Polarization Polarization Results from the Results from the
Cosmic Cosmic Background Background
ImagerImagerSteven T. Myers
Jonathan Sievers (CITA)
CITA 04 Oct. 2004
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.
Whence Polarization?Whence Polarization?
Polarization comes from Thomson Polarization comes from Thomson scattering during recombinationscattering during recombination
Quadrupole seen by electrons produces Quadrupole seen by electrons produces polarization.polarization.
Dominant source from velocity modes – Dominant source from velocity modes – so out of phase with TTso out of phase with TT
Pol’n lines up with modes, so no BB typePol’n lines up with modes, so no BB type Strongly predicted by TT – good check Strongly predicted by TT – good check
on model.on model.
No DipoleNo Dipole
No net extra No net extra radiation from radiation from left/right or left/right or top/bottom, so top/bottom, so no polarizationno polarization
Doppler shift Doppler shift makes dipole makes dipole pattern, so pattern, so moving moving electron in an electron in an isotropic field isotropic field has no has no polarization.polarization.
QuadrupoleQuadrupole More radiation More radiation
from left/right from left/right than than top/bottom. top/bottom. Electron moves Electron moves up/down, and up/down, and so scattered so scattered radiation is radiation is polarized.polarized.
E Mode OnlyE Mode Only
If velocity If velocity converges, converges, then electron then electron moves moves normal to normal to wave +Ewave +E
If diverges, If diverges, electron electron moves along moves along wave –Ewave –E
Never moves Never moves tilted, so no tilted, so no B radiationB radiation
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
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
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
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
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)
Theta/Theta_0Theta/Theta_0
Angular size of sound horizon at LSS Angular size of sound horizon at LSS should be same for TT and EE. should be same for TT and EE.
CBI only has multiple solutions (shift CBI only has multiple solutions (shift spectrum by one peak).spectrum by one peak).
DASI removes degeneracy, but less DASI removes degeneracy, but less sensitive.sensitive.
CBI+DASI give scale vs. TT of 1.02 CBI+DASI give scale vs. TT of 1.02 +/- 0.03.+/- 0.03.
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
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