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\newcommand\totaldetections{417}
\newcommand\totalstars{63}
\newcommand\farawayobjects{2}
\newcommand\sourcesremaining{352}
\newcommand\sfsources{83}
\newcommand\diffusesources{269}
\newcommand\outerexcess{0.065}
\newcommand\outermedian{64}
\newcommand\outerMAD{22}
\newcommand\outerspread{25--344}
\newcommand\innerexcess{0.241}
\newcommand\innermedian{48}
\newcommand\innerMAD{31}
\newcommand\innerspread{4--277}
\newcommand\outerexcessRot{0.067}
\newcommand\outermedianRot{74}
\newcommand\outerMADRot{44}
\newcommand\outerspreadRot{12--400}
\newcommand\innerexcessRot{0.243}
\newcommand\innermedianRot{31}
\newcommand\innerMADRot{37}
\newcommand\innerspreadRot{0--324}
\chapter{Study of AGN mechanical mode feedback in Centaurus A\protect\footnote[1]{The contents of this chapter are published in \cite{joseph2022uvit} }} % Write in your own chapter title
\label{Chap2}
\lhead{\emph{Chapter 2: Study of AGN mechanical mode feedback in
Centaurus A}} % Write in your own chapter title to set the page header
\noindent
\section{Introduction}
Centaurus A (Cen A) is a large radio source occupying 8$\degree$ $\times$ 4$\degree$ in the sky and associated with the early-type galaxy NGC 5128 \citep{israel1998centaurus}.
\cite{bolton1949positions}, based on radio observations of Cen A, was the first to note its association with NGC 5128.
The radio emission is from the AGN at the central region of NGC 5128.
Cen A has been observed in a wide range of wavelengths and studied in detail due to its proximity of 3.8 Mpc (1$''$ $\approx$ 18 pc at this distance, \citealt{harris2010}).
These studies reveal the presence of a warped disk and optical shells with associated neutral hydrogen and CO emission---they are believed to be the aftereffects of a past merger activity
\citep{quillen1993warpeddisk,
malin1983shell,
schiminovich1994neutralhydrogen,
charmandaris2000moleculargas}.
According to a recent study using simulations of Cen A, the merger occurred $\sim$2 Gyr ago \citep{wang2020mergerage}.
Post-merger galaxies show an enhancement in the neutral and molecular gas content compared to galaxies of similar stellar mass with no recent merger activity
\citep{ellison2018enhancedNeutralgas,
pan2018enhanceMolecularGas}.
Simulations suggest that the aforementioned enhancement takes place through the depletion of ionised gas \citep{moreno2019mergersimulation}.
Mergers are also known to trigger AGN activity in the local universe \citep{ellison2019mergertriggerAGN}.
Due to proximity, signatures of a recent merger, and the presence of an AGN, Cen A allows us to study the influence of AGN and merger activity on star
formation in great detail.
In Cen A, the age of observed radio structure is estimated to be of the order of a Gyr, and there could be a possibility of the AGN activity being triggered by the recent merger \citep{eilek2014dynamicmodelRadio}.
While a merger can trigger AGN activity, it may also produce tidal structures which should disappear after a few Gyrs.
Neutral and molecular gases are known to be associated with tidal structures \citep{duc2013tidesbook}.
There exist \revii{a} few observed cases where AGN interacts with the gas content located outside the galaxy to induce star formation---this is an effect known as positive AGN feedback
\citep{van1985minkowski,
van1993induced3c285,
bicknell2000jet4c41,
ngc1275canning2014filamentary}.
The presence of AGN can also inhibit star formation in the galaxy, and therefore the effect of AGN feedback is complex.
Cen A is believed to have experienced positive feedback, where the jet launched from the central black hole might have interacted with the gas present around the galaxy \revii{that was} retained from the past merger activity.
This jet ploughing through the cold (HI \& H$_2$) gas could be the trigger for star formation.
One of the pioneering studies in this regard was carried out by \cite{mould2000jetCenA}, where they discussed the observed OB associations as arising due to jet interaction with the gas cloud.
\cite{neff2015complex} argue that a galactic wind could also be at play along with the jet.
\cite{oosterloo2005anomalous} proposed that the jet interacted with a large neutral hydrogen cloud present on the northeast side of Cen A based
on kinematic information.
An aspect that has been crucial in Cen A AGN-cloud interaction studies is the complex morphology of AGN emission revealed by radio/X-ray observations
\citep{feigelson1981xray,
junkes1993radio,
dobereiner1996rosat,
kraft2000chandra,
kraft2002chandra,
hardcastle2003radio}.
The observed radio emission at scales of giant, medium and small level radio lobes has been classified in the literature and studied.
From the centre of NGC 5128, at about 15 kpc north-east (NE), lies the northern middle lobe (NML).
The NML appears to be an extension of the northern inner lobe (NIL) seen at a distance of about 8 kpc from the centre of NGC 5128---however, the connection between them seems unclear \citep{neff2015radio, mckinley2018jet}.
The origin of the NML is also of considerable interest and there exist different explanations in the literature
\citep{morganti1999centaurus,
saxton2001centaurus,
kraft2009jet,
2010gopal,
neff2015complex}.
Available observations point to the presence of young massive stars in the region, which could be induced by the relativistic jet of Cen A
\citep{rejkuba2002radio}.
Ultraviolet (UV) observations using GALEX by \cite{neff2015complex} too have shown the presence of UV bright filaments with young star clusters in a section spanning 20 kpc northward.
In the literature, these filaments are referred to as Inner filament, seen at a distance of $\sim$8 kpc from the centre of NGC 5128 and near NIL, and Outer filament at $\sim$15 kpc and inside the NML.
Collectively, we call this northward section from NGC 5128 as the northern star-forming region (NSR).
Among the various tracers to understand the nature of stars in regions with star formation, UV is particularly important due to its sensitivity towards stars formed over the past 10--200 Myr \citep{kennicutt2012star}.
It is also possible to constrain the ages of stellar populations up to several hundreds of Myrs with UV colours \citep{bianchi2011galex}.
Available GALEX observations are of low resolution, and therefore high-resolution observations in the UV band would reveal a wealth of information on the nature of the stellar population in the NSR, as well as, provide clues to the jet induced star formation activity.
The jet activity and its interaction with tidal structures in NSR make Cen A an excellent candidate for studying the AGN mechanical mode feedback.
We performed UV observations of the NSR using Ultra-Violet Imaging Telescope (UVIT) in different UV filters with an angular resolution better than 1.5 arcseconds.
This chapter presents the results from these new UV band observations.
\section{Observations}
\begin{table}
\centering
\caption{Summary of UVIT Level2 data.
$\lambda_{\text{mean} }$ and $\Delta\lambda$
values are taken from \protect\cite{tandon2020additional}.
The quoted exposure times are from the
science-ready images.
For a signal-to-noise ratio (SNR) of 3,
we estimated the corresponding AB magnitude values
for UVIT observations in each filter (given in
the 6th column).
The corresponding flux values are also provided.}
\label{tab:obs_summary}
\begin{adjustbox}{width=1\textwidth}
\begin{tabular}{@{}llrrrrr@{}}
\toprule
\multicolumn{1}{c}{Channel} &
\multicolumn{1}{c}{Filter} &
\multicolumn{1}{c}{$\lambda_{\text{mean}}$ (\AA)} &
\multicolumn{1}{c}{$\Delta\lambda$ (\AA)} &
\multicolumn{1}{c}{Exposure time (s)} &
\multicolumn{1}{c}{AB mag$_{(\text{SNR}=3)}$} &
Flux$_{(\text{SNR}=3)}$ (erg cm$^{-2}$ s$^{-1}$ \AA$^{-1}$) \\ \midrule
FUV & F148W & 1481 & 500 & 23677 & 26.24 & 1.588E-18 \\
NUV & N219M & 2196 & 270 & 10588 & 24.12 & 5.094E-18 \\
NUV & N245M & 2447 & 280 & 2148 & 24.75 & 2.281E-18 \\
NUV & N279N & 2792 & 90 & 7473 & 23.55 & 5.298E-18 \\ \bottomrule
\end{tabular}
\end{adjustbox}
\end{table}
\begin{figure}
\includegraphics[width=\textwidth]{Cen_A/showcase__collage.png}
\caption{UVIT image of Cen A with F148W filter in blue,
N219M in green, and N245M in red colours.
The image has been processed to make the
features stand out.
The central large circular image shows the
$\sim$0.5$\degree$ UVIT field of view.
The white horizontal line is shown for
scale and has a length of 3 arcminutes.
Thumbnails placed around the main image are
zoomed sections of the image chosen to
showcase the imaging capabilities of UVIT.
Here, Thumbnails 1 and 2 are part of the Outer filament,
Thumbnail 3 shows part of the Inner filament, and
Thumbnail 4 shows new candidates of jet induced
star-forming sources.
Circular thumbnails A-C highlights a few of the interesting
sources found in the image.
Circular thumbnails A and C show UV sources near the Outer
and Inner filaments, respectively.
Circular thumbnail B has a pair of stars, with one on the
left brighter in FUV than the right one.
The source on the right in Circular thumbnail B
is a RR Lyr type variable star
(J132546.5–425141.3 in \protect\citealt{kinman2014rrlyr}).
}
\label{fig:collage}
\end{figure}
The UVIT FUV and NUV observations of NSR were made with a pointing centred on RA = 201$\degree$.602291, Dec = -42$\degree$.844600.
Our observations of NSR were carried out from 2018-03-14 to 2018-03-15 (UT) with a total scheduled exposure of $\sim$24000 seconds in both the channels, which took 17 \textit{AstroSat} orbits.
We did imaging in broadband FUV (F148W), narrowband NUV (N279N), and medium-band NUV (N219M and N245M) filters with varying integration times.
Although N245M filter exposure time is $\sim$5 times less than N219M filter, N245M is $\sim$5 times more sensitive than
N219M \citep[see][table 3]{tandon2020additional}.
Table~\ref{tab:obs_summary} gives details on UVIT
FUV and NUV imaging.
The science ready UVIT images were downloaded from the ISSDC \textit{AstroSat} archive.
These images were reduced using the UVIT Level2 pipeline version 6.3 \citep{ghosh2021performance, ghosh2022automated} by the UVIT Payload Operations centre and made available to ISSDC for dissemination.
The pipeline corrected for the telescope drift of UV data in each orbit using the VIS channel and then aligned and combined the orbit-wise images.
These data were processed using the calibration database version 20190625, which contains the latest flat fielding and distortion correction information.
The astrometric calibration of the images was carried out using the Astrometry.net package \citep{lang2010astrometry}.
All NUV images were re-projected to the FUV image projection using the
flux-conserving spherical polygon intersection method of reproject package
\citep{robitaille2020reproject}.
The final images have a plate scale of 0.4169 arcseconds per pixel.
A colour composite UVIT image with a circular size of $\sim$0.5$\degree$ diameters created from F148W, N219M and N245M passbands is shown in Fig.~\ref{fig:collage}.
NGC 5128 can be seen at the bottom right part of the image.
The galaxy has a prominent UV bright disk with a dark band.
This morphology results from a strongly warped disk rich in dust and star formation
\citep{quillen2006spitzer}.
UV bright star-forming structures seen outside the galaxy disk and in the NSR are marked in red boxes in Fig.~\ref{fig:collage}.
Compared to previous GALEX observations, the higher spatial resolution of UVIT reveals the intricate structure of the star-forming regions in more detail.
\section{Source detection}
\begin{figure}
\includegraphics[width=\columnwidth]{Cen_A/CenA_showcase.png}
\caption{\textit{Left}: F148W filter image of Cen A.
The image has been processed to make the
faint and diffuse features visible.
The red box depicts the area considered
for analysis in this \revii{thesis}.
Two dashed circles represent the
Outer region (see Fig.~\ref{fig:outer_region})
and the Inner region (see
Fig.~\ref{fig:inner_region}).
\textit{Right}: 6.3 cm total intensity map of Cen A
from \protect\cite{junkes1993radio}.
The black circle of 28 arcminute diameter is
the field of view of our UVIT observations.
}
\label{fig:showcase}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{Cen_A/SF_and_nonSF_sources.png}
\caption{The \totaldetections{} sources detected in the
NSR (red box in Fig.~\ref{fig:showcase}) are plotted.
The orange stars are the \totalstars{} galactic sources,
green circles are \farawayobjects{} distant galaxies,
blue crosses are \sfsources{} star-forming sources,
and \diffusesources{} diffuse sources are depicted
by pink X shaped markers.
The red dashed line is the vector path through NSR
representing the potential path associated
with a past jet activity (defined in
section~\ref{sec:outer_region}).}
\label{fig:sources}
\end{figure}
Our study concentrates on \revii{the} recent star formation observed near and inside the Inner and Outer filaments in the NSR.
An area encompassing these filaments and their surroundings were chosen for further analysis.
New UVIT observations reveal UV bright sources in the NSR shown as a red box in Fig.~\ref{fig:showcase}.
The red box has a centre at RA = 201$\degree$.570662, DEC = -42$\degree$.860251 and a size of 17$\times$14 arcminutes.
Most of the UV bright sources are seen near the Outer filament.
Here, UV sources are roughly segregated into a double structure with a gap in an otherwise continuous distribution of sources (see figures~\ref{fig:sources} \& \ref{fig:outer_region}).
This double structure consists of a V-shaped segment and a smaller elongated segment.
When it comes to the Inner filament, UV sources are present, but not as many as in the Outer filament.
They are observed as a single elongated structure.
Between the Inner filament and NGC 5128 lies another set of UV sources with a sparse extent similar to the Inner filament.
To study such a diverse collection of sources, we attempted to detect all sources in the field, find properties, and classify them.
The sources were detected, and their properties were measured using tools provided in the Photutils package \citep{photutils}, \revii{the steps of which are described below.}
Proper estimation of the background and associated uncertainty is vital for the detection of sources as well as the accurate estimation of source fluxes.
For each filter, a low-resolution background map was created by estimating the background in each mesh of a grid that covers the image using sigma-clipped statistics.
The mesh size should not be too small so that the background gets overestimated and source fluxes underestimated.
At the same time, the size should not be too large to miss the diffuse variation in the background.
We chose 400$\times$400 pixels ($\sim$3$'$ $\times$ $\sim$3$'$) as the mesh size.
Sigma clipping is performed, up to 10 iterations, on each mesh by rejecting values outside 3 times the standard deviation from the median.
The background in each mesh is calculated as (2.5 $\times$ median) $-$ (1.5 $\times$ mean).
However, if (mean $-$ median) $\div$ std $>$ 0.3, the median value is used as background.
Each mesh's background root mean square (RMS) is also estimated.
Then final background map is calculated by interpolating the low-resolution
background map to match the image cutout size.
2D background and background RMS noise were estimated in this manner.
The NSR contains both extended and point-like sources.
Therefore, we have used the image segmentation method of Photutils.
In this method, sources are detected based on the criteria that there should be a minimum number of connected pixels (along edges or corners) that are each greater than a specified threshold value with a shape similar to the
user-provided kernel.
The threshold was set as 1.5 times the background RMS off the background level.
To separately identify detected sources, image pixels have integer labels assigned such that pixels with the same values are part of one source---such a map is called a segmentation image.
The segmentation image may contain overlapping sources detected as single sources.
The deblending function provided in the Photutils package was used to separate such sources.
Photutils deblends sources in the segmentation image using a combination of multi-thresholding and watershed segmentation.
To deblend each source, 32 exponentially spaced thresholding levels were chosen between the minimum and maximum values of the source segment with the criteria that a deblended source should contain at least 0.1\% of the flux of the blended source.
Compared to NUV, very few foreground stars are bright in the FUV channel.
Therefore, we used the F148W filter image to create a deblended source segmentation image that was also applied to NUV filter images.
To smooth the noise and maximise the detection of sources with a shape similar to the telescope point spread function (PSF), the F148W image was filtered with a Gaussian kernel of FWHM of 1.4 arcseconds.
We removed sources with fluxes at or below the background level in the NUV filter images after applying the F148W segmentation image.
Finally, the centroid estimation and isophotal photometry were carried out for all the \totaldetections{} detected sources in each filter, where photometric fluxes were measured in counts per second (CPS).
The CPS values are converted to flux in erg cm$^{-2}$ s$^{-1}$ \AA$^{-1}$
using the UVIT calibration information from \cite{tandon2017orbit} and
\cite{tandon2020additional}.
The measured fluxes are affected by dust extinction in our galaxy.
The median colour excess along the line of sight to the NSR is 0.104 with a standard deviation of 0.006.
We found no large-scale variations in the \cite{schlegel1998maps} colour excess map\footnote{\cite{schlegel1998maps} map was obtained from \url{https://irsa.ipac.caltech.edu/applications/DUST}.} upon visual inspection.
\cite{schlafly2011measuring} suggests a 14\% recalibration of \cite{schlegel1998maps} maps.
Therefore we took the colour excess value as 0.089.
We then estimated the flux extinction factors for each UVIT filter with $R_v = 3.1$ following \cite{fitzpatrick1999correcting}, and the fluxes were corrected for the Galactic extinction.
Among the \totaldetections{} sources, there are foreground (stars) and background (distant galaxies) sources.
Using Gaia distances from \cite{bailer2021estimating}, we identified \totalstars{} galactic sources, and they were removed from our list of sources (see Fig.~\ref{fig:sources}).
The filtered catalogue was then compared against the SIMBAD astronomical database to remove those objects associated with a redshift above 0.003 (with 0.001826 being the Cen A redshift).
\revii{\Numberstringnum{\farawayobjects}} sources were identified as distant galaxies and removed in this step.
Our final catalogue thus consists of \sourcesremaining{} sources.
Since we do not have redshift information for the final NSR catalogue of \sourcesremaining{} sources to conclusively ascertain their membership in
the northern star-forming region of Cen A, our list of sources should be considered as candidates (while contamination has been controlled, there can still be intruders in this list).
The NSR source catalogue is publicly available online\footnote{The catalogue can be accessed at \url{https://github.com/prajwel/Centaurus-A_NSR/blob/main/cena_nsr.fit}.}.
A sample table is shown in Table~\ref{tab:nsr_catalogue}.
HST observation of the Inner filament shows that both shock heated gas and young stellar populations are present along the structure \citep{crockett2012triggered}.
UVIT observation of the Inner filament also shows diffuse emission from the shock heated gas and concentrated emission from young stellar populations as point-like sources (see Fig.~\ref{fig:collage}, thumbnail 3).
Similar differences in emission features are observed in UV sources found near the Outer filament, with some being diffuse and others
point-like \revii{sources}.
Therefore, we assume that the diffuse UV emission comes from hot gas and point-like emission from young stellar populations in the NSR.
To differentiate the two, point-like sources in the NSR source catalogue were identified using the DAOFIND algorithm \citep{stetson1987daophot}.
We categorised point-like sources as sites of star formation and the remaining as diffuse emission sources.
\begin{table}
\centering
\caption{A sample table from the NSR source catalogue
and their properties is shown.
RA and DEC are in degrees, the isophotal areas of NSR
sources are in pc$^2$, and flux values are in
erg cm$^{-2}$ s$^{-1}$ \AA$^{-1}$.
The whole catalogue can be accessed as a FITS table at
\url{https://github.com/prajwel/Centaurus-A_NSR/blob/main/cena_nsr.fit}}.
\label{tab:nsr_catalogue}
\resizebox{\textwidth}{!}{%
\begin{tabular}{@{}rrrrrrrrrrr@{}}
\toprule
\multicolumn{1}{c}{RA\_J2000} &
\multicolumn{1}{c}{DEC\_J2000} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}Area\end{tabular}} &
\multicolumn{1}{c}{F148W flux} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}F148W flux\\ error\end{tabular}} &
\multicolumn{1}{c}{N219M flux} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}N219M flux\\ error\end{tabular}} &
\multicolumn{1}{c}{N245M flux} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}N245M flux\\ error\end{tabular}} &
\multicolumn{1}{c}{N279N flux} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}N279N flux\\ error\end{tabular}} \\ \midrule
201.4154820 & -42.9330740 & 4.3644 & 6.8203E-17 & 5.1634E-18 & 8.3704E-17 & 9.8141E-18 & 6.1774E-17 & 6.1091E-18 & 6.0927E-17 & 7.6091E-18 \\
201.4189675 & -42.8136009 & 3.5977 & 5.1847E-17 & 4.5022E-18 & 6.1014E-17 & 8.4147E-18 & 5.3870E-17 & 5.2520E-18 & 4.3801E-17 & 6.1293E-18 \\
201.4198720 & -42.9460643 & 0.2949 & 1.5659E-18 & 1.0404E-18 & 2.5296E-18 & 2.1278E-18 & 3.6963E-18 & 1.3404E-18 & 5.0530E-18 & 2.0750E-18 \\
201.4203589 & -42.8501478 & 0.2949 & 3.3262E-18 & 1.2006E-18 & 8.6239E-19 & 1.4900E-18 & 1.6674E-18 & 8.2067E-19 & 1.6105E-18 & 1.3192E-18 \\
201.4270628 & -42.8393758 & 0.5308 & 5.9493E-18 & 1.6086E-18 & 2.1877E-18 & 1.8868E-18 & 1.6640E-18 & 8.5589E-19 & 6.3417E-18 & 2.4028E-18 \\
201.4308015 & -42.9838896 & 0.4718 & 5.4323E-18 & 1.5720E-18 & 1.3038E-20 & 1.2537E-18 & 1.8899E-18 & 1.3372E-18 & 2.0131E-18 & 1.6313E-18 \\
... & ... & ... & ... & ... & ... & ... & ... & ... & ... & ... \\
201.7123104 & -42.7777452 & 2.1822 & 2.5372E-17 & 3.3228E-18 & 1.7310E-17 & 4.7520E-18 & 2.2578E-17 & 3.4386E-18 & 3.1436E-17 & 5.7720E-18 \\
201.7133760 & -42.7623472 & 0.9437 & 1.0718E-17 & 2.1710E-18 & 8.8000E-18 & 3.6816E-18 & 7.1867E-18 & 1.8518E-18 & 2.7222E-18 & 2.1107E-18 \\
201.7136741 & -42.9743428 & 1.8873 & 2.1280E-17 & 3.0789E-18 & 5.9550E-18 & 3.6667E-18 & 1.3223E-17 & 2.5992E-18 & 1.0956E-17 & 3.3486E-18 \\
201.7139861 & -42.7669313 & 0.4128 & 3.5732E-18 & 1.3393E-18 & 1.8493E-18 & 2.0008E-18 & 3.0481E-18 & 1.2401E-18 & 1.4284E-18 & 1.3460E-18 \\
201.7220010 & -42.7695121 & 0.3539 & 4.8505E-18 & 1.4020E-18 & 3.4040E-18 & 2.1360E-18 & 1.0263E-18 & 9.2078E-19 & 6.4431E-19 & 9.5644E-19 \\
201.7259025 & -42.7761188 & 4.0695 & 4.6224E-17 & 4.5108E-18 & 2.3046E-17 & 5.5320E-18 & 2.1584E-17 & 3.4222E-18 & 1.8171E-17 & 4.1800E-18 \\ \bottomrule
\end{tabular}%
}
\end{table}
\section{Regions of NSR}
We divided the NSR further into Outer and Inner regions.
The characteristics of the two regions are discussed in the following sections.
\subsection{Outer region}
\label{sec:outer_region}
\begin{figure}
\includegraphics[width=\columnwidth]{Cen_A/molecular_clouds_marked_with_sizes.png}
\caption{A closer look at the V-shaped Outer filament using
the F148W image.
The red dashed line is the vector path.
The black dashed circle has a radius of 4.5 arcminutes
with a centre at RA = 201$\degree$.5884734,
Dec = -42$\degree$.8144597.
The semi-transparent cyan circles
represent the molecular clouds,
with the radius proportional to the cloud mass.
The molecular cloud data used here is from ALMA
observations by \protect\cite{salome2017inefficient}.}
\label{fig:outer_region}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{Cen_A/junkes_TP_red.png}
\caption{6.3 cm radio contours of \protect\cite{junkes1993radio}
with contour levels
0.1, 0.15, 0.3, 0.75, 1, 2, 5, 10, 40 Jy/beam
and a half-power beamwidth of 4.3 arcminutes
overlaid on the FUV F148W image.
The image has been processed to make the
faint and diffuse features visible.
The red dashed line corresponds to a vector
connecting the AGN nucleus
to the core of 6.3 cm total power emission
in the NML.
Green 185 MHz radio contours with contour
levels 0.2, 0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6, 1.8, 2
Jy/beam and a Gaussian restoring beam of width
1.5 $\times$ 1.2 arcminutes are from
\protect\cite{mckinley2022multi}.
The broad emission observed by
\protect\cite{junkes1993radio} is likely from
the radio knots in the NML being
smoothed due to a lack of sensitivity to
small-scale structures.}
\label{fig:radio_emission}
\end{figure}
\begin{table}
\caption{Summary of selected sources with jet induced star formation from the literature.}
\label{tab:jetinduced}
\resizebox{\columnwidth}{!}{%
\begin{tabular}{|l|r|l|l|l|}
\hline
\multicolumn{1}{|c|}{Name} & \multicolumn{1}{c|}{Redshift} & \multicolumn{1}{c|}{\begin{tabular}[c]{@{}c@{}}Distance to the\\ prominent structure\end{tabular}} & \multicolumn{1}{c|}{Morphology} & \multicolumn{1}{c|}{Recent merger history} \\ \hline
Cen A & 0.001826 & $\sim$15 kpc & \begin{tabular}[c]{@{}l@{}}bifurcated \\ (this study)\end{tabular} & \begin{tabular}[c]{@{}l@{}}yes\\ \citep{wang2020mergerage}\end{tabular} \\ \hline
MO & 0.0181 & \begin{tabular}[c]{@{}l@{}}$\sim$20 kpc\\ \citep{salome2015jet}\end{tabular} & \begin{tabular}[c]{@{}l@{}}bifurcated\\ \citep{croft2006minkowski}\end{tabular} & \begin{tabular}[c]{@{}l@{}}yes (cluster level)\\ \citep{bogdan2011chandra}\end{tabular} \\ \hline
3C 285 & 0.0794 & \begin{tabular}[c]{@{}l@{}}$\sim$70 kpc\\ \citep{salome2015jet}\end{tabular} & \begin{tabular}[c]{@{}l@{}}likely bifurcated\\ \citep{van1993induced3c285}\end{tabular} & \begin{tabular}[c]{@{}l@{}}yes\\ \citep{salome2015jet}\end{tabular} \\ \hline
3C 34 & 0.689 & \begin{tabular}[c]{@{}l@{}}$\sim$120 kpc\\ \citep{best1997jet}\end{tabular} & \begin{tabular}[c]{@{}l@{}}bifurcated\\ \citep{best1997jet}\end{tabular} & unknown \\ \hline
4C 41.17 & 3.8 & \begin{tabular}[c]{@{}l@{}}$\sim$10 kpc\\ \citep{bicknell2000jet4c41}\end{tabular} & \begin{tabular}[c]{@{}l@{}}bifurcated\\ \citep{bicknell2000jet4c41}\end{tabular} & \begin{tabular}[c]{@{}l@{}}yes\\ \citep{de2005detection}\end{tabular} \\ \hline
\end{tabular}%
}
\end{table}
To study the NSR sources observed in and around the Outer filament, we define a circular region of 4.5 arcminutes radius at RA = 201$\degree$.5884734, Dec = -42$\degree$.8144597 (dashed circle in Fig.~\ref{fig:outer_region}).
The radius was chosen to encompass most of the NSR sources near the Outer filament.
The double structure consisting of a V-shaped segment and \revii{a relatively small} elongated segment can be observed here.
Part of the ribbon-like diffuse FUV emission noticed by \cite{neff2015complex} is also present.
\cite{mould2000jetCenA} suggested that the jet interacted with the gas cloud to trigger star formation.
A portion of the northern middle lobe (NML) is found in the Outer region.
The NML is part of Cen A radio structure classification in the literature,
covering a section northward of Cen A up to $\sim$30 arcminutes \citep{israel1998centaurus}.
In the box area that we have selected for studying NSR (see Fig.~\ref{fig:showcase}), there exists NML and a smaller scale radio lobe
closer to the galaxy called the northern inner lobe (NIL).
While NML is present in the Outer region, NIL is found in the Inner region (see next section).
There has been no detection of a southern middle lobe or SML \citep{neff2015radio}.
The observations by \cite{morganti1999centaurus} revealed a large-scale jet that connects the NML and NIL.
They proposed that NML could be the result of a precessing jet that underwent an interaction with the environment on the northern side of Cen A.
\cite{saxton2001centaurus} considered the scenario of NML being a buoyant bubble of plasma generated by an intermittently active jet.
According to \cite{kraft2009jet}, NML was initially formed from a previous nuclear outburst and is being re-energised by the current outburst. \cite{2010gopal} described how the radio jet could have interacted with the gas cloud to produce NML.
To address the various short-lived structures seen in and around the NML, \cite{neff2015complex} proposed that an AGN-augmented wind could be present.
Contrary to what is observed and explained by \cite{morganti1999centaurus}
as a currently active 'large-scale jet', radio observations by \cite{neff2015radio} do not detect any structure connecting NIL and NML.
\cite{mckinley2018jet} detected a collimated structure at the site of 'large-scale jet'.
The latest observations by \cite{mckinley2022multi} disfavours the existence of a presently active 'large-scale jet'.
Regardless of whether a collimated jet now exists connecting NIL to NML and
AGN-augmented wind currently energises the observed structures around Cen A,
we consider it likely that a jet activity could have been present extending to NML in the past for the following reasons:
(a) The presence of a double structure in the Outer region---the observed UV sources show a gap in its distribution, and it splits the structure into a V-shaped segment and a smaller elongated segment.
Such double structures are observed in association with other cases of jet induced star formation (See Table~\ref{tab:jetinduced}).
(b) The spatially localised anomalous gas kinematics in a large gas cloud found near the Outer filament is explained as arising due to jet interaction \citep{oosterloo2005anomalous}.
(c) The wind depends on an ongoing starburst in the galaxy, but the giant radio lobes seen on the north and south sides of Cen A have an age of the order of 1 Gyr \citep{eilek2014dynamicmodelRadio}.
Simulations predict that it is less likely for a starburst to be older than 500 Myr \citep{di2008frequency}.
Therefore, we adopt the interpretation of \cite{2010gopal}, which explains the origin of NML as arising due to jet interaction with the gas cloud.
Observations by \cite{neff2015radio} and \cite{mckinley2022multi} show that the NML has multiple radio knots.
X-ray knots were observed in the NML by \cite{kraft2009jet}.
Previous authors noted that the radio and X-ray knots may dissipate within a few Myr and requires a supply of energy to maintain them.
Based on energetic arguments, \cite{mckinley2022multi} suggested that the AGN jet is a necessary part of explaining the observed features in the NML.
We assume that the radio and X-ray knots in the NML were created by a former jet when a gas cloud would have come into contact with it.
We believe this is a reasonable assumption based on existing observations of the NML.
To find the potential path of this past jet activity through the Outer region, we used the radio continuum data of \cite{junkes1993radio} and estimated the centroid for the sigma clipped core profile of the radio emission in the NML (see Fig.~\ref{fig:radio_emission}, the bottom part of the NML can be seen extending into the Outer region).
Then, extending from the AGN nucleus, we created a vector that goes through the NML centroid.
This vector has a position angle of 37.4 degrees.
The \sourcesremaining{} NSR sources (\sfsources{} star-forming and \diffusesources{} diffuse sources) are shown in Fig.~\ref{fig:sources}, along with the vector.
The path along the vector appears to be relatively devoid of NSR sources.
The absence of NSR sources along the vector path is especially pronounced in the Outer region.
The vector goes through the gap splitting the observed double structure into two segments.
We consider the vector as the potential path of the past jet activity through NML.
Our vector is aligned to the first two radio knots observed by \cite{mckinley2022multi}.
We caution that the vector represents a hypothetical path---it may be difficult to ascertain whether the jet travelled along this path.
The ALMA observations by \cite{salome2017inefficient} reveals that there is also a lack of molecular clouds along the vector path (see Fig.~\ref{fig:outer_region}).
Detections from the ALMA CO map are overlaid in cyan colour.
The radii of circles are proportional to the cloud masses.
Most molecular clouds are located along with the ribbon-like diffuse FUV emission region.
If the diffuse UV emission comes from hot gas, the observed cluster of molecular clouds could be far from the hot gas, though they appear close in projection.
\subsection{Inner region}
\begin{figure}
\includegraphics[width=\columnwidth]{Cen_A/inner_filament_with_VLA_1.55GHz_overlay.png}
\caption{The greyscale F148W image shows
the Inner region.
Blue crosses are star-forming sources, and
pink X-shaped markers depict diffuse sources.
The red dashed line is the vector path.
The green box shows the location of
the Inner filament.
The VLA 1.55 GHz radio contours are overlaid (red)
on the figure with contour
levels 0.060, 0.097, 0.167, 0.287 Jy/beam
and a half-power beamwidth of 4.3 arcseconds.
The radio feature close to the Inner filament has only the lowest contour level.
Therefore, this might be an artefact.
VLA image credit: NRAO/VLA Archive Survey, (c) 2005-2009 AUI/NRAO.}
\label{fig:inner_region}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{Cen_A/new_star_forming_regions.png}
\caption{A section of Figure \ref{fig:inner_region}
containing the lower part of NIL is shown here.
The image was convolved with a Gaussian kernel
with FWHM comparable to the PSF.
Dashed circles B and C represent candidate
star-forming structures, and A denote diffuse emission.}
\label{fig:new_regions}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{Cen_A/subregion_B.png}
\caption{HST F606W image of the candidate site B
is shown.
The white diagonal stripe on the right
side of the figure represents the
$\sim$50 pixel gap in the ACS
detector.
The dashed circle occupies the
same sky region as the dashed circle B in
Fig.~\ref{fig:new_regions}.
The UVIT F148W contours are overlaid (blue)
with contour levels 0.00012, 0.00028, 0.00044,
0.0006 CPS.
The green circles mark the point-like
sources detected using DAOFIND.
The red-filled circles show the Gaia detected foreground
stars \citep{bailer2021estimating}.}
\label{fig:subregion_B}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{Cen_A/subregion_C.png}
\caption{HST F606W image of the candidate site C
is shown.
The white diagonal stripe on the left
represents the
$\sim$50 pixel gap in the ACS
detector.
Additionally, the ACS detector did not cover
a small section near the top left corner.
This section is also shown in white colour.
The dashed circle occupies the
same sky region as the dashed circle C in
Fig.~\ref{fig:new_regions}.
The UVIT F148W contours are overlaid (blue)
with contour levels 0.00012 and 0.00028 CPS.
The green circles mark the point-like
sources detected using DAOFIND.
The red-filled circles show the Gaia detected foreground
stars \citep{bailer2021estimating}.}
\label{fig:subregion_C}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{Cen_A/subregion_A.png}
\caption{\textit{Chandra} ACIS-I image of
candidate site A is shown with soft band flux
(0.5-1.2 keV) in yellow and hard band flux
(2.0-7.0 keV) in blue.
The diagonal blue stripe near the
bottom left corner is due to the read-out
streak in the hard band
\citep{mccollough2005impact}.
The dashed circle occupies the same sky
region as the dashed circle A in
Fig.~\ref{fig:new_regions}.
The VLA 1.55 GHz radio contours are overlaid
(red) with contour levels 0.060, 0.097, 0.167,
0.287 Jy/beam.}
\label{fig:subregion_A}
\end{figure}
Compared to the Outer filament, the Inner filament
has fewer NSR sources.
For a comparative analysis, we defined an expanded
region including the Inner filament with a circle
of 4.5 arcminutes radius (same as the Outer region) at
RA = 201$\degree$.4875502, Dec = -42$\degree$.9560958.
The inner filament sources can be seen as an
elongated structure.
Very young stars (1--4 Myr) have been observed in
the Inner filament by \cite{crockett2012triggered},
and they suggested that a jet cocoon driven bow
shock could have triggered star formation.
Close to the Inner filament, backflows from the jet have
been found \citep{hamer2015muse}.
The FUV F148W image with VLA 1.55 GHz contours reveals
the complex structure of the Inner region
where present jet activity is observed
(see Fig.~\ref{fig:inner_region}).
According to the Cen A radio structure classification,
the radio lobe seen in the Inner region is called the
northern inner lobe (NIL).
We have identified candidate sites of star formation
that could be related to AGN activity
(dashed circles B and C in Fig.~\ref{fig:new_regions}).
They appear where the collimated radio beam in
the NIL starts to diverge.
The candidate site B is mentioned in the literature
as DF 6 and has been noted for its alignment with the jet
\citep{dufour1978inner, graham2002star}.
We found Advanced Camera for Surveys (ACS)
F606W observations of the candidate sites from the HST
archive (HST programme 10597, PI: A. Jordan).
F606W is a broad V-band filter that includes the
H-alpha emission line.
The F606W images of the candidate sites are shown
in Figs \ref{fig:subregion_B} and \ref{fig:subregion_C}.
Point-like sources are seen in the F606W image
at locations where FUV emission is observed.
The green circles in Figs \ref{fig:subregion_B}
and \ref{fig:subregion_C} mark the point-like
sources detected using DAOFIND.
In Fig.~\ref{fig:subregion_B}, a cluster of point-like
sources is seen aligned with the core of the FUV
emission contours.
The alignment of candidate sites B and C with NIL
makes a case for jet induced star formation at
these locations.
There are also faint and diffuse UV sources
padded along the radio beam path (dashed
circle A in Fig.~\ref{fig:new_regions}).
Using the SciServer system and CIAO 4.13 (CALDB 4.9.6),
we merged all available \textit{Chandra} ACIS-I
observations of Cen A \citep{taghizadeh2020sciserver,
fruscione2006ciao}.
\textit{Chandra} ACIS-I image of candidate site A is shown
in Fig.~\ref{fig:subregion_A} with soft band flux (0.5-1.2 keV)
in yellow and hard band flux (2.0-7.0 keV) in blue colours.
If we compare Figs \ref{fig:new_regions} and \ref{fig:subregion_A},
hard band flux is missing at locations where diffuse
UV emission is observed.
Also, we did not observe any point-like sources in
HST F606W observations within site A.
Noting these aspects, we propose that diffuse
emission could be coming from the hot gas
present at this location.
\section{Stellar population synthesis}
\label{sec:age}
We used the evolutionary synthesis code
Starburst99 v7.0.1 to analyse the NSR sources
with recent star formation in both regions
\citep{leitherer1999starburst99,
vazquez2005optimization,
leitherer2010library,
leitherer2014effects}.
Starburst99 has already been used in studies
with UVIT data \citep{mondal2018uvit}.
\cite{salome2016star} noted that Outer
and Inner filaments have high oxygen abundances
from the Multi-Unit Spectroscopic Explorer
(MUSE) data analysis.
While the MUSE observations cover only
small sections of the Outer and Inner regions
(2 arcminute square section on the V-shaped segment
of the Outer region and 1 arcminute square covering the
inner filament), \cite{salome2016star} found
no major metallicity differences between the filaments
and no major metallicity gradients along each of the
filaments.
Therefore, we have assumed solar metallicity in both
regions.
We used a simulated simple stellar population that had
its total stellar mass distributed in a Kroupa IMF with
instantaneous star formation evolved through Geneva
isochrone tracks (solar metallicity; Z = 0.014)
to compare our observations.
To obtain bounds on the effects of massive star rotation,
we used the 0\% and 40\% of the break-up velocity isochrone
models provided in Starburst99.
Following the notation in \cite{leitherer2014effects},
we denote the 0\% rotation model with solar metallicity as
v00-h and the 40\% model as v40-h.
The method followed for the analysis is explained below.
Using the simulated high-resolution UV spectra
spanning ages up to 1 Gyr,
we generated a table of UV luminosities
in UVIT filters by convolving simulated spectra
with filter effective area functions.
The simulated luminosity $L(\lambda_{\text{mean}}$)
in erg s$^{-1}$ \AA$^{-1}$
was calculated as follows:
\begin{equation}
L(\lambda_{\text{mean}}) =
\frac{\int L(\lambda)\ EA(\lambda)\ d\lambda}
{\int EA(\lambda)\ d\lambda}
\end{equation}
where $L(\lambda)$ is the starburst99 spectra and
$EA(\lambda)$ is the effective area function given in
Table 4 of \cite{tandon2020additional}.
The $\lambda_{\text{mean}}$ is the mean of
effective area weighted wavelengths (defined in equation
3 of \citealt{tandon2017orbit}).
The luminosities were then
converted to AB magnitudes.
The simulated magnitudes are shown in
Fig.~\ref{fig:simulated_colors} for F148W, N219M, and
N245M bands with the v00-h model and
$10^5 M_{\odot}$ total stellar mass.
The observed FUV $-$ NUV colour
can be compared with the simulated colour
to estimate the age of the UV emitting
population of young stars.
From our list of \sfsources{} NSR star-forming
sources, 61 sources lie inside the Outer region and
16 are found in the Inner region.
Fig.~\ref{fig:age_attenuation} shows ratios of the simulated luminosity values between UVIT filters.
In the figure, the output from simulations using both v00-h and v40-h models are shown.
However, dust attenuation could affect UV
observations in the Outer and Inner regions.
\cite{auld2012herschel} observed dust clouds around
Cen A and interpreted that a merger with a
late-type gas-rich galaxy could have taken place.
\cite{santoro2016embedded} observed a small section
of the Outer filament using MUSE
and derived colour excess values
from $\text{H}\alpha/\text{H}\beta$
ratio for two star-forming sources.
We found that the N245M - N219M colour
remain approximately constant (see Fig.~\ref{fig:age_attenuation}).
After assuming an attenuation law with $R_v = 4.05$
from \cite{calzetti2000dust}, the simulated and observed
colours were compared to estimate the
colour excess (see Section ~\ref{sec:colour_excess}).
The flux and magnitude values were
corrected for dust attenuation.
Then, to estimate the ages of the sources,
the observed N219M $-$ F148W and
N245M $-$ F148W colours
were compared with simulated colours
from the v00-h model.
The mean of the two estimates from
N219M $-$ F148W and N245M $-$ F148W colours
was taken as the final age value for each source.
The colours and estimated ages for the Outer
and Inner regions are given in Tables~\ref{tab:inner_region_catalog}
\& \ref{tab:outer_region_catalog}, respectively.
See Table~\ref{tab:age_summary} for a
summary of results in both regions.
N279N is a narrow bandwidth filter,
which is $\sim$7 times less sensitive than N245M.
Hence, observations in this filter were not used for age calculations.
Fig.~\ref{fig:age_distribution} shows the age
distribution of the Outer and Inner regions.
The V40-h model also gives comparable age
estimates.
Compared to the Outer region, where most sources are part of
the Outer filament, the Inner region contains a more sparse
distribution of ages.
\begin{figure}
\includegraphics[width=\columnwidth]{Cen_A/simulated_UVIT_filter_colors_noRot.png}
\caption{The plot shows the UVIT filter AB magnitudes
simulated using Starburst99.
The F148W, N219M, and N245M magnitudes are
shown \revii{up to an age of 1 Gyr.}
The simulation was generated using the
v00-h model and
$10^5 M_{\odot}$ total stellar mass.}
\label{fig:simulated_colors}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{Cen_A/Starburst99_simulated_colors_for_CenA_UVIT_filters.png}
\caption{The plot shows the UVIT filter
colours simulated using Starburst99.
The N219M $-$ F148W (blue),
N245M $-$ F148W (orange),
and N245M $-$ N219M (green) colours have been
estimated for \revii{ages up to 1 Gyr.}
Strong and faint lines correspond to
simulations with v00-h and v40-h, respectively.}
\label{fig:age_attenuation}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{Cen_A/age_distribution.png}
\caption{The age distribution of the Outer and Inner regions.
Each histogram bin has a width of 20 Myr.
The vertical blue and orange lines represent the
median values of the Outer and Inner region
distributions, respectively (see Table~\ref{tab:age_summary}).}
\label{fig:age_distribution}
\end{figure}
\begin{landscape}
\begin{table}
\centering
\caption{A sample table from the NSR inner region source catalogue and their properties is shown.
RA and DEC are in degrees, the isophotal area of NSR sources are in pc$^2$, and flux values are in erg cm$^{-2}$ s$^{-1}$ \AA$^{-1}$.
The colour values used in the analysis are shown in columns
\revii{12, 13, and 14}. Age is in Myr.
The whole catalogue can be accessed as a FITS table at
\url{https://github.com/prajwel/Centaurus-A_NSR/blob/main/cena_inr.fit}.
For two sources, the observed colour values fell outside the simulated colour value range, so ages
could not be determined.
These two sources have a "nan" entry in the
age column.
}
\label{tab:inner_region_catalog}
\resizebox{\columnwidth}{!}{%
\begin{tabular}{@{}rrrrrrrrrrrrrrr@{}}
\toprule
\multicolumn{1}{c}{RA\_J2000} &
\multicolumn{1}{c}{DEC\_J2000} &
\multicolumn{1}{c}{Area} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}F148W\\ flux\end{tabular}} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}F148W\\ flux error\end{tabular}} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}N219M\\ flux\end{tabular}} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}N219M\\ flux error\end{tabular}} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}N245M\\ flux\end{tabular}} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}N245M\\ flux error\end{tabular}} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}N279N\\ flux\end{tabular}} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}N279N\\ flux error\end{tabular}} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}N219M -\\ F148W\end{tabular}} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}N245M -\\ F148W\end{tabular}} &
\multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}N245M -\\ N219M\end{tabular}} &
\multicolumn{1}{c}{Age} \\ \midrule
201.4154820 &
-42.9330740 &
4.3644 &
6.8203E-17 &
4.5787E-18 &
8.3704E-17 &
9.4170E-18 &
6.1774E-17 &
5.9277E-18 &
6.0927E-17 &
7.2280E-18 &
-0.5982 &
-0.3773 &
0.2209 &
236.6650 \\
201.4412119 &
-42.9555594 &
2.4771 &
3.4109E-17 &
3.2836E-18 &
4.0350E-17 &
6.4850E-18 &
4.1830E-17 &
5.2128E-18 &
6.1307E-17 &
7.2152E-18 &
-0.5583 &
-0.7063 &
-0.1480 &
276.9896 \\
201.4480639 &
-42.9674604 &
5.0721 &
6.4036E-17 &
4.5647E-18 &
4.3077E-17 &
6.9508E-18 &
3.6957E-17 &
4.4060E-18 &
2.5554E-17 &
5.7344E-18 &
0.0546 &
0.1121 &
0.0575 &
48.5387 \\
201.4483249 &
-42.9772165 &
21.6451 &
4.2856E-16 &
1.1280E-17 &
2.5638E-16 &
1.6911E-17 &
2.1368E-16 &
1.1057E-17 &
1.5934E-16 &
1.3038E-17 &
0.1819 &
0.2709 &
0.0889 &
44.9612 \\
201.4495844 &
-42.9762409 &
10.4982 &
2.1572E-16 &
7.9684E-18 &
1.9138E-16 &
1.4552E-17 &
1.4335E-16 &
9.4402E-18 &
1.4987E-16 &
1.2019E-17 &
-0.2459 &
-0.0410 &
0.2048 &
68.0601 \\
201.4501058 &
-42.9783131 &
8.1390 &
1.1607E-16 &
6.0756E-18 &
5.4060E-17 &
8.1737E-18 &
5.9365E-17 &
5.8119E-18 &
3.6778E-17 &
7.3107E-18 &
0.4538 &
0.2432 &
-0.2105 &
6.2405 \\
... &
... &
... &
... &
... &
... &
... &
... &
... &
... &
... &
... &
... &
... &
... \\
201.5140402 &
-42.9548405 &
32.5561 &
1.1006E-15 &
1.7209E-17 &
5.2118E-16 &
2.3844E-17 &
4.4654E-16 &
1.6551E-17 &
3.1603E-16 &
1.6565E-17 &
0.4357 &
0.4946 &
0.0589 &
nan \\
201.5153409 &
-42.9141509 &
3.3028 &
4.6056E-17 &
3.7783E-18 &
2.5608E-17 &
5.3880E-18 &
1.6732E-17 &
3.0136E-18 &
1.7467E-17 &
4.1789E-18 &
0.2614 &
0.6145 &
0.3531 &
12.0083 \\
201.5512368 &
-42.9007761 &
4.7183 &
5.9382E-17 &
4.3458E-18 &
3.7225E-17 &
6.7104E-18 &
3.3646E-17 &
4.1500E-18 &
9.9782E-18 &
3.4028E-18 &
0.1312 &
0.1320 &
0.0009 &
26.4789 \\
201.5523085 &
-42.9022168 &
3.7156 &
4.9372E-17 &
3.9368E-18 &
3.1780E-17 &
6.0076E-18 &
2.8903E-17 &
3.7015E-18 &
1.8776E-17 &
4.1279E-18 &
0.1025 &
0.0966 &
-0.0059 &
48.3958 \\
201.5578779 &
-42.9938295 &
1.9463 &
2.3509E-17 &
2.7668E-18 &
1.6702E-17 &
4.1912E-18 &
1.0703E-17 &
2.1187E-18 &
2.7618E-18 &
2.1292E-18 &
-0.0047 &
0.3695 &
0.3742 &
29.8782 \\
201.5583015 &