2017/06/08

Dust formation theory inastronomical environments
Takaya Nozawa(National Astronomical Observatory of Japan)

Contents:
1. Introduction
2. Classical (kinetic) nucleation
3. Chemical (molecular) nucleation
4. Implications

1-1. Origin of cosmic dust grains〇 Cosmic dust grains‐universally exist in the universe‐cause various astrophysical phenomena
extinction, scattering, polarization, IR emission,
molecular formation on the surface, formation of planets …

The origin of dust remains to be clarified !!
〇 Massive dust at z > 5 discoveredin the early universe, CCSNe must play
dominant roles in the enrichment of ISM
with dust~106 Msun of dust ina galaxy at z = 8.4
Laporte+2017

1-2. Key questions for dust formation
1. How much dust grains form?

2. What is the size distribution of dust?

3. When do the majority of grains form?

1-3. Observed dust mass in CC-SNe/SNRs
reverse shock
destruction??
missing
cold dust?

Dust mass
increasing
with time?

??

NIR/MIR
FIR/submm
extinction

Dust mass formed in the ejecta is dominated by cold dust

1-4. Dust mass increases with time?
Dust mass estimated fromIR emission
Gall et al. (2014, Nature)

Most of dust grains(> 0.1 Msun) form at~20 yr post-explosion

Evolution of dust mass in SN
1987A derived from extinctionof optical emission lines
Bevan & Barlow (2016)

1-5. Key questions for dust formation
1. How much dust grains form?
‐FIR/submm obs. ➜ 0.1-1 Msun
‐theoretical works ➜ 0.1-1 Msun

2. What is the size distribution of dust?
➜ what fraction of dust is destroyed by RS?
➜ smaller grains are destroyed more efficiently

3. When do the majority of grains form?
‐obs. ➜ ~20 yr (dust mass gradually increases with time)‐theory ➜ ~1-2 yr (within 5 yr)2-0. Two approaches for nucleation
1. Nucleation

2. Grain growth(formation of stable clusters)〇 Classical nucleation〇 Chemical nucleation(kinetic nucleation)(molecluar nucleation)(Kozasa+1989, 1991, Yamamoto+2001,
Todini & Ferrara 2001, Nozawa+2003,
2008, 2010, Schneider & Bianchi 2007,Fallest+2011, Keith & Lazzati 2011,Schneider+2012, Nozawa & Kozasa
2013, Lazzati & Heger 2016,Marassi+2015, Bocchio+2016)(Clayton+1999, 2001, Deneault+2003,
Cherchneff & Dwek 2009, 2010,
Sarangi & Cherchneff 2013, 2015
Biscaro & Cherchneff 2014, 2016)
Sluder+2016)

2-1. Phase transition〇 Gibbs free energy〇 Supersaturation ratio, S

gas

solidsolid stable for lnS > 0 （S>1）

gas phase

c1
p1v

p1

bulk material

2-2. Formation of clusters〇 Free energy for clusters〇 Energy involved incluster formation## capillary approximation

gas phase

c1clusters

2-3. Kinetic nucleation
c1c2

J2

c3

J3

αn-1c1cn-1
Jnβncn〇 Master equations

sticking coefficient, ηs = 1

energy barrier : ~ 10cn

2-4. Classical nucleation〇 Steady-state nucleation rate
(assuming Js = J2 = J3 = … = Jn)## formation rate of stable clusters

2-5. Basic equations for dust formation
1. Nucleation
・ Kinetic
・ Classical2. Grain growth・ free expansion

・ gas cooling(γ=1.25)

2-6. Kinetic vs. Classical・ Kinetic nucleation(n*=100)

・ Classical nucleationηs = 1

2-7. Dependence on sticking coefficient2-8. Energy barrier of clusters
chainringcage〇 Free energy for clusters

・ Classical nucleation

・ Density fluctuation theory

Mauney+2015

・ Kinetic nucleation

2-9. Dependence on surface energy
300 day

700 day‐ Increasing the surface energy can lead to lower condensation
temperature, retarding the formation of dust
‐ Dependence of sticking coefficient and energy barrier on theresulting size of dust is not strong3-1. Chemical approach〇 Master equations〇 Arrhenius expression

Empirical (fitting) formula to account for reaction
rates obtained from experiments

3-2. Reaction rates for carbon clusters

Cherchneff & Dwek (2010)

3-3. Chemical vs. Kinetic (Classical)
lnS < 0lnS > 0

green line: only for forward reactions
red line: destruction reaction C2 + O ===> CO + C
If chemical reaction rates and paths are not accurate,
the chemical approach may produce erroneous results

4-1. Mass evolution of newly formed dust

Molecules: chemical
Clusters: chemical
Grains: coagulation
Sarangi & Cherchneff (2015)

Molecules: chemical
Clusters: kinetic
Grains: accretion
Lazzati & Heger (2016)

Both nucleation approaches predict that ~0.1 Msunof dust condenses a few years after the explosion

4-2. Size distribution of newly formed dust

Molecules: chemical
Clusters: chemical
Grains: coagulation
Sarangi & Cherchneff (2015)

Molecules: chemical
Clusters: kinetic
Grains: accretion
Lazzati & Heger (2016)

The radii of newly formed dust ranges from ~0.001 µm
to ~1 µm though there are some subtle differences

4-3. Timescale of grain growth

At 20 yr, the gas density is too low to form dust
grains in the freely expanding ejecta

5. Summary of this talk1) Classical (kinetic) nucleation‐well established on the basis of thermodynamics‐still one of the good tools to describe dust formation
2) Chemical (molecular) nucleation‐consistently follows the formation of a variety ofmolecules and small clusters, given that reaction
paths and rates are well known3) Both nucleation approaches predict‐the formation of dust in the ejecta within 5 yr(seems hard to form massive dust at ~20 yr)‐dust size range of 0.001-1 µm