11institutetext: Université de Strasbourg, CNRS, Observatoire astronomique de
Strasbourg, UMR 7550, F-67000 Strasbourg, France 22institutetext: Kavli
Institute for Particle Astrophysics and Cosmology (KIPAC), Stanford
University, USA 33institutetext: Department of Astrophysics & Atmospheric
Sciences, Kyoto Sangyo University, Kamigamo-motoyama, Kita-ku, Kyoto 603-8555,
Japan

# Forgotten treasures in the HST/FOC UV imaging polarimetric archives of
active galactic nuclei

I. Pipeline and benchmarking against NGC 1068 and exploring IC 5063

T. Barnouin<EMAIL_ADDRESS>F. Marin 11 E. Lopez-
Rodriguez 22 L. Huber 11 M. Kishimoto 33

(Received July 3, 2023; accepted Month Day, 2023)

###### Abstract

Context. Over its 13 years of operation (1990 – 2002), the Faint Object Camera
(FOC) on board the Hubble Space Telescope (HST) observed 26 individual active
galactic nuclei (AGNs) in ultraviolet (UV) imaging polarimetry. However, not
all of the observations have been reduced and analyzed or set within a
standardized framework.

Aims. We plan to reduce and analyze the AGN observations that have been
neglected in the FOC archives using a consistent, novel, and open-access
reduction pipeline of our own. We then extend the method to the full AGN
sample, thus leading to potential discoveries in the near future.

Methods. We developed a new pipeline in Python that will be able to reduce all
the FOC observations in imaging polarimetry in a homogeneous way. Most of the
previously published reduced observations are dispersed throughout the
literature, with the range of different analyses and approaches making it
difficult to fully interpret the FOC AGN sample. By standardizing the method,
we have enabled a coherent comparison among the different observational sets.

Results. In this first paper of a series exploring the full HST/FOC AGN
sample, we present an exhaustively detailed account of how to properly reduce
the observational data. Current progress in cross-correlation functions,
convolution kernels, and a sophisticated merging and smoothing of the various
polarization filter images, together with precise propagation of errors, has
provided state-of-the-art UV polarimetric maps. We compare our new maps to the
benchmark AGN case of NGC 1068 and successfully reproduce the main results
previously published, while pushing the polarimetric exploration of this AGN
futher, thanks to a finer resolution and a higher signal-to-noise ratio (S/N)
than previously reported. We also present, for the first time, an optical
polarimetric map of the radio-loud AGN IC 5063 and we examine the complex
interactions between the AGN outflows and the surrounding interstellar medium
(ISM).

Conclusions. Thanks to our newly and standardized reduction pipeline, we were
able to explore the full HST/FOC AGN sample, starting with observations that
had not been previously published (e.g., IC 5063 here). This pipeline will
allow us to make a complete atlas of UV polarimetric images of the 26 unique
AGNs observed by the FOC, highlighting the importance and necessity of
(imaging) polarimeters for the upcoming new generation of 30-m class
telescopes.

###### Key Words.:

Instrumentation: polarimeters – Methods: observational – Polarization –
Astronomical data bases: miscellaneous – Galaxies: active – Galaxies: Seyfert

##  1 Introduction

Polarimetry has proven to be one of the most resourceful observational methods
in astronomy (Hildebrand, 2005; Hough, 2006). From stars to planets,
supernovae remnants to gamma-ray bursts, polarimetry has brought a wealth of
information about the geometry and composition of cosmic sources, including
magnetic field intensity and topology in both small- and large-scale
structures. However, it is probably the field of active galactic nuclei (AGNs)
that polarimetry has contributed the most (Marin, 2019, and references
therein), starting with the proposition of a unified model for AGNs from
optical and ultraviolet (UV) polarimetry (Antonucci & Miller, 1985), followed
by the uncovering of a near-infrared (NIR) polarized accretion disk spectrum
in quasars (Kishimoto et al., 2008), or, most recently, the dichotomy of
radio-loud and radio-quiet quasars in far-infrared (FIR) polarimetry (López
Rodríguez, 2023).

One of the major challenges with AGNs is that they are extra-galactic, compact
objects that cannot be resolved using conventional imaging techniques. As the
typical scale of the internal disk of an AGN is $\sim$2pc, for NGC 1068 (most
studied Type 2 AGN at $\sim$13.5Mpc), it would require a spatial resolution of
less than 10 milliarcseconds to resolve. Even interferometry is only able to
resolve a couple of the closest or most massive sources (e.g., Event Horizon
Telescope Collaboration et al., 2019; Gámez Rosas et al., 2022; Isbell et al.,
2022). This method recently was able to get to milliarcseconds resolution with
VLTI/MIDI and VLTI/MATISSE in the mid-IR and 100 microarcseconds resolution
with CHARA array in the near-IR that has allowed for the resolution the nuclei
of NGC 1068 (López-Gonzaga et al., 2014; Gámez Rosas et al., 2022), Circinus
galaxy (Tristram et al., 2014; Isbell et al., 2022), and NGC4151 (Kishimoto et
al., 2022). Polarimetry has the unique advantage of transcending spatial
constraints: polarimetric techniques can provide physical information well
below the beam of the observations because only the polarized source is
measured, while the unpolarized light does not contribute to the total
polarized light. A disk’s morphology can be easily told apart from a spherical
morphology, even if the region is beyond the resolving power of the best
imaging telescope. Using this pivotal characteristic, it is strikingly evident
why polarimetry is the key to improving our understanding of the compact and
luminous regions at the center of host galaxies known as AGNs. Their
characteristics indicate that their intrinsic luminosity is not produced by
stars. Instead, a supermassive black hole (105 – 1010 solar masses, Shankar et
al., 2004; Inayoshi & Haiman, 2016) is thought to accrete matter at the center
of the AGN, releasing thermal radiation that peaks in the blue-UV band of the
electromagnetic spectrum (Shakura & Sunyaev, 1973). Surrounding this sub-
parsec-scale central engine, there are outflows, relativistic jets, clouds of
gas with various ionization stages, and a reservoir of dust and molecular gas
and stars. The global picture of AGNs is certainly not easy to decipher and
even the most up-to-date models struggle with establishing their true
locations, compositions, and generation mechanisms of their broad variety of
structures. The most enigmatic of all structures lies in the accreting region
surrounding the central supermassive black hole (Antonucci, 1993; Urry &
Padovani, 1995; Elvis, 2000; Netzer, 2015). This is an area where polarimetry
can prove especially handy. In addition, since the accretion engine emits the
most in the UV band, where the starlight polluting contribution is weak, it
can be most efficient to observe AGNs in this specific waveband.

Today, there are no longer any far- or mid-UV polarimeters available for AGN
observations. A few telescopes mounted with spectropolarimetric instruments
reaching the near-UV band still exist (such as the VLT/FORS2 or the HST/WFPC2)
but it would be necessary to observe high-redshift sources in order to probe
the far-UV band111For a galaxy at redshift $z$ = 3, the Lyman break will
appear to be at wavelengths of about 3600 Å. This is highly limiting since
high-redshift objects are often fainter than AGNs from the nearby Universe and
the required amount of time to reach a minimal signal-to-noise ratio
(S/N$\geq$ 3) in polarization is unfeasible. To examine the UV polarization of
AGNs, we must rely on past instruments, namely the Wisconsin Ultraviolet
Photopolarimeter Experiment (WUPPE, Nordsieck & Code, 1982; Stanford et al.,
1985; Code & Nordsieck, 1989) and various instruments aboard the Hubble Space
Telescope (HST). WUPPE provided the first UV polarized spectra of 5 AGNs (NGC
4151, NGC 1068, 3C 273, Centaurus A, and Mrk 421; see Marin et al., 2018). On
the other hand, a total of 2,000 datasets were acquired by the various UV
polarimeters that equipped the HST from Cycle 0 to Cycle 22. This corresponds
to several dozens of AGNs. Among those observations, for each of these
instruments, a fraction of the observations lack any associated publication.
As an example, 19% of AGN proposals in the FOC archives are yet to be
published, implying a deep potential pool of scientific discoveries.

The FOC served as a particularly interesting polarimeter. It was one of HST’s
five instruments at launch and consisted of a long-focal-ratio, photon-
counting imager capable of taking high-resolution images in the wavelength
range 1150 – 6500 Å. When corrected by COSTAR, the field-of-view (FoV) and
pixel size of the f/96 camera were 7” $\times$ 7” (512 $\times$ 512 pixel2
format) and 0.014” $\times$ 0.014”, respectively. Other configurations were
also possible thanks to a different optical relay (f/48). The excellent
spatial resolution offered by the FOC, coupled to the very low instrumental
polarization and excellent polarizing efficiencies of the polarizers in the
f/96 relay made the FOC a unique instrument. No other polarimeter (or any non-
polarimetric instruments for that matter) have fully used the spatial
resolution capabilities of the Optical Telescope Assembly (OTA) of the HST.
Unfortunately, the FOC was replaced by the ACS during Servicing Mission 3B
(March 7, 2002).

Because the FOC was ahead of its time and was one of the most promising
instruments to achieve great discoveries in the field of AGNs, it is a pity
that 19% of the AGN proposals in the FOC archives lack any exploitation (5/26
AGNs observed with the FOC were never published) . Therefore, in this series
of papers, we have decided to propose a rigorous, systematically complete, and
consistent re-analysis of all raw HST imaging polarimetric AGN observations
from the FOC in the HST archive to enable science deferred or unachieved by
many approved programs.

In 2005, the Canadian Astronomy Data Center (CADC), in collaboration with
STScI, decided to produce the final calibration files for the science
observations and the whole FOC dataset was re-calibrated accordingly (Kamp et
al., 2006). From this data reprocessing, CADC noticed a sensible modification
of the science data due to a new ”best geometric reference.” Since this re-
calibration and the release of consistently processed data, no re-analysis of
the observation has been published for the AGN dataset. In addition, most of
the old reduced observations are dispersed throughout the literature, with
different analyses and approaches, making it difficult to fully interpret the
FOC AGN sample. This is why we decided to create a consistent, novel and open-
access reduction pipeline of our own to produce high-level, science-ready,
polarimetric products for the scientific community as well as polarimetric
data reduction packages. Ultimately, we aim to explore, download, reduce, and
present all the polarimetric images taken with the FOC in a standardized way.
A large sample of radio-loud and radio-quiet AGNs is indeed necessary to
investigate whether all the differences between pole-on and edge-on objects
can be explained by an inclination effect (Antonucci, 1993; Marin, 2016) or
whether morphological differences of the circumnuclear region must also be
taken into account (Ramos Almeida et al., 2009; Alonso-Herrero et al., 2011;
Ichikawa et al., 2015; López Rodríguez, 2023). Using a large AGN sample also
allows us to study their thermal and non-thermal physical components
(Antonucci, 2012, 2015), which, in turn, enables us to put physical constrains
in the AGN components.

In this first paper of the series, we present a detailed description of the
new reduction pipeline in Sect. 2. We test our methodology against a well-
known, previously published FOC polarimetric image of NGC 1068 in Sect. 3. We
then proceed with the reduction of a forgotten FOC observation of the
Seyfert-2 galaxy IC 5063 (PKS 2048-572) in Sect. 4. We discuss our results
Sect. 5 and present our conclusions in Sect. 6.

##  2 Reduction pipeline

In this section, we present the general reduction pipeline methodology and our
choice of various algorithms to extract as much information as possible from
the raw data. We created our new reduction pipeline in python language, making
use of this easy-to-read tool for optimized reduction methods. The pipeline is
already available to grab on the author’s
Git222git.unistra.fr/t.barnouin/FOC_Reduction. We focused our work on the FOC
instrument but it was written to be modular so that it is relatively easy to
add other instruments to the pipeline. The overall data reduction steps is
summarized in a diagram in Fig. 1. The FOC instrument measures polarization
state by performing three consecutive observations of the same target through
three polarizer filters with complementary polarization axis angles,
$\theta_{1}=0^{\circ}$, $\theta_{2}=60^{\circ}$, and $\theta_{3}=120^{\circ}$,
usually referred to as POL0, POL60, and POL120 respectively. The reduction
procedures of polarization observations with the FOC instrument call for at
least three rounds of observations with the same instrument, but through three
different filters with different properties (see Keyes, 1998, Section 8.7).
The FOC instrument itself has some photometric uncertainties that also ought
to be taken into account (see Keyes, 1998, Section 8.3) as well as specific
issues to the filter wheel, the uncertainty in the polarizer axis directions,
PSF differences, and throughput issues (see Nota & et al., 1996, Sections
4.4.3 and 11.2.6) that induce relative uncertainties between observations. To
better implement these uncertainties into our data reduction, we chose to go
back to the most generic description of the flux through a polarizer, as
described in the appendix of Kishimoto (1999). The three polarized exposures
obtained are then combined into the Stokes parameters to compute the
polarization state, as described in Section 2.7. For the remainder of this
section, actual examples will be provided using the Feb 28, 1995 (5:33AM) FOC
observation of NGC 1068 (ID: 5144), which we will explore in further detail in
Sect. 3.

Figure 1: Diagram representing the pipeline’s reduction operations from the
raw data obtained from the HST Legacy Archives to the obtained polarization
maps.

###  2.1 Data importing and selection of the region of interest

The data were imported from astrophysics standard FITS files, making use of
information in headers to optimize the whole pipeline without requiring user
inputs. The required FITS files were calibrated data products that can be
retrieved from the MAST HST Legacy Archive333archive.stsci.edu/missions-and-
data/hst.

A ”query” utility that depends on astroquery Python package allows us to
download FOC’s _c0f files from the terminal, given a target name (and possibly
a proposal id). Otherwise, the user can feed its own FITS files to the
pipeline, as long as their HEADER contain the identifying keywords defined in
the HST/FOC Data Handbook Chapter 5.2 (Keyes, 1998). We made use of the
Calibrated exposure FITS files, whose suffix is _c0f in the MAST archives. We
immediately translated each observation count as count rates, using the
EXPTIME header keyword containing the exposure time of the data set. For a
better handling of the data these count rates are conserved as such during the
whole pipeline and only translated into physical units when displaying the
relevant data through plots. This is done using the PHOTFLAM header keyword
containing the inverse sensitivity conversion factor (Nota & et al., 1996). In
our case, count rates were transformed as fluxes in erg.cm-2.s-1.Å-1. For 2D
images (e.g., FOC outputs), the observational data are processed through a
Graham’s scan algorithm (Graham, 1972) for a better selection of the region of
interest (ROI). This algorithm finds the convex hull of a set of $n$ points in
the plane with a complexity $O\left(n\log n\right)$, cropping out non-
exploitable values from the data matrix (infinite numbers, zeros, …). An
automatized function finds the optimal rectangle-shaped image that contains
only valuable data from the observation and removes the unusable empty
borders, artifacts from the finite size of the detector and non-physical
calibration procedures. The implemented version of this algorithm takes the
full set of observations and concurrently crop out the undesired edges on
every observation. To do so, it takes as the parameters the pixel step to
create the image shell (allows us to reduce the number of points to be
considered to run the algorithm), the value to be discarded, and the choice of
whether the final crop should be the intersection or the union of all
individual crops. The obtained shell is then intersected with the ones
obtained for each observations (and each half wave plate) to get an uniform
cropping across the whole dataset. An example of such preliminary data
selection can be seen in Fig. 2. On average, this procedure remove 15 – 18% of
the original raw image of 512 $\times$ 512 pixels.

Figure 2: Image of the POL0 polarizer filter for NGC 1068. The total exposure
time is 1,796 seconds. The blue rectangle delimits the cropped region of
interest after Graham’s scan, removing the borders containing non-pertinent
data for the analysis.

###  2.2 Deconvolution.

Before the installation of COSTAR, the FOC point spread function (PSF)
suffered from severe spherical aberration, which meant that a circular
aperture of 0.1” radius contained only 15 – 18% of the light from a star
instead of the expected 70%. COSTAR has restored much of the OTA capabilities,
in the sense that the COSTAR-corrected PSF contains more than 75% of the light
within a radius of 0.1” at visible wavelengths. The FOC PSF typically measures
1.6 – 1.8 pixels in the visible ($\sim$ 0.08” at full width at half maximum,
FWHM), as in Nota & et al. (1996). To recover the underlying fine structures
that has been blurred by the photo-diodes of the detector, our pipeline
implements several deconvolution algorithms that can be used to treat the raw
images before any reduction.

A linear regularized deconvolution method was implemented using a standard
Wiener filter (Wiener, 1949). It is a low-pass filter with some neighboring
pixel regularization constraint. Its simplicity is optimal for stationary and
Gaussian noise, but for spatially localized features such as singularities or
edges, it comes with drawbacks; namely, it creates oscillations along the
sharp contours and degrades the resolution.

Several iterative regularized methods were also implemented, which enforce a
set of additional constraints of positivity, support, and band limitation on a
given object, $O$. Because this process investigates the maximum likelihood in
the case of Poisson-noise induced by a PSF $P$, it has no closed-form solution
and requires an iterative approach. The algorithm evaluates the most probable
pixel in which a photon should be detected given the raw image, $I$. The Van-
Cittert method finds underlying structures in residual solutions at each
iteration and put them in the restored image:
$O^{n+1}=O^{n}+\alpha(I-(P*O^{n})),$ where $\alpha$ is a convergence parameter
generally taken to be equal to $1$ (van Cittert, 1931). The one-step gradient
method replaces this convergence parameter with a convolution of the residual
with the inverted PSF : $O^{n+1}=O^{n}+P^{*}*(I-(P*O^{n}))$. The Richardson-
Lucy method multiplies the previously computed deconvolved image with a
weighted image made up of a convolution of the data with the known PSF of the
detector : $O^{n+1}=O^{n}(\frac{I}{P*O^{n}}*P^{*})$ (Richardson, 1972).
Finally, the conjugate gradient iterative method solves the inverse problem
with PSF convolution and regularization constraint in an optimized way: the
search direction for the solution $O^{n}$ is orthogonal to the direction of
the gradient of the residual function $R^{n}(x,y)=(I-P*O^{n})(x,y)$.

In our pipeline, we let the user decides if a deconvolution should be applied
and how many times any iterative algorithm should be run. This is critical for
pre-COSTAR observation but less important in the case of post-COSTAR data, as
explained previously. In our example of NGC 1068, no deconvolution was
performed on the data.

###  2.3 Error computation and propagation.

The background noise is estimated on the calibrated data, before being
processed through data alignment and resampling. A very basic first method
searches for a common region in all observations and of user defined pixel
size (basically, $\sim$10% of the image size) with the least integrated flux.
We assume this sub-image to be background dominated and we estimate the
background by taking the root mean square of the selected sub-image (see Fig.
3). The user can check for the evolution of the background flux during each
observation (see Fig. 4) and verify that there is no transient source
involved.

Another more robust method takes into account the intensity histogram of each
image and assume that the background is the most represented intensity bin
(see Fig. 5). The binning is done with a logarithmic range, in such a way that
lower intensities get more precise binning than high intensities, and the
number of bins is given by the Freedman-Diaconis rule for a sample, $x,$ of
size, $n$:

$N_{bins}=\frac{\max(x)-\min(x)}{2\cdot\frac{IQR(x)}{\sqrt[3]{n}}},\hfill\text{\footnotesize
with $IQR$ the interquartile range.}$ (1)

If it is required by other flux statistics during the observations, the user
can also choose for the number of bins to be computed by the following rules:
square-root ($N_{bins}=\sqrt{(}n)$), Sturges ($N_{bins}=\log_{2}(n)+1$), Rice
($N_{bins}=2\sqrt[3]{n}$), and Scott
($N_{bins}=\frac{\max(x)-\min(x)}{3.5\frac{STD(x)}{\sqrt[3]{n}}}$).

This second method has little dependence on transient sources as it looks for
an intensity plateau rather than an image location. It can also better
estimate observation-dependent levels, as can be seen in the deviation of
estimated background values in Table 1. These differences in intensity levels
can come from different parameters of observation or calibration. At this
point, the background value is subtracted to the whole image. From there are
computed and quadratically summed the uncertainties in the ”correction
factors” as a percentage of the observed flux in each pixel. Following
Kishimoto (1999), the wavelength dependence of the transmittance of each
polarizer filter $\sigma_{wav}$ is taken to be 1%, the differences in PSFs
through each polarizer filter, $\sigma_{psf}$, is taken to be 3% and the
heavily smoothed flat-fielding uncertainty, $\sigma_{flat}$, is taken to be
3%.

Filter name | Observation date & time | $N_{bins}$ |  Estimated background ($10^{-4}s^{-1}$)
---|---|---|---
POL0 | 1995-02-28 05:33:12 | 6348 | 6.43
POL0 | 1995-02-28 06:07:33 | 2141 | 25.7
POL0 | 1995-02-28 07:07:54 | 5747 | 7.78
POL60 | 1995-02-28 07:37:16 | 4319 | 13.1
POL60 | 1995-02-28 08:44:26 | 6091 | 10.3
POL60 | 1995-02-28 09:06:15 | 6205 | 8.57
POL60 | 1995-02-28 10:22:57 | 4727 | 16.3
POL120 | 1995-02-28 10:37:59 | 8324 | 7.06
POL120 | 1995-02-28 12:05:37 | 8696 | 6.49

Table 1: Histogram binning and resulting estimation of the background (here in
count rates) for each observation of NGC 1068. Figure 3: Image of NGC 1068 for
the first observation. The red rectangle delimits the region considered for
background noise. The dark red pixels are considered to be below the
background intensity value. Figure 4: Background flux and error for each NGC
1068 dataset as a function of the observation time. The different colors
represent the various polarizer filters (polarization axis angle of 0∘, 60∘
and 120∘ for the FOC instrument). Figure 5: Intensity histograms on which the
background (vertical dashed line) is estimated for each observation.

###  2.4 Data alignment.

The polarized data come from multiple observations with different polarizer
filter. To extract the polarization information in the Stokes convention, we
must sum the datasets, but it is only possible if the data have been
previously aligned. To do so, our method implements a 2D image alignment to
sub-pixel precision using a factor of 10 oversampling, allowing us to align
our images to a precision up to 0.1 pixel precision, corresponding to an
alignment precision between observations of 0.0014 arcsec. This is done
through cross-correlation of the phase-space of the misaligned images, as
described in Guizar-Sicairos et al. (2008). Each image is then linearly
shifted accordingly, using the relation in Eq. 2 to compute the value in each
pixel. Once aligned using the imaged large scale structures, the uncertainty
coming from the different observations shifts is computed from the
displacement with respect to the reference dataset. This uncertainty is
computed for each pixel in the resulting image, as half of the difference of
the values in this pixel before and after shifting the data (see Eq. 3). This
uncertainty is quadratically summed to the global uncertainty inside the
pixel:

$\displaystyle\begin{aligned} I_{x,y}^{shifted}(\Delta x,\Delta y)=&uv\cdot
I_{x+\lfloor{\Delta x}\rfloor,y+\lfloor{\Delta y}\rfloor}\\\
&+u(\mathrel{{1}{-}{v}})\cdot I_{x+\lfloor{\Delta x}\rfloor,y+\lceil{\Delta
y}\rceil}\\\ &+(\mathrel{{1}{-}{u}})v\cdot I_{x+\lceil{\Delta
x}\rceil,y+\lfloor{\Delta y}\rfloor}\\\
&+(\mathrel{{1}{-}{u}})(\mathrel{{1}{-}{v}})\cdot I_{x+\lceil{\Delta
x}\rceil,y+\lceil{\Delta y}\rceil}\end{aligned},$ (2)
$\displaystyle\sigma_{x,y}^{shifted}(\Delta x,\Delta
y)=\left|\frac{{I_{x,y}-I_{x,y}^{shifted}(\Delta x,\Delta y)}}{2}\right|,$ (3)
$\displaystyle\text{with }\left\\{\begin{aligned} &\Delta x,\Delta y\text{ are
the shifts along the x and y axis},\\\ &\lfloor\Delta x\rfloor,\lceil{\Delta
x}\rceil\text{ the floor and ceiling integers of }\Delta x,\\\ &u=\Delta
x-\lfloor\Delta x\rfloor,v=\Delta y-\lfloor\Delta
y\rfloor.\end{aligned}\right.$

###  2.5 Data binning

We propose several methods to re-sample the data. Assuming the target pixel
size is larger than the original pixel size, the user can resample the data in
arcsec or pixel units and can choose to do it by averaging or summing the
resampled data. This is done by re-binning the data matrix to a smaller shape
using matrix products with rows and columns compressors. This resampling,
while reducing the spatial resolution, allows us to get better statistics in
the resized pixel that now sums or averages the events from each sub-pixels.
This is mandatory to study polarization as polarized fluxes require high
statistics to become meaningful. In the extreme case scenario, the user can
integrate the whole image down to one pixel to simulate what a polarimetric
instrument without imaging capabilities would have observed. Uncertainties
computed from previous alignment and background subtraction procedures are
propagated through re-sampling as the quadratic sum of the errors of the bin.
This uncertainty is then quadratically summed to the root mean square (RMS) of
the flux of the sub-pixels of the bin, accounting for some baseline noise:

$\displaystyle\sigma_{X,Y}^{re-
sampling}=\sqrt{{RMS_{X,Y}^{f}}^{2}+{\sigma_{X,Y}^{propag}}^{2}},$ (4)
$\displaystyle\text{with }\left\\{\begin{aligned}
RMS_{X,Y}^{f}&=\frac{\sqrt{\sum_{(x,y)\in(X,Y)}f_{x,y}^{2}}}{\sum_{(x,y)\in(X,Y)}1},\\\
\sigma_{X,Y}^{propag}&=\sqrt{\frac{\sum_{(x,y)\in(X,Y)}\sigma_{x,y}^{2}\cdot
f_{x,y}}{\sum_{(x,y)\in(X,Y)}f_{x,y}}},\end{aligned}\right.$

where each pixel of the re-binned image at coordinates, $X,Y,$ correspond to a
subset of pixels $(x,y)\in(X,Y)$ in the original image of flux, $f_{x,y}$, and
associated error, $\sigma_{x,y}$.

###  2.6 Data smoothing

Several options are available for smoothing the data. The idea behind data
smoothing is to reduce noise from a data set to allow important patterns to
more clearly stand out. A user-defined function can be convolved to the
prepared data, before summing observations that were obtained through the same
polarizer filter. The same convolution procedure can also be done after data
combination. This convolution can be applied to a weighted dataset whose
weights, $w_{i,j}$, are the inverse square of the error for each pixel $x,y$:

$S_{xy}=(s*g)_{xy}=\sum_{i,j}^{N_{pixels}}s_{ij}\cdot w_{ij}\cdot
g(\mathrel{{x}{-}{i}},\mathrel{{y}{-}{j}}),$ (5)

where $g$ is some user-defined kernel to which the data should be convoluted.
The error of the smoothed pixel is computed by convoluting the square of the
errors to the convolution kernel squared:

$\sigma_{xy}^{smoothing}=\sqrt{(\sigma^{2}*g^{2})_{xy}}=\sqrt{\sum_{i,j}^{N_{pixels}}\sigma_{ij}^{2}\cdot
w_{ij}^{2}\cdot{g(\mathrel{{x}{-}{i}},\mathrel{{y}{-}{j}})}^{2}}.$ (6)

Another finer data smoothing combines and smooth the data from multiple
observation sets at the same time using a Gaussian kernel with user-defined
FWHM. Given $N$ observations through a given polarizer filter, the obtained
combined and smoothed pixel at coordinates $(x,y)$ is given by:

$S_{xy}=\frac{\sum_{k}^{N}\sum_{i,j}s^{k}_{ij}\cdot w^{k}_{ij}\cdot
g(\mathrel{{x}{-}{i}},\mathrel{{y}{-}{j}})}{\sum_{k}^{N}\sum_{i,j}w^{k}_{ij}\cdot
g(\mathrel{{x}{-}{i}},\mathrel{{y}{-}{j}})},$ (7)

where $s^{k}_{ij}$ is the signal of the pixel at $(i,j)$ for observation $k$,
$g(\mathrel{{x}{-}{i}},\mathrel{{y}{-}{j}})=e^{-\frac{(\mathrel{{x}{-}{i}})^{2}+(\mathrel{{y}{-}{j}})^{2}}{2\sigma^{2}}}$
is a Gaussian kernel with $\sigma=\text{FWHM}/(2\sqrt{2\ln{2}}),$ and
$w^{k}_{ij}=1/{e^{k}_{ij}}^{2}$ is the weight given by the inverse-squared
error of this same pixel. The error on the combined pixel is obtained by
taking the weighted root mean square of the errors:

$\sigma_{xy}^{smoothing}=\frac{\sqrt{\sum_{k}^{N}\sum_{i,j}{e^{k}_{ij}}^{2}\cdot{w^{k}_{ij}}^{2}\cdot{g(\mathrel{{x}{-}{i}},\mathrel{{y}{-}{j}})}^{2}}}{\sum_{k}^{N}\sum_{i,j}w^{k}_{ij}\cdot
g(\mathrel{{x}{-}{i}},\mathrel{{y}{-}{j}})}.$ (8)

###  2.7 Stokes parameters and polarization components computation.

Here, we describe how we computed the Stokes parameters and the uncertainties
arising from the polarization measurement. We refer to Kishimoto (1999) and
Clarke et al. (1972, p38, p100, p171) for more details. The FOC instrument is
not equipped with a circular polarization analyzer that would allow us to
characterize the ellipticity of the observed polarization. In the following,
we assume a linear polarization, with a Stokes parameter of $V=0$.

We computed the remaining $I$, $Q$, $U$ Stokes parameters from the addition
and subtraction of the theoretical flux through three polarizer filters with
complementary polarization axis angles ($\theta_{1}=0^{\circ}$,
$\theta_{2}=60^{\circ}$, $\theta_{3}=120^{\circ}$ for the FOC). We defined the
Stokes vector as $\mathbf{S}=(I,Q,U)$. We call $F_{i}$ the theoretical
polarized flux that is not attenuated by the polarizer filter with axis angle
$\theta_{i}$. We define the theoretical polarized flux vector by
$\mathbf{F}=\left(\frac{2f_{\theta_{1}}}{t_{1}},\frac{2f_{\theta_{2}}}{t_{2}},\frac{2f_{\theta_{3}}}{t_{3}}\right),$
where $t_{i}$ is the transmittance of the polarizer filter with axis oriented
to angle $\theta_{i}$. The general formula is the following:
$\mathbf{S}=A\cdot\mathbf{F}$ and the transformation matrix, $A,$ is given by
:

$\displaystyle
A=\frac{1}{N}\left[\begin{smallmatrix}k_{2}k_{3}\sin{(-2\theta_{2}+2\theta_{3})}&k_{3}k_{1}\sin{(-2\theta_{3}+2\theta_{1})}&k_{1}k_{2}\sin{(-2\theta_{1}+2\theta_{2})}\\\
-k_{2}\sin{2\theta_{2}}+k_{3}\sin{2\theta_{3}}&-k_{3}\sin{2\theta_{3}}+k_{1}\sin{2\theta_{1}}&-k_{1}\sin{2\theta_{1}}+k_{2}\sin{2\theta_{2}}\\\
k_{2}\cos{2\theta_{2}}-k_{3}\cos{2\theta_{3}}&k_{3}\cos{2\theta_{3}}-k_{1}\cos{2\theta_{1}}&k_{1}\cos{2\theta_{1}}-k_{2}\cos{2\theta_{2}}\end{smallmatrix}\right],$
(9) $\displaystyle\begin{aligned} \text{ where
\;}N=&k_{2}k_{3}\sin{(-2\theta_{2}+2\theta_{3})}+k_{3}k_{1}\sin{(-2\theta_{3}+2\theta_{1})}\\\
&+k_{1}k_{2}\sin{(-2\theta_{1}+2\theta_{2}).}\end{aligned}$

We then define $A^{\prime}$ such that $\mathbf{S}=A^{\prime}\cdot\mathbf{f}$
where $\mathbf{f}=(f_{\theta_{1}},f_{\theta_{2}},f_{\theta_{3}})$ is the
observed polarization flux vector.

The error is propagated through the transformation of the variance-covariance
matrix of the polarization flux, $\mathbf{f}$ ($V^{\mathbf{f}}$), to that of
the Stokes parameters $\mathbf{S}$ ($V^{\mathbf{S}}$), where we assumed no
correlation between the flux obtained through the different polarization
filters:

$\displaystyle V^{\mathbf{S}}=A^{\prime}V^{\mathbf{f}}A^{\prime T},$ (10)
$\displaystyle\text{\; with
\;}V^{\mathbf{S}}=\left[\begin{smallmatrix}\sigma_{I}^{2}&\sigma_{IQ}&\sigma_{IU}\\\
\sigma_{IQ}&\sigma_{Q}^{2}&\sigma_{QU}\\\
\sigma_{IU}&\sigma_{QU}&\sigma_{U}^{2}\end{smallmatrix}\right]\text{ ,
}V^{\mathbf{f}}=\left[\begin{smallmatrix}\sigma_{f_{\theta_{1}}}^{2}&0&0\\\
0&\sigma_{f_{\theta_{2}}}^{2}&0\\\
0&0&\sigma_{f_{\theta_{3}}}^{2}\end{smallmatrix}\right].$

The statistical uncertainty is computed after the combination of the observed
polarized flux for each Stokes parameter. The uncertainty on the polarized
flux $\sigma_{f_{\theta_{j}}}$ is calculated assuming Poisson noise in the
counts and $\forall k\neq j,\,\sigma_{f_{\theta_{j}}f_{\theta_{k}}}=0,$ as
they arise from different observations:

$\displaystyle{\sigma^{stat}_{S_{i}}}^{2}$
$\displaystyle=\sum_{j=1}^{3}\left|\frac{\partial S_{i}}{\partial
f_{\theta_{j}}}\right|^{2}\cdot\sigma^{2}_{f_{\theta_{j}}}\;$
$\displaystyle\text{ for }S_{i}\in\left[I,Q,U\right],$ (11)
$\displaystyle\sigma_{f_{\theta_{j}}}$
$\displaystyle=\sqrt{\frac{r_{j}}{t_{j}}}\;$ $\displaystyle\text{ for
}f_{\theta_{j}}\in\left[f_{\theta_{1}},f_{\theta_{2}},f_{\theta_{3}}\right],$
(12)

with $\forall j$, $r_{j}$ represent the rate and $t_{j}$ is the exposure time
for the polarized flux, $f_{\theta_{j}}$. We compute the partial derivative of
$S_{i}$ with respect to $f_{\theta_{j}}$, knowing that $\forall
j,\frac{\partial A^{\prime}}{\partial f_{\theta_{j}}}=0$:

$\frac{\partial S_{i}}{\partial
f_{\theta_{j}}}=\sum_{k=1}^{3}{A^{\prime}}_{ik}\frac{\partial
f_{\theta_{k}}}{\partial f_{\theta_{j}}}=A^{\prime}_{ij}.$ (13)

The polarizer filters axis angle is known to an uncertainty of $3^{\circ}$
(Nota & et al., 1996) and this error comes into account when computing the
Stokes parameters as they explicitly depend on $\theta_{1,2,3}$ through the
transformation matrix (Eq. 9). Assuming $\sigma_{\theta}=3^{\circ}$, we
compute the uncertainties from the polarizer filters orientation as follows:

${\sigma^{axis}_{S_{i}}}^{2}=\sum_{j=1}^{3}\left|\frac{\partial
S_{i}}{\partial\theta_{j}}\right|^{2}\cdot\sigma^{2}_{\theta_{j}}\;\text{ for
}S_{i}\in\left[I,Q,U\right],$ (14)

where we compute the partial derivative of $S_{i}$ with respect to
$\theta_{j}$ assuming $\forall k\neq j,\frac{\partial
f_{\theta_{k}}}{\partial\theta_{j}}=0$:

$\frac{\partial
S_{i}}{\partial\theta_{j}}=\frac{1}{N}\left[\sum_{k=1}^{3}\frac{\partial
a^{\prime}_{ik}}{\partial\theta_{j}}f_{\theta_{j}}-S_{i}\frac{\partial
N}{\partial\theta_{j}}\right]\text{\; with }a^{\prime}=N\cdot A^{\prime}.$
(15)

These uncertainties are quadratically summed to the previously computed
propagated errors.

We then rotated Stokes parameters to have north directed up. From the header
keyword ORIENTAT providing the angle between north and the image’s y axis in
the northeast direction, we get $\alpha$ the rotation angle. We transform the
Stokes parameters and covariance matrix in the following way :

$\displaystyle\mathbf{S}_{r}=R_{I}\left(-2\alpha\right)\cdot\mathbf{S},$ (16)
$\displaystyle V^{\mathbf{S}}_{r}=R_{I}\left(-2\alpha\right)\cdot
V^{\mathbf{S}}\cdot{R_{I}\left(-2\alpha\right)}^{T},$ (17)
$\displaystyle\text{where
}R_{I}\left(-2\alpha\right)=\left[\begin{matrix}1&0&0\\\
0&\cos{(2\alpha)}&\sin{(2\alpha)}\\\
0&-\sin{(2\alpha)}&\cos{(2\alpha)}\end{matrix}\right].$

The polarization degree and angle are determined from the Stokes parameters by
the following well-known equations:

$\displaystyle P$ $\displaystyle=\frac{\sqrt{Q^{2}+U^{2}}}{I},$ (18)
$\displaystyle\theta_{P}$
$\displaystyle=\frac{1}{2}\arctan\left(\frac{U}{Q}\right).$ (19)

And the associated errors are propagated as follows:

$\displaystyle\sigma_{P}$ $\displaystyle=\frac{1}{I}$
$\displaystyle\left(\frac{Q^{2}\sigma_{Q}^{2}+U^{2}\sigma_{U}^{2}+2QU\sigma_{QU}}{Q^{2}+U^{2}}+\frac{Q^{2}+U^{2}}{I^{2}}\sigma_{I}^{2}\right.,$
(20)
$\displaystyle\;\left.-\frac{2Q}{I}\sigma_{IQ}-\frac{2U}{I}\sigma_{IU}\right)^{\frac{1}{2}}$
$\displaystyle\sigma_{\theta_{P}}$ $\displaystyle=$
$\displaystyle\frac{1}{2\left(Q^{2}+U^{2}\right)}\left(U^{2}\sigma_{Q}^{2}+Q^{2}\sigma_{U}^{2}-2QU\sigma_{QU}\right)^{\frac{1}{2}}.$
(21)

Due to the presence of noise, the normalized Stokes parameters are the only
estimates of the true normalized Stokes parameters. To correct this bias, in
the following, we refer to the polarization degree as its improved estimator:
the debiased polarization degree of $P_{debiased}=\sqrt{P^{2}-\sigma_{P}^{2}}$
(Simmons & Stewart, 1985).

##  3 Benchmarking our pipeline against NGC 1068

In order to test our pipeline, we decided to re-analyze the FOC data of NGC
1068. This is the most archetypal type-2 (edge-on) radio-quiet AGN and thus
the best target for benchmarking. It possesses the largest database of radio-
to-UV polarization measurements (Marin, 2018) and was even part of the
original catalog of Carl Seyfert (Seyfert, 1943). Its proximity to Earth
($z\approx$ 0.00379, which corresponds to a Hubble distance of $\sim$ 13.48
Mpc in the standard $\Lambda$CDM model) allows us to resolve the first
hundreds of parsecs thanks to the spatial resolution of the FOC (at $z$ =
0.00379, 1” equals 81.5 pc). NGC 1068 was observed by the FOC on Sep 30, 1993
(10:32AM) and on Feb 28, 1995 (5:33AM), with the respective program IDs 3504
and 5144. However, the first observation (1993) was badly saturated along the
AGN core direction due to an improper estimation of the expected UV flux
(Capetti et al., 1995a). We thus focus our work on the second observation
(1995). The dataset was obtained through the F253M UV filter centered around
2530 Å, together with the polarizing filters POL0, POL60, POL120. The optical
relay f/96 was selected to obtain a FoV of 7” $\times$ 7” and a pixel size of
0.014” $\times$ 0.014”. It results in a 512 $\times$ 512 pixelated image of
the source and its environment. Each polarizing filter acquired $\sim$ 3 500
seconds worth of observation for a total exposure time of 10 581 seconds. This
observation was first published by Capetti et al. (1995b) and further analyzed
by Kishimoto (1999).

Figure 6:  Total flux Fλ (erg.s-1.cm-2.Å-1, color-coded) of NGC 1068, with the
polarization information superimposed to the image using white vectors. The
linear polarization degree is proportional to the vector length while the
polarization position angle is indicated by the orientation of the vector (a
vertical vector indicating a polarization angle of 0∘). North is up, east is
left. We show the full FoV so that no potential information is lost. A spatial
bin corresponds to 0.1”. The contours are displayed from 1% to 99% every 10%
of the maximum value of $4.863\cdot 10^{-14}$ erg.s-1.cm-2.Å-1. The smoothness
of the contours is tightly linked to the amount of smoothing done in the
reduction process.

In Fig. 6, we show the total intensity map with the polarization information
superimposed to it. We rebinned the data in order to get a pixel size of 0.1”,
similarly to Capetti et al. (1995b) for a direct comparison. The pixels were
smoothed by a Gaussian kernel of standard deviation 0.2”. Only the bins with a
S/N higher than 30 in total flux and higher than 3 in polarization have their
polarization vectors shown. We display in the top-left corner of the figure
the total flux, polarization degree, and polarization angle as integrated over
the whole FoV. At 2555Å pivot wavelength we observe an integrated flux of
$(48.63\pm 3.21)\cdot 10^{-15}$ erg.s-1.cm-2.Å-1 with a polarization of
$11.4\pm 0.2$ % at position angle $97.6\pm 0.4^{\circ}$. The total flux image
is dominated by a compact region of about 3 $\times$ 3 pixels (0.3” $\times$
0.3”) that is situated at the base of the polar outflows that extend in the
northern and southern directions, although the northern part is much more
visible in total flux. The southern part suffers from slightly higher
reddening from the dust of the host galactic plane (Kishimoto, 1999). The
polarization vectors allow to highlight the double-conical morphology of the
winds, with a much higher contrast than in pure intensity. The polarization
pattern seen in the winds is centro-symmetric, pinpointing the source of
emission even if it is hidden by an optically thick dusty region. This
circumnuclear region, often called the ”torus”, is not coincident with the
brightest spot of total flux but is immediately below it ($\sim$ 0.3” towards
the south), where the total intensity decreases due to heavy absorption by the
dust and gas mixture (Kishimoto, 1999). Focusing on the regions with the
highest S/N, the structure of the bi-polar winds is revealed thanks to
polarimetry. The polarization degree in the brightest region is of the order
of 15 – 20% and significantly increases along the winds, up to 35 – 40%.

Figure 7: Comparison of the integrated polarization obtained by this pipeline
through a simulated aperture of 1” diameter (green encircled region) to the
one obtained by Antonucci et al. (1994) with the FOS spectropolarimeter. The
FOC data was binned to a pixel of 0.1” and smoothed with a Gaussian of a FWHM
of 0.2”. The polarization vectors are shown for
$\left[\text{S/N}\right]_{P}\geq 3$ and $\left[\text{S/N}\right]_{I}\geq 30$.

A direct comparison with the results of Capetti et al. (1995b) validates ours
results. The centro-symmetric pattern is well reproduced and the differences
in morphology observed between the northern and southern outflows coincides
between Fig. 2 in Capetti et al. (1995b) and our Fig. 6 with a S/N cut of 30
in total flux. We find similar polarization degrees in various positions in
the winds, with the exception of the location of the highest patch of
polarization degree. In Capetti et al. (1995b), the authors detect a 65%
polarization level immediately west of the brightest spot of total flux, while
such this region only displays 20% linear polarization in our results. This is
very likely due to the different steps between the two reduction pipelines.
While in Capetti et al. (1995b) the errors in the Stokes parameters were
computed assuming Poisson statistics, we propagated the errors from the
calibrated data from the archive. In addition, the smoothing of the image can
play a crucial role in blurring or increasing the polarization of a given
pixel. No indication on the smoothing process were given in Capetti et al.
(1995b), but we tried using different Gaussian kernels without succeeding to
find the same patch of high polarization. On the other hand, we note that
Kishimoto (1999) re-analyzed the same data and neither found this 65%
polarization spot. It indicates that there might have been a small
misalignment effect or a numerical artifact in the reduction method of Capetti
et al. (1995b). There are, in fact, no evident reasons why such a high
polarization degree should exist outside the polar winds half-opening angle,
directly west of the torus location, where the central irradiation should be
absorbed by the circumnuclear dust wall. We also note that we present a much
wider view of NGC 1068, while Capetti et al. (1995b) cropped their results to
a FoV of 3.3” $\times$ 2.9”. Integrating the total flux over the 7” $\times$
7” image with a binning of 0.10” and a Gaussian combination smoothing of a
FWHM of 0.20” gives us about 4.86 $\pm$ 0.32 $\times$ 10-14 erg.s-1.cm-2.Å-1,
which agrees with the 4.79 $\pm$ 0.20 $\times$ 10-14 erg.s-1.cm-2.Å-1 flux
recorded by the International Ultraviolet Explorer (IUE) for a 10” $\times$
20” fixed aperture at 2700 Å, see Kinney et al. (1993). The integrated
polarization degree and polarization angle are 11.4% $\pm$ 0.2% and 97.6∘
$\pm$ 0.4∘, respectively. These values are in good agreement with the WUPPE
polarization measurement of NGC 1068 made by Code et al. (1993), who found
12.9% $\pm$ 1.9% and 112∘ $\pm$ 3.8∘ for an aperture of 6” $\times$ 12”.
Through the 1” aperture of the Faint Object Spectrograph (FOS) centered on the
peak of the continuum emission, Antonucci et al. (1994) measured a degree of
polarization of 17.2% $\pm$ 1.1% and a position angle of 91.1∘ $\pm$ 1.8∘ in
the range 2460–2760 Å. By simulating a 1” diameter aperture on the FOC data,
we obtained 10.7% $\pm$ 0.1% and a position angle of 91.0∘ $\pm$ 0.7∘(see Fig.
7).

Figure 8: Direct comparison of the polarization map obtained by this pipeline
to the one obtained by Kishimoto (1999) for the same 10 pixel binning, without
smoothing and taking the intersection of both maps cut at
$\left[\text{S/N}\right]_{P}\geq 3$ and $\left[\text{S/N}\right]_{I}\geq 30$.
Figure 9: Distribution of the polarization degree obtained by this pipeline to
the one obtained by Kishimoto (1999) in the same cut at
$\left[\text{S/N}\right]_{P}\geq 3$ and $\left[\text{S/N}\right]_{I}\geq 30$.
Figure 10: Degree of alignment of the polarization angle obtained by this
pipeline to the one obtained by Kishimoto (1999) in the same cut at
$\left[\text{S/N}\right]_{P}\geq 3$ and $\left[\text{S/N}\right]_{I}\geq 30$.

Another test was made by comparing our polarization map to the one of
Kishimoto (1999). In this case, we used a 10 pixel binning, without smoothing,
and taking the intersection of both maps cut at
$\left[\text{S/N}\right]_{P}\geq 3$ and $\left[\text{S/N}\right]_{I}\geq 30$.
The results are shown in Fig. 8. The polarization pattern reproduces the shape
of the figure from Kishimoto (1999), as the exact same location of the
statistically significant pixels. We note, however, a slight difference in the
vector length, likely due to a different background estimation. In Kishimoto
(1999), the background is estimated by finding a plateau in the outskirt of
the radial flux profile as a function of the distance from the center, this
plateau value is taken to be the image background. As this sort of technique
fails to properly estimate a background value for polluted sources (as we will
see with IC 5063 in section 4), we chose to implement a more general approach,
hence the possible difference.

In Fig. 9, we compare the measured polarization degree from each analysis
pipeline using a Gaussian fit. As observed on the superimposed polarization
maps, the detected polarization degree is slightly higher from this pipeline
with a mean at 23% and a larger distribution than from Kishimoto (1999), which
shows a mean at 19% and a more peaked distribution. Hence, the two pipelines
give similar results within the uncertainties. The difference most likely
comes from the method of background subtraction and how we estimate the
uncertainties, as we use the debiased polarization degree.

To compare the alignment of the obtained polarization angles in each pixel, we
use circular statistics and introduce the metric $\zeta$ (Clark & Hensley,
2019), as defined in Eq. 22, with $\theta_{1}$ as the polarization angle from
Kishimoto (1999) and $\theta_{2}$ the one from this pipeline.

$\displaystyle\zeta=\cos{(2\delta\theta)},$ (22) $\displaystyle\text{with
}\delta\theta=\frac{1}{2}\arctan{\left[\frac{\sin{(2\theta_{1})}\cos{(2\theta_{2})}-\cos{(2\theta_{1})}\sin{(2\theta_{2})}}{\cos{(2\theta_{1})}\cos{(2\theta_{2})}+\sin{(2\theta_{1})}\sin{(2\theta_{2})}}\right],}$
$\displaystyle\text{and }\theta_{1},\theta_{2}\text{ the angles to be
compared.}$

Here, $\zeta$ is defined on the range of [$-1$, 1], such that two perfectly
aligned distributions will have $\zeta$ = 1, two perpendicular distributions
will have $\zeta$ = $-1$, and two distributions with no statistical alignment
will have $\zeta$ = 0.

From Fig. 10, we can see that both pipeline get almost identical polarization
angles, $\zeta>0.8$, where the polarized flux is stronger and where the
statistics are better. Outside of these regions of high S/N, and where
background estimation and uncertainties becomes non-negligible, the alignment
is less strong, but still in agreement. Since the whole HST/FOC dataset was
re-processed in 2005 with new geometric references and the latest filter
calibrations (Kamp et al., 2006), the archival data are intrinsically
different from the science data that were used during the FOC lifetime. This
can explain the differences in the polarization degree histogram in Fig. 9 and
the polarization angle misalignment in the clouds N-W and S-E of the nucleus
location in Fig. 10. Additionally, it became important to align the different
observation by cross-correlation and not by using the images shifts provided
by Hodge (1996). These were used for the data reduction by Kishimoto (1999)
but the new best geometric reference modified these values, as it can be seen
in Fig. 11, in which the observations are incorrectly shifted using the pixel
shifts values from Hodge (1996).

Figure 11: Same as Fig. 8, except that the alignment uses the shift values
from Hodge (1996); i.e., there is no cross-correlation, highlighting the fact
that the 2005’s re-calibrated dataset have updated geometric properties in
comparison to the dataset used in Capetti et al. (1995a, b) and Kishimoto
(1999).

A deeper examination of the flux and polarization pattern of NGC 1068 is
presented in the mosaic of Fig. 12. Here we plot zoomed-in maps of the AGN,
showing the total flux (top-left), polarized flux (top-right), polarization
degree (bottom-left), and polarization position angle (bottom-right).
Comparing the total and polarized flux map, we see that the sinuous shape of
the winds is much more emphasized by the polarized flux, where reprocessing is
clearly revealed. This makes it possible to identify the geometry of the winds
with greater precision, using the fact that polarization offers a better
contrast than total flux images.

Figure 12: Four different zoomed-in outputs of the pipeline for NGC 1068 with
the polarization map superimposed. The polarization vectors are only displayed
for the selected cut of $\left[\text{S/N}\right]_{P}\geq 3$ and
$\left[\text{S/N}\right]_{I}\geq 30$. The integrated values are computed on
the full FoV ($P^{int}$ and $\theta_{P}^{int}$). Top-left: Total flux
$F_{\lambda}$ (erg.s-1.cm-2.Å-1, in log-scale). Top-right: Polarized flux
$F_{\lambda}\cdot P$ (erg.s-1.cm-2.Å-1). Bottom-left: Polarization degree $P$
(%). Bottom-right: Polarization angle $\theta_{P}$ (in °, taken in the
trigonometric direction with north being 0°).

Different types of data smoothing were implemented in the pipeline to allow
reproduction of older data reductions and results. A simple Gaussian smoothing
with a FWHM determined by a pixel radius allow to reproduce the data reduction
as usually done by previous papers (see Capetti et al., 1995b; Antonucci et
al., 1994). However, for future works, we prefer to use smoothing weighted on
each pixel related error. A comparison between these smoothing methods can be
seen in Fig. 13 and it highlights the better S/N permitted by a simple
Gaussian smoothing and the improved definition of spatially resolved
structures using weighted methods.

Figure 13: Four different zoomed-in outputs of the pipeline for NGC 1068 with
the polarization map superimposed. The polarization vectors are only displayed
for the selected cut of $\left[\text{S/N}\right]_{P}\geq 3$ and
$\left[\text{S/N}\right]_{I}\geq 30$. This juxtaposition shows different
smoothing methods, all maps are binned to 0.1” pixels. Top-left: Without
smoothing. Top-right: Simple Gaussian smoothing of FWHM of 0.2”. Bottom-left:
Gaussian smoothing with FWHM of 0.2” where pixels are weighted with their
inverse squared error. Bottom-right: Combination and weighted Gaussian
smoothing where the different observation through a same polarizer filter are
both averaged and smoothed at the same time for a better reduction.

##  4 Uncharted FOC observation of IC 5063

Once we have made sure our pipeline produces valid polarization maps, we can
undertake the exploration of one of the unpublished AGN observations in the
FOC archives: IC 5063. We leave the remaining unexplored AGNs for the next
papers of this series.

IC 5063 is a nearby elliptical galaxy ($z\approx$ 0.01135, corresponding to a
Hubble distance of $\sim$ 48.32 Mpc in the standard $\Lambda$CDM model). It is
a radio-loud galaxy, with a bright red nucleus. The latter characteristic can
either come from a very steep non-thermal spectrum (with spectral index -4.5)
or by re-radiation from hot dust with a black-body color temperature of 650 K
(Axon et al., 1982). In 1987, a high polarization degree (17.4 $\pm$ 1.3 % at
PA $\approx 4\pm 5$° in $H$ and $K$ bands) was measured in near-infrared for a
$2.25$ arcseconds aperture centered on the nucleus (Hough et al., 1987). This
suggests a non-thermal synchrotron source for the near-IR emission from the
nucleus. The detection of a strong, broad H$\alpha$ emission seen in polarized
flux also suggests the existence of a hidden broad-line region (Inglis et al.,
1993), pointing towards a hidden type-1 AGN nested in the dusty heart of an
elliptical galaxy. Indeed, a prominent dust lane has been observed along the
long axis of IC 5063, mostly concentrated on the northern side. The
symmetrical distribution of this dust lane and its continuity outside of the
nucleus spanning a few kiloparsecs suggest an external origin, most probably a
previous merger, as such structures are unlikely to survive many dynamical
timescales (Colina et al., 1991). Finally, it has been observed that this AGN
displays strong interactions between the ISM and its radio jets (radio
position angle $\sim$ 115∘, Morganti et al., 1998) that introduce complex
emission regions along the jets (Oosterloo et al., 2000). These regions
spanning a few hundred parsecs are a perfect observational target for the FOC
thanks to its fine spatial resolution (at $z=$ 0.01135, 1” equals to 241.7
pc).

IC 5063 was observed by the FOC on Feb 25, 1998 (program ID 5918). The
observation used the F502M filter centered around 4985 Å, for an exposure time
of 5 261 seconds through each POL0, POL60 and POL120 filters. This adds up to
a total observation time of 15 783 seconds. The observation was reduced in
total flux by Dasyra et al. (2015), in particular, their Fig. 8, and allowed
for the identification of discrete gas-outflow starting points along the radio
jets. However, no polarization study has ever been published despite the
rather good quality of the data.

Some concern may arise about the potential contamination (dilution) from the
extended [O III] polar emission that could impact our resulting maps. Indeed,
we can see from Venturi et al. (2021) Fig. 1 (c) that the HST/FOC FoV is
totally embedded in the [O III] emission region. These emission lines are
formed when atoms from the polar region are photo-ionized by the continuum
radiation from the central source. Photo-ionization produces unpolarized
photons (Lee et al., 1994; Lee, 1994), so our whole map is subject to
polarization dilution by the [O III] emission. As such, it likely decreases
the observed polarization degree ($P$), but it should not change the
polarization angle ($\theta_{P}$). There should not be misleading polarization
patterns.

###  4.1 Characteristics of the optical polarization map

We processed the observation of IC 5063 through our pipeline and we present
the resulting 4985 Å-centered polarization map in Figs. 14 and 15. We show the
total intensity map with the polarization information superimposed to it. We
rebinned the data to get individual spatial bins of 0.1” and the pixels were
smoothed by a Gaussian kernel of standard deviation 0.2”. Only the bins with a
$\left[\text{S/N}\right]_{I}\geq 30$ and $\left[\text{S/N}\right]_{P}\geq 3$
have their polarization vectors shown. We lowered the cut to $3\sigma$ in
polarization degree due to lower polarized flux coming from the the AGN
compared to the $5\sigma$ cut on the observation of NGC 1068.

The total flux image is dominated by a croissant-shaped region that is
situated near the base of the jets (RA 20h52m02.4s, DEC -57°04’08”), but it
does not necessarily corresponds to the location of the hidden nucleus. We
remind the reader that the central engine is obscured by a circumnuclear
reservoir of dust, so it is not directly visible in total flux. This bright
croissant most likely results from: a) the re-emission of the ISM by the
interaction of the jet with the host galaxy and/or b) the scattering of
photons thermally emitted from the central accretion disk. The opposite jets,
invisible in UV/optical light due to Doppler beaming outside our line-of-
sight, extend towards the southeast and northwest directions. The lobes of the
jets, detected in radio and seen superimposed on the polarization map in Fig.
17, match two regions with a higher intensity than the background light,
together with specific morphologies. The northwest lobe region shows a
peculiar $V$ shape that could result from the interaction of the northern jet
with the material expelled by the central engine before the onset of jet
activity. This material is likely to be the narrow line region (NLR) across
the host galaxy that we observe in many radio-quiet AGNs (see the case of NGC
1068). In the southern part, a less intense, diffuse clumpy emission can be
seen. This can be due to the fact that the southeast jet and lobe are obscured
by the dusty disc of the host galaxy and the medium they interact with is
responsible for the observed optical/UV radiation.

Figure 14: Total flux Fλ (erg.s-1.cm-2.Å-1, color-coded) of IC 5063, with the
polarization information superimposed to the image using white vectors. The
data is re-sampled to have bins of 0.1” and smoothed with a Gaussian kernel of
FWHM of 0.2”. The polarization vectors are displayed for
$\left[\text{S/N}\right]_{I}\geq$ 30 and $\left[\text{S/N}\right]_{P}\geq$ 3
in white, for $\left[\text{S/N}\right]_{P}\geq$ 2 in red and for
$\left[\text{S/N}\right]_{P}\geq$ 1 in blue. Their lengths are proportional to
$P$. The contours are displayed from 1% to 99% every 10% of the maximum value
of $1.727\cdot 10^{-15}$ erg.s-1.cm-2.Å-1. Figure 15: Two different outputs of
the pipeline for IC 5063 with the polarization map superimposed. The
polarization vectors are only displayed for the selected cut of
$\left[\text{S/N}\right]_{I}\geq$ 30 and $\left[\text{S/N}\right]_{P}\geq$ 3
in white, for $\left[\text{S/N}\right]_{P}\geq$ 2 in red and for
$\left[\text{S/N}\right]_{P}\geq$ 1 in blue. The integrated values are
computed on the full FoV ($P^{int}$ and $\theta_{P}^{int}$). Left:
Polarization degree $P$ (%). Right: Polarized flux $F_{\lambda}\cdot P$
(erg.s-1.cm-2.Å-1).

###  4.2 Region-by-region exploration and correlation to radio and IR data

IC 5063 appears to show a lot of complex interactions between the jets, the
AGN winds and the local galactic material. Thus, we divided the HST/FOC map in
six distinct regions. These regions are listed in Tab. 2 and delimited in Fig.
16. These specific regions are individually explored through the polarization
information made available by the HST/FOC observation and correlated with
observations at other wavelengths:

  * •

In Fig. 17, we show the superposition of our HST/FOC map with the 18 GHz ATCA
map provided by Morganti et al. (1998). Due to small discrepancies between
between ATCA and HST respective WCS coordinates ($\sim$ 0.5” error), both maps
were manually aligned with the hypothesis that the hidden nucleus is right
below the croissant-shaped high flux and is the center of the radio emission.

  * •

In Fig. 18, we make use of the F606W filter of the Wide Field and Planetary
Camera 2 (WFPC2) of the HST to highlight the presence and position of the dust
lane. Due to differences of the HST pointing between 1995 and 1998 ($\sim$ 1”
error), the WFPC2 and FOC maps were manually aligned with the hypothesis that
the croissant-shaped high flux in both near-UV and near-IR are of similar
origin. We inverted the color-map for the near-IR map in order to better see
the extension of the dust-lane on the northern part of the AGN.

Region | $F_{\lambda}^{int}$ | $P^{int}$ | $\theta_{P}^{int}$ | radio PA - $\theta_{P}^{int}$
---|---|---|---|---
FoV | $611.4\pm 52.6$ | $1.9\pm 0.3$ | $87.2\pm 3.0$ |  $\sim$ 28
1 | $5.684\pm 0.085$ | $20.4\pm 2.3$ | $38.5\pm 3.4$ |  $\sim$ 77
2 | $87.02\pm 0.18$ | $0.7\pm 0.4$ | $36.8\pm 13.7$ |  $\sim$ 78
3 | $39.16\pm 0.13$ | $0.7\pm 0.6$ | $9.9\pm 21.9$ |  $\sim$ 105
4 | $4.247\pm 0.338$ | $29.4\pm 13.2$ | $88.4\pm 11.4$ |  $\sim$ 26
5 | $90.38\pm 0.32$ | $4.9\pm 0.6$ | $91.0\pm 3.1$ |  $\sim$ 23
6 | $26.75\pm 0.11$ | $5.8\pm 0.7$ | $142.4\pm 3.6$ |  $\sim$ -27

Table 2: IC 5063 optical polarization maps integrated over the specific
regions displayed on Fig. 16. The first line corresponds to the full FoV
integrated data. Fluxes are in 10-17 ergs cm-2 s-1 Å-1, $P^{int}$ in percents
and $\theta_{P}^{int}$ in degrees. The radio position angle (PA) has been
measured by Morganti et al. (1998) and is about 115∘. Figure 16: Optical
polarization map for IC 5063 obtained through the pipeline. The polarization
vectors are displayed for $\left[\text{S/N}\right]_{I}\geq$ 30 and
$\left[\text{S/N}\right]_{P}\geq$ 3 in white, for
$\left[\text{S/N}\right]_{P}\geq$ 2 in red and for
$\left[\text{S/N}\right]_{P}\geq$ 1 in blue and the overlaid regions are
listed in Tab. 2 and detailed in the text. Figure 17: 18 GHz ATCA map from
Morganti et al. (1998) superimposed onto our HST/FOC map. Both maps have been
aligned on the supposed nucleus location. The optical polarization vector have
a fixed length to better highlight their orientation. Figure 18: Total flux of
IC 5063 at $5997$ Å observed by HST/WFPC2 in 1995. The superimposed
polarization vectors, shown with a constant length for better visualization,
are taken from the polarization map at $4985$ Å from this paper. They are
displayed for the selected cut of $\left[\text{S/N}\right]_{I}\geq$ 30 and
$\left[\text{S/N}\right]_{P}\geq$ 3 in white, for
$\left[\text{S/N}\right]_{P}\geq$ 2 in red and for
$\left[\text{S/N}\right]_{P}\geq$ 1 in blue (less significative). Both maps
have been aligned on the croissant-shaped high flux region.

####  4.2.1 Region 1: Northern AGN winds

The first region we investigate corresponds to a zone that is beyond the
interaction of the northern jet and the local medium. It is relatively
unperturbed and matches the location of the extended NLR seen in [O III]
emission by Colina et al. (1991). The polarization degree we measure is high,
on the order of 36%, associated with a polarization position angle of $\sim$
30∘. Compared to the position angle of the extended [O III] emission and of
the radio jets (115∘), the polarization angle appears perpendicular. This,
together with the high degree of polarization, indicates that scattering
prevails in this region. The light we observe directly comes from the obscured
central engine through perpendicular scattering onto the winds that act like a
mirror. In addition, this result agrees with the polarization angle and degree
observed in optical by Inglis et al. (1993) ($\sim$ 10–30% at $\sim$ 30–50∘).
Any spectropolarimetric attempt to measure broaden Balmer lines in polarized
flux should then focus on this region to be free from the turbulence and
emission caused by the northern jet and lobe. Interestingly, our independent
detection of the undisturbed NLR allows us to say that IC 5063 did have polar
winds before the onset of jet activity, but the ionization cone and the NLR
structures have been almost completely wiped out by the jet within the first
arc-seconds around the core.

####  4.2.2 Region 2: Southern lobe

The second brightest spot in flux at the 4985 Å-centered optical waveband is
situated on the southwestern part of the AGN and corresponds to a zone where
the counter jet seem to interact with the local medium. This region of high
flux is almost completely depolarized. We can see from the superposition of
the radio map to the optical data (Fig. 17) that this depolarized region also
corresponds to the southern lobe. This depolarization seen in near-UV may
originate from a scattering medium perturbed by the jet and lobe, resulting in
a complex reprocessing environment producing polarized photons with various
polarization angles and, thus, resulting in a net depolarization of the photon
flux. We note, however, the presence of a circular polarization pattern where
the lobe encounters the ISM. In these region, the medium might be kinetically
aligned by the jet’s lobe pushing the medium out of its way, but the
statistical significance of the detection per pixel is below 3$\sigma$.
However, Table 2 shows that integrating the whole lobe region gives a
polarization $\sim$1% with a $\left[\text{S/N}\right]_{P}$ of 6.5. This is a
clear detection of a polarized source at a PA $\sim 15^{\circ}$, almost
perpendicular to the jet direction.

####  4.2.3 Region 3: Northern lobe

From Morganti et al. (1998), we know that this AGN is characterized by fast
gas outflows fueled from the central core. In this region located between the
hidden nucleus and the unperturbed wind, where the radio map highlight the
presence of the northern lobe, we detected a low degree of polarization ($\sim
2.6\pm 0.5$%), probably for the same reason as stated above for the southern
lobe. Also, similarly to the southern lobe, the associated PA $\sim
10^{\circ}$ corresponds to a direction that is perpendicular to the radio jet.
Furthermore, the V-shape seen in the 4985 Å–centered optical waveband most
likely indicate a highly interactive region where the radio jet, the polar
wind, and the ISM meet.

####  4.2.4 Region 4: Dust lane

On the northern part of the HST/FOC map, we can see a clear cut in logarithmic
scale on the flux intensity map. We know from Morganti et al. (1998), in
particular, their Fig. 4, that this obscured region in optical corresponds to
the extension of the dust lane, which is confirmed by the WFPC2 infrared map
(Fig. 18). Using the spatial capabilities of the FOC, we can isolate and
integrate the polarization from this dusty region. Given the low flux from
this specific region, we get higher errors but we do observe a high
polarization degree, around 18% at $\sim$ 84∘, exactly along the position
angle of the dust lane. The high polarization degree and the polarization
angle parallel to the dust lane strongly suggest dichroic absorption from
starlight in the foreground dust lane. The integrated PA could then highlight
the large-scale ordered magnetic field in the dust lane.

####  4.2.5 Region 5: Diffuse medium

The map of IC 5063 can essentially be divided in three parts : the northern
section that is dominated by the dust lane, the southeast to northwest
diagonal that corresponds to the highly asymmetric AGN, and the southern part
that is essentially the ISM, a diffuse medium where Maksym et al. (2020)
identified ”dark rays.” That is to say, the projected shadow of the
circumnuclear dusty torus. For completeness, we investigated this region and
found a low polarization degree ($\sim$ 1%) and with a polarization position
angle $\sim$ 123∘, namely, it is parallel to the jet radio axis. Because the
southern region of the map is not as much obscured as the northern region, the
observed polarization either results from dichroic absorption and re-emission
of host starlight passing through the diffuse medium, or it could be the
imprint of the magnetic field of the galaxy itself. Deeper (and longer)
observations would be needed to assess the correct interpretation.

####  4.2.6 Region 6: Highly polarized knot

This region is characterized by a high S/N associated to a strong polarized
flux. It is just north of the estimated position of the nuclei and goes across
the croissant-shaped region of highest flux. We measured a high polarization
degree at $6.1\pm 0.4$% associated with a polarization angle of $151.2\pm
1.7^{\circ}$. We learn from Lopez-Rodriguez et al. (2013) that the central 1.2
arcsec of IC 5063 in J, H, and Kn band was measured to be 2.0±0.7%, 2.5±0.9%,
and 7.8±0.5%, respectively, and that the PA of polarization is wavelength-
independent (within the error bars) and measured to be $3\pm 6^{\circ}$ in the
three filters. In this HST/FOC observation we get a high polarization degree
because we are less diluted by the host starlight in the UV than in the IR,
but the different PA we get with respect to Lopez-Rodriguez et al. (2013)
indicates some pollution by either the jet or by the dust lane. As the PA-
radioPA is similar to region 4, we estimate that we get a mix of signals from
the dust lane and additionally from a region situated further away from the
torus height. We can confirm that this is not the jet polarization, as
otherwise we would see it all along the jet structure (also, due to Doppler
boosting outside of our line-of-sight, this would not be a reasonable
explanation). It is more likely that the polarization observed in UV comes
from dichroic absorption from the dust lane of AGN core photons scattered in
our line of sight by the jet base or the ionized wind base.

##  5 Discussion

We went on to test our new reduction pipeline against NGC 1068 and applied it
to IC 5063 with the results detailed above. Here, we discuss this process,
along with two more points related to our IC 5063 analysis and to the use of a
different background noise estimator than usual.

###  5.1 Past polarimetry of IC 5063

In contrary to, for instance, NGC 1068 or NGC 4151 (Marin et al., 2018, 2020),
IC 5063 has not been extensively observed in optical polarimetry. This is due
to the fact that its optical polarization is strongly affected by both
interstellar polarization and dilution by the host galaxy, but also because of
the presence of the dust lane that hides a significant fraction of the AGN.
From the archives, we were able to retrieve four papers that present optical
and/or near-infrared polarimetric measurements of IC 5063.

Martin et al. (1983) was probably the first to measure the optical linear
polarization of IC 5063 using Pockels cell polarimeters on the Steward
observatory. The observations were made with a Corning 4-96 filter (3800 –
5600 Å) and a 4” aperture. The authors found a polarization degree of 1.28%
$\pm$ 0.14% at a polarization position angle of 10.1∘ $\pm$ 3.2∘. Broadband
optical and near-infrared polarization measurements were also undertaken by
Hough et al. (1987) with the Hatfield Optical-IR polarimeter on the 3.9m
Anglo-Australian Telescope. The authors noted that the polarization decreases
from B to J and then rises towards longer wavelength, while the polarization
angle is wavelength-independent. Inglis et al. (1993) were the first to
provide spectropolarimetric data with the same telescope as Hough et al.
(1987), mounted with a spectrograph and a rotating Thomson CCD. Strong, broad
H$\alpha$ emission was discovered in polarized flux. The polarization obtained
by Inglis et al. (1993) between 4500 and 7000 Å is approximately constant :
$\sim$ 1.7% at 3∘. Finally, Lopez-Rodriguez et al. (2013) used the infrared
polarimeter built by the University of Hertfordshire for the Anglo-Australian
Telescope and measured polarization in J, H and Kn bands at four different
sized apertures: 1.2, 2.0, 3.0, and 4.0 arcsecs. They found a larger and
aperture-dependent polarization degree than in the optical, with a constant
polarization position angle.

All archival polarimetric data are plotted in Fig. 19. We indicated the
contribution of the interstellar polarization in gray, following the standard
Serkowski’s law (Serkowski et al., 1975). We used a synthetic 1.5” radius
aperture on our IC 5063 map and checked whether we could reproduce the
observation. The data we obtain is strongly position-dependent. Targeting the
brightest spot in ultraviolet light, we only probe the jet base region, while
displacing the aperture along the jet direction or placing it inside the dust
lane region dramatically alter the observed polarization, as demonstrated in
Sect. 4. Because we do not know what was the exact pointing of the various
telescopes that obtained polarimetric data in the past, we made use of the
fact that Inglis et al. (1993) measured both the narrow emission lines in the
total flux and the broad emission line in polarized flux to estimate that the
pointing encompassed the region of the map that is dominated by the polar
winds (region 1 in Fig. 16). We thus extracted the continuum linear
polarization from this region and obtained 1.3% $\pm$ 0.3% at 173.2∘ $\pm$
4.3∘. This value is consistent with the previous measurement (see Fig. 19).

Figure 19: Compilation of published IC 5063 polarimetric measurements, prior
to interstellar and starlight dilution correction. Top: Polarization degree.
Bottom: Polarization angle minus the radio position angle of the jet
structure. The aperture used for each measurement is color-coded. The
interstellar polarization (ISP) contribution is highlighted in gray. We
simulated an aperture of radius 1 arcsec centered on the WCS reference point,
situated on the NW part of our region 3, right at the beginning of the
V-shape. We obtained a $1.0\pm 0.4\%$ polarization degree with an associated
$7.9\pm 10.5^{\circ}$ polarization angle. Our measurement is shown using a
green cross. See text for details and references.

Playing with aperture values and position centers, we easily see that a
variation of half an arcsecond can completely change the observed polarization
in a source as complicated as IC 5063. Polarization imaging at a high
resolution is thus needed to determine the polarization of each separate
region, as integrating over a too large aperture would ultimately result in a
mix of several emission and/or scattering mechanisms – thus resulting in an
erroneous explanation.

###  5.2 Background noise estimation

Estimating the background for point-like sources is rather simple: a circular
region is used for the source and a co-located, disjointed annulus is used for
the background. Generally, the background should be extracted from a region
near the source. This is a good estimation of the background as long as the
annulus does not intersect other sources, as it is independent on the
instrument biases. This technique cannot be applied to extended sources, such
as IC 5063.

What is usually done for imagery of AGNs is to study the evolution of the flux
along a virtual line that starts from the SMBH location and that extends in a
direction perpendicular to winds and jets axis. When this flux reaches a
plateau, the value of this plateau is assumed to be the background flux. This
requires that the source is extended, but not to the point of reaching the
borders of the FoV.

In order to generalize this process for complex structures with potentially
polluted background (such as the dust lane in IC 5063), we used a method that
is not common in astrophysics (see e.g. Almoznino et al., 1993) but that is
frequently used in astrophotography (Bijaoui, 1980). The method, as presented
in Sect. 2.3, is based on the counts histogram of the stacked pictures. This
mode calculation assumes the sky radiation is normally distributed around a
typical sky value. Thus if the distribution of the image intensities is
constructed, the sky pixels will practically form a Gaussian centered on the
sky level. Other radiating sources in the frame, which represent additional
photon contributions on top of the sky, will form a tail on the bright side of
the sky distribution (see Fig. 5). The advantage of this approach is that, no
matter how bright these sources are, they will not affect the location of the
peak of this histogram and hence the measured sky value. Other ”bad” pixels,
such as cosmic ray hits and defects of the CCD chip, that are either fainter
or brighter than the sky will (for the most part) not affect the peak
location. The sky value can be taken either as the exact location of the
histogram peak (mode) or as the peak of a Gaussian or parabola fitted to the
histogram in its peak region. To estimate the background noise, we constructed
the distribution of the image intensities using a logarithmic scale and a
statistic rule to bin the intensities. The background value is then chosen to
be the peak of the obtained histogram (mode).

##  6 Conclusion

In this first paper of a series, we present a general pipeline for the
reduction of UV and optical polarimetric data from the final re-calibrated
archive of the HST/FOC legacy instrument. This code, written in python
language, is designed to bring polarimetric analysis to the community. We
checked and validated our tool by re-reducing NGC 1068’s data with even a
slightly better precision that what was done a few decades ago. Moreover, it
allowed us to begin the analysis of the UV polarization map of IC 5063. We
were able to use the full power of the space-resolved polarization to divide
the analysis in regions of different characteristics. With this, the pipeline
proves to be a powerful tool to make use of the still unmatched polarimetric
capabilities of the FOC. Its ease and promptness of use will allow us to
homogeneously reduce and analyse the full AGN sample among the FOC archive to
get a better understanding of their overall properties and present them in the
subsequent papers of the series. However, due to the fact that the FOC is the
last mid- to far-UV polarimeter to have been in operation, this study can only
be completed or taken further with future instruments. This study aim then at
the preparation of future spectro-polarimeter instruments, such as POLLUX,
planned to be mounted on the Habitable Wold Observatory by NASA.

###### Acknowledgements.

The authors would like to acknowledge the referee for their comments that
helped to improved this paper. TB and FM would also like to acknowledge the
great help of Drs. Morganti and Maksym, who kindly shared their ACTA and HST
maps of IC 5063, respectively. The authors would also like to deeply thank Dr.
Antonucci for his comments and help through the pipeline creation and results
analyses.

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