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

The random motion  of stars is one of the most fundamental ingredients in the study of  the dynamics of galactic disks.
Among many examples showing the importance of stellar velocity dispersion in dynamics, there is asymmetric drift caused by density and dispersion gradients; this drift makes the rotation of stars
 lagging circular velocity. There is also the azimuthal anisotropy, which informs the structure of stellar orbits in the disk plane.
 Both of these make use of the azimuthal and radial components, $\sigma_\phi$\ and $\sigma_R$\ \citep[e.g.,][]{bin08}.
 As for the vertical component, $\sigma_z$, it is essential to
constrain the total mass surface density inside disks, thus the stellar mass-to-light ratios and luminous-to-dark
matter fractions  \citep[e.g.,][]{dms0,dms6}.

It has long been a hard task to characterize the 3D   velocity dispersion  space of stellar disks other than the Milky Way because of the
nature of observations very demanding in integration time and angular coverage.
The works of \citet{ger97}, \citet{ger00}, \citet{sha03}, and \citet{ger12} made significant contributions to this field. These authors were able to constrain the vertical-to-radial axis ratio of the dispersion ellipsoid
in eight spiral galaxies from long-slit spectroscopy measurements aligned with the disk major and minor axes kinematics.
They found   ${\sigma_z \over \sigma_R} \sim 0.3-0.9$.
 The growing amount of data from  integral field spectroscopy (IFS) now
   successfully replaces such long-slit experiments, covering the 2D kinematics of the disks
   for large samples of galaxies.  The DiskMass Survey (hereafter \dms)
  was exactly designed to measure dispersions in 30 low inclination disks by means of IFS and constrain the stellar mass density and luminous-to-dark
 mass ratio \citep{dms1,dms2,dms0,dms4,dms6}. One of the objectives of this present study  is to improve the modeling of stellar velocity dispersions from IFS data
  for a larger galaxy sample and larger disk inclinations.

Yet, a major problem in the derivation of the 3D dispersion space comes from the difficulty in modeling the observed dispersion $\sigma_{\rm los}$\
by
\begin{equation}
  \sigma_{\rm los} =    \big ( (\sigma^2_R \sin^2\phi + \sigma^2_\phi \cos^2\phi) \sin^2 i +  (\sigma_z \cos i)^2  \big)^{1/2}
 \label{eq:sigmalos}
,\end{equation}
 where  $\phi$ is the azimuthal angle in the deprojected orbit and $i$ the disk inclination, considering a stellar velocity ellipsoid
 aligned with the cylindrical coordinate system in the disk plane. Because of the competition between the components
  that have roughly comparable amplitudes, it impossible to fit the model blindly to the observations.
 To overcome that issue, one can fix one of the three parameters, preferentially $\sigma_z$, as the radial and tangential components
 can be easily  disentangled in that particular case by the variation of dispersion with azimuth.
  For example, \citet{nor08}  assumed $\sigma_\phi=\sigma_z$, which allowed these authors to constrain the dispersion ellipsoid of
  four early-type spirals, but from long-slit spectroscopy. Although this assumption
   makes the derivation easier, it has no physical justification, however.
  Another possibility is to fix the ratio between two of the components.
 For instance,  $\frac{\sigma_\phi}{\sigma_R}$\ can be guessed beforehand from the slope of the rotation curve, assuming that
   the epicyclic approximation is valid, then $\sigma_R$\ and $\sigma_\phi$\ can be deduced with the help of the equation of the asymmetric drift to finally give
  {$\sigma_z \over \sigma_R $}\ using the dispersion data \citep{ger97, ger00, sha03, cia04, ger12, dms4}.
   An alternate assumption is to consider global links between the components. The best example
  that uses such approach is \dms,\ which assumed ${\sigma_\phi \over \sigma_R}=0.7$ and
  ${\sigma_z \over \sigma_R}=0.6$  at all galactocentric radii and for every galaxy, yielding $\sigma_z$ by deprojecting
  $\sigma_{\rm los}$\ \citep[e.g.,][]{dms1,dms2,dms6}.

In this study I propose to relax most of these strong assumptions, by considering that only {$\sigma_z \over \sigma_R $}\ can be fixed, making it possible
to fit the two plane components to the data. Although still  limited in angular and spectral resolution and spatial coverage,
the current large IFS surveys such as Calar Alto Legacy Integral Field Area Survey \citep[\textsc{CALIFA},][]{califasanchez12},  Sydney-Australian-Astronomical-Observatory Galaxy Survey \citep[\textsc{SAMI},][]{samibryant15}, or Mapping Nearby Galaxies at Apache Point Observatory
\citep[MaNGA,][]{bun15}
  can yield accurate enough kinematics to make direct   fits of Eq.~\ref{eq:sigmalos} to 2D dispersion maps
  possible. The power of IFS devices    precisely lies in the ability to recover the angular variation of velocities in the sky plane.
  This is an improvement with respect to the early long-slit spectroscopy works of \citet{ger97} limited to two directions only. The strategy
  is also different from  the \dms\ work as the   proposed model  fits line-of-sight dispersions, thus avoiding   problems inherent
  to deprojections of observables when $\cos \phi$ and $\sin \phi \rightarrow 0$.
  Moreover, the strategy is technically similar to the usual fits of  velocity fields  in which $v_{\rm los}$ is the
  projection along the line of sight of model rotation velocities $v_\phi$ and noncircular radial motions $v_R$.

   Consequently,  I present the first attempt to fit 2D models of Eq.~\ref{eq:sigmalos} to a large sample of
   stellar disk dispersion fields
     with the minimum assumptions possible and
   independent of any considerations imposed by  the epicycle theory and asymmetric drift equations.  I use the stellar   kinematics
   of 93 disk galaxies from the \textsc{CALIFA}\ survey to derive the azimuthal anisotropy,
   which is the most important byproduct of this analysis (Sect.~\ref{sec:derivation}),   study
   the properties of azimuthal anisotropy (Sect.~\ref{sec:properties}), and compare the anisotropy distribution  with
   the absolute magnitude and stellar mass (Sect.~\ref{sec:massanis}) and with
   predictions of the epicycle theory (Sect.~\ref{sec:compghasp}).
   Brief discussions,  comparisons with other works, and conclusions
   are presented in Sect.~\ref{sec:discussion} and~\ref{sec:summary}.
   Finally, results from the modeling of mock datasets using a N-body numerical simulation of a Milky Way-mass disk are presented in   Appendix~\ref{sec:validation} and Appendix~\ref{sec:easimu}.
   These results show the ability of the proposed strategy to find realistic azimuthal anisotropies with weak impacts from systematic effects. They also show the negative impact on {$\sigma_z \over \sigma_R $}\ when
   the epicyclic assumption is assumed to be valid even though it is not.

    \begin{figure}[th]
 \begin{center}
 \includegraphics[width=5cm]{figeps/imsdssn257.eps}\\
 \includegraphics[width=8.3cm]{figeps/fig-siglos-anisgeneric-0218-NGC0257.eps}\\
 \includegraphics[width=8.3cm]{figeps/anisotropy-anisgeneric-0218-NGC0257.eps}
   \caption{Example of results with the galaxy NGC257.
   \textit{Top:} Composite SDSS image of the galaxy.
   \textit{Middle:} Line-of-sight dispersion profile. A rainbow color code is used to highlight the common spaxel centroids inside
   the adaptive radial rings.  The shaded area represents the standard deviation of $\sigma_{\rm los}$\ inside each adaptive
   ring. Red open circles represent the azimuthally average of $\sigma_{\rm los}$\ within each radial ring.
   The thick blue line indicates the azimuthally average of the dispersion model done with ${\sigma_z \over \sigma_R}=0.7$. The vertical dashed line shows the radius $R=R_e$.
   The last spaxel is not part of any ring and is  not used in the modeling of the dispersion ellipsoid.
   \textit{Bottom:} Profile of azimuthal anisotropy parameter (filled circles) and polynomial fits to the profile (shaded area, see text for details).
  Starred symbols indicate the values interpolated   at $R/h=0.5,1,2$ (from the polynomial fits),  open
  diamond and squares at the effective radii of the bulge ($R=R_b$) and of the galaxy ($R=R_e$). A dashed line indicates the azimuthal anisotropy expected by
  the epicyclic approximation from the circular velocity curve of the galaxy.  }
 \label{fig:n257}
 \end{center}
 \end{figure}

 \begin{figure*}[t]
  \centering
  \includegraphics[width=18cm]{figeps/fig-azimobs.eps}
  \caption{Azimuth-velocity dispersion diagrams for 9 example galaxies.
  From left to right (respectively) the columns illustrate  orbits that are more tangentially biased ($\beta_\phi \rightarrow -0.5$), isotropic ($\beta_\phi \sim 0$)
,  and more radially biased ($\beta_\phi \rightarrow 0.5$). Symbols are the \textsc{CALIFA}\ line-of-sight velocity dispersions and colored curves the best-fit anisotropic dispersion
  model (for the case {$\sigma_z \over \sigma_R $}$=0.7$). See text for information about the considered radial range of the diagrams.}
 \label{fig:azim-tanisorad}
 \end{figure*}

 \section{Derivation of anisotropic velocity dispersions from IFS data}
 \label{sec:derivation}

 The observations are the integral field data from the \textsc{CALIFA}\ sample \citep{califasanchez12,califawalcher14}.
 That sample is representative of the general galaxy population within the
 SDSS $r-$band absolute magnitude range [$-19,-23.1$] \citep{califawalcher14}.
 I used
 the third \textsc{CALIFA}\ release \citep{califasanchez16} and in particular their stellar velocity dispersion maps \citep{califalcon17}.
All galaxies but ellipticals and S0s were selected. Moreover, disks less (more, respectively) inclined than 35\degr\ (75\degr)
were discarded to prevent us from projection effects as much as possible. These effects have little impact  on  the
azimuthal anisotropy for the chosen inclination disk range, as shown in Appendix~\ref{sec:validation} from mock data based on a N-body numerical simulation,
and in Sect~\ref{sec:globalproperties}. The inclinations were deduced using the photometric ellipticity $e$ given in \cite{califalcon17} from
$\cos^2 i=((1-e)^2-q_0^2)/(1-q_0^2)$, where $q_0=0.2$ the intrinsic axis ratio of galaxies \citep[][chapter III]{hom46}.
That intrinsic ratio is known to vary with morphological type \citep{bot83}, but for simplicity I assumed this ratio to be constant.
This has no consequence on the results.
   Then, a visual inspection was carried out to
discard the most perturbed morphologies or systems, those with clear signs of merger or strong tidal features, and a couple of disks with
an axis ratio that are consistent with being less inclined than 75\degr\ but exhibit a clear edge-on morphology.

The \textsc{CALIFA}\ survey performed adaptive binning of absorption line data cubes to increase the signal-to-noise ratio of spectra. As a result,
the dispersions of spaxels that are part of a same adaptive cell are equivalent. Working with individual spaxels would thus lead to  correlated
radii when adaptive cells extend  on more than one radial ring defined below.
To avoid this effect, only the spaxel lying at the center of each cell was considered in the calculation of the ellipsoid.
Then, following cautions given in \cite{califalcon17},
any $\sigma_{\rm los}$ $< 40$ km~s$^{-1}$\ were masked to avoid the instrumental bias at observed dispersion below the spectral resolution. Also,
spurious dispersions were discarded to avoid divergent fits.
These  were identified by inspecting by eye the distribution of $\sigma_{\rm los}$\ for each galaxy.
For example, five deviant centroids above 300 km~s$^{-1}$\ for the galaxy UGC312 were masked because the
93 remaining centroids in this galaxy  are  $\sigma_{\rm los}<170$ km~s$^{-1}$, or values above 600 km~s$^{-1}$\ for NGC7824.
A radial bin or ring is then defined by a collection of at least ten spaxels and with angular size not smaller than 2\arcsec.
Such an adaptive radial sampling enabled us to perform robust least-squares fits with a number of degrees of freedom at least four times the two free parameters.

For each dispersion field, nonlinear Levenberg-Marquardt least-squares axisymmetric fits of  Eq.~\ref{eq:sigmalos} were performed at
fixed disk inclination and major axis position angle, by means of the \textsc{MPFIT} minimization package \citep{mar09}.
The fits are made with the constraint that {$\sigma_z \over \sigma_R $}\ is given and kept fixed as a function of radius. A large range of {$\sigma_z \over \sigma_R $}\ was spanned to
 study the impact of the vertical anisotropy parameter on the results. The ratio has been chosen randomly from normal laws centered on ${\sigma_z \over \sigma_R}=0.1, 0.2, 0.3, ..., 1.5$
 with a full width at half maximum of $0.1$.
The boundaries of 0.1 and 1.5 for {$\sigma_z \over \sigma_R $}\ were chosen to be consistent with the minimum and maximum values of $\beta_z$\ that \citet{kal17}
 estimated for E to Sdm \textsc{CALIFA}\ galaxies.
 This range also contains the values found by  \citet{ger12} and ratio chosen by \dms\ \citep[0.6;][]{dms1} for other galaxy samples. It also contains
 the compilation of values given in \citet{pin18}. The value
${\sigma_z \over \sigma_R}=0.7$ is the one of the thin Galactic disk component measured in the solar neighborhood \citep{bla16}.
Higher values correspond to  vertical dispersions more representative of stellar populations orbiting inside a thick disk,
\citep[e.g., $\sim 1$ for the thick Milky Way disk;][]{bla16}.

One thousand fits were performed for each central value of {$\sigma_z \over \sigma_R $}, each time
choosing randomly both the observed dispersions within the uncertainties provided by \cite{califalcon17}, a fixed value of {$\sigma_z \over \sigma_R $}\ around the central values, and the initial parameter
guesses of $\sigma_R$\ and $\beta_\phi  =1-\Big(\frac{\sigma_\phi}{\sigma_R} \Big)^2$. Normal distributions were used to select the random values.
In total, 15000 fits were thus made for each galaxy. Uniform weightings were applied to the randomly selected observed dispersions.

For each central value of {$\sigma_z \over \sigma_R $}, the azimuthal anisotropy $\beta_\phi({\sigma_z \over \sigma_R})$ is chosen as the median value of the fitted  distributions from the Monte Carlo fitting process.
Following the analysis performed in Appendix~\ref{sec:validation} with mock data,
I adopted as final anisotropy parameter and uncertainty at a given radius the median and standard deviation of the
posterior distribution made from the 15 values of $\beta_\phi({\sigma_z \over \sigma_R}$).

Finally, sample cleaning was performed by discarding the galaxies with less than three radial bins  to make
the derivation of median anisotropies possible for a sample as large as possible (93 disks).
 The sample contains 88 galaxies with an anisotropy that could be interpolated at $R=h/2$, 68 at $R=h$, 68 at $R=R_e$,
which are not necessarily the same galaxies as those at $R=h$, and
19 at $R=2h$. The photometric parameters are from \citet[][the galaxy effective radius $R_e$]{califalcon17},
and in \citet[][the disk scalelength $h$]{men17}.
Also, 46 and 78 of the 93 galaxies have measured bar and bulge properties, respectively \citep{men17}.
This information can be used to study the impact of the bulge and the bar on the anisotropy (Sect.~\ref{sec:bulbar}).
The working sample is made of 8 galaxies that are classified Sa, 9 Sab, 24 Sb, 35 Sbc, 8 Sc, 5 Scd, 2 Sd, 1 Sdm, and one Irr
within the absolute magnitude range [$-19.2, -22.8$]. The sample is thus neither uniform nor complete and the lack of objects at the faint magnitude end reflects
the difficulty of measuring absorption lines in later disk morphologies.

{It is important to note that the stellar or gaseous
rotation curves of these galaxies have not been derived. The velocity curves used to test the epicyclic approximation are those given
by \citet{kal17} for the \textsc{CALIFA}\ sample, and by \citet{epi08a,epi08b} for another galaxy sample (see Sect.~\ref{sec:compghasp}).}

{Also, for sake of comparison I  derived the azimuthal anisotropy profile of the Milky Way. For that, I used
astrometric and spectroscopic data of the Gaia mission \citep{pru16}, and particularly
the radial and azimuthal dispersions performed by D. Katz \citep[private communication, and see details in ][]{kat18}. These data consist in
 millions of FGK stars selected in the Second Gaia Data Release \citep{bro18},  lying in the Galactic disk
 ($4\le R\le 14$ kpc, $|\phi| \le 15\degr$, $|z|\le 1$ kpc). Although it does not represent kinematic measurements of the entire Galaxy, and
 though the methodology is very different from that used to model the \textsc{CALIFA}\ dispersion fields,
 this large set of  stars is enough to infer a robust Galactic anisotropy profile that is certainly of better quality
 than any of the other galaxies studied here. }

\section{Properties of azimuthal anisotropy}
 \label{sec:properties}

  \subsection{Examples of results}
  \label{sec:exampleresults}

Figure~\ref{fig:n257} {presents} typical results   obtained from the least-squares fits. The shown galaxy is NGC257 ($i=51\degr$), which is
a  Sc galaxy from the \textsc{CALIFA}\ subsample that has 206 useful spaxels spread over 12 independent adaptive radial bins. {Examples of results for 4 other galaxies are shown in Appendix~\ref{sec:othergal}.}
The middle panel shows all the spaxel values by different colors, and the expected decrease of the dispersion as a function of radius.
The azimuthally averaged dispersion profile is shown as open circles, and the  azimuthal average from the
resulting 2D dispersion model as a thick blue line, highlighting  the ability of the axisymmetric
model to capture the bulk of the random motions.

{The  azimuthal anisotropy profile is shown in Fig.~\ref{fig:n257} (bottom panel, filled circles).
The scatter of $\beta_\phi$\ at each radius remains small within the spanned range of {$\sigma_z \over \sigma_R $}\ (except at
$R \sim 1.45 h$). This  indicates that $\beta_\phi$\ is not strongly dependent on the choice of {$\sigma_z \over \sigma_R $}\ in stellar disks, whose finding agrees with the results obtained from the modeling of mock data using
a N-body simulation (App.~\ref{sec:validation}). This result is well representative of the whole sample.
The anisotropy profile of NGC257 is consistent with isotropy in the inner disk ($\beta_\phi \sim 0$) and then with more tangential stellar orbits in outer regions.
The shaded area shows the scatter of 1000 second degree polynomial fits to random anisotropy profiles chosen within a Gaussian law of standard deviation the quoted  uncertainties of the filled circles.
The polynomial fits make it possible to interpolate the profile at the characteristic radii $R=R_e$ and $R/h=0.5, 1, 2$, whenever possible.
  Table~\ref{tab:anisvalues}  lists the interpolated anisotropies at these radii as well as the median of the profile.}

  \begin{table*}
 \caption{Azimuthal anistropy of 93 disk galaxies from the \textsc{CALIFA}\ sample. Median of the anisotropy profile and interpolated  values at $R=0.5h,h,2h, R_e$. The quoted uncertainty for the median anisotropy
 is the median of the  errors of the anistropy profile. This is an excerpt of a longer table is only available online.}
 \label{tab:anisvalues}
\centering
\begin{tabular}{c|c|cc|cc|cc|cc|cc}
\hline\hline
  Galaxy  & Number of  & \multicolumn{2}{c}{$\beta_\phi$~~~~$\epsilon_{\beta_\phi}$} & \multicolumn{2}{|c}{$\beta_\phi$~~~~$\epsilon_{\beta_\phi}$}  & \multicolumn{2}{|c}{$\beta_\phi$~~~~$\epsilon_{\beta_\phi}$} & \multicolumn{2}{|c|}{$\beta_\phi$~~~~$\epsilon_{\beta_\phi}$} & \multicolumn{2}{|c}{$\beta_\phi$~~~~$\epsilon_{\beta_\phi}$} \\
  & radial bins & \multicolumn{2}{c|}{$R=h/2$} & \multicolumn{2}{c|}{$R=h$} & \multicolumn{2}{c|}{$R=2h$} & \multicolumn{2}{c|}{$R=R_e$} & \multicolumn{2}{c}{Median} \\
  \hline
IC0674          & $  3$ & $ 0.39$ & $ 0.02$ & $ 0.48$ & $ 0.03$ & -- & -- & $ 0.43$ & $ 0.02$ & $ 0.47$ & $0.03$ \\
IC1151          & $  4$ & $-0.14$ & $ 0.02$ & $ 0.04$ & $ 0.02$ & -- & -- & $ 0.31$ & $ 0.02$ & $ 0.23$ & $0.03$ \\
IC1528          & $  7$ & $-0.41$ & $ 0.05$ & $ 0.35$ & $ 0.03$ & -- & -- & -- & -- & $ 0.00$ & $0.02$ \\
IC1683          & $  4$ & $-0.71$ & $ 0.23$ & -- & -- & -- & -- & -- & -- & $-0.08$ & $0.12$ \\
IC4566          & $  5$ & $-0.04$ & $ 0.01$ & $ 0.04$ & $ 0.01$ & -- & -- & $ 0.08$ & $ 0.03$ & $-0.06$ & $0.02$ \\
\hline
\end{tabular}
\end{table*}

{Figure~\ref{fig:azim-tanisorad} presents azimuth-dispersion diagrams   at selected radii for nine galaxies.
The radial ranges are  $11.9\arcsec-22.6\arcsec$ (NGC755),  $13.3\arcsec-15.4\arcsec$ (NGC5633),  $5.4\arcsec-7.6\arcsec$ (IC1528),
  $R=1\arcsec-9.4\arcsec$ (NGC257), $5.4\arcsec-9.4\arcsec$ (NGC5016), $1.1\arcsec-8.1\arcsec$ (IC456), $7.3-13.8\arcsec$ (NGC2253), $3.2\arcsec-11.6\arcsec$ (NGC4047), and  $13.7\arcsec-22.3\arcsec$ (NGC5406).
The radial range shown for NGC257 corresponds to the isotropic orbits observed in the four innermost radial bins in Fig.~\ref{fig:n257}.
The solid lines are the model line-of-sight dispersion, as deduced from
anisotropies averaged over the considered radial ranges.
The azimuth-dispersion diagrams are evidence of many irregularities in the dispersion maps.
Some diagrams seem scattered (e.g., NGC755, NGC5633, IC4566), others present wiggles on small angular scales  (e.g., NGC4047, NGC5016, NGC5406), others show
asymmetries in the amplitude of the anisotropy from one side of the galaxy to the other (e.g.,  $\phi=\pi/2$ versus   $\phi=3\pi/2$  for NGC2253).
These asymmetries are caused by lopsidedness, spiral arms, and bisymmetric or other higher frequency perturbations in the disks. They obviously cannot be reproduced by  axisymmetric modeling. }

  \subsection{Global properties}
  \label{sec:globalproperties}

    \begin{figure}[th]
 \begin{center}
  \includegraphics[width=8.5cm]{figeps/fig-betaobsvsincl0218.eps}
   \caption{ Median anisotropy and uncertainty ($\epsilon_{\beta_\phi}$) as a function of disk inclination for the \textsc{CALIFA}\ disk galaxies. The horizontal dashed line is $\beta_\phi=0.51$ chosen by the
   DiskMass Survey \citep{dms0}.
   The solid line is not a fit to the data but the uncertainty curve deduced from the mock data of Appendix~\ref{sec:validation}, showing the consistency between the observations and  numerical modeling. }
 \label{fig:betaincl}
 \end{center}
 \end{figure}

The distribution of the median anisotropy as a function of disk inclination is shown in the top panel of Fig.~\ref{fig:betaincl}. It shows the negligible projection effect on the derived anisotropy, as
 the median anisotropy is consistent with being not strongly correlated with the inclination. Whether the slight trend
 of smaller $\beta_\phi$\ in   disks of lower inclination is genuine or an artifact from having fewer such disks in the sample is not clear. A larger sample would be helpful to clarify that point.
 What is clear however is the inclination effect with the median uncertainty (bottom panel).
 This  implies that the accuracy of the modeling is lower for lower inclinations.
  It is important to note that this trend is in good agreement with the expectations from  the analysis of the mock datasets of Appendix~\ref{sec:validation} (solid line in Fig.~\ref{fig:betaincl}).
 It is evidence that the proposed uncertainties on observed anisotropies are realistic, and that the trends
 obtained from the analysis  of mock low-resolution dispersion maps are representative of real observations.

{The  profiles of  azimuthal anisotropy as a function
of galactocentric radius for the 93 galaxies are shown in Fig.~\ref{fig:anisallpoints} (open circles). The galaxy
distances  used to transform the radius into a kpc-scale are those listed in  Nasa NASA/IPAC Extragalactic Database.
The median   profile   is also shown (filled diamonds) as well as the standard deviation on each bin of radius (dashed lines).  }
Based on prescriptions given in \citet{bin08}, several types of orbits can be identified as follows:
tangential orbits ($\beta_\phi < -0.5$), intermediate tangential-to-isotropic orbits
($-0.5<\beta_\phi<-0.25$), isotropic orbits ($|\beta_\phi| \le 0.25$, with pure isotropy at $\beta_\phi=0$), intermediate isotropic-to-radial  orbits
($0.25 < \beta_\phi < 0.5$), and radial orbits ($\beta_\phi > 0.5$). Radii with very tangential orbits $\beta_\phi << -5$ that are proxies of circular orbits ($\beta_\phi \rightarrow -\infty$)
are not observed.  {We note the effect of the orbits in the azimuthal-dispersion diagrams of Fig.~\ref{fig:azim-tanisorad}. The largest values of $\sigma_{\rm los}$\
are reached at $\phi=(0,\pi)$ for more tangential orbits, $\phi=(\pi/2,3\pi/2)$ for more radial orbits, whereas $\sigma_{\rm los}$\ is nearly flat for isotropic orbits, according to Eq.~\ref{eq:sigmalos}.}

{The median anisotropy for the  sample is  $\beta_\phi=0.25$ and the  median profile as a function of radius is consistent  with orbits that turn from isotropic at low radius
to more radially biased orbits at larger radius. This radial trend also seems to depend on the morpholigical type (see Sect.~\ref{sec:massanis}). Another consequence of Figs.~\ref{fig:betaincl} and~\ref{fig:anisallpoints}}
is the observation that  $\beta_\phi=0.51$,  as assumed by the \dms\ analysis \citep{dms1,dms2,dms6}, cannot be a value representative of nearby disks of any morphological types and at every galactocentric radii.

  \begin{figure}[t]
 \begin{center}
  \includegraphics[width=9cm]{figeps/anisotropy-0218-nbin10-total-log-points.eps}
   \caption{Azimuthal anisotropy profiles for the  sample of 93 \textsc{CALIFA}\ disk galaxies (circles).
   The filled diamonds represent the median profile derived from every galaxy and the dashed lines the standard deviation. The
   solid line indicates the anisotropy profile of the Milky Way as deduced from  Gaia Data Release 2 dispersions published in \citet{kat18},
   and an open triangle the location of the Sun.}
 \label{fig:anisallpoints}
 \end{center}
 \end{figure}

{The Gaia DR2 anisotropy profile of the Milky Way compares well with the values measured for the other galaxies
(solid line in Fig.~\ref{fig:anisallpoints}). It rises as a function of radius,
giving a solar neighborhood value consistent with radially biased orbits (open triangle).
It is important to note that the value chosen by \citet{dms1,dms2} and \citet{dms6} agrees perfectly with that of the solar neighborhood, as already reported in \citet{dms2}.}

\subsection{Impact of bars and bulges}
\label{sec:bulbar}

{The variation of anisotropy as a function of bulge-to-total (B/T) and bar-to-total r-band luminosity fractions is shown in Fig.~\ref{fig:betabulbar}. It is useful to assess globally the impact of the stellar bulges
and bars on the median velocity anisotropy in the disk planes.}

{In particular, verifications were made that the galaxies with larger bulge  contributions to the total galaxy luminosity are not systematically more isotropic/anisotropic than the rest of the sample. Indeed,
the relevance of performing fits of the planar model of Eq.~\ref{eq:sigmalos} to dispersions of stars potentially more impacted by spherical or triaxial symmetries could be questioned.
The verification is shown in the top panel of Fig.~\ref{fig:betabulbar}. No systematic trends are observed; the anisotropy of the  galaxies with a more important bulge contribution ($\rm B/T > 20\%$) remains in full agreement with the
median anisotropy of the galaxies with a smaller bulge contribution ($\rm B/T \le 20\%$, dashed line). Then, verifications were also made that
no systematic trend occurs when B/T is compared to the  anisotropy interpolated at the bulge effective radius $R=R_b$. }

 \begin{figure}[t]
 \begin{center}
  \includegraphics[width=8.5cm]{figeps/fig-betavsbulgbar.eps}
   \caption{{Median anisotropy   as a function of B/T (top) and bar-to-total (bottom) luminosity fraction in the SDSS r-band. A horizontal dashed line indicates   the median anisotropy of the galaxies with lower bulge contribution
   (bulge-to-total luminosity fraction lower than 20\%).}}
 \label{fig:betabulbar}
 \end{center}
 \end{figure}

 {A similar comparison with the luminosity contribution of the bar was carried out.
 As the dynamics of bars participate in the secular evolution of disks, it might be possible to observe an effect on the structure of the stellar orbits as a function of bar importance.
 This is however not the case, as shown in the bottom panel of  Fig.~\ref{fig:betabulbar}. As in the bulge case, the anisotropy distribution remains roughly constant as a function of the bar-to-total luminosity fraction.
 This could indicate a more important role from other mechanisms than stellar bars in shaping the global orbital structure in the plane of galactic disks.}

 \section{Evidence for a link between azimuthal anisotropy and the magnitude and morphological type}
 \label{sec:massanis}

 {The radial variation of $\beta_\phi$\  can also be measured in bins of luminosity and morphological types.
  This is shown in Fig.~\ref{fig:anisallmabsbin}, which reveals a link between the anisotropy and morphology (top).
  The  earlier the type of the disk, the more radially biased the stellar orbits. Anisotropy parameters in Sa-Sab show small
  differences with Sb types. The radial change of anisotropy seems linked to the morphology as well. Globally, it increases with radius in Sa, Sab, and  Sb types,
   increases slightly in Sbc-Sc disks, and tends to decrease in types later than Scd. Interestingly, the anisotropy seems roughly independent on type  in the innermost
  regions. }

 {The bottom panel of  Fig.~\ref{fig:anisallmabsbin} also identifies a clear link with the absolute r-band magnitude (thus with the stellar mass). Unsurprisingly, the
 relation looks similar to the top panel, in which the median anisotropy is larger in more  luminous  disks. }

 \begin{figure}[th]
  \centering
  \includegraphics[width=9cm]{figeps/fig-betamabsrlograd.eps}
  \caption{{Azimuthal dispersion profiles color-coded with the morphological type (top) and absolute r-band magnitude (bottom).}}
 \label{fig:anisallmabsbin}
 \end{figure}

 \begin{figure*}[th]
 \begin{center}
   \includegraphics[width=9cm]{figeps/fig-betavsmabsr-05rd-apex.eps}\includegraphics[width=9cm]{figeps/fig-betavsmabsr-rd-apex.eps}
   \caption{
    Absolute magnitude-anisotropy relations of \textsc{CALIFA}\ stellar disks at $R=h/2$ (left) and $R=h$ (right).
   Different colors and symbols represent different disk morphologies from Sa to Irr.  The solid line is  the most likely linear fit to $\beta_\phi$\ (at $R=h/2$ only).
   Crossed symbols and dotted lines represent the observed and best-fit relations
   predicted by the epicycle approximation for the same \textsc{CALIFA}\ disks, as deduced from circular velocity curves of \citet{kal17}. Gray circles and dashed lines are the observed and best-fit relations
   predicted by the epicycle approximation for other galaxies, as deduced from \mbox{H$\alpha$}\ rotation curves of the \ghasp\ sample of \citet{epi08a,epi08b}.    }
 \label{fig:anismagrd}
 \end{center}
 \end{figure*}

 {The link with   the luminosity  can also be studied
 at characteristic radii. Figure~\ref{fig:anismagrd}   shows for instance the azimuthal anisotropy at $R=h/2$ and $R=h$ as a function of magnitude;
 symbol shapes and colors  are coded as functions of morphological types.
  The anisotropy and magnitude at $R=h/2$  present a non-negligible degree of correlation (Pearson correlation factor of 60\%), but also non-negligible scatter.}

{A linear model $\beta_\phi =a M_r +b$  has thus been fitted to the relation.
This can be achieved by iterative least-squares fits coupled with sigma-clipping of the most deviant points. However
 a more robust solution for scattered correlations is to account for an additional intrinsic variation perpendicular to the  model \citep[e.g.,][]{hog10}.
A linear Bayesian estimation turns out to be more appropriate in this case. It has been performed with
the Python library \textsc{emcee} developed by \citet{for13}, which makes use of
the affine-invariant ensemble sampler  \citep[][]{goo10} in the Markov chain Monte Carlo fit (MCMC).
The likelihood function introducing the Gaussian variance $s$ due to the  point scattering   perpendicular to the line
is given in \citet{hog10}. The  corner plot  reporting
the projections of the posterior probability distributions of the two parameters and of $\ln(s)$  is shown in Fig.~\ref{fig:cornerlinearfitmabsanis05rd} of Appendix~\ref{sec:mcmccornerplots}. }

  The linear relation the most likely is
    \begin{equation}
    \beta_\phi = -0.14^{+0.03}_{-0.03}\, M_r - 2.84^{+0.56}_{-0.58} ~~~~~~~~~~~(R=h/2)\\
   ,\end{equation}
   where the slope, intercept, and lower and upper uncertainties are based on the 50th, 16th, and 84th percentiles of the samples in the marginalized distributions, respectively.
   The larger scatter of $\beta_\phi$\ at $R=h$  makes the correlation poorer (correlation factor of 30\%) and the linear fit difficult.
   This correlation is  mostly valid for disks brighter than with $M_r = -20$ because of the lack of observations of fainter galaxies.
   It would therefore be important to extend this type of analysis using a more complete sample at the faint magnitude end. This could only be
   achieved from more accurate and sensitive observations than \textsc{CALIFA}. Integral field spectroscopy with, for example, the Very Large Telescope MUSE instrument \citep{bac10}
   would be certainly appropriate for that work.
That absolute magnitude-anisotropy relation is translated into a stellar mass-anisotropy relation in Sect.~\ref{sec:discussion}.

   \section{Disagreement with epicyclic approximation}
   \label{sec:compghasp}
    In the framework of the epicycle theory, the azimuthal anisotropy  is linked to the slope of the circular velocity $v_c$\  \citep[e.g.,][]{bin08} by
    \begin{equation}
    \beta_{\rm EA}  =\frac{1}{2} \left( 1- \dfrac{\mathrm{d}\ln v_c}{\mathrm{d} \ln R}\right) \, .
     \label{eq:betaea}
    \end{equation}

  {The objective of this section is to present a comparative analysis of the epicycle anisotropy $\beta_{\rm EA}$\ to the stellar azimuthal anisotropy. This goal is achieved by means of
  two samples of velocity curves that make it possible to derive the difference $\Delta \beta_\phi=\beta_\phi-\beta_{\rm EA}$ and the
  distribution of anisotropies at characteristic radii ($R/h=0.5,1,2$ and $R=R_e$).}

  {The first set of data are the circular velocity curves of \textsc{CALIFA}\ galaxies derived by \citet{kal17}.  As these authors fit the mass distribution and gravitational potential
  to the data from dynamical modeling involving anisotropic multi-Gaussian expansion \citep{cap08}, they were  able to infer the circular velocity curves of the galaxies. I thus derived the profiles
  of $\beta_{\rm EA}$\ for the 68 galaxies in common with their \textsc{CALIFA}\ sample, as well as $\Delta \beta_\phi$.  An example of  an epicycle anisotropy profile is shown
 in Fig.~\ref{fig:n257} with the galaxy NGC257, and in Appendix~\ref{sec:othergal} for a few other galaxies.}

   {Moreover,   the circular velocity can  be reasonably approximated by the rotation curve $v_\phi$  of a gaseous component   because
  the  gas rotation  does not lag $v_c$\ as significantly as stars.
  This assumption allowed \citet{ger97}, \citet{ger00}, \citet{sha03},  \citet{cia04}, \citet{ger12},
  and \citet{dms4} to derive $\frac{\sigma_\phi}{\sigma_R}$\ beforehand, then find $\sigma_\phi$, $\sigma_R$\ and $\sigma_z$\ using the line-of-sight dispersions and the equation of the asymmetric drift, to finally deduce {$\sigma_z \over \sigma_R $}.
  Therefore, a second  set of kinematical data does not involve \textsc{CALIFA}, and instead uses Gassendi \mbox{H$\alpha$}\ survey of SPirals  (\ghasp), a high-resolution Fabry-Perot interferometry survey of \mbox{H$\alpha$}\ gas velocity fields and rotation curves
  of 203 nearby disk galaxies \citep{epi08a,epi08b}.
  The \ghasp\ sample presents a couple of advantages.
   First, it has negligible overlap with \textsc{CALIFA}. This implies that it can be used as an independent consistency check in the analysis.
   Then, its angular and spectral resolution is higher than \textsc{CALIFA}.
   As  the slope of $v_\phi$  is  the key factor of  Eq.~\ref{eq:betaea}, the better the resolution, the less biased the analysis of $\beta_{\rm EA}$.
   This is the reason why no attempt to derive gas rotation curves of the present \textsc{CALIFA}\ sample was performed. }

   The \ghasp\ sample   contains all types of disk morphology over a
  large  range of magnitude and   rotation velocity.    A  selection was made to keep only the
  \ghasp\  targets with available $R_c$ surface photometry from \citet{bar15}.
  {The $R_c$ magnitudes of \ghasp\  can be used as good proxies of the SDSS $r$ magnitudes,
    with a difference between the two photometric systems within $\pm 0.2$ magnitude only, on average \citep{bar15}. }
   A three-parameter velocity model was fitted to the \ghasp\ rotation curves to avoid sudden ring-to-ring change of velocity slope
   inherent to the high-resolution Fabry-Perot data. The model is the Einasto velocity profile presented in \citet{che11}.
   The disk scalelengths of  \ghasp\ are given in \citet{bar15}.
  If no scalelength is provided in \citet{bar15}, then it was deduced from the galaxy effective radius by $h=R_e/1.7$.
    An example of rotation curve and epicycle anisotropy profile  is shown in Fig.~\ref{fig:exghasp} with the galaxy UGC3809.
    The selection led to a total of 128 galaxies with $\beta_{\rm EA}$\ at $R=h$, without objects in common with the \textsc{CALIFA}\ sample.

  It is important to note that in the considered range of magnitude, the fraction of galaxies fainter than $M_r=-20.5$    is larger in \ghasp\
  than in \textsc{CALIFA}, and the fraction of galaxies brighter than $M_r=-22.1$  is larger in \textsc{CALIFA}\ than in \ghasp.
  It is indeed more difficult for \ghasp\ to detect \mbox{H$\alpha$}\ emission at high stellar mass and more difficult
   for \textsc{CALIFA}\ to detect absorption lines from colder (lower dispersion) stellar disks. This has no impact on the result, however.

 \begin{figure}[th]
 \begin{center}
    \includegraphics[width=\columnwidth]{figeps/rcghasp-ugc3809.eps}
  \caption{\mbox{H$\alpha$}\ rotation curve ($v_\phi$, open symbols and solid line) and the epicycle anisotropy profile ($\beta_{\rm EA}$,
  dotted line) of the galaxy UGC3809.
  The \mbox{H$\alpha$}\ rotation curve is from the \ghasp\ survey \citep{epi08a, epi08b}. The solid line
  indicates the Einasto model of the rotation velocity. The $\beta_{\rm EA}$\ profile is deduced from the rotation model using Eq.~\ref{eq:betaea}.
  The filled circles represent  $\beta_{\rm EA}$\ at $R=h$.}
 \label{fig:exghasp}
 \end{center}
 \end{figure}

   \begin{figure*}[th]
 \begin{center}
   \includegraphics[width=\textwidth]{figeps/fig-histanis.eps}
   \caption{Comparisons of stellar anisotropy $\beta_\phi$\ and epicycle anisotropy $\beta_{\rm EA}$. All panels show normalized distributions in \%.
   The bottom right panel compares the stellar anisotropy from \textsc{CALIFA}\ with the epicycle value derived from \mbox{H$\alpha$}\ rotation curves of the \ghasp\ sample of \citet{epi08a,epi08b},
   while all other panels compare the stellar anisotropy from \textsc{CALIFA}\ with the epicycle value derived from \textsc{CALIFA}\ circular velocity curves of \citet{kal17}.
   The top left graph is the  total distribution of  differences  $\Delta \beta_\phi=\beta_\phi-\beta_{\rm EA}$ for the 68 \textsc{CALIFA}\ galaxies with common $\beta_\phi$\ and $\beta_{\rm EA}$.
   Blue shaded histograms are those of the stellar anisotropy, and   red histograms those of the epicycle anisotropy. }
 \label{fig:histcompapex}
 \end{center}
 \end{figure*}

  \begin{figure}[h]
 \begin{center}
  \includegraphics[width=9cm]{figeps/prof-diffanisobsapex-0218.eps}
   \caption{{Radial profiles of  difference between the stellar anisotropy $\beta_\phi$\ and the epicycle anisotropy $\beta_{\rm EA}$\ ($=\Delta \beta_\phi$).
   The solid line indicates $\Delta \beta_\phi$ for the Milky Way, as derived from Gaia DR2 data published in \citet{kat18}. The location of the Sun is indicated by a triangle.}}
 \label{fig:diffanis}
 \end{center}
 \end{figure}

  {The normalized distribution of  residuals $\Delta \beta_\phi$ is shown in the top left panel of Fig.~\ref{fig:histcompapex}.
  This figure also presents the normalized distributions of $\beta_\phi$\ and $\beta_{\rm EA}$\ at  $R/h=0.5,1,2$ and $R=R_e$ ($R=h$ for \ghasp).   }

  {The distribution of epicycle anisotropy for the \ghasp\ galaxies
  is very comparable to that of \textsc{CALIFA}. A difference of $\sim 0.1$ only is observed between the two samples (\ghasp\ values tend to be smaller). This indicates a good consistency between the two datasets
  of velocity curves. Ionized gas rotation curves tend to be only slightly steeper than the circular velocity curves of \citet{kal17} at the considered radius, perhaps highlighting a small asymmetric drift in the gaseous component. }

 More interestingly,   significant discrepancies between stellar and epicycle anisotropies are evidenced.  $\Delta_{\beta_\phi}$ that are consistent with the null value within the quoted uncertainty of 0.15
   represent only 1/3 of all values.  The residuals are mainly negative. The concentration of epicyclic approximation around $\sim 0.3-0.5$  makes the theory overestimate the number of galaxies with
   intermediate isotropic-to-radial and radially biased
  orbits, up to a factor of 2-6, depending on the considered radius. { The variation of
  $\Delta \beta_\phi$ as a function of radius for the 68 galaxies in common with \citet{kal17}  is shown in Fig.~\ref{fig:diffanis}. It is seen that, on average,
  larger anisotropy residuals occur at low radius,
  as caused by the larger occurrence of isotropic orbits in inner disk regions (Fig.~\ref{fig:anisallpoints}); smaller residuals occur at larger radii, although with
  a significant scatter.}

  {I also measured the epicycle anisotropy of the Milky Way between $R=4$ and $R=13$ kpc using a third degree polynomial fit of the
  azimuthal velocity curve of stars within $|z| = 200$ pc of the disk measured
  in \citet{kat18} from Gaia DR2 data, as well as between $R=4$ and $R=8$ kpc using a Einasto model of the \mbox{H{\sc i}}\ rotation curve measured in \citet{che15}.
  I found Galactic  $\beta_{\rm EA}$ between 0.4 and 0.6, which is thus different from the real Galactic anisotropy profile of Fig.~\ref{fig:anisallpoints} by
  $\Delta \beta_\phi=0.1$ to $0.25$ inside $R \sim 7$ kpc (solid line in Fig.~\ref{fig:diffanis}). Therefore, Eq.~\ref{eq:betaea}
  of the epicyclic approximation does not apply completely to the inner Galactic kinematics either. In the solar neighborhood,
  the epicycle anisotropy matches well the stellar value (triangle symbol in Fig.~\ref{fig:diffanis}).}

  {A direct consequence of these results is the significant possibility that the azimuthal anisotropy chosen by
  \citet{ger97}, \citet{ger00}, \citet{sha03}, \citet{cia04}, \citet{dms4}, and \citet{ger12} is inappropriate,
  since these authors all assumed $\beta_\phi$\ $=$ $\beta_{\rm EA}$.  Since the impact of this assumption  is negative  on
  the estimation of the vertical-to-radial dispersion ratio (see Appendix~\ref{sec:easimu}),
  I did not attempt to derive $\beta_z$\ at fixed $\beta_{\rm EA}$. }

  {The epicycle anisotropy is shown as a function of absolute magnitude in Fig.~\ref{fig:anismagrd} at $R=h/2$ and $R=h$.
  The two values are correlated at both radii.
  The epicycle relations can be modeled by the linear equations }

   \begin{equation}
   \begin{split}
    \beta_{\rm EA} = -0.06 (\pm 0.02) M_r - 0.9 (\pm 0.4)\, \rm \, (\textsc{CALIFA}),\\
                     -0.04 (\pm 0.01) M_r - 0.6 (\pm 0.1)\, \rm \, (\ghasp),
   \end{split}
   \end{equation}
  at $R=h/2$ and
   \begin{equation}
   \begin{split}
     \beta_{\rm EA} = -0.03 (\pm 0.02) M_r - 0.2 (\pm 0.4)\, \rm \, (\textsc{CALIFA}),\\
                      -0.04 (\pm 0.01) M_r - 0.4 (\pm 0.1)\, \rm \, (\ghasp),
    \end{split}
   \end{equation}
  at $R=h$,  again
   considering $M_r \sim M_R$. This parametrization is shown as dashed {and dotted} curves in Fig.~\ref{fig:anismagrd}.
   {The slopes of the  \textsc{CALIFA}\ and \ghasp\ relationships are sensitively similar. The zero points are different, but that difference is not significant
   as it includes the systematic $\sim 0.1$ difference between the two samples mentioned above  and is within the errors. }

  {It is important to note that if the epicycle approximation was able to produce correct anisotropies, it would automatically imply an absolute magnitude-anisotropy relation.
   Even though this correlation actually has different parameters, the correlation observed between stellar anisotropy and magnitude would thus be supported by theoretical expectations.
  In reality, the epicycle relationship is shallower than the magnitude-anisotropy relation at $R=h/2$.
  This also suggests that the failed detection of a clear correlation at $R=h$ may be fortuitous. A larger sample would certainly clarify that point. }

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

    The  advent of large IFS surveys such as \textsc{CALIFA}\ \citep{califasanchez12}, \textsc{SAMI}\ \citep{samibryant15},
    and MaNGA\ \citep{bun15}  is an opportunity to understand better the
  dynamics and evolution of stellar disks. With such data, it has been shown it is possible to measure the {velocity anisotropy} in the disk plane from a simple geometric and kinematic model
  of dispersion fields, as for velocity fields, and with minimum assumptions.
  This is a major improvement with respect to early slit measurements, although not
  enough to get strong constraints on the vertical-to-radial axis ratio of the ellipsoid. A
  significant range of vertical-to-radial dispersion ratio can indeed be invoked to get the value of the azimuthal anisotropy parameter
  (Sect.~\ref{sec:globalproperties}). {This does not necessarily imply that a
  link does not exist between     $\beta_\phi$\ and $\beta_z$\ within the sample, however.}

  { The best way to determine unambiguously all parameters remains the observations of face-on disks  (e.g., the \dms\ survey) and the direct measurements
   of vertical dispersion in a wide variety of luminosities and morphologies,} and then fix $\sigma_z$\ in Eq.~\ref{eq:sigmalos}
  while fitting the dispersion maps of the present \textsc{CALIFA}\ subsample. This type of analysis will be investigated
  in future works. It is important to note that this should  work well only if
  clear relation(s) between $\sigma_z$\ and fundamental galaxy properties can be identified.

  \subsection{Relation between the stellar mass and shape of stellar orbits}

    Schwarzschild orbit modeling  is another possible way to constrain the orbital structure of stellar triaxial systems  \citep{sch79}. This method was used very recently to model
   the whole \textsc{CALIFA}\ sample, i.e.,  also including ellipticals and lenticulars  \citep{zhu17,zhu18}.
  These authors found a broad range of types of orbits  inside $R_e$ at a given stellar mass, but noticed a
  trend in the links between the stellar mass and shape of orbits.
  Counter-rotating orbits represent $\lesssim 10\%$
  of the galaxy populations; warm orbits dominate the galaxy luminosity fraction at a  level of 40\% for $\rm M_\star \lesssim 10^{11}$ \rm M$_\odot$;  the fraction of hot orbits increases
     from  $2\, 10^{10}$ \rm M$_\odot$\ and dominates at large mass,
    while that of colder orbits contribute to 10-30\%, being more important around $\rm M_\star = 10^{10}$ \rm M$_\odot$.
    These authors defined cold orbits by near circular orbits; warm orbits by those with substantive angular momentum, but harboring more extensive radial motions;
    and hot orbits by those with negligible angular momentum.

 {Making the comparison with their analysis is not straightforward as they measured a circularity parameter, which differs from $\beta_\phi$. Moreover,
 the present methodology is not designed to differentiate prograde from retrograde orbits. To force the comparison with \citet{zhu18},  I used the stellar mass given in
 \citet{califalcon17} to recast the magnitude-anisotropy relation into a mass-anisotropy relation (Fig.~\ref{fig:anisvsmass}),
 and measure the fractions of three broader families of orbits in the plane,  i.e,
 tangential ($\beta_\phi < -0.25$), isotropic ($|\beta_\phi| \le 0.25$) and radial
 ($\beta_\phi > 0.25$) orbits, in bins of 0.5 dex of stellar mass.  For each galaxy, the global anisotropy is chosen as the median value
 of the radial profile, {and the associated error is the median of the anisotropy uncertainties}.
 With those definitions, it is shown that the fraction of tangential orbits is unsurprisingly negligible
 and the fraction of isotropic orbits decreases with the stellar mass to the detriment of radial orbits, which start dominating the sample at
 $\rm \log (M_\star/M_\odot) \sim 10.5$.  Therefore, the trends measured by \citet{zhu18} are qualitatively present within the three categories of orbits if a rough parallel is made between
 warm with  isotropic orbits, hot with radial orbits and cold with tangential orbits, and with some obvious overlap between  warm with
 radial orbits and cold with isotropic orbits. These results indicate the important role of galaxy evolution in shaping the stellar orbits in  the plane.
  As the morphology changes with time and as the mass grows and is redistributed through various dynamical effects, the tangential and isotropic orbits in disks turn progressively radial.}

  {The mass-anisotropy correlation of Fig.~\ref{fig:anisvsmass} can be modeled by the following linear law:}
     \begin{equation}
      \beta_\phi = 0.26 (\pm 0.03) \log (M_\star/M_\odot) - 2.54 (\pm 0.30)
       \label{eq:massbeta}
   \end{equation}
 This model  is shown as a solid line in Fig.~\ref{fig:anisvsmass}.  Appendix~\ref{sec:mcmccornerplots} gives posterior distributions
of the MCMC fits,   again performed with a nuisance parameter controlling the scatter perpendicular
to the law.
 \begin{figure}[t]
 \begin{center}
    \includegraphics[width=\columnwidth]{figeps/fig-betastelmass.eps}
  \caption{Stellar mass-azimuthal anisotropy correlation. The top panel shows the occurrence of galaxies
  per bin of stellar mass with isotropic, radial and tangential orbits (circle, triangle, and squared symbols, respectively),
  normalized to the total number of galaxies per 0.5-dex bin of stellar mass.  The mass unit is \rm M$_\odot$. The starred symbol is for the Milky Way.
  The solid line is the most likely linear model of the mass-anisotropy relation given by Eq.\ref{eq:massbeta}.}
 \label{fig:anisvsmass}
 \end{center}
 \end{figure}

 {During the refereeing step of this article, \citet{pin18} published a
 detailed analysis of the impact of many dynamical processes on {$\sigma_z \over \sigma_R $}\ from idealized and cosmological simulations. They found that the vertical-to-radial axis of the velocity
 ellipsoid can be produced by a multitude of disk heating mechanisms (bars, mergers, and spiral arms). They also analyzed a compilation of {$\sigma_z \over \sigma_R $}\
 from photometry and spectroscopy-based observations and came to the conclusion that no correlation exists between the morphological type and vertical anisotropy parameter,
 in contrast with claims of \citet{ger12}.
 The study of a range of simulated galaxy mass larger than that of \citet{pin18} would be  useful to investigate whether
 the new magnitude and mass-anisotropy correlations shown in this work are present in cosmological numerical models as well. If present, such simulations could
 likely identify which of the secular and hierarchical mechanisms participates the most in the building of that relation.}

 {Finally, the location of the Milky Way in the stellar mass-anisotropy diagram matches perfectly  within the observed correlation. The
 mass of the Milky Way takes into account the stellar masses of the bulge, thin and superthin bars,
 thick and thin disks and outer halo, as given in \citet{bla16}. The median value is that of the
 Galactic profile shown in Fig.~\ref{fig:anisallpoints}.}

 \subsection{Epicycle anisotropy versus stellar azimuthal anisotropy}

 The difference between the  anisotropy parameters measured from stellar dispersions and predicted from the epicycle approximation
 can be seen as a  problem of slope of rotation curves  with respect to the measured anisotropies: there are too many galaxies harboring {an  almost flat velocity curve}.
  This problem is manyfold.

  {First, the rise of the galaxy rotation curves is not steep enough
    to explain the occurrence of isotropic and more tangential orbits. In the context of the epicycle approximation, isotropy can only be obtained when
    the velocity is linearly dependent on radius. As for tangential motions, $\beta_\phi = -0.5$ can only be obtained
 with $v_c \propto R^2$, assuming a spherical distribution of total dark+luminous matter.
 Besides the fact that such latter velocity shape has never been observed in galaxies, it is that of a mass distribution that increases as $R^4$ (the density linearly increases with radius),
 which is not physical.
 In  presence of almost flat velocity curves, the nominal equation of $\beta_{\rm EA}$\ thus excludes  the tangential orbits for realistic mass distributions, and,
 by extension, the circular orbits ($\beta_\phi \rightarrow -\infty$). This may seem paradoxical because the epicyclic approximation is supposed to
 explain  motions of stars very weakly perturbed, almost  circular.  }

   { Then, there are not enough steeply declining rotation curves to explain
    the occurrence of the most radial orbits ($\beta_\phi > 0.5$). It is indeed very rare to find declining curves, particularly at the radii probed here,
    knowing that the maximum of rotation curves
    are usually observed around $R=2.2h$ where the amplitude of the contribution of an exponential stellar disk is maximum \citep{fre70}. }

     {I exclude the possibility of incorrect derived anisotropies for the stellar data as origin of the discrepancy. The analysis of a numerical simulation shows that
    the azimuthal anisotropy inferred from fits of Eq.~\ref{eq:sigmalos}  is not strongly deviant from the simulated values. The
    systematic offset  is $\sim 0.1$ at most and occurs only at low inclination, and the typical uncertainty
    is 0.15 (see Appendix~\ref{sec:validation}). In other words, the level of inaccuracy of the proposed methodology is not enough to confuse
    orbits that are genuinely radial with more isotropic and tangential orbits.  }

 {It is not possible to identify the origin of the discrepancy with the current analysis.  More observations  of cold  stellar disks are necessary
 to study this problem, particularly at low disk stellar mass  where the difference is stronger. Similarly,
 other observations  probing outer regions  would be helpful to verify whether the problem still holds
 where the disks are colder and the rotation curves flatter. Moreover, numerical simulations would be helpful to assess the domain of suitability of the
 theory with realistic stellar orbits. That would imply studying both the simulated dynamics of low mass, unevolved disks, and that
 of massive, evolved disks, i.e., those which have been dynamically heated by a large  diversity of disturbing mechanisms  that the theory cannot address (tidal encounters, mergers, accretion of intergalactic gas,
 spiral arms, bars, lopsidedness, interactions between Giant Molecular Clouds, etc). The test of Eq.~\ref{eq:betaea} with the N-body simulation of a barred spiral disk
 in Apps.~\ref{sec:validation} and~\ref{sec:easimu} is a first step toward these objectives.
 {Additionally, \citet{cud94} proposed a modified version of  Eq.~\ref{eq:betaea},  but it has never been tested with extragalactic data. This possibility shall be explored in future works. }

\section{Summary}
\label{sec:summary}
In this article, I have derived the {azimuthal anisotropy of velocity dispersions in the plane of } stellar disks
by means of a simple kinematic and geometric model fitted to dispersion maps from the IFS \textsc{CALIFA}\ survey,
{assuming fixed vertical-to-radial dispersion ratios. The testing of the validity of the methodology applied to a N-body numerical simulation of
 a Milky Way-like disk gave full satisfaction. It showed the negligible impact of systematic inclination, angular resolution, and noise effects, which do not prevent
 the algorithm from finding different families of simulated stellar orbits.}

The main conclusions from this work are as follows:
\begin{itemize}

 \item Stellar disks exhibit a broad variety of tangential, isotropic, and radial orbits, yet isotropic to radially biased orbits are more frequent.

 \item Globally, stellar orbits in the plane tend to be  more and more
radial with radius. This figure nonetheless depends on the morphology and absolute magnitude of the galaxies.

 \item Evidence for an absolute magnitude-, or stellar mass-, azimuthal anisotropy correlation is presented. Disks
 with lower stellar mass exhibit more tangential and isotropic orbits, while more massive stellar disks have more radial orbits. This unsurprisingly
 suggests the important role of galaxy evolution in shaping the orbital structure in the disks.

 \item A discrepancy with expectations from the epicyclic approximation is evidenced. The epicycle  azimuthal anisotropy inferred from the shape
 of circular  velocity curves  is observed in a narrow range of values
 that is not representative of the variety of stellar orbits. This is explained by
 the large occurrence of nearly flat velocity curves that cannot reproduce more isotropic and tangential  stellar orbits and some of the most radial orbits.
 A magnitude-epicycle azimuthal anisotropy is also evidenced, but is significantly shallower than the magnitude-anisotropy
 relationship of stellar disks. Consequently, extreme caution must be taken when using
 both azimuthal and vertical anisotropy parameters
 derived in the framework of the epicyclic approximation. This study thus casts doubts on the validity of many anisotropies
 found in the works that were based on that theory.

\end{itemize}

 In the next decade, the huge quantity of absorption lines data gathered for
 nearby  disks will impact the knowledge of stellar disk dynamics and evolution,
 perhaps at the same extent as it did for early-type galaxies \citep{ems11,cap11,cap13}.
 The modeling of   dispersion fields of disks such as {that proposed here, or elsewhere but with different methodologies}
 may be first steps toward these objectives. It appears also fundamental in the future to measure the  stellar disk
 kinematics at higher spectral resolution and sampling
 to extend the discovered  trends to outer, colder regions,
 and to the large population of low stellar mass disks. {Yet, this latter point still represents a real challenge for observations.}

\begin{acknowledgements}
This research is supported by the Comit\'e Mixto ESO-Chile and the DGI at University of Antofagasta. I am very grateful
to Fran\c{c}oise Combes for many fruitful discussions, and to the referee for a critical review and constructive suggestions.
I am grateful to David Katz who provided the rotation curve and velocity dispersions
of the Milky Way from Gaia Data Release 2.
This study makes use of data from
the Calar Alto Legacy Integral Field Area (\textsc{CALIFA}) survey (http://califa.caha.es),
whose observations have been collected at the Centro Astron\'imico Hispano Alem\'an (CAHA) at Calar Alto,
operated jointly by the Max-Planck-Institut f\"ur Astronomie and the Instituto de Astrof\'isica de Andaluc\'ia (CSIC).
This work has made use of data from the European Space Agency (ESA) mission
 {\it Gaia} (\url{https://www.cosmos.esa.int/gaia}), processed by the {\it Gaia}
 Data Processing and Analysis Consortium (DPAC, \url{https://www.cosmos.esa.int/web/gaia/dpac/consortium}). Funding for the DPAC
has been provided by national institutions, in particular the institutions participating in the {\it Gaia} Multilateral Agreement.
It also makes use of \ghasp, whose data are available on the Fabry Perot database (\url{http://cesam.lam.fr/fabryperot}),
operated at CeSAM/LAM, Marseille, France. The Markov chain Monte Carlo hammer \textsc{emcee} is available at \url{http://dfm.io/emcee/current} and the MPFIT minimization library at \url{https://cow.physics.wisc.edu/~craigm/idl}.
\end{acknowledgements}

\bibliographystyle{aa}

redpajama_set_name: RedPajamaArXiv


She's the Icelandic queen of quirky, known for her outrageous outfits, which can only be described as unforgettable – remember the swan dress everyone? But what is easy to forget is just how brilliantly talented Bjork actually is.
Dressed for this occasion in a dress I can only describe as being covered in molluscs, a huge red afro, bioluminescent blue stockings and sparkly wedge heel boots), the singer bops around the stage as she belts out her unique band of songs from her Biophilia album. Currently showing numerous times a day at the Australian Centre for Moving Images (ACMI ), this viewing of the final Biophilia concert at London's Alexandra Palace is a showcase of Bjork at her best.
The show played six-week residencies in eight cities over a period of three years and was highly acclaimed by the critics. Backed by a choir of some 20 odd vocally gifted singers from her homeland, 'Director of Knobs' Matt Robertson and percussionist extraordinaire and player of 'drums and stuff' Manu Delago, not only does she sing, uttering a child like 'thank you' after each song, but Bjork has been heavily involved in the production of the show and album too.
More of a concept album, and partly recorded on a tablet computer as well as containing an iPad app suite of interactive music games, it explores the relationship between music, technology and nature. And it's not only Bjork taking this exploration on board. Reykjavik is currently running a Biophilia Educational Program, which is designed to do just that – its concept being to provide an alternative way for children to learn and explore their creativity, by merging together science and music in a hands-on approach. The slogan "Creativity as a Learning Tool" was based upon Bjork's Biophilia concept. The program was launched in collaboration with the Manchester International Festival in 2011 and has been developed further by Bjork in collaboration with the University of Iceland and Reykjavik City Schools. Interestingly, is it particularly useful in teaching children suffering from ADHD, dyslexia and other learning disabilities.
Leaving the stage with 'thank you for tonight!', it's not long before she is ushered back to the stage for not one but three encore performances, including a chant-like warning to Greenland to declare independence.
Thank you Bjork for reminding me of the magic that is you.


text:
Q: Add Multiple Members to Google Calendar I have to invite multiple members to the google calendar while creating the event and later on when event is created then he can alter the invited member from google calendar .
Here is the code to insert the multiple invitee : but can't able to insert the attendee. but i am able to insert the remaining data.
Intent intent = new Intent(Intent.ACTION_EDIT);
                                    intent.setType("vnd.android.cursor.item/event");
                                    ArrayList<String> al = new ArrayList<String>();
                                    al.add("ashis@gmail.com");
                                    al.add("sonam@gmail.com");
                                    intent.putStringArrayListExtra(CalendarContract.Attendees.ATTENDEE_EMAIL,al);
intent.putExtra(CalendarContract.Events.EVENT_LOCATION, locationName);

Update google Calendar :  Here i am able to update the value of the endTime but attendee is not been updated .
public void updateEvent(long eventID,long endTime,String calendarEventID){
        Intent intent = new Intent(Intent.ACTION_VIEW);
        intent.setData(Uri.parse("content://com.android.calendar/events/" + calendarEventID));
        ContentResolver cr = getActivity().getContentResolver();
        Uri eventUri = ContentUris.withAppendedId(CalendarContract.Events.CONTENT_URI, eventID);
        ContentValues event = new ContentValues();
        event.put(CalendarContract.Events.DTEND, endTime);
        event.put(CalendarContract.Attendees.ATTENDEE_EMAIL, "sunil@gmail.com");
        cr.update(eventUri, event, null, null);
        intent.setFlags(Intent.FLAG_ACTIVITY_NEW_TASK);
        getActivity().startActivity(intent);
    }

A: According to the Android docs in Adding Attendees, you ought to use put instead of like:
Here is an example that adds a single attendee to an event. Note that the EVENT_ID is required:
long eventID = 202;
...
ContentResolver cr = getContentResolver();
ContentValues values = new ContentValues();
values.put(Attendees.ATTENDEE_NAME, "Trevor");
values.put(Attendees.ATTENDEE_EMAIL, "trevor@example.com");
values.put(Attendees.ATTENDEE_RELATIONSHIP, Attendees.RELATIONSHIP_ATTENDEE);
values.put(Attendees.ATTENDEE_TYPE, Attendees.TYPE_OPTIONAL);
values.put(Attendees.ATTENDEE_STATUS, Attendees.ATTENDEE_STATUS_INVITED);
values.put(Attendees.EVENT_ID, eventID);
    Uri uri = cr.insert(Attendees.CONTENT_URI, values

);

redpajama_set_name: RedPajamaStackExchange


The Julia Roberts Tom Hanks W Magazine cover shoot showcases perhaps two of the biggest superstars in the world. Although the duo is known for their happy-go-lucky personalities, Julia Roberts and Tom Hanks strike serious, sophisticated and incredibly glamorous poses for the magazine's June 2011 issue.
In the accompanying Julia Roberts Tom Hanks W Magazine article, they address everything from Hank's directing skills to Roberts' interest in directing. Candid, playful and full of personality, this editorial is certainly a treat for longtime Julia Roberts and Tom Hanks fans.


text:
O Parque do Zizo é uma área de preservação ambiental privada, localizada entre os município de São Miguel Arcanjo e Tapiraí, na região de Sorocaba, a cerca de 200 quilômetros da capital paulista. Situado na Serra de Paranapiacaba, em uma das áreas remanescentes da Mata Atlântica mais bem preservada do Brasil, o Parque do Zizo é parte do entorno do Parque Estadual Carlos Botelho, que em conjunto abriga e protege várias espécies da fauna e da flora ameaçados de extinção.

Histórico
Inaugurado em 1998, o Parque do Zizo fruto de indenização paga para a família do militante da ALN Luiz Fogaça Balboni, vulgo Zizo ou "Matias", morto numa troca de tiros em 1969 durante um assalto a bancos na cidade de São Paulo. Preservar a natureza foi a maneira que familiares e amigos do Zizo encontraram para homenagear Luiz Fogaça Balboni.

Natureza local
O Parque do Zizo possui uma área de 400 hectares e está desenvolvendo projetos de Pesquisa Científica e Educação Ambiental, que inclui um programa de visitas monitoradas pelas trilhas que estão sendo implantadas, nos locais de acesso ao público.

Caminhando pela mata primária, você encontrará espécimes vegetais em risco, como a bromélia carijó e o palmito jussara, base da cadeia alimentar de aves e animais silvestres, que vem sofrendo com a ação predatória dos palmiteiros. E com um pouco mais de sorte poderá se deparar com um grupo de mono-carvoeiros ou muriquis - os maiores primatas das Américas, bugios, antas, e até mesmo jaguatiricas e onças-pardas, todos animais em via de extinção.

Administração
O Projeto é administrado pela Associação Parque do Zizo (APAZ), uma ONG criada em 1998 com o objetivo de dar sustentação aos projetos ambientais do Parque do Zizo. Responsável direta pela captação de recursos e pela interface com a comunidade, participa ativamente de movimentos em defesa do meio ambiente e na formação de uma consciência ecológica na região.

Ligações externas

Áreas verdes de São Miguel Arcanjo (São Paulo)

redpajama_set_name: RedPajamaWikipedia


State Representative Dave Williams on Denver's "Sanctuary City" situation.
State Senator Owen Hill on switchblade legislation.
Gary DeFrange talks about his time at Winter Park and the future as he gets ready to retire.


We have been hosting educational visits to the farm for several years.
Most visits are from local primary schools, but we also host visits for gardening clubs and other adult groups, as well as for older children.
Michelle is a qualified teacher, and is also CEVAS qualified. A Teacher's Information Pack is available (see link below).
For primary school children, we can tailor a visit to complement the current syllabus, for example healthy living, how plants grow, caring for the environment, using our senses.
A typical visit could last 2-3 hours, and include a range of activities - the orchard and market garden provide a safe, open environment for outdoor learning. We also have an indoor space for activities like seed sowing, and if the weather is unfavourable.
For further information, please contact Michelle (see contact page for details).


text:
Christiane Gredigk (* 15. Juli 1982) ist eine frühere deutsche Crosslauf-Sommerbiathletin.

Christiane Gredigk nahm zunächst an den Junioren-Wettbewerben der Sommerbiathlon-Weltmeisterschaften 2000 in Chanty-Mansijsk teil und erreichte dort die Plätze neun im Sprint und zehn in der Verfolgung. Mit Claudia Welscher, Dörte Krüger und Stefanie Glöckner belegte sie danach Rang vier im Staffelrennen der Frauen.

Weblinks

Biathlet (Deutschland)
Deutscher
Geboren 1982
Frau


Hello, everyone, and welcome back to your regularly scheduled Fur Face Friday. Last week, we had a special memorial post for all the darling pets we so sorely miss, and who will always be in our hearts. Now we're going to celebrate the ones who are here to heal our hearts every day.
First up, yesterdaysjam found Nell being a light in the darkness.
Edie Beale's Littledude performed his civic duty in being cute.
...while kristinbytes' Bindi suggested three heads are better than one.
Kiltedpadre's Lola reminded us that comfort is found in familiarity.
booktart's dog showed us what a big beautiful world it is.
simon-on-the-river's Tiddly reminded us to get plenty of rest.
Bertolt's Harpur and Beckett let love conquer all (after conquering each other, of course).
Hammergirl found the charming benefits of horsing around.
bio's kitten emphasized the importance of sharing relaxing activities.
...and last but certainly not least, Chuckles' Apple did her best to help us all smile at the hidden treasures in our lives.
That's it for this week, all. Our pets really are a blessing in our lives and they can hold us together even when the world is falling apart. So please share your befloofed, befinned and/or befeathered - and most importantly beloved friends!


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redpajama_set_name: RedPajamaCommonCrawl


Things people took on 2018 SLMM- and things they wished they had taken!
We asked 2018 competitors to let us know if there was something , other than Mandatory Kit that was particularly useful, or something they didn't take but wish they had taken.The list turned out to be a lot longer than expected!
Buff to wet and put round neck for cooling.
Inflatable pillow. Hardly any weight and a better night's sleep.
A gas stove extended foot, so much safer than just the canister on the ground.
A collapsible cup for scooping water out of streams whilst on the move.
Phone for decent pictures – pleased you now allow this in the rules.
A meat and potato pie for Sunday breakfast.


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Sometimes, highly energetic particles are produced by our Sun, and they get accelerated by the magnetic reconnection in solar flares or by coronal mass ejections, also known as shock waves. Such blasts of plasma and electromagnetic radiation from the Sun have the potential to seriously impact life on Earth, so it's important for us to understand them as much as we can.
In this case it was a solar proton event or SPE, a particularly intense type of solar storm where the released particles include high-energy protons.
These phenomena are called solar proton events (SPEs), and this threatens modern society in terms of navigation and communication systems, commercial aircraft operations, and space technologies.
"This was a high level of particle radiation, ten times more than has been observed in the last 70 years", Raimund Muscheler, of Lund University in Sweden, said. "If..."
Evidence of solar storms hitting Earth in the past can be found in ice cores-samples of ice that formed over the past 100,000 years. This sets off reactions that raise the production rate of radionuclides - unstable atoms with excess nuclear energy, which include carbon-14, beryllium-10, and chlorine-36.
We've seen SPEs in the past, affecting Canada in 1989 and Sweden in 2003. 774-775. The latter is the largest solar eruption known to date.
A strong wave of high-energy particles should be able to destroy most of the electronic devices which are now in use, including primary navigation and communication systems. "These produce the geomagnetic storms".
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New research indicates that solar storms can be even more powerful than measurements have shown so far via direct observations.
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You can choose your friends, but you can't choose your unbelievably distant family deciding to ennoble you, apparently.
Description: Malcolm has that 'handsomeness of indeterminate age' about him, with a still somewhat boyish grin, but crinkled laugh lines around his eyes that go with it. His brows will no doubt be wild and bushy when he is an old man, but he is not an old man, so they are strong and dark, and sketch out his exaggerated moods with perfect clarity. His expressive playfulness is the source of his charm. Otherwise unremarkable, and a little rough around the edges, he's a tall man, but not too tall; strong, but not obnoxiously so. He's clearly not a man that spends his time lifting heavy things to sculpt overt muscles.
Personality: Malcolm is perfectly suited for being a duke, if one ignores personality, training, inclination, background, motivation and goals, but aside from that, he's perfectly suited. Being told this was his new DUTY and OBLIGATION might make something in him roll over and die in complete exasperated surrender, but at his heart, he really does try to help people, even if a hefty dose of sarcasm helps him deal with what life gives him without dying of alcoholic liver failure.
Background: Malcolm is reasonably sure that his father was incapable of forming a sentence that didn't contain 'honor', 'duty', or 'responsibility'. Bentley Shepherd was exhausting that way. Getting up in the morning would be greeted with, 'it's about time you've risen, now to see to your duties' or 'our family's honor depends on how well we see to our responsibilities'. If ever there was a man that was born trying to hard to redeem his family's line for shame from three hundred years ago during the Crownbreaker Wars, it was Malcolm's father. And it wasn't as if another sometimes spear carrying soldier in the duke's army and other times farmer really had much responsibilities! But there was no telling dear old dad that. He could be asking about the chickens and it would be, "if you live life honorably, everything will fall into place. Now collect the eggs." WHAT DID THAT EVEN MEAN? How does that even follow? This, dad, is why mother left you to become a pirate.
So it came as no surprise to anyone that knew Malcolm, or talked to his father for more than three minutes, that Malcolm and his sister Bonnie left home immediately at eighteen to make their fortune in the wide 'and oft dishonorable' world, away from a parent who seemed to have taken a secret vow to never have a trace of humor or fun in his life. Malcolm immediately fell into sellswording for a living, and Bonnie became a 'naval acquisitions specialist' in the pattern of dear old mom, who apparently had made quite a name for herself at Port Defiance and around the Saffron Chain. Malcolm, unfortunately, discovered that for some reason it seemed like he just had the kind of face that screams to people, 'I have a problem. That fellow right there seems just the person to help me out with my personal tragedy, curse, adventure, expedition, or otherwise life threatening sojourn'. He has no idea why it happens. You don't just go up to a random person on the street and tell them how you need help because Little Timmy wandered into a Shardhaven or some shavs kidnapped your dog! But it led him to forming an adventuring company named the Valiant Effort with Bonnie and some friends, to at least make official the reason they would be wandering into extraordinarily regrettable situations.
Life was just approaching something close to relaxing if regularly life threatening when he received word that his father, the seemingly now knighted Sir Bentley Shepherd, had died. Very sad, exasperating old man or no. And that he had died saving Duke Gregor 'the Butcher of Graypeak' Shepherd, and had been serving for years as the House Sword. And that Duke Gregor, now succumbing to his own wounds, had made a deathbed decree re-ennobling Sir Bentley Shepherd 'to erase the stain of honor on that distant branch of House Shepherd', and effectively making Malcolm his heir, which for some mind boggling reasons his 9th cousins are actually okay with, despite Malcolm repeatedly offering it up. The letter written by his father that Malcolm received posthumously with this news read, "It is your duty to see to the restoration of the house honor, and live up to all of your responsibilities."
Oh no. It was the trifecta.
Adora Good taste in furniture. But he's not buying more when prompted. I don't like him.
Ajax An easy going Duke, promised work. He seems alright. I wouldn't mind workin' for him either.
Austen A rather talkative duke. He seems new to teh position, and anxious to redeem the name of his family. An honourable urge, I hope it works out well for him.
Beatrice The reluctant Duke. A simple man with an unbelieveable story. Common down to his excellent bone structure. Pleasantly candid.
Berenice Oh he does /try/, doesn't he? Darling.
Calandra He says he's not the Butcher Duke. He /says/. It's probably true. /Probably/.
Calarian Quite the character. I imagine the Duke will be injecting some life into House Grayson over the coming months.
Caspian I like this man! He seems to be craving adventure. I can understand his feelings. Maybe we can go on an adventure some day together?
Cedric The poor man needs help and is very wise indeed to readily and obediently take wise direction.
Cirroch For someone who is a Crownlander, he is quite good with snowballs!
Dariel A talkative, friendly duke who loves a drink and a joke.
Delilah A duke with the common touch, he dislikes paperwork, prefers rushing off into trouble, and high adventure shines in his eyes. I don't know that his coronet will ever wear him down, and I hope it won't.
Domonico A rough and ready Duke. Hopefully soon I will be able to demonstrate the advantages of regular sparring and training sessions.
Draven He didn't pay! The Hug Tax! It's okay! He seems nice! I like him lots! Maybe too serious! Too sly and serious!
Duarte The newly ennobled! Who is EVERY bit as charming as Lady Jennyva said he was. How fine!
Evaristo Duke Shepherd - and what a duke. Seems like the man you'd meet at a shady bar and that would drink you under the table and then helpfully carry you to your bed and pay your bill, and when you wake up day after all hungover and really, really tired, he'll be up at dawn climbing a mountain and come back before you even have breakfast, and speak really loudly and cheerfully at you... Ah, perhaps I should avoid drinking with this guy.
Fiora Going to give me a dog? We'll see if he's worth his word. If he does, maybe he's not so bad. If he doesn't. Well. Then.
Harlex Doesn't seem like a Duke. That's good. Amicable, too.
Iseulet One of those men that you can meet and tell he is good to his core. He laughs from his belly. I like that - I hope being a member of the Peerage doesn't steal that away from him. Keep smiling, Duke Shepherd!
Jeffeth I don't really know who he is. But I liked him. He didn't really know what to do with himself at a memorial. Some people would think that's bad, but I think that shows a good heart. So he probably has a good heart. Or I'm totally wrong and he's terrible. Let's hope the first!
Jennyva I'm confident he'll be a wonderful Duke. You can tell he's just a big softie.
Joscelin Rather joyous in the mantle of Duke, if also very new to it. Certain about some of his new role and learning about everything else. He has the makings of a great leader, in that he quite possibly could command without being demanding. A useful skill, that, one that he can hone into an impressive tool, like ... well, rather like a Shepherd, leading his people where they -want- to go, rather than forcing them somewhere they don't.
Kaia A friendly and talkative man; he seems nice!
Kenna I feeeeeellllll like he really doesn't want to be known as the butcher. Cuz that's understandable.
Lou Easily excitable, but very interested in exploration. New to his position, but much room for growth. I'm sure he'll do his family well.
Luca I'd heard there was a new Duke come to Arx and it took me a bit to meet him, but he seems like.. he's.. working on it? He's amiable, and I think that will carry him a long way in the places where he's not quite polished yet. I bet he'd be fun at dinner.
Miella If he hadn't been introduced as a Duke I would not have known. Not sure if that's a point in his favor or not.
Miranda Talking to Ribbons about her eyes... He has a dry wit I admire.
Orrin It is rare to see men of his station retain such a good-natured affect.
Pharamond Assuming the newest Duke doesn't get eaten alive I have a feeling I could come to enjoy knowing this man. He seems enthusiastic for his family.
Quenia New to his position, but not exactly in the same way I was. Still, it abrupt all the same. I couldn't help but give him a bit of advice I wish I had before taking things over. Hopefully he puts it to good use.
Reese He seems like a well spoken, charming and intelligent Duke. He seems to get things and has an alertness about him.
Sabella He seems like a man with a very creative mind who is not afraid to ask for something that he wants even if it is not on the menu! I can't wait to get to know him better! I love it when our vassals turn out to be imaginative go-getters!
Samuele Sometimes being awkward in greetings is the best way to make them. He seems cheerful at least.
Sebastian He displays in many ways that he was not born to nobility, and yet there is something appealing about the raw honesty of a man saying and doing the things he wants without fear or favor.
Sorrel This charming Crownlands duke is quite social and friendly. I hope to continue to consider him a friend in the future.
Venturo A warm enough soul, and a Duke at that. It's always a pleasure to meet those who might be future partners in the endeavors of the Raconteur and bringing food and entertainment to all of the lands of Arvum.
Videl The Duke Shepherd seems unaccustomed to his position, but well-meaning and hard working. Let's hope he learns to swim before he sinks.
Willow We've met a few times but rarely had the chance to talk. He seems to have a nice smile and a pretty killer sense of humor though.
Wyatt He's a great new cousin, and that pained expression when I start talking about trade law just shows that he bears the weight of his responsibilities seriously, and is steeling himself against missing any of it. It must continue.


text:
The Basketball Champions League Top Scorer is the annual award that is given to the professional club basketball league, the Basketball Champions League (BCL)'s Top Scorer throughout the Champions League season. The  Basketball Champions League is the European-wide 3rd-tier level league. It is the European-wide league that is two tier levels below the European top-tier level EuroLeague, and one tier level below the EuroCup.

Top scorers

References

External links
Basketball Champions League (official website)
FIBA (official website)

Basketball Champions League awards and honors


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Just two days after Uber (uber) brought on its first-ever chief marketing officer, the mobility service revealed a new logo, a new mission statement and a totally revamped identity system.
Rebecca Messina, formerly of Beam Suntory and Coca-Cola, joined Uber this week as its global CMO. Uber's previous chief brand officer, Bozoma Saint John, left in June to become CMO of Endeavor.
Wolff Olins, the Uber Brand Experience Team and MCKL Type Foundry worked for nine months on the rebranding, which AdWeek was the first to reveal. Uber's new logo, set in the custom Uber Move typeface, is more approachable and meant to reflect safety and accessibility.
"To reimagine how the world moves, we looked to design a system that connected with all modes of transportation, in all places, for all people, and ultimately delivered by all teams across Uber," Wolff Olins said in a statement.
The outgoing Uber logo was in place for just two and a half years and drew criticism for being inscrutable. And since then, the company has been slammed with with sexual harassment allegations and criminal investigations. CEO Dara Khosrowshahi, in office for just one year after founder Travis Kalanick's exit, is definitely already leaving his mark on the company, which may finally be growing up.


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