Formation of Carbon Grains in Red-supergiant Windsof Very Massive Population III Stars
Takaya Nozawa1 (takaya.nozawa@nao.ac.jp)
Sung-Chul Yoon2, Keiichi Maeda3, Takashi Kozasa4, Ken’ichi Nomoto5, Norbert Langer6
1NAOJ, 2Seoul National University, 3Kyoto University, 4Hokkaido University, 5K-IPMU, University of Tokyo, 6Universitat Bonn

○ Abstract We investigate the formation of dust in a stellar wind during the red-supergiant (RSG) phase of a very massive Population
III star with a zero-age main sequence mass of 500 Msun. We show that, in a carbon-rich wind with a constant velocity, carbon grains canform with a lognormal-like size distribution, and that all of the carbon available for dust formation finally condenses into dust for wide
ranges of the mass-loss rate ([0.1–3]x10−3 Msun yr−1) and wind velocity (1–100 km s−1). We also find that the acceleration of the wind, driven
by newly formed dust, suppresses the grain growth but still allows more than half of the gas-phase carbon to finally be locked up in dust
grains. These results indicate that, at most, 1.7 Msun of carbon grains can be produced during the RSG phase of 500 Msun Population IIIstars. Such a high dust yield could place very massive primordial stars as important sources of dust at the very early epoch of the universe if
the initial mass function of Population III stars was greatly weighted to a much higher mass than that of the present stellar population.

○ Model of a RSG with MZAMS = 500 Msun (Yoon et al. 2012)○ Model of circumstellar envelope

・ Lstar = 107.2 Lsun, Tstar = 4,440 K, Rstar = 6,750 Rsun
・ AC = 3.11x10-3, AO = 1.75x10-3 ➔ C / O = 1.78 (C-rich)・ spherically symmetry, constant wind velocity
・ density and temperature profile○ Calculations of dust formation
・ formula of non-steady-state dust formation (Nozawa & Kozasa 2013)
・ Table 1 : chemical reactions considered in this study# Mdot and vw are treated as free parameters
・ wind velocity : vw = 20 km/s
fiducial value
・ mass-loss rate : Mdot = 3x10-3 Msun yr-1
・ fc = 1, which is a fraction of carbon atoms available for dustformation after the formation of CO molecules○ Results of dust formation calculations (Fig. 1)
・ C grains form around r = 7.5 Rstar (r = 12 Rstar) for Model A (Model B)
・ Final condensation efficiency is unity for both of the models
・ Final average radius is similar in both Model A and Model B➜ the results are almost independent of chemical reactions○ Dependence on Mdot and vw (Fig. 2)
・ The average grain radius becomes larger for a higher mass-loss rate
(aave,∞ ∝ Mdot0.88) and/or a lower wind velocity (aave,∞ ∝ vw-1.75)
・ The condensation efficiency of dust is unity for the condition:

Fig. 1 – (a) Formation rate of seed clusters with n* = 100, divided by the nominal concentration of the key
molecules (I*, solid), condensation efficiency (fcon, dotted), and average grain radius (aave, dashed) as afunction of distance from the center of the star (r/Rstar), and (b) final size distribution spectrum by mass of
newly formed C grains for a mass-loss rate Mdot = 3x10-3 Msun yr-1, a wind velocity vw = 20 km s-1, and fc = 1.
The thick lines represent the results for Model A where the chemical reaction (1) in Table 1 is considered forthe formation of clusters, while the thin lines represent those for Model B with the chemical reaction (2).

・ for the fiducial case (M dot = 3x10-3 Msun yr-1, vw = 20 km s-1, fc = 1)
➜ 1.7 Msun of C grains can form over the lifetime of the RSG○ Effects of wind acceleration on dust formation (Figs. 3 and 4)
・ Momentum equation of wind acceleration (Ferrarotti & Gail 2006)

・ The wind is rapidly accelerated to > 100 km s -1, reducing the growthrate of grains and the formation rate of seed clusters
・ The formation of small grains at later phases, as well as the gradual
growth of large grains, enhances fcon,∞ up to >0.5 with very small aave,∞

Fig. 2 – Final average radius aave,∞, and final condensation efficiency fcon,∞, of C grains formed in theoutflowing gas; (a) as a function of product fc Mdot for vw = 20 km s-1, and (b) as a function of vw for fc Mdot =3x10-3 Msun yr-1. The thick solid lines represent the results for Model A, while the thin dashed lines represent
those for Model B.

○ Discussion : How efficient is dust formation?
・ Dust ejection efficiency by very massive Population III RSGs
➜ XVMS = Mdust / MZAMS < 3.4x10-3
・ Dust ejection efficiency by core-collapse supernovae (CCSNe)➜ XCCSN = (0.1-30)x10-3
Dust production efficiency of Population III RSGs is comparable
with, or slightly less than that of CCSNe➜ very massive Population III RSGs could be important sources ofdust if the IMF of Population III star was highly top-heavy

Fig. 3 – Wind velocity vw (upper panel), formation
rate of seed clusters I*, condensation efficiency fcon,
and average radius aave (lower panel) as a function ofr/Rstar for model A with the wind acceleration. The
initial wind velocity and mass-loss rate are set to bevw,0 = 30 km s-1 and Mdot= 3x10-3 Msun yr-1,respectively. The dashed lines in the lower panel are
the results without wind acceleration.

Fig. 4 – Solid lines show the dependence ofaave,, and fcon on vw,0 in the case with windacceleration for Model A with fcMdot = 3x10-3
Msun yr-1. The dashed lines show the averageradius aave,1 and condensation efficiency fcon,1
just before the grain growth is depressed bywind acceleration.