All Figures

$\begin{figure} \includegraphics[width=13.95cm,clip]{2011fig1.eps} \end{figure}$ Figure 1: 2D projected reconstructed FAM orbits for different values of $N_{\rm f}$ . The black dots represent the final (present) positions for each object. The solid lines indicate the trajectories followed by the objects as a function of time. The top-left panel shows FAM reconstructed orbits with $N_{\rm f}=1$ (Zel'dovich approximation). The top-right with $N_{\rm f}=2$ , the lower-left $N_{\rm f}=3$ and the lower-right $N_{\rm f}=6$ .
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In the text

$\begin{figure} \par\includegraphics[width=15cm,clip]{2011fig2.ps} \end{figure}$ Figure 2: Spectral characteristics for the two studied cosmological scenarios. Upper left: power spectrum P(k) (green lines) and k³P(k) (blue lines), for the $\Lambda$ CDM (continuous lines) and $\tau$ CDM (dotted lines) cosmological scenarios used in this study. Lower left: velocity power $k^3 P_{\rm v}(k)$ , the amount of velocity power per logarithmic waveband interval. Upper centre: expected bulk flow velocities (km s^-1) over a spherical (tophat) volume of radius $R_{\rm TH}$ . The solid line is the real theoretical prediction, the dashed one concerns the restricted power spectrum represented in the simulation box. Centre low: the convergence of the bulk flow, defined according to Eq. (16). Upper right: expected shear flow (km s^-1 Mpc^-1) over a spherical (tophat) volume of radius $R_{\rm TH}$ . Similar to bulk flow, the solid line concerns the full theoretical power spectrum while the dashed corresponds to the restricted power spectrum represented in the simulation box. Lower right: convergence of the shear flow, defined according to Eq. (16). Note that for the righthand frames the corresponding ordinate axis are the ones on the righthand side of the plotbox, while for the central frames it is the one on its lefthand side.
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In the text

$\begin{figure} \par\includegraphics[width=14.3cm,clip]{2011fig12.ps} \end{figure}$ Figure 12: Velocity Field Multipole Decomposition: the total N-body velocity field, involving the same one as in Figs. 13 and 14, decomposed into its four different components. The coordinate system is that defined by the tidal shear tensor, see Fig. 13. At each row we depict the velocities in the (x-y), (x-z) and (y-z) plane. Top: the locally induced velocity, approximated by the FAM₃₀ realization. Second row: the monopole component, a result of the slight local expansion due to its underdensity wrt. the global Universe. Third row: the bulk flow, of which most is concentrated in the (x-y) and (y-z) plane. Fourth row: the shear flow component.
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In the text

$\begin{figure} \includegraphics[width=15.6cm,clip]{2011fig13.ps} \end{figure}$ Figure 13: 2D projected peculiar (residual) velocities for the same mock catalog as in Figs. 7 and 8 in three perpendicular central planes of $10 ~h^{-1}~{\rm Mpc}$ width. The coordinate frame is rotated such that the bulk flow velocity is oriented along the x-direction. Within the plane perpendicular to the x-axis, the y and z axes are chosen arbitrarily. First row: the residual velocity (i.e. tidal velocity) N-body - FAM₃₀. Secondrow: residual velocities after subtraction bulk flow component. The resulting residual field is clearly dominated by a shear pattern, most notably in the y-z plane.
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In the text

$\begin{figure} \par\includegraphics[width=15cm,clip]{2011fig14.ps} \end{figure}$ Figure 14: 2D projected peculiar velocities for the same mock catalog as in Figs. 7 and 8 in three perpendicular central planes of $10 ~h^{-1}~{\rm Mpc}$ width. The coordinate frame is defined by the three eigenvectors of the shear tensor. The x-axis is aligned along the direction of the largest (stretching) eigenvalue, the y-axis is aligned along the middle eigenvalue and the z-axis along the smallest (compressional) eigenvalue. The first two rows are the same as Fig. 13, within the "shear reference system''. The third row depicts the final residual field after subtraction of the quadrupolar shear component.
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In the text

$\begin{figure} \par\includegraphics[width=15cm,clip]{2011fig15.ps} \end{figure}$ Figure 15: point-to-point comparison between the three successive residual velocities and the corresponding mock catalog N-body velocity. The three panels in each row correspond to the x, y and z velocity components. The coordinate system is the "shear reference system''. Toprow: the tidal velocity field N-body-FAM. Middle row: residual velocity field after subtraction bulk flow. Bottom row: residual velocity field after subtraction of both tidal bulk and shear components.
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In the text

$\begin{figure} \par\includegraphics[width=14.8cm,clip]{2011fig16.ps} \end{figure}$ Figure 16: Aitoff projections of the galaxy distribution of a NBG + PSCz $\Lambda$ CDM catalog. The top-most panel shows the corresponding NBG distribution, $d_{\rm sur}=[0,30]~h^{-1}~{\rm Mpc}$ . The subsequent panels depict the external galaxy distribution enclosed by the shells defined by survey depth $d_{\rm sur}=[30{-}55]~h^{-1}~{\rm Mpc}$ , $d_{\rm sur}=[55{-}70]~h^{-1}~{\rm Mpc}$ , $d_{\rm sur}=[70{-}85]~h^{-1}~{\rm Mpc}$ and $d_{\rm sur}=[85{-}100]~h^{-1}~{\rm Mpc}$ .
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In the text

$\begin{figure} \par\includegraphics[width=14cm,clip]{2011fig17.ps} \end{figure}$ Figure 17: Sky distribution of galaxies in external shell of survey depth $d_{\rm sur}=30{-}100~h^{-1}~{\rm Mpc}$ . This galaxy distribution should reflect the mass distribution inducing the local tidal velocity flow. By means of symbols we have indicated the track of the gravity dipole and quadrupole eigenvector directions (cf. Eqs. (36) and (37)) on the sky, by radially expanding outward the survey depth $d_{\rm sur}$ in steps of $1~h^{-1}~{\rm Mpc}$ , from $d_{\rm sur}=30~h^{-1}~{\rm Mpc}$ to $d_{\rm sur}=100~h^{-1}~{\rm Mpc}$ . For comparison the same symbol, but then enlarged, indicates the directions for the corresponding bulk velocity and velocity shear eigenvector directions. Diamond: dipole. Triangle: stretching component shear. Square: middle component shear. Star: compressional component shear.
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In the text

$\begin{figure} \par\includegraphics[width=12.83cm,clip]{2011fig18.ps} \end{figure}$ Figure 18: Aitoff projections of the galaxy distribution of a NBG + PSCz $\tau$ CDM catalog. The top-most panel shows the corresponding NBG distribution, $d_{\rm sur}=[0,30]~h^{-1}~{\rm Mpc}$ . The subsequent 4 panels depict the external galaxy distribution enclosed by the shells defined by survey depth $d_{\rm sur}=[30{-}55]~h^{-1}~{\rm Mpc}$ , $d_{\rm sur}=[55{-}70]~h^{-1}~{\rm Mpc}$ $d_{\rm sur}=[70{-}85]~h^{-1}~{\rm Mpc}$ and $d_{\rm sur}=[85{-}100]~h^{-1}~{\rm Mpc}$ . Bottom panel: convergence gravity dipole and quadrupole. By means of symbols we have indicated the track of the gravity dipole and quadrupole eigenvector directions (cf. Eqs. (36) and (37)) on the sky, by radially expanding outward the survey depth $d_{\rm sur}$ in steps of $1~h^{-1}~{\rm Mpc}$ , from $d_{\rm sur}=30~h^{-1}~{\rm Mpc}$ to $d_{\rm sur}=100~h^{-1}~{\rm Mpc}$ . For comparison the same symbol, but then enlarged, indicates the directions for the corresponding bulk velocity and velocity shear eigenvector directions. Diamond: dipole. Triangle: stretching component shear. Square: middle component shear.Star: compressional component shear.
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In the text

$\begin{figure} \par\includegraphics[width=16cm,clip]{2011fig19.eps} \end{figure}$ Figure 19: Cumulative gravity dipole and tidal gravity shear. As a function of survey depth $d_{\rm sur}$ the Cartesian components of the gravity dipole, g_x, g_y and g_z is followed (in equivalent velocity unit $~{\rm km~s^{-1} }$ ). The symbols at $d_{\rm sur}$ indicate the corresponding velocity dipole. Lefthandpanel: $\Lambda$ CDM. Righthand panel: $\tau$ CDM.
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In the text

$\begin{figure} \par\includegraphics[width=14cm,clip]{2011fig3.ps} \end{figure}$ Figure 3: Central slices through a mock galaxy catalog realization. Depicted is the galaxy distribution in the external ( $r>30~h^{-1}~{\rm Mpc}$ ) volume. For each catalog, we show the x-y ( left), x-z ( centre) and y-z ( right) plane. Top row: $\Lambda$ CDM mock catalog; Bottom row: $\tau$ CDM catalog.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2011fig4.eps} \end{figure}$ Figure 4: Object counts as a function of distance in the PSCz mock catalogs. Upper panel: the two histograms show the average counts in the mock samples for the $\tau$ CDM and $\Lambda$ CDM cosmological models. The continuous line show the expected counts. Lower panel: the histograms show the fractional difference between the observed and expected counts averaged over all PSCz mock samples in the two cosmological models explored.
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In the text

$\begin{figure} \par\includegraphics[width=17cm,clip]{2011fig5.ps} \end{figure}$ Figure 5: Compilation of cubic subregions and various mock subsamples of the object distribution in one of the $\Lambda$ CDM PSCz mock catalogs. The full mock catalog of objects, the PSCz look-alike volume and the NBG look-alike volume out to a radius of $100~h^{-1}~{\rm Mpc}$ , is shown in the large lefthand cubic box (with size $200 ~h^{-1}~{\rm Mpc}$ ). The boxes along the top row and those along the bottom row represent mutually exclusive object samples. The lower ones represents the inner cosmic region ( $x < 30~h^{-1}~{\rm Mpc})$ , the top row represent a corresponding part of the exterior PSCz region ( $30 ~h^{-1}~{\rm Mpc}< x < 100 ~h^{-1}~{\rm Mpc}$ ). Emanating from the complete cubic volume and running along the top row are two successive boxes which zoom in on the external PSCz mock catalog objects, with cubic sizes of $160 ~h^{-1}~{\rm Mpc}$ ( middle right cube) and $80 ~h^{-1}~{\rm Mpc}$ ( lower right cube) respectively. The lower row of two cubic volumes the central (inner) NBG mimicking object sample. The full inner sample, comprising a sphere of radius $30~h^{-1}~{\rm Mpc}$ is shown in the lower central cubic volume, whose size of $80 ~h^{-1}~{\rm Mpc}$ is equal to the central PSCz box, while the righthand cube focuses in on the $40 ~h^{-1}~{\rm Mpc}$ size central region.
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In the text

$\begin{figure} \par\includegraphics[width=16cm,clip]{2011fig6.eps} \end{figure}$ Figure 6: 2D projection of the particle distribution in one of the $\Lambda$ CDM PSCz mock catalogs ( left panel). The inner circle divides the NBG look-alike volume limited region from the PSCz flux limited one. The right panel show the 2D projected velocities in a slice of 10 $~h^{-1}~{\rm Mpc}$ cut through the inner part of the catalog.
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In the text

$\begin{figure} \par\includegraphics[width=15cm,clip]{2011fig7.ps} \end{figure}$ Figure 7: 2D projected, unsmoothed velocities at each particles position in one of the NBG- $\Lambda$ CDM mock catalogs. Each row contains three frames, corresponding to the central y-z, x-z and x-y plane through the point sample. Bottom row: projected N-body velocities. Central row: projected FAM₃₀ velocities. Bottom row: residual N-body-FAM₃₀ velocities.
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In the text

$\begin{figure} \par\includegraphics[width=14.8cm,clip]{2011fig8.ps} \end{figure}$ Figure 8: Same as Fig. 7, for the PSCz based FAM₁₀₀ reconstructions. Shown are the 2D projected, unsmoothed velocities at each particles position in the central NBG mimicking volume of the full PSCz- $\Lambda$ CDM mock catalogs, the same region as depicted in Fig. 7. Each row contains three frames, corresponding to the central y-z, x-z and x-y plane through the point sample. Bottom row: projected N-body velocities. Central row: projected FAM₁₀₀ velocities. Bottom row: residual N-body-FAM₁₀₀ velocities.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=14.5cm,clip]{2011fig9.ps} \end{figure}$ Figure 9: Point-to-point comparison (scatter plot) of four quantities related to FAM reconstructed velocities and the corresponding "real'' object velocity in the underlying N-body samples. The N-body realization, and the mock sample, concern the $\Lambda$ CDM scenario. For each quantity two panels are shown: the lefthand one is the one for FAM₃₀ reconstruction, the righthand one for the FAM₁₀₀ reconstruction. Top lefthand: the amplitude of the velocities. Top righthand: residual velocity amplitudes FAM-N-body. Bottom lefthand: FAM velocity component projected along the N-body velocity. Bottom righthand: angle $\theta$ between FAM velocity and N-body velocity, in terms of $\mu=\cos(\theta)$ .
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In the text

$\begin{figure} \par\includegraphics[angle=90,width=15cm,clip]{2011fig10.ps} \end{figure}$ Figure 10: Point-to-point comparison (scatter plot) of FAM velocity decompositions wrt. the corresponding N-body velocity of the involved $\Lambda$ CDM mock sample. Both the parallel projection $v_{\parallel }$ ( centre frames) as well as the perpendicular projection $v_{\perp }$ along the N-body velocity direction are analyzed. Top row: FAM₃₀ reconstruction against N-body velocity equivalent. Bottom row: FAM₁₀₀ reconstruction against N-body velocity equivalent. Lefthand column: $v_{\parallel }$ . Central column: $v_{\perp }$ . Righthand column: The x component of the velocity, v_x. The solid line in the righthand column frames indicates the identity line $v_{x,{\rm FAM}}=v_{x,{N-{\rm body}}}$ . The dashed line indicates the best linear fit. Evidently, the FAM₃₀ deviate systematically from the identity line. The point scatter density is characterized by the contours, indicating iso-density surfaces. See Table 3.
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In the text

$\begin{figure} \par\includegraphics[width=13.5cm,clip]{2011fig11.ps} \end{figure}$ Figure 11: Point-to-point comparison (scatter plot) of the Cartesian components of the residual velocity ${\vec v}_{\rm FAM}-{\vec v}_{N{\rm body}}$ components against corresponding N-body velocity ${\vec v}_{N{\rm body}}$ . From left to right: v_x, v_y and v_z. Top row: FAM₃₀ reconstructed velocity. Bottom row: FAM₁₀₀ reconstructed velocity.
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In the text

$\begin{figure} \par\includegraphics[width=16cm,clip]{2011fig19.eps} \end{figure}$	Figure 19: Cumulative gravity dipole and tidal gravity shear. As a function of survey depth $d_{\rm sur}$ the Cartesian components of the gravity dipole, g_x, g_y and g_z is followed (in equivalent velocity unit $~{\rm km~s^{-1} }$ ). The symbols at $d_{\rm sur}$ indicate the corresponding velocity dipole. Lefthandpanel: $\Lambda$ CDM. Righthand panel: $\tau$ CDM.
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$\begin{figure} \par\includegraphics[width=14cm,clip]{2011fig3.ps} \end{figure}$	Figure 3: Central slices through a mock galaxy catalog realization. Depicted is the galaxy distribution in the external ( $r>30~h^{-1}~{\rm Mpc}$ ) volume. For each catalog, we show the x-y ( left), x-z ( centre) and y-z ( right) plane. Top row: $\Lambda$ CDM mock catalog; Bottom row: $\tau$ CDM catalog.
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$\begin{figure} \par\includegraphics[width=16cm,clip]{2011fig6.eps} \end{figure}$	Figure 6: 2D projection of the particle distribution in one of the $\Lambda$ CDM PSCz mock catalogs ( left panel). The inner circle divides the NBG look-alike volume limited region from the PSCz flux limited one. The right panel show the 2D projected velocities in a slice of 10 $~h^{-1}~{\rm Mpc}$ cut through the inner part of the catalog.
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$\begin{figure} \par\includegraphics[width=15cm,clip]{2011fig7.ps} \end{figure}$	Figure 7: 2D projected, unsmoothed velocities at each particles position in one of the NBG- $\Lambda$ CDM mock catalogs. Each row contains three frames, corresponding to the central y-z, x-z and x-y plane through the point sample. Bottom row: projected N-body velocities. Central row: projected FAM₃₀ velocities. Bottom row: residual N-body-FAM₃₀ velocities.
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$\begin{figure} \par\includegraphics[width=13.5cm,clip]{2011fig11.ps} \end{figure}$	Figure 11: Point-to-point comparison (scatter plot) of the Cartesian components of the residual velocity ${\vec v}_{\rm FAM}-{\vec v}_{N{\rm body}}$ components against corresponding N-body velocity ${\vec v}_{N{\rm body}}$ . From left to right: v_x, v_y and v_z. Top row: FAM₃₀ reconstructed velocity. Bottom row: FAM₁₀₀ reconstructed velocity.
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