Evidence for r-process delay in very metal-poor stars
DDraft version February 9, 2021
Typeset using L A TEX twocolumn style in AASTeX63
Evidence for r-process delay in very metal-poor stars
Yuta Tarumi, Kenta Hotokezaka,
2, 3 and Paz Beniamini
4, 5 Department of Physics, School of Science, The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA Astrophysics Research Center of the Open University (ARCO), The Open University of Israel, P.O Box 808, Ra’anana 43537, Israel
Submitted to ApJLABSTRACTThe abundances of r -process elements of very metal-poor stars capture the history of the r -processenrichment in the early stage of the Milky Way formation. Currently, various types of astrophysicalsites including neutron star mergers, magneto-rotational supernovae, and collapsars, are suggestedas the origin of r -process elements. The time delay between the star formation and the productionof r -process elements is the key to distinguish these scenarios with the caveat that the diffusion of r -process elements in the interstellar medium also induces the delay in r -process enrichment because r -process events are rare. Here we study the observed Ba abundance data of very metal-poor starsas the tracer of the early enrichment history of r -process elements. We find that the gradual increaseof [Ba/Mg] with [Fe/H] requires a significant time delay (100 Myr – 1 Gyr) of r -process events fromstar formation rather than the diffusion-induced delay. We stress that this conclusion is robust tothe assumption regarding s -process contamination in the Ba abundances because the sources with nodelay would overproduce Ba at very low metallicities even without the contribution from the s -process.Therefore we conclude that sources with a delay, possibly neutron star mergers, are the origins of r -process elements. Keywords: diffusion — stars: abundances — Galaxy: evolution INTRODUCTIONNeutron-capture processes are responsible for the syn-thesis of the heaviest elements in the Universe (Sneden& Cowan 2003). Burbidge et al. (1957) classify theminto two, namely the slow-process ( s -process) and therapid-process ( r -process). The astrophysical sites thatpredominantly contribute to the production of s -processelements are the asymptotic giant branch (AGB) stars(Burbidge et al. 1957; Hollowell & Iben 1988; Travaglioet al. 2004) while the origin of r -process elements re-mains one of the biggest mysteries in nuclear astro-physics.Recently, the observations of the gravitational wavesignal and its electromagnetic counterpart from a neu- Corresponding author: Yuta [email protected] tron star merger (NSM), GW170817, provided us withevidence that NSMs eject copious amounts of r -processelements (see, e.g., Margutti & Chornock 2020 for arecent review). The merger rate and the mass of theejected r -process elements derived from the observa-tions of GW170817 agree remarkably well with thoseestimated from the r -process elemental abundances ofGalactic stars and ultra-faint dwarf galaxies (UFDs)(Eichler et al. 1989; Ji et al. 2016; Beniamini et al. 2016;Cˆot´e et al. 2018; Hotokezaka et al. 2018; Rosswog et al.2018) as well as geological measurements of radioactiveisotopes (Hotokezaka et al. 2015; Tsujimoto et al. 2017;Bartos & Marka 2019; Cˆot´e et al. 2020; Beniamini &Hotokezaka 2020).Even though the NSM scenario for the origin of r -process elements successfully explains the total amountof r -process elements in the Milky Way, it encounterspotential obstacles to the delays between binary forma-tion and merger. For example, a chemical evolution a r X i v : . [ a s t r o - ph . GA ] F e b Tarumi et al. model with a delay time distribution of ∝ ∆ t − hasdifficulty explaining the distribution of stellar Eu abun-dances at higher metallicities [Fe / H] (cid:38) − r -process elements being predomi-nantly produced by astrophysical phenomena other thanNSMs, such as magneto-rotational supernovae (MRSNe,Nishimura et al. 2015, 2017), peculiar magnetar forma-tion (Metzger et al. 2008; Thompson & ud-Doula 2018),and collapsars (Siegel et al. 2019). These latter phenom-ena are associated with the death of massive stars, andtherefore they have no delay times between star forma-tion and r -process enrichment.A critical question for the origin of r -process elementsis: do we have any direct observational evidence sup-porting the delay between star formation and the pro-duction of r -process elements, or are r -process elementspreferentially produced in the early Universe? We caninfer the history of metal enrichment in the Milky Waythrough the elemental abundance ratio and the over-all metallicity of stars, e.g., the distribution of stellarabundances on a [ r /Mg] - [Fe/H] plot. This paper aimsto infer the time delay of r -process element productionin a largely model-independent fashion and to clarifythe origin of r -process elements. Ishimaru et al. (2004)assert that the origin of the r -process elements shouldnot be the highest-mass stars using three stars with lowEu abundances at [Fe / H] ∼ −
3. However, such mea-surements can be reconciled if r -process events are suf-ficiently rare because the diffusion process delays thechemical enrichment. Here we use Ba abundances ofvery metal-poor stars ([Fe / H] < −
2) as the sample.With Ba abundances, which are available in a largernumber of stars, we can distinguish the intrinsic delayof the r -process from the diffusion delay. In section 2, webriefly describe the scenarios for the astrophysical phe-nomena suggested as the origin of r -process elements.In section 3, we give the compilation of observed dataand discuss the trend in the data. In section 4, we dis-cuss the implication of the delay on the origin of the r -process in the Universe. SCENARIOS FOR THE R -PROCESS ANDDELAY TIMESThe scenarios for the origin of r -process elements aregenerally classified into three categories according to therelation between the star formation rate (SFR) and the production rate of r -process elements: (i) the delay sce-nario (NSM model), (ii) the no-delay scenario (Rare SNmodel), and (iii) the “negative” delay scenario (Collap-sar model; the origin of “negative” delays is explainedbelow). Any astrophysical scenario for the origin of r -process elements falls into one of the three categories.For all the scenarios we assume that α -elements arepredominantly produced by normal core-collapse SNe(ccSNe) and that the r -process events are rare, e.g., ∼ / (i) The delay scenario (NSM model) : A prominentfeature of NSMs is a significant time delay after theformation of the progenitor stars. In fact, GW170817occurred in a galaxy with weak star formation activ-ity, suggesting that the time delay between the binaryformation and merger is ∼ DT D :˙ N r ( t ) ∝ (cid:90) t dt (cid:48) DT D (∆ t ) SF R ( t (cid:48) ) , (1)where ˙ N r is the rate of the r -process events, ∆ t = t − t (cid:48) is a time between binary neutron star formation andmerger, and SF R is the star formation rate. The formof
DT D is often assumed to be ∝ ∆ t − with a min-imum delay ∆ t min . Beniamini & Piran (2019) finda somewhat steeper power law, DT D ∝ ∆ t − . with∆ t min ∼
35 Myr, inferred from the orbital separationsof the Galactic binary pulsars. In addition, the red-shift distribution of short gamma-ray bursts (GRBs) isconsistent with a
DT D ∝ ∆ t − with ∆ t min ≈
20 Myr(Wanderman & Piran 2015). (ii) The no-delay scenario (Rare SN model) : PeculiarccSNe such as MRSNe and peculiar magnetar forma-tion are proposed to produce heavy r -process elements(Nishimura et al. 2015; Metzger et al. 2008; Thompson& ud-Doula 2018). Since the evolution of the fractionof these peculiar ccSNe to normal ccSNe evolves is un-known, we assume here that it is constant with timeduring the Galaxy’s evolution. The production rate of r -process elements is then proportional to that of α -elements, i.e., ˙ N r ( t ) ∝ SF R ( t ). (iii) The “negative” delay scenario (Collapsar model) :Siegel et al. (2019) propose that the massive outflowfrom the central engine of long GRBs, i.e., collapsars,can be the site of the r -process . A “negative” delay is The nucleosynthesis of heavy elements in collapsars is still underdebate (Fujibayashi et al. 2020). elay of the r-process r -processenrichment associated with the death of massive stars(which of course occurs after their birth, not before).It should instead be understood in an averaged sense.“Negative” delays from star formation to r -process en-richment are a result of the fact that long GRBs prefer-entially occur in environments with large specific SFRand low metallicities (Svensson et al. 2010; Palmerioet al. 2019). This is perhaps most clearly demonstratedby the redshift distribution of long GRB which peaks ata higher redshift than the cosmic SFR (Wanderman &Piran 2010). Therefore, we assume that the productionratio of r -process elements to α -elements decreases withtime in this scenario:˙ N r ( t ) ∝ A ( t ) SF R ( t ) , (2)where A ( t ) is a decreasing function, which takes intoaccount the enhancement of the event rate of collapsarsat the earlier times. In what follows, we assume A ( t ) ∝ t − . motivated by the relation between the long GRBrate and cosmic SFR at z (cid:46) R -PROCESS DELAY INFERRED FROM VERYMETAL-POOR STARSWe now turn to constrain the early enrichment his-tory of r -process elements by using the r -process abun-dances of very metal-poor stars. Europium (Eu) is themost commonly used as the r -process tracer element.However, since the absorption lines of Eu are not sostrong, the Eu measurements are often unavailable forvery metal-poor stars. In such cases, barium (Ba) abun-dances are used as the tracer of r -process elements in-stead of Eu (Fran¸cois et al. 2007; Duggan et al. 2018).Here we study Ba abundance evolution at the low metal-licity range of − (cid:46) [Fe / H] (cid:46) −
2. Although most Bais produced by the s -process at solar metallicity, the[Ba/Eu] ratio decreases as metallicity decreases, and at[Fe / H] < − .
0, the production of Ba is dominated bythe r -process .Figure 1 shows a schematic figure of the [Ba/Mg] evo-lution against [Fe/H]. The Galaxy was metal-poor atearly times, and as a result, stars formed very earlyshape the curve on the left. At such extremely lowmetallicities, the chemical inhomogeneity of the inter-stellar medium (ISM) plays an important role becausethe event rate of the r -process is much lower than nor- The exception is the s -enhanced carbon-enhanced metal-poor(CEMP- s ) stars. These stars are part of binaries, and the com-positions of the stars are dominated by mass-transfer from thecompanions. Such stars are not included in this work. [ B a / M g ] s-processr-process D i ff u s i o n e ff e c t NSMSNecollapsar
Figure 1.
A schematic figure showing the evolution of[Ba/Mg] against [Fe/H]. A sharp increase of the median[Ba/Mg] is expected at very low [Fe/H]. This is as a result ofthe inhomogeneity effect described in the text, which holdsfor times short relative to the mixing time, where the Baenrichment at a given location is largely dominated by oneevent. At − . (cid:46) [Fe / H] (cid:46) − . r -process enrichment. At − . (cid:46) [Fe / H] contributionsfrom s -process becomes important and we see the increase in[Ba/Mg] with increasing [Fe/H]. mal SNe. The r -process elements in the ISM at a givenlocation originate from a single enrichment event (Be-niamini & Hotokezaka 2020). The volume fraction ofthe highly enriched ISM is very small and therefore typ-ical stars (outside of the enriched areas) have very low[Ba/Mg]. This inhomogeneity effect quickly disappearsas more events start to contribute to the enrichmentat each location, and the [Ba/Mg] track now representsthe intrinsic delay of r -process element production. At[Fe / H] (cid:38) −
2, the s -process starts to contribute signif-icantly to the Ba abundances. As we are interested inconstraining the r -process enrichment, in what follows,we will focus on very metal poor stars with [Fe / H] (cid:46) − µ (Ba / Mg) is defined as: µ (Ba / Mg) = 1 N star N star (cid:88) i [Ba / Mg] i , (3)where the index i runs from 1 to the number of starsin each [Fe/H] bin. We ignore stars with upper limits.The curves were mostly unchanged even if we assumeall upper limit stars to have [Ba / Mg] = − Tarumi et al. [ B a / M g ] Observation
JINAbasemean median Neutron star mergermean 1-zonemean (JINA) [Fe/H] [ B a / M g ] Supernovamean 1-zonemean (JINA) [Fe/H]
Collapsarmean 1-zonemean (JINA)
Figure 2.
Evolution of [Ba/Mg] against [Fe/H] in observed stars and in our diffusion model. Top-left panel: observeddistribution. The data is obtained in JINAbase (Abohalima & Frebel 2018). Stars with high carbon abundance ([C / Fe] > . ∝ t α and here wechoose α = 1 in all the cases. For the NSM model, we use a power-law DTD ∝ t − with a minimum delay time of 20Myr. Forthe SNe model r -process enrichment occurs concurrently with star formation. For the collapsar model we assume the rate to beproportional to SF R ( t ) × t − . , so that the r -process enrichment preferentially occur before the Fe and Mg enrichment. Thediffusion coefficient D is set to D = 0 . / Gyr for all the models. The curves labeled by 1-zone are the result of the one-zonemodeling, in which the instantaneous mixing is assumed, i.e., D → ∞ . pseudo-increasing trend on the median even withouttime delay, as we have shown in Figure 1. This is be-cause the abundance distribution has a long tail on thehigh-abundance end. The skewed abundance distribu-tion naturally arises in the elemental abundance distri-bution of the ISM in a galaxy. Initially, one r -processevent enriches a small portion of the ISM to a very highdegree, and it dilutes to the whole galaxy as time passes.If we measure the distribution of the r -process elementabundances of the ISM before complete mixing, the me-dian would always be less than the “one-zone” predic-tion, for which instantaneous mixing is assumed.In contrast, the linear mean, µ ([Ba / Mg]), is robust tothe inhomogeneity of the distribution of r -process ele-ments. It gives appropriate weights to both r -rich and r -poor gas. The deviation from a one-zone model arises because we are comparing the medians, which overesti-mate the importance of volumetrically dominant r -poorgas. If we assume that Mg and Fe distributions are ho-mogeneous, and we sample the whole system with a suf-ficient resolution, the linear mean exactly matches theone-zone model with the instant mixing approximation.Therefore we conclude that the increase in the linearmean µ ([Ba / Mg]) is a result of the time delay betweenthe production of Mg and r -process elements. The re-maining problems are the validity of the assumptions.Namely, (i) the homogeneity of the denominator (Mg)and the x-axis (Fe), and (ii) a sufficient sampling of thevolume. Although validating these conditions is diffi-cult, we expect that such effects would deviate the lin-ear mean symmetrically from the one-zone calculation.Therefore it is unlikely that the inhomogeneity effect elay of the r-process r -rich bubbles. Herewe estimate the range (∆[Fe / H]) from [Ba / Mg] ∼ − . / Mg] ∼ − . is ∼ − .
5. The volume of each r -richbubble (1 σ region) is ∼ σ . The median of [Ba/Mg]roughly converges to [Ba/Mg] when the total vol-ume fraction of r -rich bubbles becomes ∼
1. The typ-ical volume of each bubble and the number of bubblesgrow as ∝ t / and t α +1 , respectively. Here we have as-sumed ( SF R density ) ∝ t α . Thus the total volumefraction V tot , σ grows as ∝ t α +5 / . Since [Fe/H] in-creases logarithmically with the number density of starsformed, we have [Fe / H] ∼ (1+ α ) log ( t )+ const. There-fore, the value of [Fe/H] when the [Ba/Mg] converges to[Ba/Mg] is[Fe / H] ≈ log ( V tot , σ ) · ( α + 1)( α + 5 /
2) + const. (4)We can follow the same procedure to derive the [Fe/H]when the median of [Ba/Mg] surpasses [Ba/Mg] − . V tot , σ = 3 · V tot , σ for V tot , σ . Fi-nally, ∆[Fe / H] can be derived as ∆[Fe / H] ≈ log (3 ) · ( α + 1) / ( α + 5 / . (cid:46) ∆[Fe / H] < . α >
0. However, the observational data show a slowerincrease, ∆[Fe / H] ∼ .
0, which a diffusion-induced in-crease cannot reproduce.To demonstrate the effects we have discussed, we runa Monte Carlo simulation of the chemical enrichment ofthe early phase of the Milky Way evolution, < SF R ∝ t α for t < r -process events at ∼ / Assuming a Gaussian distribution, 10 − . × e − . (cid:39) e − . = e − . / , therefore a region of size √ . σ (cid:39) σ has [Ba/Mg] valuehigher than [Ba/Mg] − .
5. The volume of a 3 σ region is 3 times that of the 1 σ region. Therefore the total volume fractionof the 3 σ regions becomes 1 when that of 1 σ regions is 1 / . We follow the dilution of the produced Fe, Mg, and r -process elements in the ISM via turbulent mixing withthe method used in Hotokezaka et al. (2015); Beniamini& Hotokezaka (2020). The number density of an element X at position (cid:126)r at time t is: n X ( (cid:126)r, t ) = (cid:88) t j
2. We also performeda simulation with
DT D ∝ ∆ t − . motivated by Beni-amini & Piran (2019) and obtain a result similar to thatwith DT D ∝ ∆ t − . Finally, we have examined the casewith a constant delay time, i.e., the production of r -process elements occurs with a fixed time delay ∆ t fromstar formation. Although this model generally results ina fast rise in [Ba/Mg], we found that some combinationof SF R ( t ) and ∆ t ∼
100 Myr can also be consistent withthe gradual rise in [Ba/Mg].Figure 3 shows the [Ba/Mg] distribution for stars inclassical dwarf galaxies. Remarkably, the same increas-ing [Ba/Mg] - [Fe/H] relation holds also for dwarf galax-ies. It supports our conclusion as it shows that the trend Once K j reaches the volume of the box, we fix K j in orderto avoid an artificial leakage of the elements (Beniamini & Ho-tokezaka 2020). Tarumi et al. [Fe/H] [ B a / M g ] FORNAXCARINASAGITTARIUS SEXTANSLEOISCULPTOR URSAMINORCANESVENATICIDRACO
Figure 3. [Ba/Mg] - [Fe/H] plot for classical dwarf galaxies.Circles are detections and downward triangles are upper lim-its. The data for these galaxies are obtained from the SAGAdatabase (Suda et al. 2017). The gray dots are stars in MW.The dwarf galaxies are on the same track of the Milky Waystars, supporting the interpretation that the gradual rise of[Ba/Mg] is caused by the intrinsic delay of r -process events. does not depend on the details of the star formation his-tories. Note that we omit UFDs as they are so smallthat they likely have experienced none or only one r -process event in the past (Beniamini et al. 2016). Inthis case, the distribution of the stellar r -process abun-dances is significantly different from that of galaxies ex-perienced multiple events and does not reflect the delay(Safarzadeh & Scannapieco 2017; Beniamini et al. 2018;Tarumi et al. 2020b). CONCLUSIONS AND DISCUSSIONSThe observed abundance distribution of [Ba/Mg] ofthe Galactic very metal poor stars clearly shows that[Ba/Mg] significantly increases as [Fe/H] increases at[Fe / H] < − .
0. Such an increase is attributed to the in-trinsic time delay of the r -process events and/or the de-lay induced by chemical diffusion in the ISM. We showedthat the increase of the linear mean and the gradual in-crease of the median require an intrinsic time delay ofthe production of r -process elements and cannot be ex-plained solely by the diffusion-induced delay. Thereforewe conclude that r -process element production occurswith significant delays at this metallicity range, whichis naturally expected in the NSM scenario (Figure 2and see also Matteucci et al. 2014; Hirai et al. 2015;Wehmeyer et al. 2015; Cˆot´e et al. 2019; Simonetti et al.2019; van de Voort et al. 2020). Any rare SN such asMRSNe and collapsars are not expected to have a signif-icant time delay between the r -process production andMg production. Consequently, SN models overproduceBa at very low metallicities even if the contribution ofthe s -process to the Ba abundances is completely ig- nored. Therefore such sources are incompatible withthe observed trend. We conclude that this is a new lineof evidence supporting NSMs as the origin of r -processelements at least in low metallicity environments [Fe/H] (cid:46) − r -process source. The existence of such an event is alsosupported from Ba abundances of UFDs (Tarumi et al.2020a). In this case, the intrinsic increase of [ r /Mg] maybe steeper than suggested by the Ba observations. How-ever, our argument regarding the increasing mean stillholds: stars with such low Ba abundances do not affectthe linear mean [Ba/Mg] anyway.Further investigation would be needed to explain the[Eu / Mg] ∼ r -processevents. One difference from the lower [Fe/H] regimeis the timescale. At the relatively higher metallicities,[Fe / H] (cid:38) −
1, where [Eu / Mg] ∼ − < [Fe / H] < − / Mg] ∼
0, they alsofound increasing [Ba / Mg], which is clear evidence of thedelayed contribution from AGB stars. Recently, Mat-suno et al. (2021) studied the r -process enrichment ofGaia-Enceladus stars. While they found a significantexcess in the r -process abundance normalized by an α -element, i.e., [Eu / Mg] ∼ .
3, [Eu / Mg] does not evolvewith [Fe/H]. The fact that r -process delays are seen at[Fe / H] (cid:46) − / H] (cid:38) − r /Mg] at the lowest metallicity stars requires a delayof 100 Myr ∼ r -process elements. No-delay and neg-ative delay sources are incompatible with the observed elay of the r-process r -process in the Universe. ACKNOWLEDGMENTSWe thank Yutaka Hirai and Tadafumi Matsuno foruseful comments. Y. T. is supported by JSPS KAK-ENHI Grant Number 20J21795. K. H. is supported byJSPS Early-Career Scientists Grant Number 20K14513.The research of P. B. was funded by the Gordon andBetty Moore Foundation through Grant GBMF5076.REFERENCES Abohalima, A., & Frebel, A. 2018, ApJS, 238, 36,doi: 10.3847/1538-4365/aadfe9Banerjee, P., Wu, M.-R., & Yuan, Z. 2020, ApJL, 902, L34,doi: 10.3847/2041-8213/abbc0dBartos, I., & Marka, S. 2019, Nature, 569, 85,doi: 10.1038/s41586-019-1113-7Beniamini, P., Dvorkin, I., & Silk, J. 2018, MNRAS, 478,1994, doi: 10.1093/mnras/sty1035Beniamini, P., & Hotokezaka, K. 2020, MNRAS, 496, 1891,doi: 10.1093/mnras/staa1690Beniamini, P., Hotokezaka, K., & Piran, T. 2016, ApJ, 832,149, doi: 10.3847/0004-637X/832/2/149Beniamini, P., & Piran, T. 2019, MNRAS, 487, 4847,doi: 10.1093/mnras/stz1589Blanchard, P. K., Berger, E., Fong, W., et al. 2017, ApJL,848, L22, doi: 10.3847/2041-8213/aa9055Buder, S., Sharma, S., Kos, J., et al. 2020, arXiv e-prints,arXiv:2011.02505. https://arxiv.org/abs/2011.02505Burbidge, E. M., Burbidge, G. R., Fowler, W. A., & Hoyle,F. 1957, Reviews of Modern Physics, 29, 547,doi: 10.1103/RevModPhys.29.547Cˆot´e, B., Fryer, C. L., Belczynski, K., et al. 2018, ApJ, 855,99, doi: 10.3847/1538-4357/aaad67Cˆot´e, B., Eichler, M., Arcones, A., et al. 2019, ApJ, 875,106, doi: 10.3847/1538-4357/ab10dbCˆot´e, B., Eichler, M., Yag¨ue, A., et al. 2020, arXiv e-prints,arXiv:2006.04833. https://arxiv.org/abs/2006.04833Duggan, G. E., Kirby, E. N., Andrievsky, S. M., & Korotin,S. A. 2018, ApJ, 869, 50, doi: 10.3847/1538-4357/aaeb8eDvorkin, I., Daigne, F., Goriely, S., Vangioni, E., & Silk, J.2020, arXiv e-prints, arXiv:2010.00625.https://arxiv.org/abs/2010.00625Eichler, D., Livio, M., Piran, T., & Schramm, D. N. 1989,Nature, 340, 126, doi: 10.1038/340126a0Fran¸cois, P., Depagne, E., Hill, V., et al. 2007, A&A, 476,935, doi: 10.1051/0004-6361:20077706Fujibayashi, S., Shibata, M., Wanajo, S., et al. 2020,PhRvD, 102, 123014, doi: 10.1103/PhysRevD.102.123014 Hirai, Y., Ishimaru, Y., Saitoh, T. R., et al. 2015, ApJ, 814,41, doi: 10.1088/0004-637X/814/1/41Hollowell, D., & Iben, Icko, J. 1988, ApJL, 333, L25,doi: 10.1086/185279Hotokezaka, K., Beniamini, P., & Piran, T. 2018,International Journal of Modern Physics D, 27, 1842005,doi: 10.1142/S0218271818420051Hotokezaka, K., Piran, T., & Paul, M. 2015, NaturePhysics, 11, 1042, doi: 10.1038/nphys3574Ishimaru, Y., Wanajo, S., Aoki, W., & Ryan, S. G. 2004,ApJL, 600, L47, doi: 10.1086/381496Ji, A. P., Frebel, A., Chiti, A., & Simon, J. D. 2016,Nature, 531, 610, doi: 10.1038/nature17425Levan, A. J., Lyman, J. D., Tanvir, N. R., et al. 2017,ApJL, 848, L28, doi: 10.3847/2041-8213/aa905fMargutti, R., & Chornock, R. 2020, arXiv e-prints,arXiv:2012.04810. https://arxiv.org/abs/2012.04810Matsuno, T., Hirai, Y., Tarumi, Y., et al. 2021, arXive-prints, arXiv:2101.07791.https://arxiv.org/abs/2101.07791Matteucci, F., Romano, D., Arcones, A., Korobkin, O., &Rosswog, S. 2014, MNRAS, 438, 2177,doi: 10.1093/mnras/stt2350Metzger, B. D., Thompson, T. A., & Quataert, E. 2008,ApJ, 676, 1130, doi: 10.1086/526418Nishimura, N., Sawai, H., Takiwaki, T., Yamada, S., &Thielemann, F. K. 2017, ApJL, 836, L21,doi: 10.3847/2041-8213/aa5deeNishimura, N., Takiwaki, T., & Thielemann, F.-K. 2015,ApJ, 810, 109, doi: 10.1088/0004-637X/810/2/109Palmerio, J. T., Vergani, S. D., Salvaterra, R., et al. 2019,A&A, 623, A26, doi: 10.1051/0004-6361/201834179Reichert, M., Hansen, C. J., Hanke, M., et al. 2020, A&A,641, A127, doi: 10.1051/0004-6361/201936930Roederer, I. U. 2013, AJ, 145, 26,doi: 10.1088/0004-6256/145/1/26Rosswog, S., Sollerman, J., Feindt, U., et al. 2018, A&A,615, A132, doi: 10.1051/0004-6361/201732117