The new Planck polarization data at large angular scales
Transcripción
The new Planck polarization data at large angular scales
The new Planck polarization data at large angular scales Anna Mangilli On behalf of the Planck Collaboration ! Institut d’Astrophysique Spatiale ! Paris Sud University Instituto de Física Teórica (IFT), Universidad Autónoma de Madrid (UAM) OUTLINE The CMB polarization at large angular scales! ! ! The challenge for Planck: systematics and statistics! ! ! The new Planck HFI results! ! The Planck Coll. A&A 2016: “Planck constraints on the reionization history” (arxiv:1605.03507) !The Planck Coll. A&A 2016: “Improved large angular scale polarization data”(arxiv:1605.02985) Anna Mangilli (IAS) - IFT, Universidad Autónoma de Madrid (UAM) - 20th June 2016 The CMB polarization Polarization Planck CMB polarization signal: orders of magnitude weaker than temperature E-modes • • Electric type polarization field. ! Generated by scalar density perturbations. B-modes • • • Magnetic type polarization field. ! Can be generated only by primordial tensor modes i.e. primordial gravitational waves ! Contribution from lensing Anna Mangilli (IAS) - IFT, Universidad Autónoma de Madrid (UAM) - 20th June 2016 Generation of the CMB polarization Planck Collaboration: Planck constraints on re erage ionized fraction of the gas in the Universe rapidly increased until hydrogen became fully ionized. Empirical, anaDECOUPLING lytic, and numerical models of the reionization process have highlighted many pieces of the essential physics that led to the birth to the ionized intergalactic medium (IGM) at late times (Couchman & Rees 1986; Miralda-Escude & Ostriker 1990; Meiksin & Madau 1993; Aghanim et al. 1996; Gruzinov & Hu REIONIZATION 1998; Madau et al. 1999; Gnedin 2000; Barkana & Loeb 2001; Ciardi et al. 2003; Furlanetto et al. 2004; Pritchard et al. 2010; Pandolfi et al. 2011; Mitra et al. 2011; Iliev et al. 2014). Such studies provide predictions on the various reionization observables, including those associated with the CMB. The most common physical quantity used to characterize reionization is the Thomson scattering optical depth defined as Z t0 Planck Collaboration: Reionisation history ⌧(z) = ne T cdt0 , (1) fraction rea rameterizat tical depth reionizatio onset of th constructio full compl mainly det z. This is logical pap to z = 1.7 reionizatio A reds flexible des process (e. 2015). A by the co t(z) Thomson scattering of star-for diffuse gas in the Universe is mostly ionized up to a redshift Thomson scattering optical depth optical depth:0 where ne is the number density of free electrons time t , T probes suc 6 (Fan et al. 2006). Z ⌘at z_reio 0 is star the Thomson t(z) (Faisst et a The cosmological evolution of galaxies, of the formationscattering cross-section, t0 ⌧is =the timeantoday,d⌘, e TequaRobertson is the time at of redshift z, and we can use the Friedmann and of the integrated luminosity of AGNs as a function 0 tion to convert dt to dz. The reionization history is conveniently choices of shift is constrained by surveys of individual galaxies in the ulexpressed terms where of the nionized (z) mialatora exp number xdensity ofe (z)/n free Helectrons co e (z) ⌘ n e is the fraction iolet (HST), visible light (HST and large ground basedinteleTheseatwo where n (z) is the hydrogen number density. time ⌘, is the Thomson scattering cross-section, is t H T pes), far-infrared and sub-millimeter wavelengths (space obadopt here In this study, we define the redshift of reionization, z ⌘ factor and ⌘ is the conformal time today. The reionisat re 0 vatories ISO, SPITZER, HERSCHEL), and millimeter (with Enhancement of the E&B which reio z , as the redshift at which x = 0.5 ⇥ f . Here the normalizatory is conveniently expressed in terms of the ionised % formation e und based millimeter telescopes SPT, ACT). 50 The modes at large angular we have tion, f = 1 + fHe = x1e (z) + nHe /n , takes into account electrons in-scales: H(z)/n = n (z) where n (z) is the Hydrogen numb e H H structures in the universe predicts that small masses detach jected into the IGM by the first ionization of helium (correspondREIONIZATION BUMP m the general expansion to collapse and virialize and if they sity. 25 eV),Autónoma which is assumed to- 20th happen roughly the beginning same the(UAM) following, defineatthe and the Mangillithe (IAS)lowest -ing IFT, to Universidad deIn Madrid Junewe 2016 ch a high enough temperature Anna to excite electronic The CMB E & B angular power spectra CMB anisotropies: l<20 (low-l) Large scale reionization bump CℓEE τ r CℓBB r = 0.1 lensing τ, r r = 0.03 r / Einflation Scientific goals Reionization history: CℓEE at large angular scales to constrain τ Inflation: CℓBB at large and intermediate scales to constrain r Anna Mangilli (IAS) - IFT, Universidad Autónoma de Madrid (UAM) - 20th June 2016 OUTLINE The CMB polarization at large angular scales! ! ! The challenge for Planck: systematics and statistics! ! ! The new Planck HFI results! ! The Planck Coll. A&A 2016: “Planck constraints on the reionization history” (arxiv:1605.03507) !The Planck Coll. A&A 2016: “Improved large angular scale polarization data”(arxiv:1605.02985) Anna Mangilli (IAS) - IFT, Universidad Autónoma de Madrid (UAM) - 20th June 2016 The Planck satellite ➡ 9 frequency bands (7 polarized: 30GHz-353GHz) ➡ Two instruments: ! LFI: 30GHz, 44GHz, 70GHz HFI: 100GHz, 143GHz, 217GHz 353GHz, 545GHz, 857GHz Channels for CMB characterization Foregrounds characterization 30GHz 44GHz 70GHz 100GHz 143GHz 217GHz 353GHz 545GHz 857GHz Anna Mangilli (IAS) - IFT, Universidad Autónoma de Madrid (UAM) - 20th June 2016 Large scale polarization issues • Planck detectors are sensitive to one polarization direction Polarization reconstruction: detector combinations ! • Mismatch between detectors will create spurious polarization signal Major systematics in polarization at large angular scales: ! ! Intensity to Polarization leakage LFI: negligible residuals with respect to noise, LFI 70GHz released HFI has higher sensitivity, lower noise: residuals systematics HFI 100GHz, 143GHz, 217GHz NOT used for the 2015 low-l analysis NEW HFI results 2016 Anna Mangilli (IAS) - IFT, Universidad Autónoma de Madrid (UAM) - 20th June 2016 The challenge I: control of systematics Measuring the large scale polarization is difficult! Major HFI systematic residuals: • inter-calibration leakage • ADC non-linearity residuals • correlated 1/f noise residuals • foreground residuals All these effects are important at low-l E-Modes: noise&systematics Planck Collaboration: Large angular scale data, reionization Planck-HFI 2015 Signal Planck-HFI NEW Signal Fig. 16. E-mode polarization pseudo spectra, plotted as C` to emphasise low multipoles, computed the plotted maps distributed in the Fig. 16. de E-mode polarization pseudo spectra, as C` to empha Anna Mangilli (IAS) - IFT, Universidad Autónoma Madrid (UAM) - 20th June 2016 from The ogy ethodology challenge II: low-l data analysis Statistical method(s) optimized to CMB analysis @ large angular scales Polarized CMB from 70 GHz Gaussian in the m=[T,Q,U] maps, with CMB Multivariate GaussianPlanck likelihood in the m=[T,Q,U] maps, with CMBin So farlikelihood (WMAP, 2013, 2015): Gaussian likelihood noise matrix M :matrix M : signal covariance plus noise covariance map space 1. Low ell CMB polarization in Planck 2014 comes from 70 GHz. 2. Out of eight surveys, we exclude Polarized CMB from 70 fromGHz the dataset survey 2 and 4 ow-l Commander temperature map because the exhibit unusual B mode excess, presumably connected with 013, the low-l temperature likelihood is based on sidelobe contamination. M= CMB signal+noise covariance matrix T,Q,U maps are of foreground emission and residual are cleaned of cleaned foreground emission and residual 3. Templates (30 and 353) are built U 1. Low ell CMB polarization in Planck Q systematics: : from full mission data. eground-cleaned Commander map like 2013, the 2014 map also incorporates the 9WMAP data and the 408 MHz Haslam 2014map comes from ore frequencies better fg model more clean sky 70 GHz. 4. Working resolution is nside = 16, Out of eight surveys, we exclude a. In2. T, Commander multiband CMB down sampled from highsolution resolution T, Commander multiband CMB solution from the dataset survey 2 and 4 noise weighting. No because the exhibit unusual B through mode smoothing is applied in polarization In Q,U polarized CMB isby provided 70 GHz, after excess, presumably connected with Q,U b. polarized CMB is provided Planck by 70 Planck GHz, after 5. The analysis mask retains 47% of the Stokes Q sidelobe contamination. template fitting for built polarized synchrotron dust, based sky. 3. Templates (30 and 353) aresynchrotron mplate fitting for polarized and dust, and based from full mission data. on Planck 30 and 353 GHz, and their polarization leakage Planck 304.Problem: and 353 GHz, and Working resolution is nside = 16, their polarization leakage noise covariance matrix reconstruction down sampled from high resolution corrections. Preliminary rections. ee Wehus’ talk tomorrow for more details Stokes Q ysis chain: erform component separation at 1 resolution efine narrow 2–based processing mask to emove obvious residuals ll mask with a constrained Gaussian realization Stokes U mooth to 440’ FWHM, and repixelize at Nside=16 efine proper side=256 2–based confidence mask at his year fsky = 0.93, which is up from 0.87 in 2013 owngrade mask, and apply to Nside=16 map accuracy through noise weighting. No smoothing is applied in polarization ange of different 2 thresholds considered; no systematic ases or trends found in power spectrum until fsky 0.97 • • 5. The analysis mask retains 47% of the sky. Stokes U Can compromise parameter reconstruction in particular for the high sensitivity of HFI channels! Preliminary of noise bias/residual systematics Difficult handling Anna Mangilli (IAS) - IFT, Universidad Autónoma de Madrid (UAM) - 20th June 2016 Cross-spectra likelihood at large scales [Mangilli, Plaszczynski, Tristram (MNRAS 483 2015)] ! Use cross-spectra likelihood at large scales! ! Noise bias removed. Exploit cross dataset informations! Better handling of residual systematics/foregrounds! Two solutions to solve for the non-Gaussianity of the estimator distributions at low multipoles • Analytic approximation of the estimators: works for single-field and small mask • Modified Hamimeche&Lewis (2008) likelihood for cross-spectra (oHL) Full temperature and polarization analysis Anna Mangilli (IAS) - IFT, Universidad Autónoma de Madrid (UAM) - 20th June 2016 In eq.14, f id f id @ f`id B C`TBBBB@ B ` ` C ` C CCC C`EB A 10 + o BB C`BB ` -15 A Cross-spectra likelihood at large scales C1/2 f id TB C is the square root of the C` matrix: ` C`EB C`BB used Figure 6. The o↵ tensor cross-spectra and -16 so [Mangilli, that:0 Plaszczynski,1Tristram (MNRAS 483 2015)] ol ∝ ol ol 10 for a given fiducial model and the function (g[D(P)]) refers to the (mode E T BC BBBC T T C TLewis 2008): A⇥B A⇥B10-16 C 0 C 0transformation: 1 C [X (C )] ! [OX ] = [X (O(C ))] . (18) ` ` ` CCC likelihood ` g ` g ` X `cross-spectra T TE g T`B C BBBC TB B • Modified Hamimeche&Lewis p C 0 10 15 (2008) for (oHL) C C B th T 1 5 ` ` C C BBB `B C 2lnL (C` ln(x) |Ĉ` ) = 1)), [Xg ]` [M f(16) ]``0 [Xg ]`0 . B TE EECCC= sign(x EB C -14 (13) l g(x) 1) (2(x B C 10 C = (15) B C C C B C ` B C T E EE EB The (oHL hereafter) reads: BBB new CCC `C` o↵set C` = BBBC (15) 0 C`` CCCH&L` likelihood `` ` 1/2 1/2 BBBapplied CCC consi B C X to the eigenvalues of the matrix P = C Ĉ C , where A data @ T@B T BEB A EB BB mod1 mod A⇥B BB A⇥B T Figure 6. The o↵se 1 0 Figure 6. The o↵set functions o of the o C C C` C `C2lnL C ` The [M ] is the inverse of the C -covariance matrix that allows 0 0 (C | Ĉ ) = [OX ] [M ] [OX ] , (19) ` ` to the `` ` ` ` ` g `` g ` Cmod and Ĉdata are, respectively, the matrices ` off the sampled C ` and ` f cross-spectra and forcross-spectra the six di↵erent combin and f 0 to quantify the ` ` and the correlations of the T, E, B fields. The `` the data. given fiducial model and the function (g[D(P)]) refers to the ven• fiducial model and the function toat the vector [Xg(g[D(P)]) ]for the H&Lrefers transformed C` angular vector defined as: in ge The problem is that and large ` iscross-spectra “Gaussianization” formation: The variable transformation g(x) is now modified for the cross-15 ⇣ positive ⌘ scalesp the P matrix is no longer guaranteed to be definite. In rmation: 10 1/2 1/2 T tions spectra to regularize the likelihood around zero so (16) [X ] = vecp C U(g[D(P)])U C . (14) -14 that Eq. g(x) = sign(x 1) (2(x ln(x) 1)), (16) g ` f id 10 fact, as shown of the cross- f id p in Eq. (2) that describes the distribution funct now reads: estimators 1/2 1/2can -14 spectra Ĉ , the Ĉ be negative. In order to solve g(x) = sign(x 1) (2(x ln(x) 1)), (16) ` data ed to the eigenvalues of the matrix P = CmodInĈeq.14, ,1/2 where 10 data Cmod C is the square root of the C matrix: ` cial m f id for this issue, we propose a modification of the H&L likelihood that and Ĉdata are, respectively, the matrices of the sampled C` and 1/2 1/2 g(x) ! sign(x)g(|x|). (20) Planc consists in adding an e↵ective o↵set o to the cross-spectra on the to the eigenvalues of the matrix P = Cmod Ĉdata` Cmod , where ata. diagonal of the C` matrices the positive definiteXYin order to ensure early 0 1 -16 The o↵set function o can be derived from simulations. We TheĈproblem is that for cross-spectra and at large angular nd are, respectively, the matrices of the sampled C and 10 TE T BC ` matrix. In particular, data ` re-define BBBC T Twe C ness of the cross-spectra P each C C C 8 guaranteed Mangilli, Plaszczynski, Tristram ` -15 ` C lines BBB ` ensuring 0 s the matrix is no longer to be positive definite. In • P C estimate the o↵sets from the MC distributions that the P 10 C “Offset” terms: N a. eff (eq. 15) matrix C` Covariance matrix as: BBBcorrelations) CCC (l-l and T-E-B T E EE EB C` =for (15) the b C as shown in Eq. (2) that describes the distribution of thedefinite crossBBBC`moreCthan C ` ` C matrix reconstructed is positive 99% of our 0 1 C BB@ angular CCA he problemĈ`is, thethat for cross-spectra and at large that: ⌧ and the scalar T T T T T E T B B C ra estimators Ĉ can be negative. In order to solve B C of tho↵ T B EB BB data C + o C C BBB `the o↵sets CCCthe simulations. Given⇣ that are to C distri` ` needed `shift C C C Figure 7. The ` ⌘⇣ ⌘ ` XY f id In ` ` ing accordingly t -15 BBBXY tolikelihood C XY f id that he P matrix is noa longer guaranteed be positive definite. XY A⇥B XY is issue, we propose modification of the H&L C A⇥B[M A⇥B 10 EE 0 ) sim EB the v ]``0 ` =field h) (C i MC , CCC (21) 2⌧ (so cross-spectra C` for !f each O(C = BBB`T,) sim (17) `+negative C`T EBC`to avoid C`(C o`EE C`0 Ceigenvalues butions E, on the A = A e at ` CCC TT s ` B sts in adding an e↵ective o↵set o to the cross-spectra on the ` B for a given fiducial model and the function (g[D(P)]) refers to the shown in Eq.P(2) that describes the of the crossB@ distribution C HFI⇥Planck-143 the⌧ fia straints of the T B EB BB BB Athe C distriXY XY A⇥B matrix, the o↵set functions depend on the shape of ` C C C + o where C ⌘ (C ) , and X, Y = {T, E, B}. onal of the C` matrices in order `to ensure definite-` ` ` ` transformation: usedWe in choose the sime ` the positive -16 estimators Ĉ , the Ĉ can be negative. In order to solve the (m li ` P matrix. data bution at each `.it In depend on10report the noise Since willparticular, be we useful inthe theo↵sets following, we also the levelstensor modes of the cross-spectra In particular, re-define each p 0 5 15 soequations that: the 10 set of tion Planck g(x) = sign(x 1) (2(x ln(x) 1)), (16) of the modified oHL likelihood in the case of the single issue, we propose a modification of the H&L likelihood that (model 2) andl bla atrix (eq. 15) as:of the maps involved in the cross-spectra and on the mask used. each ` independe Full temperature andwe polarization A⇥BIn particular, A⇥B analysis field approximation. are interested in applying the [Xof )]` the ! [OX (O(C ))] . more(18) 0 Ine↵ective 1g ]` = [Xgat 1/2 1/2 to de g (C `are ` ` s in adding an o↵set o to cross-spectra on the fact, the tails the C distributions each ` negative ent methods, sett ` ` applied to eigenvalues of the- matrix PEE=A⇥B Cmod Ĉdata Cmod , where EE T E(IAS) B Autónoma BBBC T T + method CCC cross-spectra Mangilli - IFT, Universidad de Madrid (UAM)C 20th June 2016 ) polarization EE-only ⌘ (C oT T Anna to Cthe C Tthe A⇥B ` ` Cross-spectra oHL: τ estimation 0.4 0.2 [Mangilli, Plaszczynski, Tristram (MNRAS 483 2015)] 0.0 0.00 Large-scale CMB cross-spectra likelih 0.02 0.04 0.06 0.08 0.10 0.12 τ τ posterior from realistic MC simulations, different noise levels, l=[2,20] 1.0 0.8 1.0 WMAPxPlanck-70 WMAPxPlanck-100 WMAPxPlanck-143 Planck-70xPlanck-100 Planck-70xPlanck-143 Planck-100xPlanck-143 0.8 0.6 Unbiasedness 0.6 fsky=0.8 fsky=0.5 Cross-spectra 0.4 0.4 0.2 0.0 0.00 0.2 0.02 0.04 0.06 τ 0.08 0.10 Optimality WMAPxPlanck-70 WMAPxPlanck-100 WMAPxPlanck-143 Planck-70xPlanck-100 100x143 Planck-70xPlanck-143 Planck-100xPlanck-143 0.6 0.4 0.0 0.00 ( f sky = 0.8) WMAP⇥Planck-70 0.0108 WMAP⇥Planck-100 0.0075 WMAP⇥Planck-143 0.0079 ⌧ ( Planck-70⇥Planck-100 0.0069 Large-scale CMB cross-spectra like 0.02 0.04 0.06 0.08 Planck-70⇥Planck-143 τ 0.10 0.0065 0.12 estimation at better than 1010% s 0.2 0.0 0.00 0.12 ⌧ Planck-100⇥Planck-143 0.0049for ⌧-r and ⌧ Table 3. Results of the joint constraints Figure 11. Validationwith of the The plots show theoHL full multi-fields temperaturelikelihood. and polarization oHL like that the oHL likelihood computed combining the simulations T, E and B fields acmodel used in the is theand ⇤CDM Bestfiducial constraints expected counting for both multipole results with ⌧ fand 0.078correlations and ln(1010gives (A s ) funbiased For r id =fields id ) = 3.09. from HFI 100GHzx143GHz on the estimation ofTable the reionization parameter ⌧. The r f idoptical = Results 0.1.depthoftothe 3. joint constraints for ⌧-r and top ⌧-ln( panel shows the ⌧ posterior six di↵erent when 20% of with the for fullthe temperature and cross-spectra polarization oHL likelihood. the sky is masked (cial f sky model = 0.8), while thesimulations bottom panel ⌧shows r the results used in the is the ⇤CDM Planck 10 for a bigger mask with = 0.5. The Adashed line and refers value ⌧ = f sky 0.078, ln(10 r to = the 0.1.input The results s ) = 3.09 ⌧ r ⌧ best f it best f it Comparison pixel-based ⌧ f id = 0.078 used inPlanck-100⇥Planck-143 the simulations. with the cross-spectra simulations with f 0.0772727 0.00492517 0.0971194 approach: compatible error bars 10 ) ⌧ ⌧ln(10 s A ) ln(10A10 1.0 0.8 Table 2. Results on the estimation of the ⌧ parameter w perature and polarization oHL likelihood. The fiducial m WMAPxPlanck-70 WMAPxPlanck-100 simulation is the Planck 2015 ⇤CDM best fit with ⌧ f id = WMAPxPlanck-143 shows the comparison between the estimates obtained w Planck-70xPlanck-100 sky cuts: . the small mask with with f sky = 0.8 and a Planck-70xPlanck-143 Planck-100xPlanck-143 f sky = 0.5. 0.02 0.04 0.06 τ 0.08 0.10 0.12 ⌧best f it (ln(10 A s ))best ⌧ ⌧best f it (ln(1010 fAits ))best(ln( ⌧ f it 0.0770 0.0050 3.0632 0.0 0.0775020 0.00501646 3.08478 ⌧ r ⌧best f it rbest f it ⌧ Figure11. 11.Validation Comparison posterior distributions of the ⌧ parameter Figure of of thethe oHL multi-fields likelihood. The plots showobfor current and 0.0049 future CMB experiments. We0.0 Annathe Mangilli (IAS) - IFT,and Universidad Autónoma de Madrid (UAM) 0.0777 0.0703 tained with full temperature polarization oHL likelihood (blue) and - 20th June 2016 Cross-spectra oHL: τ-r estimation [Mangilli, Plaszczynski, Tristram (MNRAS 483 2015)] l=[2,20], full temperature and polarization oHL likelihood! MC simulations Planck 100x143 with correlated noise 0.10 1.0 0.8 0.09 0.8 0.6 0.08 0.6 τ 1.0 Mangilli et al. 2015 0.4 0.07 0.2 0.06 0.2 0.0 0.05 0.0 0.1 0.4 0.2 0.3 0.4 r ⌧-r) and (⌧-A s ). The plot shows the joint constraints obtained with the full temperature and Anna Mangilli (IAS) - IFT, Universidad Autónoma de Madrid (UAM) - 20th June 2016 OUTLINE The CMB polarization at large angular scales! ! ! The challenge for Planck: systematics and statistics! ! ! The new Planck HFI results! ! The Planck Coll. A&A 2016: “Planck constraints on the reionization history” (arxiv:1605.03507) !The Planck Coll. A&A 2016: “Improved large angular scale polarization data”(arxiv:1605.02985) Anna Mangilli (IAS) - IFT, Universidad Autónoma de Madrid (UAM) - 20th June 2016 The new Planck-HFI results • Large scale Polarization l=[4-20] + lmin=2,3! ! • E-modes 100GHzx143GHz cross spectra (PCL, Xpol)! Planck Collaboration: Planck constraints on reionization history ! • Sky fraction: 50% + validation 60%! ! • multipoles. The idea behind this approach is that the noise can be considered as uncorrelated between maps and that systematics will be considerably reduced in cross-correlation compared to auto-correlation. At low multipoles and for incomplete sky coverage, the C` s are not Gaussian distributed and are correlated between multipoles. lollipop uses the approximation presented in Hamimeche & Lewis (2008), modified as described in Mangilli et al. (2015) to apply to cross-power spectra. The idea is to apply a change of variable C` ! X` so that the new variable X` is Gaussian. Similarly to Hamimeche & Lewis (2008), we define 0 1 q e` + O` CC q BBB C f CCA C f + O` , X` = C` + O` gB@ (A.1) ` C ` + O` p e` are the measured crosswhere g(x) = 2(x ln(x) 1), C power spectra, C` are the power-spectra of the model to evaluate, C`f is a fiducial model, and O` are the o↵sets needed in the case of cross-spectra. For multi-dimensional CMB modes (i.e., T , E, and B), C` is a 3 ⇥ 3 matrix of power-spectra: 0 TT TE TB 1 C C CC BBB C C B ET EE B C C EB CCCC , C` = BB@ C (A.2) A C BT C BE C BB ` Polarization foreground cleaning ! ! Fig. A.1. Galactic mask used for the lollipop likelihood, covering 50 % of the sky. Planck frequencies corrected for polarization leakage: ! • - 30GHz for polarized synchrotron - 353GHz for polarized dust e` C 1/2 . and the g function is applied to the eigenvalues of C` 1/2C ` In the case of auto-spectra, the o↵sets are replaced by the noise bias e↵ectively present in the measured power-spectra. For cross-power spectra, the noise bias is null and here we use the e↵ective o↵sets defined from the C` noise variance: r 2 C` ⌘ O` . (A.3) 2` + 1 Cross-spectra based likelihood analysis oHL (Mangilli et al. MNRAS 2015) The distribution of the new variable X can be approximated Fig. A.2. Distribution of the peak value of the posterior distrias Gaussian, with a covariance given by the covariance of the bution for optical depth from end-to-end simulations including e` is then noise, systematic e↵ects, Galactic dust signal, and CMB with the C` s. The likelihood function of the C` given the data C fiducial value June of ⌧ = 2016 0.06. X Anna Mangilli (IAS) - IFT, Universidad Autónoma de Madrid (UAM) - 20th T 1 e 0 Planck HFI 100GHzx143GHz E-modes at low-l: ! Planck Collabo first τ constraint from CMB polarization data alone z = 0.5), for the various data combinations are: Planck, Collaboration: Planck constraintslolli on reion ⌧ = 0.053+0.014 0.016 ⌧ = 0.058+0.012 0.012 , 14 lollipop+Plan Départemen Quai E. Ans 15 ⌧ , lollipop+PlanckTT+len Departamen 38206 La La 16 ⌧ , lollipop+PlanckTT+ Departamen s/n, Oviedo, 17 We can see an improvement of the posterior width Department Nijmegen, P temperature anisotropy data to the lollipop lik 18 Department comes from the fact that the temperature anisotrop Columbia, 6 other ⇤CDM parameters, in particular theCanada normal 19 initial power spectrum As , and its spectralDepartment index, n College of ing also helps to reduce the degeneracy with As , L California, 20 Department rid of the tension with the phenomenological lensi London WC AL when using PlanckTT only (see Planck Colla 21 Department 2016), even if the impact on the error barsBrighton is smal BN 22 Department the posteriors in Fig. 6 with the constraints from Pla Helsinki, He Anna Mangilli (IAS) - IFT, Universidad Autónoma de Madrid (UAM) - 20th June 2016 = 0.058+0.011 0.012 = 0.054+0.012 0.013 (see figure 45 in Planck Collaboration XI 2016) s asured crossel to evaluate, ed in the case des (i.e., T , E, (A.2) e` C 1/2 . C` 1/2C ` placed by the er-spectra. For re we use the e: (A.3) approximated ariance of the e` is then ata C (A.4) ed via Monte -field approxbased only on We use a conwith a Galactic mplitude meaodized using a seudo-C` estio polarisation) and 143 GHz rst two multicontamination boration XLVI 14 Département de Physique Théorique, Université de Genève, Quai E. Ansermet,1211 Genève 4, Switzerland 15 Departamento de Astrofı́sica, Universidad de La Laguna (ULL) 38206 La Laguna, Tenerife, Spain 16 Departamento de Fı́sica, Universidad de Oviedo, Avda. Calvo So s/n, Oviedo, Spain 17 Department of Astrophysics/IMAPP, Radboud Univer Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands 18 Department of Physics & Astronomy, University of Bri Columbia, 6224 Agricultural Road, Vancouver, British Colum Canada 19 Department of Physics and Astronomy, Dana and David Dorn College of Letter, Arts and Sciences, University of South California, Los Angeles, CA 90089, U.S.A. 20 Department of Physics and Astronomy, University College Lond London WC1E 6BT, U.K. 21 Department of Physics and Astronomy, University of Sus Brighton BN1 9QH, U.K. 22 Department of Physics, Gustaf Hällströmin katu 2a, Universit Helsinki, Helsinki, Finland Fig. A.2. Distribution of the peak value of the posterior distri23 Department of Physics, Princeton University, Princeton, New Jer bution for optical depth from end-to-end simulations including U.S.A. noise, systematic e↵ects, Galactic dust signal, and CMB with the 24 Department of Physics, University of California, Berke fiducial value of ⌧ = 0.06. California, U.S.A. 25 Department of Physics, University of California, One Shi Avenue, Davis, California, U.S.A. To validate the choice of multipole and the stability of the re26 Department of Physics, University of California, Santa Barb sult on ⌧, we performed several consistency checks on the Planck California, U.S.A. 27 data. Among them, we varied the minimum multipole used (from Department of Physics, University of Illinois at Urbana-Champa ` = 2 to ` = 4) and allowed for larger sky coverage (increasing 1110 West Green Street, Urbana, Illinois, U.S.A. 28 to 60 % of the sky). The results are summarized in Fig. A.3. Dipartimento di Fisica e Astronomia G. Galilei, Università d Studi di Padova, via Marzolo 8, 35131 Padova, Italy 29 Dipartimento di Fisica e Astronomia, Alma Mater Studior Appendix B: Impact on ⇤CDM parameters Università degli Studi di Bologna, Viale Berti Pichat 6/2, I-401 Bologna, Italy In addition to the restricted parameter set shown in Fig. 6, 30 Dipartimento di Fisica e Scienze della Terra, Università di Ferr we describe here the impact of the lollipop likelihood on Via Saragat 1, 44122 Ferrara, Italy 31 ⇤CDM parameters in general. Figure B.1 compares results from Dipartimento di Fisica, Università La Sapienza, P. le A. Mor lollipop+PlanckTT with the lowP+PlanckTT 2015. The new Roma, Italy 32 low-` polarization are sufficiently that they Dipartimento di Fisica, Università degli Studi di Milano, Fig. A.3. Posterior results distributions for opticalpowerful depth, showing the Celoria, 16, Milano, Italy break between ns choices and ⌧. The contours ⌧ and e↵ectthe of degeneracy changing two of the made in ourforanalysis. 33 Anna likelihood Mangilli (IAS) - IFT, Universidad Autónoma (UAM) - 20th di June 2016Università di Roma Tor Vergata, Via d Fisica, As , where the lollipop dominates the constraint, arede MadridDipartimento End-to-end simulations Sky fraction (2014) and Planck Collaboration XIII (2016); however, some tension still remains. +0.014 ⌧ = 0.053 0.016 , with Combining with VHL data gives compatible results, consistent error bars. The slight shift toward lower+0.012 ⌧ value (by ⌧ = 0.058 0.012 ,alone ) is related to the fact that the PlanckTT likelihood Combination0.3 of low-l HFI with: pushes towards higher ⌧ values (see Planck Collaboration +0.011 XIII ⌧ = 0.058 0.012 , 1. +Planck 2016), TT/lensing (2015) while the addition of New VHL data helps to some extent in +0.012 reducing the tension on ⌧experiments between high-`(ACT and low-` polarization. 2. +Very High-l ground-based & SPT) cosmology corresp Planck low-l polarization + other data 4.2. Kinetic Sunya lolli The Thomson sca lollipop+Pla trons induces seco reionization proce ⌧ = 0.054 0.013 , thelollipop+ e↵ect of photo velocity, which is We can see an improvement theItpost kSZ of e↵ect. is co neous” temperature anisotropy data to kSZ the e↵ect lol (e.g., Ostriker & V comes from the fact that the temperatur neous) reionizatio other ⇤CDM parameters,during in particular the process bubbles initial power spectrum As ,ionized and its specta nents can be desc ing also helps to reduce the degenerac computed analytic rid of the tension phenomenolo Collaborati Planck 2015 with thePlanck homogeneous AL when using PlanckTTononly (see Pls In the followin 2016), even if the impact given on the by error b the posteriors in Fig. 6 with the constrai (see figure 45 in Planck Collaboration where D` = `(` + deed, the polarization likelihood kSZ” standisforsuffi “h breaks the degeneracy between and spectively.nsFor the template power sp ⇤CDM parameters is small, typically Fig. 5. Posterior distribution forAutónoma ⌧ fromdethe various combinations Anna Mangilli (IAS) - IFT, Universidad Madrid (UAM) - 20th June 2016 with a simulation mum level allowed by the luminosity density constraints at redshifts zagreement < 9, then the currently observed galaxy population at Better with astrophysical MUV < 17 seems to be sufficient to comply with all the observational constraints without the need for high-redshift (z = 10– 15) galaxies. WMAP9, Planck 2015 data The scientific results that we present today are a produc the Planck Collaboration, including individuals from m than 100 scientific institutes in Europe, the USA and Cana optical depth & redshift WMAP Planck NEW Bouwens et al. (2015) Robertson et al. (2015) Ishigaki et al. (2015) • integrated optical depth for the symmetric model (tanh, δz = 0.5). • models from Bouwens et al. (2015), Robertson et al. (2015), Ishigaki et al. (2015), using high redshift galaxy UV and IR flux and/or direct measurements. Planc projec Europea Agenc instru provide scie Consort by ESA stat partic lead co France a w contri from (USA tele refle provid collab between a sci Consor and fu Den Fig. 17. Reioniza eterization comp piled by Bouwens of ionized fractio limits. The dark a 95 % allowed inte Although the Fig. 16. Evolution of the integrated optical depth for the tanh above, understand preliminary M. Tristram Japan, Dec. 2015 B-mode from Space, Kavli IPMU in the Universe i functional Anna form (with z = 0.5, blue shaded area). The Mangilli (IAS) - IFT, Universidad Autónoma de Madrid (UAM) - 20th June 2016 redshift andusing duration of thevanishing EoR, finding are plotted in Fig. 11. In such a model, the end of reionization C be modelled a tanh (Lewis 2008): z <function 10.2 (95 %ionized CL, ,Ontimes sults fractionat3 low xprior) early strongly depends on theunform constraint redshift. the `ot e at strongly depends on the constraint at low redshift. On the other hand, theredshifts. constraints on z only slightly depend the lo can hand, the constraints on z only slightly depend on the lowat low When calculating theone↵ect " !# z < 4.6 (95 % CL). (13) redshift prior. This results shows that the Universe is ionized vely z <f 6.8+0.9 (95y % ytoCL, prior zend width > 6)to. the(i.etr redshift prior. This results shows that the Universe is ionized at +1.0 re necessary a non-zero regive less than the 10 % level above z = 9.4 ± 1.2. z = 8.5 (uniform prior) , (14) z = 8.0 (uniform prior) , less than the 10 % level above z = 9.4 ± 1.2. re xe (z) re= 1 + tanh , (2) 1.1 1.1 aints be modelled 20 2 y using a tanh function (LewisPla +0.9 5.2. Redshift-asymmetric parameterization " . 5.2. Redshift-asymmetric parameterization tio anck z = 8.5 (prior zend >f 6) zre = 8.8+0.9 (prior z > 6) . (15) re end y yre 0.9 0.9 We now explore more complex reionization histories us 3 3/2 1/2 Fig. 10. Posterior distributions (in blue) of z and z for a bee reionization histories using x (z) = 1 + tanh Fig. 10. Posterior distributions (in blue) of z and z for a We now explore more complex e where y = (1 + z) and y = (1 + z) z. The key parameters of x (z) described VHL redshift-symmetric 2 y of x (z)parameterization described in using the CMB likelihoods2 the redshift-asymmetric parameterization redshift-symmetric parameterization using the CMB likelihoods the redshift-asymmetric parameterization tail Sect. 3. In the same manner as in Sect. 5.1, also examine in polarization and temperature (lollipop+PlanckTT). The are also thus examinezre the, which measures the redshift at which the ionized in polarization and temperature (lollipop+PlanckTT). The Sect. 3. In the same manner as in Sect. 5.1, additional constraint from the Gu This redshift is lower than the values derived previously green contours and lines show the distribution after imposing e↵ect of imposing the 3/2 ude. e↵ect of imposing the additional constraint from the Gunn3 pa- 1/2(H green contours and lines show the distribution after imposing fraction reaches half its maximum and a width z. The tanh Peterson e↵ect. where y = (1 + z) and y = z. the additional prior z > 6. Peterson e↵ect. 2 (1 + z) the additional prior z > 6. The distributions of the two parameters, z and z mea, 10 ACT SPT pos- from WMAP-9 data, in combination The distributions of the twowith parameters, z and z and , are are thus zre12. , us which measures theopredshift rameterization of the EoR transition allows to compute the plotted in Fig. With the redshift-asymmetric parameteri plotted in Fig. 12. With the redshift-asymmetric parameteriza4 aon reaches wiz in The10.3 posterior is shown in Fig.a10 after fraction tion, we obtain z redshift-symmetric =half 10.4its maximum (imposing the and prior tical depth of (1) for one-stage almost The posterior distribution of z is shown in Fig. 10 after tion, we obtain zz re = 10.4 (imposing the distribution prior on z of ), z Eq. (Hinshaw et al. 2013), namely = ± 1.1. It is of marginalizing 6 marginalizing overionized z, with and without the additional constraint rameterization which disfavours anyofmajor to the ionized fract the contribution EoR transition allows u over z, with and without the additional constraint which disfavours any major contribution to the fraction pan reionization transition, where the redshift interval between the > z > 6. This suggests that the reionization process occurred at from sources that could form as early as z 15. ⇠ > z > 6. This suggests that the reionization process occurred at from sources that could form as early as z 15. also lower than the value zre = 11.1 ±⇠ onset 1.1 ofderived in tical depth of Eq. (1) for a one-stage almost ten the reionization processreionization and its half completion transition, where is the(by redshift i Planck Collaboration XVI (2014), based on Planck 2013 data construction) between half completion 9 equal to the interval onset of the reionization processand and itsple ha (H full completion. In this parameterization, depth between is construction) the equaloptical to the interval and the WMAP-9 polarization likelihood. red full completion. In with this parameterization, 11. Posterior distributions on the mainly determined by zFig. almost degenerate the width re and Although the uncertainty is now smaller, this new determined by2015 zre andcosmoalmost degen sul z. This is the model used in themainly Planck 2013 and reionization, i.e., z and z , using the end beg z. This is the model used in the Planck pro 201 with forthe TT) reionization redshift value is entirely consistent logical papers, which we have fixed z = 0.5 (corresponding rameterization without (blue) and with logical papers, for which we have fixed z (g = to z = 1.73). In this case, we usually talk about “instantaneous” Planck 2015 results (Planck Collaboration XIII 2016) for DM to z = 1.73). In this case, we usually talk ab +1.8 reionization. Planck Collaboration: Reionization history = 9.9 1.6 orreionization. in combinah z PlanckTT+lowP alone, zre Planck A redshift-asymmetric parameterization A redshift-asymmetric parameterization is a better, more 4. Collaboration: history +1.3 Reionization In addition to the posteriors for zre a s (in tion with other data sets, width zPlanck 8.8While (specifically for flexible description of numerical simulation re z=Collaboration: flexible description of numerical simulations of the reionization = 0.5. there is still some debate on whether heof redshift (Lewis et al. 2006). The 1.2 Planck constraints on reionization history Planck Collaboration: Planck constraints on reionization history symmetric parameterization, the distri process (e.g., Ahn et al. 2012; Park et al. 2 Planck Collaboration: Reionization history n: Planck constraints on reionization process (e.g., al. 2006). 2012; Park et al.for2013; Douspisexotic et al.uselium could be inhomogeneous and extended (and ful investigating reioni the PlanckTT+lowP+lensing+BAO) estimated with z fixed toAhn 0.5. Re dth z= 0.5. While there ishistory still some debate onreionization whether heof redshift (Lewis etetal. They should be particularly 2015). A function with zthis (i.e., behaviour beginning ofof reionization, zin99 thusextended have an early start, ful Worseck etAal.function 2014), we have checked reionization Cen (2003). Howeve end redshift2015). with this behaviour is also suggested These values are within 0.4 the results for the m reionization could be inhomogeneous and (and for investigating exotic reionization histories, e.g., double by the constraints from ionizing backgro d in The constraint from lollipop+PlanckTT when fixing z to 0.5 width z = 0.5. While there is still some debate on whether heof redshift (Lewis et al. 2006). They should be particularly u redshift can break this degeneracy. This is illustrated in Fig. 10, redshift can break this degeneracy. Thisthat is illustrated in helium Fig. 10,reionization varying the redshift between 2.5 and 4.5 10) polarization anisotropies are are plotted in Fig. 11. In such a model, symmetric model. For the duration of the EoR, the upper limits by the constraints from ionizing background measurements pre < of star-forming galaxies and +1.0 lium reionization could be inhomogeneous and extended (and ful for investigating exotic reionization histories, e.g., dou us have an early start, Worseck etthe al. 2014),ofchanges we have checked reionization Cen(in (2003). However, thevalue CMB large-scale (`low-re where we show green) the results of the same analysis withfrom ⇠ show (in green) results the same analysis with most iswhere zre =we 8.2 . This slightly lower value (compared to the one the total optical depth by less than 1 %. all of the optical depth, z are of star-forming galaxies and from low-redshift line-of-sight probes such as quasars, Lyman-↵ emitte 1.2 kS strongly depends on the constraint at lo thus have an early start, Worseck et al. 2014), we haveonchecked reionization Cenare (2003). However, the CMB large-scale (`w an additional prior z > 6. In this case, we find z < 1.3 at 95 % at varying the helium reionization redshift between 2.5 and 4.5 10) polarization anisotropies mainly sensitive to the overend an additional prior zletting > 6.varying Inthe thisreionization case, we find z <width 1.3redshift atand 95 % tude the reionization bump inovI simplest most widely-used deend that (Faisst et al. of 2014; Chornock et al. probes asparameterizations quasars, Lyman-↵ emitters, or -ray bursts the heliumThe reionization between 2.5such and 4.5 10) polarization anisotropies are mainly sensitive to2014; the over obtained when be free) is explained ele CL, which corresponds to a reionization duration (z z ) of hand, the constraints on z only sligh beg end beg anges the total optical depth by less than 1 %. all value of the optical depth, which determines the ampliCL, which correspondschanges to a reionization duration zend of1 %. transition between Fig. have the im scribes the(zEoR as a)step-like essentially beg Robertson et3). al.We 2015; Bouwens et al. 2015 zvalue <an10.2 (95 % CL, unform prior) ,estimated (18) the total optical depth by less than all Chornock of the optical depth, which determines the amp (Faisst et al. 2014; et al. 2014; Ishigaki et al. 2015; 3 onal by theand shape the degeneracy surface. Allowing larger duredshift prior. This results shows that th( ferent models (tanh andspectrum power tude of the reionization bump in the EE power spectrum (seelaw vanishing ionized fraction xefor at early times, to a of value of unity The simplest mostofwidely-used parameterizations dechoices of redshift-asymmetric parameteri tude the reionization bump in the > EE power The simplest and most widely-used parameterizations deRobertson et al. 2015; Bouwens et al. 2015). The two simplest z < 6.8 (95 % CL, prior z 6) . (19) z < 4.6 (95 % CL). (13) end EE ofofredshift EE zscribes < 4.6 % as CL). (13) found di↵erences less tha exponential functions (D atavalue low When calculating the e↵ect on anisotropies itmial istheorand Fig. 3).less We have estimated the impact on Cthe for the two d the(95 EoR step-like transition between an essentially low theration keeping the same of ⌧ pushes towards higher than 10 % level above z = 9.4 ± Fig. 3). We have estimated the impact on C for two difribes EoR aswhen a step-like transition between anredshifts. essentially ` 4.1 choices of redshift-asymmetric parameterizations are polyno` 3 EoR: z beg and duration re re e e end end re respondables, including those associated with the CMB. ing toThe 25 eV), isnassume d ltoquantit happen the same most which commo physica y roughly used to at charact erize time as hydrog We define the beginn and the reionization isen thereioniz Thomsation. on scatteri ng optical depthing defined end of the EoR by the redshifts zbeg ⌘ z10 % and zend ⌘ z99 % as at Z t0 which xe = 0.1⇥ f and 0.99⇥ f , respectively. 0 The duration of the 2, (1) EoR is then defined as⌧(z)z = = z10 %ne zT99cdt % . Moreover, to ensure t(z) that the Universe is fully reioniz ed at low redshift, we impose where the conditi ne is onthe thatnumbe the EoR r density is comple of free ted electro beforenstheatsecond time t0 ,he-T is thereioniz lium Thoms on scatteri ation phase ng (corres cross-s pondin ection, g tot054 is eV), the time noting today, thatt(z) it isiscommo the time nlyatassume redshif d tthat z, and quasars we can are necessa use the ryFriedm to produc ann eequathe tion photon hard to conver s needed t dt to dz. to ionize The reioniz heliumation . To history be explici is conven t about iently how express we treat ed theinlowest terms redshif of the tsionized we assume fraction thatxethe (z) full ⌘ nereioniz (z)/nHa(z) where tion of helium nH (z) ishappen the hydrog s fairly en numbe sharplyr density at zHe =. 3.5 (Becker et al. 2011), In followi this study, ng a we transiti define on the of hyperb redshifolic t oftangen reioniz t ation, shape zwith re ⌘ z502% , as the redshift at which xe = 0.5 ⇥ f . Here the normalizais that tinelectro practice we tion,The f =reason 1 + this fHe =is not 1 +defined nHe /nHsymmet , takes rically into accoun ns inhave tighter ntsby on the the end reioniza on the beginni ng. jected intoconstrai the IGM firstofionizat iontion ofthan helium (corres ponding to 25 eV), which is assumed to happen roughly at the same time as hydrogen reionization. We define the beginning and the end of the EoR by the redshifts zbeg ⌘ z10 % and zend ⌘ z99 % at which xe = 0.1⇥ f and 0.99⇥ f , respectively. The duration of the EoR is then defined as z = z10 % z99 % .2 Moreover, to ensure that the Universe is fully reionized at low redshift, we impose the condition that the EoR is completed before the second helium reionization phase (corresponding to 54 eV), noting that it is commonly assumed that quasars are necessary to produce the hard photons needed to ionize helium. To be explicit about how we treat the lowest redshifts we assume that the full reionization of helium happens fairly sharply at zHe = 3.5 (Becker et al. 2011), following a transition of hyperbolic tangent shape with +1.9 1.6 end beg re beg end end beg The reason this is not defined symmetrically is that in practice we have tighter constraints on the end of reionization than on the beginning. end end beg +1.9 1.6 beg e 2 These parameterizations in ⌧fact double reionization model, Fig. ferent models andatwo power law) having the⌧are same = ve 0 necessary atimes, non-zero width the(tanh transition, and it(tanh can ionizedto fraction xetoat early to a value oftounity ferent models and power law) having the same = 0.06 nishing ionized fraction3 xe atvanishing early times, a value ofgive unity mial or exponential functions of redshift (Douspis et al. 2015). EE adopt here a is power defined two param and found di↵erences of than 4% for `given <by 10. at low redshifts. When calculating the e↵ect anisotropies it is2008): C` less quitelaw weak, theEven actu be modelled using a tanhonfunction (Lewis Th and found di↵erences of less than 4 % for ` < 10. Even for low redshifts. When calculating the e↵ect on anisotropies it is These two parameterizations are in fact very similar, and we which reionization ends (z ); and the expo a double reionization model, Fig. 4 shows that the impact end necessary to give a non-zero width to the transition, and it can cannot be distinguished relative to " !# tro 5.2. Redshift-asymmetric parameteriz EE we have af adopt double model, Fig. 4(i.e., shows that impact cessary to give a non-zero width to theusing transition, and it(Lewis can 2008): quite weak, given theeven actual measured value ofon⌧, a herereionization by two parameters: the atexperim be modelled a tanh function 8 the ya power yre Claw for a redshift full-sky `9 isdefined > of EE x (z) = 1 + tanh , (2) > f ✓not of forspre zm< e cannot be distinguished relative to the cosmic variance > which reionization ends (z ); and the exponent ↵. Specifically C is quite weak, given the actual measured value ⌧, and modelled using a tanhSymmetric function (Lewis 2008): " !# Planck data do allow for < end model: Asymmetric model: ◆ 2 y ` ↵ xemore =and Werelative now explore complex reion Fig. 13. Posterior distributions for z(z)rein using the at tr f (in blue) y of yre zwe have > zz z checked (i.e., even for a full-sky experiment). We also > Fig. Posterior distributions and z for a > tion of x redshift bins. Princ re cannot be distinguished to the cosmic variance spread f for z> e x (z) = 1 + tanh , (2) : Fig. 11.10. Posterior distributions on the end and beginning of 8 e z z " !# Planck data do not allow for model-independent reconstr sca 2 y the redshift-asymmetric parameterizatio asymmetric parameterization without (blue) with (g > 1/2 been proposed as anand explicit appr > redshift-symmetric the CMB f x✓parameters for z < z , f i.e., zend andyparameterization where y = (1 using + z)3/2 and ypa= 32even (1likelihoods + z)for z.a The key reionization, zbegy, reusing the redshift-symmetric (i.e., full-sky experiment). We also checked that end > tion of in redshift bins. Principal component analysis h < ◆↵thethe e dit x (z) = 1 + tanh , (2) In following, we fix z = 20, the red tails of the reionization history i e early Sect. 3. In same manner as in Sec x (z) = (3) prior z > 6. > are thus z , which measures the redshift at which the ionized z z rameterization (blue) prior > 6. 3/2 (green) 1/2 zendPlanck early re3the in polarization and temperature been> proposed as an explicit approach to tryreconstructo capture the data end doeThe not allow for model-independent where y = (1 + z)with and y =(lollipop+PlanckTT). z. The key parameters 2 without yand > f for z > z . the& the first emitting sources form, and at which : 2 (1 + z) end (Hu & Holder 2003; Mortonson z z early end fraction reaches half its maximum and a width z. The tanh patails of the reionization history in a small set of paramet e↵ect of imposing the additional con are thus z , which measures the redshift at which the ionized tionafter of xeimposing in redshift bins. Principal component analysis green contours and relines show the distribution xe (z) tomethods the ionized fraction left overhas from siz are generally considered rameterization of the EoR transition allows us to compute the op(Hu & Holder 2003; Mortonson & Hu 2008). Although tht fraction reaches half its maximum and a width z. The tanh pa3 3/2 1/2 Peterson e↵ect. checked that our results are not sensitive to been proposed as an explicit approach to try to capture the de(IAS) - IFT, Universidad Autónoma Madrid (UAM) 20thzare June 2016 4 considered additional 6. thedefollowing, we -fix = 20, the redshift which they here y = (1 + z)theand y = (1prior +Anna z) zMangilli key parameters tial in fact based on a description of endz.>The early methods generally to bearound non-parametric, tical depth of Eq. (1) for aIn one-stage almost redshift-symmetric early early end Improved and lower τ: impact on parameters nck constraints on reionization history 2015 New Lowl HFI (4) (5) (6) (7) ding This o fix f the enstting meter XIII aring lone 2015 New Lowl HFI Anna Mangilli (IAS) - IFT, Universidad Autónoma de Madrid (UAM) - 20th June 2016 e show only ⌧the results 0.016 , = 0.053 lollipop ; > 6. (4)In this case, we find z < an additional prior zend nds to approximatively+0.012 +1.0 Conclusions CL, which(uniform corresponds to(5) a ,reionization duration (zb z = 8.5 prior) (14) ⌧ = 0.058 , lollipop+PlanckTT ; re 1.1 y looking at constraints 0.012 +0.9 ic models using z = 8.8 . (95 % CL).(15) ⌧ = Planck 0.058+0.011 , lollipop+PlanckTT+lensing ; > (6) z <6) 4.6 re 0.9 (prior zend 0.012 we introduce the VHL+0.012 ⌧ = 0.054 , lollipop+PlanckTT+VHL . (7) 0.013 This redshift is lower than the values derived om the • kSZ Aamplitude. significantly lower value for the reionization optical depth:previously from WMAP-9 data, in combination with ACT and SPT ts that follow fromsee posWe can an improvement of the posterior width when adding - is consistent with a fully reionized Universe at z ∼ 6 al.the 2013), namely zre = This 10.3 ± 1.1. It is pleted at temperature a redshift of anisotropy 6 (Hinshaw dataet to lollipop likelihood. - 6. is infrom better with astrophysical constraints ! alsothat lower thanrecent the value zre =help 11.1 ± 1.1 derived in rior zend > comes theagreement fact the temperature anisotropies to fix - disfavors Planck Collaboration (2014), basedofon Planck 2013 data reionization tailXVI and complicated reionization histories! other ⇤CDM high-z parameters, in particular the normalization the and the WMAP-9 polarization likelihood. - makes the quest of B-modes at low-l more challenging! initial power spectrum A , and its spectral index, n . CMB lenss s on Although the uncertainty is now smaller, this new ing also helps to reduce the degeneracy with As , while getting • τ constraint: tighter constraints cosmological reionization redshift value lensing is on entirely consistent parameters with the emperature (PlanckTT) ridImproved of the tension with the phenomenological parameter Planck 2015 results (Planck Collaboration XIII 2016) for σ8, Σm s, n s, using ν constraints ⇤CDM ALAon when PlanckTT only (see Planck Collaboration XIII +1.8 PlanckTT+lowP alone, z = 9.9 or in combinare dshift zre2016), and width z the impact on the error bars is small. Comparing even if 1.6 The Planck Coll. A&A 2016: “Planck constraints on the reionization history” (arxiv:1605.03507) +1.3 n. Figure 10posteriors shows (inin2016: tion other data sets, zrePlanckTT = 8.8alone Fig. 6 with the constraints from aints on the kSZ amplitude at `“Improved = 3000 using Thethe Planck Coll. A&A large angular scale polarization data”(arxiv:1605.02985) 1.2 (specifically for arginalization over the PlanckTT+lowP+lensing+BAO) estimated fixed 0.5. anckTT+VHL likelihoods. three Collaboration cases corre(see figure 45 inThe Planck XI 2016) shows that with in- zFig. 6. to Constraint ent kSZAs templates. eters. discussed in The constraint lollipop+PlanckTT when z to 0.5 deed, the polarization likelihoodfrom is sufficiently powerful that it fixing ogy from PlanckT +1.0 anisotropies are the almost is zre =between 8.2 1.2 .nThis value (compared to the one breaks degeneracy ⌧. Thelower impact on other s andslightly likelihood from P What’s next:! nction. We thus recover obtained when letting the reionization width be free) is explained ⇤CDM parameters is small, typically below 0.3 (as shown likelihood. The to sis. The data presented here provide the best conmposingmore an byAppendix thedata shape of the degeneracy surface. are Allowing for larger du• additional Further Planck improvement at map-making level on going explicitly in B). The largest changes for the bottom panels on the kSZ power and is a factor of 2 lower than on fraction at very low ration when keeping the same value of ⌧ pushes towards higher • ⌧ and A , where the lollipop likelihood dominates the conPrimordial B-modes at low-ell: s ted in George et al. (2015). Our limit is certainly parameter shiftspretowards smaller val- The with the straint. homogeneous kSZ template, 8which improved S/N, lensing is not a slightly contaminant 1.79 µK2 .ues However, not leaveismuch room by- about 1 needed: . This in the right to help resolve fullit does sky future CMBdirection satellites (PIXIE, LiteBIRD, M5,IGM ?)9 wa that the onal kSZ power patchy reionization. some coming of the from tension with cluster abundances and weak galaxy places a lower lim Universidad with George et al. (2015),Anna weMangilli find(IAS) the- IFT, total kSZ Autónoma de Madrid (UAM) - 20th June 2016 Thank you! CITA – ICAT UNIVERSITÀ DEGLI STUDI DI MILANO ABabcdfghiejkl