PoS(Cosmology2009)015 p into a part http://pos.sissa.it/ satellite. ce. e quadrupole and octopole, the rom the he quadrupole aligns with the axis f the octopole does not. However, ss, our analysis of the axis of evil st one axis aligning by chance in an e then determine the preferred axes for on map, which serves as a statistically Cosmology2009, ive Commons Attribution-NonCommercial-ShareAlike Licen , in the WMAP polarization data. We split the polarization ma ∗ axis of evil [email protected] [email protected] correlated with the temperature and an uncorrelated part.the W quadrupole and octopole in theindependent uncorrelated probe polarizati of the axis ofof evil. We evil find within that our the measurement axis ofwith precision, t our whereas measurement the uncertainty, axis the o probability of at lea isotropic is of thepromises order to be of a 50 powerful per tool when cent. applied to Neverthele data expected f We search for an unusualso-called alignment of the preferred axes of th Speaker. ∗ Copyright owned by the author(s) under the terms of the Creat c International Workshop on Cosmic Structure andSeptember Evolution 23-25, - 2009 Bielefeld, Germany Mona Frommert The axis of evil – a polarization perspective Max-Planck-Institut für Astrophysik, Garching, Germany E-mail: Torsten A. Enßlin Max-Planck-Institut für Astrophysik, Garching, Germany E-mail:

PoS(Cosmology2009)015 (2.1) . When ◦ 3 . : L Mona Frommert [3, 1, 11, 16, 15]. MB) is one of the strongest re map. To this end, we use de Oliveira-Costa et al. [3], axis of evil d ILC map in Fig. 1, most of e planes are roughly the same hysical origin as the primordial adrupole and octopole extracted able significance, which seem to . B temperature map have led to a ) s the rization map which is uncorrelated ological origin of them. ˆ nt years, there have been claims of n easurement, or whether it is actually into spherical harmonics, which are lar momentum operator oise in the temperature data [2], and nt between the preferred axes of the polarization map, so that a detection ( ation in the CMB temperature map, if direction that can be picked out in the de Oliveira-Costa et al. came up with primordial Universe [4, 12, 17, 8, 13, perature map also manifest themselves be of the axis of evil. Chance fluctua- e map as well. lm and thus to question the cosmological Y liarities as the latter, if these are intrinsic T lm a ng anomalies in the temperature map. For example, if m , l ∑ tion maps [6]. ary effect on the CMB such as the integrated Sachs-Wolfe ≡ 2 ) ˆ n ( However, since the polarization is not statistically in- l T 1 l ∑ )= ˆ n ( T (ILC) map from WMAP smoothed with a kernel of 18 To define the preferred axis, we use the statistic proposed by We start by searching for the axis of evil in the CMB temperatu The observed isotropy of the cosmic microwave background (C Note, though, that this is not generic for all models exibiti Since the polarization fluctuations of the CMB have the same p internal linear combination 1 working on large scales, wewe can decide safely to neglect neglect the residual detector foregrounds in n the temperatur which has been introduced in ordersmoothed to temperature quantify the map preferred by eye.the hot and When cold looking blobs at seemfrom the to the be smoothe lying ILC on map thefor show same plane. the the two The same qu multipoles. behaviour Inthe [see, order following e.g., to statistic. 3], quantify and this Theeigenfunctions alignment, th temperature of maps the square are and expanded the z-component of the angu dependent of the temperature, chance fluctuations in the tem in the polarization [6].with Here, the we temperature thus map use astions the a in part statistically the of independent temperature pro the maps pola of do the not anomalies affect in the the latter uncorrelated would be a hint to an actual cosm 2. The axis of evil in temperature the 1. Introduction The axis of evil evidences for the isotropy ofanomalies the detected Universe. in the However, CMBbreak in temperature rece statistical map isotropy with of consider principle. the Among temperature these fluctuations anomalies,quadrupole there and is the a octopole, strong which alignme is commonly referred to a the peculiarities in the temperature maps are due to a second effect, we would not expect them to be present in the polariza The claims of thediscussion existence about of whether this a is preferred simply dueit direction to can in a be chance the blamed fluctu on CM localdue structures to or a on systematics preferred in direction the18, intrinsic m 10]. to the geometry of the temperature fluctuations, they should exhibit similar pecu to the geometry of the primordial Universe. PoS(Cosmology2009)015 corr P (2.2) ). ) ◦ Mona Frommert denote galactic 60 b , ◦ , is the linear com- P and 110 l − ( . ≈ 2 | ) ) ap, in which we are then going b , where of the ILC map in Fig. 2. Both ′ alactic plane in the polarization ce the results from de Oliveira- , ) ˆ n l ◦ ( ( sponding to 33, 41, and 61 GHz), le (right panel) for the ILC map. We lm ible at our resolution. 63 , ization data are highly contaminated larization map, a obtained in a coordinate system with ◦ | e quadrupole and the octopole of ihood in the 5 year WMAP likelihood 2 by simply rotating the z-axis into every lm m d the axis of evil. n 120 a for which the expectation value of the z- t al. find m − ∑ n measurement precision. The axes of quadrupole ( = and downgraded to a resolution of NSIDE=8. ≈ i ◦ l ) 3 . T b 3 | , l 2 ( | L · ′ ˆ n | | l T h ′ ˆ n max ≡ , we determine the z-axis ˆ l ˆ n -direction. We determine the axis ˆ ′ n , is maximised: L · n , ˆ L denotes the spherical hamonic coefficient ILC map, smoothed with a beam of 18 ) ′ ˆ n Preferred axis of the quadrupole (left panel) and the octopo ( lm a Let us now move on and obtain the uncorrelated polarization m We plot the preferred axes of the quadrupole and the octopole Figure 1: Figure 2: The axis of evil reproduce the results of de Oliveira-Costa et al. within our and octopole point in the same direction, which has been name Then, for every multipole Here, longitude and latitude, respectively (de Oliveira-Costa e component of the z-axis pointing in ˆ bination of the maps of thewhich Ka, are Q, used and for V determining frequencycode bands the [9]. (corre low-l We polarization furthermore likel use the P06 mask [14] to mask out the g to search for the axis ofby evil. detector Unfortunately, noise the and WMAP polar galactic foregrounds. Our observed po 3. Splitting of the polarization map pixel centre and checking for the maximum, which is well feas ends of every axis are markedCosta et by al. a within cross our in measurement the precision: maps. the axes We of reprodu th point in the same direction, which is roughly PoS(Cosmology2009)015 cmb P (3.3) (3.2) (3.1) Observed , with i † Mona Frommert TT in order to obtain ≡ h Top panel: Part of the polarization T raw uncorr S P and with the WMAP temperature octopole for the uncorrelated i † ion maps: : T P Bottom panel: cmb P n the uncorrelated map, we would like . , map: ps). , which is highly contaminated by noise. ection 2. As we have already mentioned, ≡ h , P . Note that the index “rec” indicates that corr T corr , T . We show the Stokes Q and U maps of the P P 1 S − T − WP rec S . We obtain the correlated polarization map by uncorr uncorr T P − , P cmb P 4 P P S rec . uncorr ≡ P in galactic coordinates are shown in the top panel of ≡ ≡ P rec uncorr corr P raw P uncorr uncorr P P , in the bottom panel of Fig. 3. rec uncorr because we only observe P from the observed polarization map cmb P : corr cmb WP P from corr P Stokes Q (left) and U (right) part of the following polarizat denotes the sky mask. We then perform a Wiener filtering on , and a part uncorrelated with that, corr W P We now determine the preferred axes of the quadrupole and the We now split the WMAP polarization map into a part correlated uncorrelated polarization map, Figure 3: The axis of evil polarization map, again using the technique introduced in s 4. The axis of evil in the uncorrelated polarization map map uncorrelated with the temperature map, polarization maps (linear combination of Ka, Q, and V band ma the map we obtain is a Wiener reconstruction of the noise-reduced uncorrelated polarization map map. The Stokes Q and U parameters for where Fig. 3. map, simply translating the temperature map into a polarization We therefore subtract being the noiseless CMB-polarization map. Into order subtract to obtai However, we do not know where the signal covariance matrices are defined as PoS(Cosmology2009)015 . . ◦ ts σ 20 rec uncorr rec uncorr P − P ◦ . To this of evil. If . The colour , and the one rec , we have run uncorr ◦ P Mona Frommert rec uncorr P der to reduce the rec uncorr P s uncorrelated with the gnment between the axes of the , whereas we would not expect ly of each other. The probability n the maps, and the colour coding le (right panel) for conditional on the measured data, e therefore do not obtain evidence . The axis of evil lies inside the 1 es and their uncertainties for in from the axes of pective pixels in 5000 MC samples. rred axes of the quadrupole and the n the respective pixel. The axis of the ◦ ssed extensively in earlier works. In l in polarization. rec ic to the geometry of the primordial uncorr as given, and assume that the axes of arization data will result in an uncer- ered the uncorrelated polarization map P nties in the axes of T with an uncertainty of 42 uncorr . P ) ry of the primordial Universe from nt precision, whereas the axis of the octopole ◦ rec 36 uncorr , P ◦ 79 5 yields an uncertainty in the axes of about 10 − ) = ( b , Planck l ( with an uncertainty of 48 aligning with the axis of evil in an isotropic Universe amoun ) ◦ 0 , ◦ rec uncorr P 17 − , and used it as a statistically independent probe of the axis ) = ( b rec uncorr , l P if it were due to chance fluctuations in the temperature. In or ( rec uncorr P Preferred axis of the quadrupole (left panel) and the octopo are distributed isotropically over the sky and independent We have computed the part of the WMAP polarization map which i What can we learn from this result? The significance of the ali rec uncorr the axis of evil wereUniverse, due we to would some expect preferred its direction signature intrins to be present in temperature map, With this, we will have a powerful test to probe the axis of evi 5. Conclusions to see it in noise contained in the polarization maps, webefore have Wiener computing filt the axes. We have then determined the prefe Nevertheless, a very crude estimate for for at least one of the axes of to about 50 per cent,for due or to against a the preferred large direction uncertainties intrinsic to we the have. geomet W P quadrupole and octopole in the temperaturethis map work, has been we asse only look at the additional information we obta region of the quadrupole, but not of the octopole of Figure 4: The axis of evil end, let us take the preferred axis in the temperature map coding counts the number ofquadrupole MC aligns samples with the whose axis axisdoes of came not. evil to within lie our o measureme the mask, residual foregrounds andtainty detector in noise the in preferred the axes. pol In order to obtain the uncertai Monte Carlo (MC) simulations, drawingfor realisations which we of then determine the preferred axes. We plot the ax in Fig. 4. Again, bothcounts ends how of many every times axis the are preferred marked axisThe by came axis to a of lie cross on the i the quadrupole res points to of the octopole to PoS(Cosmology2009)015 Jour- Phys. , 363:29–39, (LAMBDA), Mona Frommert e mask, detector MNRAS nsen, M. Reinecke, and hat greatly improved this scretization and Fast Anal- parse Anisotropic Universe microwave background. Hamilton. Significance of the nalysis with polarization maps s of evil, whereas the axis of the . We acknowledge the use of the , 690:1807–1819, January 2009. teagudo, Christoph Räth, Claudia n predictions for models of CMB The imprints of local superclusters A. Wuensche. Alignment tests for with Planck. ments, and Martin Reinecke, Mari- onditional on the observational data. ibuted isotropically. This probability ApJ , 69(6):063516, March 2004. d direction intrinsic to the primordial ugh alignment with the axis of evil for rrelation: The observer’s manual. data, due to the large uncertainties in the HEALPix , 10:11, October 2005. , 622:759–771, April 2005. Phys. Rev. D 6 ApJ , 74(6):063506, September 2006. , 77(6):063008, March 2008. Phys. Rev. D Legacy Archive for Microwave Background Data Analysis Phys. Rev. D . In order to assess the uncertainty in the axes coming from th [5]. rec uncorr P , which will yield much more significant results. , 70(8):083536, October 2004. package [7], the Planck isotropy anomalies. nal of and Astro-Particle Physics October 2005. largest scale CMB fluctuations in WMAP. on the Sunyaev-Zel’dovich signals and their detectability Rev. D low CMB multipoles. M. Bartelmann. HEALPix: A Frameworkysis for of High-Resolution Data Di Distributed on the Sphere. Models and Application to the Five-Year WMAP Data. 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