The r-process in proto-neutron-star wind revisited
aa r X i v : . [ a s t r o - ph . S R ] M a y Draft version October 11, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
THE r -PROCESS IN PROTO-NEUTRON-STAR WIND REVISITED Shinya Wanajo Draft version October 11, 2018
ABSTRACTWe examine the r -process in the neutrino-driven proto-neutron-star (PNS) wind of core-collapsesupernovae in light of the recent findings of massive neutron stars in binaries as well as of an indicationof neutron-richness in the PNS ejecta because of the nucleon potential corrections on neutrino opacities.To this end, a spherically symmetric, general relativistic, steady-state wind model is applied for awide range of PNS masses between 1 . M ⊙ and 2 . M ⊙ with the latter reaching the causality limit.Nucleosynthesis calculations with these PNS models are performed by assuming a time evolution ofelectron fraction with its minimal value of Y e = 0 .
4, which mimics recent hydrodynamical results.The fundamental nucleosynthetic aspect of the PNS wind is found to be the production of Sr, Y andZr in quasi-equilibrium and of the elements with A ≈ r -process, which can be anexplanation for the abundance signatures in r -process-poor Galactic halo stars. PNSs more massivethan 2 . M ⊙ can eject heavy r -process elements, however, with substantially smaller amount thanwhat is needed to account for the solar content. PNS winds can be thus the major origin of lighttrans-iron elements but no more than 10% of those heavier than A ∼ . M ⊙ . Subject headings: nuclear reactions, nucleosynthesis, abundances — stars: abundances — supernovae:general INTRODUCTION
Proto-neutron-star (PNS) wind of core-collapse super-novae (CCSNe), the outflows driven by neutrino heat-ing, has long been suggested to be the major site ofthe r -process (rapid neutron-capture process) since early1990’s (Meyer et al. 1992; Woosley et al. 1994). One ofthe problems in these early works was the very highentropy in the wind, S ∼ k B nucleon − ( k B is theBoltzmann constant), which was not confirmed by sub-sequent works ( S ∼ k B nucleon − , Takahashi et al.1994; Qian & Woosley 1996). General relativistic ef-fects were found to increase entropy (Cardall & Fuller1997) but needed a PNS more massive than M ≈ . M ⊙ for robust r -processing (Otsuki et al. 2000; Wanajo et al.2001; Thompson et al. 2001). Another problem wasan unacceptable overproduction of some species suchas Sr, Y, and Zr (Woosley et al. 1994; Wanajo et al.2001). More seriously, hydrodynamical simulationsof CCSNe with elaborate neutrino transport indicatedproton-richness in the wind ejecta (Fischer et al. 2010;H¨udepohl et al. 2010). These works seemed to excludethe PNS wind scenario as the r -process site.Recent works on the effect of nucleon potential cor-rections for neutrino opacities seem, in part, to re-vive the PNS wind scenario (Reddy et al. 1998; Roberts2012; Mart´ınez-Pinedo et al. 2012; Roberts et al. 2012;Horowitz et al. 2012). These works predict that the elec-tron fraction ( Y e ; number of protons per nucleon) dropsoff from an initially proton-rich value to the minimalvalue of ∼ . ∼ . National Astronomical Observatory of Japan, 2-21-1 Osawa,Mitaka, Tokyo 181-8588, Japan; [email protected] systems with a precision measurement of M = 1 . ± . M ⊙ for PSR J1614-2230 (Demorest et al. 2010) andan inferred mass of M ∼ . M ⊙ for PSR B1957+20(van Kerkwijk et al. 2011) are also encouraging for thePNS wind scenario.In this Letter we aim to revisit the issue of the r -processin PNS winds in light of these recent findings. This is toextend and improve the previous nucleosynthesis studies,which were based on limited hydrodynamical outcomes(e.g., Woosley et al. 1994; Arcones & Montes 2011) orsemi-analytic solutions with a few selected parametersets (e.g., M = 1 . M ⊙ and 2 . M ⊙ ; Wanajo et al. 2001)with Y e evolutions that were incompatible with the re-cent works. To this end, a semi-analytical wind model(Wanajo et al. 2001) is applied for a wide range of M between 1 . M ⊙ and 2 . M ⊙ (Section 2). Nucleosynthe-sis calculations are performed with the wind solutions byassuming a time evolution of Y e (Section 3) that mimicsthe result of Roberts et al. (2012). The nucleosynthe-sis yields are mass-integrated to compare with the solar r -process abundances as well as those in Galactic halostars. We then discuss whether PNS winds can be thesources of r -process elements in the Galaxy. WIND MODEL
Although the underlying physics what causes theexplosions of CCSNe has been under debate (e.g.,Janka et al. 2012), it is known that the neutrino-drivenoutflows after evacuation of the early convective ejectaare well described by the steady-state (semi-) ana-lytical 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 symmet-ric, general relativistic, semi-analytic wind model inWanajo et al. (2001, for more detail, see their Section 2). Wanajo time [s] L ν [ e r g s - ] -1 time [s] R [ k m ] S [ k B nu c - ] M = M sun τ [ m s ] M = M sun S / τ / [ k B nu c - m s - / ] M = M sun Y e = 0.450.400.350.300.250.20 time [s] d M / d t [ M s un s - ] -7 -6 -5 -4 -3 -2 -1 M = M sun Fig. 1.—
Time evolutions of L ν (top left) and R (top right) adopted in this study. Resulting S (middle left), τ (middle right), S/τ / (bottom left), and ˙ M (bottom right) are shown as functions of t . In the bottom-left panel, the Y e ’s, above which the production of A ∼ The average neutrino energies are taken to be 12, 14, and14 MeV for electron neutrino, electron antineutrino, andheavy lepton neutrinos, respectively (according to, e.g.,Fischer et al. 2010; H¨udepohl et al. 2010). The equationof state for ions (ideal gas) and arbitrarily degenerate, ar-bitrarily relativistic electrons and positrons is taken fromTimmes & Swesty (2000).Each wind (i.e., transonic) solution can be obtainedfor a given set of (
M, R, L ν ); we assume the PNS ra-dius R to be the same as the neutrinosphere and theneutrino luminosities of all the flavors to have the samevalue L ν . We consider the models of M/M ⊙ = 1 . L ν and R , phenomenological time evolutions during the first10 s after core bounce ( t = 0 .
20 s ≤ t ≤ t = 10 s)are adopted as follows. To roughly mimic recent re-sults of long-term simulations over the PNS coolingphase (e.g., Fischer et al. 2010; H¨udepohl et al. 2010),we assume L ν ( t ) = L ν, ( t/t ) − with L ν, (erg s − ) =10 . = 3 . × (Fig. 1; top left). We also assume R ( L ν ) = ( R − R )( L ν /L ν, ) + R with R = 30 kmand R = 10 km so that each wind solution can beobtained from a given set of ( M, L ν ). This is equiva-lent to set R ( t ) = ( R − R )( t/t ) − + R (Fig. 1; topright). Note that R ( t ) = 10 . -Process in proto-neutron-star wind 3 time [s] Y e Y e, min = 0.40 Y e, min = 0.45time [s] f M = M sun Fig. 2.—
Top: time evolution of Y e adopted for nucleosyn-thesis calculations ( Y e , min = 0 .
40; solid curve). The case with Y e , min = 0 .
45 is also shown by the dashed curve. Bottom: valuesof f (Eq. [1]) as functions of t . The cases for Y e , min = 0 . f = 1 and f = 1,respectively, above which the production of A ∼
200 and A ∼ bound of the constraint for cold NSs (with M = 1 . M ⊙ ),10 . ≤ R ≤ . . M ⊙ model reaches thesmallest radius ( ≈ . R & . M/M ⊙ ) km (Lattimer 2011). The PNSwith M = 2 . M ⊙ should be thus taken as the absoluteextreme model. Wind solutions for each M model are computed forlog L ν (erg s − ) = 52 . , . , . . . , .
90 ( t ≤ t ≤ t ;171 L ν ’s). The middle and bottom panels (Fig. 1)illustrate the resulting basic properties. We confirmthe previous results (Otsuki et al. 2000; Wanajo et al.2001; Thompson et al. 2001) that the asymptotic en-tropy ( S ; middle left) increases with time, being sys-tematically greater for more massive PNSs. We furtherfind a strong sensitivity of S to M for > . M ⊙ , whichreaches 338 k B nucleon − for M = 2 . M ⊙ . This is a con-sequence of the general relativistic effects that are par-ticularly important when M/R is close to the causalitylimit (Cardall & Fuller 1997). We also find systemati- Wanajo et al. (2001) showed that, with inclusion of generalrelativistic effects, nucleosynthetic outcomes were roughly scaledwith
M/R . Nucleosynthetic results of
M/M ⊙ = 1 . R =10 km here would be thus similar to those of, e.g., M/M ⊙ = 1 . R = 12 km. cally 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 val-ues at t ∼ S/τ / (with a fixed Y e ) serves as the measure ofthe strength of r -processing. We find in the bottom-leftpanel (Fig. 1) that S/τ / increases with time and sat-urates at t ∼ τ thatcounterbalances the increasing S . That is, the strengthof r -processing becomes mostly independent of time for t & Y e is kept constant. The dashed lines in-dicate the values of Y e above which the production of A ∼
200 nuclei are expected, according to the analyti-cal formula in Hoffman et al. (1997, their Eq. (19)). Wefind that an unacceptably low Y e ( < .
25) is required for M = 1 . M ⊙ . If a currently predicted minimal value of Y e ∼ . M = 2 . M ⊙ forthe production of heavy r -process nuclei. The bottom-right panel shows the mass ejection rates ( ˙ M ) that aresystematically smaller for more massive PNS models andquickly decrease with time. This indicates that the windejecta are dominated by the early components with small S/τ / . The very late ejecta for t >
10 s (if any; not con-sidered in this study) would be unimportant.The time evolution of Y e , which is needed fornucleosynthesis calculations, is assumed as Y e ( t ) = c cosh[ c ( t − t min )] + c (Fig. 2; top), where c = 1 . t < t min = 3 . c = 0 .
10 for t > t min . The coef-ficients c and c are determined to satisfy Y e ( t min ) = Y e , min and, for t < t min and t > t min , respectively, Y e ( t ) = 0 .
55 and Y e ( t ) = 0 .
50. This roughly mimics thehydrodynamical result by Roberts et al. (2012, see theirFig. 5). We adopt Y e , min = 0 .
40 (solid curve in the toppanel of Fig. 2), the value slightly smaller than ∼ . Y e drops in responseto the PNS contraction, the increasing neutrinosphericdensity suppresses the charged current neutrino inter-actions by Pauli blocking and Y e cannot decrease atlate times (Fischer et al. 2012). Note that the α -effect(McLaughlin et al. 1996; Meyer et al. 1998), which werenot considered in Roberts et al. (2012), would slightlyshift Y e towards ∼ .
5. The value of Y e , min here maythus be taken as the absolute lower limit for PNS winds.The lower panel (Fig. 2) shows the condition formaking the third peak nuclei ( A ∼ f = ( S/ k B nucleon − )( Y e / . τ /
20 ms) / & , . . Y e . . . (1)This reflects the value of Y e in addition to the com-bination S/τ / (Fig. 1; bottom left). We find thatonly the extreme model of M = 2 . M ⊙ satisfies thiscondition (the region above the horizontal solid line).Also indicated by the horizontal dashed line is the con- Otsuki et al. (2000) and Wanajo et al. (2001) showed that thewind of (
M, L ν ) = (2 . M ⊙ , erg s − ) with Y e = 0 .
40 led to arobust r -process. Their PNS radius was, however, fixed to 10 km,which was appreciably smaller than our more reasonable, time-dependent value of R ( L ν = 10 erg s − ) = 15 km. Wanajo
TABLE 1Ejecta masses (in units of − M ⊙ ) M/M ⊙ He 122 92.7 71.9 56.9 45.8 37.4 31.0
A >
100 2.19 2.75 2.76 2.27 1.78 1.37 0.893Sr 3.61 1.92 1.09 0.627 0.346 0.177 0.0764Ba 0.00 0.00 0.00 0.00 0.0420 0.0373 0.0199Eu 0.00 0.00 0.00 0.00 0.00452 0.00585 0.00305 mass number a bund a n ce
50 100 150 200 25010 -9 -8 -7 -6 -5 -4 -3 -2 M = M sun mass number r e l a ti v e t o s o l a r r- a bund a n ce
50 100 150 200 25010 -2 -1 M = M sun Fig. 3.—
Top: mass-integrated nuclear abundances, which arecompared with the solar r -process abundances (circles) that shiftedto match the third peak height ( A ∼ . M ⊙ model.Bottom: ratios of mass-integrated abundances relative to the solar r -process abundances (scaled at A = 90). dition for making the second peak ( A ∼ f ≈ . f &
1. It indicates that only the mod-els with M & . M ⊙ can reach the second peak of the r -process abundances. The f curves with Y e , min re-placed by 0.45 are also shown in Figure 2, implyingslightly weaker r -processing. NUCLEOSYNTHESIS
The nucleosynthetic yields for all the (
M, L ν ) setsare computed with the reaction network code describedin Wanajo et al. (2001, 2011b). Reaction rates areemployed from the latest library of REACLIB V2.0(Cyburt et al. 2010) for the experimental evaluationswhen available and the rest from the theoretical es-timates in BRUSLIB (Xu et al. 2013) based on theHFB-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 slightlyshift Y e by the α -effect, are not included. Using ther-modynamic trajectories of PNS winds, the calculationsare started when the temperature decreases to 10 GK,assuming initially free protons and neutrons with massfractions Y e and 1 − Y e , respectively. The nucleosynthetic abundances are mass-integrated(Fig. 3; top) by adopting ˙ M for each PNS model. Forcomparison purposes, the solar r -process compositions(circles) are also plotted to match the third peak height( A ∼ M = 2 . M ⊙ model. As anticipatedfrom the lower panel of Figure 2, only the extreme modelof M = 2 . M ⊙ satisfactorily accounts for the productionof heavy r -process nuclei up to Th ( A = 232) and U ( A =235 and 238). The 2 . M ⊙ model reaches the third peakabundances but those beyond. The 2 . M ⊙ model reachesthe second ( A ∼ r -processing for the models with M < . M ⊙ .We find, however, quite robust abundance patternsbelow A ∼ A ≈
56 and 90 with a trough between them are formedin quasi-nuclear equilibrium (QSE; & N = 50 species Sr, Y, Zr (Woosley et al. 1994; Wanajo et al. 2001) are notprominent in our result. This is due to the short du-ration of moderate S ( < k B nucleon − ; Fig. 1) with Y e ∼ .
45 (Fig. 3), in which the N = 50 species copiouslyform in QSE. The lower panel of Figure 3 shows the ra-tios of nucleosynthetic abundances relative to their solar r -process values (normalized at A = 90). For 2 . M ⊙ and2 . M ⊙ models, the ratios are more or less flat between A = 90 and 200, although deviations from unity are seeneverywhere.Table 1 provides the masses (in units of 10 − M ⊙ ) of thetotal ejecta, He, those with
A > He 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 massesof Sr range a factor of 50 with the greater amount forless massive models. Ba and Eu are produced only inthe massive models with M ≥ . M ⊙ .Studies of Galactic chemical evolution estimate the av-erage mass of Eu per CCSN event (if they were the ori-gin) to be ∼ − M ⊙ (Ishimaru & Wanajo 1999), thatis, ∼ a few10 − M ⊙ for the nuclei with A > M ≥ . M ⊙ reach 30%–60% of this requirement. The fraction of events with suchmassive PNSs would be limited to no more than ∼ & M ⊙ ). The masses of Eufrom these massive PNSs are, therefore, about 10 timessmaller than the requirement from Galactic chemical evo- We examined only the Y e , min = 0 .
40 case with t min = 3 . t min did not qualitatively changeour result. The cases with Y e , min = 0 .
45 corresponded to roughlyre-scaling M ’s with ∼ . . M ⊙ smaller values. Note also thatthe presence of the preceding SN ejecta that give rise to thetermination-shocks (Arcones et al. 2007) do not change the grossabundance features (Wanajo 2007; Kuroda et al. 2008). -Process in proto-neutron-star wind 5 atomic number a bund a n ce
40 60 80-4-202 M = M sun atomic number a bund a n ce
40 60 80-4-202 M = M sun atomic number r e l a ti v e t o HD
40 60 80-2-1012 M = M sun atomic number r e l a ti v e t o C S -
40 60 80-2-1012 M = M sun Fig. 4.—
Mass-integrated elemental abundances compared to the stellar abundances (top panels) and their ratios (bottom panels). TwoGalactic halo stars, HD 122563 (left, Honda et al. 2006; Roederer et al. 2012) and CS 31082-001 (right Siqueira Mello Jr. et al. 2013) aretaken as representative of r -process-poor/rich stars, respectively. The nucleosynthetic abundances are normalized at Z = 40. lution (the same holds for Ba). Note that, for massivePNS cases, the ejecta masses would be further reducedby fallback or black-hole formation (Qian et al. 1998;Boyd et al. 2012). For Sr, the required mass per CCSNevent is estimated to be ∼ × − M ⊙ from the solar r -process ratio of Sr/Eu = 16.4 (Sneden et al. 2008). Thelow mass PNS models, which may represent the majorityof 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 < 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 Jr. et al. 2013) stars withthe metallicities [Fe/H] = − . − .
9, respectively.These stars have [Eu/Fe] = − .
52 and +1 .
69, respec-tively, well below and above the average value of ≈ +0 . ≈ −
3. The top and bottom panels show, re-spectively, the mass-integrated abundances and their ra-tios relative to the stellar abundances, which are normal-ized to the stellar abundances at Z = 40.In the left panels, we find that the 1 . M ⊙ and 1 . M ⊙ models result in reasonable agreement with the stellarabundances between Z = 38 (Sr) and Z = 48 (Cd). The2 . M ⊙ model nicely reproduces the abundance patternof HD 122563 up to Z = 68 (Er) but somewhat overpro- duces the elements of Z = 46–48 (Pd, Ag, Cd). It couldbe thus possible to interpret that the abundance signa-tures of r -process-poor stars were due to a weak r -processthat reaches Z ∼
50 (
M < . M ⊙ ) or 70 ( M = 2 . M ⊙ )with or without additional sources for Z >
50, respec-tively. In the right panels, we find that the stellar abun-dances between Z = 38 (Sr) and Z = 47 (Ag) are wellreproduced by massive models with M ≥ . M ⊙ . Themodels with M = 2 . M ⊙ and 2 . M ⊙ produce the heavierelements with a similar pattern to that of CS 31082-001but with a smaller ratio. Because of the insufficient pro-duction of Eu (Table 1), our PNS models would not ac-count for the high [Eu/Fe] value in this star. The windsfrom such massive PNSs ( M & . M ⊙ ) could be, how-ever, still the source of the low-level abundances (fac-tor of several 10 smaller than the average values) of Srand Ba in numerous metal-poor stars (Roederer 2013;Aoki et al. 2013). CONCLUSION
We revisited the issue of the r -process in neutrino-driven PNS winds in light of recent findings of the mas-sive NSs as well as of the neutron-richness in the PNSejecta. Nucleosynthesis calculations were performed withthe semi-analytical wind models over a wide range ofthe PNS masses (1 . ≤ M/M ⊙ ≤ . Y e .Based on our result, including the extreme model( M = 2 . M ⊙ ) that encounters the causality limit, it Wanajowould be safe to conclude that neutrino-driven PNSwinds were excluded as the major origin of heavy r -process elements. Note that some previous works havesuggested several mechanisms that help to increase S and reduce τ , e.g., strong magnetic field (Thompson2003; Suzuki & Nagataki 2005) and highly anisotropicneutrino emission (Wanajo 2006). Our conclusion wouldnot be changed if such mechanisms (associated to proba-bly rare events) were considered, as far as the dominantdriving source of the wind is neutrino heating (whichsets ˙ M ). Other driving mechanisms such as magnetoro-tationally (Metzger et al. 2007; Winteler et al. 2012) oracoustic-wave driven outflows are beyond the scope ofthis Letter and cannot be excluded as the r -process ori- gins on the basis of our result.Neutrino-driven PNS winds are, however, promisingsources 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 ofCCSNe (Wanajo et al. 2011a). If not the main origin ofthe r -process elements beyond A ∼ < −
1) found in extremely metal-poor stars.Future surveys or indications of massive NSs, long-termhydrodynamical simulations of PNS winds, and galac-tic chemical evolution studies will be important to makeclear the role of PNS winds in the enrichment historiesof galaxies.This work was supported by the JSPS Grants-in-Aidfor Scientific Research (23224004).1) found in extremely metal-poor stars.Future surveys or indications of massive NSs, long-termhydrodynamical simulations of PNS winds, and galac-tic chemical evolution studies will be important to makeclear the role of PNS winds in the enrichment historiesof galaxies.This work was supported by the JSPS Grants-in-Aidfor Scientific Research (23224004).