Nucleosynthesis signatures of neutrino-driven winds from proto-neutron stars: a perspective from chemical evolution models
Fiorenzo Vincenzo, Todd A. Thompson, David H. Weinberg, Emily J. Griffith, James W. Johnson, Jennifer A. Johnson
MMNRAS , 1– ?? (2021) Preprint 10 February 2021 Compiled using MNRAS L A TEX style file v3.0
Nucleosynthesis signatures of neutrino-driven winds fromproto-neutron stars: a perspective from chemical evolution models
Fiorenzo Vincenzo ★ , Todd A. Thompson , David H. Weinberg , , Emily J. Griffith ,James W. Johnson , Jennifer A. Johnson Department of Astronomy & Center for Cosmology and AstroParticle Physics, The Ohio State University, Columbus, OH 43210, USA Institute for Advanced Study, Princeton, NJ 08540, USA
10 February 2021
ABSTRACT
We test the hypothesis that the observed first-peak (Sr, Y, Zr) and second-peak (Ba) s-processelemental abundances in low metallicity Milky Way stars ([Fe/H] < ∼ − . . 𝑃 ∼ 𝑣 rot between 150 and 300 km s − , can explain the observedabundance levels reasonably well for [Fe/H] < −
2. These models overpredict [Sr/Fe] and[Mo/Fe] at higher metallicities, but with a tuned dependence of 𝑣 rot on stellar metallicity theymight achieve an acceptable fit at all [Fe/H]. If many proto-NSs are born with strong magneticfields and short spin periods, then their neutrino-driven winds provide a natural source for Sr, Y,Zr, Mo, Ru, and Ba in low metallicity stellar populations. Spherical winds from unmagnetizedproto-NSs, on the other hand, overproduce the observed Sr, Y, and Zr abundances by a largefactor. Key words:
Galaxy: abundances – stars: abundances – stars: magnetars
Isotopes with nucleon number larger than that of iron-peak ele-ments (
A ≈
56) are prevented by an increasingly large Coulombbarrier from being synthesized by any charged-particle-inducedthermonuclear reaction in stellar interiors. The existence of thevast majority of the trans-iron elements is explained by a series ofneutron-capture processes followed by 𝛽 -decays, starting from seednuclei of iron-peak elements (Burbidge et al. 1957; Cameron 1957).Neutron-capture nucleosynthesis can operate by means of two pro-cesses, depending on whether the rate of neutron-capture is slow(s-process) or rapid (r-process) with respect to the rate of 𝛽 -decay.Nearly all trans-iron elements are produced by a mixture of s- andr-process events, except for a number of stable s-only nuclei which ★ email: [email protected] are shielded from any r-process contribution by the presence of astable, neutron-rich r-only nucleus with equal A .In the classical picture, the s-process proceeds along the so-called valley of 𝛽 -stability, giving rise to three distinctive peaks inthe Solar abundance template, which correspond to the magic neu-tron numbers N 𝑛 =
50 (e.g., Sr, Y, Zr), N 𝑛 =
82 (e.g.,
Ba),and N 𝑛 =
126 (e.g.,
Pb). Such peaks in the Solar abundance pat-tern are due to the fact that the stable heavy-element isotopes with amagic neutron number have a neutron-capture cross-section whichis much lower than that of the other isotopes of the 𝛽 -stability valley,creating a bottleneck in the s-process path.The main site of the s-process nucleosynthesis in astrophysicalenvironments is found in the late evolutionary stages of low- andintermediate-mass (LIM) stars, during the asymptotic giant branch(AGB) phase (e.g., Ulrich 1973). The main source of free-neutronsin AGB stars is provided by the reaction C( 𝛼 , 𝑛 ) O (Iben &Renzini 1982; Hollowell & Iben 1989), which is active at energies © a r X i v : . [ a s t r o - ph . GA ] F e b F. Vincenzo et al. 𝐸 ≈ C-pocket in the Heintershell during the interpulse period of AGB stars represents thekey physical mechanism responsible for the s-process nucleosyn-thesis in LIM stars (Iben & Renzini 1982; Hollowell & Iben 1989;Straniero et al. 1995; Gallino et al. 1998; Straniero, Cristallo, &Gallino 2009). The continuous recurrence of the third-dredge upand interpulse periods makes s-process nucleosynthesis in AGBstars very effective for a relatively extended period of time, pro-ducing remarkable effects in the chemical abundance distributionobserved in the stars of our Galaxy (see, for example, Busso et al.2001; Karakas & Lattanzio 2007; Cristallo et al. 2009; Karakas &Lugaro 2016).S-process nucleosynthesis can also take place during the evo-lutionary stage of core He-burning of massive stars, which – beforeexploding as core-collapse supernovae (SNe) – can pollute the in-terstellar medium (ISM) of our Galaxy through radiatively-drivenstellar winds, enriched with He, C, N, O, and traces of s-processelements. In particular, massive stars provide a prompt s-processcontribution to the chemical evolution of our Galaxy at low metal-licities, before low-mass stars reach the AGB phase and enrich theISM with their nucleosynthetic products. An interesting study is thatof Cescutti et al. (2013), who proposed that a prompt s-process con-tribution from rapidly-rotating massive stars (Frischknecht, Hirschi,& Thielemann 2012) – predicted to be more abundant at low metal-licities, where stars are more compact and hence rotate faster – canhelp explain the shape of the scatter in [Sr/Ba] in metal-poor halostars (see also the review of Frebel 2010).The r-process works by rapidly piling up neutrons in an increas-ingly heavy nucleus. As the neutron-capture proceeds, the nucleonbinding energy becomes increasingly low, until an equilibrium isreached between the photo-disintegration and the neutron-capture,which temporarily freezes out the neutron number. The 𝛽 -decay ofthe neutron-rich nucleus then breaks the deadlock, allowing the r-process to resume. It then proceeds rapidly until a new equilibriumis reached again (see, for example, the classical books of Clayton1983; Rolfs & Rodney 1988).The r-process is the main physical mechanism behind the nu-cleosynthesis of the neutron-rich heavy elements observed in MilkyWay (MW) stars at all metallicities, but it also provides a non-negligible contribution to the majority of neutron-capture elementswhich are observed in metal-poor stars. The signature of r-processevents is very pervasive, and it is observed at all metallicities in thestars of our Galaxy.The astrophysical environments of r-process events in the cos-mos usually involve explosive physical conditions, because veryhigh neutron densities are required. The neutron-rich isotopes pro-duced along the r-process path have a very short half-life, causingthe neutron-rich nuclei to beta-decay over timescales of the order ofmilliseconds, if they did not undergo further rapid neutron-capture.Examples of r-process sites that have been proposed and investigatedby theoretical studies include (i) neutrino-driven winds from proto-neutron stars (NSs) (Woosley et al. 1994; Takahashi, Witti, & Janka1994; Qian & Woosley 1996; Hoffman, Woosley, & Qian 1997; Ot-suki et al. 2000; Thompson, Burrows, & Meyer 2001; Wanajo et al.2009; Wanajo 2013); (ii) neutrino-driven winds from highly mag-netic and potentially rapidly rotating proto-magnetars (Thompson2003; Thompson, Chang, & Quataert 2004; Metzger, Thompson, &Quataert 2007, 2008; Vlasov, Metzger, & Thompson 2014; Vlasovet al. 2017; Thompson & ud-Doula 2018); ( iii) neutrino-drivenwinds around the accretion disk of a black hole (Pruet, Thompson,& Hoffman 2004; Metzger, Thompson, & Quataert 2008; Wanajo &Janka 2012; Siegel, Barnes, & Metzger 2019); (iv) electron-capture SNe (see, for example, Wanajo et al. 2009; Cescutti et al. 2013;Kobayashi, Karakas, & Lugaro 2020); (v) magneto-rotationally-driven SNe (Burrows et al. 2007; Winteler et al. 2012; Cescutti& Chiappini 2014); and (vi) neutron-star mergers (Lattimer et al.1977; Freiburghaus, Rosswog, & Thielemann 1999; Argast et al.2004; Goriely, Bauswein, & Janka 2011; Rosswog 2013; Matteucciet al. 2014; Cescutti et al. 2015; Vincenzo et al. 2015; Kobayashi,Karakas, & Lugaro 2020). Since it is likely that all these mecha-nisms have contributed to r-process nucleosynthesis at some level,the theoretical studies have focused on exploring the frequency ofeach event and the predicted template of the corresponding r-processejecta.Due to the large uncertainties in the r-process nucleosynthesiscalculations, the working strategy of the first MW chemical evo-lution models was to assume empirical yields for the r-process,which were tuned to reproduce the abundances of light and heavyneutron-capture elements at low metallicity. After doing this, it waspossible to discuss the conditions for the different r-process sites toproduce enough material to explain the neutron-capture elementalabundances and their dispersion in metal-poor stars (e.g., Travaglioet al. 2004; Cescutti et al. 2006; Cescutti 2008). Another strategywas employed by Prantzos et al. (2018), who emphasize the ro-tating massive star contribution and fit the metallicity dependenceof stellar rotation empirically by reproducing observed abundancetrends (see also Prantzos et al. 2020). Kobayashi, Karakas, & Lu-garo (2020) recently explored the impact of a variety of differentscenarios to the observed abundances of neutron-capture elements.In this work we explore the hypothesis that neutrino-drivenwinds from proto-NSs can explain the abundances of the first peak(Sr, Y, Zr) and second peak (Ba) of the s-process elemental abun-dance distribution. We test this hypothesis by assuming that mas-sive stars enrich the ISM at their death through (i) radiative-drivenmass loss; (ii) core-collapse SNe; and – after the explosion – (iii) neutrino-driven winds from the proto-NS that may have been leftafter the explosion. To test this hypothesis, we also look at the abun-dances of Mo and Ru, which can be synthesized in p-rich outflowsof proto-NSs (Hoffman et al. 1996; Fröhlich et al. 2006; Pruet et al.2006). Throughout this paper, when we consider proto-NS windswe mean both purely neutrino-driven proto-NS winds and proto-magnetar models with strong magnetic fields and potentially rapidrotation as described in Vlasov et al. (2017). We emphasize thelatter scenario, which achieves good agreement with observations,while also showing that existing yield predictions for the windsfrom unmagnetized, non-rotating proto-NSs overproduce some ob-served abundances by a large factor (Hoffman et al. 1996; Hoffman,Woosley, & Qian 1997). Recent studies indicate that ∼
40 per cent ofNS births produce magnetar-strength fields (Beniamini et al. 2019).Moreover, recent work by Sukhbold & Thompson (2017) arguesthat normal Type IIP supernovae may arise from magnetars withfew-ms spin period. Nevertheless, while the spin distribution ofNSs with magnetar-strength fields is highly uncertain, the observedspin distribution of normal pulsars indicates that their NSs are bornrotating slowly; a typical average value of the initial spin period is (cid:104) 𝑃 (cid:105) =
300 ms, with 𝜎 𝑃 =
150 ms (Faucher-Giguère & Kaspi 2006,table 6).Our paper is organized as follows. In Section 2 we describeour chemical evolution model. In Section 3 we present our results.Finally, in Section 4, we draw our conclusions.
MNRAS , 1– ?? (2021) ucleosynthesis signatures of proto-NS winds Figure 1.
The predictions of chemical evolution models including a con-tribution to Sr, Y, and Zr from neutrino-driven winds of proto-NSs withdifferent rotation period (Vlasov et al. 2017) (green dashed-dotted line: 𝑃 = 𝑃 = 𝑃 = 𝑃 =
10 ms). These models are compared with a model which doesnot assume proto-NS winds (red dashed curve), but only chemical enrich-ment from stellar winds of AGB stars (Cristallo et al. 2016) and massive stars(Sukhbold et al. 2016), and core-collapse SNe (Sukhbold et al. 2016). Theobservational data are from Zhao et al. (2016, black error bars), Misheninaet al. (2019, orange star symbols), and Chaplin et al. (2020, red star symbol).For Y, we also show the observational data from GALAH-DR2 (Buder etal. 2018), which are represented by the gray colour-code two-dimensionalhistogram, as well as by the average binned data (yellow triangles with errorbars), by selecting only dwarf stars with log ( 𝑔 ) > . >
20. Model curves (not shown) that adopt the predicted yieldsof spherical winds from unmagnetized proto-NSs would be mostly off thetop of these plots, exceeding the observed abundance ratios by 1-1 . We develop a chemical evolution model for the abundances in theISM of our Galaxy, which makes the following assumptions for thevarious stellar and SN chemical enrichment sources.(i) For AGB stars, we assume the stellar nucleosynthesis yields
Figure 2.
The predicted [Ba/Fe]-[Fe/H] abundance pattern from our refer-ence chemical evolution model including neutrino-driven winds of massiveproto-NSs (blue solid curve) as compared with a model which does not as-sume proto-NS winds (red dashed curve, like in Fig. 1). For these predictionswe base the Ba yield on the calculations of Wanajo (2013) rather than themuch lower Ba yields computed by Vlasov et al. (2017) (see §2). The twopanels focus on different sets of observational data, which are from Zhaoet al. (2016, green error bars), Mishenina et al. (2019, cyan filled circles),and Chaplin et al. (2020, red star symbol). The observational data fromGALAH-DR2 (Buder et al. 2018) are shown as in Fig. 1. as computed by Straniero, Gallino, & Cristallo (2006), Cristalloet al. (2007, 2009, 2011, 2015a,b, 2016), Piersanti, Cristallo, &Straniero (2013), and Straniero, Cristallo, & Piersanti (2014), whichare publicly available online at the FRUITY database website . Ourassumed set of stellar yields for AGB stars includes the followingmetallicities 𝑍 = . . . . . . . . . .
01, 0 . .
02, with stellar masses in therange 1 . < 𝑀 < . (cid:12) .(ii) We consider two alternatives for massive star yields. Ourreference model assumes the stellar nucleosynthesis yields as com-puted by Sukhbold et al. (2016) for non-rotating stars with masses inthe range 9 ≤ 𝑀 <
120 M (cid:12) at solar metallicity, which account forblack hole formation and “failed” SNe (e.g., see Ugliano et al. 2012;Pejcha & Thompson 2015; Ertl et al. 2016; Sukhbold & Adams 2020for simulations and models, and Smartt 2009; Gerke, Kochanek, &Stanek 2015; Adams et al. 2017; Basinger et al. 2020 for an obser-vational perspective). Specifically, we use the yields provided forthe Z9.6 model below 12 M (cid:12) and the W18 model at higher masses.Sukhbold et al. (2016) compute yields at solar metallicity, which weapply at all metallicities. With the W18 central engine, most starsbetween 22-25 M (cid:12) and above 28 M (cid:12) form black holes without ex-plosion, but they still produce enrichment through stellar winds. Ouralternative massive star yields use the calculations of Limongi &Chieffi (2018, set R) with stellar rotation velocity 𝑣 rot =
150 km s − and the following grid of iron abundances: [ Fe/H ] = − − − http://fruity.oa-teramo.inaf.it MNRAS , 1– ?? (2021) F. Vincenzo et al.
Figure 3.
Predictions for [Mo/Fe]-[Fe/H] (upper panel) and [Ru/Fe]-[Fe/H](lower panel). The black curve correspond to the models with p-rich outflowsfrom proto-NSs (Pruet et al. 2006), by assuming a production factor (PF)of 10 (black solid curve) and 30 (black dashed curve). The model withoutthe contribution of proto-NS winds is the red dashed line, like in Fig. 1.The observational data are from Peterson (2013, blue filled circles), Hansen,Andersen, & Christlieb (2014, orange filled circles), Spite et al. (2018, greenfilled circles), Mishenina et al. (2019, red filled circles), Mishenina et al.(2020, violet filled circles) . We note that Limongi & Chieffi (2018) also account for failedSNe, by assuming a sharp transition at 𝑀 >
25 M (cid:12) . Above thisthreshold mass, the chemical enrichment is provided only by thestellar winds.(iii) The average yields of Sr, Y, and Zr from neutrino-drivenwinds from proto-NSs are taken from the models of Vlasov et al.(2017) with rotation periods 𝑃 =
2, 3, 5, and 10 ms. For Ba, ourreference model assumes an average yield 𝑀 Ba,r = × − M (cid:12) ,which is of the order of magnitude predicted in the winds of themost massive proto-NSs by Wanajo (2013). Note that Vlasov et al.(2017) find very little Ba production in all of their models. However,they did not systematically consider higher-mass proto-NSs andthey did not include the effects of General Relativity (GR), both ofwhich enhance heavy-element production (Cardall & Fuller 1997),and were considered by Wanajo (2013). Conversely, Wanajo (2013)did not consider the effects of a strong magnetic field and rapidrotation on the nucleosynthesis, which Vlasov et al. (2017) findhave important consequences for production of elements 𝑍 < These stellar yields are publicly available at the following website: http://orfeo.iaps.inaf.it
Figure 4.
Predictions for [Ba/Fe]-[Fe/H] (upper panel), [Sr/Fe]-[Fe/H] (mid-dle panel), and [Mo/Fe]-[Fe/H] (lower panel), focusing on the trend atlow metallicities in order to reproduce the observations of Roederer etal. (2014, gray pengatons), which have also been binned in the range − . ≤ [Fe/H] < − . 𝑣 rot =
150 km s − ), the AGB stellar yields of Cristallo et al. (2016), andneutrino-driven winds from proto-NSs (Sr from Vlasov et al. 2017, Ba fromWanajo 2013, and Mo from Pruet et al. 2006). The various curves and theremaining observational data are the same as in Fig. 2. We also show forcomparison the prediction of the model with Sukhbold et al. (2016, S16;thin black dotted curve) yields with chemical enrichment from massive starsand proto-NS winds with 𝑃 = more like the Wanajo (2013) yields. This inconsistency points to theurgent need for a next generation of magnetic and rapidly rotatingproto-NS wind models including GR, a range of proto-NS masses,and dynamical magnetospheres (see Thompson & ud-Doula 2018).(iv) We assume that the production factors for the most abundantisotopes of Mo and Ru, 𝑃 Mo,Ru , are in the range 10-30, according tothe predictions of the models of Pruet et al. (2006), with the average
MNRAS , 1– ?? (2021) ucleosynthesis signatures of proto-NS winds yield of 𝑖 = Mo, Ru being defined as 𝑀 𝑖, pnw ( 𝑚 ) = 𝑃 𝑖 × 𝑋 (cid:12) ,𝑖 × 𝑀 tot-ej,SN ( 𝑚 ) , (1)where 𝑋 (cid:12) ,𝑖 is the Solar abundance by mass of 𝑖 = Mo, Ru (Asplundet al. 2009), and 𝑀 tot-ej,SN ( 𝑚 ) is the total ejected mass in the core-collapse SN explosion of a massive star with initial mass 𝑚 .(v) For Type Ia SNe, we assume the empirically motivated delay-time distribution function (DTD) (Maoz & Mannucci 2012):DTD Ia ( 𝑡 ) = 𝐴 Ia 𝑡 − . , (2)where 𝐴 Ia is chosen in order to have two Type Ia SNe over 13 . M (cid:12) of stellar mass formed (Bell et al. 2003; Maoz, Man-nucci, & Nelemans 2014; Vincenzo, Matteucci, & Spitoni 2017).In this work, we assume a minimum delay-time 𝜏 min,Ia =
150 Myr.The stellar yields of Type Ia SNe are from Iwamoto et al. (1999).
The star formation rate — We assume that the star formationrate (SFR) follows a linear Kennicutt law, namely SFR ( 𝑡 ) = SFE × 𝑀 gas ( 𝑡 ) , where SFE represents the star-formation efficiency and 𝑀 gas ( 𝑡 ) is the total gas mass in the Galaxy. The accretion rate — The simulated galaxy is assumed toform from the accretion of primordial gas from the circumgalacticenvironment. The gas infall rate obeys the following law: I( 𝑡 ) = 𝐴 I × 𝑒 − 𝑡 / 𝜏 inf , where 𝐴 I is a normalization constant that determinesthe total amount of gas accreted over the Hubble time, defining theso-called infall-mass, 𝑀 inf , of the models. The outflow rate — The model can account for the effect ofgalactic outflows, which carry gas and metals out of the galaxypotential well. The galactic winds are assumed to proceed with arate proportional to the SFR, namely O( 𝑡 ) = 𝜔 SFR ( 𝑡 ) , where 𝜔 is the so-called mass-loading factor. We note in advance that ourreference chemical evolution model – for simplicity – does notassume outflow activity ( 𝜔 = The chemical-enrichment rate — The chemical enrichmentfrom winds of AGB stars and massive stars, core-collapse SNe, TypeIa SNe, and neutrino-driven winds from proto-NSs is included inour chemical evolution model according to the following equation: R 𝑖 ( 𝑡 ) = 𝑚 cutoff ∫ 𝑚 TO ( 𝑡 ) d 𝑚 IMF ( 𝑚 ) SFR ( 𝑡 − 𝜏 𝑚 ) 𝑝 𝑖 (cid:0) 𝑚, 𝑍 ( 𝑡 − 𝜏 𝑚 ) (cid:1) + 𝑝 𝑖, Ia ∫ 𝑡𝜏 min,Ia d 𝜏 DTD Ia ( 𝜏 ) SFR ( 𝑡 − 𝜏 ) , (3)which describes the chemical-enrichment rate of the 𝑖 -th chemicalelement at the time 𝑡 from all the assumed dying nucleosyntheticsources. In the reference model, we assume the initial mass function(IMF) of Kroupa, Tout, & Gilmore (1993) and the stellar lifetimes, 𝜏 𝑚 , of Kobayashi (2004). Note that the Kroupa, Tout, & Gilmore(1993) IMF is quite different from the one usually referred to asa “Kroupa IMF” (Kroupa 2001). It has a high mass slope of − . − .
3, and it therefore predicts lower IMF-averaged yieldsfrom massive stars for a given SFR.The quantity 𝑚 TO ( 𝑡 ) in equation (3) represents the turn-offmass, which is derived from the assumed inverse stellar lifetimesof Kobayashi (2004); the quantity 𝑚 cutoff =
100 M (cid:12) representsthe maximum stellar mass, which is assumed to form in the star-formation events; the quantity 𝑝 𝑖 ( 𝑚, 𝑍 ) represents the stellar nu-cleosynthetic yields of the 𝑖 -th chemical element from all stars withmass 𝑚 and metallicity 𝑍 ; finally, 𝑝 𝑖, Ia is the average nucleosynthe-sis yield from Type Ia SNe. Note that 𝑝 𝑖 ( 𝑚, 𝑍 ) includes the nucle-osynthesis yields from stellar winds of AGB stars and massive stars,core-collapse SNe, and neutrino-driven winds from proto-NSs. We [Fe/H] = − . 𝑣 rot / [km/s] [Sr/Fe] [Y/Fe] [Zr/Fe] [Ba/Fe] [Mo/Fe]0 − . − . − . − . − . − . − . − . − . − . . − . − .
24 0 . − . [Fe/H] = − . 𝑣 rot / [km/s] [Sr/Fe] [Y/Fe] [Zr/Fe] [Ba/Fe] [Mo/Fe]0 − . − . − . − . − . − . − . − . − . − . .
41 0 .
57 0 .
85 1 .
10 0 . [Fe/H] = − . 𝑣 rot / [km/s] [Sr/Fe] [Y/Fe] [Zr/Fe] [Ba/Fe] [Mo/Fe]0 − . − . − . − . − . .
58 0 .
33 0 . − . − . .
41 1 .
51 1 .
81 2 .
02 1 . [Fe/H] = 𝑣 rot / [km/s] [Sr/Fe] [Y/Fe] [Zr/Fe] [Ba/Fe] [Mo/Fe]0 − . − . − . − . − . .
37 0 . − . − . − . .
39 0 .
71 0 . − . − . Table 1.
The IMF-averaged yield of [X/Fe] ( 𝑋 = Sr, Y, Zr, Ba, and Mo)as predicted by the massive star models of Limongi & Chieffi (2018), as afunction of [Fe/H] and rotation velocity. The assumed IMF is that of Kroupa,Tout, & Gilmore (1993). The values in the table are computed by using gross stellar nucleosynthetic yields, namely including also the contributionof the ejected material which was present at the stellar birth and remainedunprocessed. The IMF-averaged stellar yields are computed by using thecode
VICE (Johnson & Weinberg 2020). These yields are reported in termsof [X/Fe], where Fe is the IMF-averaged iron yield from massive stars only. assume that proto-NS winds arise for stars with progenitor masses8 ≤ 𝑚 <
20 M (cid:12) and that more massive progenitors produce blackhole remnants with no proto-NS winds.
The chemical evolution equations — Using all quantities de-fined above, our model solves the following differential equationfor the evolution of the gas mass in the form of the 𝑖 -th chemicalelement in the ISM of the galaxy as a function of time: 𝑀 g ,𝑖 ( 𝑡 ) 𝑑𝑡 = − 𝑋 𝑖 ( 𝑡 ) SFR ( 𝑡 ) + R 𝑖 ( 𝑡 ) + I( 𝑡 ) − O( 𝑡 ) , (4)where 𝑋 𝑖 ( 𝑡 ) = 𝑀 g ,𝑖 ( 𝑡 )/ 𝑀 gas ( 𝑡 ) is the ISM abundance by mass ofthe 𝑖 -th chemical element at the time 𝑡 . In our reference chemicalevolution model, we assume SFE = − , 𝜏 inf = 𝜔 = ( 𝑀 inf / M (cid:12)) = .
5, which are tuned to reproduce the observedchemical abundance patterns of [ 𝑋 /Fe]-[Fe/H], where 𝑋 = O, Sr, Y,Zr, Ba, Mo, and Ru, at the Solar neighbourhood. These values areconsistent with previous works (e.g., Minchev, Chiappini, & Martig2013; Nidever et al. 2014; Spitoni et al. 2015; Vincenzo, Matteucci,& Spitoni 2017; Magrini et al. 2018). In contrast to the models ofAndrews et al. (2017) and Weinberg et al. (2017), we are able toobtain solar metallicities with 𝜔 = MNRAS , 1– ?? (2021) F. Vincenzo et al.
The predictions of our reference chemical evolution model for thefirst peak s-process elemental abundance ratios are shown in Fig. 1.For [Y/Fe], the observational data are from the second data releaseof the GALactic Archaeology with HERMES (GALAH) spectro-scopic survey (Buder et al. 2018, two dimensional histogram withthe gray color-coding), considering only dwarf stars with surfacegravity log ( 𝑔 ) > . >
20. To under-stand the average trend of the data, we also show the mean [Y/Fe]from GALAH with the corresponding ± 𝜎 dispersion as a functionof [Fe/H] (yellow triangles with error bars). Finally, we show the[Y/Fe] ratio as measured by Chaplin et al. (2020) in a bright starbelonging to the inner MW halo ( 𝜈 Indi) (red star symbol), for whichthey measured an asteroseismic age of ≈
11 Gyr from the analysisof the TESS oscillation spectrum of the star. For [Zr/Fe], the ob-servational data are from Chaplin et al. (2020, red star symbol) andZhao et al. (2016, black data with error bars) for a sample of starsin the Solar neighbourhood. For [Sr/Fe] we show the abundancemeasurements of Mishenina et al. (2019, yellow star symbols). Allobservational data shown in Fig. 1 are measured by accounting fornon-local thermodynamic equilibrium (NLTE) effects in the abun-dance analysis.When accounting only for the chemical enrichment from core-collapse SNe, Type Ia SNe, and the stellar winds of AGB stars andnon-rotating massive stars (pink dashed curve in Fig. 1), we cannotreproduce the observed abundance ratios of [X/Fe] of the first-peaks-process elements ( 𝑋 = Sr, Y, Zr). In particular, our chemicalevolution model consistently underpredicts the abundance ratiosat metallicities below [Fe/H] ≈ − .
5. Including the additional r-process contribution from neutrino-driven winds of proto-NSs withrotation periods in the range 2 ≤ 𝑃 ≤ 𝑃 =
10 ms the model underpredictsthe observed [Sr/Fe] ratios at [Fe/H] ≈ −
1, though agreement with[Y/Fe] and [Zr/Fe] is acceptable. For 𝑃 =
10 ms the proto-NSis effectively “non-rotating” in the sense that the predicted yieldswould not decrease much for still longer periods.Although we do not show them in Fig. 1, we have also com-puted models using the yields of the “spherical” calculations ofVlasov et al. (2017) for non-rotating, unmagnetized proto-NS. Thesemodels overpredict the observed [Y/Fe], [Zr/Fe], and [Sr/Fe] ratiosby 1-1 . 𝑡 < ∼ [ Fe/H ] (cid:46) − . − . (cid:46) [ Fe/H ] (cid:46) − . [ Fe/H ] ≈ − .
6, [Y/Fe] increases because
Figure 5.
Model predictions of [Ba/Fe] (upper panel), [Sr/Fe] (intermediatepanel), and [Mo/Fe] (bottom panel) as a function of [Fe/H], as computed byusing the nucleosynthetic stellar yields of Limongi & Chieffi (2018) models.The black dotted curve corresponds to 𝑣 rot = − , the black dashedcurve to 𝑣 rot =
150 km s − , and the black solid to 𝑣 rot =
300 km s − . Theobservational data are the same as in Figs. 2-4. of the large amounts of Y produced by AGB stars per unit time,which is eventually overcome by Type Ia SNe at [ Fe/H ] > ∼
0. Asimilar explanation is valid for the predicted trends of [Sr/Fe] and[Zr/Fe], in agreement with discussion of [Sr/Fe] by Johnson &Weinberg (2020). However, without a proto-NS wind contribution,these trends lie below the data by ∼ . 𝑀 Ba,r = × − M (cid:12) per event) pro-vide excellent agreement with the bulk of the observational datafrom the GALAH survey (Buder et al. 2018) as well as with Zhaoet al. (2016) and Chaplin et al. (2020), all including NLTE effectsin their abundance analysis. Without this contribution, the modelunderpredicts observed abundances at [Fe/H] (cid:46) − MNRAS , 1– ?? (2021) ucleosynthesis signatures of proto-NS winds It has been shown that the p-rich outflows of proto-NSs can behighly effective in the nucleosynthesis of Mo and Ru (Pruet et al.2006). In order to test this scenario, in Fig. 3 we compare the predic-tions of our models for [Mo/Fe] (upper panel) and [Ru/Fe] (lowerpanel) with a set of observational data (Peterson 2013; Hansen,Andersen, & Christlieb 2014; Spite et al. 2018; Mishenina et al.2019, 2020). Similarly to what we find for the first- and second-peak s-process elements, our chemical evolution model includingproto-NS winds with a production factor 𝑃 =
30 produces a goodmatch to the bulk of the observational data of [Mo/Fe] and [Ru/Fe]as a function of [Fe/H], while the model without proto-NS windsfalls far short.
The Sukhbold et al. (2016) yields are available only at solar metal-licity, and they assume non-rotating massive star progenitors. Toaddress both of these potential shortcomings, we consider the al-ternative yields of Limongi & Chieffi (2018). Table 1 reports theIMF-averaged [X/Fe] ratios ( 𝑋 = Sr, Y, Zr, Ba, and Mo) as predictedwhen assuming these yields, for different [Fe/H] abundances and ro-tation velocities. Larger rotation velocity causes an enhancement ofthe s-process production in massive stars (see also figure 4 of John-son & Weinberg 2020); this is due to the so-called rotation-inducedmixing, which can bring material from the convective H-burningshell (in particular, N nuclei produced in the CNO cycle) to theHe-burning core, where the reaction Ne( 𝛼 , 𝑛 ) Mg takes place(the main source of free neutrons in massive stars). When the Nnuclei reach the He-core, they can capture two 𝛼 -particles to pro-duce Ne, eventually giving rise to more s-process events. Thisphysical mechanism, which enhances the s-process nucleosynthesisin massive stars, was originally proposed by Frischknecht, Hirschi,& Thielemann (2012) to explain the s-process nucleosynthesis atvery low-metallicity (see also Cescutti et al. 2013).The rotation velocity of massive stars is highly uncertain. Onebenchmark study is that of Ramírez-Agudelo et al. (2013), whofound that the distribution of the projected rotation velocities ina sample of massive stars in the Tarantula Nebula has a peak at ∼
80 km/s, with the 80th percentile being at ≈
300 km/s. Therefore,in the context of the stellar models of Limongi & Chieffi (2018), avalue of 𝑣 rot ≈
300 km/s should be considered as an approximateupper limit from an observational point of view, with the majorityof the stars likely rotating with velocities in the range 0 < 𝑣 rot <
150 km/s. However, typical rotation speeds could be different atvery low metallicities.In Fig. 4, we show the predictions of chemical evolution mod-els assuming the stellar nucleosynthesis yields of Limongi & Chieffi(2018) for 𝑣 rot =
150 km/s with and without proto-NS winds (bluesolid curve and red dashed curve, respectively, for [Ba/Fe] in theupper panel). We assume yields are constant below [Fe/H] = − 𝑃 = − ≤ [ Fe/H ] ≤ −
2. Conversely, when weinclude our standard estimate of the r-process contribution fromproto-NS winds, we obtain better agreement with the average trendof the observational data at low [Fe/H]. The [Sr/Fe] comparisonprefers the higher proto-NS yields of the 𝑃 = 𝑣 rot =
150 km/s and proto-NS winds systematically overestimates [Sr/Fe] at [ Fe/H ] (cid:38) −
2. This disagreement can be alleviated bytransitioning to low rotation speeds for [ Fe/H ] (cid:38) −
2, thus mov-ing towards the black dashed curve computed with Sukhbold et al.(2016) stellar yields.If we assume still higher rotation velocities at low metallicity,then it becomes possible to reproduce the data without the additionof proto-NS winds. Fig. 5 compares the observed chemical abun-dance ratios of [Ba/Fe] (upper panel), [Sr/Fe] (intermediate panel),and [Mo/Fe] (bottom panel) with the predictions of models assum-ing the stellar nucleosynthetic yields of Limongi & Chieffi (2018) for 𝑣 rot =
0, 150, and 300 km s − . At least in overall level, the observed[Sr/Fe] and [Ba/Fe] ratios at low metallicities can be explained bymodels with rotation velocities in the range 150 < 𝑣 rot <
300 km/s,without the need of a significant r-process contribution from addi-tional sources. Reproducing the observed [Mo/Fe] requires typicalrotation speeds at the top of this range.
In this work, we have tested the hypothesis that the observed abun-dances of first-peak (i.e. Sr, Y, Zr) and second-peak (i.e. Ba) s-process elements, as well as the abundances of Mo and Ru, canbe explained by incorporating an additional r-process contributionat low metallicities from neutrino-driven winds from proto-NSs.To this aim, we have developed chemical evolution models for theevolution of the elemental abundances in our Galaxy includingproto-NS winds, also investigating the impact of different assump-tions for the chemical enrichment of massive stars, which can beimportant s-process contributors of light neutron-capture elementsat low [Fe/H] (Frischknecht, Hirschi, & Thielemann 2012; Cescuttiet al. 2013).We base our proto-NS wind yields on the calculations ofVlasov et al. (2017, for Y, Sr, Zr), Wanajo (2013, for Ba), andPruet et al. (2006, for Mo, Ru). We caution that the Wanajo (2013)Ba yield of ≈ × − 𝑀 (cid:12) per event is much higher than the Ba yieldpredicted by Vlasov et al. (2017), so we regard our Ba predictionsas more uncertain (see Section 2 for details). For massive stars, weconstruct models using the non-rotating models of Sukhbold et al.(2016) computed at [Fe/H] =
0, and alternative models using theyields of Limongi & Chieffi (2018, set R), which are available fordifferent rotation velocities and [Fe/H] abundances. Both Sukhboldet al. (2016) and Limongi & Chieffi (2018) massive star modelsaccount for failed SNe, but Sukhbold et al. (2016) compute an ex-plosion landscape based on a neutrino-driven central engine, whileLimongi & Chieffi (2018) impose a mass threshold for black holeformation at 25 M (cid:12) .Our main conclusion can be summarized as follows.(i) Adding the predicted proto-NS wind yields to the Sukhboldet al. (2016) massive star yields, and our standard choice of TypeIa supernova and AGB yields, leads to good agreement with theobserved trends of [Y/Fe], [Zr/Fe], [Sr/Fe], [Ba/Fe], [Mo/Fe], and[Ru/Fe] (see Figs. 1-3). The best agreement for Sr, Y, and Zr isobtained for proto-NS rotation periods 𝑃 ∼ − 𝑃 ∼
10 ms (which are effectively in the non-rotating limit forour purposes) underpredict the observed [Sr/Fe]. For Mo and Ru,production factors of 10-30 (see equation 1) are required, similar tothe proto-NS wind predictions of Pruet et al. (2006). Without proto-NS winds the models underpredict the observations by 0 . − < ∼ − .
5, though for Y, Sr, and Ba the AGBcontribution leads to acceptable agreement near solar metallicity.
MNRAS , 1– ?? (2021) F. Vincenzo et al. (ii) Because the Sukhbold et al. (2016) yields assume non-rotating, solar metallicity progenitors, we have also consid-ered the alternative yield sets of Limongi & Chieffi (2018)for [Fe/H] = − , − , − , 𝑣 rot = , ,
300 km s − . For 𝑣 rot =
150 km s − , we find rea-sonable agreement with observed [Ba/Fe] and [Sr/Fe] trends for − < [Fe/H] < − 𝑃 = − < − − < ∼ [Fe/H] < ∼ − .
5, models with the Limongi &Chieffi (2018), 𝑣 rot =
150 km s − overpredict the observed [Sr/Fe],even without proto-NS winds (see Fig. 4). This conflict suggests thatrotation velocities of massive stars must be lower than 150 km s − at these metallicities.(iv) The predicted s-process yields of low metallicity massivestars are sensitive to rotation, increasing by 1-3 orders of magnitudefor 𝑣 rot =
300 km s − vs. 𝑣 rot =
150 km s − (see Table 1). Evenwithout proto-NS winds, models with yields intermediate betweenthese two cases could reproduce the observed levels of Ba and Srat [Fe/H] < − 𝑣 rot =
300 km s − yieldscould reproduce the observed levels of Mo, though not the detailedtrend. The observations of Ramírez-Agudelo et al. (2013) in theTarantula nebula favor typical rotation velocities <
150 km s − ,but higher rotation might be possible at low metallicity because ofreduced mass loss and associated angular momentum loss. Veryhigh rotation velocities are disfavoured in some recent chemicalevolution models such as those of Prantzos et al. (2018, 2020) andKobayashi, Karakas, & Lugaro (2020).(v) Models that adopt the Vlasov et al. (2017) yields for sphericalwinds from non-rotating, unmagnetized proto-NS are strongly ruledout, overpredicting the observed Sr, Y, and Zr abundances by 1-1.5 dex, in agreement with previous studies (Woosley et al. 1994;Hoffman et al. 1996; Hoffman, Woosley, & Qian 1997; Roberts,Woosley, & Hoffman 2010).In summary, the winds from proto-NS with rotation periods 𝑃 ∼ − < − .
5, where models without this contribution fall shortby 0 . 𝑃 ∼
10 ms models investigated here can be viewed asa near lower limit to the neutrino-driven wind contribution in theVlasov et al. (2017) models, as they have strong magnetic fields butminimal rotation, and they are already close to producing the ob-served levels of Sr, Y, and Zr. Further reducing the predicted yieldsof these elements would require changing the electron fraction evo-lution in the cooling proto-NS models, by changing the ratio of theelectron- and anti-electron neutrino fluxes in the first moments aftersuccessful SN explosion.
We thank Tuguldur Sukhbold for providing the set of stellar yieldsassumed in our chemical evolution models. We thank Anna Porre-don and Sten Hasselquist for useful remarks. This work was sup-ported by NSF grant AST-1909841. F.V. acknowledges the support of a Fellowship from the Center for Cosmology and AstroParticlePhysics at the Ohio State University. TAT is supported in part byNASA grant
DATA AVAILABILITY
The data underlying this article will be shared on reasonable requestto the corresponding author.
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