The Cosmic Background Imager – U. Kansas, 29 Nov 2004 2 CMB Polarization Results from the Cosmic...

2The Cosmic Background Imager – U. Kansas, 29 Nov 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


The Cosmic Microwave Background

• Discovered 1965 (Penzias & Wilson)– 2.7 K blackbody– Isotropic– Relic of hot “big bang”– 3 mK dipole (Doppler)

• COBE 1992– Blackbody 2.725 K– Anisotropies ≤10-5


The Expanding Universe• space is expanding with time

– measured by scale factor a – or “redshift” z ~ inverse scale factor– a = 1 now; a = 0 at “Big Bang”– all linear scales (like wavelengths) expand as a

• all else follows from this expansion!– radiation temperature T scales with 1/a – matter density 1/a3 ; radiation density 1/a4

• rate of expansion = H “Hubble constant”– controlled by matter and radiation density of Universe– H-1 “expansion time”, currently ~13 Gyr– expansion should be decelerating with time

• accelerating !? “dark energy” with negative pressure!

– speed of light c limits “horizon” of causality• isotropy of Universe suggests early phase of “inflation”

za

1

1


Thermal History of the Universe

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

““First 3 minutes”:First 3 minutes”:very hot (10 million very hot (10 million °°K)K)like interior of Sunlike interior of Sunnucleosynthesis!nucleosynthesis!

After “recombination”:After “recombination”:cooler, transparent, cooler, transparent, neutral hydrogen gasneutral hydrogen gas

Before “recombination”:Before “recombination”:hot (3000hot (3000°°K)K)like surface of Sun like surface of Sun opaque, ionized plasmaopaque, ionized plasma

““Surface of last scattering” Surface of last scattering” TT≈≈30003000°°K zK z≈≈10001000THIS IS WHAT WE SEE AS THIS IS WHAT WE SEE AS THE CMB!THE CMB!


Matter History of the Universe

• we see “structure” in Universe now– density fluctuations ~1 on 10 Mpc scales– clusters of galaxies!

• must have been smaller in past (fluctuations grow)– in expanding Universe growth is approximately linear– CMB @ a = 0.001 density fluctuations ~ 0.001

• NOTE: density higher in past, but density fluctuations smaller!

Courtesy A. Kravtsov – http://cosmicweb.uchicago.edu


Angular Power Spectrum

• brightness fluctuations on surface of last scattering– due to the small (~0.1%) density variations– gravity causes flows (velocities)– radiation pressure resists compression bounces– acoustic waves!

• Fourier analysis– break angular ripple pattern into spherical harmonics (waves)– look for power on particular angular frequencies– like a cosmic Spectrum Analyzer!– acoustic waves + expansion fundamental + overtones

• fundamental = scale of first compression since horizon crossing• scale set by sound crossing time at last scattering


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 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)



only transverse only transverse polarization can be polarization can be transmitted on scattering!transmitted on scattering!

CMB Polarization

• Due to quadrupolar intensity field at scattering


NOTE: polarization maximum NOTE: polarization maximum when velocity is maximum when velocity is maximum (out of phase with compression (out of phase with compression maxima)maxima)


CMB Polarization• E & B modes: translation invariance

– E (even parity, “gradient”, aligned 0° or 90° to k-vector) • from scalar density fluctuations predominant!

– B (odd parity, “curl”, at ±45° to k-vector) • 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


Traditional Inteferometer – The VLA• The Very Large Array (VLA)

– 27 elements, 25m antennas, 74 MHz – 50 GHz (in bands)– independent elements Earth rotation synthesis


CMB Interferometer – The CBI• The Cosmic Background Imager (CBI)

– 13 elements, 90 cm antennas, 26-36 GHz (10 channels)– fixed to 3-axis platform telescope rotation synthesis!


Other CMB Interferometers: DASI, VSA

• DASI @ South Pole

• VSA @ Tenerife


CBI milestones• 1980’s

– 1984 OVRO 40m single-dish work (20 GHz maser Rx!)– 1987 genesis of idea for CMB interferometer

• 1990’s– 1992 OVRO systems converted to HEMTs– 1994 NSF proposal (funded 1995)– 1998 assembled and tested at Caltech– 1999 August shipped to Chile– 1999 November Chile first “light”

• 2000+– 2000 January routine observing begins– 2001 first paper; 2002 first year results; 2003 2yrs; 2004 pol– 2002 continued NSF funding to end of 2004– exploring funding prospects to operate until end of 2006


CBI Site – Northern Chilean Andes

• Elevation 16500 ft.!


CBI in Chile


The CBI Adventure…

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

need to dig the truck out!


CMB Interferometry


dmdlvmuljemlIvuV ..2.),(),(

Interferometers

• Spatial coherence of radiation pattern contains information about source structure– Correlations along wavefronts

• Equivalent to masking parts of a telescope aperture– Sparse arrays = unfilled aperture– Resolution at cost of surface brightness sensitivity

• Correlate pairs of antennas– “visibility” = correlated fraction of total signal

• Fourier transform relationship with sky brightness– Van Cittert – Zernicke theorem


CBI Instrumentation


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


Polarization of radiation

• Electromagnetic Waves– Maxwell: 2 independent linearly polarized waves

– 3 parameters (E1,E2,) polarization ellipse

• 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)

Rohlfs & Wilson

The Poincare SphereThe Poincare Sphere


Polarization Interferometry

• CBI receivers can observe either RCP or LCP– correlation products RR, RL, LR, or LL from antenna pair

• Correlations to Stokes parameters (I,Q,U,V) :

• co-polar: RR = I + V LL = I – V – CMB not circularly polarized, ignore V (RR = LL = I)– co-polar correlations measure intensity (CMB temperature)

• cross-polar: RL = [Q + i U] e-i2 LR = [Q – i U] ei2 – cross-polar visibilities measure linear polarization– electric vector position angle EVPA = ½ tan-1(U/Q)– rotates with parallactic angle of detector on sky


Polarization Interferometry

• Stokes I,Q,U to E and B:

• Q + i U = [E + i B] ei2 RL = [E + i B] ei2( – counter-rotates with wave vector angle = ½ tan-1 (v/u)

• polarization covariances: TT,EE,BB,TE,TB,EB• visibility covariances:

– <RR RR*> = TT <RR RL*> = TE <RL RL*> = EE + BB

• interferometry works in Fourier domain– multipole l = 2 B / for baseline B– power spectrum from amplitude of visibility covariances– circularly polarized interferometer “directly” measures E and B!


Interferometry Equations

• Our co-polar and cross-polar visibilities are:

RLij

iijij

RLij

ijeBiEPdV

e)](~

)(~

[)()( )(22 vvvvvu

E & B response smeared by phase variation over aperture A

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

RRijijij

RRij TPdV e)(

~)()( 2 vvvu

piijij eAP xvvuv

2)(~

)(


Errors: leakage

• instrumental polarization– “leaks” L into R, R into L (level ~1%-2%)

– e.g. Robs = R + d L

• measure on bright source– use standard data analysis to determine d-terms

• to first order:– TT unaffected– TT leaks into TE & TB

– TE & TB leak into EE, BB, EB

• include in correlation analysis– just complicates covariance matrix calculation


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)


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


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)

Carlstrom et al. 2003 astro-ph/0308478


CBI Current Polarization Data

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


CBI Upgrade: Polarization

• CBI instrumentation– Use quarter-wave devices for linear to circular conversion– Single amplifier per receiver: either R or L only per element

• 2000 Observations– One antenna cross-polarized in 2000 (Cartwright thesis)– Only 12 cross-polarized baselines (cf. 66 parallel hand)– Original polarizers had 5%-15% leakage– Deep fields, upper limit ~8 K

• 2002 Upgrade– Upgrade in 2002 using DASI polarizers (J. Kovac)– Observing with 7R + 6L starting Sep 2002– Raster scans for mosaicing and efficiency– New TRW InP HEMTs from NRAO


CBI Upgrade: New NRAO HEMTs

• 2002 Upgrade– New TRW InP HEMTs from NRAO

Ka-band Receiver

0

2

4

6

8

10

12

14

16

18

20

26 28 30 32 34 36 38 40

Frequency (GHz)

No

ise

Tem

per

atu

re (

K)


Calibration from WMAP Jupiter

• Old uncertainty: 5%• 2.7% high vs. WMAP Jupiter• New uncertainty: 1.3%• Ultimate goal: 0.5%


CBI Polarization Mosaics

• Four mosaics = 02h, 08h, 14h, 20h at = 0° (70 °) – 02h, 08h, 14h 6 x 6 fields, 20h deep strip 6 fields [45’ centers]


CBI observational issues

• short (100) baselines– can see the Sun if it is up observe at night only– can see the Moon within 60 observe 60 from Moon

• CMB fields on equator observe SZE clusters when blocked by moon!

– far-field at 100m atmosphere imaged along with CMB• Atacama site very good, little data lost to clouds

• plus platform (no delay tracking)– need to reject common mode signals (which correlate)

• 120db isolation between antennas (shields + phase shifters)

– strong (>1 Jy) ground signal (polarized)• orientation dependence (see mountains around site!)• removed by differencing (or scan projection)


Before ground subtraction:

• I, Q, U dirty mosaic images:


After ground subtraction:

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


Foregrounds – Sources

• Foreground radio sources– Predominant on long baselines – Located in NVSS at 1.4 GHz, VLA 8.4 GHz– Measured at 30 GHz with OVRO 40m

• new 30 GHz GBT receiver available late 2004

• “Projected” out in power spectrum analysis– 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 & 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)

• NOTE: scatter at high l is due to “bandpower noise”

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


k b cdm ns m h

CBI Mosaic Observation

2.5o

THE PILLARS OF INFLATION

1) super-horizon (>2°) anisotropies2) acoustic peaks and harmonic pattern (~1°)3) damping tail (<10')4) Gaussianity5) secondary anisotropies6) polarization7) gravity waves

But … to do this we need to measure a signal which is 3x107 timesweaker than the typical noise!

geometry baryonic fraction cold dark matter primordial dark energy matter fraction Hubble Constant optical depthof the protons, neutrons not protons and fluctuation negative press- size & age of the to last scatt-universe neutrons spectrum ure of space universe ering of cmb

The CBI measures these fundamental constants of cosmology:


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]


Cosmology from EE Polarization

• 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…

• 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)


Breaking degeneracy

• Are temperature peaks intrinsic or dynamical?– if dynamical (standard model) then polarization shifted– if intrinsic (non-standard) then polarization aligned with TT

• however, would not expect EE only! still…

nearly degenerate TT spectranearly degenerate TT spectradashed: broken scale invariancedashed: broken scale invariance

& suppressed acoustic oscillations& suppressed acoustic oscillations

dashed: polarization aligned with TTdashed: polarization aligned with TT

solid: standard modelsolid: standard modelpolarization half-cyclepolarization half-cycle

shift w.r.t. TTshift w.r.t. TT


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)


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

= 0= 0°° : EE prediction: EE prediction = 180= 180°°: aligned with TT: aligned with TT



• 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 Projections

• Run through 2006: EE 2.7× & BB 3.5× improvement


CBI Projections

• EE phase: end of 2004 vs. end of 2006


CBI Projections

• The goal: EE and BB (lensing)


CBI Projections

• Will BB (lensing) be foreground limited?


Future

• CBI– 6 months more data in hand finer l bins– more detailed papers: data tests, analysis, parameters– plan to run to end of 2006 (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!)


SZE with CBI: z < 0.1 clusters

P. Udomprasert thesis (Caltech)Udomprasert et al. 2004 (astro-ph/0408005)


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 – U. Kansas, 29 Nov 2004 2 CMB Polarization Results from the Cosmic...

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