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<!-- DOI: 10.1051/0004-6361/200911997 -->

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

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<h2 class="sec"><a name="SECTION00090000000000000000"></a>Appendix A: Graphical representation  of the 3D temperature correction, <IMG
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  the quality  of the fit, <I>QF</I>, and the sensitivity of the fit, 
<!-- MATH: ${\sigma_{{T}_{eff}}}$ -->
<IMG
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<tr><td><!-- init Label --><A NAME="fig2">&#160;</A><!-- end Label--><A NAME="750"></A><A NAME="figure617"
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<td class="img-txt"><span class="bold">Figure A.1:</span><p>
The temperature differences (3D - 1D) using 1D&nbsp;models with <IMG
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 ALT="$\alpha $">&nbsp;= 0.5, <IMG
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 ALT="$\alpha $">&nbsp;= 1.0 and <IMG
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 ALT="$\alpha $">&nbsp;= 2.0, for H<IMG
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H<IMG
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and&nbsp;H<IMG
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for all of the six models considered. The uncertainties related to each temperature difference measurement are displayed as boxes. The value of the uncertainty on the <I>x</I>-axis corresponds to the associated 
<!-- MATH: $\sigma_{T_{\rm eff}}$ -->
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(sensitivity) values, while the uncertainty on the <I>y</I>-axis corresponds to the associated <I>QF</I> (quality of fit) values. See Table&nbsp;<a href="/articles/aa/full_html/2009/29/aa11997-09/aa11997-09.html#tab2">2</a> and the text for details.</p></td>
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<h2 class="sec"><a name="SECTION000100000000000000000"></a>
Appendix B: 3D-1D temperature correction  and the lithium abundance in metal-poor F-type dwarfs
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<tr><td><!-- init Label --><A NAME="fig3">&#160;</A><!-- end Label--><A NAME="717"></A><A NAME="figure625"
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<td class="img-txt"><span class="bold">Figure B.1:</span><p>
3D-1D abundance correction versus effective temperature difference for the
test case of a metal-poor F-type dwarf. For details see&nbsp;text.</p></td>
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Here we present an example where it is advantageous to use a 1D&nbsp;model corrected for the 3D-1D&nbsp;temperature difference when deriving the chemical abundance from spectral line analysis: the abundance of lithium in a metal-poor F-type dwarf obtained from the 670.7&nbsp;nm resonance line. We
performed   a 3D-NLTE&nbsp;spectrum synthesis calculation for the line on the 3D&nbsp;model with 
<!-- MATH: $\ensuremath{T_{\rm eff}}$ -->
<IMG
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 ALT="\ensuremath{T_{\rm eff}}">&nbsp;= 6280&nbsp;K, 
<!-- MATH: $\ensuremath{\log g}$ -->
<IMG
 WIDTH="30" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
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 ALT="\ensuremath{\log g}">&nbsp;= 4.0, [M/H]&nbsp;= -2.0 (cf.&nbsp;Table&nbsp;<a href="/articles/aa/full_html/2009/29/aa11997-09/aa11997-09.html#tabmod">1</a>).  We considered the resulting spectrum as representing an observation. Unlike a real observation, however, the underlying lithium abundance and stellar parameters are exactly known.  According to Table&nbsp;<a href="/articles/aa/full_html/2009/29/aa11997-09/aa11997-09.html#tab3">3</a> the temperature correction from H<IMG
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fitting amounts to 74&nbsp;K in this case, i.e.&nbsp;the 1D&nbsp;model that fits the 3D&nbsp;H<IMG
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 ALT="$\alpha $">&nbsp;profile best is 74&nbsp;K cooler than the 3D&nbsp;model.  We then calculated for a series of thirteen 1D&nbsp;(LHD)&nbsp;models of different effective temperatures 1D&nbsp;lithium line profiles in LTE and NLTE. In the 1D&nbsp;spectrum synthesis, we assumed a microturbulence velocity of 1&nbsp;km&nbsp;s<sup>-1</sup>; however, the actual value is not important since the line was chosen to be very weak. We derived for each model the lithium abundance matching the line strength obtained in&nbsp;3D. Figure&nbsp;<a href="/articles/aa/full_html/2009/29/aa11997-09/aa11997-09.html#fig3">B.1</a> depicts the resulting abundance differences between  the underlying lithium abundance assumed in the 3D&nbsp;model and the derived 1D&nbsp;abundance, versus the effective temperature differences between 1D&nbsp;models and the 3D&nbsp;model. As evident from the plot, one reduces the abundance error resulting from the erroneous effective temperature of the 1D&nbsp;model when applying the 3D-1D&nbsp;temperature correction. This holds irrespective of whether the 1D&nbsp;abundance analysis is performed in LTE or&nbsp;NLTE. Not surprisingly, the figure also shows that the correction of the effective temperature does not result in a perfect match of the lithium abundances in a&nbsp;1D&nbsp;analysis.

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