Polarization Polarization Results from the Results from the

Cosmic Cosmic Background Background

ImagerImagerSteven T. Myers

Jonathan Sievers (CITA)

Cosmo 04

Continued…

The CBI CollaborationThe CBI CollaborationCaltech 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.

The InstrumentThe Instrument 13 90-cm Cassegrain 13 90-cm Cassegrain

antennasantennas 78 baselines78 baselines

6-meter platform6-meter platform Baselines 1m – 5.51mBaselines 1m – 5.51m

10 1 GHz channels 26-36 GHz10 1 GHz channels 26-36 GHz HEMT amplifiers (NRAO)HEMT amplifiers (NRAO) Cryogenic 6K, Tsys 20 KCryogenic 6K, Tsys 20 K

Single polarization (R or L)Single polarization (R or L) Polarizers from U. ChicagoPolarizers from U. Chicago

Analog correlatorsAnalog correlators 780 complex correlators780 complex correlators

Field-of-view 44 arcminField-of-view 44 arcmin Image noise 4 mJy/bm 900sImage noise 4 mJy/bm 900s

Resolution 4.5 – 10 arcminResolution 4.5 – 10 arcmin

The CBI Adventure…The CBI Adventure… Two winters a year! Two winters a year!

The roads fill with The roads fill with snow.snow.

The CBI Adventure…The CBI Adventure… Steve Padin wearing the Steve Padin wearing the

cannular oxygen system cannular oxygen system (CBI site >5000 meters)(CBI site >5000 meters)

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

erupts in 2001erupts in 2001

CBI in ChileCBI in Chile

CMB Interferometry

why, what, how?

CMB InterferometersCMB Interferometers CMB issues:CMB issues:

Extremely low surface brightness fluctuations < 50 Extremely low surface brightness fluctuations < 50 KK

Large monopole signal 3K, dipole 3 mKLarge monopole signal 3K, dipole 3 mK Polarization less than 10% Polarization less than 10% signal < 5 signal < 5 KK

No compact features, approximately Gaussian No compact features, approximately Gaussian random fieldrandom field

Foregrounds both galactic & extragalacticForegrounds both galactic & extragalactic Traditional direct imagingTraditional direct imaging

Differential horns or focal plane arraysDifferential horns or focal plane arrays InterferometryInterferometry

Inherent differencing (fringe pattern), filtered imagesInherent differencing (fringe pattern), filtered images Works in spatial Fourier domainWorks in spatial Fourier domain Element-based errors vs. baseline-based signalsElement-based errors vs. baseline-based signals Limited by need to correlate pairs of elementsLimited by need to correlate pairs of elements Sensitivity requires compact arraysSensitivity requires compact arrays

The Fourier RelationshipThe Fourier Relationship

RRk

ikk

RRk

ikkk

RRk

k

kk

eIAd

eIAdV

e)(~

)(~

e)()()(

22

)(22

xv

xxu

vvuv

xxxxu

A parallel hand “visibility” in sky and Fourier planes:A parallel hand “visibility” in sky and Fourier planes: direction direction xxkk and and uukk = = BBkk//kk for baseline for baseline BBkk

other correlation LL measures same Iother correlation LL measures same I The aperture (antenna) size restricts responseThe aperture (antenna) size restricts response

convolution in uv plane = loss of Fourier resolutionconvolution in uv plane = loss of Fourier resolution multiplication on sky = field-of-viewmultiplication on sky = field-of-view

loss of ability to localize wavefront directionloss of ability to localize wavefront direction Small apertures = wide field = higher Fourier resolutionSmall apertures = wide field = higher Fourier resolution

The uv plane and The uv plane and ll space space The sky can be uniquely described by spherical The sky can be uniquely described by spherical

harmonicsharmonics CMB power spectra are described by multipole CMB power spectra are described by multipole ll

( the angular scale in the spherical harmonic ( the angular scale in the spherical harmonic transform)transform)

For small (sub-radian) scales the spherical harmonics For small (sub-radian) scales the spherical harmonics can be approximated by Fourier modescan be approximated by Fourier modes The conjugate variables are (The conjugate variables are (u,vu,v) as in radio ) as in radio

interferometryinterferometry The uv radius is given by The uv radius is given by ll / 2 / 2

The projected length of the interferometer baseline The projected length of the interferometer baseline gives the angular scale gives the angular scale Multipole Multipole ll = 2 = 2 BB / /

An interferometer naturally measures the transform An interferometer naturally measures the transform of the sky intensity in of the sky intensity in ll space space

uv uv coverage of a close-packed coverage of a close-packed arrayarray

13 antennas13 antennas 78 baselines78 baselines 10 frequency channels 10 frequency channels 780 instantaneous 780 instantaneous

visibilitiesvisibilities frequency channels give radial spread in uv planefrequency channels give radial spread in uv plane

Baselines locked to platform in pointing directionBaselines locked to platform in pointing direction Baselines always perpendicular to source directionBaselines always perpendicular to source direction Delay lines not neededDelay lines not needed

Pointing platform rotatable to fill in Pointing platform rotatable to fill in uvuv coverage coverage Parallactic angle rotation gives azimuthal spreadParallactic angle rotation gives azimuthal spread

uvuv plane is over-sampled plane is over-sampled inner hole (1.1D), outer limit dominates PSFinner hole (1.1D), outer limit dominates PSF many more visibilities than independent many more visibilities than independent uvuv

“patches”“patches”

MosaicingMosaicing 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 ℓCBI 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 better if we follow a wave for more ℓResolution in better if we follow a wave for more ℓ

periodsperiods We want larger area, therefore observe mosaics of We want larger area, therefore observe mosaics of

fieldsfields Final resolution is FT of entire mapFinal resolution is FT of entire map

CBI observes 6x6 pointings in polarizationCBI observes 6x6 pointings in polarization Coverage is 4.5 x 4.5 degrees per mosaicCoverage is 4.5 x 4.5 degrees per mosaic ℓ ℓ resolution goes from 420 to ~70resolution goes from 420 to ~70 Means peaks can be observedMeans peaks can be observed

uv uv coverage with mosaic coverage with mosaic beambeam

Polarization – Stokes Polarization – Stokes parametersparameters CBI receivers can observe either RCP or LCPCBI receivers can observe either RCP or LCP

cross-correlate RR, RL, LR, or LL from antenna paircross-correlate RR, RL, LR, or LL from antenna pair Mapping of correlations (RR,LL,RL,LR) to Stokes parameters Mapping of correlations (RR,LL,RL,LR) to Stokes parameters

(I,Q,U,V) :(I,Q,U,V) :

Intensity I plus linear polarization Q,U importantIntensity 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 Iparallel hands RR, LL measure intensity I cross-hands RL, LR measure polarization Q, Ucross-hands RL, LR measure polarization Q, U

R-L phase gives Q, U electric vector position angleR-L phase gives Q, U electric vector position angle

E and B modesE and B modes A useful decomposition of the polarization signal A useful decomposition of the polarization signal

is into “gradient” and “curl modes” – E and B:is into “gradient” and “curl modes” – E and B:

uv1tan v

vvvvv 2)(~

)(~

)(~

)(~ ieBiEUiQ

RLk

ikk

RLk

keBiEPdV e)](~

)(~

[)()( )(22 vvvvvu

E & B response smeared by phase variation over aperture A

interferometer “directly” measures E & B!

CBI Current Polarization CBI Current Polarization DataData Observing since Sep 2002Observing since Sep 2002

compact configuration, maximum sensitivity, new NRAO compact configuration, maximum sensitivity, new NRAO HEMTsHEMTs

Four mosaics Four mosaics = 02 = 02hh, 08, 08hh, 14, 14hh, 20, 20hh at at = 0 = 0°° 02h, 08h, 14h 6 x 6 fields, 20h deep strip 6 fields , 45’ 02h, 08h, 14h 6 x 6 fields, 20h deep strip 6 fields , 45’

centerscenters Scan subtraction/projectionScan subtraction/projection

observe scan of 6 fields, 3observe scan of 6 fields, 3mm apart = 45’, remove mean 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 brightestneed 30 GHz GBT measurements to know brightest

Massive computations Massive computations parallel codes 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 using 256 node/ 512 proc McKenzie cluster at CITACITA

CBI & DASI FieldsCBI & DASI Fieldsgalactic projection – image WMAP “synchrotron” galactic projection – image WMAP “synchrotron”

(Bennett et al. 2003)(Bennett et al. 2003)

Foregrounds – SourcesForegrounds – Sources Foreground radio sourcesForeground radio sources

Predominant on long baselines Predominant on long baselines Located in NVSS at 1.4 GHz, VLA 8.4 GHzLocated in NVSS at 1.4 GHz, VLA 8.4 GHz Projected out in power spectrum analysisProjected out in power spectrum analysis

Project ~3500 sources in TT, ~550 in Project ~3500 sources in TT, ~550 in polarizationpolarization

No evidence for contribution of sources in No evidence for contribution of sources in polarization – our approach very conservativepolarization – our approach very conservative

““masking” out much of sky – need GBT masking” out much of sky – need GBT measurements to reduce the number of measurements to reduce the number of sources projectedsources projected

Data TestsData Tests

Data split by frequency (26-31 GHz, 31-36 Data split by frequency (26-31 GHz, 31-36 GHz) – no sign of foreground, but GHz) – no sign of foreground, but sensitivity lowsensitivity low

Data split by epochData split by epoch RR only vs. LL only TT spectraRR only vs. LL only TT spectra Polarization spectra omitting mosaicsPolarization spectra omitting mosaics Lead-trail subtractionLead-trail subtraction

No evidence for inconsistencies

Spectra!Spectra!

We measure TT, EE, BB, TE spectraWe measure TT, EE, BB, TE spectra Spectra with Spectra with ΔℓΔℓ=150 for plots=150 for plots Fine bin spectra (Fine bin spectra (ΔℓΔℓ~75) for ~75) for

cosmology etc. More information cosmology etc. More information contained, but hard to interpret contained, but hard to interpret visually due to large error bars, visually due to large error bars, correlationscorrelations

Single shaped band spectra for Single shaped band spectra for consistency with WMAP predictions consistency with WMAP predictions

Spectra!Spectra!

We measure TT, EE, BB, TE spectraWe measure TT, EE, BB, TE spectra Spectra with Spectra with ΔℓΔℓ=150 for plots=150 for plots Fine bin spectra (Fine bin spectra (ΔℓΔℓ~75) for cosmology ~75) for cosmology

etc. More information contained, but etc. More information contained, but hard to interpret visually due to large hard to interpret visually due to large error bars, correlationserror bars, correlations

Single shaped band spectra for Single shaped band spectra for consistency with WMAP predictions consistency with WMAP predictions

Also Also ΔℓΔℓ=150 spectra with bins offset by =150 spectra with bins offset by 7575

Consistency w/ WMAPConsistency w/ WMAP

Spectra consistent with the Spectra consistent with the cosmological model from WMAPext cosmological model from WMAPext datasetdataset

χχ22 = 7.98 TT, 3.77 EE, 4.33 BB (vs. = 7.98 TT, 3.77 EE, 4.33 BB (vs. 0), and 5.80 TE for 7 dof.0), and 5.80 TE for 7 dof.

New: Shaped CNew: Shaped Cll fits fits Use WMAP’03 best-fit Cl in signal Use WMAP’03 best-fit Cl in signal

covariance matrixcovariance matrix bandpower is then relative to fiducial power bandpower is then relative to fiducial power

spectrumspectrum compute for single band encompassing all compute for single band encompassing all llss

Results for CBI data (sources projected Results for CBI data (sources projected from TT only)from TT only) EE likelihood vs. zero : equivalent EE likelihood vs. zero : equivalent

significance significance 8.9 8.9 σσ

Parameters w/CBIParameters w/CBI Paramaters calculated using Antony Lewis’s Paramaters calculated using Antony Lewis’s

MCMC code, COSMOMCMCMC code, COSMOMC Old CBI mosaics (Readhead et al. 2004) Old CBI mosaics (Readhead et al. 2004)

overlap with polarization mosaics. Not overlap with polarization mosaics. Not allowed to combine sample-limited part of allowed to combine sample-limited part of spectra.spectra.

Thermal limited ( >1000) old spectrum ℓThermal limited ( >1000) old spectrum ℓincluded. New spectrum only for <1000.ℓincluded. New spectrum only for <1000.ℓ

First time EE included for measuring First time EE included for measuring parameters (though impact of EE quite small)parameters (though impact of EE quite small)

Blue=WMAPRed=WMAP+currentGreen=WMAP+current+CBI7 high-ℓ

Params, contd…Params, contd…

Measuring the PhaseMeasuring the Phase Peak/valley locations of EE strongly predicted by TTPeak/valley locations of EE strongly predicted by TT We model EE spectrum as :We model EE spectrum as :CCℓℓ==ff + + ggsin(sin(kk +ℓ+ℓ φφ) then fit ) then fit

for for ff, , gg, , kk, and , and φφ.. For For ff and and gg 2 2ndnd order rational functions, fit is very order rational functions, fit is very

good, RMS deviation = 0.7 good, RMS deviation = 0.7 μμKK22

For given value of phi, expected EE spectrum For given value of phi, expected EE spectrum calculated using window functions calculated using window functions

Calculate Calculate χχ22 using correlation in fine bin spectrum and using correlation in fine bin spectrum and gaussian errors – gaussian errors – χχ22 = ( = (q-mq-m))TT(F(FEEEE))-1-1((q-mq-m))

New: CBI EE Polarization New: CBI EE Polarization PhasePhase Peaks in EE should be offset one-Peaks in EE should be offset one-

half cycle vs. TThalf cycle vs. TT functional fit to envelope of EE plus functional fit to envelope of EE plus

sinusoidal modulation:sinusoidal modulation:25°±33° rel. phase (2=1)

2(0°)=0.56

CBI Fine EE w/ Best Fit PhaseCBI Fine EE w/ Best Fit Phase

EE Amplitude and PhaseEE Amplitude and Phase

Can check for both amplitude and phase Can check for both amplitude and phase agreement. agreement.

CBI finds both amplitude and phase CBI finds both amplitude and phase agree well with WMAP predictionagree well with WMAP prediction

Contours saturate at 3Contours saturate at 3σσ (gaussian) (gaussian)

New: CBI, DASI, CapmapNew: CBI, DASI, Capmap

The CBI Adventure…The CBI Adventure…

sunsetsunset

Foregrounds – SourcesForegrounds – Sources Foreground radio sourcesForeground radio sources

Predominant on long baselines Predominant on long baselines Located in NVSS at 1.4 GHz, VLA 8.4 Located in NVSS at 1.4 GHz, VLA 8.4

GHzGHz Measured at 30 GHz with OVRO 40mMeasured at 30 GHz with OVRO 40m

new 30 GHz GBT receivernew 30 GHz GBT receiver

New: Shaped CNew: Shaped Cll fits fits Use WMAP’03 best-fit Cl in signal Use WMAP’03 best-fit Cl in signal

covariance matrixcovariance matrix bandpower is then relative to fiducial power bandpower is then relative to fiducial power

spectrumspectrum compute for single band encompassing all compute for single band encompassing all llss

Results for CBI data (sources projected Results for CBI data (sources projected from TT only)from TT only) EE likelihood vs. zero : equivalent EE likelihood vs. zero : equivalent

significance significance 8.9 8.9 σσ