Cosmological-scale coherent orientations of quasar optical polarization vectors in the $Planck$ era Investigating the Galactic dust contamination scenario

Gigaparsec scale alignments of the quasar optical polarization vectors have been proven to be robust against a scenario of contamination by the Galactic interstellar medium (ISM). This claim has been established by means of optical polarization measurements of the starlight surrounding the lines of sight of the 355 quasars for which reliable optical polarization measurements are available. In this paper, we take advantage of the full-sky and high quality polarization data released by the \textit{Planck} satellite to provide an independent, complementary, and up-to-date estimation of the contamination level of the quasar optical polarization data by the Galactic dust. Our analysis reveals signatures of Galactic dust contamination at the two sigma level for about 30 per cent of the quasar optical polarization data sample. The remaining 70 per cent of the lines of sight do not show Galactic dust contamination above the two sigma level, suggesting low to negligible contamination of the quasar optical polarization signal. We further found arguments suggesting that Galactic thermal dust cannot fully account for the reported quasar optical polarization alignments. Based on the measurements of the ratio of the polarized intensity of the dust in the submillimeter to the degree of linear polarization of the quasar in the optical, we provide a new and independent quality criteria to apply to the quasar optical polarization sample. We argue that, unless correction is applied, such a criterion should be imposed on the data for future investigations in the framework of the cosmological-scale correlations of quasar optical polarization vector orientations that still could compete with the isotropic principle of the cosmological paradigm.


Introduction
have reported alignments of quasar optical linear polarization vectors extending over cosmological-scale regions of the Universe (see also Jain et al. 2004;Pelgrims & Cudell 2014;Hutsemékers et al. 2014;Pelgrims & Hutsemékers 2015, 2016 and Pelgrims 2016 for a recent review).The very large scales at which these coherent orientations take place suggest either a cosmological origin or a correlation between objects or fields over cosmological scales, up to ∼ 1 Gpc at redshift z ≃ 1 − 2. These observations have been recognized as pointing at missing ingredients to the well accepted concordance cosmological model.Since their observational discovery, a wide variety of scenarios have been proposed to explain these alignments.A non-exhaustive list of these includes: fundamental constant variations, cosmic strings, cosmic birefringence, cosmological magnetic fields, new dark matter particle candidates, anisotropic or rotational cosmological mod-A&A proofs: manuscript no.P-2 The eventuality of instrumental bias has been discussed by Hutsemékers et al. (1998;2005) and Sluse et al. (2005).Briefly, their conclusion is that instrumental bias is very unlikely because the quasar optical polarization sample contains data from different observational campaigns, measured by different authors, using different techniques and/or with different instruments.Additionally, the global significance of the patterns of polarization alignments have been assessed using dedicated statistical techniques, specifically based on the reshuffling of the polarization vectors on the source positions, that would have take into account a global bias when computing the prior of randomness (see Jain et al. 2004;Hutsemékers et al. 2005).
As discussed further in Sect.2, the combination of magnetic fields and dust grains in our Galaxy is well known to polarize optical light from distant stars and to be at the origin of alignment patterns of star polarization vectors (e.g.Mathewson & Ford 1970;Axon & Ellis 1976;Planck Collaboration Int. XXI 2015).While the quasar light is certainly contaminated to some degree by the traversed ISM, Hutsemékers et al. (1998;2005) made sure it cannot be at the origin of the large-scale quasar polarization vector alignments.First, they used Burstein & Heiles (1982) extinction maps to evaluate the contamination of the quasar polarization data by the ISM.As a consequence they imposed severe selection criteria on the quasar polarization data to eliminate at best potentially strong contaminated data points.Second, they considered the polarized Galactic star catalogs of Axon & Ellis (1976) and Heiles (2000) to compare the quasar polarization vector orientations with those of the nearest polarized Galactic stars.The detection of the large-scale alignments of the quasar polarization vectors were found to be robust against the scenario of a Galactic dust contamination.Similar conclusion was also found in (Payez et al. 2010) where a basic modeling of the ISM contamination was investigated.
In this paper, our aim is to verify independently and with up-to-date data sets that the degree of contamination of the quasar optical polarization sample is indeed low and to verify that complex Galactic dust features could not account for the alignments.We will make use of the diffuse thermal dust polarized emission measured by the Planck satellite 1 at 353 GHz (Planck Collaboration Int. XIX 2015) to evaluate the level of contamination of the optical quasar polarization by the Galactic dust grains.This analysis should yield independent quality criteria for the quasar data and possibly allows, in the future, for the refinement of our understanding of these striking alignments of the quasar polarization vectors.
The paper is structured as follow.In Sect.2, we motivate the choice and subsequently present the data sets that we use to evaluate the ISM contamination of the quasar optical polarization data.Sect. 3 contains the core of our analysis and we present and discuss thereby the main results.We conclude in Sect. 4. Appendix A contains details about our treatment of the dust polarization maps.The robustness of our analysis regarding the choice of the adopted smoothing length of the polarization maps is discussed in Appendices B and C. In Appendix D, we reproduce the main results presented in the rest of the paper but obtained by means of another polarization ratio discussed by Martin (2007) and used in (Planck Collaboration Int.XXI 2015).
1 http://www.esa.int.Planck  Planck Collaboration Int. XXI 2015).If the magnetic field is coherent in a given region of the sky, dust grains align with the lines of the field in that region (Martin 2007 and references therein for viable physical models producing the alignment).The polarization state of an incident light beam passing through this region is then modified.The electric component perpendicular to the magnetic field is anisotropically dimmed by diffusion on the dust grains.An un-polarized incident light beam therefore exits the dusty region with a net polarization parallel to the magnetic field.The diffuse Galactic dust also emits thermally polarized light in the submillimetre spectral band.The polarization of this light is to be preferentially perpendicular to the lines of the magnetic field in which the dust grains are embedded (see, e.g., Martin 2007 for a discussion).

Data sets
As a consequence, for a given line of sight, polarization vectors in the submillimetre and in the visible are expected to be orthogonal one another if the optical polarization is only due to dust.If the background quasar has an intrinsic polarization then the dust contamination can be modeled as the vectorial addition of an ISM polarization (perpendicular to the dust polarized emission) to the intrinsic quasar polarization.An offset towards the perpendicularity can, in principle, be detected statistically.The relative orientations of the polarization vectors from both wave bands appear to be an easy-to-interpret indicator of contaminated quasar optical polarization data.
In this paper we shall take advantage of the full-sky maps of the thermal dust polarization signal from the Planck survey to proceed to our analysis.Compared to previous studies that rely on starlight polarization, the use of the Planck polarized dust data has the considerable advantage to probe the whole line of sight through the Milky Way.Some differences between the results obtained using starlight polarization and thermal dust are thus to be expected.The data sets that we use in this work are described below.

Quasar optical polarization catalog
The current sample of quasar optical polarization measurements from which the very large-scale alignments of the polarization vectors are studied is made of 355 sources.This sample contains reliable polarization measurements for quasars located in both Galactic hemispheres.195 quasars are located in the Northern hemisphere and 160 in the Southern one.The quasars that make the sample have been selected to avoid at best the ISM Galactic contamination according to the following requirements: |b| ≥ 30 • , p V ≥ 0.6% and σ ψ V ≤ 14 • which is about to corresponds to p V ≥ 2 σ p V .b is the Galactic latitude of the source, p V the degree of linear polarization, σ p V its error and σ ψ V the error on the polarization position angle.We denote the quasar optical polarization position angle ψ V which is defined in the IAU convention (North-to-East) and is expressed in degree.It takes values in the range 0 -180 • .The subscript V is used throughout for quasar polarization quantities.This choice also indicates that the quasar data are from the optical domain, mostly in the V-band (Sluse et al. 2005).
The redshift of the quasars of the final sample varies from 0.06 to 3.95.Despite the fact that all Galactic longitudes are covered, the sky coverage of the sample is unfortunately not ho-mogeneous (see Hutsemékers et al. 2005 and Pelgrims 2016 for details).
Up to now and to the best of our knowledge it is the only publicly available2 large and reliable sample of linear polarization data of quasars at optical wavelengths.We refer the reader to Hutsemékers et al. (2005) for a detailed description of this sample, which consists in a compilation of 'new' observations obtained at that time (Hutsemékers 1998;Hutsemékers & Lamy 2001;Hutsemékers et al. 2005;Sluse et al. 2005) and of ancillary data from the literature.
To proceed to our analysis, we first convert the quasar sky coordinates from B1950 to the J2000.Then, we convert them into Galactic coordinates (l, b).The quasar polarization position angles are transformed accordingly using, e.g.Eq. 16 of Hutsemékers (1998).

Planck 353 GHz polarized sky and dust data
The diffuse thermal dust polarized emission is the dominant Galactic foreground present in measurements of the polarization of the Cosmic Microwave Background (CMB) emission at frequency above 100 GHz (e.g., Planck Collaboration Int. XXII 2015).The Planck satellite recorded this emission and it provided unprecedented full-sky coverage maps of this Galactic emission in intensity I S and polarization, measuring the Q S and U S Stokes parameters.We use the subscript S to refer to the polarization quantities in the submillimetre.
We use the Planck single-frequency polarization maps at 353 GHz which are available on the Planck Legacy Archive3 .We refer the reader to Planck Collaboration Int.XIX (2015); Planck Collaboration Int.XXI (2015) for details and discussions regarding these data.The Planck HFI 353 GHz maps have a native resolution4 of about 4.86' (Planck Collaboration Int.XIX 2015) and a HEALPix5 grid tessellation corresponding to N side = 2048 (Górski et al. 2005).At the instrument resolution, the 353-GHz polarization maps are noise dominated (Planck Collaboration Int. XIX 2015).This is particularly true at high Galactic latitudes (|b| ≥ 30 • ) where the ISM is more diffuse.In order to increase the signal to noise ratio of the Planck HFI measurements of the diffuse ISM we smooth the Stokes parameter maps.From a physical point of view, the larger the smoothing value we adopt, the larger the angular scales of the ISM variations we consider.For our comparative analysis to be meaningful, there is a compromise between maintaining high resolution data and dealing with reliable dust polarization quantities.
As shown in Appendix A, we found convenient to smooth the polarization maps with a Gaussian kernel of full width at half maximum (FWHM) of 15' (due to the map intrinsic resolution, the effective beam is then about 15.8').This choice provides us with more than eighty per cent of the quasar lines of sight that fulfill the condition p S ≥ 2 σ p S , where p S is the degree of linear polarization of the dust emission and σ p S its uncertainty (see Appendix A).As a comparison, only about forty per cent of these lines of sight fulfill the above quality criterion if we consider the original maps.The analyses presented in Sect. 3 and 4 have also been conduced in parallel using a smoothing kernel with FWHM of 5', 10' and 20'.We choose to report only the results for FWHM of 15' in the core of the paper.The results with the other kernel FWHM values are very consistent as shown in Appendix A and B.
At 353 GHz, thermal dust is, by large, the principal source of the polarized signal.The dispersion arising from CMB polarization anisotropies is much lower than the instrumental noise for Q S and U S (Planck Collaboration VI 2014).Its impact on our analysis is thus expected to be negligible.The cosmic infrared background (CIB) is assumed to be unpolarized (Planck Collaboration XXX 2014).At this frequency, only small contributions are expected in the intensity map either from the CMB, the CIB and the zodiacal light (e.g., Planck Collaboration Int.XXI 2015).As we use only this map to reinforce other results only, we found unnecessary to correct the map from these contributions.
For each quasar we identify the HEALPix pixel corresponding to its position on the sky and we estimate the thermal dust emission quantities from the smoothed maps.Note that quasars of our sample are point-like sources having angular size below the arc second level (Sluse et al. 2005).Their contribution, or the contribution of their host Galaxy, to the 353-GHz signal collected by Planck are considered as negligible due to the instrument resolution at 353 GHz and the (approximate) pixel size of 1.71'.
From the I S , Q S and U S of the smoothed maps, we derive the dust linear polarization intensity P S , computed as P 2 S = Q 2 S + U 2 S , the degree of linear polarization p S = P S /I S , and ψ S the dust polarization position angle that we define in the IAU convention as We force to polarization position angle to be in the range 0 -180 • .The evaluation of the errors on these quantities is explained in Appendix A.
For our analysis, we also make use of the full-sky dust extinction map derived in (Planck Collaboration XI 2014).We refer the reader to that paper for discussions and details.This quantity, directly related to the optical depth of the ISM towards the quasars, helps at evaluating the level of contamination of the quasar light by the Galactic dust (see Planck Collaboration Int.XXI 2015 and our Sect.3).For consistency, we also smooth the E(B − V) map with the same Gaussian kernel FWHM values as for the polarization maps.

Dust-to-quasar polarization correlation quantities
As discussed in Sect.2, optical polarization that would be due only to depolarization by dust is predicted to be perpendicular to the submillimetre polarization emitted by the dust grains.The relative angle between the measured polarization vectors in the two wavebands might thus be considered as an indicator for dust contamination of the quasar optical data.The relative angle between the two polarization vectors is computed as where the angles are expressed in degree.The consecutive absolute values take into account the axial nature of the polarization vectors.∆ S/V is defined in the range 0 -90 • .For a sample of lines of sight, any deviation from uniformity of the ∆ S/V distribution could indicate a possible contamination of the sample.Therefore, we consider the ∆ S/V as our first dust-to-quasar contamination gauge.The ∆ S/V distribution of the 355 comparison measurements is shown in Fig. 1.A clear departure from uniformity is observed.We quantify and discuss it in the next subsection.Notice, that a departure from uniformity would not provide a sufficient argument to conclude for a contamination.Coincidental position angle correlations need to be taken into account.
We proceed to such consideration in Sect.3.3.
We complement our study using two polarization ratios discussed in (Martin 2007) and used in (Planck Collaboration Int.XXI 2015) to derive ISM physical properties by comparing polarized light from stars in the optical domain (V-band) and thermal dust emission from the same Planck data that we are using here.
The first polarization ratio we consider is defined as and has units of polarized intensity (here K CMB ).For Galactic star related studies, this ratio is used to characterize the efficiency of the dust grains at producing polarized submillimetre emission compared to their ability at polarizing starlight in the visible.
Here, the fundamental difference with starlight based studies is that the quasars of our sample are thought to have an intrinsic degree of linear polarization while the starlight are assumed to be un-polarized.The R P/p values are therefore expected to be much lower in our study than in (Planck Collaboration XXI 2015) for example.Large values of the R P/p require at the same time a large polarized dust emission and a low degree of linear polarization of the quasars.The first condition implies dusty regions with a significant alignments of non-spherical dust grains which, in turns, implies an efficient polarizability of incident optical light.The second condition is fulfilled for quasars that are more prone to be affected by dust contamination.Because dust contamination can be modeled as a vectorial addition of an ISM polarization to the intrinsic quasar polarization, the smaller the intrinsic degree of linear polarization, the more noticeable the dust contamination.
The other polarization ratio that we consider is defined as where τ V is the optical depth to the quasar, measured in the Vband.We compute this quantities from the extinction E(B − V) .086 with R V , the ratio of total to selective extinction (e.g.Planck Collaboration Int.XXI 2015.We adopt R V = 3.1 which is the indicated value for the diffuse ISM (e.g.Fitzpatrick 2004).Our results are independent of this value which only acts as a scaling factor.While R P/p is defined such that it is sensitive to the polarizing grains alone, R S/V also involves nonaligned grains.This non-dimensional ratio somehow weights R P/p by the amount of total dust and its extinction effect on the light of the background source.The phenomenology from this ratio is similar to the one with R P/p .The larger the R S/V value, the more prone to dust contamination the optical polarized signal.Our aim at considering this quantities is to cross check the results obtained with R P/p .For clarity, we base our discussion in the core of the paper on R P/p .The results with R S/V are shown in the Appendix D.
From a phenomenological point of view and if the optical data set is affected by the Galactic dust at a detectable level, one might expect to observe a correlation between the angle ∆ S/V and the polarization ratios.The larger the value of the polarization ratios, the more likely perpendicular the polarization vectors should be.We search for such correlation in Sect.3.3.Fig. 2 shows the scatter plot of the pairs (R P/p , R S/V ) for the quasar sample.

Preliminary results
We present the distribution of the 355 ∆ S/V measurements in Fig. 1.The blue histogram corresponds to the ∆ S/V that are com-puted from the position angles of the quasar optical polarization vectors and the 353-GHz dust polarization vectors built from the maps smoothed with a Gaussian kernel of FWHM of 15'.The departure from uniformity is significant and is robust even accounting for observational uncertainties as illustrated in red in Fig. 1.A two-sided Kolmogorov-Smirnov test gives a probability that the blue histogram is drawn from a parent-uniform distribution of about 2.4 10 −6 .This probability (P KS ) is independent on the number of bins.
Beside, the cumulative-binomial probability to observe, out of 355, 212 or more data points with ∆ S/V > 45 • is found to be P bin = 1.5 10 −4 .This shows that the excess towards the perpendicularity is significant.
Alternatively, we consider the mean of the cosines of the relative angles, denoted cos(∆ S/V ) .Under the hypothesis that these angle are uniformly distributed in the range 0 -90 • , the expectation value of this mean is 2/π ≃ 0.6366.Based on Monte Carlo simulations, in which the relative angles are randomly generated according to a flat distribution, we compute the probability to observe by chance a value of cos(∆ S/V ) as extreme as the one from the data, the p-value of the observation.Out of 10 6 random realizations, none managed to reach the value obtained for the data, leading to a p-value of p value 10 −6 .This is more than a 5σ deviation from uniformity.
From the sample of 355 quasars, several sub-samples were considered in the literature (e.g.Hutsemékers et al. 1998;2005;Jain et al. 2004;Pelgrims & Cudell 2014) to identify the regions of the parameter space where the quasars have their polarization the more aligned.For completeness and for comparison with these works, we apply such historical cuts and test the uniformity of the corresponding ∆ S/V distributions.We thus separate in two approximately equal parts the sample (i) by means of the sky location of the quasars (we separate the Northern Galactic sky to the Southern one), (ii) by means of the degree of linear polarization, and (iii) by means of the redshift z of the quasars.We also consider combinations of these selection criteria.Table 1 summarizes the results using the cos(∆ S/V ) -uniformity test.The two other tests lead to very similar results.
Under the assumption that the departure from uniformity of the ∆ S/V distribution with an excess towards 90 • indicates a contamination of the optical polarization data by Galactic dust, inspection of Table 1 reveals that, the contamination is more noticeable for the part of the quasar sample with a low degree of linear polarization.The contamination of the quasar sample could be significant for the whole Southern Galactic sky, even if the departure from uniformity and the predominance for the perpendicularity appears to be stronger for the low-redshift part and/or for the low-degree of linear polarization part of the sample.In the Northern Galactic cap, however, the contamination seems to involve preferentially the low-redshift part of the sample.The high-redshift part presents even a small deficit, and not an excess, of polarization vectors at more than 45 • to the dust polarization vectors; as opposed to what contamination would produce.It is specifically in that region of the space (angular and redshift coordinates) that the extreme-scale alignments of the quasar optical polarization vectors have been shown to be the more significant (Hutsemékers et al. 2005).
The conclusions from this investigation using dust polarization data agree with those obtained in (e.g., Hutsemékers et al. 2005;Payez et al. 2010) based on polarized starlight.All their discussions on the implication of the dust contamination on the pertinence of the cosmological-scale alignments of the quasar polarization vectors are thus expected to hold.
Table 1.Results of uniformity test and historical sub-samples.Probabilities are in per cent.N is the number of data points in the considered sub-sample, p V the degree of linear optical polarization and z the redshift of the quasars.cos(∆ S/V ) is measured from the sub-sample and the probabilities p value are set using 10 6 random simulations of samples of size N.In Table 2, we report the same kind of investigation but using the median of the polarization ratio R P/p to define the subsample.Inspection of this table suggests that it is the part of the sample that corresponds to large values of the polarization ratio that is responsible for the significant departure from uniformity of the ∆ S/V distribution.Indeed, cutting the samples in two equal-size sub-samples always leaves a ∆ S/V distribution compatible with uniformity for the low values of the polarization ratio.At the contrary, the part of large values are found to deviate very significantly to uniformity.This dichotomy is quantified using a two-sample Kolmogorov-Smirnov test on the ∆ S/V distributions.The probability that the ∆ S/V distributions of the low and large R P/p -value parts are drawn from the same parent distribution is found to be P 2KS (R P/p ) = 0.441%.We investigate further this point in Sects.3.3 and 3.4.

Correlation between ∆ S/V and R P/p
As discussed in Sect.3.1, R P/p (and R S/V ) represents a good parameter according to which the hypothesis of dust contamination can be investigated.In Sect.3.2 we found that R P/p could be cor- related to the degree of uniformity of the ∆ S/V distribution.Here we go further in the investigation of this apparent correlation.In Fig. 3 we show the scatter plot of the couple (cos(∆ S/V ), R P/p ).
In that figure, we also present binned data (blue points).The adopted sampling is such that each bin contains a fair -and approximately equal-amount of data points and in the meantime, leave us with as much bins as possible in order to allow for a detailed study in terms of the R P/p values.As observed, in Fig. 3, the larger the R P/p value, the smaller the cos(∆ S/V ) value, which implies a trend towards the perpendicularity of the optical polarization vectors from the submillimetre ones.We quantify this correlation using the Spearman's rank-order correlation test.Applied on the pairs (∆ S/V , R P/p ), the obtained correlation coefficient is 0.24 and the two-sided probability of obtaining this result by chance is 5.5 10 −6 .We further verify this result by means of a permutation test with 10 6 random simulations to evaluate the random distribution of the correlation coefficient.The random realizations were obtained by shuffling the values of the polarization ratio on the ∆ S/V values.The resulting distribution of the correlation coefficients corresponds to the (blue-) filled histogram in Fig. 4. The (one-sided) p-value of the observed correlation, marked by the (red) vertical line, is computed as being 2.0 10 −6 .
We test this result considering experimental errors on the position angles of the quasars and the dust polarization vectors.We generate the polarization position angles according to normal distributions centered on the observations and with their corresponding width 6 .For each of the 10 6 realizations we compute the Spearman correlation coefficient.The distribution of these correlation coefficients corresponds to the (orange-) unfilled histogram in Fig. 4. The Spearman's rank-order correlation coefficient is 0.22 ± 0.02 which corresponds to a 4.1 ± 0.4 sigma detection of a correlation between ∆ S/V and R P/p . 6The errors are taken from the catalog for the quasars and as deriving from the approximated calculation given in Appendix A for the dust.The robustness of our analysis with respect to the value of the FWHM of the Gaussian kernel to smooth the dust polarization maps is discussed in Appendix B. 7 Statistical uncertainties are also discussed in Appendix C. As shown in Appendix D, this result is also confirmed using the polarization ratio R S/V instead of R P/p .
For the sake of completeness, we have searched for similar correlations than those observed between the cos(∆ S/V ) and R P/p but with the various observables, either from the quasar data, the dust data or a mix of those.These observable are the two polarization ratios R P/p and R S/V , the dust related quantities τ V , P S , p S , I S and the quasar quantities b, l, z, p V , all defined above.We led this investigation using the Spearman rank-order correlation test.The results are given in Table 3. Very significant correlations are detected with the polarization quantities related to Galactic dust.
We also detect a significant correlation between cos(∆ S/V ) and the redshift of the quasars.This actually reflects the redshift dependence of the preferred orientation of the quasar optical polarization vectors (at least in the Northern Galactic hemisphere).Indeed, in the Northern hemisphere, quasars seem to have -on average-their polarization vectors randomly oriented with respect to the dust (second line of Table 1).Interestingly, low redshift quasars have their polarization vector preferentially perpendicular to the dust polarization vectors.The tendency is at the opposite for high redshift quasars.Compatible conclusion has been reached already in (Hutsemékers et al. 1998;2001;2005) considering starlight.This observational fact actually proves that dust contamination cannot fully account for the extreme-scale alignments of the quasar optical polarization vectors.Indeed, and as explored in details in (Payez et al. 2010), correcting for a Galactic contamination at low redshift automatically implies Table 3. Correlation between cos(∆ S/V ) and the observables : the polarization ratios R P/p and R S/V , the dust related quantities τ V , P S , p S , I S and the quasar related quantities b, l, z, p V .The two-sided probabilities obtained by the Spearman's rank-order correlation test are reported along with the corresponding correlation coefficient ρ. a much stronger alignments at high redshift.The reverse is also true.This means that quasars have their optical polarization vectors effectively aligned one another in at least one of the two regions of the space defined by Hustemékers et al. towards the North Galactic pole.

Robustness tests
As mentioned in Sect.3.2, any deviation from uniformity of the distribution of the ∆ S/V angles indicates a possible contamination of the optical polarization sample by foreground Galactic dust.However, a non-uniform ∆ S/V distribution is not a selfconsistent proof for a contamination.Coincidental correlation of the position angles needs to be investigated.To that concern, the correlation we have found between ∆ S/V and the polarization ratio R P/p (and R S/V ) is more convincing as arguments in favor of a measurable contamination of the quasar optical polarization sample.Furthermore, the shuffling procedure that we applied in the previous sub-section on the pairs (∆ S/V , R P/p ) and (∆ S/V , R S/V ) proves that the departure from uniformity of the ∆ S/V distribution is unlikely accidental but is likely due to contamination by dust.
To test further the robustness of the observed correlations against a scenario of fortuitous locations of lines of sight, we proceed to the following additional test.
We rotate the Planck dust polarization maps by steps of five degrees around the North-Galactic pole, from 5 • to 355 • .For each finite rotation we compute the relative angles between the quasar and dust polarization vectors, the two polarization ratios and finally the Spearman correlation coefficients, as for the data.We further invert the Southern and Northern hemisphere and proceed to the same analysis.This provides us with a distribution of 140 Spearman's correlation coefficients with which to compare the one from the real observations.
Out of the 140 realizations by rotation, none shows a correlation coefficient of the pairs (∆ S/V , R P/p ) as extreme as for the data.The same conclusion holds for the pairs (∆ S/V , R S/V ).According to this additional test, the probability that the observed correlations happen by chance is lower than 1%.The Spearman correlation coefficient from the measurements are 0.02 ±0.06 for the two polarization ratios.Given the values of the correlation coefficients for the data, the significance of the observed correla-Fig.5. Shown in red is the cos(∆ S/V value from the data as a function of the fraction of the sample that is removed according to the R P/p values of the data points (see text).The red shaded regions mark the one and two sigma contours from the observational errors on the polarization position angles (dust and quasar).The gray shaded regions correspond to the one and two sigma deviations around the expected value (black horizontal line), assuming a uniform distribution of ∆ S/V angles.Truncation of 20% of the sample is sufficient to obtain a distribution that agrees with uniformity.
tions is about 3.8 sigma8 away.A coincidental non-uniformity of the ∆ S/V distribution is therefore shown as being very unlikely.

Towards an unbiased quasar optical polarization sample
Fig. 3 shows that the departure from uniformity of the ∆ S/V distribution is likely due to the lines of sight having large values of the polarization ratio R P/p .It is therefore appealing to introduce a quality criterion of the quasar optical polarization based on the values of this ratio.We provide the first investigation in that direction.We show below that this parameter can be used to remove those data points that are significantly affected by dust and therefore obtain a sample of quasar optical polarization measurements free of Galactic dust contamination.
In Fig. 5, starting with the original sample of 355 ∆ S/V measurements, we systematically reduce the sample size by removing those data points having largest value of the polarization ratio R P/p .It is shown that removing twenty per cent of the sample is sufficient to retrieve a cos(∆ S/V ) distribution for which the hypothesis of uniformity cannot be rejected at the two sigma level.
We further show, in Fig. 6 that the polarization ratio is a good parameter at discriminating dust contaminated quasar optical polarization data.To that aim, we compare the < cos(∆ S/V ) > obtained after removing the 20% largest R P/p values from the sample to that when randomly removing 20% of the sample.It is shown that (i) the < cos(∆ S/V ) > values obtained by random truncation of the sample keep deviating significantly from the hypothesis of uniformity, (ii) the value of < cos(∆ S/V ) > corresponding to the sample truncated by means of R P/p does not correspond to a random truncation of the sample and, finally,  (iii) that the latter value agrees with a uniform distribution of the ∆ S/V angles.
In Appendix D, we show that similar result is obtained for R S/V and also for the other values of the FWHM of the Gaussian kernel used to smooth the dust maps.In a search of reliable optical polarization measurements, it appears relevant to discriminate the data points with respect to their value of the polarization ratios.In order to deal with an optical polarization sample for which the dust contamination is negligible, our analysis suggests to remove -from the original sample-all data points with either R P/p ≥ 57 µK CMB (or R S/V ≥ 9.4 10 −3 ).9Our results also show that Galactic ISM contamination is not detected for eighty per cent of the quasar optical polarization sample presented by Hutsemékers et al. (2005).
We have checked that the sky coordinates and the redshift distributions of the quasar polarization sample with and without the selection based on R P/p are similar.This provides a strong argument against the hypothesis that Galactic contamination would be at the origin of the extreme-scale alignments of the quasar optical polarization vectors.Hutsemékers et al. (1998;2001;2005) have reported alignments of quasar optical linear polarization vectors extending over cosmological-scale regions of the Universe.Severe quality criteria, that considerably limit the sample size, were adopted to reduce at best the Galactic contamination of the quasar optical polarization data by dust.The authors concluded that even if the resulting sample is unavoidably contaminated to some level by the ISM, this contamination would never be able to fully account for the extreme-scale alignments.The redshift dependence of the alignment directions is one of the characteristic of the alignments that cannot be explained with Galactic foregrounds (see also Payez et al. 2010).

Conclusions
In this paper, we re-investigate the degree of contamination of these optical polarization data by Galactic dust using Planck data instead of starlight optical polarization measurements.Our goal was to check independently and with up-to-date data sets that the contamination level of the quasar optical polarization sample is indeed low and to verify that complex Galactic dust features could not account for the alignments.We led our investigation using the Planck full-sky maps at 353 GHz which captures the diffuse thermal dust polarized emission.This observable is complementary and independent to starlight-based polarization estimation of the ISM.Moreover it has the advantage to have an homogeneous sky sampling and to be representative of the whole integration through the Galaxy of the dust along the line of sight.
First, our analysis reveals a significant deviation (> 5σ) from uniformity of the distribution of the relative angles between the polarization vectors of the quasars and of the dust (∆ S/V ).There is a significant tendency towards the perpendicularity of those vectors.Second, we found significant correlations (∼ 4σ) between the relatives angles and to polarization ratios that are computed for each line of sight to a quasar.The larger the values of the polarization ratios (R P/p or R S/V ), the more perpendicular the optical polarization vectors to the dust polarization vectors.So, using external data set (the dust maps), we were able to show that the dust contamination has a measurable effect on the quasar data, i.e. that the dust contamination might be higher than previously thought.However, our analysis also shows that the significant contamination involves only about 20% of the quasar sample.In order to avoid at best the ISM contamination, we suggest a new quality criteria based on the polarization ratio values.Applying such selection, we showed that the resulting ∆ S/V distribution agrees with the hypothesis of uniformity which we consider as an indication for negligible contamination of the optical polarization data.
In a sens, our work reinforces previous claim according to which the ISM cannot be responsible for the cosmological-scale alignments of the quasar optical polarization vectors.This is because about eighty per cent of the quasar sample presented by Hutsemékers et al. (2005) do not show trace of a contamination by the Galactic ISM.The cosmological relevance of the extremescale alignments of the quasar polarization vectors is thus expected to be unchanged as also discussed at the end of Sects.3.3 and 3.5.The proof of this claim, being beyond the purpose of this work, is postponed to future analyses.Meanwhile, we have found a strong argument against Galactic contamination for the quasars that have high redshift and that are located in the Northern Galactic cap.The tendency of the ∆ S/V distribution is indeed opposed to what a contamination would produce.
Further inquiries require that one reproduces the analyses presented in Hutsemékers et al. (2005) and Pelgrims & Cudell (2014) with the restricted sample, i.e. applying the polarizationratio selection.Alternatively, providing a simplistic model of Galactic dust contamination of the optical polarization data, a decontamination of the sample should be investigated.The observational characteristics of the extreme-scale alignments of the quasar polarization vectors shall be adapted accordingly.While this is well beyond the purpose of this work, this task is mandatory in a search for the physical scenario responsible for these striking observations.For such an inquiry, additional quasar optical polarization data will be required.Quasars showing a low degree of linear polarization should particularly be included to the sample as they could provide upper limits to the dust contribution of the optical polarized signal.Together with polarization data of Galactic starlight, they could be used to fit the parameters of the contamination model.Unfortunately, and to the best of our knowledge, there is yet no publicly available large quasar optical polarization sample of that sort.Hopefully this work would motivate the elaboration of such a sample.
Large-scale correlations of the quasar polarization vectors have also been observed at radio wavelengths (8.4 GHz) (Pelgrims & Hutsemékers 2015).While their were arguments against the hypothesis of strong Galactic contamination, it should be worth to performed a similar comparison as the one presented here but between the synchrotron full-sky map released by Planck and the flat-spectrum radio source polarization vectors.To this regards, the polarization maps of the diffuse emission and the point-like source catalog at low frequencies (11 -20 GHz) that will be released by the RADIOFOREGROUNDS project 10 will constitute a considerable advantage to lead such inquiries in the Northern equatorial hemisphere.
Appendix A: Dust polarized data: smoothing and error estimation We use the Planck HFI 353 GHz Stokes polarization maps (I S , Q S and U S ) obtained from the full mission with the five fullsky surveys.These maps have a native resolution of about 4.86'.At the instrument resolution, the 353 GHz maps are noise dominated (Planck Collaboration Int. XXII 2015).This is particularly true at high Galactic latitudes (|b| ≥ 30 • ) where the ISM is the more diffuse and where we conduct our analysis.We smooth the original maps in order to increase the signal-to-noise ratio or, accordingly, to reduce the variance in pixel.The price to pay is a loss in resolution of the maps altogether with an increase in beam difference between the diffuse dust emission and the pointlike quasar.We shall thus find the smallest smoothing length that leads to reliable dust polarization quantities.
We use the smoothing function from the Python HEALPix package (Górski et al. 2005).This function uses a Gaussian kernel for the smoothing of input maps and allows to handle easily polarization quantities.We investigated four values of the full width at half maximum (FWHM) of the Gaussian kernel: 5', 10', 15' and 20'.Due to the intrinsic map resolution, this corresponds to an effective resolutions of about 6.99 ', 11.13', 15.78' and 20.59', respectively.From these maps we can compute smoothed polarization quantities.
We evaluate the uncertainties in the smoothed maps using a Monte Carlo approach via the covariance maps released by Planck.We adopt the gross approximation that the errors on Stokes parameters are independent an Gaussian11 .We proceed as follow: (i) For each pixel, and for each Stokes parameter Ŝi , we generate a random realization according to a normal distribution centered on the data with a standard deviation taken as the square root of the corresponding diagonal element from the covariance matrix given in the Planck data, C SS i .(ii) We proceed to the smoothing of the polarization maps, keeping the N side parameter to 2048.(iii) We extract the Stokes parameters in pixels that contain the quasars and we compute the relevant quantities.(iv) We run from (i) to (iii) 100 times.This allow us to evaluate the mean and the standard deviation for the smoothed quantities.For the dust polarization position angle uncertainties, we adopt the (approximated) standard relation (Serkowski et al. 1975) σ ψ S = 28.65 • × σ p S /p S .
For the four smoothing FWHM values used to smooth the polarization maps, we have computed the degree of linear polarization p S of the dust and its associated uncertainties σ p S .For the 355 lines of sight towards the quasars, the fractions that pass the selection p S ≥ 2 σ p S are 69.6%,76.7%, 83.1% and 87.6% for the FWHM smoothing kernel of 5', 10', 15' and 20' respectively.We choose the FWHM value of 15' to conduct our discussion in the core of the paper as it leads to more than eighty per cent of the lines of sight having reliable polarization measurements.Meanwhile, and as demonstrated in the next sections, we conducted our analysis in parallel for the other FWHM values and found consistent results.Furthermore, in the core of the paper, we took into account the observational uncertainties (on the polarization position angles) while deriving the most important results.

Fig. 1 .
Fig. 1.Histogram of the 355 relative angles ∆ S/V computed as in Eq. 2. The observed distribution is not uniform.The central values and the error bars given in red are obtained by considering, for each line of sight, observational uncertainties on both polarization position angles, from the quasar and from the dust, as explained in Sect.3.3.They correspond to the mean and the dispersion obtained in each bin by computing the histogram for the first 10 4 realizations.

Fig. 2 .
Fig.2.Scatter plot in the plane (R P/p , R S/V ) of the 355 measurements of the polarization ratios measured from the Planck maps smoothed with a Gaussian kernel of FWHM of 15' and the quasar data.Horizontal and vertical dashed-line mark the cuts suggested in Sect.3.5 in order to retrieve a ∆ S/V distribution that agrees with the hypothesis of uniformity at the 2σ level.Quasars corresponding to polarization ratio values below these thresholds are expected to have an optical polarization not significantly affected by Galactic dust.

Fig. 3 .
Fig.3.Scatter plot in the plane (cos(∆ S/V ), R P/p ) and binned data.The error bars correspond to the errors on the mean of cos(∆ S/V ) in bin that are due to experimental uncertainties.Statistical errors in bin are about two times larger.Vertical gray lines show the borders of each bins.They were chosen such that each bin contains 51 data points, except the last one which contains 48 of those.The horizontal-tick line shows the expected mean under the assumption of uniformity in bin and the horizontal-dashed lines show the one standard deviation from this mean, computed for 51 data points.

Fig. 4 .
Fig. 4. Spearman's rank-order correlation coefficients between ∆ S/V and R P/p .(Blue-)filled histogram corresponds to the distribution obtained by shuffling 10 6 time the R P/p on the relative angles.(Orange-)unfilled histogram is for the distribution obtained by taking into account the observational uncertainties on the polarization position angles.The (red) vertical line corresponds to the correlation coefficient obtained from the data.

Fig. 6 .
Fig.6.The filled blue histogram is for the distribution of < cos(∆ S/V ) > for 10 6 realizations of uniform ∆ S/V distributions for a sample size of 0.8× 355.The red unfilled histogram corresponds to the values obtained for the data when removing the 20% of the sample with the higher values of the R P/p ratio.This distribution takes into account the errors on the polarization position angles.The green unfilled histogram is for 10 6 realizations of 20% random truncation of the original sample.

Table 2 .
Results of uniformity test and polarization-ratio sub-samples.
Probabilities are in per cent, R P/p in µK CMB .N is the number of data points in the considered sub-sample.cos(∆ S/V ) is measured from the sub-sample and the probabilities p value are set using 10 6 random simulations of samples of size N.