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 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

4. IPAM – Jan 30, 2004 4 CMB Interferometers: DASI, VSA DASI @ South Pole VSA @ Tenerife

5. IPAM – Jan 30, 2004 5 CMB Interferometers: CBI CBI @ Chile

6. IPAM – Jan 30, 2004 6 The Cosmic Background Imager

7. IPAM – Jan 30, 2004 7 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

8. IPAM – Jan 30, 2004 8 3-Axis mount : rotatable platform

9. IPAM – Jan 30, 2004 9 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

10. IPAM – Jan 30, 2004 10 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

11. IPAM – Jan 30, 2004 11 Site – Northern Chilean Andes

12. IPAM – Jan 30, 2004 12 A Theoretical Digression

13. IPAM – Jan 30, 2004 13 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

14. IPAM – Jan 30, 2004 14 Thermal History of the Universe Courtesy Wayne Hu – http://background.uchicago.edu

15. IPAM – Jan 30, 2004 15 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

16. IPAM – Jan 30, 2004 16 Primary Anisotropies Courtesy Wayne Hu – http://background.uchicago.edu

17. IPAM – Jan 30, 2004 17 Primary Anisotropies Courtesy Wayne Hu – http://background.uchicago.edu

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

19. IPAM – Jan 30, 2004 19 Images of the CMB BOOMERANG WMAP Satellite ACBAR

20. IPAM – Jan 30, 2004 20 WMAP Power Spectrum Courtesy WMAP – http://map.gsfc.nasa.gov

21. IPAM – Jan 30, 2004 21 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

22. IPAM – Jan 30, 2004 22 CMB Imaging/Analysis Problems Time Stream Processing (e.g. calibration) Power Spectrum estimation for large datasets –MLM, approximate methods, efficient methods –Extraction of different components –From PS to parameters (e.g. MCMC) Beyond the Power Spectrum –Non-Gaussianity –Bispectrum and beyond Other –Optimal image construction –“object” identification –Topology –Comparison of overlapping datasets

23. IPAM – Jan 30, 2004 23 CMB Interferometry

24. IPAM – Jan 30, 2004 24 The Fourier Relationship An interferometer “visibility” in the sky and Fourier planes: The aperture (antenna) size smears out the coherence function response –Lose ability to localize wavefront direction = field-of-view –Small apertures = wide field

25. IPAM – Jan 30, 2004 25 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

26. IPAM – Jan 30, 2004 26 CBI Beam and uv coverage 78 baselines and 10 frequency channels = 780 instantaneous visibilities –Frequency channels give radial spread in uv plane 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) Pointing platform rotatable to fill in uv coverage –Parallactic angle rotation gives azimuthal spread –Beam nearly circularly symmetric CBI uv plane is well-sampled –few gaps –inner hole (1.1D), outer limit dominates PSF

27. IPAM – Jan 30, 2004 27 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 !

28. IPAM – Jan 30, 2004 28 Mosaicing in the uv plane offset & add phase gradients

29. IPAM – Jan 30, 2004 29 Power Spectrum and Likelihood Statistics of CMB (Gaussian) described by power spectrum: Break into bandpowers Construct covariance matrices and perform maximum Likelihood calculation:

30. IPAM – Jan 30, 2004 30 Power Spectrum Estimation Method described in CBI Paper 4 –Myers et al. 2003, ApJ, 591, 575 (astro-ph/0205385) The problem - large datasets –> 10 5 visibilities in 6 x 7 field mosaic –~ 10 4 distinct per mosaic pointing! –But only ~ 10 3 independent Fourier plane patches More problems –Mosaic data must be processed together –Data also from 4 independent mosaics! –Polarization “data” x3 and covariances x6! –ML will be O(N 3 ), need to reduce N!

31. IPAM – Jan 30, 2004 31 Covariance of Visibilities Write with operators Covariance But, need to consider conjugates v = P t + e = P P † + E E = (~diagonal noise) = P P t = P P t

32. IPAM – Jan 30, 2004 32 Conjugate Covariances On short baselines, a visibility can correlate with both another visibility and its conjugate

33. IPAM – Jan 30, 2004 33 Gridded Visibilities Solution - 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 Digression: Another Approach Could also attempt reconstruction of Fourier plane –v = P t + e → v = M s + e e.g. ML solution over e = v – Ms –x = H v = s + n H = (M t N -1 M) -1 M t N -1 n = H e see Hobson & Maisinger 2002, MNRAS, 334, 569 –applied to VSA data

35. IPAM – Jan 30, 2004 35 Covariance of Gridded Visibilities Or Covariances Equivalent to linear (dirty) mosaic image  = R t + n R = Q P + Q P n = Q e + Q e* M = = R R † + N N = = QEQ † + QEQ † M = = R R t + N N = = QEQ t + QEQ t

36. IPAM – Jan 30, 2004 36 Complex to Real pack real and imaginary parts into real vector put into (real) likelihood equation

37. IPAM – Jan 30, 2004 37 Gridded uv-plane “estimators” Method practical & efficient –Convolution with aperture matched filter –Reduced to 10 3 to 10 4 grid cells –Not lossless, but information loss insignificant –Fast! (work spread between gridding & covariance) Construct covariance matrices for gridded points –Complicates covariance calculation Summary of Method –time series of calibrated visibilities V –grid onto D, accumulate R and N (scatter) –assemble covariances (gather) –pass to Likelihood or Imager –parallelizable! (gridding easy, ML harder)

38. IPAM – Jan 30, 2004 38 The Computational Problem

39. IPAM – Jan 30, 2004 39 Gridded “estimators” to Bandpowers Output of gridder –estimators  on grid (u i,v i ) –covariances N, C T, C src, C res, C scan Maximum likelihood using BJK method –iterative approach to ML solution –Newton-Raphson –incorporates constraint matrices for projection –output bandpowers for parameter estimation –can also investigate Likelihood surface (MCMC?) Wiener filtered images constructed from estimators –can IFFT  (u,v) to image T(x,y) –apply Wiener filters  ‘=  –tune filters for components (noise,CMB,srcs,SZ)

40. IPAM – Jan 30, 2004 40 Maximum Likelihood Method of Bond, Jaffe & Knox (1998)

41. IPAM – Jan 30, 2004 41 Differencing & Combination Differencing –2000-2001 data taken in Lead-Trail mode Independent mosaics –4 separate equatorial mosaics 02h, 08h, 14h, 20h

42. IPAM – Jan 30, 2004 42 Constraints & Projection Fit for CMB power spectrum bandpowers Terms for “known” effects –instrumental noise –residual source foreground –incorporate as “noise” matrices with known prefactors Terms for “unknown effects” –e.g. foreground sources with known positions –known structure in C –incorporate as “noise” matrices with large prefactors –equivalent to downweighting contaminated modes in data noise projected fitted

43. IPAM – Jan 30, 2004 43 Window Functions Bandpowers as filtered integral over l Minimum variance (quadratic) estimator Window function:

44. IPAM – Jan 30, 2004 44 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

45. IPAM – Jan 30, 2004 45 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

46. IPAM – Jan 30, 2004 46 Example – Mock deep field Raw CMB Noise removed Sources

47. IPAM – Jan 30, 2004 47 CBI Results

48. IPAM – Jan 30, 2004 48 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

49. IPAM – Jan 30, 2004 49 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

50. IPAM – Jan 30, 2004 50 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

51. IPAM – Jan 30, 2004 51 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

52. IPAM – Jan 30, 2004 52 CBI 2000 Mosaic Power Spectrum

53. IPAM – Jan 30, 2004 53 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

54. IPAM – Jan 30, 2004 54 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

55. IPAM – Jan 30, 2004 55 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)

56. IPAM – Jan 30, 2004 56 New : Calibration from WMAP Jupiter Old uncertainty: 5% 2.7% high vs. WMAP Jupiter New uncertainty: 1.3% Ultimate goal: 0.5%

57. IPAM – Jan 30, 2004 57 New: CBI 2000+2001 Results

58. IPAM – Jan 30, 2004 58 CBI 2000+2001 Noise Power

59. IPAM – Jan 30, 2004 59 CBI 2000+2001 and WMAP

60. IPAM – Jan 30, 2004 60 CBI 2000+2001, WMAP, ACBAR

61. IPAM – Jan 30, 2004 61 The CMB From NRAO HEMTs

62. IPAM – Jan 30, 2004 62 Example: Post-WMAP parameters

63. IPAM – Jan 30, 2004 63 CBI Polarization

64. IPAM – Jan 30, 2004 64 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

65. IPAM – Jan 30, 2004 65 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

66. IPAM – Jan 30, 2004 66 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)

67. IPAM – Jan 30, 2004 67 Polarization Interferometry “Cross hands” sensitive to linear polarization (Stokes Q and U): where the baseline parallactic angle is defined as:

68. IPAM – Jan 30, 2004 68 E and B modes A useful decomposition of the polarization signal is into gradient and curl modes – E and B:

69. IPAM – Jan 30, 2004 69 CBI-Pol 2000 Cartwright thesis

70. IPAM – Jan 30, 2004 70 Pol 2003 – DASI & WMAP Courtesy Wayne Hu – http://background.uchicago.edu

71. IPAM – Jan 30, 2004 71 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!

72. IPAM – Jan 30, 2004 72 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

73. IPAM – Jan 30, 2004 73 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

74. IPAM – Jan 30, 2004 74 Beyond Gaussianity Objects in CMB data –our galaxy: diffuse, structure, different spectral components see WMAP papers for example of template filtering –discrete source foregrounds known sources catalogued, can project out or fit faint sources merge into “Gaussian” foreground –scattering of CMB from clusters of galaxies (SZE) The Sunyaev-Zeldovich Effect –Compton upscattering of CMB photons by keV electrons –decrement in I below CMB thermal peak (increment above) –negative extended sources (absorption against 3K CMB) –massive clusters mK, but shallow profile θ -1 → exp(-v)

75. IPAM – Jan 30, 2004 75 Spectral distortion of CMB Dominated by massive halos (galaxy clusters) Low-z clusters: ~ 10’-30’ z=1: ~1’  expected dominant signal in CMB on small angular scales Amplitude highly sensitive to  8 A. Cooray (astro-ph/0203048) P. Zhang, U. Pen, & B. Wang (astro-ph/0201375) 2 nd ary SZE Anisotropies

76. IPAM – Jan 30, 2004 76 SZE with CBI: z < 0.1 clusters P. Udomprasert thesis (Caltech)

77. IPAM – Jan 30, 2004 77 CBI SZE visibility function dominated by shortest baselines

78. IPAM – Jan 30, 2004 78 CL 0016+16, z = 0.55 (Carlstrom et al.) SZE:  = 15  K, contours =2  X-Ray

79. IPAM – Jan 30, 2004 79 CMB Interferometry Issues? process issues –more clever compression (e.g. S/N eigen., MC) –uv-plane exploration (e.g. Hobson & Maisinger) –incorporation of time-series (e.g. calibration) –beyond ML (MCMC?), also projection and marginalization –application to general radio interferometry (e.g. mosaicing) multi-components –spectral components (uv-coverage vs. frequency) –spatial components (CMB, SZE, point sources, diffuse fg) –non-Gaussianity (bispectrum etc., image-plane?) SZE issues –modelfitting or multiscale imaging? –removal of CMB –substructure

80. IPAM – Jan 30, 2004 80 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.

81. IPAM – Jan 30, 2004 81