Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 1
Crystallization Mechanism of Cometary Grains
T. Yamamoto & T. ChigaiNagoya University
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 2
Detection of crystalline silicate feature in C/Halley
0
0.2
0.4
0.6
0.8
1
8 9 10 11 12 13
Em
issi
vity
Wavelength (µm)
9.2 10.0 10.55 11.2 11.9
Halley Dec.1985Halley Jan.1986
(Campins and Ryan 1989, Bregman et al. 1987)
• Similar features have been observed in several comets.
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 3
Crystalline silicate in various kinds of objects
Hanner 1999, 2003
1. Observed in
• evolved stars
C-rich giant star, post-AGB star
• YSOs at a late stage & young MS stars
Herbig Ae/Be stars & β-Pic
• comets
• ZL dust (Honda et al. 2003)
• IDPs
2. Not observed in
• ISM & molecular clouds
• YSOs at an early stage
(Molster et al. 1999)
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 4
Characteristics of crystalline silicate
• Similar features
• Variety of objects: hot & cool
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 5
Origin of cometary silicate
Mixture of amorphous & crystalline silicates
1. amorphous: interstellar dust survived in the solar nebula
2. crystalline: annealing or condensation in the solar nebula
• Need high temperature
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 6
Origin of cometary silicate
Mixture of amorphous & crystalline silicates
1. amorphous: interstellar dust survived in the solar nebula
2. crystalline: annealing or condensation in the solar nebula
• Need high temperature
Present model:
• “Cool” crystallization mechanism
• Need not mixing
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 7
Greenberg’s model of cometary dust
silicate core + organic refractory (OR) + icy mantle
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 8
Crystallization mechanism
1. Moderate heating of dust by solar radiation
• Dust temperature (300 – 500K) is not enough for silicate
crystallization but enough for icy mantle sublimation
2. Trigger chain chemical reactions in the OR
3. Energy released by the reactions heats the silicatecore.
• Er ∼ several to 10 eV ∼ 105 K
4. Lead to partial crystallization of the silicate core.
Chemical heating model
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 9
Chemical heating model
organic refractory
amorphoussilicate
solar radiation
heat
crystallinesilicate
chemical reaction
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 10
Basic equations
1. Degree of crystallinity (Haruyama et al. 1993)
∂fc
∂t=
1 − fc
tc
=1 − fc
Ae−Ec/kT
• tc = AeEc/kT : crystallization time scale
• Ec: activation energy of crystallization
• Ec = 3.5 eV for amorphous ol. and px. (Kimura et al. 2002)
A = 10−12 to 10−13 s
2. Temperature in the silicate core
∂T
∂t− χ
r2
∂
∂r
(r2∂T
∂r
)=
Hc
ρcp
∂fc
∂t
• Hc: Latent heat of crystallization per unit volume
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 11
Initial condition
Instantaneous heat source on the silicate core surface
• Duration of heating of the surface due to reactions isshort enough.
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 12
Temperature in the silicate core
0
50
100
150
200
250
300
0.9 0.92 0.94 0.96 0.98 1
T/T
0
r/a
10-3
10-4
10-2
24χt/a = 10−5time
Substantial temperature increase near the core surface
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 13
Key parameter of crystallization
θ0 =kΩ
µmHcp
nrhr
(χA)1/2
Er
Ec
∝ nr : density of reactive molecules in OR
θ-value determines crystallization degree
• crystallized volume as θ0 • Possible values of θ0 (Greenberg particle)
θ0 = 0.6 to 6 for nr = 1021 for 1022 cm−3
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 14
Volume fraction of crystalline region
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
fc
r/a
3 1θ0 = 6
• Substantial crystallization near the core surface for θ0 > 1
• volume fraction: 2 - 40% for nr = 1021 - 1022 cm−3
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 15
Does the crystalline fraction explain the observed spectra?
1. Calculations of the spectra
• individual grain: am. core + xtal. mantle structure
• Spectra of aggregates: MG in the Rayleigh regime
• varying volume fraction of the crystalline region
2. Optical const (n, k) data for Mg2SiO4
• amorphous: Scott & Duley 1996
• crystalline: Sogawa et al. 1999
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 16
Spectra vs volume fraction of crystalline forsterite
0
0.2
0.4
0.6
0.8
1
1.2
8 9 10 11 12 13
Q /
a (
1/µm
)
λ (µm)
Maxwell-Garnett
f=20%
15%
10%
amorphous
obs.
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 17
Comparison with observed spectrum
• Crystalline volume fraction f of 10 – 20 % can repro-duce the observed crystalline feature.
f-value: within the range expected from the chem-ical heating model
best fit: f ' 15 %
• Detailed fitting is another problem.
mixing pyroxene & other materials
varying Mg/Fe ratio
grain size distribution
particle shape
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 18
Conclusions
1. Chemical heating mechanism works.
• Crystallization degree (∼ 15%) needed to explain the ob-
served spectra can be realized.
2. Chemical heating model
• Need not high temperature and mixing of amor-phous & crystalline silicate
• Preserve ices of interstellar composition
• Applicable to crystallization in protoplanetary disks & other
objects
• Amount of energy deposition in the OR is a keyquantity.
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 19
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
8 9 10 11 12 13
Q /
a (
1/µm
)
λ (µm)
amorphous core-crystalline mantle
+ organic mantlerOR:rm:rc=100:70:66.5
rm:rc=70:66.5=100:95
Figure 1: Effect of the outer organic mantle on the spectrum. The blue curve shows Q/a of a small spherecomposed of an amorphous forsterite core and a crystalline forsterite mantle, and the red one shows Q/a addingan organic outer mantle. Optical constant data of the organic mantle are adopted from Greenberg & Li (1996)A&A 309, 258.
Crystallization of Cometary Silicate/ T. Yamamoto & T. Chigai IAU JD14, Sydney, 03/07/22, HM3 20
0
2
4
6
8
10
12
8 9 10 11 12 13
Wavelength (µm)
Q /
a (
1/µm
)
(1 - rc / rm) = 1
.75
.5
.25
00
0.5
1
1.5
2
2.5
8 9 10 11 12 13
Wavelength (µm)Q
/ a
(1/
µm)
.25
.2
.15
.1
.05
0
Figure 2: Q/a for amorphous core-crystalline mantle silicate small spheres. Amorphous forsterite (Mg2SiO4)from Scott & Duley (1996) ApJS 105, 401 core- crystalline olivine (Mg2SiO4) from Sogawa et al. (1999) ISASLPS 32, 179 mantle grains.