2013/08/06

Non-steady-state dust formation inthe ejecta of Type Ia supernovae
Takaya Nozawa(Kavli IPMU, University of Tokyo)

Collaborators:
Takashi Kozasa (Hokkaido University)
Keiichi Maeda, Ken’ichi Nomoto (Kavli IPMU)

1-1. Sources of dust in the early universe
huge amounts of dust grains (>108 Msun) are detectedin host galaxies of quasars at redshift z > 5 (< 1 Gyr)
➔ Type II SNe arising from short-lived massive stars(> 8 Msun) must be main producers of dust
➔ 0.1 Msun of dust per SN is needed (e.g., Dwek+07)－ theoretical works predict that 0.1-1.0 Msun of dust
can form in Type II SNe (e.g., Nozawa+03; Nozawa+10)－ FIR observations with Herschel discovered ~0.1 Msunof cool dust in Cas A, SN 1987A, and Crab(Barlow+10; Matsuura+11; Gomez+12b)

What are the main composition and typical size of newly
formed dust in the ejecta of SNe?

1-2. Dust formation in Type Ia SNe〇 Type Ia supernovae (SNe Ia)－ thermonuclear explosions of C+O white dwarfs withthe mass close to Chandrasekhar limit (~1.4 Msun)－ synthesize a significant amount of heavy elements➔ possible sources of interstellar dust?

〇 No evidence for dust formation in SNe Ia－ no cool dust in Kepler and Tycho SNRs (Gomez+12a)
detection of warm dust of 10^-4
Msun in Tycho (Ishihara+10)

What causes the differencein dust formation process?

KeplerTycho

1-3. How do dust grains form?
chemical approachgaseous atoms nucleation approach(e.g. Cherchneff+09)

molecules
formation of seed nuclei(steady-state nucleation rate)

reaction rates unknown!

clusters

steady-state nucleation ratecannot be applied in rarefied
astrophysical environments(e.g., Donn & Nuth 1985)

dust grains

2-1. Concept of nucleation theoryc1c(2)J2c(3)

J3

αn-1c1cn-1 c(n)Jnβncn・ master equations

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

where μ = 4πa02σ / kT・ non-steady-state dust formationn＊= 100

2-3. Basic equations for dust formation
・ Equation of mass conservation(cluster)(grain)・ Equation of grain growth= c10 x 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-3

c10 = 108 cm-3
CMgSiO3・ dashed line : non-steady model・ dotted line : steady model

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 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 grains with n＊ = 100
・ Is : formation rate of grains with n = nc

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
MgSiO3The combined size distribution of clusters andgrains is in good agreement with the grain size
distribution calculated with the steady-state
nucleation rate

3-5. Scaling relation of average grain radius
CMgSiO3

Λon: ratio of supersaturation timescale to gas collisiontimescale at the onset time of dust formation

Λon = τsat/τcoll ∝ τcool ngas
where τcool = ton / 3 (γ – 1)
Nozawa & Kozasa, submitted

3-6. Scaling relation of average grain radius
CMgSiO3

average radiuscondensation
efficiency

Nozawa & Kozasa, submitted

4-1. Dust formation in Type Ia SN○ Type Ia SN modelW7 model (C-deflagration) (Nomoto+84; Thielemann+86)－ Meje = 1.38 Msun

－ E51 = 1.3－ M(56Ni) = 0.6 Msun

4-2. Results of dust formation calculations
Λon = 30

4-3. Mass of dust formed in Type Ia SNein units of M sun

Dust species

SteadyNon-steadyC

8.08x10-3

3.99x10-3

Mg2SiO4

8.79x10-3

1.21x10-5

MgSiO32.34x10-2

3.64x10-6

SiO2

3.40x10-2

8.39x10-3Al2O3

1.89x10-3

0.00FeS

6.06x10-2

2.83x10-3Si

1.10x10-1

9.04x10-2Fe

4.72x10-2

4.71x10-2Ni

1.10x10-2

1.09x10-2

Total

0.305

0.164

4-4. Discussion on dust formation in SNe Ia〇 Issues to be addressed－ sticking probability: s = 1 in the calculations➔ if s < 0.1, any dust grain cannot condense－ SN (W7) model: massive carbon (Mc ~ 0.05 Msun)➔ observationally estimated carbon mass in
SNe Ia : Mc < 0.01 Msun (Marion+06; Tanaka+08)－ M(56Ni) ~ 0.6 Msun in SNe Ia (cf. ~0.06 Msun in SNe II)➔ energetic photons and electrons resulting from
56Ni decay destroy small clusters (e.g., Nozawa+11)

5. Summary of this talk
〇 Steady-state nucleation rate is a good approximation
if the gas density is high (τsat / τcoll >> 1)➔ otherwise, non-steady effect becomes remarkable,
leading to a lower fcon,∞ and a larger aave,∞〇 Steady-state nucleaition 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〇 Effect of non-steady state is remarkable in SNe Ia➔ Masses of silicate/oxide grains are significantly
reduced, compared to the results by steady model

5-1. Dependence on t0
c10 = 107 cm-3

c10 = 105 cm-3

5-2. Dependence on gas cooling rate (γ)
c10 = 107 cm-3

c10 = 105 cm-3

5-3. Dependence on n＊
c10 = 106 cm-3

c10 = 105 cm-3
MgSiO3