高赤方偏移銀河の金属量非一様性と初代星初期質量関数への影響

Metallicity inhomogeneity
inside high-z galaxies andits effects on Pop-III IMF

Yuta Tarumi (Tokyo University),in collaboration withTilman Hartwig andMattis Maggmetal dilution in high-z galaxies

Stellar archaeology to IMF❖

Direct observation of Pop-III stars is quite difficult.

❖-> Can we investigate indirectly?

❖Pop-III properties (like IMF) affects…

❖❖

Metal yields❖

Radiation flux

Using semi-analytical model, we search for pop-III IMF that best
reproduces the observation.

metal dilution in high-z galaxiesWhat is semi-analytical model(SAM)?
❖Simplified simulation of galaxy
4in each DM halo: FASTTime❖

No resolution inside each halo❖

→ Assume homogeneity

T. Hartwig, V. Bromm, R. S.
Hartwig+15

metal dilution in high-z galaxies

How inhomogeneous??
❖The metallicity can differ
by 5 orders ofmagnitude (!!!)❖Usually SAM assumehomogeneity insidevirial radius→ Inhomogeneity can play
an important role !

Z ≡ log10(metal mass)− log10(0.02)[ (total mass) ]metal dilution in high-z galaxies

How inhomogeneous??
❖

The metallicity can differ
by 5 orders ofmagnitude (!!!)❖

Usually SAM assume
homogeneity insidevirial radius→ We take inhomogeneity
into account…

Z ≡ log10(metal mass)− log10(0.02)[ (total mass) ]metal dilution in high-z galaxies

How inhomogeneous??
❖

The metallicity can differ
by 5 orders ofmagnitude (!!!)❖

Usually SAM assume
homogeneity insidevirial radius

By introducing
a new parameter dZdZ

Z ≡ log10(metal mass)− log10(0.02)[ (total mass) ]metal dilution in high-z galaxies

What is semi-analytical model(SAM)?
❖Simplified simulation of galaxy
4in each DM halo: FASTTime❖

No resolution inside each halo❖

→ Assume homogeneity

T. Hartwig, V. Bromm, R. S.
Hartwig+15

metal dilution in high-z galaxies

What is semi-analytical model(SAM)?
❖Simplified simulation of galaxy
4in each DM halo: FASTTime❖❖

No resolution inside each halo
→ Assume homogeneity, or
introduce a parameter to takeinhomogeneity into accountUse cosmological simulation
to calibrate this parameter!!

T. Hartwig, V. Bromm, R. S.
Hartwig+15

metal dilution in high-z galaxies

Motivation❖

I want to…
❖❖

predict [Fe/H] of stars in a halo, only by❖total metal mass❖

total hydrogen massand obtain better prediction on Pop-III IMF through SAM
calibration.

metal dilution in high-z galaxies

Method1: cosmological simulation❖

Introduce a parameter “dZ” as:Z ≡ log10(metal mass)− log10(0.02)[ (total mass) ]dZ = Zdense − ZalldZ < 0dZ > 0metal dilution in high-z galaxies

Result1: correlation matrix❖

dZ = Zdense − Zallis correlated with:❖Zdense

❖

Zall

❖

Mpop2

❖

Mpop3

There’s something between
stellar mass and dZ!

metal dilution in high-z galaxies

Result1: distribution of dZ
dZ distribution is different between internal and externalenrichment.

❖

In internal enrichment, dZ distributes around 0: well mixed❖

In external enrichment, dZ is mostly negative, and the absolutevalue can be quite large (~ -5 or more)dZ❖

Bimodality!!

log10(Stellar mass)metal dilution in high-z galaxies

Result1: distribution of dZ❖

In internal enrichment, dZ distributes around 0: well mixed❖

In external enrichment, dZ is mostly negative, and the absolutevalue can be quite large (~ -5 or more)

Bimodality!!

log10(Stellar mass)dZ

dZ distribution is different between internal and externalenrichment.

dZ❖

Metallicity of all gas Zall

metal dilution in high-z galaxies

Result1: distribution of dZ❖

In external enriched haloes, typically dZ ~ -1❖

Previous works assume good dZ distribution for internalenrichment.
ExternalComparison-1

metal dilution in high-z galaxies

Result1: distribution of dZ
Why the externally enriched halos have negative dZ?

metal-rich wind❖

Pristine gas collapse happens earlier, and thenenrichment wind cannot penetrate into the cloud.

−4Metallicity❖

metal-poorgalaxyCenter remains
pristine−6metal dilution in high-z galaxies

Method2: the semi-analytical modelI

Table 2. Parameter values in our fiducial model. This set
parameters best reproduces the MDF at [Fe/H] 3 as we shobelow.

❖❖

SAM has many parameters.

ParameterValue

Pop III SFE
fraction of faint SNe
metal fallback fraction
metal ejection fraction
lower IMF limit
upper IMF limit
IMF slope ↵⌘III = 10 1 ⇠ 10 6
ffaint = 0.0 ⇠ 1.0
ffallback = 0% ⇠ 100%
feject = 100% ⇠ 0%
Mmin = 1 ⇠ 10M
Mmax = 100 ⇠ 1000M
1.0(flat) ⇠ 1.35(Salpeter)

SAM is mainly calibrated by:
the SMHM relation M*(Mhalo)(to Renaissance, abundance matching)❖Internal enrichment fraction(to Renaissance)❖

metallicity distribution function(to observation)❖

Behroozi+13, Garrison-Kimmel+14

metal dilution in high-z galaxies

Result2: MDF and IMF
Overall MDF looks similar.
[Fe/H] distribution function

Stellar mass❖

[Fe/H]

metal dilution in high-z galaxies

Result2: MDF and IMF
Overall MDF looks similar.
[Fe/H] distribution function

IMF comparison

Stellar mass❖

[Fe/H]

log10(Mstar)metal dilution in high-z galaxies❖

Increase # of stars in-5 < [Fe/H] < -4.

❖Stars with [Fe/H] < -5
are mostly fromexternal enrichment.

❖However, the effect on
IMF seems small:
IMF prediction is notmuch affected by theinhomogeneity.

Stellar mass

Result2: The effects of dZdZ effect[Fe/H]

metal dilution in high-z galaxies

Summary❖(high-z) galaxy is inhomogeneous. The inhomogeneity
is prominent in externally enriched halos. Dense gas ismetal-poor, because metal-rich wind cannot penetrate
into gas cloud.

❖We may observe [Fe/H] < -4 stars more often thanpreviously we have imagined.

❖metallicity inhomogeneity only plays a minor role on
MDF and consequently on IMF.

Introduction

Importance of mixing

https://www.ipmu.jp/ja/20190524-FirstStars

Mixing inside galaxy
2CONROY, GRAVES & VAN DOKKUM

1.2
uumcontinNa I

1.0

Mixing connects source
event and current
observations.

Fe I+Ti Iflux

❖

Fe I

Fe I
HαTiO

Na I + TiO

TiO

Mg ITiO

0.8
Fe I
CH

0.6
0.4
0.2
0.4

Ca I
Ca IIMgH

13.5 Gyr, Zsol
σ=350 km/s

0.5

0.6

0.7

λ (μm)

0.8

0.9

metal dilution in high-z galaxies

Method2: Star formation in the SAM❖

Initially halos are “pristine”.

❖If each halo satisfies all the criteria, it forms PopIII/II stars
and enrich the halo.
PopIII criteria:・The halo is massive enough❖star formation can alsoenrich neighboring halos

・The halo is pristine・The Lyman-Werner feedback is not too strong

PopII criteria:
・The halo is massive enough・The halo contains enough coolants

metal dilution in high-z galaxies

CEMP fraction

metal dilution in high-z galaxies

Method1: cosmological simulation❖“Renaissance simulation”: Large volume, Good resolution
https://rensimlab.github.io/showcase.html

107M⊙