Chemical Abundances in the Universe: Connecting First Stars toPlanets
c 2009 International Astronomical Union
Proceedings IAU Symposium No. 265, 2009
K. Cunha, M. Spite & B. Barbuy, eds.
DOI: 00.0000/X000000000000000X

Chemo-dynamical simulations of galaxies
Chiaki Kobayashi1
1

The Australian National University, Mt. Stromlo Observatory, Cotter Rd., Weston ACT
2611, email: chiaki@mso.anu.edu.au

Abstract. We simulate the formation and evolution of galaxies with a self-consistent 3D hydrodynamical model including star formation, supernova feedback, and chemical enrichment.
Hypernova feedback plays an essential role not only in solving the [Zn/Fe] problem, but also
reproducing the cosmic star formation rate history and the mass-metallicity relations. In a MilkyWay type galaxy, kinematics and chemical abundances are different in bulge, disk, and thickdisk because of different star formation histories and the contribution of Type Ia Supernovae.

1. Introduction
While the evolution of the dark matter is reasonably well understood, the evolution of
the baryonic component is much less certain because of the complexity of the relevant
physical processes, such as star formation and feedback. With the commonly employed,
schematic star formation criteria alone, the predicted star formation rates (SFRs) arehigher than what is compatible with the observed luminosity density. Thus feedback
mechanisms are in general invoked to reheat gas and suppress star formation. Supernovae inject not only thermal energy but also heavy elements into the interstellar medium,
which can enhance star formation. Chemical enrichment must be solved as well as energy
feedback. “Feedback” is also important for solving the angular momentum problem andthe missing satellite problem, and for explaining the existence of heavy elements in intracluster medium and intergalactic medium, and the mass-metallicity relation of galaxies(Kobayashi et al. 2007, hereafter K07).
In the next decade, high-resolution multi-object spectroscopy (HERMES) and spaceastrometry mission (GAIA) will provide kinematics and chemical abundances of a million
stars in the Local Group. Since different heavy elements are produced from different supernovae with different timescales, elemental abundance ratios can provide independent
information on “age”. Therefore, stars in a galaxy are fossils to untangle the history of
the galaxy. The galactic archeology technique can be used to study the galaxy formation and evolution in general. Metallicities are measured in various objects with different
galaxy mass scale and as a function of redshift/time. The internal structure of galaxies
have being observed with integral field spectrographs (e.g., the SAURON project, SINFONI on VLT). Chemodynamical simulations can provide useful predictions and physicalinterpretation of these observations.

2. Chemical Enrichment Sources
Hypernovae (HNe) — Although the explosion mechanism of core-collapse supernovae is a debated issue, the ejected explosion energy and 56 Ni mass (which decayed to56Fe) can be directly estimated from the observations, i.e., the light curve and spectra fitting of individual supernova. As a result, it is found that many core-collapse supernovae
have more than ten times larger explosion energy (E51 ∼> 10) and produce a significant
amount of iron. We calculate the nucleosynthesis yields for wide ranges of metallicity(Z = 0 − Z⊙ ) and the explosion energy (normal SNe II and HNe). Assuming that a halfof supernovae with 6 20M⊙ are HNe, the evolution of the elemental abundance ratios
1

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Chiaki Kobayashi

Figure 1. Evolutions of heavy element abundance ratios [X/Fe] against [Fe/H] for one-zone
models with only SNe II (long-dashed line), with our new yields and SN Ia model (short-dashedline), with the double-degenerate scenario of SNe Ia (dotted line), and with AGB stars (solidline). The dots are observational data (see K06 for the references).

from carbon to zinc are in good agreement with observations in the solar neighborhood,bulge, halo, and thick disk (Kobayashi et al. 2006, hereafter K06).
Figure 1 shows the evolutions of heavy element abundance ratios [X/Fe] against [Fe/H]
with our new yields (short-dashed lines), and with only SNe II (long-dashed lines, Nomoto
et al. (1997)’s yields adopted). The star formation history and total number of SNe Ia
are determined to meet the observed metallicity distribution function. In the early stageof galaxy formation, only SNe II explode, and [α/Fe] stays constant. Because of thedelayed Fe production by SNe Ia, [α/Fe] decreases toward 0. α-elements, O, Mg, Si, S,
and Ca, show the plateau at [Fe/H] ∼< − 1. Ti is underabundant overall, which could be
solved with 2D calculation. The observed decrease in the odd-Z elements (Na, Al, andCu) toward low [Fe/H] is reproduced by the metallicity effect on nucleosynthesis. The
iron-peak elements (Cr, Mn, Co, and Ni) are consistent with the observed mean values at−2.5 ∼< [Fe/H] ∼< − 1, and the observed trend at the lower metallicity can be explainedby the energy effect under the assumption of inhomogeneous enrichment. Note that Cr
II observations are plotted.
The most important improvement is in Zn. The observed abundance of Zn ([Zn/Fe]∼ 0) can be explained only by such large contribution of HNe. Since the observed [Zn/Fe]
shows an increase toward lower metallicity (Primas et al. 2000; Nisesn et al. 2007), theHN fraction may be larger in the earlier stage of galaxy formation. Since neutron-richisotopes 66−70 Zn are produced at high metallicity, the HN fraction can be as small as
1%. In the following chemodynamical simulations, we adopt ǫHN = 0.5, 0.5, 0.4, 0.01 for
Z = 0, 0.001, 0.004, 0.02. Pair-instability supernovae, which produce much more Fe, more
[S/Fe], and less [Zn/Fe], should not contribute in the galactic chemical evolution.
Type Ia Supernovae (SNe Ia) — The progenitors of the majority of SNe Ia aremost likely the Chandrasekhar (Ch) mass white dwarfs (WDs). For the evolution ofaccreting C+O WDs toward the Ch mass, two scenarios have been proposed: One is the
double-degenerate (DD) scenario, i.e., merging of double C+O WDs with a combined
mass surpassing the Ch mass limit, although it has been theoretically suggested that it
leads to accretion-induced collapse rather than SNe Ia. The other is our single-degenerate(SD) scenario, i.e., the WD mass grows by accretion of hydrogen-rich matter via masstransfer from a binary companion.

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We construct a new model of SNe Ia, based on the SD scenario, taking account of
the metallicity dependences of the WD wind (Kobayashi et al. 1998) and the massstripping effect on the binary companion star (Kobayashi & Nomoto 2009). Our model
naturally predicts that the SN Ia lifetime distribution spans a range of 0.1 − 20 Gyrwith the double peaks at ∼ 0.1 and 1 Gyr. While the present SN Ia rate in ellipticalgalaxies can be reproduced with the old population of the red-giants+WD systems, thelarge SN Ia rate in radio galaxies could be explained with the young population of themain-sequence+WD systems. Because of the metallicity effect, i.e., because of the lack ofwinds from WDs in the binary systems, the SN Ia rate in the systems with [Fe/H] ∼< − 1,
e.g., high-z spiral galaxies, is supposed to be very small. We succeed in reproducing thegalactic supernova rates with their dependence on the morphological type of galaxies,
and the cosmic SN Ia rate history with a peak at z ∼ 1. At z ∼> 1, the predicted SN Ia
rate decreases toward higher redshifts and SNe Ia will be observed only in the systems
that have evolved with a short timescale of chemical enrichment. This suggests that theevolution effect in the supernova cosmology can be small.
From [Fe/H] ∼ −1, SNe Ia start to occur producing more Fe than α-elements, andthus [α/Fe] decreases toward the solar abundance. The decreasing [Fe/H] depends on the
SN Ia progenitor model. Our SN Ia model can give better reproduction of the [(α, Mn,
Zn)/Fe]-[Fe/H] relations in the solar neighborhood than other models such as the DD
scenario (dotted lines). With the DD scenario, the typical lifetimes of SNe Ia are ∼ 0.1
Gyr, which results in the too early decrease in [α/Fe] at [Fe/H] ∼ −2. Even with our SD
model, if we do not include the metallicity effect, [α/Fe] decreases too early because of
the shortest lifetime, ∼ 0.1 Gyr, of the MS+WD systems. In other words, the metallicity
effect is more strongly required in the presence of the young population of SNe Ia.
Asymptotic Giant Branch (AGB) stars — Stars with initial masses between
about 0.8−8M⊙ (depending on metallicity) produce light elements such as C and N, while
the contribution of heavier elements are negligible in the galactic chemical evolution (solidlines). The nucleosynthesis yields of AGB stars involves uncertainties due to convection
and mass loss. We introduce the new calculation by Karakas (2009), which is based on
Karakas & Lattanzio (2007). The Na overproduction problem has been solved with theupdated reaction rates (Karakas 2009).
Needless to say, the envelope mass and pre-existing heavy elements are returned bystellar winds from all stars. Surprisingly, in many hydrodynamical simulations, this contribution is not included, which should affect the metallicity and star formation history.

3. Chemodynamical Model
The details of our chemodynamical models are described in Kobayashi (2004), and canbe summarized as follows. i) The Smoothed Particle Hydrodynamics (SPH) method isadopted with individual smoothing lengths and timesteps. For the simulations of individual galaxies, the gravity is calculated in direct summation using the special purpose
computer GRAPE (GRAvity PipE). For cosmological simulations, we basically use an
SPH code GADGET-2 by Springel (2005), being modified with the physical processes
in Kobayashi (2004). ii) Radiative cooling is computed using a metallicity-dependentcooling function (Sutherland & Dopita 1993). iii) Our star formation criteria are thesame as in Katz (1992); (1) converging flow; (∇ · v)i < 0, (2) rapid cooling; tcool < tdyn ,and (3) Jeans unstable gas; tdyn < tsound . The star formation timescale is proportional
to the dynamical timescale (tsf ≡ 1c tdyn ), where the star formation timescale parameterc = 0.1 is adopted (Kobayashi 2005). If a gas particle satisfies the above star formation
criteria, a fractional part of the mass of the gas particle turns into a star particle. Since
an individual star particle has a mass of 105−7 M⊙ , it dose not represent a single star, but

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Chiaki Kobayashi

Figure 2. Age-metallicity relations (upper panels) and [O/Fe]-[Fe/H] relations (lower panels)in the solar neighborhood (a and b), thick disk (c and d), and bulge (e and f). The contours
show the mass density for the simulation. The dots show the observations of stars in the solar
neighborhood.

an association of many stars. The mass of the stars associated with each star particle isdistributed according to an initial mass function (IMF). We adopt a Salpter IMF with aslope x = 1.35, which give good agreement with many observations except for the [α/Fe]
problem in elliptical galaxies. iv) For the feedback of energy and heavy elements, we
do not adopt the instantaneous recycling approximation. Via stellar winds, SNe II, and
SNe Ia, thermal energy and heavy elements are ejected from an evolved star particle asfunctions of time and metallicity, and are distributed to all surrounding gas particles out
to a constant radius of 1 kpc (§4), or with the number of feedback neighbors NFB = 405(§5). v) The photometric evolution of a star particle is identical to the evolution of asimple stellar population (SSP). SSP Spectra are taken from Kodama & Arimoto (1997)
as a function of age and metallicity.

4. Chemodynamical Evolution of the Milky Way Galaxy
We simulate the chemodynamical evolution of the Milky Way-type galaxy from the
CDM initial fluctuation. The initial condition is similar to those in Kobayashi (2004,
2005), but with the initial angular momentum of λ ∼ 0.1, the total mass of ∼ 1012 M⊙ ,and ∼ 120000 particles. We choose an initial condition where the galaxy does not undergo
major mergers, otherwise no disk galaxy can form. The cosmological parameters are set
to be H0 = 70 km s−1 Mpc−1 , Ωm = 0.3, and ΩΛ = 0.7.
In the CDM scenario, any galaxies form through the successive merging of subgalaxies
with various masses. In our simulation, the merging of subgalaxies induces an initial
starburst and the bulge forms by z ∼> 3. 80% of bulge stars (r 6 1 kpc) are older than
∼ 10 Gyr. According to the late gas accretion, the disk structure is seen at z <∼ 2.Inthe solar neighborhood (r = 7.5 − 8.5 kpc, |z| 6 0.5 kpc), 50% of disk stars are younger
than ∼ 8 Gyr, and old stars tend to have small rotation velocity v and large velocity
dispersion σ. When we define thick disk as v/σ < 1.5, 80% of thick disk stars are older
than ∼ 8 Gyr.
The age-metallicity relations are shown in the upper panels of Figure 2. (a) In the solar
neighborhood, [Fe/H] increases to ∼ 0 at t ∼ 2 Gyr, which is broadly consistent with

Chemo-dynamical simulations of galaxies

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the observation (Nordström et al. 2004). (c) In the thick disk, the relation is similar as
in the solar neighborhood, but most stars are populated in the region with old age andlow [Fe/H]. (e) In the bulge, [Fe/H] increases more quickly than in the disks. Metal-richstars with [Fe/H] ∼ 1 appear at t ∼ 2 Gyr.
The [O/Fe]-[Fe/H] relations are shown in the lower panels of Figure 2, and we obtain
similar results for other α elements. (b) In the solar neighborhood, we can reproduce theobservational trend. [α/Fe] decreases because of the delayed iron enrichment of SNe Ia.
If we do not include the metallicity effect on SNe Ia, or if we do not include HNe, wecannot reproduce the plateau at [Fe/H] ∼< −1, and the scatter of [α/Fe] at [Fe/H] ∼< −1 istoo large. At [Fe/H] ∼> − 1, the scatter is large. This may be because the mixing of heavy
elements among gas particles has not been included in our chemodynamical model.
(d) In the thick disk, chemical enrichment timescale is so short that [α/Fe] tends tobe larger than in the thin disk, which is consistent with the observations (Bensby etal. 2004). (f) In the bulge, chemical enrichment timescale is shorter than in the disks,
the [α/Fe] plateau continues to [Fe/H]∼ 0, which is consistent with some observations(Zoccali et al. 2008). The star formation has not been terminated in the simulation, andsome new stars are forming also in the bulge. Such young stars tend to have large [Fe/H]
and low [α/Fe] in our simulation, and the observed stars in Cunha et al. (2007) may beaffected by inhomogeneity, or some uninvolved physics. Particularly, if the relations of
O and Mg are different, we may have to include non-supernova physics such as strong
stellar winds.
We predict the time evolution of [X/Fe]-[Fe/H] diagrams as a function of location(Kobayashi 2009). From statistical comparison for the frequency distribution along therelations, chemodynamical models should be tested and improved, and then can be used
to untangle when, where, how the stars with given abundance pattern have formed.
Origin of thick disk? — Tracing the orbit of star particles, we discuss the originof the thick disk. The fractions of stars that have formed in the disk (z < 1 kpc) are∼ 40%. The rest, more than half of thick disk stars have formed in merging subgalaxies
before they accrete onto the disk. In this sense, the CDM picture seems not to conflictwith the Milky Way Galaxy. However, it is very hard to find initial condition to form
disk galaxies (with this resolution) because major mergers brake the disk structure, andlate star formation caused by slow gas accretion is not enough to re-generate (contrary to
Steinmetz & Navarro 2002). For the frequency of disk galaxies, the CDM picture seems
to have a problem, although it should be tested with cosmological simulations.

5. Cosmological Simulations
The story is not closed yet. Since the resolution is not enough to describe the small-scale
physics, the modelling of feedback involves a parameter. The model has to be checkedwith a different scale of observational constraints. The most stringent one is the massmetallicity relation of galaxies. We simulate the evolution of dark matter, gas, and stellar
systems from the cosmological initial condition of a 10h−1 Mpc cubic box with periodic
boundary, NDM = Ngas = 963 particles, H0 = 70 km s−1 Mpc−1 , Ωm = 0.3, ΩΛ = 0.7,
Ωb = 0.04, n = 1, and σ8 = 0.9.
With the larger energy ejection by HNe, the SFR starts to be suppressed from z ∼ 6
onwards, and is overall reduced by a factor of 3 at 0 ∼<z∼< 3. We then succeed in reproducing both the observed cosmic SFRs and stellar density evolution (K07). The present
stellar fraction is less than 10% being consistent with the recent observational estimate(Fukugita & Peebles 2004), while 25% of baryons turn into stars without feedback.
The metal enrichment timescale depends on the environment. In large galaxies, enrichment takes place so quickly that [O/H] reaches ∼ −1 at z ∼ 7, which is consistent

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Chiaki Kobayashi

Figure 3. (a) Mean metallicities of cold gas (T < 104 K) within 10 kpc, plotted against the
total stellar mass. The lines are observational data: Tremonti et al. (2004, z = 0), Savaglio etal. (2005, z = 0.7), Erb et al. (2006, z = 2.2), and Maiolino et al. (2008, z = 3.5). (b) Mean
stellar metallicities within 10 kpc, V-band luminosity-weighted. Kobayashi & Arimoto (1999,
solid line) from metallicity gradients, Gallazzi et al. (2005, dashed line), and Quider et al. (2009,z = 2 − 3) for lensed galaxy.

with the sub-solar metallicities of the Lyman break galaxies (Pettini et al. 2001). The
low metallicities of DLA systems (Prochaska et al. 2003) are also consistent with ourgalaxies, provided these systems are dwarf galaxies or the outskirts of massive galaxies.
The low [C/H] of the IGM (Schaye et al. 2003) can be explained if the IGM is enriched
only by SNe II and HNe. The average metallicity of the universe reaches [O/H] ∼ −2
and [Fe/H] ∼ −2.5 at z ∼ 4 , but reaches the same values at z ∼ 3 in the IGM.
How are heavy elements ejected from galaxies to the IGM? In the simulation, we cantrace the orbit of gas particles over time. Exploiting this, we define as wind particles
those that are not in galaxies now, but have been in galaxies before (Fig. 15 in K07).
In this simulation, ∼ 10% of baryons turn into stars, ∼ 10% of the gas stays in galaxies(∼ 8% is hot), and ∼ 20% is ejected as galactic winds. The rest, half of the baryons,
never accretes onto galaxies. Tracing the orbits of gas particles, we can also examine fromwhich galaxies the wind gas particles are ejected, and measured the ejected wind massfrom each galaxy (Fig. 16 in K07). Winds are efficiently ejected from small galaxies, with
∼ 80% of accreted baryons being ejected from Mtot ∼ 1011 M⊙ galaxies. A similar relationis also found for the ejected metal fraction, i.e. the ratio between the wind metal mass
to the total metal mass. It is interesting that the wind fraction and the ejected metal
fraction correlate well with the stellar metallicity. Based on this finding, we conclude thatthe origin of the mass-metallicity relation is the mass-dependent galactic winds.
Figure 3 shows of the mass-metallicity relations of simulated galaxies (dots) and observations (lines). For the gas-phase metallicity, there are uncertainties such as inhomogeneity and aperture effect, and a large scatter is seen. The simulation is comparable
to observations upto z ∼ 2, but there is an offset at z = 3.5. This may be a problem,
but the normalization of observations needs to be checked. For the stellar metallicity, atight relation is present since z = 5 in the simulation. At high redshifts, observations areavailable for only 2 lensed galaxies, which is remarkably consistent with the simulation.
References
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Kobayashi, C., Tsujimoto, T., Nomoto, K., Hachisu, I, & Kato, M. 1998, ApJ, 503, L155
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