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