All Figures

$\begin{figure} \par\includegraphics[width=12.9cm]{6813f01.eps}\end{figure}$ Figure 1: Velocity diagrams of halo 6 out to $R=r_{\rm v}$ in the mass centre rest frame of reference seen in different projections and with different types of interlopers. Filled and empty circles indicate halo particles and interlopers respectively. In the top left corner of each panel we mark the projection axis and the criterion for interloper identification (> $r_{\rm v}$ , > $2r_{\rm v}$ or > $v_{\rm esc}$ for particles beyond $r_{\rm v}$ , $2r_{\rm v}$ and unbound particles respectively). In the bottom left corner we give numbers of halo particles and interlopers which are seen on a given velocity diagram.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.8cm,clip]{6813f02.eps}\end{figure}$ Figure 2: The top panel shows the velocity diagram of halo 4 in projection along z axis. Filled and empty circles indicate particles bound and unbound to this halo respectively. Middle and bottom panels show respectively the dispersion profiles and the results of the fitting procedure in the form of 68.3, 95.4 and 99.73 percent probability contours in the $M_{\rm v}-c$ parameter plane assuming isotropic orbits. The different types of lines correspond to different subsamples of particles used to calculate the dispersion profile: dotted lines are for the whole sample with interlopers included, solid ones for bound particles, dashed ones for particles below $2r_{\rm v}$ and dotted-dashed lines for particles below $r_{\rm v}$ . The cross marks the concentration parameter and virial mass found in 3D analysis of the mass distribution in the halo.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{6813f03.eps}\end{figure}$ Figure 3: Maximum velocity profiles. The dark gray area in the background indicates maximum velocity reached by bound particles. Medium and light gray strips correspond respectively to the formula (4) and (5) with the mass profile given by the mass estimator (6). Widths of the shaded areas are given by the dispersions following from averaging over the whole sample of velocity diagrams.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{6813f04.eps}\end{figure}$ Figure 4: Illustration of successive steps in $v_{\rm max}(1)$ method of interloper removal for halo 6 in projection along the y axis. The method uses the maximum velocity profile (5) and mass profile (6). The top and bottom panels show successive mass profiles and maximum velocity profiles separating interlopers from halo particles respectively. Filled and empty circles mark particles bound and unbound to the halo. Numbers indicate successive steps of the procedure which are described by the lines of different types. Final maximum velocity profiles (number 4) are drawn with dashed-dotted lines.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{6813f05.eps}\end{figure}$ Figure 5: Dependence of the results of the interloper removal method based on the analysis of the velocity dispersion of binned data on the maximum number of bins $n_{\rm max}$ . The left panel shows the fraction of identified unbound particles $f_{\rm i}$ and the right one the fraction of bound particles taken for interlopers by mistake $f_{\rm g}$ . Widths of both profiles (dark gray) are given by the dispersions following from averaging over the sample of velocity diagrams. Light gray strip in the background indicates the best range of $n_{\rm max}$ .
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.9cm,clip]{6813f06.eps} % \end{figure}$ Figure 6: Results of the $3\sigma _{\rm los}(R)$ method for halo 6 in three projections (x, y and z from top to bottom). Left column panels show velocity diagrams with final $\pm 3\sigma _{\rm los}(R)$ lines separating interlopers from halo particles. Filled and empty circles on velocity diagrams indicate bound and unbound particles respectively. Right column panels show the line-of-sight velocity dispersion profiles obtained in successive steps of the procedure (solid lines from top to bottom). The dashed line with error bars is the dispersion profile measured for bound particles.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{6813f07.eps}\end{figure}$ Figure 7: Boundary lines $v_{\rm lim}$ of the area occupied by halo particles with probability $p_{\rm lim}=0.9973$ for three values of the concentration parameter c=1,5,10. The velocity diagram is assumed to have a cut-off in radius at $R_{\rm max}=r_{\rm v}$ and $v_{\rm lim}$ is expressed in units of the local value of the projected velocity dispersion $\sigma _{\rm los}(R)$ .
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{6813f08.eps}\end{figure}$ Figure 8: Histograms of the ratio $M_{\rm P}/M_{\rm VT}$ for different subsamples of particles. Subsamples are identified in the upper right corner of each panel: the lower right panel is for all particles, upper left for bound particles and the remaining two for particles inside $r_{\rm v}$ or $2r_{\rm v}$ . All histograms are normalized to unity.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.6cm,clip]{6813f09.eps} % \end{figure}$ Figure 9: The ratio of mass estimators $M_{\rm P}$ and $M_{\rm VT}$ , their derivatives $\Delta M/(\Delta n_{\rm rem}M)$ and fractions of unbound $f_{\rm i}$ and bound $f_{\rm g}$ particles removed in the procedure based on jackknife statistics as a function of the total number of removed particles $n_{\rm rem}$ . All profiles are averaged over the whole sample of 30 velocity diagrams and the shaded areas indicate the dispersion of values. The solid and dashed lines in the lower right panel correspond respectively to $M_{\rm VT}$ and $M_{\rm P}$ .
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=16cm,clip]{6813f10.eps}\end{figure}$ Figure 10: Stacked velocity diagrams in projection along x, y and z axes.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{6813f11.eps}\end{figure}$ Figure 11: Surface density ( left column) and velocity histograms ( right column) of interlopers on stacked velocity diagrams in different projections marked in the upper left corner of each panel. Solid, dashed and dotted lines correspond to unbound particles and particles beyond $2r_{\rm v}$ and $r_{\rm v}$ respectively. Both surface density and velocity histograms are normalized to the number of a given type of interlopers averaged over 10 velocity diagrams in a given projection.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{6813f12.eps}\end{figure}$ Figure 12: The velocity histogram and the fitted probability distribution given by (15) for the outer bin of a stacked velocity diagram in projection along the x axis.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{6813f13.eps}\end{figure}$ Figure 13: Left column panels show dispersion profiles obtained by fitting the probability distribution (15) to velocity histograms for composite haloes in different radial bins (filled circles). Black lines plot dispersion profiles of bound particles with shaded strips indicating the $3\sigma$ range of variability among the velocity diagrams. Right column panels show profiles of the probability $\alpha (R)$ measured for particles beyond $r_{\rm v}$ (dotted lines) or $2r_{\rm v}$ (dashed lines) and for unbound particles (solid lines). Dashed-dotted broken lines represent results of the fitting procedure. Each row of panels corresponds to a different projection direction of the stacked velocity diagram marked in the bottom left corner.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{6813f14.eps}\end{figure}$ Figure 14: Left column panels show the results of the Bayesian analysis in the form of contours in the c- $\alpha _{\rm p}$ parameter plane corresponding to 68.3, 95.4 and 99.73 percent confidence levels. In the right column we plot $\alpha (R)$ probability profiles calculated for different types of interlopers: particles beyond $r_{\rm v}$ (dotted lines) or $2r_{\rm v}$ (dashed lines) and unbound particles (solid lines). Shaded areas indicate $\alpha (R)$ values corresponding to c and $\alpha _{\rm p}$ parameters from the inside of the 99.73 percent probability contours. The rows of panels from top to bottom are for the x, y and z projections respectively.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{6813f03.eps}\end{figure}$	Figure 3: Maximum velocity profiles. The dark gray area in the background indicates maximum velocity reached by bound particles. Medium and light gray strips correspond respectively to the formula (4) and (5) with the mass profile given by the mass estimator (6). Widths of the shaded areas are given by the dispersions following from averaging over the whole sample of velocity diagrams.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7cm,clip]{6813f07.eps}\end{figure}$	Figure 7: Boundary lines $v_{\rm lim}$ of the area occupied by halo particles with probability $p_{\rm lim}=0.9973$ for three values of the concentration parameter c=1,5,10. The velocity diagram is assumed to have a cut-off in radius at $R_{\rm max}=r_{\rm v}$ and $v_{\rm lim}$ is expressed in units of the local value of the projected velocity dispersion $\sigma _{\rm los}(R)$ .
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8cm,clip]{6813f08.eps}\end{figure}$	Figure 8: Histograms of the ratio $M_{\rm P}/M_{\rm VT}$ for different subsamples of particles. Subsamples are identified in the upper right corner of each panel: the lower right panel is for all particles, upper left for bound particles and the remaining two for particles inside $r_{\rm v}$ or $2r_{\rm v}$ . All histograms are normalized to unity.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=16cm,clip]{6813f10.eps}\end{figure}$	Figure 10: Stacked velocity diagrams in projection along x, y and z axes.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7cm,clip]{6813f12.eps}\end{figure}$	Figure 12: The velocity histogram and the fitted probability distribution given by (15) for the outer bin of a stacked velocity diagram in projection along the x axis.
Open with DEXTER