2013/09/11

天文学的ダスト形成環境における非定常ダスト形成過程の定式化(Formulation of Non-steady-state Dust Formation
Process in Astrophysical Environments)
to be published in ApJ (arXiv:1308.1873)

野沢 貴也（Takaya Nozawa）(Kavli IPMU, University of Tokyo)and小笹 隆司（Takashi Kozasa）(Hokkaido University)

1-1. Core-collapse SNe as sources of dust
・Discoveries of massive dust at high redshifts➔ CCSNe must be main producers of dust grains

・Dust formation in the ejecta of CCSNe－ theoretical works predict that 0.1-1.0 Msun of dust
can form in CCSNe (e.g., Nozawa+03; Nozawa+10)－ FIR observations with Herschel reported ~0.1 Msunof cool dust in Cas A, SN 1987A, and Crab(Barlow+10; Matsuura+11; Gomez+12)## Some of dust grains formed in the ejecta are## destroyed by the reverse shock (e.g., Nozawa+07)

Necessary to reveal the dust mass and size distribution!

1-2. Aim of this study
・How do dust grains form?
atoms ➔ molecules ➔ clusters➔ bulk grains??
reaction coefficients unknown!

Cherchneff & Dwek (2011)

・Nucleation accompanied by chemical reactions－ kinetics of dust formation process is controlled by
key molecule: gas species with the least collision
frequency among reactants(Kozasa & Hasegawa 1987)－ steady-state nucleation rate may not be applied in
rarefied environments (e.g., Donn & Nuth 1985)
The aim of this study is to formulate a non-steady-state
formation process of dust grains

2-1. Formulation of dust formation
c1c2

J2

c3

J3

αn-1c1cn-1 cn
Jn

βncn

・ master equations

2-2. Steady-state nucleation rate
・ steady-state nucleation rate: Js➔ assuming Js = J2 = J3 = ・・・ = J∞

whereμ = 4πa02σ / kT
σ：surface tension

S : supersaturation ratio( S = p1 / p1v )2-3. Non-steady-state dust formation
・ non-steady-state dust formationn＊= 100

・ Non-steady model: solving master equations
・ Steady model: using a steady-state nucleation rate

2-4. Basic equations for dust formation
・ Equation of mass conservation(clusters)(grains)・ Equation of grain growth∝ fcon・ Evolutions of gas density and temperature(γ = 1.1-1.7)

Parameters: c0, γ, t0 (the time at which lnS = 0)fiducial values: γ = 1.25, t0 = 300 day3-1. Steady vs. Non-steady (1)c10 = 108 cm-3C

c10 = 108 cm-3
MgSiO3decrease in temperature  increase in S  increase in I＊ (Is) grain growth  consumption of gas  decrease in I＊ (Is)The results for steady and non-steady models
are essentially the same for high gas densities

3-2. Steady vs. Non-steady (1): size distributionc10 = 108 cm-3C

c10 = 108 cm-3
MgSiO3The size distribution of grains for steady andnon-steady models are identical➔ The steady-state nucleation rate is a goodapproximation for higher initial densities

3-3. Steady vs. Non-steady (2)c10 = 105 cm-3C

c10 = 105 cm-3
MgSiO3・ I＊: formation rate of clusters with n＊ = 100
・ Is : formation rate of clusters with n = nc (<100)for τcoll/t0 << 1 ➔ Is = … = In = In+1 = … = I＊
for τcoll/t0 << 1 ➔ Is > … > In > In+1 > … > I＊

3-4. Steady vs. Non-steady (2): size distributionc10 = 105 cm-3C

c10 = 105 cm-3
MgSiO3For lower gas densities, the steady model
overestimates the condensation efficiency
and underestimates the average grain radius

3-5. Scaling relation of average grain radius
CMgSiO3

Λon > 30

Λon > 30

‐Λon = τsat/τcoll : ratio of supersaturation timescale to gas
collision timescale at the onset time (ton) of dust formation‐ton : the time at ｗhich fcon reacｈes 10-10・ fcon,∞ and aave,∞ are uniquely determined by Λon・ steady-state nucleation rate is applicable for Λon > 30

3-6. Scaling relation of average grain radius
CMgSiO3

average radius‐a ~ 0.1 μm in Type II-P SNe (Nozawa+03)‐a ~ 0.001 μm in Type IIb SNe (Nozawa+10)

condensation
efficiency## Λon = τsat/τcoll ∝ τcool ngas

5. Summary of this talkWe develop a new formulation describing nonsteady-state
formation of small clusters and grains in a self-consistentmanner, taking account of chemical reactions〇 Steady-state nucleation rate is a good approximation
if the gas density is high enough (τsat / τcoll >> 1)➔ otherwise, non-steady effect becomes remarkable,
leading to a lower fcon,∞ and a larger aave,∞〇 Steady-state nucleation rate is applicable for Λon > 30
➔ fcon,∞ and aave,∞ are determined by Λon = τsat / τcollat the onset time (ton) of dust formation➔ The approximation formulae for fcon,∞ and aave,∞are given as a function of Λon