2. The Cosmic Background Imager – Berkeley, 28 Sep 2004 2 CMB Polarization Results from the Cosmic Background Imager Steven T. Myers National Radio Astronomy Observatory Socorro, NM

3. The Cosmic Background Imager – Berkeley, 28 Sep 2004 3 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

4. The Cosmic Background Imager – Berkeley, 28 Sep 2004 4 The CMB Landscape

5. The Cosmic Background Imager – Berkeley, 28 Sep 2004 5 Thermal History of the Universe Courtesy Wayne Hu – http://background.uchicago.edu

6. The Cosmic Background Imager – Berkeley, 28 Sep 2004 6 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

7. The Cosmic Background Imager – Berkeley, 28 Sep 2004 7 CMB Acoustic Peaks Compression driven by gravity, resisted by radiation ≈ “j ladder” series of harmonics + projection corrections peaks: ~  l s j troughs: ~  l s (j ± ½)

8. The Cosmic Background Imager – Berkeley, 28 Sep 2004 8 CMB Secondary Anisotropies Courtesy Wayne Hu – http://background.uchicago.edu SPH (512 3 ) [Wadsley et al. 2002] Bond et al. 2002 MMH (512 3 ) [Pen 1998] SZESecondary  8 =1.0, 0.9

9. The Cosmic Background Imager – Berkeley, 28 Sep 2004 9 CMB Polarization Due to quadrupolar intensity field at scattering Courtesy Wayne Hu – http://background.uchicago.edu

10. The Cosmic Background Imager – Berkeley, 28 Sep 2004 10 CMB Polarization E & B modes: translation invariance –E (gradient) from scalar density fluctuations predominant! –B (curl) from gravity wave tensor modes, or secondaries Courtesy Wayne Hu – http://background.uchicago.edu

11. The Cosmic Background Imager – Berkeley, 28 Sep 2004 11 Polarization Power Spectrum Hu & Dodelson ARAA 2002 Planck “error boxes” Note: polarization peaks out of phase w.r.t. intensity peaks

12. The Cosmic Background Imager – Berkeley, 28 Sep 2004 12 The Gold Standard: WMAP + “ext” WMAP ACBAR

13. The Cosmic Background Imager – Berkeley, 28 Sep 2004 13 The Cosmic Background Imager

14. The Cosmic Background Imager – Berkeley, 28 Sep 2004 14 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

15. The Cosmic Background Imager – Berkeley, 28 Sep 2004 15 Other CMB Interferometers: DASI, VSA DASI @ South Pole VSA @ Tenerife

16. The Cosmic Background Imager – Berkeley, 28 Sep 2004 16 CBI Site – Northern Chilean Andes Elevation 16500 ft.!

17. The Cosmic Background Imager – Berkeley, 28 Sep 2004 17 The CBI Adventure… Steve Padin wearing the cannular oxygen system –because you never know when you need to dig the truck out!

18. The Cosmic Background Imager – Berkeley, 28 Sep 2004 18 3-Axis mount : rotatable platform

19. The Cosmic Background Imager – Berkeley, 28 Sep 2004 19 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

20. The Cosmic Background Imager – Berkeley, 28 Sep 2004 20 The uv plane The projected baseline length gives the angular scale multipole: l = 2  B/λ = 2  u ij | shortest CBI baseline: central hole 10cm

21. The Cosmic Background Imager – Berkeley, 28 Sep 2004 21 CBI Beam and uv coverage Over-sampled uv-plane –excellent PSF –allows fast gridded method (Myers et al. 2000) primary beam transform: θ pri = 45' Δ l ≈ 4D/λ ≈ 360 mosaic beam transform: θ mos = n×45' Δ l ≈ 4D/nλ

22. The Cosmic Background Imager – Berkeley, 28 Sep 2004 22 CBI 2000+2001, WMAP, ACBAR, BIMA Readhead et al. ApJ, 609, 498 (2004) astro-ph/0402359 SZESecondary CMBPrimary

23. The Cosmic Background Imager – Berkeley, 28 Sep 2004 23 CMB Interferometry

24. The Cosmic Background Imager – Berkeley, 28 Sep 2004 24 Polarization of radiation Electromagnetic Waves –Maxwell: 2 independent linearly polarized waves –3 parameters (E 1,E 2,  )  polarization ellipse Rohlfs & Wilson

25. The Cosmic Background Imager – Berkeley, 28 Sep 2004 25 Polarization of radiation Electromagnetic Waves –Maxwell: 2 independent linearly polarized waves –3 parameters (E 1,E 2,  )  polarization ellipse Stokes parameters (Poincare Sphere): –intensity I (Poynting flux) I 2 = E 1 2 + E 2 2 –linear polarization Q,U (m I) 2 = Q 2 + U 2 –circular polarization V (v I) 2 = V 2 Rohlfs & Wilson The Poincare Sphere

26. The Cosmic Background Imager – Berkeley, 28 Sep 2004 26 Polarization of radiation Electromagnetic Waves –Maxwell: 2 independent linearly polarized waves –3 parameters (E 1,E 2,  )  polarization ellipse Stokes parameters (Poincare Sphere): –intensity I (Poynting flux) I 2 = E 1 2 + E 2 2 –linear polarization Q,U (m I) 2 = Q 2 + U 2 –circular polarization V (v I) 2 = V 2 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)

27. The Cosmic Background Imager – Berkeley, 28 Sep 2004 27 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

28. The Cosmic Background Imager – Berkeley, 28 Sep 2004 28 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°)

29. The Cosmic Background Imager – Berkeley, 28 Sep 2004 29 E and B modes A useful decomposition of the polarization signal is into “gradient” and “curl modes” – E and B: E & B response smeared by phase variation over aperture A interferometer “directly” measures (Fourier transforms of) E & B!

30. The Cosmic Background Imager – Berkeley, 28 Sep 2004 30 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)

31. The Cosmic Background Imager – Berkeley, 28 Sep 2004 31 Power Spectrum and Likelihood Break C l into bandpowers q B : Covariance matrix C sum of individual covariance terms: maximize Likelihood for complex visibilities V: known foregrounds (e.g point sources) residual (statistical) foreground scan (ground) signal fiducial power spectrum shape (e.g. 2  / l 2 )  =1 if l in band B; else  =0 noise projected fitted

32. The Cosmic Background Imager – Berkeley, 28 Sep 2004 32 CBI Polarization Data Processing Massive data processing exercise –4 mosaics, 300 nights observing –more than 10 6 visibilities total! –scan projection over 3.5° requires fine gridding more than 10 4 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 mosaicing phase factor Matched filter gridding kernel

33. The Cosmic Background Imager – Berkeley, 28 Sep 2004 33 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)

34. The Cosmic Background Imager – Berkeley, 28 Sep 2004 34 Detail: leakage Leakage of R  L (d-terms): “true” signal 1 st order: DI into P 2 nd order: DP into I 2 nd order: D 2 I into I 3 rd order: D 2 P* into P

35. The Cosmic Background Imager – Berkeley, 28 Sep 2004 35 CBI Polarization New 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)

36. The Cosmic Background Imager – Berkeley, 28 Sep 2004 36 2002 DASI & 2003 WMAP Polarization Courtesy Wayne Hu – http://background.uchicago.edu Carlstrom et al. 2003 astro-ph/0308478

37. The Cosmic Background Imager – Berkeley, 28 Sep 2004 37 New: DASI 3-year polarization results! 16Sep04!Leitch et al. 2004 (astro-ph/0409357) 16Sep04! –EE 6.3 σ –TE 2.9 σ –consistent w/ WMAP+ext model –BB consistent with zero –no foregrounds (yet)

38. The Cosmic Background Imager – Berkeley, 28 Sep 2004 38 New: DASI 3-year polarization results! 16Sep04!Leitch et al. 2004 (astro-ph/0409357) 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  K 2 at l = 300 –NO POLARIZED FOREGROUNDS DETECTED !

39. The Cosmic Background Imager – Berkeley, 28 Sep 2004 39 CBI Current Polarization Data Observing since Sep 2002 (processed to May 2004) –compact configuration, maximum sensitivity

40. The Cosmic Background Imager – Berkeley, 28 Sep 2004 40 CBI Polarization Mosaics Four mosaics  = 02 h, 08 h, 14 h, 20 h at  = 0° –02h, 08h, 14h 6 x 6 fields, 20h deep strip 6 fields [45’ centers]

41. The Cosmic Background Imager – Berkeley, 28 Sep 2004 41 Before ground subtraction: I, Q, U dirty mosaic images:

42. The Cosmic Background Imager – Berkeley, 28 Sep 2004 42 After ground subtraction: I, Q, U dirty mosaic images (9 m differences):

43. The Cosmic Background Imager – Berkeley, 28 Sep 2004 43 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

44. The Cosmic Background Imager – Berkeley, 28 Sep 2004 44 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 14 h field (in North Polar Spur) 50% worse Rely on CBI frequency leverage (26-36 GHz) –synchrotron spectrum -2.7 vs. thermal –also l 2 vs. CMB in power spectrum

45. The Cosmic Background Imager – Berkeley, 28 Sep 2004 45 CBI & DASI Fields galactic projection – image WMAP “synchrotron” (Bennett et al. 2003)

46. The Cosmic Background Imager – Berkeley, 28 Sep 2004 46 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

47. The Cosmic Background Imager – Berkeley, 28 Sep 2004 47 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!

48. The Cosmic Background Imager – Berkeley, 28 Sep 2004 48 Shaped C l 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 l s Results for CBI data (sources projected from TT only) –q B = 1.22 ± 0.21 (68%) –EE likelihood vs. zero : equivalent significance 8.9 σ Conservative - project subset out in polarization also –q B = 1.18 ± 0.24 (68%) –significance 7.0 σ

49. The Cosmic Background Imager – Berkeley, 28 Sep 2004 49 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 (Readhead et al. 2004a) [overlaps ‘04]

50. The Cosmic Background Imager – Berkeley, 28 Sep 2004 50 New: CBI Polarization Parameters 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!

51. The Cosmic Background Imager – Berkeley, 28 Sep 2004 51 New: CBI Polarization Parameters 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…

52. The Cosmic Background Imager – Berkeley, 28 Sep 2004 52 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)

53. The Cosmic Background Imager – Berkeley, 28 Sep 2004 53 Example: Acoustic Overtone Pattern Sound crossing angular size at photon decoupling –fiducial model WMAP+ext : θ 0 = 1.046 WMAP WMAP+CBI’04 WMAP+CBI’04+CBI’02 grand unified: θ = 1.044±0.005 θ/θ 0 =0.998±0.005 θ/θ 0 = 0.998±0.005(WMAP+CBI’04+CBI’02)

54. The Cosmic Background Imager – Berkeley, 28 Sep 2004 54 Example: Acoustic Overtone Pattern Sound crossing angular size at photon decoupling –fiducial model WMAP+ext : θ 0 = 1.046 –CBIPol + WMAP + “ext” : θ/θ 0 = 0.998 ± 0.005 Overtone pattern –equivalent to “j ladder” –TT extrema spaced at j intervals –EE spaced at j+½ (plus corrections)

55. The Cosmic Background Imager – Berkeley, 28 Sep 2004 55 New: CBI EE Polarization Phase Parameterization 1: envelope plus shiftable sinusoid –fit to “WMAP+ext” fiducial spectrum using rational functions

56. The Cosmic Background Imager – Berkeley, 28 Sep 2004 56 New: CBI EE Polarization Phase Peaks in EE should be offset one-half cycle vs. TT –fix amplitude a=1 and allow phase  to vary slice at: a=1  = 25°±33° rel. phase (   2 =1)   2 (1, 0°)=0.56

57. The Cosmic Background Imager – Berkeley, 28 Sep 2004 57 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: a=0.94  = 24°±33° (   2 =1)   2 (1, 0°)=0.56

58. The Cosmic Background Imager – Berkeley, 28 Sep 2004 58 New: CBI EE Polarization Phase Scaling model: spectrum shifts by scaling l –same envelope f,g as before fiducial model: θ 0 = 1.046 (“WMAP+ext”) θ sound crossing angular scale

59. The Cosmic Background Imager – Berkeley, 28 Sep 2004 59 New: CBI EE Polarization Phase Scaling model: spectrum shifts by scaling l –allow amplitude a and scale θ to vary overtone 0.67 island: a=0.69±0.03 excluded by TT and other priors other overtone islands also excluded

60. The Cosmic Background Imager – Berkeley, 28 Sep 2004 60 New: CBI EE Polarization Phase Scaling model: spectrum shifts by scaling l –allow amplitude a and scale θ to vary best fit: a=0.93 slice along a=1: θ/θ 0 = 1.02±0.04 (   2 =1) zoom in: ± one-half cycle

61. The Cosmic Background Imager – Berkeley, 28 Sep 2004 61 New: CBI, DASI, Capmap

62. The Cosmic Background Imager – Berkeley, 28 Sep 2004 62 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: suppressed by DASI DASI phase lock: θ/θ 0 =0.94±0.06 θ/θ 0 = 0.94±0.06 a=0.5 (low DASI)

63. The Cosmic Background Imager – Berkeley, 28 Sep 2004 63 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: suppressed by DASI data other overtone islands also excluded CBI+DASI phase lock: θ/θ 0 =1.00±0.03 θ/θ 0 = 1.00±0.03 a=0.78±0.15 (low DASI)

64. The Cosmic Background Imager – Berkeley, 28 Sep 2004 64 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

65. The Cosmic Background Imager – Berkeley, 28 Sep 2004 65 CBI Polarization Projections

66. The Cosmic Background Imager – Berkeley, 28 Sep 2004 66 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!)

67. The Cosmic Background Imager – Berkeley, 28 Sep 2004 67 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.