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

Radio galaxies are ideal probes of large-scale structure as they are biased tracers of the underlying mass and can be easily detected out to high redshifts. By using biased galaxies populations, one can efficiently trace huge super-structures (i.e clusters of clusters of galaxies) which are still in the linear regime and can therefore be directly traced back to rare fluctuations in the initial density field at recombination. However, in order to be useful probes, it is vital to understand how different populations of radio galaxies trace the underlying dark matter (i.e. their bias) and how this has evolved with time.

Different populations of galaxies demonstrate a range of clustering strengths as measured by the clustering length, $r_0$. For example $r_0$ $\approx$ 8.1$\pm$0.9 Mpc ($h$=0.7) for $L_\star$ elliptical galaxies \citep{nor02} and $r_0$ $\approx$ 5.4 Mpc for IRAS selected galaxies \citep{fis}. The power-law fit to the correlation function can also be applied to galaxy cluster surveys. For clusters of galaxies selected from the APM survey, the correlation length has been measured to be $r_0$ $\approx$ 20.4$\pm$3.4 Mpc for Abell Richness Class (ARC) $>$1 clusters \citep{dal} and $r_0$ $\approx$ 30.4 Mpc for ARC $>$2 \citep{crof}. Hence as one would expect from high-peak bias effects \citep{kai}, clusters are more strongly clustered than galaxies. The clustering of radio galaxies will follow that of the underlying host galaxy population but it may also be affected by the radio triggering mechanism in different populations and/or environments.

Because of the difficulties in obtaining large, complete radio galaxy redshift surveys, the clustering properties of radio galaxies are relatively poorly constrained. For local radio galaxies, \citet{pn} find a correlation length of $r_0$ $\approx$ 15.7 Mpc ($h$=0.7). \citet{mag04} calculate $r_0$ = 13.0$\pm$0.9 Mpc for 2dFGRS/FIRST radio galaxies with AGN signatures in their optical spectra (before correcting for redshift space distortions). These radio galaxies therefore cluster with a strength between that of normal galaxies and rich clusters of galaxies. This is consistent with their preferential location in poor groups of galaxies. By deprojecting the angular correlation function of NVSS radio sources, \citet{bw} find a correlation length of $r_0$ $\approx$ 8.6 Mpc. In this case, the clustering signal comes from radio galaxies with a median redshift of $z\sim$1 but the correlation function has been corrected for growth of clustering under linear theory \citep{pee}.

With the advent of large area radio surveys down to fainter flux densities (\citealt{con}; \citealt{bwh}), we can define lower radio flux density limited surveys over large areas of the sky. We have defined a new radio galaxy redshift survey: the Texas-Oxford NVSS Structure (TONS) survey. This survey comprises the largest complete spectroscopic sample of low luminosity (predominantly FRI) radio galaxies over large contiguous areas yet compiled.  By going to fainter radio flux densities ($s_{\rm{1.4}}\ge$3 mJy) and imposing optical limits ($E\approx R\ltsimeq$19.5), the TONS survey is optimised for looking at clustering of objects in a region of moderate (0 $\ltsimeq$ $z$ $\ltsimeq$ 0.5) redshifts. The radio flux density limit of $s_{\rm{1.4}}\ge$3 mJy increases the space density of radio galaxies powered by AGN but does not go so deep that the sample becomes dominated by galaxies whose radio emission originates from star formation mechanisms.

In this paper, we determine the clustering strength of the low luminosity TONS radio galaxies at moderate redshifts. From the correlation length we will be able to estimate the bias of this population and compare it to previous estimates of both higher luminosity radio galaxies and similar radio galaxies in the local Universe. By cross-matching radio surveys with large spectroscopic surveys such as the Sloan Digital Sky Survey (SDSS; \citealt{aba04}) and 2dF galaxy redshift survey \citep{col} with NVSS and FIRST, even larger samples can now be compiled (see e.g., Jarvis, Clewley \& Brand in prep.).

The paper will be structured in the following way: In Sec. 2 we summarise the selection techniques used in the Texas-Oxford NVSS Structure (TONS) redshift survey of radio galaxies: this technique has already been discussed in detail for the TONS08 sub-sample \citep{brand}. We present the full TONS12, TONS08w and TONS16w sub-samples and their spectra in Sec. 3. Sec. 4 summarises the method used to obtain a model redshift distribution and compares this to the observed redshift distribution of each of the TONS sub-samples. In Sec. 5 and Sec. 6, we describe the method used to calculate the two point correlation function and present the results for the different sub-samples. Sec. 7 is a discussion which compares the results to previous work. The main conclusions are summarized in Sec. 8.

Unless otherwise stated, we assume a spatially flat $\Lambda$CDM Universe throughout the paper with the following values for the cosmological parameters:
Hubble constant: $H_{0}=70~ {\rm km~s^{-1}Mpc^{-1}}$; $h=H_{0}/100=0.7$; matter density parameter at $z$=0: $\Omega_ {\rm M}(0)=0.3$; vacuum density parameter at z=0: $\Omega_ {\Lambda}(0)=0.7$.

\section{SAMPLE SELECTION}
\label{sec:selection}

The Texas-Oxford NVSS Structure (TONS) survey comprises three independent regions on the sky selected in the same areas as the 7CRS \citep{wil02} and the TexOx-1000 (TOOT) survey \citep{hr}. The TONS08 (Texas-Oxford NVSS Structure 08$^h$) sub-sample is the subject of \citet{brand}. The TONS12, TONS16w and TONS08w surveys are presented in this paper. The sky regions surveyed by these sub-samples are shown in Table.~\ref{tab:radec}. Table.~\ref{tab:samples} summarises the properties of the different TONS sub-samples in addition to the various radio galaxy samples that are used or referred to throughout this paper. TONS08 and TONS12 have the faintest radio flux densities limit ($s_{\rm{1.4}}\ge$3 mJy), while TONS08w and TONS16w were designed to survey larger areas but due to limited telescope time, were less radio deep ($s_{\rm{1.4}}\ge$30 mJy). TONS08w was specifically designed to determine the spatial extent of the TONS08 super-structures which appeared to be unbounded by the TONS08 survey \citep{brand}.

\begin{table*}
\begin{center}
\begin{tabular}{rrr}
\hline\hline
sample & RA & Dec\\
\hline
TONS08                    & $08^h10^m20^s\le$ RA $\le08^h29^m20^s$ & $24^\circ10^\prime00^{\prime\prime}\le$ DEC $\le29^\circ30^\prime00^{\prime\prime}$\\
TONS12                    & $12^h48^m00^s\le$ RA $\le13^h12^m00^s$ & $33^\circ00^\prime00^{\prime\prime}\le$ DEC $\le38^\circ00^\prime00^{\prime\prime}$\\
TONS08w                   & $08^h00^m00^s\le$ RA $\le08^h41^m00^s$ & $21^\circ50^\prime00^{\prime\prime}\le$ DEC $\le31^\circ50^\prime00^{\prime\prime}$\\
TONS16w                   & $16^h24^m00^s\le$ RA $\le16^h56^m00^s$ & $42^\circ00^\prime00^{\prime\prime}\le$ DEC $\le51^\circ00^\prime00^{\prime\prime}$\\
\hline\hline
\end{tabular}
{\caption[]{\label{tab:radec} The RA and DEC limits for the different TONS sub-samples.}}
 \end{center}
 \end{table*}

Unlike the low-frequency selected 7CRS and TOOT, the TONS survey is selected at 1.4 GHz from the NVSS. For objects of typical spectral index, the TONS08 and TONS12 sub-samples go to fainter radio flux densities than TOOT (which has a 151 MHz flux density $s_{\rm{151}}$ limit of 100 mJy, corresponding to $s_{\rm{1.4}}\approx$20 mJy for radio spectral index\footnote{$\alpha$ is the spectral index for radio sources where the radio flux density $s_{\rm{\nu}} \propto \nu^{-\alpha}$, where $\nu$ is the observing frequency}$\alpha\approx$0.8). In addition, TONS has an optical magnitude limit ($E\approx R\approx$19.5) and colour cut ($B$-$R >$1.8) imposed on it. This means that we can efficiently trace large-scale structure at moderate ($z<$0.5) redshifts using AGN-fuelled radio galaxies.

Full details of the sample selection, observations and data reduction of the TONS08 survey can be found in \citet{brand}. TONS12, TONS16w and TONS08w were all selected, observed and reduced using the same procedure. The only exception to this is in the selection of the TONS08w sample: sample members were selected by only considering candidates with an angular distance of $\le$10 arcsec between the optical and radio positions. This sample may therefore suffer from some incompletenesses.

\begin{table*}
\begin{center}
\begin{tabular}{rrrrrrl}
\hline\hline
Survey & Type & radio limits & optical limits & colour cut & area (sr.) & ref. \\
\hline
TONS08 & $ROz$ & $s_{1.4}>$3 & $E<$19.83 & $B-R >$1.8 & 0.00688 & {\scriptsize \citet{brand}}\\
TONS12  & $ROz$ & $s_{1.4}>$3 & $E<$19.64 & $B-R >$1.8 & 0.00744 & {\scriptsize this paper}\\
TONS16w & $ROz$ & $s_{1.4}>$30 & $E<$19.5  & $B-R >$1.8 & 0.0151 & {\scriptsize this paper}\\
TONS08w & $ROz$ & $s_{1.4}>$30 & $E<$19.5  & $B-R >$1.8 & 0.02786 &{\scriptsize this paper}\\
Lacy    & $ROz$ & $s_{1.4}>$20 &17$<E<$20.2& APM$^{5}$ &0.0122&{\scriptsize \citet{lac}}\\
TOOT    & $Rz$  & $s_{151}>$100 & NONE               &NONE&& {\scriptsize \citet{hr}}\\
7CII    & $Rz$  & $s_{151}>$500 & NONE               &NONE&& {\scriptsize\citet{wil02}}\\
Sadler  & $ROz$ & $s_{1.4}>$2.8 &14$<B_j<$19.4& AGN$^{1}$ &0.099& {\scriptsize\citet{sad}}\\
2dF     & $Oz$  & NONE          & $B_j<$19.4 & NONE & 0.61 & {\scriptsize\citet{col}} \\
NVSS$^{2}$ & $R$& $s_{1.4}>$2.5  & NONE & NONE &10.36 & {\scriptsize\citet{con}}\\
FIRST$^{3}$& $R$& $s_{1.4}>$2  & NONE & NONE & 2.61 & {\scriptsize\citet{bwh}}\\
PN & $Rz$ & $s_{1.4}>$500 & NONE$^{4}$ & NONE & 9.3 & {\scriptsize\citet{pn}}\\
\hline\hline
\end{tabular}
{\caption[Surveys]{\label{tab:samples} Table summarising the various samples used in and/or referred to in this paper. $R$ denotes radio galaxy surveys, $O$ denotes surveys with an optical magnitude cut and $z$ denotes spectroscopic redshift surveys. The radio limits are in mJy. Notes: 1. AGN were identified using Principal Component Analysis (PCA) applied to the spectra \citep{fol}. 2. NVSS is 50 per cent complete at 2.5 mJy and 99 per cent complete at 3.5 mJy. 3. FIRST is 95 per cent complete at the given limiting flux densities. 4. \citet{pn} impose a redshift limit of $z$=0.1. 5. Galaxies were identified from APM charts.
}}
 \end{center}
 \end{table*}

The selection criteria for all TONS surveys were based on cross-matching positions of objects in radio and optical surveys. An initial selection was made of NVSS targets \citep{con} in the chosen area of sky with 1.4 GHz flux densities, $s_{1.4}>$3 mJy. The NVSS positions were matched with APM positions \citep{mcm} of objects with $E<$19.5. We selected any objects with APM and NVSS positions with an offset of $\le$ 20 arcsec from each other. We then plotted radio contours from the FIRST survey \citep{bwh} over optical POSS-II images and overplotted the positions of the APM and NVSS objects, identifying real identifications by eye. For full details of this technique we refer the reader to \citet{brand}.

To correct for plate-to-plate variations in the magnitudes obtained from the APM survey, we modified the $O$ and $E$ magnitudes using corrections derived from comparison of the APM magnitudes to GSC-2 magnitudes for each POSS-II plate (R. White priv. com.). We modified the magnitude cut from our original target of 19.5 to 19.83 and 19.64 in the TONS08 and TONS12 sub-sample respectively (the magnitude corresponding to the new limit of the most shallow plate). All following analysis uses these corrected values.

The final selection criteria was that $O-E\ge$1.8. This cuts out all the bluer objects which tend to be stars (which by coincidence lie close to the line of sight to the radio source), quasars (which can lie at much higher redshifts) and star-burst galaxies (which tend to be at low redshifts due to their low radio luminosity).

Table.~\ref{tab:the_samples} summarises the total number of objects in each of the TONS sub-samples as well as the predicted number from a model redshift distribution described in Sec.~\ref{sec:nz}.

\begin{table}
\begin{center}
\begin{tabular}{rrr}
\hline\hline
sample & total number & predicted number\\
\hline
TONS08                    & 84 & 95.1$\pm4.5$ \\
TONS12                    & 107& 97.6$\pm4.5$ \\
TONS08w                   & 47 & 74.8$\pm3.5$ \\
TONS16w                   & 40 & 40.6$\pm1.9$  \\
\citet{lac}               & 36 & 47.5$\pm2.7$  \\
\citet{sad}               & 433&428.0$\pm27.9$ \\
TONS0812                 & 191 &192.7 $\pm6.4$\\
TONS0812$\textunderscore$SS              & 92 &46.9 $\pm3.4$\\
TONS0812$\textunderscore$nonSS           & 99 &145.8$\pm5.4$\\
\hline\hline
\end{tabular}
{\caption[]{\label{tab:the_samples} The total number of radio galaxies in each of the TONS sub-samples compared to that predicted by the model redshift distribution. TONS0812 is the combined TONS08 and TONS12 sub-samples, TONS0812$\textunderscore$SS and TONS0812$\textunderscore$nonSS are the combined TONS08 and TONS12 sub-samples within super-structure regions and out of super-structure region respectively (see Sec.~\ref{sec:ssreg}).
}}
 \end{center}
 \end{table}

\section{OBSERVATIONS}
\label{sec:tons_obs}

Optical spectra were obtained during the period October 2000 - May 2003 on the 2.6m Nordic Optical Telescope (NOT) using the Andalucia faint object spectrograph, the 4.2m William Herschel telescope (WHT) using ISIS, the 2.7m Smith reflector at McDonald with the Imaging grism instrument (IGI) \citep{hill02}, and the Hobby-Eberly telescope (HET) using the Marcario low resolution spectrograph (LRS) \citep{hill98}.

The spectra were reduced using standard {\small IRAF} procedures. Spectra and redshifts for the TONS08 sub-sample have been presented in \citet{brand}. Spectra for the observed radio galaxies (with no previously known redshift) for the TONS12, TONS08w and TONS16w sub-samples are shown in Fig.~\ref{fig:12spectra}, Fig.~\ref{fig:08wspectra} and Fig.~\ref{fig:16spectra} respectively. As found for the TONS08 sub-sample, the vast majority of objects in the entire TONS survey were identified as moderate redshift radio galaxies.
All spectra are smoothed for presentation purposes and sorted by redshift for clarity. In most cases, redshifts were determined from absorption lines (very few objects exhibited emission lines). The estimated redshifts are presented in Table.~\ref{tab:12summary}, Table.~\ref{tab:08wsummary} and Table.~\ref{tab:16summary}. These were checked by performing a cross-correlation between the spectra and both a rest frame composite spectrum obtained from the TONS08 data \citep{brand} and an evolved population GISSEL model \citep{bc}.

Of all the sub-samples, only TONS16w overlaps with the second data release of the Sloan Digital Sky Survey (SDSS; \citealt{aba04}). 11/40 of the TONS16w sample have spectroscopic redshifts in SDSS. In all cases, the redshifts agree to within 0.003.

\begin{figure}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(50,35)
\put(70,-5){\special
{psfile="12s_1298.ps"
vscale=22 hscale=30 angle=90}}
\end{picture}
\end{center}
{\caption[junk]{\label{fig:12spectra} Spectra of all the radio galaxies in TONS12 that are not in TOOT, reported by Benn (priv. comm.) and/or do not have redshifts from the literature. See Table.~\ref{tab:12summary} for details. The Flux density is in units of 10$^{-20}\ \rm{W}\rm{m}^{-2}\rm{\AA}^{-1}$. Shown here is an example spectrum. Plots of all the spectra can be found in the version to be published in MNRAS in early 2005.
}}
\end{figure}

\begin{figure}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(50,35)
\put(70,-5){\special
{psfile="08w_4525.ps"
vscale=22 hscale=30 angle=90}}
\end{picture}
\end{center}
{\caption[junk]{\label{fig:08wspectra} Spectra of all the radio galaxies in TONS08w that are not in TONS08, TOOT08 and/or not not have redshifts from the literature. See Table.~\ref{tab:08wsummary} for details. The flux density is in units of 10$^{-20}\ \rm{W}\rm{m}^{-2}\rm{\AA}^{-1}$. Shown here is an example spectrum. Plots of all the spectra can be found in the version to be published in MNRAS in early 2005.
}}
\end{figure}

\begin{figure}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(50,35)
\put(70,-5){\special
{psfile="16w_2338.ps"
vscale=22 hscale=30 angle=90}}
\end{picture}
\end{center}
{\caption[junk]{\label{fig:16spectra} Spectra of all the radio galaxies in TONS16 that are not in TOOT16 and/or do not have redshifts from the literature. See Table.~\ref{tab:16summary} for details. The flux density is in units of 10 $^{-20}\ \rm{W}\rm{m}^{-2}\rm{\AA}^{-1}$. Shown here is an example spectrum. Plots of all the spectra can be found in the version to be published in MNRAS in early 2005.
}}
\end{figure}

\input{the_table12}
\input{the_table08w}
\input{the_table16w}

\section{THE TONS REDSHIFT DISTRIBUTIONS}

\subsection{Obtaining a universal N(z)}
\label{sec:nz}

To perform clustering analysis on a survey, it is crucial to know the underlying redshift distribution of the population under study. This is often obtained by simply using a redshift distribution that is either smoothed or fitted to the data itself (e.g. \citealt{ste}). However, the obvious presence of large-scale structure in our sub-samples means that this will not be representative of the true underlying redshift distribution.

We required a model redshift distribution derived from a data set over a sufficiently large area to reduce the effects of large-scale structure and which we could modify for different optical magnitude and radio flux density limits of each of our sub-samples. There are currently no model redshift distributions derived from surveys going down to NVSS / FIRST flux densities in the literature. \citet{dp} and \citet{wil01} model the radio luminosity function of relatively bright ($s_{\rm{1.4}}>$100 mJy) radio galaxies from which a redshift distribution can be extrapolated to lower flux densities and the correct radio frequency. However these models can display unphysical spikes at low redshifts and the extrapolation results in large uncertainties. These models were not accurate enough for our purposes.

Instead, we used a maximum likelihood technique \citep{mar} to fit our own bivariate (radio and optical) luminosity function (BLF) to radio galaxies in the 2dF galaxy redshift survey \citep{sad}. These data are over a sufficiently large area to smooth over any large-scale structure. The BLF can be integrated over any optical apparent magnitude and radio flux density limits to obtain a model redshift distribution for each of the TONS sub-samples. \citet{brand} described the form of the bivariate luminosity function that was modelled and the best fit parameters of this model. Note that because to TONS survey extends out only to moderate redshift, the redshift evolution is not well constrained. \citet{cj} found that the lower luminosity (FR I dominated) AGN population is consistent with a constant co-moving space density with redshift. Fixing the BLF to a model with no evolution with redshift, resulted in no significant difference in the model redshift distribution.

\noindent Because the TONS survey optical apparent magnitude limits were defined in the $E(\approx R)$ band but the BLF is defined for the $b_j$ band, we converted the apparent $R$-band magnitude limits to absolute $R$ magnitude for each redshift and applied a colour correction of $B-R$=1.52 (calculated from the difference in flux in the rest-frame of a template SED of an evolved stellar population \citep{bc} measured in the 2 different bands). We assumed a colour correction of $B_j-B=-$0.11 \citep{fre}.

The redshift distribution of the \citet{sad} radio galaxies is shown is Fig.~\ref{fig:sad}. Overplotted is the fitted model redshift distribution. We note that although this survey is is over 13 times the area of TONS08, it still exhibits features due to large-scale structure and this may bias the resulting fit of the BLF. We minimised this effect by effectively smoothing the redshift distribution (by modifying the redshifts of each radio galaxy by an amount drawn from a Gaussian distribution of FWHM 0.05).

\begin{figure}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(150,135)
\put(-2,60){\special
{psfile="sad_z_distn.ps"
vscale=45 hscale=45 angle=0}}
\put(-2,-10){\special
{psfile="sad_z_distn_substr.ps"
vscale=45 hscale=45 angle=0}}
\end{picture}
\end{center}
{\caption[junk]{\label{fig:sad} The redshift distribution of the \citet{sad} sample with the model redshift distribution overplotted (solid line). The $\pm 1\sigma$ errors on the model are overplotted (dashed lines). We plot the distribution using 16 and 55 redshift bins between $z$=0 and $z$=0.5 for the top and bottom figures respectively. Even with 433 radio galaxies over a larger area, the redshift distribution is not smooth.
}}
\end{figure}

\subsection{Errors}

We found the errors on the redshift distribution using the following method to allow for the deviations in the derived model parameters. We split the parameter space into discrete grid spaces. For each grid space, we calculated the maximum likelihood, $S$ of this parameter combination and converted it to a probability ($P\propto \exp(-S/2)$). We then normalised the probabilities so that the total probability in all grid spaces added up to one and converted to a cumulative probability. We calculated the number of radio galaxies expected for each redshift interval given the survey limits and the parameter values in that box. We then weighted this by multiplying by the probability of the parameter combination. By adding up the weighted number of galaxies for each redshift interval, we should have obtained a very similar redshift distribution to that obtained by the best fit parameter values. The advantage of this procedure is that if there is more than one parameter combination which fits the BLF well, these will also have an influence on the final redshift distribution.

To calculate the errors, we performed a Monte-Carlo simulation in which we chose 5000 random numbers between 0 and 1. Because the cumulative probabilities for all parameter space grid spaces were normalised to run from 0 to 1, each random number could be associated with a unique parameter combination. Those parameter combinations which have higher relative probabilities occupy a larger proportion of this probability space and will therefore have had a greater chance of being selected. The redshift distribution was then calculated for all parameter combinations that were selected. The minimum and maximum $\pm$1$\sigma$ errors at each redshift interval were calculated by determining where 67 per cent of the measurements fell.

It is likely that other quantities will also have contributed to the error in the measurement of the redshift distribution. Errors may have been introduced by incompletenesses in both the radio and optical surveys at faint flux densities: The NVSS catalogue is $\approx$ 90 per cent complete at $s_{1.4}$=3 mJy \citep{con}. Before correcting for plate-to-plate variations, the APM magnitudes have a global rms uncertainty of 0.5 mag \citep{mcm}. We assumed an error of 0.3 mag, which is the difference between the magnitude corrections of the two POSS-II plates in the TONS08 region. We incorporated this into the total error on each redshift bin by determining the $R$ magnitude limit in the Monte Carlo simulations as a Gaussian distributed value with a standard deviation of 0.3 about the magnitude limit.

\subsection{A comparison of the TONS sub-samples with their model redshift distributions}

Table.~\ref{tab:the_samples} shows the number of radio galaxies observed and predicted by our model redshift distribution in all the TONS sub-samples. These numbers are significantly different in most cases. However, it is not surprising that there are large variations in these numbers due to the presence of super-structures and voids which occur on similar scales to that of the survey size ($\sim$100 Mpc diameter at $z\sim$0.3).

Fig.~\ref{fig:zdist_all} shows the redshift distributions overplotted with the model redshift distributions for the TONS08, TONS12, TONS08w and TONS16w sub-samples. In all cases, large-scale structure has changed the redshift distribution of our sub-sample significantly from that expected for a typical area of sky.

\begin{figure*}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(150,130)
\put(-2,60){\special
{psfile="08s_z_distn.ps"
vscale=40 hscale=40 angle=0}}
\put(70,60){\special
{psfile="12s_z_distn.ps"
vscale=40 hscale=40 angle=0}}
\put(-2,-10){\special
{psfile="08w_z_distn.ps"
vscale=40 hscale=40 angle=0}}
\put(70,-10){\special
{psfile="16w_z_distn.ps"
vscale=40 hscale=40 angle=0}}
\put(28,127){\large\bf TONS08}
\put(100,127){\large\bf TONS12}
\put(28,57){\large\bf TONS08w}
\put(100,57){\large\bf TONS16w}
\end{picture}
\end{center}
{\caption[]{\label{fig:zdist_all} The redshift distribution of the TONS08, TONS12, TONS08w and TONS16w sub-samples (top left to bottom right) with the model redshift distribution overplotted (solid line). The $\pm 1\sigma$ errors on the model are also shown (dashed lines). We plot the distribution using 28 redshift bins between $z$=0 and $z$=0.5.
}}
\end{figure*}

Within the TONS08 sub-sample, there are two prominent spikes at $z\approx$0.27 and $z\approx$0.35 with, perhaps, void-like regions at lower redshifts, accounting for the low overall number of radio galaxies. Analysis of these redshift spikes; their significance and their implications for structure formation theories and/or radio galaxy bias is performed in \citet{brand}. The TONS12 survey covers a similar area to that of TONS08 but in a different region of sky. It too shows two redshift peaks above that expected from the model redshift distribution (but at redshifts $z\approx$0.23 and $z\approx$0.31). That redshift spikes are found in both sub-samples is important as it demonstrates that redshift spikes are probably a universal feature of radio galaxy distributions.

The TONS08w and 16w surveys are wider area samples with higher flux density limits. Within the TONS08w sub-sample, there are fewer radio galaxies than we would expect. However, this may simply be due to incompletenesses in this survey. We may have missed sources with a large offset between the radio and optical positions - something more likely for higher power radio galaxies. Within the TONS16w sub-sample, we observed a similar number of radio galaxies to that predicted from the model redshift distribution. Although there is an excess of radio galaxies at a redshift $z$=0.2-0.3, the number density of radio galaxies is insufficient to determine if there is a significant overdensity. This is perhaps not surprising given the lack of evidence for significant redshift spikes in previous surveys with a similar flux density limit (see \citealt{brand} sec.~5.3).

\section{RADIO GALAXY CLUSTERING}
\label{sec:corr_fn}

\subsection{Calculating the two point correlation function}

The spatial two-point correlation function is the traditional tool for measuring the strength of clustering and hence provides an easy comparison with other surveys. It is also perhaps the most intuitive and simple measure of clustering. It provides fundamental information about the galaxy distribution in the sense that it is the Fourier transform of the power spectrum of the density fluctuations and (when the clustering is still in the linear regime and the bias is known) can be directly related back to fluctuations in the primordial density field. The two-point correlation function measures the excess probability over random d$P$ of finding a pair of objects in two volumes d$V_1$ and d$V_2$ with a separation, $r$ (e.g. \citealt{pn}):

\begin{equation}
\rm{d}P=\rho_{0}^2 [1+\xi(r)] \rm{d}V_{1}\rm{d}V_{2},
\end{equation}

\noindent where $\rho_{0}$ is the average number density. The form of the correlation function is generally well approximated by a power-law:

\begin{equation} \label{eqn:r0}
\xi(r)=\left(\frac{r}{r_0}\right)^{-\gamma},
\end{equation}

\noindent where $r_0$ is the correlation scale length (the separation at which $\xi$=1) and $\gamma$ is the slope of the correlation function and is usually assumed to be equal to 1.8 (e.g. \citealt{gp}). Thus, the strength of any clustering can be estimated by obtaining a value for $r_0$. The larger the value of $r_0$, the greater the clustering signal of the sample.

In practise, the correlation function is calculated using an estimator. There are several different forms of this estimator, but they all involve counting pairs of objects within the real catalogue, a random catalogue and between the two at different separations, $r$. \citet{ker} find that on small (r$\approx$4.4$h^{-1}$Mpc) scales, the estimators are comparable. However, for larger scales (r$\approx$115$h^{-1}$Mpc), the estimator of \citet{lasz} significantly outperforms the rest:

\begin{equation} \label{eq:xi}
\xi(r)=\frac{DD(r)-2DR(r)+RR(r)}{RR(r)},
\end{equation}

\noindent where DD(r) is the number of data-data pairs, RR is the number of random-random pairs and DR is the number of data-random pairs all calculated for separation $r$. This is the estimator that we have used for this analysis.

In order to calculate the two-point correlation function, a set of random catalogues was constructed. These catalogues allow a comparison of the data to randomly distributed objects on the sky. The random catalogues were all constructed with the same number of objects as the real catalogue and the same selection function. They were all assigned a random RA and DEC within the sample boundaries and a random redshift selected from the redshift distribution expected for objects in the survey. We used the redshift distribution calculated in Sec.~\ref{sec:nz}.  The RR and DR pairs used in the calculation of the correlation function were obtained by averaging 1000 simulations of the random catalogue to reduce to negligible any errors due to statistical variations within the random samples.

\subsection{Corrections to the two-point correlation function}

Small survey volumes that are unrepresentative of the overall field must be corrected for the ``integral constraint''. Because the TONS survey sizes are comparable to scales at which the number density of galaxies in the volume can significantly differ from field to field, we need to account for the fact that they are not representative of the general field. Because the correlation function is only calculated for a finite survey volume, in practise the observed number density $n$ is used instead of the global number density $<n>$.

Unlike most studies, we have corrected for the sample being under- or over-dense due to large-scale structure. This is possible because, in calculating the model redshift distributions for each subsample, we have already estimated the underlying number density of radio galaxies in the TONS sub-samples. The observed correlation function, $\xi(r)_{\rm obs}$ was modified to the true correlation function, $\xi(r)_{\rm true}$ by a normalisation term, $n/<n>$:

\begin{equation}\label{eq:xi_cor}
(1+\xi(r)_{\rm true})=(1+\xi(r)_{\rm obs})\left(\frac{n}{<n>}\right)^2,
\end{equation}

\noindent \citep{pea} where $n$ is the total number of objects in the sample and $<n>$ is the total number of objects expected in the sample as calculated from our model redshift distribution (see Table.~\ref{tab:the_samples}). In an under-dense region, the number of random-random pairs calculated in the correlation function will be under-estimated and hence the correlation function will be over-estimated and must be corrected downwards. Applying this formula is essentially the same as changing the number of random objects in equation.~\ref{eq:xi} from the number of objects in the sample to the number of objects expected.

The observed correlation function is also modified because it is measured not in real space, but in redshift space. In practise, the redshift measurements will be affected by large-scale coherent velocities and small-scale virialised motions. This will tend to skew the correlation function and boost the value of $r_0$. The linear analysis of \citet{kai87} implies a boost in the redshift space correlation function by a factor of 1.2 \citep{pea99}. Because of uncertainties in this effect, and because there are other large uncertainties, we have not corrected for this effect.

Finally, to allow for redshift evolution in the clustering of radio galaxies, an evolution term can be incorporated into the definition of the correlation length:

\begin{equation}\label{eq:arr_nort}
r_0(z)=r_0(0)\left(1+z\right)^{-(3+\epsilon-\gamma)/\gamma},
\end{equation}

\noindent (e.g. \citealt{ove}; \citealt{bro03}). $\epsilon$=0 and $\epsilon$=$\gamma$-3 represent scenarios in which the clustering is fixed in physical or co-moving co-ordinates respectively. $\epsilon$=$\gamma$-1 represents growth of clustering under linear perturbation theory \citep{pee}. Unless otherwise stated, in all following analysis, $r_0(0)$ refers to the correlation function at $z$=0 assuming growth of clustering under linear theory.

\subsection{Calculating the errors on the two-point correlation function}

The Poisson errors on the correlation function at a given separation $r$ are given by:

\begin{equation}
\sigma_\xi(r)=\frac{1+\xi(r)}{\sqrt{DD(r)}}
\end{equation}

\noindent (e.g. \citealt{pn}). Poisson statistics assume that all pairs are independent of each other which is not the case. The Poisson errors will therefore be an underestimate of the true error. We also used the bootstrap method to estimate the errors (e.g. \citealt{bbs}; \citealt{lbf}; \citealt{mjb}). This involved re-sampling of the data to generate further data sets with a population distribution identical to that of the real data set. We did this by selecting a random sample of $N$ objects from the real catalogue and re-calculating the two-point correlation function for the new sample. The bootstrap estimate of the standard deviation $\sigma_i$ of the re-sampled correlation function $\xi^{*}$ is given by:

\begin{equation}
\sigma_i^2=\sum_{k=0}^{N-1}\frac{(\xi^{*}_{i}-<\xi^{*}_{i}>)^2}{N-1},
\end{equation}

\noindent where $<\xi^{*}>$ is the mean value of $\xi^{*}$ in separation bin $i$. We calculated this for 1000 re-sampled datasets ($N$=1000). Because some galaxies were counted more than once, there were a large number of real-real pairs in the smallest separation bin. Although this is not therefore a good estimate of the mean, it does provide a good estimate of the internal error.

Because the bootstrap method calculates the internal variance of the sample, the errors will always be an underestimate of the true error as they don't include the error in the underlying number density. However, we have already corrected for this from the model redshift distribution. The only uncertainty will be from the error in our knowledge of the underlying number density. We have already estimated the 1$\sigma$ errors associated with the total number of radio galaxies expected in each sample (Table.~\ref{tab:the_samples}). This was determined from the $\pm$1$\sigma$ errors on the model redshift distribution calculated in Sec.~\ref{sec:nz}. To estimate our total error, we added the fractional errors in quadrature (including twice the fractional error on $<n>$ because $\xi(r)\propto <n>^2$).

\subsection{Estimating $r_0$}
\label{sec:croft}

Because each galaxy can contribute to multiple close pairs, the correlation function obtained in neighbouring bins may be correlated and hence in order to obtain the correlation length it is not strictly correct to simply calculate the best fit to a power-law function (Equation.~\ref{eqn:r0}). Ideally we would obtain the full covariance error matrices using our bootstrap error estimate:

\begin{equation}
\sigma_{ij}^2=\sum_{i=0}^{N-1}\frac{(\xi^{*}_{i}-<\xi^{*}_{i}>)(\xi^{*}_{j}-<\xi^{*}_{j}>)}{N-1}.
\end{equation}

\noindent However, to calculate this, each of the data points must be independent. \citet{mad} overcome this problem by dividing their survey area into contiguous regions and selecting areas at random (instead of the standard bootstrap method in which galaxies are selected at random). A similar approach is that of jackknife re-sampling (see e.g. \citealt{zeh}). Because our sample volume was too small to divide into enough regions (each required to be larger than the separation distances under consideration), we instead chose to estimate the value of the correlation length by using the Levenberg-Marquardt technique to perform a non-linear least squares fit of a power-law function (Equation.~\ref{eqn:r0}) to the binned correlation function data \citep{pre}. In this way, we incorporated the calculated errors rather than assuming simple Poisson errors. Because we were using only the diagonal terms of the covariance matrix, we cannot guarantee that we have obtained an unbiased estimate of the correlation length. However, the goodness of fit suggests that any such bias is negligible.

\subsection{Relating the correlation length to the bias}

The simplest models relating the galaxy distribution to that of the underlying dark matter is a linear bias: $\rho_{\rm{gal}}= b \times \rho_{\rm{mass}}$ where $b$ is a constant bias factor. The bias is therefore related to the correlation function by:

\begin{equation}
\xi_{\rm{gal}}(r)=b^2 \xi_{\rm{mass}}(r).
\end{equation}

\noindent This can be understood intuitively: clusters of galaxies will form preferentially at the sites of high-density peaks in the primordial density field, and will consequently have a larger bias.

The bias of radio galaxies $b_{\rm{rg}}$ with respect to the bias of another type of galaxy, $b_{\rm{gal}}$ is therefore related to their scale-lengths $r_0$ and power law indices $\gamma$ by:

\begin{equation}\label{eq:b_r}
\frac {b_{\rm{rg}}}{b_{\rm{gal}}}=\frac{ \left( r_{0 ~\rm{rg}} \right) ^{\gamma_{\rm{rg}}/2} } {\left(  r_{0 ~\rm{gal}}\right) ^{\gamma_{\rm{gal}}/2} }
\end{equation}

\section{Results}

In this section, we discuss the correlation function and its corresponding correlation length obtained for each of the TONS sub-samples. We summarise the correlation lengths obtained along with values obtained in other studies in Table.~\ref{tab:rnort}.

\begin{table*}
\begin{center}
\begin{tabular}{rrrrrr}
\hline\hline
Survey & mean $z$ & $r_0(z)$ (Mpc $h^{-1}$) & $r_0(z)$ (Mpc) & $r_0$(0) (Mpc) & $b/b_{\rm opt}$ \\
\hline
\citet{nor02} (L$_{\star}$ ellipticals 2dfGRS) & local &5.7$\pm$0.6 & 8.1$\pm$0.9 & {\bf 8.1$\pm$0.9} & 1.0\\
\citet{nor02} (brightest ellipticals 2dfGRS) & $\sim$0.1 &9.7$\pm$1.2 & 13.9$\pm$1.7 & {\bf 15.1$\pm$1.9} & 1.7$\pm$0.3\\
\citet{dal} (APM ARC$>$1 clusters) & local &14.3$\pm$2.4 & 20.4$\pm$3.4 & 20.4$\pm$3.4 & 2.3$\pm$0.5\\
\citet{crof} (APM ARC$>$2 clusters) & local &21.3$\pm^{11.1}_{9.3}$ &  30.4$\pm^{15.9}_{13.3}$ & 30.4$\pm^{15.9}_{13.3}$ & 3.3$\pm^{1.9}_{1.6}$ \\
\citet{pn} (local radio galaxies) & local &11.0$\pm$1.2 & 15.7$\pm$1.7 & 15.7$\pm$1.7 & 1.8$\pm$0.3 \\
\citet{bw} (NVSS radio galaxies) & $\sim$1.0 & -  & -  & 8.6 & 1.05 \\
\citet{mag04} (2dFRS radio galaxies) & $\sim$0.1 & -  & 13.0$\pm$0.9  & 14.2$\pm$1.0 & 1.7$\pm$0.3 \\
TONS08 & $\sim$0.3 & - & 8.0$\pm$2.4 & 10.2$\pm$3.0 & 1.2$\pm$0.4 \\
TONS12 & $\sim$0.3 & - & 11.3$\pm$1.8 & 14.3$\pm$2.3 & 1.7$\pm$0.4 \\
TONS08/12 & $\sim$0.3 & -  & 8.7$\pm$1.6 & {\bf 11.0$\pm$2.0} & 1.3$\pm$0.3 \\
\citet{lac} & $\sim$0.3 &17.9$\pm$7.4 & 12.5$\pm$5.2 & 15.9$\pm$6.6 & 1.5$\pm$0.7 \\
TONS08w/16w/\citet{lac} & $\sim$0.3 & -  & 8.8$\pm$4.4 & 11.2$\pm$5.6 & 1.4$\pm$0.8 \\
\hline\hline
\end{tabular}
{\caption[Surveys]{\label{tab:rnort} Table summarising the measured two-point correlation length, $r_0(z)$ ($h^{-1}$ Mpc), the measured two-point correlation length assuming $h$=0.7, $r_0(z)$ (Mpc), the correlation function corrected to $z$=0 assuming growth of clustering by linear theory, $r_0$(0) (Mpc) and the corresponding bias with respect to L$_{\star}$ elliptical galaxies in the 2dfGRS \citep{nor02}. \citet{nor02} look at clustering properties of different types of galaxies in the 2dfGRS. We take the clustering lengths of L$_{\star}$ ellipticals. We assume this is a local measurement and use this value as  $b_{\rm opt}$. The brightest ellipticals are defined as M$_{\rm b_{j}}$-5log$_{10}h^{-1}$=-21.0-22.0. To convert to $r_0$(0) we assume the median redshift of this population is $z$=0.1. \citet{bw} calculate a rough value for the angular clustering of NVSS ($s_{1.4}>$10 mJy) radio galaxies. The value $r_0(0)$ has already been corrected for growth of clustering under linear theory assuming a median redshift of $z$=1.
}}
 \end{center}
 \end{table*}

\subsection{The TONS08 and TONS12 sub-samples}

Fig.~\ref{fig:corrfn_08} shows the two-point correlation function calculated for the TONS08 and TONS12 sub-samples. In the case of TONS08, there are less radio galaxies than predicted. The number of radio galaxies in the random sample is effectively increased and the correlation function has therefore been corrected downwards. Conversely, the TONS12 sample has more radio galaxies than predicted and the correlation function was corrected upwards.

In both cases, a power-law function provided a poor fit to the correlation function. This is due to the presence of an excess number of pairs of galaxies with separations of 30-80 Mpc and is probably caused by the presence of super-structures in the sub-samples (see Sec.~\ref{sec:ssreg}). The error bars become large in the low separation bins due to small number statistics. The bootstrap errors also become larger when the discrepancy between $n$ and $<n>$ becomes large. This is due to the multiplication factor of $(n/<n>)^2$ in equation.~\ref{eq:xi_cor} for each bootstrap realisation. Because of the large uncertainties, we fixed $\gamma$ to the canonical value of $\gamma$=1.8. We fitted a power-law function to the correlation function out to separations of $r$=200 Mpc. Our best fit values for the correlation length are $r_0(z)$=8.0$\pm$2.4 Mpc and $r_0(z)$=11.3$\pm$1.8 Mpc (1$\sigma$) for the TONS08 and TONS12 sub-samples respectively. The best fit power-law models are overplotted in Fig.~\ref{fig:corrfn_08}. Assuming that the sub-samples have a median redshift of $z$=0.3 and that clustering grows according to linear theory, we used Equation.~\ref{eq:arr_nort} to determine that the equivalent correlation length at $z$=0 are $r_0(0)$=10.2$\pm$3.0 Mpc and $r_0(0)$=14.3$\pm$2.3 Mpc (1$\sigma$). The higher value for the correlation length in the TONS12 sample is probably in part due to the presence of an excess number of pairs of galaxies with separations of 10-20 Mpc which will tend to pull the fitted function up to higher values of $r_0$.

\begin{figure*}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(150,65)
\put(-2,-10){\special
{psfile="08s_corr_func_err.ps"
vscale=45 hscale=45 angle=0}}
\put(70,-10){\special
{psfile="12s_corr_func_err.ps"
vscale=45 hscale=45 angle=0}}
\end{picture}
\end{center}
{\caption[junk]{\label{fig:corrfn_08} The two-point correlation function for the TONS08 and TONS12 sub-samples. The data are binned in 10 Mpc separation bins. The errors plotted are obtained from a combination of the bootstrap method and the error due to the uncertainties in the predicted number of radio galaxies. The diamonds show the extent of the Poisson errors. The solid line shows the fitted power-law correlation function with $r_0$=8.0 Mpc (TONS08) and $r_0$=11.3 Mpc (TONS12) and a fixed slope of $\gamma$=1.8. The dotted line shows the correlation function fitted by \citet{pn} for local radio galaxies evolved to $z$=0.3 assuming linear theory ($r_0$=6.1 Mpc).
 }}
\end{figure*}

To obtain better number statistics, we computed the correlation function for the combined TONS08 and TONS12 sub-samples. Fig.~\ref{fig:corrfn_08_12} shows that the combined correlation function has much smaller errors than is obtained for the separate sub-samples. This is partly because of the increased sample size and also because when TONS08 and TONS12 are combined, the number of radio galaxies observed is very similar to the number expected (see Table.~\ref{tab:the_samples}).

The best fit correlation length for the combined samples is $r_0(z)$=8.7$\pm$1.6 Mpc (1$\sigma$) (fitting the power-law function out to separations of 30 Mpc). This corresponds to $r_0(0)$=11.0$\pm$2.0 Mpc (1$\sigma$). Using Equation.~\ref{eq:b_r} and taking $r_{0 ~\rm{gal}}(0)$=8.1$\pm$0.9 Mpc \citep{nor02} and $b_{\rm{gal}}$=1.0, this corresponds to a bias of $b_{\rm{rg}}$=1.3$\pm$0.3.

\begin{figure*}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(150,90)
\put(20,-15){\special
{psfile="08_12_corr_func_err.ps"
vscale=60 hscale=60 angle=0}}
\end{picture}
\end{center}
{\caption[junk]{\label{fig:corrfn_08_12} The two-point correlation function for the combined TONS08 and TONS12 sub-samples. The data are binned in 10 Mpc separation bins. The errors plotted are obtained from a combination of the bootstrap method and the error due to the uncertainties in the predicted number of radio galaxies. The diamonds show the extent of the Poisson errors. The solid line shows the fitted power-law correlation function with $r_0$=8.7 Mpc and a fixed slope of $\gamma$=1.8. The dotted line shows the correlation function fitted by \citet{pn} for local radio galaxies evolved to $z$=0.3 assuming linear theory ($r_0$=6.1 Mpc).
 }}
\end{figure*}

\subsection{Super-structure regions}
\label{sec:ssreg}

By re-dividing our combined sample into those within and out of super-structure regions, we directly determined if there are any differences in the clustering properties of radio galaxies in different large-scale environments. We combined the TONS08 and TONS12 sub-samples and redivided the combined sample into radio galaxies that were within super-structure regions and those that were not. We defined super-structure members as radio galaxies with redshifts in the intervals $z$=0.233-0.285 and $z$=0.33-0.367 for the TONS08 sub-sample and $z$=0.21-0.25 and $z$=0.285-0.34 for the TONS12 sub-sample. Using this criteria, this resulted in 50/84 and 42/107 radio galaxies defined as being in a super-structure and 34/84 and 65/107 radio galaxies defined as being outside of super-structures in TONS08 and TONS12 respectively. The total sample size was 92 radio galaxies within super-structures and 99 out of super-structures. From our model redshift distribution, we calculated that we would expect 22.3$\pm$2.4 and 24.6$\pm$2.4 radio galaxies within the super-structure regions and 72.8$\pm$3.8 and 73.0$\pm$3.8 radio galaxies outside super-structure regions in the TONS08 and TONS12 sub-samples respectively (see Table.~\ref{tab:the_samples}).

The two-point correlation functions for the combined TONS08 and TONS12 super-structure and non-super-structure regions are shown in Fig.~\ref{fig:corrfn_08_12_ss}. In these cases, we calculated the two-point correlation functions without correcting for the underlying number density of radio galaxies because we were determining differences in the shape and strength of the correlation function in over- and under-dense regions rather than trying to determine a universal correlation length. The two-point correlation functions have very different shapes. The two-point correlation function in non-super-structure regions appears to conform to a well-behaved power-law relation whereas the correlation function in super-structure regions strongly deviates from a simple power-law. The enhanced number of pairs at large separations seen in the correlation functions of both the TONS08 and TONS12 samples are due to radio galaxies in super-structure regions. This is unsurprising given that we would expect a clustering signal on larger scales in regions that we see super-structures. \citet{wild04} use the relative bias of galaxies in the 2dFGRS to rule out an exact linear bias. The deviation from a simple power-law in super-structure regions supports the view that bias may be a more complicated function.

The two plots illustrate nicely how a power-law is only a good fit either out of super-structure regions or in surveys that are less biased and large enough for their contribution to be negligible. In a survey consisting of biased tracers of the mass, such super-structures will be common and thus a power-law will never be a good approximation.

\begin{figure*}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(150,65)
\put(-2,-10){\special
{psfile="08_12_corr_func_err_ss.ps"
vscale=45 hscale=45 angle=0}}
\put(70,-10){\special
{psfile="08_12_corr_func_err_nonss.ps"
vscale=45 hscale=45 angle=0}}
\end{picture}
\end{center}
{\caption[junk]{\label{fig:corrfn_08_12_ss} The two-point correlation function for the radio galaxies within (left) and outside of (right) super-structure regions in the combined TONS08 and TONS12 sub-samples. The data are binned in 10 Mpc separation bins. The errors plotted are obtained from a combination of the bootstrap method and the error due to the uncertainties in the predicted number of radio galaxies. The diamonds show the extent of the Poisson errors. The dotted line shows the correlation function fitted by \citet{pn} for local radio galaxies evolved to $z$=0.3 assuming linear theory ($r_0$=6.1 Mpc).
 }}
\end{figure*}

\subsection{The TONS08w, TONS16w and Lacy sub-samples}

We also computed the two-point correlation function for the sub-samples with a higher radio flux-density limit.

\citet{lac} analysed an independent sample of similar ($s_{1.4}>20$ mJy) radio galaxies in a different area of the sky but with a much smaller sample size. To compare our use of a different method and in particular, a different redshift distribution, we compared the correlation length that we obtain with that obtained by \citet{lac}. Without correcting for the fact that the region is under-dense, we obtained a correlation length of $r_0(z)=15.3\pm7.1$ Mpc. The correlation length obtained by \citet{lac} is $r_0=17^{+7}_{-12}$ Mpc. Our results agree with this well within the error bars. When we corrected the correlation function to that for the underlying number density, we found $r_0(z)=12.5\pm5.2$ Mpc. This shows that the effects of calculating $\xi$ over a small survey volume are large. Assuming a median redshift of $z$=0.3, this corresponds to a correlation length at $z$=0 of $r_0(0)=15.9\pm6.6$ Mpc.

As demonstrated for the \citet{lac} sample, the small numbers combined with the smaller number density of the higher flux density radio galaxies in the TONS08w and TONS16w sub-samples means that the errors are too large to determine a reliable value of $r_0$ for each individual sub-sample. We therefore combined the TONS08w, TONS16w and \citet{lac} samples to improve the small number statistics. Although the \citet{lac} sample has slightly different selection criterion, the populations are sufficiently similar to add the samples together to increase the number statistics and still obtain meaningful results.

The combined two-point correlation function is shown in Fig.~\ref{fig:corrfn_highf}. Because of the possibility of incompletenesses in the TONS08w sub-sample, we assumed that the underlying number density of radio galaxies in the TONS08w survey was equal to the number observed (Equation.~\ref{eq:xi_cor}). The error bars are too large to obtain a reasonable estimate of $r_0$. A number of reasons may be accountable for the lack of signal and the large error bars. An intrinsic reason may be the smaller number density of the higher flux density radio galaxies. Perhaps there are too few luminous radio galaxies triggered at small separations. Indeed, there are only four, one and zero radio galaxy pairs with separations $<$ 10 Mpc in the \citet{lac}, TONS16w and TONS08w sub-samples respectively. The \citet{lac} sample gives a particularly high clustering signal (even after it is corrected for being an under-dense region). This is in contrast to the TONS08w and TONS16w sub-samples which appear to have much weaker clustering signals.

We obtained a clustering length of $r_0(z)$=8.8$\pm$4.4 Mpc (1$\sigma$). Assuming a median redshift of $z$=0.3, this corresponds to a correlation length at $z$=0 of $r_0(0)$=11.2$\pm$5.6 Mpc (1$\sigma$). This is consistent with the findings of \citet{mag04} who found no difference in the clustering properties of radio-AGNs of different radio luminosity in the 2dFGRS and \citet{ove} who found that the angular correlation function of NVSS radio galaxies is approximately constant between flux density limits of $s_{1.4}$=3 - 40 mJy. \citet{mag04} concluded that once radio activity is triggered in low luminosity radio galaxies, there is no evidence for a connection between black-hole mass and the level of radio output. However our errors are so large that one can rule out only very dramatic differences in the clustering properties of the two samples.

\begin{figure}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(150,65)
\put(-2,-10){\special
{psfile="highf_corr_func_err_nocorr.ps"
vscale=45 hscale=45 angle=0}}
\end{picture}
\end{center}
{\caption[junk]{\label{fig:corrfn_highf} The two-point correlation function for the combined TONS08w, TONS16w and \citet{lac} samples assuming that the predicted number of radio galaxies in TONS08w is equal to the number observed. The data are binned in 10 Mpc separation bins. The errors plotted are obtained from a combination of the bootstrap method and the error due to the uncertainties in the predicted number of radio galaxies. The diamonds show the extent of the Poisson errors. The solid line shows the power-law correlation function with $r_0$=8.8 Mpc and a fixed slope of $\gamma$=1.8. The dotted line shows the correlation function fitted by \citet{pn} for local radio galaxies evolved to $z$=0.3 assuming linear theory ($r_0$=6.1 Mpc).
 }}
\end{figure}

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

By combining the TONS08 and TONS12 sub-samples, we found a correlation length of $r_0(z)$=8.7$\pm$1.6 Mpc. Even after correcting for the increase in clustering under linear theory between $z\sim$0.3 and the local Universe ($r_0(0)$=11.0$\pm$2.0 Mpc), this value is significantly smaller than the local value of $r_0(0)$=15.7$\pm$1.7 Mpc derived by \citep{pn} and that obtained by \citet{mag04} ($r_0(0)$=14.2$\pm$1.0 Mpc). The reason for this discrepancy is unclear as we should be looking at a comparable sample in terms of the mean radio luminosity of the population (see Fig.~\ref{fig:lz_relation}). This may be evidence for a redshift evolution in the clustering of low luminosity radio galaxies but we note that the sign of the supposed effect (radio galaxies are less biased at $z \sim$0.3 than at $z \sim$0) runs counter to the inferences drawn from systematic changes in the environment of weak radio galaxies with redshift \citep{hl}. However, a number of different effects could contribute to this apparent discrepancy including a marginal statistical difference (see errors on biases in Table.~\ref{tab:rnort}), small number statistics, redshift space distortion effects and the assumptions that have to be adopted when transforming the clustering measurements at different redshifts to that in the local Universe.

We obtained a larger correlation length than that obtained from the projection of the angular correlation function of NVSS radio galaxies (\citealt{bw}; \citealt{ove}). Any discrepancy in this case is easier to explain: Fig.~\ref{fig:lz_relation} illustrates how the \citet{bw} sample is dominated by more powerful FRII radio galaxies near the break in the RLF. \citet{mclu} showed that although the scale size and optical luminosity of the host galaxy is correlated with the radio power for FRII's, this relation does not hold for FRI radio galaxies. If FRI radio galaxies have more luminous host galaxies, they should also have a larger clustering length. The radio activity in these populations may be triggered by a different mechanism. This is hinted at by the recent result of \citet{cj} who found that although it is well known that the co-moving number density of powerful FRII radio galaxies falls dramatically at low redshifts, the co-moving number density of lower luminosity AGN remains constant. The clustering strength of FRII radio galaxies may therefore be more complex than simply tracing the clustering of the underlying host galaxy population. However, these measurements may have significantly underestimated the correlation length for two reasons. Firstly, deep cleaning of the NVSS images may have caused a deficit of galaxy pairs with separations $\theta\sim$0.2 deg, which may have resulted in a spuriously low power-law fit and hence correlation length \citep{bla04}. Secondly, the assumed redshift distribution used to deproject the angular correlation function has an unphysical spike at low redshifts which would also have suppressed the correlation signal. When these effects are accounted for, the correlation length obtained was $r_0(0)$=15.1$\pm$0.7 (C. Blake, private communication).

\begin{figure*}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(150,90)
\put(20,-15){\special
{psfile="lumz.ps"
vscale=60 hscale=60 angle=0}}
\end{picture}
\end{center}
{\caption[junk]{\label{fig:lz_relation} 1.4 GHz Luminosity as a function of redshift for the TONS08 (circles) and TONS12 (squares) sub-samples. Also plotted is the luminosity corresponding to the radio galaxy flux density limits over the appropriate redshift range for the TONS08/12 sub-samples ($s_{\rm 1.4}$=3 mJy; solid line), the \citet{pn} sample ($s_{\rm 1.4}$=0.5 Jy; long dashed line) and the \citet{bw} sample ($s_{\rm 1.4}$=10 mJy; short dashed line). Various critical values of the radio luminosity are marked: the star-burst (SB) / AGN break ($L_{\rm 1.4 GHz} \sim 10^{22} {\rm W Hz^{-1} sr^{-1}}$); the FRI/FRII break ($L_{\rm 1.4 GHz} \sim 3 \times 10^{24} {\rm W Hz^{-1} sr^{-1}}$) and the RLF break ($L_{\rm 1.4 GHz} \sim 10^{25.7} {\rm W Hz^{-1} sr^{-1}}$).
 }}
\end{figure*}

\citet{nor01} showed that the strength of galaxy clustering depends on the galaxies intrinsic optical luminosity. The mean luminosity of the TONS08/12 radio galaxies is $\sim$2.5 $L_\star$. From the relation: $b/b_\star=0.85+0.15L/L_\star$ \citet{nor01}, we expect the sample to have a relative bias of $b$=1.2. From \citet{nor02} fig.10, the expected bias of 2.5$L_\star$ early-type galaxies has a slightly higher bias of $b$=1.3. Using equation.10, the TONS08/12 (linear theory evolution corrected) clustering length corresponds to a bias of $b$=1.3$\pm$0.3. Although the uncertainties are large, this suggests that the clustering strength of the TONS radio galaxies is consistent with that of the underlying host galaxy population. If, as suggested by the results of \citet{mclu}, the clustering signal measured by \citet{bw} and \citet{ove} was dominated by galaxies with smaller ($\sim L_\star$) optical luminosities, we would indeed expect them to measure a smaller clustering signal.

\citet{brand} postulated that the radio galaxy bias of low luminosity radio galaxies needs to be $b\sim$3-4 to explain the number of super-structures found within the TONS08 volume. In this paper, we have shown that redshift spikes are a common phenomena in radio galaxies redshift surveys at NVSS flux density levels and $z\sim$0.3 (corresponding to FRI-like radio galaxies well below the RLF break). The discrepancy in the bias inferred here and by \citet{brand} may be related to the inadequacy of a simple linear bias model for the way radio galaxies trace the underlying dark matter.

\section{CONCLUSIONS}

The results of this investigation can be summarized as follows.

\begin{itemize}
\item We have demonstrated that redshift spikes corresponding to super-structure size overdensities are a common phenomenon within radio galaxy redshift surveys.
\item We computed a universal redshift distribution for radio galaxy redshift surveys of given optical magnitude and radio flux density limits.
\item The spatial clustering of low luminosity (predominantly FRI) radio galaxies at $z\sim$0-0.5 has been measured directly for the first time.
\item We used our model redshift distribution to correct the clustering signal for our sample being under- or over-dense due to large-scale structure.
\item The best fit correlation length for our low flux density limit ($s_{1.4}>$3 mJy) sample is $r_0(z)$=8.7$\pm$1.6 Mpc, corresponding to $r_0(0)$=11.0$\pm$2.0 Mpc at $z$=0 (assuming an increase in clustering under linear theory). This is consistent with the clustering strength of the underlying host galaxy population.
\item  We found that the clustering of low luminosity radio galaxies is not significantly different for our low and high flux density limited samples.
\item By comparing the two-point correlation function for radio galaxies within and outside of super-structure regions, we showed that a power-law function is only a good approximation outside super-structure regions or in surveys that are less biased and large enough for their contribution to be negligible. In a survey consisting of biased tracers of the mass, such super-structures will be common and thus a power-law will never be a good approximation.
\end{itemize}

\section{ACKNOWLEDGEMENTS}

We thank Chris Blake, Michael Brown, Idit Zehavi, Mark Lacy and John Peacock for useful discussions and Devinder Sivia, Will Percival, Jenny Grimes and Steve Croft for use of code and software. We also thank Amanda Bauer, Filipe Abdalla and Ewan Mitchell for obtaining some of the spectra and Chris Benn and Jasper Wall for redshifts of unpublished spectra of some of the radio galaxies in TONS12.
We thank the staff at McDonald, NOT and the WHT for the  technical support they have provided. This research has made use of APM, NVSS, FIRST \& POSS-II web-based databases. We thank the staff of the Hobby-Eberly Telescope. The HET is operated by McDonald Observatory on behalf of The University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universitaet Muenchen, and Georg-August-Universitaet Goettingen.
The Nordic Optical Telescope is operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.
The WHT is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. This material is based in part upon work supported by the Texas Advanced Research Program under Grant No. 009658-0710-1999.
Kate Brand was supported for the majority of this work by a PPARC studentship. Steve Rawlings thanks PPARC for a Senior Research Fellowship.

\bibliographystyle{mn2e}

redpajama_set_name: RedPajamaArXiv


The fake notice claims the agency promises to refund 35% of the victims' investment in BitConnect.
The Texas state regulator on Friday warned Texans about persons that approach victims of the now-defunct pyramid scheme BitConnect claiming that, for a $250 fee, they can help them recover their investments.
This type of activity is typical of the fraud mechanism known as a 'recovery room.' Although the agency could help people who have lost money, they don't charge a fee, guarantee money back, or give special preference to anyone who files a formal complaint.
While there are many variations of these tactics, the investor should be cautious of any person or organization that claims to know about his expertise and offers to help return their money.
Texas' watchdog is one of the most active state regulators in the crypto arena, joining federal authorities in going after businesses trying to avoid proper registrations. BitConnect itself received two cease-and-desist letters from state authorities after the self-described "self-regulating financial system" used celebrities to promote its scam.
Divyesh Darji, the Indian head of BitConnect and believed to be a core promoter of the scheme, was arrested in August.
These recovery scams are simply defrauding the victims one more time, and according to the regulator, consumers should look for some red flags. In most cases, victims are contacted by someone pretending to be affiliated with a government entity to perform investigations or other services.
They use a variety of lies to add credibility to their pitch, and once the victim shows interest, a series of official-looking documents are sent to assure the investor that money is waiting in an account and can be recovered for a fee.


text:
Greece: Highlights of Athens in One Day
Posted by ITKT Featured Writer | Feb 14, 2020 | Europe, Greece, ITKT Blogs, Spotlight | 0
The Acropolis: Birthplace of Democracy, Philosophy, Theatre, Sciences, and Art ©Pixabay Dias 12
Yes, I have just eight hours to see Athens and am pleasantly surprised at how much I am able to do. I climb to the top of the Acropolis and admire the four main structures up there. I wander the streets of Plaka, the old city, and even have time for lunch at a charming sidewalk cafe whose "sidewalk" is a set of stairs leading straight up. I enjoy some quiet time on a bench in Syntagma Square. And I watch the guards at the Tomb of the Unknown Soldier perform elaborate maneuvers to honor the fallen hero.
My first job is to familiarize myself with the metro. It is easy to use and much faster than buses and taxis. There are three main stops for all of these destinations–"Akropoli", "Monastiraki", and "Syntagma". I decide to tour the Acropolis first while I still have plenty of energy and it is not too hot. I take the Red Line to the "Akropoli" stop which is conveniently located a block or so away from the ticket booths. After visiting the Acropolis I decide to walk (downhill) to Plaka and Syntagma Square because I enjoy walking and experiencing the city along the way.
The Parthenon, a masterpiece of classic Doric architecture ©2019 Elizabeth von Pier
The Birthplace of Democracy, Athens' Ancient Acropolis
"Acropolis" is a generic term meaning a citadel or fortified area of an ancient Greek city, typically built on a hill with very steep sides and serving defensive purposes. There are many acropoleis in Greece, but most people associate "Acropolis" with the one high up in the ancient fortified area of Athens. The one in Athens is the one with a capital "A".
The significance of this particular acropolis stems from its age""dating back to the 5th century BC""and the magnificent structures built on it. These include the Parthenon, said to be one of the finest examples of classical architecture.
As my excitement and anticipation build, a sign announces that I am now entering the "heart of Ancient Athens", the place where "the most essential aspects of the European identity emerged: Democracy, Philosophy, Theatre, Sciences, Arts. EUROPE STARTS HERE!" I am psyched.
I start along the path leading up to the Acropolis and am encouraged. The incline is slight and there are shade trees along the side. But that changes pretty quickly. It is a long daunting way up to the fortress-like setting at the top. I have to keep a close watch for where I step because the gently sloping pathway quickly turns into a steep, hazardous, and slippery marble staircase. Even first thing in the morning there are many tourists and they tend to make the trek up dangerous because they stop suddenly and without warning to take a sip of water or to take a photo. A collision up here could be disastrous.
Along the way, I pass the ancient stone theater, Odion Theater of Herodes Atticus, on the southwestern slope. This is a concert venue and a spectacular setting when it is lit up at night. The semi-circular amphitheater appears to have been carved out of the natural rock and faces a 28-meter-high stone structure with arched openings that at one time held statues. It was built in 161 AD by Herodes Atticus in honor of his wife and is considered to be the birthplace of European theater.
The Propylaea is the first set of structures as I reach the Acropolis. It and the other buildings up here at the apex were built to thank the gods and celebrate the Athenian victory over the invading Persians. It marks the entryway to the temple complex and today can be identified by the numerous columns and steep walkways. It is a building of the Doric order with a few Ionic columns. I make note of the columns outlining what once must have been a fabulous structure, but what I remember most is the winding and slippery marble staircase used to ascend to the top. Crowds slowly make their way up, taking care to drink plenty of water and not lose their balance. It feels dangerous but exciting.
Once I reach the peak and emerge from the Propylaea, the three-quarter view of the Parthenon is awesome. One of the glories of Western architecture, this majestic showpiece of the Acropolis was built to be the focus of the building complex. It was built in the fifth century BC as a temple to Athens' patron goddess, Athena, the Greek goddess of wisdom and war and was meant to house an immense statue of Athena that was made out of gold and ivory by the famous sculptor Pheidias. This statue has been lost since the Roman Empire conquered Athens in the second century BC.
The sky is a perfect clear blue and the structure, made out of 22,000 tons of white marble, stands out brilliantly against it. It has fifty Doric columns arranged in perfect classical order, and the top is open to the sky because of a fire that broke out in the 3rd century AD and destroyed the roof and most of the sanctuary's interior.
The Erechtheion also is of the Age of Pericles, the 5th century BC. It is the elegant building to the left of the path leading to the Parthenon and is distinguished by six caryatids, fluted pillars of draped women who hold up the roof over the porch. These are exact copies of the originals which have been removed to the Acropolis Museum and the British Museum in order to prevent further decay. Named for Erechtheos, a mythological king of Athens, the temple has over its long history been used as a church, a palace, a harem, and a military powder magazine. It was restored after Greece gained her independence from the Turks in 1821.
I stop to take a breath and look around at the majesty before me""the juxtaposition of the ancient structures up here and the magnificent modern city below.
The building off to the right of the Parthenon is the Temple of the goddess, Athena Nike. Early in its history, the temple was used as a worship place for deities. It is considerably smaller than the other temples on the Acropolis and its parapet was used to defend the Acropolis from military attack. It also served to prevent people and objects from falling over the steep edge.
A Restaurant in the old town Plaka district ©2019 Elizabeth von Pier
Plaka, The Old Town
Sitting at the base of the Acropolis is Plaka, the "old town". This is a picturesque area of narrow winding streets, shops, restaurants, and interesting neoclassical churches and buildings. The two main roads through Plaka are fairly flat, whitewashed, and mainly for pedestrians. But side streets can be challenging. Many are built on the side of the Acropolis and consist of a series of steep staircases leading up. Notwithstanding the inconvenience, shops and restaurants have sprung up on these vertical "streets" and are doing a lively business. Shop doors open onto the steps, and restaurants set up tables here, an unlikely but charming spot for an outdoor patio. I stop to enjoy a luscious Greek salad and a glass of wine at one of these "sidewalk" cafes. There is nothing like a Greek salad made in Greece with its fresh ripe tomatoes, cucumbers, red onions, olives, feta cheese, and extra virgin olive oil. My mouth still waters at the memory.
The Athens Cathedral of the Annunciation, popularly known as the Metropolis, sits in the main square of Plaka. Marble from 72 demolished churches was used to construct the massive walls of the cathedral. Next to it is a tiny Byzantine-era chapel, known as the Little Metropoli. It was built at the turn of the 13th century on the ruins of an ancient temple using old stone and monuments taken from earlier churches.
Tourist shops generally are pretty much the same everywhere, but I found here the occasional artist-owned gold shop that offers exquisite hand-designed gold jewelry at a fraction of the price I would pay in the States because the cost of labor is so cheap here.
Handmade sandals are also popular. I search out the unique workshop of Stavros Melissinos. Stavros is called the poet sandal maker and he, along with his son Pantelis, has been writing poetry and making sandals here in Athens for over sixty years. His designs are based on the footwear of notables such as Socrates, Plato, and Helen of Troy and his clients include the Beatles, Jacqueline Kennedy-Onassis, Barbara Streisand, Rudolph Nureyev, and Sophia Loren. I bought some of his sandals twenty-five years ago and am still wearing them.
Tomb of the Unknown Soldier in Syntagma Square, Athens ©2019 Elizabeth von Pier
Syntagma Square and The Tomb of the Unknown Soldier
Syntagma (Constitution) Square is a few blocks down the hill from Plaka. It is the heart of the city, near many tourist destinations, and a common meeting place as well as the scene of occasional demonstrations. Close-by is the Greek parliament building and the tomb of the Unknown Soldier. The old world and luxurious Hotel Grande Bretagne sits on the northwest corner of the square and is a nice place to stop for dessert and a cup of tea.
A moving shrine to people who have died in war, the Tomb of the Unknown Soldier, sits above Syntagma Square. It is a simple monument that was designed and built in the early 1930s and is guarded by the Evezones, the elite force of the Greek army and part of the Presidential Guard. Standing proudly above the Tomb is the old Royal Palace, built in 1843 as the first modern royal palace and, since 1934, home to the Greek parliament.
Periodically the two guards on duty perform a series of maneuvers to honor the dead. They wear red hats, taupe suits, white tights, and shoes adorned with black pompoms. Their maneuvers are uniform and well-orchestrated, as though to the beat of music, and last for about thirty minutes. I feel moved to be here honoring the fallen heroes. A ceremonial guard change occurs every Sunday at 11:00 am when marching bands and the Presidential guard parade from their barracks behind the parliament building.
When you go:
I visited Athens on a Holland America cruise entitled "11-Day Ancient Empires" which traveled round-trip to and from Civitavecchia (Rome). Ports of call included Kusadasi (Ephesus), Turkey; Katakolon (Olympia), Greece; Piraeus (Athens), Greece; Mykonos, Greece; Rhodes, Greece; Santorini, Greece; and Salerno (Amalfi Coast, Pompeii, Sorrento), Italy.
Written by: Elizabeth von Pier
Elizabeth von Pier loves to travel. After she retired from her lifetime career in banking, she has been traveling the world, photographing, and writing. She has been published in the Los Angeles Times and many online travel magazines including In the Know Traveler, Go Nomad, WAVEjourney, Travelmag""The Independent Spirit, and Travel Thru History. She also recently published her first book, "Where to Find Peace and Quiet in London" and is now working on another volume in this series, "Where to Find Peace and Quiet in Paris" which is expected in 2020. Ms. von Pier lives in Hingham, MA.
For more ITKT travel stories about Greece
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redpajama_set_name: RedPajamaCommonCrawl


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Interior Minister Matteo Salvini has threatened to send the passengers back to Libya.
The Italian coast guard ship Diciotti has arrived in the Sicilian city of Catania with 177 migrants awaiting word on which countries will take them following another standoff between Malta and Italy.
Though the ship made port late on Monday, the Italian government is not allowing the migrants to disembark pending a decision by the European Union on where they will go.


Qatar is located in southwest Asia surrounded by the waters of the Persian Gulf and Saudi Arabia.
It's a country born from natural gas and oil and the rapidly the capital grown. This is Doha. Winters are mild and summers are humid, so humid that your clothes stick to you even though we were in November. We started with a visit to Al Shaqab thoroughbred Arabian horses, known as Qatar Equestrian Federation. In the stables, horses stood quietly, just had finished eating and were willing to "chat ". Near the stables was riding with air conditioning field where they were trained and prepared for competitions.Then we went to another farm this time... camels. Souq Waqif is a commercial area like "market " actually a bazaar where we found all kinds of clothes, jewelry , traditional sweets , spices, souvenirs.
Beside them were terraces , restaurants Lebanese , Italian , Malay , Iraq. Also there you could have a coffee at a cafe French French .
By the time we arrived it was pretty deserted but tonight , the market became crowded and small.
Although on at least 100 years old, was rebuilt and renovated recently , is keeping her former glory .
There I found some shops where they began negotiations Arabian perfumes ... after many " attempts " , had come to seem to me that all were about the same smell .
Then I got in the animals' . From colorful cages were heard beeps , whistles , mieuneli and all sorts of other sounds difficult to identify.
You could easily lose a few hours there but we unfortunately had to keep our program.
There was a lovely but short ride on the Doha Corniche where we admired the newly built district , West Bay, the financial center with giant buildings where large firms and were based . Guide took us by bus and took a tour through the small town of steel and glass . Then we returned to the hotel, we rested a bit and went to another mall, more affordable and less luxurious than the Villagio . And there was a house where you could exchange any currency exchange their currency - Qatari Riyal . In the evening we all had dinner at a Lebanese restaurant that looks a little more luxurious than a canteen - my honest opinion . I was disappointed not specific menu , though incomparable with what we offered at the hotel as the place itself , presentation, smell dark ... well I'm not left a good impression but taking the pulse of the streets , admire the lights of the cliff , to breathe air with dusk became more bearable ... was a kind of balance, so after all I must say it was a pretty cool experience.


Girls in Trinidad and Tobago are being introduced to the oval ball through global programmes like Get Into Rugby. Photo: World Rugby.
How did a Kiwi synchronised swimmer become the global head of women's rugby? Suzanne McFadden talks to Katie Sadleir, who's responsible for empowering women in rugby, inspired by young girls from Mongolia to Uganda and Syria.
Twelve-year-old Ugandan Lucky Nirere is one incredible young woman.
She started playing tag rugby at the age of two, and began coaching the sport as soon as she started primary school.
At nine, she represented Uganda at the 2015 Rugby World Cup as a ball deliverer, leading the Australian and Welsh men's sides onto the field at Twickenham.
Now, as she starts high school, Nirere is a coach educator - working with 50 grassroots rugby coaches – and is proudly "the best junior referee in Uganda".
Nirere hopes to follow her mother, Fortunate, into the Ugandan national women's rugby team, the Lady Cranes. Only then, will she be allowed to play rugby in boots – not bare feet.
Although they are 6500km apart, and have never met in person, Nirere and Katie Sadleir – a Kiwi Olympian living in Dublin - have become firm friends.
And although Sadleir represented New Zealand in synchronised swimming, winning a Commonwealth bronze medal, it's rugby that's brought the two together.
It's girls like Nirere who inspire and drive Sadleir in her role as World Rugby's first general manager of women's rugby.
"She's so passionate about rugby and what she's doing in the game. It's just amazing," Sadleir says of Nirere, who she was introduced to her by Regina Lunyolo Okoit, the manager of the Lady Cranes.
When Sadleir sent some World Rugby paraphernalia to Nirere - like a backpack, and a diary - she sent back a video of herself unwrapping the gifts in front of her village. "She's such a special kid – I thanked for being such an inspiration," Sadleir says.
Encouraging young women around the world like Nirere to play and stay in the game, by giving her opportunities on and off the field, is all part of Sadleir's brief to accelerate the global development of women in rugby.
The women's game is already growing at an astounding rate.
In New Zealand alone, female players rose to 27,838 this season - with 3500 new players signing up. NZ Rugby's head of women's development, Cate Sexton, put the almost 15 percent growth down to more resources being poured into the women's game here.
Globally, it's a similar success story. Since 2013, the number of female rugby players has increased by 60 percent, so more than a quarter of the 9.1 million people who play rugby are women and girls.
While Sadleir wants to ensure that growth remains healthy, another of her goals is to strengthen the 15s game. "There's been this question: should women's rugby be sevens only, especially since it became an Olympic sport? Is that the game to follow?" says Sadleir, during a visit home for New Zealand Rugby's inaugural Women in Governance Conference.
One way is to build the traditional game is to close the gap in winning margins between countries that qualify for the 2021 Women's Rugby World Cup (which New Zealand and Australia are bidding to host). World Rugby has just reviewed the high performance programmes of the top 22 women's unions, and are looking at ways to lift the competitiveness of the bottom six nations.
There's also a review into the international calendar to ensure there are more tournaments for the 15s women's sides – which could mean more regional competitions.
"One of the challenges we have as a sport globally is that there are so many different formats of rugby – 15s, sevens, even snow and beach rugby. And we're responsible for them all," she says.
Yep, snow rugby is a sport - and it's played by women. As part of developing the new strategy for the global women's game, Sadleir went to Mongolia, where they play snow rugby.
It was there she saw little girls in Mongolian orphanages running around dressed in Hong Kong team rugby gear.
Asia is a real focus for rugby expansion. Sadleir has spoken to the general manager of Syrian Rugby about the future of the game there. Syria's women's sevens team made their international debut in a tournament in Lebanon earlier this year.
"It's really opened my mind to the challenges women and girls around the world face to play rugby," Sadleir says.
Katie Sadleir sees herself as a "myth buster" in World Rugby. "When I started, people said 'There's no way World Rugby will have women on its council'. Now there are 17."
Sadleir admits she's never played a game of rugby in her 54 years. She was a water baby.
Born in Scotland, and raised in Canada, Sadleir came to New Zealand with her family as a teenager, and immersed herself in synchronised swimming and water polo. She went to the 1984 Los Angeles Olympics in synchronised swimming with her sister Lynette, and won bronze for her solo routine at the 1986 Edinburgh Commonwealth Games.
Eight years later, Sadleir returned to the New Zealand team as their deputy chef de mission for the 1994 Commonwealth Games in Canada - the beginning of an illustrious career in sports administration.
When she received a Sport New Zealand lifetime achievement award two years ago, her citation described her as "the architect of many of the systems and programmes fundamental to the high performance sport system in New Zealand today".
She led the establishment of the New Zealand Academy of Sport in the late 1990s, and had ground-breaking roles in SPARC. But her career has been all about sport - she had major leadership roles at ACC and Wellington City Council; and was the project director at Te Auaha, the New Zealand Institute of Creativity in Wellington, when the rugby job came up.
Part of her unofficial job title is "myth buster", she says. "When I started, people said 'There's no way World Rugby will have women on its council'. Now there are 17.
"I came to work in an organisation which had been governed since 1886 by a council of men. Thirty men were on the highest decision-making council, and not a single woman. We were at the bottom of the pecking order," she says.
Last year, World Rugby created a new strategic direction – that by 2025, women in rugby would have equity on and off the field, through the five pillars of participation, performance, leadership, profile and investment.
When the discussion moved to leadership, and setting quotas for unions, Sadleir spoke up. "I said, 'You know what you guys? We cannot start setting quotas for people around the globe unless we address the elephant in the room – what's happening at World Rugby'," she says.
Beaumont agreed, and led a drive to create dramatic change - increasing the council by 17 members, and all of them women. "We went from zero to 35 percent in the first year," says Sadleir.
She knows she has some work to do to help balance the boards of the world's rugby unions. A World Rugby survey of six regional associations and 14 unions around the globe showed only one had 33 percent women on its board – the recognised percentage for effective impact. New Zealand Rugby has just one woman – Dr Farah Palmer – among its nine board members.
It's also Sadleir's job to look at "great things" happening globally in women's sport and learn from other codes.
She has a close working relationship with fellow Kiwi, Sarai Bareman, the chief women's football officer for FIFA. "We were appointed around the same time, and we made a commitment to share and engage with each other," Sadleir says. They also catch up regularly with former English cricketer Holly Colvin, who's the women's cricket manager for the ICC.
"I'm always very conscious of the fact that these people are not there to represent women in rugby; they are there for rugby," she says.
But until that day, Sadleir is revelling in her role, and happy living in Dublin. The global nature of the job brings her back home often to see her daughter, Abbey.


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text:
Свиня Альбрехта Дюрера () — порода свиней, виведена шляхом зворотньої селекції домашньої свині часів середньовіччя. При виведенні цієї породи селекціонери спиралися на малюнки і гравюри німецького художника Альбрехта Дюрера.

Історія
В ході подальшої селекції така домашня свиня, яка існувала в часи середньовіччя, вимерла. Про те, як виглядали домашні свині в той час, можна дізнатися завдяки німецькому художнику Альбрехту Дюреру, який реалістично відтворив тогочасних домашніх свиней на багатьох своїх малюнках і гравюрах. Спираючись на твори Дюрера селекціонери змогли вивести домашню свиню часів середньовіччя.

Сьогодні свиню Альбрехта Дюрера тримають переважно в зоопарках, аби продемонструвати відвідувачам зовнішній вигляд домашньої свині близько 1500 року. Деякі екземпляри цієї породи можна побачити, наприклад, в лісопарку Гундсгаптен у районі Форхгайм, Верхня Франконія або у Франконському музеї просто неба в Бад-Віндсгаймі.

Примітки

Посилання
 Свиня Альбрехта Дюрера на сайті zootierliste.de

Альбрехт Дюрер
Породи свиней
Свині в культурі

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text:
Carriera

Giocatore
Cresciuto nella , esordì in Serie A a 18 anni, con la maglia della Lazio il 4 maggio 1980, anno in cui vinse il premio di Miglior Giocatore del Torneo di Viareggio.
Dopo qualche mese al Milan, passò all', in massima serie, nell'estate 1980 e vi rimase fino all'ottobre 1981, quando andò in Serie C1 all'. Dopo 2 stagioni passò al  in Serie C2 e poi al  in Serie C1.

Tornato all'Empoli nell'estate del 1985, fu dirottato in autunno in Interregionale alla , dove giocò 10 gare segnando 6 reti.
Seguirono 4 annate in serie C con , ,  e . Con i falchetti giocò 98 gare e segnò 41 reti contribuendo alla promozione in Serie B del 1991.
Nel 1992 passò al  (con cui fu autore di una tripletta alla Juventus in Coppa Italia).
Nel 1994 passò al  in Serie B, dove, nella trasferta di  del 23 ottobre, mise a segno 5 gol nell'1-7 ottenuto dai rosanero, eguagliando il record stabilito da Carlo Dell'Omodarme nel 1959-1960.
Nella stagione 1995-1996, dopo aver iniziato alla  in Serie C, approdò in Serie B all' del presidente Sibilia, con cui retrocesse in C. Giocò in seguito 2 anni nel  disputando 49 gare e siglando 22 reti. Militò inoltre nel  in Serie C2, e nuovamente in Serie D alla Puteolana nella stagione 1999-2000, con cui ottenne la promozione in Serie C2.

Chiuse la carriera nel .

Allenatore e dirigente
Direttore sportivo alla Casertana nelle stagioni di Serie D 2000-2001, 2002-2003.

Ha iniziato nel 2002 nella squadra dove ha giocato, la Casertana, in Campionato Nazionale Dilettanti e l'Ariano Irpino in serie D, salvandolo dalla retrocessione vincendo i play-out col Marsala. Nel 2004 passa alla , portandola dalla C2 ai playoff persi per la promozione in B. Nella stagione 2005-2006 porta la Cavese in serie C1 dopo aver battuto il 15 aprile il Sassuolo 2-1. L'estate 2007 passa al Foggia, ma nel gennaio 2008 è esonerato dopo una prima metà di campionato disastrosa rispetto alle aspettative della squadra e dei tifosi. Il 7 ottobre 2008 diventa allenatore dell' al posto di Giuseppe Incocciati. L'inizio è positivo, nella trasferta di  pareggia 1-1; nell'impegno successivo interno col , arriva la 1ª vittoria, l' vince 2-1.
Conclude l'esperienza Irpina con retrocessione in Lega Pro Prima Divisione. Il 16 giugno 2009 diventa allenatore dell'Empoli, in sostituzione di Silvio Baldini. Il 6 giugno 2010 gli subentra Alfredo Aglietti.

L'8 gennaio 2011 diventa allenatore del Frosinone, in Serie B in cui aveva militato in attività, subentrando a Guido Carboni. Chiude il campionato all'ultimo posto con retrocessione in Lega Pro Prima Divisione.

Il 7 gennaio 2012 diventa allenatore della  a seguito dell'esonero di Gaetano Auteri. Con lui arriva tutto il suo staff: allenatore in 2ª Alessandro Tatomir, preparatore atletico Nicola Albarella, preparatore-portieri Franco Cotugno. Il 23 gennaio, dopo 2 sconfitte e l'ultimo posto in classifica, rescinde consensualmente il contratto.

Il 6 luglio 2012 diventa allenatore dell'Ischia Isolaverde, esordendo nel 2-1 col CTL Campania, primo turno di Coppa Italia Serie D 2012-2013 e il 2 settembre in campionato col 3-0 sul Sant'Antonio Abate. Con l'Ischia vince il campionato con 5 giornate di anticipo e scudetto dilettanti.

Il 20 gennaio 2014 è esonerato dall'Ischia dopo Chieti-Ischia 3-0. Il 2 luglio 2014 firma al  neoretrocesso in Serie D ma circa 2 mesi più tardi (prima d'inizio campionato) rescinde consensualmente il contratto. Il 24 novembre 2014 diventa allenatore della Casertana al posto dell'esonerato Angelo Gregucci.

Il 10 novembre 2015 diventa allenatore del  succedendo all'esonerato Michele Cazzarò. ma il 27 gennaio 2016 viene sollevato dall'incarico.

L'8 gennaio 2017 subentra a Massimo Costantino sulla panchina della Vibonese non riuscendo a salvare il team dalla retrocessione dalla Lega Pro.
Il campionato successivo riparte dalla Serie D ma il 14 novembre 2017 si dimette.
Il 24 dicembre 2018 firma per il  con cui conclude il campionato di Serie D al quinto posto nel girone H.

Il 17 settembre 2019 viene chiamato a subentrare a Francesco Moriero sulla panchina della Cavese, militante in Serie C.

Inizialmente non confermato per la stagione successiva viene richiamato dalla Cavese il 28 dicembre 2020.

Il 14 dicembre 2021 subentra a Tony Lio come nuovo allenatore del Lamezia Terme, militante in Serie D.

Il 18 ottobre 2022 subentra a Salvatore Marra sulla panchina della Puteolana, che staziona all'ultimo posto nella classifica del girone H di Serie D. L' 8 gennaio seguente viene esonerato, con la squadra sempre sull' ultimo gradino della classifica.

Statistiche

Statistiche da allenatore
Statistiche aggiornate al 14 dicembre 2021.

Palmarès

Giocatore

Club

Juve Stabia: 1978-1979 (girone F)
Puteolana: 1999-2000 (girone G)

Empoli: 1982-1983 (girone B)
Casertana: 1990-1991 (girone B)

Individuale
Miglior Giocatore del Torneo di Viareggio: 1
1980

Allenatore

Cavese: 2005-2006 (girone B)

Cavese: 2005-2006

Ischia Isolaverde: 2012-2013 (girone H)

Ischia Isolaverde: 2012-2013

Note

Bibliografia

Collegamenti esterni

Dirigenti della Casertana F.C.