Astronomy. Astrophysics. Joint 3D modelling of the polarized Galactic synchrotron and thermal dust foreground diffuse emission

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1 DOI: / / c ESO 2011 Astronomy & Astrophysics Joint 3D modeing of the poarized Gaactic synchrotron and therma dust foreground diffuse emission L. Fauvet 1, J. F. Macías-Pérez 1, J. Aumont 2,3, F. X. Désert 1,4,5,T.R.Jaffe 3,6,A.J.Banday 3,7, M. Tristram 8, A. H. Waekens 7, and D. Santos 1 1 LPSC, Université Joseph Fourier Grenobe 1, CNRS/IN2P3, Institut Nationa Poytechnique de Grenobe, 53 avenue des Martyrs, Grenobe Cedex, France e-mai: macias@psc.in2p3.fr 2 Institut d AstrophysiqueSpatiae, Centre Universitaire d Orsay, Bat. 121, Orsay Cedex, France 3 Centre d Etude Spatiae des Rayonnements, 9 avenue du Coone Roche, Tououse, France 4 Laboratoire d astrophysique de Grenobe, OSUG, Université Joseph Fourier, BP 53, Grenobe Cedex 9, France 5 Institut Nee, 25 rue des Martyrs, BP 166, Grenobe Cedex 9, France 6 Jodre Bank Centre for Astrophysics, Schoo of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK 7 Max-Panck Institute for Astrophysics, Kar Schwarzschid Str. 1, Garching, Germany 8 Laboratoire de Accéérateur Linéaire, BP 34, Orsay Cedex, France Received 23 March 2010 / Accepted 19 October 2010 ABSTRACT Aims. We present for the first time a coherent mode of the poarized Gaactic synchrotron and therma dust emissions that are ikey to form the predominant diffuse foregrounds for measuring the poarized CMB fuctuations by the Panck sateite mission. Methods. We produced 3D modes of the Gaactic magnetic fied incuding reguar and turbuent components, and of the distribution of matter in the Gaaxy incuding reativistic eectron and dust grain components. By integrating aong the ine of sight, we constructed maps of the poarized Gaactic synchrotron and therma dust emission for each of these modes and compared them to currenty avaiabe data. We consider the 408 MHz a-sky continuum survey, the 23 GHz band of the Wikinson Microwave Anisotropy Probe, and the 353 GHz Archeops data. Resuts. The best-fit parameters obtained are consistent with previous estimates in the iterature based ony on synchrotron emission and pusar rotation measurements and this aows us to reproduce the arge-scae features observed in the data. Unmodeed oca Gaactic structures and the effect of turbuence make it difficut to accuratey reconstruct observations in the Gaactic pane. Concusions. Finay, using the best-fit mode we are abe to estimate the expected poarized foreground contamination at the Panck frequency bands. For the CMB bands, 70, 100, 143 and 217 GHz, at high Gaactic atitudes athough the CMB signa dominates in genera, a significant foreground contribution is expected at arge anguar scaes. In particuar, this contribution wi dominate the CMB signa for the B modes expected from reaistic modes of a background of primordia gravitationa waves. Key words. Gaaxy: genera poarization cosmic background radiation 1. Introduction ΔT T CMB The Panck sateite mission, currenty in fight, wi provide measurements of the CMB anisotropies both in temperature and poarization over the fu sky at unprecedented accuracy. Panck, which observes the sky over a wide range of frequency bands from 30 to 857 GHz, has a combined sensitivity of and an anguar resoution from 33 to 5arcmin(Consortia 2004). Of particuar cosmoogica interest is the possibiity of measuring the so-caed poarization B modes, the existence of which impies that tensor fuctuations from primordia gravitationa waves are generated during infation. Panck shoud be abe to measure the tensor-to-scaar ratio, r, downto0.1(betoue et a. 2009; Efstathiou et a. 2009) in the case of a nomina mission (2 fu-sky surveys) and to 0.05 with an extended mission of 4 fu-sky surveys (Efstathiou & Gratton 2009). The vaue of r sets the energy scae of infation (Peiris et a. 2003) and then provides constraints on infationary modes (Baumann 2009). To achieve this high eve of sensitivity, it is necessary to accuratey estimate the temperature and poarization foregrounds that arise both from diffuse Gaactic emission components and from point-ike and compact sources of Gaactic and extragaactic origins. Indeed, in the Panck frequency bands these foreground components may dominate the poarized CMB signa and therefore must be either masked or subtracted prior to any CMB anaysis. For this purpose, the Panck coaboration pans to use component separation techniques (see Leach et a. 2008, for a summary) in addition to the traditiona masking of highy contaminated sky regions incuding identified point-ike and compact sources. As these component separation techniques wi be mainy based on Panck data aone, one of the main issues wi be to estimate the residua foreground contamination on the fina CMB temperature and poarization maps. These residuas wi transate into systematic biases and arger error bars on the estimation of the temperature and poarization power spectra of the CMB fuctuations (see Betoue et a. 2009, fora recent study). Thus, they wi affect the precision to which cosmoogica information can be retrieved from the Panck data. Artice pubished by EDP Sciences A145, page 1 of 13

2 The main poarized foreground contributions wi come from the diffuse Gaactic synchrotron and therma dust emission. Using Wmap (Wikinson Microwave Anisotropy Probe) observations, Page et a. (2007) have shown that the emission from reativistic eectrons is highy poarized, up to 70%, between 23 and 94 GHz. Furthermore, Benoîteta.(2004); Ponthieu et a. (2005) have observed significanty poarized therma dust emission, up to a eve of 15% at the 353 GHz Archeops channe. By contrast the diffuse free-free emission is not intrinsicay poarized and the anomaous dust-correated microwave emission has been measured to be weaky poarized, %(Battistei et a. 2006). Finay, at the Panck frequency bands the poarized contributions from compact and point sources are expected to be weak for both radio (Nota 2009) and dust (Désert et a. 2008) sources. The spatia and frequency distribution of both Gaactic synchrotron and therma dust poarized emissions at the Panck frequencies are not we known and the ony avaiabe informations come from microwave and submiimetre observations. For synchrotron, Faraday rotation (Burn 1966) makes it very difficut to extrapoate the poarized observed radio emissions (Woeben et a. 2006; Woeben 2007; Carretti 2009) to the microwave domain. For therma dust, poarized observations are not currenty avaiabe in the infrared and the current optica data (Heies 2000) are too sparses (Page et a. 2007) for a reiabe extrapoation to ower frequencies. The diffuse Gaactic synchrotron emission is produced by reativistic eectrons spiraing around the Gaactic magnetic fied ines with the direction of poarized emission orthogona both to the ine-of-sight and to the fied ines (Rybicki & Lightman 1979). Based on these statements, Pageet a. (2007) proposedto mode the poarized synchrotron Gaactic emission observed by the Wmap sateite using a 3D mode of the Gaaxy incuding the distribution of reativistic eectrons and the Gaactic magnetic fied structure. Athough this mode aowed them to expain the observed poarization ange at the 23 GHz band where the synchrotron emission dominates, it was not used for the CMB anaysis. Instead, the 23 GHz data were adopted as a tempate for poarized synchrotron emission and extrapoated to higher frequencies. Independenty, Han et a. (2004, 2006) useda3d mode of the free eectrons in the Gaaxy (Cordes & Lazio 2002) and of the Gaactic magnetic fied that incuded reguar and turbuent components to expain the observed rotation measures towards known pusars. Based on previous work, Sun et a. (2008) performed a combined anaysis of the poarized Wmap data and of the rotation measurements of pusars using the pubicy avaiabe Hammurabi code (Waekens et a. 2009) for computing the integrated emission aong the ine-of-sight. This work has been extendedby Jaffe eta.(2010) for the study of the Gaactic pane using an MCMC agorithm to expore the parameter space of the modes, and by Jansson et a. (2009) for the fu sky using a ikeihood anaysis for parameters estimation. Therma dust emission arised from dust grains in the Interstear Medium (ISM) which are heated by stear radiation (Désert et a. 1998). They are considered to be obate in shape and to aign their ongitudina axis perpendicuary to the magnetic fied ines (Davis & Greenstein 1951). When aigned they rotate with their anguar moment parae to the magnetic fied ines. Since the therma dust emission is more efficient aong the ong axis, inear poarization is generated orthogona to the magnetic fied ines and to the ine-of-sight. The poarization fraction of the emission depends on the size distribution of the grains and is about a few percent at miimeter waveengths (Hidebrand et a. 1999; Vaiancourt 2002). Ponthieu et a. (2005) concuded that the poarized emission observed in the 353 GHz Archeops data was associated with the therma dust emission and proposed a simpe magnetic fied pattern to expain the measured poarization on the Gaactic pane. Page et a. (2007) suggested that part of the observed poarized emission of the 94 GHz Wmap data was aso due to therma dust. They modeed it using the observed poarization of stear ight (Heies 2000) which has a direction perpendicuar to that of therma dust. With the prospect of data from the Panck sateite mission in mind, we present here consistent physica modes of the synchrotron and therma dust emissions based on the 3D distribution of reativistic eectrons and dust grains in the Gaaxy, and on a 3D pattern of the Gaactic magnetic fied. The paper is structured as foows: Sect. 2 describes the 408 MHz a-sky continuum survey (Hasam et a. 1982), the five-year Wmap data set (Page et a. 2007)andtheArcheops data (Ponthieu et a. 2005) used in the anaysis. In Sect. 3 we describe in detai modes for the poarized emissions, which are statisticay compared to the data in Sect. 4. In Sect. 5 we discuss the impact of poarized foregrounds on the measurement of the poarized CMB emission with the Panck sateite, before presenting our concusions in Sect Observationa data 2.1. Diffuse Gaactic synchrotron emission The synchrotron mechanism emission is an important contributor to the diffuse sky emissions at both radio and microwave observation frequencies. Athough its SED is not accuratey known, it is considered to be we represented by a power aw in antenna temperature T ν ν β s with the synchrotron spectra index ranging from 2.7to 3.3(Kogut et a. 2007; God et a. 2009). Radio frequency information such as the Leiden 408 MHz and 1.4 GHz surveys (Brouw & Spoestra 1976; Woeben et a. 2006), the Parkes survey at 2.4 GHz (Duncan et a. 1999), and the MGLS survey (Medium Gaactic Latitude Survey) at 1.4 GHz (Uyaniker et a. 1999) are generay used to provide insight the Gaactic diffuse synchrotron emission in poarized intensity. However, Faraday rotation introduces compications into the interpretation of such data since strong depoarization is expected for frequencies ower than 10 GHz (Burn 1966; Sun et a. 2008; Jaffe et a. 2010; Jansson et a. 2009; La Porta et a. 2008, 2006). Consequenty, the best poarized Gaactic diffuse synchrotron tracers are at high frequency such as the Wmap survey at 23 GHz (Page et a. 2007) MHz a-sky continuum survey In the foowing we use the 408 MHz a sky continuum survey (Hasam et a. 1982) as a tracer of the Gaactic synchrotron emission in temperature. We use the HEALPix (Gòrski et a. 2005) format map avaiabe on the LAMBDA website 1. The caibration scae of this survey is caimed to be accurate to better than 10% and the zero eve has an uncertainty of ±3 Kasexpained in Hasam et a. (1982). To subtract the free-free emission at 408 MHz we use the five-year pubic Wmap free-free foreground map at 23 GHz generated from the maximum entropy method (MEM) described in Hinshaw et a. (2007). We have found that the free-free correction has no impact on the fina resuts presented in this paper. We start from the fu sky HEALPix maps at N side = 512 (pixe size of 6.9 arcmin) and downgrade them to N side = 32 (pixe size of 27.5 arcmin). We 1 A145, page 2 of 13

3 L. Fauvet et a.: Gaactic poarized foreground for PLANCK Fig. 1. Intensity maps at 408 MHz in K RJ units for the Hasam data (eft) and buit with the mode of synchrotron emission with an MLS magnetic fied for the best fit mode parameters (right). then subtract from the Hasam data the free-free component extrapoated from the K-band assuming a power-aw dependence of ν 2.1 as in Dickinson et a. (2003). The eft pane of Fig. 1 shows the free-free corrected 408 MHz a-sky survey where we ceary observe the Gaactic pane and the north poar spur at high Gaactic atitude Five-year WMAP poarized data at 23 GHz To trace the poarized synchrotron emission we used the a sky five-year Wmap Q and U maps at 23 GHz (Page et a. 2003; God et a. 2009) avaiabes on the LAMBDA website in the HEALPix pixeisation scheme at N side = 512. These maps have then been downgraded to N side = 32 to increase the signa-tonoise ratio as we are ony interested on very arge anguar scaes and the anaysis wi be performed on Gaactic atitude profies. We assumed anisotropic white noise on the maps and computed the variance per pixe using the variance per observation provided on the LAMBDA website and maps of the number of observations. We ignored arge anguar scae correations in the noise but beieved that this has no affect the fina resuts since very simiar resuts have been obtained from a pixe-based anaysis at N side = 16 using the fu noise correation matrix. The second and third pots in the eft coumn of Fig. 2 show the 23 GHz Q and U maps. We can ceary observe the Gaactic pane but aso arge-scae high Gaactic structures Therma dust The therma dust emission in intensity is we traced by the IRAS (Schege et a. 1998) a sky observations in the infrared, the COBE-FIRAS (Bouangeret a. 1996) a sky observations in the radio and miimeter domains and the Archeops (Macías-Pérez et a. 2007; Benoît et a. 2004) data in the miimeter domain over roughy one-third of the sky. Eary observations by Hitner (1949); Ha (1949) and ater by Heies (2000) demonstrated that staright emission in the optica domain was poarized, and therefore we can expect the therma dust emission at miimeter waveengths aso to be poarized. This was confirmed by the Archeops observations at 353 GHz (Ponthieu et a. 2005) that yieded a poarization fraction of about 10% in the Gaactic pane. Recent modes of poarized dust emission by Draine & Fraisse (2009) suggest that the dust poarization fraction coud be as high as 15% at 353 GHz. Here we used the Archeops 353 GHz Q and U maps as tracers of the poarized therma dust emission. As shown in the fifth and sixth pots of the eft coumn of Fig. 2 they coverabout 30% of the sky with 13 arcmin resoution. In contrast with the Wmap data at 23 GHz, the dominant signa is concentrated on the Gaactic pane. These maps are then downgraded to N side = 32 to increase the signa-to-noise ratio. The noise is assumed to be anisotropic white noise on the maps and we compute the variance per pixe using information provided by the Archeops coaboration (Macías-Pérez et a. 2007). 3. 3D modeing of the gaaxy We present in this section a reaistic mode of the diffuse poarized synchrotron and dust emissions using a 3D mode of the Gaactic magnetic fied and of the matter density in the Gaaxy. We wi consider the distribution of reativistic cosmic-ray eectrons (CREs), n CRE, for the synchrotron emission and the distribution of dust grains, n dust, for the therma dust emission. The tota poarized foreground emissions observed at a given position on the sky n and at a frequency ν can be computed by integrating aong the ine of sight as foows. Synchrotron For the synchrotron emission (Rybicki & Lightman 1979) we write: diν sync = ɛ sync (ν) n CRE (n, z) (1) ( B (n, z) 2 + B t (n, z) 2) (s+1)/4 dz we obtain I sync ν (n) = Q sync ν (n) = U sync ν (n) = di sync ν, (2) di sync ν cos(2γ(n, z)) p sync, (3) di sync ν sin(2γ(n, z)) p sync, (4) where I, Q and U are the Stokes parameters and ɛ sync (ν) isan emissivity term. γ is the poarization ange. B n is the magnetic fied component aong the ine of sight, n, andb and B t the magnetic fied components on a pane perpendicuar to the ineof-sight. z is a 1D coordinate aong the ine-of-sight. s is the exponent of the power-aw representing the energy distribution of reativistic eectrons in the Gaaxy. The poarization fraction, p sync, is reated to s, as foows p sync = s + 1 s + 7/3 (5) A145, page 3 of 13

4 Fig. 2. Form top to bottom: maps in intensity, I, and poarization Q and U at 23 GHz for the WMAP 5-year data (eft) and the mode of synchrotron emission with MLS magnetic fied for the best fit mode parameters (right) and at 353 GHz for the Archeops data (eft) and the mode of therma dust emission with MLS magnetic fied for the best fit mode parameters (right). The 353 GHz maps are rotated by 180 for better visuaization. A the maps are in K RJ units. A145, page 4 of 13

5 L. Fauvet et a.: Gaactic poarized foreground for PLANCK Fig. 3. Schematic view of the poarization direction of the Gaactic synchrotron and dust therma emissions as functions of the Gaactic magnetic fied direction. In the foowing we wi assume a constant vaue of 3 for s so that the synchrotron emission wi be proportiona to the square of the perpendicuar component of the Gaactic magnetic fied to the ine of sight and p sync = 0.75 (Rybicki & Lightman 1979). Locay, the direction of poarization wi be orthogona to the magnetic fied ines and to the ine-of-sight. Then, the poarization ange γ is given by γ(n, s) = 1 2 arctan 2B (n, z)b t (n, z) B 2 (n, z) (6) B2 t (n, z) Therma dust For therma dust emission we have di dust ν (n) = ɛ dust (ν) n dust (n, z)dz (7) we can write Iν dust (n) = Q dust ν (n) = U dust ν (n) = di dust ν, (8) diν dust p dust cos(2γ(n, z)) f g (n, z) f ma (n, z), (9) diν dust p dust sin(2γ(n, z)) f g (n, z) f ma (n, z), (10) where ɛ dust is the dust emissivity, p dust is the poarization fraction, γ is the poarization ange, and, f g and f ma are poarization suppression factors (see beow). The poarization fraction p dust wi be considered a free parameter in the anaysis. As discussed before, dust grains in the ISM are obates and wi aign their arge axis (see Fig. 3) perpendicuary to the magnetic fied ines (Davis & Greenstein 1951; Lazarian 1995; Lazarian et a. 1997; Lazarian 2009). Therefore, the poarization direction for therma dust emission wi be perpendicuar both to the magnetic fied ines and the ine-of-sight as was aready the case for the synchrotron emission. Then, the poarization ange γ wi be the same for the synchrotron and therma dust emissions. However, as the dust grains rotate with their spin axis parae to the magnetic fied, we aso need to account for a geometrica suppression factor. For instance, if the magnetic fied ines are parae to the ine-of-sight, we expect the dust poarized emission to be fuy suppressed. The suppression factor can be expressed as f g = sin 2 (α) whereα is the ange between the magnetic fied ines and the ine-of-sight. By construction, we observe that γ and α are the same ange. The process of aignment of the dust grains with the magnetic fied is very compex (Mathis 1986; Goodman & Whittet 1995; Lazarian 1995; Lazarian et a. 1997; Lazarian 2009) and its accurate representation is out of the scope of this paper. Then, to account for misaignment between the dust grains and the magnetic fied ines we define an empirica factor f ma. The exact form of this factor is unknown but we have empiricay observed that the geometrica suppression seems to be more important than expected for the Archeops data. Therefore, we have taken f ma to be sin(α). We have observed that the resuts presented in this paper are robusts with respect to the parameter Matter density mode In gaactocentric cyindrica coordinates (r, z, φ) the reativistic eectrons density distribution can be written as (see Drimme & Sperge 2001) e r n CRE,r n CRE (r, z) = n 0,e cosh 2 (z/n CRE,h ), (11) where n CRE,h defines the width of the distribution verticay and is set to 1 kpc in the foowing. n CRE,r defines the distribution radiay and it is a free parameter of the mode. Notice that we expect these two parameters to be strongy correated, hence we decided to fix one of them as in previous anayses (Sun et a. 2008; Jaffe et a. 2010). The density distribution of dust grains in the Gaaxy is poory known and we therefore eect to describe it in the same way as for reativistic eectrons: e r n d,r n d (r, z) = n 0,d cosh 2 (z/n d,h ), (12) where n d,r and n d,h are the radia and vertica widths of the distribution. In the foowing we set them to 3 and 1 kpc respectivey. We have tested different vaues of these two parameters and found no impact on the fina resuts Gaactic magnetic fied mode According to observations many spira gaaxies over a range of redshifts show evidences of a arge scae magnetic fied with intensity of few μg, and a direction spatiay correated with the spira arms (Sofue et a. 1986; Beck et a. 1996; Wieebinski 2005). For our Gaaxy, the magnetic fied direction aso seems to foow the spira arms but with a compex spatia distribution (Wieebinski 2005; Han et a. 2006; Beck 2006). Indeed, there are hints for oca reversas in the fied direction and radia dependency of the intensity (Han et a. 2006; Beck 2001). Pusar Faraday rotation measurements (Han et a. 2004, 2006; Sofue et a. 1986; Brown et a. 2007) have been used to fit the Gaactic arge-scae magnetic fied with various modes incuding both axisymmetric and bisymmetric forms, or a fied that reverses in the inter-arm regions, etc. Pusar Faraday rotation measurements aso indicate the presence of a turbuent component of the magnetic fied (Han et a. 2004). As discussed in Jaffe eta.(2010) the turbuent Gaactic magnetic fied can be separated into an isotropic and an anisotropic component. The atter, aso caed A145, page 5 of 13

6 ordered random component, wi be not considered in this paper because it cannot be distinguished from the arge-scae magnetic fied when studying poarization intensity ony Large-scae magnetic fied In the foowing we consider a modified ogarithmic spira (MLS) mode of the arge-scae magnetic fied based on the Wmap team mode presented in Page et a. (2007). It assumes a ogarithmic spira to mimic the shape of the spira arms (Sofue et a. 1986) to which we have added a vertica component. In gaactocentric cyindrica coordinates (r, z, Φ) it reads ( r B(r) = B reg (r)[cos(φ + β)n ( r cos(φ + β)n r 0 r 0 ) sin(p)cos(χ)u r ) cos(p)cos(χ)u φ + sin(χ)u z ], (13) where p is the pitch ange and β = 1/ tan(p). r 0 is the radia scae and χ(r) = χ 0 (r)(z/z 0 ) is the vertica scae. Foowing Tayor & Cordes (1993) we restrict our mode to the range 3 < r < 20 kpc. The ower imit is set to avoid the center of the Gaaxy for which the physics is poory constrained and the mode diverges. The intensity of the reguar fied is fixed using pusar Faraday rotation measurements by Han et a. (2006) B reg (r) = B 0 e r R R B (14) where the arge-scae fied intensity at the Sun position is B 0 = 2.1 ± 0.3 μg andr B = 8.5 ± 4.7 kpc. The distance between the Sun and the Gaactic center, R is set to 8 kpc (Eisenhauer et a. 2003; Reid & Brunthaer 2005). We aso study the spira mode of Stanev (1997); Sun et a. (2008), hereafter ASS. In cyindrica coordinates it is given by Br D = D 1 (r, Φ, z)d 2 (r, Φ, z)sin(p) (15) BΦ D = D 1(r, Φ, z)d 2 (r, Φ, z)cos(p) (16) Bz D = 0 (17) where D 1 accounts for the spatia variations of the fied and D 2 for asymmetries or reversas in the direction. The pitch ange is defined as for the MLS mode described above. D 1 (r, z) is given by B 0 exp( r R D 1 (r, z) = R 0 z z 0 ) r > R c B c r R c. (18) where R is the distance of the Sun to the center of the Gaaxy and it is set to 8 kpc as before. R c is a critica radius and it is set to 5 kpc foowing the ASS+RING mode in Sun et a. (2008). InthesamewayR 0 is fixed to 10 kpc, B 0 to 6 μg andb c to 2 μg. The fied reversas are as in Sun et a. (2008) athough it is important to notice that the synchrotron and therma dust poarized emissions depend ony on the orientation and not on the sign of the magnetic fied and therefore are not sensitives to fied reversas Turbuent component In addition to the arge-scae Gaactic magnetic fied, Faraday rotation measurements on pusars in our vicinity have reveaed a turbuent component on scaes smaer than a few hundred pc (Lyne & Smith 1989). Moreover it seems to be present on arge anguar scaes (Han et a. 2004) with an ampitude estimated to be of the same order of magnitude as that of the reguar one (Han et a. 2006). The magnetic energy E B (k) associated with the turbuent component is we described by a power spectrum of the form (Han et a. 2004, 2006) ( ) α k E B (k) = C (19) k 0 where α = 0.37 and C = (6.8 ± 0.3) erg cm 3 kpc. As discussed before, we ony consider here an isotropic random Gaactic magnetic fied, modeing an ordered component is beyond the scope of this paper Fina mode Finay the tota magnetic Gaactic fied B tot (r) can be written as B tot (r) = B reg (r) + B turb (r) (20) where B reg (r) is the reguar component, either MLS or ASS, and B turb (r) is the turbuent one. We define A turb as the reative intensity of the turbuent component with respect to the reguar one and it is a free parameter of the mode. The turbuent component is computed from a 3D random reaization of the power aw spectrum presented above over a box of points of 56 pc resoution. In this paper we do not consider the hao component presented by Sun et a. (2008); Jansson et a. (2009) as reativistic eectrons and dust grains are not expected to be concentrated on the hao Emissivity mode in poarization As discussed in the previous section, the poarized emission in the 23 GHz Wmap data shows compex structures both on the Gaactic pane and in oca high Gaactic atitude structures such as the north poar spur (Page et a. 2007). An accurate representation of this compexity cannot be achieved using our simpified mode. A simiar degree of compexity is observed in the 353 GHz poarization maps athough the morphoogy of the structures is rather different. To account for this, the Q and U estimated for synchrotron and therma dust modes are corrected using intensity tempates of these components extrapoated to the observation frequencies (23 and 353 GHz) using constant spectra indices. For the synchrotron emission we have ( ν Q s = I Has ( ν U s = I Has ) βs Q sync ν Iν sync, (21) ) βs U sync ν Iν sync, (22) where I Has is the reference map in intensity constructed from the 408 MHz a sky continuum survey (see Sect ) after subtraction of the free-free emission and ν is the frequency of A145, page 6 of 13

7 L. Fauvet et a.: Gaactic poarized foreground for PLANCK Tabe 1. Latitude and ongitude bands for the Gaactic profies used in the anaysis. Latitude interva (deg) [0, 30] [30, 90] [90, 120] [120, 180] [180, 270] [270, 330] [330, 360] Longitude interva (deg) [ 90, 50] [ 50, 20] [ 20, 5] [ 5, 5] [5, 50] [50, 70] [70, 90] Tabe 2. Parameters of the 3D Gaactic mode. Parameter Range Binning p (deg) [ 80.0, 80.0] 10.0 A turb [0, 2.5] B reg 0.25 n CRE,r (kpc) [0.0, 10.0] 1 β s [ 4.3, 2.4] 0.1 p dust [0.00, 0.30] 0.01 observation. Notice that we do not use the synchrotron MEM intensity map at 23 GHz (Hinshaw et a. 2007) as a synchrotron tempate to avoid any possibe spinning dust contamination (the Wmap team made no attempt to fit for the atter component). The spectra index β s used to extrapoate maps at various frequencies is a free parameter of the mode. For the therma dust emission we write Q dust ν Q d = I sfd, (23) Iν dust Uν dust U d = I sfd, (24) Iν dust where I sfd is the reference map in intensity at 353 GHz generated using mode 8 from Finkbeiner et a. (1999). We compute the I, Q and U maps for synchrotron and therma dust with a modified version of the Hammurabi code (Waekens et a. 2009). Each map is generated by integrating in 100 steps aong each ine-of-sight defined by the HEALPix N side = 128 pixe centres. The integration continues out to 25 kpc from the observer situated 8.5 kpc from the Gaactic centre. 4. Gaactic-profies comparison 4.1. Gaactic-profies description In order to compare the modes of Gaactic poarized emissions to the avaiabe data, we compute Gaactic ongitude and atitude profies for the modes and for the data in temperature and poarization using the sets of atitude and ongitude bands defined in Tabe 1. In both cases, we use bins of ongitude of 2.5. In the foowing discussions, we ony consider Gaactic atitude profies because equivaent resuts are obtained with the ongitudina profies. We compute error bars incuding intrinsic instrumenta uncertainties and the extra variance induced by the presence of a turbuent component. The atter is estimated from the RMS within each of the atitude bins foowing Jansson et a. (2009). For the 408 MHz a sky continuum survey we account for intrinsic uncertainties due to the 10% caibration errors described in Sect. 2. FortheWmap 23 GHz data we have computed 600 reaizations of Gaussian noise maps from the number of hits per pixe and the sensitivity per hit given on the Wmap LAMBDA web site. We have computed Gaactic atitude profies in poarization for these simuated maps and estimated intrinsic errors from the standard deviation within each atitude bin. For the Archeops data we use the noise simuations discussed in Macías-Pérez et a. (2007) and proceed as for the Wmap data. Fig. 4. Gaactic profies in temperature at 408 MHz buit using the Hasam data (back) and the mode of synchrotron emission with MLS for various vaues of the pitch ange p 70, 30 and 50 degrees (from green to red). Gaactic atitude profies are computed for a grid of modes obtained by varying the pitch ange, p, the turbuent component ampitude, A turb, the dust fraction of poarization, p dust, the radia scae for the synchrotron emission, n CRE,r, and the synchrotron spectra index, β s. The atter is assumed to be spatiay constant on the sky. Deaing with a more reaistic varying spectra index (see Kogut et a. 2007; La Porta et a for detaied studies) is beyond the scope of this paper. However, we ensured that this hypothesis does not impact the resuts for the other free parameters in the mode. Indeed, we produced simuated Wmap observations at 23 GHz with spatiay varying synchrotron spectra index and anaysed them assuming a constant one. No significant bias was observed for any of the other parameters and the error bars were compatibes with those in the cases of a constant spectra index. The range and binning step considered for each of the above parameters are given in Tabe 2. A the other parameters of the modes of the Gaactic magnetic fied and matter density are fixed to vaues proposed in Sect. 3. Notice that to be abe to compare the dust modes to the Archeops 353 GHz data, the simuated maps are mutipied by a mask to account for the Archeops incompete sky coverage. Figure 4 shows in back Gaactic atitude profies in temperature for the 408 MHz a sky continuum survey with error bars A145, page 7 of 13

8 Fig. 5. Gaactic profies in poarization Q and U at 23 GHz buit with the five-year WMAP data (back) and the mode of synchrotron emission with MLS magnetic fied for various vaues of the pitch ange p, 70, 30 and 50 degrees (from green to red). computed as discussed above. In coor, we show for comparison the expected gaactic diffuse synchrotron emission from the MLS Gaactic magnetic fied mode for various vaues of the pitch ange p from 80 to 80 degrees in steps of 20 degrees. In Fig. 5 we present the poarization Gaactic atitude profies for the Wmap 23 GHz data (back) and the expected poarized diffuse synchrotron emission for the previous MLS modes (coor). Finay, Fig. 6 shows the poarization Gaactic atitude profies for the 353 GHz Archeops data (back) compared to the same MLS modes (coor). From these figures we can see that the current avaiabe data do have discriminative power between the different modes and therefore a ikeihood anaysis is justified Likeihood anaysis The data and mode Gaactic atitude profies are compared using a ikeihood anaysis where the tota ikeihood function is obtained from L tot =Π 3 d=1 L d (25) where for each of the 3 data sets described above the ogikeihood function is given by og L d = i N on 1 j=0 N at 1 k=0 (D d i, j,k Md i, j,k )2 σ d 2 i, j,k (26) where i represents the poarization state meaning intensity ony for the 408 MHz a-sky survey, and, Q and U poarization for the 23 GHz WMAP and 353 GHz Archeops data. j and k represent the ongitude bands and atitude bins respectivey. D d i, j,k and Mi, d j,k correspond to the data set d and mode for the i poarization state, j ongitude band and k atitude bin, respectivey. σ d i, j,k is the error bar associated with M d i, j,k. Tabe 3 presents the best-fit parameters for the three individua data sets described above and aso for their combination (abeed A in the tabe). Resuts are presented both for the MLS and ASS modes of the Gaactic magnetic fied. The best-fit vaues for the pitch ange, p, are in agreement within 1-σ error A145, page 8 of 13

9 L. Fauvet et a.: Gaactic poarized foreground for PLANCK Fig. 6. Gaactic profies in temperature and poarization Q and U at 353 GHz with the ARCHEOPS data (back) and for various vaues of the pitch ange p, 70, 30 and 50 degrees, for the mode in poarization of therma dust emission with MLS magnetic fied (from green to red). Tabe 3. Best-fit parameters for the MLS and ASS modes of the Gaactic magnetic fied. Data Magnetic fied mode p (deg) A turb n CRE,r β s p dust (%) χ 2 min 408 MHz MLS <1.00 (95.4% CL) ASS <1.0 (95.4% CL) WMAP 23 GHz MLS <1.25 (95.4% CL) <20 (95.4% CL) ASS <1.5 (95.4% CL) (95.4% CL) Archeops 353 GHz MLS <2.25 (95.4% CL) ASS <2.25 (95.4% CL) <0.25 (95.4% CL) A MLS ASS <0.25 (95.4% CL) bars for the three data sets. From the fu data set, we can concude that the pitch ange favoured by the data is around 30 degrees with error bars of the order of 10 to 20 degrees both for the MLS and ASS modes. The fina error bars on this parameter are in agreement with the dispersion observed from different data sets, except for the Archeops ASS case. These resuts are compatibe with the pitch ange vaues presented in Sun et a. (2008); Page et a. (2007); Mivie-Deschênes et a. (2008). The reative ampitude of the turbuent component, A turb, is poory constrained and the data do not seem to favour a strong turbuent component either in the case of MLS or ASS modes. However, our resuts are compatibes with the ones presented in A145, page 9 of 13

10 Fig. 7. From eft to right and from top to bottom: power spectra C TT,C EE,C BB,C TE,C TB,C EB at 23 GHz buit with the 5-year Wmap data (back) and the mode of synchrotron emission with MLS magnetic fied for the best fit mode parameters, excuding the Gaactic region defined by b < 5. Sun et a. (2008); Mivie-Deschênes et a. (2008); Han et a. (2004, 2006) at the 2-σ eve. The eectron density radia scae, n CRE,r, is poory constrained by the data both for MLS and ASS modes athough our resuts are compatibe with those of Sun et a. (2008). We aso tested the possibiity of a oca contribution to the eectronic density as proposed by Sun et a. (2008). We found that adding this oca component improves neither the fit nor the constraint on the radia scae. The best-fit vaue for the spectra index of the synchrotron emission seems to be significanty ower than the one in Sun et a. (2008); Page et a. (2007). This may due to differences between the intensity tempate. Notice that we rescae the poarization intensity using the 408 MHz a sky continuum survey to obtain a more reaistic mode. Finay, we observe that the constraints on the poarization fraction for dust, p dust are weak but they are in agreement with the resuts in Ponthieu et a. (2005) Temperature and poarization anguar power spectra Using the best-fit parameters of the MLS mode, p = 30.0, A turb = 0.0, n CRE,r = 4andβ s = 3.4, we have constructed simuated maps of the sky at 408 MHz and 23 and 353 GHz. Notice that for A turb we ony had an upper-imit from the anaysis and therefore, we have decided to set it equa to zero to maximize the possibe foreground emissions in the foowing study. These maps are shown on right-hand side of Figs and 2. Athough for the Gaactic profies the fit can be considered reativey good, the fake temperature map at 408 MHz ooks very different from the 408 MHz a-sky survey map (eft side of the pot), in particuar at the North Poar Spur (Woeben 2007), as no oca structures were incuded in the mode. This supports a posteriori our correction of the poarization synchrotron mode using an intensity tempate as presented in Sect. 3. InQ and U poarization, the 23 GHz simuated maps seem to reproduce quaitativey the structures observed in the Wmap data (eft side of the pot). However in temperature the mode and the data are very different as we have not accounted for spatiay variabe synchrotron spectra nor for any extra component as discussed in Page et a. (2007); Kogut et a. (2007); Mivie-Deschênes et a. (2008). Finay, the mode of therma dust emission is abe to reproduce quaitativey the Archeops data at 353 GHz. I, Q and U maps can be decomposed in spherica harmonics eading to the a T,m, ae,m and ab,m coefficients. The auto and crosscorreation of the atter form the 9 temperature and poarization anguar power spectra, C XY = a,m X, ay,m,wherex and Y can be either T, E or B. Figures 7 and 8 show the temperature and poarization anguar power spectra for the 23 GHz Wmap and 353 GHZ Archeops data compared to the best-fit MLS mode for synchrotron and dust, respectivey. As discussed before, the temperature auto power spectrum of the 23 GHz data is very different from the mode as no extra components in temperature were considered. However in poarization we have quaitativey a good agreement. However, we ceary observe that the mode does not account for a the observed emission. At 353 GHz the agreement between the data and the mode quaitativey and quantitativey is good. For poarization most of the data sampes at ess than 3-σ from the mode. In temperature the mode is not A145, page 10 of 13

11 L. Fauvet et a.: Gaactic poarized foreground for PLANCK Fig. 8. From eft to right and from top to bottom: power spectra C TT,C EE,C BB,C TE,C TB,C EB at 353 GHz computed from Archeops data (back) and the mode of therma dust emission with MLS magnetic fied for the best fit mode parameters (red) for the fu sky. as accurate as in poarization but we notice that the fitting was restricted to poarization data ony. 5. Gaactic foreground contamination to the CMB measurements by the PLANCK sateite We can use the best-fit mode of poarized synchrotron and dust emissions to estimate the poarized foregrounds contamination to the CMB at the Panck sateite observation frequencies. Notice that the aim of this section is not to obtain an accurate tempate of the poarized Gaactic foreground emissions to be subtracted from the Panck data for subsequent CMB anaysis. However, we are interested in comparing the predicted foregrounds contribution to the CMB emission. For this purpose, we have produced simuated maps of the Gaactic poarized foreground emissions using the best-fit mode parameters for each of the Panck CMB frequencies, 70, 100, 143 and 217 GHz. The therma dust poarized emission have been extrapoated using a constant spectra index of 2.0 in antenna temperature. We have computed the temperature and poarization power spectra of these maps and compared them to the expected CMB ones for the Wmap best-fit ΛCDM mode (avaiabe on the LAMBDA website) to which we added a tensor component assuming a tensor to scaar ratio of 0.1. Note that neither noise, systematics nor resoution effects are considered. Figure 9 shows these power spectra at 100 GHz. The expected CMB signa is represented in red. The poarized diffuse foreground emissions for Gaactic atitude cuts of b < 15,30 and 40 are shown as soid back, bue and cyan ines, respectivey. 1-σ errors in the mode are represented as dashed ines. In temperature, the CMB C TT dominates at a the anguar scaes considered as coud be expected from the Wmap and Archeops data. For poarization, the CMB C EE dominates at high vaues but we observe significant foreground contamination at the owest vaues ( <20). In the same way, the CMB C TE dominates at 100 GHz but for very ow vaues. However, the CMB C BB is significanty smaer than the foreground contribution at a the anguar scaes considered even for such a arge vaue of the tensor to scaar ratio. The CMB C TB and C EB are expected for most cosmoogica modes to be nu and therefore, the foregrounds contribution dominates the signa. These resuts are consistent with previous estimates by La Porta et a. (2006) who considered ony synchrotron emission and with those of Ponthieu et a. (2005) who modeed ony the dust emission. As the Gaactic poarized foreground emissions seem to dominate the observed emission at the Panck CMB frequencies, specia care shoud be taken when estimating the CMB emission using standard tempate subtraction techniques and component separation agorithms. The assessment of the fina errors is crucia and it is ikey that modes of the poarized foreground emissions such as those presented in this paper can be of substantia hep in this task. A145, page 11 of 13

12 Fig. 9. From eft to right and from top to bottom: power spectra C TT,C EE,C BB,C TE,C TB,C EB at 100 GHz for the mode of Gaactic poarized emission appying a Gaactic cut of b < 15 (back) 30 (bue) and 40 (cyan). The dashed curves indicate the 1-σ error bars in the modes. We compared them to the expected CMB ones (red) for the Wmap best-fit ΛCDM mode (Komatsu et a. 2009) to which we added a tensor component assuming a tensor to scaar ratio of Summary and concusions We have presented in this paper a detaied study of the poarized Gaactic foregrounds due to diffuse synchrotron and therma dust emissions. We have constructed coherent modes of these two foregrounds based on a 3D representation of the Gaactic magnetic fied and of the distributions of reativistic eectrons and dust grains in the Gaaxy. For the Gaactic magnetic fied we have assumed a arge-scae reguar component pus a turbuent one. The reativistic eectrons and dust grains distributions have been modeed with exponentias peaking at the Gaactic center. From these anaysis we have been abe to study the main parameters of the modes, the magnetic fied pitch ange, p, the radia width of the reativistic eectron distribution, h er,thereative ampitude of the turbuent component, A turb and spectra index of the synchrotron emission β s. We have been abe to set constraints ony on the pitch ange and the synchrotron spectra index. An upper imit on the reative ampitude of the turbuent component is obtained athough the data seems to prefer no turbuence at arge anguar scaes. With the current data we are not abe to constrain the radia width of the reativistic eectron distribution. Notice that our constraints are compatibe with those in the iterature. Using the best-fit parameters we have constructed maps in temperature and poarization for the synchrotron and therma dust emissions at 23 and 353 GHz and compared them to the Wmap and Archeops data at the same frequencies. We find good agreement between the data and the mode. However, when comparing the temperature and poarization power spectra for the data and mode maps, we observe that the synchrotron emission mode is not reaistic enough. For dust the mode seems to reproduce the data in better detai, but it is important to reaize that the errors on the Archeops data are much arger. From this, we can concude that the modes presented in this paper cannot be used for direct subtraction of poarized foregrounds for CMB purposes. However, they can be of great hep in estimating the impact of the poarized Gaactic foreground emissions on the reconstruction of the CMB poarized power spectra. Indeed, we have extrapoated the expected poarized Gaactic foreground emissions to the Panck CMB frequencies, 70, 100, 143 and 217 GHz and found that they dominate the emissions at ow, vaues where the signature of important physica processes such as reionization are expected in the poarized CMB power spectra. Furthermore, the Gaactic poarized foreground emissions seem to dominate the B modes for which we expect a unique signature from primordia gravitationa waves. Because of this, we propose the use of modes simiar to those presented in this paper to assess the errors in the reconstruction of the CMB emission when using tempate subtraction techniques or component separation agorithms. References Battistei, E., Reboo, R., Rubinõ Martin, J., et a. 2006, ApJ, 645, 141 Baumann, D. E. 2009, in AIP Conf. Proc., 1141 Beck, R. 2001, Space Sci. Rev., 99, 243 A145, page 12 of 13

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