All Figures

$\begin{figure} \par\includegraphics[width=4.9cm,clip]{587fig1a.eps}\hspace*{5mm}... ...1b.eps}\hspace*{5mm} \includegraphics[width=5cm,clip]{587fig1c.eps} \end{figure}$ Figure 1: RS ( left image), kSZ ( central image) and the sum of both effects ( right image), for a pair of merging clusters with masses $10^{15}~M_\odot$ (left cluster) and $5\times 10^{14}~M_\odot$ (right cluster), with zero angular momentum, when observed with projection angle $80\hbox {$^\circ $ }$ , and a physical separation of 1 Mpc. Contour lines in all plots correspond to (-64, -16, -4, -1, 1, 4, 16, 64) times the maximum of the map (dotted-lines for negative regions and solid lines for positive ones).
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{587fig2a.eps}\hspace*{5mm} \... ....eps}\hspace*{5mm} \includegraphics[width=5.2cm,clip]{587fig2c.eps} \end{figure}$ Figure 2: Same as Fig. 1, but considering angular momentum, and with a larger projection angle. Here, $\hat{\i}= 60\hbox{$^\circ$ }$ , and the velocity vector is defined by the spherical angles $(60\hbox {$^\circ $ },60\hbox {$^\circ $ })$ . Contours have the same meaning as in Fig. 1.
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In the text

$\begin{figure} \par\includegraphics[width=7.15cm,clip]{587fig3.eps} \end{figure}$ Figure 3: Dependence of the measured quadrupole (Q_xx) on the projection angle $\hat{\i}$ . These curves have been derived for the case of $M_1 = 10^{15}~M_\odot$ (left cluster), M₂ = 5 $\times$ $10^{14}~M_\odot$ (right cluster), separation of 1 Mpc, $\phi _v = 0\hbox {$^\circ $ }$ and the clusters placed along the X-axis (so Q=|Q_xx|) and we use $\hat{\i}= \theta_v$ (i.e. zero angular momentum). We performed the computation of the quadrupole in the whole image (quoted as "all''), and masking the region that in the y-parameter map has a signal above the 10% of the peak intensity (quoted as "outer''). We can see that when doing this, the quadrupole signal is dominated by the RS component. The flux is given in mJy, at the cross-over frequency of the tSZ effect ( $\nu=217~{\rm GHz}$ ). The merging system is assumed to be at $300~{\rm Mpc}$ .
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In the text

$\begin{figure} \par\includegraphics[width=7.1cm,clip]{587fig4.eps} \end{figure}$ Figure 4: Dependence of the measured dipole modulus ( $d=\sqrt {d_x^2+d_y^2}$ ) with the projection angle $\hat{\i}$ . We consider exactly the same case and notation as in Fig. 3, but here we also show the dipole signal from the region where the 90% of the tSZ emission comes from (quoted as "inner''), as well as the complementary "outer'' region.
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In the text

$\begin{figure} \par\includegraphics[width=7.3cm,clip]{587fig5.eps} \end{figure}$ Figure 5: Dependence of the measured quadrupole (Q_xx) on the separation between clusters. We consider the case $M_1 = 10^{15}~M_\odot$ , M₂ = 5 $\times$ $10^{14}~M_\odot$ , $\phi _v = 0\hbox {$^\circ $ }$ (so Q_yy=0) and we use $\hat{\i}= \theta_v=80\hbox{$^\circ$ }$ (zero angular momentum). Notation and units are the same as in Fig. 3. Separations are measured from the most massive to the less massive cluster, so in this picture a positive separation represents a pre-merger state, where the two clusters are approaching each other, while a negative separation represents a post-merger state.
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In the text

$\begin{figure} \par\includegraphics[width=7.35cm,clip]{587fig6.eps}\end{figure}$ Figure 6: Recovery of $\phi _{v} - \alpha _{{\rm CM}}$ from $2 \alpha_{\vec{Q}^{T}} - \alpha_{\vec{Q}^{{\rm tSZ}}}$ . Thick solid line excludes that area containing 90% of the tSZ emission, whereas thin solid line considers the entire map. The dotted line gives the expected scaling $2 \alpha_{\vec{Q}^{T}} - \alpha_{\vec{Q}^{{\rm tSZ}}} = \phi_v - \alpha_{{\rm CM}}$ . A projection angle of $\hat{\i}= 60\hbox{$^\circ$ }$ was used in the calculation.
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In the text

$\begin{figure} \par\includegraphics[width=7.45cm,clip]{587fig7.eps}\end{figure}$ Figure 7: Dependence of |Q^T_xy | with the absolute value of the projected component of the angular momentum, |J_z|. We use the same physical parameters of the previous figure, and computed for each value of $\phi _v$ the projected Z-component of the angular momentum (note that, for $\phi _v = 0\hbox {$^\circ $ }$ and $\phi _v=180\hbox {$^\circ $ }$ , $\vec{J}=0$ ). Under the symmetry of our system (clusters along the X-axis), the kSZ residual affects mostly the Q^T_xx values, leaving the crossed term Q^T_xy practically unaltered.
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{587fig2a.eps}\hspace{5mm} \... ....eps}\hspace{5mm} \includegraphics[width=5.2cm,clip]{587fig2c.eps} \end{figure}$	Figure 2: Same as Fig. 1, but considering angular momentum, and with a larger projection angle. Here, $\hat{\i}= 60\hbox{$^\circ$ }$ , and the velocity vector is defined by the spherical angles $(60\hbox {$^\circ $ },60\hbox {$^\circ $ })$ . Contours have the same meaning as in Fig. 1.
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$\begin{figure} \par\includegraphics[width=7.1cm,clip]{587fig4.eps} \end{figure}$	Figure 4: Dependence of the measured dipole modulus ( $d=\sqrt {d_x^2+d_y^2}$ ) with the projection angle $\hat{\i}$ . We consider exactly the same case and notation as in Fig. 3, but here we also show the dipole signal from the region where the 90% of the tSZ emission comes from (quoted as "inner''), as well as the complementary "outer'' region.
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