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\begin{document}
\title*{Search for Turbulent Gas through Interstellar Scintillation}
\author{Moniez M., Ansari R., Habibi F., Rahvar S.}
% \thanks{Present address: Fluid Mech Inc., 24 The Street, Lagos, Nigeria.},
% \and Susanne H{\"o}fner$^2$}
\institute{Moniez \at Laboratoire de l'Acc\'{e}l\'{e}rateur Lin\'{e}aire,
{\sc IN2P3-CNRS}, Universit\'e de Paris-Sud, B.P. 34, 91898 Orsay
Cedex, France, \email{moniez@lal.in2p3.fr}
}
\maketitle
\abstract{
Stars twinkle because their light propagates through the atmosphere.
The same phenomenon is expected when the light of remote stars
crosses a Galactic -- disk or halo -- refractive medium
such as a molecular cloud.
%LSST is an ideal setup to search for this signature of gas
%thanks to the fast readout and to the wide and deep field.
We present the promising results of a test performed with the ESO-NTT
and the perspectives.
\keywords{Galaxy:structure, dark matter, ISM}
}
\section{What is interstellar scintillation?}
Refraction through
an inhomogeneous transparent cloud (hereafter called screen)
distorts the wave-front of incident electromagnetic waves
(Fig.\ref{front}) \cite{Moniez};
%The phase delay induced by a screen at distance $z_0$
%can be described by a function $\Phi(x_1,y_1)$ in the plane
%transverse to the observer-source line.
%the luminous amplitude in the observer's plane after propagation
%is described by the Huygens-Fresnel diffraction theory.
For a {\it point-like} source,
the intensity in the observer's plane is affected by
interferences which, in the case of stochastic inhomogeneities,
takes on the speckle aspect.
At least 2 distance scales characterise this speckle:
\begin{itemize}
\item
The diffusion radius $R_{diff}(\lambda)$ of the screen,
defined as the transverse separation
for which the root mean square of the phase difference at wavelength
$\lambda$ is 1 radian.
%This radius characterizes
%the structuration of the inhomogeneities
%of the cloud, which are related to the turbulence.
\item
The refraction radius
\begin{equation}
%{\rm The\ refraction\ radius}
R_{ref}(\lambda)=\frac{\lambda z_0}{R_{diff}(\lambda)} \sim
30860\, km \left[\frac{\lambda}{1\, \mu m}\right]
\left[\frac{z_0}{1\, kpc}\right]\left[\frac{R_{diff}(\lambda)}{1000\, km}\right]^{-1}
\end{equation}
where $z_0$ is the distance to the screen.
This is the size, in the observer's plane, of the diffraction spot from a patch
of $R_{diff}(\lambda)$ in the screen's plane.
%\item
%In addition, long scale structures of the screen can induce
%local focusing/defocusing configurations that also
%produce intensity variations.
\end{itemize}
%\subsection{Expectations from simulation: intensity modulation, time
%scale, chromatic effects}
After crossing a fractal cloud described by the Kolmogorov turbulence
law (Fig. \ref{front}, left), the light from a {\it monochromatic
point} source produces an illumination
pattern on Earth made of speckles of size $R_{diff}(\lambda)$ within
larger structures of size $R_{ref}(\lambda)$ (Fig. \ref{front}, right).
\begin{figure}[h]
\begin{center}
\includegraphics[width=11.cm]{principe_OSER.eps}
\end{center}
\caption[]
{\it
Left: a 2D stochastic phase screen (grey scale), from
a simulation of gas affected by Kolmogorov-type turbulence.
Right: the illumination pattern from a point source (left) after crossing
such a phase screen.
The distorted wavefront produces structures at scales $\sim R_{diff}(\lambda)$
and $R_{ref}(\lambda)$ on the observer's plane.
}
\label{front}
\end{figure}
The illumination pattern from a stellar source of radius $r_s$ is
the convolution of the point-like intensity pattern with the projected
intensity profile of the source
%(projected radius
%$R_S=r_s\times z_0/z_1$ where $z_1$ is the distance to the source)
(Fig. \ref{simuscint}, up-right).
\begin{figure}[h]
\centering
\parbox{8cm}{
\includegraphics[width=8cm]{15260fg2a.eps}
\includegraphics[width=8cm]{15260fg2b.eps}
}
\hspace{0.1cm}
\parbox{3.4cm}{\caption[]
{\it
Simulated
illumination map at $\lambda=2.16\mu m$ on Earth from a point source (up-left)-
and from a K0V star ($r_s=0.85R_{\odot}$, $M_V=5.9$) at $z_1=8\, kpc$ (right).
The refracting cloud is assumed to be at $z_0=160\, pc$
with a turbulence parameter $R_{diff}(2.16\mu m)=150\, km$.
The circle shows the projection of the stellar disk ($r_s\times z_0/z_1$).
The bottom maps are illuminations in the $K_s$ wide band
($\lambda_{central}=2.162\mu m$, $\Delta\lambda = 0.275\mu m$).
}
\label{simuscint}}
\end{figure}
%
%\begin{figure}[h]
%\centering
%\parbox{5.cm}{
%\includegraphics[width=4.5cm,height=4.cm]{mod_index.eps}
%}
%\parbox{5.cm}{\caption[]
%{\it
%The intensity modulation index $m_{scint.}=\sigma_I/\bar I$
%decreases when the ratio of the projected
%stellar disk $R_S$ to the refraction scale $R_{ref}(\lambda)$ increases.
%%Intensity modulation index $m=\sigma_I/\bar I$
%%of illumination patterns from simulated diffused stellar light
%%as a function of $x=R_S/R_{ref}$.
%The modulation index is
%essentially contained between the curves represented by functions
%$F_{min}(x)$ and $F_{max}(x)$.
%}
%\label{modindex}}
%\end{figure}
%shows a significant modulation, that varies with the ratio
%$R_S/R_{ref}=r_s R_{diff}/\lambda z_1$ (Fig.3).
%This pattern sweeps across the Earth as
%As the line of sight of the star crosses the transparent cloud
%with the relative transverse velocity $V_T$,
%This pattern sweeps across the Earth at the speeed of the cloud
%relative to the line of sight.
%same speed.
%velocity $V_T$ of the screen,
The cloud, moving with transverse velocity $V_T$
relative to the line of sight, will induce stochastic
%the pattern sweeps across the Earth at the same speed, inducing
intensity fluctuations of the light received from the star
at the characteristic time scale
%\vspace{-0.3cm}
\begin{equation}
t_{ref}(\lambda) = \frac{R_{ref}(\lambda)}{V_T} \sim
5.2\, minutes\left[\frac{\lambda}{1\mu m}\right]\left[\frac{z_0}{1\, kpc}\right]\left[\frac{R_{diff}(\lambda)}{1000\, km}\right]^{-1}\left[\frac{V_T}{100\, km/s}\right]^{-1}.
%\vspace{-0.2cm}
\label{dureescint}
\end{equation}
with modulation index $m_{scint.}=\sigma_I/\bar I$ given by
\begin{eqnarray}
m_{scint.} &=& 0.12 \, \left[\frac{\lambda}{1 \mu m}\right] \left[\frac{z_0}{10 pc}\right]^{-1/6}
\left[\frac{R_{diff}(\lambda)}{1000 km}\right]^{-5/6} \left[\frac{r_s/z_1}{R_\odot/10 kpc}\right]^{-7/6}.
\label{xparam}
\end{eqnarray}
This modulation index decreases when the apparent stellar radius increases.
{\bf Signature of the scintillation signal:}
The first two signatures
%are probably the best ones for the scintillation, because they
point to a propagation effect, which is incompatible with
any type of intrinsic source variability.
%The 3rd and 4th are statistical properties.
\begin{itemize}
\item
Chromaticity:
Since $R_{ref}$ varies with $\lambda^{-1/5}$, one expects
a small variation of the characteristic time scale $t_{ref}(\lambda)$
between the red side of the optical
spectrum and the blue side.
\item
Spatial decorrelation:
%Synchronized observations with distant telescopes would
%allow one to distinguish between intrinsic variabilities (that appear
%simultaneous everywhere) and propagation effects (that produce
We expect a decorrelation between the
light-curves observed at different telescope sites, increasing with
their distance.
\item
Correlation between the stellar radius and the modulation index:
Big stars scintillate less
than small stars through the same gaseous structure.
%This characteristics
%signs the limitations from the spatial coherence of the source and
%can be used to statistically distinguish the scintillating population
%from other variable stars.
\item
Location:
The probability for scintillation is correlated with the
foreground gas column-density.
%Regarding the invisible gas,
Therefore, extended structures may induce
scintillation of apparently neighboring stars
looking like clusters.
%induce clusters of neighboring scintillating stars.
%Such clustering without apparent cause
%is not expected from other categories of variable stars.
\end{itemize}
{\bf Foreground effects, background to the signal:}
Atmospheric {\it intensity} scintillation is negligible
through a large telescope \cite{dravins}.
Any other atmospheric effect should be easy
to recognize as it affects all stars.
Asterosismology, granularity of the
stellar surface, spots or eruptions
produce variations of very different amplitudes and time scales.
A rare type of recurrent variable stars exhibit emission
variations at the minute scale, but such objects could be identified
from their spectrum.
\section{Preliminary studies with the NTT}
%Test observations have been made with the ESO-NTT for scintillation
%of SMC stars due to {\it invisible} gas and for scintillation of
%Galactic stars located behind {\it visible} nebulae.
During two nights of June 2006,
4749 consecutive exposures of ${T_{exp}=10\,s}$
have been taken with the infra-red
SOFI detector in $K_s$ and $J$ through nebulae B68, cb131, Circinus and
towards SMC \cite{resultNTT}.
%The results from this test have been published in \cite{resultNTT}.
A candidate has been found towards B68
(Fig. \ref{candidate}), but the poor photometric precision in $K_s$ and
other limitations prevent us from definitive conclusions.
Nevertheless, we can conclude from the rarity of stochastically
fluctuating objects
that there is no significant population of stars that can
mimic scintillation effects, and future searches
should not be overwhelmed by background of fakes.
\begin{figure}[h]
%\vspace{-0.3cm}
\centering
\parbox{7cm}{
\includegraphics[width=7.cm]{15260fg11a.eps}
\caption[]{\it
Light-curves for the two nights of observation (above) and images of the
candidate found toward B68 during a low-luminosity phase (up-right)
and a high-luminosity phase (bottom); North is up, East is left.
\label{candidate}}
}
\hspace{0.3cm}
\parbox{4cm}{
\includegraphics[width=3.5cm]{15260fg11b.eps}
}
\end{figure}
From the observed SMC light-curves we also
established upper limits
%(not yet competitive, but already excluding
%a major contribution of strongly turbulent gas)
on invisible gaseous structures as a function of their diffusion radius
(Fig. \ref{limits}). This limit, although not really competitive,
already excludes a major contribution of strongly turbulent gas to the
hidden Galactic matter.
%The possible $R_{diff}$ domain for the hidden gas clumpuscules expected
%from the model of Pfenniger and Combes\cite{fractal} and their maximum
%contribution to the optical depth are indicated by the gray zone.
These constaints are at the moment limited by the statistics
and by the photometric precision.\\
\begin{figure}[h]
%\vspace{-0.3cm}
\centering
\parbox{5.5cm}{
\includegraphics[width=5.5cm,height=3.5cm]{15260fg13b.eps}
}
\hspace{0.3cm}
\vspace{-0.3cm}
\parbox{5.cm}{\caption[]{\it
The $95\%\,CL$ maximum optical depth of structures with $R_{diff}(1.25\mu m)