Polarization Results from the Cosmic Background Imager Steven T. Myers Jonathan Sievers (CITA) CITA 04 Oct Continued…

The CBI Collaboration Caltech Team: Tony Readhead (Principal Investigator), John Cartwright, Clive Dickinson, Alison Farmer, Russ Keeney, Brian Mason, Steve Miller, Steve Padin (Project Scientist), Tim Pearson, Walter Schaal, Martin Shepherd, Jonathan Sievers, Pat Udomprasert, John Yamasaki. Operations in Chile: Pablo Altamirano, Ricardo Bustos, Cristobal Achermann, Tomislav Vucina, Juan Pablo Jacob, José Cortes, Wilson Araya. Collaborators: Dick Bond (CITA), Leonardo Bronfman (University of Chile), John Carlstrom (University of Chicago), Simon Casassus (University of Chile), Carlo Contaldi (CITA), Nils Halverson (University of California, Berkeley), Bill Holzapfel (University of California, Berkeley), Marshall Joy (NASA's Marshall Space Flight Center), John Kovac (University of Chicago), Erik Leitch (University of Chicago), Jorge May (University of Chile), Steven Myers (National Radio Astronomy Observatory), Angel Otarola (European Southern Observatory), Ue-Li Pen (CITA), Dmitry Pogosyan (University of Alberta), Simon Prunet (Institut d'Astrophysique de Paris), Clem Pryke (University of Chicago). The CBI Project is a collaboration between the California Institute of Technology, the Canadian Institute for Theoretical Astrophysics, the National Radio Astronomy Observatory, the University of Chicago, and the Universidad de Chile. The project has been supported by funds from the National Science Foundation, the California Institute of Technology, Maxine and Ronald Linde, Cecil and Sally Drinkward, Barbara and Stanley Rawn Jr., the Kavli Institute,and the Canadian Institute for Advanced Research.

Whence Polarization? Polarization comes from Thomson scattering during recombination Polarization comes from Thomson scattering during recombination Quadrupole seen by electrons produces polarization. Quadrupole seen by electrons produces polarization. Dominant source from velocity modes – so out of phase with TT Dominant source from velocity modes – so out of phase with TT Pol’n lines up with modes, so no BB type Pol’n lines up with modes, so no BB type Strongly predicted by TT – good check on model. Strongly predicted by TT – good check on model.

No Dipole No net extra radiation from left/right or top/bottom, so no polarization No net extra radiation from left/right or top/bottom, so no polarization Doppler shift makes dipole pattern, so moving electron in an isotropic field has no polarization. Doppler shift makes dipole pattern, so moving electron in an isotropic field has no polarization.

Quadrupole More radiation from left/right than top/bottom. Electron moves up/down, and so scattered radiation is polarized. More radiation from left/right than top/bottom. Electron moves up/down, and so scattered radiation is polarized.

E Mode Only If velocity converges, then electron moves normal to wave +E If velocity converges, then electron moves normal to wave +E If diverges, electron moves along wave –E If diverges, electron moves along wave –E Never moves tilted, so no B radiation Never moves tilted, so no B radiation

The Instrument cm Cassegrain antennas cm Cassegrain antennas 78 baselines 78 baselines 6-meter platform 6-meter platform Baselines 1m – 5.51m Baselines 1m – 5.51m 10 1 GHz channels GHz 10 1 GHz channels GHz HEMT amplifiers (NRAO) HEMT amplifiers (NRAO) Cryogenic 6K, Tsys 20 K Cryogenic 6K, Tsys 20 K Single polarization (R or L) Single polarization (R or L) Polarizers from U. Chicago Polarizers from U. Chicago Analog correlators Analog correlators 780 complex correlators 780 complex correlators Field-of-view 44 arcmin Field-of-view 44 arcmin Image noise 4 mJy/bm 900s Image noise 4 mJy/bm 900s Resolution 4.5 – 10 arcmin Resolution 4.5 – 10 arcmin

The CBI Adventure… Two winters a year! The roads fill with snow. Two winters a year! The roads fill with snow.

The CBI Adventure… Steve Padin wearing the cannular oxygen system (CBI site >5000 meters) Steve Padin wearing the cannular oxygen system (CBI site >5000 meters)

The CBI Adventure… Volcan Lascar (~30 km away) erupts in 2001 Volcan Lascar (~30 km away) erupts in 2001

CBI in Chile

CMB Interferometry why, what, how?

CMB Interferometers CMB issues: CMB issues: Extremely low surface brightness fluctuations < 50  K Extremely low surface brightness fluctuations < 50  K Large monopole signal 3K, dipole 3 mK Large monopole signal 3K, dipole 3 mK Polarization less than 10%  signal < 5  K Polarization less than 10%  signal < 5  K No compact features, approximately Gaussian random field No compact features, approximately Gaussian random field Foregrounds both galactic & extragalactic Foregrounds both galactic & extragalactic Traditional direct imaging Traditional direct imaging Differential horns or focal plane arrays Differential horns or focal plane arrays Interferometry Interferometry Inherent differencing (fringe pattern), filtered images Inherent differencing (fringe pattern), filtered images Works in spatial Fourier domain Works in spatial Fourier domain Element-based errors vs. baseline-based signals Element-based errors vs. baseline-based signals Limited by need to correlate pairs of elements Limited by need to correlate pairs of elements Sensitivity requires compact arrays Sensitivity requires compact arrays

The Fourier Relationship A parallel hand “visibility” in sky and Fourier planes: A parallel hand “visibility” in sky and Fourier planes: direction x k and u k = B k / k for baseline B k direction x k and u k = B k / k for baseline B k other correlation LL measures same I other correlation LL measures same I The aperture (antenna) size restricts response The aperture (antenna) size restricts response convolution in uv plane = loss of Fourier resolution convolution in uv plane = loss of Fourier resolution multiplication on sky = field-of-view multiplication on sky = field-of-view loss of ability to localize wavefront direction loss of ability to localize wavefront direction Small apertures = wide field = higher Fourier resolution Small apertures = wide field = higher Fourier resolution

The uv plane and l space The sky can be uniquely described by spherical harmonics The sky can be uniquely described by spherical harmonics CMB power spectra are described by multipole l ( the angular scale in the spherical harmonic transform) CMB power spectra are described by multipole l ( the angular scale in the spherical harmonic transform) For small (sub-radian) scales the spherical harmonics can be approximated by Fourier modes For small (sub-radian) scales the spherical harmonics can be approximated by Fourier modes The conjugate variables are (u,v) as in radio interferometry The conjugate variables are (u,v) as in radio interferometry The uv radius is given by l / 2  The uv radius is given by l / 2  The projected length of the interferometer baseline gives the angular scale The projected length of the interferometer baseline gives the angular scale Multipole l = 2  B / Multipole l = 2  B / An interferometer naturally measures the transform of the sky intensity in l space An interferometer naturally measures the transform of the sky intensity in l space

uv coverage of a close-packed array 13 antennas 13 antennas 78 baselines 78 baselines 10 frequency channels  780 instantaneous visibilities 10 frequency channels  780 instantaneous visibilities frequency channels give radial spread in uv plane frequency channels give radial spread in uv plane Baselines locked to platform in pointing direction Baselines locked to platform in pointing direction Baselines always perpendicular to source direction Baselines always perpendicular to source direction Delay lines not needed Delay lines not needed Pointing platform rotatable to fill in uv coverage Pointing platform rotatable to fill in uv coverage Parallactic angle rotation gives azimuthal spread Parallactic angle rotation gives azimuthal spread uv plane is over-sampled uv plane is over-sampled inner hole (1.1D), outer limit dominates PSF inner hole (1.1D), outer limit dominates PSF many more visibilities than independent uv “patches” many more visibilities than independent uv “patches”

Mosaicing Resolution of 1 field is FT of primary beam (in radians) Resolution of 1 field is FT of primary beam (in radians) CBI has single pointing FWHM of 420 in ℓ CBI has single pointing FWHM of 420 in ℓ Too poor to resolve peaks and dips in CMB Too poor to resolve peaks and dips in CMB Resolution in ℓ better if we follow a wave for more periods Resolution in ℓ better if we follow a wave for more periods We want larger area, therefore observe mosaics of fields We want larger area, therefore observe mosaics of fields Final resolution is FT of entire map Final resolution is FT of entire map CBI observes 6x6 pointings in polarization CBI observes 6x6 pointings in polarization Coverage is 4.5 x 4.5 degrees per mosaic Coverage is 4.5 x 4.5 degrees per mosaic ℓ resolution goes from 420 to ~70 ℓ resolution goes from 420 to ~70 Means peaks can be observed Means peaks can be observed

uv coverage with mosaic beam

Polarization – Stokes parameters CBI receivers can observe either RCP or LCP CBI receivers can observe either RCP or LCP cross-correlate RR, RL, LR, or LL from antenna pair cross-correlate RR, RL, LR, or LL from antenna pair Mapping of correlations (RR,LL,RL,LR) to Stokes parameters (I,Q,U,V) : Mapping of correlations (RR,LL,RL,LR) to Stokes parameters (I,Q,U,V) : Intensity I plus linear polarization Q,U important Intensity I plus linear polarization Q,U important CMB not circularly polarized, ignore V (RR = LL = I) CMB not circularly polarized, ignore V (RR = LL = I) parallel hands RR, LL measure intensity I parallel hands RR, LL measure intensity I cross-hands RL, LR measure polarization Q, U cross-hands RL, LR measure polarization Q, U R-L phase gives Q, U electric vector position angle R-L phase gives Q, U electric vector position angle

E and B modes A useful decomposition of the polarization signal is into “gradient” and “curl modes” – E and B: A useful decomposition of the polarization signal is into “gradient” and “curl modes” – E and B: E & B response smeared by phase variation over aperture A interferometer “directly” measures E & B!

CBI Current Polarization Data Observing since Sep 2002 Observing since Sep 2002 compact configuration, maximum sensitivity, new NRAO HEMTs compact configuration, maximum sensitivity, new NRAO HEMTs Four mosaics  = 02 h, 08 h, 14 h, 20 h at  = 0° Four mosaics  = 02 h, 08 h, 14 h, 20 h at  = 0° 02h, 08h, 14h 6 x 6 fields, 20h deep strip 6 fields, 45’ centers 02h, 08h, 14h 6 x 6 fields, 20h deep strip 6 fields, 45’ centers Scan subtraction/projection Scan subtraction/projection observe scan of 6 fields, 3 m apart = 45’, remove mean observe scan of 6 fields, 3 m apart = 45’, remove mean lose only 1/6 data to differencing (cf. ½ previously) lose only 1/6 data to differencing (cf. ½ previously) Point source projection (important for TT) Point source projection (important for TT) list of NVSS sources (extrapolation to 30 GHz unknown) list of NVSS sources (extrapolation to 30 GHz unknown) need 30 GHz GBT measurements to know brightest need 30 GHz GBT measurements to know brightest Massive computations  parallel codes Massive computations  parallel codes grid visibilities and max. likelihood (Myers et al. 2003) grid visibilities and max. likelihood (Myers et al. 2003) using 256 node/ 512 proc McKenzie cluster at CITA using 256 node/ 512 proc McKenzie cluster at CITA

CBI & DASI Fields galactic projection – image WMAP “synchrotron” (Bennett et al. 2003)

Foregrounds – Sources Foreground radio sources Foreground radio sources Predominant on long baselines Predominant on long baselines Located in NVSS at 1.4 GHz, VLA 8.4 GHz Located in NVSS at 1.4 GHz, VLA 8.4 GHz Projected out in power spectrum analysis Projected out in power spectrum analysis Project ~3500 sources in TT, ~550 in polarization Project ~3500 sources in TT, ~550 in polarization No evidence for contribution of sources in polarization – our approach very conservative No evidence for contribution of sources in polarization – our approach very conservative “masking” out much of sky – need GBT measurements to reduce the number of sources projected “masking” out much of sky – need GBT measurements to reduce the number of sources projected

Data Tests Data split by frequency (26-31 GHz, GHz) – no sign of foreground, but sensitivity low Data split by frequency (26-31 GHz, GHz) – no sign of foreground, but sensitivity low Data split by epoch Data split by epoch RR only vs. LL only TT spectra RR only vs. LL only TT spectra Polarization spectra omitting mosaics Polarization spectra omitting mosaics Lead-trail subtraction Lead-trail subtraction No evidence for inconsistencies

Spectra! We measure TT, EE, BB, TE spectra We measure TT, EE, BB, TE spectra Spectra with Δℓ=150 for plots Spectra with Δℓ=150 for plots Fine bin spectra (Δℓ~75) for cosmology etc. More information contained, but hard to interpret visually due to large error bars, correlations Fine bin spectra (Δℓ~75) for cosmology etc. More information contained, but hard to interpret visually due to large error bars, correlations Single shaped band spectra for consistency with WMAP predictions Single shaped band spectra for consistency with WMAP predictions

Spectra! We measure TT, EE, BB, TE spectra We measure TT, EE, BB, TE spectra Spectra with Δℓ=150 for plots Spectra with Δℓ=150 for plots Fine bin spectra (Δℓ~75) for cosmology etc. More information contained, but hard to interpret visually due to large error bars, correlations Fine bin spectra (Δℓ~75) for cosmology etc. More information contained, but hard to interpret visually due to large error bars, correlations Single shaped band spectra for consistency with WMAP predictions Single shaped band spectra for consistency with WMAP predictions Also Δℓ=150 spectra with bins offset by 75 Also Δℓ=150 spectra with bins offset by 75

Consistency w/ WMAP Spectra consistent with the cosmological model from WMAPext dataset Spectra consistent with the cosmological model from WMAPext dataset χ 2 = 7.98 TT, 3.77 EE, 4.33 BB (vs. 0), and 5.80 TE for 7 dof. χ 2 = 7.98 TT, 3.77 EE, 4.33 BB (vs. 0), and 5.80 TE for 7 dof.

New: Shaped C l fits Use WMAP’03 best-fit Cl in signal covariance matrix Use WMAP’03 best-fit Cl in signal covariance matrix bandpower is then relative to fiducial power spectrum bandpower is then relative to fiducial power spectrum compute for single band encompassing all l s compute for single band encompassing all l s Results for CBI data (sources projected from TT only) Results for CBI data (sources projected from TT only) EE likelihood vs. zero : equivalent significance 8.9 σ EE likelihood vs. zero : equivalent significance 8.9 σ

Parameters w/CBI Paramaters calculated using Antony Lewis’s MCMC code, COSMOMC Paramaters calculated using Antony Lewis’s MCMC code, COSMOMC Old CBI mosaics (Readhead et al. 2004) overlap with polarization mosaics. Not allowed to combine sample- limited part of spectra. Old CBI mosaics (Readhead et al. 2004) overlap with polarization mosaics. Not allowed to combine sample- limited part of spectra. Thermal limited (ℓ>1000) old spectrum included. New spectrum only for ℓ 1000) old spectrum included. New spectrum only for ℓ<1000. First time EE included for measuring parameters (though impact of EE quite small) First time EE included for measuring parameters (though impact of EE quite small) Blue=WMAP Red=WMAP+current Green=WMAP+current+CBI7 high-ℓ

Params, contd…

Measuring the Phase Peak/valley locations of EE strongly predicted by TT Peak/valley locations of EE strongly predicted by TT We model EE spectrum as :C ℓ =f + gsin(kℓ+φ) then fit for f, g, k, and φ. We model EE spectrum as :C ℓ =f + gsin(kℓ+φ) then fit for f, g, k, and φ. For f and g 2 nd order rational functions, fit is very good, RMS deviation = 0.7 μK 2 For f and g 2 nd order rational functions, fit is very good, RMS deviation = 0.7 μK 2 For given value of phi, expected EE spectrum calculated using window functions For given value of phi, expected EE spectrum calculated using window functions Calculate χ 2 using correlation in fine bin spectrum and gaussian errors – χ 2 = (q-m) T (F EE ) -1 (q-m) Calculate χ 2 using correlation in fine bin spectrum and gaussian errors – χ 2 = (q-m) T (F EE ) -1 (q-m)

New: CBI EE Polarization Phase Peaks in EE should be offset one-half cycle vs. TT Peaks in EE should be offset one-half cycle vs. TT functional fit to envelope of EE plus sinusoidal modulation: functional fit to envelope of EE plus sinusoidal modulation: 25°±33° rel. phase (   2 =1)  2 (0°)=0.56

CBI Fine EE w/ Best Fit Phase

EE Amplitude and Phase Can check for both amplitude and phase agreement. Can check for both amplitude and phase agreement. CBI finds both amplitude and phase agree well with WMAP prediction CBI finds both amplitude and phase agree well with WMAP prediction Contours saturate at 3σ (gaussian) Contours saturate at 3σ (gaussian)

New: CBI, DASI, Capmap

Theta/Theta_0 Angular size of sound horizon at LSS should be same for TT and EE. Angular size of sound horizon at LSS should be same for TT and EE. CBI only has multiple solutions (shift spectrum by one peak). CBI only has multiple solutions (shift spectrum by one peak). DASI removes degeneracy, but less sensitive. DASI removes degeneracy, but less sensitive. CBI+DASI give scale vs. TT of / CBI+DASI give scale vs. TT of /

CBI Only

Dasi Only

CBI+DASI

The CBI Adventure… sunset sunset

Foregrounds – Sources Foreground radio sources Foreground radio sources Predominant on long baselines Predominant on long baselines Located in NVSS at 1.4 GHz, VLA 8.4 GHz Located in NVSS at 1.4 GHz, VLA 8.4 GHz Measured at 30 GHz with OVRO 40m Measured at 30 GHz with OVRO 40m new 30 GHz GBT receiver new 30 GHz GBT receiver

New: Shaped C l fits Use WMAP’03 best-fit Cl in signal covariance matrix Use WMAP’03 best-fit Cl in signal covariance matrix bandpower is then relative to fiducial power spectrum bandpower is then relative to fiducial power spectrum compute for single band encompassing all l s compute for single band encompassing all l s Results for CBI data (sources projected from TT only) Results for CBI data (sources projected from TT only) EE likelihood vs. zero : equivalent significance 8.9 σ EE likelihood vs. zero : equivalent significance 8.9 σ