text:
\section{Introduction}
\label{ch:intro}

The interstellar medium is a rarefied medium which fills the space between stars in galaxies. The ISM includes interstellar gas (molecular, atomic, ionized), dust, electromagnetic fields and cosmic rays. All the components of the ISM are closely related to each other due to the constant circulation of matter and energy in the galaxy. The ISM is highly turbulent \citep{TurbISM2014}, with high Reynolds numbers \citep[$R_e\gg10^3$, e.g.,][]{Combes2000}. Turbulence can be caused by processes on a wide range of scales (from pc to kpc), e.g., the interaction of cosmic rays and the interstellar plasma, stars and the interstellar medium, as well as rotation of the Galaxy, collisions between the stellar and gas components \citep{Elmegreen_2004}, etc.

When a radio wave passes through turbulent ionized gas of the ISM, it encounters stochastic free-electron density fluctuations on its way, which cause fluctuations in the refractive index of the medium. Thus, wavefronts will be randomly distorted, resulting in scattering of radio emission \citep{Ferrire2019}. Scattering may distort the images of compact radio sources in a number of ways \citep[e.g.,][]{2008A&A...489L..33S,Pushkarev2013,2014ApJ...794L..14G,2018ApJ...865..104J}, this complicates the interpretation of their observations. The study of radio wave scattering effects makes it possible to reconstruct the intrinsic characteristics of a scattered source. It is important to consider the phenomena of radio wave scattering when measuring the brightness temperatures of AGNs, which is crucial for theoretical models of relativistic jets \citep{Johnson2016}. At the same time, radiation scattering contains the most important information about properties of the turbulent medium, and a detailed study of this effect allows to investigate the properties of the ISM in our Galaxy \citep[e.g.,][]{Pushkarev15}. The AGN VLBI radio core (or shortly AGN core) that is generally observed in the region where the jet stops being opaque to synchrotron radiation is compact enough to probe the scattering properties of the ISM. The advantage of these sources over pulsars is that they are (i) more numerous, (ii) uniformly distributed over the sky, and (iii) their emission passes through the entire depth of the scattering screens in the Galaxy.

According to the studies of the radio wave scattering based on pulsar observations, it has been shown that scattering screens in our Galaxy consist of two main components: (1) a nearly uniform medium with a characteristic length-scale of the density fluctuations of about 500~pc and (2) a clumped medium with a scale of 100~pc, with an approximate size of one clump about 1~pc \citep{Cordes1985,Cordes86}. The typical size of such a substructure is important since it directly determines how the scattering manifests itself. For example, large-scale inhomogeneities lead to the refractive scattering effects, e.g., angular wandering of the apparent source position \citep{Clegg_1998}, extreme scattering effects \citep{Fiedler1987,Pushkarev2013}, `slow' intensity variations \citep{Rickett1984}. Fluctuations at smaller scales lead to diffractive scattering effects, e.g., angular broadening \citep{Duffett_Smith1976}, `fast' intensity scintillations in time and frequency \citep{Jauncey2020}.

There are two competing models of scattering screens: the Gaussian screen model \citep{Gauss_screen,Ratcliffe_1956} and the model with a power-law spectrum of electron density fluctuations \citep{Lovelace1970, Cordes1985}. The brightness distribution of a point source seen through the Gaussian scattering screen is Gaussian (unresolved core surrounded by a halo) with an angular size proportional to wavelength squared, i.e., $\theta\propto\lambda^{k}$, where $k = 2.0$ \citep{Narayan1985,Cordes86}. A power-law spectrum of turbulence assumes that the spectrum of free electron density fluctuations can be approximated as a Kolmogorov power-law \citep{Kolmogorov41,Cordes86,Rickett1990,Armstrong95}. In this case, the scattering angle of a point source is proportional to wavelength to the power of 2.2, i.e., $\theta\propto\lambda^{k}$, where $k = 2.2$.

If there is no intermediate scattering screen, then the observed angular size of a compact background source will coincide with its intrinsic size. For example, in the case of an apparent jet base in active galactic nuclei, an observed size will be proportional to $\lambda^{k}$, where $k = 1$ for conical jet shape \citep{BK79,Konigl1981}. This assumption works for 15~GHz and lower frequencies. At higher frequencies, VLBI observations of nearby AGNs might probe innermost jet regions characterized by quasi-parabolic shape \citep{Asada2012,Kovalev2020}.

In this work we further develop the study made by \cite{Pushkarev15}. For that, we use a larger sample of the observed AGNs, and introduce new methods for modelling the apparent jet base structure of active galactic nuclei and a completely new approach to study the scattering effects in our Galaxy.

\section{AGN VLBI core size measurements}
\label{ch:size_measurements}

Our analysis is based on the VLBI observations of AGN jets at frequencies ranging from 1.4 to 86~GHz (see \autoref{tab:table_freqs} for details) compiled in the Astrogeo database\footnote{\url{ http://astrogeo.org/vlbi_images/}}. We rely on the measured interferometric visibilities and do not analyse the corresponding restored images. The Astrogeo database collects geodetic VLBI observations \citep{2009JGeod..83..859P,2012A&A...544A..34P,2012ApJ...758...84P}, the VLBA\footnote{Very Long Baseline Array of the National Radio Astronomy Observatory, Socorro, NM, USA} calibrator surveys (VCS; \citealt{2002ApJS..141...13B,2003AJ....126.2562F,2005AJ....129.1163P,2006AJ....131.1872P,2007AJ....133.1236K,2008AJ....136..580P}), the MOJAVE VLBA program (\citealt{2018ApJS..234...12L} and references therein) and other VLBI networks including EVN\footnote{European VLBI Network}, LBA\footnote{Long Baseline Array} and GMVA\footnote{Global millimeter VLBI array} \citep{2007ApJ...658..203H,2008AJ....136..159L,2011AJ....142...35P,2011MNRAS.414.2528P,2011AJ....142..105P,2012MNRAS.419.1097P,2013AJ....146....5P,2015ApJS..217....4S,2017ApJS..230...13S,2017ApJ...846...98J,2019MNRAS.485...88P,2019A&A...622A..92N,2021AJ....161...14P,2021AJ....161...88P}. This dataset contains 17\,474 sources observed from 1994 to 2021, comprising more than $100\,000$ individual observations. The majority of them were performed at 2, 5, 8, or 15~GHz.

The AGN VLBI core is the apparent jet origin. We apply the model-fitting of interferometric visibilities approach and describe the apparent structure with two Gaussian components: the core and the extended jet emission. We use nested sampling to make fitting completely automatic and independent of initial guesses. The brightest component of the two is first selected as the core; if the jet orientation at a lower frequency is opposite to that at a higher frequency, we switch the two components. \cite{plavin2022} present and discuss this in details as well as evaluate this fitting approach used to measure jet directions. Nested sampling provides principled uncertainty estimates on all parameters, including the core component size. We find these uncertainties directly useful for our analysis even though they are fundamentally underestimated: calibration and self-calibration effects are not accounted here. Specifically, we drop the measurements with uncertainty in the core size exceeding 50~per~cent of the value itself. We find that the unresolved sources are also removed by this criterion and we do not perform any additional selection. \autoref{tab:exp_data} contains eight randomly selected AGN for which the core size was measured.

\begin{table}
	\caption{Central frequencies of the used observing bands.}
	\centering
	\begin{tabular}{|*{3}{c|}}
		\hline
		\hline
		 Band   & Central frequency range (GHz) \\
		\hline
		L & 1.3 -- 1.6   \\
		S & 2.2 -- 2.3   \\
		C & 4.1 -- 5.1   \\
		X & 7.6 -- 8.7   \\
		U & 13.8 -- 15.6 \\
		K & 23.9 -- 24.4 \\
		Q & 43.1 -- 43.9 \\
		W & 86.2 -- 86.3 \\
		\hline
	\end{tabular}
	\label{tab:table_freqs}
\end{table}

\begin{table*}
    \centering
    \caption{Apparent angular sizes of the AGN VLBI core measured at frequencies ranging from 1.4 to 86~GHz with separate records for every epoch.}
    \label{tab:exp_data}
        \begin{tabular}{lrcccrr}
        \hline
        \hline

            Name            & $\mathrm\nu$ & Epoch      & $\theta_\mathrm{core}$ & $\theta_{\mathrm{core}}^\mathrm{err}$  & $b$        & $l$\\
                            & (GHz)        &            & (mas)                  & (mas)                  & (deg) & (deg)\\
            (1)             & (2)          & (3)        & (4)                    & (5)                    & (6)        & (7)\\
            \hline
             J0006$-$0623   & 1.40         & 2010-08-23 & 2.601                  & 0.007                 & $-66.65$  & 93.51    \\
             J0825$+$0831	& 2.31         & 2005-07-20 & 1.483                  & 0.074                 & 24.66     & 215.92   \\
             J1842$+$7946	& 4.36         & 2020-12-13 & 0.945                  & 0.098                 & 27.07	 & 111.44 \\
             J0158$+$2124   & 8.68         & 2014-08-09 & 0.686                  & 0.006                 & $-38.86$  & 142.95   \\
             J1337$-$1257   & 15.4         & 1995-07-28 & 0.091                  & 0.010                 & 48.37     & 320.02   \\
             J1048$-$1909 & 24.4          & 2002-08-25 & 0.057                  & 0.003
             & 34.91 & 266.75\\
             J2258$-$2758	& 43.1         & 2003-09-13 & 0.089                  & 0.002                 & $-64.92$  & 24.39   \\
             J0136$+$4751	& 86.3         & 2002-04-20 & 0.028                  & 0.001                 & $-14.32$  & 130.79    \\
        \hline
        \end{tabular}
        \begin{tablenotes}
            \item The columns are as follows: (1) source name in the J2000.0 notation; (2) central observing frequency; (3) epoch; (4) measured AGN core size; (5) formal model depended error of the source size fitting; (6) Galactic latitude; (7) Galactic longitude.
            The table is published in its entirety in the machine-readable format as supplementary material. Eight randomly selected records are shown here for guidance regarding its form and content.
        \end{tablenotes}
\end{table*}

\section{Angular broadening of the AGN core size}
\label{ch:angular_broadening}

To study the scattering properties of the interstellar medium in our Galaxy, we have analyzed the VLBI core size measurements described in \autoref{ch:size_measurements}. There are 61\,230 measurements of 8\,959 active galactic nuclei which pass our filtering criterion. These AGNs are located over the entire sky, except for the region of far southern latitudes of the celestial sphere due to the lack of robust observational data in this area.

Electron density fluctuations in the ISM lead to angular broadening of radio sources. Scattering material spreads throughout the Galaxy, but it mostly concentrates in a thin disc of about 100~pc in width, likely associated with HII regions, stellar wind bubbles and supernova explosions \citep{Geldzahler1981, Cordes1984, spangler1986interstellar}. \autoref{fig:size_vs_gallat} shows the AGN core sizes as a function of the absolute value of the Galactic latitude $|b|$ at all observing frequencies between 1.4~GHz and 86~GHz. These figures demonstrate that the median size of cores increases significantly when a source is seen through the Galactic plane ($|b| < 10^\circ$). This effect is most noticeable at low frequencies 2, 5, or 8~GHz, being most sensitive to scattering of radio wave and, accordingly, to angular broadening of the observed AGN core size.

\begin{figure*}
    \centering
    \includegraphics[width=0.45\linewidth]{figures/size_vs_gallat_Lband.pdf}
    \includegraphics[width=0.45\linewidth]{figures/size_vs_gallat_Sband.pdf}
    \includegraphics[width=0.45\linewidth]{figures/size_vs_gallat_Cband.pdf}
    \includegraphics[width=0.45\linewidth]{figures/size_vs_gallat_Xband.pdf}
    \includegraphics[width=0.45\linewidth]{figures/size_vs_gallat_Uband.pdf}
    \includegraphics[width=0.45\linewidth]{figures/size_vs_gallat_Kband.pdf}
    \includegraphics[width=0.45\linewidth]{figures/size_vs_gallat_Qband.pdf}
    \includegraphics[width=0.45\linewidth]{figures/size_vs_gallat_Wband.pdf}
    \caption{The AGN VLBI core sizes as a function of the absolute value of the Galactic latitude measured at frequencies ranging from 1.4~GHz to 86~GHz. Each dot represents an individual source for which the median size for all epochs was taken. The red curve is the running median which demonstrates an increase of the median sizes of the AGN cores as they approach the Galactic plane. The running median was taken over a range of $5^\circ$ of $|b|$ at 2\,--\,8 GHz and $10^\circ$ for 15~GHz, 24~GHz. The blue shaded area shows the standard deviation of the median value of the angular size.}
    \label{fig:size_vs_gallat}
\end{figure*}

The isotropic distribution of the investigated sources over the sky allowed us to map out a sky distribution of the source sizes at different frequencies to visualise the angular broadening effect (\autoref{fig:size_colormaps}). We measured the angular diameter for 3541, 4544, and 7039 AGN cores at 2, 5, 8~GHz, respectively. At other frequencies, the number of sources is considerably smaller. To create these maps, we excluded all the sources with core sizes greater than 20 mas for 2~GHz data, greater than 15~mas for 5~GHz data and greater than 10~mas for 8 GHz~data. These sources with very large sizes introduce a lot of noise to the resulting map. Each $1^\circ\times1^\circ$ pixel of the map contains the average (Gaussian function weighted) observed core size of AGN which falls into a circular area of $10^\circ$ radius around a given pixel. The empty area around the South pole is the region where we do not have enough observational data yet.

The distributions of AGN core sizes over the sky for the three frequencies are shown in \autoref{fig:size_colormaps}. A characteristic increase of the average value of measured sizes in the Galactic plane for all frequencies is observed. It is also notable that the average sizes of the sources in the Galactic plane at lower frequencies are much larger, (e.g., the map for 2~GHz, \autoref{fig:size_colormaps}, top panel) than at higher frequencies (e.g., 8~GHz, \autoref{fig:size_colormaps}, bottom panel). This effect is a result of a power-law frequency dependence of the observed AGN core size $\theta\propto\nu^{-k}$, where $k$ is expected to be 1 for the sources with undetected scattering \citep{BK79,Konigl1981} and close to 2 for the scattered ones \citep{Cordes86,Rickett1990,Armstrong95}. \autoref{tab:median_sizes} shows the median sizes of sources in the Galactic plane and outside of it derived for different frequencies. The difference between the median size values is especially noticeable at low frequencies, while at high frequencies there is almost no difference between the median sizes within and outside the Galactic plane.

\begin{table}
	\caption{Median sizes of the measured AGN VLBI cores as presented at \autoref{fig:size_vs_gallat}.}
	\centering
	\begin{tabular}{rcrcr}
		\hline
		\hline
		$\nu$ & $\theta_\mathrm{med}\,\,(|b|<10^\circ)$ & $N$ & $\theta_\mathrm{med}\, (|b|>10^\circ)$ & $N$\\
		(GHz) & (mas)  & & (mas) & \\
	    (1) & (2) & (3) & (4) & (5)\\
		\hline
		1.4  & $2.142\pm0.895$   & 14 & $1.666\pm0.132$ & 121\\
		2    & $1.838\pm0.084$   & 510 & $1.132\pm0.012$ & 3031\\
		5    & $1.036\pm0.050$   & 544 & $0.764\pm0.012$ & 4000\\
		8    & $0.394\pm0.011$   & 979 & $0.331\pm0.003$ & 6060\\
		15   & $0.174\pm0.016$   & 64 & $0.139\pm0.004$ & 606\\
		24   & $0.127\pm0.013$   & 49 & $0.107\pm0.004$ & 210\\
		43   & $0.094\pm0.006$   & 15 & $0.064\pm0.003$ & 190\\
		86   & $0.038\pm0.012$   & 7 & $0.043\pm0.003$ & 41\\
		\hline
	\end{tabular}
	\begin{tablenotes}
       \item The columns are as follows: (1) frequency band, see \autoref{tab:table_freqs} for details; (2) median AGN core size within the Galactic plane and its error estimated with the bootstarp method; (3) number of sources used to estimate (2); (4) median AGN core size outside the Galactic plane and its error estimated with the bootstarp method; (5) number of sources used to estimate (4).
    \end{tablenotes}
    \label{tab:median_sizes}
\end{table}

\begin{figure*}
	\includegraphics[scale=1.54]{figures/sphere_size_Sband_Gaussianweight.pdf}
	\includegraphics[scale=1.54]{figures/sphere_size_Cband_Gaussianweight.pdf}
	\includegraphics[scale=1.54]{figures/sphere_size_Xband_Gaussianweight.pdf}

    \caption{The observed AGN core size distribution maps. The colour of each pixel reflects the average size of sources at this location. The average size was estimated based on the sources which fall into a circular area of $10^\circ$ radius around this central point (pixel). The red colour corresponds to the larger observed AGN core sizes (dominance of scattering), and the dark blue colour means the smaller values of the observed AGN core sizes (weak or no scattering). All the spheres presented in this work are shown in the Galactic coordinates over the celestial sphere in the Mollweide equal-area projection. The maps are published in the FITS format as supplementary material.}
    \label{fig:size_colormaps}
\end{figure*}

The red color on the map (\autoref{fig:size_colormaps}) corresponds to the largest observed sizes of AGN cores with the exception of those that we removed to smooth and reduce map noise, as we mentioned earlier. These sources are concentrated within a narrow band in the center of the map, where the Galactic longitude ($l$) is in a range of $-120^\circ~<~l~<~120^\circ$ for 2~GHz. The Galactic centre region is located approximately in the range of longitudes of $-20^\circ\leqslant~l \leqslant~20^\circ$. As expected, the smallest number of sources with large observed sizes is in the regions of longitudes $l~>~150^\circ$ and $l~<~-150^\circ$ --- this is the Galactic anti-centre, which contains much less scattering material. It is also clearly seen that the sources at high Galactic latitudes ($|b|>10^\circ$) are not subject to significant angular broadening. As it was demonstrated, the sources with small angular sizes fill almost the entire sphere, with the exception of some regions in the Galactic plane. This means that there are certain Galactic regions which cause strong scattering at this frequency range.

Interestingly, there are indications of scattering near the edge of the empty region. As we will see later in \autoref{ch:two_freqs_method}, the data near the edge have poorer accuracy due to the following reasons: (i) a smaller number of sources, see \autoref{fig:sphere_2_and_8_GHz}, and (ii) the angular resolution is lower because of a larger restoring beam size for the low-declination sources.
We compared the sky distribution of the local regions with cloud interaction presented in Figure~2 of \cite{Linsky2008} with the scattering maps obtained in our work, for example, the core size distribution at 2~GHz (\autoref{fig:size_colormaps}, top). There are some correspondences in the location of the scattering regions, e.g, the screen around the Cygnus supernova remnant and the region in the Galactic plane near the Galactic longitude of about $-90^\circ$. However, we do not observe a full correspondence of the detected regions of significant or possible scattering, as our data are sensitive not only to the local but also more distant screens in the Galaxy.

It is widely known that a distinctive feature of AGNs is their high intrinsic variability across the whole electromagnetic spectrum on scales from hours to years \citep[e.g.,][]{1997ARA&A..35..607Z,2019ARA&A..57..467B,2019MNRAS.485.1822P}. To search for the characteristic time scales of the external variability of scattering properties, we used our measured multi-epoch data of the AGN VLBI core sizes at 2~GHz and 8~GHz. We calculated the size variability at a given frequency, which exceeds the variability allowed by the estimated error. In \autoref{fig:variability} we show the size variability at 2~GHz. Namely, the difference between two measured source sizes at all available time intervals $\Delta t$. All possible time periods were used for each source. Approximately 8~per~cent of all calculated amplitudes at 2~GHz and 6~per~cent at 8~GHz were excluded from the analysis, because they do not exceed the estimated error for this amplitude.
Results can be summarized as follows.
We observe the same general properties of the core sizes at 2~GHz and 8~GHz:
(i) variability on long time scales is much higher than on short time scales;
(ii) variability outside the Galactic plane is higher than the variability within the plane for $\Delta t$ more than a few years, reflecting time scales of the intrinsic changes of the core size;
(iii) on average, variability does not exceed 20~per~cent for timescales more than a year; for time scales less than a year, median amplitude remains constant. This indicates that the observed variability is dominated by internal AGN evolution rather than scattering. Thus, we did not manage to reveal the characteristic timescale of variability of scattering in the Galaxy due to the lack of data at close epochs and dominating internal AGN variability.

\begin{figure}
    \centering
	\includegraphics[width=0.95\linewidth]{figures/variability_Sband_nearb.png}
	\includegraphics[width=0.95\linewidth]{figures/variability_Sband_awayb.png}
    \caption{Amplitude of the variability of the AGN core size at 2~GHz over a wide range of time covered by observations (days to tens of year). Each dot in these plots represents the relative amplitude of a change of the AGN core sizes at 2~GHz. The running median (the red curve) was taken over a range of 100 days.}
    \label{fig:variability}
\end{figure}

\section{Single power-low approximation of the $k$-index}
\label{ch:two_freqs_method}

The diffraction phenomena associated with the radiation scattering in a turbulent interstellar medium cause the angular broadening of a distant background radio source. Thus, the observed distribution of the source brightness is a convolution of the intrinsic structure of the source with the scattering function. The measured angular diameter of the AGN core should correspond to a convolution of the intrinsic and scattered components of the size \citep{Lazio08}:
\begin{gather}
    \theta_\mathrm{obs}^2 =\theta_\mathrm{int}^2 + \theta_\mathrm{scat}^2
	\label{eq:formula1},
\end{gather}
\begin{gather}
    \theta_{\mathrm{int}} = \theta_\mathrm{int1} \cdot \nu^{-k_{\mathrm{int}}}
	\label{eq:formula1_1},
\end{gather}
\begin{gather}
    \theta_{\mathrm{scat}} = \theta_\mathrm{scat1} \cdot \nu^{-k_\mathrm{scat}}
	\label{eq:formula1_2},
\end{gather}
where $\theta_\mathrm{obs}$ is the measured AGN core size at the observing frequency, $\theta_\mathrm{int}$ and $\theta_\mathrm{scat}$ are the intrinsic and scattered AGN core sizes at the observing frequency, $\theta_\mathrm{int1}$ and $\theta_\mathrm{scat1}$ are the intrinsic and scattered AGN core sizes at 1~GHz, $\nu$ is the frequency of observation (GHz), $k_{\mathrm{int}}$ is the power-law index from the frequency dependence of the intrinsic core size and $k_{\mathrm{scat}}$ is the power-law index from the frequency dependence of the scattered AGN core size.

\begin{figure}
	\includegraphics[width=\linewidth]{figures/sphere_irregularity4.pdf}
    \caption{Top panel: Sky distribution of the measured AGN core sizes. The red dots represent 2614 AGNs for which the angular size was simultaneously measured at 2~GHz and 8~GHz. The grey triangles are 7039 AGNs measured only at 8~GHz. The bottom panel shows the averaged density distribution map for simultaneously measured AGN core sizes at 2~GHz and 8~GHz. Each pixel of the map reflects the number of the sources which fall into a circular area of $10^\circ$ radius around this central point (pixel).}
    \label{fig:sphere_2_and_8_GHz}
\end{figure}

If we consider a simple approximation to Equations~\ref{eq:formula1}--\ref{eq:formula1_2}, it can be expressed as $\theta_{\mathrm{obs}}\propto\nu^{-k}$. It is expected that the index $k$ is approximately equal to 2, if scattering dominates and is equal to 1 when the radiation coming from a source is not scattered. This power-law $k$ index reflects the strength of scattering of the source and will allow us to analyse its distribution over the sky, similar to the distribution of the observed AGN core sizes at different frequencies, which we showed in \autoref{fig:size_colormaps}.

To estimate the index $k$, we can use the data of simultaneous multi-epoch measurements of the AGN core sizes at two frequencies, 2~GHz and 8~GHz. We calculated the index $k$ for 2614 AGNs. If a source has more than one observation epoch, the median value of the $k$ index was used. \autoref{fig:sphere_2_and_8_GHz} (top panel) demonstrates the sky distribution of these sources (red dots). We also plotted in \autoref{fig:sphere_2_and_8_GHz} (top panel) the sources measured only at 8~GHz (gray triangles). \autoref{fig:sphere_2_and_8_GHz} (bottom panel) also shows a source density distribution map based on the data from simultaneous observations at 2~GHz and 8~GHz. Each pixel of the map reflects the average number of sources that fall into a circular area of $10^\circ$ radius around this central pixel.

The derived $k$ index values are shown in \autoref{fig:k_28_hists}, separately for 462 and 2614 sources seen through the Galactic plane (\autoref{fig:k_28_hists}, left) and outside of it (\autoref{fig:k_28_hists}, right), with the median $k$ values 1.29 and 1.01, respectively. The distributions of $k$ indices were fitted using the Gaussian functions: two Gaussians for data within the Galactic plane to separate contributions of scattered and unscattered sources and a single Gaussian for the region outside the Galactic plane. The obtained parameters of the Gaussian curves are presented in \autoref{tab:table_gaussians}.

\begin{figure*}
    \centering
    \includegraphics[width=0.48\linewidth]{figures/hist_k28_simult_gauss_1.pdf}
    \includegraphics[width=0.49\linewidth]{figures/hist_k28_simult_gauss_2.pdf}
    \caption{Histograms of the $k$ indices, derived from simultaneous measurements of the AGN core sizes $\theta\propto\nu^{-k}$ at 2~GHz and 8~GHz. The left histogram is the distribution of indices in the Galactic plane ($|b| < 10^\circ$), fitted with two Gaussian curves representing unscattered and scattered sources. The right histogram is the distribution of indices outside the Galactic plane ($|b| > 10^\circ$), fitted by a single Gaussian curve. All the parameters of the fitting functions are listed in \autoref{tab:table_gaussians}. The red curve presented on the left histogram shows the distribution formed by the sum of the first (solid) and the second (dashed) Gaussian curves.}
    \label{fig:k_28_hists}
\end{figure*}

\begin{figure}
	\includegraphics[width=\linewidth]{figures/hist_k28_simult_2hists.pdf}
    \caption{Amplitude-normalised histogram of the $k$ indices, derived from simultaneous measurements of the AGN core sizes at 2~GHz and 8~GHz in the Galactic plane (grey histogram) is plotted on top of the histogram of the $k$ values measured outside the Galactic plane (blue histogram).}
    \label{fig:k28_another_variant}
\end{figure}

\autoref{fig:k28_another_variant} is the amplitude-normalised histogram of the $k$ indices, where the data in the Galactic plane is plotted on top of the $k$ values measured outside the Galactic plane. That shows that the values of the $k$ index outside of the Galaxy (\autoref{fig:k_28_hists}, right) cluster around a value of $k = 1.02~\pm~0.01$ and the first Gaussian curve within the Galaxy (\autoref{fig:k_28_hists}, left) with a peak at $k = 0.99~\pm~0.02$ describe the distributions of sources showing similarly insignificant levels of scattering. Notably, the obtained peak values of the $k$ indices are in good agreement with the theoretically expected $k = 1$ for the frequency dependence $\theta_{\mathrm{obs}}\propto\nu^{-k}$ of the intrinsic AGN core sizes \citep{BK79,Konigl1981}.
Note that this value is also in a good agreement with the often observed core-shift dependence $r\propto\nu^{-1}$, see for details \citet{2011A&A...532A..38S,2014MNRAS.437.3396K}.
The second Gaussian curve on the left histogram (\autoref{fig:k_28_hists}) with a peak at $k = 1.60 \pm 0.02$ describes the contribution of the scattered sources to the distribution of the $k$ indices in the Galactic plane. All the errors here are estimated as the standard deviations of the means of samples. The resulting $k$ index value differs significantly from the theoretically expected value $k\approx2$ for the scattered sources. The index value close to $k = 2$ is observed for a small number of sources in the Galactic plane. We used a simple approximation for the frequency dependence of the observed AGN core size for these calculations. It is the main reason for underestimating this value of the $k$ index for the scattered sources. All of the obtained results of the $k$ are very similar to those obtained by an earlier study by \cite{Pushkarev15}.

The presence of two modes in the $k$ indices distribution in the Galactic plane indicates that a significant number of sources are not scattered even though lie at low latitudes, and the signal from these sources passes through the most densely populated part of our Galaxy. Thus, we can expect many scatter--free regions in the Galactic plane.

\begin{figure*}
	\includegraphics[scale=1.6]{figures/sphere_k28_gaussweight.pdf}
	\includegraphics[scale=1.6]{figures/sphere_k_error.pdf}
    \caption{Top: Distribution map of the power-law $k$ index derived from the AGN core sizes $\theta\propto\nu^{-k}$ simultaneously measured at 2~GHz and 8~GHz over the sky. The magnitude and colour of each pixel of the map reflect the average over $10^\circ$ area value of the $k$ index at this location. The red colour corresponds to higher values of the $k$ index (dominance of scattering), the dark blue colour corresponds to the lower values of the $k$ index (the sources with undetected scattering). Bottom: The distribution map of the standard deviation of the estimated average index $k$. The darker the map area, the greater the error of the estimated average value of the $k$ index in this direction of the sky. The maps are published in the FITS format as supplementary material.}
    \label{fig:k28_map}
\end{figure*}

Using the obtained values of the $k$ indices calculated for 2614 sources uniformly distributed over the sky, we created the distribution map of scattering power in the Galaxy (\autoref{fig:k28_map}). To create this map, we excluded the sources outside the interval $0.5 \leqslant k \leqslant 2.5$, because too small and too large index values introduce needless noise. The resulting $k$ index distribution map replicates the pattern of the AGN core size distribution map at low frequencies, for example, at 2~GHz (compare with \autoref{fig:size_colormaps}, top). According to the map, we can highlight the regions of strong scattering in the Galactic plane ($|b| < 10^\circ$):
\begin{enumerate}
\item the region at $-20^\circ\leqslant l\leqslant20^\circ$ encompasses the Galactic centre and Galactic bar. This central region also contains Sagittarius~A$^\ast$ hosting a supermassive black hole surrounded by a hot radio-emitting gas cloud approximately 1.8~pc in diameter \citep{Downes1971};
\item Cygnus supernova remnant is located at $(l, b)~=~(74\fdg0, -8\fdg6)$;
\item Cassiopeia~A is a supernova remnant located at $(l, b)~=~(111\fdg7, -2\fdg1)$;
\item Vela supernova remnant is located at $(l, b)$ = $(-96\fdg5, -2\fdg8)$;
\item Taurus A supernova remnant is located at $(l, b)~=~(-175\fdg4, -5\fdg8)$ in the constellation of Taurus;
\item and also an area of moderate scattering in a direction to the Orion Nebula M42, the closest region of massive star formation at $(l, b) = (-151\fdg0, -19\fdg4)$. \cite{Koay2019} identified the region of Orion-Eridanus superbubble as an important scattering region even at 15~GHz due to the detection of 11 radio sources of interday variability on these sightlines.
\end{enumerate}

We also derived the $k$ indices using the two-frequency method mentioned above and the data from non-simultaneous observations of the AGN core sizes at frequency pairs 2~GHz and 8~GHz (3324 sources), 2~GHz and 5~GHz (1178 sources), 5~GHz and 8~GHz (2833 sources). For each source, the median observed core size at a given frequency was taken. A common feature for all three cases is that the $k$ index distribution for the AGNs in the Galactic plane ($|b|<10^\circ$) does not have a clear two-peak structure and cannot be reliably fitted by two Gaussian curves. The distributions of $k$ for the sources outside the Galactic plane obtained from the non-simultaneous measurements look similar and almost do not differ from the distribution represented in \autoref{fig:k_28_hists}, right. The peak of all obtained histograms is concentrated around the value $k = 1$. We conclude that simultaneous measurements are required to properly address the joint case of intrinsic and external effects of the core size. For this reason, we prefer the results from the simultaneous observations at two frequencies for the further analysis in this paper.

\section{Connection between scattering properties and rotation measure, electron density, and $\mathrm{H\alpha}$ distributions in the Galaxy}
\label{ch:corellation_tests}

The strength of scattering of radio wave emission which passes through clumpy distributed plasma is related to the length-scales and amplitude of the density inhomogeneities of the medium along the line of sight. Therefore, we can expect an enhancement of the scattering strength in regions with a high concentration of free electrons. For this reason, in this section, we will test the connection between the distribution of the scattering strength and the parameters measured in our Galaxy which are related to free electrons concentration, namely the rotation measure \citep[$RM$,][]{Taylor09}, the scattered size distribution based on the NE2001 model \citep[$\theta_{\mathrm{NE2001}}$,][]{NE2001} and the distribution of the $\mathrm{H\alpha}$ radiation intensity in the Galaxy \citep[$\mathrm{H\alpha}$,][]{Finkbeiner03}. The distribution of the scattering strength in the Galaxy, as we have already noted, can be reflected by the distribution of the AGN core sizes measured at low frequency, for example, at 2~GHz (see \autoref{ch:angular_broadening}
for details), and also by the distribution of the power-law $k$ indices from the frequency dependence of the AGN core sizes (see \autoref{ch:two_freqs_method} for details).

We used Kendall's $\tau$ non-parametric rank correlation coefficient to assess the magnitude of the correlation between the compared parameters. The errors of $\tau$ are estimated as standard deviations of the obtained by bootstrap parameter distributions. The results of Kendall's $\tau$ tests are shown in \autoref{tab:correlation_results}. The strongest correlation is traced between the AGN core sizes $\theta_\mathrm{obs,2\,GHz}$ obtained from the observations at 2~GHz and the $\mathrm{H\alpha}$ radiation intensity distribution in the Galaxy. Thus, we can conclude that there is a direct relationship between the regions of a high $\mathrm{H\alpha}$ intensity and the distribution of scattering screens in the Galaxy. The correlations of $\theta_\mathrm{obs,2\,GHz}$ with other parameters are also significant.

\autoref{fig:theta_vs_Halpha} shows the distribution map of the $\mathrm{H\alpha}$ radiation intensity in the Galaxy \citep{Finkbeiner03}. The Finkbeiner's full sky $\mathrm{H\alpha}$ map was created using the data from several surveys: the Wisconsin H-Alpha Mapper\footnote{\url{ http://www.astro.wisc.edu/wham/}}, the Virginia Tech Spectral-Line Survey\footnote{\url{http://www1.phys.vt.edu/~halpha/}}, and the Southern H-Alpha Sky Survey Atlas\footnote{\url{http://amundsen.swarthmore.edu/SHASSA/}}. The $\mathrm{H\alpha}$ data in Cartesian projection with 6$'$ resolution are available on the D.~Finkbeiner's website\footnote{\url{https://faun.rc.fas.harvard.edu/dfink/skymaps/}}. On top of the $\mathrm{H\alpha}$ maps, we plotted contours of the average observed AGN core sizes measured at 2~GHz, $\theta_\mathrm{obs,\,2\,GHz}$. For the contours, we used the sources with the core sizes less than 20~mas to avoid unnecessary noise introduced by large individual sources. These contours largely repeat the locations of high-intensity $\mathrm{H\alpha}$ clouds. This result confirms the expectation because the $\mathrm{H\alpha}$ emission observed in spiral galaxies is a direct indicator of a hot ionised interstellar medium \citep[HII,][]{Reynolds1983}. Previously, \cite{Lovell2008} also reported on very significant correlation between scintillations caused by the turbulent interstellar medium and the line-of-sight $\mathrm{H\alpha}$ emission in the Galaxy.

\begin{figure*}
	\includegraphics[scale=1.8]{figures/sphere_Halpha.pdf}
    \caption{Distribution map of the $\mathrm{H\alpha}$ radiation intensity in the Galaxy, on top of which the observed AGN core size distribution $\log\theta_\mathrm{obs,\,2\,GHz}$~(mas) contours are plotted. The colour of the map reflects intensity in Rayleighs (1$R$ = $10^6$ photons $\mathrm{cm}^{-2}$ $\mathrm{s}^{-1}$ $\mathrm{sr}^{-1}$). The contour levels denote $\theta_\mathrm{obs,\,2\,GHz}\,=\,1.6,\,2.5,\,4.0,\,6.3\,\,\mathrm{mas}$.}
    \label{fig:theta_vs_Halpha}
\end{figure*}

We note that the correlations with $\mathrm{H\alpha}$ data may result in a higher Kendall's $\tau$ value than others due to the higher $\mathrm{H\alpha}$ data resolution. Additionally, $RM$ values partly depend on magnetic field strength, while it has no effect on scattering. In this sense, $\mathrm{H\alpha}$ turns out to be an optimal tracer of the ionized hot plasma.

\begin{table}
	\caption{Fitted parameters of the Gaussian curves for the distributions of the $k$ indices derived from the data of simultaneous observations of the AGN core sizes at 2~GHz and 8~GHz.}
	\centering
	\begin{tabular}{|*{5}{c|}}
		\hline
		\hline
		$|b|$       & $\mu$ & $\sigma$ & $\mu_{2015}$ & $\sigma_{2015}$ \\
		(1)         &(2)    &(3)       &(4)           &(5)\\
		\hline
		$<10^\circ$ & 0.99  & 0.30     & 0.91         & 0.33\\
		            & 1.60  & 0.28     & 1.76         & 0.28\\
		$>10^\circ$ & 1.02  & 0.37     & 0.90         & 0.44\\
		\hline
	\end{tabular}
	\begin{tablenotes}
        \item The columns are as follows: (1)~$|b|$ is the absolute range of the Galactic latitude ($^\circ$); (2)~$\mu$ is the mathematical expectation obtained in this work; (3)~$\sigma$ is the standard deviation obtained in this work; (4)~$\mu_{2015}$ is the mathematical expectation obtained in \cite{Pushkarev15}; (5)~$\sigma_{2015}$ is the standard deviation obtained in \cite{Pushkarev15}.
    \end{tablenotes}
	\label{tab:table_gaussians}
\end{table}

\section{Two-component model of the frequency-dependent AGN core size}
\label{ch:k_scatter_modeling}

This section presents Monte-Carlo simulations of the intrinsic and scattered components of the observed source size $\theta_\mathrm{obs}$. Also, we present two methods for estimating the characteristic value of the scattering index $k_\mathrm{scat}$ and then compare all the obtained results with the theoretical predictions.

\subsection{Multi-frequency fitting of observed core sizes}
\label{sec:section6_1}

Given a large amount of experimental data, we determined (\autoref{ch:two_freqs_method}) that the exponent $k$ for the sources with undetected scattering equals 1 with a high accuracy. Therefore, we can set $k_\mathrm{int}$ in Equations~\ref{eq:formula1}--\ref{eq:formula1_2} equal to 1 and determine the unknown parameters of these equations for each selected source, namely $k_\mathrm{scat}$, $\theta _\mathrm{int1}$, $\theta_\mathrm{scat1}$.

\autoref{fig:freq_vs_size} shows how the AGN core size changes depending on the observing frequency for sources used as two clearly different examples: J0433+0521, which is the source with undetected scattering, and J0359+5057, which is a highly scattered one. Therefore, as discussed and shown above, the observational data for J0433+0521 can be fitted by the size-frequency dependence $\theta_\mathrm{obs}\propto\nu^{-1}$. The frequency dependence for the scattered source J0359+5057 is best fitted by a sum of two spectral components with different slopes, $k_\mathrm{int}=1$ and $k_\mathrm{scat}=2$ in the logarithmic scale.

\begin{figure}
    \centering
	\includegraphics[width=\linewidth]{figures/freqs_vs_thetas2.pdf}
    \caption{Example of the frequency dependence of the AGN core size for two sources: (1) the source with undetected scattering J0433+0521 (blue open circles) located at $(l,b)=(-169\fdg6,-27\fdg4)$ and (2) the scattered source J0359+5057 (red circles) located at $(l,b) = (150\fdg4,-1\fdg6)$. The size measurement error is not shown in the plot, since its value does not exceed the radius of the plot markers (red and blue circles). The dotted lines represent a fit according to the equations mentioned in the legend.}
    \label{fig:freq_vs_size}
\end{figure}

Using the multi-frequency observational data of the AGN core sizes in the Galactic plane ($|b|<10^\circ$) according to Equations~\ref{eq:formula1}--\ref{eq:formula1_2}, we can estimate the characteristic value of the scattering index $k_\mathrm{scat}$, which will correspond to the best fit of the intrinsic $\theta_\mathrm{int1}$ and scattered $\theta_\mathrm{scat1}$ sizes at 1~GHz setting $k_\mathrm{int}=1$.
For each source, the average observed core size at a given frequency was taken.
We performed fitting for three frequency sub-groups.
The obtained values of the scattering index $k_\mathrm{scat}$ are summarised in \autoref{tab:table_k_scatter_results}.
Note, in this section we used the distribution generated by bootstrap method to estimate the parameter confidence interval. Hence the errors of the values were estimated as the standard deviation of the obtained parameter distribution.

We compared the core size at 15~GHz from our two-component circular Gaussian modelfits with that from more detailed models from the 2-cm VLBA Survey \citep{2cmPaperIII} and its successor, the MOJAVE program \citep{MOJAVE_XVIII}, filtering out about 25~per~cent of cases when the core feature is fitted with delta-function and using geometric average in those cases (about 19~per~cent) where the core is an elliptical Gaussian. In total, we compared 5891 models of 503 sources and found that a distribution of the ratio $\theta_{\rm core}^{\rm 2comp}/\theta_{\rm core}^{\rm MOJAVE}$ peaks at 1 but has a heavier right tail that shifts the median to about 1.5.
\begin{table*}
	\caption{Results of the correlation Kendall's $\tau$-test between values obtained in this work and the other measured characteristics of the Galaxy.}
	\centering
	\resizebox{\textwidth}{!}{
	\begin{tabular}{l|cccc|cccc|ccc}
		\hline
		\hline

		 & & $|b| < 10^\circ$ &&& & $|b| > 10^\circ$ &&& & All sky &\\

		                      & $\tau$           & $N$ & $p$                 && $\tau$          & $N$    & $p$               && $\tau$          & $N$   & $p$ \\
		\hline

		$k$ -- $RM$                            & $0.122\pm0.031$  & 462 & $8.7\times10^{-5}$  && $0.065\pm0.013$ & 2614 & $5.9\times10^{-7}$  && $0.121\pm0.012$ & 3076  & $7.6\times10^{-24}$\\[2pt]

		$k$ -- $\theta_{\mathrm{NE2001}}$      & $0.206\pm0.030$  & 462 & $4.0\times10^{-11}$ && $0.071\pm0.013$ & 2614 & $4.4\times10^{-8}$  && $0.150\pm0.012$ & 3076  & $1.4\times10^{-35}$\\[2pt]

		$k$ -- $\mathrm{H\alpha}$              & $0.300\pm0.028$  & 462 & $6.2\times10^{-22}$ && $0.097\pm0.013$ & 2614 & $9.9\times10^{-14}$ && $0.173\pm0.012$ & 3076  & $3.4\times10^{-47}$\\[2pt]

		$\theta_{\mathrm{obs,2\,GHz}}$ -- $RM$ & $0.124\pm0.028$  & 510 & $2.8\times10^{-5}$ && $0.048\pm0.012$ & 3031 & $8.0\times10^{-5}$ && $0.111\pm0.012$ & 3541  & $4.8\times10^{-23}$\\

		$\theta_{\mathrm{obs,2\,GHz}}$ -- $\theta_{\mathrm{NE2001}}$ & $0.271\pm0.027$  & 510 & $6.3\times10^{-20}$ && $0.043\pm0.013$ & 3031 & $3.3\times10^{-4}$ && $0.140\pm0.012$ & 3541  & $5.3\times10^{-36}$\\

		$\theta_{\mathrm{obs,2\,GHz}}$ -- H$\alpha$& $0.369\pm0.028$  & 510 & $1.2\times10^{-35}$ && $0.084\pm0.013$ & 3031 & $3.3\times10^{-12}$ && $0.176\pm0.011$ & 3541  & $2.4\times10^{-55}$\\

		\hline
	\end{tabular}
	}
	\begin{tablenotes}
        \item Note: $k$ is the power-law index calculated by the two-frequency method (see \autoref{ch:two_freqs_method} for details) using the simultaneous observational data at 2~GHz and 8~GHz; $RM$ is the rotation measure; $\theta_\mathrm{NE2001}$ is the scattered AGN core size at 1~GHz obtained based the NE2001 model; $\mathrm{H\alpha}$ is the intensity of the $\mathrm{H\alpha}$ radiation in the Galaxy; $\theta_\mathrm{obs,2\,GHz}$ is the AGN core sizes measured at 2~GHz. $\tau$ is the Kendall's correlation coefficient, $N$ is the number of the sources, $p$ is the probability of chance correlation.
    \end{tablenotes}
	\label{tab:correlation_results}
\end{table*}

This indicates that at relatively high frequencies where scattering is weak, we overestimate the core size to some degree applying the two-component approach to modelfit the observed source brightness distribution, which works better at lower frequencies. This leads to an underestimation of the $k$-index in the multi-frequency analysis. Thus, we conclude that the most robust and least biased estimate of $k$ in \autoref{tab:table_k_scatter_results} is for the 2-5-8~GHz fit which is based on the low-frequency data. For the same reason, we excluded the AGN core size measurements at 86~GHz from the multi-frequency analysis.

\begin{table}
	\caption{Scattering indices $k_\mathrm{scat}$ derived from different sets of the measured AGN core sizes at the Galactic plane.
	\label{tab:table_k_scatter_results}}
	\centering
	\begin{tabular}{lrc}
		\hline
		\hline
		Subgroup & $N$ & $k_{\mathrm{scat}}$ \\
		(1) & (2) & (3)\\
		\hline

		All combinations            & 174  & $1.83\pm0.07$   \\[4pt]

		$\textbf{2,\,\,5,\,\,8}$ \textbf{GHz} & \textbf{130} & $\textbf{2.01$\pm$0.13}$   \\[4pt]

		$2,\,8,\,15$ GHz     & 58   & $1.83\pm0.07$   \\

		\hline
	\end{tabular}
	\begin{tablenotes}
       \item Columns are as follows: (1) frequency bands over which the subgroups of the sources were selected for fitting; (2) the number of the sources used to estimate the scattering index value; (3) the scattering index value.
       \item `All combinations' means that all  frequencies were used for each source, when measurements at more than three bands were available, but without 86~GHz. The most robust result is highlighted in bold (see \autoref{sec:section6_1}, paragraph 4 for details).
    \end{tablenotes}
\end{table}

\begin{figure*}
    \centering
    \includegraphics[width=0.486\linewidth]{figures/hist_theta_inn_fitted.pdf}
    \includegraphics[width=0.474\linewidth]{figures/hist_theta_scatt_fitted.pdf}
    \caption{Histograms of the intrinsic ($\theta_\mathrm{int1}$, left) and scattered ($\theta_\mathrm{scat1}$, right) sizes of the AGN cores at 1~GHz obtained from the simulation. The blue contour histogram shows the size distribution for the sources in the Galactic plane. The grey solid histogram shows the size distribution outside the Galactic plane. The black dashed histogram shows the size distribution of the sources from the entire sky. The values given in the legend after the `\#' sign indicate the number of the sources for this set of the data.}
    \label{fig:theta_scat_and_int}
\end{figure*}

\begin{figure*}
    \centering
    \includegraphics[width=0.45\linewidth]{figures/theta_int_vs_gallat2.pdf}
    \hspace{0.5cm}
    \includegraphics[width=0.45\linewidth]{figures/theta_scat_vs_gallat2.pdf}
    \caption{Intrinsic ($\theta_\mathrm{int1}$, left) and scattered ($\theta_\mathrm{scat1}$, right) AGN core sizes at 1~GHz obtained from the simulation, depending on the absolute value of the Galactic latitude. Each dot represents an individual source and is plotted only for AGN cores with the significant scattered component. The running median (the red curve) was taken over a range of $10^\circ$ of $|b|$. The blue shaded area shows the standard deviation of the median value of the angular size.}
    \label{fig:inn_scatt_vs_gallat}
\end{figure*}

Using the obtained values of $k_\mathrm{scat}$ from \autoref{tab:table_k_scatter_results}, we can separate the contribution of the intrinsic, $\theta_\mathrm{int1}$, and scattered, $\theta_\mathrm{scat1}$, component size to the observed one, $\theta_\mathrm{obs}$. To find $\theta_\mathrm{int1}$ and $\theta_\mathrm{scat1}$, we put the found value of the scattering index into Equations~\ref{eq:formula1}-\ref{eq:formula1_2}. For these calculations, the value $k_\mathrm{scat}=2.01\pm{0.13}$ was used due to the most robust combination of bands, as mentioned above. The sources from the entire sky that have more than three observing frequencies were selected for this analysis. The intrinsic, $\theta_\mathrm{int1}$, and scattered, $\theta_\mathrm{scat1}$, sizes were estimated at 1~GHz for 1411 AGN. The results are listed in \autoref{tab:table_thetas}. The obtained results are also presented in \autoref{fig:theta_scat_and_int}.

\begin{table}
	\caption{The intrinsic and scattered sizes of 1411 AGN VLBI cores at 1~GHz.}
	\centering
	\begin{tabular}{lrrrrr}
		\hline
		\hline
		Name & $b$ & $\theta_{\mathrm{int1}}$& $\theta_\mathrm{int1}^\mathrm{err}$ & $\theta_{\mathrm{scat1}}$& $\theta_{\mathrm{scat1}}^\mathrm{err}$\\
		     & (deg) & (mas) & (mas)& (mas)& (mas) \\
		(1) & (2) & (3) & (4) & (5) & (6) \\
		\hline
        J0042$+$5708 & $-5.71$	& 0.86	  & 0.03    & 26.34     & 0.30 \\
        J0407$-$1211 & $-41.76$	& 2.23    & 0.02    & 3.19      & 0.11  \\
        J0805$+$6144 & 32.35	& 2.13	  & 0.02    & 1.91      & 0.24 \\
        J0809$+$3455 & 30.35	& 1.42	  & 0.04    & 5.25      & 1.27 \\
        J0909$+$4253 & 42.84	& 1.82	  & 0.03    & 1.06      & 0.47 \\
        J1217$+$3007 & 82.05	& 1.05	  & 0.05    & 3.64      & 0.15  \\
        J1305$-$1033 & 52.16	& 2.36	  & 0.02    & $<0.10$   & $\dots$ \\
        J1436$+$2321 & 65.95 	& 0.76    & 0.01    & $<0.10$   & $\dots$ \\
        J1728$+$3838 & 31.97	& 0.89    & 0.06    & 5.15      & 0.38 \\
        J2102$+$4702 &  0.34    & 1.01    & 0.07    & 14.19     & 0.49\\
		\hline
	\end{tabular}
    \begin{tablenotes}
        \item Columns are as follows: (1)~name of source; (2)~Galactic latitude; (3)~the value of calculated intrinsic size of the source; (4)~the intrinsic size calculation error estimated using the bootstrap method; (5)~the value of calculated scattered size of the source; (6)~the scattered size calculation error estimated using the bootstrap method.
        The full table is published in its entirety in the machine-readable format as supplementary material. Ten randomly selected records are shown here for guidance regarding its form and content.
    \end{tablenotes}
	\label{tab:table_thetas}
\end{table}

The distribution of the intrinsic sizes (\autoref{fig:theta_scat_and_int}, left) has one peak. The median value of the intrinsic sizes in the Galactic plane (blue contour histogram) and outside of it (solid gray histogram) is 2.6 and 2.1~mas, respectively. There is a slight shift between the medians of the blue and gray histograms. We also analysed the dependence of the obtained intrinsic sizes on the absolute value of the Galactic latitude, which is shown in \autoref{fig:inn_scatt_vs_gallat}, left. As seen, the running median retains its value through the whole range of $|b|$ even within the Galactic plane. It is assumed that the intrinsic sizes do not depend on the Galactic latitude.

The distribution of the obtained scattered sizes of the AGN cores is presented in \autoref{fig:theta_scat_and_int}, right. For this distribution, a completely different picture is observed. The histogram has a two-peak structure.
The left peak is populated by the sources for which the scattered component of the measured size $\theta_\mathrm{scat1}$ is estimated to be very close to zero within the errors. This means that the contribution of scattering to the observed angular diameter is negligible; these are the sources with insignificant scattering.
The right peak of the distribution corresponds to the sources for which the contribution of scattering is dominant or at least significant. For this peak, there is a significant shift between the distribution of the scattered sizes in the Galactic plane and outside of it. Compare blue and gray histograms in \autoref{fig:theta_scat_and_int}, right. The median values of scattered sizes in the Galactic plane (blue contour histogram) and outside of it (grey solid histogram) in \autoref{fig:theta_scat_and_int} are 16.1 and 4.8~mas, respectively. Therefore, we conclude that the contribution of the scattered component to the observed AGN core size in the Galactic plane is systematically larger than that of outside the Galactic plane, and this difference is significant.
\autoref{fig:inn_scatt_vs_gallat} shows the dependence of the obtained scattered sizes on the absolute value of the Galactic latitude. We plotted only those sources for which the scattered component of the observed size is significant. The running median demonstrates a large increase in the median scattered sizes as it approaches and crosses the Galactic plane ($|b| = 10^\circ$).

\begin{figure*}
    \centering
	\includegraphics[width=\linewidth,trim=0cm 0.6cm 0cm 0cm]{figures/hist_vs_map2.pdf}
    \caption{Histogram of the Galactic longitude for the sources with an insignificant scattered component of the observed AGN core size (bottom) against the map of the $k$ index distribution (top panel) corresponding to \autoref{fig:k28_map}, cropped at latitudes ($|b|=10^\circ$) and projected onto the plane. The axes of the Galactic longitudes in both panels coincide.}
    \label{fig:theta_zeros_vs_shpere}
\end{figure*}

We determined that for about 30~per~cent of AGN in the Galactic plane the contribution of the scattered component of the observed core size is negligible. It means that this fraction of the observed sources in the Galactic plane is not subject to significant scattering for frequencies down to at least 2 GHz. \autoref{fig:theta_zeros_vs_shpere} demonstrates that the sources with $\theta_{\mathrm{scat}1}\approx0$ are concentrated in the areas where the sources with insignificant scattering ($k\approx1$) are located. We note that the results presented on two panels in \autoref{fig:theta_zeros_vs_shpere} being obtained using different methods and data sets, are in good agreement with each other. Therefore, we can conclude that most of the sources with insignificant scattering are located in the region of the Galactic anti-centre ($|l|>150^\circ$).

\begin{figure}
    \centering
	\includegraphics[width=0.95\linewidth]{figures/theta_scat_vs_NE2001.pdf}
    \caption{Comparison of the results obtained from our modelling of the scattered AGN core sizes $\theta_\mathrm{scat1}$ with the sizes predicted by the NE2001 model  at 1~GHz. See \autoref{ch:corellation_tests} for details. The green arrow points to 677 missing sources lying outside the plot (their y-axis positions are marked). The values given in the legend after the `\#' sign indicate the number of the sources for this dataset.}
    \label{fig:NE2001_vs_theta_scatt}
\end{figure}

The free electron density distribution in the Galaxy model NE2001 \citep{NE2001} is mainly based on radio observations of pulsars which provide the information about the properties of the local ionized interstellar medium. Pulsars being Galactic radio sources are not optimal for studying large-scale scattering properties. The pulsar data can provide reliable information only in the Galactic plane. Nevertheless, we performed a comparison of the estimated scattered sizes $\theta_\mathrm{scat1}$ obtained in our work, with the scattered sizes obtained on the basis of the NE2001 model ($\theta_\mathrm{NE2001}$) at 1~GHz. In \autoref{fig:NE2001_vs_theta_scatt} we show the sources lying in the Galactic plane and outside of it in different colors. The scattering sizes determined on the basis of the NE2001 model in the region $|b|>10^\circ$ are mainly concentrated around $\theta_\mathrm{NE2001} \approx 1$~mas (black circles), but according to our results the $\theta_\mathrm{scat1}$ sizes of these sources cover the range from 0.1~mas to more than 10~mas. The extragalactic objects, the path to which lies through the Galactic plane (red triangles), have a better agreement between the compared sizes. The red dots are scattered around the line of equality $\theta_\mathrm{scat1}=\theta_\mathrm{NE2001}$. Nearly half of the sources (677) lie outside the plot, we mark them along the y-axis. These are the sources for which the scattering does not dominate according to our calculations, $\theta_\mathrm{scat1}\approx0$, but the NE2001-model sizes are distributed from 0.1~mas to about 8~mas. Thus we conclude that the scattering of these sources predicted by the NE2001 model was not confirmed by the results of our estimates made on the basis of multi-frequency VLBI AGN data.

\subsection{Modeling observed core size distributions at 2~GHz and 8~GHz}

In this section we describe an alternative method for estimating the scattering index $k_\mathrm{scat}$ using the AGN VLBI core size measurements at two frequencies. For simplicity, we here assume that sources seen outside the Galactic plane ($|b|>10^\circ$) are not subject to scattering at all. In \autoref{fig:k_28_hists}, we showed that the distribution of the observed AGN core sizes in the Galactic plane ($|b|<10^\circ$) contains both sources with insignificant (about 30~per~cent) and significant scattering. Therefore, the size distribution of the sources from this area contains the contribution of both types of sources.

We also assume that the observed size distribution of the scattered sources could be fitted with a generalization of half-Gaussian distribution or half-Student's distribution. We performed an iteration over all parameters of these distributions. For example, for the Student's function: $do\!f$ and $\sigma$ are degrees of freedom and width of the distribution, respectively. We generated a random sample of sizes, and then added in quadrature to the observed sizes of the sources outside the Galactic plane (the sources with insignificant scattering), that is $\theta_{\mathrm{int}}$ according to \autoref{eq:formula1}. The result of these steps is the distribution $\theta_\mathrm{fit}$, which we will compare with the distribution obtained from the observational data for the sources in the Galactic plane $\theta_\mathrm{obs}$ ($|b|<10^\circ$). If these distributions are similar, the selected analytical distribution with its parameters is an appropriate description of $\theta_\mathrm{scat}$ distribution at a given frequency.

\begin{figure}
    \centering
    \includegraphics[width=\linewidth]{figures/student_hist_Sband.pdf}
    \includegraphics[width=\linewidth]{figures/student_hist_Xband.pdf}
    \caption{
    Histograms of the observed AGN core sizes $\theta_\mathrm{obs}$. The gray histogram represents the AGNs in the Galactic plane while the green contour histogram shows the distribution outside the plane. The blue curve is the distribution of the scattered sizes at a given frequency $\theta_{\mathrm{scat}}$ (see \autoref{eq:formula1}) applying half-Student's distribution. The fitting parameters for half-Student's function are shown on the right side of the plots; $do\!f$ is degrees of freedom, $\sigma$ is the standard deviation. The black contour histogram depicts total distribution of the source sizes $\theta_\mathrm{fit}$, which is the squared sum of half-Student's distribution and the distribution of the sources with insignificant scattering ($|b|>10^\circ$). The values given in the legend after the `\#' sign indicate the number of the sources for a given dataset.
    \label{fig:size_distribution_fitting}
    }
\end{figure}

We minimize the Kolmogorov-Smirnov (KS) test statistic between the observed and fitted size distributions.
The smallest values of these statistics, i.e., the greatest similarity of distributions, is obtained when we used the Student's distribution to fit the scattered size $\theta_{\mathrm{scat}}$. \autoref{fig:size_distribution_fitting} shows the data fitting results at two frequencies, 2~GHz and~8 GHz (black contour histograms).

We searched for the best widths $\sigma$ at 2~GHz and 8~GHz with a fixed value of the degree of freedom, $do\!f$, for both frequencies. Thus, the found parameters of $\sigma$ for 2~GHz and 8~GHz can be used to derive the value of the scattering index, similarly to the two-frequency method (see \autoref{ch:two_freqs_method} for details). We reached the maximum similarity with the following parameters of the Student's function: $do\!f = 0.83\pm0.06$, $\sigma= 0.811\pm0.077$ for 2~GHz, $\sigma= 0.058\pm0.008$ for 8~GHz. Thus, using this alternative method, the scattering index $k_\mathrm{scat} = 2.00 \pm 0.05$ was inferred. All the errors were estimated as standard deviations of the obtained by bootstrap parameter distributions.

\subsection{The special case of Sagittarius~A$^\ast$}

\cite{2018ApJ...865..104J} have shown that for Sagittarius~A$^\ast$, the most heavily scattered source on the sky, the power-law index for density fluctuations $\beta<3.47$, which is shallower than expected for a Kolmogorov spectrum ($\beta=11/3$). At the same time they found $\lambda^2$ dependence of the angular size ($k=2.0$) at $\lambda>1$~cm, as the scattering is in a strong regime, with the diffractive scale smaller than the dissipation scale of the turbulence. In this case, the source angular size follows the $\lambda^2$ scaling regardless of a spatial spectrum slope. In our case, the sources are more weakly scattered, and the obtained value of $k$ indicates that the spatial spectrum of inhomogeneities is steeper ($\beta\simeq 4$) than that for a Kolmogorov turbulence.

\section{Summary}
\label{s:summary}

We used the largest to~date number of experimental VLBI data from multi-frequency observations of AGNs to study the ISM scattering properties in the Galaxy. We analyzed the dependencies of the observed AGN core sizes on the Galactic latitude and found significant angular broadening of the measured core sizes for the sources seen through the Galactic plane. This effect is especially strong at low frequencies, particularly at 2~GHz. We established that scattering screens containing density fluctuations of hot plasma are concentrated mainly in the Galactic plane. Outside the Galactic plane, we did not detect regions with strong scattering. We created the sky distribution maps of the measured AGN core sizes at 2, 5, and 8~GHz, marking the distribution of scattering screens in the Galaxy.

We calculated the power-law index $k$ from the frequency dependence of the AGN core size $\theta\propto\nu^{-k}$ derived from simultaneous observations at 2~GHz and 8~GHz for 2614 sources. The mean value $k = 1.02\pm0.01$ derived for the sources outside the Galactic plane is in good agreement with the theoretical prediction $\theta\propto\nu^{-1}$ for the AGN cores with undetected scattering with synchrotron self-absorption. For the scattered sources, we obtained a characteristic value $k = 1.60\pm0.02$ ignoring the contribution of the intrinsic structure, hence it is less than the predicted $k \simeq 2$. Using the $k$-index values calculated between 2~GHz and 8~GHz, we constructed the first detailed sky distribution map of scattering properties in the Galaxy based on VLBI experimental data.

The regions of the Galaxy characterized by a high $\mathrm{H\alpha}$ radiation intensity show a significant spatial correlation with the areas of strong scattering. One of them is positionally associated with the Cygnus constellation region, which contains active star-forming regions and the supernova remnant W78. In the locations of Taurus~A, Vela and Cassiopeia~A supernova remnants, as well as in the location of Orion nebula (M42), we also found an increase of the scattering strength of the ISM. The region with the strongest scattering is the Galactic centre, which extends in the Galactic plane at $-20^\circ\leqslant l\leqslant20^\circ$.

Using the AGN VLBI core sizes derived from multi-frequency data, we separated the contribution of the intrinsic and scattered sizes to the observed angular diameter for 1411 AGN. As expected, the contribution of scattered components of the observed size for the sources in the Galactic plane is systematically larger than for those observed outside the Galactic plane. We found that about 30~per~cent of the AGN observed in the Galactic plane are not subject to scattering. This reflects that the interstellar medium of our Galaxy is highly inhomogeneous. Most of the sources with insignificant scattering are located in the direction of the Galactic anti-centre.

Applying different methods to derive the power-law scattering index, we obtained virtually the same values $k_\mathrm{scat} \simeq 2.0$. This strongly supports the Gaussian screen model. At the same time, we do not exclude that new targeted observing campaigns to study main scattering screens individually may deliver for some screens different results that will be more consistent with the Kolmogorov turbulence model.

\section*{Acknowledgements}

We thank the anonymous referee and Eduardo Ros for comments which have helped to improve the manuscript as well as Elena Bazanova for language editing.
We thank Michael Johnson for providing the data of the scattered size estimated based on the NE2001 model.
We are grateful to the teams referred to in \autoref{ch:size_measurements} for making their fully calibrated VLBI FITS data publicly available and Leonid Petrov for maintaining the database with these data.
This research was supported by the Russian Science Foundation project 21-12-00241.
This research has used the MOJAVE database maintained by the MOJAVE team \citep{2018ApJS..234...12L}. This study has also used the VLBA data from the Blazar Monitoring Programs BEAM-ME and VLBA-BU-BLAZAR, funded by NASA through the \emph{Fermi} Guest Investigator Program.
This research has made use of NASA's Astrophysics Data System.

\section*{Data Availability}

The analysis is based on the data compiled in the Astrogeo database\footnote{\url{ http://astrogeo.org/vlbi_images/}} that collects VLBI observations. The dataset contains 17\,474 sources observed from 1994 to 2021, more than $100\,000$ individual observations. The majority of them were performed at 2, 5, 8 or 15~GHz. Details are presented in \autoref{ch:size_measurements}. The data underlying this study is available in the paper and in its online supplementary materials.

\bibliographystyle{mnras}

redpajama_set_name: RedPajamaArXiv


Cave and Karst Science's August 2017 issue is now available.
Volume 44, Number 2 carries six main articles, starting with 'Deeply submerged speleothems in Keld Head, Kingsdale, Yorkshire' by John Cordingley, David Lowe and Tony Waltham, which examines the significance of a deposit of laminated flowstone lying at a depth of 9m, 550m into the Marble Steps Branch of the cave. The paper is well-illustrated with surveys, diagrams and photographs and goes into the implications of the deposit for both the history of the cave system and the timing of the Quaternary deepening of Kingsdale. The paper provides a fascinating glimpse of what Keld Head might have looked like at the time when its deepest flowstone was growing, and the system appears to exhibit the deepest known calcite speleothems in any British underwater cave. A date for the flowstone is awaited.
A paper by Georgios Lazaridis, Konstantinous Trimmis and Spyridoula Pappa on travertine caves in Almopia, Greece provides information on seven caves that have been explored and surveyed within two travertine terraces in Greece's Almopia region. Of the two, the Aspi terrace is less faulted than the Baina Terrace, and the differences between them could be related to the degree of faulting. In travertine caves, the age of the cave formation is contemporary with that of the host rock, which differs from karst caves which are formed by dissolution of significantly older rocks. The photographs are excellent and several surveys show how short many of these caves are in comparison with karst caves.
Phil Murphy makes some further observations on two iconic landforms, Gordale Scar and Malham Cove, and looks at their settings and relationships with an emphasis on their differences and how or why these might have arisen. This short paper provides an interesting contrast between two features that will be familiar to many cavers. An eight-page paper by Slovenian karst scientist France Šušteršič proposes a conceptual model of Dinaric solution doline dynamics, and discusses a simplified model of the dynamics of solution dolines. The author makes it clear that firm conclusions cannot be drawn and that any statements are to be taken as no more than initial guidelines for future investigations. Despite the simplified nature of the paper, the content is heavily mathematical, as are the numerous diagrams.
Peter Wilson, Tom Lord and Ángel Rodés examine the glaciation and deglaciation age of the Stump Cross area in the Yorkshire Dales as determined by terrestrial cosmogenic nuclide (10Be) dating. The ages of gritstone boulders in the vicinity of Stump Cross Cavern provide evidence of glacier ice in the area at the Wharfe-Nidd interfluve and the results show that the deglaciation of the Dales was likely to have been well-advanced around 18 – 16 thousand years ago. In the final paper, Charles Young and David Lowe look at the Hydrogeology of the Banff Hot Springs, Banff National Park, Canada, from a karst perspective. At 12 pages, this is the longest paper in the issue, but it is well supplied with diagrams, surveys and photos and their conclusions contribute to a broader understanding of the area and its watercourses.
The issue starts on a sad note with an obituary of caver and cave scientist Noel Christopher written by John Gunn, which includes a list of his various publications. At the end of the issue, the Forum section has a review by Duncan Price of the recent publication Adventures Underground by Dave Haigh and John Cordingley and a short, personal account on the historical scientific interest of dating the Dales caves by Tony Waltham.
Cave and Karst Science is published three times a year and is free to paid up members of the British Cave Research Association. Non-members can obtain copies for an annual subscription of £28 (+ postage for non-UK destinations). A discounted student subscription is available. Details are available from the BCRA bookshop.The publication contains a wealth of information and represents excellent value for money for anyone with an interest in the title subject. It is well-presented throughout, with a clear, attractive layout.


A Cambodian garment factory worker (L) shouts slogans during a protest in front of Phnom Penh Municipal hall, Sept. 5, 2013.
Four trade unions on Tuesday demanded that Cambodia's garment and footwear manufacturers raise the minimum wage of their workers and provide them with additional benefits, threatening a nationwide strike and demonstrations if they do not comply.
In a joint letter to the Van Sou Ieng, president of the Garment Manufacturers Association in Cambodia (GMAC), an employers' organization, the unions called for nearly double the U.S. $80 per month minimum wage announced by the government in March, and which took effect two months later.
"We are demanding an increase in the minimum wage to U.S. $154 [per month], as well as six additional workers' benefits," said the letter, which was signed by the unions, including the National Independent Federation Textile Union of Cambodia (NIFTUC).
The government has indicated that it would allow an increase in the minimum wage, but didn't say by how much.
"Even though we cannot say how much the wage would be raised, the government policy is that they will raise the wage in January 2014," the Cambodia Daily quoted Prak Chanthoeun, director-general of the Labor Ministry's labor conflict committee, as saying.
Among the benefits demanded in the union joint missive on Tuesday were an additional U.S. $3 per day for food, that factories maintain a sovereignty fund in the national bank for workers in case of unexpected closures, and an end to short term contracts.
The letter also called for an end to powerful government officials backing factories and for authorities to prosecute anyone connected to a factory who threatens or harms workers.
A government advisory committee established by Cambodia's ministry of labor has scheduled tripartite talks on the minimum wage issue between the worker unions, GMAC and government representatives for Wednesday.
NIFTUC President Mom Nhim told RFA's Khmer Service that the workers are preparing for the meeting as a way to "coordinate efforts on the minimum wage," but said the unions would prefer to meet one on one with GMAC as a way to get to the heart of the issue.
"We want to have bilateral talks first and the talks must be honest," she said.
But Mom Nhim said that if a solution could not be found that was amenable to the unions, workers would begin mass protests.
"For the first stage [in case talks are not productive], we will hold strikes in every factory, but in the case that there is still no resolution we will hold demonstrations," she said.
"We will hold a discussion in response to the demands, but we don't want to see any threats of strikes or demonstrations attached to those demands," he said.
Following a tripartite meeting between the government, unions, and GMAC in March, workers' minimum wages earnings were raised from U.S. $61 to U.S. $73, plus an additional U.S. $5 as a form of health benefit. GMAC later agreed to add an additional U.S. $2 per month following a request by Prime Minister Hun Sen, bringing the total to U.S. $80.
The increase of U.S. $19 per month in minimum wage represented only a U.S. $8 bump up from the GMAC's position of U.S. $72 when negotiations opened at the end of February.
The unions had originally demanded U.S. $120, but dropped down to U.S. $100 after one day of talks.
In July, two weeks before national elections, Cambodia's umbrella Free Trade Union (FTU) threw its weight behind the opposition Cambodian National Rescue Party (CNRP), citing the party's commitment to raising the minimum wage for factory workers.
The CNRP had proposed a minimum monthly wage of U.S. $150 for garment workers and U.S. $250 for civil servants. There is no minimum salary as such for civil servants, who are largely exempt from the country's labor laws.
In September, Prime Minister Hun Sen's ruling Cambodian People's Party (CPP) was officially declared the winner of the July 28 polls, despite widespread allegations of election irregularities, and the CNRP's plans for wage increases never came to fruition.
Reported by Khe Sonorng for RFA's Khmer Service. Translated by Samean Yun. Written in English by Joshua Lipes.
300,000 workers making average $80 per month.
300,000 x $80 = $24,000,000 per month slave labor wages.
$240,000,000 x 12 = $288,000,000 per annual slave labor wages.
Each year Cambodia export about $4 billion dollars garment worth annually.
Someone is making a HUGE profit on slave labors back. If they doubled the slave wages to $150 per month, that would only cost them $576,000,000 per year on labor. That still leaves them over $3.7 billion dollars, someone still making a HUGE profit.
Congratulation, at least someone can do math here. Unfortunately, this person had no knowledge of Cost Accounting. Let's start with opearation costs(fix and variable costs), raw materials, taxes and etc.... . Hello..... go back to school and take some accounting classes.


National Coffee Day is upon us this Friday, Sept. 29, and you know what that means: free coffee!
Free coffee is available from a wide variety of restaurants (Dunkin' Donuts, Tim Hortons) and convenience stores (Wawa, 7-Eleven) for National Coffee Day 2017, but not Starbucks, apparently. In some cases free coffee can be yours beyond just the main "holiday" itself on Friday.
Krispy Kreme is offering free coffee, with no purchase required and no strings attached, for Friday, Saturday, and Sunday of National Coffee Day weekend. Some other participants are making their National Coffee Day freebies available after National Coffee Day itself as well.
Cinnabon: Each customer can get a free 12-ounce coffee on Friday, September 29, no purchase required.
Cumberland Farms: Text the phrase FREECOFFEE to 64827 on Friday and you'll get a mobile coupon good for a free coffee (or tea, cappuccino, or hot chocolate), in any size, at Cumberland Farms retail locations in the Northeast and Florida. What's more, Cumberland Farms is giving customers free coffee every Friday in October, no coupon or purchase required.
Dunkin' Donuts: On September 29, Dunkin' Donuts customers get a free medium cup of coffee with the purchase of another medium, large, or extra-large cup of coffee.
Einstein Bros. Bagels: Every customer can get a free coffee on Friday, no purchase required.
Krispy Kreme: National Coffee Day has been transformed into National Coffee Weekend at Krispy Kreme, where hot or iced coffee is available for free, in any size, from Friday, September 29, through Sunday, October 1. No purchase or coupon is required.
Lyft: Catch a ride with Lyft on National Coffee Day in select cities—Austin, Dallas, Los Angeles, Philadelphia, Portland, San Francisco, and Seattle—and you'll get a free can of High Brew Coffee in flavors like Mexican vanilla and dark chocolate mocha.
Peet's Coffee & Tea: Coffee bean purchases are 25% off on Friday, and any customer who buys a bag of beans gets a free coffee.
Pilot Flying J: You'll get a free small cup of coffee or another hot beverage on Friday if you show the online coupon available here or at Pilot Flying J's Facebook page.
7-Eleven: Members of 7-Eleven's 7Rewards app will get a coupon good for one free coffee in any size, redeemable anytime Friday through Sunday.
Stewart's Shops: All customers get a choice of free hot, iced, or cold-brewed coffee from noon until closing at Stewart's Shops, which are concentrated in upstate New York.
Tim Hortons: Download the Tim Hortons mobile app and you'll get one free hot or iced coffee, in any size, between September 29 to October 8.
Wawa: On Friday, customers get a free coffee in any size.


text:
Solar energy project kills over 3,500 birds in California
A solar energy project has killed as many as 3,500 birds in California, USA, a report said, Pravda.Ru reports.
The Ivanpah project, a 377-megawatt solar energy array in San Bernardino County, California, has killed an estimated 3,504 birds during the first year of operation, Pravda.Ru reports. The array is a collection of mirrors that direct sunlight to three tall towers, which create steam to run a turbine.
According to the paper, researchers found up to 83 different bird species that had been killed in the area, Pravda.Ru says. However, the report says that the deaths are a "minimal proportion of local, regional or national populations."
"We were pleased that the report said our impact is minimal but the entire process, including this report, is about knowing your impact so you can reduce it further," an official with NRG Energy, which operates the project, told the Sun.
Read article on the Russian page of Pravda.Ru
Also read: Birds are capable of scanning future
Solar Impulse: The future of flying
In pictures: Clouds of migratory birds in the sky
Slideshow of wildlife

redpajama_set_name: RedPajamaCommonCrawl


Magnificent home located in family-friendly subdivision with AMAZING views! Endless features include a spacious master suite with Corian double vanity, garden tub, & separate shower. Kitchen with SS appliances & Corian counters/sink. Gas fireplaces with blower fans on 2 levels. Decks/balconies on all 3 levels. Fenced backyard. Tons of storage!


text:
Pakistan Doesn't Like us; We give them money, but not for long?
First, some insights from Pakistan:
Pakistan's military says it has rejected recent reports in The New York Times criticizing the Pakistani army and the country's powerful intelligence agency, known as the ISI.
Major General Athar Abbas said the articles in the U.S. publication are part of a "vilifying campaign."
The New York Times published an editorial and an article last week linking the ISI to the death of a Pakistani journalist who had written scathing reports about the infiltration of militants into the military. (here)
Zulfiqar Khan has denied selling nuclear secrets to North Korea and has said the US aims to rollback the Pak nuclear programme by defaming the agencies and retired generals.
Talking to our sources, he said America had targeted the nuclear programme of Pakistan and wanted to control it and roll it back. "For this purpose, sometimes they talk of the Taliban and sometimes of the command and control system of Pakistan," he said, adding the recently published letter written by North Korea to Dr Abdul Qadeer Khan showed that America wanted to develop distrust in the people of Pakistan against the country's armed forces and security agencies, so as to achieve its evil designs against the nuclear programme of Pakistan.
About the claim of American newspaper 'The Washington Post' that he and former chief of army staff Gen (R) Jehangir Karamat had received big money from North Korea, Zulfiqar said the accusation was absolutely wrong and based on ill intentions. (here)
And let's not forget this little piece of Propaganda which Pakistan regularly does to insight unrest in the States.
And now? Well now it seems that the U.S. is starting to wise up. According to the New York Times, the President is going to suspend 1/3 in aid (who not all?) to Pakistan:
The Obama administration is suspending and, in some cases, canceling hundreds of millions of dollars of aid to the Pakistani military, in a move to chasten Pakistan for expelling American military trainers and to press its army to fight militants more effectively.
Altogether, about $800 million in military aid and equipment, or over one-third of the more than $2 billion in annual American security assistance to Pakistan, could be affected, three senior United States officials said.
This aid includes about $300 million to reimburse Pakistan for some of the costs of deploying more than 100,000 soldiers along the Afghan border to combat terrorism, as well as hundreds of millions of dollars in training assistance and military hardware, according to half a dozen Congressional, Pentagon and other administration officials who were granted anonymity to discuss the politically delicate matter.
So… what do we have? We have two countries, Afghanistan and Pakistan, who are taking lots of money from us to essentially use against us. When are we going to stop this, and I mean all of this?
Abdul Qadeer Khan, Afghanistan, Athar Abbas, Jehangir Karamat, New York Times, north korea, Pakistan
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text:
Australian Paper launched an information centre in Morwell for its proposed energy from waste project today. The company is completing a feasibility study to assess the viability of the project, which would convert household waste into energy to be used at the Maryvale mill. The feasibility study began last year and is expected to take about a year to complete. The company will need to attract about $600 million in investment for the project. Both state and federal governments are contributing $2.5 million to the $7.5 million study, which will look into the technical, environmental, social and economic challenges of the project. Australian Paper national manager of sustainability and communications Craig Dunn said the project represents a "unique opportunity" for the region. "Australian Paper is the largest user of natural gas in Victoria and that leaves us really exposed to the vagaries of that market, to pricing changes," he said. "We are really looking to stabilise our future energy footprint, our future energy requirements through this project." Mr Dunne said energy generation from waste was "well-proven technology", however the company hopes to gather broad community feedback to proceed. "That is really why we are here today, for the information centre, to promote the fact that we are looking for that broader social licence from the local community," he said. According to Australian Paper, the project could divert about 650,000 tonnes of waste from landfill in south east Melbourne and Gippsland and could create up to 800 construction jobs and more than 40 ongoing jobs. Federal member for Gippsland Darren Chester said the energy from waste project was important in terms of establishing long-term, sustainable jobs in the region. "Jobs is big issue in the [Latrobe] Valley," he said. "We need to work with the local community on sustainable long-term employment opportunities, we need to work with existing local businesses that have a proven track record of success. "All levels of government working with the business community, working with local residents making sure we have dedication and absolute focus on the opportunities for young people, particularly in our region." Member for Eastern Victoria Harriet Shing said the project had "great opportunities" ahead as an emerging market in Gippsland. "It will enable us, when the proof of concept is delivered in the middle of 2018, to grow local jobs and opportunities, to manage our carbon footprint, to take advantage of technology which is already functioning very successfully in other jurisdictions around the world and to really make the most of cutting-edge technology as it grows and develops in the waste and energy markets," she said.
https://nnimgt-a.akamaihd.net/transform/v1/crop/frm/storypad-6vw4HdPJmTwUKT8teC8K4L/fb83e15c-ac66-4228-98a8-b94e1e8852f1.jpg/r0_163_6000_3553_w1200_h678_fmax.jpg
March 19 2018 - 12:00AM
Community space for energy from waste
Heidi Kraak
Australian Paper launched an information centre in Morwell to gain community feedback about a proposed energy from waste project which could be established at its Maryvale mill. photograph heidi kraak
Australian Paper launched an information centre in Morwell for its proposed energy from waste project today.
The company is completing a feasibility study to assess the viability of the project, which would convert household waste into energy to be used at the Maryvale mill.
The feasibility study began last year and is expected to take about a year to complete.
The company will need to attract about $600 million in investment for the project.
Both state and federal governments are contributing $2.5 million to the $7.5 million study, which will look into the technical, environmental, social and economic challenges of the project.
Australian Paper national manager of sustainability and communications Craig Dunn said the project represents a "unique opportunity" for the region.
"Australian Paper is the largest user of natural gas in Victoria and that leaves us really exposed to the vagaries of that market, to pricing changes," he said.
"We are really looking to stabilise our future energy footprint, our future energy requirements through this project."
Mr Dunne said energy generation from waste was "well-proven technology", however the company hopes to gather broad community feedback to proceed.
"That is really why we are here today, for the information centre, to promote the fact that we are looking for that broader social licence from the local community," he said.
According to Australian Paper, the project could divert about 650,000 tonnes of waste from landfill in south east Melbourne and Gippsland and could create up to 800 construction jobs and more than 40 ongoing jobs.
Federal member for Gippsland Darren Chester said the energy from waste project was important in terms of establishing long-term, sustainable jobs in the region.
"Jobs is big issue in the [Latrobe] Valley," he said.
"We need to work with the local community on sustainable long-term employment opportunities, we need to work with existing local businesses that have a proven track record of success.
"All levels of government working with the business community, working with local residents making sure we have dedication and absolute focus on the opportunities for young people, particularly in our region."
Member for Eastern Victoria Harriet Shing said the project had "great opportunities" ahead as an emerging market in Gippsland.
"It will enable us, when the proof of concept is delivered in the middle of 2018, to grow local jobs and opportunities, to manage our carbon footprint, to take advantage of technology which is already functioning very successfully in other jurisdictions around the world and to really make the most of cutting-edge technology as it grows and develops in the waste and energy markets," she said.
Discuss "Community space for energy from waste "


Kentucky Coach Joker Phillips has tried to maintain a sense of humor during what has been a difficult season and mounting questions about his job status.
"I was coming over here today, and I got in the car, and my seat was hot," he said. "And I looked up, and I had hit the seat warmer."
Enduring a third straight losing season, questions regarding Phillips' future and Kentucky's struggles are no laughing matter, though.
The Wildcats (1-8, 0-6 Southeastern Conference) lost their seventh straight game Saturday at Missouri, putting them on pace for their worst finish since going 2-9 in 2004.
Injuries have forced Phillips to play 26 freshmen against one of the nation's toughest schedules. That hasn't stopped Wildcats fans from expressing their frustration: calling for his dismissal on radio talk shows and not showing up for games � attendance has fallen off at 67,942-seat Commonwealth Stadium.
Players say they still support Phillips and will try to finish the season with three wins to help the embattled coach.
"He's still here, he's still our coach, we're still playing for him and I'm going to play hard for him," junior right tackle Kevin Mitchell said.
"We don't actually say anything to him" about his situation, "but we come out and we practice hard. We're keeping it going, we just continue as a team. We're all pushing each other hard. Practicing hard shows him that we still care, that we still believe and that we're not giving up."
Phillips, 12-22 and in his third season at Kentucky, is one of several SEC coaches facing uncertain futures � joining Auburn's Gene Chizik, Tennessee's Derek Dooley and Arkansas' John L. Smith.
But Phillips has remained upbeat through the turmoil, saying that he's been too busy focusing on his team to pay attention to what has been or said about him. When asked again if he has talked to Kentucky Athletic Director Mitch Barnhart about his status, Phillips came back with his standard response that the two friends have talked without being specific.
"Just small talk," Phillips said. "Talking like friends do weekly."
Kentucky spokesman Tony Neely declined an interview request with Barnhart about Phillips, saying via email, "As was stated before the season, and as we do with each program, an evaluation will be done at the end of the season."
GATOR WR OUT: No. 8 Florida will be without receiver Solomon Patton for the rest of the season.
Patton, a junior from Mobile, Ala., broke his left arm in Saturday's 17-9 loss to Georgia. Patton has just one reception for 17 yards this season. But he has 14 carries for 140 yards and has played an integral role on special teams.
GET WELL SOON: South Carolina Coach Steve Spurrier led the cheers of more than 1,000 people who turned out yesterday to wish injured star Marcus Lattimore a quick recovery and a happy 21st birthday.
"This is not a memorial service," Spurrier said. "This is a happy birthday to Marcus and an appreciation for everything he's done and is going to continue to do for South Carolina."
And then Spurrier gave out a gift of hope to worried Gamecock fans.
"The message he gave me was, 'I'll be back,' " Spurrier said. "So he's coming back."
That was the last thing on anyone's mind after watching Lattimore's devastating injury. His right knee was dislocated and sustained significant ligament damage requiring surgery and maybe needing more than a year of rehabilitation. Lattimore was released from the hospital Sunday night.
Playing again, though, wasn't what yesterday's gathering was about. Fans filled the area in front of the McKissick Museum on the school's historic Horseshoe, many wearing Lattimore's No. 21. They signed large cards of support, brought birthday balloons and sang "Happy Birthday" to their beloved star.
TEXAS STICKS WITH ASH: Texas is going with sure and steady over swashbuckling. The Longhorns are sticking with David Ash as starting quarterback over Case McCoy.
Despite pulling Ash late in the game against Kansas, Coach Mack Brown said Ash gets to keep his job for Texas' trip to Lubbock to play No. 20 Texas Tech (6-2, 3-2 Big 12) on Saturday.
"David's body of work has been pretty good," Brown said, adding that he "would not hesitate" to pull him for McCoy if Ash doesn't play well.
McCoy, a junior and the younger brother of former Texas quarterback Colt McCoy, has shown a flair for delivering in clutch moments for Texas, but Ash has been one of the top-rated passers in the country this season.
"Case did an outstanding job. We're so proud of the job he did for us," Brown said.
VAZ IN FOR BEAVERS: Oregon State Coach Mike Riley has decided to start junior Cody Vaz at quarterback Saturday against Arizona State.
Vaz had started two games for the No. 13 Beavers while starter Sean Mannion recovered from arthroscopic knee surgery. Mannion returned Saturday to start against Washington but threw four interceptions before Vaz replaced him in a 20-17 loss.
"It's one of those things that's not easy," Riley said. "You look at the integrity of the competition and you try to make a decision for the team that's right this minute."
"It's a little disappointing, but at the same time I know it's about the team, it's not about any one player," Mannion said.
Vaz, who hadn't started a game since high school, stepped in during Mannion's recovery and led the Beavers to a 42-24 win at BYU and a 21-7 victory at home against Utah.
ROBINSON WILL RETURN: Michigan, it seems, got a scare and not a long-term problem when Denard Robinson injured a nerve in his right elbow against Nebraska.
"He should be fine," Wolverines Coach Brady Hoke said. "He should be ready to go on Saturday."
Michigan lost its one dimension on offense in a 23-9 loss Saturday to Nebraska when Robinson was running for a first down. He cut back for extra yards instead of going out of bounds and aggravated a nerve in his elbow that he injured against Illinois.
"It gets numb and tingly," Hoke said.
The team's medical staff is working on protective equipment that Robinson can wear in an attempt to prevent his throwing arm from getting banged up again in the same spot.
BADGERS QB DONE: Wisconsin quarterback Joel Stave is done for the season after breaking his left collarbone against Michigan State.
Coach Bret Bielema announced the news two days after the Badgers' 16-13 overtime loss to the Spartans. Doctors determined the redshirt freshman would not need surgery to repair the injury.
Stave completed 70 of 118 attempts for 1,104 yards and six touchdowns in seven games. He threw three interceptions.
He was the top quarterback in spring practice, but junior transfer Danny O'Brien earned the starting slot in fall camp ahead of Stave and fifth-year senior Curt Phillips. Stave replaced O'Brien in the second half of Wisconsin's 37-26 victory against UTEP on Sept. 15 because of a handful of turnovers by O'Brien, and Bielema named Stave the starter going forward.
O'Brien and Phillips will vie for the starting spot for Wisconsin (6-3, 3-2 Big Ten), which has a bye week before playing Indiana (1-3, 3-5) on Nov. 10 in Bloomington.
CYCLONES LB OUT: Iowa State senior linebacker Jake Knott is likely out for the season with a left shoulder injury.
Cyclones Coach Paul Rhoads said Knott, the reigning Big 12 defensive player of the week and a first-team All-Big 12 pick in 2011, had surgery yesterday in Chicago. Rhoads said Knott might make it back for a potential bowl game. But the Cyclones won't know more until later in the week.
Knott injured his shoulder Oct. 20 against Oklahoma State, but he returned and had 11 tackles and forced a fumble in Iowa State's 35-21 win on Saturday over Baylor.