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\shorttitle{FEPS: dust processing in TTS systems}
\shortauthors{Bouwman et al.}

\begin{document}

\title{The formation and evolution of planetary systems: \\
Grain growth and chemical processing of dust in T~Tauri systems.}

\author{J.\,Bouwman and Th.\,Henning}
\affil{Max Planck Institute for Astronomy, K\"onigstuhl 17, D-69117, Heidelberg, Germany}
\and
\author{L. A. \,Hillenbrand}
\affil{Department of Astronomy, California Institute of Technology, Pasadena, CA 91125.}
\and
\author{M.R.\,Meyer}
\affil{Steward Observatory, University of Arizona, 933 N. Cherry Ave., Tucson, AZ 85721-0065}
\and
\author{I.\,Pascucci}
\affil{Steward Observatory, University of Arizona, 933 N. Cherry Ave., Tucson, AZ 85721-0065}
\and
\author{J.\,Carpenter}
\affil{Department of Astronomy, California Institute of Technology, Pasadena, CA 91125.}
\and
\author{D.\,Hines}
\affil{Space Science Institute,4750 Walnut Street, Suite 205 Boulder, CO 80301.}
\and
\author{J.S.\,Kim and M.D.\,Silverstone}
\affil{Steward Observatory, University of Arizona, 933 N. Cherry Ave., Tucson, AZ 85721-0065}
\and
\author{D.\,Hollenbach}
\affil{NASA Ames Research Center, Moffet Field, CA 94035}
\and
\author{S.\,Wolf}
\affil{Max Planck Institute for Astronomy, K\"onigstuhl 17, D-69117, Heidelberg, Germany}


\begin{abstract}
This paper is one in a series presenting results obtained within the Formation
and Evolution of Planetary Systems (FEPS) Legacy Science Program on the {\it Spitzer
Space Telescope}. Here we present a study of dust processing and growth
in seven protoplanetary disks within the FEPS sample.
The infrared silicate emission features of these protoplanetary disks indicate dust grains substantially different form those in the interstellar medium (ISM).
First, the amorphous silicates have growth to sizes at least 10 times larger. Second, there is a non-negligible 
($sim$5\% in mass fractions) contribution from crystalline species.
We find a correlation
between the strength of the amorphous silicate feature and the shape of the
spectral energy distribution. This latter result is consistent with the growth
and subsequent gravitational settling of dust grains towards the disk mid-plane.
We find that the average size of the crystalline silicates grains is much smaller and
not related to that of the amorphous silicate grains. This suggests that either
the crystallisation occurred at early evolutionary stages before substantial
growth of the amorphous material occurred or that the crystalline material
formed separately from the gas-phase. Further, we find a change in the relative
abundance of the different crystalline species: more enstatite relative to forsterite is observed in the inner warm dust population at about $\sim$1 AU, while forsterite dominates in the colder outer regions at about $\sim$15 AU. 
This change in the relative abundances suggests differences in the formation mechanism of
the crystalline silicates as a function of radius, and argues for a localised
crystallisation process rather than a radial mixing scenario where
crystalline silicates are being transported outwards from a single formation
region in the hot inner parts of the disk. Last, we report the detection of
emission from polycyclic aromatic hydrocarbon molecules in five out of seven
sources. We find a tentative PAH band at 8.2~$\mu$m, previously undetected in 
the spectra of disks around low-mass pre-main-sequence stars.
\end{abstract}



\keywords{pre-main-sequence stars -- circumstellar disks --- circumstellar dust --- planetary systems}

\section{Introduction}

The circumstellar disks surrounding the pre-main-sequence Brown Dwarfs (BD), T~Tauri stars (TTS)
and Herbig~Ae/Be (HAEBE) systems are believed to be the sites of ongoing planet
formation \citep[e.g.][from here on we will refer to these disks as protoplanetary disks]{Luhman2007,Natta2007}.
As most of the youngest ($<$1~Myr) solar-mass stars have circumstellar disks
\citep{Strom1989}, with typical masses \citep{beckwith1990} and sizes
\citep{mcCaughrean1996, Dutrey1996} comparable to the expected values for the
primitive solar nebula, these disks are the natural candidates for the
birth-sites of planets. The sub-micron sized dust grains present initially
in these disks can coagulate to form larger objects and
eventually earth-like planets \citep[e.g.][]{weidenschilling1997,henning2006}.
By deriving the composition of the circumstellar dust, and identifying the
processes governing the chemistry and coagulation, valuable insights can be
gained in the workings of protoplanetary disks
\citep[e.g.][]{processing,hd100546,Roy2003,Roy2005,Przygodda2003,
Kessler-Silacci2006, Sargent2006} and thus the planet formation process. The
results of these analyses can be compared directly with the investigation of
solar system objects like comets, meteorites and interplanetary dust particles
(IDPs), which preserve a record of the early phases in the evolution of the solar
system.  

With the IRAS and ISO missions, a tremendous advance in our knowledge of
protoplanetary disks was achieved. However, the spectroscopic studies with
these missions were limited to relatively nearby and luminous stars of
spectral type A and B, and provided only limited knowledge of the evolution of
solar-mass systems. With the launch of the  {\it Spitzer Space
Telescope} \citep{Werner2004}, these less luminous systems became accessible to
observations. The FEPS {\it Spitzer} Legacy program probes the circumstellar dust
properties around a representative sample of protoplanetary disks and debris
disks, spanning a wide range of circumstellar disk properties and covering the
major phases of planet system formation and evolution \citep{meyer2007}

We present an analysis of the infrared (IR) spectra of
protoplanetary disks around seven pre-main sequence systems
observed within the FEPS legacy program. These are the only systems among the 
328 FEPS targets showing spectroscopic features from solid state dust components.
\citep[See][for a detailed description of the FEPS parent sample]{meyer2007}.
In Table~\ref{tbl:stars} the astrophysical parameters
of these seven stars are compiled.
Five of the systems,
RX J1842.9-3532,       
RX J1852.3-3700,       
1RXS J132207.2-693812, 
RX J1111.7-7620, and
1RXS J161410.6-230542 ,
were identified in \cite{Silverstone2006}
as optically-thick primordial disks on the basis
of their IRAC colors and excess emission at wavelengths shorter than 8~$\mu$m. 
\cite{Silverstone2006} provide a literature review for the
five stars identified in their study. In addition to these five systems,
HD~143006 and RX~J1612.6-1859A also show evidence for
optically-thick disks and solid state features. We give a literature review for the latter two stars in Appendix~A. HD~143006 was added to the FEPS sample on the basis of its IRAS excess
emission, in order to search for remnant gas
in that system \citep[e.g.][]{pascucci2006}.  The solid state
features in RX~J1612.6-1859A were noticed from visual inspection
of each spectrum as it was reduced.  No other sources in the
FEPS sample show evidence for solid state emission features.
Of these 321 sources, most lack excess in the IRS wavelengths,
and a few exhibit optically-thin emission from debris.
No other optically-thick circumstellar disk sources are
present in the data other than the seven with solid state
emission features discussed here.


We study the compositional properties of the systems listed in
Table~\ref{tbl:stars} using 5-35~$\mu$m spectra obtained with the Infrared
Spectrograph \citep[IRS;][]{Houck2004} on-board the {\it Spitzer Space Telescope}. We focus
on silicate grain processing (silicates make up the bulk of the refractory
dust mass assuming solar system abundances) and perform a quantitative analysis
of the observed solid state emission.  Using a consistent analysis
method for the entire sample, the derived grain composition of the individual
systems can be compared directly. This enables us look for signs of silicate grain processing. Apart from analyzing the 10~$\mu$m spectral
region, also accessible to ground-based studies, {\it Spitzer} provides access to the
silicate resonances at longer wavelengths. This enables us to study the
dust composition of not only the warmest dust (temperatures between $\sim$ 500
-- 1000 K), located in the inner parts ($\sim0.1-1$~AU) of the protoplanetary
disks around solar-like stars, but also the cold ($\sim$ 100 K) dust component in the outer regions
($\sim$15~AU) of the disks.  

This paper is organized in the following way: In section~2 we discuss the data
reduction, introduce the main dust components and present the method used to
analyze the Spitzer IRS spectra. In section~3 modelling results are presented
and in section~4 we discuss implications for the evolution of the dust
in the circumstellar disks around solar-mass stars.

\section{Observations and Dust Models}
\subsection{The IRS Low-Resolution Spectra}

We obtained low-resolution ($R=\sim60-120$) spectra with
the IRS instrument on-board {\it Spitzer}. A high accuracy IRS or PCRS
peak-up (with a 1$\sigma$ pointing uncertainty of 0.4" radius) 
was used to acquire targets in
the spectrograph slit, thus minimizing slit losses and assuring high photometric
accuracy to about 10\%. Two nod positions per cycle were obtained in standard staring mode
with a minimum of six cycles per target for redundancy and to allow
the rejection of artifacts introduced by bad pixels or cosmic ray hits. The
integration times were 6s and 14s for the brightest and faintest sources,
respectively. The targets were observed with the full spectral coverage of the
IRS low-resolution instrument between 5.2 and 35~$\mu$m. Beyond 35~$\mu$m the
spectra suffer from excess noise \citep{Houck2004} and can not be used.

Our spectra are based on the {\tt droopres} intermediate data product processed
through the SSC pipeline S12.0.2. Partially based on the {\tt SMART} software
package \citep[][for details on this tool and extraction methods]{Higdon2004},
our data is further processed using spectral extraction tools developed for the
FEPS {\it Spitzer} science legacy program.  As a first step, we correct for the
background emission and stray-light by subtracting the associated pairs of
imaged spectra of the two nodded positions along the slit for each module and
order. In this way we also correct for pixels having an anomalous dark current.
Pixels flagged by the SSC data pipeline as ``bad'' were replaced with a value
interpolated from an 8 pixel perimeter surrounding the errant pixel. We then
extracted the spectra from the resulting set of images using a 6.0 pixel and 5.0
pixel fixed-width aperture in the spatial dimension for the observations with
the short- (5.2 - 14~$\mu$m) and long-wavelength (14-35~$\mu$m) modules,
respectively. The low-level fringing at wavelengths $>$20~$\mu$m was removed
using the {\tt irsfringe} package \citep{lahuis2003}.

Absolute flux calibration was achieved in a self-consistent manner using the
ensemble of FEPS observations. As the majority of the 328 FEPS program stars
exhibit stellar photospheres throughout the shorter wavelength range of the IRS, this data set
is unique for calibrating the IRS instrument. From our full set of
FEPS observations we selected a subset of the spectra which complied with the following
criteria: 1) colors (24-33~$\mu$m) within 1$\sigma$ of an extrapolated best-fit model
photosphere \citep[e.g.][]{meyer2004, carpenter2006} 
and 2) Signal-to-noise ratio (SNR) larger than 50 with no artifacts
within the spectra. This resulted for the first order of the short wavelength
module (SL1) and the long wavelength module spectra (LL1, LL2) in a set of 16
stars and for the shorter wavelength orders (SL2) in a subset of 10 stars. Together
with the stellar photospheric models for these two subsets, we used these spectra to derive the relative spectral response functions (RSRFs) for the
absolute flux calibration. For the relative (point to point) calibration, we
derived RSRFs using six calibration stars observed at different epochs with the
Cohen photospheric models provided by the SSC, having a superior SNR. This procedure ensures
that the RSRFs used to calibrate our protoplanetary disk spectra have the highest possible SNR
and an estimated absolute flux calibration uncertainty of $\sim$10\%. For further
details on the flux calibration see the explanatory supplement for the FEPS
data, delivered to the {\it Spitzer} data archive (Hines et al. 2005).

The resulting calibrated spectral energy distributions are shown in
Fig.~\ref{fig:specta}. A detailed view of these spectra in three wavelength
bands, showing more clearly the solid-state
emission features is presented in Fig.~\ref{fig:fit}. As one can see from
Fig.~\ref{fig:specta}, a wide range in spectral shape and emission feature
strength can be observed. In the next section we will discuss the analysis
methods and the different silicate components and grain models used to interpret
the spectra shown in Fig.~\ref{fig:fit}.


\subsection{Outline of Spectral Analysis Methods}
\label{sec:analysis}

For the analysis and interpretation of our observations we use a two-fold
approach. First, we characterize the spectra by measuring the
strengths and positions of spectral features. Second, we decompose the observed emission features to  determine the relative contribution of different silicate grains.
For the spectral characterization we employ a method similar to schemes previously used
to analyse IR spectra from the Infrared Space Observatory
\citep[e.g.][]{molster2002B,molster2002A} and ground-based observations
\citep[e.g.][]{Roy2005}. To measure the emission band strengths and positions,
we first fit a low order polynomial (second order in the 10~$\mu$ region, fifth order for $\lambda > 15$~$\mu$m) to the spectral data points excluding obvious
spectral features (e.g. the continuum). As a next step we normalize our spectra to the fitted
continuum as 
$F_{\nu,\mathrm{norm}} = 1 + (F_{\nu,\mathrm{obs}}-F_{\nu,\mathrm{cont}})/<F_{\nu,\mathrm{cont}}>$,
where $F_{\nu,\mathrm{obs}}$ is the observed 
Spitzer flux,  $F_{\nu,\mathrm{cont}}$ is the fitted continuum, and $<F_{\nu,\mathrm{cont}}>$ the mean continuum value over the fitted wavelength interval. This 
normalization allows us to directly compare the different spectra and, ensures 
that the shape of the spectral features remains identical to that in the original, 
unnormalised, spectra.

To characterise the 10~$\mu$m amorphous silicate
band we determined the fluxes at different wavelengths across the silicate
feature in the normalized spectra. The results of this analysis are presented in Section~3.  Amorphous
silicates also show a band at around 18~$\mu$m. However, this band blends with
the (often rising) continuum emission, as can for instance be seen in
Fig.~\ref{fig:specta}. This makes it difficult, if not impossible, to determine the
band strength and position with sufficient accuracy for a meaningful analysis.
We, therefore, opted not to use this band in our analysis.  At longer
($>$20~$\mu$m) wavelengths the emission features are mainly produced by
crystalline silicates.  To measure the observed band positions and strengths, we
simultaneously fitted a Gaussian to each of the main spectral features in the normalized
spectra. The results of this analysis are also presented in Section~3.  For the
crystalline silicate emission bands in the 10~$\mu$m wavelength region, a
slightly modified analysis method has to be applied. In this wavelength range,
the emission bands overlap with, and can be dominated by emission from small
amorphous silicate grains. Also, PAH molecules may contribute to the observed
emission in the short wavelength range, overlapping with the emission features
of the crystalline silicates. Therefore, the crystalline contribution can only
be estimated by fitting a detailed grain model (discussed in the next section)
determining the contribution of the amorphous silicates and PAH molecules. After
subtracting the fitted contribution of the amorphous silicate and PAH molecules,
we applied an analysis for estimating the different crystalline silicate band
strengths in the 10~$\mu$m wavelength region, similar to that for the longer
wavelength crystalline bands. 

\subsection{Dust Models}
\label{sec:model}

The grain model and analysis method for determining the physical properties of
the dust grains contributing to the observed emission are similar to those
successfully applied in previous studies of the 10~$\mu$m region \citep[see][for further
discussion]{processing,Roy2005}. Here,  we also apply this
method to the silicate emission at longer ($\sim$20-30~$\mu$m) wavelengths. Dust in 
protoplanetary disks has most likely the structure of highly irregular
aggregates containing many different dust constituents, like
the interplanetary dust particles collected in the Earth's upper atmosphere. Calculating the optical properties of such
complex structure has proven to be extremely difficult \citep[ e.g.][]{henning1996}. 
However, assuming that the aggregates are extremely porous, the
individual constituents making up the aggregate may interact with the radiation
field as separate entities, as is the case of IDPs \citep[][]{molster2003}. 
Therefore, we assume that the observed emission can be represented by the sum of the
emission of individual dust species. Table~\ref{tbl-species} summarises the dust
species used in our analysis, including all dust species commonly identified in protoplanetary disks \citep[e.g.][]{Sargent2006,Roy2005,processing}. 


Crystalline silicates such as forsterite (Mg$_2$SiO$_4$) and enstatite (MgSiO$_3$) have many strong and narrow resonances in the wavelength range covered by the IRS spectrograph.
These rotational/vibrational bands allow for an accurate determination of the chemical composition,
grain size and shape/porosity of the crystalline dust species. We find, like in the above mentioned studies, that the pure magnesium end-members of the olivine and pyroxene families, together with the assumption of an inhomogeneous grain structure and/of non-spherical grain shape gives the best match to the observed spectral features. Here we use a distribution of hollow spheres \citep[DHS;][]{min2005} which gives an excellent match to the observed band positions and shapes;\citep[see][ for a further discussion of grain shape and porosity effects]{voshchi2006,min2006}. 
Based on the comparisson between the in our spectra observed band positions and strengths,
and laboratory measurements \citep{Fabian2001,Koike2003}, we find no evidence for iron containing crystalline silicates.

For the amorphous iron/magnesium silicates the exact composition and grain shape can not be constrained as well as for the crystalline silicates. Models of the broad amorphous silicate
resonances at $\sim$10~$\mu$m and $\sim$18~$\mu$m are to some extent degenerate. Silicate models with varying magnesium to iron ratios and different grain shapes/homogeneity can reproduce the observed bands \citep[e.g.][]{Min_ISM}. To allow for a direct comparison with previous studies,
we assume here that the amorphous silicates have an equal magnesium to iron atomic ratio, and
stoichiometries consistent with olivine and pyroxene. Further, for the amorphous iron-magnesium silicates we assume homogeneous, spherical grains for which we calculate the absorption coefficients using the Mie theory \citep[e.g.][]{bohren1983} and the optical constants listed in
Table~\ref{tbl-species}. 

To take into account the effect of grain size, we calculated for each of the different grain
species the opacities for three volume equivalent grain radii of 0.1~$\mu$m, 1.5~$\mu$m
and 6.0~$\mu$m, respectively. These grain sizes sample the range of
spectroscopically identifiable grain sizes at infrared wavelengths at the SNR of
our data. The resulting calculated opacities for three successive wavelength
regimes are shown in Figs.~\ref{fig:kappa_short}, \ref{fig:kappa_mid} and
\ref{fig:kappa_long}. We present our analysis of the various dust species in
Sections ~\ref{sec:coagulation}, \ref{sec:settling}, and 
~\ref{sec:crystalline}. 

Apart from the silicate dust species, PAH molecules also
contribute to the observed emission bands within the spectral range of the IRS
instrument. These large molecules are not in thermal
equilibrium with the radiation field, but are stochastically heated. Though many
of the observed spectral features can be linked to specific vibrational modes
and ionisation states of the molecules, the exact composition remains unclear.
As our main focus in this paper is the solid-state component in the protoplanetary disks,
we opted to use a template spectrum, based on observed profiles by
\cite{peeters2002} and \cite{diedenhoven2004}, for estimating the contribution of PAH molecules
to the spectra. We present this analysis in Section~\ref{sec:pah}.

The thermal infrared emission from protoplanetary disks is
determined by the complex spatial distribution of individual dust species,
and the radial and vertical optical depth and temperature distributions. A
completely self-consistent model of protoplanetary disks, such as a full
radiative transfer calculation, would also have to account for processes such as
radial and vertical mixing of circumstellar material and chemical and structural
alteration of the dust grains under varying physical conditions in different
parts of the disk. Further, to uniquely constrain such models, spatially
resolved observations as a function of wavelength \citep[e.g.][]{Thamm1994} are necessary.  
Instead, we employ a more simplistic approach which has
been demonstated to successfully reproduce the silicate emission features of
HAEBE and TTS systems. Detailed self-consistent models \citep[e.g.][]{menshchikov1997,CG,dullemond2001} have shown that the 
emission features originate from a warm optically thin disk surface layer on top an optically thick disk interior, producing continuum emission.
The basic assumption of our simple model is that the disk emission features can be reproduced 
by a sum of emissivities at a given temperature T$_\mathrm{dust}$, and the continuum emission by the emission of a black body at a given temperature T$_\mathrm{cont}$, which could be interpreted as the typical color temperature of the underlying continuum at a given wavelength. 

We thus fit the following emission model 
using a linear least square minimization to the Spitzer low-resolution spectra:
\begin{equation}
\label{eq:1}
F_\nu = B_\nu(T_\mathrm{cont}) C_0 + B_\nu(T_\mathrm{dust}) \left(\sum_{i=1}^3\sum_{j=1}^5 C_{i,j} 
\kappa_\nu^{i,j} \right) + C_\mathrm{PAH} I_\nu^\mathrm{PAH},
\end{equation}
where $B_\nu(T_\mathrm{cont})$ denotes the Planck function at the characteristic 
continuum temperature $T_\mathrm{cont}$,
$B_\nu(T_\mathrm{dust})$ the Planck function at the characteristic silicate grain 
temperature $T_\mathrm{dust}$, $\kappa_\nu^{i,j}$ is the mass absorption coefficient for 
silicate species $j$ (five in total) and grain size $i$ (three in total), 
$I_\nu^\mathrm{PAH}$ is the PAH template emission 
spectrum, and $C_0$, $C_{i,j}$ and $C_\mathrm{PAH}$ are the weighting factors of the continuum, 
the silicate components and the PAH contribution, respectively. For the single temperature 
approximation to be meaningful, the width of the spectral region, and thus the temperature 
range, needs to be sufficiently narrow. Therefore, we have split the observed spectra 
into three bands: from 6 to 13~$\mu$m, from 17 to 26~$\mu$m, and from 
26 to 36~$\mu$m. Apart from the previous considerations, these wavelength boundaries 
also ensure that both continuum and spectral features can be well characterized, and that 
multiple bands of the main crystalline silicates can be modeled simultaneously. 
We have limited the maximum temperature in our fits to 1500~K, above which all silicate dust is expected to be vaporized.

Fig.~\ref{fig:fit} shows the resulting best-fit models for the three spectral
regions. As one can see, a good agreement between model and observations can be 
obtained using the dust species discussed in this section, without the need for additional components.
The resulting model parameters are listed in
Table~\ref{tab:t2_fs:fits}. We estimate the uncertainties in the derived band
strengths and positions and the best-fit dust compositions by the following method: 
We generate a set of 100 spectra for
each observation  by
randomly adding Gaussian noise with a 1~$\sigma$ distribution equal to the error
in the spectral extraction determined for each spectral data point. For each of
these simulated spectra, we applied the analysis methods described above. Our
quoted results represent the mean values of the derived quantities and the error
is the 1~$\sigma$ standard deviation in the mean. 

\section{Results}

Following the dust modeling and spectral decomposition, our main science
results are in the areas of dust coagulation from the analysis of the 10 $\mu$m
amorphous silicate feature, dust settling from the additional analysis of the
overall SED shape, crystallinity from the analysis of the various silicate dust
species, and PAHs, which remain in the residual emission after subtracting the identified
silicates.

\subsection{Coagulation in protoplanetary disks}
\label{sec:coagulation}

Grain size strongly influences the infrared opacities, as can be seen in
Fig.~\ref{fig:kappa_short} to \ref{fig:kappa_long}. Typically, for the
observations presented here, grain sizes (assuming compact grains) of up to
10~$\mu$m can be inferred spectroscopically. This is two orders of magnitude
larger than the grain sizes typically derived for dust grains in the ISM ($\le 0.1$~$\mu$m). 
For larger grains,
the spectral signatures become too weak to distinguish them from continuum
emission. Amorphous iron-magnesium silicates, making up the bulk of the solid
state material in the ISM, show two broad spectral features at about 10~$\mu$m and
18~$\mu$m from which grain sizes can in principle be determined. The latter
band, however, often blends with continuum emission from the disk interior and
colder dust grains at larger radii, making it difficult to determine the
grain size. For this reason, the 10~$\mu$m silicate band gives
the most accurate information concerning amorphous silicate grain sizes. Many
previous studies have shown that both the shape \citep[][]{processing} and
strength \citep[][]{Roy2003,Roy2005,Przygodda2003,schegerer2006,Kessler-Silacci2005,
Kessler-Silacci2006} of the 10~$\mu$m silicate features observed in HAEBE and TTS 
systems are mainly determined by the size of the amorphous silicate grains.

Fig.~\ref{fig:cor_shape} shows the
correlation between the shape and strength of the 10~$\mu$m silicate feature as
measured by the relation between the peak over continuum strength of the
10~$\mu$m silicate feature and the ratio of normalized fluxes at 11.3 to
9.8~$\mu$m (filled symbols) and at 8.6 to 9.8~$\mu$m (open symbols). Though crystalline silicate emission bands will also influence the shape of the 10~$\mu$m silicate band, the
correlations of Fig.~\ref{fig:cor_shape} can be best explained by a change in the 
typical size of the emitting dust grains. 
The dashed line shows the expected correlation for an amorphous
silicate of olivine stoichiometry with a grain size changing continuously from
0.1~$\mu$m (lower right) to 2~$\mu$m (upper left). The only exception is
the 8.6 over 9.8~$\mu$m ratio of RX~J1612.6-1859A (\#3), where the ratio is
dominated by an unusually strong  emission from enstatite and
silica.  Fig.~\ref{fig:cor_size_mass} shows the relation between the mass weighed 
grain size of the amorphous iron-magnesium silicates (open symbols; right axis) as derived
from our spectral decomposition of 0.1, 1.5 and 6~$\mu$m grains and the 
peak over continuum value of the 10~$\mu$m silicate band. 
This correlation demonstrates that the peak
to continuum ratio is correlated to the estimated size of the emitting amorphous iron-magnesium silicate grains.

As a note of caution, recall that
the exact values for the grain sizes derived  are
linked to the grain model used in the spectral decomposition. For reasons
discussed in Section~\ref{sec:model}, we use homogeneous spheres to model the
amorphous silicates.  More complex grain structures, like fractal high-porosity grains give
qualitatively similar results \citep[e.g.][]{voshchi2006, min2006}, but require much larger
aggregates to reproduce the observed band strengths.

\subsection{Coagulation and dust settling}
\label{sec:settling}

Having explored grain growth for our sample of T Tauri disks
compared to the ISM grain population, we now ask what
effect coagulation could have on the disk structure itself. As we do not have
spatially resolved observations, we use the shape of the SED to infer the geometry of the disks. 
It is long known that the disk geometry strongly influences the
shape of the SED \citep[e.g.][]{kenyon1987}. Strongly flaring disks,
intercepting a substantial fraction of the radiation from the central star at large radii,
show a rising SED peaking at around 100~$\mu$m.
'Flattened' disks, on the other hand, intercept far less
of the radiation from the central star, and show a
power-law-like SED decreasing with wavelength. 
\cite{HerbigOverview} showed that the disks in HAEBE systems
can be divided into two groups based on the shape of their SEDs.
\cite{HerbigOverview} interpret this bi-modal behaviour of the SED in terms of a
bi-modal disk geometry, having either a flaring or a 'flattened' disk structure.
 Recent spatially resolved observations seem to confirm the interpretation that the
different SEDs can be linked to different disk geometries
\citep[e.g.][]{leinert2004}. As an explanation for the different disk geometries
two different models have been proposed: (1) grain growth and gravitational settling towards the
disk mid-plane, and (2) 'self shadowing' of the disk surface at larger radii by the inner ($\sim0.1$~AU) disk.

%Though dust grains constitute only $\sim$1~\% of the mass of
%the circumstellar disk assuming solar abundances, they completely dominate the
%IR emission. Grain dynamics are, however, determined by the gas under the
%condition that both are well coupled and the gas mass density exceeds the dust mass density. 
%An increase in grain size can cause the dust grains to decouple from the gas. 

Coagulation models show that if the dust
grains in the upper layers of a flared disk become sufficiently large, 
they will gravitationally settle towards
the mid-plane of the disk, resulting in a flattened disk geometry \citep[e.g.][]{Schraepler2004,nomura2006}.
Recent model calculations concerning the effect of grain coagulation and settling on the SED show 
that the changing dust geometry from a flaring towards a flattened geometry due to the grain settling results in SEDs consistent with observations \citep[][]{allessio2006,dullemond_settling2004}. 

As an alternative, \cite{dullemond2004} explain the variation in observed SED shapes for HAEBE
and TTS systems as differences in disk heating caused by differences in the
self-shadowing of the disk surface. If the central
star can not directly irradiate the outer disk surface due to a puffed-up inner disk
(causing the surface of the outer disk to lay in the shadow of the inner disk), the temperature and
thus the scale height of the shadowed region will be substantially lower compared
to a disk with a directly irradiated surface. This lower temperature will result in a 
smaller pressure scale height of the disk and thus in a 'flattened' geometry.

A way to test these models is to look for a relation between the measured grain sizes and the 
geometry of the disk. In Fig.~\ref{fig:cor_slope} we explore the relation between the amorphous
silicate grain sizes, as measured by the strength of the 10~$\mu$m silicate
feature, and the disk flaring angle, as measured by the 33~$\mu$m over 24~$\mu$m
(top figure) and 70~$\mu$m over 13~$\mu$m flux ratio (lower panel) flux ratios.
Here, the 13, 24 and 33~$\mu$m fluxes are synthetic photometry points derived from our IRS
spectra using an ~$\sim$1~$\mu$m wide box centered on the quoted wavelenghts. The 70$\mu$m fluxes are derived from MIPS observations.
Larger flaring angles of the disk produce larger flux ratios because of enhanced
emission from cooler grains further out in the disk that are exposed to the 
stellar flux by the flaring.
With increasing grain size (decreasing 10~$\mu$m silicate band) the flaring
angle of the disk appears to decrease (as traced by the slope of the SED towards longer
wavelengths). Our results are in qualitative agreement with the model
predictions of \cite{allessio2006} and \cite{dullemond_settling2004},
and provide direct spectroscopic evidence
for the link between the typical size of the dust grains and the disk structure.
These results suggest that in TTS systems it is coagulation and grain settling 
towards the mid-plane which determines the disk geometry and thus the SED, 
rather then self-shadowing by the disk.




\subsection{The crystalline silicates in protoplanetary disks}
\label{sec:crystalline}

The analysis of features produced by crystalline silicates  provides important
information on dust processing in protoplanetary disks. Presently, no
crystalline silicates have been observed in the diffuse ISM. \cite{kemper2005}
place an upper limit of 1\% on the crystalline silicate mass fraction of the
diffuse ISM. The much higher mass fractions observed in protoplanetary disks 
\citep[e.g.][$\sim$5\% in this study]{processing,Roy2005}
therefore, imply that the observed crystalline silicates had to be formed in the
disks themselves, rather then being incorporated directly from the ISM into the
disk \citep[see][]{henning2005}. This makes crystalline silicates a 
tracer of dust processing and evolution in protoplanetary disks.
Figs.~\ref{fig:young_disks_short_no_amorf} and
\ref{fig:young_disks_long_no_cont} show the observed crystalline silicate bands
at mid- and far-IR wavelengths, respectively, for our TTS sample. As described
in Section~\ref{sec:analysis} the spectra have been normalized and, for the 10 $\mu$m
regime, corrected for the amorphous silicate contribution. These normalised
spectra clearly show the emission bands characteristic of emission from the
crystalline dust species forsterite, enstatite and silica. Using the opacities
plotted in Figs.~\ref{fig:kappa_short} to \ref{fig:kappa_long}, these three
crystalline dust species, in combination with the amorphous silicates, produce an
excellent fit to the Spitzer spectra as shown in Fig.~\ref{fig:fit}. 
The overall mass fraction of crystalline silicates based on the spectral decomposition
of the 10 $\mu$m silicate band is around $\sim$5\% (see also Table~\ref{tab:t2_fs:fits}).
We find no conclusive evidence for other crystalline silicates.
Interestingly, other crystalline dust species, like iron
sulfides or oxides can be expected to exist in protoplanetary disks
\citep[e.g.][]{pollack1996}. Looking at Figs.~\ref{fig:fit} and
\ref{fig:young_disks_long_no_cont}, weak features at 25.5~$\mu$m (source
number 0 and 5) and 30.5~$\mu$m (source number 0 and 3) can be observed which are
not properly reproduced by our dust model. These features, however,
are 1) not conclusively seen in the other targets; 2) the bands do not coincide with
known bands of materials like iron-sulfide or iron-oxide \citep{begemann1994,henning1995};
and 3) no clear relation between these weak bands can be observed. 
The possibility that these very weak bands are an
instrumental artifact in the form of some residual fringing can not be ruled out
at this stage.

\subsubsection{Crystallinity and grain size}

As for amorphous dust grains, the shape, strength and wavelength
positions of the emission bands of the crystalline dust species yield
information on the typical size of the emitting dust grains. As the crystalline
silicates have many narrow spectral features sensitive to shape, size and
composition of the dust grains, an excellent determination of the grain
properties can be made. Using the analysis method described in Section~\ref{sec:analysis},
Figs.~\ref{fig:cor_band_pos} and \ref{fig:cor_bands} show the correlations between the measured
position and strengths of the main forsterite resonances in our TTs sample.  
The observed band positions hardly vary from
the nominal position expected for 0.1~\micron~ sized grains (filled triangles). This is in sharp
contrast to the results for the amorphous silicate component, where grain sizes
of at least 6~\micron~ are required to reproduce our observations. Also, the band
ratios between the main forsterite resonances do not substantially vary from
source to source, leading to a linear relation between the various bands
reflecting differences in the crystalline mass fractions in different sources. 

From the spectral decomposition in the 10~$\mu$m wavelength region (see also
Table~\ref{tab:t2_fs:fits}), we determined the relative mass fraction of
crystalline silicates contributing to the crystalline emission bands.
Fig.~\ref{fig:cor_size_mass} also shows the relation between
the observed amorphous silicate grain size and the crystalline silicate mass
fraction. From this figure, it is clear that the crystallinity and
grain size of the (bulk) amorphous dust are not correlated. Determining the mass
fraction of crystalline silicates depends on how well one can determine the
mass fraction of the amorphous dust component. Within the 10~$\mu$m spectral
region, probing the warmest dust, this poses no problem as the amorphous
silicates show a clear spectral signature. At the longer ($\sim$20~$\mu$m)
wavelengths, probing the colder dust at larger disk radii, however, amorphous
silicates lack clear spectral signatures, which makes it difficult
to determine the physical properties of the
colder grains. However, the strengths of the emission bands over the local
continuum in the $\sim$20 - 30~$\mu$m spectral region, still provide a measure
of the relative crystalline mass fraction as a function of wavelength, and thus
as a function of temperature and hence as a function of radial distance in the disk. Fig.~\ref{fig:cor_xbands}
compares the strength of the 10~\micron~ silicate band -a measure of the typical
grain size of the amorphous silicates- to the observed band strengths and
positions of three of the main crystalline silicate bands. 
No apparent correlation between the amorphous and
crystalline bands can be seen. As both the observed crystalline mass fraction
and size of the crystals are not correlated with the grain size of the amorphous
dust,grain growth and crystallization appear to be unrelated.

At first glance the spectrum of a source like 1RXS~J161410.6-230542
(lower left panel in Fig.~\ref{fig:fit}) seems to exhibit a much higher
crystalline mass fraction than a source like RX~J1842.9-3532 (upper left panel
Fig.~\ref{fig:fit}). The apparently more pronounced crystalline silicate bands
in the former TTS system, however, do not reflect a larger crystalline mass
fraction but rather less amorphous silicate emission.  As the amorphous grains
grow with respect to the crystalline silicates, their relative opacities
decrease and hence their contribution to the observed spectra diminishes. It is,
therefore, crucial to have an accurate determination of the grain size of the
(bulk) amorphous silicates. If we would have used a smaller maximum grain size
in our spectral decomposition, we would have estimated that no amorphous
silicates are present in the 1RXS~J161410.6-230542 system, leading to a 100~\%
crystalline silicate mass fraction. This would, consequently, have led to a
relation between the grain size of the amorphous dust and the crystallinity, as
was noted by \cite{Roy2005}. This result could be
an artifact from underestimating the maximum grain size in their ground based observations, leading to a lower mass estimate of the amorphous dust component. 
Compared with these ground-based studies, 
we should note that the \emph{Spitzer} data have the advantage to allow for a
determination of the continuum outside of the spectral window accessable from
the ground. This results in a better characterization of the strength of the
10~$\mu$m silicate band, and thus of the grain size, especially in the case of
very weak emission features.

\subsubsection{The crystallization process}

Apart from the comparison between the crystalline  and the amorphous emission
bands, the inter-comparison between the crystalline spectral features
can provide crucial information. 
Though we are not spatially resolving the protoplanetary disks, from model calculations of 
the temperature distribution in the disk around a typical TTS, one can make an estimate of the size of the emitting region at a given wavelength \citep[e.g]{Kessler_size}.  \cite{Kessler_size}
aregue that the silicate feature at around 10~$\mu$m originates from the disk surface 
at round 1~AU from the central star. 
The spectral features observed at the longest wavelengths, at around 30~$\mu$m,
correspond to a temperature of $\sim$120~K; the temperature at which a black body would emit most of his radiation at the given wavelength. 
Assuming a $\lambda^{-1}$ dependency for the dust opacity, and a
typical stellar temperature and radius of 5500 K and 1 $R_{\odot}$,
respectively, dust grains attain a temperature of 120 K at a radius 
of about 15~AU from the central star. The implies that with the IRS instrument we can probe the inner $\sim$15~AU of a disk in a TTS system. 
The dust composition of the disks outward of $\sim$15~AU can not be determined as the dust grains at these large radii are to cold to emit at wavelengths covered by the IRS spectrograph.
Comparing the relative band strengths of forsterite in the
10~$\mu$m wavelength region probing the warmest dust, 
with the forsterite bands at longer wavelengths probing the colder dust component 
further out in the protoplanetary disks, a trend can be observed
(see Fig.~\ref{fig:cor_far_ir_bands}). Those systems
showing the strongest forsterite emission bands in the 10~$\mu$m spectral
region also show the strongest bands at the longer wavelengths. 
We interpret this correlation as evidence of a global crystallization process, where the
crystallinity of the inner $\sim$10~AU of the disk is increased from non-detectable ISM values to
the observed mass fractions of about $\sim$5\% as measured in the 10~$\mu$m spectral region.
Weather this means that the crystalline silicates are formed throughout the entire inner disk,
or formed locally and then redistributed throughout the inner disk will be discussed in Section~\ref{sec:discussion}.   
One should note that due to the uncertainties in determining the amorphous mass fractions in a
quantatitive way at the longer wavelengths (see also Section~\ref{sec:model}),
the radial density profile of the crystalline silicates remains uncertain.
It is possible that in colder parts of the disk, at larger
radial distances, the fraction of crystalline grains deviates from that determined for the inner
parts. However, our results show that, irrespective of the exact radial
profile, the crystallinity of the very inner ($\sim$1~AU as measured at 10~$\mu$m) and outer ($\sim$5-15~AU as measured at wavelengths $\sim20-30$~$\mu$m) disk regions
are related.

A similar comparison for the enstatite emission bands is difficult as at the
longer wavelengths our spectra show no features which can be uniquely identified
with enstatite. Comparing the strength of the main enstatite band at 9.2~$\mu$m
and the longer wavelength bands of forsterite we find no clear correlation.
 This suggests that both crystalline species are to a certain extent
unrelated, and a general increase of forsterite abundance seems not to correspond to a
similar increase in enstatite abundance. Although the crystalline silicate mass relative to
that of the amorphous silicates can not be determined at the longer wavelengths, 
our spectral decomposition as a function of wavelength, and thus radius of the emitting regions,
can determine the mass ratios between the different crystalline silicates. In Fig.~\ref{fig:cor_xsil_mid_far_ir} the relation
between the enstatite fraction of the crystalline grain populations as measured
within the 10~$\mu$m wavelength region, 
and that determined from the longer wavelength spectral regions, is
plotted. Surprisingly, these results imply that the mass fraction of enstatite
varies in the radial direction, with a larger enstatite fraction in the warmer
inner disk than in the colder outer ($\sim$5 to 15~AU) regions. Another
difference between the forsterite and enstatite grain population is the typical grain size.
The grain size  of the enstatite grains ($\sim$1~$\mu$m)
is larger than that of the forsterite grains ($\sim$0.1~$\mu$m). Again this
points towards differences in the formation mechanism and/or conditions
producing these crystalline species. The implications of the above results will
be discussed in Section~\ref{sec:discussion}.


\subsection{PAH emission in protoplanetary disks around T~Tauri stars}
\label{sec:pah}
So far, little is known about the presence of PAH molecules in disks around
low-mass pre-main sequence stars. Systems with a relatively strong UV field can
readily excite PAH molecules, as is observed for the more massive and luminous
Herbig~Ae/Be systems where clear PAH emission signatures can be seen \citep[e.g.][]{HerbigOverview,sloan2005}. 
Though observations of UV poor reflection nebula and PAH 
laboratory measurements and models \citep[][]{Li2002,Mattioda2005}
show that longer wavelength photons can also excite PAH molecules, little
evidence has been found for IR emission bands from stochastically heated
molecules or very small grains from the circumstellar disks around low-mass
stars as studied in this paper. After carefully fitting our silicate model, a
residual feature centered at 8.2~$\mu$m could be seen in the model subtracted spectrum of
five of the observed targets, which we tentatively identify
with emission from stochastically heated PAH molecules. Fig.~\ref{fig:pah} shows
the normalised residual spectrum after subtraction of the best-fit silicate model. 
The strongest bands can be seen in the residual spectrum of HD~143006 (\#2), the
most luminous source in our sample (G6/8 spectral type), 
which also shows clear evidence for emission bands at 6.2~\micron~ and 11.2~\micron. 

As the PAH molecules require stellar photons to be excited, the molecules
contributing to the emission bands have to be located at the optically thin
surface layers of the disk, in direct view of the central star. As many papers
have shown for the Herbig~Ae/Be systems \citep[e.g.][]{HerbigOverview, acke_iso_spec2004}, 
there exists a direct correlation between the presence of PAH emission bands and the shape of
the SED, a measure of the flaring angle of the disk. Those disks having an SED
consistent with a flattened disk structure, and hence a less illuminated disk
surface show little or now evidence of PAH emission. These results are also
confirmed by spatially resolved spectroscopy showing the PAH emission bands to
come from the flaring surface at larger radii of the disk
\citep[][]{vanboekel2004}. We can observe a similar trend, where those sources
having SEDs consistent with more flattened disk structures show no clear
evidence for the 8.2~$\mu$m feature. This apparent correlation between the lack
of the 8.2~$\mu$m feature and the flaring angle of the disk, therefore, suggests
that this emission band is not due to an unidentified dust species in thermal
equilibrium, but rather a  stochastically heated large molecule or very small
grain species at the disk surface.

Surprisingly, the observed band in the 8~$\mu$m region is not centered between
7.7 to 7.9~$\mu$m, where PAH emission is usually observed. The band position
at 8.2~$\mu$m has only been  measured in the spectra of a few other sources. 
\cite{peeters2002} observed this band position in two post-AGB stars,
and \cite{sloan2005} observed the feature in the HAEBE system HD~135344.
The observed bands in these three objects, however, show a slightly
broader profile than is observed in the TTS systems. The observed relatively weak
or absent 6.2~\micron~ and 11.2~\micron~ features with respect to the 
8.2~\micron~ band is consistent with the \cite{peeters2002} and \cite{sloan2005}
studies. Further, the HAEBE system from the latter study showing the
8.2~$\mu$m PAH band, has the lowest UV-flux of the four systems discussed in
that paper, which would be consistent with our observations of lower
luminosity systems. Presently, no conclusive explanation for the carrier of the
8.2~\micron~ feature has been put forward. We can only speculate that the
chemistry, ionisation state and/or structure should be substantially different
for our sources compared to the PAH population in HAEBE systems. \cite{Li2002} argue that in an
environment low in UV where longer wavelength photons excite the PAHs, 
the PAH molecules have to be ionised and/or large to be excited. The presumably 
much stronger X-ray emission in the TTS systems with respect to their higher mass 
counterparts may play also a role here, driving a different chemistry and ionisation state.
On the one hand, X-ray photons may increase the electron abundance in the gas which would 
reduce the PAH ionization. On the other hand, a strong X-ray field could directly (multpiple times) ionize the PAH molecules due to the Auger effect, and thereby change them or even 
destoy the smallest. 

\section{Discussion}
\label{sec:discussion}

The circumstellar disks in T~Tauri star systems are believed to be the sites of
on-going planet formation, and thus represent an analogue for the proto-solar
nebula. As the disks evolve with time, the sub-micron sized dust grains present
at the formation time of the disks coagulate to form larger objects and
eventually planet(esimal)s \citep{Beckwith2000, henning2006}. 
By studying the characteristics and evolution of the
disk and its dust composition, valuable insights can be obtained into the
processes leading to the formation of planets, and important constraints on disk
and planet formation models can be derived. Also, by analogy, TTS systems 
can provide clues into the early evolution of the solar system.
In the following we will discuss the implications of our findings presented in the previous sections, for the evolution of the dust in protoplanetary disks of TTS systems.

\subsection{Grain growth and disk structure}
Based on our analysis of low-resolution infrared spectra of seven TTS systems
obtained with the Spitzer Space Telescope, we find clear evidence of processing
and growth of the silicate dust species present in their protoplanetary disks.
We interpret observed variations in the thermal emission from amorphous silicate dust
species as evidence for grain sizes which are substantially different from those
observed in the ISM, and argue for grain growth within the protoplanetary disks.
For the first time, we find a clear correlation between the strength of the
amorphous silicate feature, measuring the typical grain size of these
grains, and the shape of the mid-infrared spectral energy distribution,
measuring the disk scale height, i.e., flaring of the disk.  In the literature, two
possible explanations have been put forward to explain the differences in disk flaring:
First, self-shadowing of the disk due to an enhanced scale height of the very
inner parts. This prevents the central star from illuminating the surface of
the outer disk, required to sufficiently heat the disk for it to flare
\citep[][]{dullemond2004}. Second, grain growth and consequent gravitational
settling toward the disk mid-plane  \citep[e.g.][]{Schraepler2004,nomura2006,allessio2006,dullemond_settling2004}. 
Our results, linking an increase in grain size to a decrease of the disk flaring, 
clearly argue for the latter explanation. 

An earlyer study by \cite{Apai2004}, studying the brown dwarf system CFHT-BD-Tau 4, also suggested 
a correlation between the strength of the silicate emission band and the shape of the SED.
\cite{acke_iso_spec2004} studied a sample of HAEBE systems observed with the
Infrared Space Observatory (ISO). Because no correlation could be found between
the observed silicate emission bands and the shape of the SED, the authors
concluded that their observations were consistent with the self-shadowing disk
model rather than coagulation and grain settling.  In apparent contradiction,
\cite{acke_mm_grainsize2004} showed a correlation between grain size, as
measured by the (sub) millimeter slope of the SED, and disk flaring angle, based on
the ratio of the near- to mid-IR excess.  The latter results argue for
coagulation and grain settling towards the mid-plane as the explanation for the
observed bi-modal distribution of SEDs, consistent with our findings here for
lower mass solar-type stars. 

We suspect that the correlation from IR
spectroscopy of the derived grain size and the disk flaring has been missed so
far for the HAEBE systems are due to the at least one order
of magnitude higher stellar luminosity of A and B type stars compared to the
later-type stars studied here. Observations of HAEBE systems
will, therefore,  probe a much larger region of the circumstellar disk 
than the observations of TTS or brown dwarf systems for any given wavelength,
by at least a factor 2 to 3. Given that coagulation
and settling are a function of density and thus radius, gradients in the observed
grain size and disk structure are to be expected. Probing a much larger region of the 
disk, therefore, could lead to the loss of any clear correlations In the HAEBE systems.

\subsection{The formation of crystalline silicates}
All systems studied in this paper show emission from crystalline silicates,
further evidence for dust processing within the protoplanetary disks as
interstellar dust, the material present at the formation time of the disks,
shows no evidence for crystalline silicates.  The results of the spectral
analysis of the crystalline silicate emission can be summarised as follows:
\begin{enumerate}
\item All observed targets show emission bands of crystalline silicates at both
higher ($\sim$300 - 500~K) temperatures, probed in the 10~$\mu$m spectral window,
and lower ($\sim$100~K) temperatures, probed in the 30~$\mu$m spectral region.
\item The observed emission bands are consistent with emission from the pure magnesium
silicates forsterite and enstatite, and silica. No conclusive evidence for other
species has been found. 
\item The average grain size of the crystals is much
smaller than that of the amorphous silicates. While amorphous silicates
requires grain sizes up to 6~$\mu$m, the crystalline emission is
more consistent with a size of $\sim$0.1 to 1~$\mu$m. 
\item The crystallinity is not correlated to the grain size of the amorphous silicates. 
\item The average grain size of the enstatite grains as derived from the modelling of the 10~$\mu$m
spectral region is systematically larger than that of the forsterite grains. 
\item The strength of the forsterite emission features in the 10~$\mu$m wavelength region and
those at the longer wavelengths are correlated. This can be interpreted as evidence that the 
crystalline mass fraction is increased from ISM values to the observed mass fractions of about $\sim$5\%, throughout the entire inner $\sim$15~AU of the
disk. 
\item We find a change in the relative abundance of the different
crystalline silicates from the very inner ($\sim$1~AU) warm dust population, which is
dominated by enstatite, compared to the population at the colder outer
disk regions at larger radii ($\sim$5-15~AU), dominated by forsterite. This change in relative
abundances points towards a radial dependence of either the formation mechanism
of the crystalline silicates, or the (non) equilibrium conditions under which
they formed, and also argues against substantial radial mixing of processed material from the 
inner to the outer parts of the disk (see paragraphs below for a detailed discussion).
\end{enumerate}

How can we interpret the above results for the crystalline silicates in a
consistent picture of the physical processes occurring in a protoplanetary disk? As
all our targets show similar crystalline mass fractions and compositions, these
physical processes can be expected to occur in all protoplanetary disks. The
formation of forsterite and enstatite requires temperatures above $\sim$1000~K
\citep[e.g.][]{hallenbeck2000,fabian2000}. Such high temperatures are reached near the central
star where dust grains can be readily heated by the stellar radiation field.
In an early active disk phase, the accretion energy can
provide an additional heat source for the dust in the mid-plane regions of the inner disk
\citep[e.g.][]{bell2000}. At these high temperatures, crystalline silicates can
be formed either through annealing  of the amorphous silicates \citep[see][for
an overview]{wooden2005} or by gas-phase condensation/annealing and gas-solid reactions
in a cooling gas \citep{davis2003, petaev2005}. Our observations show, however,
that a substantial fraction of the crystalline silicates have temperatures
($\sim$100~K) far below the required crystallisation temperature. This implies
that either large scale radial mixing has to occur, transporting the crystalline
silicates from the hot inner parts to the cooler outer disk
\citep[e.g.][]{dominique2002}, or that an additional localised and/or transient
heating mechanism is operating in the cooler regions of the disk, at larger
radial distances from the central star. Such additional heating mechanism might
be provided by shock-waves in which gas and dust grains are heated to the
required temperatures of above a 1000~K \citep{harker2002,Desch2005}.

The question is now if our results can distinguish between different 
formation mechanisms and locations for the crystalline silicates.
The presence of forsterite
and enstatite, respectively the magnesium rich end members of the olivine and
pyroxene solid-solution series, with no evidence for crystalline silicates
containing substantial amounts of iron, suggest they formed as high-temperature,
gas-phase condensates \citep[][]{davis2003, gail2004}. The presence of
high-temperature condensates at lower temperatures indicates that complete
equilibrium condensation is not taking place in protoplanetary disks, else these
species would have been transformed to other ferromagnesian silicates during
cooling. Though the exact order in which the different dust species condense out
from a cooling gas depends on the gas pressure and isolation of the condensed
dust grains from the surrounding gas \citep{petaev2005}, most models predict
forsterite to be condensed out first, followed by the formation of enstatite at
slightly lower temperatures through solid-gas reactions between forsterite and
SiO$_2$ gas. Iron will condense out slightly before or after forsterite as
metallic iron grains rather than being incorporated into silicates. The slightly
larger grain size of enstatite compared to forsterite can be the result from the
gas-solid reactions and the broader temperature range (and thus a longer
formation window in a slowly cooling gas) under which enstatite can be formed
and is stable.

An alternative formation mechanism for forsterite and enstatite is annealing of
amorphous silicates without evaporating/recondensating the parent grain. 
The annealing process critically depends on the structure
of the amorphous material and the oxygen partial pressure of the surrounding gas
(i.e. reducing or oxidising conditions). To prevent the formation of iron
containing olivine and pyroxene minerals, the amorphous grains have to be
annealed under reducing conditions. \cite{davoisne2006} show that carbon
combustion locking up the oxygen in the form of CO rather then in FeO, will
cause the iron the precipitate as metallic particles, and not get incorporated
into a silicate. \cite{thompson2002} showed that forsterite and silica,
independent of the stoichiometry of the amorphous metarial, will always form,
but that the formation of enstatite follows through solid-solid reactions 
between forsterite and silica. The effectiveness and speed of this reaction
critically depends on the structure of the amorphous grains. In highly porous
grains, like those formed from smokes, the contact surfaces between the
individual sub-units will be small and, therefore, reactions will be slow and require
substantial structural modification (like melting) of the amorphous grain. For
compact glassy amorphous silicates, the formation of enstatite can proceed
immediately.  Similar as with direct condensation, this secondary formation of
enstatite through forsterite alteration could also explain why we observe a
slightly larger grain size for enstatite compared to forsterite.

Apart from the above considerations two additional observational constraints can
be imposed to distinguish between annealing or condensations as the main
formation mechanism for crystalline silicates, namely summary points (3) and
(4). The implication of these two observations is that the simultaneous
presence of both large amorphous grains and small crystalline grains is
\emph{not} caused by a preferential transformation of small amorphous grains
into crystalline silicates, leaving the larger amorphous grains. Or with other words,
the observed change in grain size towards larger grains is not caused by grain growth
but removal of the smaller amorphous grain population trough crystallization
in a distribution of grain sizes. 
If this would have been the case, a correlation between amorphous grain size and crystalline
mass fraction would have been observed. This together with the fact that no
large crystalline grains are observed implies that either the crystals form as
gas-phase condensates, the large amorphous aggregates are disrupted before
annealing, or that the main crystallisation process occurred before coagulation.

Gas-phase condensation can naturally explain any difference in grain size
between the amorphous and crystalline grains. In case of an
evaporation/condensation zone in the disk, where first the amorphous grains are
evaporated after which crystalline species can condense out if the gas cools, no
relation between the original grain size distribution of the amorphous dust and
that of the crystalline grains will exist. Annealing of large amorphous grains,
on the other hand, will lead to the formation of large crystals. It is,
therefore, necessary to disrupt the larger aggregates before they get annealed.
A gradual heating of dust grains as they approach the hot inner disk is unlikely
to fullfill this requirement. Annealing by shock waves could be a more plausible
scenario, as it could also provide the mechanism to disrupt the larger amorphous
aggregates. This formation mechanism would be similar as the formation scenario 
of chondrules \citep[e.g.][]{Desch2005}.

In case of an early formation time of the
crystalline silicates before coagulation, during the high accretion
phases, viscous dissipation can efficiently heat the disk to in a region
extending several AU from the central star \citep[e.g][]{bell2000}. An early
formation time would imply that the crystalline silicate content of
protoplanetry disks would remain fixed during their further evolution. This is
consistent with previous studies who reported no correlations between the
processing of the silicates and systemic ages
\citep[e.g.][]{Roy2005,Kessler-Silacci2006, Kessler-Silacci2005}, though any
correlation might also be lost due to the large uncertainties in age
determinations. On the other hand, all systems studied in this paper show
crystalline silicates. Studies of on average younger samples show that a
substantial fraction of disks show no crystalline silicates \citep[e.g.
50~\%][]{Kessler-Silacci2006}. This would argue in favour of crystallinity
increasing with time.  Further, a recent study of FU~Orionis, the proto typical
case of its class, shows no signs of crystalline silicates
\citep[][]{Quanz2006}. If the notion is correct that the FU~Orionis type objects
represent the early high accretion stages of TTS evolution, crystalline
silicates should be present if the bulk of the crystalline silicates would form
during the early evolution of the disks. Interestingly, \cite{Quanz2006} show
that FU~Orionis already shows signs of grain growth. If coagulation sets in this
early, an alternative scenario for the formation of crystalline silicates is
required.

%One should keep in mind, however,
%that this could be a selection effect as we are studying those systems with the longest
%surviving disk, which might also have the most favourable initial conditions for
%crystalline silicate production.

Note that there is no difference in coagulation behaviour between crystalline
and amorphous silicates. The difference in grain size between the crystalline
and amorphous silicates can be interpreted in terms of the optical properties of
larger composite aggregates. Suppose a population of small, predominantly
amorphous dust grains coagulates into larger aggregates. These larger aggregates
will obviously consists mainly of amorphous material but with few, from each
other isolated crystalline grains which will therefore react with the radiation
field as separate entities. The optical properties of such composite aggregates
will likely resemble that of the combined properties of a larger amorphous grain
with smaller crystalline particles, similar as is observed in cometary spectra
and IDPs. 

The two remaining summary points, (6) and (7), to be discussed here, place
further constaints on the formation mechanism of the crystalline silicates and
on the location in the disk where the crystalline silicates are forming. On the
one hand we observe a general increase in the crystalline mass fraction in the
inner $\sim$15~AU of the disks, on the other hand we observe a gradient in the
crystalline dust composition within this inner region. The changing forsterite
over enstatite mass ratio points to differences in the condensation or annealing
conditions. As discussed in the previous paragraphs, the formation of enstatite
follows after the formation of forsterite. The absence or much lower enstatite
mass fraction derived from the longer wavelength bands, probing the cooler dust
at about 5-15~AU compared to the mass ratio derived from the 10~$\mu$m wavelength
region, shows that none or much less of the forsterite is converted into
enstatite at larger radial distances from the central star. In the case of
gas-phase condensation as the formation mechanism for the crystalline silicates,
this implies non-equilibrium condensation conditions at larger disk radii, in contrast to the
very inner disk regions. If forsterite forms locally at $\sim$15~AU in the disk it has to be isolated from the surrounding gas by for instance coagulation, or followed by rapid cooling, both inhibiting the gas-solid reactions leading to the formation of enstatite. 
Alternatively, in case forsterite is formed through annealing of ISM material, the low enstatite
to forsterite ratio implies a rather porous structure of the amorphous silicates
and brief heating events, preventing the formation of enstatite at an radial distance of about 5 to 15~AU from the central star.

The high temperature region in the inner disk near the central star, is the
natural location where crystallisation can occur. If so, the presence of
crystalline silicates at lower temperatures together with the observed general
increase of the crystalline mass fraction in the inner $\sim$15~AU of the disks,
implies that efficient radial mixing of the processed dust from the inner disk
to larger radii must occur. At the early, high accretion phases of the disk, the
transport of angular momentum is expected to efficiently mix material from the
hot inner to the cold outer parts of the disk
\citep[][]{dominique2002,dullemond2006}. Though at a first glance this scenario
would be able to explain our observations, an argument against it is the radial
dependency of the crystalline silicate composition: If the crystalline silicates
originates from a single formation region before being distributed through the
disk, the composition of the processed material would be constant with radius.
Indeed, detailed disk models by \cite{gail2004}, taking into account radial
mixing, predicting the dust composition as a function of radius, show exactly
this counter argument.  While  \cite{gail2004} predict the composition of the
crystalline silicates in inner regions of the disk to be dominated by enstatite,
consistent with our observations, the radial mixing model will also predict a
large mass fraction of enstatite at larger radii, in contradiction with our
results. The only way to save the radial mixing scenario is if during the active
mixing phase, non-equilibrium conditions prevailed in the inner parts of the
disk, forming only forsterite. This might be achieved by very rapid outward
transportation of the formed forsterite preventing prolonged heating of the
grains or substantial gas-solid reactions which could lead to the formation of
enstatite. During the passive, low accretion disk phases, the phase were we are
observing our TTS sample, were radial mixing is not expected to be efficient,
equilibrium conditions might be reached again, resulting in the observed large
fraction of enstatite in the inner disks. At present, however, there is no
theoretical foundation for this scenario.
 
An alternative model to explain the summary points (6) and (7) is the in-situ
formation of crystalline silicates at radii of about 5-15~AU. As stellar radiation
is not efficient in heating the dust to sufficiently high temperatures for
crystallisation to occur, an alternative heating mechanism is required. A
promissing model is the local heating of dust and gas by shock waves
\citep[][]{harker2002, Desch2005}.  For typical densities and shock speeds,
small dust grains should be efficiently heated to high temperatures up to disk
radii of about 10~AU. A possible source for the shocks could be gravitational
instabilities or planetary mass companions within the disk. Shock heating could
provide sufficiently brief heating events such that equilibrium conditions or
prolonged annealing will not occur, preventing the formation of enstatite at
larger radii. In the very inner ($\sim$1~AU) disk, at higher densities,  apart
from eating by the central star, cooling can be expected to be longer such that
equilibrium conditions could be reached. The overall increase of the forsterite
mass fraction in the  inner $\sim$15~AU of the disks, might reflect that spiral
waves could affect the entire disk region, causing shock to occur over a large
range of radii or simply that the forsterite, produced at 5-15~AU from the
central star, is accreated inwards to smaller radii. This shock-wave scenario
could explain why some systems do not show any evidence for the presens of
crystalline silicates at the longest or even all wavelengths
\citep[e.g.][]{Kessler-Silacci2006}: these systems might not (yet) have produced
disk instabilities or sufficiently large planetary sized objects to produce
shock-waves.

Ideally, the spatial distribution of the different silicate species, should be
directly determined by spatially resolved spectroscopy. Due to observational
difficulties, this is at present limited to the much brighter HAEBE and the most
nearby TTS systems. Using mid-IR interferometric observations obtained with the
VLTI/MIDI instrument, \cite{roy2004} could spatially separate contribution to
the IR emission coming from the inner $\sim$2~AU of the disk, and that coming
from larger radii, for a sample of HAEBE systems. These observations clearly
showed that the crystalline silicates in the observed HAEBE systems are mainly
consentrated in the inner, high temperature, parts of the disk, and have a
composition consistent with a formation  under (near) equilibrium conditions.
However, befor concluding that all crystalline silicates form in the inner parts
of the disk, one has to realize that of the by \cite{roy2004} studied systems,
show no or substantially weaker crystalline silicate bands at the longer
(20-30~$\mu$m) wavelengths in their Spitzer and ISO spectra \citep[][Bouwman et
al, in prep.]{HerbigOverview}. This suggest that these HAEBE systems, in
contrast to the in disks in our TTS sample, did not witnessed substantial radial
mixing or in-situ formation of crystalline silicates at larger radii, with only the very
inner regions of the HAEBE disks containing observable quantities of  
crystalline silicates.

\subsection{PAH molecules in disks surrounding T~Tauri stars.}
Though the main focus of this paper is the silicate dust processing we report
the tentative detection of emission bands from polycyclic aromatic hydrocarbon
molecules. Emission bands of PAH molecules are commonly found in environments with a
strong UV flux like the circumstellar disks around HAEBE stars. 
As PAH molecules can contain a substantial fraction of the available carbon, and are spectroscopically
easier detectable as carbon in larger grains, they can provide us with important clues concerning 
the carbon chemistry of circumstellar environments. Also, these stochastically heated molecules 
strongly influence the gas temperature through photo-electric heating, and consequenly 
the disk structure as it depends on the gas pressure and thus gas temperature. 
Five out of seven TTS systems show an, for these low mass systems, previously
undetected band at 8.2~$\mu$m.  The fact that we only observe a PAH band at
8.2~$\mu$m rather than the commonly observed band position between 7.7 to 7.9$\mu$m suggests a fundamental
difference in carbon chemistry between our sample and the more luminous HAEBE
and F~type TTS systems. At this point we can only speculate that the difference
in carbon chemistry could be linked to differences in X-ray fluxes or stellar
wind properties of the intermediate-mass systems compared to those of low-mass pre-main-sequence stars.
If so this could also influence the possibility and chemical path by which more
complex pre-biotic organic molecules can be formed in protoplanetary disks. 


\appendix

\section {HD~143006}

HD~143006 is a well-studied \citep[e.g.][]{Garcia-Lario1990, Walker1988, 
sylvester1996, Coulson1998, Natta2004, Dent2005}
classical T Tauri star of spectral type G6/8 which appears
to be member of the Upper Scorpius OB association \citep[][]{Mamajek2004}.
It displays many T~Tauri characteristics including infrared to millimeter
excess \citep[][]{Odenwald1986}, 
optical emission lines \citep[][]{Stephenson1986}, 
and coronal activity revealed through x-rays \citep[][]{Sciortino1998}.
It is thus an ``old" accretion disk system, with an age og 3-5~Myr.

\section {RX~J1612.6-1859A}

RX~J1612.6-1859A and RX~J1612.6-1859B are the names assigned in the nomenclature of
\cite{Martin1998}
for a pair of emission line sources in the $\rho$~Oph vicinity.  The former object is an M0 
star also known as 2MASS~J16123916-1859284 or GSC~06209-01312 that has been studied
only by optical spectroscopy \citep{Martin1998,The1964}. 
The latter object, by contrast, is a well-known T Tauri star, also known as ScoPMS~52 
\citep[][]{Walter1994} or Wa~Oph~3 \citep[][]{Walter1986}.
This K0 star was, in fact, the target of
the FEPS observations and the source discussed in our companion paper \citep{Silverstone2006}
as not having any excess emission out to 8 $\mu$m (and indeed not out to 24 $\mu$m;
Carpenter et al., in preparation).  For our IRS observations of this source, however,
the IRS peak-up routine centerd on to the mid-IR bright 
object RX~J1612.6-1859A in the slit rather than RX~J1612.6-1859B 20" away.  The observations 
discussed herein are thus of RX~J1612.6-1859A, an M0 emission line object.

\acknowledgements  

JB and ThH acknowledge support from the
EU Human Potential Network contract No. HPRN-CT-2002000308.  


\bibliographystyle{aa}
\bibliography{reference_list,publication_list}

\clearpage
\begin{deluxetable}{llccccccccc}
\tabletypesize{\scriptsize}
\rotate
\tablecaption{Astrophysical parameters of program stars.\label{tbl:stars}}
\tablewidth{0pt}
\tablecolumns{11}
\tablehead{
\colhead{ID\#} & \colhead{Name} & \colhead{$\alpha$} & \colhead{$\delta$} & \colhead{$d$} & \colhead{log(Age)} & \colhead{Sp. Type} & \colhead{Ref.} & \colhead{$T_{\rm eff}$} & \colhead{$A_V$} & \colhead{L$_star$}\\
\colhead{} & \colhead{}  &   \colhead{(2000)} & \colhead{(2000)} & \colhead{[pc]} & \colhead{[yr]} & \colhead{} & \colhead{[K]} & \colhead{} & \colhead{[mag]}  & \colhead{[L$_\odot$]}
}
\startdata
0 &RX J1842.9-3532       &18:42:57.98  &-35:32:42.73 & 145 & 6.63  (4 Myr) & K2    & 2,3,1 & 4995  & 1.03 & 1.0\\
1 &RX J1852.3-3700       &18:52:17.30  &-37:00:11.93 & 145 & 6.5-7 (4 Myr) & K3    & 2,3,1 & 4759  & 0.92 & 0.6\\
2 &HD 143006             &15:58:36.92  &-22:57:15.35 & 145 & 6.70  (5 Myr) & G6/8  & 7,8,9 & 5884  & 1.63 & 2.5\\
3 &RX J1612.6-1859A      &16:12:39.18  &-18:59:28.0  & 145 & 6.70  (3 Myr) & M0    & 11    & 3800  & 1.80 & 0.5\\
  &(2MASS J16123916-1859284)&             &            &     &               &       &       &       &      &    \\
4 &1RXS J132207.2-693812 &13:22:07.53  &-69:38:12.18 &  86 & 7.23  (17 Myr) & K1IVe & 10    & 5228  & 1.22 & 1.3\\
  &(PDS 66)              &             &            &     &               &       &       &       &      &    \\
5 &RX J1111.7-7620       &11:11:46.32  &-76:20:09.21 & 163 & 6.69  (5 Myr) & K1	   & 5,3,4 & 4621  & 1.30 & 1.6\\
6 &1RXS J161410.6-230542 &16:14:11.08  &-23:05:36.26 & 145 & 6.70  (5 Myr) & K0    & 7,8,6 & 4963  & 1.48 & 3.2\\
  &([PZ99] J161411.0-230536)&             &            &     &               &       &       &       &      &    \\
\tableline
\enddata

\tablenotetext{~}{
References for distance, age, spectral type -- 
(1) Neuhauser et al. 2000;
(2) Neuhauser \& Forbrich 2007;
(3) Hillenbrand et al. 2007, in preparation;
(4) Alcala et al. 1995;
(5) Luhman 2007;
(6) Preibisch et al. 1998;
(7) de Zeeuw et al. 1999;
(8) Preibisch et al. 2002;
(9) Houck \& Smith-Moore 1988;
(10) Mamajek et al. 2002;
(11) Martin et al. 1998.
}
\tablenotetext{~}{
Notes for temperature, extinction, luminosity --
Spectral types are from optical spectroscopy as cited above.
B-V and V-K colors are used in conjunction with spectral types
to estimate effective temperatures and visual exinction values;
see Carpenter et al. 2007, in preparation, for details.
In the case of RX J1612.6-1859A J-H and H-K colors are used and
luminosity is computed from J-band bolometric correction.
}
\end{deluxetable}



\begin{figure}
\begin{center}
\resizebox{0.7\hsize}{!}{\includegraphics[angle=0]{f1.eps}}
  \caption{The spectral energy distributions the the TTS systems observed within the FEPS legacy program. 
   Shown are the Spitzer low-resolution spectra scaled to the adopted 
   distance and luminosity of the individual stars as listed in Table~\ref{tbl:stars}.
   For clarity the spectra are off-set from each other, ordered from top to bottom based on the
   observed slope of the SED, by multiplying by 20, 5, 0.75, 1, 2.2, 0.25 and 0.2, respectively.
}
   \label{fig:specta}
\end{center}
\end{figure}

\begin{figure*}
\begin{center}
\resizebox{0.7\hsize}{!}{\includegraphics[angle=0]{f2.eps}}
  \caption{Spitzer low-resolution spectra  of 7 TTS observed within the FEPS legacy program.
The left panels show the spectra in the wavelength region between 8 and 13~$\mu$m. 
The central panels show the spectral region between 17 and 26~$\mu$m, 
and the right panels the spectral region between 26 and 36~$\mu$m. The spectra are ordered from top to bottom according to the decreasing strength above continuum 
of the 10~$\mu$m silicate band. Also plotted in this figure is a compositional fit to the spectra (light grey lines). For details on the 
model fits see \ref{sec:model}. }
   \label{fig:fit}
\end{center}
\end{figure*}

\clearpage

\begin{deluxetable}{llllll}
\tabletypesize{\small}
\tablewidth{0pt}
\tablecolumns{6}
\tablecaption{Overview of dust species used. For each component we specify
 its lattice structure, chemical composition, shape and reference to the 
 laboratory measurements of the optical constants. For the homogeneous
 spheres we used Mie theory to calculate the opacities. For the inhomogeneous
 spheres, we used the distribution of hollow spheres \citep[DHS;][]{min2005}, to simulate
 grain deviating from perfect symmetry. \label{tbl-species} }
\tablehead{\colhead{\#}&\colhead{Species}&\colhead{state}&\colhead{Chemical}&\colhead{Shape}&\colhead{Ref} \\
 \colhead{}& \colhead{}&\colhead{} & \colhead{ formula}  &  \colhead{}  & \colhead{} } 

\startdata
1 & Amorphous silicate  & A  &  MgFeSiO$_{4}$       & Homogeneous   & (1)  \\
  & (Olivine stoichiometry)&  &                     &                &  \\
2 & Amorphous silicate  & A  &  MgFeSi$_{2}$O$_{6}$ & Homogeneous   & (1)  \\
 & (Pyroxene stoichiometry)&  &                     &                &  \\
3 & Forsterite   & C  &  Mg$_{2}$SiO$_{4}$   & Inhomogeneous & (2)   \\
4 & Clino Enstatite    & C  &  MgSiO$_{3}$         & Inhomogeneous & (3) \\
5 & Silica       & A  &  SiO$_{2}$           & Inhomogeneous & (4)  \\
\tableline
\enddata
\tablerefs{(1)\citet{dorschner1995}; (2)\citet{servoin1973}; (3)\citet{jaeger1998}; (4)\citet{Henning1997};}
\end{deluxetable}

\begin{figure}
\figurenum{3a}
\begin{center}
\resizebox{0.8\hsize}{!}{\includegraphics[angle=0]{f3a.eps}}
  \caption{To unity scaled opacities between 8 and 13~$\mu$m for the different dust species 
  listed in Table~\ref{tbl-species}. The solid lines represent opacities for a grain size 
  of 0.1~$\mu$m, the dashed lines for 1.5~$\mu$m and the dot-dash lines for 6~$\mu$m. 
  Also indicated in each panel are the scaling factors for each of the opacity curves.
}
   \label{fig:kappa_short}
\end{center}
\end{figure}

\begin{figure}
\figurenum{3b}
\begin{center}
\resizebox{0.8\hsize}{!}{\includegraphics[angle=0]{f3b.eps}}
  \caption{To unity scaled opacities between 17 and 26~$\mu$m for the different dust species
  listed in Table~\ref{tbl-species}. The solid lines represent opacities for a grain size
  of 0.1~$\mu$m, the dashed lines for 1.5~$\mu$m and the dot-dash lines for 6~$\mu$m.
  Also indicated in each panel are the normalization factors for each of the opacity curves.
}
   \label{fig:kappa_mid}
\end{center}
\end{figure}

\begin{figure}
\figurenum{3c}
\begin{center}
\resizebox{0.8\hsize}{!}{\includegraphics[angle=0]{f3c.eps}}
  \caption{To unity sacled opacities between 26 and 36~$\mu$m for the different dust species
  listed in Table~\ref{tbl-species}. The solid lines represent opacities for a grain size
  of 0.1~$\mu$m, the dashed lines for 1.5~$\mu$m and the dot-dash lines for 6~$\mu$m.
  Also indicated in each panel are the normalization factors for each of the opacity curves.
}
   \label{fig:kappa_long}
\end{center}
\end{figure}

\clearpage

\begin{deluxetable}{@{} rlllllllllllllll @{}}
\setlength{\tabcolsep}{0.02in} 
\tabletypesize{\tiny}
\rotate
\tablecaption{ The best fit values of the parameters in our compositional fits to the 8 to 13~$\mu$m spectral region.The abundances of the various dust species are given
as a percentage of the total dust mass, \emph{excluding} the dust responsible
for the continuum emission. Also listed is the mass averaged grain size of the different dust species.
If a species was not found, or unconstrained by the spectra, this is indicated by a -~symbol.
The PAH and continuum flux contributions are listed as percentages of the total integrated 
flux over the 10\,$\mu$m region, contained in these components. 
These are measures for the relative flux contributions, but cannot be interpreted as relative dust masses.
The resulting best fit model spectra are plotted in Fig.~\ref{fig:fit} (light grey lines).
\label{tab:t2_fs:fits} }
\tablewidth{0pt}
\tablecolumns{16}


%\fontsize{6}{10pt}\selectfont
%\linespread{1.3}%
%\selectfont

\tablehead{
\colhead{\#} & \colhead{$\chi^2$} & \colhead{$T_{c}$\,[K]} & \colhead{$T_{dust}$\,[K]} &
\colhead{Cont.}  & \multicolumn{2}{c}{Amorph. Olivine}  & \multicolumn{2}{c}{Amorph. Pyroxene}  &
\multicolumn{2}{c}{Forsterite}  & \multicolumn{2}{c}{Enstatite}  &
\multicolumn{2}{c}{Silica}  &\colhead{PAH} \\
  \colhead{}  &   \colhead{}    & \colhead{}     &    \colhead{}        & \colhead{contr.} &  
\colhead{mass } &\colhead{ $<a>$ }  & \colhead{mass}   & \colhead{$<a>$}  & \colhead{mass } &
\colhead{$<a>$} &\colhead{mass}   & \colhead{$<a>$ }  & \colhead{mass } & \colhead{$<a>$} &\colhead{contr.}
}

\startdata
\multicolumn{16}{l}{\bf 8-13$\mu$m spectral region} \\
0 & 11.1$\pm$0.5 & 1500.0$_{-0.0}^{+0.0}$ & 324.6$_{-5.6}^{+6.9}$ & 0.5214$_{-0.0009}^{+0.0009}$ & 
0.7902$_{-0.0063}^{+0.0063}$ & 1.16$_{-0.09}^{+0.09}$ & 
0.1787$_{-0.0072}^{+0.0071}$ & 1.12$_{-0.08}^{+0.09}$ & 
0.0146$_{-0.0004}^{+0.0004}$ & 0.1$_{-0.0}^{+0.0}$ & 
0.0165$_{-0.0015}^{+0.0016}$ & 1.20$_{-0.09}^{+0.08}$ & 
  -    &   -  & 
0.0066$_{-0.0004}^{+0.0004}$\\
1 & 3.4$\pm$0.3 & 1500.0$_{-0.0}^{+0.0}$ & 257.4$_{-6.2}^{+3.9}$ & 0.6361$_{-0.0025}^{+0.0027}$ & 
0.9872$_{-0.0058}^{+0.0042}$ & 3.08$_{-0.13}^{+0.07}$ & 
0.0016$_{-0.0014}^{+0.0064}$ & 0.1$_{-0.0}^{+0.0}$ & 
0.0016$_{-0.0009}^{+0.0011}$ & 0.1$_{-0.0}^{+0.0}$ & 
0.0091$_{-0.0038}^{+0.0036}$ & 1.41$_{-0.32}^{+0.08}$ & 
0.0006$_{-0.0006}^{+0.0030}$ & 1.5$_{-0.0}^{+0.0}$ & 
0.0082$_{-0.0017}^{+0.0015}$\\
2 & 17.2$\pm$0.7 & 1459.0$_{-13.5}^{+17.1}$ & 296.2$_{-2.6}^{+5.3}$ & 0.6255$_{-0.0013}^{+0.0011}$ & 
0.4225$_{-0.0053}^{+0.0120}$ & 0.13$_{-0.03}^{+0.47}$ & 
0.5296$_{-0.0137}^{+0.0047}$ & 5.30$_{-0.05}^{+0.06}$ & 
0.0149$_{-0.0003}^{+0.0003}$ & 0.1$_{-0.0}^{+0.0}$ & 
0.0330$_{-0.0011}^{+0.0010}$ & 1.496$_{-0.02}^{+0.004}$ & 
   -        &            - & 
0.0246$_{-0.0003}^{+0.0003}$\\
3 & 8.8$\pm$0.7 & 1030.6$_{-94.7}^{+77.5}$ & 369.9$_{-44.0}^{+66.4}$ & 0.6792$_{-0.0210}^{+0.0263}$ & 
0.2933$_{-0.2375}^{+0.2511}$ & 6.00$_{-0.009}^{+0.0}$ & 
0.6452$_{-0.2529}^{+0.2366}$ & 4.85$_{-1.94}^{+0.34}$ & 
0.0141$_{-0.0018}^{+0.0044}$ & 0.15$_{-0.04}^{+0.24}$ & 
0.0342$_{-0.0054}^{+0.0061}$ & 1.13$_{-0.13}^{+0.13}$ & 
0.0133$_{-0.0027}^{+0.0040}$ & 0.37$_{-0.22}^{+0.27}$ & 
0.0103$_{-0.0021}^{+0.0031}$\\
4 & 11.1$\pm$0.5 & 778.8$_{-14.6}^{+2.7}$ & 183.8$_{-14.8}^{+1.2}$ & 0.6054$_{-0.0011}^{+0.0031}$ & 
0.6369$_{-0.0412}^{+0.0367}$ & 5.57$_{-0.05}^{+0.08}$ & 
0.3279$_{-0.0370}^{+0.0404}$ & 2.27$_{-0.75}^{+0.45}$ & 
0.0114$_{-0.0005}^{+0.0003}$ & 0.1$_{-0.0}^{+0.0}$ & 
0.0238$_{-0.0026}^{+0.0013}$ & 0.97$_{-0.07}^{+0.04}$ & 
  -     &  -  & 
0.0126$_{-0.0004}^{+0.0007}$\\
5 & 4.0$\pm$0.4 & 1500.0$_{-0.0}^{+0.0}$ & 236.6$_{-7.2}^{+6.5}$ & 0.8544$_{-0.0010}^{+0.0011}$ & 
0.8236$_{-0.0160}^{+0.0138}$ & 6.0$_{-0.0}^{+0.0}$ & 
0.1060$_{-0.0133}^{+0.0153}$ & 0.1$_{-0.0}^{+0.0}$ & 
0.0272$_{-0.0023}^{+0.0025}$ & 0.97$_{-0.06}^{+0.05}$ & 
0.0349$_{-0.0022}^{+0.0023}$ & 1.39$_{-0.08}^{+0.07}$ & 
0.0083$_{-0.0015}^{+0.0019}$ & 0.35$_{-0.21}^{+0.27}$ & 
0.0022$_{-0.0005}^{+0.0005}$\\
6 & 6.9$\pm$0.4 & 617.0$_{-7.1}^{+13.2}$ & 305.1$_{-5.8}^{+5.6}$ & 0.8206$_{-0.0096}^{+0.0055}$ & 
0.5862$_{-0.1153}^{+0.0810}$ & 6.0$_{-0.0}^{+0.0}$ & 
0.3728$_{-0.0802}^{+0.1200}$ & 5.999$_{-0.016}^{+0.001}$ & 
0.0058$_{-0.0005}^{+0.0005}$ & 0.1$_{-0.0}^{+0.0}$ & 
0.0249$_{-0.0024}^{+0.0022}$ & 1.21$_{-0.09}^{+0.08}$ & 
0.0104$_{-0.0009}^{+0.0009}$ & 0.1$_{-0.0}^{+0.0}$ & 
0.0066$_{-0.0011}^{+0.0008}$\\
\tableline
\multicolumn{16}{l}{\bf 17-26$\mu$m spectral region} \\
0 & 28.3$\pm$1.4 & 46.3$_{-1.4}^{+3.8}$ & 118.0$_{-0.0}^{+0.0}$ & 0.0321$_{-0.0018}^{+0.0022}$ & 
0.9592$_{-0.0071}^{+0.0066}$ & 1.5$_{-0.0}^{+0.0}$ & 
0.0161$_{-0.0069}^{+0.0073}$ & 0.80$_{-0.67}^{+0.67}$ & 
0.0192$_{-0.0005}^{+0.0009}$ & 0.14$_{-0.04}^{+0.11}$ & 
    -     &       -        & 
0.0055$_{0.0005}^{+0.0005}$ & 1.5$_{0.0}^{+0.0}$ & 
     -             \\
1 & 7.0$\pm$0.7 & 105.3$_{-0.6}^{+30.1}$ & 84.95$_{-0.0}^{+0.05}$ & 0.2529$_{-0.0289}^{+0.0186}$ & 
0.8650$_{-0.0119}^{+0.0136}$ & 1.61$_{-0.09}^{+0.14}$ & 
0.1141$_{-0.0136}^{+0.0122}$ & 1.5$_{-0.0}^{+0.0}$ & 
0.0099$_{-0.0013}^{+0.0011}$ & 0.72$_{-0.24}^{+0.21}$ & 
0.0007$_{-0.0006}^{+0.0015}$ & 0.1$_{-0.0}^{+0.0}$ & 
0.0104$_{-0.0007}^{+0.0007}$ & 1.5$_{-0.0}^{+0.0}$ & 
        -       \\
2 & 18.8$\pm$1.0 & 33.0$_{-3.3}^{+5.4}$ & 112.7$_{-3.9}^{+0.3}$ & 0.0096$_{-0.0024}^{+0.0047}$ & 
0.7384$_{-0.0195}^{+0.1520}$ & 1.5$_{-0.0}^{+0.0}$ & 
0.2459$_{-0.1474}^{+0.0201}$ & 5.84$_{-0.08}^{+0.10}$ & 
0.0100$_{-0.0004}^{+0.0005}$ & 0.1$_{-0.0}^{+0.0}$ & 
     -       &      -       & 
0.0057$_{0.0004}^{+0.0008}$ & 1.5$_{0.0}^{+0.0}$ & 
 -             \\
3 & 5.9$\pm$0.6 & 18.2$_{-3.2}^{+6.0}$ & 197.7$_{-6.4}^{+7.9}$ & 0.0013$_{-0.0006}^{+0.0010}$ & 
0.1214$_{-0.0353}^{+0.0348}$ & 1.5$_{-0.0}^{+0.0}$ & 
0.8628$_{-0.0348}^{+0.0369}$ & 5.67$_{-0.03}^{+0.04}$ & 
0.0130$_{-0.0007}^{+0.0007}$ & 0.1$_{-0.0}^{+0.0}$ & 
    -      &     -           & 
0.0029$_{-0.0008}^{+0.0008}$ & 0.71$_{-0.55}^{+0.71}$ & 
      -           \\
4 & 13.0$\pm$0.8 & 106.0$_{-7.4}^{+5.4}$ & 152.6$_{-3.9}^{+2.6}$ & 0.1748$_{-0.0388}^{+0.0513}$ & 
0.3846$_{-0.0594}^{+0.0912}$ & 1.5$_{-0.0}^{+0.0}$ & 
0.5881$_{-0.0967}^{+0.0614}$ & 4.99$_{-0.39}^{+0.18}$ & 
0.0226$_{-0.0023}^{+0.0039}$ & 0.1$_{-0.0}^{+0.0}$ & 
0.0001$_{-0.0001}^{+0.0014}$ & 0.1$_{-0.0}^{+0.0}$ & 
0.0047$_{-0.0009}^{+0.0010}$ & 1.13$_{-0.68}^{+0.34}$ & 
     -                 \\
5 & 5.3$\pm$0.5 & 177.0$_{-2.6}^{+3.9}$ & 294.5$_{-31.3}^{+34.6}$ & 0.7317$_{-0.0104}^{+0.0120}$ & 
0.0328$_{-0.0311}^{+0.0784}$ & 6.0$_{-0.0}^{+0.0}$ & 
0.8255$_{-0.0717}^{+0.0368}$ & 1.5$_{-0.0}^{+0.0}$ & 
0.0996$_{-0.0071}^{+0.0090}$ & 1.26$_{-0.10}^{+0.10}$ & 
0.0206$_{-0.0077}^{+0.0088}$ & 0.1$_{-0.0}^{+0.0}$ & 
0.0215$_{-0.0051}^{+0.0052}$ & 0.15$_{0.05}^{+0.56}$ & 
      -             \\
6 & 3.9$\pm$0.5 & 340.0$_{-110.6}^{+9.7}$ & 155.1$_{-13.1}^{+71.6}$ & 0.6692$_{-0.1003}^{+0.0308}$ & 
   -            &     -          & 
0.9643$_{-0.0255}^{+0.0060}$ & 1.43$_{-0.83}^{+0.85}$ & 
0.0321$_{-0.0051}^{+0.0157}$ & 0.52$_{-0.29}^{+0.23}$ & 
0.0025$_{-0.0021}^{+0.0040}$ & 0.1$_{-0.0}^{+0.0}$ & 
0.0012$_{-0.0011}^{+0.0106}$ & 0.1$_{-0.0}^{+0.0}$ & 
          -               \\
\tableline
\multicolumn{16}{l}{\bf 26.5-35.5$\mu$m spectral region} \\
0 & 15.3$\pm$2.0 & 25.7$_{-1.6}^{+4.9}$ & 96.7$_{-2.7}^{+5.2}$ & 0.0726$_{-0.0115}^{+0.0282}$ & 
0.0458$_{-0.0396}^{+0.1059}$ & 2.95$_{-2.71}^{+2.75}$ & 
0.9341$_{-0.1055}^{+0.0392}$ & 0.66$_{-0.45}^{+0.65}$ & 
0.0165$_{-0.0009}^{+0.0012}$ & 0.74$_{-0.30}^{+0.29}$ & 
0.0036$_{-0.0014}^{+0.0016}$ & 1.08$_{-0.78}^{+0.41}$ & 
    -          &     -        & 
        -       \\
1 & 3.1$\pm$0.6 & 31.2$_{-10.8}^{+43.9}$ & 89.3$_{-13.5}^{+12.2}$ & 0.0515$_{-0.0350}^{+0.2006}$ & 
0.5475$_{-0.3181}^{+0.3822}$ & 3.47$_{-2.11}^{+2.39}$ & 
0.4425$_{-0.3891}^{+0.3170}$ & 1.78$_{-1.19}^{+3.33}$ & 
0.0054$_{-0.0012}^{+0.0013}$ & 0.82$_{-0.63}^{+0.52}$ & 
0.0011$_{-0.0009}^{+0.0014}$ & 0.48$_{-0.38}^{+1.01}$ & 
0.0035$_{-0.0035}^{+0.0331}$ & 0.89$_{-0.83}^{+0.63}$ & 
       -           \\
2 & 6.0$\pm$1.0 & 33.6$_{-10.0}^{+16.2}$ & 134.0$_{-6.8}^{+21.5}$ & 0.1070$_{-0.0649}^{+0.1931}$ & 
0.2973$_{-0.2574}^{+0.1866}$ & 5.16$_{-3.46}^{+0.81}$ & 
0.6921$_{-0.1864}^{+0.2567}$ & 0.47$_{-0.35}^{+1.79}$ & 
0.0101$_{-0.0009}^{+0.0017}$ & 0.47$_{-0.31}^{+0.42}$ & 
0.0003$_{-0.0003}^{+0.0012}$ & 0.1$_{-0.0}^{+0.0}$ & 
0.0002$_{-0.0002}^{+0.0045}$ & 0.1$_{-0.0}^{+0.0}$ & 
       -         \\
3 & 5.2$\pm$0.8 & 26.9$_{-16.9}^{+147.2}$ & 173.8$_{-37.5}^{+343.9}$ & 0.0980$_{-0.0921}^{+0.8132}$ & 
0.1832$_{-0.1675}^{+0.2281}$ & 4.90$_{-4.52}^{+1.07}$ & 
0.7364$_{-0.3726}^{+0.2133}$ & 1.10$_{-0.97}^{+0.95}$ & 
0.0708$_{-0.0529}^{+0.5710}$ & 0.55$_{-0.37}^{+0.42}$ & 
0.0061$_{-0.0061}^{+0.0638}$ & 0.1$_{-0.0}^{+0.0}$ & 
   -    &   -   & 
    -        \\
4 & 6.8$\pm$0.9 & 21.0$_{-5.3}^{+6.2}$ & 104.4$_{-4.5}^{+1.9}$ & 0.0259$_{-0.0108}^{+0.0163}$ & 
0.0866$_{-0.0577}^{+0.0621}$ & 4.37$_{-2.80}^{+1.45}$ & 
0.8956$_{-0.0619}^{+0.0581}$ & 0.28$_{-0.18}^{+0.51}$ & 
0.0154$_{-0.0008}^{+0.0010}$ & 0.32$_{-0.17}^{+0.21}$ & 
      -          &      -        & 
0.0024$_{-0.0023}^{+0.0089}$ & 0.1$_{-0.0}^{+0.0}$ & 
     -          \\
5 & 3.2$\pm$0.6 & 33.2$_{-16.6}^{+39.1}$ & 186.2$_{-33.5}^{+142.1}$ & 0.1327$_{-0.1136}^{+0.3108}$ & 
0.0230$_{-0.0213}^{+0.1883}$ & 2.27$_{-1.28}^{+3.91}$ & 
0.9521$_{-0.1950}^{+0.0218}$ & 2.39$_{-1.95}^{+1.61}$ & 
0.0165$_{-0.0023}^{+0.0043}$ & 0.38$_{-0.25}^{+0.37}$ & 
0.0079$_{-0.0032}^{+0.0049}$ & 0.82$_{-0.61}^{+0.60}$ & 
0.0005$_{-0.0005}^{+0.0053}$ & 0.1$_{-0.0}^{+0.0}$ & 
     -                \\
6 & 4.2$\pm$0.6 & 15.85$_{-5.5}^{+59.8}$ & 174.5$_{-19.7}^{+121.1}$ & 0.0266$_{-0.0193}^{+0.3374}$ & 
0.0448$_{-0.0443}^{+0.1745}$ & 5.67$_{-5.89}^{+0.34}$ & 
0.9216$_{-0.1567}^{+0.0524}$ & 1.09$_{-0.89}^{+0.60}$ & 
0.0193$_{-0.0022}^{+0.0060}$ & 0.76$_{-0.32}^{+0.28}$ & 
   -    &  -  & 
0.0137$_{-0.0101}^{+0.1975}$ & 0.1$_{-0.0}^{+0.0}$ & 
     -               \\
\tableline
\enddata
%\linespread{1}%
%\selectfont
\end{deluxetable}


\setcounter{figure}{3}
\begin{figure}[t]
\begin{center}
\resizebox{0.9\hsize}{!}{\includegraphics[angle=0]{f4.eps}}
  \caption{Correlations between the strength and the shape of the 10~$\mu$m silicate band.
The filled symbols show the correlation between the peak over continuum ratio 
of the 10~$\mu$m silicate
band and the ratio of the normalized flux at 11.3~$\mu$m over 9.8~$\mu$m (left axis). 
The open symbols show the correlation between the peak over continuum ratio and the ratio 
of the normalized flux at 8.6~$\mu$m over 9.8~$\mu$m (right axis).
The numbers correspond to the ID numbers of our target stars as listed in Table~1. 
Also plotted in this figure, represented by the dashed lines, is the calculated behaviour for both flux ratios of amorphous olivine grains for a continuous changing grain size from 0.1~$\mu$m (lower right) 
to 2.0~$\mu$m (upper left).}
   \label{fig:cor_shape}
\end{center}
\end{figure}

\begin{figure}[t]
\begin{center}
\resizebox{0.9\hsize}{!}{\includegraphics[angle=0]{f5.eps}}
  \caption{Correlation between the derived mass fraction of crystalline silicates 
(filled symbols; left axis) and the peak-over-continuum ratio of the 10~$\mu$m silicate 
band and the mass averaged grain size of the amorphous silicates (open symbols; right axis) emitting at this wavelength region. As one can see, as the amorphous grains become bigger the 10~$\mu$m silicate band
 becomes weaker. No correlation between the mass fraction of crystalline silicates and the 
typical grain size of the amorphous silicates can be observed.
}
   \label{fig:cor_size_mass}
\end{center}
\end{figure}

\begin{figure}[t]
\begin{center}
\resizebox{0.5\hsize}{!}{\includegraphics[angle=0]{f6a.eps}}
\resizebox{0.5\hsize}{!}{\includegraphics[angle=0]{f6b.eps}}
\caption{Correlation between the far-IR slope of the spectral energy distribution, a measure for disk geometry, and the peak-over-continuum ratio of the 10~$\mu$m silicate band, a measure for the typical grain size. The far-IR slope is measured  by the ratio of the flux at 33~$\mu$m over 24~$\mu$m (top figure) and the 70~$\mu$m over 13~$\mu$m flux ratio (lower panel). A clear correlation can be seen: As the 10~$\mu$m silicate band becomes weaker, the slope of the 
spectral energy distribution decreases. The 13, 24 and 33~$\mu$m fluxes are synthetic photometry points derived from the \emph{Spitzer} low-resolution spectra, the 70~$\mu$m fluxes are photometric data from the MIPS instrument on-board  the \emph{Spitzer Space Telescope}.
}
   \label{fig:cor_slope}
\end{center}
\end{figure}

\begin{figure}[t]
\begin{center}
\resizebox{0.6\hsize}{!}{\includegraphics[angle=0]{f7.eps}}
  \caption{The emission bands of crystalline silicates in the 10~$\mu$m spectral
   window. Shown are the Spitzer low-resolution spectra normalized to the fitted amorphous silicate, PAH,
   and continuum model (see also Section~\ref{sec:model}). The normalized spectra
  all have the same vertical scale between 0.97 and 1.15 but are offset for clarity. The spectra
  are ordered from top to bottom by decreasing 10~$\mu$m silicate band strength. The ID numbers
  correspond to those listed in Table~\ref{tbl:stars}.
  Also indicated in this figure are the positions of the main emission bands of silica,
   forsterite, enstatite dust grains. }
  \label{fig:young_disks_short_no_amorf}
\end{center}
\end{figure}

\begin{figure}[t]
\begin{center}
\resizebox{0.6\hsize}{!}{\includegraphics[angle=0]{f8.eps}}
  \caption{Continuum normalized spectra of the FEPS TTS sample. Shown are the 
Spitzer low-resolution spectra between 17 and 36~$\mu$m normalized to the fitted
continuum using a low order polynomial (see also Section~\ref{sec:model}). The normalized spectra 
all have the same vertical scale between 0.97 and 1.15 but are offset for clarity. The spectra 
are ordered from top to bottom by decreasing 10~$\mu$m silicate band strength. The ID numbers
correspond to those listed in Table~\ref{tbl:stars}. Also indicated in this figure with the 
dashed and dotted lines are the positions of the main spectral features of forsterite and silica.}
  \label{fig:young_disks_long_no_cont}
\end{center}
\end{figure}

\begin{figure}[t]
\begin{center}
\resizebox{0.7\hsize}{!}{\includegraphics[angle=0]{f9.eps}}
\caption{Comparison between the forsterite band position at 27.8~$\mu$m and that of the 
 33.5~$\mu$m feature (top panel) and the 23.4~$\mu$m feature (lower panel). Also indicated are the 
   calculated nominal band positions for 0.1~$\mu$m forsterite grains (filled triangles). }
  \label{fig:cor_band_pos}
\end{center}
\end{figure}

\begin{figure}[t]
\begin{center}
\resizebox{0.8\hsize}{!}{\includegraphics[angle=0]{f10.eps}}
  \caption{Comparison between the measured strength of the forsterite bands at 11.3~$\mu$m (plotted on x-axis) and 10.1~$\mu$m (filled circles), between the 33.5~$\mu$m (plotted on x-axis) and the 27.8~$\mu$m spectral features (open circles) and the 23.4~$\mu$m (plotted on x-axis) and the 27.8~$\mu$m spectral features (filled triangles).}
  \label{fig:cor_bands}
\end{center}
\end{figure}

\begin{figure}[t]
\begin{center}
\resizebox{0.9\hsize}{!}{\includegraphics[angle=0]{f11.eps}}
  \caption{Correlations between the peak over continuum ratio of the 10~$\mu$m silicate band and 
 the band strengths (filled symbols; left axis) and positions (open symbols; right axis) 
of three spectral emission bands of crystalline silicates.
 The top, middle and bottom panels show the correlations for the 23.4~$\mu$m, 27.8~$\mu$m, and the 33.5~$\mu$m band, respectively. 
 As one can see, both position and normalized band strength of these crystalline
 silicate bands show almost no variations and are not correlated to the silicate emission at 10~$\mu$m.
  }
   \label{fig:cor_xbands}
\end{center}
\end{figure}



\begin{figure}[t]
\begin{center}
\resizebox{0.5\hsize}{!}{\includegraphics[angle=0]{f12a.eps}}
\resizebox{0.5\hsize}{!}{\includegraphics[angle=0]{f12b.eps}}
  \caption{Correlations between the measured band strengths of the crystalline silicate
   features in the 20 to 35~$\mu$m wavelength region and those observed in the  10~$\mu$m spectral region.
  The top figure shows the comparison between the band strength of the 11.3~$\mu$m and that of the 33.5~$\mu$m spectral feature (open circles), the 27.8~$\mu$m band (filled circles)
 and 23.4~$\mu$m band (open squares), respectively. The lower figure shows a
  similar comparison but with the band strength of the 10.1~$\mu$m spectral feature.}
  \label{fig:cor_far_ir_bands}
\end{center}
\end{figure}


\begin{figure}[t]
\begin{center}
\resizebox{\hsize}{!}{\includegraphics[angle=0]{f13.eps}}
  \caption{Correlation between the enstatite mass fraction of the crystalline silicates as
   measured in the 10~$\mu$m spectral window and the enstatite mass fraction of the crystalline silicates
   derived from analyzing the longer wavelength features between 20 to 35~$\mu$m.}
  \label{fig:cor_xsil_mid_far_ir}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\resizebox{0.8\hsize}{!}{\includegraphics[angle=0]{f14.eps}}
  \caption{Observed PAH emission bands in the spectra of the FEPS TTS sample.
     Shown are the Spitzer low-resolution spectra normalized to the fitted silicate model 
   (see also Section~2.2 and Table~\ref{tab:t2_fs:fits}). The first 5 spectra clearly show an
    emission feature at 8.2~$\mu$m we assign to emission from PAH molecules. Shown at the
   bottom of the figure is the average spectrum of source \# 0,1,3 and 4, over-plotted with the 
   PAH template spectrum used in our fitting procedure. The dashed lines mark the positions of the main PAH bands.
}
   \label{fig:pah}
\end{center}
\end{figure}

%\begin{figure}[t]
%\begin{center}
%\resizebox{\hsize}{!}{\includegraphics[angle=0]{cor_forst_silica.ps}}
%  \caption{Correlation between the mass ratio of forsterite and silica. 
%  The filled circles show the values determined from the 8-13~$\mu$m spectral region, while the filled diamonds
%   show the values determined from the analysis of the 17-26~$\mu$m spectral region.
%  The dashed lines represent the measured annealing behavior of the of the amorphous
%  magnesium silicates smectite dehydroxylate (SMD; upper curve) and serpentine dehydroxylate
%  (SD; lower curve). }
%  \label{fig:cor_forst_silica}
%\end{center}
%\end{figure}


\end{document}
