THE r-PROCESS IN PROTO-NEUTRON-STAR WIND REVISITED

Proto-neutron-star (PNS) wind of core-collapse supernovae (CCSNe), the outflows driven by neutrino heating, has long been suggested to be the major site of the r-process (rapid neutron-capture process) since early 1990s (Meyer et al. 1992; Woosley et al. 1994). One of the problems in these early works was the very high entropy in the wind, S ∼ 400 k_B nucleon⁻¹ (k_B is the Boltzmann constant), which was not confirmed by subsequent works (S ∼ 100 k_B nucleon⁻¹; Takahashi et al. 1994; Qian & Woosley 1996). General relativistic effects were found to increase entropy (Cardall & Fuller 1997) but needed a PNS more massive than M ≈ 2.0 M_☉ for robust r-processing (Otsuki et al. 2000; Wanajo et al. 2001; Thompson et al. 2001). Another problem was an unacceptable overproduction of some species such as Sr, Y, and Zr (Woosley et al. 1994; Wanajo et al. 2001). More seriously, hydrodynamical simulations of CCSNe with elaborate neutrino transport indicated proton-richness in the wind ejecta (Fischer et al. 2010; Hüdepohl et al. 2010). These works seemed to exclude the PNS wind scenario as the r-process site.

Recent works on the effect of nucleon potential corrections for neutrino opacities seem, in part, to revive the PNS wind scenario (Reddy et al. 1998; Roberts 2012; Martínez-Pinedo et al. 2012; Roberts et al. 2012; Horowitz et al. 2012). These works predict that the electron fraction (Y_e, number of protons per nucleon) drops off from an initially proton-rich value to the minimal value of ∼0.42–0.45 and increases again toward ∼0.5 in the late wind phase, behavior not expected in previous works. Recent discoveries of massive neutron stars (NSs) in binary systems with a precision measurement of M = 1.97 ± 0.04 M_☉ for PSR J1614−2230 (Demorest et al. 2010) and an inferred mass of M ∼ 2.4 M_☉ for PSR B1957+20 (van Kerkwijk et al. 2011) are also encouraging for the PNS wind scenario.

In this Letter, we aim to revisit the issue of the r-process in PNS winds in light of these recent findings. This is to extend and improve the previous nucleosynthesis studies, which were based on limited hydrodynamical outcomes (e.g., Woosley et al. 1994; Arcones & Montes 2011) or semi-analytic solutions with a few selected parameter sets (e.g., M = 1.4 M_☉ and 2.0 M_☉; Wanajo et al. 2001) with Y_e evolutions that were incompatible with the recent works. To this end, a semi-analytical wind model (Wanajo et al. 2001) is applied for a wide range of M between 1.2 M_☉ and 2.4 M_☉ (Section 2). Nucleosynthesis calculations are performed with the wind solutions by assuming a time evolution of Y_e (Section 3) that mimics the result of Roberts et al. (2012). The nucleosynthesis yields are mass-integrated to compare with the solar r-process abundances as well as those in Galactic halo stars. We then discuss whether PNS winds can be the sources of r-process elements in the Galaxy.

Although the underlying physics of what causes the explosions of CCSNe has been under debate (e.g., Janka et al. 2012), it is known that the neutrino-driven outflows after evacuation of the early convective ejecta are well described by the steady-state (semi-) analytical solutions of PNS wind models (Duncan et al. 1986; Qian & Woosley 1996; Cardall & Fuller 1997; Otsuki et al. 2000; Wanajo et al. 2001; Thompson et al. 2001). In this study, we use the spherically symmetric, general relativistic, semi-analytic wind model in Wanajo et al. (2001; for more details, see their Section 2). The average neutrino energies are taken to be 12, 14, and 14 MeV for electron neutrino, electron antineutrino, and heavy lepton neutrinos, respectively (according to, e.g., Fischer et al. 2010; Hüdepohl et al. 2010). The equation of state for ions (ideal gas) and arbitrarily degenerate, arbitrarily relativistic electrons and positrons is taken from Timmes & Swesty (2000).

Each wind (i.e., transonic) solution can be obtained for a given set of (M, R, L_ν); we assume the PNS radius R to be the same as the neutrinosphere and the neutrino luminosities of all the flavors to have the same value L_ν. We consider the models of M/M_☉ = 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, and 2.4, which cover the range of measured and estimated masses of NSs (Demorest et al. 2010; van Kerkwijk et al. 2011; Lattimer 2011). For L_ν and R, phenomenological time evolutions during the first 10 s after core bounce (t₀ = 0.20 s ⩽ t ⩽ t₁ = 10 s) are adopted as follows. To roughly mimic recent results of long-term simulations over the PNS cooling phase (e.g., Fischer et al. 2010; Hüdepohl et al. 2010), we assume L_ν(t) = L_{ν, 0}(t/t₀)⁻¹ with L_{ν, 0} (erg s⁻¹) = 10^52.4 = 3.98 × 10⁵² (Figure 1, top left). We also assume R(L_ν) = (R₀ − R₁)(L_ν/L_{ν, 0}) + R₁ with R₀ = 30 km and R₁ = 10 km so that each wind solution can be obtained from a given set of (M, L_ν). This is equivalent to set R(t) = (R₀ − R₁)(t/t₀)⁻¹ + R₁ (Figure 1, top right). Note that R(t₁) = 10.4 km matches the lower bound of the constraint for cold NSs (with M = 1.4 M_☉), 10.4 km ⩽ R ⩽ 12.9 km, inferred by Steiner et al. (2013). With this assumption, the 2.4 M_☉ model reaches the smallest radius (≈10.3 km) allowed by the causality limit (the speed of sound must not exceed the speed of light), R ≳ 4.3 (M/M_☉) km (Lattimer 2011). The PNS with M = 2.4 M_☉ should be thus taken as the absolute extreme model.¹

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Wind solutions for each M model are computed for log  L_ν(erg s⁻¹) = 52.60, 52.59, ..., 50.90 (t₀ ⩽ t ⩽ t₁, 171 L_ν's). The middle and bottom panels (Figure 1) illustrate the resulting basic properties. We confirm the previous results (Otsuki et al. 2000; Wanajo et al. 2001; Thompson et al. 2001) that the asymptotic entropy (S, middle left) increases with time, being systematically greater for more massive PNSs. We further find a strong sensitivity of S to M for >2.0 M_☉, which reaches 338 k_B nucleon⁻¹ for M = 2.4 M_☉. This is a consequence of the general relativistic effects that are particularly important when M/R is close to the causality limit (Cardall & Fuller 1997). We also find systematically smaller expansion timescales (τ, defined as the e-folding time of temperature below 0.5 MeV; Otsuki et al. 2000) for more massive PNSs, which take minimal values at t ∼ 1–2 s and increase with time (Figure 1, middle right).

As analytically shown by Hoffman et al. (1997), the ratio S/τ^1/3 (with a fixed Y_e) serves as the measure of the strength of r-processing. We find in the bottom left panel (Figure 1) that S/τ^1/3 increases with time and saturates at t ∼ 5 s as a result of the increasing τ that counterbalances the increasing S. That is, the strength of r-processing becomes mostly independent of time for t ≳ 5 s if Y_e is kept constant. The dashed lines indicate the values of Y_e above which the production of A ∼ 200 nuclei is expected, according to the analytical formula in Hoffman et al. (1997; their Equation (19)). We find that an unacceptably low Y_e (<0.25) is required for M = 1.4 M_☉. If a currently predicted minimal value of Y_e ∼ 0.42–0.45 were taken, one would need a PNS with the mass close to the extreme case of M = 2.4 M_☉ for the production of heavy r-process nuclei.² The bottom right panel shows the mass ejection rates ($\dot{M}$) that are systematically smaller for more massive PNS models and quickly decrease with time. This indicates that the wind ejecta are dominated by the early components with small S/τ^1/3. The very late ejecta for t > 10 s (if any, not considered in this study) would be unimportant.

The time evolution of Y_e, which is needed for nucleosynthesis calculations, is assumed as Y_e(t) = c₁cosh [c₂(t − t_min)] + c₃ (Figure 2, top), where c₂ = 1.0 for t < t_min = 3.0 s and c₂ = 0.10 for t > t_min. The coefficients c₁ and c₃ are determined to satisfy Y_e(t_min) = Y_{e, min} and, for t < t_min and t > t_min, respectively, Y_e(t₀) = 0.55 and Y_e(t₁) = 0.50. This roughly mimics the hydrodynamical result by Roberts et al. (2012; see their Figure 5). We adopt Y_{e, min} = 0.40 (solid curve in the top panel of Figure 2), the value slightly smaller than ∼0.42–0.45 in Roberts et al. (2012). While Y_e drops in response to the PNS contraction, the increasing neutrinospheric density suppresses the charged current neutrino interactions by Pauli blocking and Y_e cannot decrease at late times (Fischer et al. 2012). Note that the α-effect (McLaughlin et al. 1996; Meyer et al. 1998), which were not considered in Roberts et al. (2012), would slightly shift Y_e toward ∼0.5. The value of Y_{e, min} here may thus be taken as the absolute lower limit for PNS winds.

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The lower panel (Figure 2) shows the condition for making the third peak nuclei (A ∼ 200) according to Hoffman et al. (1997),

$$\begin{eqnarray} &&f_{200} = \frac{(S / 230\, k_\mathrm{B}\, \mathrm{nucleon}^{-1})}{(Y_\mathrm{e}/0.40)(\tau / 20\, \mathrm{ms})^{1/3}} \gtrsim 1,\quad 0.38 \lesssim Y_\mathrm{e} \lesssim 0.46.\nonumber \\ \end{eqnarray} \tag{ 1 }$$

This reflects the value of Y_e in addition to the combination S/τ^1/3 (Figure 1, bottom left). We find that only the extreme model of M = 2.4 M_☉ satisfies this condition (the region above the horizontal solid line). Also indicated by the horizontal dashed line is the condition for making the second peak (A ∼ 130) nuclei, f₁₃₀ ≈ 1.34 f₂₀₀ ≳ 1. It indicates that only the models with M ≳ 2.0 M_☉ can reach the second peak of the r-process abundances. The f₂₀₀ curves with Y_{e, min} replaced by 0.45 are also shown in Figure 2, implying slightly weaker r-processing.

The nucleosynthetic yields for all the (M, L_ν) sets are computed with the reaction network code described in Wanajo et al. (2001, 2011a). Reaction rates are employed from the latest library of REACLIB version 2.0 (Cyburt et al. 2010) for the experimental evaluations when available and the rest from the theoretical estimates in BRUSLIB (Xu et al. 2013) based on the HFB-21 mass predictions (Goriely et al. 2010). The β-decay rates are taken from the gross theory predictions (GT2; Tachibana et al. 1990) obtained with the HFB-21 masses. Neutrino interactions, which would slightly shift Y_e by the α-effect, are not included. Using thermodynamic trajectories of PNS winds, the calculations are started when the temperature decreases to 10 GK, assuming initially free protons and neutrons with mass fractions Y_e and 1 − Y_e, respectively.³

The nucleosynthetic abundances are mass-integrated (Figure 3, top) by adopting $\dot{M}$ for each PNS model. For comparison purposes, the solar r-process compositions (circles) are also plotted to match the third peak height (A ∼ 195) for the M = 2.4 M_☉ model. As anticipated from the lower panel of Figure 2, only the extreme model of M = 2.4 M_☉ satisfactorily accounts for the production of heavy r-process nuclei up to Th (A = 232) and U (A = 235 and 238). The 2.2 M_☉ model reaches the third peak abundances but those beyond. The 2.0 M_☉ model reaches the second (A ∼ 130) but the third peak abundances. We find no strong r-processing for the models with M < 2.0 M_☉.

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We find, however, quite robust abundance patterns below A ∼ 110, which appears a fundamental aspect of nucleosynthesis in PNS winds. The double peaks at A ≈ 56 and 90 with a trough between them are formed in quasi-nuclear equilibrium (QSE; ≳ 4 GK). Note also that the overproduction of N = 50 species ⁸⁸Sr, ⁸⁹Y, ⁹⁰Zr (Woosley et al. 1994; Wanajo et al. 2001) is not prominent in our result. This is due to the short duration of moderate S (<100 k_B nucleon⁻¹; Figure 1) with Y_e ∼ 0.45 (Figure 3), in which the N = 50 species copiously form in QSE. The lower panel of Figure 3 shows the ratios of nucleosynthetic abundances relative to their solar r-process values (normalized at A = 90). For 2.2 M_☉ and 2.4 M_☉ models, the ratios are more or less flat between A = 90 and 200, although deviations from unity are seen everywhere.

Table 1 provides the masses (in units of 10⁻⁵ M_☉) of the total ejecta, ⁴He, those with A > 100, Sr, Ba, and Eu, for all the PNS models. The total ejecta masses span a factor of six with smaller values for more massive PNSs. The larger fractions of ⁴He in more massive models, however, lead to the ejecta masses for A > 100 (total masses of r-process nuclei) ranging only a factor of 2.5. The masses of Sr range a factor of 50 with the greater amount for less massive models. Ba and Eu are produced only in the massive models with M ⩾ 2.0 M_☉.

Studies of Galactic chemical evolution estimate the average mass of Eu per CCSN event (if they were the origin) to be ∼10⁻⁷ M_☉ (Ishimaru & Wanajo 1999), that is, ∼a few 10⁻⁵ M_☉ for the nuclei with A > 100. Taken at the face value, the Eu masses for M ⩾ 2.0 M_☉ reach 30%–60% of this requirement. The fraction of events with such massive PNSs would be limited to no more than ∼20% of all CCSN events (e.g., ≳ 25 M_☉). The masses of Eu from these massive PNSs are, therefore, about 10 times smaller than the requirement from Galactic chemical evolution (the same holds for Ba). Note that, for massive PNS cases, the ejecta masses would be further reduced by fallback or black hole formation (Qian et al. 1998; Boyd et al. 2012). For Sr, the required mass per CCSN event is estimated to be ∼2 × 10⁻⁶ M_☉ from the solar r-process ratio of Sr/Eu = 16.4 (Sneden et al. 2008). The low-mass PNS models, which may represent the majority of CCSNe, thus overproduce Sr by about a factor of 10. The amount of QSE products such as Sr, Y, and Zr is, however, highly dependent on the multi-dimensional Y_e distribution in early times (t < 1 s; Wanajo et al. 2011b).

Figure 4 compares the mass-integrated abundances with those of Galactic halo stars. Two well-known objects are taken as representative of r-process-poor (HD 122563, left panels; Honda et al. 2006; Roederer et al. 2012) and r-process-rich (CS 31082-001, right panels; Siqueira Mello et al. 2013) stars with the metallicities [Fe/H] =−2.7 and −2.9, respectively. These stars have [Eu/Fe] =−0.52 and +1.69, respectively, well below and above the average value of ≈+0.5 at [Fe/H] ≈−3. The top and bottom panels show, respectively, the mass-integrated abundances and their ratios relative to the stellar abundances, which are normalized to the stellar abundances at Z = 40.

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In the left panels, we find that the 1.2 M_☉ and 1.4 M_☉ models result in reasonable agreement with the stellar abundances between Z = 38 (Sr) and Z = 48 (Cd). The 2.0 M_☉ model nicely reproduces the abundance pattern of HD 122563 up to Z = 68 (Er) but somewhat overproduces the elements of Z = 46–48 (Pd, Ag, Cd). It could be thus possible to interpret that the abundance signatures of r-process-poor stars were due to a weak r-process that reaches Z ∼ 50 (M < 2.0 M_☉) or 70 (M = 2.0 M_☉) with or without additional sources for Z > 50, respectively. In the right panels, we find that the stellar abundances between Z = 38 (Sr) and Z = 47 (Ag) are well reproduced by massive models with M ⩾ 1.6 M_☉. The models with M = 2.2 M_☉ and 2.4 M_☉ produce the heavier elements with a similar pattern to that of CS 31082-001 but with a smaller ratio. Because of the insufficient production of Eu (Table 1), our PNS models would not account for the high [Eu/Fe] value in this star. The winds from such massive PNSs (M ≳ 2.0 M_☉) could be, however, still the source of the low-level abundances (factor of several 10 smaller than the average values) of Sr and Ba in numerous metal-poor stars (Roederer 2013; Aoki et al. 2013).

We revisited the issue of the r-process in neutrino-driven PNS winds in light of recent findings of the massive NSs as well as of the neutron-richness in the PNS ejecta. Nucleosynthesis calculations were performed with the semi-analytical wind models over a wide range of the PNS masses (1.2 ⩽ M/M_☉ ⩽ 2.4), assuming phenomenological time evolutions of Y_e.

Based on our result, including the extreme model (M = 2.4 M_☉) that encounters the causality limit, it would be safe to conclude that neutrino-driven PNS winds were excluded as the major origin of heavy r-process elements. Note that some previous works have suggested several mechanisms that help to increase S and reduce τ, e.g., strong magnetic field (Thompson 2003; Suzuki & Nagataki 2005) and highly anisotropic neutrino emission (Wanajo 2006). Our conclusion would not be changed if such mechanisms (associated with probably rare events) were considered, as far as the dominant driving source of the wind is neutrino heating (which sets $\dot{M}$). Other driving mechanisms such as magnetorotationally (Metzger et al. 2007; Winteler et al. 2012) or acoustic-wave-driven outflows are beyond the scope of this Letter and cannot be excluded as the r-process origins on the basis of our result.

Neutrino-driven PNS winds are, however, promising sources that eject light trans-iron elements made in QSE (Sr, Y, and Zr) and by a weak r-process (up to Pd, Ag, and Cd), in addition to the early convective ejecta of CCSNe (Wanajo et al. 2011b). If not the main origin of the r-process elements beyond A ∼ 110, they could be the sources of low-level abundances of Sr and Ba (e.g., [(Sr, Ba)/Fe] < − 1) found in extremely metal-poor stars. Future surveys or indications of massive NSs, long-term hydrodynamical simulations of PNS winds, and galactic chemical evolution studies will be important to make clear the role of PNS winds in the enrichment histories of galaxies.

This work was supported by the JSPS Grants-in-Aid for Scientific Research (23224004).