On Neutron Star Mergers As the Source of R-Process Enhanced

Draft version March 27, 2019 Preprint typeset using LATEX style emulateapj v. 12/16/11

ON NEUTRON STAR MERGERS AS THE SOURCE OF R-PROCESS ENHANCED METAL POOR STARS IN THE MILKY WAY Mohammadtaher Safarzadeh, Richard Sarmento, and Evan Scannapieco School of Earth and Space Exploration, Arizona State University Draft version March 27, 2019

ABSTRACT We model the history of Galactic r-process enrichment using high-redshift, high-resolution zoom cosmological simulations of a Milky Way (MW) type halo. We assume that all r-process sources are neutron star mergers (NSMs) with a power law delay time distribution. We model the time to mix pollutants at subgrid scales, which allows us to to better compute the properties of metal poor (MP) and carbon enhanced metal poor (CEMP) stars, along with statistics of their r-process enhanced subclasses. Our simulations underpredict the cumulative ratios of r-process enhanced MP and CEMP stars (MP-r ,CEMP-r ) over MP and CEMP stars by about one order of magnitude, even when the minimum coalescence time of the double neutron stars (tmin) is set to 1 Myr. No r-process enhanced stars form if tmin = 100 Myr. Our results show that even when we adopt the r-process yield estimates observed in GW170817, NSMs by themselves can only explain the observed frequency of r-process enhanced stars if the birth rate of double neutron stars per unit mass of stars is boosted to −4 −1 ≈ 10 M .

1. INTRODUCTION earliest r-process sources. Therefore, a successful theory The recent aLIGO/aVirgo detection of gravitational for the source of the r-process should be able to explain waves from the merger of two neutron stars (GW170817; the observed statistics of MP-r and CEMP-r stars in the Abbott et al. 2017a), and the subsequent kilonova ob- MW’s halo (Barklem et al. 2005; Abate et al. 2016). served across the entire electromagnetic spectrum (Ab- In fact, the very existence of CEMP-r stars poses new bott et al. 2017b; Coulter et al. 2017) have confirmed challenges for the origin of r-process elements in the early that r-process elements are made in copious amounts in universe. These stars are believed to form at high red- neutron star mergers (NSMs; Abbott et al. 2017c; Kasen shifts and in low mass halos where Population III (Pop. et al. 2017). This discovery could be the sine qua non for III) stars have polluted the halo with their carbon rich showing that NSMs are the primary source of r-process ejecta. In such low mass halos, for a CEMP-r star to elements in the Milky Way (Côtéet al. 2018b). form, an r-process source that acts on a timescale similar On the other hand, while it is clear that NSMs are one to Pop. III stars (i.e., ≈10 Myr) is needed (Ramirez-Ruiz of the sources of r-process enrichment, it remains an open et al. 2015). question if they are the most important source. To ad- Could the observed statistics of different classes of r- dress this question, several theoretical studies have mod- process enhanced stars be explained by NSMs as the sole eled r-process enrichment of a Milky Way (MW) type source of r-process in the early universe? In this study, halo and its ultra faint dwarf (UFD) satellites by NSMs. we address this question, by carrying out a set of zoom van de Voort et al.(2015a) carried out a zoom simulation cosmological simulations of a MW type halo and model- of a MW type halo to z = 0 and concluded that NSM ing NSMs as the sources of the r-process material. We events can explain the observed [r-process /Fe] abun- improve on crucial aspects of previous such simulations on three fronts: (i) Modeling the coalescence timescales dance ratios assuming 10−2M r-process mass is ejected of double neutron stars (DNSs) as drawn from distribu- into the ISM in each NSM event. Shen et al.(2015) stud- tions motivated by population synthesis analyses (Fryer ied the sites of r-process production by post-processing arXiv:1812.02779v2 [astro-ph.GA] 25 Mar 2019 et al. 1998; Dominik et al. 2012; Behroozi et al. 2014). “Eris” zoom simulations, and found that r-process ele- (ii) Identifying Pop. III stars by following the evolution of ments can be incorporated into stars at very early times, pristine gas in each simulation cell with a subgrid model a result that is insensitive to modest variations in the de- of turbulent mixing that is crucial for properly identify- lay distribution and merger rates. Separately, Safarzadeh ing Pop. III stars whose ejecta are the precursor to the & Scannapieco(2017) studied r-process enrichment in formation of CEMP stars (Sarmento et al. 2017; Naiman the context of UFDs and concluded that natal kicks can et al. 2018); (iii) Adopting a high dark matter particle affect the r-process enhancement of subsequent stellar mass resolution in order to resolve halos where the MP generations. and CEMP stars form in the early universe. In each of these studies, it is observations of metal The structure of this work is as follows: In §2 we de- poor (MP) and carbon enhanced metal poor (CEMP) scribe our method in detail. In §3 we present our results stars that are most constraining. Such stars encode a and compare them to observations of MW halo stars. wealth of information about the formation of the first In §4 we discuss our results and conclusions. Through- stars in the universe (Beers & Christlieb 2005; Frebel out this paper, we adopt the Planck 2015 cosmologi- & Norris 2015), and similarly their r-process enhanced cal parameters (Planck Collaboration et al. 2016) where subclasses (MP-r and CEMP-r ), provide insight into the ΩM = 0.308, ΩΛ = 0.692, Ωb = 0.048 are total matter, 2 vacuum, and baryonic densities, in units of the critical For the full hydrodynamic simulations, this zoom re- density ρc, h = 0.678 is the Hubble constant in units of gion is refined to a base level of 12, and 13 for two dif- 100 km/s/Mpc, σ8 = 0.82 is the variance of linear fluc- ferent sets of simulations corresponding to a dark matter −1 5 4 tuations on the 8 h Mpc scale, ns = 0.968 is the tilt particle mass of mDM≈1.2 × 10 M and 1.4 × 10 M of the primordial power spectrum, and YHe = 0.24 is the respectively. The zoom region has sides 4.4 × 4.2 × 6.4 primordial helium fraction. comoving Mpc h−1 .

2. METHOD 2.2. Star formation and feedback The stellar particle mass in the simulation is m∗ = We used ramses (Teyssier 2002), a cosmological adap- 3 tive mesh refinement (AMR) code, which implements an ρth∆xminN where ∆xmin is the best resolution cell size unsplit second-order Godunov scheme for evolving the achievable and N is drawn from a Poisson distribution Euler equations. ramses variables are cell-centered and N¯ P (N) = exp(−N¯), (2) interpolated to the cell faces for flux calculations, these N! are then used by a Harten-Lax-van Leer-Contact Rie- mann solver (Toro et al. 1994). where ρ∆x3 We performed a set of zoom cosmological simulations ¯ N = 3 ∗, (3) of a MW type halo in order to address if NSMs can be ρth∆xmin considered the primary source of r-process enrichment in and the star formation efficiency ∗ was set to 0.01 the early universe. We adopted three different minimum (Krumholz & Tan 2007) in our simulations. Setting timescales for the coalescence of the DNSs: tmin = 1, 10, Lmax, the maximum refinement in the simulation, to 24, and 100 Myrs. We also adopted three different energy for 3 50 together with n∗ = 17 H/cm as the threshold for star the NS merger event and run simulations: ENSM = 10 , 51 52 formation in the cells results in a stellar particle mass of 10 , and 10 ergs. In all cases, we stopped the simu- ≈ 50 M . This is massive enough to host the two su- lations at z ≈ 8 − 9 when reionization is complete and pernovae needed to create a double neutron star. Lmax the formation of the metal poor stars largely diminishes. is the maximum refinement level in the simulation. A The statistics of different classes of stars displaying a further limitation on star particle formulation is that no high abundance of r-process elements are then compared more than 90% of the cell’s gas mass can be converted against MW’s halo stars. into stars. In this study, we only modeled r-process elements pro- 2.1. Simulation setup and Milky Way initial conditions duction by NSMs and slow s-process channels were not To initialize our simulations, we first ran a dark matter modeled. Consequently, we did not model elements such only simulation down to redshift zero in a periodic box as barium that have both r-process and s-process origin. with a comoving size of 50 Mpc h−1. Initial conditions Also, we did not model SN Ia because of their long aver- (ICs) were generated from music (Hahn & Abel 2011) age delay times of the order of 200-500 Myr (Raskin et al. for a Planck 2015 cosmology. The virial mass and ra- 2009). Given the stellar particle mass (≈ 50M ), 50% of dius of the halos are derived from the HOP halo finder all such particles were assumed to host one core-collapse (Eisenstein & Hut 1998). We used a halo mass cut of supernova (CCSN), assigned stochastically. Therefore, 12 half of the stellar particles generated a CCSN ejecting 1 − 2 × 10 M to ensure we only identified halos with a a total mass of msn = 10 M with a kinetic energy of mass similar to the MW. We found 275 such halos within 51 the desired mass range in our simulation box. We fur- ESN = 10 erg 10 Myr after the star was formed. The ther refined our MW-type halo candidates by requiring metallicity yield for each CCSN is set to ηSN = 0.1, mean- them to be isolated systems. We estimated this based ing one solar mass of metals is ejected in each CCSN event. on the tidal isolation parameter (τiso) approach (Grand et al. 2017). The isolation parameter for each halo is For each newly formed star particle, the ejected mass computed as: and energy were deposited into all cells whose centers are within 20 pc of the particle, and if the size of the 3 τiso,i = M200,i/M200 × (R200/ri) , (1) cell containing the particle is greater than 20 pc, the energy and ejecta are deposed into the adjacent cells where M200 and R200 are the virial mass and radius of the (Dubois & Teyssier 2008). Here the total mass of the halo of interest, and M200,i and ri are the virial mass of ejecta is that of the stellar material plus an amount and distance to the i-th halo in the simulation, respec- of the gas within the cell hosting the star particle (en- tively. We computed τiso,max for all halos with masses trained gas) such that mej = msn + ment, and ment ≡ 12 3 between 1 − 2 × 10 M , by searching within a distance min(10 msn, 0.25 ρcell ∆x ). Similarly, the mass in met- of 10 Mpc h−1 centered on the location of each halo. als added to the simulation is taken to be 15% of the The most isolated halos, i.e., those with lowest values of SN ejecta plus the metals in the entrained material, τiso,max are our candidate MW-like halos. Zej mej = ment Z + 0.15 msn. Next, we traced the dark matter (DM) particles within We separately tracked the metals generated by Pop III 2 × R200, for the top five candidates with the lowest val- stars. These are dubbed ‘primordial metals’ and their ues for τiso,max, back to the starting redshift. The lo- mass is taken to be ZP,ej mej = ment ZP + 0.15 msn P? cations of these DM particles determine the Lagrangian since the scalar P? captures the mass fraction of the star enclosing box. The halo with the smallest box, now our particle that represents Pop III stars. SN feedback is zoom region, was chosen for our simulations to reduce the dominant driver of turbulence in our simulation and the computational costs. we have modeled the feedback to be purely in kinetic Neutron Star Mergers and r-process Enhanced Metal Poor Stars 3 form. Lastly, we note that we do not model black hole formation and its feedback because its impact is expected TABLE 1 to be negligible at this redshift (Scannapieco & Oh 2004; Mass fractions of metals Scannapieco et al. 2005; Croton et al. 2006; Sijacki et al. X/Z X/ZP 2007) Element 1 Gy 60 M Pop. III SNe 2.3. Cooling C 1.68 ×10−1 7.11 ×10−1 Fe 5.39 ×10−2 2.64 ×10−12 We used CLOUDY (Ferland et al. 1998) to model cool- 4 The mass fractions of metals for selected elements used to model ing at temperatures & 10 K. Below this temperature the normal and primordial metallicity of star particles in our sim- we used Rosen & Bregman(1995) and allowed the gas ulation. Data for gas typical of 1 Gyr post BB provided by F. X. to cool radiatively to 100 K. However, adiabatic cooling Timmes (2016). Data for 60M Pop. III SN provided by Heger can result in gas falling below this temperature. (2016). Additionally, we supplemented the cooling in the pri- Similarly, the elemental abundance pattern for regular mordial gas with an H2 cooling model based on Martin metals, is accounted for by a single scalar Z. By tracking et al.(1996). We computed the cooling rate for each these values for each star particle in the simulations, and simulation cell based on its density, temperature, and convolving them in post-processing, we can explore the H fraction, f . We set the primordial H fraction ac- 2 H2 2 composition of our star particles through cosmic time, cording to Reed et al.(2005) with f = 10−6. H2 by using a variety of yield models for both Pop. III and Although we did not explicitly model radiative trans- Pop. II SNe. fer, we modeled the Lyman-Werner flux from our star Our pristine mass fraction scalar, P , modeled the particles since these photons destroy H2. We used ηLW = 4 mass-fraction of gas with Z < Zcrit in each simulation 10 photons per stellar baryon (Greif & Bromm 2006) cell. Star formation took place at much smaller scales and assumed optically thin gas throughout the simula- than the best resolution of typical cosmological simu- tion volume. The total number of stellar baryons, N∗,b, lations. Modeling P allowed us to follow the process of was computed each step by totaling the mass in star par- metal mixing at subgrid scales by quantifying the amount ticles assuming a near-primordial composition (X=0.73, of pristine gas within each cell as a function time. Y =0.25). The value of f was then updated every sim- H2 Most simulations instantaneously update cells’ average ulation step: metallicity once they are contaminated with SN ejecta. However, mixing pollutants typically takes several Eddy (fH2,old Ngas − NLW) fH2,new = , (4) turnover times (Pan & Scannapieco 2010; Pan et al. 2013; Ngas Ritter et al. 2015). By tracking the evolution of P , we where can model the formation of Pop. III stars in areas of the simulation that would normally be considered polluted above Z ; in effect increasing the chemical resolution NLW = N∗,b ηLW. (5) crit of the simulation. Our model for the pristine fraction We did not model the formation of H2 since subsequent is based on accepted theoretical models (Pan & Scanna- cooling is dominated by metals shortly after the first stars pieco 2010) and has been calibrated against numerical are formed. Lastly, we included a UV background model simulations that model the dynamical time required to based on Haardt & Madau(1996) model. mix pollutants, due to SN stirring, in an astrophysical context (Pan et al. 2013). 2.4. Turbulent mixing As stellar particles are formed within a cell, they in- We made use of the work described in Sarmento et al. herit Z, P and ZP, from the gas. This allowed us to (2017) to generate and track new metallicity-related calculate the fraction of stellar mass in a given star par- quantities for both the gas and star particles. Specifi- ticle that represents metal-free stars, P?, as well as the cally, for each cell in the simulation we tracked the av- relative contributions that metals from Pop. III and Pop. erage primordial metallicity, ZP, which tracks the mass II stars make to the stars that are enriched, ZP,?/Z?. fraction of metals generated by Pop. III stars, and the The ejecta composition for Pop. II and Pop. III stars pristine gas mass fraction, P , which models the frac- are indicated in Table1. Properly accounting for turbu- tion of unpolluted gas within each simulation cell with lent mixing enables us to identify the Pop. III stars whose Z < Zcrit. We briefly describe these scalars here, and a stellar yields (carbon rich ejecta) are different than Pop. more thorough discussion is presented in Sarmento et al. II stars and are responsible for the formation of CEMP (2017). stars. We express the abundance ratios of a star com- The primordial metallicity scalar, ZP, tracked the pared to that of the Sun as metallicity arising from Pop. III stars. This scalar allowed us to track the fraction of Pop. III SN ejecta in N N [A/B] = log A − log A , (6) subsequent stellar populations. Yields from Pop. III stars NB NB are likely to have non-solar elemental abundance ratios star (Heger & Woosley 2002; Umeda & Nomoto 2003; Ishi- The solar abundance of Eu (log Eu) is assumed to be gaki et al. 2014) and contribute to the unusual abun- 0.52 (Asplund et al. 2009) in the notation of log X = dances patterns seen in the halo and UFD CEMP stars. log(NX/NH)+12 where NXand NH are the number densi- Knowing both ZP and the overall metallicity of the gas, ties of element X and hydrogen, respectively. Likewise for Z, allowed us to estimate the abundances of various el- carbon we adopt log C = 8.43 and for iron log Fe = 7.5. ements, without having to track each one individually. We note that subgrid turbulent mixing is only modeled 4 for the metals and not the r-process ejecta. However, due to the high resolution of these simulations, we observe a negligible difference in metal enrichment due to the Time since Big Bang [Myr] computation of subgrid turbulent mixing. Therefore, we 958 785 658 562 487 379 306 253 215 assume the same holds for r-process material as it is -1 treated as another scalar field similar to the metals in the code. -2 ] 3

2.5. Modeling neutron star mergers c p

M -3

We have modeled the formation of DNSs to take place / −3 r for a tiny fraction (10 ) of stellar particles chosen to y /

5 ¯ go SNe. This corresponds to one DNS per 10 M of -4 M [ stars, that translates into a neutron star merger rate of −4 D ≈ 10 /year at z = 0 (van de Voort et al. 2015b). R F -5 reionization S The particle chosen to host a DNS ﬁrst undergoes two g o CCSN explosions, corresponding to the two progenitor l fiducial Sarmento+ 18 stars. Afterwards, the particle was assigned a delay time -6 this work, high res Barai+ 18 −1 Xu+ 16 normal Johnson+ 13 distribution drawn from a power law tmerge ∝ t (e.g. Xu+ 16 void Finkelstein+ 16 Dominik et al. 2012; Mennekens & Vanbeveren 2016) -7 Sarmento+ 17 Madau & Dickinson 14 with minimum of t =1, 10, or 100 Myr (for three min 6 7 8 9 10 12 14 16 18 separate simulations) and maximum of tmax =10 Gyr re- redshift spectively. Note that this time is after the formation of the second neutron star in the binary. Once the merger 1.6 time has elapsed we simulated the generation of r-process z > 14 51 elements via a third explosion with ENSM = 10 erg in z > 12 50 1.4 our ﬁducial run, while we explored ENSM = 10 , and z > 10 1052 erg cases separately. z > 9 1.2 z > 8.2 2.5.1. Europium yield

We set the ﬁducial value of the europium yield in 1.0 the NSM events in our simulations based on the NS-

NS merger detected by aLIGO/Virgo (GW170817). We F −5 D 0.8 adopted the estimated Eu yield of 1.5×10 M for each

NS merger event in our simulation. This number reflects M the lanthanide-rich material ejected in the post-merger 0.6 accretion disk outflow in a NS-NS merger event with the maximum value of 0.04 M (Cowperthwaite et al. 2017) multiplied by the abundances pattern of the solar 0.4 r-process residuals (Côtéet al. 2018b). The disk wind ejecta could be lanthanide-rich depending on the lifetime 0.2 of the hyper-massive neutron star prior to collapsing into a black hole (Metzger & Fernández 2014; Siegel & Met- 0.0 zger 2017). We adopted this value since in order to an- 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 swer the question of whether NSMs could by themselves explain the statistics of the r-process enhanced stars in [Fe/H] the MW’s halo, one needs to be conservative in the assigned yields. Fig. 1.— Top panel: the comoving SFR density of the T1E51 simulation (solid black line), and the higher resolution simulation (T10E51; dashed black line ). Also shown are data from the Re- 2.6. Simulation parametrizations naissance simulation, for both the normal and void regions (Xu We carried out five different simulations in this paper. et al. 2016), as well as simulations by Sarmento et al.(2017), Barai & de Gouveia Dal Pino(2018), and Johnson et al.(2012). We also We name the simulations as TxEy, where x stands for the include observations by Madau & Dickinson(2014) and a LF-based minimum time for coalescence of the NSMs, and y stands SFRD by Finkelstein(2016). Our SFRD is in good agreement with for the energy for the NSM event in cgs unit. For example observations and the other simulations at z < 10 and in reason- T10E51 stands for the simulation with minimum time able agreement with the other simulations at z > 10 where the uncertainty is larger. Bottom panel: the metallicity distribution for the merging of the NSMs set to 10 Myr with ENSM = function (MDF) as a function of formation redshift of the stars in 1051 erg . The dark matter particle mass resolution is the simulation: The MDF for all the stars that are formed prior to 5 mp ≈ 1.2 × 10 M , and our stellar particle mass is fixed z=(14,8.2) is shown in (blue, black), while other redshifts are color coded as shown in the legend. to be 50 M . We stopped the simulation at z ≈ 8. All the five simulations are summarized in Table2.

3. RESULTS We start by showing the overall star formation history of our MW type galaxy and its corresponding metallicity Neutron Star Mergers and r-process Enhanced Metal Poor Stars 5

the dominant formation scenario of the CEMP stars is TABLE 2 not through the mass transfer from a binary compan- Simulations parameters ion. Moreover, the discovery of damped Ly-α systems t (Myr) E (erg) z with enhanced carbon: Cooke et al.(2011, 2012) suggests min NSM final that these stars are born in halos that are pre-enriched T1E51 1 1051 8.2 50 by carbon (Sharma et al. 2018). T10E50 10 10 8.9 Left panel of Figure3 shows the distribution of the T10E51 10 1051 8.9 T10E52 10 1052 8.9 stars in [C/Fe] − [Fe/H] plane. Each point is a star par- T100E51 100 1051 8.9 ticle color coded given its age (i.e. the red shows the stars that formed at the highest redshift in the simula- The characteristics of the simulations presented in this paper. tion). The adopted Fe and C yields from Pop. II and We adopt the notation of TxEy to name each simulation, where x Pop. III SNe is listed in Table1. Each star formation stands for the minimum time for coalescence of the NSMs, and y event traces a line with a negative slope in this plane. stands for the energy for the NSM event in cgs unit. The simulation 51 The oldest stars trace a line with more negative slope with minimum time for merging of 1 Myr and ENSM = 10 erg is named T1E51. The simulation with minimum time for merging compared to the younger stars formed in the simulation. of the binaries set to 100 Myr is named T100E51. All these three Since carbon is primarily generated from Pop. III stars, 5 simulations have dark matter particle mass of 1.2 × 10 M . The and Pop. III stars are formed in metal poor regions, nat- first column indicates the minimum timescale for merging of the DNSs in a power law distribution. The second column corresponds urally we see higher carbon enrichment towards lower to the energy of the NSM event, and the last column is the stopping metallicities. This is consistent with the observations of redshift of the simulation. the CEMP stars where higher percentage of the stars show [C/Fe] > 1 towards lower metallicities. The loca- evolution. The top panel of Figure1 shows the comov- tion of the stars in [C/Fe] − [Fe/H] plane that defines a ing star formation rate density (SFRD) of T1E51 simu- CEMP star is outlined with dashed blue line. lation that we ran down to redshift z = 8.2. The cyclic Right panel of Figure3 shows the cumulative frac- SFR trend with overall increase towards lower redshift is tion of the MP stars that are CEMPs as a function of characteristics of all simulations while the exact level of redshift. The black star indicates the observed cumu- the SFR can vary depending on the overdensity which is lative ratio of ≈ 5% (Lee et al. 2013) which is based re-simulated at higher resolution (Xu et al. 2016). The on the SDSS/SEGUE data and consistent with other improved DM mass resolution in the Renaissance simu- groups (Frebel et al. 2006; Carollo et al. 2011; Placco lation allows it to track star formation in smaller over et al. 2014). The orange hexagon is the updated analysis densities at earlier times. Hence we see a higher SFRD from Yoon et al.(2018). We note that in this plot we at early times for the normal case as compared to simula- have adopted [C/Fe] > 0.7 for the definition for CEMP tions with lower DM mass resolution. The Renaissance star to be consistent with the statistics presented in (Lee simulation has a comoving resolution of 19 pc as com- et al. 2013) and Yoon et al.(2018). The cumulative ra- pared to our resolution of 5 pc, however their DM parti- tio of the CEMP stars to all the MP stars drops with cle mass is 2.9 × 104 as compared to our 1.2 × 105 M . redshift and reaches the observed ratio around z ∼ 8. The bottom panel of Figure1 shows the metallicity distribution function (MDF) for stars grouped based on 3.2. Formation of metal poor r-process stars their formation redshift. The MDF for stars formed at Figure4 shows the distribution of stars in in [Fe /H] − z > 14 is shown in blue and those that are formed at z > [Eu/H], [C/Fe] − [Eu/Fe], and [Fe/H] − [Eu/Fe] planes 8.2 shown in black. As expected the overall metallicity in T10E51 at z ≈ 9. Each data point indicates one star increases with time while the rate of change of the MDF particle in the simulation and we show a random sample slows down towards lower redshifts. These are all the of 20% of all the stars in the simulation box. Each data stars in the simulation, not categorized per halo mass. point is color coded by the stellar age. Figure2 shows rendered images of the dark matter, Close inspection of the distribution of stars in the hydrogen, r-process , and metals in the T10E51 simula- [Fe/H] − [Eu/H] plane shows that star formation events tion at z ≈ 9. The fact that DNSs are born with delay trace lines with different slopes, mostly from linear in time distributions causes some halos to be only enriched the early times to vertical at later cosmic times. A hor- with metals and no r-process . We note that modeling izontal line indicates a star formation event in a region DNSs’ kicks will pronounce this feature that we present where the gas has a dispersion in [Fe/H] but europium in an upcoming work. is well mixed, while the opposite holds for a vertical line as we go to more metal rich stars. These are on average 3.1. Formation of CEMP stars younger stars that have recently formed in halos enriched Modern surveys of the Galactic halo, as well as UFDs, by iron. These halos are enough old for the iron to be indicate that CEMP stars (defined as those with [C/Fe]> well mixed, however, a recent NSM event explains the 1 and [Fe/H]< −1) become more prevalent as over- large dispersion along the [Eu/H] axis. The correlation all metallicity decreases (Beers & Christlieb 2005). In between [Eu/H] and [Fe/H] at high metallicities which fact, these surveys indicate that the fraction of CEMP are shown by young stars is an imprint of the fact that stars is as high as 25% for stars with [Fe/H] < −2.0 stars start to form in halos where there have been pre- (Komiya et al. 2007) and possibly as high as 40% for enrichment by both SNe II and DNSs. stars with [Fe/H] < −3.5 (Lucatello et al. 2006). Hansen The middle panel of Figure4 shows the distribution et al.(2016) found that only about 17% ±9% of all the of the stars in [Eu/Fe] − [C/Fe] plane. One can use the CEMP-no stars (that display no enhancement to s or distribution of the stars in this plane to select CEMP-r r-process elements), exhibit binary orbits. Therefore, stars. Each line traces one star formation event and as 6

Fig. 2.— 3D perspective snapshot of the T10E51 simulation. Clockwise from top left panel we show the dark matter, hydrogen, r-process, and metals distribution at z = 8.95. The metals are produced by CCSN and the r-process by the NSM, which follow a power law delay time distribution with a minimum time for merging of 10 Myr. When comparing the metal and r-process distribution, we see the fact that the delay in NSMs caused some halos to be enriched with metals but no r-process material. can be seen the lines have a positive slope, indicating that cation of the stars in this plane is used to define different those stars that are carbon enriched, and therefore born category of metal poor r-process enhanced stars. in halos enriched with Pop. III ejecta, also show higher [Eu/Fe] values. This is because Pop. III star formation 3.3. Comparison with observations of r-process results both in supernovae that eject large amounts of enhanced metal poor stars carbon into their surroundings, and DNSs that are strong Metal poor stars encode a wealth of information about sources of europium. This leads to the observed correla- the conditions in the early universe when these stars tion for old stars. As can be seen, older stars are clus- were formed (Frebel & Norris 2015). Such stars are di- tered towards the lower end of [C/Fe] and do not show vided into two categories, MP-rI and MP-rII , based on the strong correlation between [Eu/Fe] and [C/Fe] as is the r-process element abundance in their spectra. MP- seen for the young stars. This is due to the fact that the rI stars are metal poor stars that show mild enhance- metal production dominates over that of carbon in more ment of r-process elements, namely (0.3 < [Eu/Fe] < 1) massive halos, and in general as the formation of Pop III and ([Fe/H] < −1.5). MP-rII stars are defined as stars cease, the new stars in the halo are born with lower those with higher levels of r-process abundance, namely [C/Fe]. In such systems, a single NSM event will leads (1 < [Eu/Fe]) and ([Fe/H] < −1.5). These two cate- to large dispersion along the [Eu/Fe] axis, as is observed gories are outlined in the right panel of Figure4. Based by how the old stellar particles are clustered towards the on the Hamburg/ESO r-process Enhanced Star survey lower end of [C/Fe]. (HERES; Barklem et al. 2005), out of 253 metal poor In the middle panel, we also show the 5 stars in the stars with −3.8 < [Fe/H] < −1.5, about 5% are MP-rII ultra-faint dwarf galaxy Reticulum II (Ji et al. 2016) and another 15-20% are MP-rI stars. Separately, based that have measured abundances in both carbon and eu- on the SAGA database of stellar abundances, Abate et al. ropium. The fact that there are practically no stars in (2016) reported that out of 451 metal poor stars with Eu our simulation that match Ret II abundances in both and Ba abundance, 26 (∼ 6%) are found to belong to of these elements, potentially shows that the europium MP-rII class. yield or NSM merger rate adopted as a fiducial value in The left panel of Figure5 shows the cumulative frac- our simulations needs to be boosted by a large factor. tion of all the MP stars that are MP-rI . This is cumu- We return to this point in the next section. lative in the sense that it indicates the fraction of all the The right panel of Figure4 shows the distribution of MP stars formed by redshift z that belong to the MP-rI the stellar particles in the [Fe/H]−[Eu/Fe] plane. The lo- class. We show the results for T1E50 (solid-blue),T1E51 Neutron Star Mergers and r-process Enhanced Metal Poor Stars 7

0.40 T1E51 CEMP 0.35 P

M 0.30 / P 0.25 M E C

0.20 e v i t 0.15 a l u

m 0.10 u C 0.05

0.00 7 8 9 10 11 12 13 14 z

Fig. 3.— Left panel: the distribution of the stars in [C/Fe] − [Fe/H] plane. Each point is a star particle color coded given its age (i.e. the red points are stars formed at the highest redshift in the simulation). The adopted Fe and C yields from Pop. II and Pop. III SNe is listed in Table1. Right panel: the cumulative ratio of CEMP stars to MP stars in the simulation as a function of redshift. The black line shows T1E51 simulation but the result is identical for all other simulations. The black star indicates the observed cumulative ratio of ≈ 5% (Lee et al. 2013) from the SDSS/SEGUE database, and the orange hexagon is the updated analysis from Yoon et al.(2018). We note that in this comparison we have adopted [C/Fe] > 0.7 for the deﬁnition for a CEMP star to be consistent with the statistics presented in (Lee et al. 2013) and Yoon et al.(2018).

CEMP-r MP-rII Ret II

MP-rI

Fig. 4.— The distribution of stars in the T10E51 simulation at z ≈ 8.9 in [Eu/H] − [Fe/H] (left panel), [C/Fe] − [Fe/H] (middle panel) and [C/Fe] − [Eu/Fe] plane (right panel). Each point is a star particle color coded given its age (i.e. the red shows the stars that formed at the highest redshift in the simulation). The adopted Fe and C yields from Pop. II and Pop. III SNe is listed in Table1. The Eu yield per −5 NS merger event is set to 1.5 × 10 M based on the yield estimates from NS-NS merger detected by aLIGO/Virgo (GW170817). This reﬂects the lanthanide-rich material ejected in the wind ejecta from a NS-NS merger events. In the middle panel, we also show the ﬁve stars in Reticulum II whose abundances in both carbon and europium is measured. (dashed-green), T1E52 (dot-dashed red), and T1E51 in adopted rate of their formation and assigned r-process solid black respectively. T100E51 simulation results in yield. zero MP-rI stars and is not shown in the plots. The Our results should be thought of in the context of black dot shows the ratio of MP-rI over MP stars from the imposed delay time distributions. When a minimum observations of the MW’s halo stars which is about 20% timescale of 1 Myr is considered for merging of the DNSs (Abate et al. 2016). Our simulations predict that the ra- when they are formed, given the power law distribution, tio is more than an order of magnitude below the level ob- the median merging timescale of the DNSs is about 100 served if the source of r-process is solely NSMs given the Myr. When the minimum timescale is changed to 0 or 8

10 Myr, the median timescale for merging changes from We performed cosmological zoom simulations of a MW 3 to 300 Myr respectively. These median timescales mat- type halo with dark matter particle mass resolution that 7 8 ter in that they need to be compared to a typical phase can resolve halos of mass ∼ 10 − 10 M with spatial of star formation that lasts in a given MW progenitor resolution of ∼ 5 pc. These high resolution zoom sim- halo. Longer merging timescales relative to star forma- ulations are aimed at explaining the observed high fre- tion timescale would lead to a NSM event that does not quency of r-process enriched stars in the MW’s halo. effectively enrich the medium such that r-process mate- We assume that the only r-process sources are NSMs rial gets recycled into the stars formed after the event. that are assigned delay time distribution drawn from a This is either because the star formation has ceased after power law, as predicted in population synthesis codes the NSM event, or because a new phase of star formation (Dominik et al. 2012). We assign europium yield to the occurs with a delay long enough to make the r-process NSM events representative of assuming 0.04 M wind material gets too diluted before getting recycled into the ejecta with solar r-process pattern residual possible for new stars. This is clearly shown in the simulation with GW170817 (Côtéet al. 2018b). a minimum merging timescale of 100 Myr, in that no We track the formation of MP and CEMP stars and MP-rI stars is born in that simulation. their r-process enriched counterpart MP-rI , MP-rII and The middle panel of Figure5 shows the cumulative CEMP-r stars and we study the impact of two parame- fraction of the MP stars that are categorized as MP-rII ters in our study: (i) The minimum time scale for merg- . The lines are the same as in the left panel. The ratio of ing after the a DNS is formed, and (ii) the impact of MP-rII stars to MP stars predicted in the simulation is ENSMon mixing the r-process material in a halo. Our about an order of magnitude less than the observed level simulations underpredict the observed ratio of r-process in the MW halo. enhanced stars to their parent category by about an or- The right panel of Figure5 shows the cumulative frac- der of magnitude. We note that implementing the natal tion of CEMP-r to all the CEMP stars. CEMP-r stars kicks would further reduce this enrichment level. are defined as a subclass of CEMP stars with [Eu/Fe] > 1 Our findings show that increasing the minimum and [Ba/Eu] < 0, and there are a handful of theories re- timescale for merging of the DNSs results in a drop in the garding their formation (Abate et al. 2016). The location overall statistics of the r-process enhanced metal poor of this category of stars is outlined with dashed brown stars. This is due to the fact that a longer minimum lines in the middle panel of Figure4. Out of 56 CEMP timescale for merging of the DNSs leads to lower overall stars with barium and europium abundances, Abate et al. NSM events during a given timespan, while increasing (2016) found 5 to be CEMP-r stars and 26 to be CEMP- the median merging timescale of the DNSs. For exam- r /s stars. About a few percent of all the CEMP stars ple, the median timescale for merging of DNSs is (3,100, are CEMP-r in our simulation which is an order of mag- 300) Myr if the minimum timescale is set to (0, 1, 10) nitude less than the observed frequency of this class of Myr respectively. Similarly, the lower the energy of the stars. NSM event, the r-process material experience less mix- The impact of the ENSM is understood in that lower ing in the halo and this actually leads to higher levels of energies tend to disperse the r-process material in a r-process enhancement for the subsequent stars formed smaller volume and therefore the higher concentration of in the halo. The impact of the assumed ENSMis subdom- r-process leads to the formation of r-process enhanced inant compared to the impact that the merging timescale stars. The impact of the ENSMis subdominant compared has on the final level of r-process enrichment. to the effect of the minimum time considered for the de- Given that with increasing the minimum time for lay time distribution. Lower delay times (1 Myr, black merging from 1 Myr to 100 Myr, we are not able to form line) leads to more NSM events in a halo, while large any MP-rI or CEMP-r stars, fast merging channels for minimum times (as in T100E51 simulation) results in the DNSs seems to be a requirement to make NSMs con- formation of no r-process enhanced stars. tribute modestly to r-process enrichment of the Galaxy In all three panels of Figure 5, the thin black dashed at high redshifts. lines indicate an assumed NSM merger rate of ≈ 2 × In order to match the observed enrichment, we can −4 −1 −4 10 M or equivalently a europium yield of 3×10 M think of two options: (i) adopting a higher Eu yield, which matches the statistics of the r-process MP stars. and (ii) increasing the DNS birth rate. Regarding the This boosted NSM merger rate, however, overpredicts first option, it is highly unlikely that higher Eu yields the same statistics for the CEMP star. The mismatch are possible from an NSM event. The adopted yield is between what Eu yield is required to match the observa- estimated from GW170817 (Cowperthwaite et al. 2017; tions, either shows we need more robust statistical data Côtéet al. 2018b) with assuming a disk ejecta of mass for the CEMP stars, or the r-process MP stars have been 0.04 M . However, we note that in Naiman et al.(2018), enriched by a separate source in addition to the NSMs. the adopted yield is three times higher that what we have adopted in our study. 4. SUMMARY AND DISCUSSION Regarding the second option, there is a large tension While both core-collapse supernovae and neutron star between the observed NS merger rates and the rates mergers could explain the observed abundance of r- predicted from population synthesis models (Belczynski process elements in the Galaxy (Cowan et al. 1991; et al. 2017; Chruslinska et al. 2018). The value of one 5 Woosley et al. 1994; Rosswog et al. 1999, 2000; Argast merger per 10 M of stars adopted in this work cor- −4 et al. 2004; Kuroda et al. 2008; Wanajo 2013; Wehmeyer responds to MW rate of NSMs of RMW ≈ 10 /year et al. 2015), only r-process production in NSMs has been (van de Voort et al. 2015b). This rate is on the as- measured directly, and therefore we model the produc- sumption that the minimum time scale for merging of tion of r-process through NSMs. Neutron Star Mergers and r-process Enhanced Metal Poor Stars 9

1 10 MP rI/MP MP rII/MP CEMP r/CEMP − − − 0 10 o i t a r

-1

e 10 v i t a

l -2

u 10

m T1_E_NSM_1E51 u

C -3 T10_E_NSM_1E50 10 T10_E_NSM_1E51 T10_E_NSM_1E52 -4 10 8 9 10 11 12 13 8 9 10 11 12 13 8 9 10 11 12 13 z z z

Fig. 5.— Cumulative fraction of different class of stars in the simulation as a function of redshift. Left panel: the cumulative fraction of all the MP stars that are MP-rI . Middle panel: the cumulative fraction of all the MP stars that are MP-rII . Right panel: the cumulative fraction of all the CEMP stars that are CEMP-r . We show the results for T1E50 (solid-blue),T1E51 (dashed-green), T1E52 (dot-dashed red), and T1E51 in solid black respectively. In all panels, the black dots indicate the observed ratio in the MW halo stars from Abate et al. (2016). The simulations severely under predict all the observed ratios by about an order of magnitude in the case of T1E51 simulation (black lines) and more so when the minimum time for merging is increased to 10 Myr. Moreover, we see that although lower explosive energy of the NSM event helps increase the fraction of r-process stars, this is subdominant when compared to the impact of minimum timescale for merging. The thin dashed lines in all three panels indicate the T1E51 result scaled by a factor of 20, translating into NSM −4 −1 merger rate of ≈ 2 × 10 M . This higher assumed higher NSM merger rate would match the observed frequency of the r-process MP stars but it overpredicts that of CEMP stars. the binaries is 30 Myr and the final stellar mass of the hanced stars. Similar conclusions has been reached based 10 MW is about 3 × 10 M . This rate corresponds to al- on chemical evolution studies of the Galaxy (Côtéet al. most the maximum rate predicted in population synthe- 2018a) and been suggested a second source of r-process is sis models with various variations, and about an order needed in order to explain the observed trends in MW’s of magnitude above the observational estimates based disk. Moreover, the long delay between GW170817 and on galactic double pulsars (Kim et al. 2015). How- the star formation activity of its host galaxy, NGC 4993 ever, translating this rate into local rate, we would (Levan et al. 2017), indicates that the merger rate at be similar to the LIGO/Virgo merger rate estimate of short delay times is different at high redshifts. Whether +3200 −3 −1 either of such choices would be consistent with the ex- 1540−1220Gpc yr (Abbott et al. 2017a). The NSM birth rate is subject to the details of the pected theoretical calculations of the r-process yield in models implemented in the population synthesis codes NS merger events or the metallicity evolution at highest (Belczynski et al. 2002, 2008; Dominik et al. 2012). In the redshift remains to be explored. Upcoming data from the standard model assumed in these models, which mostly R-Process Alliance is projected to increase the detected concerns with the assumptions governing the common number of MP-rII stars to 125, and over 500 new MP- envelope (CE) phase during the formation of a compact rI stars in the next several years (Hansen et al. 2018; binary system, we find that with the adopted Kroupa Sakari et al. 2018). Moreover, upcoming data on the initial mass function (Kroupa & Weidner 2003) the DNS frequency of CEMP-r stars from high-resolution obser- 5 vations of a sample of approximately 200 bright CEMP birth rate is about 2.5 per 10 M of stellar mass modeled. However, this birth rate can be boosted by a factor stars by Rasmussen et al. (in prep) is likely to provide of three in variation of their standard model (for example a much improved estimate of the frequencies of CEMP in variation 15 of Dominik et al. 2012), which translate subclasses. into NSM birth rates of about 6 times of what we have assumed in this study. While increasing the r-process 5. FUTURE WORK yield will not impact the star formation history of our We have not modeled the natal kicks of the DNSs in galaxy and simply will shift the stellar particles up and this work. However, their impact is expected to be sig- down in [Eu/Fe] or [Eu/H] axis, we could not treat birth nificant specifically if natal kicks and delay times are not rates similar to the yields. Higher birth rates will affect correlated for a DNS. DNSs are thought to be the precur- the iron yield from the CCSN as their number density sors of the short gamma-ray bursts (sGRBs) and the lo- would be affected. In other words, while in our simula- cation of sGRBs with respects to galaxies in the field can tion there is one DNS born per 1000 CCSNe, changing provide clues into the natal kick distribution of the DNSs. that to one DNS per 100 CCSNe will significantly impact By studying host-less GRBs, Fong & Berger(2013) de- the metallicity trends in our halos. rived natal kick velocities in the range of 20-140 km s−1 Based on our results higher yields or higher birth rates with a median value around 60 km s−1. with fast merging timescales are needed to match the From a theoretical perspective, population synthesis observations of the MW halo’s metal poor r-process en- analysis of DNSs (Fryer et al. 1998) where binary sys- 10 tems with different initial masses for each star, initial ec- Another avenue to improve on the present work would centricity and orbital separation are simulated to merge be to model the s-process enrichment of the stars so and arrive at the outcome natal kick velocity after the that comparisons could be made with the statistics of second star goes off as a SNe. Such models arrive at na- the CEMP-s stars in the MW. For that we would need tal kick distributions with an exponential profile and a to model the formation of the AGB stars (Sharma et al. median of 180 km s−1 (Behroozi et al. 2014). Safarzadeh 2018). This work could be expanded to a whole suite & Côté(2017) studied the impact of DNS’s natal kick on of MW type halos in large simulations such as Auriga the Galactic r-process enrichment and concluded that (Grand et al. 2017) and Caterpillar suite of simulations almost 50% of all the NSMs that have occurred in the (Griffen et al. 2016) to achieve a reliable halo-to-halo star formation history of a MW type system do not con- scatter. tribute to the r-process enrichment as the DNSs merge well outside the galaxy’s effective radius. For systems with shallow potential wells such as the Ul- 6. ACKNOWLEDGEMENTS 7−9 tra Faint Dwarfs (UFDs, with halo mass of ∼ 10 M ; We are thankful to the referee for useful comments. Simon et al. 2011), and their progenitors at high redshifts We are also thankful to Enrico Ramirez-Ruiz, Tim Beers, (Safarzadeh et al. 2018) small natal kicks on the order of Brian Metzger, Jeff Andrews, Daniel Siegel, and Tassos 10-20 km s−1 can make DNS escape their hosts (Kelley Fragos for valuable discussions. This work was supported et al. 2010; Safarzadeh & Côté 2017). This can severely in by the National Science Foundation under Grants impact the level of enrichment of the halos and should AST-1715876 & PHY-1430152 (the Joint Institute for leave a clear mark on CEMP-r /CEMP ratio specifically Nuclear Astrophysics - Center for the Evolution of the since CEMP stars only formed early on before the halo Elements), and NASA theory grant NNX15AK82G. We is heavily enriched with metals, and would be almost im- thank the Texas Advanced Computing Center (TACC) possible to make CEMP-r stars if the DNSs escape their and the Extreme Science and Engineering Discovery En- host halo. vironment (XSEDE) for providing HPC resources.

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