1. IPAM – Jan 30, 2004 1 Interferometric Imaging & Analysis of the CMB Steven T. Myers National Radio Astronomy Observatory Socorro, NM

2. IPAM – Jan 30, 2004 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

3. IPAM – Jan 30, 2004 3 Radio Interferometers Connected-element “radio” interferometers: –The Very Large Array (VLA) @ New Mexico –Owens Valley Millimeter-wave Array @ California –BIMA Millimeter-wave Array @ California –Coming: CARMA (combined OVRO & BIMA) ALMA Millimeter-wave Array @ Chile CMB interferometers –Ryle Telescope @ UK –DASI @ South Pole –VSA @ Tenerife –CBI @ Chile

4. IPAM – Jan 30, 2004 4 Example: The VLA 27 elements –25m apertures –Maxiumum baseline 36km (A-config) –Y-pattern, 4 configurations (36km,10km,3.6km,1km)

5. IPAM – Jan 30, 2004 5 CMB Interferometers CMB issues: –Extremely low surface brightness fluctuations < 50  K –Polarization less than 10% –Large monopole signal 3K, dipole 3 mK –No compact features, approximately Gaussian random field –Foregrounds both galactic & extragalactic Traditional direct imaging –Differential horns or focal plane arrays Interferometry –Inherent differencing (fringe pattern), filtered images –Works in spatial Fourier domain –Element gain effect spread in image plane –Limited by need to correlate pairs of elements –Sensitivity requires compact arrays

6. IPAM – Jan 30, 2004 6 CMB Interferometers: DASI, VSA DASI @ South Pole VSA @ Tenerife

7. IPAM – Jan 30, 2004 7 CMB Interferometers: CBI CBI @ Chile

8. IPAM – Jan 30, 2004 8 The Cosmic Background Imager

9. IPAM – Jan 30, 2004 9 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

10. IPAM – Jan 30, 2004 10 3-Axis mount : rotatable platform

11. IPAM – Jan 30, 2004 11 CBI Instrumentation Correlator –Multipliers 1 GHz bandwidth –10 channels to cover total band 26-36 GHz (after filters and downconversion) –78 baselines (13 antennas x 12/2) –Real and Imaginary (with phase shift) correlations –1560 total multipliers

12. IPAM – Jan 30, 2004 12 CBI Operations Observing in Chile since Nov 1999 –NSF proposal 1994, funding in 1995 –Assembled and tested at Caltech in 1998 –Shipped to Chile in August 1999 –Continued NSF funding in 2002, to end of 2004 –Chile Operations 2004-2005 pending proposal Telescope at high site in Andes –16000 ft (~5000 m) –Located on Science Preserve, co-located with ALMA –Now also ATSE (Japan) and APEX (Germany), others –Controlled on-site, oxygenated quarters in containers Data reduction and archiving at “low” site –San Pedro de Atacama –1 ½ hour driving time to site

13. IPAM – Jan 30, 2004 13 Site – Northern Chilean Andes

14. IPAM – Jan 30, 2004 14 A Theoretical Digression

15. IPAM – Jan 30, 2004 15 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

16. IPAM – Jan 30, 2004 16 Thermal History of the Universe Courtesy Wayne Hu – http://background.uchicago.edu

17. IPAM – Jan 30, 2004 17 CMB Anisotropies Primary Anisotropies –Imprinted on photosphere of “last scattering” “recombination” of hydrogen z~1100 –Primordial (power-law?) spectrum of potential fluctuations Collapse of dark matter potential wells inside horizon Photons coupled to baryons >> acoustic oscillations! –Electron scattering density & velocity Velocity produces quadrupole >> polarization! –Transfer function maps P(k) >> C l Depends on cosmological parameters >> predictive! –Gaussian fluctuations + isotropy Angular power spectrum contains all information Secondary Anisotropies –Due to processes after recombination

18. IPAM – Jan 30, 2004 18 Primary Anisotropies Courtesy Wayne Hu – http://background.uchicago.edu

19. IPAM – Jan 30, 2004 19 Primary Anisotropies Courtesy Wayne Hu – http://background.uchicago.edu

20. IPAM – Jan 30, 2004 20 Secondary Anisotropies Courtesy Wayne Hu – http://background.uchicago.edu

21. IPAM – Jan 30, 2004 21 Images of the CMB BOOMERANG WMAP Satellite ACBAR

22. IPAM – Jan 30, 2004 22 WMAP Power Spectrum Courtesy WMAP – http://map.gsfc.nasa.gov

23. IPAM – Jan 30, 2004 23 CMB Polarization Due to quadrupolar intensity field at scattering E & B modes –E (gradient) from scalar density fluctuations predominant! –B (curl) from gravity wave tensor modes, or secondaries Detected by DASI and WMAP –EE and TE seen so far, BB null Next generation experiments needed for B modes –Science driver for Beyond Einstein mission –Lensing at sub-degree scales likely to detect –Tensor modes hard unless T/S~0.1 (high!) Hu & Dodelson ARAA 2002

24. IPAM – Jan 30, 2004 24 CMB Interferometry

25. IPAM – Jan 30, 2004 25 The Fourier Relationship An interferometer “visibility” in the sky and Fourier planes: The aperture (antenna) size smears out the coherence function response –Like a double-slit experiment with widening slits –Interference plus diffraction pattern –Lose ability to localize wavefront direction = field-of-view –Small apertures = wide field

26. IPAM – Jan 30, 2004 26 The uv plane and l space The sky can be uniquely described by spherical harmonics –CMB power spectra are described by multipole l ( the angular scale in the spherical harmonic transform) 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 l / 2  The projected length of the interferometer baseline gives the angular scale –Multipole l = 2  B / An interferometer naturally measures the transform of the sky intensity in l space

27. IPAM – Jan 30, 2004 27 CBI Beam and uv coverage 78 baselines and 10 frequency channels = 780 instantaneous visibilities –Frequency channels give radial spread in uv plane Pointing platform rotatable to fill in uv coverage –Parallactic angle rotation gives azimuthal spread –Beam nearly circularly symmetric Baselines locked to platform in pointing direction –Baselines always perpendicular to source direction –Delay lines not needed –Very low fringe rates (susceptible to cross-talk and ground)

28. IPAM – Jan 30, 2004 28 Field of View and Resolution An interferometer “visibility” in the sky and Fourier planes: The primary beam and aperture are related by: CBI: CMB peaks smaller than this !

29. IPAM – Jan 30, 2004 29 Mosaicing in the uv plane

30. IPAM – Jan 30, 2004 30 Power Spectrum and Likelihood Statistics of CMB (Gaussian) described by power spectrum: Break into bandpowers Construct covariance matrices and perform maximum Likelihood calculation:

31. IPAM – Jan 30, 2004 31 Power Spectrum Estimation Method described in Paper IV (Myers et al. 2003) Large datasets –> 10 5 visibilities in 6 x 7 field mosaic –~ 10 3 independent Gridded “estimators” in uv plane –Convolution with aperture matched filter –Fast! Reduces number of points for likelihood –Not lossless, but information loss insignificant Construct covariance matrices for gridded points Maximum likelihood using BJK method Output bandpowers Wiener filtered images constructed from estimators

32. IPAM – Jan 30, 2004 32 Covariance of Visibilities Write with operators Covariance Problem –Size of v, P >10 5 visibilities, 10 4 distinct per mosaic pointing! v = P t + e = P P † +

33. IPAM – Jan 30, 2004 33 Gridded Visibilities Convolve with “matched filter” kernel Kernel Normalization –Returns true t for infinite continuous mosaic  = Q v + Q v* Deal with conjugate visibilities

34. IPAM – Jan 30, 2004 34 Covariance of Gridded Visibilities Covariance Or Problem –Reduced to 10 3 to 10 4 grid cells –Complicates covariance calculation, loss of information = Q Q † + conjg. = Q P P † Q † + Q Q † + conjg. = R R † +  = R t + n R = Q P + Q P n = Q e

35. IPAM – Jan 30, 2004 35 The Computational Problem

36. IPAM – Jan 30, 2004 36 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

37. IPAM – Jan 30, 2004 37 Wiener filtered images Covariance matrices can be applied as Wiener filter to gridded estimators Estimators can be Fourier transformed back into filtered images Filters C X can be tailored to pick out specific components –e.g. point sources, CMB, SZE –Just need to know the shape of the power spectrum

38. IPAM – Jan 30, 2004 38 Example – Mock deep field Raw CMB Noise removed Sources

39. IPAM – Jan 30, 2004 39 CBI Results

40. IPAM – Jan 30, 2004 40 CBI 2000 Results Observations –3 Deep Fields (8h, 14h, 20h) –3 Mosaics (14h, 20h, 02h) –Fields on celestial equator (Dec center –2d30’) Published in series of 5 papers (ApJ July 2003) –Mason et al. (deep fields) –Pearson et al. (mosaics) –Myers et al. (power spectrum method) –Sievers et al. (cosmological parameters) –Bond et al. (high-l anomaly and SZ) pending

41. IPAM – Jan 30, 2004 41 Calibration and Foreground Removal Calibration scale ~5% –Jupiter from OVRO 1.5m (Mason et al. 1999) –Agrees with BIMA (Welch) and WMAP 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 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 –Projected out in power spectrum analysis

42. IPAM – Jan 30, 2004 42 CBI Deep Fields 2000 Deep Field Observations: 3 fields totaling 4 deg^2 Fields at  ~0  =8 h, 14 h, 20 h ~115 nights of observing Data redundancy  strong tests for systematics

43. IPAM – Jan 30, 2004 43 Mosaic Field Observations 3 fields totaling 40 deg^2 Fields at  ~0  =2 h, 14 h, 20 h ~125 nights of observing ~ 600,000 uv points  covariance matrix 5000 x 5000 CBI 2000 Mosaic Power Spectrum

44. IPAM – Jan 30, 2004 44 CBI 2000 Mosaic Power Spectrum

45. IPAM – Jan 30, 2004 45 Cosmological Parameters wk-h: 0.45 10 Gyr HST-h: h = 0.71 ± 0.076 LSS: constraints on  8 and  from 2dF, SDSS, etc. SN: constraints from Type 1a SNae

46. IPAM – Jan 30, 2004 46 SZE Angular Power Spectrum Smooth Particle Hydrodynamics (512 3 ) [Wadsley et al. 2002] Moving Mesh Hydrodynamics (512 3 ) [Pen 1998] 143 Mpc  8 =1.0 200 Mpc  8 =1.0 200 Mpc  8 =0.9 400 Mpc  8 =0.9 [Bond et al. 2002] Dawson et al. 2002

47. IPAM – Jan 30, 2004 47 Combine CBI & BIMA (Dawson et al.) 30 GHz with ACBAR 150 GHz (Goldstein et al.) Non-Gaussian scatter for SZE –increased sample variance (factor ~3)) Uncertainty in primary spectrum –due to various parameters, marginalize Explained in Goldstein et al. (astro-ph/0212517) Use updated BIMA (Carlo Contaldi) Constraints on SZ “density” Courtesy Carlo Contaldi (CITA)

48. IPAM – Jan 30, 2004 48 Flat HST-h Priors LSS parameters from Surveys Courtesy J.R. Bond

49. IPAM – Jan 30, 2004 49 SZE with CBI: z < 0.1 clusters

50. IPAM – Jan 30, 2004 50 New : Calibration from WMAP Jupiter Old uncertainty: 5% 2.7% high vs. WMAP Jupiter New uncertainty: 1.3% Ultimate goal: 0.5%

51. IPAM – Jan 30, 2004 51 New: CBI 2000+2001 Results

52. IPAM – Jan 30, 2004 52 CBI 2000+2001 Noise Power

53. IPAM – Jan 30, 2004 53 CBI 2000+2001 and WMAP

54. IPAM – Jan 30, 2004 54 CBI 2000+2001, WMAP, ACBAR

55. IPAM – Jan 30, 2004 55 The CMB From NRAO HEMTs

56. IPAM – Jan 30, 2004 56 Post-WMAP Unification

57. IPAM – Jan 30, 2004 57 weak prior: t > 10 10 yr 0.45 < h < 0.9  m > 0.1 LSS prior: constraint on amplitude of  8 and shape of  eff (Bond et al. Ap.J. 2003) CBI + COBE

58. IPAM – Jan 30, 2004 58 weak prior: t > 10 10 yr 0.45 < h < 0.9  m > 0.1

59. IPAM – Jan 30, 2004 59 CBI Polarization

60. IPAM – Jan 30, 2004 60 CBI 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 (switchable) –Observing with 7R + 6L starting Sep 2002 –Raster scans for mosaicing and efficiency –New TRW InP HEMTs from NRAO

61. IPAM – Jan 30, 2004 61 Polarization Sensitivity CBI is most sensitive at the peak of the polarization power spectrum Theoretical sensitivity  ±  of CBI in 450 hours (90 nights) on each of 3 mosaic fields 5 deg sq (no differencing), close-packed configuration. EE TE The compact configuration

62. IPAM – Jan 30, 2004 62 Stokes parameters CBI receivers can observe either R or L circular polarization CBI correlators can cross-correlate R or L from a given pair of antennas Mapping of correlations (RR,LL,RL,LR) to Stokes parameters (I,Q,U,V) Intensity I plus linear polarization Q,U important –CMB not circularly polarized, ignore V (RR = LL = I)

63. IPAM – Jan 30, 2004 63 Polarization Interferometry “Cross hands” sensitive to linear polarization (Stokes Q and U): where the baseline parallactic angle is defined as:

64. IPAM – Jan 30, 2004 64 E and B modes A useful decomposition of the polarization signal is into gradient and curl modes – E and B:

65. IPAM – Jan 30, 2004 65 CBI-Pol 2000 Cartwright thesis

66. IPAM – Jan 30, 2004 66 Pol 2003 – DASI & WMAP Courtesy Wayne Hu – http://background.uchicago.edu

67. IPAM – Jan 30, 2004 67 Polarization Issues Low signal levels –High sensitivity and long integrations needed –Prone to systematics and foreground contamination –Use B modes a veto at E levels Instrumental polarization –Well-calibrated system necessary –Somewhat easier to control in interferometry –Constraint matrix approach possible (e.g. DASI) Stray radiation –Sky (atmosphere) unpolarized (good!) –Ground highly polarized (bad!) –Scan differencing or projection necessary Computationally intensive!

68. IPAM – Jan 30, 2004 68 CBI Current Polarization Data Observing since Sep 2002 Four mosaics 02 h, 08 h, 14 h, 20 h –02h, 08h, 14h 6 x 6 fields, 45’ centers –20h deep strip 6 fields Currently data to Mar 2003 processed –Preliminary data analysis available –Only 02h, 08h (partial), and 20h strip

69. IPAM – Jan 30, 2004 69 CBI Polarization Projections CBI funded for Chile ops until 2003 Dec 31 –Projections using mock data available NSF proposal pending for ops through 2005 –Projections using mock data available

70. IPAM – Jan 30, 2004 70 Conclusions from CBI Data Definitive measurement of diffusive damping scale Measurements of 3 rd & 4 th Acoustic Peaks At Low L  consistent with other experiments At High L (>2000)  indications of secondary anisotropy?

71. IPAM – Jan 30, 2004 71 Conclusions from CBI Data Definitive measurement of diffusive damping scale Measurements of 3 rd & 4 th Acoustic Peaks At Low L  consistent with other experiments At High L (>2000)  indications of secondary anisotropy? Small Scale Power ~3 sigma above expected intrinsic anisotropy Not consistent with likely residual radio source populations (more definitive characterization needed) Suggestive of secondary SZ anisotropy, although this would imply sigma8 ~ 1 Other possible foregrounds not ruled out at this point

72. IPAM – Jan 30, 2004 72 Conclusions from CBI Data Definitive measurement of diffusive damping scale Measurements of 3 rd & 4 th Acoustic Peaks At Low L  consistent with other experiments At High L (>2000)  indications of secondary anisotropy? Small Scale Power ~3 sigma above expected intrinsic anisotropy Not consistent with likely residual radio source populations (more definitive characterization needed) Suggestive of secondary SZ anisotropy, although this would imply sigma8 ~ 1 Other possible foregrounds not ruled out at this point Polarization Observations commenced Sep 2003 Upper limits so far Should have sensitivity to measure spectrum (esp. to 2005)

73. IPAM – Jan 30, 2004 73 The CBI Collaboration Caltech Team: Tony Readhead (Principal Investigator), John Cartwright, 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.

74. IPAM – Jan 30, 2004 74