\documentclass{article}
\usepackage{a4wide}

\begin{document}
\title{\textbf{Practice Work Session P7 (2.5h)}\\Preparing VLTI
  observations}
\author{G. Duch\^ene\\
        Laboratoire d'Astrophysique de Grenoble (LAOG)}
\date{\textbf{Euro Summer School}\\
  \emph{Observation and Data reduction with the Very Large Telescope
    Interferometer} \\
4-16 June 2006, Goutelas (France)}
\maketitle

\begin{abstract}
  This session draws on those conducted during the previous Practice
  Work Sessions. Its objective is to prepare a VLTI observing run,
  considering both AMBER and MIDI observations, in order to determine
  what is feasible with these instruments and how useful the planned
  observations would be to solve a particular scientific problem.
\end{abstract}

\section*{Practical considerations}

These exercises will be conducted with the VLTI-dedicated version of
ASPRO. We will run the web-based version of the software from the
local server, as we did in session P5, because we will also try to
identify adequate calibrators. If the network fails, we will resort to
the versions used in previous Practice Work Sessions and skip the
calibrators part.

\section{Astrophysical problems}

In this session, we shall consider two projects. In both cases, the
goal is twofold: 1) to determine the adequate VLTI configurations that
allow the observations, and 2) to decide which instrument is useful in
constraining the system's properties. Furthermore, we want to obtain
quantitative results that can be used as arguments in an ESO proposal:
e.g., adequate period to conduct the observations, expected range of
visibilities, ...

The first problem consists in spatially resolving a spectroscopic
binary system in order to constrain the system inclination and,
therefore, its total mass. In this project, we will try to use both
AMBER and MIDI and determine which instrument is most appropriate.

The second problem consists in studying an object surrounded by a
circumstellar disk with AMBER. In this case, the goal is to determine
the relative flux of the star and of the disk, the typical size of the
disk, as well as the minimum number of measurements needed.

\section{Binary system}

\subsection{Setting the problem}

Here we consider a ``test'' spectroscopic binary system, namely
HD\,147889. Let us assume that this source is a spectroscopic binary
(consisting of unresolved stars), with a maximum projected semi-major
axis of 0.4\,mas, along position angle 25$^o$ (we will consider this
position angle as a sure thing for the purpose of this exercise). If
we observe the binary system at a random point in time, its projected
separation is 0.2\,mas; at apoastron, the projected separation reaches
0.6\,mas. We further assume that the binary has a magnitude difference
of 0.25\,mag, constant throughout the near- and mid-infrared. This
flux ratio is estimated from the guessed masses for the stars and thus
to be considered uncertain: it will remain an unknown in our problem.

The goal of the observation is to try and determine the binary
separation and flux ratio at a certain wavelength with a satisfactory
accuracy so that the stellar masses can be determined.

\subsection{AMBER observations}

Here we decide to use AMBER with 3 UTs in snapshot mode: select
\texttt{AMBER with 3 Telescopes} in the \texttt{Choose...} menu.

\subsubsection{Setting the object}

In the {\it Object} menu, use the CDS link to define the target. Note
that you must use an \texttt{underscore} sign instead of a
\texttt{space} in the object name. Click on \texttt{GO}. If the
network fails, the J2000 coordinates of HD\,147889 are
$\alpha$=16:25:24.32 and $\delta$= -24:27:56.6. Set the object's
magnitudes to MV=7.95, MH=4.94, and MK=4.58.

Set the model of the object with the parameters indicated above, using
the ``observation at a random time'' projected separation. Proceed to
the observational set-up.

\subsubsection{Observability of the target}

Before choosing a particular instrumental configuration, we must first
determine the dates of observation. Click on the \texttt{Source
Observability...} button and check that the target is above elevation
30$^o$ during most of the night (this is indicated by the black
segment). Check also that the delay lines are able to follow the
target during that interval (this is the red segment). Test other
triplets of UTs. When should the observations be conducted (propose 2
months)?  Does it depend on the selected baselines?

\subsubsection{Choosing the AMBER configuration}

AMBER offers three spectral resolutions. It would be preferable to use
the highest resolution possible, in case some physical insight on the
system could be gained, for instance by comparing in- and
out-of-spectral line visibilities. However, the object brightness may
prevent us from using the highest resolution of AMBER.

Select a certain resolution and click on the \texttt{GO (Show/Add UV
track)} button. If the object is too faint to be observed with the
requested resolution, an error window pops-up. What configuration can
be used for this object?

\subsubsection{Testing a first interferometer configuration}

For the time being, select a central wavelength of 2.2$\mu$m, and
UT1-UT2-UT3 as baselines. Use a 60\,min sampling periodicity and,
opening the \texttt{Less used observing constraints}, choose to follow
the motion of the target in the hour angle range [-0.5h;0.5h], i.e. we
will obtain a single measurement (snapshot) with 3 visibilities
(remember to click on the \texttt{click here to validate entries}
button).

With this setup, click on the \texttt{GO (Show/Add UV track)} button
to see the Fourier transform of the object and the {\it uv} points
that will be sampled. Click on the \texttt{Proceed to visibility
  panel} to obtain a plot of visibilities as a function of projected
baseline. The uncertainties that are shown correspond to the object
brightness and the instrumental configuration.

Do you think that this configuration can help constraining the actual
separation and flux ratio of the binary?

\subsubsection{Testing other configurations}

Experiment with other combinations of UTs as well as a different
central wavelength within the range of AMBER to decide whether it is
possible to measure the binary separation at a random phase in its
orbit. If so, what configuration do you propose?

Repeat the same exercise with the projected separation corresponding
to the apoastron passage. 

In conclusion, what configuration and time constraint (if any) do you
suggest for conducting these observations?

\subsubsection{Accuracy on the binary separation}

With the selected configuration, click on the \texttt{Proceed to UV
fitting} after having plotted the visibilities. In this panel, we
shall estimate the accuracy on the binary separation that the
observations would provide. {\it Note that this is not the best method
for estimating this accuracy; this will be discussed later in the
Summer School (see discussion on Model Fitting next Wednesday). Still,
ASPRO provides an estimate of the uncertainties that will be found
when fitting a model to visibilities.}

In the \texttt{AMBER\_3T UV fit control panel}, choose to fit a binary
to the data. In the fit, we can fix 4 out of 6 parameters: the model
is located at (0,0), its total flux is unity and the position angle is
set to be 25$^o$. Since we usually do not know ahead of time the
actual separation and flux ratio of the binary, try ``random''
guesses, flux ratio ranging from 0.1 to 1 and separation ranging from
0.2 to 5\,mas. To set a parameter to a fixed value, use \texttt{-1} as
``number of starts''; to let it free, use \texttt{0}.

For each set of initial guesses, run the fit 3-5 times: the fitting
routine introduces a noise-imitating random process that yields
different results every time. The r.m.s. of the fit results is
actually a better estimate of the uncertainty we would obtain on the
model parameters. Note the values and uncertainties on the flux ratio
and separation. Repeat the process with different initial guesses.

What accuracy can we hope to get on the flux ratio and the separation
with the proposed observations?

\underline{NB}: If you want to run the same fitting procedure with
another instrumental configuration (changing baseline and/or
wavelength), you must return all the way to the ``object definition''
section and re-enter the parameters of the model.

\subsubsection{Check with VisCalc}

Use the \texttt{VisCalc} tool\footnote{It is available under
``Exposure Time Calculators'' on the ESO webpages at {\it
http://www.eso.org/observing/etc}} to check the square visibilities
that were obtained with ASPRO. Be careful that ESO's convention on
position angles is reverse from ASPRO's. It is always wise to double
check one's results!

\subsubsection{Finding a calibrator}

Before going ahead and writing a proposal, we must check that there
are adequate calibrators around our target. Use the SearchCal tool
available in this version of ASPRO, following the same instructions as
during Practical Work Session P4. Use a small search region around the
target (20\,min in RA, 3$^o$ in Dec and a magnitude range [3.;6.] to
match the target brightness).

Indicate possible calibrators and the accuracy on their
visibilities. Will this accuracy limit our ability to determine the
binary properties?

\subsection{MIDI observations}

We now want to determine whether using MIDI instead of AMBER for this
project is more appropriate. We must exit ASPRO and restart it,
selecting \texttt{MIDI on UTs}. Since we cannot use 3 telescopes at
once with MIDI, we will keep the default [-12.;+12.] hour angle range,
i.e. we will observe the target for an entire transit. Follow the same
procedure as with AMBER (for this object, MN=3.30).

With what instrument configurations (beam combiner and spectral
resolution) is it possible to observe this target given its
brightness? Is it possible to use the ATs (on which the pressure is
much lower) instead of the UTs to observe this target?

Can you find an instrumental setup (baseline and observing wavelength)
that allows to determine the binary separation and flux ratio in the
mid-infrared?

Conclusion: in a proposal concerning this target, would you ask for
AMBER or MIDI? What if the binary separation were 5\,mas instead?

\section{Circumstellar disk}

If time permits, repeat the same exercise with a different geometrical
model for the target.

This time, we will use AMBER with 3 Telescopes in snapshot mode (hour
angle range [-0.5;0.5]) and will consider that our target consists of
the sum of two components: an unresolved point source and a circular
Gaussian structure that mimics a face-on circumstellar disk. The
unknown parameters are the flux ratio between the two components and
the FWHM of the Gaussian profile.

With a disk:star flux ratio of 1:4 (make sure the sum of the fluxes
for each component is equal to unity, otherwise the visibilities will
be incorrect) and a Gaussian FWHM of 3\,mas, find the most appropriate
telescope configurations and observing wavelengths to determine the
unknown parameters with good accuracy.

\underline{NB}: When running the fitting routine, set all parameters
to fixed values, except for the flux and FWHM of the Gaussian profile
(all we really care about is its flux {\it relative to the point
source}).

Estimate the accuracy with which the properties of the Gaussian
component can be determined. Increase the hour angle coverage to add
more measurements and determine the smallest number of observations
needed to get a good constraint.

Repeat the exercise if the disk:star flux ratio is 1:10. In this case,
is it at all possible to constrain the Gaussian component with the
current capabilities of AMBER?

\end{document}





