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<!-- DOI: 10.1051/0004-6361/200810972 -->

<h2 class="sec">Online Material</h2>

<p>

<p>

<h2 class="sec"><a name="SECTION00090000000000000000"></a>
<A NAME="ap:sed_just"></A>
Appendix A: (Circum)Stellar parameters from SED fits
</h2>
<div class="inset-old">
<table>
<tr><td><!-- init Label --><A NAME="fig:rob06_mdot">&#160;</A><!-- end Label--><A NAME="2834"></A><A NAME="figure2182"
 HREF="img81.png"><IMG
 WIDTH="199" HEIGHT="67" SRC="Timg81.png"
 ALT="\begin{figure}
\mbox{ \epsfig{file=10972A1a.eps, height=6.0cm} \epsfig{file=10972A1b.eps, height=6.0cm} \epsfig{file=10972A1c.eps, height=6.0cm} }\end{figure}"></A><!-- HTML Figure number: 5 --></td>
<td class="img-txt"><span class="bold">Figure A.1:</span><p>
Comparison between mass accretion rates from the literature
and those derived from SED fits for the sample of T-Tauri stars
considered in <A NAME="aaref50"></A><a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob06">Robitaille et&nbsp;al. (2006)</a>. SED fits and determination of parameter
ranges were performed as for the <IMG
 WIDTH="10" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img6.png"
 ALT="$\rho $">&nbsp;Ophiuchi objects discussed in this
paper. Panel&nbsp;<B> a)</B> compares the literature data with results of
SED fits using all the available photometry, including optical bands.
Panel&nbsp;<B> b)</B> is analogous, but only photometry longward of 1&nbsp;<IMG
 WIDTH="11" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.png"
 ALT="$\mu $">m
was used for the SED fits. Panel&nbsp;<B> c)</B> compares the
results of SED fits with and without optical photometry. Reduced&nbsp;<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.png"
 ALT="$\chi ^2$">
values and mean absolute distances from the bisector, both
computed considering uncertainties on the abscissa only, are reported
within each panel.</p></td>
</tr><tr><td colspan="2"><a href="http://dexter.edpsciences.org/applet.php?pdf_id=5&DOI=10.1051/0004-6361/200810972" target="DEXTER">Open with DEXTER</a></td></tr>

</table></div>
<p>
In this appendix, we describe how we constrained some stellar and
circumstellar parameters of the objects in our sample by comparing
their SEDs with the theoretical models of <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob06">Robitaille et&nbsp;al. (2006)</a>. These consist
of a grid of 200&nbsp;000&nbsp;model SEDs that include contributions from the
central star, the circumstellar disk, and the envelope, parametrized
with 14&nbsp;parameters. The models that best approximate the observed SEDs
were found with the aid of the Web-based tool presented by
<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob07">Robitaille et&nbsp;al. (2007)</a>. As stated by <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob07">Robitaille et&nbsp;al. (2007)</a>, and in accord with basic
principles, this method does not allow the simultaneous determination
of all 14&nbsp;physical parameters, since the SEDs are often defined by
less than 14&nbsp;independent fluxes. However, depending on the available
fluxes, <I>some</I> of the parameters can be constrained more narrowly
than others. We are interested here, in particular, in obtaining the
range of values compatible with the observed SEDs for: i) the
extinction toward our objects; ii) their disk accretion rates.

<p>

<h3 class="sec2"><a name="SECTION00091000000000000000"></a>
<A NAME="ap:sed_method"></A>
A.1 The method and its validation
</h3>

<p>
Our procedure follows closely that of <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob07">Robitaille et&nbsp;al. (2007)</a>: from the Web
interface we obtain, for each object, a list of the 1000&nbsp;models that
best approximate the observed SEDs, i.e. those with the smallest&nbsp;<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.png"
 ALT="$\chi ^2$">.
Our ``best guess'' parameter values and associated
confidence intervals are then derived by selecting a set of <I>statistically reasonable</I> models and computing the median and the
<IMG
 WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img82.png"
 ALT="$\pm$"><IMG
 WIDTH="20" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img83.png"
 ALT="$1\sigma$">
quantiles of the parameter values for these models. The
statistically reasonable models were defined as those with reduced

<!-- MATH: $\chi^2 < (\chi^2_{\rm best}+3)$ -->
<IMG
 WIDTH="88" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img84.png"
 ALT="$\chi^2 < (\chi^2_{\rm best}+3)$">,
where 
<!-- MATH: $\chi^2_{\rm best}$ -->
<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img85.png"
 ALT="$\chi^2_{\rm best}$">
refers to
the best fit model, or if this condition results in less than 10&nbsp;models, the 10&nbsp;models with smallest&nbsp;<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.png"
 ALT="$\chi ^2$">.
Note that, because
the uncertainties on the observed SEDs are not well defined (see
below), and the parameter space is sampled only discretely by the
adopted grid of models, the statistical significance of the thus
derived confidence intervals cannot be easily assessed.

<p>
A similar method<A NAME="tex2html26"
 HREF="#foot2835"><sup><IMG  ALIGN="BOTTOM" BORDER="1" ALT="[*]" SRC="/icons/foot_motif.png"></sup></A> was tested by <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob07">Robitaille et&nbsp;al. (2007)</a> by considering a sample of
Taurus-Auriga objects for which stellar and circumstellar parameters
had been derived independently in the literature and comparing these
parameters with those obtained from fitting the SEDs, defined from the
optical to millimeter wavelengths. In the case of our heavily absorbed
<IMG
 WIDTH="10" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img6.png"
 ALT="$\rho $">&nbsp;Ophiuchi YSOs, the SEDs lack, with the exception of one star,
data in the optical bands, i.e. those more directly affected by the
accretion-shock emission. In order to test our ability to constrain
the accretion rates in the absence of optical information, we repeated
the SED fits of the Taurus-Auriga stars of <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob07">Robitaille et&nbsp;al. (2007)</a>, using the
same datapoints to define the SEDs, and both including and excluding
the optical magnitudes. The results are shown in
Fig.&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#fig:rob06_mdot">A.1</a>. Panel&nbsp;<I>a</I>), analogous to Fig.&nbsp;2b in
<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob07">Robitaille et&nbsp;al. (2007)</a>, compares the accretion rates derived from the SED fits,
including optical data, with independent values from the literature.
Panel&nbsp;<I>b</I>) compares the results of the SED fits without the optical
magnitudes with the literature data. The agreement between the two
quantities is acceptable and may actually be considered better than in
the former panel: the reduced&nbsp;<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.png"
 ALT="$\chi ^2$">,
computed from the identity
relation considering only uncertainties on 
<!-- MATH: $\dot{M}_{\rm SED}$ -->
<IMG
 WIDTH="34" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img86.png"
 ALT="$\dot{M}_{\rm SED}$">,
is indeed
reduced from <IMG
 WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img12.png"
 ALT="$\sim$">12 to&nbsp;1.7. This can in part be attributed to the
increased error bars; note, however, that the average of the unsigned
differences, abs(
<!-- MATH: $\dot{M}_{\rm SED}-\dot{M}_{\rm Lit.}$ -->
<IMG
 WIDTH="77" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img87.png"
 ALT="$\dot{M}_{\rm SED}-\dot{M}_{\rm Lit.}$">), is almost
unchanged, 0.49&nbsp;dex for panel&nbsp;<I>a</I>) and 0.48&nbsp;dex for panel&nbsp;<I>b</I>).
Panel&nbsp;<I>c</I>) compares the&nbsp;<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img14.png"
 ALT="$\dot{M}$">
from the SED fits with and without
optical magnitudes, showing that the two sets of values agree within
uncertainties.  We conclude that the SEDs defined from&nbsp;IR to
millimeter wavelengths are indeed sensitive to the accretion rate, at
least in the <IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img14.png"
 ALT="$\dot{M}$">
range covered by the Taurus-Auriga sample:
log&nbsp;
<!-- MATH: $\dot{M}=[-8.5,-6]$ -->
<IMG
 WIDTH="90" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img88.png"
 ALT="$\dot{M}=[-8.5,-6]$">.

<p>
This is due to the effect of viscous heating affecting the disk
thermal structure. To exemplify this effect we plot in
Fig.&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#fig:sed_colors">A.2</a>, as a function of accretion rate, the ratio
between the IRAC&nbsp;3 band and the <I>J</I>-band flux, for the <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob06">Robitaille et&nbsp;al. (2006)</a>
models for stars with mass between&nbsp;0.7 and 1.3&nbsp;<IMG
 WIDTH="22" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.png"
 ALT="$M_\odot $">,
age between&nbsp;1 and 2&nbsp;Myr (implying little or no circumstellar envelope), and low
disk inclination with respect to the line of sight (
<!-- MATH: $i<60^\circ$ -->
<IMG
 WIDTH="44" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img89.png"
 ALT="$i<60^\circ$">).
We plot with different symbols models with disk inner radii in
different ranges, since the inner hole affects the flux at the IRAC&nbsp;3
wavelength (5.8&nbsp;<IMG
 WIDTH="11" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.png"
 ALT="$\mu $">m). A relation between the two quantities is
seen for models with moderate inner disk holes, apparently
characterized by different regimes in three different&nbsp;<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img14.png"
 ALT="$\dot{M}$">ranges: 
<!-- MATH: $\log(\dot{M}/M_{\odot})\la-11$ -->
<IMG
 WIDTH="107" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img90.png"
 ALT="$\log(\dot{M}/M_{\odot})\la-11$">,

<!-- MATH: $-11\la\log(\dot{M}/M_{\odot})\la-9$ -->
<IMG
 WIDTH="140" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img91.png"
 ALT="$-11\la\log(\dot{M}/M_{\odot})\la-9$">,
and 

<!-- MATH: $\log(\dot{M}/M_{\odot})\ga-9$ -->
<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img92.png"
 ALT="$\log(\dot{M}/M_{\odot})\ga-9$">.
The factor of <IMG
 WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img12.png"
 ALT="$\sim$">2 scatter
around this relation may likely be attributed to model variations
within the specified parameter ranges and to the several other
unconstrained model parameters. Similar and even more pronounced
trends are apparent in analogous plots using fluxes in longer
wavelength IRAC and MIPS bands, with the expected difference that at
the longer wavelengths, emitted farther out in the disk, the size of
the inner hole has a much smaller effect. The three regimes in
Fig.&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#fig:sed_colors">A.2</a> can be understood as follows: i) for
large accretion rates, 
<!-- MATH: $\log(\dot{M}/M_{\odot})\ga-9$ -->
<IMG
 WIDTH="100" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img92.png"
 ALT="$\log(\dot{M}/M_{\odot})\ga-9$">,
the flux in
the IRAC band, emitted by the inner disk (<I>R</I>&lt;1&nbsp;AU), is significantly
affected by viscous accretion (<A NAME="aaref13"></A><A NAME="tex2html63"
 HREF="#dal98">D'Alessio et&nbsp;al.  1998</A>,<A NAME="tex2html64"
 HREF="#dal99">1999</A>); ii) for

<!-- MATH: $-11\la\log(\dot{M}/M_{\odot})\la-9$ -->
<IMG
 WIDTH="140" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img91.png"
 ALT="$-11\la\log(\dot{M}/M_{\odot})\la-9$">
disk heating is
dominated by the stellar photospheric emission and, consequently, no
relation between the IRAC flux and&nbsp;<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img14.png"
 ALT="$\dot{M}$">
is observed; iii) for

<!-- MATH: $\log(\dot{M}/M_{\odot})\la-11$ -->
<IMG
 WIDTH="107" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img90.png"
 ALT="$\log(\dot{M}/M_{\odot})\la-11$">
we again observe a direct
relation between the IRAC&nbsp;3 flux and&nbsp;<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img14.png"
 ALT="$\dot{M}$">,
which we attribute to
the fact that these low accretion rates correspond, in the
<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob06">Robitaille et&nbsp;al. (2006)</a> model grid, to very low disk masses (
<!-- MATH: $M_{\rm disk}\la10^{-6}~M_\odot$ -->
<IMG
 WIDTH="98" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img93.png"
 ALT="$M_{\rm disk}\la10^{-6}~M_\odot$">
for the <IMG
 WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img12.png"
 ALT="$\sim$">1&nbsp;solar mass stars
plotted in Fig.&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#fig:sed_colors">A.2</a>). Since, in the model grid, disk
mass and accretion are directly correlated and such low mass disks are
optically thin (<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob06">Robitaille et&nbsp;al.  2006</a>), lower accretion rates imply lower disk
mass and lower emission in the IRAC band. The IRAC&nbsp;3 flux vs.
<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img14.png"
 ALT="$\dot{M}$">
correlation in this regime does not therefore imply that
that the mid-IR SED carries <I>direct</I> information on disk
accretion. 

<p>
As a result of this discussion, in the derivation of accretion rates
for our <IMG
 WIDTH="10" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img6.png"
 ALT="$\rho $">&nbsp;Ophiuchi sample from the SED fits, we decided not to
use values below  
<!-- MATH: $10^{-9}~M_{\odot}$ -->
<IMG
 WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img94.png"
 ALT="$10^{-9}~M_{\odot}$">&nbsp;yr<sup>-1</sup>. In such cases we
instead conservatively assigned upper limits to&nbsp;<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img14.png"
 ALT="$\dot{M}$">
equal to the
maximum between 
<!-- MATH: $10^{-9}~M_{\odot}$ -->
<IMG
 WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img94.png"
 ALT="$10^{-9}~M_{\odot}$">&nbsp;yr<sup>-1</sup> and the upper end of
the&nbsp;<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img14.png"
 ALT="$\dot{M}$">
confidence interval (see above).

<p>
<div class="inset-old">
<table>
<tr><td><!-- init Label --><A NAME="fig:sed_colors">&#160;</A><!-- end Label--><A NAME="2837"></A><A NAME="figure2251"
 HREF="img95.png"><IMG
 WIDTH="96" HEIGHT="99" SRC="Timg95.png"
 ALT="\begin{figure}
{
\epsfig{file=10972A2.eps, height=8.8cm} }\end{figure}"></A><!-- HTML Figure number: 6 --></td>
<td class="img-txt"><span class="bold">Figure A.2:</span><p>
Scatter plot of the ratio between the flux in the IRAC&nbsp;1
band over that in&nbsp;<I>J</I>, as a function of
disk accretion rate, according to the <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob06">Robitaille et&nbsp;al. (2006)</a> models for a solar
mass stars. Each point corresponds to one of the <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob06">Robitaille et&nbsp;al. (2006)</a> models
satisfying the following conditions: mass of the central object
between&nbsp;0.7 and 1.3&nbsp;<IMG
 WIDTH="22" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.png"
 ALT="$M_\odot $">,
age between&nbsp;1 and 2&nbsp;Myr, and disk
inclination with respect to the line of sight &lt;60<IMG
 WIDTH="9" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img9.png"
 ALT="$^\circ $">.
Different
symbols indicate models with an inner disk radius in one of
five ranges as indicated in the legend.</p></td>
</tr><tr><td colspan="2"><a href="http://dexter.edpsciences.org/applet.php?pdf_id=6&DOI=10.1051/0004-6361/200810972" target="DEXTER">Open with DEXTER</a></td></tr>

</table></div>
<p>

<h3 class="sec2"><a name="SECTION00092000000000000000"></a>
<A NAME="ap:sed_rhoOph"></A>
A.2 The <IMG
 WIDTH="10" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img6.png"
 ALT="$\rho $">
Ophiuchi sample
</h3>

<p>
We collected photometric measurements and uncertainties (when
available) for our <IMG
 WIDTH="10" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img6.png"
 ALT="$\rho $">
Ophiuchi sample from several sources: <I>J</I>,
<I>H</I>, and <IMG
 WIDTH="17" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img96.png"
 ALT="$K_{\rm s}$">
magnitudes (or upper limits) were taken for almost all
objects from 2&nbsp;MASS<A NAME="tex2html29"
 HREF="#foot2838"><sup><IMG  ALIGN="BOTTOM" BORDER="1" ALT="[*]" SRC="/icons/foot_motif.png"></sup></A>; <I>Spitzer</I> IRAC (bands&nbsp;1-4) and MIPS (bands&nbsp;1 &amp;
2) photometry was collected from the c2d database<A NAME="tex2html30"
 HREF="#foot2265"><sup><IMG  ALIGN="BOTTOM" BORDER="1" ALT="[*]" SRC="/icons/foot_motif.png"></sup></A> (<A NAME="aaref19"></A><a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#eva03">Evans et&nbsp;al.  2003</a>); 1.2&nbsp;mm
fluxes were collected from <A NAME="aaref54"></A><a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#stan06">Stanke et&nbsp;al. (2006)</a> and 1.3&nbsp;mm fluxes from
<A NAME="aaref2"></A><a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#and94">Andre &amp; Montmerle (1994)</a><A NAME="tex2html31"
 HREF="#foot2839"><sup><IMG  ALIGN="BOTTOM" BORDER="1" ALT="[*]" SRC="/icons/foot_motif.png"></sup></A>. Optical 
<!-- MATH: ${\it UBVR}$ -->
<IMG
 WIDTH="39" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img97.png"
 ALT="$ {\it UBVR}$">&nbsp;photometry for one object
with small absorption (DoAr&nbsp;25) was taken from <A NAME="aaref63"></A><a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#yak92">Yakubov (1992)</a>. Table&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#tab:sed_input">A.1</a> lists all the photometric flux densities collected
from the literature.  

<p>
Finally, we complement the photometric data with flux densities from
the IRS spectra (cf. Sect.&nbsp;&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#sect:data_spitzer">2.1</a>). We computed flux
densities between&nbsp;10 and 18&nbsp;<IMG
 WIDTH="11" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.png"
 ALT="$\mu $">m, at regular wavelength intervals
spaced by 0.5&nbsp;<IMG
 WIDTH="11" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.png"
 ALT="$\mu $">m. Each flux density was taken as the average of the
spectral bins in 0.2&nbsp;<IMG
 WIDTH="11" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.png"
 ALT="$\mu $">m intervals centered at the nominal
wavelength. For the four stars with two IRS observations, we have
taken the average of the two spectra. (In three cases the
wavelength-averaged fluxes differ by less than 0.1&nbsp;dex, while in one
case, EL29/GY214, the difference is 0.4&nbsp;dex. In all cases we verified
that the results of the model fits did not change appreciably choosing
either of the two spectra). Table&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#tab:sed_input_IRS">A.2</a> lists the
flux densities from the IRS spectra. As stated in
Sect.&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#sect:data_spitzer">2.1</a>  our sky subtraction procedure does not
take into account diffuse nebular emission. In order to assess the
significance of diffuse emission on the object flux densities, we have
considered the IRS spectra of the 13 YSOs in our sample observed in
the context of the <I>Spitzer</I> legacy program <I>From Molecular
Cores to Planet-Forming Disks</I> (``c2d'', <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#eva03">Evans et&nbsp;al.  2003</a>). As with the
entire c2d&nbsp;sample, the reduced/sky-subtracted IRS spectra have been
analyzed (and made publicly available) by the c2d team, using a
sophisticated extraction and sky subtraction method based on the
modelling of the cross dispersion profiles (<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#lah07">Lahuis et&nbsp;al.  2007</a>). We have
compared the flux densities derived from the c2d-reduced spectra with
those derived from the same spectra reduced by us. We find the spectra
to be similar, with both the maximum and the wavelength-averaged
discrepancy decreasing with object intensity. The maximum discrepancy
falls below&nbsp;10% for the 9&nbsp;YSOs with c2d-reduced spectra that have an
average flux &gt;0.5&nbsp;Jy. Based on this comparison, and noting that the
c2d objects are representative of our sample in their position with
respect to nebulosity seen in IRAC and MIPS maps, we decided to use
the IRS-derived fluxes to define the SEDs of the 17 stars with average
IRS flux &gt;0.5&nbsp;Jy. 

<p>
As suggested by <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob07">Robitaille et&nbsp;al. (2007)</a>, in order to account for systematic
uncertainties, underestimation of the measurement errors, and
intrinsic object variability over time, a lower limit of&nbsp;25%, 10%,
and&nbsp;40% was imposed on the uncertainties of optical, NIR/MIR, and 
millimeter fluxes, respectively. 

<p>
Figure <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#fig:sed_examples">A.3</a> exemplifies the ``fitting'' procedure
described in Sect.&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#ap:sed_method">A.1</a> for three of our YSOs. It shows
the SEDs with the best fit models and the distributions of two fit
parameters, <IMG
 WIDTH="19" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.png"
 ALT="$A_{\rm V}$">
and 
<!-- MATH: $\dot{M}_{\rm disk}$ -->
<IMG
 WIDTH="33" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img75.png"
 ALT="$\dot{M}_{\rm disk}$">,
both for the 1000&nbsp;models with lowest&nbsp;<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.png"
 ALT="$\chi ^2$">
and for the <I>statistically reasonable</I>
ones (cf. <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#ap:sed_method">A.1</a>). SEDs and best fit models for the 28&nbsp;YSOs in our sample are shown in Fig.&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#fig:sed_all">A.4</a>.

<p>
<div class="inset-old">
<table>
<tr><td><!-- init Label --><A NAME="fig:sed_examples">&#160;</A><!-- end Label--><A NAME="2843"></A><A NAME="figure2289"
 HREF="img98.png"><IMG
 WIDTH="200" HEIGHT="132" SRC="Timg98.png"
 ALT="\begin{figure}
{
\epsfig{file=10972A3a.ps, width=5.80cm}\epsfig{file=10972A3b.ps...
...972A3h.ps, width=5.95cm}\epsfig{file=10972A3i.ps, width=5.95cm} }\end{figure}"></A><!-- HTML Figure number: 7 --></td>
<td class="img-txt"><span class="bold">Figure A.3:</span><p>
Examples of SED fits for three objects in our sample with
[Ne&nbsp;II] detections. <I> From left to right</I>: DoAr25/GY17, WL20/GY240, and
IRS44/GY269. The first is classified as Stage/Class&nbsp;II, the other two as
Stage/Class&nbsp;I. The upper row shows the SEDs and the best fit models as
produced by the Web interface provided by <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob06">Robitaille et&nbsp;al. (2006)</a>. For the
datapoints, detections and upper limits are indicated by circles and
triangles, respectively. The lower two rows represent distributions of
two fit parameters, <IMG
 WIDTH="19" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.png"
 ALT="$A_{\rm V}$">
and 
<!-- MATH: $\dot{M}_{\rm disk}$ -->
<IMG
 WIDTH="33" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img75.png"
 ALT="$\dot{M}_{\rm disk}$">.
The empty histograms
refer to the 1000&nbsp;model fits with lowest&nbsp;<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.png"
 ALT="$\chi ^2$">
and the green
histograms to the <I> statistically reasonable</I> samples of models defined in
Sect.&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#ap:sed_method">A.1</a>. The solid and dashed vertical lines indicate
the median and the&nbsp;1<IMG
 WIDTH="13" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img3.png"
 ALT="$\sigma $">
dispersion for these latter samples. For the
panels in the second row, the symbols close to the upper axis indicate
the <IMG
 WIDTH="19" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.png"
 ALT="$A_{\rm V}$">&nbsp;values inferred from the&nbsp;<I>A</I><SUB><I>J</I></SUB> in
Table&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#tab:target_litdata">2</a> (circles) and from the X-ray-derived&nbsp;<IMG
 WIDTH="21" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img11.png"
 ALT="$N_{\rm H}$">in Table&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#tab:droxo_irs_results">4</a> (squares). </p></td>
</tr><tr><td colspan="2"><a href="http://dexter.edpsciences.org/applet.php?pdf_id=7&DOI=10.1051/0004-6361/200810972" target="DEXTER">Open with DEXTER</a></td></tr>

</table></div><div class="inset-old">
<table>
<tr><td><!-- init Label --><A NAME="fig:sed_all">&#160;</A><!-- end Label--><A NAME="2851"></A><A NAME="figure2314"
 HREF="img99.png"><IMG
 WIDTH="208" HEIGHT="265" SRC="Timg99.png"
 ALT="\begin{figure}
{
\epsfig{file=10972A3a.ps, width=4.60cm}\epsfig{file=10972A4a.p...
...0972A4k.ps, width=4.60cm}\epsfig{file=10972A4w.ps, width=4.60cm} }\end{figure}"></A><!-- HTML Figure number: 8 --></td>
<td class="img-txt"><span class="bold">Figure A.4:</span><p>
SEDs and best fit models, as produced by the Web interface
provided by <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob06">Robitaille et&nbsp;al. (2006)</a>, for the 28&nbsp;YSOs in our sample.</p></td>
</tr><tr><td colspan="2"><a href="http://dexter.edpsciences.org/applet.php?pdf_id=8&DOI=10.1051/0004-6361/200810972" target="DEXTER">Open with DEXTER</a></td></tr>

</table></div>
<p>
Following visual examination of the SED fits and of the distributions
of model parameters used to define the confidence intervals, we
decided to modify the input datapoints for two objects: for
IRS45/GY273 we excluded the&nbsp;1.2 and 1.3&nbsp;mm datapoints from
<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#stan06">Stanke et&nbsp;al. (2006)</a> and <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#and94">Andre &amp; Montmerle (1994)</a>; including these
points significantly worsened the quality of the fit and had a
significant effect on the values of the parameters. The 1.2&nbsp;mm flux
is &gt;20&nbsp;times higher than the 1.3&nbsp;mm flux (an upper limit) and
can probably be attributed to an extended source that <I>includes</I>
our YSO. For&nbsp;GY289, a source with average IRS flux &lt;0.5&nbsp;Jy, we
decided to include the IRS datapoints because: i) they agree quite
well with the MIPS fluxes at similar wavelengths; ii) the quality of
the model fit is reasonable (
<!-- MATH: $\chi^2_{\rm best}\sim 2$ -->
<IMG
 WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img100.png"
 ALT="$\chi^2_{\rm best}\sim 2$">)
and; iii) the
confidence intervals of the model parameters are narrower but
compatible with those from the fit performed without these points. 

<p>
For one object, WL5/GY246, we could not obtain a unique fit with the
above procedure. The object was previously classified as a deeply
absorbed Class&nbsp;III star with an F7 spectral type (<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#gre95">Greene &amp; Meyer  1995</a>), and
our SED was defined by <I>J</I>, <I>H</I>, <I>K</I>, <I>Spitzer</I> IRAC&nbsp;1-4 and
1.2/1.3&nbsp;mm fluxes. Fits both with and without the mm fluxes, likely
contaminated by nearby sources (cf. <A NAME="tex2html65"
 HREF="#stan06">Stanke et&nbsp;al.  2006</A>; <A NAME="tex2html66"
 HREF="#and94">Andre &amp; Montmerle  1994</A>),
consistently yield high envelope and/or disk accretion rates, typical
of a Class&nbsp;I object, but having  little effect on the NIR/MIR part of
the SED due to the associated large inner disk radii. The NIR/MIR SED
can however be fit equally well by purely photospheric ``Phoenix''
models, as suggested by the same <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob07">Robitaille et&nbsp;al. (2007)</a> web interface used to
fit the star/disk/envelope models. We thus decided to assume that
WL5/GY246 is a Class&nbsp;III object and to derive its extinction,
effective temperature, and stellar mass using the&nbsp;<I>J</I>, <I>H</I>, and <I>K</I>&nbsp;photometry, the spectral type, and the calibrations tabulated by
<A NAME="aaref37"></A><a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#kh95">Kenyon &amp; Hartmann (1995)</a>. Uncertainties were estimated from the assumed
uncertainty on the spectral type, one subclass, and the range of
values obtained by estimating the absorption from the 
<I>J</I>-<I>H</I>, <I>H</I>-<I>K</I>, and
<I>J</I>-<I>K</I>&nbsp;colors.

<p>
Table&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#tab:sed_results">3</a>, introduced in the main text (Sect.&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#sect:anc_SED">2.3</a>), lists the outcome of the SED-fit process: the
quality of the fit (the&nbsp;<IMG
 WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.png"
 ALT="$\chi ^2$">
of the ``best-fit'' model), the
object extinction (the sum of interstellar and envelope extinction),
the stellar effective temperature and mass, the disk mass, the disk
and envelope accretion rates, the evolutionary Stage. The last
quantity was assigned following <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob07">Robitaille et&nbsp;al. (2007)</a>. Stage&nbsp;I: 
<!-- MATH: $\dot{M}_{\rm
env}/M_* > 10^{-6}$ -->
<IMG
 WIDTH="96" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img101.png"
 ALT="$\dot{M}_{\rm
env}/M_* > 10^{-6}$">;
Stage&nbsp;II: 
<!-- MATH: $\dot{M}_{\rm env}/M_* \le 10^{-6}$ -->
<IMG
 WIDTH="95" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img102.png"
 ALT="$\dot{M}_{\rm env}/M_* \le 10^{-6}$">
and

<!-- MATH: $M_{\rm disk}/M_* > 10^{-6}$ -->
<IMG
 WIDTH="99" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img103.png"
 ALT="$M_{\rm disk}/M_* > 10^{-6}$">;
Stage&nbsp;III: 
<!-- MATH: $\dot{M}_{\rm env}/M_* \le
10^{-6}$ -->
<IMG
 WIDTH="95" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img102.png"
 ALT="$\dot{M}_{\rm env}/M_* \le 10^{-6}$">
and 
<!-- MATH: $M_{\rm disk}/M_* \le 10^{-6}$ -->
<IMG
 WIDTH="98" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img104.png"
 ALT="$M_{\rm disk}/M_* \le 10^{-6}$">.
As indicated in the main
text, in order to use a designation more familiar to researchers in
the field, we also refer to the ``Stages'' as ``Classes''. 

<p>
Figures <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#fig:sedAv_vs_lit">A.5</a> and <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#fig:sedTe_vs_lit">A.6</a> compare the
extinction values&nbsp;(<IMG
 WIDTH="19" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.png"
 ALT="$A_{\rm V}$">)
and stellar&nbsp;
<!-- MATH: $T_{\rm eff}$ -->
<IMG
 WIDTH="23" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img105.png"
 ALT="$T_{\rm eff}$">
obtained
from the SED&nbsp;fits with the same parameters listed in
Table&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#tab:target_litdata">2</a> for Class&nbsp;II and Class&nbsp;III stars.
Given the considerable uncertainties of both determinations, the SED
fits yield results similar to those obtained with the method of
<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#nat06">Natta et&nbsp;al. (2006)</a>. A similar comparison with the accretion rates derived
from the Pa<IMG
 WIDTH="11" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img39.png"
 ALT="$\beta$">
and Br<IMG
 WIDTH="10" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img40.png"
 ALT="$\gamma$">&nbsp;NIR&nbsp;line fluxes (in 
Table&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#tab:target_litdata">2</a>) is less conclusive due to the large number
of upper limits and to the large uncertainties that affect the
spectroscopic measurements as well as the SED fits. Seven objects can
be used for the comparison, having accretion rate estimates or upper
limits from both methods. For only two stars, both methods yield
estimates: those for IRS&nbsp;54 are in good agreement; for WL&nbsp;16 the
spectroscopic estimate is 2.6&nbsp;dex higher than the value from the SED
fits, 
<!-- MATH: $\dot{M}\sim 10^{-8}$ -->
<IMG
 WIDTH="58" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img106.png"
 ALT="$\dot{M}\sim 10^{-8}$">&nbsp;<IMG
 WIDTH="22" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.png"
 ALT="$M_\odot $">&nbsp;yr<sup>-1</sup>. The discrepancy is
however reduced to 1.2&nbsp;dex when comparing the result of the SED fit
with the <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#nat06">Natta et&nbsp;al. (2006)</a> value. Moreover, the derivation of&nbsp;<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img14.png"
 ALT="$\dot{M}$">from the Pa<IMG
 WIDTH="9" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img107.png"
 ALT="$_\beta$">&nbsp;line with the method of <A HREF="#nat06">Natta et&nbsp;al. (2006, see also Sect.&nbsp;<A HREF="aa10972-08.right.html)</A>sect:anc_SED">2.3</A># is better suited for cool stars and is
likely to yield inaccurate results for WL&nbsp;16 (
<!-- MATH: $T_{\rm
eff}\sim10^4$ -->
<IMG
 WIDTH="59" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img108.png"
 ALT="$T_{\rm
eff}\sim10^4$">&nbsp;K).  An independent estimate by <A NAME="aaref45"></A><a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#naj96">Najita et&nbsp;al. (1996)</a> yielded
an upper limit compatible with the SED value: 
<!-- MATH: $\dot{M}\la
2\times10^{-7}$ -->
<IMG
 WIDTH="81" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img109.png"
 ALT="$\dot{M}\la
2\times10^{-7}$">&nbsp;<IMG
 WIDTH="22" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.png"
 ALT="$M_\odot $">&nbsp;yr<sup>-1</sup>. Three other stars have
<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img14.png"
 ALT="$\dot{M}$">
estimates from the SED fits and upper limits from
Table&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#tab:target_litdata">2</a>: in two cases, IRS&nbsp;51 and IRS&nbsp;47,
the confidence intervals from the SED fits are consistent with the
upper limits; for DoAr&nbsp;25/GY17, the only star with optical
magnitudes, the SED fit yields an accretion rate that is 1.6&nbsp;dex
higher than the upper limit from the Pa<IMG
 WIDTH="9" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img107.png"
 ALT="$_\beta$">&nbsp;line. Finally, for two
stars, WL&nbsp;10 and WL&nbsp;11, the spectroscopic estimates are 0.4&nbsp;dex and
0.1&nbsp;dex larger than the upper limits from the SED fits. The
discrepancy is however reduced to 0.24&nbsp;dex for WL&nbsp;10 and disappears
for WL&nbsp;11 if the slightly larger <IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img14.png"
 ALT="$\dot{M}$">&nbsp;values from <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#nat06">Natta et&nbsp;al. (2006)</a>
are considered instead of those in Table&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#tab:target_litdata">2</a>.

<p>

<h3 class="sec2"><a name="SECTION00093000000000000000"></a>
A.3 Summary
</h3>

<p>
In this Appendix we have shown that the SED models of <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob06">Robitaille et&nbsp;al. (2006)</a>,
although undeniably approximate, can be useful to constrain parameters
such as the line-of-sight absorption and the disk accretion  rate,
even in the absence of optical photometry. Although resulting
uncertainties in these parameters are often large, the constraints are
by and large compatible with independent determinations obtained with
more direct methods.

<p>

<p>
<div class="inset-old">
<table>
<tr><td><!-- init Label --><A NAME="fig:sedAv_vs_lit">&#160;</A><!-- end Label--><A NAME="2853"></A><A NAME="figure2402"
 HREF="img110.png"><IMG
 WIDTH="99" HEIGHT="99" SRC="Timg110.png"
 ALT="\begin{figure}
{\epsfig{file=10972A5.eps, width=8.8cm} }\end{figure}"></A><!-- HTML Figure number: 9 --></td>
<td class="img-txt"><span class="bold">Figure A.5:</span><p>
Comparison of the <IMG
 WIDTH="19" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.png"
 ALT="$A_{\rm V}$">values derived from fitting the SEDs with the <a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#rob06">Robitaille et&nbsp;al. (2006)</a> models
with values derived from 2MASS photometry (cf. Table&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#tab:target_litdata">2</a>).
Objects of different SED Class are indicated by different symbols as
shown in the legend.</p></td>
</tr><tr><td colspan="2"><a href="http://dexter.edpsciences.org/applet.php?pdf_id=9&DOI=10.1051/0004-6361/200810972" target="DEXTER">Open with DEXTER</a></td></tr>

</table></div>
<p>
<div class="inset-old">
<table>
<tr><td><!-- init Label --><A NAME="fig:sedTe_vs_lit">&#160;</A><!-- end Label--><A NAME="2855"></A><A NAME="figure2410"
 HREF="img111.png"><IMG
 WIDTH="99" HEIGHT="98" SRC="Timg111.png"
 ALT="\begin{figure}
\par {\epsfig{file=10972A6.eps, width=8.8cm} }\end{figure}"></A><!-- HTML Figure number: 10 --></td>
<td class="img-txt"><span class="bold">Figure A.6:</span><p>
Same as Fig.&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#fig:sedAv_vs_lit">A.5</a> for the effective
temperatures.</p></td>
</tr><tr><td colspan="2"><a href="http://dexter.edpsciences.org/applet.php?pdf_id=10&DOI=10.1051/0004-6361/200810972" target="DEXTER">Open with DEXTER</a></td></tr>

</table></div>
<p>
<A NAME="tab:sed_input"></A><p class="inset-old"><a href="/articles/aa/full_html/2009/38/aa10972-08/tableA.1.html"><span class="bold">Table A.1:</span></a>&#160;&#160;
Flux densities, in mJy, collected from the literature (cf. Sect.&nbsp;<a href="/articles/aa/full_html/2009/38/aa10972-08/aa10972-08.html#ap:sed_rhoOph">A.2</a>) and used for the SED fits.</p>
<p>
<A NAME="tab:sed_input_IRS"></A><p class="inset-old"><a href="/articles/aa/full_html/2009/38/aa10972-08/tableA.2.html"><span class="bold">Table A.2:</span></a>&#160;&#160;
Flux densities, in Jy, obtained from the IRS spectra for the
SED fits.</p>
<p>
<br>

</div></body></html>