Mineralogia delle polveri nelle prime fasi della formazione di stelle ...

α
α
α

µ
µ

µ
µ

H B−V

α
µ
µ
σfea Afea λfea
λfea
Lmm/Lbol
µ

α
µ
µ
σfea Afea λfea
λfea
Lmm/Lbol
µ

α
µ
µ
σfea Afea λfea
λfea
Lmm/Lbol
µ

µ
•
•
•
µ
•

µ
•
•
•
µ
•

2

5 6 ⊙
3 4 ⊙
• ∼
∼ 10 − 20 ⊙
• ρ
≤ ⊙
• ∼
10 −2
⊙ 2 ⊙
18
3
H2 ≥ 4 −3 ∼

µ
ρ(r) ∝ r −2
ρ(r) ∝ r −2
BE 2 s
s kT µ
µmH
H
ρcoreρnubecritico ∼
BE
B µ

Bonnor-Erbert
ρ ∼
ρ(r) ∝ r −2
AB 6 7
∼ 5 H2 ≥ 5 −3

ρ ∝ r −p
ΦBπ 2 flat
flat flat
3π
τff =
32Gρ
BE
flat Bcritico
ρ

ρ ∝−2 v0
as =
µmH
µ
H
s ∼ 0.2 −1
kT
Rinfall = a × t
5
s −1 infall ∼

≤ infall
≥ infall
Static
Infall
Rinf = at
Dense
Core
Infall
Expansion
Wave
3
˙M
m0a
=
G
s −1 0 ∼
˙ M ∼ ×−6⊙
Rc (t) = G3 M 3 ⋆ Ω 2
16a 8 ∼ G3 ˙ M 3 Ω 2
16a 8 t 3 ∝ t 3

Ω −1 −1
× 5
˙M ∼ × −6 ⊙ −1 c ∼
Ω −1 −1
∼ c
acc ˙ M
∼ ∼
∼c
a
ρSIS (r) = a2
2πG r−2
MSIS (r < R) = 2a2
R
G

2GMacc (t)
vff (r, t) = −
r
acc
M ˙ 2 = 4πr ρff (r, t) |vff (r, t) | ρff
ρff =
Macc = ˙ Mt ˙ M =
ρff = a2
4πG
˙M
4π 2GMacc (t) r−3/2
m0a 3
G
m0
2a r−3/2 t −1/2
−2 −1.5
infall ·
·
Mff (r < Rinfall, t) = MSIS (r < Rinfall) − Macc (t) = 2a2
G Rinfall − ˙ Mt
Mff (r < Rinfall, t) = 2a2
G
3 m0a 1
at − t
G 2
2a2
× at
G
Mff (r < Rinfall, t) 1
2 × MSIS (r < Rinfall)
MSIS (r < R = a · t)
Macc (t) = M⋆ (t) + Mdisco (t) 1
2 × MSIS (r < R = at)
ρff (r, t)

Infall Static
ρ (r) ∝ r −1.5
ρ (r) ∝ r −2
R < Rinfall = a · t ρff(r,t) ∝ r −3/2 t −1/2
Mff (r ≤ R < Rinfall, t) ∝ t −1/2
ρ
∼ 5
5 s −1
infall
θ ∼
ρ
nube

MSIS (r < 4200AU) 0.4M⊙ × Tnube
10K
a
a 2 s + a 2 turb + a2 magn
s
Mturb+magn (r < 4200AU) = 4 × MSIS (r < 4200AU) 1.5M⊙ × Tnube
10K
µ µ
αIR =
d log (λSλ)
d log (λ)

• αIR ≥
• ≤ αIR
• αIR
inv⋆
S int
2 d
1.3mm × /Lbol ≥ 0.2Jy/L⊙
160pc
int
1.3mm bol
mm ⋆
mm
•
∼
µ
•

•
∼ 6
4
5

•
∼ 6
4
5

•
∼ 6
4
5

• ∼ 2 ∼
6
⊙ ∼
6 −3

•
−3
•
α β
−3
•
•
•
⊙

⋆ ≤⊙
−7 −4 ⊙ −1
5
−3 −3 ⊙ −2 −1

−3
10 −2 −1 −1
−1
−2.6
2 2 3
2
6

Time
Stardust
Interstellar
dust
Molecular
cloud dust
Protostellar
dust
Interplanetary
dust

x
2
2
66
2
2

Reaction Time
H-C-C-H
-
50nm
Coagulation
Surface Growth
and Coagulation
Particle Inception
Particle Zone
PAHs
Molecular
Zone
0.5nm
Aromatic
rings
Acetylene
2

+
+
−3
⊙ −2 −1 −3 ⊙ −2 −1
4 −3
5
7

5
6 −3 ≤
dIν
ds = −kνIν + jν
ν
dτν =
−kνds τν
dIν
dτν
= −Iν + jν
τν τνr
Iν = Iν (0) e −τνr +
τνr
0
kν
jν
kν
e −τν dτν
Iν (0) τν = τνr jν
kν
τνr Iν Bν

Bν (T ) = 2hν3
c 2
1
e hν
kT − 1
jν
kν
j ∗ ν = k ∗ νBν (T )
Iν = Iν(0)e −τνr + Bν (T ) 1 − e −τνr
λ
λ
Aλ = −2.5log Fν
Fν (0)
= 1.086NdustQeσdust
Fν (0) Ndust
−2 σdust
Qe
sν
jνS
Qs
Qs/Qe
jνS (k) = ndustQsσdust
Iν (k ′ ) F (k − k ′ ) dω ′
k k ′
dω ′ F (k − k ′ )
k k ′ F
Qa
Qe Qs
jνE = ndustQaσdustBν (Ts)

Ts
Aλ
∆m (λ)
λ1 λ2
∆m (λ)
Aλ ∆m (λ1)
∆m (λ2)
∆m (λ1) − ∆m (λ2) = ∆ (Aλ1 − Aλ2)
Aλ
Aλ1 − Aλ2
E (λ1, λ2) λ1 λ2
E (λ1, λ2) =
EB−V EB−V

2
EB−V
α 2
2
NH =
5.9 × 10 21 EB−V mag −1 cm −2
E (λ1, λ2) EB−V λ2
λ
1/λ µ

ā× −6
ā× −6 ā× −6
× −6
RV
RV = AV
EB−V
RV E (∞, V ) /EB−V
Aλ RV

Aλ
µ ∼ µ
∼ µ ∼

Aλ
µ ∼ µ
∼ µ ∼

µ
µ ∼
λ

λ (µm) (K)
(0.7 ÷ 1) − 5 740 − (3000 ÷ 5200)
5 − (25 ÷ 40) (93 ÷ 140) − 740
(25 ÷ 40) − (200 ÷ 350) (11 ÷ 19) − (93 ÷ 140)
λ
∼

VOLI DI PALLONI, AEREI E SATELLITI
∼
µ
µ
µ
µ
µ
µ
µ
µ
µ
µ

µ

• µ
•
µ
• µ
• µ
λ ∼
∆λ
∼
µ

λ (µm)
µ
µ µ
µ

µ µ µ
µ µ µ
µ
µ µ

µ µ µ
µ µ µ
µ
µ µ

−7 −7
−7 −7
−7 −7
−7 −7
−7 −7

−16
λ

λ (µm)
−16
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
µ

µ µ µ µ

µ µ µ µ

µ

3
µ µ
++
µ

3
µ µ
++
µ

CO2(aq) + H2Oi = H2CO3(aq)
H2CO3 + H2O = H3O + + HCO − 3
− 3
HCO − 3 + H2O = H3O + + CO −−
3

Ca ++ + 2HCO − 3 = CaCO3 + H2O + CO2
•
3
2
•
CaCO3 + H3O + + HCO − 3 = Ca ++ + 2HCO − 3 + H2O

3 3
3
3

−2
3
λ
−2
3

2−
−2
3
λ3 µ
λt λl
λt λl

2−
−2
3
λ3 µ
λt λl
λt λl

µ
λt (µm) λl (µm) ∗
λ u 1
λ2
λ u 3
λ u 4
λ g
1 αxx αyy
λ g
2
λ g
3 αxx
λ g
4 αxx αxy
λ5
λ6
λ7
λ8
λ9
λ10
λ11
λ12
λ13 αxz
λ14 αxz

µ
λt (µm) λl (µm) ∗
λ u 1
λ2
λ u 3
λ u 4
λ g
1 αxx αyy
λ g
2
λ g
3 αxx
λ g
4 αxx αxy
λ5
λ6
λ7
λ8
λ9
λ10
λ11
λ12
λ13 αxz
λ14 αxz

4
⊙
2
12
∼ 6 −3
⊙
ρ
µ

2
∼
µ
∼

2
⊙

α
bolmm
⊙
∼ ∼
⊙
∼
∼

12 + 2
H2∼ 6 −3
+
2
⊙

∼
2
ρ
∼⊙ ⊙
2
∼µ

⊙

α
⊙
⊙

ρ
⊙
ρ
∼
5
⊙
α
α ∼⊙
µ
⊙

µ ◦
⊕
α
α α
α
α
α
α

µ
∼ ⊙
∼ α

α
α
α

⊙
⊙
∗
α
α
∗
∗
α

•
•

•
•
µ

±

σ
σ

σ
σ

•
•

α

µ
µ
µ
kλ
kλ = k0(λ0/λ) β
β

∼
Iλ =
BB(λ, Ti) · [1 − exp[τi(60µm) · (60/λµm) βi ] · Ωi
i
BB(λ, Ti) Ti
λ τi βi Ti
Ωi
χ2
µ
µ
λ ≤µ

µ

µ
µ

µ
µ
µ
µ
µ
µ
µ
µ
µ µ

µ

µ
µ
µ

µ
µ
α
µ µ
µ
µ
µ µ
• λfea
σfea Afea
•
µ α
∼µ µ

µ
µ
63µ
2 414 − 303
113.763µ µ

µ
α

µ
µ
Afea σfea λfea
λ ≥ 98 µ
λ ≤ 97 µ

µ
σfea Afea λfea
σfea
µ

µ
µ λfea
σfea Afea λfea µ
σfea µ
Afea
∗
λfea σfea
TWarm τWarm λfea σfea fea
⊙ µ µ −2−1 µ−1
<
<
<
<
<
<
<
∗
<
α
α
∗ <
∗
α

µ
λfea σfea fea
λfea bol
λfea

cold warm

Minviluppo/M⋆
Lmm/Lbol
∼ 4

µ

µ
3
µ
µ
∼µ
∼µ
µ
3
µ µ
µ
µ
2 3 4
µ

µ
•
3 3 3 3 3 3 3 3
λu 1
λu 2
λu 3
λu 4
λ g
1
λ g
2
λ g
3
λ g
4
•

µ
k60µm −1 2
6 −3
M = τ60µm
k60µm
· S
S = π · R 2
d · θ
2
R =
θ k
N(s)
N(s)
Wλ
Wλ ∝
riga
[Iν(τ) − Iν(0)]dν ∝
riga
τνdν ∝
ldv
N(s)ds

M = N · S
S = π · R 2
d · θ
R =
2
θ
Calcite Calcite
Warm
Warm α
Calcite Calcite Warm
−2 −2 ⊕ 2 ⊕ %
5.7 2.0 6.7 0.3
14.6 3.5 17.6 0.2
2.0 0.2 0.7 0.2
3.0 3.1 8.3 0.4
11.6 3.0 5.7 0.5
8.6 4.0 4.0 0.9
0.8 0.1 1.3 0.07
1.0 0.1 2.3 0.4
1.0 0.1 1.0 1
4.0 2.0 2.7 0.8
2.3 0.15 0.07 2
1.0 0.15 0.6 0.2
1.7 0.15 2.3 0.05
1.3 0.1 0.2 0.7
α 6.6 1.2 6.0 0.2
0.2 0.01 0.03 0.5
α 0.3 0.2 0.02 6
−6

M = N · S
S = π · R 2
d · θ
R =
2
θ
Calcite Calcite
Warm
Warm α
Calcite Calcite Warm
−2 −2 ⊕ 2 ⊕ %
5.7 2.0 6.7 0.3
14.6 3.5 17.6 0.2
2.0 0.2 0.7 0.2
3.0 3.1 8.3 0.4
11.6 3.0 5.7 0.5
8.6 4.0 4.0 0.9
0.8 0.1 1.3 0.07
1.0 0.1 2.3 0.4
1.0 0.1 1.0 1
4.0 2.0 2.7 0.8
2.3 0.15 0.07 2
1.0 0.15 0.6 0.2
1.7 0.15 2.3 0.05
1.3 0.1 0.2 0.7
α 6.6 1.2 6.0 0.2
0.2 0.01 0.03 0.5
α 0.3 0.2 0.02 6
−6

M = N · S
S = π · R 2
d · θ
R =
2
θ
Calcite Calcite
Warm
Warm α
Calcite Calcite Warm
−2 −2 ⊕ 2 ⊕ %
5.7 2.0 6.7 0.3
14.6 3.5 17.6 0.2
2.0 0.2 0.7 0.2
3.0 3.1 8.3 0.4
11.6 3.0 5.7 0.5
8.6 4.0 4.0 0.9
0.8 0.1 1.3 0.07
1.0 0.1 2.3 0.4
1.0 0.1 1.0 1
4.0 2.0 2.7 0.8
2.3 0.15 0.07 2
1.0 0.15 0.6 0.2
1.7 0.15 2.3 0.05
1.3 0.1 0.2 0.7
α 6.6 1.2 6.0 0.2
0.2 0.01 0.03 0.5
α 0.3 0.2 0.02 6
−6

M = N · S
S = π · R 2
d · θ
R =
2
θ
Calcite Calcite
Warm
Warm α
Calcite Calcite Warm
−2 −2 ⊕ 2 ⊕ %
5.7 2.0 6.7 0.3
14.6 3.5 17.6 0.2
2.0 0.2 0.7 0.2
3.0 3.1 8.3 0.4
11.6 3.0 5.7 0.5
8.6 4.0 4.0 0.9
0.8 0.1 1.3 0.07
1.0 0.1 2.3 0.4
1.0 0.1 1.0 1
4.0 2.0 2.7 0.8
2.3 0.15 0.07 2
1.0 0.15 0.6 0.2
1.7 0.15 2.3 0.05
1.3 0.1 0.2 0.7
α 6.6 1.2 6.0 0.2
0.2 0.01 0.03 0.5
α 0.3 0.2 0.02 6
−6

M = N · S
S = π · R 2
d · θ
R =
2
θ
Calcite Calcite
Warm
Warm α
Calcite Calcite Warm
−2 −2 ⊕ 2 ⊕ %
5.7 2.0 6.7 0.3
14.6 3.5 17.6 0.2
2.0 0.2 0.7 0.2
3.0 3.1 8.3 0.4
11.6 3.0 5.7 0.5
8.6 4.0 4.0 0.9
0.8 0.1 1.3 0.07
1.0 0.1 2.3 0.4
1.0 0.1 1.0 1
4.0 2.0 2.7 0.8
2.3 0.15 0.07 2
1.0 0.15 0.6 0.2
1.7 0.15 2.3 0.05
1.3 0.1 0.2 0.7
α 6.6 1.2 6.0 0.2
0.2 0.01 0.03 0.5
α 0.3 0.2 0.02 6
−6

M = N · S
S = π · R 2
d · θ
R =
2
θ
Calcite Calcite
Warm
Warm α
Calcite Calcite Warm
−2 −2 ⊕ 2 ⊕ %
5.7 2.0 6.7 0.3
14.6 3.5 17.6 0.2
2.0 0.2 0.7 0.2
3.0 3.1 8.3 0.4
11.6 3.0 5.7 0.5
8.6 4.0 4.0 0.9
0.8 0.1 1.3 0.07
1.0 0.1 2.3 0.4
1.0 0.1 1.0 1
4.0 2.0 2.7 0.8
2.3 0.15 0.07 2
1.0 0.15 0.6 0.2
1.7 0.15 2.3 0.05
1.3 0.1 0.2 0.7
α 6.6 1.2 6.0 0.2
0.2 0.01 0.03 0.5
α 0.3 0.2 0.02 6
−6

µ
µ ∼µ ∼µ
2

µ

µ

µ

α
α

&
µ 2
CO2

&
µ 2
CO2

&
µ 2
CO2

&

2

2