deletions | additions       diff --git a/Results.tex b/Results.tex  index ff47d90..23600ff 100644  --- a/Results.tex  +++ b/Results.tex 
...
Most of the imaging of YSO winds traces molecular lines and low-ionizations stages, e.g. \ion{O}{1} or \ion{Fe}{2}. These lines are formed in low-temperature regions, but not in a hot post-shock plasma. Thus, one could expect to see a hole that is filled by hot post-shock plasma form the stelalr wind. However, no such hole is resolved in any CTTS imaging. This limits the maximal size of the stellar wind region to a few AU. Our calculations show that this scenario is compatible with the known properties of the stellar wind.   \subsection{X-ray luminosities}  \label{sect:LX}  The post-shock plasma is less dense than the typical stellar corona and can thus be treated in the so-called coronal approximation, meaning that the plasma is optically thin and line ratios for prominent X-ray lines are in the low-density limit. We use the shock models of \citet{2007A&A...466.1111G} to predict the fraction of the total pre-shock kinetic energy that will be emitted in the X-ray range. \citet{2011AN....332..448G} published a grid of X-ray spectra\footnote{Available at http://hdl.handle.net/10904/10202} with pre-shock velocities between 300 and 1000~km~s$^{-1}$ in increments of 100~km~s$^{-1}$. We integrate all emission between 0.3 and 3~keV for each spectrum. At 300~km~s$^{-1}$ only 2\% of the available energy is emitted between 0.3 and 3~keV, so we set the fraction to zero for pre-shock velocities of 0, 100 and 200~km~s$^{-1}$, which are not covered by the model grid. The fraction of energy emitted in X-rays is independent of the density except for a few density-sensitive emission lines with negligable contribution to the integrated flux. The physical size of the post-shock region depends strongly on the density, but total energy available only depends on the pre-shock velocity and density. Thus, the X-ray luminosity $L_X$ does not change, if the post-shock region is compressed by some external presure and the calculated values of $L_X$ is robust.  The highest post-shock temperatures are generally reached at the base of the jet when the stellar wind encounters the inner disk rim or at large $z$ when the shock front intersects the jet axis. In our fiducial model (Fig.~\ref{fig:result}, solid red line), the pre-shock velocity is $>250$~km~s${-1}$ at $z<5$~AU and $z>20$~AU. Given the large solid angle covered by the inner disk rim, the $z<5$~AU region contributes significantly to the total $L_X$. However, in most YSOs the central object is highyl absorbed. Therefore, all $L_X$ values given are calculated taking into account only regions with $z>5$~AU. Paper~I already showed that in DG~Tau a small fraction, about $10^{-3}$, of the total mass loss rate in the outflow is enough to power the observed X-ray emission at the base of the jet. In our fiducial model, this small fraction corresponds to the mass flow close to the jet axis, where the pre-shock velocities are highest.  diff --git a/bibliography/biblio.bib b/bibliography/biblio.bib  index c4cb62b..85b86b9 100644  --- a/bibliography/biblio.bib  +++ b/bibliography/biblio.bib 
...
adsurl = {http://adsabs.harvard.edu/abs/2011AN....332..448G},  adsnote = {Provided by the SAO/NASA Astrophysics Data System},  }  @INPROCEEDINGS{2006SPIE.6270E..60F,  author = {{Fruscione}, A. and {McDowell}, J.~C. and {Allen}, G.~E. and {Brickhouse}, N.~S. and {Burke}, D.~J. and {Davis}, J.~E. and {Durham}, N. and {Elvis}, M. and {Galle}, E.~C. and {Harris}, D.~E. and {Huenemoerder}, D.~P. and {Houck}, J.~C. and {Ishibashi}, B. and {Karovska}, M. and {Nicastro}, F. and {Noble}, M.~S. and {Nowak}, M.~A. and {Primini}, F.~A. and {Siemiginowska}, A. and {Smith}, R.~K. and {Wise}, M.},  title = {{CIAO: Chandra's data analysis system}},  booktitle = {Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series},  year = {2006},  series = {Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series},  volume = {6270},  month = {jul},  doi = {10.1117/12.671760},  adsurl = {http://adsabs.harvard.edu/abs/2006SPIE.6270E..60F},  adsnote = {Provided by the SAO/NASA Astrophysics Data System},  }  @ARTICLE{2012ApJ...756..128F,  author = {{Foster}, A.~R. and {Ji}, L. and {Smith}, R.~K. and {Brickhouse}, N.~S.},  title = {{Updated Atomic Data and Calculations for X-Ray Spectroscopy}},  journal = {\apj},  archiveprefix = {arXiv},  eprint = {1207.0576},  primaryclass = {astro-ph.HE},  keywords = {atomic data, atomic processes, X-rays: general},  year = {2012},  month = {sep},  volume = {756},  eid = {128},  pages = {128},  doi = {10.1088/0004-637X/756/2/128},  adsurl = {http://adsabs.harvard.edu/abs/2012ApJ...756..128F},  adsnote = {Provided by the SAO/NASA Astrophysics Data System},  }  @ARTICLE{1994AJ....108.1872K,  author = {{Kenyon}, S.~J. and {Dobrzycka}, D. and {Hartmann}, L.},  title = {{A new optical extinction law and distance estimate for the Taurus-Auriga molecular cloud}},  journal = {\aj},  keywords = {Astronomical Catalogs, Infrared Astronomy, Interstellar Extinction, Light (Visible Radiation), Molecular Clouds, Stellar Evolution, Stellar Spectrophotometry, Visible Spectrum, Astronomical Maps, Infrared Photometry, Spectrographs, Spectroscopic Telescopes, Stellar Luminosity},  year = {1994},  month = {nov},  volume = {108},  pages = {1872-1880},  doi = {10.1086/117200},  adsurl = {http://adsabs.harvard.edu/abs/1994AJ....108.1872K},  adsnote = {Provided by the SAO/NASA Astrophysics Data System},  }  diff --git a/figures/DGTaufit/DGTaufit.png b/figures/DGTaufit/DGTaufit.png  new file mode 100644  index 0000000..b2231bc  Binary files /dev/null and b/figures/DGTaufit/DGTaufit.png differ diff --git a/figures/DGTaufit/caption.tex b/figures/DGTaufit/caption.tex  new file mode 100644  index 0000000..3bb3672  --- /dev/null  +++ b/figures/DGTaufit/caption.tex 
...
\caption{\label{fig:fit}  Observed X-ray spectrum of DG~Tau. The best-fit model is shown in red; the orange lines represent the weakly absorbed recollimations shock (dominating at low energies) and the strongly absorbed thermal emission component (dominating at high energies).  }  diff --git a/figures/DGTaufit/size.tex b/figures/DGTaufit/size.tex  new file mode 100644  index 0000000..2fcf78b  --- /dev/null  +++ b/figures/DGTaufit/size.tex 
...
height = 700\nwidth = 500  diff --git a/fitDGTau.tex b/fitDGTau.tex  new file mode 100644  index 0000000..4844538  --- /dev/null  +++ b/fitDGTau.tex 
...
\subsection{Fit to DG Tau data}  In this section we perform a formal fit of our model to the \emph{Chandra} data of DG~Tau. There are some limitations inherent in the model (see discussion in Section~\ref{sect:modelassumptions}) and in the fitting process (see below), but the resulting best-fit model reproduces the observations with parameters that are in line with the observational limits discussed above and thus shows that our model is consistent with the data.  We download and extract the following \emph{Chandra} ObdIDs from the archive: \dataset[ADS/Sa.CXO#obs/04487]{4487}, \dataset[ADS/Sa.CXO#obs/06409]{6409}, \dataset[ADS/Sa.CXO#obs/07246]{7246}, and \dataset[ADS/Sa.CXO#obs/07247]{7247}. These datasets have been used and are described in \citet{2008A&A...478..797G,2008A&A...488L..13S} and paper~I and we refer the reader to those publications for more details. We processed the data with CIAO~4.6 \citep{2006SPIE.6270E..60F}, extracting the CCD spectrum from DG~Tau and a larger, source-free background region on the same chip with the ``specextract'' script. Because the number of counts in the soft component is low and we are not interested in the rapid changes seen in the hard emission attributed to the stellar corona \citep{2008A&A...478..797G} we combine all four source spectra. We bin them to 25 counts per bin and subtract the background. We fit a model with two thermal optically thin plasma emission components \citep[APEC][]{2012ApJ...756..128F} each with its own cold absorber analogous to \citep{2008A&A...478..797G} in the Sherpa fitting tool. We then replace the cooler APEC component by our recollimation shock model. Since the numerical evaluation of this model is slow, we fix the properties of the hot component at the values obtained in the privious fit to reduce the number of free parameters. To further reduce the number of parameters, we set $P_0 = 100\times P_\infty$ and $h=5$~AU. For each set of parameters, our model is evaluated as follows: We solve the ODE in eqn.~\ref{eqn:ode} numerically as above and calculate mass flux and pre-shock velocity for each numerical step. To take the high absorbing column density to DG~Tau itself into account we discard all step with $z<5$~AU. We bin the remaining mass flux according to the pre-shock velocity in each step in bins of 250-350, 350-450, ... 950-1050~km~s$^{-1}$. For each bin we select the appropriate post-shock cooling spectrum from the model grid discussed in Section~\ref{sect:LX} and scale it with the mass flux and an assumed distance to DG~Tau of 140~pc \citep{1994AJ....108.1872K}. We use Sherpa to adjust $\dot M$, $P_0$, $v_\infty$, and the absorbing column density $N_\textrm{H}$ to simultaneously reproduce the observed X-ray spectrum and the position of the shock. \citet{2008A&A...488L..13S} and \citet{2011ASPC..448..617G} give distances of 25-45~AU between DG~Tau and the soft X-ray emission, but do not calculate formal errors for the position. For the purpose of a $\chi^2$ fit we compare the position where the shock front comes back to the jet axis to the value $z_{max} = 30\pm5$~AU.  The best-fit parameters for the shock model are given in table~\ref{tab:fiducial}, $N_\textrm{H}=X$ for the shock, and the parameters of the hot coronal component are $N_\textrm{H}=2.6\times10{22}$~cm$^{-2}$, plasma temperature $kT = 2.2$~keV, and volume emission measure $VEM=5\times10^{52}$~cm$^{-5}$. The best-fit has $z_{max} = 30.4$~AU and $\chi^2_{red}= 1.1$. The fitted spectrum is shown in Figure~\ref{fig:fit}.  diff --git a/justificationassumption.tex b/justificationassumption.tex  index c057251..aab77ad 100644  --- a/justificationassumption.tex  +++ b/justificationassumption.tex 
...
\subsection{Justification of model assumptions}  \label{sect:modelassumptions}  In this section we explain the assumptions made in the derivation of the equations above.  diff --git a/layout.md b/layout.md  index b7e8d49..437e589 100644  --- a/layout.md  +++ b/layout.md 
...
Results.tex  figures/result/result.png  figures/rhocool/rhocool.png  fitDGTau.tex  figures/DGTaufit/DGTaufit.png  Discussion.tex  Summary.tex  diff --git a/parameters.tex b/parameters.tex  index e76b2ad..ac33a38 100644  --- a/parameters.tex  +++ b/parameters.tex 
...
\begin{table}  \label{tab:fiducial}  \caption{Values for fiducial model}  \begin{tabular}{cc} \begin{tabular}{ccc}  \hline\hline  parameter & value\\ fiducial & fit to DG~Tau\\  \hline  $v_\infty$ & 600 km s$^{-1}$\\  $\dot M$ & $10^{-8}\;M_\odot\textrm{yr}^{-1}$\\  $\omega_0$ & 0.01 AU & = 0.01  AU\\ $P(z)$ & $P_\infty+P_0\exp\left(-\frac{z}{h}\right)$ &  $P_\infty+P_0\exp\left(-\frac{z}{h}\right)$\\ $P_\infty$ & $5\cdot 10^{-6}$ Ba\\  $P_0$ & $5\cdot 10^{-4}$ Ba\\  $h$ & 2 AU & = 5  AU\\ \hline  \end{tabular}  \end{table}