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\author{}
\title {\vspace{-6ex} \LARGE\bf 
        Title
       }
\title {\vspace{-8ex}\hphantom{a}}
\date{}


\begin{document}

\maketitle

\hA\vspace{-18ex}\hA\par
\section{Introduction}

\section{Primary scientific goal}

\section{Secondary scientific goal: Population analysis}

  The secondary goal of the project is to investigate the relationship 
between compactness, spectral index at kiloparsec scale (angular size at 
arcsecond level), spectral index at parsec scale (angular size at 
milliarcsecond level), source size and its morphology at parsec scales
from VLBA images and kiloparsec scales using VLA images from NVSS and 
VLASS. The key scientific questions are

\begin{itemize}\renewcommand{\labelitemi}{$\mathbf\circ$}\setlength{\itemsep}{0.5ex}
   
   \item Which parts of an AGN dominates in emission at different 
         frequencies and different resolutions?

   \item Can the spectral index be used as a discriminator of radio source
         properties? If yes, which properties and what are the eliminations?

   \item How different the statistics of VLBI detected sources drawn from
         flat-spectrum biased parent samples are different from the 
         statistics drawn from unbiased samples? How many compact sources 
         do we miss? For instance, CRATES catalogue of flat spectrum sources
         \citep{r:crates} was used by {\it Fermi} mission for associations 
         of $\gamma$-rays sources with AGNs. How many AGN associations were
         missed due to the selection bias?
\end{itemize}

  This will be achieved by analysis of four \Blb{complete} samples: 
1)~the Northern Polar Cap Survey drawn from NVSS \citep{r:nvss} with 
flux density limit S(1.4~GHz) $>250$~mJy, $\delta > 75^\circ$; 
2)~Ecliptic band drawn from GB6 and PMN catalogues \citep{r:gb6,r:pmn} 
at ecliptic latitude $|\beta| < 7.5^\circ$ and S(4.8~GHz) $>70$~mJy; 
3)~AT20G sample \citet{r:at20g}at $-40^\circ < \delta < 0^\circ$ 
and S(20~GHz) $>40$~mJy; and 4)~CLASS sample at $0^\circ < \delta < 75^\circ$ 
and S(8.4~GHz) $>50$~mJy, spectral index $\alpha > -0.5$. In the current
we will observe remaining flat-spectrum sources in order to reach 
completeness of our sample.

  We will also observe remaining sources from CRATES catalogue brighter
50~mJy and $\delta > -40^\circ$ that have not been observed before. 
CLASS is limited only to $\delta>0^\circ$, while CRATES is the all-sky
catalogue. The main motivation is not to miss a gravitational lens
or a close binary source in the declination zone 
$-40^\circ < \delta < 0^\circ$. CRATES is not complete, however observing
CLASS and CRATES, we will extend the list of all {\it known} flat
spectrum sources observed with VLBI and brighter 50~mJy at 8~GHz to the 
area $[-40^\circ < \delta < +90^\circ]$, i.e. 82\% the sky. Since all 
known AT20G sources at $-40^\circ$ have already been observed with VLBA,
the list of VLBI detected sources with flat spectrum can be very high.
Comparing statistics of detected and non-detected flat-spectrum sources 
in the declination zone [0, $-40^\circ$] and [0, +$40^\circ$], we will
estimate the completeness of the sample of VLBI detected sources with 
flat spectrum in the [0, $-40^\circ$] zone. Its deviation from the 
complete sample will provide us a measure of flat spectrum sources missed
in the AT20G sample.

   We started observing flat spectrum sources in August 1984, and 36 years 
later we will be in a position to say that there are no known flat spectrum
sources brighter 50~mJy at $\delta > -40^\circ$ that have not been observed.


\begin{table}
   \caption{Sample of sources observed or to be observed with VLBI.
            The columns are: the total number of sources in the sample,
            the number of sources observed with VLBA, the number of
            of detected sources, the number of non-detected sources,
            and the number of remaining sources. A given source may
            be a member of more than one sample.}
   \par\smallskip\par
   \begin{center}
      \begin{tabular}{lrrrrr}
         \hline
          Sample       & \# Tot & \# Obs & \# Det & \# Ndt & \# Rem \\
         \hline
          NPCS         &   482  &   482  &   156  &   326  &     0  \\
          GB6+PMN      &  5780  &  5769  &  2198  &  3571  &    11  \\
          AT20G        &  3580  &  3571  &  3288  &   283  &     9  \\
          CLASS        &  5788  &  4696  &  4610  &    86  &  1092  \\
          CRATES       &  8521  &  6732  &  6504  &   228  &  1789  \\
          CRATES+CLASS &  9496  &  7284  &  7049  &   235  &  1977  \\
         \hline
      \end{tabular}
   \end{center}
\end{table}

\section{Proposed observations}

  Analysis of prior VLBA surveys, such as BP242 program showed that the 
overall efficiency is about 20 sources per hour, including overheads for 
slewing and observations of atmospheric calibrators. 
Therefore, we request in total 99 hours at wide C-band receiver, at 4.3 and 
7.6~GHz sub-bands simultaneously for observing 1977 targets mentioned above
in one scan of 60 seconds at 2048~Mbps in a mode used in VCS7--9 surveys 
(Petrov in preparation 2020\footnote{See the on-line project report at 
\web{http://astrogeo.org/vcs9}}). In order to optimize the use of the VLBA, 
we request  79~hours in the filler mode and five 4~hour blocks in the 
non-filler mode. The filler time schedules will be generated by the array 
operators on-demand using the web-based tool that we have developed and used 
in past filler projects. The targets are uniformly distributed over right 
ascensions, but according to our experience, available filler time in not 
uniformly distributed. Requested five 4-hour blocks are intended to cover the 
area that is inaccessible for the filler time. Since we do not know 
beforehand which area will not be covered with the filler time, we are going 
to schedule five 4-hour blocks after we use 79 hours of filler time. 
Therefore, we ask to extend the project over two semesters.

\section{\large Data release plan}

  We wave the proprietary period. Images and source positions will be 
available from the project web site immediately upon processing, typically 
with a lag of one month of observations. Upon completion the project the 
positions will augment the Radio Fundamental Catalogue and the images will
be be submitted to the the Astrogeo VLBI FITS image database.

\begin{thebibliography}{9}

   \bibitem[Condon et~al.(1998)]{r:nvss}
           Condon,~J.~J. et al., \aj, 115, 1693

  \bibitem[Gregory et~al.(1996)]{r:gb6}
     Gregory,~P.~C., et al., 1996, ApJS, 103, 427

  \bibitem[Healey et al.(2007)]{r:crates}
     Healey, S.~E. at al., 2007, AJSS, 171, 1.

  \bibitem[Murphy et al.(2010)]{r:at20g}
     Murphy,~T. et al., 2010, MNRAS, 402, 2403.

  \bibitem[Myers et al.(2003)]{r:class}
     Myers, S.~T. et al., 2013, MNRAS, 341, 1.

   \bibitem[Wright et~al.(1996)]{r:pmn}
            Wright,~A.~E., et al. 1996, ApJS, 103, 145

\end{thebibliography}

\end{document}