the cosmic background imager – berkeley, 28 sep 2004 2 cmb polarization results from the cosmic...

2The Cosmic Background Imager – Berkeley, 28 Sep 2004

CMB Polarization Results from the

Cosmic Background ImagerSteven T. Myers

National Radio Astronomy Observatory

Socorro, NM


The Cosmic Background Imager

• A collaboration between– Caltech (A.C.S. Readhead PI, S. Padin PS.)– NRAO– CITA– Universidad de Chile– University of Chicago

• With participants also from– U.C. Berkeley, U. Alberta, ESO, IAP-Paris, NASA-MSFC,

Universidad de Concepción

• Funded by– 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 CMB Landscape


Thermal History of the Universe

Courtesy Wayne Hu – http://background.uchicago.edu


CMB Primary Anisotropies

• Low l (<100)– primordial power spectrum (+ S-W, tensors, etc.)

• Intermediate l (100-2000)– dominated by acoustic peak structure– position of peak related to sound crossing angular scale angular diameter distance to last scattering

– peak heights controlled by baryons & dark matter, etc.– damping tail roll-off with

• Large l (2000-5000+)– realm of the secondaries (e.g. SZE)



CMB Acoustic Peaks

• Compression driven by gravity, resisted by radiation≈ “j ladder” series of harmonics + projection corrections

peaks: ~ peaks: ~ llss jjtroughs: ~ troughs: ~ llss ( (jj ±± ½½))


CMB Secondary Anisotropies


•SPH (5123) [Wadsley et al. 2002]

Bond et al. 2002

•MMH (5123) [Pen 1998]

SZE SZE SecondarySecondary

8=1.0, 0.9


CMB Polarization

• Due to quadrupolar intensity field at scattering



CMB Polarization

• E & B modes: translation invariance– E (gradient) from scalar density fluctuations predominant!– B (curl) from gravity wave tensor modes, or secondaries



Polarization Power Spectrum

Hu & Dodelson ARAA 2002

Planck “error boxes”Planck “error boxes”

Note: polarization peaks Note: polarization peaks out of phase w.r.t. out of phase w.r.t. intensity peaksintensity peaks


The Gold Standard: WMAP + “ext”WMAP

ACBAR


The Cosmic Background Imager


The Instrument

• 13 90-cm Cassegrain antennas– 78 baselines

• 6-meter platform– Baselines 1m – 5.51m

• 10 1 GHz channels 26-36 GHz– HEMT amplifiers (NRAO)

– Cryogenic 6K, Tsys 20 K

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

• Analog correlators– 780 complex correlators

• Field-of-view 44 arcmin– Image noise 4 mJy/bm 900s

• Resolution 4.5 – 10 arcmin


Other CMB Interferometers: DASI, VSA

• DASI @ South Pole

• VSA @ Tenerife


CBI Site – Northern Chilean Andes

• Elevation 16500 ft.!


The CBI Adventure…

• Steve Padin wearing the cannular oxygen system– because you never know when you

need to dig the truck out!


3-Axis mount : rotatable platform


The CMB and Interferometry

• The sky can be uniquely described by spherical harmonics– CMB power spectra are described by multipole l

• 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 uv radius is given by |u| = l / 2• An interferometer naturally measures the transform of

the sky intensity in l space convolved with aperture

e)(~

)(~

e)()()(

22

)(22

p

p

i

ip

eIAd

eIAdV

xv

xxu

vvuv

xxxxu


The uv plane

• The projected baseline length gives the angular scale

multipole:multipole:

ll = 2 = 2B/B/λ λ = 2= 2uuijij||

shortest CBI baseline:shortest CBI baseline:

central hole 10cmcentral hole 10cm


CBI Beam and uv coverage

• Over-sampled uv-plane– excellent PSF– allows fast gridded method (Myers et al. 2000)

primary beam transform:primary beam transform:

θθpripri= 45= 45' ' ΔΔll ≈ 4D/ ≈ 4D/λλ ≈ 360 ≈ 360

mosaic beam transform:mosaic beam transform:

θθmosmos= = nn××4545' ' ΔΔll ≈ 4D/ ≈ 4D/nnλλ


CBI 2000+2001, WMAP, ACBAR, BIMA

Readhead et al. ApJ, 609, 498 (2004)Readhead et al. ApJ, 609, 498 (2004)

astro-ph/0402359astro-ph/0402359

SZE SZE SecondarySecondaryCMB CMB

PrimaryPrimary


CMB Interferometry


Polarization of radiation

• Electromagnetic Waves– Maxwell: 2 independent linearly polarized waves

– 3 parameters (E1,E2,) polarization ellipse

Rohlfs & Wilson





• Stokes parameters (Poincare Sphere):– intensity I (Poynting flux) I2 = E1

2 + E22

– linear polarization Q,U (m I)2 = Q2 + U2

– circular polarization V (v I)2 = V2

Rohlfs & Wilson

The Poincare SphereThe Poincare Sphere





• Stokes parameters (Poincare Sphere):– intensity I (Poynting flux) I2 = E1

2 + E22

– linear polarization Q,U (m I)2 = Q2 + U2

– circular polarization V (v I)2 = V2

• Coordinate system dependence:– I independent– V depends on choice of “handedness”

• V > 0 for RCP

– Q,U depend on choice of “North” (plus handedness)• Q “points” North, U 45 toward East• EVPA = ½ tan-1 (U/Q) (North through East)


Polarization – Stokes parameters• CBI receivers can observe either RCP or LCP

– cross-correlate RR, RL, LR, or LL from antenna pair

• CMB intensity I plus linear polarization Q,U important– CMB not circularly polarized, ignore V (RR = LL = I)

– parallel hands RR, LL measure intensity I

– cross-hands RL, LR measure complex polarization P=Q+iU• R-L phase gives electric vector position angle = ½ tan-1 (U/Q)

• rotates with parallactic angle of detector on sky

V

U

Q

I

eie

eie

VI

eUiQ

eUiQ

VI

ee

ee

ee

ee

ii

ii

i

i

LL

RL

LR

RR

1001

00

00

1001

22

22

2

2

*

*

*

*


Polarization Interferometry

• Parallel-hand & Cross-hand correlations– for antenna pair i, j and frequency channel :

– where kernel P is the aperture cross-correlation function

– and the baseline parallactic angle (w.r.t. deck angle 0°)

RLij

iijij

RLij

RRijijij

RRij

ijeUiQPdV

IPdV

e)(~

)(~

)()(

e)(~

)()(

22

2

vvvvu

vvvu

ijiijijij eAP xvvuv

2)(~

)(

01tan ijijijij uv


E and B modes

• A useful decomposition of the polarization signal is into “gradient” and “curl modes” – E and B:

uv1tan v

vvvvv χieBiEUiQ 2)(~

)(~

)(~

)(~

RLij

iijij

RLij

ijeBiEPdV

e)](~

)(~

[)()( )(22 vvvvvu

E & B response smeared by phase variation over aperture A

interferometer “directly” measures (Fourier transforms of) E & B!


Power Spectrum of CMB

• Statistics of CMB field– Gaussian random field – Fourier modes independent– described by angular power spectrum

– 4 non-zero polarization covariances: TT,EE,BB,TE (plus EB, TB)

)'()'(~

)(~

2)'()'(*~

)(~

2

2

vvvv

vvvvv

CTT

CTT

)'()'(*~

)(~

)'()'(*~

)(~

)'()'(*~

)(~

)'()'(*~

)(~

)'()'(*~

)(~

)'()'(*~

)(~

22

22

22

vvvvvvvv

vvvvvvvv

vvvvvvvv

EBTB

BBTE

EETT

CBECBT

CBBCET

CEECTT


Power Spectrum and Likelihood• Break Cl into bandpowers qB:

• Covariance matrix C sum of individual covariance terms:

• maximize Likelihood for complex visibilities V:

BB

BCqC shape

BBEBEETBTETT

CqCqCqCqCC BB

B

,,,,,

scanscan

resres

srcsrc

N

known foregrounds (e.g

point sources)

residual (statistical) foreground

scan (ground) signal

fiducial power spectrum shape (e.g. 2/l2)

=1 if l in band B; else =0

noise projected fitted


CBI Polarization Data Processing

• Massive data processing exercise– 4 mosaics, 300 nights observing– more than 106 visibilities total!– scan projection over 3.5° requires fine gridding

• more than 104 gridded estimators

• Method: Myers et al. (2003)– gridded estimators + max. likelihood– tested in CBI 2000, 2001-2002 papers

• Parallel computing critical– both gridding and likelihood now parallelized using MPI

• using 256 node/ 512 proc McKenzie cluster at CITA• 2.4 GHz Intel Xeons, gigabit ethernet, 1.2 Tflops!• currently 4-6 hours per full run (!)• current limitation 1 GB memory per node

kiiikk

i

kik eA

z

wQ xuuu 2)(

~

k

kiki VQ

mosaicing phase factor

Matched filter gridding kernel


Tests with mock data

• The CBI pipeline has been extensively tested using mock data– Use real data files for template– Replace visibilties with simulated signal and noise– Run end-to-end through pipeline– Run many trials to build up statistics

w/o source projection(×½)


Detail: leakage

• Leakage of R L (d-terms):

dldmemleidd

eded

eimlEV

dldmemledd

iedied

emlEV

mvluiχiLj

Ri

χiLj

χiRi

χi

sky

RLij

RLij

mvluiχiRj

Ri

χiRj

χiRi

χi

sky

RRij

RRij

ijijji

jiji

ji

ijijji

jiji

ji

2)(*

)(*)(

)(

2)(*

)(*)(

)(

),](U)Q(

)VI()VI(

U)Q)[(,(

),](V)-(I

U)(QU)(Q

V)I)[(,(

““true” signaltrue” signal

11stst order: order:DD••I into PI into P

22ndnd order: order:DD•P into I•P into I

22ndnd order: order:DD22•I into I•I into I

33rdrd order: order:DD22•P* into P•P* into P


CBI PolarizationNew Results!

Brought to you by:A. Readhead, T. Pearson, C. Dickinson (Caltech)

S. Myers, B. Mason (NRAO),J. Sievers, C. Contaldi, J.R. Bond (CITA)

P. Altamirano, R. Bustos, C. Achermann (Chile)& the CBI team!

astro-ph/0409569 (24 Sep 2004)


2002 DASI & 2003 WMAP Polarization


Carlstrom et al. 2003 astro-ph/0308478


New: DASI 3-year polarization results!

• Leitch et al. 2004 (astro-ph/0409357) 16Sep04! 16Sep04! – EE 6.3 σ – TE 2.9 σ – consistent w/ WMAP+ext model– BB consistent with zero– no foregrounds (yet)


New: DASI 3-year polarization results!

• Leitch et al. 2004 (astro-ph/0409357) 16Sep04! 16Sep04! – CMB thermal spectrum =0 : found =0.11±0.13– vs. synchrotron = -2.0 to -3.0– no point sources seen in images (>15 mJy)– test against synchrotron (diffuse and point) foregrounds– relative to 8.5 K2 at l = 300– NO POLARIZED FOREGROUNDS DETECTED !


CBI Current Polarization Data

• Observing since Sep 2002 (processed to May 2004)– compact configuration, maximum sensitivity


CBI Polarization Mosaics

• Four mosaics = 02h, 08h, 14h, 20h at = 0°– 02h, 08h, 14h 6 x 6 fields, 20h deep strip 6 fields [45’ centers]


Before ground subtraction:

• I, Q, U dirty mosaic images:


After ground subtraction:

• I, Q, U dirty mosaic images (9m differences):


CBI Calibration & Foregrounds

• Calibration on TauA (Crab) & Jupiter– use TauA to calibrate R-L phase (26 Jy of polarized flux!)– secondary calibrators also (3C274, Mars, Saturn, …)

• Scan subtraction/projection– observe scan of 6 fields, 3m apart = 45’– lose only 1/6 data to differencing (cf. ½ previously)

• Point source projection– list of NVSS sources (extrapolation to 30 GHz unknown)– 3727 total for TT many modes lost, sensitivity reduced– use 557 for polarization (bright OVRO + NVSS 3 pol)– need 30 GHz GBT measurements to know brightest


CBI Diffuse Foregrounds

• Mid-High galactic latitudes (25°– 50° vs. 60° DASI) • Galactic cosmic rays (synchrotron emission)

– from WMAP template (Bennett et al. 2003)– mean, rms, max not significantly worse than in DASI fields– except 14h field (in North Polar Spur) 50% worse

• Rely on CBI frequency leverage (26-36 GHz)– synchrotron spectrum -2.7 vs. thermal

– also l2 vs. CMB in power spectrum


CBI & DASI Fields

galactic projection – image WMAP “synchrotron” (Bennett et al. 2003)


New: CBI Polarization Power Spectra

• 7-band fits (l = 150 for 600<l<1200)• bin positions well-matched to peaks & valleys• offset bins run also• narrower bins (l = 75) – scatter from F-1

• bin resolution limited by signal-to-noise


Data Tests

• Test robustness to systematic effects, such as:– instrumental effects (amplitude, polarization)– foregrounds (synchrotron, free-free, dust)

• Numerous 2 and noise tests– few discrepant days found no difference to results

• Conduct series of splits and “jack-knife” tests, e.g.:– primary vs. secondary calibrators (calibration consistency)– first half vs. second half of data (time-variable instrument)– “jack-knife” on antennas (bad single antenna)– “jack-knife” on fields (bad single field)– high vs. low frequency channels (e.g. foregrounds)

NO SIGNIFICANT DEVIATIONS FOUND!


Shaped Cl fits

• Use WMAP’03 best-fit Cl in signal covariance matrix– bandpower is then relative to fiducial power spectrum– compute for single band encompassing all ls

• Results for CBI data (sources projected from TT only)– qB = 1.22 ± 0.21 (68%)

– EE likelihood vs. zero : equivalent significance 8.9 σ

• Conservative - project subset out in polarization also– qB = 1.18 ± 0.24 (68%)

– significance 7.0 σ


New: CBI Polarization Parameters

• use fine bins (l = 75) + window functions (l = 25) • cosmological models vs. data using MCMC

– modified COSMOMC (Lewis & Bridle 2002)

• Include:– WMAP TT & TE– WMAP + CBI’04 TT & EE (Readhead et al. 2004b = new!)– WMAP + CBI’04 TT & EE l <1000

+ CBI’02 TT l >1000 (Readhead et al. 2004a) [overlaps ‘04]



• use fine bins (l = 75) + window functions (l = 25) • Include:

– WMAP TT & TE– CBI 2004 Pol TT, EE (Readhead et al. 2004b = new)– CBI 2001-2002 TT (Readhead et al. 2004a)

• NOTE: parameter constraints dominated by higher precision TT from CBI 2001-2002 data!



• NOTE: parameter constraints dominated by higher precision TT from CBI 2001-2002 (and to lesser extent 2002-2004) data!

• To discern what polarization data is adding, will need to be more subtle…


Cosmology from EE Polarization

• Standard Cosmological Model ™– EE “predictable” from TT– constraints dominated by more precise TT measurements

• Beyond the Standard Model– derive key parameters from EE alone – check consistency– add new ingredients (e.g. isocurvature)


Example: Acoustic Overtone Pattern

• Sound crossing angular size at photon decoupling– fiducial model WMAP+ext : θ0 = 1.046

WMAPWMAP

WMAP+CBI’04WMAP+CBI’04

WMAP+CBI’04+CBI’02WMAP+CBI’04+CBI’02

1 s

grand unified:grand unified:

θθ == 1.0441.044±0.005±0.005

θθ//θθ00 = = 0.998±0.0050.998±0.005(WMAP+CBI’04+CBI’02)(WMAP+CBI’04+CBI’02)


Example: Acoustic Overtone Pattern

• Sound crossing angular size at photon decoupling– fiducial model WMAP+ext : θ0 = 1.046

– CBIPol + WMAP + “ext” : θ/θ0 = 0.998 ± 0.005

• Overtone pattern– equivalent to “j ladder” – TT extrema spaced at j intervals– EE spaced at j+½ (plus corrections)

21

j

j

sEEj

sTTj


New: CBI EE Polarization Phase

• Parameterization 1: envelope plus shiftable sinusoid– fit to “WMAP+ext” fiducial spectrum using rational functions

kgfa

C EE

sin

1



• Peaks in EE should be offset one-half cycle vs. TT – fix amplitude a=1 and allow phase to vary

slice at: slice at: aa=1=1

== 2525°±°±3333°° rel. phase ( rel. phase (22=1)=1)

22(1, 0(1, 0°°)=0.56)=0.56



• Peaks in EE should be offset one-half cycle vs. TT– allow amplitude a and phase to vary

best fit: best fit: aa=0.94=0.94

== 2424°±°±3333°° ( (22=1)=1)

22(1, 0(1, 0°°)=0.56)=0.56



• Scaling model: spectrum shifts by scaling l – same envelope f,g as before

0

0

sin

1

ss

EE

AAa

kgfa

C

fiducial model:fiducial model:

θθ00== 1.0461.046(“WMAP+ext”)(“WMAP+ext”)

θθ sound crossingsound crossingangular scaleangular scale



• Scaling model: spectrum shifts by scaling l – allow amplitude a and scale θ to vary

overtone 0.67 island: overtone 0.67 island: aa=0.69=0.69±±0.030.03

excluded by TTexcluded by TTand other priorsand other priors

other overtone islandsother overtone islands

also excludedalso excluded



• Scaling model: spectrum shifts by scaling l – allow amplitude a and scale θ to vary

best fit: best fit: aa=0.93=0.93

slice along a=1:slice along a=1:

θθ//θθ00== 1.021.02±±0.04 (0.04 (22=1)=1)

zoom in: zoom in:

± one-half cycle± one-half cycle


New: CBI, DASI, Capmap


New: DASI EE Polarization Phase

• Use DASI EE 5-bin bandpowers (Leitch et al. 2004)– bin-bin covariance matrix plus approximate window

functions

a=0.5, 0.67 overtone islands:a=0.5, 0.67 overtone islands:

suppressed by DASIsuppressed by DASI

DASI phase lock:DASI phase lock:

θθ//θθ00== 0.94±0.060.94±0.06a=0.5 (low DASI)a=0.5 (low DASI)


New: CBI + DASI EE Phase

• Combined constraints on θ model:– DASI (Leitch et al. 2004) & CBI (Readhead et al. 2004)

CBI a=0.67 overtone island:CBI a=0.67 overtone island:

suppressed by DASI datasuppressed by DASI data

other overtone islandsother overtone islands

also excludedalso excluded

CBI+DASI phase lock:CBI+DASI phase lock:

θθ//θθ00== 1.00±0.031.00±0.03a=0.78a=0.78±0.15±0.15 (low DASI) (low DASI)


Conclusions

• CMB polarization interferometry (CBI,DASI)– straightforward analysis {RR,RL} → {TT,EE,BB,TE}– polarization systematics minimized

• CMB polarization results– EE power spectrum measured

• consistent with Standard Cosmological Model™

– EE acoustic spectrum• peaks phase one-half cycle offset from TT

• sound crossing angular scale independently consistent (3%)

– BB null, no polarized foregrounds detected– TE difficult to extract in wide bins

• more data, narrower bins


CBI Polarization Projections


Future

• CBI– 6 months more data in hand finer l bins– more detailed papers: data tests, analysis, parameters– run to end of 2005 (pending funding)– also: SZE clusters (e.g. Udomprasert et al. 2004)

• Beyond CBI QUIET– detectors are near quantum & bandwidth limit – need more!– but: need clean polarization (low stable instrumental effects)– large format (1000 els.) coherent (MMIC) detector array– polarization B-modes! (at least the lensing signal)

• Further Beyond– Beyond Einstein (save the Bpol mission!)


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.

the cosmic background imager – berkeley, 28 sep 2004 2 cmb polarization results from the cosmic...

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