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Observational Constraints on The Evolution of Dust in ...

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Evoluti<strong>on</strong> <strong>of</strong> <strong>Dust</strong> <strong>in</strong> Protoplanetary Disks 89<br />

Figure 4.6 – IRS spectra <strong>of</strong> the disk sources <strong>in</strong> Serpens. Object number is <strong>in</strong>dicated <strong>in</strong> each panel.<br />

In gray are the orig<strong>in</strong>al spectra, while <strong>in</strong> black a b<strong>in</strong>ned versi<strong>on</strong> (us<strong>in</strong>g a Savitzky–Golay (Savitzky<br />

& Golay 1964) filter <strong>of</strong> order 0 and degree 3) is overplotted.<br />

and shift to l<strong>on</strong>ger wavelengths.<br />

A statistical analysis <strong>of</strong> these two features can be d<strong>on</strong>e us<strong>in</strong>g the follow<strong>in</strong>g quantities:<br />

S 10µm<br />

peak is a measure <strong>of</strong> the strength <strong>of</strong> the feature centered at 10 µm and S 11.3/S 9.8<br />

is a proxy for the shape <strong>of</strong> the feature (the smaller this value, the more peaked the<br />

feature is); S 20µm<br />

peak measures the strength <strong>of</strong> the 20 µm feature, while S 23.8/S 19 is a<br />

proxy for this feature shape. Follow<strong>in</strong>g Kessler-Silacci et al. (2006), S λ is def<strong>in</strong>ed as:<br />

S λ = 1 + 1 2δ<br />

In this paper, we use δ = 0.1 µm.<br />

∫ λ+δ<br />

λ−δ<br />

F λ − C λ<br />

C λ<br />

dλ. (4.1)<br />

Kessler-Silacci et al. (2006) found a global trend (best fit to observati<strong>on</strong>s) for both<br />

features (Figure 9 <strong>in</strong> their paper and Figure 4.9 <strong>in</strong> this <strong>on</strong>e), <strong>in</strong>dicat<strong>in</strong>g that the<br />

feature shape and strength are physically related, as expected if the silicate features

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