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

IPAM – Jan 30, 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

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

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

IPAM – Jan 30, 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

IPAM – Jan 30, CMB Interferometers: DASI, VSA South Pole Tenerife

IPAM – Jan 30, CMB Interferometers: CBI Chile

IPAM – Jan 30, The Cosmic Background Imager

IPAM – Jan 30, The Instrument cm Cassegrain antennas –78 baselines 6-meter platform –Baselines 1m – 5.51m 10 1 GHz channels 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

IPAM – Jan 30, Axis mount : rotatable platform

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

IPAM – Jan 30, 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 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

IPAM – Jan 30, Site – Northern Chilean Andes

IPAM – Jan 30, A Theoretical Digression

IPAM – Jan 30, 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 K –Anisotropies 10 -5

IPAM – Jan 30, Thermal History of the Universe Courtesy Wayne Hu –

IPAM – Jan 30, 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

IPAM – Jan 30, Primary Anisotropies Courtesy Wayne Hu –

IPAM – Jan 30, Primary Anisotropies Courtesy Wayne Hu –

IPAM – Jan 30, Secondary Anisotropies Courtesy Wayne Hu –

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

IPAM – Jan 30, WMAP Power Spectrum Courtesy WMAP –

IPAM – Jan 30, 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

IPAM – Jan 30, CMB Interferometry

IPAM – Jan 30, 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

IPAM – Jan 30, 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

IPAM – Jan 30, 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)

IPAM – Jan 30, 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 !

IPAM – Jan 30, Mosaicing in the uv plane

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

IPAM – Jan 30, 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

IPAM – Jan 30, 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 † +

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

IPAM – Jan 30, 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

IPAM – Jan 30, The Computational Problem

IPAM – Jan 30, 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

IPAM – Jan 30, 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

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

IPAM – Jan 30, CBI Results

IPAM – Jan 30, 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

IPAM – Jan 30, 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 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

IPAM – Jan 30, 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

IPAM – Jan 30, 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

IPAM – Jan 30, CBI 2000 Mosaic Power Spectrum

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

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

IPAM – Jan 30, 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/ ) Use updated BIMA (Carlo Contaldi) Constraints on SZ “density” Courtesy Carlo Contaldi (CITA)

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

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

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

IPAM – Jan 30, New: CBI Results

IPAM – Jan 30, CBI Noise Power

IPAM – Jan 30, CBI and WMAP

IPAM – Jan 30, CBI , WMAP, ACBAR

IPAM – Jan 30, The CMB From NRAO HEMTs

IPAM – Jan 30, Post-WMAP Unification

IPAM – Jan 30, weak prior: t > 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

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

IPAM – Jan 30, CBI Polarization

IPAM – Jan 30, 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

IPAM – Jan 30, 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

IPAM – Jan 30, 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)

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

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

IPAM – Jan 30, CBI-Pol 2000 Cartwright thesis

IPAM – Jan 30, Pol 2003 – DASI & WMAP Courtesy Wayne Hu –

IPAM – Jan 30, 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!

IPAM – Jan 30, 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

IPAM – Jan 30, 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

IPAM – Jan 30, 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?

IPAM – Jan 30, 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

IPAM – Jan 30, 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)

IPAM – Jan 30, 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.

IPAM – Jan 30,