text:
\section{Introduction}

From January to November 1983 the Infrared Astronomical Satellite (IRAS),
a joint project of the US, UK and the Netherlands \cite[]{neugebauer84},
performed a survey of 98\% of the sky at four wavelengths :
12, 25, 60 and 100 $\mu$m.
IRAS lead to numerous scientific discoveries spanning a broad range of
astrophysical subjects, from comets, circumstellar disk to interacting
galaxies. The satellite was designed to optimize the reliablility of point
sources detection and photometry;
one of the great legacies of IRAS is certainly its catalog of
more than 250~000 point sources. On the other hand, the relative stability
of its detectors also allowed mapping
of extended emission. In fact IRAS made a significant contribution to our
understanding of Galactic diffuse emission by revealing the interstellar dust
emission of infrared cirrus, that can be observed in any direction on the
sky \cite[]{low84}.

A first set of extended emission maps (the SkyFlux atlas)
was released in 1984 and 1986 along with the IRAS Point Source Catalog.
It was then clear that significant improvements of the sensitivity
and photometric accuracy could be obtained based on the acquired knowledge
of the instrument. The IRAS data were later reprocessed based
on the knowledge of the instrumental response available at that time but also
by applying a zodiacal light correction and a destriping method.
This second generation processing, which increased
the sensitivity by a factor up to five, lead to
the the IRAS Sky Survey Atlas (ISSA) published in 1991 and 1992.
The IRAS Sky Survey Atlas Explanatory Supplement \cite[]{wheelock93}
describes in detail the processing and analysis of this atlas.

Since its publication, the ISSA has been a tremendously useful data product,
used to study various aspects of Galactic (e.g. \cite{boulanger88})
and extra-galactic (e.g. \cite{miville-deschenes2002b})
diffuse emission. The ISSA plates
have become an essential data set for any multi-wavelength analysis of the
interstellar medium.
Unfortunately, even after the heroic processing done by the IRAS team,
the ISSA plates still suffer from defects (striping, calibration,
zero level, zodiacal light) that can limit significantly their use.
In the context of the numerous ongoing and future
infrared/submm/mm missions (Spitzer, Herschel, Planck, JWST, ASTRO-F...),
IRAS data could still be highly valuable,
even with their relatively coarse angular resolution ($\sim$4').
This was our main motivation
to reprocess the ISSA plates of all IRAS bands, in order to improve
their sensitivity and absolute calibration.

This new generation of IRAS maps,
a product named IRIS (for Improved Reprocessing of the IRAS Survey),
will be of particular interest for the Planck mission dedicated
to the study of the Cosmic Microwave Background (CMB). Planck will perform
an all-sky survey in the 350~$\mu$m-10~mm wavelength range with an angular
resolution in the high frequency bands comparable to IRAS.
One of the main anticipated challenges of this mission
 will be the
separation of all the components, including dust, that contribute
to the signal in this wavelength range (as it is for WMAP, \citep[]{bennett2003a}).
Several studies of dust emission at high Galactic latitudes
showed large variations of dust properties at all scales,
even in the diffuse interstellar medium
\cite[]{boulanger90,lagache98,bernard99,miville-deschenes2002,stepnik2003}.
To improve on the dust models available (e.g. \cite{finkbeiner99})
and bring them to an accuracy
level required for Planck, dust evolution should be understood
in a more general way, including the properties of the
smaller grain populations that give some informations on the
evolutionary stage of dust (coagulation, fragmentation) and
on the properties of the bigger grains that contribute to
the submm/mm emission.
Small grains have also been suggested \cite[]{draine98} to
be responsible for the anomalous microwave emission
(e.g. \cite{lagache2003b}).
In this context, well calibrated, arcminute resolution and
all-sky dust emission maps at
12, 25, 60 and 100~$\mu$m  would be of tremendous help to understand
and model dust emission in the Planck bands.
This is one of the main motivations of the present work.

The present paper describes in detail the procedure we
followed to reduce significantly the striping of the ISSA maps and to
rescale them to have an absolute calibration
coherent with both the DIRBE and IRAS Point Source Catalog photometry.
In \S~\ref{section_issa}
we describe in detail the ISSA product. Our reprocessing
of the ISSA plates, which include an automatic deglitching,
an improved destriper and an absolute calibration and zero level correction,
is described in \S~\ref{section_cleaning} and \S~\ref{section_calibration}.
The overall properties of the IRIS product are discussed
in \S~\ref{section_properties}.
The whole IRIS data set is available at {\bf http://www.cita.utoronto.ca/~mamd/IRIS}
and at {\bf http://www.ias.u-psud.fr/iris/}.

\section{The IRAS Sky Survey Atlas}

\label{section_issa}

\subsection{Processing of the ISSA plates}

During its 10 months operation period, IRAS made two surveys of 98\% of the
sky and a third one of 75\% of the sky. To confirm point source detection,
each survey, called an HCON for Hours CONfirmation,
consisted of two coverages of the sky separated by up to 36 hours.
The first two HCONs (HCON-1 and HCON-2) were done concurrently with
the second one behind the first one by a few weeks. The third survey (HCON-3)
began after the first two were completed. Due to
exhaustion of the liquid helium supply the third HCON could not be completed
and it thus covers only 75\% of the sky.

The ISSA is a set of 430 fields of $500\times500$ pixels of 1.5'.
Each field is a $12.5^\circ \times 12.5^\circ$ region centered every
$10^\circ$ in declination. All HCONs represent the sky surface brightness at
the 4 wavelengths from which an estimate of the zodiacal light was subtracted.
The HCONs were destripped, checked for zero level stability and visually
examined for artifacts and glitches. The processed HCONs were then co-added,
using sky coverage maps, to produce one final map (named HCON-0) per field
and per wavelength.

\subsection{Diffuse emission photometry}

Special care has been taken to have a consistent diffuse emission
calibration through the Atlas. But, as the IRAS mission was designed
to provide absolute photometry for point sources only,
the ISSA images give only relative photometry on spatial scales
larger than $\sim$5' and cannot be used
directly to determine the absolute surface brigthness of diffuse emission.
The uncertainty on the zero level is dominated by
uncertainties in the zodiacal light model at 12 and 25 $\mu$m,
and by detector drifts at 60 and 100 $\mu$m.

As it was designed to study the cosmic infrared background,
the DIRBE (Diffuse Infrared Background Experiment) experiment on board the
COBE (Cosmic Background Explorer) satellite has made absolute surface
brightness measurements of the sky at scales larger than 0.7$^\circ$.
Moreover the DIRBE data were corrected with a better zodiacal light model
\cite[]{kelsall98} than the one used for the ISSA.
Fortunately DIRBE and IRAS had very similar filters and therefore the DIRBE
data can be used to determine the absolute IRAS calibration at scales larger
than 0.7$^\circ$. Some efforts have been put in the comparison between DIRBE
data and individual HCON images. \cite{wheelock93} showed that
the amplitude of the 60 and 100 $\mu$m  intensity fluctuations
are overestimated in the ISSA maps with respect to DIRBE.
\cite{wheelock93} suggest a linear relation between the IRAS and DIRBE
surface brightness that also takes into account the difference in zero level:
\begin{equation}
I_{\lambda}^{DIRBE}(\alpha, \delta) = G_\lambda \times I_{\lambda}^{ISSA}(\alpha, \delta)
+ B_{\lambda}(\alpha,\delta).
\end{equation}
The gain correction factors ($G_\lambda$) given in Table~\ref{table_issa}
were originally obtained on spatial scales of the order of an IRAS scan
($\sim 8^\circ$).
We have performed a detailed comparison of the DIRBE and IRAS data
on numerous regions covering a broad range of brightness and
we conclude that these factors vary with angular scale and brightness.
This issue is discussed in detail in \S~\ref{section_gain}.
Regarding the zero point of the ISSA maps, \cite{schlegel98} showed that the
100 $\mu$m  offset $B_{100}(\alpha,\delta)$ varies significantly across the sky.
Our analysis show that this is the case at all wavelengths
(see \S~\ref{section_offset}).

\begin{table*}
\begin{center}
\caption{\label{table_issa} Compilation of IRIS related quantities}
\begin{tabular}{lcccc}\hline
 & \multicolumn{4}{c}{Wavelength ($\mu$m)}\\ \cline{2-5}
Quantity & 12 & 25 & 60 & 100\\\hline
1. IRAS resolution (arcmin) &  $0.75\times 4.5$ &  $0.75\times 4.6$ &
$1.5\times 4.7$ &  $3.0\times 5.0$\\
2. IRIS resolution (arcmin) & $3.8\pm0.2$ &
$3.8\pm0.2$ & $4.0\pm0.2$ & $4.3\pm0.2$ \\
3. ISSA noise level (MJy/sr) & $0.04\pm0.01$ & $0.05\pm0.02$ & $0.04\pm0.01$ & $0.07\pm0.03$ \\
4. IRIS noise level (MJy/sr) & $0.04\pm0.01$ & $0.05\pm0.02$ & $0.03\pm0.01$ & $0.06\pm0.02$ \\
5. DC/AC & 0.78 & 0.82 & 0.92 & 1.00\\
6. $G_\lambda$ & $1.06\pm0.02$ & $1.01\pm0.02$ & $0.87\pm0.05$ & $0.72\pm0.07$\\
7. DIRBE S(gain) (\%) & 5.1 & 15.1 & 10.4 & 13.5\\
8. DIRBE S(offset) (MJy/sr) & $6.0\times10^{-5}$ & $8.3\times10^{-5}$ &
0.027 & 0.027 \\\hline
\end{tabular}
\end{center}
Note. -- Row 1: Effective instrumental resolution of the IRAS
detectors \cite[]{wheelock93}. Row 2: Angular resolution of the ISSA and IRIS
plates (see \S~\ref{section_resolution}).
Row 3-4: The ISSA and IRIS noise level given here are representative
of the median instrumental noise of the whole plates.
The noise level varies from one plate to the other as a function of coverage
(see \S~\ref{section_noise}). Row 5-6: DC/AC and IRAS/DIRBE corrections given
by the IRAS team \cite[]{wheelock93}.
Row 7-8: DIRBE gain and offset uncertainties from \cite{hauser98}.
\end{table*}

\subsection{Point Source Photometry}

By staring at point sources, the IRAS team clearly showed
\cite[]{wheelock93} that the instantaneous (AC) and long-term (DC)
responsivity of the IRAS detectors were different. For a survey
mission like IRAS, this introduces a responsivity difference
between point-like object and diffuse emission. The ISSA plates
are DC calibrated which means that point source fluxes estimated
on a ISSA plate have to be corrected for the DC/AC responsivity
difference (see Table~\ref{table_issa}).
Even if the ISSA product was not optimized for point sources
\cite{wheelock93} showed that, when corrected for the appropriate
DC/AC factor, point source fluxes measured
on ISSA plates are photometrically consistent with the IRAS Point Source
Catalog to within 10\%.
We have verified this by comparing the DIRBE and ISSA (convolved by the
DIRBE beam) fluxes of several stars. We also found a general good
agreement between these two data sets.

\subsection{Post-processing of the ISSA plates}

Beside the responsivity variation and zero level problems,
the ISSA plates have also relatively strong stripes,
related to the scanning on the sky, that participate significantly
to the noise. The main goals of the present work were first to reduce the
amplitude of those stripes to lower the noise level and second to
correct the ISSA plates calibration to match both the DIRBE
and the Point Source Catalog photometry.

In the next sections we describe how we have addressed all of
these problems. First we discuss how we have deglitched
automatically the individual HCONs (\S~\ref{section_deglitching}).
Then we describe our destriping algorithm (\S~\ref{section_destriping}).
Finally we describe how we use the comparison of the IRAS and
DIRBE data to establish a calibration and a zero level correction that is
coherent both for point sources and diffuse emission
(\S~\ref{section_calibration}).

Through out the processing we have taken great care to work
on individual HCONs to improve the destriping of the maps and
to be able to estimate the noise level in the final averaged maps.
This specific point is discussed in \S~\ref{section_noise}.

\section{Cleaning the ISSA plates}

\label{section_cleaning}

\subsection{Deglitching}

\label{section_deglitching}

Before co-adding the individual HCONs, the IRAS team inspected them
visually
to identify artifacts like moving objects (e.g. asteroids) or residual
glitches. To allow for further validity checks of point sources seen
(or not) in the co-added maps, the IRAS team decided to provide the
individual HCONs that include those artifacts. As we are working directly
on the individual HCONs we had to redo the deglitching but we took
advantage of the fact that the co-added maps (HCON-0) have already been
deglitched.

First, using the method described in \S~\ref{section_point_source}
we identified point sources both in the individual HCONs and in the co-added
map. In a given map the identified pixels were then gathered together into
regions by consecutively labelling all the detecting regions
with a unique region index
\footnote{We use the label\_region function of IDL}.
Then we computed the central position
(taken as the position of the brightest pixel) and the maximum radius
of each region. For each region found in the individual HCON (1,2 or 3) we
derived the distance to all regions found in the co-added map.
Each HCON region with no counterpart in the co-added map
at distance lower than the sum of the two regions maximum radius
is considered as a glitch.
The corresponding pixels in the HCON are then set to the background
level at that position.

This automatic method worked very well to identify automatically residual glitches
and moving objects on most of the ISSA plates. It was not as performant in
very bright regions were the diffuse emission varies significantly
at small scales. Therefore we did not deglitch regions brighter that
200 MJy/sr at 100~$\mu$m. We also dealt manually with Saturn due to its
large extend in the affected HCONs.

\subsection{Destriping}

\label{section_destriping}
The ISSA plates have relatively strong stripes that are related to the
scanning on the sky. We describe in this part our destriping algorithm that
reduces significantly the amplitude of those stripes.
The destriping is done in Fourier space for each HCON. For typical HCONs,
the stripes have one or two directions but there exists more complicated
regions where there are several directions (up to 5 for example near the
Large Magellanic Cloud). In the Fourier space, such stripes give extra-power
in well-defined azimuthal directions that can be identified and corrected
(Fig. \ref{HCON_stripes}).

To be able to identify clearly the striping pattern in Fourier space, two
effects have to be dealt with: point-like sources and large scale gradients.
Point sources introduce contaminating power in Fourier space
in every direction and with a flat power spectrum. Their main effect is to
lower significantly the contrast of stripes in Fourier space, especially
at large wavenumbers $k$. On the contrary,
a large scale gradient across an image produces extra-power
in privileged directions in Fourier space (horizontal and vertical)
that mimics stripes.
To get rid of this effect it is quite common to apodize the image (see \cite{schlegel98}
for example) but this destroies the information on the edge of the image.

To get round these difficulties we used a wavelet decomposition
(``a trou'' algorithm) of every HCON and worked
only on an image that is the sum of the first five scales
(2, 4, 8, 16 and 32 pixels of 1.5'). This filtered map contains only small scale
structures, usually dominated by the stripes, and is thus free of any
large scale gradient (Fig. \ref{HCON_stripes}).
To increase the contrast of the striping pattern we removed point sources
at each scale of the wavelet decomposition prior to summing them;
we cliped all the wavelet coefficients higher than 7$\sigma$, where $\sigma$
is computed at each scale.
The original HCON was then decomposed into
three components: a large scale emission map (scales larger than 32 pixels),
small scale emission map (scales smaller than 32 pixels) and a point sources
map. The following destriping algorithm was only applied on the small scale
emission map.

Each small scale emission map was Fast Fourier Transformed (FFT) and
the averaged magnitude of the FFT was computed as a function of
angle $\theta$ in 360 bins of $1^\circ$ wide.
We identified the bins with averaged magnitude greater than N$\sigma$
and replaced them by the averaged azimuthal magnitude.
This is equivalent to replace the identified bins by the power spectrum
of the clean bins. This procedure was repeated twice
on artificially rotated FFT pattern (to detect stripes with direction falling between two bins).
During this process, we progressively decreased N from 7 to 5.
We then made the inverse transform of the cleaned FFT and added the result
to the large scale emission and point source maps.

This procedure can only be applied on fully defined HCONs.
For each plate, the missing data were iteratively replaced by the destriped
data of the companion HCONs. When large regions have not been observed by the
3 HCONs, we used the DIRBE data, corrected for the appropriate gain and
offset values.

Our procedure has been extensively tested on simulations.
We simulated typical interstellar diffuse regions using
fractional Brownian motion images
\cite[]{miville-deschenes2003b} with a similar power spectrum to
what is observed in the ISM (spectral index of -3 \cite[]{gautier92}).
We added to this map typical random noise together with stripes that were
simulated in Fourier Space (note that we cannot inject in our simulations
empirically derived stripes from real data since such maps, obtained
by wavelet filtering real data visually dominated by stripes, are also
contaminated by the instrumental noise).
The simulated map were then processed through the whole
destriping procedure.
An example of such a simulated map  for a typical high latitude region
at 12~$\rm \mu$m (where the amplitude of the stripes are of the same
order than the signal) is shown
on Fig. \ref{simu_destripe}, together with the result of the destriping algorithm.
We computed the power spectrum of the input noisy interstellar map and that
of the recovered map. In such regions, we modified the power spectrum at small
scales by only about 3$\%$. This demonstrates that we have supressed
the contribution of the stripes (that was four times higher than the signal
on the power spectrum at small scales in this case) without adding extra-noise. In
brighter regions, the contribution of the stripes becomes smaller compared
to the galactic emission, leading to a still better recoverage
of the simulated map. These simulations clearly show the robustness
and efficiency of our destriping process.

\begin{figure}
\includegraphics[width=\linewidth]{f1}
\caption{\label{HCON_stripes} Illustration of the destriping algorithm.
The image (plate number 83 at 60 $\rm \mu$m) is choosen such that it
contains point sources, diffuse emission and undefined regions.
Top-left: HCON; Top-right: wavelet filtered HCON; Middle-left:
FFT of the filtered HCON; Middle-right: modified FFT; Bottom-left: destriped
HCON; Bottom-right: ratio of the power spectrum of the HCON and the destriped
HCON.}
\end{figure}

\begin{figure*}
\includegraphics[width=\linewidth]{f2}
\caption{\label{simu_destripe} Simulated high latitude cirrus region with
noise and stripes. Top-left: cirrus (P(k)$\propto$ k$^{-3}$);
Top-middle: random noise; Top-right: stripes;
Bottom-left: total simulated map; Bottom-middle: destriped map;
Bottom-right: power spectrum of the cirrus (continuous line),
cirrus+noise (dashed line), cirrus+noise+stripes (diamonds),
and the recovered map after the destriping process
(dashed-dotted line), in arbitrary units. The dashed and
dashed-dotted lines are superimposed (the difference is at the order
of 3$\%$ at very small scales).
}
\end{figure*}

\section{Calibrating the ISSA plates}

\label{section_calibration}

\subsection{Infrared photo-detectors}

\label{sec_isocam}

\cite{wheelock93} showed that the responsivity of all IRAS detectors are
affected by memory effects that introduce a calibration difference between
diffuse emission and point sources.
Since IRAS, and especially with the ISO mission, several
studies have been done to understand the response of infrared photo
conductors like the IRAS 60 and 100 $\mu$m  Ge:Ga detectors.
Using solid state and semiconductor physics,
\cite{vinokurov91} and \cite{fouks95} have studied the response of
such detectors. They showed that the instantaneous response depends
on the illumination and on the history of the detector. A simplify
version of their model was successfully applied to ISOCAM observations
\cite[]{coulais2000}. This non-linear model is rather complex and it is
not the purpose of the present paper to describe it in detail. But to
feel how the response of infrared photo detectors behaves, lets
consider the simple case of a detector stabilized at flux
$J_0$ that is suddenly illuminated at flux $J_1$ at time $t=0$.
In this case, the response $J(t)$ of the detector as a function of
time is described by:
\begin{equation}
\label{fouks}
J(t) = \beta J_1 + \frac{(1-\beta)J_1
  J_0}{J_0 + (J_1 - J_0) \exp (-t  J_1 / \lambda)}.
\end{equation}
The $\beta$ and $\lambda$ parameters depends on the physical
properties of the detector.
An example of this model is shown in Fig.~\ref{exemple_fouks}
where we illustrate what would be the response of a detector
when the flux is double ($J_1 = 2 \times J_0$), for three values
of the initial flux $J_0$.
We see that the response of the detector is very sensitive
to the flux value; for lower flux value, the detector
takes more time to stabilize. Therefore, for a given
integration time, an intensity fluctuation on a low
surface brigthness region will be systematically
underestimated in comparison to a brighter one.

This has an important consequence on survey
observations like the IRAS mission that scanned the sky
with a fixed integration time.
It is likely that, at low flux value,
the integration time was shorter than the stabilization time of the
detector. Therefore the amplitude of the fluctuations on the sky
are systematically underestimated in faint regions.
This type of memory effect should leave another signature
on maps with a fixed integration time.
As the satellite scans the sky it observes structures with various
angular scales. These structures can be seen as flux steps like
in Fig.~\ref{exemple_fouks}. Then, when the satellite goes through
a small scale structure, it is likely that the observed flux will never
reach the stabilization level. On the other hand, for very large scale
structures, the detector has enough time to stabilize.
Therefore, the amplitude of the intensity fluctuations are
underestimated at low flux but also at small scales.

\begin{figure}
\includegraphics[width=\linewidth]{f3}
\caption{\label{exemple_fouks} Illustration of the response of an
 infrared photo detector based on Eq.~\ref{fouks} \cite[]{fouks95}.
The response to upward and downward flux steps are shown for three
values of the flux $J_1$ = 2, 6 and 10.
To illustrate the behavior of the detector when the flux value is double,
the lower flux value is $J_1/2$ for each case.
The response of the detector is very sensitive to the flux value;
for lower flux value, the detector takes more time to stabilize.}
\end{figure}

\subsection{Responsivity of the 12 and 25 $\mu$m  detectors}

Similar effects were indeed observed by the IRAS team.
By staring at several stars of different brightness,
\cite{wheelock93} showed that the responsivity $R$
of the 12 and 25 micron detectors depends on time and therefore on angular
scale, as the satellite is scanning the sky at a fixed rate
(3.85 arcmin/sec). The responsivity was observed to be constant
for angular scales larger than 2$^\circ$ but it decreased
at smaller scales, in accordance with the model described earlier.
On the other hand the IRAS team reports no variations of
the responsivity as a function of brightness for these detectors.
In Table~\ref{table_gain} we give the responsivity
variation with angular scale from \cite{wheelock93} for the 12 and
25~$\mu$m  detectors but one must be aware that this variation of the
responsivity with scale was not applied
to the ISSA plates. Instead a constant responsivity factor was used
to match the responsivity at large scale (i.e. the ISSA plates are
DC calibrated) which means that the brightness fluctuations at scales
smaller than $\sim2^\circ$ are systematically underestimated at 12
and 25~$\mu$m.

\begin{table*}
\begin{center}
\caption{\label{table_gain} Responsivity factors}
\begin{tabular}{ccc|ccccccc}\hline
$l$ & 12 $\mu$m  & 25 $\mu$m  & $l$ & & 60 $\mu$m  & & & 100 $\mu$m \\
(degree) & $R_0$ & $R_0$ & (degree) &
$R_0$ & $A$ & $B$ &
$R_0$ & $A$ & $B$ \\\hline
0.067 & 0.78 & 0.82 & 0.067 & 0.92 & 0.0 & 0.0 & 1.0 & 0.0 & 0.0\\
0.1 & 0.90 & 0.90 & 1.25 & 1.00 & 0.08 & -5.0e-5 & 0.96 & 0.008 & -4.8e-5\\
0.2 & 0.92 & 0.93 & 2.5 & 1.01 & 0.01 & -4.0e-5 & 0.99 & 0.011 & -6.5e-5\\
0.5 & 0.98 & 0.97 & 5.0 & 1.05 & 0.014 & -6.0e-5 & 1.08 & 0.012 & -8.0e-5\\
1.0 & 1.00 & 0.98 & 10.0 & 1.13 & 0.014 & -9.0e-5 & 1.25 & 0.08 & -5.9e-5\\
1.5 & 1.00 & 1.00 \\
2.0 & 1.00 & 1.00 \\\hline
\end{tabular}
\end{center}
The responsivity $R$ at a given wavelength, scale and brightness
is given by Eq.~\ref{eq_gain}. The responsivity at 12 and 25~$\mu$m  does not
depend on brightness ($A=0$, $B=0$). The value of the responsivity at
the smallest scale (0.067 degree) is the DC/AC factor
(see Table~\ref{table_issa}) needed to recover the correct point source
calibration.
\end{table*}

\subsection{Responsivity of the 60 and 100~$\mu$m  detectors}

\label{section_gain}

At 60 and 100~$\mu$m  the situation is complicated by the fact that the
responsivity depends both on time (i.e. angular scale) and brightness.
\cite{wheelock93} did not give any prescription to address this
problem. To evaluate the variation of the responsivity with scale
and brightness of the 60 and 100~$\mu$m  detectors
we compared the IRAS and DIRBE data using a wavelet analysis.

To study the variations of the 60 and 100~$\mu$m  responsivity
we have looked at variations of $\Delta IRAS/\Delta DIRBE$ as
a function of scale and brightness.
For a given diffuse structure on the sky the quantity
$\Delta IRAS/\Delta DIRBE$
represents the ratio of the brightness fluctuation (above the background) of
that structure seen in the IRAS and DIRBE data. If we take the DIRBE
calibration as an absolute reference, the quantity $\Delta IRAS/\Delta DIRBE$
is equal to the IRAS responsivity $R$ to a brightness fluctuation.
To compute  $\Delta IRAS/\Delta DIRBE$ as a function of scale and brightness
we first put the two dataset on a common
grid and at the same angular resolution.
For each ISSA plate we have constructed a larger map ($600\times600$ pixels)
by mosaicking neighbouring plates. This step is necessary in order to
avoid edge effects in further convolutions. Next this bigger ISSA plate
is convolved by the DIRBE beam.
The DIRBE data are then projected on the ISSA grid.
Finally both maps are convolved by a Gaussian beam of FHWM 40'
to smooth out the DIRBE pixelisation \cite[]{schlegel98}
and the extra 50 pixels wide edges are removed.
At that point the angular resolution and size of both maps are
of 1 degree and $500\times500$ respectively.

To compute the variation of $\Delta IRAS/\Delta DIRBE$ with scale and
brightness we used a wavelet transform (the ``a trou'' algorithm -
\cite{starck98})
that allows us to study the brightness variations as a function of scale.
An exemple of such a decomposition is shown in Fig.~\ref{simul_wavelet}
on a fractional Brownian motion (fBm) image
\cite[]{miville-deschenes2003b} with a similar power spectrum to
what is observed in the ISM (spectral index of -3) and convolved the
same way the IRAS and DIRBE data were.
On the top row of Fig.~\ref{simul_wavelet} we show two fBm images,
$m_1$ and $m_2$,
where $m_2$ was constructed by simply applying a constant multiplicative
factor to $m_1$ ($m_2 = Q\times m_1$).
On the four bottom rows we show the wavelet coefficients at four differents
scales (1.25, 2.5, 5 and 10 degrees). The important result
here is that the slope of the linear regression of the wavelet coefficients
gives exactly the multiplicative factor $Q$ at each scale.

An exemple of the same wavelet decomposition
for a typical 60~$\mu$m  field is shown in Fig.~\ref{exemple_wavelet}.
One would notice that the wavelet coefficients of the IRAS and DIRBE are
very well fitted by a linear fit with relatively small dispersion.
One noteworthy result here is the increase with scale of the slope
($\Delta IRAS/\Delta DIRBE$) of the linear regression between
DIRBE and IRAS data. The trend seen
in Fig.~\ref{exemple_wavelet} is totally
representative of what is generally observed.

\begin{figure}
\begin{center}
\includegraphics[width=\linewidth]{f4}
\caption{\label{simul_wavelet}
Illustration of the use of the wavelet decomposition
to compute a gain difference between two maps at different scales.
Here the $m_1$ and $m_2$ are identical fBm images
(shown in the top row) with a constant multiplicative factor
between the two ($m_2 = 1.389 \times m_1$). The four
bottom rows shows the wavelet decomposition of $m_1$ and $m_2$.
The right column shows the correlation between $m_2$ and $m_1$
for the whole map and at each scale. The slope $a$
of the linear regression is given in each panel.}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=\linewidth]{f5}
\caption{\label{exemple_wavelet}
Example of a wavelet decomposition of a typical 60~$\mu$m  image.
See Fig.~\ref{simul_wavelet} for details.}
\end{center}
\end{figure}

We have perform this analysis at 60 and 100~$\mu$m, on all the ISSA plates
with no undefined values, to also study the variation
of $R=\Delta IRAS/\Delta DIRBE$
with brightness $<I_\lambda>${\footnote{Note here that, as stated at the
end of this section,  $<I_\lambda>$ is the median value
of the DIRBE data to limit the effect of variations of
the IRAS zero level}}.
The results of this analysis are compiled in
Figures~\ref{reponse_60} and \ref{reponse_100} where we show the variation
of $R$ with brightness at the four scales studied.
>From these two figures we found that the IRAS responsivity $R$ increases
with brightness for the two bands. The increase of $R$
with scale described previously is also seen in these two figures.
In addition the values of $R$ are systematically above 1.0
at large scale which confirms that IRAS brightness fluctuations are
overestimated at large scales in the ISSA plates. The values obtained here at
scales of 10$^\circ$ and for brightness of $\sim 3$ and $\sim 10$ MJy/sr at
60 and 100~$\mu$m  are compatible with the IRAS-DIRBE correction factors given
by \cite{wheelock93} (see Table~\ref{table_issa}).

The increase of $R$ with scale and brightness indicates
that the IRAS responsivity is generally lower for small scale
and faint brightness fluctuations than for large scale and
large brightness fluctuations.
This behavior is in complete accordance with what
is expected for typical photo-conductors (see \S~\ref{sec_isocam}).

\begin{figure}
\begin{center}
\includegraphics[width=\linewidth]{f6}
\caption{\label{reponse_60}
Responsivity of the 60~$\mu$m  IRAS data compared to DIRBE as a
function of the 60~$\mu$m  DIRBE brightness and for four different scales.
The dotted lines are the slope of the linear regression of IRAS vs DIRBE
and DIRBE vs IRAS. The solid line is the average of the two dotted lines.
The dashed line is the fit to the average slope using Eq.~\ref{eq_gain}.}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=\linewidth]{f7}
\caption{\label{reponse_100}
Responsivity of the 100~$\mu$m  IRAS data compared to DIRBE as a function of
the 100~$\mu$m  DIRBE brightness and for four different scales.
See Fig.~\ref{reponse_60} for details.}
\end{center}
\end{figure}

The dotted lines in Figures~\ref{reponse_60} and \ref{reponse_100}
represent
the slope of the linear regression of IRAS vs DIRBE and DIRBE vs IRAS,
and the solid line is the average of the two. Computing both linear
regressions allows us to conclude
that the trend observed here is not due to noise. The effect of
detector noise is clearly seen
at small scale and at low brightness where the dispersion of the
slope values is increasing.
There is also an increase of the dispersion at large scales
(very clear at 60~$\mu$m), due to the large scale drift
of the detector responsivity or to a bad zodiacal light correction.
These two effects produce an additive effect with spatial variations
at scales larger than a few degrees, affecting predominantly
the slope measured at larger scales and at low brightness.

The curves in figures~\ref{reponse_60} and \ref{reponse_100} can be
resonably well fitted by the following fonctional:
\begin{equation}
\label{eq_gain}
R = R_0 + A<I_\lambda>+ B<I_\lambda>^2.
\end{equation}
The values of $R_0$, $A$ and $B$, which all depend on
$\lambda$ and scale $l$, are given in Table~\ref{table_gain}.
The brightness $<I_\lambda>$ is the median value
of the DIRBE data, to limit the effect of variations of
the IRAS zero level.

\begin{figure}
\includegraphics[width=\linewidth]{f8}
\caption{\label{fig_gain}
Responsivity correction factor ($G=1/R$) for the four bands as a function
of angular scale. For the 60 and 100~$\mu$m  bands the gain factor is given for
three values of mean brightness. The solid, dotted and dashed lines are
respectively for 1, 10 and 50
MJy/sr at 100~$\mu$m  and 0.3, 3 and 15 MJy/sr at 60~$\mu$m. The shaded grey area
represents the angular scales on which DIRBE data are used to scale the IRAS
data.}
\end{figure}

\subsection{Reponsivity correction}

In the previous sections we showed that the IRAS responsivity to diffuse
emission varies with scale and, at 60 and 100~$\mu$m,
also with brightness. At these wavelengths we were able
to establish an analytical form of the responsivity variations
(Eq.~\ref{eq_gain}) by comparing the IRAS and DIRBE data.
This expression is also valid for the 12 and 25~$\mu$m  bands; in this case
it reduces to $R=R_0$ as the responsivity does not depend on the brightness
($A=0$ and $B=0$).

The responsivity correction to apply to the ISSA plates is the inverse of
the expression given in Eq.~\ref{eq_gain} ($G=1/R$).
In Fig.~\ref{fig_gain} we show the responsivity correction factor as function
of scale for the four bands. For the 60 and 100~$\mu$m  bands we
present three curves to show the variation of the responsivity correction
with brightness.

\begin{figure}
\includegraphics[width=\linewidth]{f9}
\caption{\label{fig_avant_apres_12} Plate number 81 at 12~$\mu$m.
Comparison of the ISSA (top-left) and IRIS (top-right) maps.
The difference between the two (ISSA-IRIS) is shown in the bottom-left
panel. The ratio of the power spectra of the IRIS and ISSA maps
is shown in the bottom-right panel. }
\end{figure}

\begin{figure}
\includegraphics[width=\linewidth]{f10}
\caption{\label{fig_avant_apres_25} Plate number 81 at 25~$\mu$m.
See Fig.~\ref{fig_avant_apres_12}.}
\end{figure}

\begin{figure}
\includegraphics[width=\linewidth]{f11}
\caption{\label{fig_avant_apres_60} Plate number 81 at 60~$\mu$m.
See Fig.~\ref{fig_avant_apres_12}.}
\end{figure}

\begin{figure}
\includegraphics[width=\linewidth]{f12}
\caption{\label{fig_avant_apres_100} Plate number 81 at 100~$\mu$m.
See Fig.~\ref{fig_avant_apres_12}.}
\end{figure}

The implementation of such a correction is made difficult by the
fact that it depends on brightness (at 60 and 100~$\mu$m).
We need to apply a correction that depend on scale but
also on position to take into account brightness variations across
the map. To achieve this we use a local approch based on a
wavelet decomposition of each ISSA HCON.

To avoid discontinuity problems between adjacent plates
each HCON is put in a $600\times600$ map and the undefined
regions are filled using other HCONs or, when IRAS data are unavailable,
by DIRBE (properly scaled to take into account the gain difference
between the two data sets).
For each HCON at each wavelength, we first separated point sources from diffuse emission
(see \S~\ref{section_point_source}).
To correct the diffuse emission map we decomposed it
(using the ``a trou'' algorithm) for the first 6 scales
(corresponding to 3', 6', 12', 24', 48', 1.6$^\circ$, 3.2$^\circ$).
Then we computed the proper gain correction factor at each scale
and for each pixel of the map using Eq.~\ref{eq_gain}.
To compute this correction at 12 and 25~$\mu$m  bands we simply use the
responsivity values given in Table~\ref{table_gain} and interpolate
at the 6 corresponding scales (from 3' to 3.2$^\circ$). At the 60
and 100~$\mu$m  we do the same but we also use the DIRBE brightness
to compute the brightness dependance part of the
responsivity correction.

The wavelet coefficients of the diffuse emission map were then
recombined to form the responsivity corrected diffuse emission map. Finally the
point sources map, properly calibrated by applying the corresponding
DC/AC factor (see Table~\ref{table_issa})
was added to the corrected diffuse emission map.
The responsivity correction applied here does not correct the emission
at scales larger than 3.2$^\circ$ degrees. We take care of this in the next
and step of the processing.

\subsection{Zero level correction}

\label{section_offset}

As it was mentioned earlier the zero level of the IRAS data
is not well determined, due to detector drifts and/or residual
zodiacal emission. To correct this large scale
responsivity and the spatially varying zero level
of the ISSA maps we again used the DIRBE data that were better
calibrated and that used a better zodiacal emission model. Here we make the
assumption that the zero level does not vary on scales
smaller than 1$^\circ$ which is reasonable as detector drifts
and zodiacal emission are not expected to vary on such scales.

As for the responsivity correction we computed the offset map
for every HCON,
enlarged to $600\times600$ to make sure that we keep
the continuity between adjacent ISSA plates. Empty pixels were
filled with the average map (HCON0), previously corrected
for the responsivity variation, or DIRBE data when necessary.
The HCON map was then convolved by the DIRBE beam and by a
Gaussian beam (FWHM=40') to smooth out the DIRBE pixelisation.
The DIRBE data were projected on this enlarged HCON map and convolved
by the same Gaussian beam. At that point both data sets are on the same
grid and at a $1^\circ$ resolution\footnote{It is worth mentioning that
point sources were removed
in the IRAS and DIRBE data to compute the offset.
Even after the gain correction, which reconciliate the calibration
of point sources and diffuse emission, we had to remove point sources
for the offset computation as bright sources at 12 and 25~$\mu$m
have relatively strong tails that increase significantly their
flux when convolved by the DIRBE beam.}.
We then computed the difference
between the two maps (DIRBE-IRAS). This difference map was added
to the HCON. When all the 3 HCONs were corrected we computed the
average map (HCON-0) using the appropriate coverage maps.
This is the final step of the processing.

\begin{figure}
\includegraphics[width=\linewidth]{f13}
\caption{\label{fig_noise_iris} {\bf Top:}
Typical 100~$\mu$m  IRIS image (left)
together with its noise map (right). These two maps
are in MJy/sr. {\bf Bottom:} Coverage map (left)
showing the number of data points averaged at each position ($N_{tot}(x,y)$).
The power spectra of the 100~$\mu$m  map and of its noise map
are shown in the right panel.}
\end{figure}

\section{Properties of the IRIS plates}

\label{section_properties}

The processing of the 4893 HCON plates was done using the McKenzie cluster
of the Canadian Institute for Theoretical Astrophysics. This Beowulf
cluster is composed of 512 2.4 GHz Xeon processors with a total of 256 GB of
RAM. We effectively used only 40 CPUs of the cluster at the same time
and the total computation time for the whole processing
(deglitching, destriping, responsivity and offset correction) was
$\sim$20 hours.\\

Figures~\ref{fig_avant_apres_12} to \ref{fig_avant_apres_100}.
present the ISSA and IRIS plate number 81
at the four wavelengths. Are also shown the difference between
the ISSA and IRIS maps and the ratio of their power spectra.
These figures show that the destriping described in \S~\ref{section_destriping}
removed very efficiently the stripes at all wavelengths.
The second more noticeable improvement is the modification of
large scale structures in each maps, due to the responsivity and zero level
corrections. These two corrections removed very well residual
zodiacal light and detector drifts and improved significantly the
calibration of the data. The correction of the large scale structures
of the maps (that is due both to responsivity and zero level corrections)
is clearly seen in the ratio of the power spectra.

One interesting property seen on Figures~\ref{fig_avant_apres_12}
and \ref{fig_avant_apres_25} is that, even after
the destriping, the power spectra ratio of the 12 and 25~$\mu$m  images
is $\sim 1$ on scales between 5' and 1$^\circ$. This is due to the
responsivity correction applied (see Fig.~\ref{fig_gain}) that is higher
than 1.0 at those scales. The noise reduction resulting in improved signal-to-noise
ratios obtained from the
destriping is almost counterbalanced by the multiplication of all the
small scale fluctuations (including noise)
by a factor greater than 1. Nevertheless the noise properties
of the IRIS plates are much more easy to handle as they are now
homogeneous.
On the other hand, at 60 and 100~$\mu$m  the responsivity correction
is not as important and there is a noise reduction that
is about 15-20$\%$ at scales 5-15'. \\

Finally, notice that the areas of the sky not covered by the
IRAS survey are left empty in the IRIS product.

\subsection{Noise}

\label{section_noise}

Following the method described by \cite{miville-deschenes2002b}
one can estimate the power spectrum of the noise of each IRIS map.
To do so we take advantage of the fact that each final IRIS map is
composed of a combination of up to three HCONs. Here we argue that
the difference between two HCONs is dominated by the instrumental
noise and that the
power spectrum of such a difference map is equal to the power spectrum
of the noise, multiplied by a scaling factor that depends on the coverage
maps.

If we make the assumption that the noise level $B$ of the IRAS detectors
is stationary, and if we neglect the photon noise (i.e. the noise level
is dominated by the readout noise),
the noise level at position $(x,y)$ of the $i^{th}$ HCON map is
\begin{equation}
\sigma_{i}(x,y) = \frac{B}{\sqrt{N_i(x,y)}}
\end{equation}
where $N_i(x,y)$ is the coverage map of the $i^{th}$ HCON map.
An example of a typical coverage map is shown on Fig.~\ref{fig_noise_iris}.

The noise level of the co-added map (HCON-0) is
\begin{equation}
\sigma_{0}(x,y) = \frac{B}{\sqrt{N_{tot}(x,y)}}
\end{equation}
where $N_{tot}(x,y)=N_1(x,y)+N_2(x,y)+N_3(x,y)$.
Similarly the noise level of the difference between two HCON maps ($i$ and $j$) is
\begin{eqnarray}
\sigma_{i-j}(x,y) & = & \sqrt{\sigma_i^2 + \sigma_j^2}\nonumber\\
& = & B\sqrt{\frac{1}{N_i(x,y)} + \frac{1}{N_j(x,y)}}.
\end{eqnarray}
Combining the last two equations, the noise level
of the co-added map becomes:
\begin{equation}
\label{eq_noise_weight}
\sigma_0(x,y) = \sigma_{i-j}
\sqrt{\frac{N_i(x,y) N_j(x,y)}{N_{tot}(x,y)(N_i(x,y)+N_j(x,y))}}
\end{equation}

To estimate the power spectrum of the noise of a given IRIS plate
we first compute the difference map between two HCONs. The difference map
is then normalized following Eq.~\ref{eq_noise_weight} to take into
account the spatial coverage of every HCON. An example of such
a normalized difference map is shown in Fig.~\ref{fig_noise_iris}
together with its power spectrum and the power spectrum of the
corresponding IRIS plate. At small scale (high $k$) these two power
spectra meet perfectly which validates our processing.

It is important to point out that the difference map used here to compute
the power spectrum of the noise is by no mean a noise level map.
It does not provide a way to estimate the noise level of every pixel
in the map but it is only used to estimate the global properties
of the noise (i.e. power spectrum, average level).

The average noise level of an IRIS map can be estimated
by taking the standard deviation of the difference map.
Typical noise level values are given in Table~\ref{table_issa}
for the four bands. Within 10\%  the IRIS noise level
is the same as the ISSA noise level.
This is due to the fact that the power spectrum of the noise
is not flat (its slope varies from -1.5 to 0). Therefore
the standard deviation of the difference map may be dominated
by large scale structures in the noise.
In such case, integral of the ISSA and IRIS noise power spectra
on selected scales allows a better comparison.
For large scales (1-10$\rm ^o$), the noise level in the IRIS plates
is about 30$\%$ smaller than that of the ISSA plates, for the four
wavelengths. At smaller scales, as explained in \S \ref{section_properties},
we gain in sensitivity only at 60 and 100 $\mu$m.
The gain is about 15-20$\%$ for scales 5-15'.

\subsection{Effective angular resolution}

\label{section_resolution}

Due to the geometry of the IRAS detectors, the IRAS data have a higher
spatial resolution in the in-scan direction than in the cross-scan
(see Table~\ref{table_issa}).
\cite{wheelock93} have computed the PSF on few (4 to 5) point sources
in each band. They showed that the PSF is non-circular due to
difference in the in-scan and cross-scan resolution. They conclude that
the angular resolution of the ISSA plates is between 4 and 5 arcmin
in each band.

Following \cite{miville-deschenes2002b} we used the power spectrum of ISSA
plates to estimate the effective Point Spread Function (PSF) of the ISSA.
If we make the assumption that the effective PSF is described by a Gaussian,
the power spectrum of an image dominated by interstellar
fluctuations can be expressed by the following equation:
\begin{equation}
P(k) = \exp\left(\frac{-k^2}{2\sigma_k^2}\right)\times Ak^\beta
\end{equation}
where $Ak^\beta$ describes the cirrus emission power
spectrum \cite[]{gautier92}. We have done such a fitting for several
IRIS plates at the 4 wavelengths. We have selected plates with relatively
bright interstellar emission (not to be affected by noise) from which we have
removed the bright point sources. The effective resolution of the four
IRIS bands are given in Table~\ref{table_issa}.
We have checked that these values are compatible with Gaussian fitting
on point sources.

\begin{figure*}
\includegraphics[width=\linewidth]{f14}
\caption{\label{fig_compare_image} Comparison of a ISSA, IRIS and
Schlegel et al. $250\times250$ sub-image at 100~$\mu$m. All the maps
are in MJy/sr. The IRIS
map combined the higher angular resolution of the ISSA map
and the destriping and zero level correction
of the Schlegel et al. map. In addition the IRIS map
was corrected for the variation of the IRAS responsivity with
scale and brightness and it also includes
properly calibrated point sources.}
\end{figure*}

\begin{figure}
\includegraphics[width=\linewidth]{f15}
\caption{\label{fig_compare_pk} Comparison of the power
spectrum of a typical 100~$\mu$m  image with IRIS and Schlegel et al.
{\bf Left:} Power spectra of the IRIS (point sources subtracted) and
Schlegel et al. plates. {\bf Right:} Ratio of the IRIS
and Schlegel et al power spectra. The two plates have a very similar
power spectrum except at high-$k$ due to the higher angular
resolution of the IRIS plate.}
\end{figure}

\subsection{Calibration uncertainties}

At 60 and 100~$\mu$m, the responsivity correction we applied at scales smaller
than 1.25$^\circ$ depends on an interpolation between the DC/AC factor
(responsivity at 5' scale) and the responsivity at scale of 1.25$^\circ$
(deduced from the comparison of IRAS and DIRBE with scale and brightness -
see \S~\ref{section_gain}).
The largest responsivity difference between these two scales is for bright
regions where it reaches $\sim$20\% (see Fig.~\ref{fig_gain}).
We estimate that the typical uncertainty on the responsivity
at scales smaller than 1.25$^\circ$ is $\sim$5\%, for the four bands.

At scales larger than 1.25$^\circ$ the IRAS data are forced to match
the DIRBE data by applying an offset map (see \S~\ref{section_offset}).
The application of such an offset map takes care of responsivity
variations at scales larger than 1.25$^\circ$ but it also sets the
zero level correctly.
The uncertainty on the responsivity at large scales is thus limited
by the DIRBE gain uncertainties which varies from 5.1 to 15.1\%
(see Table~\ref{table_issa}). Considering the relatively small
uncertainty of the responsivity at sub-degree scales we estimate
that the overall uncertainty on the IRIS calibration is dominated
by the uncertainty on the DIRBE data (including the uncertainty
on the zodiacal model).\\

In the comparison of the IRAS and DIRBE data, an additional uncertainty
comes from the slight differences of the system spectral responses. To take into account
these differences, the DIRBE data should have been multiplied by the ratio of the
IRAS to DIRBE color correction prior to any comparison with the IRAS data
(see \S~\ref{section_color_correction}). This ratio
depends on the details of the wavelength response of the system
but also on the
shape of the intrinsic energy distribution that is unkown for each sky direction (especially
at short wavelengths).
No correction was therefore applied to the DIRBE data.
This induces an additional uncertainty  at 100, 60, 25 and 12 microns
that is less than typically 6, 10, 3 and 10$\%$ for the diffuse medium
respectively.

\subsection{Comparison with Schlegel et al.}

A first attempt to produce well calibrated 100~$\mu$m  IRAS maps was done by
\cite{schlegel98}. These authors improved the destriping and
zero level of the ISSA plates in a similar fashion as we did.
One of the great improvement of the IRIS 100 $\rm \mu$m
data compared to \cite{schlegel98} is that we take into account the
variation of the responsivity with brightness at scales smaller
than 1$^\circ$ (while they apply a constant factor of 0.87).
In addition the product given by \cite{schlegel98} does not
include point sources.

In Fig.~\ref{fig_compare_image} we present a comparison of a 100~$\mu$m
$250\times250$ pixels sub-image of the same region in
ISSA, IRIS and \cite{schlegel98}. One striking feature of this figure
is the striping that is completely removed in the IRIS and \cite{schlegel98}
images. One
feature of the IRIS product is also the fact that it includes point sources.
One would also note the difference in angular resolution
between the IRIS and \cite{schlegel98} data. Contrary to \cite{schlegel98}
we have taken great care to keep the full ISSA resolution.
The difference in angular resolution between IRIS and \cite{schlegel98}
is well seen in Fig.~\ref{fig_compare_pk} where we compare the power
spectrum of a typical 100~$\mu$m  map\footnote{Point sources have been
subtracted from the IRIS map prior to compute the power spectrum.}.
There is a very good agreement between
these two data sets at scales larger than $\sim30'$ but there is
a significant difference at smaller scales due to the difference in
the responsivity correction and also to the lower resolution of the
\cite{schlegel98} data (6.1').

\section{Conclusion}
We have built a new generation of IRAS maps that are
rescaled to an absolute calibration
coherent with both the DIRBE and the IRAS Point Source Catalog
photometry.
These maps are also much less contaminated by stripes
than the previous IRAS images.
This new generation of IRAS maps is named IRIS
for Improved Reprocessing of the IRAS Survey.
The IRIS data are available at {\bf http://www.cita.utoronto.ca/~mamd/IRIS} and
{\bf http://www.ias.u-psud.fr/iris}. They can also be obtained from {\bf http://www.ipac.caltech.edu}
and through the Centre de Donn\'ees astronomiques
de Strasbourg (CDS - {\bf http://www.cdsweb.u-strasbg.fr}) via
{\it Aladin}. The data products are detailed in Appendix~\ref{data_products}.\\

Compared to the previous products (namely the ISSA and \cite{schlegel98}),
we made a major improvement of the calibration
and zero level at all wavelengths
(but especially at 12 and 25~$\mu$m) by comparing with DIRBE
and remove significantly the stripes using an
efficient iterative process
that involve a wavelet decomposition of the map.
Considering the relatively small
uncertainty of the IRAS responsivity at sub-degree scales we estimate
that the overall uncertainty on the IRIS calibration is dominated
by the uncertainty on the DIRBE data (including the uncertainty
on the zodiacal model). One other great interest of the IRIS maps is that
they contain all the IRAS small scale information (including point-like
sources) properly calibrated.
With IRIS, we have reached the limit of the post-processing of the ISSA plates.
Improvements over the IRIS product will be only possible
by working directly on the raw IRAS data.\\

The IRIS data will be of great use for the whole community.
In the context of the numerous ongoing and future
infrared/submm/mm missions (Spitzer, Herschel, Planck, JWST, ASTRO-F...),
they will be very helpful to prepare and analyse the observations.
In particular, with an angular resolution comparable to the
high frequency bands of Planck, these data will be very complementary,
providing unique dust templates. These data can also be used by themselves
to conduct still original science.
As an example, in a forthcoming paper, we will present a study of the properties
of the cirrus dust emission.

\section*{Acknowledgments}
We warmly thanks S. Wheelock, N. Gautier, F. Boulanger
and J.-L. Puget for the help and support they give to this work.
Thanks to all the IRAS team for providing us with the great legacy
ISSA product. The processing of the IRIS plates has been done on the
Beowulf cluster of the Canadian Institute for Theoretical Astrophysics.

redpajama_set_name: RedPajamaArXiv


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Documented training on hazard analysis methodologies from a recognized training organization is required. Experience with combustible dust or dust hazard analysis is highly desirable. 40 hour HAZWOPER training is desirable.
A high degree of proficiency with common computer programs, such as Word, PowerPoint, and Excel is required along with excellent interpersonal and communication skills. The ability to solve complex technical problems and provide expert technical support is a must.
Demonstrated ability to successfully engage with multiple levels of the organization and the proven ability to lead cross functional teams. Demonstrated leadership and technical capabilities. Successful track record at self-directed task accomplishments.
A Professional Engineer license is highly desirable.
This position requires basic physical requirements such as standing, walking (indoors and outdoors), and stairway access.


text:
Q: Documentation Bug? FB Graph API explorer cannot return /me/address I am playing FB graph API explorer which is a fantastic tool to test graph API. But I met a weird case.
First of all, I have a access token with all permissions to access myself account.
Here is my query:
me?fields=id,name,address

But I only got:
{
  "id": "alongnumber",
  "name": "stringname"
}

Where is "address" returned?
Thanks
Derek
@Tobi suggests it might be a documentation bug. Can anyone confirm it?

A: There is no such field as address. Have a look at

*

*https://developers.facebook.com/docs/graph-api/reference/user
to see which fields are currently available. To get the current location, you can use me?fields=id,location{id}, and then request the location.id object in a second request to get the location details.

A: There is no field like Address though there is current_address & current_location but they also don't seem to work with basic permissions.
Check this for all the field names which you can get from the API. https://developers.facebook.com/docs/reference/fql/user#columns

redpajama_set_name: RedPajamaStackExchange


text:
Home » News and events » Events » What Is the Future of Individual Tax Residence Under the Proposed Rules?
What Is the Future of Individual Tax Residence Under the Proposed Rules?
Crawford School of Public Policy | Tax and Transfer Policy Institute
4.00pm–5.00pm
Molonglo Theatre , Level 2, JG Crawford Building 132, Lennox Crossing, ANU
Dr John Minas, Curtin University
diane ! paul () anu ! edu ! au
This seminar focuses on an analysis of the proposed rewrite of the residence rules for individual taxpayers in Australia. We evaluate whether the proposed rules are more aligned with the tax policy objectives of simplicity, certainty, equity, and integrity, than the current law, by applying them to the facts of some key individual residence cases and comparing the approach and outcomes with the current law. The proposed rules appear to increase the incidence of taxpayers who would become residents, which, arguably, alters Australia's jurisdictional claim. The "borderline" cases on residence, that are the subject of litigation, may persist in the event of the new rules being implemented. Furthermore, litigation in a particular area of tax law is not, of itself, evidence of complexity in that area. Although simplicity is a goal of tax policy, the tax reform process in Australia has typically proceeded on an incremental basis. Implementation of a completely new set of rules may increase uncertainty and add to complexity. It would also require taxpayers, tax practitioners, and the tax administration to become well acquainted with a new set of rules. By comparing the current law with the proposed rules, one of the contributions of the research may be to promote debate and discussion about alternative reform pathways.
Dr John Minas is a Senior Lecturer in Taxation (Curtin Law School, Curtin University) and an Adjunct Research Fellow in the Griffith Law Futures Centre. His research interests are taxation law and policy.
Please register your attendance at the registration tab above.

redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction}\label{sec:intro}

Star forming galaxies are the leading candidate for the source of ultraviolet photons required to reionize the universe. Several lines of evidence indicate that reionization was underway by $z=11$ and ended a few hundred Myr later at $z\simeq6$--7 (e.g., \citealt{schenker2012,mortlock2011,hinshaw2012}). Deep near-IR imaging with the Hubble Space Telescope has provided good constraints on the UV luminosity density of star forming galaxies during the reionization epoch (e.g., \citealt{ellis2013,oesch2013}) which indicate that the ongoing star formation is likely capable of producing the required ionizing flux. However, it is unclear whether this radiation is able to escape from galaxies and actually ionize the intergalactic medium (IGM). Based on estimates of the total UV luminosity density and IGM clumping factor, the required escape fraction $f_{esc}$ of hydrogen-ionizing photons is $\gtrsim 0.2$ (e.g., \citealt{robertson2013}). The precise value of $f_{esc}$ is a key uncertainty in determining the role of galaxies in reionization.

Direct measurements of $f_{esc}$ during the reionization epoch are essentially impossible, not only because of the faint apparent luminosity, but also because foreground IGM attenuates the ionizing flux to undetectable levels even at $z\gtrsim4$. Direct imaging and composite spectra of galaxies at lower redshift has established a modest average $f_{esc} \simeq 0.05$ for Lyman break galaxies (LBGs) at $z=3$ \citep{bogosavljevic2010}. If star forming galaxies dominated reionization, $f_{esc}$ must have been higher at earlier times. This paper is concerned with improving the constraints on $f_{esc}$ at higher redshifts for which direct measurements are not practical. Our methodology is as follows: $f_{esc}$ is set by the areal covering fraction of hot stars by H {\sc i} such that $f_{esc} = 1 - f_c$, and $f_c$ can be inferred from intermediate dispersion spectroscopy of interstellar UV absorption lines.
The difficulty, of course, is that LBGs at redshift $z>3$ are very faint, so securing suitably high quality absorption line spectra of individual examples is a very challenging proposition. In an earlier paper \citep{jones2012} we therefore analyzed the average properties of LBGs at $z\simeq4$--5 derived from composite spectra in a manner similar to that pioneered at $z\simeq3$ by \citet{shapley2003}.

A particular motivation for the present study was the discovery of a marked reduction with increasing redshift in the equivalent width of low-ionization absorption lines at fixed UV luminosity, suggestive of changes in either the kinematic profile or the covering fraction of neutral gas \citep{jones2012}. Additionally, spectra of individual galaxies show a trend of increasing Ly$\alpha$\ emission equivalent width with redshift which we argued could reflect evolution in the H~{\sc i} covering fraction \citep{stark2010}, especially given the strong correlation of Ly$\alpha$\ and low-ionization absorption lines \citep{shapley2003,jones2012}.
A lower covering fraction for the neutral gas within typical LBGs would be particularly important as it could imply a higher escape fraction of ionizing photons. The composite spectra discussed by \citet{jones2012} did not have adequate resolution to distinguish the effects of reduced covering fraction and kinematics, and so the present paper takes this investigation one step further by attempting to resolve this important ambiguity. Here we present higher resolution spectra of 3 gravitationally lensed $z\simeq4$ LBGs. Although their unlensed luminosities are typical of the constituent galaxies comprising the \citet{jones2012} composite, their individual lensed magnitudes are much brighter enabling comparable signal to noise to the stack of LBGs discussed in our earlier paper.

Throughout the paper we adopt a flat $\Lambda$CDM cosmology with $\Omega_{\Lambda}=0.7$, $\Omega_{M}=0.3$, and H$_0 = 70$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi Mpc$^{-1}$. All magnitudes are in the AB system \citep{oke1974}.

\section{Gravitationally-Lensed $z\simeq4$ Galaxies}\label{sec:data}

The spectra comprising the composite published by \citet{jones2012} were taken with the 600 line mm$^{-1}$ DEIMOS grating with a resolution of $\simeq$3.5 \AA, although uncertain systemic redshifts led to reduced resolution of the composite spectrum (corresponding to a velocity resolution of $\sim 450$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi\ FWHM). The composite comprised galaxies with $z'_{AB}=24$--26 with 90\% completeness to $z'_{AB}=25$ at $z\simeq4$. The stacked spectrum reveals multiple low ionization lines such as Si {\sc ii} $\lambda$1260, O {\sc i} $\lambda$1302 + Si {\sc ii} $\lambda$1304, and C {\sc ii} $\lambda$1334 in the region where the signal/noise is optimal. As discussed by \citet{jones2012}, these lines are normally saturated so the line depth at a given velocity provides a measure of the areal covering fraction $f_c$ of O and B stars by neutral H {\sc i} gas along the line of sight.

Typical LBGs are too faint for detailed line profile studies even at $z=2$, but strong gravitational lensing can boost the brightness of representative examples making such studies of individual sources a practical proposition. Studies of several lensed $z\simeq2$--3 LBGs have found that absorption velocities of low-ionization metal transitions range from $\sim-1000$ to +500 \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi\ with typical line centroids $v \sim -200$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi\ \citep{pettini2002,quider2009,quider2010,dessauges-zavadsky2010}. The mean low ionization absorption velocity in the \citet{jones2012} composite is similar, $v_{LIS} = -190$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi.

In a similar fashion, for the present analysis we have located 3 gravitationally-lensed LBGs at $z\simeq4$. Two are independent sources lensed by the well-studied cluster Abell 2390 and the third was located in the cluster J1621+0607 in the Sloan Digital Sky Survey. A2390\_H3 and H5 represent two distinct highly-elongated pairs of lensed images that were spectroscopically confirmed to be at different redshifts by, respectively, \citet{frye1998} and \citet{pello1999}. The tangential arc system in J1621+0607 was spectroscopically confirmed by \citet{bayliss2011}. The gravitational magnification factor is $\simeq$10 in each case \citep{pello1999}. We summarize the key properties in Table~\ref{tab:arcs}. The redshifts and absolute UV luminosities are representative of sources studied by \citet{jones2012}. In addition, for comparison purposes, we include an analysis of high quality spectra for 3 further lensed $z=2$--3 sources (courtesy of M. Pettini) in Table~\ref{tab:arcs}. These include the `Horseshoe' ($z$=2.38, \citealt{quider2010}), cB58 ($z$=2.73, \citealt{pettini2002}) and the `Cosmic Eye' ($z$=3.07, \citealt{quider2009}).

Spectra were taken with the 1200 line mm$^{-1}$ DEIMOS grating during two runs in October 2011 and June 2012. This provides a resolution of $\simeq$1.7 \AA\, corresponding to a velocity resolution of $\simeq$70 km s$^{-1}$, considerably better than for the composite discussed by \citet{jones2012}. Spectra of each galaxy covered wavelengths corresponding to at least 1175$-$1675 \AA\ in the rest frame.
The lensed sources in Abell 2390 were observed simultaneously with a multi-slit mask that sampled two images of each source. Seeing varied between 0\farcs4 and 1\farcs4 FWHM during the observations, and the bulk of the data used has seeing in the range 0\farcs7-0\farcs9. Some exposures ($\sim 10$\%) were affected by cirrus and are not included in the final addition. Total observing times for the final spectra are given in Table~\ref{tab:arcs}.

The DEIMOS spectra were reduced and calibrated using the {\sc Spec2D} pipeline following the techniques discussed in detail by \citet{stark2010}. In the case of A2390\_H3, care was taken to ensure that the extracted spectrum was not contaminated by light from a nearby cluster member. Data from the October 2011 and June 2012 runs were reduced separately and the resulting one-dimensional spectra were combined with an inverse-variance weighted mean. Spectra of J1621 are affected by poor sky subtraction residuals, while the Abell 2390 arc spectra are of excellent quality. Spectra of different images of the Abell 2390 arcs were scaled to the same flux level before combining to a common wavelength scale with 0.7 \AA\, pixels, roughly Nyquist sampled. The final spectra, shown in Figure~\ref{fig:spectra}, reach an average continuum S/N per 70 \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi\, resolution element of 5 for J1621, 9 for A2390\_H3, and 10 for A2390\_H5 over the rest-frame wavelength range 1250--1650 \AA. This is comparable to that in the composite spectrum in \citet{jones2012} which has S/N equivalent to $\sim 10$ at the improved resolution of 70 \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi of our new data.

\section{Analysis}\label{sec:analysis}

\subsection{Systemic Redshift}\label{sec:redshift}

Accurate systemic redshifts are required in order to examine the kinematics of gas seen in absorption and the techniques for estimating these are discussed in detail in \citet{jones2012}. This is straightforward when nebular emission lines are visible, such as is the case in both J1621+0607 (O~{\sc iii}] $\lambda\lambda$1661,6) and A2390\_H5 (O {\sc iii}] $\lambda\lambda$1661,6, He {\sc ii} $\lambda$1640, C {\sc iv} $\lambda\lambda$1548,51). The strong emission from highly ionized species such as  He {\sc ii} and C {\sc iv} seen in A2390\_H5 is uncommon but has been observed in some high redshift starburst galaxies and signifies an extremely young, metal-poor, and hot stellar population (e.g. \citealt{fosbury2003,erb2010}). Alternatively they may signify the presence of an active galactic nucleus, but the narrow line widths ($50-185$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi\, FWHM, corrected for instrumental resolution) suggest an origin in star-forming H{\sc ii} regions.

No appropriate features are detected in the spectrum of A2390\_H3 and so we estimate the systemic redshift from low-ionization absorption lines using the method of \citet{jones2012}. This gives $z = 4.043 \pm 0.002 = z_{IS} + 190$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi, with uncertainty dominated by an rms difference $\sim 125$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi\, between redshifts derived from absorption lines and that obtained from nebular emission \citep{steidel2010}. The adopted systemic arc redshifts are listed in Table~\ref{tab:arcs}.

\subsection{Low-Ionization Covering Fraction}\label{sec:fcov}

Ideally we would measure the covering fraction of neutral hydrogen directly from spatially resolved H {\sc i} absorption. However, the only available transition (Ly$\alpha$) is dominated by strong emission with net equivalent width $W_{\rm Ly\alpha} = 20-100$ \AA, and the observed line profile is complicated by resonant scattering in the extended circumgalactic medium (CGM; \citealt{steidel2011}). These effects are apparent from the Ly$\alpha$\ line profiles which show redshifted emission as well as strong absorption arising from both the CGM and Ly$\alpha$\ forest (Figure~\ref{fig:spectra}).
We therefore estimate the covering fraction of neutral hydrogen from absorption lines of heavier low-ionization species which arise in H {\sc i} gas, i.e., those with ionization potentials less than 1 Rydberg.

The covering fraction of any ion is related to its absorption line optical depth $\tau$ and residual intensity $I$ via
\begin{equation}\label{eq:fcov}
\frac{I}{I_0} = 1 - f_c (1 - e^{-\tau})
\end{equation}
where $I_0$ is the continuum level. Optical depth is in turn related to column density as
\begin{equation}\label{eq:N}
\tau = f \lambda \frac{\pi e^2}{m_e c} N = f \lambda \frac{N}{3.768 \times 10^{14}}
\end{equation}
where $f$ is the ion oscillator strength, $\lambda$ is the transition wavelength expressed in \AA, and $N$ is the ion column density in cm$^{-2}$\,(\ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi)$^{-1}$. Combining equations~\ref{eq:fcov} and \ref{eq:N} yields an expression for $f_c$ as a function of $I$ and $N$. In cases where two or more transitions are measured for the same ion, from the same ground state, with different values of $f \lambda$, it is possible to solve these equations for $N$ and $f_c$. In the following analysis we will treat all variables as functions of velocity, i.e., $f_c(v)$.

For the low ionization species of interest, our spectra cover three such transitions of Si {\sc ii} at 1260, 1304, and 1526 \AA\, which we use to measure the covering fraction as a function of velocity $f_c(v)$, for each galaxy. Si {\sc ii} $\lambda$1304 is only used in the velocity range $v \gtrsim -200$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi\, where it is not contaminated by O {\sc i} $\lambda$1302. We resample the spectrum of each transition to a common velocity scale, and find the values of $N$ and $f_c$ which minimize the least-square residual $\chi^2 = \sum (I_{obs} - I_{N,f_c})^2 / \sigma_{obs}^2$ in each velocity bin. We additionally find the range of $N$ and $f_c$ for which $\chi^2$ is within 1 of the minimum value, and adopt this as the 1$\sigma$ uncertainty.

The best-fit $f_c$ and uncertainty calculated for each arc are shown as a function of velocity in Figure~\ref{fig:fcov}. Since Si {\sc ii} is the dominant ion of silicon in H {\sc i} gas, this is approximately equal to the covering fraction of H {\sc i} (provided that it is enriched with Si) which impedes the escape of ionizing radiation.

\subsection{Average Low-Ionization Absorption Profile}

A simple and complementary alternative to the method outlined in Section~\ref{sec:fcov} is to estimate the covering fraction from saturated transitions. In cases where $\tau \gg 1$,
Equation~\ref{eq:fcov} simplifies to
\begin{equation}\label{eq:profile}
f_c = 1 - I/I_0.
\end{equation}
Several of the strongest absorption lines covered by our spectra are typically saturated, including: Si {\sc ii} $\lambda$1260, O~{\sc i} $\lambda$1302, Si {\sc ii} $\lambda$1304, C {\sc ii} $\lambda$1334, and Si {\sc ii} $\lambda$1526 which are all tracers of H {\sc i} gas. In order to minimize the statistical uncertainty we calculate the average intensity of these transitions as a function of velocity using an inverse-variance weighted mean, taking care not to use the wavelength region where O {\sc i} $\lambda$1302 and Si {\sc ii} $\lambda$1304 are blended (roughly $-300 \lesssim v \lesssim -200$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi\, depending on the kinematics of each source). These profiles are shown in Figure~\ref{fig:fcov} together with the covering fraction measured from Si {\sc ii}. We note that the covering fraction derived from Equation~\ref{eq:profile} is a strict lower limit.

\section{Results}\label{sec:discussion}

This work was motivated in large part by the need to disentangle kinematics and covering fractions of absorbing gas. In particular, we seek to explain the extent to which decreased absorption line equivalent widths measured from composite spectra in our earlier work \citep{jones2012} result from changes in gas kinematics compared to covering fractions, and the implications of this result for the escape of ionizing radiation. We are limited in examining the redshift evolution of these properties by the small number of sources with suitable spectra, and we caution that this sample is not necessarily representative of the LBG population at these redshifts. Nonetheless we can examine general trends within the existing data from this work and others in the literature \citep{pettini2002,quider2009,quider2010,dessauges-zavadsky2010}.
Following the methods in Section~\ref{sec:analysis} we show the average absorption profiles and Si {\sc ii} covering fractions (derived from unblended transitions at 1260, 1526, and 1808 \AA) of well-studied $z=2$--3 galaxies for comparison in Figure~\ref{fig:fcov}. To quantify trends in the absorption line profiles, the velocity extent and maximum absorption depth for each galaxy are shown as a function of redshift in Figure~\ref{fig:abs}.

In the case of Abell 2390, we take the most conservative approach noting that the interpretation of the absorbing gas is complicated by the physical proximity and similar redshift of the two arcs. Their projected separation is $\sim 70$ kpc \citep{pello1999} and it is unclear which source lies in the foreground. At lower redshifts, \citet{steidel2010} have shown that low-ionization absorption seen in a background source at $b = 70$ kpc has a detectable average equivalent width $\sim 0.4$ \AA\ for the transitions of interest. Since we lack specific information about the 3-D geometry, the following analysis does not include any contribution from this effect. If anything, our results will overestimate the true covering fraction and therefore yield a more conservative constraint on the escape fraction.

\subsection{Kinematics}

The kinematics of foreground low-ionization gas are revealed in the absorption line profiles shown in Figure~\ref{fig:fcov}. In all cases we see significant blueshifted absorption indicating outflows, as expected given the high star formation surface densities \citep{heckman2002}. The maximum outflow velocity at which absorption is detected is $-700$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi\, in A2390\_H3, with an uncertainty of $\sim125$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi\, since we do not directly measure the systemic redshift. A2390\_H5 reveals weak absorption extending to $-600$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi, seen also in higher-ionization Si {\sc iv} and C {\sc iv} lines, although it is only marginally detected at $<-300$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi. The maximum outflow velocity in J1621 is $-300$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi.

The outflowing low-ionization gas attains a somewhat lower ($\sim30$\% on average) maximum velocity at higher redshift. This trend is not due to lower quality data as it remains evident in Figure~\ref{fig:fcov} if we consider alternative measures such as the FWHM or an absorption threshold at 25\% of the continuum flux. However all galaxies except J1621 have similar maximum velocities ranging from $600-800$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi. Likewise the extent of redshifted absorption is approximately $+200$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi\ for all sources, with the notable exception of the Cosmic Eye as discussed in detail by \citet{quider2010}; this indicates little difference in line broadening from rotation or other internal kinematic structure. Therefore, in this limited sample, the low-ionization gas kinematics are similar with a somewhat lower average velocity extent at higher redshift.

\subsection{Covering Fraction}

The covering fraction of each galaxy as a function of gas velocity is estimated from the methods described in Section~\ref{sec:analysis} and shown in Figure~\ref{fig:fcov}. Both methods are generally in good agreement indicating that Equation~\ref{eq:profile} is a valid approximation.
Si {\sc ii} covering fractions derived for the Cosmic Eye are systematically higher than indicated by the average absorption profile; this is largely an artifact caused by additional absorption at the wavelength of Si {\sc ii} $\lambda$1260 from intervening gas at $z=2.66$ \citep{quider2010}. It is also apparent from Figure~\ref{fig:fcov} that the Si {\sc ii} covering fraction is poorly constrained in regions of weak absorption due to the marginal significance of individual absorption lines. This is most problematic in the high-velocity wings. The strong anticorrelation between absorption line strength and covering fraction, as well as results at lower redshift \citep{martin2009}, suggest that the most likely solution for such ambiguous cases is a low covering fraction of optically thick gas. We therefore opt to compare galaxies on the basis of their average absorption line profile as this quantity is simpler to define and less susceptible to the uncertainties described above. Nonetheless the Si {\sc ii} results are an important verification that the average profile accurately traces $f_c$.

We can now compare the covering fractions measured at $z=4$ with sources at lower redshift. Figure~\ref{fig:abs} shows the maximum absorption depth for each galaxy as a function of redshift. The $z=4$ galaxies have maximum absorption depths corresponding to $f_c=0.3$--0.9, in each case occurring at $v\sim-100$ \ifmmode\,{\rm km}\,{\rm s}^{-1}\else km$\,$s$^{-1}$\fi. There is a large scatter in Figure~\ref{fig:abs} with $\sigma(f_{c,max}) = 0.26$ and no strong redshift dependence. Galaxies at $z=4$ do, however, have covering fractions which are lower on average by 25\% or $\Delta f_{c,max} = 0.16$ compared to $z=2$--3.

\subsection{Trends with Ly$\alpha$}

We now turn to trends with Ly$\alpha$\ equivalent width. Previous sections focused on possible redshift evolution of low-ionization absorption lines in our quest to examine whether this may signify an increasing ionizing escape fraction. The connection with Ly$\alpha$\ is a natural one to explore given there is a strong correlation between its equivalent width $W_{\rm Ly\alpha}$ and low-ionization absorption \citep{jones2012,shapley2003}. Since our previous work has suggested that the distribution of $W_{\rm Ly\alpha}$ for LBGs of a fixed luminosity increases with redshift \citep{stark2010,stark2011,schenker2012}, we can hope to derive inferences about the low ionization absorption in sources for which Ly$\alpha$\ measurements are now widely available.

Each galaxy in Figure~\ref{fig:abs} is color-coded according to $W_{\rm Ly\alpha}$. This value refers only to the equivalent width of Ly$\alpha$\ emission, differing from the conventional net sum of emission and absorption. The maximum outflow velocity is lower on average in galaxies with stronger Ly$\alpha$\ emission, consistent with well-quantified results from composite spectra \citep{shapley2003}. More interestingly, Figure~\ref{fig:abs} reveals a trend of lower absorption depth (implying lower $f_c$) with stronger Ly$\alpha$\ emission at $3.5\sigma$ significance. We show this relation in Figure~\ref{fig:lya}. In contrast, the trend of lower average $f_c$ at higher redshift has limited significance ($1.1\sigma$) and is explained by Ly$\alpha$\ demographics within the sample. Although limited by the small sample size, this is an important first quantitative result at these redshifts.
Since the frequency and equivalent width of Ly$\alpha$\ emission increases in LBGs at higher $z=3\rightarrow6$, these results imply that the average covering fraction of low-ionization gas should decrease with redshift.

\subsection{Ionizing Escape Fraction}

Direct measurements of the ionizing flux are impractical at the redshifts of interest in this paper both because of the faint apparent magnitudes of LBGs and the high opacity of the Ly$\alpha$\ forest. Nonetheless we can provide important constraints on $f_{esc}$ using indirect tracers of H {\sc i}.

Before doing so, we consider the potential systematic uncertainties which may limit our ability to estimate the true value of $f_{esc}$ from metal absorption lines. Results at $z\simeq3$ have shown that $f_{esc}$ is indeed dependent on low-ionization absorption strength \citep{bogosavljevic2010} although this relation is not one-to-one, likely due to the factors described below. While in general these preclude accurate estimates of the escape fraction, the maximum absorption depth (Figures~\ref{fig:fcov}, \ref{fig:abs}) is a valuable constraint on H {\sc i} spatial homogeneity and sets a stringent upper limit on $f_{esc}$.

1. We measure covering fraction as a function of velocity, yet gas at different velocities may cover different spatial regions and we lack the spatial resolution needed to evaluate this effect. The maximum absorption depth {\em at a given velocity} is thus a lower limit on the total H {\sc i} covering fraction and an upper limit on $f_{esc}$.

2. Metal-free H {\sc i} is not detected. To date only two instances of metal-free gas have been found at these redshifts \citep{fumagalli2011} and so this is likely insignificant. Again, this possibility implies that covering fractions measured in Section~\ref{sec:analysis} yield upper limits on $f_{esc}$.

3. Low column density gas will not be detected, although such gas will not affect $f_{esc}$ unless it has very low metallicity $\lesssim 0.1$ Z$_{\odot}$. The optical depth of metal transitions used here compared to Lyman continuum at $\sim900$ \AA\ is $\frac{\tau}{\tau_{\rm LyC}} = 1.7$ for the weakest line (Si {\sc ii} $\lambda$1304) and 10--20 for the strongest transitions (Si {\sc ii} $\lambda$1260, C {\sc ii} $\lambda$1334, O {\sc i} $\lambda$1302) for solar abundance ratios \citep{asplund2009}. Galaxies in the $z=2$--3 sample with measured interstellar abundance ratios have Z $\gtrsim0.4$ Z$_{\odot}$ for the relevant elements, such that the attenuation of weaker Si lines is roughly equal to that of ionizing radiation.

4. There may be narrow components with uniform covering fraction which are spectroscopically unresolved. However, such smooth absorption and column density profiles would require a remarkably regular spacing of discrete narrow components, and so a partial covering fraction appears more likely (see \citealt{pettini2002,quider2009}).

5. Si {\sc ii} and C {\sc ii} are present in both H {\sc i} and H {\sc ii} regions. We have therefore confirmed that O {\sc i}, with essentially the same ionization potential as H {\sc i}, gives consistent results in all cases.

6. We measure a covering fraction at 1260--1526 \AA, but the stars which are bright at these wavelengths do not necessarily emit at $<$912 \AA. Our measurements therefore correspond to a constraint on the relative escape fraction $f_{esc} = L_{\rm LyC} / L_{1500}$ as commonly used in the literature. However, the spatial distribution of $L_{1500}$ is similar to ionizing emission as traced by Balmer lines in $z\simeq1-3$ galaxies (e.g., \citealt{jones2010}), indicating that this effect may be minimal.

With these caveats in mind, we now summarize what can be learned about the ionizing escape fraction at $z=4$. The depth of low-ionization absorption lines gives upper limits $f_{esc} < 0.7$ for A2390\_H5, $<0.3$ for A2390\_H3, and $<0.1$ for J1621. The true values are likely well below the upper limits and in three lower-redshift galaxies we can verify that this is the case. \citet{quider2010} show that the Cosmic Eye has an H {\sc i} covering fraction of $\simeq 95$\% implying $f_{esc} < 0.05$ based on damped Ly$\alpha$\ absorption, more stringent than the $f_{esc} < 0.1$ from our analysis. Secondly, no ionizing radiation is detected from the Horseshoe in deep UV imaging (B. Siana, private communication) nor from the spectrum of Q0000-D6 ($f_{esc} < 0.16$; \citealt{giallongo2002}) despite low maximum covering fractions (Figures~\ref{fig:fcov}, \ref{fig:abs}). Non-uniform coverage of low-ionization metals is evidently a necessary, but not sufficient, condition for the escape of ionizing radiation. Results derived in this paper should therefore be strictly interpreted as upper limits. Nonetheless, our measurements at $z=4$ are readily compatible with the value $f_{esc} \gtrsim 0.2$ required for galaxies to reionize the universe \citep{robertson2013}.

\section{Discussion}

In our previous work \citep{jones2012} we found a decrease in the low-ionization absorption equivalent width with redshift in composite LBG spectra, but were unable to distinguish whether gas kinematics and/or covering fraction were the cause. The new data presented in this paper now resolve this ambiguity. Although the sample of LBGs with high quality spectra at $z>2$ is small and not necessarily representative,  the present data show an approximately equal decrease of $\sim25$\% in the gas velocity and covering fraction with redshift. The much stronger dependence of low-ionization absorption with Ly$\alpha$\ emission appears to be predominantly due to the covering fraction of neutral hydrogen.

The main limitation of methods used in this work to constrain $f_{esc}$ is that we do not directly measure the fraction of ionizing emission covered by H {\sc i}. While the spectrally-resolved covering fraction of heavy elements provides an important measure of the ``patchiness'' of H {\sc i}, gas at different velocities may cover different spatial regions and so we can derive only a lower (upper) limit on $f_c$ ($f_{esc}$). Deep integral field spectroscopy with good spatial resolution may resolve this issue and provide better constraints on $f_c$ and $f_{esc}$.

We have successfully measured the kinematics and covering fraction of low-ionization (H~{\sc i}) gas in $z=4$ LBGs from high quality rest-UV spectra. Resulting upper limits on the ionizing escape fraction $f_{esc} \leq 1 - f_c$ are readily consistent with that required for star-forming galaxies to reionize the universe (e.g., \citealt{robertson2013}). Importantly, the new data enable these measurements at a time $< 1$ Gyr from the reionization epoch, much earlier than was previously possible. We note that in order for galaxies to reionize the universe, the escape fraction must increase rapidly from $\left< f_{esc} \right> = 0.05$ measured at $z=3$ \citep{bogosavljevic2010} to a value $f_{esc} \gtrsim 0.2$ at $z=7$ \citep{robertson2013,kuhlen2012}.  While the trends with redshift are poorly constrained, the available data reveal a reduced covering fraction with increasing $W_{\rm Ly\alpha}$ indicating that galaxies with moderate or strong Ly$\alpha$\ emission are likely to have larger $f_{esc}$. This is supported by direct evidence at $z=3$, where galaxies with detectable ionizing flux have stronger Ly$\alpha$\ emission and weaker low-ionization absorption than LBGs with lower $f_{esc}$ \citep{bogosavljevic2010}. Clearly the distribution of (metal-enriched) H {\sc i} is patchier in galaxies with stronger Ly$\alpha$\ emission, and therefore more likely that ionizing radiation can escape.  Since the frequency and strength of Ly$\alpha$\ emission in typical LBGs increases with redshift \citep{stark2010,stark2011}, our results provide new evidence that the covering fractions decrease (and therefore $f_{esc}$ increases) with redshift.

\acknowledgements

We thank Max Pettini for providing ESI spectra of the $z=2$--3 galaxies used as a comparison sample.
T.A.J. acknowledges support from the Southern California Center for Galaxy Evolution through a CGE Fellowship.
D.P.S. acknowledges support from NASA through Hubble Fellowship grant \#HST-HF-51299.01 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc, for NASA under contract NAS5-265555.
The analysis pipeline used to reduce the DEIMOS data was developed at UC Berkeley with support from NSF grant AST-0071048.
This work relies on data obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration, and was made possible by the generous financial support of the W.M. Keck Foundation.
We wish to recognize the significant cultural role that the summit of Mauna Kea has within the indigenous Hawaiian community; we are most fortunate to have the opportunity to conduct observations from this mountain.

\medskip


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