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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 133<br />

10 % <strong>of</strong> each <strong>of</strong> the Serpens and Taurus samples, so the statistical results derived here<br />

should not be affected by this removal. <strong>The</strong> f<strong>in</strong>al sample <strong>of</strong> 139 sources analysed is<br />

composed <strong>of</strong> 60 objects <strong>in</strong> Serpens, 66 <strong>in</strong> Taurus, 9 objects <strong>in</strong> Upper Scorpius, and<br />

4 <strong>in</strong> η Chamaele<strong>on</strong>tis. <strong>The</strong> statistical uncerta<strong>in</strong>ties <strong>of</strong> the spectra were estimated as<br />

expla<strong>in</strong>ed <strong>in</strong> Ol<strong>of</strong>ss<strong>on</strong> et al. (2009).<br />

<strong>The</strong> great majority <strong>of</strong> the objects studied here are low-mass stars (spectral types<br />

K and M, see Tables A.1 and A.2). <strong>The</strong> study <strong>of</strong> m<strong>in</strong>eralogical evoluti<strong>on</strong> across stellar<br />

mass is not the focus <strong>of</strong> this paper. Such a study would require a separate paper,<br />

<strong>in</strong> which the same techniques are used for low- and <strong>in</strong>termediate-mass stars. Thus,<br />

the statistical results derived <strong>in</strong> the follow<strong>in</strong>g secti<strong>on</strong>s c<strong>on</strong>cern T Tauri stars, and not<br />

necessarily apply to <strong>in</strong>termediate-mass Herbig Ae/Be stars.<br />

6.3 Spectral Decompositi<strong>on</strong> and the B2C Method<br />

In order to reproduce the observed IRS spectra <strong>of</strong> these circumstellar disks the B2C<br />

decompositi<strong>on</strong> method, expla<strong>in</strong>ed <strong>in</strong> detail and tested extensively <strong>in</strong> Ol<strong>of</strong>ss<strong>on</strong> et al.<br />

(2010), is applied. Two dust gra<strong>in</strong> populati<strong>on</strong>s, or comp<strong>on</strong>ents, at different temperatures<br />

(warm and cold) are used <strong>in</strong> the method, <strong>in</strong> additi<strong>on</strong> to a c<strong>on</strong>t<strong>in</strong>uum emissi<strong>on</strong>.<br />

<strong>The</strong> warm comp<strong>on</strong>ent reproduces the 10 µm feature, while the cold comp<strong>on</strong>ent reproduces<br />

the n<strong>on</strong>-negligible residuals at l<strong>on</strong>ger wavelengths, over the full spectral range<br />

(see Figure 6.1). Each comp<strong>on</strong>ent, warm and cold, is the comb<strong>in</strong>ati<strong>on</strong> <strong>of</strong> five different<br />

dust species and three gra<strong>in</strong> sizes for amorphous silicates or two gra<strong>in</strong> sizes for<br />

crystall<strong>in</strong>e silicates.<br />

Figure 6.1 – Example <strong>of</strong> the B2C model<strong>in</strong>g for object #15 <strong>in</strong> Serpens. <strong>The</strong> down-most black l<strong>in</strong>e is<br />

the estimated c<strong>on</strong>t<strong>in</strong>uum for this source. <strong>The</strong> dark gray l<strong>in</strong>e is the fit to the warm comp<strong>on</strong>ent (fitt<strong>in</strong>g<br />

well the 10 µm feature) and the black l<strong>in</strong>e is the fit to the cold comp<strong>on</strong>ent (c<strong>on</strong>tribut<strong>in</strong>g mostly to<br />

l<strong>on</strong>ger wavelengths). <strong>The</strong> light gray l<strong>in</strong>e is the f<strong>in</strong>al fit to the entire spectrum. <strong>The</strong> orig<strong>in</strong>al spectrum<br />

is shown <strong>in</strong> black with its uncerta<strong>in</strong>ties <strong>in</strong> light grey. (A color versi<strong>on</strong> <strong>of</strong> this figure is available <strong>in</strong><br />

the <strong>on</strong>l<strong>in</strong>e journal)<br />

<strong>The</strong> three amorphous species are silicates <strong>of</strong> oliv<strong>in</strong>e stoichiometry (MgFeSiO 4 ),<br />

silicates <strong>of</strong> pyroxene stoichiometry (MgFeSiO 6 ), and silica (SiO 2 ). <strong>The</strong> two crystall<strong>in</strong>e<br />

species are both Mg-rich end members <strong>of</strong> the pyroxene and oliv<strong>in</strong>e groups, enstatite

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