 400 Myr. This estimate is equivalent to the rate of r-process production by NS merger of 1 per 1370 CCSNe. The rate is in fairly good agreement with the estimate of 1 per 1000−2000 CCSNe that was made from the correlation of stellar abundances between [Fe/H] and [Eu/H] in dSphs, as well as from Galactic chemical evolution (Tsujimoto & Shigeyama 2014a). We reanalyze its frequency from abundance correlation between [Mg/H] and [Eu/H] among Galactic stars to avoid uncertainties in the chemical enrichment process in dSphs and contributions from Type Ia supernovae. By inputting the Mg nucleosynthesis yield from a CCSN deduced by the observed two quantities, i.e., an average Fe mass of 0.07 M_⊙ (light curve analysis: Hamuy 2003) and the plateau of [Mg/Fe] = 0.4 among halo stars, we obtain a frequency of 1 per ∼1400 CCSNe for Eu production.