Contribution of collapsars, supernovae, and neutron star mergers to the evolution of r-process elements in the Galaxy
Yuta Yamazaki, Toshitaka Kajino, Grant J. Mathews, Xiaodong Tang, Jianrong Shi, Michael A. Famiano
aa r X i v : . [ a s t r o - ph . GA ] F e b Contribution of collapsars, supernovae, and neutron star mergers to the evolution ofr-process elements in the Galaxy
Yuta Yamazaki , , ∗ Toshitaka Kajino , , , Grant J. Mathews , ,Xiaodong Tang , Jianrong Shi , and Michael A. Famiano , Graduate School of Science, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 11-0033, Japan National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan School of Physics, and International Research Center for Big-Bang Cosmology and Element Genesis,Beihang University, Beijing 100083, P. R. China Department of Physics and Center for Astrophysics,University of Notre Dame, Notre Dame, IN 46556, USA Institute of Modern Physics, Chinese Academy of Science, Lanzhou, Gansu 730000, P. R. China Key Laboratory of Optical Astronomy, National Astronomical Observatories,Chinese Academy of Science, Beijing 100012, P. R. China and Physics Department, Western Michigan University, Kalamazoo, MI 49008-5252 USA (Dated: February 12, 2021)We study the evolution of rapid neutron-capture process (r-process) isotopes in the Galaxy. Weanalyze relative contributions from core collapse supernovae (CCSNe), neutron star mergers (NSMs)and collapsars under a range of astrophysical conditions and nuclear input data. Although the r-process in each of these sites can lead to similar (or differing) isotopic abundances, our simulationsreveal that the early contribution of r-process material to the Galaxy was dominated by CCSNe andcollapsar r-process nucleosynthesis, while the NSM contribution is unavoidably delayed even underthe assumption of the shortest possible minimum merger time.
The origin by rapid neutron capture (r-process) ofnearly half of the heavy atomic nuclides from iron to ura-nium remains an open question [1]. The neutrino-drivenwind (NDW) of core collapse supernovae (CCSNe) isnow believed to produce only light r-process elements [2].The magneto-hydrodynamically driven jet (MHDJ) fromrapidly rotating, strongly magnetized CCSNe is an alter-native site [3]. Also, there is a growing consensus [4, 5]that neutron star mergers could be the dominant con-tributor to r-process elements in the Galaxy. This is duein part to the discovery of gravitational waves from thebinary neutron star merger (NSM) GW170817 and its as-sociated kilonova and GRB170817A [6, 7]. There is alsoevidence [8, 9] for massive ejection of r-process materialwithout associated supernova enrichment in the dwarfgalaxy Reticulum II.Of interest to this letter is that in addition to the abovesources, a single massive star collapsing to a black hole(collapsar) may also be a viable site for the main r-processabundances [10]. It has been argued [11] that extra pro-duction site for the r-process may be required that wasactive in the early Galaxy but fades away at higher metal-licity. Otherwise, it is not possible to account for thedecrease of r-process elements with iron after the onsetof Type I supernovae (at [Fe/H] ∼ − ∼ yr) it is inevitable that neutronstar binaries are formed with a distribution of separationdistances and merger timescales. This leads to a delayin the arrival of r-process material in the solar neigh-borhood, and constrains the NSM contribution to thesolar-system abundances.SNe and collapsars result when a single massive starthat completes its evolution within a few Myr. Theycan enrich r-process elements in the interstellar medium(ISM) of the Galactic disk from the earliest times. Onthe other hand, NSMs involve the remnants of previouslyexploded massive stars. Their observed occurrence rate is ∼ . −
1% of the observed galactic SN rate. The observedorbital properties of binary pulsars imply a coalescencetimescale ranging from a few hundred Myr to longer thanthe Hubble time [12].The universal elemental abundance pattern observedin metal-poor halo stars and the solar system (universal-ity) [13] suggests that only a single site contributed tothe the r-process elements [4, 11, 14–16]. However, theisotopic abundance patterns can be quite different eventhough the elemental Z -distributions are universally sim-ilar [10, 17, 18].This motivates the study described herein of the rel-ative contributions of multiple r-process sites (CCSNe,NSMs and collapsars) and their cosmic evolution. Wehave utilized a widely employed GCE model [19] adaptedto calculate r-process contributions from various sourcesin the solar neighborhood. We have explored a largeparameter space of r-process models, nuclear input, andastrophysical parameters to examine the general featuresof the evolution of r-process abundances.We find that CCSNe and collapsars must dominate ther-process abundances in the early Galaxy, while NSMscan only arrive later when the metallicity has alreadybeen enriched to -1 < [Fe/H]. This is independent of theminimum timescale for binary neutron-star coalescenceand is a consequence of the unavoidable distribution ofbinary separation distances at formation.The observed cosmic star formation rate (SFR) [20]as well as SPH galactic chemo-dynamical evolution(GCDE) models of spiral galaxy evolution [21] and dwarfspheroidal galaxy evolution [22] all indicate that the SFRat first rises and then diminishes with time. The GCEmodel [19] adopted in this study produces a SFR similarto that observed and deduced from GCDE simulations.This GCE model also reproduces well the chemical evo-lution of light elements from hydrogen to zinc [19]. Inthis study we have extended this model to include the r-process contributions from NDW, MHDJ, collapsars andNSM.Gas evolution involves a cycle of star formation, stel-lar evolution and nucleosynthesis; ejection of materialinto the interstellar medium (ISM); mixing of ejecta withthe ISM; and formation of the next generations of stars.We adopt an exponentially declining galactic inflow ratewith timescale of 4 billion years consistent with the hi-erarchical clustering paradigm. Although, the merger ofdwarf galaxies into the galactic halo can bring some r-process enriched stars, the bulk of the inflowing gas con-sists of r-process depleted material from the circumgalac-tic medium [23].The Surface density σ i of isotope i in the ISM thenobeys,˙ σ i ( t ) = X µ ǫ µ Z m h m l E i,µ B ( t − τ ( m )) φ ( m ) dm + ǫ NSM
Z Z Z M h M l dq da P a ( a ) P q ( q ) × E i, NSM B ( t − τ ( m ) − τ g ( a )) φ ( M ) dM − B ( t ) σ i σ gas , (1)where the first and second terms on the r.h.s. describe theenrichment of newly produced nuclei by explosive nucle-osyntheses in different astrophysical sites, i.e µ = NDW,MHDJ, Collapsars, and NSMs, respectively. The thirdterm accounts for the loss from the ISM due to star for-mation, where σ gas is the total gas surface density. E i,µ is the yield of isotope i from each astrophysical site µ . The quantity B ( t ) is the star formation rate, and φ ( m )is the initial mass function which we adopt from [24].For the present illustration we adopt the abundancedistribution of r-process nuclei in the NDW model fromthe 1.8 M ⊙ proto-neutron star yields of [2]. We adoptyields from the NSM model of [18], and the MHDJ modelyields are taken from [25]. For the collapsar model, weadopt the yields of [26, 27].In Eq. (1), the enrichment of r-process nuclei from su-pernovae and collapsars in the ISM is delayed by theperiod τ (m) from star formation to the death of the pro-genitor star of mass m . We adopt lifetimes from [28] formassive stars and from [29] for stars with m ≤
10 M ⊙ .In [29] it was estimated that the metallicity effect on theprogenitor lifetime is only about ∼
5% and is ignored.The quantities ǫ µ and ǫ NSM are the fractions of starsresulting in each event in a given mass range m l ∼ m h or M l ∼ M h for a single or binary system. In this study, wetake these as efficiency parameters, which are adjustedto the solar r-process abundances. We here define theabundance of solar r-process nuclei as the sum of nuclidesin mass range 90 ≤ A ≤ τ g in addition to τ (m).We adopt a paradigm whereby main-sequence binaries oftotal mass M = m + m are formed within a gas cloud.The heavier star with mass m explodes first to form aneutron star or black hole, followed by the second CCSNof the lighter progenitor.Binary population synthesis studies indicate that theminimum coalescence time is ∼
100 My. This is in rea-sonable agreement with the lower limit estimated fromobserved binary pulsars [12]. In the quadrupole limit,the coalescence time τ g from an initial binary separation a scales as a . We ignore the dependence on eccentricityas tidal interactions should circularize the orbits.The event rate of NSMs in Eq.(1), includes the uniformprobability P q ( q ) for a given mass ratio of the secondaryto total mass, q ≡ m /M , and the probability P a ( a ) ∝ /a , of an initial separation a . This is consistent with theobservationally inferred coalescence time, P τ g ∝ τ g − [30,31]. The lower limit of the initial separation a constrainsthe minimum coalescence time.The observed lower limit of the coalescence timescaleof binary neutron stars is ∼
50 My [12]. However, thereare several effects that might shorten coalescence time.If the binary system is perturbed by the third stellarobject or if there exits a common envelope, these wouldaccelerate orbital energy loss rate. We therefore treat τ g as a parameter, and allow shorter minimum coalescetimes, i.e τ g = 1, 10 and 100 My in our GCE calculations.We consider two combinations of multiple astrophysi-cal sites for r-process nucleosynthesis: One set of modelsincludes only CCSNe and NSM contributions to the r- TABLE I. .Model sym − asym − sym+ asym+˜ χ process. The other includes the collapsar contribution.We also considered two sets of nuclear physics input.One adopts a symmetric fission fragment distribution(FFD) and the other an asymmetric FFD. The FFDstrongly affects abundances near r-process peaks as dis-cussed below. The four models are labeled as follows:Model sym- and asym- ignore the collapsar contribution,adopting symmetric and asymmetric FFDs respectively.Model sym+ and asym+ include collapsars with sym-metric and asymmetric FFDs respectively.We take efficiency parameters ǫ µ in Eq. (1) as freeparameters adjusted so as to best fit the solar-systemr-process abundances at the time of solar-system forma-tion. The reduced chi square for the fitted abundancepattern for each of the four models is shown in Table 1.The collapsar contribution improves the goodness offit even after accounting for the extra degree of freedom.The collapsar abundances do not exhibit an underpro-duction near A = 140 −
145 which appears in most previ-ous r-process calculations [1]. The r-process in collapsarsundergoes fission recycling so many times that the fissionfragments enhance the abundances at A ≈ − A = 140 − A < A ≈ Y e ∼ . FIG. 1. The time-varying isotopic abundance patterns at[Fe/H]=0.0, -1.5, -3.0 from top to bottom. The black linesshow the total calculated r-process abundances. The red andgreen lines represent the contributions from NSMs and CC-SNe (including the NDW and MHDJ), respectively. The bluelines show the contribution from collapsars. which causes the r-process path to run along extremelyneutron-rich isotopes. The reaction flow quickly reachesheavy fissile nuclei in the region A = 250 − A = 100 −
180 and evenheavier isotopes [17]. When a symmetric FFD [18] is usedin the NSM r-process, the second peak around A ∼ A >
100 are produced, andthe third peak is slightly shifted towards the heavier massregion since the neutron-number density remains high af-ter freezeout in tidal ejecta from NSM.The abundance pattern in the collapsar r-process (blueline in Fig. 1) has three unique features due to the veryrapid-neutron captures caused by the relatively high val-ues of the neutron density at freezeout [27]. First, ther-process peaks are shifted systematically towards theheavier mass region. This is caused by residual neutroncaptures after freezeout of the r-process. This causes adiscrepancy away from the observed solar r-process abun-dance pattern around the third peak A ∼
195 (Fig. 1).Secondly, an odd-even pattern manifests in the lan-thanide abundance hill. This is a typical feature resultingfrom very rapid-neutron captures and the sudden freeze-out. We note, however, that the calculation of Ref. [10]adopts a different ejecta model and shows a smootherpattern. Thirdly, the second peak in the collapsar modelis broadened to higher mass region A= 140 −
150 as men-tioned previously.The properties of neutron-rich unstable nuclei and thephysical conditions of the trajectory dynamics are thusintricately connected in any nucleosynthesis simulations.However, if some characteristic features, such as thosediscussed here, were measured in the isotopic abundancesof r-process enhanced metal-deficient stars, this couldconfirm that the heavy nuclei in those stars originatefrom a single or a few very similar r-process events.Our simple GCE model indicates a time-metallicity re-lation given by t/10 y ≈ [Fe / H] . However, this re-lation is broken in the extremely metal-deficient region[Fe/H] < -2. This is because of the inhomogeneous na-ture of the stochastic Galactic star formation [22] at lowmetallicity. Nevertheless, metallicity remains a reason-able measure of the time evolution of the Galaxy downto -2 < [Fe/H].Figure 1 shows the abundances of r-process nucleifrom each contribution from NDW, MHDJ, NSMs andcollapsars as snapshots in metallicity or time. Amongthese possible astrophysical sites, CCSNe (i.e. NDWand MHDJ) and collapsars make the predominant con-tribution in the early Galaxy. The NSM contributiongrows gradually with increasing metallicity and eventu-ally reaches 1 % of the total abundance of solar r-processelements at [Fe/H] = -1.5, -1.3, and -0.7 for models with aminimum coalescence times of τ g = 1, 10, and 100 My, re-spectively. We thus conclude that the NSM contributionwas negligibly small in the early Galaxy and has arrivedlater in Galactic evolution due to the long coalescencetime delay τ g . This conclusion is nearly independent ofthe model selection of astrophysical sites and input nu-clear physics.However, the detailed time variation of the abun-dance pattern does depend on the input nuclear physicsor models of the ejecta used in r-process simulations.A typical example of the dependence on input nuclearphysics is the FFD. As discussed previously, symmetricand asymmetric FFDs can lead to very different abun-dance patterns over the entire mass range. Althoughthe MHDJ r-process (green line) explains well the abun- dance peaks around A ∼
130 and 195 and the hill oflanthanides around A ∼ A = 140 ∼
150 remains in either FFD model. In-deed, most r-process nucleosynthesis calculations under-produce the heavier isotopes just above the second peak[1].In Model sym+, NSMs change the total abundancepattern only slightly when the Galaxy has evolved tonear solar metallicity [Fe/H]=0. This is because theNSM contribution fraction is only about 1%. In themetal-deficient region [Fe/H] < − .
5, the NSM contribu-tion does not change the total abundance pattern be-cause the r-process nuclei are dominated by CCSNe orcollapsars. On the other hand, the abundance patternchanges drastically as a function of metallicity at [Fe/H] < − .
5. Figure 1 exhibits a very busy abundance pat-tern because of the odd-even structure in the collapsarr-process yields. There are significant shifts of the secondand third peaks towards heavier mass numbers as shownby the black lines.Figure 2 displays the calculated elemental abundancepatterns as a function of atomic number Z in Modelsym+, compared with observational data in the r-processenhanced metal-poor halo stars, BD+173248 ([Fe/H] =-2.1) [36] and CS22892-052 ([Fe/H] = -3.1) [37].They exhibit a more or less similar elemental abun-dance pattern for any metallicity, except for severalatomic numbers to be discussed below. In particular,around the lanthanide hill near Dy ( Z = 66), they agreewith each other independently of any models. This fea-ture is known as the universality of the r-process ele-mental abundance pattern [13]. Such similarity is dueto the fact that there are many isotopes contributing tothe same atomic number Z with different mass numbers A [17]. The most abundant isotopes smooth the detailedstructure apparent in the mass distributions of Fig. 1.The peak height around Te ( Z = 52) and Os ( Z = 78)depends on the models. This model dependence arisesfrom the different contribution fractions from the fourastrophysical sites. Unfortunately, the second peak ele-ments except for Te [36] have not been observed in metal-deficient halo stars.The elemental abundances are in reasonable agreementwith observational data. Interestingly, the actinides alsoare remarkably enhanced in the collapsar r-process. Thisis because the extremely high neutron number density incollapsars causes the r-process path to proceed along veryneutron-rich nuclei and produce neutron-rich isotopes be-yond the third peak. Such a remarkable enhancement ofactinides is indeed observed in actinide-boost stars [38].One finds a discrepancy for lighter elements Zr-Sn( Z = 38 −
48) in CS 22892-052. A remarkable enhance-ment of these elements has been reported in so-calledHonda stars [39]. Our present theoretical interpretationis that the universality between the second and thirdpeaks including the lanthanide hill around Z ≈
66 and
FIG. 2. Comparison of calculated r-process elemental abun-dance patterns (blue lines) with the observed abundances(points) of the solar system (top) and metal poor stars,BD+173248 (middle) and CS 22892-052(bottom). beyond is satisfied in any cases, although the variationin a wider mass range can be reasonably explained byinhomogenity in the early galaxy.To summarize, we have studied the cosmic evolution ofthe r-process abundance pattern in the context of GCEmodels that take into account multiple astrophysical sitessimultaneously (i.e. NDW and MHDJ CCSNe, NSMsand collapsars). The NSM r-process calculations werecarried out with different input nuclear physics includingsymmetric and asymmetric FFDs. We then find that ther-process elements in the early Galaxy are dominated bythe yields from CCSNe and collapsars, while the NSMcontribution is inevitably delayed due to the cosmologi-cally long coalescence timescale for very slow GW radi-ation. The relative NSM contribution rapidly increaseswith cosmic time. However, it does not reach even 1% ofthe total solar r-process composition until the metallic-ity is enriched to [Fe/H] ≥ -1.5. This conclusion does not change for a wide range of minimum coalescence times τ g = 1 - 100 My in any GCE models including multiplesites and different input nuclear physics.We also find that significant differences among ourmultiple-site GCE model calculations arise in the isotopicabundance pattern as a function of mass number A , whilestill satisfying the universality of elemental abundancesfor metal-poor halo stars. This is in contrast to previousstudies that focused on only a single r-process site or acombination of at most two astrophysical sites in orderto explain the universality of the elemental abundancepattern.Several unique features of each astrophysical site arestill expected in the GCE of the isotopic mass A -abundance pattern. In particular, the collapsar contri-bution dominates from the very beginning of the earlyGalaxy since its progenitor is a very massive star. Thecollapsar r-process shows an odd-even pattern over theentire mass range and also both the collapsar and NSMthe abundance peaks shift towards the heavier mass re-gion due to a high residual neutron-flux during the freeze-out of the r-process.Although the elemental Z -abundance patterns aremore or less similar to one another among the models,one can find exceptional differences in the actinides orlight r-process elements Z <
42. Therefore, these arethe important indicators of the dominant r-process site.Also, the peak structure is model dependent due to thedifferent contribution fractions from the four astrophysi-cal sites considered here.It is therefore highly desirable to carry on spectroscopicobservations with next generation telescopes such as theThirty Meter Telescope [40]. These could provide themetallicity dependence of the abundance ratios of ac-tinides, lanthanides and lighter elements as well as theabundance peaks simultaneously. A separation of each r-process element into isotopes should provide constraintson the evolution of the NSM, MHDJ and collapsar modelconstruction beyond that of a single r-process site as dis-cussed in this article.This work is supported in part by Grants-in-Aidfor Scientific Research of JSPS (20K03958, 17K05459).Work at the University of Notre Dame supported byDOE nuclear theory grant DE-FG02-95-ER40934. 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