1 / 81

Interferometric Imaging & Analysis of the CMB

Interferometric Imaging & Analysis of the CMB. Steven T. Myers. National Radio Astronomy Observatory Socorro, NM. Interferometers. Spatial coherence of radiation pattern contains information about source structure Correlations along wavefronts

quynh
Download Presentation

Interferometric Imaging & Analysis of the CMB

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Interferometric Imaging & Analysis of the CMB Steven T. Myers National Radio Astronomy Observatory Socorro, NM

  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. CMB Interferometers • CMB issues: • Extremely low surface brightness fluctuations < 50 mK • 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. CMB Interferometers: DASI, VSA • DASI @ South Pole • VSA @ Tenerife

  5. CMB Interferometers: CBI • CBI @ Chile

  6. The Cosmic Background Imager

  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. 3-Axis mount : rotatable platform

  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. 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. Site – Northern Chilean Andes

  12. A Theoretical Digression

  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. Thermal History of the Universe Courtesy Wayne Hu – http://background.uchicago.edu

  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) >> Cl • Depends on cosmological parameters >> predictive! • Gaussian fluctuations + isotropy • Angular power spectrum contains all information • Secondary Anisotropies • Due to processes after recombination

  16. Primary Anisotropies Courtesy Wayne Hu – http://background.uchicago.edu

  17. Primary Anisotropies Courtesy Wayne Hu – http://background.uchicago.edu

  18. Secondary Anisotropies Courtesy Wayne Hu – http://background.uchicago.edu

  19. Images of the CMB WMAP Satellite BOOMERANG ACBAR

  20. WMAP Power Spectrum Courtesy WMAP – http://map.gsfc.nasa.gov

  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. 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. CMB Interferometry

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

  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 / 2p • The projected length of the interferometer baseline gives the angular scale • Multipole l = 2pB / l • An interferometer naturally measures the transform of the sky intensity in l space

  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. CMB peaks smaller than this ! Field of View and Resolution • An interferometer “visibility” in the sky and Fourier planes: • The primary beam and aperture are related by: CBI:

  28. Mosaicing in the uv plane offset & add phase gradients

  29. Power Spectrum and Likelihood • Statistics of CMB (Gaussian) described by power spectrum: Construct covariance matrices and perform maximum Likelihood calculation: Break into bandpowers

  30. Power Spectrum Estimation • Method described in CBI Paper 4 • Myers et al. 2003, ApJ, 591, 575 (astro-ph/0205385) • The problem - large datasets • > 105 visibilities in 6 x 7 field mosaic • ~ 104 distinct per mosaic pointing! • But only ~ 103 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(N3), need to reduce N!

  31. Covariance of Visibilities • Write with operators • Covariance • But, need to consider conjugates v = P t + e < v v†> = P < t t † > P† + E E =<ee†> (~diagonal noise) < v v t> = P < t t t> P t = P < t t † > P t

  32. Conjugate Covariances • On short baselines, a visibility can correlate with both another visibility and its conjugate

  33. Gridded Visibilities • Solution - convolve with “matched filter” kernel • Kernel • Normalization • Returns true t for infinite continuous mosaic D = Q v + Q v* Deal with conjugate visibilities

  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 = (MtN-1M)-1MtN-1 n = H e • see Hobson & Maisinger 2002, MNRAS, 334, 569 • applied to VSA data

  35. D = R t + n R = Q P + Q P n = Q e + Q e* M = < DD†> = R < t t † > R† + N N = <nn†> = QEQ†+ QEQ† M = < DD t> = R < t t t > Rt + N N = <nn t> = QEQt+ QEQt Covariance of Gridded Visibilities • Or • Covariances • Equivalent to linear (dirty) mosaic image

  36. Complex to Real • pack real and imaginary parts into real vector • put into (real) likelihood equation

  37. Gridded uv-plane “estimators” • Method practical & efficient • Convolution with aperture matched filter • Reduced to 103 to 104 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. The Computational Problem

  39. Gridded “estimators” to Bandpowers • Output of gridder • estimators D on grid (ui,vi) • covariances N, CT, Csrc, Cres, Cscan • 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 D(u,v) to image T(x,y) • apply Wiener filters D‘=FD • tune filters for components (noise,CMB,srcs,SZ)

  40. Maximum Likelihood • Method of Bond, Jaffe & Knox (1998)

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

  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 projected noise fitted

  43. Window Functions • Bandpowers as filtered integral over l • Minimum variance (quadratic) estimator • Window function:

  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. Wiener filtered images • Covariance matrices can be applied as Wiener filter to gridded estimators • Estimators can be Fourier transformed back into filtered images • Filters CX 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. Example – Mock deep field Noise removed Raw CMB Sources

  47. CBI Results

  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. 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. CBI Deep Fields 2000 • Deep Field Observations: • 3 fields totaling 4 deg^2 • Fields at d~0 a=8h, 14h, 20h • ~115 nights of observing • Data redundancy  strong tests for systematics

More Related