Takaya Nozawa • Institute for the Physics and Mathematics of the Universe • Graduate School of Science, Hokkaido University Collaborators; T. Kozasa (Hokkaido Univ.), H. Umeda (Univ. of Tokyo) H. Hirashita (ASIAA), K. Maeda (IPMU), N. Tominaga (NAOJ) K. Nomoto (Univ. of Tokyo, IPMU), A. Habe (Hokkaido Univ.) E. Dwek (NASA Goddard Space Flight Center) T. T. Takeuchi (Nagoya Univ.), T. T. Ishi (Kyoto Univ.) MATHEMATICS OF THE UNIVERS 1
1. Evidence of dust in the high-z universe 2. Dust formation in primordial SNe 3. Dust evolution in primordial SNRs 4. Extinction curves expected at high redshift 5. Role of dust in the early universe
• 30% of z > 5 quasars have shown the presence of large amounts of dust grains with mass larger than 10^8 Msun y (Bertoldi et al. 2003; Priddey et al. 2003; Robson et al. 2004; Beelen et al. 2006; Wang et al. 2008, Fan's talk) SDSS J1148+5251 at z=6.4 AS, 351, L29) a rapid enrichment with dust V formed in the ejecta of SNe Dust of 0.1-1 Msun per SN is 1 required to form to explain a large content of dust at high-z galaxies (Morgan & Edmunds 2003, Maiolino et al. 2006; Dwek et al. 2007, Dwek's Talk) 3
SDSS J1048+4637 at z=6.2 Broad absorption line (BAL) quasars Maiolino et al. (2004, Nature, 431, 533) different dust properties from those in low redshifts,
• Dust absorbs stellar light and re-emits it by thermal radiation → plays a crucial role in interpreting the SFR and the IMF, of the early generation of stars from high-z observations (e.g., Loeb & Haiman 1998) • Dust has great impacts on the formation processes of stars — providing additional cooling pathways of gas through thermal emission (e.g., Schneider et al. 2003, Omukai et al. 2005) — forming molecules (mainly H₂) on the surface (e.g., Cozax & Spaans 2004) — controlling the energy balance in the interstellar medium
In the previous studies, the composition and size of dust are assumed to be the same as those in Galaxy, and the amount is treated as a parameter. Absorption and thermal emission by dust grains ( are sensitive to the composition, size, and amount It is essential to clarify the properties of dust in the early epoch of the universe! We aim at revealing the composition and size, amount of dust by treating self-consistently the formation and destruction processes of dust. MATHEMATICS OF THE UNIVERS
• At z > 5, the main formation sites of dust are considered to be in the ejecta of supernovae (SNe) • first stars (Population III stars) very massive M =100-500 Msun In the early universe • Type II SNe (SNe II) ; M pr=8−40 M sun •  pair-instability SNe ; M n =140−260 M sun (Heger et al. 2003)
Todini & Ferrara (2001, MNRAS, Type II SN model (Z = 0-0.02) by Woo one-zone model within He core formation and destruction of CO and initial gas density and temperature fo Kl Al,O, 10 Progenitor mass 8
Nozawa et al. (2003, ApJ, 598, 785) Type II SN (Z=0) and PISNe model by Umeda & Nomoto (2002) mixing of elements within He-core → two extreme cases unmixed case (onion-like structure) uniformly mixed case (retaining the density profile) gas temperature; solving radiative transfer calculation formation of CO and SiO molecules is complete
grain radius (cm) • Various species of dust form, reflecting the elemental composition of each layer. •C, SiO2, and Fe grains are lognormal-like with relatively large average radii, while other grains are power-law-like.
• Because oxygen is rich,  only silicate (MgSiO 3 , Mg 2 SiO 4 , SiO 2 ) and oxides (Fe₃O₄, Al₂O₃) form. • The size distribution of each dust species except for Al,O 3 is lognormal-like
• Total dust mass increases with increasing progenitor mass SNe II : Mdust = 0.1-2 Msun  PISNe : Mdust = 10-60 Msun • Dust mass for the mixed case is generally larger than for the unmixed case
Maiolino et al., (2004, Nature, 431, 533)
● Basic equations (spherical symmetry)   1  ∂ (r²ρυ) = 0 dt ∂P 1  ρυ )十r²ユr dr ρυ² ਹ 1  | ρυ² r2 r²ホr dt 2 2 V (nenhAgas(T) + Aic(T) + Ad(nh,T)) Agas(T) : cooling function of gas by the atomic process (Sutherland & Dopita 1993; Smith et al. 2001) Aic(T) : inverse Compton cooling (Ikeuchi & Ostriker 1986) Λic(T) = 5.41×10−32(1+z)4ne(T/104 K) (we adopt z = 20) Λα(nH,T) : cooling of gas through thermal emission of dust · numerical code : flux splitting method (van Albada et al. 1982)
● deceleration of dust due to drag force (Baines et al. 1965)
wd ; velocity of dust relative to gas Pd ; bulk density of a grain n; ; number density of gas species i
● dust destruction by sputtering (e.g., Dwek et al. 1996)
Y i (E i = c i k T ) ; sputtering yield at normal incidence Msp ; average mass of the sputtered atoms
O  Models of Pop III SNe (Umeda & Nomoto 2002) • M r=13, 20, 25, and 30 M ⊙ (E 51=1) O The ambient medium (e.g., Kitayama et al. 2004) • gas temperature ; T = 10 4 K • gas density ; nH,o =  0.1, 1, and 10 cm -³ O  Dust in the He core (Nozawa et al. 2003) • size distribution and spatial distribution of each grain species formed in the ejecta • dust grains → test particles The calculation is performed from 10 yr up to ~10 6 yr.
(Nozawa et al. 2007, ApJ, 666, 955) Model : Mpr=20 M ⊙ (E51=1) nh,o =  1 cm-³ Downward-pointing arrows: forward shock in upper panel reverse shock in lower panel The temperature of the gas swept up by the shocks → 106-108 K Dust grains residing in this hot gas are eroded by sputtering
(Nozawa et al. 2007, ApJ, 666, 955) Model : Mpr=20 M ⊙ (E 51=1) nh,o =  1 cm-3 Dust grains in the He core collide with reverse shock at (3-13)x10³ yr The evolution of dust heavily depends on the initial radius and composition aini = 0.01 μm  (dotted lines) → completely destroyed aini = 0.1 μm (solid lines) → trapped in the shell t aini = 1 μm (dashed lines) → injected into,the ISM
The size distribution of surviving dust is greatly deficient in small-sized grains, compared with that at its formation → Dust in the early universe is dominated by large grain
Total mass of dust surviving the destruction for Type II SNRs;; 0.1-0.8 M ্ for the unmixed grain model (n H,o = 0.1-1 cm -3) 0.06-0.7 M ω for the mixed grain model (n H,o = 0.1 cm -3) → high enough to explain dust content at high-z galaxies (Morgan & Edmunds 2003, Maiolino et al. 2006; Dwek et al. 2007)
flat extinction curve at high redshifts ! Hitashita, T. N. et al. (2008, 384, 1725, MNRAS)
Priddey et al. (2003, MNRAS, 344, L74) Maiolino et al. (2004, A&A, 420, 2
(2004, ApJ, 616, 147) 1
1/λ (μm ¹)

Stratta et al. (2007, ApJ, 661, L9) Li et al. (2008, astro-ph/0712.2622) coagulation of grains in dense clouds evaporation of smaller grains by GRB destruction of small grains by shock
GRB 050904 at z=6.3

Tsuribe & Omukai (2006, ApJ, 378, 973)
Population II.5 stars : the 2nd-generation stars formed in the dense shell of Pop III SNRs (Mackey et al. 2003; Salvattera et al. 2004; Machida et al. 2005) dust grains surviving the destruction but not injected into the ISM are piled up in the dense shell in 105-106 yr • elemental composition of these piled-up grains →  elemental abundance of Population II.5 stars metallicity and metal abundance patte comparing with observations of HMP a
<   Fe/HIく[Mg, Si/Fe] ＜ 21 Elemental composition of f dust piled up in the shell / can reproduce abundance patterns in HMP stars The transport of dust segregated from metal-rich gas f can be responsible for the elemental composition of 7 Population II.5 stars formed in the dense SN shell.
1. The fate of newly formed dust within primordial SNRs strongly depends on the initial radii and compositions. 2. Size distribution of dust surviving in SNRs is weighted to large size. 3. Extinction curves in the early universe is expected to be flat. 4. Dust grains in the early universe play crucial roles in the formation of metal-deficient low-mass stars. 5. Dust formed in the ejecta has great impacts on the composition and formation of Population II.5 stars.