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CMB Polarization

CMB Polarization. Theory: yet another Holy Grail Origin of CMB polarization Q,U, E, B & all that The heroic past Discovery of CMB polarization (2003-2009) Challenges Systematics Calibration Foregrounds Future ambitions. Generation of polarized CMB radiation by Thomson scattering (Hu).

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CMB Polarization

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  1. CMB Polarization • Theory: yet another Holy Grail • Origin of CMB polarization • Q,U, E, B & all that • The heroic past • Discovery of CMB polarization (2003-2009) • Challenges • Systematics • Calibration • Foregrounds • Future ambitions Rencontres de Moriond 2010

  2. Generation of polarized CMB radiation by Thomson scattering (Hu) Scalar quadupole moment Tensor quadrupole moment Rencontres de Moriond 2010

  3. Scalar Polarization • Naturally produced by adiabatic fluctuations at last scattering • “Large” polarization: photons travel significant distance between scatterings (!) • Only on causally-connected angular scales (< 1°) • acoustic peaks when generated at last scattering • Large scales when generated by re-ionization • A bit smaller-scale than structure in total intensity: • driven by gradients in brightness • Polarized brightness up to 10% of total intensity fluctuations on small scales. Rencontres de Moriond 2010

  4. Planck Energy LHC Tensor Polarization • Driven by very-large scale gravitational waves, generated at inflation. • Tensor-to-scalar power ratio depends on inflationary energy scale: r≈(V1/4/3.31017GeV)4 • Nearly negligible on ‘causal’ scales, strongest @ ~2° Rencontres de Moriond 2010

  5. Polarization pattern on sky can be separated into two orthogonal modes: E-mode or gradient mode B-mode or curl mode For plane waves, E-modes polarized alternately parallel & perpendicular to wave vector B-modes at 45° B-modes have opposite parity to E-modes B-modes only generated by tensor fluctuations Names based on obscure & confusing analogy with EM fields; ignore! (Polarization always refers to electric field orientation) E-mode vs B-mode Rencontres de Moriond 2010

  6. E-mode vs B-mode Wayne Hu Rencontres de Moriond 2010

  7. Polarization normally represented by Stokes parameters I  |Ex|2 + |Ey|2 Total intensity Q  |Ex|2 – |Ey|2 U  Re(ExEy*) Linear poln V  |ER|2 - |EL|2 Circular poln But depend on coordinate system defining x and y Polarization is “Spin-2” quantity orientation but no direction Analyse in terms of “spin-2 spherical harmonics”±2Ylm Harmonic coefficients can be summed & differenced to yield pure E- and B-modes E mode parity (-1)ℓ B mode parity (-1)ℓ+1 almE,B Coefficients coord-dependent, but not Cℓ ±2Ylm:Spin-2 Spherical Harmonics Rencontres de Moriond 2010

  8. E-mode peaks interleave with total power E-mode correlated with Temp (Stokes I), alternately positive & negative B-mode uncorrelated due to opposite parity Note bump at ℓ < 10 due to scattering after re-ionization Tensor mode only separable from scalar in B-mode pol (no scalar contribution) B-mode amplitude assumes maximum possible scalar-to-tensor ratio r Polarization Cℓ Spectra T E B Blens Rencontres de Moriond 2010

  9. Cosmology • E-modes: • Direct probe of last scattering surface • Best constraint on early re-ionization (z ~ 10) • Independent check on cosmological model fitted to Temperature data • (Nearly) independent of temperature pattern: eventually reduces cosmic variance (needs better SNR) • Gravitational lensing B-modes: • Sensitive probe of mass distribution: σ8, mass vs light, tests of GR consistency. • Primordial B-modes: • “Holy Grail of Cosmology”. • Relic from inflationary epoch: t = 10-37 s, • Fixes inflation energy scale: big clue to relevant physics • Non-guassian B-modes sensitive test of defects Rencontres de Moriond 2010

  10. King Arthur inherits kingdom in anarchy & chaos. Gathers knights of the round table, pacifies kingdom, conquers the Roman Empire, institutes ideal kingdom. Knights see vision of Holy Grail at feast in Camelot, set off to search for Holy Grail. Failure, disappointment, disillusion, death; no knight finds Grail and returns to tell the tale. Fellowship of the Round Table never recovers. Kingdom collapses into anarchy & chaos. High History of the Holy Grail(abridged) Rencontres de Moriond 2010

  11. WMAP, L2, 2003 Discovery! Cosmic Background Imager, Chajnantor, 2004 E-modes! DASI Team South Pole, 2002 Boomerang 2003, Somewhere in Antarctica Rencontres de Moriond 2010

  12. CMB Polarization 2005 Rencontres de Moriond 2010

  13. Uses old DASI mount QUaD Rencontres de Moriond 2010

  14. QUaD: E vs B amplitude E-mode only Signal! B-mode only Noise! Rencontres de Moriond 2010

  15. QUaD: E-mode Peaks Rencontres de Moriond 2010

  16. South Pole: BICEP1 Rencontres de Moriond 2010

  17. BICEP Polarization NB Scale Difference! Chiang et al, ApJ, this week Rencontres de Moriond 2010

  18. Current results • Dominated by BICEP at ℓ < 300, QUaD at higher ℓ • Best limit: • r < 0.72 (95%) (BICEP) • 1 more year of BICEP, full year of QUIET data already taken. • Expect modest improvement. Chiang et al, ApJ, this week Rencontres de Moriond 2010

  19. Double take • B-mode limit gives r < 0.72 • …but WMAP claim r < 0.24 (Jarosik et al 2010)?? • Current best limit on tensor amplitude comes from total intensity (+BAO etc) not B-modes • But limited by cosmic variance… • …so tight limits on B-modes needed to do better. • Current race (Planck vs BICEP2 vs others) is to get to r = 0.1 • Slow race: energy scale  r1/4 • but B-mode amplitude on sky  r 1/2 Rencontres de Moriond 2010

  20. } or vice versa Challenges of CMB Polarization • Good news: • Q  |Ex|2 – |Ey| U  Re(ExEy*) …differencing and cross-correlation are two good ways to eliminate systematics • Polarization signals are weak, don’t drive systematics • Sky rotates around detector: automatic “chopping” • Bad news: • Leakage from unpolarized signal • Lack of bright polarized calibrators • 4 times more complicated Rencontres de Moriond 2010

  21. Complex field description (Jones Matrix): Power description (Mueller Matrix): J: 8 real numbers (including irrelevant overall phase) M: 16 real numbers M allows for incoherent combination of modes. Original Modified Being systematic about systematics Rencontres de Moriond 2010

  22. Being systematic about systematics? • Output at one pixel is whole-sky integral over matrix-valued beam times sky • Matrices vary with • frequency, • sky position (polarized beam) • time • Often we only have one output signal, not four, i.e. one row of matrix • Effective matrix at given sky pixel is weighted response from many visits with different orientations: “beam” different at each pixel. • Each polarimeter architecture has characteristic strengths & weaknesses, including additive artefacts not included in matrices. Rencontres de Moriond 2010

  23. First-order beam artefacts • Hu, Hedman & Zaldarriaga analysis: • First-order perturbations around gaussian beam • Monopole, dipole quadrupole terms • Structure smaller than beam by definition. Graphic: Epic Study Rencontres de Moriond 2010

  24. Trends 2001-2010 • Interferometers give way to large focal plane arrays • Surface brightness limitations for interferometers • Very broad-band systems • Bandpass mis-match major source of leakage from I to (Q,U): requires careful calibration • Corrugated horns (for very clean beams) replaced by focal plane detector arrays • Requires elaborate baffling to cut out stray light. • Bolometric systems Rencontres de Moriond 2010

  25. To amplify or not? • Amplification: allows replication of signal, saves √2 or 2 in SNR for polarimetry • But inevitably adds noise even in ideal case, especially at hν >~ kTb • To avoid amplification, need very cold (0.1K) detectors, held at very stable temperature. • Upshot: bolometers best at > 100 GHz, amplifiers best below 50 GHz. Rencontres de Moriond 2010

  26. Two planes of absorbing mesh, with orthogonal wires. Each rejects ‘wrong’ polarization with 90-95% efficiency Used on Boomerang 2003 flight, QUaD experiment, Planck HFI, etc. Polarization-Sensitive Bolometers Rencontres de Moriond 2010

  27. Getting absolute angles surprisingly difficult Astronomers don’t need angles to absolute precision better than a few degrees Astronomical “calibrators” known to 2° at best Use physical polarization reference Calibration BICEP wire-grid Calibrator Rencontres de Moriond 2010

  28. Thermal Dust: COBE FIRAS, Planck HFI, PILOT Anomalous Dust: COSMOSOMAS, WMAP, Planck LFI, QUIJOTE Free-free / Synchrotron: Arecibo, C-BASS, Planck LFI Foregrounds Rencontres de Moriond 2010

  29. Polarized Foreground SED (???) RMS Q,U on 1° scales (maybe!) Rencontres de Moriond 2010

  30. CMB polarization splits into orthogonal modes: E-modes fix optical depth to re-ionization dramatic reduction in parameter degeneracy B-modes define energy scale of inflation Obscured by Galactic foreground emission minimum at ~60GHz synchrotron below dust above. C-BASS Foreground vs CMB signal E 60 GHz B V1/4 = 2×1016 GeV Lensing Rencontres de Moriond 2010

  31. “Last word” in CMB temperature observations: accuracy set by foreground residuals Polarization: Not formal mission goal Best we can do without putting extra constraints on the hardware best power spectrum yet Low SNR but 12 million pixels First chance of detecting primordial B-mode polarization ESA’s Planck mission Rencontres de Moriond 2010

  32. Launch: May 18th 2009 CPV Phase: July-August Survey started: Aug 13th 2009 >95% of sky now covered once Baseline Survey ends: Oct 2010, one year extension approved. End of proprietary period on 1st year of data: October 2012. Planck Cryo Qualification Model under test at CSL, Liège. Planck mission status Rencontres de Moriond 2010

  33. Space Planck CMBPOL/EPIC BPOL Balloon EBEX PILOT (Dust) SPIDER Ground-based: QUIET1 (40/90 GHz) C-BASS (5 GHz) QUIJOTE1 (10-18, 30 GHz) BICEP2 (150 GHz) GEM-P (5 GHz) ABS (145 GHz) POLARBear (150 GHz) QUIET2 (30/40/90) QUIJOTE2 (30) Keck Array (100/150/220) QUBIC Projects ongoing and planned Rencontres de Moriond 2010

  34. State-of-the art Receivers • MIC Amplifiers up to 120 GHz • cool to 15K • Tsys=10 K at 33 GHz, state of the art. • Rule of thumb is 1/3 K per GHz. • 7 times worse than quantum limits, limited by internal noise • 20% bandwidth, defined (not very well) by tuned circuits • Bolometers 100 GHz to infrared. • cooled to 0.1K • 30-50% bandwidth • Custom filters (Cardiff University) • 7 times worse that quantum limits, limited by losses in filters etc (nearly perfect detectors) Rencontres de Moriond 2010

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