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The Astrophysical Journal, 666:955Y966, 2007 September 10# 2007. The American Astronomical Society. All rights reserved. Printed in U.S.A.

EVOLUTION OF DUST IN PRIMORDIAL SUPERNOVA REMNANTS: CAN DUST GRAINS FORMED
IN THE EJECTA SURVIVE AND BE INJECTED INTO THE EARLY INTERSTELLAR MEDIUM?
Takaya Nozawa,1 Takashi Kozasa,1 Asao Habe,1 Eli Dwek,2 Hideyuki Umeda,3Nozomu Tominaga,3 Keiichi Maeda,4 and Ken’ichi Nomoto3,5
Received 2007 March 15; accepted 2007 May 30

ABSTRACT
We investigate the evolution of dust that formed at Population III supernova (SN ) explosions and its processing
through the collisions with the reverse shocks resulting from the interaction of the SN ejecta with the ambient
medium. In particular, we investigate the transport of the shocked dust within the SNR and its effect on the chemicalcomposition, the size distribution, and the total mass of dust surviving in SNRs. We find that the evolution of thereverse shock, and hence its effect on the processing of the dust, depends on the thickness of the envelope retained by
the progenitor star. Furthermore, the transport and survival of the dust grains depend on their initial radius, aini , andcomposition: for Type II SNRs expanding into the ISM with a density of nH;0 ¼ 1 cm3, small grains with aini P
0:05 m are completely destroyed by sputtering in the postshock flow, while grains with aini ¼ 0:05Y0:2 m aretrapped into the dense shell behind the forward shock. Very large grains of aini k 0:2 m are ejected into the ISM
without decreasing their sizes significantly. We find that the total mass fraction of dust that is destroyed by the reverse
shock ranges from 0.2 to 1.0, depending on the energy of the explosion and the density of the ambient ISM. The
results of our calculations have significant impact on the abundance pattern of the second-generation stars that form in
the dense shell of primordial SNRs.
Subject headinggs: dust, extinction — early universe — shock waves — supernova remnants —supernovae: general
Online material: color figures
allicity of 106 to 105 Z (Omukai et al. 2005; Schneider et al.
2006), although very massive stars of k100 M are considered to
be formed up to Z ’ 103:5 Z without the effect of dust (Bromm
et al. 2001). Finally, dust obscures the nature of underlying stellar
populations (e.g., Hines et al. 2006) and physical processes in theearly universe. Understanding the origin and the complex evolutionary history of dust is therefore one of the most importantgoals in astrophysics.
During the first billion years of cosmic history, supernovae(SNe) are the only possible source of interstellar dust, since lowmass stars have not had time to evolve off the main sequence andinject the dust that forms in their quiescent outflows into the ISM.
Theoretical studies aimed at determining the composition andyield of dust in the ejecta of primordial Type II SNe (SNe II ) andpair-instability SNe (PISNe) were conducted by Todini & Ferrara(2001), Nozawa et al. (2003), and Schneider et al. (2004). These
works have shown that even the first SNe evolving from zerometal progenitor stars can efficiently produce dust at 150Y800 days
after the explosion. The ratio of the total dust mass to the progenitor mass Mpr is 0.02Y0.05 for SNe II with Mpr ¼ 12Y35 M
and 0.15Y0.3 for PISNe with Mpr ¼ 140Y260 M. The composition of the newly formed dust grains is controlled by theelemental composition inside the He core, and their sizes range
from 0.001 to 1 m, depending on the concentration of the gas
species forming dust and the time evolution of temperature anddensity of gas.
The results of these calculations have been applied to study thehigh-redshift dust. Maiolino et al. (2004b) demonstrated a SN
origin for high-redshift dust, showing that the extinction curveof the z ¼ 6:2 quasar SDSS 1048+46 can be nicely fitted by the
SN II dust models from Todini & Ferrara (2001). Dust producedin the unmixed SNe II by Nozawa et al. (2003) can also successfully reproduce the extinction curve of the quasar SDSS
1048+46 by weighting the progenitor mass with the Salpeter

1. INTRODUCTION
Recent far-infrared to millimeter observations of quasars with
redshifts k5 have revealed the presence of large amounts of dustwith masses in excess of 108 M ( Bertoldi et al. 2003; Priddey
et al. 2003; Robson et al. 2004; Beelen et al. 2006). The presenceof these large quantities of dust at such an early epoch, when theuniverse was P1 Gyr old, suggests the rapid enrichment withdust that formed in the explosive ejecta of short-lived massive
stars (Morgan & Edmunds 2003; Maiolino et al. 2004b; Dwek
et al. 2007). In addition, Maiolino et al. (2004a) have reported
that the dust extinction curve of the broad absorption line quasar
SDSS 1048+46 at z ¼ 6:2 is quite different than those of quasars at z < 4, suggesting different dust sources and evolutionary
histories.
Dust plays a pivotal role in the interstellar processes that determine the state of the interstellar medium ( ISM ). Dust affects
the thermal and chemical balance of the ISM by reprocessing theradiative outputs from stars, providing photoelectrons that heat
the gas, and depleting the gas of refractory elements that are important cooling agents of the ISM. Dust also serves as a catalyst
for chemical reactions, especially the formation of H2 moleculeson the surface of dust grains (Hirashita & Ferrara 2002; Cazaux& Spaans 2004). In addition, the cooling of gas through thermalradiation from dust triggers the fragmentation of a star-forming
cloud into low-mass gas clumps of 0.1Y1 M even for the met1
Department of Cosmosciences, Graduate School of Science, Hokkaido
University, Sapporo 060-0810, Japan; tnozawa@mail.sci.hokudai.ac.jp.
2
Laboratory for Astronomy and Solar Physics, NASA Goddard Space Flight
Center, Greenbelt, MD 20771.
3
Department of Astronomy, School of Science, University of Tokyo,
Bunkyo-ku, Tokyo 113-0033, Japan.
4
Max-Planck-Institut für Astrophysik, 85741 Garching, Germany.
5
Research Center for the Early Universe, School of Science, University ofTokyo, Bunkyo-ku, Tokyo 113-0033, Japan.

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NOZAWA ET AL.

initial mass function (Hirashita et al. 2005). Adopting the dust
models by Nozawa et al. (2003), Nozawa et al. (2006, hereafter
NKH06) investigated the destruction of dust in the early ISM by
the high-velocity shocks driven by SNe and derived the timescale of dust destruction in the early universe as a function of the
explosion energy of SNe and the gas density in the ISM. It should
be pointed out here that these studies implicitly assumed that dust
grains formed in SNe are injected into the ISM without their composition and size distribution being reprocessed.
However, the interaction of the SN ejecta with the surrounding
medium will create a reverse shock that will process the grainsthat condensed in the He core before their injection into the ISM.
Once the newly formed dust grains encounter the reverse shock,they acquire the high velocities relative to the gas and penetrate
into the hot gas created by the passage of the reverse shock andforward shock. These dust grains are eroded by the kinetic sputtering and are also decelerated by the drag force of the gas. Small
grains decelerate efficiently, and become trapped in the hot gas,
where they are efficiently destroyed by thermal sputtering. On
the other hand, large grains can maintain their high velocities,
pass through the shocked gas and the outwardly expanding shock
front, and be injected into the ISM without significant destruction.
The net amount and composition of the dust that is eventually
returned to the ISM by SNe differ substantially from the dust thatwas in the SN ejecta shortly after its formation.
In this paper we study the evolution of dust formed in primordial SNe II and PISNe, considering its processing through thecollisions with the reverse shocks and its transport within supernova remnants (SNRs), based on the dust formation calculations
by Nozawa et al. (2003). The questions that we pose here arewhat fraction of dust grains formed in Population III SNe cansurvive the hostile circumstances within SNRs and how theirsize distributions can be altered by sputtering in the postshock
flow. This subject has not been fully explored to date. Recently,
Bianchi & Schneider (2007) have studied the evolution of newly
condensed grains through the passage of the reverse shock byusing a semianalytical model and have showed that the fractionof dust mass survived ranges between 2% and 20% depending on
the density in the ISM. However, they consider only the dust evolution in the nonradiative phase of SNRs up to about (4Y8) ; 10 4 yr
from the SN explosion, without taking into account the motionof dust relative to gas caused by the drag force, which strongly
affects the destruction process and evolution of dust in SNRs. In
the calculations, we carefully treat the dynamics and destructionof dust and the time evolution of the temperature and density of
the gas within SNRs until 105 Y106 yr extending over a periodof the radiative phase, in order to reveal how much dust is finallyinjected into the ISM or destroyed completely. Although we
focus on Population III SNe in this paper, this study can also
give great insight into the evolution of dust in Galactic SNRs.
In x 2 we describe the initial conditions for the evolution of
SNRs, the model of dust inside the He core, and the physics ofdust and gas within SNRs. In x 3 we present and discuss the results of calculations. In x 4 we discuss the effects of the thicknessof the hydrogen envelope on the evolution of dust in SNRs. Asan application of the result, we investigate the abundance patternsof the second-generation stars formed in the dense shell of Population III SNRs in x 5. The summary is presented in x 6.

Vol. 666

of the ambient gas (Truelove & McKee 1999). In this paper we
focus on the evolution of ejecta expanding into a uniform ambient medium whose elemental composition is primordial. To
investigate the dependence of the efficiency of dust destruction
on the ambient gas density, we consider three cases for the hydrogen number density in the ISM: nH;0 ¼ 0:1, 1, and 10 cm3.
The temperature of gas T0 in the ISM can also affect the evolution of SNRs, since the ambient pressure regulates the deceleration of blast waves. However, we have confirmed that the resultsof calculations are almost independent of the value of T0 , provided that T0 ¼ 10 3 Y105 K. Thus, we assume here T0 ¼ 10 4 K
regardless of the gas density in the ISM, referring to the studies
showing that the radiative feedback from the massive pre-SN stars
can cause the ambient ISM to heat up to T0  10 4 K (Kitayama
et al. 2004; Machida et al. 2005).
The initial conditions for the structures of density and velocity
in the ejecta are taken from the hydrodynamic models of Population III SNe by Umeda & Nomoto (2002). We adopt six SN
models: four SNe II and two PISNe. The explosion energy of
SNe II with Mpr ¼ 13, 20, 25, and 30 M is 10 51 ergs, and thatof PISNe with Mpr ¼ 170 and 200 M is 2 ; 10 52 and 2:8 ;10 52 ergs, respectively. It should be mentioned here that themassive metal-free stars cannot lose significant mass during their
lifetime due to pulsations and line-driven stellar winds, which
are considered to be important at high metallicities (Baraffe et al.
2001). Although Smith & Owocki (2006) have suggested thatthe mass loss of very massive stars above roughly 40Y50 M
may be possible by continuum-driven winds or hydrodynamic
explosions being insensitive to metallicity, the mechanism totrigger such a mass loss is an open question. Thus, we consider
that Population III SNe II and PISNe have retained their thickhydrogen envelopes at the time of explosion.
2.2. Dust Model inside the He Core

2. THE MODEL OF CALCULATIONSIn the ejecta of SNe, dust grains can nucleate and grow only inthe metal-rich cooling gas, and their composition and size distribution largely depend on the elemental abundance inside the
He core (Kozasa et al. 1989). Accordingly, Nozawa et al. (2003)
have calculated the dust formation in Population III SNe by considering two cases for the elemental composition inside the He
core. They found that in the unmixed ejecta with the original onionlike structure, a variety of grain species condense in each layer.
The main grain species are C grain in the carbon-rich He layer;
Al2O3 , Mg2SiO4 , and MgO grains in the O-Mg-Si layer; Al2O3,
MgSiO3, and SiO2 grains in the O-Si-Mg layer; Si and FeS grainsin the Si-S-Fe layer; and Fe grain in the innermost Fe-Ni core. On
the other hand, oxide (Al2O3 and Fe3O4) and silicate ( MgSiO3,
Mg2SiO4, and SiO2) grains are formed in the uniformly mixed
ejecta with C/O < 1, where the efficiency of unity is assumed forthe formation of CO and SiO molecules.
Dust grains inside the He core are never processed by kinetic
or thermal sputtering before they hit the reverse shock because
they move with the same velocities as the gas, and the gas temperature within the He core is too low for dust grains to be destroyed by the thermal sputtering. Therefore, as the initial conditionof dust residing within the He core, we adopt the size distribution, mass fraction, and spatial distribution of each dust species
calculated by Nozawa et al. (2003). In what follows, we refer tothe dust grains created in the unmixed and mixed ejecta as theunmixed grain model and the mixed grain model, respectively.

2.1. The Initial Conditions for the Evolution of SNRs

2.3. Physics of Gas and Dust in SNRs

The evolution of SNRs is described by three characteristic parameters: explosion energy, ejecta mass, and the density profile

The collision of the expanding SN ejecta with the surrounding ISM simultaneously creates a forward shock at the interface

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DUST EVOLUTION IN PRIMORDIAL SNRs

between the ejecta and the ISM and a reverse shock that penetrates into the ejecta. Once the reverse shock encounters dust
grains inside the He core, the dust grains are decoupled from thecomoving gas to ballistically intrude into the hot gas heated by
the reverse shock, and then they are eroded via the kinetic sputtering because of high velocities relative to gas. If dust grains aretrapped into the postshock flow owing to the gas drag, they aredestroyed via the thermal sputtering caused by the thermal motion of gas. These dust particles are also heated by the collisions
with the gas and radiate the thermal emission to cool the postshock gas. The rates of deceleration, erosion by sputtering, andheating of dust grains depend on not only their chemical composition and size but also the temperature and density of the gas
in the postshock flow.
Recently, NKH06 have calculated the dust destruction in thehigh-velocity interstellar shocks driven by SNe in the early universe, by carefully treating the dynamics, erosion, and heating of
dust grains and taking account of their size distribution and thetime evolution of the temperature and density of the gas in thepostshock flow. The present calculations of the dust evolution
within SNRs follow the method described in NKH06 (see NKH06
for details). We briefly mention the outline, focusing on the difference in the cooling function used in the calculations.6
We assume that the spherically symmetric ejecta collides with
the ISM in 10 yr after the explosion. With the initial conditions
described in x 2.1, the time evolution of the gas in SNRs is numerically solved with the flux-splitting method (van Albada et al.
1982; Mair et al. 1988). In the calculations, we include three processes of the radiative cooling in the equation of the conservationof energy. The first is the thermal emission from dust collisionally heated in the postshock flow, and the second is the inverse
Compton cooling, whose rate is calculated at the redshift ofz ¼ 20. The third is the cooling of gas by the atomic process. For
the gas with the primordial composition in the hydrogen envelope and behind the forward shock, we adopt the atomic cooling
function for the zero-metal case given by Sutherland & Dopita(1993) that is limited to the gas temperature of T  10 4 K. In
order to calculate the evolution of the gas in the dense shell thatappears at the later phase of SNRs, we extrapolate the cooling rate of gas at T < 10 4 K as follows. Referring to Machida
et al. (2005), the atomic cooling rate at T < 10 4 K is approximately proportional to T 4 ; the cooling rate decreases from gas ’
1023 ergs cm3 s1 at T ¼ 10 4 K to gas ’ 1027 ergs cm3 s1
at T ¼ 10 3 K. Therefore, we simply evaluate the atomic coolingrate as gas ¼ T44 gas
4 , where T4 is the gas temperature in units ofistheatomic cooling rate at T ¼ 10 4 K. For the
104 K and gas4
metal-rich He core, we assume that the gas is only composed ofoxygen, which is the most abundant gas species inside the He
core, and employ the cooling functions from Smith et al. (2001)
for T  105 K and Raymond & Smith (1977) for T < 105 K. In
the calculations, we ignore the contribution of cooling by metal
ions released from dust by sputtering for simplicity.
6
Note that in the calculation we neglect the effect of Coulomb drag on the
motion of dust: the ratio of the Coulomb drag force to the gas drag force is givenby  2 ln ½Gplasma (s)/Gcoll (s) ( Draine & Salpeter 1979), where  is the dimensionless potential parameter,  is the Coulomb cutoff factor, and s is defined bys 2 ¼ mwd2 /2kT, with m the mass of gas and wd the velocity of dust relative to gas.
Gplasma /Gcoll < 1 for 0 < s < 1 ( Draine & Salpeter 1979), ln   30Y40 in
SNRs ( Dwek & Arendt 1992), and  is evaluated to be 105 /T for the gas temperature of T k105:5 K ( McKee et al. 1987). Thus, the Coulomb drag is negligible
compared with the gas drag for T k106 K; otherwise, it can play an important rolein the deceleration of dust. However, the erosion rate of dust grains by thermal
sputtering quickly decreases at T P106 K ( NKH06). As a result, the Coulomb
drag does not significantly affect the motion and destruction of dust grains considered in this paper.

957

Fig. 1.— Structures of (a) the density and (b) the temperature of the gas at given
times within the SNR generated from the explosion of the star with M pr ¼ 20 M
and expanding into the ISM with nH;0 ¼ 1 cm3 (the standard model). The positions of the forward and reverse shocks are indicated by the downward-pointing
arrows in (a) and (b), respectively.

The dynamics and destruction of dust after colliding with thereverse shocks are calculated as follows. By treating dust as a test
particle and ignoring the effect of charge on dust grains, the deceleration rate of dust due to the gas drag is calculated for eachsize of the dust to evaluate the velocity relative to gas and the position. Then we calculate the dust destruction by sputtering andthe heating by collisions with the gas, using the relative velocity
and the temperature and density of gas at the position. The sputtering yield of each dust species is calculated with the formuladerived by NKH06. Dust grains are considered to be completely
destroyed when their sizes become smaller than the radius of thenominal monomer of condensate. The cooling of gas throughthermal emission of dust is calculated by balancing the heating of
dust resulting from the collisions with electrons. The calculations
are performed by the truncation time at which the forward shock
velocity decelerates below 20 km s1.
3. RESULTS
In this section we present the results of the calculations of dust
evolution within primordial SNRs. In x 3.1 we demonstrate thetime evolution of temperature and density of gas in the SNR, andin x 3.2 we show the transport and destruction of dust grains
within SNRs. In x 3.3 we provide the resulting size distributionof survived dust and elucidate the dependence of the efficiency of
dust destruction on the progenitor mass and the gas density in theISM.
3.1. Time Evolution of the Gas in the SNRs
Figure 1 shows the time evolution of the density ( Fig. 1a) andtemperature ( Fig. 1b) of gas by 2 ; 10 4 yr in the SNR generated
from the explosion of the star with Mpr ¼ 20 M and expanding

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NOZAWA ET AL.

Fig. 2.— Time evolution of (a) the position Rrs and (b) the velocity Vrs of thereverse shock. The thick solid lines represent the results for the standard modelwith Mpr ¼ 20 M and nH;0 ¼ 1 cm3, and the thin solid lines for the model with
Mpr ¼ 170 M and nH;0 ¼ 1 cm3. The results that do not include the cooling by
thermal emission from dust are also shown by the thick and thin dashed lines for
Mpr ¼ 20 and 170 M , respectively. [See the electronic edition of the Journal
for a color version of this figure.]

into the ISM with nH;0 ¼ 1 cm3. The unmixed grain model istaken as the model of dust inside the He core, and the cooling ofgas by dust is taken into account. In what follows, we refer to thismodel as the standard model.
The forward shock resulting from the interaction of the ambient gas with the ejecta of the SN is specified by the steep rise of thegas temperature and the increase of the gas density by 4 times
that in the ISM. The downward-pointing arrows in Figure 1a show
the positions of the forward shock. We can also identify the formation of the reverse shock from the high temperature of gas
heated by the compression, and we indicate its position for eachtime by the downward-pointing arrows in Figure 1b.
The position Rrs (Fig. 2a) and velocity Vrs (Fig. 2b) of thisreverse shock as a function of time are depicted by the thick solidlines in Figure 2. The reverse shock is decelerated by the shocked
gas in the ejecta while it initially expands outward, and then returns back at a distance of 5 pc (1:5 ; 1019 cm) with the velocity of a few hundred kilometers per second. The trajectory of
the reverse shock is affected by the detailed structure of density
in the ejecta. The collision with the locally high-density gas inside the He core causes the reverse shock to move outward again
at 5200 yr. After 1:1 ; 10 4 yr, the reverse shock goes inward
through the He core, increasing its velocity up to >1000 km s1.
Hence, dust grains crossing the reverse shock acquire the different velocities relative to gas, depending on the time of collision
with the reverse shock, and are efficiently eroded by the kinetic
sputtering if the relative velocity is 500Y1300 km s1.

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It can be seen from Figure 1 that the temperature of the gas in
the region between the forward and reverse shocks is higher than
106 K. Thus, dust grains staying in this region are subject to thethermal sputtering. However, the erosion rate of dust decreases
as the SNR evolves because the density decreases with time.
Around the truncation time (’8 ; 105 yr for the standard model),the gas density within the SNR is more than 100 times lower thanthat in the ISM, and the gas temperature becomes low (several
times 105 K) enough for dust grains not to be sputtered efficiently; thus, the destruction of dust via the sputtering is extremely inefficient.
The influence of the cooling by dust on the SNR evolution isclarified by comparing the results of calculations with and without
the cooling by dust emission. The evolution of the reverse shock
without the dust cooling for Mpr ¼ 20 M and nH;0 ¼ 1 cm3 isshown by the thick dashed lines in Figure 2, where the coolingof gas by dust can cause the velocity of the reverse shock to be
reduced by 10%. The thin lines in Figure 2 show the evolutionof the reverse shock penetrating into the ejecta of the PISN with
Mpr ¼ 170 M calculated for nH;0 ¼ 1 cm3. Because the thermal emission from dust increases with increasing dust mass,
the effects of cooling by dust are significant for the remnants of
PISNe, where the mass of dust formed in the ejecta is a few tensof solar masses. As we can see from the figure, the velocity of
the reverse shock including dust cooling (thin solid line) decreases
to 0.6 times that not including the cooling (thin dashed line) at
k7000 yr. In addition, the dust cooling decreases the gas temperature by 20%, compared with that calculated without dust
cooling. However, it should be noted that the efficiency of dust
destruction is little affected by the dust cooling because most of
the dust grains are predominantly destroyed by the thermal sputtering and the erosion rate is not sensitive to the gas temperature
as long as T > 106 K ( NKH06). Note that the cooling by theoxygen line has no influence on the results, since the temperature within the He core during the passage of the reverse shock
is above 107 K, where the dominant cooling process of gas is
free-free emission.
3.2. Transport and Destruction of Dust in SNRs
The time evolutions of the positions (Fig. 3a) and sizes (Fig. 3b)of dust grains within the SNR for the standard model are given
in Figure 3. In Figure 3a, the trajectories of the forward andreverse shocks are also depicted by the thick solid lines, alongwith the position of the surface of the He core. Among nine dust
species in the unmixed grain model are shown C, Mg2SiO4, andFe grains with the initial sizes of 0.01 m (dotted lines), 0.1 m(solid lines), and 1 m (dashed lines). Each grain species initially moves coupling with the gas with the velocity of 1300,
900, and 400 km s1 for C, Mg2SiO4, and Fe grains, respectively, and collides with the reverse shock at 3650 yr for C grains
formed in the outermost He core, 6300 yr for Mg2SiO4 grains in theoxygen-rich layer, and 13,000 yr for Fe grains condensed in the
innermost He core.
The collision time of the reverse shock with dust grains depends on the initial velocity and position of dust, the thicknessof the hydrogen envelope, and the density in the ISM. Figure 4
gives the collision time tcoll of the reverse shock with the He corefor different progenitor mass and gas density in the ISM. We cansee that the collision time is shorter for PISNe than SNe II, in
spite of the fact that PISNe have the thicker hydrogen envelopes.
The reason is that the gas velocities (2000Y3000 km s1) at theoutermost He core for PISNe with the explosion energies higher
than 1052 ergs are a few times higher than those for SNe II. For
nH;0 ¼ 0:1Y10 cm3, the collision times are ’103 Y104 yr andNo. 2, 2007

DUST EVOLUTION IN PRIMORDIAL SNRs

959

Fig. 4.— Collision time tcoll of the reverse shocks with the He core vs. theprogenitor stellar mass for different gas density in the ISM. The results for nH;0 ¼
0:1, 1, and 10 cm3 are connected by the dot-dashed, dashed, and dotted lines,
respectively. [See the electronic edition of the Journal for a color version of thisfigure.]Fig. 3.— Time evolutions of (a) the positions and (b) the ratios of size to theinitial size of dust grains within the SNR for the standard model. The positionsof the forward and reverse shocks are depicted by the thick solid lines in (a),along with the position of the surface of the He core. Among nine dust species
for the unmixed grain model are shown C, Mg2SiO4, and Fe grains with initial
sizes of 0.01 m (dotted lines), 0.1 m (solid lines), and 1 m (dashed lines).

decrease with increasing ambient gas density. Note that this result is not consistent with the observations of the Cas A SNR,
where thermal emission from dust heated by the reverse shock
has already been detected at ’330 yr after the explosion (Enniset al. 2006 and references therein). This is because the progenitor
of the Cas A is believed to have lost the considerable hydrogenenvelope during their evolution (Young et al. 2006), in contrast
to the Population III SNe considered in this paper. We discuss theeffect of the thickness of the hydrogen envelope on the evolutionof dust in the SNR in x 4.
The fates of dust grains within SNRs heavily depend on theirinitial sizes aini , as well as the chemical composition reflecting
the difference in the sputtering yield and bulk density, as shownin Figure 3. For the standard model, the relatively small grains
with aini ¼ 0:01 m are efficiently decelerated due to the gas
drag and are fully trapped into the hot plasma to be completely
destroyed by the thermal sputtering. Note that the gas drag on
grains with small radii is more efficient than that on larger grains
because the deceleration rate of a grain is inversely proportional
to its size (NKH06). Actually, the grains with the initial sizes lessthan 0.05 m are trapped into the hot gas between the forward
and reverse shocks and continue to be eroded by the thermal sputtering even at over 105 yr until they are completely destroyed.
Larger grains of aini ¼ 0:1 m undergo the kinetic and thermal
sputtering while streaming in the hot gas. Thanks to the high bulk
density, Fe grains with aini ¼ 0:1 m are injected into the ISM,
reducing the size by 52%. On the other hand, C and Mg2SiO4
grains with aini ¼ 0:1 m are trapped and eroded by the thermal
sputtering in the denser region behind the forward shock, andtheir surface layers whose thicknesses are 43% and 69% of theirinitial sizes are eroded, respectively, until 2 ; 105 yr when the
SNR enters into the radiative phase and the dense SN shell isformed behind the forward shock. These dust grains remain in

the dense shell without further processing because the gas cools
down quickly below 106 K. Thus, the decrease of sizes of thesegrains is truncated at a given size, and the erosion of dust withaini ¼ 0:05Y0:2 m results in the final size of 0.001Y0.1 m,
depending on their initial sizes. For 1 mYsized C, Mg2SiO4 ,and Fe grains, the kinetic sputtering reduces their sizes by 0.7%,
6%, and 8%, respectively. Note that large grains with aini k
0:2 m can go across even the forward shock and be injected
into the ISM because the deceleration due to the gas drag is very
inefficient.
We should mention here that the degree of the erosion of dust
is a complex function of the initial position and initial size of thedust, as well as the sputtering yield. Fe grains formed in the innermost He core and traveling through the oxygen-rich gas undergo
the efficient erosion, since the sputtering yield by an oxygen ion is50 times larger than that by a proton. In contrast, the degree ofthe erosion of C grains in the outermost He core is relatively small
because they can quickly escape from the He core after the collision with the reverse shock and also have the sputtering yield
lower than those of other dust species. Furthermore, without being decelerated efficiently, the larger grains with high velocities
relative to gas are more efficiently eroded by sputtering in the relatively dense region near the forward shock front. However, thegrains with sizes larger than a given size can evade the erosion in
the shocked hot gas within SNRs and are expelled into the ISM.
Although the processing of dust in the ISM is not the main
subject of this paper, here we simply show the processing of dust
injected into the ISM as a consequence of dust evolution in SNRs.
Dust grains injected into the ISM can be consumed through the
kinetic sputtering because of the difference in velocity between theambient cool gas and the dust grains, while the grains can also be
decelerated by the direct collisions with the gas. In this case, theratio of the final radius aBn to the initial size aini of dust is dependent only on the escape velocity w0, defined as the velocity
with which dust is injected into the ISM passing through theforward shock, and is given by
"
#
!Z
w0 X
2msp
aBn
dw
0
¼ exp Ai Yi (w)
;
ð1Þ
w
aini
3g
wf
i

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NOZAWA ET AL.

Vol. 666

Fig. 5.— Ratio of the final size aBn to the initial size aini of dust eroded by the
kinetic sputtering in the ISM with the primordial gas composition as a function of
the escape velocity w0, where the final relative velocity wBn is taken as 10 km s1.
The results are shown for C, Si, Mg2SiO4, Fe3O4, and Fe grains. [See the electronic edition of the Journal for a color version of this figure.]

where msp is the average atomic mass of the elements sputteredfrom the grain, g is the mean molecular weight of the gas, andYi 0 (w) is the sputtering yield at normal incidence by gas species i
whose number abundance is Ai .
Figure 5 shows the results calculated by equation (1) for theprimordial gas composition as a function of the escape velocity. In the calculations, the final relative velocity wBn is taken as
10 km s1, which is small enough for dust grains not to be erodedby the kinetic sputtering. Also we assume that the escape velocity equals the initial velocity inside the He core, since very large
grains are ejected to the ISM with high velocities, not being decelerated efficiently. Hence, the calculated aBn gives the lower
limit of the final size realized in the ISM. The final size acquiredby each dust species is different, depending on the sputtering yieldYi0 and the average atomic mass msp , and decreases with increasing escape velocity. The ratio of the final size to the initial size
is ’0.8 for C grains with w0  1300 km s1, ’0.5 for Mg2SiO4
grains with w0  900 km s1, and ’0.5 for Fe grains with w0 
400 km s1. Thus, the sizes of very large grains supplied fromSNe are decreased to 0.5Y0.8 times those at the time of the ejection but are not completely destroyed in the ISM. For PISNe with
explosion energies higher than 1052 ergs, the sizes of Fe grains
with the initial velocities of ’1000 km s1 decrease by 70% in the
ISM, although the sizes of C and Mg2SiO4 grains whose initial
velocities are in the range of 2000Y3000 km s1 are not significantly different from those calculated for the standard model. Notethat dust grains in the ISM are also processed by the high-velocity
interstellar shocks driven by the ambient SNe ( NKH06), whichis the major mechanism of the dust destruction in the ISM.
3.3. Efficiency of Dust Destruction
The results described in x 3.2 imply that the size distribution ofsurvived dust is greatly deficient in small-sized grains, comparedwith that at the time of dust formation. In Figure 6 we present theinitial size distribution at the time of dust formation ( Fig. 6a) andthe size distribution of dust at the truncation time (Fig. 6b) for the
standard model. The comparison of these figures clearly indicates that grains with radii below a few tens of angstroms are
missing for almost all dust species. In particular, Al 2O3 grainsare completely destroyed because their initial sizes are smaller

Fig. 6.— Size distribution of each dust species for the standard model: (a) for
the initial size distribution before destruction and (b) for the resulting size distribution of survived dust after destruction. [See the electronic edition of the
Journal for a color version of this figure.]

than 0.02 m. We can also see that the sizes of the relatively large
grains are shifted to small sizes due to the erosion by sputtering.
It should be pointed out here that the size distribution of survived
dust is different from that by Bianchi & Schneider (2007): they
have found that the final size distribution shows a flattening toward smaller sizes without any abrupt truncation. The main reason
for this difference is considered as follows. Bianchi & Schneider(2007) assumed that newly formed grains remain confined andtrapped at their initial positions in the ejecta. Therefore, dust grains
remaining at their initial positions cease to be eroded by sputtering on the timescale of (4Y8) ; 10 4 yr due to the decrease of thegas density caused by expansion. As shown in x 3.2, our results
show that even small grains of aini  0:05 m penetrate into the
hot plasma between the forward and reverse shocks and aretrapped and completely destroyed in the hot gas with relatively
high density. On the other hand, the erosion of grains with theradii of 0.05Y0.2 m produces the grains with the final sizes of
0.001Y0.1 m remaining in the dense shell.
The critical size below which dust is completely destroyed in
SNRs is sensitive to the gas density in the ambient medium. Although the critical size weakly depends on the dust species andtheir initial positions, we can roughly estimate the average critical

No. 2, 2007

DUST EVOLUTION IN PRIMORDIAL SNRs

TABLE 1The Main Results of Calculations for the Unmixed Grain Model
Mpr
(M)

dest

ejectshellttr(106 yr)H
Mshell4(10 M)TABLE 2The Main Results of Calculations for the Mixed Grain Model
Mpr
(M)

dest

3

0.240
0.386
0.198
0.383
0.562
0.746

0.756
0.610
0.800
0.614
0.438
0.247

0.004
0.004
0.002
0.003
<0.001
0.007

0.698
0.752
0.517
0.785
0.958
0.997

0.256
0.231
0.474
0.206
0.040
0.002

2.13
2.05
2.12
2.11
4.58
5.13

2.96
2.58
2.89
2.83
34.4
50.2

13..........................
20..........................
25..........................
30..........................
170........................
200........................

0.775
0.664
0.747
0.569
0.742
0.751

0.936
0.942
0.851
0.920
0.999
1.00

0.004
0.013
0.103
0.042
<0.001<0.001

0.212
0.311
0.245
0.415
0.258
0.248

0.013
0.025
0.008
0.016
<0.001
0.001

2.14
2.05
2.10
2.10
4.55
5.12

2.96
2.57
2.82
2.80
33.7
49.8

0.814
0.767
0.800
0.788
1.81
2.00

2.07
1.71
1.95
1.86
24.8
34.2

0.309
0.301
0.316
0.308
0.726
0.817

1.33
1.21
1.38
1.29
17.8
26.0

nH;0 ¼ 1 cm3
0.046
0.017
0.009
0.009
0.002
0.001

0.814
0.767
0.800
0.790
1.81
2.02

2.07
1.72
1.97
1.88
25.4
35.2

13..........................
20..........................
25..........................
30..........................
170........................
200........................

0.995
0.907
0.988
0.920
0.993
0.989

nH;0 ¼ 10 cm3
13..........................
20..........................
25..........................
30..........................
170........................
200........................

shellH
Mshell4(10 M)nH;0 ¼ 0:1 cm

nH;0 ¼ 1 cm3
13..........................
20..........................
25..........................
30..........................
170........................
200........................

ejectttr(106 yr)3nH;0 ¼ 0:1 cm
13..........................
20..........................
25..........................
30..........................
170........................
200........................

961

0.060
0.045
0.046
0.038
<0.001<0.001

0.001
0.075
0.009
0.060
0.007
0.011

0.004
0.018
0.003
0.020
<0.001<0.001nH;0 ¼ 10 cm3
0.308
0.301
0.310
0.309
0.723
0.825

1.31
1.21
1.33
1.31
18.0
27.1

Notes.— For a given nH;0 , the mass fraction of dust destroyed dest , piled up
in the dense shell shell , and ejected to the ISM eject as a function of the progenitor mass Mpr for the unmixed grain model. The truncation time ttr and the hyH
in the dense SN shell are given by the units of 106 yr anddrogen mass Mshell
104 M, respectively.

size for different gas density in the ISM. For nH;0 ¼ 0:1 cm3, theupper limit of the initial size of dust completely destroyed is0.01 m, and the lower limit of that ejected to the ISM is0.03 m. For nH;0 ¼ 10 cm3, the grains with aini P 0:2 m
are destroyed, and the grains with aini k 0:5 m are injected in
the ISM. Note that the above critical sizes are true for the grain
species except for C grains. The critical size of C grains is 0.006,
0.02, and 0.07 m for nH;0 ¼ 0:1, 1, and 10 cm3, respectively,
and is a few times smaller than other dust species because C grains
are located at the outermost He core and also have the lower
erosion rate by sputtering. Note that the initial sizes of Fe grains
injected into the ISM are smaller than those of others by a factorof 2 because of the high bulk density and are k0.02, 0.1, and0.25 m for nH;0 ¼ 0:1, 1, and 10 cm3, respectively.
On the other hand, the critical size for each grain species is almost independent of the progenitor mass as long as the explosion
energy of SNe is the same because the time evolution of temperature and density of gas within SNRs is similar. For PISNe with
explosion energies higher than 1052 ergs and more massive hydrogen envelopes, the critical size increases approximately by afactor of 3, compared with that for SNe II. However, the initialsize of dust ejected to the ISM is less than 2 times that for SNe II
because the high initial velocity inside the He core makes thedust grains easily escape from SNRs. These results lead to theconclusion that the large-sized grains dominate the mass of dust
injected from SNe into the ISM.
Tables 1 and 2 summarize the mass fraction of dust destroyeddest , piled up in the dense shell shell , and ejected to the ISM eject
for the unmixed and mixed grain models, respectively. In Figures 7a and 7b we also present the total mass of survived dust for

13..........................
20..........................
25..........................
30..........................
170........................
200........................

1.00
0.988
1.00
0.995
1.00
1.00

0.
0.002
0.
<0.0010.
0.

<0.0010.010<0.001
0.005<0.0010.

Note.— Same as Table 1, but for the mixed grain model.

both grain models, respectively, along with their initial total mass.
We can first see that the mass of dust destroyed increases with increasing surrounding gas density. In particular, for nH;0 ¼ 10 cm3,
all or almost all (k85%) of dust grains formed in the ejecta aredestroyed, and the mass of survived dust is less than 0.1 M forall models considered in this paper. The reason for this is as follows: the erosion of dust takes place in the hot gas between theforward and reverse shocks, whose density increases with the ambient gas density. Therefore, the higher ISM gas density leads tothe efficient erosion and deceleration of dust through the more frequent collisions with the hot gas. Next, we find that the mass fraction of dust destroyed is generally higher for the mixed grain model
than the unmixed grain model; for SNe II with nH;0 ¼ 1 (0.1) cm3,
dest ¼ 0:5Y0:8 (0.2Y0.4) for the unmixed grain model, whiledest ¼ 0:9Y0:99 (0.57Y0.78) for the mixed grain model. This
reflects the fact that the mixed grain model lacks the grains larger
than 0.05 (0.01) m in comparison with the unmixed grain model.
Finally, it can be seen that dust grains formed in PISNe are more
efficiently destroyed than those in SNe II, since the newly formed
dust grains are dominated by the small-sized grains and the criticalsize is much larger. Thus, for nH;0 ¼ 1 cm3, the mass of dust
survived in PISNe is 0.1Y1 M for both grain models and isalmost the same as that (0.07Y0.5 M) in the SNe II, although themass of dust formed in PISNe is a few tens times higher than thatin SNe II. Note that the dust destruction by reverse shocks ismore effective than that by high-velocity interstellar shocks forthe dust grains with the same size distribution (NKH06).
The destruction efficiency, defined as the ratio of the mass ofdust destroyed to the initial dust mass, is given in Tables 3 and 4
for each dust species in the unmixed and mixed grain model, respectively. As mentioned above, the efficiency of dust destruction is greatly influenced by what fraction of the initial dust mass
is occupied by the sizes larger than the critical size. Thus, the962

NOZAWA ET AL.
distributions are not sensitive to the metallicity of progenitor
stars ( Todini & Ferrara 2001; Nozawa 2003). Also the cooling
function of gas for Z  103 Z is independent of the metallicity(Sutherland & Dopita 1993). Thus, the results of calculations
presented in this paper can be directly applied to the evolution ofdust in the ejecta of SNe II expanding into the ambient medium
whose metallicity is less than 103 Z. The increase of the metallicity in the ambient medium to the solar value greatly enhances
the cooling of gas behind the forward shock and causes the timeof the transition from nonradiative phase to radiative phase to be
reduced to less than half of that for the zero-metallicity case.
Nevertheless, the destruction efficiency of each grain species for
Z ¼ Z decreases at most by 15% of that for Z ¼ 0. Therefore,
the results of the present study could be useful for evaluating thedust evolution in SNRs generated from SNe II, regardless of theinitial metallicity of progenitor stars and ambient medium. However, as is demonstrated in the next section, the thickness of thehydrogen envelope strongly affects the motion and destruction ofdust within SNRs.
4. THE EFFECT OF THE THICKNESS OF THE HYDROGENENVELOPE ON THE EVOLUTION OF DUST IN SNRs

Fig. 7.— Total mass of survived dust for the various progenitor masses andthe gas density in the ISM (a) for the unmixed grain model and (b) for the mixed
grain model. The results for nH;0 ¼ 0:1, 1, and 10 cm3 are connected by the dotdashed, dashed, and dotted lines, respectively. The solid lines are for the initial
total mass of dust at the time of dust formation. [See the electronic edition of the
Journal for a color version of this figure.]

destruction efficiency for a given dust species is very sensitive tothe initial size distribution. Note that it is difficult to find the clear
dependence of the destruction efficiency of each dust species on
the progenitor mass because the size distribution of dust at thetime of dust formation is different from model to model. However, for example, the efficiency of destruction of Al2O3 grains
with aini P 0:02 m is 1 for almost all cases considered in thispaper. For the unmixed grain model, FeS and MgSiO3 grains arealso predominantly destroyed. On the other hand, Fe, Si, and C
grains, for which most of the mass is locked into the grains larger
than 0.05 m, have relatively small destruction efficiencies. For
the mixed grain model, SiO2 grains are the main dust species thatare left in SNRs and /or are injected into the ISM. Therefore, we
conclude that the chemical composition, size distribution, andamount of dust grains supplied from SNe to the ISM are quite
different from those at the time of dust formation.
Here we discuss the dependence of the metallicity on the present results of calculations. First, it should be pointed out thatthe species of dust formed in the ejecta of SNe II and their size

As mentioned in x 3.2, for the SNe with the thick hydrogenenvelopes, it takes more than 1000 yr for the reverse shocks tocollide with the dust condensed inside the He core. On the other
hand, the infrared observations of the Cas A SNR ( Dwek et al.
1987; Lagage et al. 1996; Arendt et al. 1999; Douvion et al.
2001; Hines et al. 2004; Ennis et al. 2006) have revealed thethermal emission from warm dust formed in the ejecta at ’330 yr
after the explosion. This difference of the time at which dust
grains inside the He core are swept up by the reverse shocks is
attributed to the difference in the thickness of the hydrogen envelope of SNe. Therefore, in this section we investigate the effecton the evolution of dust in the SNR.
In order to illustrate the evolution of dust in the SNR generated
from the SN whose hydrogen envelope is very thin, we adopt
the model of ejecta with Mpr ¼ 20 M from Umeda & Nomoto(2002) and modify it by artificially reducing the mass of thehydrogen envelope from 13 to 0.7 M at the time of explosion.
Keeping the structure of the density, we simply scale up the gas
velocity so that the explosion energy can equal 1051 ergs. We also
assume that the dust inside the He core is the same as that formedin the primordial SN II with Mpr ¼ 20 M.
Figure 8 illustrates the trajectories (Fig. 8a) and time evolutions of sizes (Fig. 8b) of C, Mg2SiO4, and Fe grains with aini ¼
0:01 and 0.1 m in the SNR calculated for nH;0 ¼ 1 cm3. As
can be expected, because the hydrogen envelope is very thin andthe initial velocities of dust grains are very high (2000Y5000 km s1
depending on their initial positions), the dust grains inside the He
core collide with the reverse shock at much earlier times: 120 yr
for C grains, 570 yr for Mg2SiO4 grains, and 1300 yr for Fe grains.
Contrary to SNe II with thick hydrogen envelopes, even the grains
with aini ¼ 0:1 m can be ejected to the ISM without decreasing
their sizes significantly: C and Mg2SiO4 grains with aini ¼ 0:1 m
reduce their sizes only by less than 6%, while the sizes of Fe
grains with aini ¼ 0:1 m decrease by 18% because the time they
stay in the hot gas is long, compared with C and Mg2SiO4 grains.
The grains with aini ¼ 0:01 m are trapped into the hot gas andare completely destroyed. In this case, the critical size below which
dust is completely destroyed is 0.04 m, and the lower limit of
the initial size of dust supplied to the ISM is 0.04 m, which is
5 times smaller than that for a SN II. Therefore, the thin hydrogen envelope, as well as the high initial velocity of dust, causes almost all survived dust grains to be injected into the ISM without

TABLE 3
The Destruction Efficiency of Each Dust Species for the Unmixed Grain Model
Mpr
(M)

Fe

Si

FeS

MgSiO3

SiO2

Al2O3

Mg2SiO4

MgO

C

0.297
0.518
0.086
0.277
0.441
0.438

1.00
1.00
0.999
0.992
1.00
1.00

0.349
0.437
0.201
0.543
0.776
0.865

0.615
0.440
0.520
0.412
0.772
0.820

0.048
0.146
0.080
0.299
0.284
0.210

0.882
0.926
0.369
0.745
0.998
0.992

1.00
1.00
1.00
1.00
1.00
1.00

0.964
0.961
0.719
0.989
1.00
1.00

0.997
0.925
0.934
0.946
1.00
1.00

0.520
0.447
0.284
0.842
0.985
0.996

0.995
1.00
1.00
0.958
1.00
1.00

1.00
1.00
1.00
1.00
1.00
1.00

1.00
1.00
0.998
1.00
1.00
1.00

1.00
1.00
1.00
1.00
1.00
1.00

0.893
0.896
0.727
0.990
1.00
1.00

3

nH;0 ¼ 0:1 cm
13................................
20................................
25................................
30................................
170..............................
200..............................

0.209
0.210
0.089
0.099
0.644
0.712

0.257
0.127
0.061
0.077
0.273
0.787

0.939
0.881
0.693
0.636
1.00
1.00

0.892
0.945
0.570
0.901
0.987
0.990
nH;0 ¼ 1 cm3

13................................
20................................
25................................
30................................
170..............................
200..............................

0.715
0.661
0.379
0.405
0.999
0.989

0.660
0.493
0.289
0.349
0.872
0.999

1.00
0.999
0.984
0.970
1.00
1.00

0.998
0.999
0.968
0.997
1.00
1.00
nH;0 ¼ 10 cm3

13................................
20................................
25................................
30................................
170..............................
P200 ...........................

0.958
0.961
0.861
0.824
1.00
1.00

0.894
0.851
0.699
0.706
0.999
1.00

1.00
1.00
1.00
1.00
1.00
1.00

1.00
1.00
1.00
1.00
1.00
1.00

Note.— For a given nH;0 , the mass fraction of dust destroyed as a function of the progenitor mass Mpr for each grain species in the unmixed grainmodel.

TABLE 4
The Destruction Efficiency of Each Dust Species
for the Mixed Grain Model
Mpr
(M)

Al2O3

MgSiO3

Mg2SiO4

SiO2

Fe3O4

0.868
0.788
0.877
0.620
0.957
0.995

0.676
0.518
0.596
0.461
0.585
0.615

0.788
0.992
0.999
0.999
1.00
0.999

0.999
0.977
1.00
0.951
1.00
1.00

0.988
0.850
0.976
0.875
0.989
0.983

0.999
1.00
1.00
1.00
1.00
1.00

1.00
1.00
1.00
0.996
1.00
1.00

0.999
0.980
1.00
0.976
1.00
1.00

1.00
1.00
1.00
1.00
1.00
1.00

3

nH;0 ¼ 0:1 cm
13..........................
20..........................
25..........................
30..........................
170........................
200........................

1.00
1.00
1.00
0.997
1.00
1.00

0.862
0.913
0.910
0.802
0.961
0.984
nH;0 ¼ 1 cm3

13..........................
20..........................
25..........................
30..........................
170........................
200........................

1.00
1.00
1.00
1.00
1.00
1.00

0.999
0.996
1.00
0.994
1.00
1.00
nH;0 ¼ 10 cm3

13..........................
20..........................
25..........................
30..........................
170........................
P200 .....................

1.00
1.00
1.00
1.00
1.00
1.00

1.00
1.00
1.00
1.00
1.00
1.00

Note.— Same as Table 3, but for each grain species in the mixed grain model.

Fig. 8.— Time evolutions of (a) the positions and (b) the ratios of size to theinitial size of dust grains within the SNR from the SN with the hydrogen envelope of 0.7 M and the explosion energy of 10 51 ergs for nH;0 ¼ 1 cm3. The
positions of the forward and reverse shocks are depicted by the thick solid lines
in (a), along with the position of the surface of the He core. Among nine dust
species for the unmixed grain model are shown C, Mg2SiO4, and Fe grains with
the initial sizes of 0.01 m (dotted lines) and 0.1 m (solid lines).

964

NOZAWA ET AL.

being trapped into the gas within the SNR. The mass fraction ofdust destroyed is 0.38, which is lower than 0.75 for the standard
model, and thus more dust grains are supplied to the ISM. The
result of calculation shows that the fates of dust grains formedin the ejecta strongly depend on the thickness of the hydrogenenvelope.
However, we adopt the model of dust formed in a SN II andalso consider the uniform ambient medium. The significant massloss of massive stars during their evolution results in a circumstellar medium that is not uniform and homogeneous. In addition, the time evolution of the temperature and density of gas in
the ejecta of SNe without hydrogen envelopes such as Type Ib/c
SNe is expected to be different from that in SNe II, which influences the dust formation in the ejecta. Therefore, we must clarify
the size distribution and amount of dust grains formed in the ejecta
to investigate the dependence of the evolution of dust on the typeof SNe. This subject will be reported in a forthcoming paper.
5. ELEMENTAL ABUNDANCESOF THE SECOND-GENERATION STARS
Some extremely metal-poor ( EMP) stars with ½Fe/H P 2:5
discovered in the Galactic halo have peculiar abundance patterns
showing modest or large (1Y100 times) enhancements of C, N,
O, Mg, and Si relative to solar ( Venkatesan et al. 2006 and references therein). In particular, two hyperYmetal-poor (HMP) stars
with ½Fe/H P 5, HE 01075240 (½Fe/H ¼ 5:2; Christlieb
et al. 2002) and HE 13272326 (½Fe/H ¼ 5:4; Frebel et al.
2005), show extreme (k10 2 times) overabundances of C, N, andO relative to iron. Because the elemental composition of HMP
stars expected to be the very early generation may strongly reflect the nucleosynthesis in Population III stars, several scenarios
have been proposed to explain the origin of elemental abundances in low-mass HMP stars: the mixing fallback in a corecollapse SN (Umeda & Nomoto 2005; Iwamoto et al. 2005), thenucleosynthesis and mass transfer in a first-generation binary
star (Suda et al. 2004; Komiya et al. 2007), the pollution by thegas with heavy elements in the ISM (Shigeyama et al. 2003), andthe combinations of these scenarios described above (Christlieb
et al. 2004).
Recently, Venkatesan et al. (2006) have proposed that EMP
stars are the second-generation stars formed in the dense shell ofprimordial SNRs and their peculiar abundances can be reproducedby the segregated transport of newly formed dust decoupled fromthe metal-rich gas in SNe. Adopting the dust models by Todini &Ferrara (2001) and Schneider et al. (2004), they calculated the
sputtering and the transport of dust driven by the UV radiation
field from the stellar cluster within a SNR. They have concluded
that the progenitor mass range of 10Y150 M qualitatively explains the enhancement of the elements composing dust grains (C,O, Mg, and Si) in EMP stars, although they did not compare theirresults with the abundance data on these metal-poor stars.
The results of the transportation and destruction of dust given
in x 3.2 show that all dust grains remaining in primordial SNRs
without being completely destroyed by sputtering can be accumulated in the dense SN shell at 10 5 Y10 6 yr after the explosion.
Thus, it is considered that the formation of the second-generationstars with solar mass scales could be possible in the shell contaminated with dust grains, as is investigated by Schneider et al.
(2006). In this case, we can expect that the elemental compositions of dust grains piled up into the dense shell reflect the metalabundance patterns of the second-generation stars.
The iron-bearing dust species with the most important element Fe are Fe and FeS grains for the unmixed grain model andFe3O4 grains for the mixed grain model. Note that C grains

Vol. 666
TABLE 5
Elemental Abundances in SN Shell

Mpr
(M)

[ Fe/ H ][C/ Fe][O/ Fe][ Mg / Fe][Si / Fe]

0.2300.034
0.500
0.739

1.92
0.410
0.5520.866

0.459
1.16
0.407
1.09

1.01
1.87
0.989
1.26

3.89
1.80
0.232
1.23

0.599
2.14
2.34
2.66

3

nH;0 ¼ 0:1 cm
13........................
20........................
25........................
30........................

6.43
5.20
5.90
5.56

0.274
0.117
1.11
0.566

0.699
0.595
1.42
0.043nH;0 ¼ 1 cm3
13........................
20........................
25........................
30........................

5.15
5.53
5.23
5.11

1.11
0.992
1.09
0.797

0.5550.585
0.4120.242

nH;0 ¼ 10 cm3
13........................
20........................
25........................
30........................

4.13
4.92
5.10
5.11

0.284
0.946
1.60
0.207

2.54
2.15
0.122
0.375

Note.—[ Fe/ H ] and abundances of C, O, Mg, and Si relative to Fe in theshell of primordial Type II SNRs for given Mpr and nH;0 with the unmixed grainmodel.

cannot be formed in the mixed ejecta because the ejecta is
oxygen-rich, and Fe3O4 grains with aini P 0:05 m are dominantly
destroyed in the postshock flow and are rarely accumulated in the
SN shell for nH;0 ¼ 1 and 10 cm3. Hence, we show only the results calculated for the unmixed grain model. In addition, Fe
and FeS grains are not significantly piled up in the shell of PISN
remnants, since most of them are completely destroyed or are
injected into the ISM. Thus, we focus on the results for Type II
SNRs.
The abundances of C, O, Mg, and Si relative to Fe in the denseshell are summarized in Table 5, where we neglect the contribution of metal atoms sputtered from the grains crossing the denseshell because the largest sized grains are only eroded by less thanH
1% of their radii. The hydrogen mass in the dense SN shell Mshellat the truncation time is given in Table 1. It can be seen from
Table 5 that all models considered here predict the value of [Fe/H]
less than 4, and most of them exhibit the value of [ Fe/ H ] ranging from 6 to 5. Thus, two HMP stars are considered to beformed in the dense shell of primordial SNRs. For the ninemodels with 6  ½Fe/ H  5, the abundances of Mg and Si
are in the range of 1:2  ½Mg/Fe  1:2 and 0:6  ½Si/Fe 
2:7, respectively, and eight models can produce the overabundances of Mg and/or Si. This result suggests that the dust formedin the unmixed ejecta of SNe II can be responsible for the peculiar abundance patterns of Mg and Si in HMP stars. Althougha few models (20 and 30 M for nH;0 ¼ 1 cm3 and 25 M for
nH;0 ¼ 0:1 cm3) result in the overabundances of C and O, aswell as Mg and Si, [C/ Fe] and [O/ Fe] are limited to <1.6 and<0.6, respectively.
For comparison, we apply the present calculations to the models of dust formation in the SN II with Mpr ¼ 22 M by Todini& Ferrara (2001) and in the PISN with Mpr ¼ 195 M by Schneider
et al. (2004). Because the sizes of the dust grains calculated bythem are considerably small (P0.04 m) except for the C grain,
the grain species that can survive the destruction through the collisions with the reverse shocks is only the C grain for the ambientgas density of nH;0 ¼ 0:1Y10 cm3. Thus, their dust models

No. 2, 2007

DUST EVOLUTION IN PRIMORDIAL SNRs

cannot explain the abundance patterns of the metals except for C
observed in HMP and EMP stars.
6. SUMMARY
We investigate the evolution of dust formed at Population III
SN explosions through the collision with the reverse shocks
within SNRs. We adopt the models of dust grains obtained fromthe calculation of dust formation in Population III SNe by Nozawa
et al. (2003) and take into account their spatial distribution andsize distribution as the initial condition. The calculations carefully treat the dynamics, erosion, and heating of dust grains, andthe evolution of temperature and density of gas in sphericallysymmetric shocks is solved as a function of time. We also discuss
the effect of the thickness of the hydrogen envelope on the evolution of dust in the SNR. Furthermore, from the analysis of thetransport and destruction of dust within SNRs, we investigate theabundances of elements related to dust in the second-generationstars formed in the dense shell of primordial SNRs.
Our main results are summarized as follows:
1. The time that the reverse shock encounters the dust thatcondensed inside the He core depends on the thickness of the H
envelope that was retained by the progenitors of the Population
III SNe. If the progenitor stars did not undergo significant massloss, the reverse shock will encounter the dust ’103 Y104 yr after
the explosion, depending on the density of gas in the ISM.
2. Once dust grains inside the He core collide with the reverse
shocks, they will follow different trajectories depending on theirinitial sizes, resulting in the differential transport and destructionof dust in SNRs. For Type II SNRs expanding into the ISM witha density of nH;0 ¼ 1 cm3, small grains with aini P 0:05 m are
rapidly trapped into the postshock flow and are completely destroyed by sputtering. Grains with aini ¼ 0:05Y0:2 m are trapped
and remain in the dense shell behind the forward shock. Very large
grains with aini k 0:2 m are ejected to the ISM through the forward shock without significantly decreasing their sizes.
3. The critical size below which dust is completely destroyedin SNRs is sensitive to the gas density in the ambient medium
and spans the range of 0.01Y0.2 m for nH;0 ¼ 0:1Y10 cm3.
The resulting size distribution of survived dust is greatly deficient965

in small-sized grains, compared with that at the time of dust formation, although the erosion of large grains produces the smaller
sized grains. Thus, the mass of dust injected from SNe into the
ISM is dominated by the large grains.
4. The total mass fraction of dust destroyed in SNRs ranges
from 0.2 to 1 and increases with increasing ambient gas densityand explosion energy of SNe. The destruction efficiency of each
dust species is very sensitive to the initial size distribution, andthe dust species whose mass is predominantly occupied by thesizes larger than the critical size can survive. Therefore, the chemical composition, size distribution, and amount of dust grains supplied from SNe to the ISM are quite different from those at thetime of dust formation.
5. The results for the evolution of dust in SNRs presented
in this paper can be directly applied for the initial metallicity ofprogenitor stars and ambient medium less than Z  103 Z andcould be useful for evaluating the evolution of dust in the Galactic SNRs generated from SNe II.
6. The fates of dust grains formed in the ejecta strongly depend on the thickness of the hydrogen envelope. For the SNR
generated from the SN with the very thin hydrogen envelope, thecollision time of the reverse shock with dust grains inside the He
core is much earlier. As long as the model of dust for SNe II isemployed for the calculation, the mass of dust supplied to the
ISM is larger than SNe II with thick hydrogen envelopes.
7. If the elemental compositions of dust grains piled up in the
SN shell reflect the metal abundance patterns of the secondgeneration stars formed in the dense shell of primordial SNRs,
the dust formed in the unmixed ejecta of SNe II can be responsible for the peculiar abundance patterns of Mg and Si in HMP
stars. However, another scenario could be necessary to produce
the large overabundances of C and O observed in HMP stars.

The authors are grateful to the anonymous referee for criticalcomments that improved the manuscript. This work has been
supported in part by a Grant-in-Aid for Scientific Research fromthe Japan Society for the Promotion of Sciences (16340051 and
18104003).

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