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2The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CMB Polarization Results from the
Cosmic Background ImagerSteven T. Myers
National Radio Astronomy Observatory
Socorro, NM
3The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
4The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
The CMB Landscape
5The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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!
6The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
7The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
8The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
9The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CMB Acoustic Peaks
• Compression driven by gravity, resisted by radiation≈ “j ladder” series of harmonics + projection corrections
peaks: ~ peaks: ~ llss jjtroughs: ~ troughs: ~ llss ( (jj + ½+ ½))
10The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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)
Courtesy Wayne Hu – http://background.uchicago.edu
11The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
Courtesy Wayne Hu – http://background.uchicago.edu
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)
12The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
Courtesy Wayne Hu – http://background.uchicago.edu
13The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
14The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
The Gold Standard: WMAP + “ext”WMAP
ACBAR
15The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
The Cosmic Background Imager
16The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
17The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
Traditional Inteferometer – The VLA• The Very Large Array (VLA)
– 27 elements, 25m antennas, 74 MHz – 50 GHz (in bands)– independent elements Earth rotation synthesis
18The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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!
19The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
Other CMB Interferometers: DASI, VSA
• DASI @ South Pole
• VSA @ Tenerife
20The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
21The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CBI Site – Northern Chilean Andes
• Elevation 16500 ft.!
22The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CBI Instrumentation
23The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CBI in Chile
24The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
The CBI Adventure…
• Steve Padin wearing the cannular oxygen system– because you never know when you
need to dig the truck out!
25The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
The CBI Adventure…
• the snow in Chile falls mainly on the road! 2 winters/yr
26The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
The CBI Adventure…• Volcan Lascar (~30 km away) erupts in 2001
27The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CMB Interferometry
28The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
Fourier transform relationshipFourier transform relationship
29The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
30The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
31The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
Polarization of radiation
• Electromagnetic Waves– Maxwell: 2 independent linearly polarized waves
– 3 parameters (E1,E2,) polarization ellipse
Rohlfs & Wilson
32The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
Polarization of radiation
• 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
33The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
Polarization of radiation
• 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)
• Statistical Quantities for CMB– T ( I in temperature units )– E & B polarization modes
• even and odd parity
• independent of coordinate system choice
• well-defined in Fourier plane
34The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
*
*
*
*
35The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
36The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
E and B modes
• Decomposition into E and B Fourier modes:
where
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!
37The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
Power Spectrum of CMB
• Statistics of CMB field– Gaussian random field – Fourier modes independent– Temperature covariance described by angular power spectrum
– 4 non-zero polarization covariances: TT,EE,BB,TE – EB, TB should be zero due to parity (but check on systematics)
)'()'(~
)(~
2)'()'(*~
)(~
2
2
vvvv
vvvvv
CTT
CTT
)'()'(*~
)(~
)'()'(*~
)(~
)'()'(*~
)(~
)'()'(*~
)(~
)'()'(*~
)(~
)'()'(*~
)(~
22
22
22
vvvvvvvv
vvvvvvvv
vvvvvvvv
EBTB
BBTE
EETT
CBECBT
CBBCET
CEECTT
38The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
39The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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– does average out with parallactic angle
• include in correlation analysis– just complicates covariance matrix calculation
40The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
Errors: 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
41The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CBI PolarizationResults!
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)Science 306, 836-844
42The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
43The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CBI Polarization Observations
• Observing since Sep 2002 (processed to May 2004)– compact configuration, maximum sensitivity
44The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
45The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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)
46The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
Calibration from WMAP Jupiter
• Old uncertainty: 5%• 2.7% high vs. WMAP Jupiter• New uncertainty: 1.3%• Ultimate goal: 0.5%
47The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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]
48The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
• 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)• no ground (or Sun) shield• orientation dependence (see mountains around site!)• removed by differencing (or scan projection)
49The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
Calibration and Foreground Removal
• Ground emission removal– Strong on short baselines, depends on orientation– Differencing between lead/trail field pairs (8m in RA=2deg)
• Use scanning for 2002-2003 polarization observations
50The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
Before ground subtraction:
• I, Q, U dirty mosaic images (6 fields 3m spacing):
51The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
After ground subtraction:
• I, Q, U dirty mosaic images (9m differences):
52The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
53The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CBI & DASI Fields
galactic projection – image WMAP “synchrotron” (Bennett et al. 2003)
54The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CBI Polarization Power Spectra• 7-band fits (l = 150 for 600<l<1200) matched to peaks & valleys
55The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CBI Polarization Power Spectra• narrower bins (l = 75) – increased scatter from F-1
56The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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!
57The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
58The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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:
59The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CBI Cosomological Parameters• use fine bins (l = 75) +
window functions• cosmological models vs.
data using MCMC– modified COSMOMC
(Lewis & Bridle 2002)
• Include:– WMAP TT & TE
– WMAP + CBI’04 TT & EE (Readhead et al. 2004b)
– WMAP + CBI’04 TT & EE l <1000 + CBI’02 TT l >1000 (Readhead et al. 2004a)
60The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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)
61The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
62The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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)
63The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
64The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
New: CBI EE Polarization Phase
• 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
65The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
New: CBI EE Polarization Phase
• Scaling model: spectrum shifts by scaling l – same envelope functions 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
66The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
New: CBI EE Polarization Phase
• 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
67The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
New: CBI EE Polarization Phase
• 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
68The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
New: CBI, DASI, Capmap
69The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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)
70The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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)
71The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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
72The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CBI Projections
• Run through 2006: EE 2.7× & BB 3.5× improvement
73The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CBI Projections
• EE phase: end of 2004 vs. end of 2006
74The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CBI Projections
• The next generation: EE and BB (lensing)
75The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
CBI Projections
• Will BB (lensing) be foreground limited?
76The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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!)
77The Cosmic Background Imager – Jodrell Bank, 28 Feb 2005
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.