Using failed supernovae to constrain the Galactic r-process element production
B. Wehmeyer, C. Frohlich, B. Côté, M. Pignatari, F.-K. Thielemann
MMon. Not. R. Astron. Soc. , 1745 (2019)
Using failed supernovae to constrain the Galactic r-processelement production
B. Wehmeyer, , (cid:63) C. Fr¨ohlich, , B. Cˆot´e, , , M. Pignatari, , , , and F.-K. Thielemann , Department of Physics, North Carolina State University, 2401 Stinson Dr, Raleigh, NC 27695-8202, USA Konkoly Observatory, Research Centre for Astronomy and Earth Sciences,Hungarian Academy of Sciences, Konkoly-Thege Mikl´os ´ut 15-17, H-1121 Budapest, Hungary E.A. Milne Centre for Astrophysics, Dept. of Physics & Mathematics, University of Hull, HU6 7RX, United Kingdom Univ. Basel, Dept. Phys., Klingelbergstr. 82, CH-4056 Basel, Switzerland GSI Helmholtzzentrum f¨ur Schwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany Joint Institute for Nuclear Astrophysics - Center for the Evolution of the Elements NuGrid Collaboration, http://nugridstars.org
Accepted 2019 May 05. Published 2019 May 16; in original form 2018 December 31
ABSTRACT
Rapid neutron capture process (r-process) elements have been detected in a largefraction of metal-poor halo stars, with abundances relative to iron (Fe) that varyby over two orders of magnitude. This scatter is reduced to less than a factor ofthree in younger Galactic disk stars. The large scatter of r-process elements in theearly Galaxy suggests that the r-process is made by rare events, like binary compactmergers and rare sub-classes of supernovae. Although being rare, neutron star mergersalone have difficulties to explain the observed enhancement of r-process elements in thelowest-metallicity stars compared to Fe. The supernovae producing the two neutronstars already provide a substantial Fe abundance where the r-process ejecta fromthe merger would be injected. In this work we investigate another complementaryscenario, where the r-process occurs in neutron star - black hole mergers in addition toneutron star mergers. Neutron star - black hole mergers would eject similar amountsof r-process matter as neutron star mergers, but only the neutron star progenitorwould have produced Fe. Furthermore, a reduced efficiency of Fe production fromsingle stars significantly alters the age-metallicity relation, which shifts the onset ofr-process production to lower metallicities. We use the high resolution ((20 pc) /cell)inhomogeneous chemical evolution tool “ICE” to study the outcomes of these effects.In our simulations, an adequate combination of neutron star mergers and neutronstar-black hole mergers qualitatively reproduces the observed r-process abundances inthe Galaxy. Key words:
Galaxy: abundances, Galaxy: evolution, nuclear reactions, nucleosyn-thesis, abundances, Supernovae: general
The r -process (e.g., Cowan et al. 1991; Arnould et al. 2007;Thielemann et al. 2011; Cowan et al. 2019, and referencestherein) is one of the dominant sources of elements heav-ier than Fe. At present, it is still unclear whether neutronstar mergers (NSMs, since recently the only observed andconfirmed r-process site) are the exclusive site of this pro-cess (e.g., Cescutti et al. 2015; Hirai et al. 2015; Ishimaru,Wanajo & Prantzos 2015; Shen et al. 2015; van de Voort et (cid:63) [email protected] al. 2015; Wehmeyer et al. 2015; Thielemann et al. 2017; Cˆot´eet al. 2018; Hotokezaka et al. 2018; Ojima et al. 2018; Siegelet al. 2018; Cowan et al. 2019; Haynes & Kobayashi 2019).While early scientific studies argued that neutrino fluxesin core-collapse supernovae (CCSNe) would have the rightproperties to host neutrino-driven nucleosynthesis (e.g., Ar-cones & Thielemann 2013, and references therein) whichmight include the r-process (e.g., Woosley et al. 1994, Taka-hashi et al. 1994), later and more advanced calculations (e.g.,Liebend¨orfer et al. 2003) pointed to proton-rich conditions intheir innermost ejecta, rather causing a νp process (Fr¨ohlichet al. 2006a,b; Pruet et al. 2005, 2006; Wanajo 2006, 2013) c (cid:13) a r X i v : . [ a s t r o - ph . GA ] A ug Wehmeyer et al. instead of the r-process. However, the collapse of the core ofa massive star leads either to a CCSN and a neutron star(NS) or the formation of a black hole (BH, e.g., Heger etal. 2003). When two NSs merge (e.g., Lattimer & Schramm1974; Paczynski 1986; Eichler et al. 1989, but see also morerecent works, e.g., Rosswog et al. 2018), conditions for theonset of the r -process are met (Freiburghaus et al. 1999;Panov et al. 2008; Korobkin et al. 2012; Bauswein et al. 2013;Rosswog 2013; Rosswog et al. 2014; Wanajo 2014; Eichler etal. 2015; Just et al. 2015). This site has been confirmed bygravitational wave detection GW170817 (e.g., Abbott et al.2017a), followed by its optical counterpart, kilonova SSS17a,showing evidence of the successful production of r -processelements (e.g., Abbott et al. 2017b, Abbott et al. 2017c).Hence, NSMs are a confirmed source of Galactic r -process el-ements. Considering this site as the exclusive r -process site,however, comes with two distinct issues:(i) r -process elements are abundant already at very lowmetallicities. Two CCSNe must have occurred before theNSM event in order to produce the two involved NSs. Hence,the interstellar medium (ISM) hosting the NSM is alreadypolluted by the Fe-rich ejecta of those two CCSNe. Manystars with low metallicity already show high r -process abun-dances compared to Fe, up to two orders of magnitudelarger than solar (e.g., Sneden et al. 2008; Roederer et al.2010; Hansen et al. 2018). Such enhancements are difficultto explain by a scenario where NSM act as the exclusive r-process element production source (e.g., Argast et al. 2004;Wehmeyer et al. 2015).(ii) r -process elemental abundances in low metallicitystars show a large scatter in comparison to solar metal-licity stars. The observed abundance scatter in alpha ele-ments with respect to Fe remains rather small throughoutthe entire chemical evolution. Instead, r -process elementsshow a much larger scatter in abundances at low metallic-ities (Roederer et al. 2010, Beers et al. 2018). Since alphaelements are made mostly by CCSNe, this suggests that r -process elemental production events should occur at a lowerfrequency than CCSNe (e.g., Thielemann et al. 2017).Recent works to address these open questions have mostlyconsidered two scenarios, i.e., adding a rare sub-class of su-pernova as second early r-process site, or considering sub-halos of the Galaxy as independent building blocks that willlater merge to form the Galaxy. The former approach isbased on the assumption that there could be a second, rare r -process production site, e.g., (the sub-class of) magnetoro-tationally driven supernovae (or “jet-supernovae”, see, e.g.,Winteler et al. 2012; M¨osta et al. 2015; Nishimura et al. 2017;Halewi & M¨osta 2018). Since this site would eject r -processelements and negligible amounts of Fe, r -process elementscould be released into a region of lower metal content thana NSM could (those require two NSs to be present and thustwo previous supernovae, already enhancing the ISM withmetals), if the occurrence rate of such a supernova would below (as expected due to the required high magnetic fields)in comparison to “regular” CCSNe. Stars being polluted bysuch an event would inherit high r -process abundances in Among the stable alpha elements are C, O, Ne, Mg, Si, S, Ar,and Ca. comparison to stars polluted by regular CCSNe. This wouldalso allow to explain the large scatter seen in r -process abun-dances in low metallicity stars.These considerations were already discussed in Cescuttiet al. (2015) and Wehmeyer et al. (2015). However, despitethe fact that 10 Gauss NSs as remnants of this distinctsupernova channels have been detected, this scenario stillhas to wait for an observational confirmation (Fujimoto etal. 2006, Fujimoto et al. 2008, Winteler et al. 2012, M¨ostaet al. 2014). Furthermore, this nucleosynthesis site involvesthe difficulty of high resolution treatments of the magneto-rotational instability (e.g., M¨osta et al. 2015; Rembiasz et al.2016; Sawai & Yamada 2016; Nishimura et al. 2017; Ober-gaulinger et al. 2018).A second approach to solve the difficulties (i) and (ii)above, is to consider dwarf galaxies as individually develop-ing sub-systems that will merge to later form the Galactichalo (e.g., Hirai et al. 2015). Observations of dwarf galaxysystems show that these systems have lower star formationefficiency (Kirby et al. 2013) and higher gas outflow rates(see predictions from cosmological simulations, e.g., Mura-tov et al. 2015; Pillepich et al. 2018). These features allowthe contribution of NSMs to already take place at low metal-licities (because lower star formation efficiency slows downthe temporal evolution of [Fe/H], which allows NSMs to ap-pear at lower [Fe/H] values with respect to the star forma-tion rate, cf., Ishimaru, Wanajo & Prantzos 2015) and pro-vide large abundance scatter (among others, because of gasoutflows in chemodynamical models, cf., Hirai et al. 2015,and the stochastic nature of dwarf systems, cf., Ojima et al.2018). Although such systems are observationally confirmedto have seen r -process production events (Ji et al. 2016;Marshall et al. 2018), it is yet unclear whether a stochasticchemical evolution model featuring low star formation effi-ciencies is applicable to the bulk of these kind of systems(Kirby et al. 2013; Ojima et al. 2018).In this paper, we study an alternative scenario with re-spect to the ones discussed above: We consider BH - NSmergers (BHNSM) as second r -process elemental produc-tion site in addition to NSMs. This site has one major dif-ference compared to NSMs: BHNSM require only one NS tobe present in the system. This means that only one
CCSNis required in the system before the r -process event. Thisallows BHNSMs to occur at lower initial metallicities thanNSMs. Also, the slower overall increase of metallicity due toless successful CCSNe permits the presence of r-process richstars at lower metallicities.This work is organized as follows. In section 2, we dis-cuss the astronomical observations relevant for this work. Insection 3, we introduce the model used to compute the evo-lution of abundances. In section 4, we present the influenceof the different r- and non-r-process sites on the evolution.In section 5, our results are summarized and discussed. Galactic chemical evolution (GCE) is a powerful tool tostudy the contributions of the different elemental produc-tion sites to stellar abundances. For many lighter elements c (cid:13) , 1745 sing failed supernovae to constrain the Galactic r-process element production (e.g., Mg, O, C) the production sites are well known. BeyondFe, the r-process contributions provide about half of the ele-ment abundances in the solar system, and are the dominantsource in the Universe of several elements like Ir, Pt and Au(for a recent review see Cowan et al. 2019). Eu is the mostobserved r-process element, and it is used as a diagnostic tostudy the history of the r-process enrichment of the Galaxy(e.g., Burris et al. 2000). Eu abundances are derived usingmostly the two UV lines at 4192 .
70 and 4205 .
05 Angstr¨om(e.g., Bi´emont et al. 1982).We make use the abundance database SAGA (StellarAbundances for Galactic Archaeology, e.g., Suda et al. 2008,2011; Yamada et al. 2013), with [Eu/Fe] abundances mainlyfrom Francois et al. (2007); Simmerer et al. (2004); Barklemet al. (2005); Ren et al. (2012); Roederer et al. (2010,2014a,b,c); Shetrone, Cˆot´e, Stetson (2001); Shetrone et al.(2003); Geisler et al. (2005); Cohen & Huang (2009); Letarteet al. (2010); Starkenburg et al. (2013); McWilliam et al.(2013). We exclude carbon enhanced metal poor (“CEMP”)stars i.e., stars with [C/Fe] (cid:62) (cid:54) −
1) and starswith binary nature, since the surface abundances of suchobjects are expected to be affected by pollution from a bi-nary companion (Ryan et al. 2005), which is beyond thescope of the present study. When comparing the observedEu abundances as a function of [Fe/H] with those of lighteralpha elements (primarily those made by CCSNe) it is verystriking to see that the two curves behave similarly closeto solar metallicities, but differ greatly at low metallicities(e.g., Thielemann et al. 2017; Cowan et al. 2019), makingmetal-poor stars to unique tracers of the early evolution ofGalactic r-process nucleosynthesis (e.g., Sneden et al. 2008;Frebel 2018; Horowitz et al. 2018).
The detection of the gravitational wave event GW170817(e.g., Abbott et al. 2017a) has been interpreted as a coa-lescence of two compact objects with masses in the range1 . (cid:12) (cid:54) m (cid:54) . (cid:12) . The GW emission was followedby the detection of a kilonova (SSS17a) whose light curvesuggests r-process element production (e.g., Chornock et al.2017; Cowperthwaite et al. 2017; Tanaka et al. 2017; Villaret al. 2017). Lanthanides as Eu were produced in the event(e.g., Tanvir et al. 2017; Wollaeger et al. 2018). While themajority of the literature suggests that the coalescence oftwo NSs was the origin of this astronomical event (Abbott etal. 2018a), it cannot be ruled out that the event was actuallythe coalescence of a NS and a BH (Hinderer et al. 2018). Fur-thermore, Hinderer et al. (2018) showed that the GW only and the electromagnetic only observations can only rule outa BHNSM for an extreme range of the parameter space andfind that 40% of the parameter space set by the nuclear andastrophysical uncertainties would permit a BHNSM eventinstead of a NSM event in the case of GW170817/SSS17a.A possible formation channel for a required stellar mass BH- considered in this study - is that it originates in a failedSN (e.g., Heger et al. 2003), which will be discussed in sec-tions 3.2.3 & 3.2.4. Another possible origin of the requiredstellar mass BH is e.g., in primordial fluctuations in the early We use the notation [A/B]= log(A / B) star − log(A / B) (cid:12) M tot Total infall mass 10 M (cid:12) τ time scale of infall decline 5 × yrs t max time of the highest infall rate 2 × yrs t final duration of the simulation 13 . × yrs Table 1.
Main infall parameters. See Wehmeyer et al. (2015) fordetails on the parameters.
Universe. A probable formation channel of such objects isdescribed in e.g., Garcia-Bellido et al. (1996); Carr et al.(2016); Garcia-Bellido (2018). However, their occurrence fre-quency in BHNSMs is hard to predict, therefore we do notinclude them here explicitly.
In comparison to homogeneous GCE models, inhomoge-neous models track the location of the nucleosynthesis sites.This permits to reproduce the scatter of abundances in-stead of predicting a linear evolution. On the other hand,large scale effects (e.g., galaxy collisions, spiral arms mixing)can only be approximated in such models. In this study weuse the inhomogeneous chemical evolution model describedin Wehmeyer et al. (2015). In the following sections, werecall the main components of the model for convenience(sections 3.1, 3.2.1, and 3.2.2) and highlight the improve-ments made to the model for the purpose of this study, es-pecially the treatment of the additional r-process site relatedto BHNSMs (sections 3.2.3 and 3.2.4).
We set up a cube of (2 kpc) in the Galaxy which is cut into100 sub cubes with an edge length of 20 pc. During eachtime step of 1 My, the following calculations are performed:(i) Primordial matter is assumed to fall uniformly intoeach simulation sub-cube. The total amount of gas fallinginto the simulation volume is calculated via a˙ M ( t ) = at b e − t/τ , (1)prescription, which permits two main infall components: Aninitial constant rise of infall following by an exponential de-cay of the infall rate. While τ and the total Galaxy evolutiontime t final are fixed initially, the parameters a and b can bedetermined alternatively from M tot (the total infall massintegrated over time), defined by M tot = (cid:90) t final at b e − t/τ dt , (2)and the time of maximal infall t max , given by t max = bτ . (3)See table 1 for the applied parameters.(ii) The total gas mass in the volume is calculated andstar formation is triggered. We use a Schmidt law with adensity power α = 1 . c (cid:13)487
We set up a cube of (2 kpc) in the Galaxy which is cut into100 sub cubes with an edge length of 20 pc. During eachtime step of 1 My, the following calculations are performed:(i) Primordial matter is assumed to fall uniformly intoeach simulation sub-cube. The total amount of gas fallinginto the simulation volume is calculated via a˙ M ( t ) = at b e − t/τ , (1)prescription, which permits two main infall components: Aninitial constant rise of infall following by an exponential de-cay of the infall rate. While τ and the total Galaxy evolutiontime t final are fixed initially, the parameters a and b can bedetermined alternatively from M tot (the total infall massintegrated over time), defined by M tot = (cid:90) t final at b e − t/τ dt , (2)and the time of maximal infall t max , given by t max = bτ . (3)See table 1 for the applied parameters.(ii) The total gas mass in the volume is calculated andstar formation is triggered. We use a Schmidt law with adensity power α = 1 . c (cid:13)487 , 1745 Wehmeyer et al. in the current time step. This number is then divided by theintegrated initial mass function (“IMF”, Salpeter type witha slope of − .
35) to obtain the number of stars formed pertime step.(iii) Once the number of newly born stars is calculated,star forming cells are selected randomly. Since star formationcan be triggered by events as cloud-cloud interactions (e.g.,shells of supernova remnants), we prefer cells with higherdensities as location for newly born stars.(iv) Once a star forming cell is selected, we choose themass of the newly born star randomly, with mass probabil-ities obeying a Salpeter type IMF with a slope of − .
35, inthe mass range of 0 . (cid:12) (cid:54) m (cid:54) (cid:12) . In order to permitstellar masses to be well distributed (i.e., no bottom heavyIMF) we permit star formation only in cells containing atleast 50M (cid:12) of gas. We consider stars with birth masses be-low 8M (cid:12) as low and intermediate mass stars (LIMS), andstars more massive than 8M (cid:12) as high mass stars (HMS)(v) The newly born star inherits the composition of theISM out of which it is formed. From its birth mass andmetallicity, we obtain its life expectation using the GenevaStellar Evolution and Nucleosynthesis Group (cf. Schalleret al. 1992; Schaerer et al. 1993a,b; Charbonnel et al. 1993)predictions, given by:log( t ) = (3 .
79 + 0 . Z ) − (3 .
10 + 0 . Z )log( M )+ (0 .
74 + 0 . Z )log ( M ), (4)where t is the expected life time of a star in My, Z is themetallicity with respect to solar, and M the star’s mass insolar masses.(vi) Once a star has reached the end of its calculated lifetime, a stellar death event is triggered (according to its birthmass), as discussed below. Low and intermediate mass stars (LIMSs) produce most ofC and N in the Galactic disk (e.g., Kobayashi & Nakasato2011). During the Asymptotic Giant Branch (AGB) phase,LIMSs produce the bulk of the slow neutron capture (“s-process”) abundances beyond Sr present in the solar system(e.g., K¨appeler et al. 2011; Bisterzo et al. 2014, and refer-ences therein). LIMSs do not make significant contributionsto the Galactic Fe or Eu inventory. Therefore, we only con-sider them as objects locking up gas for the duration of theirlife time for the purpose of our simulation. LIMSs return asignificant amount of H and He in the ISM, marginally af-fecting the [Fe/H] ratios in the ISM. However, results andconclusions presented in this work are not affected. Oncedying, LIMS give back portions of their locked up gas viastellar winds (resulting in a planetary nebula), leaving be-hind a white dwarf. Since planetary nebulae have observedsizes of a few tenths of to a few light years (e.g., Cat’s eyenebula NGC 6543 with a 0.2 light year diameter, Reed etal. 1999, Helix nebula with 2.87 light years, O’Dell et al. In this manuscript - when referring to stellar masses (excludingNSs and BHs) - we refer to the zero age main sequence mass ofthe star.
Since many stars in the Galaxy are born in double star sys-tems (e.g., Duchˆene & Kraus 2013), there is a chance that anewly born star has a companion that meets the prerequi-sites to let the double star system later undergo a supernovaevent of type Ia (SNIa). We follow the analytical suggestionof Greggio (2005) to simplify all associated stellar and bi-nary evolution aspects to one probability ( P SNIa = 9 × − )for a newly born intermediate mass star (IMS, stars withmasses in the range 1M (cid:12) (cid:54) m (cid:54) (cid:12) ) to be born in asystem that will later end up as a SNIa. This is equivalentto a rate of 7 . × − SNIa events per unit solar mass ofstars formed. At the end of the life time of the second IMS,we inject 10 erg of energy at the location of the event andemit the event specific yields (cf. Iwamoto et al. 1999, modelCDD2). As in Wehmeyer et al. (2015), we simply eject thesame amount of Fe at all metallicities. This might be un-realistic (e.g., Timmes et al. 2003; Thielemann et al. 2004;Travaglio et al. 2005; Bravo et al. 2010; Seitenzahl et al.2013; Leung & Nomoto 2018), but this approximation doesnot strongly affect the outcomes of our simulation. SNIa donot contribute to the r-process production, but they are thedominant source of Fe in the Galactic disk (e.g., Matteucci& Greggio 1986). Therefore, we need to take into accountthe SNIa contribution to reproduce the chemical evolutionof the [Eu/Fe] ratio in the Galaxy. Stars more massive than 10M (cid:12) will experience all evolu-tionary stages until Si burning and the formation of anFe core (e.g., Jones et al. 2013). With the loss of its cen-tral energy source, the star cannot withstand the gravita-tional inward pull anymore and collapses. The core is com-pressed until it reaches nuclear densities, a so-called proto-NS. Neutrinos originating from the proto-NS lead to neu-trino and anti-neutrino capture on neutrons and protons,which heat up matter in the so-called gain region (e.g., Bur-rows 2013; Janka et al. 2016; Janka 2017; Burrows et al.2018) and lead to a successful explosion if the deposited en-ergy is sufficient. This is the case for a large fraction of initialstellar masses beyond 10M (cid:12) , but dependent on the stellarstructure/compactness inherited from the pre-collapse stel-lar evolution this mechanism fails and results in the for-mation of a BH (e.g., Heger et al. 2003). In order to beable to determine when a star fails to explode instead ofending up in a supernova, the explosion energy predictionsof the CCSN simulation suite PUSH (Perego et al. 2015;Curtis et al. 2019; Ebinger et al. 2019) are used to un-derstand under which conditions massive stars collapse toa BH instead of exploding in a CCSN and leaving behinda NS. Their conclusions are that stars in the mass region22 . (cid:12) (cid:54) m (cid:54) . (cid:12) (at Z = Z (cid:12) ) do not have sufficientexplosion energies to withstand the gravitational collapse.These stars failing to explode in the CCSN simulations areconsidered in the GCE suite in the following way: they col-lapse to a BH, without ejecting Fe. Since most massive stars c (cid:13) , 1745 sing failed supernovae to constrain the Galactic r-process element production have at least one companion (e.g., Duchˆene & Kraus 2013),we then use these results to constrain the BHNSM rate andthe implications of this second r -process site on the chemi-cal evolution of the Galaxy (see section 3.2.4 for a detaileddiscussion of the implementation of BHNSMs/NSMs).While we do have prescriptions for the explodabilityand thus the production of metals by HMS at the end oftheir life time for solar metallicity HMSs, it is expected thatfor low metallicities, in contrast to to solar metallicities, alarger fraction of massive stars ends as BHs rather than CC-SNe, due to smaller opacities and smaller amounts of massloss during the hydrostatic phase. Therefore, we employ thepredictions made by these studies only close to solar metal-licities and make different assumptions for lower metallic-ity HMSs: Since the explodability tends to scale with theprogenitor compactness (Ebinger 2017; Ebinger et al. 2019;Curtis et al. 2019; Ebinger et al., in prep.), we employ thecompactness of low metallicity progenitors at the time ofthe onset of the gravitational collapse as indicator whetherthe individual low metallicity progenitors will later undergoa successful CCSN. Lower opacity due to less metal contentleads to less radiation scatter in the outer layers of lowermetallicity stars. This stellar wind loss has an effect on thecompactness of stars: It leaves lower metallicity stellar coresat a higher compactness in comparison to their solar metal-licity counterparts. Since the explosion calculations withinthe PUSH model have not yet been completed for lowermetallicities, we utilize a simplified concept: In addition tothe known explodability of solar metallicity HMSs, we testthree extreme cases: all stars (cid:62) (cid:12) ( (cid:62) (cid:12) , (cid:62) (cid:12) )at metallicities Z (cid:54) − Z (cid:12) (chosen to be metallicity-wisein between the current Curtis et al. 2019; Ebinger et al. 2019predictions at Solar metallicity, and Ebinger et al., in prep.,predictions for [Fe/H]= −
4) are doomed to die in a failedSN at the end of their life time. This permits to account forthe extent of the effects of the stellar wind mass losses, andtherefore for the varied compactness of a lower metallicityHMS.
If a double star system consists of two HMS, both endtheir life either in a failed or in a successful supernova (e.g.,Nomoto et al. 2013). If the two remaining objects (two NSsin the case of two successful CCSNe, two BHs in the caseof two failed SNe, and one NS and one BH in the case ofone successful CCSN and one failed SN) survive the super-nova kicks and remain gravitationally bound (e.g., Tauris etal. 2017), this bound system emits gravitational waves andmerges later. In this case, a compact binary merger (CBM,either a NSM or a BHNSM) event occurs. BHNSMs canbe an important source of r-process material. Korobkin etal. 2012 give results for the merger of a 1 . (cid:12) NS witheither a 5M (cid:12) or a 10M (cid:12)
BH, which produce comparableyield curves and ejecta masses to NSMs. NSMs, on the otherhand require two NSs and thus two successful CCSNe beforethe CBM event, so the surrounding ISM is already pollutedwith the ejecta of these two CCSNe and thus already en-riched in metals. This means that the CBM products areejected into a region where the metallicity is already highin comparison to the case of a BHNSM, where only one
NSis required, which means that only one
CCSN polluted the ISM with metals . Theoretical predictions for NSM ratesvary strongly (e.g., Kalogera et al. 2004), while the rates forBHNSMs are very controversial (e.g., Mennekens & Van-beveren 2014). Also, different nucleosynthesis (e.g., Abbottet al. 2017a; Chornock et al. 2017; Cowperthwaite et al.2017; Kasen et al. 2017; Tanaka et al. 2017; Wang et al.2017; Gompertz et al. 2018; Hotokezaka et al. 2018; Rosswoget al. 2018) and GCE studies (e.g., Matteucci et al. 2014;Cescutti et al. 2015; Hirai et al. 2015; Ishimaru, Wanajo& Prantzos 2015; Shen et al. 2015; Wehmeyer et al. 2015;Komiya & Shigeyama 2016; Haynes & Kobayashi 2019) usedifferent rates for this kind of event. Cˆot´e et al. (2017) havecompiled several modern GCE calculations involving NSMevent probabilities and found that the rate assumptions dif-fer by two orders of magnitude from study to study. Thisfact originates - among others - in the different treatmentof infall prescriptions, differences in star forming prescrip-tion, employed IMF, CCSN/SNIa ejecta, and total ejectedmass per NSM. When the assumptions in these studies arenormalized to the same IMF, Fe yields, and Eu yields, thenthe number of NSMs per unit of stellar mass formed foundin different studies converges within a factor of 4 (see Cˆot´eet al. 2017). While these theoretical prescriptions for NSMper unit volume or unit stellar mass formed vary greatly,a new approach helps us to determine the actual rate ofCBMs in the local Universe: the detection of gravitationalwaves. While the first detections were attributed to BH -BH mergers (and are thus of less importance for this study)more recent ones have detected a NSM event (e.g., Abbottet al. 2018a,b, which predict a NSM rate of 1540 +3200 − Gpc − yr − ). In order to reduce the number of free parameters inthe formation channel, we use a simpler approach: We usean effective probability factor P r-proc , which represents theprobability for a newly born HMS to be in a system that willend up as a NSM/BHNSM, producing the r-process. We use P r-proc = 4%, which translates to (assuming a Salpeter ini-tial mass function with a slope of − .
35, and a standardCosmic star formation history with constant CBM delaytimes - see Cˆot´e et al. 2017 for the details of this conver-sion) 1 . × − CBM events per unit solar mass of starsformed. This rate is arguably high (see above and Cˆot´e etal. 2017 for a rate comparison of recent GCE models), butwould correspond to an event rate of ≈ − yr − ,which is well within the rate predicted by LIGO/Virgo.However, this approach has one major caveat: If theBH in the binary system is too massive (or does not havesufficient angular momentum), this will lead to the NS ei-ther being swalled without disruption, or being disruptedand forming a disc, but inside the last stable orbit, i.e., notleading to mass ejection. The upper limit for BH massesto permit ejecta depends on the NS equation of state, theBH mass, and the BH spin (e.g., Belczynski et al. 2017).With present knowledge (see Rosswog 2015), an upper limitseems to be in the range of 10 to 14M (cid:12) for the BH mass.Consequently, it is important how massive the resulting BHswould be after a star has undergone a failed SN. Two points Following this argumentation, BH - BH mergers might occur ina region where no CCSN has occured and is thus metal-free. How-ever, since BH - BH mergers do not eject any r-process enrichedmaterial, we do not consider this case here.c (cid:13)487
35, and a standardCosmic star formation history with constant CBM delaytimes - see Cˆot´e et al. 2017 for the details of this conver-sion) 1 . × − CBM events per unit solar mass of starsformed. This rate is arguably high (see above and Cˆot´e etal. 2017 for a rate comparison of recent GCE models), butwould correspond to an event rate of ≈ − yr − ,which is well within the rate predicted by LIGO/Virgo.However, this approach has one major caveat: If theBH in the binary system is too massive (or does not havesufficient angular momentum), this will lead to the NS ei-ther being swalled without disruption, or being disruptedand forming a disc, but inside the last stable orbit, i.e., notleading to mass ejection. The upper limit for BH massesto permit ejecta depends on the NS equation of state, theBH mass, and the BH spin (e.g., Belczynski et al. 2017).With present knowledge (see Rosswog 2015), an upper limitseems to be in the range of 10 to 14M (cid:12) for the BH mass.Consequently, it is important how massive the resulting BHswould be after a star has undergone a failed SN. Two points Following this argumentation, BH - BH mergers might occur ina region where no CCSN has occured and is thus metal-free. How-ever, since BH - BH mergers do not eject any r-process enrichedmaterial, we do not consider this case here.c (cid:13)487 , 1745
Wehmeyer et al. need to be considered, (a) the mass loss during stellar evo-lution, and (b) which part of the pre-collapse star ends upin the BH and which part is still ejected in a failed SN. Pos-sible options are that at least the H-envelope or all matteroutside the CO core (or even more) is ejected. Looking attables and figures in Thielemann et al. (2018) and Ebingeret al. (2019), referring to stellar models from Hirschi (2007);Limongi & Chieffi (2006a,b) - and Woosley et al. (2002);Woosley & Heger (2007), respectively - with different rota-tion rates and metallicities, it turns out that for high (butcredible, e.g., Hirschi et al. 2005) rotation rates a 30M (cid:12) starcan loose half of its mass and an 80M (cid:12) star can even end ina final pre-collapse mass of 20M (cid:12) . Including also the mostrecent results of Limongi & Chieffi (2018), we find He-coremasses below the above mentioned upper mass limit (for thedisruption of the NS by the BH under ejection of r-processmatter) for stars with initial masses below 25 to 30M (cid:12) , andCO-masses below these limits up to initial masses of 40M (cid:12) .Thus, while a point of caution should be kept in mind re-garding the BHNSM scenario, it will clearly not be excluded.The occurrence rates utilized here should, however, be takenas an upper limit.
Using our model, we study the effect of using BHNSMsas additional r -process production site. Our results suggestthat the discussed deficiencies of using NSMs as exclusive r -process element production site can be cured by addingthis second site. As can be seen in fig. 1, both challengesmentioned in the introduction can be solved by using ourmodel and including BHNSMs. Model stars (red, green, andblue squares) are(i) abundant in a very low metallicity region,(ii) show a large abundance scatter at lower metallicites,while this scatter is reduced towards higher metallicities,and(iii) are in qualitative agreement with the observations(magenta crosses)This can be explained in the following way: Regarding point(i) BHNSMs require only one previous CCSN event (sincethey only require one NS before the r -process event as op-posed to two previous CCSNe for NSM. This implies thatthis r -process event potentially happens at lower metallici-ties compared to NSM. See also section 3.2.4 for discussion,and fig. 2 for illustration. Additionally, another effect is rel-evant here: A model where a certain amount of stars fail toexplode in a CCSN (and thus do not contribute to the Feinventory of the Galaxy) slow down the [Fe/H] enrichmentover time, compared to a model where every star succeedsto explode and thus contributes to the Fe evolution. Thisreduces the number of CCSNe per time step. See section 4.2for discussion.(ii) Since BHNSMs can occur while ejecting less Fe per r -process event (as discussed above), their event specific[Eu/Fe] (including the previous CCSN) is a factor of twohigher in comparison two NSMs (where two CCSNe are re-quired in order to form the two NSs). This potentially allows Figure 1.
Effect of the different choices of the prescriptions forfailed SN at low metallicities on the GCE of [Eu/Fe]: Magentacrosses represent observations. Red (green, blue) squares repre-sent GCE models where all stars (cid:62) (cid:12) ( (cid:62) (cid:12) , (cid:62) (cid:12) )at metallicites Z (cid:54) − Z (cid:12) are forming failed SNe at the end oftheir life. Figure 2.
Locations of NSM/BHNSM events in the [Eu/Fe] vs.[Fe/H] space of our fiducial model (failed SNe for m (cid:62) (cid:12) at metallicity lower than Z (cid:54) − Z (cid:12) ). Magenta crosses repre-sent observations. Red squares represent all model stars. Greenand blue squares are the locations where BHNSMs or NSMs oc-cur, respectively. This allows us to determine at what point thedifferent r-process events contribute to the Galactic r-process el-ement inventory. Note that the first r-process events always haveto occur in a r-process element free/poor environment, and thusare located at or near [Eu/Fe]= −∞ . We put green and blue tri-angles at the [Fe/H] locations above where the first BHNSM orNSM occur. them to boost the abundances in terms of [Eu/Fe] muchstronger than NSMs can. As can be seen in section 4.3, thenumber of BHNSMs is higher in the beginning and subse-quently lowers substantially. This leads to a decrease in theabundance boost and hence to less scatter in [Eu/Fe] abun-dances at higher metallicities.Furthermore, if the mass range of failed supernovae inthe IMF increases for lower metallicities, the event rate ofBHNSMs increases accordingly and thus their nucleosyn-thetic influence towards low metallicities increases. This willbe discussed in section 4.3. In a model where no failed SNe are allowed, all HMS die ina CCSN. So, all HMS eject Fe at the end of their life, andcontribute it to the Galactic Fe inventory. Opposed to that, a c (cid:13) , 1745 sing failed supernovae to constrain the Galactic r-process element production Figure 3.
Illustration of a shifted age-metallicity relation. Blue(red) squares represent model stars in a model that does (not)permit failed SNe. A model that permits failed SNe produces lessFe per time step, so the [Fe/H] enrichment is delayed in compar-ison to a model which does not allow failed SNe. model where failed SNe are allowed, some stars collapse intoa BH. This means that those stars do not contribute to theGalactic Fe. If the same star formation rate for both of thesemodels is assumed, a model permitting failed SNe has thusless CCSN events per time step compared to a model whereall stars die in a CCSN. This leads to a slower increase in[Fe/H] vs. time. This also has implications on the GCE of r-process elements: All CBMs have a coalescence time betweenthe death of the two stars and the merger event. When (ina model with enabled failed SNe) the [Fe/H] enrichment isslowed down with respect to time, the coalescence time scaleof CBMs is of less importance. In other words, less nearbyCCSN occur during the coalescence time. This allows CBMproducts to be ejected into a region that is less Fe rich thanin a comparable model with no failed SNe permitted. Seefig. 3 for illustration.
Since in this simulation individual stars and nucleosynthe-sis sites are followed, we can keep track of the number ofindividual events per time step. This allows us to deter-mine which site (BHNSMs or NSM) is the dominant sitecontributing to the r-process element production through-out the history of the Galaxy. Since NSMs seem to be thedominant site ( (cid:62)
50% of all CBM events at all times), weconsider the relative importance of BHNSMs with respect tooverall CBMs (=BHNSMs+NSMs) in fig. 4. While the firstr-process production events at early Galactic stages seem tobe approximately equally performed by both types of CBMs,this changes rapidly towards NSMs as dominant r-processsite. Already in early Galactic evolution stages ( t (cid:62) ≈
10% of all CBMs. Thisoriginates in the fact that a large portion of stars (all stars m (cid:62) (cid:12) ) at lower metallicity ([Fe/H] (cid:54) −
2) will end upas a BH, while at higher metallicities only the stars in therange 22 . (cid:12) (cid:54) m (cid:54) . (cid:12) will end up as BHs, accordingto the PUSH calculations utilized here. B HN S M s / C B M s [ % ] time [Gy] Figure 4.
Relative occurrence of BHNSMs with respect to allCBMs (BHNSMs+NSMs) using a model where stars (cid:62) (cid:12) at lower metallicity (Z (cid:54) − Z (cid:12) ), and stars 22 . (cid:12) (cid:54) m (cid:54) . (cid:12) at higher metallicity die in a failed SN instead of a CCSN. In this work, we have shown that the two major issues ofthe GCE of r -process elements, namely a) the large scat-ter in abundances in comparison to alpha-elements at lowermetallicities, and b) that r -process elements are abundantat low metallicities, can be explained explained in our GCEmodel by including BHNSMs as a second r -process elementproduction site in addition to NSMs.This scenario is complementary to magneto-rotationalsupernovae, or even collapsars, related to single stars andtheir early appearance in Galactic evolution, but the presentstudy shows that BHNSMs could already produce the re-quired effect.The main advantage of BHNSMs acting as a second r -process site is that, contrary to NSMs, only one NS (plusone BH) is required to perform an r -process event. Henceonly one previous successful CCSN is required, so the sur-rounding ISM is only polluted by Fe once as opposed to twice for NSMs. This advantage permits that BHNSMs occur inenvironments with less Fe content than the environment ofNSMs. A second advantageous effect is that due to a higherfailed SN rate at lower metallicities, i.e., less Fe-producingCCSNe, the overall enhancement of [Fe/H] is progressingslower in time, reducing the significance of the coalescencetime scales of CBM.Furthermore, we have shown that, despite that at earlyGalactic stages the r-process contribution of BHNSMs andNSMs to the Galactic r -process content is comparable, thecontribution of NSMs is dominant over BHNSMs at laterGalactic stages. This can be explained by more successfulCCSN explosions with respect to failed SN explosion com-pared to lower metallicities, leading to a larger number ofNSMs than BHNSMs.There remains a number of open questions in this work,related to the stochastic nature of this GCE approach (asalready addressed in Wehmeyer et al. 2015), as well as thespecific implementation utilized this work.(i) We did not include CCSNe as r -process element c (cid:13)487
Relative occurrence of BHNSMs with respect to allCBMs (BHNSMs+NSMs) using a model where stars (cid:62) (cid:12) at lower metallicity (Z (cid:54) − Z (cid:12) ), and stars 22 . (cid:12) (cid:54) m (cid:54) . (cid:12) at higher metallicity die in a failed SN instead of a CCSN. In this work, we have shown that the two major issues ofthe GCE of r -process elements, namely a) the large scat-ter in abundances in comparison to alpha-elements at lowermetallicities, and b) that r -process elements are abundantat low metallicities, can be explained explained in our GCEmodel by including BHNSMs as a second r -process elementproduction site in addition to NSMs.This scenario is complementary to magneto-rotationalsupernovae, or even collapsars, related to single stars andtheir early appearance in Galactic evolution, but the presentstudy shows that BHNSMs could already produce the re-quired effect.The main advantage of BHNSMs acting as a second r -process site is that, contrary to NSMs, only one NS (plusone BH) is required to perform an r -process event. Henceonly one previous successful CCSN is required, so the sur-rounding ISM is only polluted by Fe once as opposed to twice for NSMs. This advantage permits that BHNSMs occur inenvironments with less Fe content than the environment ofNSMs. A second advantageous effect is that due to a higherfailed SN rate at lower metallicities, i.e., less Fe-producingCCSNe, the overall enhancement of [Fe/H] is progressingslower in time, reducing the significance of the coalescencetime scales of CBM.Furthermore, we have shown that, despite that at earlyGalactic stages the r-process contribution of BHNSMs andNSMs to the Galactic r -process content is comparable, thecontribution of NSMs is dominant over BHNSMs at laterGalactic stages. This can be explained by more successfulCCSN explosions with respect to failed SN explosion com-pared to lower metallicities, leading to a larger number ofNSMs than BHNSMs.There remains a number of open questions in this work,related to the stochastic nature of this GCE approach (asalready addressed in Wehmeyer et al. 2015), as well as thespecific implementation utilized this work.(i) We did not include CCSNe as r -process element c (cid:13)487 , 1745 Wehmeyer et al. sources, although there might be a chance for a small con-tribution to the abundance of r-process elements or a con-tribution to the “weak” r-process by CCSNe.(ii) Also, we did not include the contribution of sub-halos(such as dwarf galaxies) to the chemical enrichment of theGalaxy.(iii) Furthermore, we did not include magneto-rotationaljet-supernovae or collapsars. They would have a similar, oreven stronger (essentially emitting no Fe) effect, as describedhere for BHNSMs, but require strong assumptions on mag-netic fields and stellar rotation, which would need to be con-firmed observationally.(iv) The predicted rates for CBMs required to explain thechemical evolution are arguably high. They are well at theupper end of the spectrum in comparison to similar GCEcalculations as inferred by Cˆot´e et al. (2017). Still, these arein overall agreement with the LIGO detection rates.(v) It has been shown by recent population synthesisstudies (e.g., Dominik et al. 2012; Belczynski et al. 2017;Chruslinska et al. 2018), that parameterized delay time dis-tributions (DTDs) should be used for CBMs instead of fixedcoalescence time scales. Thus, our approach over-simplifiesthe GCE of r -process elements in the metallicity region of[Fe/H] (cid:62) −
1, omitting the modelling difficulties associatedwith employing probably more realistic DTDs. See Cˆot´e etal. (2017, 2018), and Hotokezaka et al. (2018) for a discus-sion of this issue. A further effect, not yet considered here,could be that the coalescence time for massive binary sys-tems containing one BH is possibly shorter than for NSMs.(vi) Since the direct swallowing of a NS by a BH proba-bly leaves no r-process matter behind, we did not considerthis case here. Hence, our predicted r-process element pro-duction rate in section 3.2.4 omits this channel and thus hasto be seen as a lower limit of a gravitational wave emissionrate. However, this event would not alter the conclusions ofsection 4.2, since the effect mentioned in that section orig-inates only in the absence of Fe ejection by failed SNe (asopposed to successful Fe ejection in a case where all
CCSNeeject Fe).Future work towards the better understanding of the originor the r -process elements will probably require(i) Detailed predictions of the explodability of low-metallicity stars being employed in a GCE model insteadof a parametrized approach.(ii) The efforts taken in this work should be re-examinedusing CCSN explodability predictions of different groups,e.g., Ugliano et al. (2012); Ertl et al. (2016); Sukhbold etal. (2016), and it should be examined whether this wouldchange the required CBM event frequency, as well as theevolution of the BHNSMs/NSM ratio.(iii) Future work should address the implications ofCCSN kicks on the survival probability and dislocation ofstellar binary systems (e.g., Belczynski & Bulik 1999): Ifa kick by a CCSN was strong enough to make the binarysystem leave the supernova remnant bubble, the succeed-ing CBM event might take place in an area of the Galaxythat has not been polluted by CCSN ejecta before. Suchan event might even contribute r -process elements at evenlower metallicities than the CBMs happening inside a CCSNbubble considered in this work. (iv) Future work should include DTDs instead of fixedcoalescence time scales in this model.(v) A future effort should be to include Jet-SNe as wellas NSMs and BHNSMs as r -process element source. Ofcourse, this would increase the level of complexity, since thiswould add another degree of freedom to the evolution of theGalaxy.(vi) The next LIGO/Virgo run will probably provide uswith a more accurate rate of CBMs. As soon as those areavailable, refined GCE calculations should be performed us-ing these improved rates. ACKNOWLEDGEMENTS
We thank Maria Lugaro, Chiaki Kobayashi, Albino Perego,Raphael Hirschi, Stephan Rosswog, Tim Beers, C. GarethFew, and Brad K. Gibson for fruitful discussions. We furtherextent our gratitude to Sanjana Curtis and Kevin Ebingerwho have provided us with the PUSH predictions which playa crucial role for the considerations in this study.BW is supported by a fellowship of the Swiss NationalScience Foundation (SNF). BW and CF acknowledge sup-port from the Research Corporation for Science Advance-ment through a Cottrell Scholar Award. CF was partiallysupported by the United States Department of Energy,Office of Science, Office of Nuclear Physics (award num-bers SC0010263 and DE-FG02-02ER41216). FKT was sup-ported by the European Research Council (FP7) under ERCAdvanced Grant Agreement No. 321263 - FISH, and theSNF. MP acknowledges the support from the SNF and the“Lend¨ulet-2014” Programme of the Hungarian Academy ofSciences (Hungary), of STFC, through the University of HullConsolidated Grant ST/R000840/1, and access to viper ,the University of Hull High Performance Computing Fa-cility. BW, BC, and MP acknowledge the support fromthe ERC Consolidator Grant (Hungary) funding scheme(project RADIOSTAR, G.A. n. 724560). BW, CF, BC, andMP acknowledge support of the National Science Founda-tion (USA) under grant No. PHY-1430152 (JINA Centerfor the Evolution of the Elements). This article is basedupon work from the “ChETEC” COST Action (CA16117),supported by COST (European Cooperation in Science andTechnology).
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