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\title[The LBA Calibrator Survey --- LCS2]{The Second LBA Calibrator Survey
of southern compact extragalactic radio sources --- LCS2}
\author[Petrov et al.]{
  \parbox[t]{\textwidth}{
     Leonid Petrov$^{1}$\thanks{E-mail:Leonid.Petrov@nasa.gov},
     Alet de Witt$^{2}$, 
     \mbox{Elaine M.~Sadler}$^{4}$, 
     Chris Phillips$^{5}$, and
     Shinji Horiuchi$^{6}$,
  }
\vspace{1.0ex} \\
$^{1}$NASA, Goddard Space Flight Center, 8800 Greenbelt Rd, MD 22071, USA \\
$^{2}$Hartebeesthoek Radio Astronomy Observatory, P.O.Box 443, Krugersdorp 1740, South Africa \\
$^{3}$Sydney Institute for Astronomy, School of Physics, The University of Sydney, NSW 2006, Australia \\
$^{4}$CSIRO Astronomy and Space Science, PO Box 76, Epping, NSW 1710,
      Australia \\
$^{5}$CSIRO Astronomy and Space Science, Canberra Deep Space Communication Complex, 
            PO Box 1035, Tuggeranong, ACT 2901, Australia
}

% These dates will be filled out by the publisher
\date{Accepted XXX; Received YYY; in original form ZZZ}

\pagerange{\pageref{firstpage}--\pageref{lastpage}}

\begin{document}

\maketitle
\label{firstpage}


\begin{abstract}

   We present the second catalogue of accurate positions and correlated flux
densities for 1100 compact extragalactic radio sources that were not observed
before 2008 at high angular resolution. The catalogue spans the declination 
range $[-90\degr, -30\degr]$ and was constructed from nineteen 24-hour VLBI 
observing sessions with the Australian Long Baseline Array at 8.3~GHz. The 
catalogue presents the final part of the program that was started in 2008.
The goals of that campaign are 1)~to extend the number of compact radio sources
with precise coordinates and measure their correlated flux densities, which can be 
used for phase referencing observations, geodetic VLBI, search for sources 
with significant offset with respect to \Gaia\ positions, and space navigation;
2)~to extend the complete flux-limited sample of compact extragalactic sources
to the southern hemisphere; and 3)~to investigate the parsec-scale
properties of sources from the high-frequency AT20G survey. The median 
uncertainty of the source positions is 3.5~mas. As a result of this VLBI 
campaign, the number of compact radio sources south of declination $-40\degr$ 
which have measured VLBI correlated flux densities and positions known to
milliarcsecond accuracy has increased by a factor of 6.4. 

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\end{abstract}

\begin{keywords}
  astrometry --
  catalogues --
  instrumentation: interferometers --
  radio continuum --
  surveys
\end{keywords}

\section{Introduction}

   Until recently, the method of very long baseline interferometry
(VLBI) proposed by \citet{r:mat65} was the only way to measure
positions of extragalactic radio sources that are almost exclusively
active galactic nuclea (AGNs) with sub-nanoradian accuracy. In 2016,
it has been demonstrated \citep{r:gaia_dr1} that \Gaia\ is able to 
get the position accuracy in par with VLBI. However, comparison of VLBI 
and \Gaia\ matching sources showed \citep{r:gaia_icrf2,r:gaia1} that there 
is a population of sources with statistically significant position offsets.
A more detailed analysis by \citet{r:gaia2}, later extend by \citet{r:gaia4} 
revealed that VLBI/\Gaia\ offsets have a preferred direction along the jet 
with the mean offset in a range of 1--2~mas that was interpreted as 
a manifestation of the contribution of optical jet to the centroid position. 
This allowed \citet{r:gaia3} to make a conclusion that VLBI/\Gaia\ difference 
is due to the fact VLBI and \Gaia\ see different part of a source and further 
improvement in accuracy beyond 1--2~mas level will not result in 
a reconciliation of VLBI and \Gaia\ coordinates of active galaxies. Recent 
publication of \citet{r:gaia5} provided further compelling evidence of it.
Moreover, the VLBI/\Gaia\ offsets brings an important signal that allows us 
to make an inference about milliarcsecond scale source structure of AGNs that
currently cannot be observed directly. As a consequence, if we need achieve 
accuracy better 1--2~mas, we cannot borrow \Gaia\ positions of matching 
sources, but have to rely on VLBI determination of source coordinates for 
applications that needs high accuracy, such as space navigation, Earth 
orientation parameter monitoring, and comparison of positions of pulsars 
determined with VLBI and timing.

   In this context, it becomes increasingly important to have an all-sky,
deep, and precise catalogue of positions of extragalactic sources from
radio observations. The most productive instrument for absolute 
radio astrometry is the Very Long Baseline Array. Using VLBA, one
can easily determine positions of sources at declinations 
[-$30\degr$, +$90\degr$] 
\citep{r:vcs1,r:vcs3,r:vcs4,r:vcs5,r:vcs6,r:obrs1,r:obrs2,r:astro_vips,
r:vgaps,r:bessel_search,r:v2m,r:vcs-ii,r:vcs9};
with some difficulties positions of sources at declinations 
[-$45\degr$, -$30\degr$] \citep{r:vcs2}; but with some exceptions one 
cannot observe sources with declinations below -$45\degr$. The sequence 
of VLBA Calibrator Surveys~1--9 (VCS) \citep[e.g.,][and references 
therein]{r:vcs6} provided a dense grid of calibrator sources.

  The lack of a VLBA analogue in the southern hemisphere resulted in the 
past in a significant hemisphere disparity of the source distribution in 
absolute radioastrometry catalogues. To alleviate this problem, we launched
a program for observing radio sources at declinations 
[-$90\degr$, -$40\degr$] with Long Baseline Array (LBA) in 2008. The main
goal of the program was to increase the density of calibrator sources with 
positions known at milliarcsecond level in the southern hemisphere to make 
an analogue of VCS in the south. Unlike to the VCS surveys at the northern 
hemisphere, we used predominately AT20G at 20~GHz from Australia Telescope 
Compact Array (ATCA) observations for drawing the candidate list for LBA 
observations. 

  The results of the first part of this campaign for observing the 
brightest sources, the catalogue LCS--1 was published by 
\citep{r:lcs1}. Here we present results of the second, final part
of the campaign. In the following sections we describe observations, 
data analysis, analysis of reported errors, and provide a brief discussion
of results.

\section{Observations}

\subsection{Network}

   The network of observing station includes 11 stations listed in
Table~\ref{t:lba}, although only a subset of stations participated at any 
given observing session. The list of VLBI experiments, observation dates,
and the participating network is shown in Table~\ref{t:lcs_exp}. The 
network, except station {\sc hartrao} is shown in Figure~\ref{f:network}. 
Station {\sc askap} participated in three experiments, station 
{\sc tidbinbilla} observed only during 4--8 hours intervals. The 64~m 
station {\sc parkes} was scheduled in every experiment and in every scan 
of target sources since it is the most sensitive antenna of the network 
and therefore, the sensitivity at baselines with {\sc parkes} is the 
highest.

\begin{table}
    \caption{The LBA network. The typical system equivalent flux
             density (SEFD) at 8.3~GHz at elevation angles $> 45\degr$
             achieved in LCS experiments is shown in the last column.}
    \begin{tabular}{l @{\hspace{1.0em}} l @{\hspace{1.0em}} l @{\hspace{1.0em}} r @{\hspace{1.0em}} l @{\hspace{1.0em}} r}
       \hline
       Code & Name   &  \ntab{c}{$\phi_{gc}$}   &
                        \ntab{c}{$\lambda$}     & Diam & SEFD \\
       \hline
       As & \sc askap       & -$26\degr.53$  & $116\degr.63$ &            12 m & 8300 Jy  \\
       At & \sc atca        & -$30\degr.15$  & $149\degr.57$ & $5 \times 22$ m &  140 Jy  \\
       Cd & \sc ceduna      & -$31\degr.70$  & $133\degr.81$ &            32 m &  600 Jy  \\
       Ha & \sc hartrao     & -$25\degr.74$  & $ 27\degr.69$ &            26 m & 1200 Jy  \\
       Ho & \sc hobart26    & -$42\degr.62$  & $147\degr.44$ &            26 m &  850 Jy  \\
       Ke & \sc kath12m     & -$14\degr.28$  & $132\degr.15$ &            12 m & 3000 Jy  \\
       Mp & \sc mopra       & -$31\degr.10$  & $149\degr.10$ &            22 m &  400 Jy  \\
       Pa & \sc parkes      & -$32\degr.82$  & $148\degr.26$ &            64 m &   50 Jy  \\
       Td & \sc tidbinbilla & -$35\degr.22$  & $148\degr.98$ &            34 m &  120 Jy  \\
       Yg & \sc yarra12m    & -$28\degr.88$  & $115\degr.35$ &            12 m & 3000 Jy  \\
       Ww & \sc wark12m     & -$36\degr.25$  & $174\degr.66$ &            12 m & 3000 Jy  \\
       \hline
    \end{tabular}
    \label{t:lba}
\end{table}

\begin{figure}
    \includegraphics[width=0.48\textwidth]{lba_lcs2.pdf}
    \caption{The LBA stations network. Station Hh ({\sc hartrao}), 60~km
             north-west of Johannesburg, South Africa, is not shown.}
    \label{f:network}
\end{figure}

  Stations {\sc atca, ceduna} and {\sc mopra} were equipped with the LBA VLBI 
backend consisting of an Australia Telescope National Facility (ATNF) Data 
Acquisition System (DAS) with an LBADR recorder. The ATNF DAS only allows two 
simultaneous intermediate frequencies (IFs): either 2 frequencies or 
2 polarizations. For each of these IFs the input 64~MHz analog IF is digitally 
filtered to 2~contiguous 16~MHz bands. Stations {\sc atca} and {\sc mopra} were 
equipped with two LBDAR recorders, however because of hardware limitations 
additional recorders could not be used for expanding the bandwidth , but could 
be used for recording both polarizations. Thus, the stations equipped with the 
ATNF backend could record two bands 32~MHz wide. This imposed a limitation on 
the frequency setup: spreading the frequencies too narrow would result in 
degradation  of group delay accuracy and spreading the frequencies two wide 
would results in group delay ambiguities with very narrow group delay 
ambiguities spacings. Our choice was to spread 32~MHz sub-bands at 256~MHz 
that allowed us to determine group delay with uncertainly 123~ps when the 
signal to noise ratio is 10 and with ambiguity of 3.9125~ns.

  Other stations were equipped with Mark-4 data acquisition terminals
that were replaced with Mark-5 during to the course of the campaign. Station
{\sc ceduna} was upgraded from the ATNF backend to Mark-5 in 2015 and used 
Mark-5 in last three observing sessions. The stations equipped with Mark-5 
recorded 256~MHz bandwidth, except {\sc tidbinbilla} that prior 2016 was able 
to record only 128~MHz and station {\sc askap} that could record a single 
bandwidth 64~MHz, dual polarization. The stations equipped with Mark-4 or 
Mark-5 recorded more 16~MHz wide frequency channels with 320~MHz wide bandwidth
that partly overlapped with the frequency channels recorded by the stations 
with the ATNF backend In every experiment network stations used from 2 to 5 
different setups and these setups were changing from the experiment to 
experiment. Figure~\ref{f:v271i_freq_setup} shows as an example the frequency 
setup of v271i experiment. The versatility of the DiFX-2 correlator 
\citep{r:difx2} allowed to cross-correlate the overlapping regions of such 
experiments. The heterogeneity of the available VLBI hardware made 
correlation more difficult but fortunately, did not introduced noticeable 
systematic errors in group delay. The most profound effect of this frequency 
allocation is ambiguities in group delay at baselines with stations that 
record with the ATNF backend.

  The telescopes at NASA's Deep Space Network (DNS) located at Tidbinbilla 
(Td), near Canberra participated in the network were, when available. 
These are Deep Space Station 34 (DSS-34, 34m, for v271h,j,m, and v441a),  
DSS-45 (34m, for v271a,b,l), and 43 (70m, for v493a). Their primary mission 
is to support communication with spacecraft but also support VLBI for 
celestial reference frame maintenance (for navigation) and astronomy for 
limited amount of time. For LBA, usually short blocks of 3-5 hour 34m 
time are available during time not suited for deep space communication. 
Mark5a system was used to record 8x16MHz channels for this series except 
v493a recorded 2x64MHz with LBA-DR. System temperatures at single-band 8GHz 
mode the are 22K, 20K, and 12K for DSS-45, DSS-34, and DSS-43, 
respectively \citet{r:dsn}. DSS-45 has been decommissioned in November 2016 
after operation for 34 years.

\begin{table}
   \caption{List of the LBA Calibrator Survey experiments. 
            The first column shows the campaign segment, the second 
            and third show the observing session and experiment ID, 
            and the last segment shows the network of participating
            stations.}
   \begin{tabular}{ @{\hspace{-0.0em}} l @{\hspace{1.0em}} l 
                    @{\hspace{1.0em}} l @{\hspace{1.0em}} l}
      \hline
      LCS--1 & 20080205\_r  & v254b & At-Cd-Ho-Mp-Pa    \\
      LCS--1 & 20080810\_r  & v271a & At-Cd-Ho-Mp-Pa-Td \\
      LCS--1 & 20081128\_r  & v271b & At-Cd-Ho-Mp-Pa-Td \\
      LCS--1 & 20090704\_r  & v271c & At-Cd-Ho-Mp-Pa \\
      \hline
      LCS--2 & 20091212\_r  & v271d & At-Cd-Ho-Mp-Pa \\
      LCS--2 & 20100311\_r  & v271e & At-Cd-Ho-Mp-Pa \\
      LCS--2 & 20100725\_p  & v271f & At-Cd-Ho-Mp-Pa \\
      LCS--2 & 20101029\_p  & v271g & At-Cd-Mp-Pa \\
      LCS--2 & 20110402\_p  & v271h & At-Cd-Ho-Hh-Ww-Td \\
      LCS--2 & 20110723\_p  & v271i & As-At-Cd-Ho-Hh-Mp-Pa-Td-Ww \\
      LCS--2 & 20111111\_p  & v271j & At-Cd-Ho-Hh-Mp-Td \\
      LCS--2 & 20111112\_p  & v441a & At-Cd-Ho-Hh-Mp-Td \\
      LCS--2 & 20120428\_p  & v271k & At-Cd-Ho-Hh-Mp-Pa-Ww-Yg \\
      LCS--2 & 20130315\_p  & v271l & As-At-Cd-Ho-Hh-Mp-Pa-Ww-Td \\
      LCS--2 & 20130615\_p  & v271m & At-Cd-Ho-Hh-Mp-Pa-Ww-Td \\
      LCS--2 & 20140603\_p  & v493a & At-Cd-Ho-Hh-Mp-Pa-Td \\
      LCS--2 & 20150407\_p  & v271n & At-Cd-Ho-Hh-Ke-Pa-Ww-Yg \\
      LCS--2 & 20150929\_q  & v271o & As-At-Cd-Ho-Hh-Ke-Pa-Ww-Yg \\
      LCS--2 & 20160628\_q  & v493c & As-At-Cd-Ke-Mp-Pa-Yg \\
      \hline
   \end{tabular}
   \label{t:lcs_exp}
\end{table}


\begin{figure}
    \includegraphics[width=0.48\textwidth]{v271i_freq_setup.pdf}

    \caption{The frequency allocation in v271i experiment. The channel
             width is 16~MHz for all stations, except As, which has
             the channel width 64~MHz. Single polarization channels are
             shown with light-gray color and dual polarization channels
             are shown with dark-Gray color.
             }
    \label{f:v271i_freq_setup}
\end{figure}

  The Australia Telescope Compact Array (ATCA) consists of six 22~m antennas.
Five of them can be phased up and record signal as a single element of the 
VLBI network. The position  of the ATCA phase center can be specified by 
the user. This feature became available in 2009. %\Note{Chris, correct?}.
However, we exercised a caution in using phased ATCA since attempts to
use phased Westerbork array for astrometry revealed significant phase 
fluctuations which rendered it highly problematic for precise astrometry 
(Sergei Pogrebenko, private communication, 2010). Therefore, we 
investigated performance of phase ATCA in a special 4~hour long test 
experiment that we ran on May 08, 2010. Stations {\sc atca, ceduna, 
hobart26, mopra}, and {\sc parkes} recorded the same frequency setup as 
in the LCS experiments. For the first 60 seconds of a 4 minute long scan 
ATCA recorded signal from the single antenna at pad with ID 104 (see LCS1 
paper for the nomenclature of ATCA pads), then it switched to the phased 
array with the phase center at the same pad and recorded for 90 second. 
Finally, ATCA switched back to recording the signal from a single station. 
In total, 232 scans of strong sources were recorded. The typical plots of 
the normalized uncalibrated fringe amplitude and fringe phase as 
a function of time within a scan are shown in figure ~\ref{f:frplot}. 

\begin{figure}
    \includegraphics[width=0.48\textwidth]{frplot_atca_parkes.pdf}
    \caption{The fringe plot at {\sc atca/parkes}, source {\sf J2225-0457}
             during vt10k test experiment. The upper plot shows fringe phase,
             the lower plot shows fringe amplitude. Light-gray area ``1'' 
             denotes the interval when single ATCA station records. 
             The dark-gray area ``3'' denotes the interval when the 
             phased-array records. The medium-gray area ``2'' denotes 
             the intermediate interval.}
    \label{f:frplot}
\end{figure}

  We see that for 18 seconds after switching to the phased-up mode the fringe
amplitude is steadily drops by 15\% and then suddenly returns back and stays 
stable within 2\%. We consider this as transitional interval. The fringe phase
does not show change greater 0.01 rad just after switching back to the phased 
mode, but shows a sudden change in a range of 0.1--0.2~rad after the end of
the transitional interval and immediately after switching from the phased
to the single antenna record mode.

  We computed average fringe phases, phase delay rates, group delays, and 
group delay rates by running the fringe fitting algorithm trough the same data 
three times. During the first processing run we masked out single antenna
recording mode and the first 18~s of the phased recording mode keeping 
72~s long data in each scan when ATCA recorded in the phased mode. During 
the second processing run we masked out the data when ATCA recorded in the 
phased mode. During the third run we processed first 60~s and last 90~s of 
each scan when ATCA recorded in the single antenna mode. We referred group 
delay and fringe phases to the same common epoch within a scan and formed 
their differences. 

  The differences in group delay between phased and single antenna 
recording mode at different baselines with ATCA is shown on 
Figure~\ref{f:atca_grdel} with green color. The weighted root mean square
(wrms) of the differences is 38~ps. For comparison, the differences in group 
delays computed using the first 60 seconds and last 90~seconds of a 4~minute 
long scan recorded at ATCA in the single antenna mode and referred to the 
same middle epoch are shown with blue color. The wrms of these differences
is 59~ps. The differences in fringe phase between recording at ATCA with 
phased model and single antenna mode are shown in Figure~\ref{f:atca_phase}.
The wrms of phase differences is 0.12~rad.

  We analyzed dependence if the differences versus elevation, azimuth and 
parallactic angle, but found no pattern. The uncalibrated averaged fringe 
amplitude at baselines with ATCA data recorded as a phased array is a factor
of~2.27 greater than the uncalibrated fringe amplitude with ATCA data 
recorded as a single antenna, which is within 2\% of $\sqrt{5}$.

  We conclude that phasing ATCA up does not introduce noticeable systematic
errors in group delay and fringe phases. The differences in group delays
is a factor of 1.5 less than the difference in group delay computed from
two subset of data separated by 90~s. The differences in phases is the random
noise with wrms is 0.12~rad, which corresponds to 0.6~mm. Therefore, we 
concluded that using of phased ATCA as an element of the VLBI network does
not introduce systematic errors, but improves sensitivity of ATCA by a factor
of 2.27. This was the first use of phased array as an element of a VLBI
network for absolute astrometry.

\begin{figure}
    \includegraphics[width=0.48\textwidth]{vt10k_grdel_diff.pdf}
    \caption{Differences in group delays from the same observations in
             test vt10k experiment. The solid green circles show
             the differences in group delay between ATCA phased-array
             and ATCA-single stations. The wrms of the differences is 38~ps. 
             For comparison, the whole blue circles show the differences 
             in group delay from first 60 sec and last 90 seconds of 
             the integration interval.}
    \label{f:atca_grdel}
\end{figure}

\begin{figure}
    \includegraphics[width=0.48\textwidth]{vt10k_phs_diff.pdf}
    \caption{Differences in fringe phase delays between ATCA phased-array
             and ATCA-single recording from the same observations in
             test vt10k experiment. The wrms of the differences ins 0.12~rad.}
    \label{f:atca_phase}
\end{figure}


\subsection{Source selection}

   We selected for observations the target sources that were previously 
detected with single dish observations or with connected interferometers
at baseline 0.1--5~km. The input catalogues provided the estimates of flux
density at angular resolutions 1--$100''$. The response of an 
interferometer to an extended source depends on its compactness and the 
size of the interferometer. The baseline projection lengths of the LCS 
network vary in a range of 5--300~M$\lambda$. That means the interferometer
will be sensitive for emission from the compact components of 
milliarcsecond size. The response to extended emission with a size more 
than 1~mas at the longest baselines and 50~mas at the shortest baselines
will be attenuated, and the interferometer will not detect signal
from emission with size a more than a factor 2--5 beyond that level.

   In order to maximize the number of detected sources, we have to
select the targets with the highest compactness: the ratio of the correlated
flux density at 5--300~M$\lambda$ to the total flux density. As a marker
of high compactness we initially used spectral index defined as
$S \sim f^\alpha$, where $f$ is the frequency. As a result of synchrotron
self-absorption the emission from the optically thick jet based that 
is morphologically referred to as the core of an AGN, has flat ($\alpha 
\approx 0$) or inverted spectrum ($\alpha > 0$). The optically think 
emission from the extended jet and extended radio-lobes that are a result 
of interaction of the jet with surrounding interstellar medium usually has 
steep spectrum ($\alpha < 1$). Therefore, one can expect the sources with 
flat spectrum, on average, will have a higher compactness, which was 
confirmed with observations \citep[e.g.,][]{r:vcs1}.

  For the coarse of the 8-year long campaign our sources selection strategy
gradually evolved, but all the time it was focused on selecting the sources 
with brightest correlated flux density. In the first three experiments we
selected the sources with spectral index $>-0.50$ from the quarter-Jansky
survey \citep{r:qJy} brighter 200~mJy. In following experiments were used
several criteria for selecting the targets. In experiments v271c--v271m we 
selected the candidate sources brighter 150~mJy with spectral index $>-0.55$
from the AT20G catalogue \citep{r:at20g}. In addition to that, we selected
the sources brighter 180~mJy and spectral index $>-0.55$ from the PMN
catalogue \citep{r:pmn1,r:pmn2,r:pmn3,r:pmn4,r:pmn5,r:pmn6,r:pmn7}.
In v271k--v271m experiments we selected the sources brighter 170~mJy and 
spectral index $>-0.55$ from the ATPMN catalogue \citep{r:atpmn}. 
The priority was given to sources with declinations $-40^\circ$, although
a small fraction of sources with declinations in a range 
[$-30^\circ, -40^\circ$] was also observed. We should not here that we 
selected {\it some} sources from these pools and did not have intention 
to select {\it all} the sources.

  However, an approach of selecting flat spectrum sources does not provide
a good prediction for correlated flux density for the sources within
5--$7^\circ$ of the Galactic plane. First, the Galactic plane is crowded
and a chance to make an error in cross-matching the sources observed with
instruments at different angular resolutions and poor positional accuracy 
is rather high. This will result in a gross mistake in the estimate of the 
spectral indices. Second, the density of galactic sources with flat spectrum, 
such as supernova remnants and ultra-compact H~II regions is much higher within
the Galactic plane. An attempt to observe flat spectrum sources in the Galactic
plane by cross-matching the MGPS-2 catalogue at 843 MHz \citep{r:mgps2} 
with other catalogues resulted in a detection rate of $\sim\! 10\%$. 
To overcome this problem, we used another approach to find candidate sources 
in the Galactic plane: we analyzed IR color-color diagram. \citet{r:massaro11} 
noticed that the blazars occupied a special zone in the color-color diagram
3.4--4.6~$\mu$m and 4.6--12~$\mu$m. We analyzed this dependence independently
and delineated the zone that encompasses over 85\% compact radio-loud AGNs
from the cumulative VLBI catalogue RFC (Petrov \& Kovalev, 2019, in 
preparation\footnote{Preview is available at \href{http://astrogeo.org/rfc}
{http://astrogeo.org/rfc}}). See section 4.2 in \citet{r:aofus2} for detail. 
After the failure with cross matching MGPS-2 with higher frequency radio 
catalogues, we tried the second approach: we selected all the sources within 
$5^\circ$ of the Galactic plane and declinations below $-40^\circ$ and flux 
density $> 50$~mJy and left those that have cross-matches against IR WISE 
catalogue \citep{r:wise,r:neowise} within $30''$. Then we threw away the 
sources that are beyond the zone of the 3.4--4.6~$\mu$m and 4.6--12~$\mu$m 
diagram that contains 85\% radio loud AGNs. We observed the brightest 
sources from the remaining sample. The detection rate of this sample 
was 57\%.

  In addition to these selection methods, we observed in three experiments,
v441a, v493a, and v493c, the flat spectrum sources brighter 10~mJy that were
detected at 5 and 9~GHz by the Australia Telescope Compact Array (ATCA) 
within its error ellipse, i.e. 2--$5'$ of unassociated sources $\gamma$-ray
sources detected with \Fermi\ mission \citep{r:fermi_1FGL} that 
we found in a dedicated program \citep{r:aofus1,r:aofus2,r:aofus3} focused in 
finding the most plausible radio counterparts of $\gamma$-ray source. Since 
radio-loud $\gamma$-ray AGNs tend to be very compact, the presence of
a radio source detected with a connected interferometer within the error 
ellipse of a $\gamma$-ray raises the probability of being detected with
VLBI. Observing such sources, first fits the primary goal of the LCS program,
second, allows to find an association to \Fermi\ objects that previously were
considered unassociated.

\subsection{Scheduling}

  The experiment schedules were generated automatically with program 
{\sf sur\_sked} in a sequence that minimizes the slewing time and obeys
a number of constraints. Target sources were observed in three to four scans 
for 2 to 4 minutes long each, except weak targets of candidates to \Fermi\ 
associations that were observed for 5--10~minutes. VLBI experiments had 
a nominal duration of 24 hours. During each session, 80--100 target sources
were observed. The minimum gap between consecutive observations of the same 
source was set to 2.5~hours. Station {\sc parkes} was required to participate 
in each scan, since it is the most sensitive antenna of the array. After 
1.5~hours of observing targets sources, a block of so-called calibrator
sources was inserted. These are the sources picked from the pool of known 
compact objects stronger 300~mJy. The block consists of 4 sources, with two
of them observed at each station in the elevations in the range of 
10--$30^\circ$ (30--$40^\circ$ for {\sc parkes} that have elevation limit 
$31^\circ$) and two observed at elevations 55--$85^\circ$. The goal of 
these observations: 1)~to improve the estimate of the atmosphere path delay
in zenith direction; 2)~to connect the LCS catalogue to the accumulative 
catalogue of compact radio sources; 3)~to use these sources as bandpass 
calibrator; 4)~to use these sources as amplitude calibrators for elevation 
gain corrections.

\section{Data analysis}

   The antenna recorded voltage sampled with 2-bits and the aggregate
bit rate from 256 to 1024 millions of samples per second. The first
step of data analysis is correlation that is performed at the dedicated
facility followed by post-correlator analysis that computes group 
delays and phase delay rates using the spectrum of cross-correlated data,
followed by astrometric analysis that computes source positions, followed 
by amplitude analysis that either produces source images or estimates 
of the correlated flux density at the specified range of the lengths 
of projected baselines.

\subsection{Correlation and post-correlation analysis}

  The first four experiments were correlated with the Bonn Mark4 Correlator.
The data from \atca, \ceduna, and \mopra, originally recorded in LBADR format,
were transformed to the Mark5B format before correlation. Correlation of the 
data from LBADR data acquisition rack against the data from the Mark-4 data
acquisition terminal was complicated since this is a non-standard
operation. Post-correlation analysis of these data was performed at the 
correlator using software program {\sc fourfit}, the baseline-based fringe 
fit offered within the Haystack Observatory Package Software ({\sc hops}) 
to estimate the residual group delay and phase delay rate. More detail about
processing these experiments can be found in \citet{r:lcs1}.

  Other experiments were correlated with the DiFX software correlator 
\citep{r:difx2} at the International Centre for Radio Astronomy Research,
the joint venture between Curtin University and the University of Western 
Australia. The output of DiFX correlator was converted to FITS-IDI format
and further processed with PIMA VLBI data analysis software \citep{r:vgaps}.
The correlator provided the time series of the auto- and cross-spectrum of
the recorded signal with spectral resolution 0.25~MHz and time resolution 
0.25~s. Such a choice of correlation parameters allowed us to detect a sources 
within several arcminutes of the pointing direction, i.e., everywhere within 
the primary beam of {\sc parkes} radio telescope that has full with half 
maximum (FWHM) at 8.4~GHz close to $2'$.

   The post-correlator analysis chain includes the following steps:

\begin{itemize}
   \item Coarse fringe fitting that is performed using an abridged grid
         of group delays and delay rates without further refinement.
         The goals of this step is to find at each baseline 10--15 
         observations with the highest signal to noise ratio (SNR) 
         and detect failures at one or more IFs.

   \item Computation of a complex bandpass using the 12 observations 
         with the highest SNR. The complex bandpass describes a distortion
         of the phase and amplitude of the recorded signal with respect
         to the signal that reached the antennas. We flagged at this step
         the IFs that either were not recorded or failed. We used 
         12 observations for redundancy in order to evaluate the statistics 
         of residual deviation of the phase and amplitude as a function of 
         frequency from the ideal after applying the bandpass computed over
         the 12 observations using least squares. Large residuals triggered 
         detailed investigation that in a case of serious hardware 
         problem resulted in flagging affected spectral channels.

   \item Fine fringe fitting that is performed using the
         complex bandpass and the bandpass mask derived in the previous 
         step. The preliminary value of the group delay and phase delay 
         is found as the maximum element of the two-dimensional Fourier 
         transform of the time series of cross-correlation spectrum sampled
         over time and frequency with a step 4 times finer over each dimension
         than the original data. The fine value of the group delay and phase 
         delay rate is adjusted from phases of the cross-correlation function
         (also known as fringe phases) as small corrections to the preliminary 
         values using least squares. Phase residuals of the cross-correlation 
         spectrum are analyzed and additive corrections to the a~priori weights 
         are computed on the basis of this analysis. The uncertainties of 
         estimates of group delays are derived from uncertainties of fringe
         phases and additive weights corrections. The uncertainties of fringe
         phases depend on fringe amplitudes. The explicit expression can be
         found on page 233 of \citet{r:tms}.

   \item Computation of total group delays and phase delay rates. The 
         group delays and phase delay rates derived at the previous 
         step are corrections to the a~priori delays and phase delay rates
         used during correlation. The mathematical model of the a~priori group 
         delay and phase rate used by the correlator is expanded over polynomials
         of the 5th order at 2~minute long intervals that cover the time range of 
         a VLBI experiment. Using these coefficients, the a~priori group delays 
         and phase delay rates are computed to a common epoch within a scan for 
         the event of arriving the wavefront at a reference station of a baseline. 
         Using these a~priori group delays and phase delay rates, the total group 
         delays for that epoch are formed. 
\end{itemize}

\subsection{Astrometric analysis}

  Total group delay is the main observable for astrometric analysis. During 
further analysis, the a~priori model of group delay, more sophisticated than 
that used for correlation, is computed, and the differences between observed 
and theoretical path delays are formed. The partial derivatives of this model 
over source coordinates, station positions, the Earth ordination parameters, 
atmosphere path delay in zenith direction, and clock function are computed.
Then corrections to that parameters are adjusted using least squares.

  The frequency setup used for this campaign, selected due to hardware 
limitation, see as an example the setup for v271i segment in 
Figure~\ref{f:v271i_freq_setup}, posed a challenge in data analysis. The 
Fourier transform over frequency over baselines with {\sc atca, ceduna, mopra} 
in this example that uses LBDAR data acquisition system has strong secondary 
maxima (see Figure~\ref{f:drf}). The amplitude of the 2nd maximum is 0.98, the 
third maximum 0.93, and the fourth maximum 0.83 with respect of the global 
maximum. Due to the noise in data and phase distortion, the fringe fitting 
process cannot reliably distinguish the primary and the secondary maxima,
and as a result, group delay is determined with the ambiguity of 
$N \times 1/2.56 \cdot 10^{8} \approx 3.9$~ns, where $N$ is a random integer 
number, typically in a range [-2,2].

\begin{figure}
    \includegraphics[width=0.48\textwidth]{drf.pdf}
    \caption{The normalized fringe amplitude as a function of group delay 
             between stations that had LBDAR recording system. The fringe 
             amplitude is divided by the amplitude at the global maximum.
            }
    \label{f:drf}
\end{figure}

  The first stage of the astrometric data analysis is to use for least squares
the so-called narrow-band group delays derived as an arithmetic average of 
group delays computed over each IF independently. The dataset of narrow-band
group delays is to be cleaned for outliers during the residual analysis 
procedure. The narrow-band delays do not have ambiguities, but are one order 
of magnitude less precise than group delays computed over the entire band. 
The estimated parameters at this stage are station positions and coordinates 
of target sources, as well as atmospheric path delays in zenith direction 
and clock function in a form of expansion over the B-spline basis. 
The contribution of the adjusted parameters to path delay computed using 
the narrow-band delays is substituted to the group delay residuals and then 
used for initial resolving group delay ambiguities. The procedure for group 
delay ambiguity resolution is described in detail in \citet{r:lcs1}.

  After the group delay ambiguities are resolved, the dataset is cleaned for
outliers in group delay. If necessary, the parametric model of clock is refined 
for incorporating discontinuities at specified epochs. Initial data weights 
were chosen to be reciprocal to the group delay uncertainty $\sigma_g$. Then 
the additive baseline-dependent wight corrections $a$ were computed for each 
observing session to make the ratio of the weighted sum of residuals be close 
to their mathematical expectation. These weights we used in the initial 
solution. The weights used in the final solution had a form
%
\beq
  w = \Frac{1}{k \cdot \sqrt{\sigma_g^2 + a^2 + b^2}},
\eeq{e:e1}
%
where $k$ is a multiplicative factor and $b$ an additive weight correction 
for taking into account mismodeled ionosphere contribution to group delay 
(see below). Such clean dataset of group delays is used in further analysis.

  The final LCS catalogue was derived using all dual-band X/S (8.4/2.3 GHz)
observations since 1980 through July 2018 under geodesy and astrometry 
programs that are publicly available and 19 LCS X-band experiments in a single 
least square solution. The estimated parameters are split into three groups:
global parameters that are adjusted for the entire dataset, local parameters
that are specific for a given experiment, and segmented parameters that 
are specific for a time interval shorter than the observing session duration. 
The global estimated parameters are coordinates of all observed sources, 
positions and velocities of all observing stations, harmonic variations of 
station positions at annual, semi-annual, diurnal, and semi-diurnal 
frequencies, as well as B-spline coefficients that describe discontinuities 
and non-linear motion of station caused by seismic activity. The local 
parameters are pole coordinates UT1 and their first time derivative. The 
segmented parameters are clock function for all the station except the 
reference one, and residual atmosphere path delay in zenith direction.

   For the course of LCS campaign, a number of target sources were observed 
in follow-up VLBI experiments. We excluded these sources from dual-band 
experiments in our LCS solution. The position of LCS target sources were 
derived using only LCS 8.3~GHz data. Observations of these sources were 
later used for evaluation of errors of the LCS catalogue and computation 
of the multiplicative weight correction $k$.

  Since equations of electromagnetic wave propagation are invariant with 
respect to rotation of the celestial coordinate system, as well as 
translation and rotation of terrestrial coordinate system, the system of 
equations have a rank deficiency and determines only a family of solutions. 
In order to define the solution from that family, we applied no-net-rotation 
constraints for source coordinates requiring the new positions of 212 
so-called defining sources have no net-rotation with with respect to their 
positions in the ICRF1 catalogue \citep{r:icrf1}. Similarly, we imposed the 
no-net-rotation and no-net-translation constraints on station positions 
and velocities.

\subsection{Imaging analysis}

  Since the median number of observations is 30, generation images 
using LCS data is problematic. Considering the scarcity of data and
a poor $uv$-coverage, direct imaging either produces a map with 
a dynamic range 1:10 to 1:100 with a high chance of an imaging artefact 
be unnoticed or, if to pursue elimination of artefacts aggressively, the 
image will be close to a point-source or a single component Gaussian.

  Recognizing these challenges, we limited our amplitude analysis to 
evaluation of a simplified source model. In this paper we limited 
our analysis to evaluation of the mean correlated flux density 
estimates in three ranges of lengths of the baseline projections 
onto the plane tangential to the source, without inversion of 
calibrated visibility data using the same technique as we used for
processing first 4 LCS experiments \citep{r:lcs1}. A reader is 
referred to this publication for detail. Here we outline the procedure.

   At the first step, we analyze system temperature, remove outliers,
evaluate the radiative atmosphere temperature, compute receiver
temperature, interpolate it for restoring missing data, and generate
a cleaned dataset of system temperatures. Dividing it by the a~priori 
elevation-dependent antenna gain, we get the a~priori system equivalent
flux density (SEFD). 

  At the second step, we estimate station-dependent multiplicative gain 
corrections to calibrated fringe amplitudes of calibrator sources with 
least squares by using a number of sources with known 8~GHz images that 
can be found in the Astrogeo VLBI FITS image 
database\footnote{Available at \href{http://astrogeo.org/vlbi\_images/}
{http://astrogeo.org/vlbi\_images/}}
that we maintain. During this procedure, we iteratively exclude those 
images which resulted in large residuals. Due to variability, the flux 
density of some individual sources may raise or decline, but the average 
flux density of a sample of sources is expected to be more stable than 
the flux density of individual objects.

  At the third step, we apply adjusted SEFDs and compute the correlated flux
densities of target sources. Then we sort the fringe amplitude over 
baseline projection lengths and compute median estimates of the correlated
flux density in three ranges: 0--10~M$\lambda$ ($<360$~km), 
10--40~M$\lambda$ (360-1440~km) and 40--300~M$\lambda$ (1400--10800~km).
These parameters characterize the strength of a source, and it has to be 
accounted for scheduling the observations. The accuracy of this procedure 
is estimated at a level of 20\% judging on residuals of gain adjustments.

  The list of 49915 estimates of correlated flux densities from individual 
observations of 1100 target sources and 368 calibrator sources is presented 
in the machine-readable table datafile3. The table contains  the following 
information: source name, date of observations, baseline name, $u$- and $v$- 
projections of the baseline vector, the correlated flux density and their 
formal uncertainty, the signal to noise ratio, the instants system 
equivalent flux density for this observation, and the observing session 
code.

\section{Error analysis}

  Single-band group delays are affected by the contribution of the ionosphere.
Considering the ionosphere as a thin shell at a certain height above the Earth
surface (typically 450 km), the group delay can be expressed as
%
\beq
  \tau_{\rm iono} = \Frac{\alpha}{f^2_{\mbox{eff}} } \: 
                \mbox{TEC} \: \Frac{1}{\cos{\beta}},
\eeq{e:e2}
%
  where $f_{\mbox{eff}}$ is the effective frequency, $\beta$ is the zenith 
angle at the ionosphere piercing point, TEC is the total electron contents 
in the zenith direction at the ionosphere piercing point, and  $\alpha$ is 
a constant (see \citet{r:sovers98} for detail). We have computed the a~priori 
ionosphere contribution to group path delay using TEC maps from analysis 
of Global Navigation Satellite System (GNSS) observations. Specifically,
we used CODE TEC time series \citep{r:schaer99}\footnote{Available at 
\href{ftp://ftp.aiub.unibe.ch/CODE}{ftp://ftp.aiub.unibe.ch/CODE}} with 
a resolution of $5^\circ \times 2.5^\circ \times 1^h$ 
($5^\circ \times 2.5^\circ \times 2^h$ before December 19, 2013).

  The TEC model from GNSS observation is an approximation, and the accuracy
of a~priori $\tau_{\rm iono}$ from such a model is noticeably lower than the
accuracy of $\tau_{\rm iono}$ computed from the linear combination of group
delays at X and S (or X and C) bands from dual-band observations. The errors
of $\tau_{\rm iono}$ from such observations is at level of several picoseconds
according to \citet{r:hob05}. We consider the contribution of mismodeled 
ionospheric path delay as the dominating source of systematic errors and, 
therefore, we investigated it in detail.
  
  We used the global dataset of VLBI observations after July 01, 1998 for 
investigation of the residual ionospheric contribution to group delay after
applying the a~priori path delay delay derived from CODE global TEC maps.
For each dual-band observing sessions, we decompose the slant ionospheric 
path delay from X/S observations at the product of the path delay in 
zenith direction and the mapping function, the ratio of the ionospheric 
path delay in a given elevation to the ionospheric path delay in 
zenith direction. Then we computed the rms of the total $\tau_{\rm iono}$ 
in zenith direction from CODE global TEC maps, $\sigma_t$, and the rms of 
the differences in $\tau_{\rm iono}$ in zenith direction computed using
the CODE global TEC maps and the dual-band X/S group delays, $\sigma_r$. 
The ratio of these two statistics, variance admittance 
$A = \frac{\sigma^2_r}{\sigma^2_t}$, is a measure of the model goodness. 
Assuming $A$ is stable, we can predict, unknown to us, statistics of 
$\sigma^2_r$ for single-band observations using $\sigma^2_t$ that we can 
compute from TEC model. We derived time series of parameter $A$ from 
analysis of all dial-band observations after July 01, 1998.

  Parameter $A$ is not stable with time. Since $A$ is computed as a ratio
of variances, we sought an empirical regression models where $A$ enters 
as a multiplicative factor. We computed the global total electron content 
(GTEC), by averaging the TEC over the sphere. As it was show by \citet{r:gtec},
such a parameter characterizes the global state of the ionosphere. 
Figure~\ref{f:gtec} shows the dependence of $A$ on GTEC. We represent this
dependence with a broken linear function with A=0.6 at GTEC=7.0, A=0.35 at 
GTEC=20.0 and A=0.25 at GTEC=60.0.

\begin{figure}
    \includegraphics[width=0.48\textwidth]{alpha_gtec.pdf}
    \caption{The dependence of the variance admittance factor $A$ on the 
             global total electron contents. The so-called TEC units 
             ($10^{16}$ electrons over zenith direction) are used for GTEC.}
    \label{f:gtec}
\end{figure}

  Using this dependence, for a given experiment we computed the GTEC, averaged
it over the period of experiment duration, computed parameter $A$ using the 
linear regression, computed the time series of the ionospheric contribution 
from the GTEC model for each station of a baseline, and then computed the 
variances of the mismodeled contribution of the ionosphere to group delay in 
zenith direction for the first and second station  of a  baseline, $\Cov_{11}$ 
and $\Cov_{22}$, as well as their covariances. Then for each observation we 
computed the predicted rms of mismodeled ionospheric contribution as

{\small \beq
  b = A \sqrt{\Cov_{11}^2 \, M_1^2(e) - 2 \Cov_{12} \, M_1(e) \, M_2(e) + 
         \Cov_{22}^2\, M_2^2(e) }, \hspace{-0.75em}
\eeq{e:e3} }
%
  where $M_1(e)$ and $M_2(e)$ are mapping function of the ionospheric path
delay. These parameters $b$ were used for weight corrections in 
expression~\ref{e:e1}.

  Parameter A varied from 0.35 to 0.59 with the mean 0.48 for the LCS campaign.
This means that applying the ionospheric contribution from the CODE TEC maps, 
we reduce the variance of the total contribution by a factor of 2, and the 
mismodeled part of the contribution is accounted in inflating uncertainty
of group delay. The known deficiency of this approach is that first, the 
regression dependence of parameter on $A$ on GTEC is rather coarse, and second, 
the correlations between residual ionospheric contributions are neglected.

  For a check of the contribution of remaining systematic errors, we compared 
our source positions derived from X-band only LCS experiments with results 
of dial-band observations that included some LCS target sources. In 2017, 
the SOuthern Astrometry Program (SOAP) of dual-band follow-up observations at 
stations Hh-Ho-Ke-Yg-Wa-Ww-Pa at 2.3/8.4 GHz commenced. The goal of the program 
is to improve positions of bright sources with declinations below $-45^\circ$. 
Buy August 2018, 10 twenty-hour experiments were observed. In two of them, 
{\sc parkes} station participated. The sources as week as 70~mJy were observed 
in experiments with {\sc parkes}, 2--3 scans per sources, and objects brighter 
250~mJy were observed in other experiments, 8--10 scans per source. These 
experiments were made in the so-called geodetic frequency setup: 6 IFs of 
16~MHz wide were spanned between 2.20 and 2.304 GHz (S-band) and 10 IFs of 
16~MHz wide were spanned between 8.198 and 8.950~GHz (X-band). Group delays 
were computed for X and S band separately, and the ionosphere-free 
combinations of group delays were formed. At the moment of writing, 
the program has not finished, and a detailed analysis will be presented in 
the future upon completion of the program. Meanwhile, we use these 
10 experiments to compare results and assess the errors.

\begin{figure}
    \includegraphics[width=0.48\textwidth]{lcs2_norm_distr.pdf}
    \caption{The distribution of the normalized arc lengths between LCS
             X-band only positions of 269 sources and their X/S positions 
             from the follow-up campaigns (Green dots). For comparison,
             the Rayleigh distribution with $\sigma=1$ parameter is shown
             with a blue line.}
\end{figure}

  We ran a reference global solution using all dual band X/S observations 
of the LCS target sources including the SOAP observations and excluding 
LCS observations. The reference and the LCS solutions differed 1) in 
the list of sessions that were used in the solutions and 2) in treatment
of the atmosphere. The reference solution used ionosphere-free linear
combinations of S and X-band observables, while the LCS solution used X-band
only group delays and during data reduction applied the ionosphere 
contribution to group delay using the CODE TEC maps. The reference solution 
used weights according to expression \ref{e:e1} with k=1 and b=0.


\begin{figure}
    \includegraphics[width=0.48\textwidth]{lcs2_err_cumul_hist.pdf}
    \caption{The cumulative distribution of the LCS position errors.}
    \label{f:lcs2errs}
\end{figure}

   We have compared the positions of 373 LCS target sources that 
are common with the reference solution. We did not find any outlier 
exceeding 20~mas that can be caused by errors in group delay ambiguity 
resolution. That means that all observations with unreliable ambiguity 
resolution were correctly flagged out and did not degrade the solution. 
At the same time, we found that the arc lengths divided by the their 
uncertainties, so-called normalized arcs, were larger than expected with 
the mean value 1.89. We attributed this discrepancy to the 
underestimation of errors of LCS observations. To alleviate this 
underestimation, we varied the multiplicative factor $k$ in expression 
\ref{e:e1} in such a way the distribution of normalized arcs be as close 
to the Rayleigh distribution with $\sigma=1$ as possible. We found that 
when $k=1.80$ is used for analysis of LCS observations, it approximates 
the distribution of normalized arcs over 269 sources that have at least 
16 observations the Rayleigh distribution the best way. The mean
arc length is 3.4~mas and the median value is 2.5~mas. The cumulative
distribution of the final LCS position errors is shown in 
Figure~\ref{f:lcs2errs}.

\section{The catalogue}

  The first 8 rows of the LCS catalogue are presented in Table~\ref{t:lcscat}
The catalogue presents source positions, position uncertainties, the 
number of used observations, flux densities in three ranges of baseline 
projection lengths, and their formal uncertainties. In total, the catalogue
has 1100 entries. The median semi-major error ellipse axes of reported 
positions is 3.6~mas. The flux densities are in a range from 3~mJy to 2.5~Jy,
with the median 102~mJy. For completeness, the list of 405 sources that have 
been observed, but not observed is given in the machine-readable table 
datafile2. The flux densities of such sources turned out below the detection
limit that at baselines {\sc parkes}/{\sc atca}, {\sc parkes}/{\sc hobart26}, 
{\sc parkes}/{\sc ceduna} is typically 6--8~mJy.

\begin{table*}
   \hspace{-2.0em}
   \scalebox{0.88}{
      \begin{tabular}{rrrrrrrrrrrrrr}
          \hline
            \ntab{c}{(1)}  & \ntab{c}{(2)}  & \ntab{c}{(3)}  & \ntab{c}{(4)}  & \ntab{c}{(5)}  & 
            \ntab{c}{(6)}  & \ntab{c}{(7)}  & \ntab{c}{(8)}  & \ntab{c}{(9)}  & \ntab{c}{(10)} & 
            \ntab{c}{(11)} & \ntab{c}{(12)} & \ntab{c}{(13)} & \ntab{c}{(14)}                  \\
                           &   & hh mm ss.fffff \hphantom{.} & $ {}^\circ \hspace{1em} {}' \hspace{1em} {}'' \hphantom{aaa}$   & mas & mas & & & Jy & Jy & Jy & Jy & Jy & Jy \\
          \hline
          LCS J0001$-$4155 & 2358$-$422 & 00 01 32.75494 & $-$41 55 25.3367 &  215.1 & 92.3 & -0.904 &    5 &  0.008 &  0.007 & -1.0  &  0.001 & 0.002 & -1.0 \\
          LCS J0002$-$6726 & 2359$-$677 & 00 02 15.19280 & $-$67 26 53.4337 &   89.6 & 32.8 &  0.553 &    5 &  0.006 &  0.007 & -1.0  &  0.001 & 0.001 & -1.0 \\
          LCS J0002$-$5621 & 0000$-$566 & 00 02 53.46830 & $-$56 21 10.7831 &   23.8 &  9.3 &  0.421 &    8 &  0.172 &  0.052 &  0.141&  0.013 & 0.012 &  0.031 \\
          LCS J0003$-$5444 & 0000$-$550 & 00 03 10.63084 & $-$54 44 55.9923 &   42.1 & 10.7 & -0.112 &    9 &  0.006 &  0.006 & -1.0  &  0.001 & 0.001 & -1.0 \\
          LCS J0003$-$5247 & 0000$-$530 & 00 03 19.60042 & $-$52 47 27.2834 &   39.0 & 18.5 & -0.291 &    8 &  0.013 &  0.014 & -1.0  &  0.002 & 0.002 & -1.0 \\
          LCS J0004$-$4345 & 0001$-$440 & 00 04 07.25762 & $-$43 45 10.1469 &    4.0 &  3.0 &  0.163 &   44 &  0.188 &  0.205 &  0.214&  0.030 & 0.024 &  0.046 \\
          LCS J0004$-$5254 & 0001$-$531 & 00 04 14.01314 & $-$52 54 58.7099 &    8.8 &  3.7 &  0.039 &   36 &  0.027 &  0.027 &  0.018&  0.002 & 0.003 &  0.003 \\
          \hline
      \end{tabular}
   }\hfill
   \caption{The first 8 rows of the LCS catalogue. Columns: (1) source ID; 
            (2) alternative source name; (3) J2000 right ascension; 
            (4) J2000 declination; (5) uncertainty in right ascension without $\cos\delta$ factor;
            (6) uncertainty in declination; (7) correlation between right
            ascension and declination estimates; (8) the number of 
            observations used in the solution; (9) the median correlated 
            flux density at baseline projection lengths in a range 
            0--10~M$\lambda$; (10) the median correlated flux density at 
            baseline projection lengths in a range 10--40~M$\lambda$; 
            (11) the median correlated flux density at baseline projection 
            lengths in a range 40--300~M$\lambda$; 12) the median uncertainty
            of the correlated flux density at baseline projection lengths 
            in a range 0--10~M$\lambda$; (13) the median uncertainty of the 
            correlated flux density at baseline projection lengths in a range 
            10--40~M$\lambda$; (14) the median uncertainty of the correlated 
            flux density at baseline projection lengths in a range 
            40--300~M$\lambda$.
%
            This table is available in its entirety in machine-readable
            table datafile1 and Virtual Observatory (VO) forms in the online 
            journal. A portion is shown here for guidance regarding its form
            and content. }
    \label{t:lcscat}
\end{table*}

  The distribution of LCS sources on the sky is shown in 
Figure~\ref{f:skydist}. The distribution is rather uniform and does not have
avoidance zones. For comparison, the sources known priori the LCS 
campaign are shown with blue color.

\begin{figure}
    \includegraphics[width=0.48\textwidth]{lcs2_map.pdf}
    \caption{The sky distribution of compact radio sources at the southern
             hemisphere. Blue light color denotes 186 sources with 
             declinations $< -40^\circ$ with VLBI positions known prior 
             the LCS program. Green dark color denotes 1100 sources 
             detected in LCS program. Red line shows the Galactic plane.}
    \label{f:skydist}
\end{figure}

\section{Discussion}

  The median position uncertainty, 3.6~mas, cannot be called the VLBI state 
of the art nowadays. There are four factors that played the role. First, 
the contribution of the ionosphere cannot be computed using GNSS TEC models 
with the same level of accuracy as using simultaneous dual-band observations. 
Second, the scale of the network, less than 1700 km for the most observations 
degraded the sensitivity of observations to source positions, since the 
source position uncertainty is reciprocal to the baseline length. Station 
{\sc hartrao} participated in less than 25\% observations. Third, the 
spanned bandwidth was limited to 320~MHz, compare with 720~MHz typically 
used in geodetic VLBI. Position uncertainty is approximately reciprocal to 
the spanned bandwidth. Fourth, observed sources were rather week: 25\% 
target sources are weaker 46~mJy.

  Nevertheless, position accuracy of several milliarcseconds is sufficient 
for phase referencing. Figure~\ref{f:caldens} shows the probability to 
find a phase calibrator brighter 30~mJy within $2^\circ$ of any target with 
$\delta < -40^\circ$. For 88\% of the area, such a calibrator can be found.
Learning the flux densities of detected sources and striking out undetected
ones that are supposed to be weaker 6--8~mJy, greatly facilitates future
follow-up observations of the sources which positions are sought to be 
known with a higher accuracy.

\begin{figure}
    \includegraphics[width=0.48\textwidth]{lcs2_dens_mas.pdf}
    \caption{The sky density of calibrator sources in the zone with 
             declinations $< -40^\circ$ defined as the number of compact sources
             with flux density $> 30$ mJy in a circle of $2^\circ$ radius.
             The Galactic plane is shown with the red line.}
    \label{f:caldens}
\end{figure}

   Among 1100 LCS sources, there are 725 counterparts with \Gaia\ DR2 
\citep{r:gaia2} with the probability of false detection below 0.0002. 
See \citet{r:gaia1} for detail of the VLBI and \Gaia\ association procedure.
\citet{r:gaia4} showed that comparison of over 9,000 matched VLBI/\Gaia\
sources reveled that 9\% have statistically significant offsets at 
the level exceeding $4\sigma$. They presented extensive argumentation that 
these offsets are real and are manifestation of the presence of optical
jets that affect positions of optic centroid reported by \Gaia. The LCS
dataset has 53 (7.2\%) outliers with arc length exceeding $4\sigma$. The 
lower fraction of outliers is explained by worse position accuracy. These 
outliers were excluded from further analysis, since they do not characterize
errors of the catalogues. The median arc length of position differences is 
3.2~mas, while the median semi-major error ellipse axes of LCS positions of 
matched sources is 3.3~mas and the median semi-major error ellipse of \Gaia\ 
positions of matched sources is 0.3~mas. This comparison demonstrates that
the median position differences between LCS and \Gaia\ positions is very 
close to the reported median of LCS semi-major error axis. 

  For analysis of LCS completeness we computed the so-called logN--logS 
diagram --- the dependence of the logarithm of the number of sources 
on the logarithm of the total flux density recovered from VLBI observations.
The dependence is approximated with a straight line within that range 
of flux densities the catalogue is considered complete. With a decrease
of flux densities, at some point the diagram deviates from the straight 
line. That point is considered the limit, below which the catalogue 
is incomplete. The diagram in Figure~\ref{f:lognlogs} shows the completeness 
level of the LCS subsample at $\delta < -40^\circ$ drops below 95\% at
flux densities 120~mJy.

\begin{figure}
    \includegraphics[width=0.48\textwidth]{lcs2_logn_logs.pdf}
    \caption{The log N--log S diagram for the LCS catalogue (low green 
             line) using only the sources with $\delta < -40^\circ$.
             The upper red line shows similar diagram for the 
             sources with $\delta > +40^\circ$.}
    \label{f:lognlogs}
\end{figure}

  For comparison, we computed a similar diagram at the northern hemisphere 
at declinations $>+40^\circ$ using the Radio Fundamental Catalogue. The 
northern hemisphere catalogue has more weak sources, but surprisingly, its 
completeness drops below 95\% level at flux densities 150~mJy. At the same 
time, the northern hemisphere catalogue has 23\% more sources. 
One explanation is the total number of sources in the southern hemisphere 
is indeed $\sim\! 20$\% less due to a large scale fluctuation of the source 
distribution over the sky. Another explanation is a selection bias. 
The parent catalogue of the LCS is AT20G at 20~GHz, while the parent 
catalogues of the northern hemisphere sources were observed at lower 
frequencies: 5--8~GHz. Selecting sources based in their emission at 20~GHz 
may result in omitting the objects with falling spectrum. The logN--logS 
dependencies for southern and northern hemispheres are almost parallel in 
a range of 0.15--0.65~Jy. If we accept the hypothesis that selecting 
candidate sources based on AT20G catalogue causes a bias, we have to admit 
that using AT20G as a parent sample we lose sources as bright as 0.5~Jy, 
which is difficult to swallow up. We think the problem of completeness 
of the LCS is open, and more observations are needed in order to 
resolve it.


%% \section{Population analysis}
%% 
%% \Grb{Elaine: this is the part where I anticipate your contribution. 
%% I suggest to take all the cross-matches between AT20G and VLBI, not limiting
%% ourselves to LCS2 only. The majority of matches will be from LCS1,2 but I 
%% do not think we should exclude the sources from VLBI.
%% }
%% 
%% \Grb{
%% I bear in mind compactness analysis (ration of VLBI to AT20G flux density), 
%% correlation  between compactness and spectral indices. Anything else?
%% }

\section{Summary}

   The LCS VLBI observing program provided positions of 1100 compact radio 
sources at declinations below $-30^\circ$ known with accuracies at 
a milliarcsecond level and estimates of their flux density at 8.3~GHz. 
As a result, the number of compact radio sources south of declination 
$-40\degr$ which have measured VLBI correlated flux densities and positions 
known to milliarcsecond accuracy has increased by a factor of 6.4. 
The internal LCS completeness test based on the logN--logS diagram shows it 
is complete at 95\% at a level of 120~mJy. At the same time, comparing LCS 
with the northern hemisphere catalogue, we found a $\sim\! 20$\% difference 
in the source count. The LCS may have a deficiency of $\sim\! 20$\% sources 
because of using AT20G as a parent sample. It is yet to be resolved whether 
using high-frequency sample catalogue results in systematic loss of sources 
with falling spectrum. The LCS catalogue is the southern hemisphere 
counterpart of the VLBA Calibrator Survey. The major outcome of this campaign
is elimination of the hemisphere bias that the VLBI catalogues suffered in 
the past. However, technical limitations of the southern hemisphere 
telescopes provided position accuracy one order of magnitude worse than 
the accuracy of similar catalogues in the northern hemisphere. Future 
observations will target LCS sources for improvement of their positions, 
and the first such follow-up observing campaign started in 2017.

\section*{Acknowledgments}
  
  The authors would like to thank \ldots.
The Long Baseline Array is part of the Australia
Telescope National Facility which is funded by the Commonwealth of
Australia for operation as a National Facility managed by CSIRO.

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