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Thehistoryofr-processenrichmentinthemilkyway
Shen,Sijing;Cooke,RyanJ;Ramirez-Ruiz,Enrico;Madau,Piero;Mayer,Lucio;Guedes,Javiera
Abstract:Weinvestigatetheproductionsitesandtheenrichmenthistoryofr-processelementsinthe
Galaxy,astracedbythe[Eu/Fe]ratio,usingthehighresolution,cosmologicalzoom-insimulation‘Eris’.
Atz = 0,ErisrepresentsacloseanalogtotheMilkyWay,makingittheideallaboratorytounderstand
thechemicalevolutionofourGalaxy.Erisformallytracestheproductionofoxygenandirondueto
Type-IaandType-IIsupernovae.Weincludeinpost-processingtheproductionofr-processelements
fromcompactbinarymergers.Unlikepreviousstudies,wendthatthenucleosyntheticproductsfrom
compactbinarymergerscanbeincorporatedintostarsofverylowmetallicityandatearlytimes,even
withaminimumdelaytimeof100Myr.Thisconclusionisrelativelyinsensitivetomodestvariationsin
themergerrate,minimumdelaytime,andthedelaytimedistribution.Byimplementingarst-order
prescriptionformetal-mixing,wecanfurtherimprovetheagreementbetweenourmodelandthedata
forthechemicalevolutionofboth[α /Fe]and[Eu/Fe].Wearguethatcompactbinarymergerscouldbe
thedominantsourceofr-processnucleosynthesisintheGalaxy.
DOI:https://doi.org/10.1088/0004-637X/807/2/115
PostedattheZurichOpenRepositoryandArchive,UniversityofZurich
ZORAURL:https://doi.org/10.5167/uzh-121971
JournalArticle
AcceptedVersion
Originallypublishedat:
Shen,Sijing;Cooke,RyanJ;Ramirez-Ruiz,Enrico;Madau,Piero;Mayer,Lucio;Guedes,Javiera(2015).
Thehistoryofr-processenrichmentinthemilkyway.TheAstrophysicalJournal,807(2):115.
DOI:https://doi.org/10.1088/0004-637X/807/2/115
arXiv:1407.3796v2 [astro-ph.GA] 9 Apr 2015
DRAFT VERSION AP RIL 10, 2015
Preprint typeset using L
A
T
E
X style emulateapj v. 5/2/11
THE HISTORY OF R-PROCESS ENRICHMENT IN THE MILKY WAY
SIJING SHEN
1
, RYAN J. COOKE
2
, ENRICO RAMIREZ-RUIZ
2
, PIERO MADAU
2
, LUCIO MAYER
3
AND JAVIERA GUEDES
4
Draft version April 10, 2015
ABSTRACT
We investigate the production sites and the enrichment history of r-process elements in the Galaxy, as traced
by the [Eu/Fe] ratio, using the high resolution, cosmological zoom-in simulation ‘Eris’. At z = 0, Eris repre-
sents a close analog to the Milky Way, making it the ideal laboratory to understand the chemical evolution of
our Galaxy. Eris formally traces the production of oxygen and iron due to Type-Ia and Type-II supernovae. We
include in post-processing the production of r-process elements from compact binary mergers. Unlike previous
studies, we find that the nucleosynthetic products from compact binary mergers can be incorporated into stars
of very low metallicity and at early times, even with a minimum delay time of 100 Myr. This conclusion is rel-
atively insensitive to modest variations in the merger rate, minimum delay time, and the delay time distribution.
By implementing a first-order prescription for metal-mixing, we can further improve the agreement between
our model and the data for the chemical evolution of both [α/Fe] and [Eu/Fe]. We argue that compact binary
mergers could be the dominant source of r-process nucleosynthesis in the Galaxy.
Subject headings: stars: abundances — Galaxy: abundances — Galaxy: evolution — methods: numerical
1. INTRODUCTION
The chemical abundance patterns of Galactic halo stars en-
code precious information about the various stellar progen-
itor systems that existed prior to their birth. These ancient
halo stars therefore provide an insight into the nucleosynthe-
sis processes that occurred early in the history of the Milky
Way. Of particular interest in this regard is the heavy ele-
ment composition of Galactic halo stars (Truran et al. 2002;
Cowan & Sneden 2006). For stars with an [Fe/H] metallic-
ity in the range ≈ 10
−2
to ≈ 10
−3
solar, elements in the mass
region above Ba have been found to be consistent with en-
richment by a pure r-process with a distribution that is char-
acteristic of solar system matter but with a large star-to-star
bulk scatter in their concentrations with respect to the lighter
elements such as Mg (Sneden, Cowan, & Gallino 2008). The
presence of these heavy nuclei in such primitive stars demon-
strates that the r-process has operated in a fairly robust man-
ner over large periods of time in Galactic history, while the
large dispersion in their abundance relative to lighter nuclei
suggests an early, chemically unmixed and inhomogeneous
Milky Way (Fields et al. 2002). At later times, these localized
inhomogeneities would be smoothed out as subsequent events
take place and heavy element products are given more time to
migrate throughout the Galaxy (Travaglio et al. 2001).
Nucleosynthesis theory has identified the specific physical
conditions and nuclear properties required for the r-process
(Burbidge et al. 1957). However, the astrophysical site for
this process has not been unambiguously identified. The orig-
inal work on this subject suggested that the neutron-rich re-
gions outside a nascent neutron star in a Type II supernova
(Woosley et al. 1994; Takahashi et al. 1994) or the ejecta from
the last seconds of a merger between a neutron star (NS)
and a compact binary companion are the most likely for-
1
Institute of Astronomy, University of Cambridge, Madingley Road,
Cambridge, CB3 0HA, United Kingdom
2
Department of Astronomy and Astrophysics, University of California,
1156 High Street, Santa Cruz, CA 95064, USA
3
Institute of Theoretical Physics, University of Zürich, Winterthur-
erstrasse 190, CH-9057 Zürich, Switzerland
4
Teralytics AG, Zollstrasse 62, 8005 Zürich, Switzerland
mation sites (Lattimer et al. 1977; Freiburghaus et al. 1999).
Compact mergers involving a neutron star are much rarer
than SN II (Cowan & Thielemann 2004) and should occur
far from their birth sites (e.g. Kelley et al. 2010). Further-
more, these two mechanisms eject different quantities of r-
process material. These differences should surely be im-
printed in the enrichment pattern of r-process elements and
may ultimately identify the dominant production mecha-
nism (Argast et al. 2004; Matteucci et al. 2014; Cescutti et al.
2013; Tsujimoto & Shigeyama 2014; Cescutti & Chiappini
2014).
The build-up of the elements in our Galaxy, including that
of the r-process, can be studied in detail by using realistic
galactic chemical evolution (GCE) models (e.g. Pagel 2009).
3D hydrodynamic simulations that incorporate the details of
chemical evolution (often referred to as chemodynamical sim-
ulations) have been widely used in the literature to study the
enrichment history and distribution of various elements in
galaxies (e.g. Kawata & Gibson 2003; Kobayashi & Nakasato
2011; Rahimi et al. 2011; Few et al. 2012; Pilkington et al.
2012; Minchev et al. 2013; Brook et al. 2014; Few et al.
2014). Because such simulations follow the dynamics and
chemical evolution self-consistently, they are better equipped
to address the inhomogeneous enrichment of the ISM and
the mixing of metals. In addition, simulations performed
in a cosmological context (e.g., Kobayashi & Nakasato 2011;
Rahimi et al. 2011; Pilkington et al. 2012; Brook et al. 2014;
Few et al. 2014) are able to capture the larger scale mixing
mechanisms including gas inflows, satellite mergers, galac-
tic winds and fountains, and instabilities in rotationally sup-
ported disks, all of which are undoubtedly important to un-
derstand the enrichment and dispersal of heavy elements. On
the other hand, since cosmological simulations today are lim-
ited by resolutions of a few tens to hundreds of parsecs, they
inevitably involve “sub-grid” models for star formation, stel-
lar feedback, and/or turbulent mixing. As such, large uncer-
tainties still exist at the hundred parsec scale. Investigating
the distribution of chemical elements in these simulations and
comparing them extensively with the observational data can,
in turn, provide important constraints on these sub-resolution
2 SHEN ET AL.
models and improve the modeling of astrophysical fluids.
The origin and evolution of the r-process elements,
however, are mostly addressed using analytical or semi-
analytical models (e.g. Argast et al. 2004; Matteucci et al.
2014; Cescutti et al. 2013; Tsujimoto & Shigeyama 2014;
Cescutti & Chiappini 2014; although see van de Voort et al.
2015), possibly because most simulations have not imple-
mented the production of r-process elements due to their un-
certain origins described above. In this Paper we employ Eris,
one of the highest resolution cosmological simulations of the
formation of a Milky Way-size galaxy (Guedes et al. 2011),
to investigate the synthesis of the heavy r-process elements in
our Galaxy, as traced by the [Eu/Fe] ratio.
2. METHODS
2.1. The Eris Simulation
We use the high resolution, zoom-in cosmological simu-
lation of a Milky Way Galaxy analog “Eris” to track the
production and transportation of r-process elements. A
detailed description of the Eris simulation is provided by
Guedes et al. (2011). Here we briefly outline the aspects rel-
evant to this study. The simulation was performed with the
parallel TreeSPH code GASOLINE (Wadsley, Stadel, & Quinn
2004) in a WMAP-3 cosmology. The run includes a uniform
UV background (Haardt & Madau 1996), Compton cooling,
atomic cooling and metallicity dependent radiative cooling at
T < 10
4
K. Star formation is modelled by stochastically form-
ing “star particles” out of gas that is sufficiently cold (T < 3×
10
4
K) and reaches a threshold density of n
SF
= 5 atoms cm
−3
.
The local star formation rate follows dρ
∗
/dt = 0.1ρ
gas
/t
dyn
∝
ρ
1.5
gas
, where ρ
∗
and ρ
gas
are the stellar and gas densities, respec-
tively, and t
dyn
is the local dynamical time. Each star particle
has initial mass m
∗
= 6000 M
⊙
and represents a simple stel-
lar population that follows a Kroupa, Tout, & Gilmore (1993)
initial mass function (IMF), and inherits the metallicity of its
parent gas particle. Star particles inject energy, mass and met-
als back into the ISM through Type Ia, Type II SNe and stel-
lar winds (Stinson et al. 2006). Eris’ high resolution enables
the development of an inhomogeneous ISM which allows re-
alistic clustered star formation and strong cumulative feed-
back from coeval supernova explosions. Large scale galac-
tic winds are launched as a consequence of stellar feedback,
which transports a substantial quantity of metals into the cir-
cumgalactic medium and enriches the subsequent gas accre-
tion (Shen et al. 2013). At z = 0, Eris forms an extended, rota-
tionally supported stellar disk with a small bulge-to-disk ratio.
The structural properties, the mass budget in various compo-
nents and the scaling relations in Eris are simultaneously con-
sistent with observations of the Galaxy (Guedes et al. 2011).
The simulation follows Raiteri, Villata, & Navarro (1996)
to model metal enrichment from SN II and SN Ia. Metals are
distributed to gas within the SPH smoothing kernel (which
consists of 32 neighboring particles). For SN II, metals are
released as the main sequence progenitors die, and iron and
oxygen are produced according to the following fits to the
Woosley & Weaver (1995) yields:
M
Fe
= 2.802 × 10
−4
m
∗
M
⊙
1.864
M
⊙
, (1)
and
M
O
= 4.586 × 10
−4
m
∗
M
⊙
2.721
M
⊙
. (2)
For SN Ia, each explosion produces 0.63 M
⊙
of iron
and 0.13 M
⊙
of oxygen (Thielemann, Nomoto, & Yokoi
1986). Stellar wind feedback is based on
Kennicutt, Tamblyn, & Congdon (1994), and the returned
mass fraction was determined following Weidemann (1987).
The returned gas inherits the metallicity of the star particle.
We adopt the Asplund et al. (2009) solar abundance scale
for elements other than O and Fe, that are not tracked in the
simulation.
We note that there are several limitations to our modeling.
First, because the smallest gas resolution element is an en-
semble of gas particles within the smoothing kernel rather
than individual particles, forcing the newly-formed star par-
ticle to inherit metallicity only from its parent gas particle
may amplify sub-resolution metallicity variances between gas
particles. Second, the simulation used a traditional SPH for-
malism where metals advect with the fluid perfectly, without
mixing due to microscopic motions (such as turbulence). Both
caveats may cause an artificially inhomogeneous chemical
distribution (Wiersma et al. 2009; Shen, Wadsley, & Stinson
2010). While improved runs within the Eris suite include
a model for turbulent diffusion (Shen et al. 2013), for this
study we have used a simulation without mixing so that our
r-process injection method is consistent with the production
and distribution of O and Fe in the simulation. In Section 3,
we explore a simple diffusion model to illustrate the effect
of mixing. Instead of using the metallicity of the parent gas
particle, we average the metallicity over 128 neighboring gas
particles to determine the metallicity of the newly-formed star
particle.
In addition, despite being one of the highest resolution
galaxy formation simulations that evolves to z =0, our model
still lacks the spatial and temporal resolution to correctly fol-
low the formation and enrichment of the first generation of
Population III stars as well as early Population II stars. It is
a common practice in the literature to introduce a metallicity
“floor” at high redshift to account for the unresolved earli-
est population (e.g., Krumholz & Gnedin 2011; Kuhlen et al.
2013; Hopkins et al. 2014). The floor metallicity is typically
around 10
−4
to 10
−3
Z
⊙
, motivated by detailed simulations of
Population III star formation and primordial metal enrichment
(e.g. Wise et al. 2012). Although a metallicity floor was not
included in Eris during the run, in Section 3 we investigate the
affect of a modest metallicity floor (10
−4
Z
⊙
) implemented
in post-processing. This is achieved by assigning a mini-
mum abundance of [Fe/H] = −4.0 to every gas particle, and
an α-enhancement of [O/Fe] +0.4, corresponding to the IMF-
weighted alpha-enhancement estimated from models of zero-
metallicity stellar nucleosynthesis (Woosley & Weaver 1995;
Heger & Woosley 2010; Limongi & Chieffi 2012).
2.2. R-Process Production Sites and Injection History
The key ingredient in our analysis is the realistic star for-
mation history (SFH) of a galaxy simulated in a cosmolog-
ical context which at redshift z = 0 is a close analog of the
Milky Way (Guedes et al. 2011). In this section we describe
our post-processing implementation for NS mergers. The im-
portant elements of our model include: (1) The delay-time
distribution (DTD) of mergers; (2) the merger rate and the
yield of r-process elements; and (3) the spatial distribution of
injection sites and their sphere of influence.
2.2.1. Delay-time distribution, merger rates and r-process yields
R-PROCESS ENRICHMENT IN THE MILKY WAY 3
FIG. 1.— The SN II rate (blue curve, left axis), which closely traces the
SFR, is compared with the NS merger rate derived from the Eris SFR and the
DTD (red curve, right axis).
The merger DTD, P(t), is well-modeled by a power-
law (Piran 1992; Kalogera et al. 2001), although there is
significant uncertainty on the value of the exponent (e.g.
Behroozi et al. 2014, and references therein). Herein, we
adopt P(t) ∝ t
−n
for t > t
cut
and zero probability otherwise,
where t
cut
is the initial time delay after a burst of star forma-
tion before the first merger occurs. Herein we consider two
power-law indices, n = 2 and n = 1, and assume conservative
values of t
cut
= 100 Myr and t
cut
= 200 Myr (Fryer et al. 1999;
Belczynski et al. 2006).
Our fiducial model assumes that each merger event
produces a mass M
rp
= 0.05 M
⊙
of r-process elements
(e.g. Just et al. 2014). We also consider a model where
M
rp
= 0.01 M
⊙
is produced, which reflects the mass of
dynamically ejected material (Lattimer & Schramm 1974;
Rosswog et al. 1999; Metzger et al. 2010; Roberts et al.
2011; Bauswein et al. 2013; Grossman et al. 2014;
Ramirez-Ruiz et al. 2014). For each merger event, we track
the production of europium, which we assume is produced
in solar relative proportions such that M
Eu
/M
rp
= 9.3 × 10
−4
(Sneden, Cowan, & Gallino 2008).
The NS merger rate is then determined by convolving the
SFH extracted from the simulation with the DTD:
R(t) = A
Z
t
H
t
cut
˙
M
∗
(t −τ) P(τ) dτ (3)
where A is a constant that is fixed by the total number of
merger events,
˙
M
∗
is the star formation rate (SFR) and t
H
is
the Hubble time. To calculate A, we impose that the abun-
dance of Eu/O in the final simulation output corresponds to
the solar value (i.e. [Eu/O] = 0.0). There are ∼ 260 mil-
lion massive stars formed in Eris that end their life as a Type
II SN, and the IMF-weighted O yield per Type II SN event
is ≃ 1 M
⊙
in our model. Assuming a solar number ratio,
log(Eu/O)
⊙
= −8.14, the total mass of Eu needed to obtain
the solar [Eu/O] abundance is ∼ 18 M
⊙
. Thus, the total mass
of r-process elements produced during the chemical evolution
of Eris needs to be 18 800 M
⊙
. If we now assume that each
compact binary merger contributes M
rp
= 0.05 M
⊙
(0.01 M
⊙
)
of r-process, then we require ≈ 3.76 × 10
5
(1.88 × 10
6
) merg-
ers in 13.8 Gyr to explain the observed solar Eu/O ratio. The
constant A is therefore fixed by requiring that the integral of
the merger rate (Eq. 3) over the lifetime of Eris is equal to
3.76 × 10
5
(1.88 × 10
6
). The resulting NS merger history is
shown in Figure 1 as the solid red curve, for M
rp
= 0.05 M
⊙
,
which is in good agreement with the expected rates calculated
by Abadie et al. (2010). For reference, we also present the
Eris SN II rate as a function of time as the blue curve in Fig-
ure 1.
2.2.2. Injection History
Compact binary mergers are expected to predominantly
occur within ∼ 10 − 100 kpc of a Milky Way-like host
galaxy (Bloom, Sigurdsson, & Pols 1999; Belczynski et al.
2006; Kelley et al. 2010). Therefore, the spatial distribution
of NS mergers broadly follows the stellar distribution of the
host galaxy. We have thus adopted a post-processing imple-
mentation to include NS mergers in Eris. Our approach is jus-
tified since the momentum imparted to the surrounding gas
by a merger is much less than that of a SN explosion, despite
releasing an energy that is similar in magnitude to a SN. The
gas dynamics is therefore largely unchanged.
In the top-left panel of Figure 2, we present a face-on il-
lustration of the projected surface mass density of Eris’ stars
at redshift z = 2. By construction, this panel represents the
distribution of merger injection sites. Similarly, in the top-
right panel of this figure, we present the SFR surface density,
which traces SN II. In the bottom panels of Figure 2, we show
the surface mass density of gas on two different spatial scales,
which are enriched by these events and later form a new gen-
eration of stars.
Using the above formalism, we calculate the number of
NS mergers that occur between adjacent timesteps and ran-
domly select a corresponding number of star particles from
a uniform distribution to act as the merger injection sites.
The surrounding gas particles are then enriched with a to-
tal Eu mass M
tot
Eu
= 4.65 × 10
−5
M
⊙
(corresponding to M
rp
=
0.05 M
⊙
), which is distributed over the 32 neighboring gas
particles according to the smoothing kernel, as outlined in
Wadsley, Stadel, & Quinn (2004). We note that the oxygen
and iron enrichment follow an identical scheme. The evolu-
tion of each gas particle is tracked for subsequent timesteps.
When a stellar particle is born in the non-diffusion case, it
inherits the Eu/Fe ratio from the parent gas particle. In our
simple mixing model, the stellar particle inherits the average
abundance of Eu, O and Fe from 128 neighbouring gas parti-
cles as described in Section 2.1. Hereafter, when comparing
with observations, we only consider star particles present in
the z = 0 snapshot.
3. R-PROCESS ENRICHMENT IN THE MILKY WAY
Our baseline set of model parameters include: an r-process
mass of M
rp
= 0.05 M
⊙
ejected per event, a merger DTD
that has a minimum merger delay-time of t
cut
= 100 Myr
and a power law of the form t
−1
, a mixing length corre-
sponding to the 128 nearest neighbors, and an alpha-enhanced
([α/Fe]=+0.40) metallicity floor of [Fe/H] = −4.0. Hereafter,
we refer to this set of parameters as our fiducial model.
We now investigate the chemical evolution of the α (traced
by O), Fe and r-process elements in Eris. The top-left panel
of Figure 3 displays the [α/Fe] abundance for a representative
sample (1:1000) of Eris star particles in the z = 0 snapshot as a
function of their formation time. Although most stars exhibit
super-solar [α/Fe] values, there are a non-negligible number
of stars with strongly sub-solar values. This effect is more
pronounced at the lowest metallicity, as shown in the bottom-
left panel of Figure 3, where the distribution of [α/Fe] values
is represented by dark and light green contours that respec-
tively enclose 68 and 95 per cent of the Eris stars at a given
4 SHEN ET AL.
FIG. 2.— A face-on illustration of the projected surface mass density of stars (top-left panel), SFR surface density (top-right panel) and gas in different scales
(bottom panels) for Eris at redshift z = 2. The units of all axes are in kpc.
metallicity. When [Fe/H] . −1.5, the [α/Fe] distribution bi-
furcates into a high and low [α/Fe] channel. The low [α/Fe]
channel corresponds to star particles predominantly enriched
by SN Ia (which, in our implementation, produce an O mass
that is five times less than the Fe mass), whereas the high
[α/Fe] channel represents the star particles enriched solely by
SN II.
To compare with observations, we overplot a sample
of [α/Fe] measurements for Milky Way thin disk, thick
disk, and halo stars (Fulbright 2000; Reddy et al. 2003;
Cayrel et al. 2004; Cohen et al. 2004; Simmerer et al. 2004;
Venn et al. 2004; Barklem et al. 2005; Reddy et al. 2006;
Mishenina et al. 2013; Roederer et al. 2014). We divide the
observational sample into stars where α (typically Mg, Si,
Ca), Fe, and Eu are all measured (blue symbols), and stars
where only α and Fe are measured (orange symbols). Over-
all, there is a reasonable agreement between the observations
and the upper envelope of the simulated stars. Moreover,
the ‘knee’ in the α/Fe ratio near a metallicity [Fe/H] ≃ −1.0,
which marks the increased contribution of SN Ia (e.g. Tinsley
1979), is well-reproduced by the Eris simulation.
The discrepancy between Eris and the observations at low
metallicity is the result of gas particles being predominantly
enriched by SN Ia, and illustrates a limitation of the traditional
SPH formalism; once a gas particle is enriched with metals, it
cannot share its metals with neighboring particles. Many tech-
niques have been developed to incorporate metal diffusion in
simulations, using either subgrid turbulent diffusion models
(Greif et al. 2009; Shen, Wadsley, & Stinson 2010), or simply
smoothing the metals within the SPH kernal (Wiersma et al.
2009). Our goal is to provide a simple demonstration of
the importance of metal diffusion for studying chemical evo-
lution. We have therefore post-processed Eris to include a
metallicity floor (as described in Section 2.1) and we paint
newly formed star particles with a metallicity corresponding
to the mass-weighted average of the 128 nearest neighbors.
The choice of 128 is based on the following estimation: At
our star formation threshold density of 5 atoms cm
−3
, this cor-
responds to a size that the gas can cross within the free-fall
time, assuming the typical velocity dispersion of the molecu-
lar cloud. The corresponding mixing length of 128 particles
peaks around 50 − 120 pc at all redshifts. Only in very rare
![FIG. 3.— Top panels: The chemical evolution of O and Fe for a representative sample (1:1000) of Eris’ z = 0 star particles (blue symbols) as a function of the formation time. The centroid of the distribution is shown by the solid dark blue line, whilst the thinner lines enclose 68 and 95 per cent of the stars. The top-left displays the raw simulation output, without a metallicity floor and without a prescription for metal diffusion. The ‘excess’ scatter at low [α/Fe] is reduced considerably when we include a simple physical model for metal diffusion and a metallicity floor, as shown in the top-right panel (see text for further details). Bottom panels: The dark and light green contours show the [α/Fe] distributions that respectively enclose 68 and 95 per cent of Eris’ z = 0 star particles. The observational data are represented by blue symbols for stars where α, Fe, and Eu were all measured, or by orange circles when only α and Fe are reported. The dashed line represents the solar value. Our simple mixing prescription and introducing a metallicity floor of Z = 10−4 Z⊙ significantly improves the agreement with the observational data.](/figures/fig-3-top-panels-the-chemical-evolution-of-o-and-fe-for-a-2h4usczw.webp)
![FIG. 4.— Same as Figure 3, but illustrates the chemical evolution of [Eu/Fe] for our fiducial model, which corresponds to a mass ejection of Mrp = 0.05 M⊙ per merger, a merger DTD that has a power law form (P(t) ∝ t−1) and a minimum merger delay-time of tcut = 100 Myr. In this figure, orange symbols represent stars where only Eu and Fe are reported and blue symbols show stars where α, Eu and Fe are measured.](/figures/fig-4-same-as-figure-3-but-illustrates-the-chemical-20kp7xl9.webp)
![FIG. 8.— Comparing our fiducial model for the chemical evolution of Eu relative to Fe, with the recent simulations by van de Voort et al. (2015). The dark and light green contours enclose 68 and 95 per cent of Eris’ star particles. The solid yellow curve shows the distribution centroid of the fiducial model considered by van de Voort et al. (2015), and the dashed yellow contours enclose 68 per cent of their star particles. The black dashed line represents the solar level of [Eu/Fe].](/figures/fig-8-comparing-our-fiducial-model-for-the-chemical-d5y9xmwj.webp)
![FIG. 7.— The chemical evolution of O and Eu relative to Fe for our fiducial model. The dark and light green contours enclose 68 and 95 per cent of Eris’ star particles. The blue curve shows the average abundance of the cold gas in Eris at each timestep that is about to form a new generation of stars (i.e. the equivalent of a one-dimensional chemical evolution model). Note the strong dissimilarity between the Eris results (green contours) and the completely-mixed Eris model (blue curves). The red curve illustrates model Mod1NS’ from Matteucci et al. (2014); this chemical evolution model shares the closest similarity to our NS merger prescription. The horizontal dashed black line represents the solar level of [Eu/Fe].](/figures/fig-7-the-chemical-evolution-of-o-and-eu-relative-to-fe-for-1tuon3hi.webp)
![FIG. 5.— A demonstration of how the simulated [Eu/Fe] contours depend on our model parameters. We make the following changes to our fiducial model: (1) change the DTD to be P(t) ∝ t−2 (top left panel); (2) increase the merger rate and reduce the yield per event by a factor of 5 (top right panel); (3) double the merger time delay to tcut = 200 Myr (bottom left panel); and (4) less efficient mixing, by averaging 32 nearest neighbors when a star particle is formed (bottom right panel). The dark and light green contours show the [Eu/Fe] distributions that respectively enclose 68 and 95 per cent of Eris’ star particles, with our mixing prescription applied. The observational data are represented by blue symbols for stars where α, Fe, and Eu were all measured, or by orange symbols for stars that only have Eu and Fe measured. The dashed line in these panels represents the solar [Eu/Fe].](/figures/fig-5-a-demonstration-of-how-the-simulated-eu-fe-contours-298hefgk.webp)
