Evolution of Dust in Primordial Supernova
Remnants and Its Influence on the Elemental
Composition of Hyper-Metal-Poor StarsTakayaNozawa , Takashi Kozasa, Asao Habe , Eli Dwek† , Hideyuki
Umeda , Nozomu Tominaga , Keiichi Maeda‡,§ and Ken’ichi Nomoto ,‡Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo
060-0810, Japan†
Laboratory for Astronomy and Solar Physics, NASA Goddard Space Flight Center, Greenbelt,
MD 20771
Department of Astronomy, School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033,
Japan‡
Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba
277-8568, Japan§
Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Strasse 1, 85741 Garching, GermanyAbstract.
The calculations for the evolution of dust within Population III supernova remnants (SNRs) arepresented, based on the models of dust formed in the unmixed ejecta of Type II SNe. We show thatonce dust grains collide with the reverse shock penetrating into the ejecta, their fates strongly dependon the initial radius aini . For SNRs expanding into the interstellar medium (ISM) with nH  0  1 cm 3 ,grains of aini 0 05 µ m are trapped in the hot gas to be completely destroyed; grains of aini 0.05–
0.2 µ m are piled up in the dense shell formed behind the forward shock; grains of aini 0 2 µ m
are injected into the ISM without being eroded significantly. The total mass of surviving dust is
0.01 to 0.8 M for nH  0  10 to 0.1 cm 3 . We also investigate the influence of the piled-up dust on
the elemental abundances of the second-generation stars formed in the dense shell of Population IIISNRs. The comparison of the calculated elemental abundances with those observed in hyper-metalpoor (HMP) and ultra-metal-poor (UMP) stars indicates that the transport of dust separated frommetal-rich gas can be an important process in determining the abundance patterns of Mg and Si in
HMP and UMP stars.
Keywords: dust; extinction, early universe, supernovae: general, stars; abundances, Population III
PACS: 95.30.Lz, 95.30.Wi, 97.10.Tk, 97.20.Wt, 97.60.Bw, 98.38.Mz

INTRODUCTION
Dust grains in the early universe have great impacts on the evolutional history of theuniverse: Dust grains control the energy balance in interstellar space through absorptionof stellar light and re-emission of it, and play critical roles in the formation processes ofstars and galaxies. In particular, their thermal emission greatly increases the efficiency
of cooling of gas in metal-poor circumstances, which causes the star-forming gas cloud
to fragment into low-mass gas clumps of 0.1–1 M for metallicity of 10 6 to 10 5
Z [1, 2, 3]. The absorption and thermal emission by dust grains heavily depend ontheir composition, size, and amount. Thus, it is one of the most important subjects inastrophysics to elucidate the origin and evolution of dust grains.

The dominant sources of dust in the early universe are considered to be supernovae(SNe) evolving from the early generations of massive stars. Theoretical studies haveinvestigated the formation of dust in primordial Type II SNe (SNe II) [4, 5] and pairinstability SNe [5, 6], and have revealed the composition, size, and mass of dust formedin the ejecta; for SNe II, dust grains of 0.1–2 M are formed, which is in good agreement with the amount required to account for dust content in high-redshift galaxies [7,8]. However, the reverse shock induced by the interaction of the SN ejecta with the surrounding medium reprocesses the newly condensed dust grains and makes their size andmass significantly different from those at the time of dust formation [9, 10].
In this proceedings, we present the calculations for the processing of dust through thecollisions with the reverse shocks and its transport within Population III SN remnants(SNRs), in order to reveal the size and amount of dust injected from SNe into the interstellar medium (ISM). The results of calculations show that a part of the surviving dust
grains are accumulated in the dense SN shell. These piled-up grains may have significant influences on the elemental abundances of the second-generation stars formed there.
Therefore, assuming that the composition of the piled-up grains reflects the elemental
composition of those stars, we explore the abundance patterns of the stars formed in thedense shell of Population III SNRs and compare to those observed in hyper-metal-poor(HMP) and ultra-metal-poor (UMP) stars.

EVOLUTION OF DUST IN PRIMORDIAL SNRSThe calculations of the dust evolution in SNRs are described in detail by Nozawa et al.
(2007) [10]. By taking the size distribution and spatial distribution of each dust species
from the dust formation model by [5] as the initial conditions, the transport of dust andits destruction by sputtering are calculated. The time evolution of the gas temperatureand density in SNRs expanding into the uniform ISM with the hydrogen number densityof nH 0 0.1, 1, and 10 cm 3 are calculated by adopting the hydrodynamic models ofPopulation III SNe by [11]. In what follows, we present the results for the evolution ofthe dust formed in the unmixed ejecta of SNe II with the progenitor masses of Mpr 13,20, 25, and 30 M and explosion energy of 1051 ergs.
In Figure 1a, we show the time evolutions of positions of C, Mg2 SiO4 , and Fe grains
within the SNR for Mpr 20 M and nH 0 1 cm 3 , and the time evolutions of theirradii are given in Fig 1b. The thick solid lines in Fig. 1a depict the positions of theforward shock, the reverse shock, and the surface of the He core. C, Mg2 SiO4 , and Fe
grains comove with the gas until they encounter the reverse shock at 3650 yr, 6300 yr,and 13000 yr, respectively. Once dust grains intrude into the reverse shock, their fatesstrongly depend on their initial radii aini and compositions. Because the deceleration
rate of a grain is inversely proportional to its radius, the relatively small grains withaini 0 01 µ m (dotted lines) are efficiently decelerated by the gas drag and are trappedin the hot gas of 106 K created by the passage of the reverse and forward shocks. Thesesmall grains captured in the hot gas are completely destroyed by the thermal sputtering.
C, Mg2 SiO4 , and Fe grains with aini 0 1 µ m (dashed lines) penetrating into the hotgas are eroded due to the kinetic and/or thermal sputterings, and their radii are reducedby 43%, 69%, and 52%, respectively. C and Mg2 SiO4 grains of aini 0 1 µ m are finally















FIGURE 1. Time evolutions of (a) positions of C, Mg2 SiO4 , and Fe grains within the SNR for Mpr  20M and nH  0  1 cm 3 and (b) ratios of their radii to the initial ones. The evolution of dust with aini 0.01, 0.1, and 1 µ m is denoted by the dotted, dashed, and solid lines, respectively. In (a), the positions of
the forward shock, the reverse shocks, and the surface of the He core are indicated by the thick solid lines.

trapped in the dense SN shell formed at 2 105 yr, where the dust grains are no longer
eroded by the thermal sputtering because the gas temperature drops down quickly below
105 K [12]. The 0.1 µ m-sized Fe grains with higher bulk density are ejected into theISM. Since the deceleration by the gas drag is inefficient, grains with aini 1 µ m (solidlines) also go across the outwardly expanding shock front and are injected into the ISM
without being processed significantly,
The behaviors of the transport and destruction of dust in a SNR heavily depend on thedensity of gas in the ISM; as the ISM gas density is higher, the density of the shocked
gas is higher, which leads to the efficient deceleration and erosion of dust through more
frequent collisions with the hot gas. As a result, the lower limit of the initial radius of dust
injected into the ISM increases with increasing the ISM density and is 0.03, 0.2, and 0.5µ m for nH 0 0.1, 1, and 10 cm 3 , respectively. Furthermore, the initial radius below
which dust is completely destroyed is enhanced by the increase of the density in the ISM,
and is 0.01, 0.05, and 0.2 µ m for nH 0 0.1, 1, and 10 cm 3 . Accordingly, as shownin Figure 2, the total mass of the surviving dust decreases with increasing the ambientdensity and spans the range of 0.01–0.8 M for nH 0 10 to 0.1 cm 3 , depending on
the progenitor mass. In any cases, the resulting size distribution of the dust that survives
the destruction shows a serious lack of small-sized grains, in comparison with that at thetime of dust formation. Note that the evolution of dust within a SNR does not dependon the progenitor mass considered here because the same explosion energy results in thesimilar time evolution of the gas temperature and density.
FIGURE 2. Total mass of surviving dust vs. the progenitor mass. The results for nH  0  0.1, 1, and 10
cm 3 are connected by the dot-dashed, dashed, and dotted lines, respectively.

ELEMENTAL ABUNDANCES IN THE DENSE SN SHELL

Currently known most iron-deficient stars, HE 0107-5240 with [Fe/H]
5 3 ([13, 14])and HE 1327-2326 with [Fe/H]
5 45 ([15, 16]) show peculiar abundance patterns:
more than 100 times excesses of C, N, and O and 1–100 times enhancements of Mg andSi relative to Fe. Also, UMP star, HE 0557-4880 with [Fe/H]
4 75 ([17]) exhibitsa large ( 50 times) overabundance of C. Although the elemental compositions of theselow-mass stars are expected to reflect the nucleosynthesis in the very early generationsof stars, the origin of the abundance patterns in HMP and UMP stars is still an openquestion.
The results for the evolution of dust within a SNR presented in this paper show thatthe dust grains which are not injected into the ISM but survive the destruction throughthe collision with the reverse shock are accumulated in the dense SN shell in 105 –106
yr. This transport of dust to the SN shell may not only enable the formation of stars
with solar mass scales there [1, 2, 3] but also influence the elemental abundance of thosestars. Therefore, based on the composition of the piled-up grains, we investigate themetal abundance patterns of the stars formed in the dense shell of SNRs and compare
to those observed in HMP and UMP stars, assuming that they are the second-generationstars formed in the shell of Population III SNRs.
The results for the elemental composition and metallicity in the dense shell aresummarized in Table 1 for various progenitor masses and ambient densities. Metallicity
in the shell is in the range from 10 6 up to 10 4 Z , which is high enough to form
low-mass stars with 0.1–1 M [1, 2, 3]. We can also see that most of calculated [Fe/H]
spans the range of 6 to 4 5, which are in good agreement with those for HMP andUMP stars.
In Figure 3a, we show the abundances of Mg and Si (upper panel) and C and O





TABLE 1. Elemental composition and metallicity in the dense shell of primordial SNe II for variousprogenitor masses and ambient densities.
Mpr (M )13202530[Fe/H][C/Fe]

 6 43

 0 274

 5 900 117
1 110 566

 5 20 5 56[O/Fe]

 0 699
 0 595
 1 42
 0 043[Mg/Fe]nH  0[Si/Fe]0 1 cm 0 230

1 92
0 410
 0 552
0 866

0 034
 0 500
0 739[Al/Fe][S/Fe]

log Z  Z 

 3

 2 60 1 97

 0 563
0 905

0 239
0 242
0 242
0 242

 5 89
 5 44
 5 55
 5 33



13202530 5 15
 5 53
 5 23
 5 11

1 110 992
1 090 797

 0 5550 585
 0 4120 242

nH  0  1 cm 3

 0 459

1 01
1 87
0 989
1 26

1 160 407
1 09–––
 5 72

 2 18
0 200
0 241
0 242

 4 72
 4 68
 4 79
 4 60

13202530 4 13
 4 92
 5 10 5 110 284
0 946
1 60
 0 207 2 54
 2 150 122
0 375

nH  0  10 cm 3

 3 89
 1 800 232
 1 230 599
2 142 34
2 66––––––
 1 45
 0 696

 4 40 4 09

 3 91
 3 84(lower panel) in the dense shell as a function of [Fe/H] for the ISM density of 1 cm 3 .
The results of calculations are drawn by the filled symbols, and the observational dataof HMP and UMP stars are plotted by the open symbols. We can see that in addition toFe, the calculated abundances of Mg and Si can also reproduce the observations of HMP
stars with 1–100 times overabundances seen in HMP stars. Some models (such as Mpr20 and 30 M for nH 0 0 1 cm 3 ) also show the modest overabundances for both Mg
and Si (see Table 1). Because the elemental composition of dust piled up in the shell
can reproduce the abundance patterns of refractory elements such as Mg, Si, and Fe in
HMP and UMP stars, we can conclude that the transport of dust separated from metalrich gas within SNRs can be responsible for the abundance patterns in HMP and UMP
stars, if they are the second-generation stars formed in the dense shell of primordial
SNRs. However, more than one hundred times excesses of C and O observed in HMP
and UMP stars cannot be reproduced by any models considered here.
The reasons is that in the calculation we assumed that the metal-rich gas in the ejectaof SN does not mix with the gas in the shell. Then, as an extreme case, we examine theabundance patterns in the shell by considering that in addition to the piled-up grains,
the gas outside the innermost Fe layer of the SN is incorporated into the shell. Theresults are shown by the filled symbols in Figure 3b. This case can produce the extreme
overabundances ( 1000 times) of C and O, but results in unreasonable excesses ( 100times) of Mg and Si, which is not in agreement with the observations. Nevertheless, it
might be possible to reproduce the elemental abundances of HMP stars if the Si-Mgrich layer is not mixed with the gas in the shell. Anyway, it is necessary to examine what
extent of the gas in the SN ejecta can mix with the gas in the shell when the secondgeneration stars form in the SN shell. In the future works, we will consider this subject.






FIGURE 3. Abundances of Mg and Si (upper panel) and C and O (lower panel) in the shell of the SNRfor nH  0  1 cm 3 ; (a) the elemental abundances obtained from the grains piled up in the shell, and (b) theelemental abundances including the gas outside the innermost Fe layer as well as the piled-up grains. The
results of calculations are shown by the filled symbols. The observational data for HMP and UMP stars
are denoted by the open symbols and are taken from [14, 15, 16, 17, 18].

ACKNOWLEDGMENTS
This work has been supported in part by a Grant-in-Aid for Scientific Research from theJapan Society for the Promotion of Sciences (19740094, 18104003).

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