Constraining Collapsar r-Process Models through Stellar Abundances
DD RAFT VERSION M AY
14, 2019Typeset using L A TEX twocolumn style in AASTeX62
Constraining Collapsar r -Process Models through Stellar Abundances P HILLIP M ACIAS
1, 2
AND E NRICO R AMIREZ -R UIZ
1, 21
Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA DARK, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark
ABSTRACTWe use observations of heavy elements in very metal-poor stars ([Fe/H] < -2.5) in order to place constraintson the viability of collapsar models as a significant source of the r -process . We combine bipolar explosionnucleosynthesis calculations with recent disk calculations to make predictions of the observational imprintsthese explosions would leave on very metal-poor stars. We find that a source of low ( ≈ . − . M (cid:12) ) Fe masswhich also yields a relatively high ( > . M (cid:12) ) r -process mass would, after subsequently mixing and formingnew stars, result in [ r /Fe] abundances up to three orders of magnitude higher than those seen in stars. In order tomatch inferred abundances, 10-10 M (cid:12) of Fe would need be efficiently incorporated into the r -process ejecta.We show that Fe enhancement and hence [ r /Fe] dilution from other nearby supernovae is not able to explainthe observations unless significant inflow of pristine gas occurs before the ejecta are able to form new stars.Finally, we show that the inferred [Eu/Fe] abundances require levels of gas mixing which are in conflict withother properties of r -process enhanced metal-poor stars. Our results suggest that early r -process production islikely to be spatially uncorrelated with Fe production, a condition which can be satisfied by neutron star mergersdue to their large kick velocities and purely r -process yields. INTRODUCTIONThe gravitational wave discovery of the binary neutron starmerger (NSM) GW170817 (Abbott et al. 2017) along withthe intensive multi-wavelength electromagnetic observationsof the ensuing kilonova SSS17a/AT2017gfo (e.g., Coulteret al. 2017; Cowperthwaite et al. 2017; Drout et al. 2017;Shappee et al. 2017) provided definitive evidence of NSMsbeing a viable source of r -process elements in the galaxyand universe as a whole. Since then, a number of interest-ing questions have arisen regarding the physics of NSMs aswell as the implications of NSMs being the only significantsource of the r -process throughout cosmic time (see Siegel2019, for a summary of current issues with the merger-onlymodel).One puzzle exhibited by the kilonova is the large mass oflanthanide rich ejecta ( ≈ . M (cid:12) ) inferred through mod-eling (e.g., Kasen et al. 2017). While the mass of dynami-cal ejecta expelled by tidal forces is expected to be at most ≈ − M (cid:12) (e.g., Radice et al. 2018), the kilonova requiredseveral times this mass in order to explain the peak lumi-nosity and subsequent evolution. This requires an additionalsource of heavy r -process ejecta, with one theoretically pre-dicted candidate being outflows from a remnant accretiondisk. These outflows, which originally were thought to bepowered by neutrino irradiation and thus result in a relativelyweak r -process , may be instead launched by nuclear recom-bination and viscous dissipation, maintaining a low Y e andresulting in a heavy r -process (e.g., Wu et al. 2016). In addition, while numerous studies have implicated a rare(in comparison to standard core-collapse supernovae) chan-nel for the r -process at both early and late times (Hotokezakaet al. 2015; Ji et al. 2016; Macias & Ramirez-Ruiz 2018),some issues have arisen with NSMs being a dominant chan-nel in the context of galactic chemical evolution. In par-ticular, the expected / observed delay time distribution t − of NSMs predicts a flat [Eu/Fe] trend in stars with [Fe/H]metallicities > -1, where we use the standard notation [El/H]= log ( N El / N H ) − log ( N El / N H ) (cid:12) , where N El is the columndensity of a given element. This is not seen in the data, asthe [Eu/Fe] exhibits a “knee" at around [Fe/H]=-1, similar tothat of alpha elements produced in CCSNe. This discrepancyimplies that there may be another early, possibly dominant,channel of r -process production that has yet to be directlydetected (Côté et al. 2018), or that the delay-time distribu-tion of NSMs differs from that of Type Ia supernovae (e.g.,Simonetti et al. 2019).One solution recently detailed by Siegel et al. (2019) is thecollapsar model proposed by Woosley (1993), in which thecore of a massive ( (cid:38) M (cid:12) ) rotating star collapses to forma black hole. The resultant explosion does not unbind theentirety of the star, leaving behind material with sufficientangular momentum to form an accretion disk (MacFadyen& Woosley 1999; Lee & Ramirez-Ruiz 2006). Due to thelarge ( > − M (cid:12) s − ) accretion rates achieved at early times,the midplane of the disk may attain high enough density tosuppress positron creation, thus capturing electrons only andproducing neutron rich material. The ejection of this material a r X i v : . [ a s t r o - ph . H E ] M a y M ACIAS & R
AMIREZ -R UIZ through a disk wind would then produce a strong r -process .This scenario, motivated by the inferred accretion disk windsof SSS17a, would result in significant heavy element produc-tion immediately following star formation events, thus repro-ducing the trend in [Eu/Fe] at late times. However, due to thelarge progenitor masses required, collapsars are inherentlyrare (even compared to NSMs) and must produce a largemass of r -process ejecta per event in order to be consistentwith the average mass production-rate inferred for the MilkyWay of ∼ − M (cid:12) yr − (Bauswein et al. 2014).Here we discuss the implications of such large r -processejecta masses and compare to observations of stars that havebeen formed from gas that has been enriched by at most a fewnucleosynthetic production events. In Section 2, we derivepredictions for stellar abundance measurements within thecollapsar scenario to compare to observations of very metal-poor stars and discuss mixing of the r -process elements. InSection 3 we comment on the implications of our findings inthe context of r -process progenitors. AN OBSERVATIONAL CONSTRAINT ON THECOLLAPSAR MODEL2.1.
Comparison with Theoretical Models
In order to make predictions of [ r /Fe] for our sample stars,we employ the nucleosynthesis calculations of Maeda &Nomoto (2003). They calculate bipolar (jetted) explosionmodels of 25 and 40 M (cid:12) stars while varying energy andopening angle as well as spherical “normal" supernovae. Weinclude results for only their bipolar explosions though thespherical results are qualitatively indistinguishable. We donot include their model 40D, which would have the largestdiscrepancy with the observational data due to an anoma-lously low Fe mass of ∼ − M (cid:12) caused by a larger initialremnant mass.These calculations provide us with Fe and Mg yields, aswell as the [Fe/H] which depends on the mass over which theexplosion diluted, given by M dilution = 5 . × M (cid:12) E . n − . C − / , (1)where E is the explosion energy in units of 10 ergs, n isthe ambient hydrogen number density in units of 1 cm − , and C is the local sound speed in units of 10 km s − (Shigeyama& Tsujimoto 1998). The Fe masses they obtain range be-tween 0.078-0.54 M (cid:12) . The calculations do not follow thenucleosynthesis in a remnant accretion disk and focus on theexplosion itself, as the full calculation remains computation-ally prohibitive. Instead, we combine their calculations withthe recent work by Siegel et al. (2019), in which only theremnant accretion disk is simulated and r -process nucleosyn-thetic calculations are performed.In order to derive a mass of r -process elements necessarilysynthesized in a single collapsar event to explain the Milky Way production rate, Siegel et al. (2019) convolve the longGRB and star formation rate with the average mass produc-tion of r -process elements in the Milky Way in order to derivea mass of 0 . − . M (cid:12) per event given the uncertainties.This is attainable within their simulations, thus introducingthe viability of the collapsar model within their framework.In our analysis we adopt their lowest event yield of 0.08 M (cid:12) ,thus deriving a lower bound on the expected [ r /Fe] abun-dances.After the collapsar event, the r -process material formedwithin the disk should efficiently mix with the ejecta synthe-sized in the explosion, thus leaving behind a chemical imprinton the subsequent generation of stars formed. With this, weare able to derive a simple equation to determine the expected[ r /Fe] enhancement given by[ r / Fe] = log ( M r-p / M Fe ) collapsar − log ( M r-p / M Fe ) (cid:12) , (2)where M r-p and M Fe are the total mass of r -process elementsand Fe produced in either the collapsar or contained withinthe solar abundance pattern. The solar abundance pattern istaken from Lodders (2003) and the r -process residual patternfrom Arnould et al. (2007). For the solar r -process pattern,we consider elements starting from mass number A=69.This can be directly applied to any r -process element, as-suming a solar abundance pattern is attained within the to-tal r -process mass. The application of this equation to thelighter r -process elements may be less justified, as there isevidence of some variation within e.g. first-peak elementscompared to the Sun. However its application to heavier el-ements is observationally motivated by the robustness of theheavy r -process solar pattern across decades in [Fe/H] metal-licity (e.g., Frebel 2018).To test this prediction, we utilize JINAbase (Abohalima& Frebel 2018) to gather stars with an [Fe/H] metallicity of< -2.5, from which measurements have also been made ofMg (alpha), Sr (first peak), Ba (second peak), and Eu (lan-thanide). We employ an additional cut of [Ba/Eu] < -0.5 inorder to avoid any early s -process contaminants (Simmereret al. 2004). We do not include stars with upper-limits onany of the elements we are considering. This brings our totalsample to a size of 186 stars. At these low metallicities, starsformed should retain memory of at most a few nucleosyn-thetic events having polluted the gas from which they form(Audouze & Silk 1995; Shigeyama & Tsujimoto 1998).With this we are able to directly compare the observationsof heavy element abundances in our sample with predictionsof the collapsar scenario. The results for Eu, Ba, and Sr areshown in Figure 1. We compare against the solar r -processvalues for Sr and Ba by adjusting for the fact that the s -process contribution to the present day solar pattern is 75%and 85%, respectively. This only results in an offset in our OLLAPSARS AS AN r - PROCESS S OURCE [ M g / F e ] M rp = 0.08 M collapsarJINAbase sample 4.00 3.75 3.50 3.25 3.00 2.75 2.50[Fe/H]0123 [ E u / F e ] [ B a / F e ] r p [ S r / F e ] r p Figure 1.
Stellar abundances from JINAbase are shown in black along with single-event predictions from the collapsar models of Maeda &Nomoto (2003) combined with r -process calculations from Siegel et al. (2019) in red. Average error bars are ∼ r -process abundances are much higher than seen in observations. Shown in the dashed lineis the trajectory a parcel of gas would take due to dilution in Fe from nearby supernovae that provide Fe but no r -process elements. plot as the correction is applied to both data and the modelsand does not inform any differences between them. As canbe seen, the collapsar models consistently over-predict theobservations of heavy elements. The top left panel shows thegood agreement between predictions for Mg and our samplethat is not seen in the r -process elements. We note that thelargest discrepancies of ∼ r -process material, thus increas-ing the predicted [ r /Fe] and exacerbating the discrepancy.Furthermore, though the Y e electron fraction distribution mayhave a significant effect on limited to main r -process abun-dance ratios compared to Solar, the fact that the model pre-dictions overshoot the data near all three r -process peaksdoes not allow for any reasonable abundance distribution torelieve the tension. For example, moving all of the r -processejecta closer to the first peak, while conserving total mass,would only increase the predicted [Sr/Fe]. One possible resolution would be the dilution of [ r /Fe] bytypical core collapse supernovae that may not provide sig-nificant r -process enrichment. The red dashed line shows theresult of such dilution. Since the Fe enhancement would onlyincrease the denominator on the y-axis while increasing thenumerator on the x-axis, this would result in the plotted linewith slope -1 through the plot. This line does not intersect thedata more than marginally for any star and is thus still diffi-cult to reconcile with the observations. It may be possiblehowever that the [ r /Fe] of the gas is enhanced with Fe frommany nearby supernovae, taking it downward along the redtrajectory drawn in Figure 1. Then, at [Fe/H] metallicity of ∼ -2 is diluted in both Fe and Eu equally by pristine inflow-ing material, lowering the [Fe/H] and pushing it horizontallyback toward the data.Another possibility is continued expansion of an Eu andFe-containing collapsar ejecta mixing significantly beyond M dilution . If material expands into ejecta from many nearbysupernovae, it will not maintain the [Eu/Fe] characteristicof its own yields, but rather obtain an [Fe/H] (and thus[Eu/Fe]) corresponding to the average [Fe/H] of the com-bined sources. Although this would violate the long-held andoften utilized “single-event" nature of these stars, which hasbeen used to compare to lighter element abundances against M ACIAS & R
AMIREZ -R UIZ
SN models, we discuss the implications of this scenario be-low.2.2.
Observational Implications within the Collapsar Model
As mentioned above we can also ask the inverse ques-tion from our JINAbase sample. That is, given the in-ferred [Eu/Fe] and assuming an Eu mass of M Eu , collapsar = X Eur-p , (cid:12) M r-p , collapsar = 8 × − M (cid:12) , we can invert Equation 2 tosolve for the mass of Fe that the Eu mixes with. Further-more, we can then calculate the mass of pristine material thatthe total Fe must be spread over in order to maintain the low[Fe/H]. This method is independent of the models of Maeda& Nomoto (2003), as we now take the [Eu/Fe] abundancesfrom our sample as an input to the equation as opposed tojust comparing against them. ( M H [ M ]) l og ( M F e [ M ]) Figure 2.
Fe mass mixed with Eu producing events required toexplain inferred [Eu/Fe] abundances are shown along the y-axis,and total Hydrogen mass in order to maintain the [Fe/H] in the starsis shown on the x-axis for our JINAbase sample of stars.
Figure 2 shows the result of this experiment. We immedi-ately see a ∼ dynamic range in both the inferred sweptFe masses and the Hydrogen dilution masses necessary to re-produce the observations. In the most extreme cases, we findHydrogen dilution masses of ≈ M (cid:12) . This is well beyondthe typical dilution masses of ∼ M (cid:12) , requiring a verylarge-scale mixing process which may be disfavored by theobserved dispersion of r -process element abundances at earlytimes, the rarity of the r -I/II stars ([Eu/Fe] > +0.3), as well asdisputing the single-event nature of stars below our [Fe/H] <-2.5 selection.We propose that a more likely resolution is that the r -process production site is spatially uncorrelated with any Feproduction, and thus the r -process material is naturally di-luted by the time it comes into contact with any Fe (Shenet al. 2015; van de Voort et al. 2015; Naiman et al. 2018).This may be the case for a NSM, in which substantial kicksduring the preceding SNe may push NSM progenitors far from their birthplace before merging. While this argumentdoes not solve the outstanding puzzle of the [Eu/Fe] “knee"seen in the chemical evolution trend, it does argue against an r -process source synthesizing Fe, unless its mixing processis extreme. DISCUSSIONOur analysis finds that any r -process source that is phys-ically associated with Fe production seems to be disfavoredby observations of heavy elements within very metal-poorstars. While this finding is consistent with aspects of previ-ous analyses (c.f., Qian & Wasserburg 2007, and referencestherein), we place direct constraints on the collapsar modelof r -process enrichment. This poses a challenge to the col-lapsar scenario, instead lending further credence to a NSM orNS black-hole (NSBH) merger that should result in minimalFe production and likely take place far from their birth sites.This does not rule out standard CCSNe as a source of alighter r -process , as they may produce substantially lesse.g. Sr per event given their rates and may still be consistentwith the abundances. The abundances also are not in con-flict with a magnetorotational jet-driven supernova (Winteleret al. 2012; Nishimura et al. 2015), as the mass of r -processis decreased by a factor of 10 and still consistent with mostof the data in Figure 1 provided external Fe enhancement.However, this scenario may require very high ( ∼ G)pre-collapse magnetic fields to produce elements such as Eu(Mösta et al. 2018).Recent kinematic studies of the highly r -process enhanced r -II stars show evidence of clustering in phase space (Roed-erer et al. 2018), suggesting they may have been strippedfrom small dwarf galaxies like the highly r -process enhancedReticulum II (Ji et al. 2016). If this is the case, measure-ments of total r -process masses of say Eu may not be reli-able, as the abundances may be driven by environmental ef-fects such as low star formation efficiency in these galaxiesas opposed to probing the event itself. However given theirlow gas mass, the amount of dilution shown in Figure 2 nec-essary to maintain both the [Eu/Fe] and [Fe/H] may be moredifficult to attain. We also note that observations of r -processenhanced stars are biased toward the halo and thus may beprobing a primarily ex-situ population. Future observationsof r -process enhanced bulge MW stars may distinguish if theproduction scenario is different between these two compo-nents.Crucial to our analysis is the assumption that the r -processelements are well mixed with the Fe by the time the nextgeneration of stars form. As the Fe is primarily produced ina jet and the r -process may be launched in a more equato-rially concentrated disk outflow, it is possible that their dif-ferent ejection speeds and times may inhibit efficient mix-ing, though again this may be in conflict with hydrodynami- OLLAPSARS AS AN r - PROCESS S OURCE > suppression required forour lowest metallicity stars.If this inefficient mixing scenario is what occurs, we arestill able to state that the abundances in metal-poor starsobserved argue against spatial correlation of r -process pro-duction with Fe, as this would result in a similar trajectoryto those shown by the red dashed-lines in Figure 1. Thisspatial correlation is to be expected in a collapsar that ex-plodes promptly following a star-formation event and wouldnot have time to migrate far from its birthplace.While SSS17a/AT2017gfo served as the long sought afterdirect evidence of significant r -process production in NSMs,there remain many outstanding questions regarding their rolethroughout cosmic time. There is certainly still room if notevidence for multiple progenitor channels contributing sig- nificantly. Future observations of electromagnetic counter-parts to gravitational wave sources will continue to elucidateremaining open questions in r -process nucleosynthesis andhopefully reveal new mysteries to explore.We thank the referee for comments which have improvedthe quality of this manuscript. We thank Stephan Ross-wog and Charli Sakari for useful comments on an earlierversion of this manuscript. This research has made use ofNASA’s Astrophysics Data System. P.M. is supported inpart by the Heising-Simons Foundation. E.R.-R. is supportedin part by David and Lucile Packard Foundation and theNiels Bohr Professorship from the DNRF. The UCSC teamis supported in part by NASA grant NNG17PX03C, NSFgrant AST-1518052, the Gordon & Betty Moore Foundation,the Heising-Simons Foundation, and the David and LucilePackard Foundation. Software:
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