Astronomy & Astrophysics

All Figures

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fig1.eps}}\end{figure}$ Figure 1: The redshift distribution of the sample of 355 quasars, illustrated for the NGP and the SGP regions separately.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{3337fig2.eps}\end{figure}$ Figure 2: The distribution of the polarization degree for the sample of 355 quasars. The median is $p \simeq 1.38\%$ . The last bin contains all objects with $p > 6\%$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{3337fig3.eps}\end{figure}$ Figure 3: The logarithmic significance level of the statistical tests applied to the sample of 355 quasars. $n_{\scriptscriptstyle \rm V}$ is the number of nearest neighbours around each quasar and involved in the calculation of the statistics.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fi4a.eps}}\\ [0.2cm] \resizebox{8.8cm}{!}{\includegraphics*{3337fi4b.eps}}\end{figure}$ Figure 4: Hammer-Aitoff projection of the Z_c^m ( top) and $S_{\scriptscriptstyle\!\!D}$ ( bottom) statistics averaged over $n_{\scriptscriptstyle \rm V}$ = 37 to 43, as a function of the equatorial coordinates $\alpha _{\rm p}$ and $\delta _{\rm p}$ of the northern pole of an arbitrary coordinate system. The less significant the statistics for a given coordinate system or pole position, the darker the corresponding ( $\alpha _{\rm p}$ , $\delta _{\rm p}$ ) point in the map. Note that ( $\alpha _{\rm p} + 180\hbox {$^\circ $ }$ , $\delta _{\rm p}$ ) is equivalent to ( $\alpha _{\rm p}$ , $- \delta _{\rm p}$ ). The full sample of 355 QSOs is used.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{3337fi5a.eps}\\ [0.3cm] \includegraphics[width=8cm,clip]{3337fi5b.eps}\end{figure}$ Figure 5: Same as Fig. 3 but for two sub-samples with different cutoffs of the polarization degree. When SL is smaller than 10^-5 (i.e. unresolved with 10⁵ simulations), we arbitrarily fix its value to SL = $8\times 10^{-6}$ .
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fig6.eps}}\end{figure}$ Figure 6: Distributions of the quasar polarization position angles for different sub-samples. The labels refer to the samples defined in Table 2.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fi7a.eps}}\\ [0.4cm] \resizebox{8.8cm}{!}{\includegraphics*{3337fi7b.eps}}\end{figure}$ Figure 7: Maps of quasar polarization vectors in the NGP region, together with the corresponding distributions of polarization degree and angle. The regions illustrated are delimited in right ascension and declination by $168\hbox {$^\circ $ }\leq \alpha \leq 218\hbox {$^\circ $ }$ and $\delta \leq 50\hbox {$^\circ $ }$ , and in redshift by $0.0 \leq z < 1.0$ ( top, 43 objects) and $1.0 \leq z \leq 2.3$ ( bottom, 56 objects; region A1). The darker polarization angle histograms refer to quasars with $p \geq 1.2\%$ , that is 2 times higher than the cutoff $p \geq 0.6\%$ adopted for the full sample.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fi8a.eps}}\\ [0.4cm] \... ...ps}}\\ [0.4cm] \resizebox{8.8cm}{!}{\includegraphics*{3337fi8c.eps}}\end{figure}$ Figure 8: Maps of quasar polarization vectors in the SGP region, together with the corresponding distributions of polarization degree and angle. The regions illustrated are delimited in right ascension by $320\hbox {$^\circ $ }\leq \alpha \leq 360\hbox {$^\circ $ }$ , and in redshift by $0.0 \leq z < 0.7$ ( top, 27 objects), $0.7 \leq z \leq 1.5$ ( middle, 29 objects; region A3) and $1.5 < z \leq 3.0$ ( bottom, 23 objects). The darker polarization angle histograms refer to quasars with $p \geq 1.2\%$ . Right ascensions should be read modulo 360 $^\circ$ .
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fi9a.eps}}\\ [0.4cm] \resizebox{8.8cm}{!}{\includegraphics*{3337fi9b.eps}}\end{figure}$ Figure 9: Maps and corresponding distributions of the interstellar polarization measured from stars matching at best the positions of the quasars illustrated in Figs. 7 and 8 ( top: NGP region; bottom: SGP region). Only stars at distances $d_{\star }\geq$ 100 pc and with a polarization angle uncertainty $\sigma _{\theta _{\star }} \leq 14\hbox {$^\circ $ }$ are considered. Since $\sigma_{\theta_{\star}} = 28\hbox{$.\!\!^\circ$ }65 \; \sigma_{p_{\star}} / p_{\star}$ , the latter condition discards stars with $p_{\star }\simeq 0$ . The NGP is located at $\alpha =192\hbox {$^\circ $ }$ , $\delta =27\hbox {$^\circ $ }$ and the SGP at $\alpha =12\hbox {$^\circ $ }$ , $\delta =-27\hbox {$^\circ $ }$ .
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fi10.eps}}\end{figure}$ Figure 10: Distributions of the acute angle $\Delta \theta$ between the polarization position angles of quasars and nearest stars. The objects represented are those considered in Figs. 7-9. The regions of the sky towards the NGP and the SGP are shown separately. Two cutoff in stellar distances are considered: $d_{\star }\geq$ 100 pc and $d_{\star }\geq$ 200 pc. Darker histograms illustrate distributions of $\Delta \theta$ including only quasars with $p \geq 1.2\%$ .
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fi11.eps}}\end{figure}$ Figure 11: The local statistics s_i of the $pS_{\scriptscriptstyle\!\!D}$ and pZ_c^mtests computed with $n_{\scriptscriptstyle \rm V}$ = 40 are represented here as a function of the redshift. The full sample of 355 quasars is considered. The s_i, which have been multiplied by a constant factor for convenience, are averaged over redshift bins $\Delta z = 0.5$ ; the error bars represent the uncertainty of the mean. The highest values of s_i indicate the strongest departures to uniform distributions of polarization angles. The line joins the mean s_i values from the $pS_{\scriptscriptstyle\!\!D}$ and pZ_c^mtests. Since the s_i are computed for $n_{\scriptscriptstyle \rm V}$ = 40, the data points are not independent. Redshifts are counted positively for objects located in the North Galactic Cap and negatively for those ones in the South Galactic Cap. The histograms give the number of quasars in each redshift bin.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fi12.eps}}\end{figure}$ Figure 12: Same as Fig. 11, except that a comoving distance scale is used and that only those quasars along the A1-A3 axis are considered. Redshifts are transformed into comoving distances using $r~ = 6\times ~ (1 - (1+z)^{-1/2}) ~\; h^{-1}$ Gpc, where h is the Hubble constant in units of 100 km s^-1 Mpc^-1. Bin size is $\Delta r = 0.4 ~ h^{-1}$ Gpc. Distances are counted positively for objects located in the North Galactic Cap and negatively for those ones in the South Galactic Cap.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fi13.eps}}\end{figure}$ Figure 13: The quasar polarization angles as a function of the redshift. Redshifts are counted positively for objects located in the North Galactic Cap and negatively for those ones in the South Galactic Cap. Polarization angles are vectorially averaged over redshift bins $\Delta z = 0.05$ . The full sample of 355 quasars is used. To facilitate detection of patterns, each data point (z, $\theta$ ) is replicated at (z, $\theta$ +180 $^\circ$ ) and (z, $\theta$ +360 $^\circ$ ).
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fi14.eps}}\end{figure}$ Figure 14: The quasar polarization angles, vectorially averaged over redshift bins $\Delta z = 0.5$ , as a function of the redshift. Redshifts are counted positively for objects located in the North Galactic Cap and negatively for those ones in the South Galactic Cap. Only the 183 quasars belonging to the A1-A3 axis are considered here. Error bars represent 68% angular confidence intervals for the circular mean (Fisher 1993); they must be seen with caution when the number of quasars per redshift bin is small, i.e. at large z. Errors are higher at $z \simeq -0.7$ and $z \simeq 1.2$ in agreement with previous results. Data points are replicated at (z, $\theta$ ), at (z, $\theta$ +180 $^\circ$ ) and at (z, $\theta$ +360 $^\circ$ ) as in Fig. 13. The fitted line is given by $\bar{\theta} = 268\hbox{$^\circ$ }- 42\hbox{$^\circ$ }~ z$ (see text).
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fi15.eps}}\end{figure}$ Figure 15: Same as Fig. 14, except that a comoving distance scale is used (cf. Fig. 12). Bin size is $\Delta r= 0.6 ~ h^{-1}$ Gpc. The superimposed line is $\bar{\theta} = 268\hbox{$^\circ$ }- 31\hbox{$^\circ$ }~ r$ , where r is the comoving distance in h^-1 Gpc.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fi16.eps}}\end{figure}$ Figure 16: Hammer-Aitoff projection of the quasar positions on the sky, in Galactic coordinates. The 355 objects are plotted. The radius of the circles is given by $\rho_i \propto \exp s_i - 0.9$ , where s_irefers the statistic defined in Sect. 6.1 for the pZ_c^m test and $n_{\scriptscriptstyle \rm V}$ = 40; the larger the circle the more significant the alignment at that point. The superimposed line gives the location of the celestial equator.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fi17.eps}}\end{figure}$ Figure 17: Maps of quasar polarization vectors and the corresponding distributions of polarization degree and angle for the low-redshift ( $z \leq 1$ ) objects located in the region of the sky defined in galactic coordinates by $b_{\scriptscriptstyle \rm II}\geq 30\hbox {$^\circ $ }$ and by $35\hbox {$^\circ $ }\leq l_{\scriptscriptstyle \rm II}\leq 175\hbox {$^\circ $ }$ (i.e. in the upper right quadrant of Fig. 16). Positions and polarization angles are projected in a coordinate system of northern pole [ $\alpha _p = 0\hbox {$^\circ $ }$ , $\delta _p = 30\hbox {$^\circ $ }$ ] and denoted by "P''. The distribution of polarization angles is weakly coherently oriented with $P_{\scriptscriptstyle\rm\! HP} = 2\times 10^{-2}$ and a preferred direction of 37 $\hbox {$^\circ $ }$ in that coordinate system.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fig1.eps}}\end{figure}$	Figure 1: The redshift distribution of the sample of 355 quasars, illustrated for the NGP and the SGP regions separately.
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$\begin{figure} \par\includegraphics[width=8.2cm,clip]{3337fig2.eps}\end{figure}$	Figure 2: The distribution of the polarization degree for the sample of 355 quasars. The median is $p \simeq 1.38\%$ . The last bin contains all objects with $p > 6\%$ .
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$\begin{figure} \par\includegraphics[width=8cm,clip]{3337fig3.eps}\end{figure}$	Figure 3: The logarithmic significance level of the statistical tests applied to the sample of 355 quasars. $n_{\scriptscriptstyle \rm V}$ is the number of nearest neighbours around each quasar and involved in the calculation of the statistics.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{3337fi5a.eps}\\ [0.3cm] \includegraphics[width=8cm,clip]{3337fi5b.eps}\end{figure}$	Figure 5: Same as Fig. 3 but for two sub-samples with different cutoffs of the polarization degree. When SL is smaller than 10^-5 (i.e. unresolved with 10⁵ simulations), we arbitrarily fix its value to SL = $8\times 10^{-6}$ .
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$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fig6.eps}}\end{figure}$	Figure 6: Distributions of the quasar polarization position angles for different sub-samples. The labels refer to the samples defined in Table 2.
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$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics*{3337fi15.eps}}\end{figure}$	Figure 15: Same as Fig. 14, except that a comoving distance scale is used (cf. Fig. 12). Bin size is $\Delta r= 0.6 ~ h^{-1}$ Gpc. The superimposed line is $\bar{\theta} = 268\hbox{$^\circ$ }- 31\hbox{$^\circ$ }~ r$ , where r is the comoving distance in h^-1 Gpc.
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