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Dust Continuum. Intensity Column density Mass. Dust emission. 1.3 mm dust emission (Motte & Andre 2001). Simple case:. If τ
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Dust Continuum
Intensity Column density Mass
Dust emission
1.3 mm dust emission (Motte & Andre 2001)
Schnee et al, 2007, ApJ
If τand Td=constant
Dust Temperature Td and emissivity spectral index can be solved!
Under Rayleigh-Jeans limit and τ
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Sν ∝κ ν B(Td )∝ν α
∝ν β ⋅ν 2 = ν β +2
∴ spectral index α = β +2
Simple case:
Beckwith & Sargent (1991):
-1<<1
power law envelope
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density
ρ ∝ r−p
temperature
T ∝ r−q
emissivity
κ ν ∝νβ
⇒ Sν ∝νβ +2 ⋅r−( p+q )
Motte (1998) :
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T ∝ r−0.4
Beckwith & Sargent (1991):
-1<<1
Mundy et al. (2000), PPVI
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ρ ∝ r−1.5 ~ r−2.0
Dust modeling:Spitzer (1977): Chap 7-9Draine & Le (1984)Draine, 2003, ARA&A