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21CMA/ PAST   data analysis Ue-Li Pen  彭威礼 Chris Hirata Xiang-Ping Wu  武向平 , Jeff Peterson
Reionization <ul><li>First objects:  </li></ul><ul><li>21 cm @ z>6 </li></ul><ul><li>50-200 Mhz </li></ul><ul><li>Δ T = 23...
Foreground: Synchrotron 408 MHz  Haslam Much brighter than signal, but no spectral structure
Detectability <ul><li>Luminosity proportional to object volume: bigger structures easier to find </li></ul><ul><li>Noise d...
21CMA/ PAST  Site
21CMA/ PAST  Strategy <ul><li>Fast track to data: avoid custom design, off-the-shelf only.  </li></ul><ul><li>Use existing...
Antenna Design <ul><li>Noise dominated by galaxy:  T gal =280 (150Mhz/f) 2.5  K @ NCP </li></ul><ul><li>sensitivity : 10 4...
Ulastai Ustir station 42º 55’ N   86º 45’  E elev  2600m Urumqi   150  km Ground shield : 5 000 m   mountains on all sides
 
 
Software correlator
U-V map data Almost no interference, excellent u-v coverage
Protype data, Feb, 2005 12 working pods of 127 antenna each 100-200 Mhz, 10 o  FOV 3C061.1 NCP
CMB Analogy <ul><li>Searching for very low surface brightness sources </li></ul><ul><li>Potentially severe foregrounds </l...
CMB map making <ul><li>Linear algebra approach to map making </li></ul><ul><li>Used by most experiments, including WMAP, P...
Data Flow <ul><li>raw time stream </li></ul><ul><li>Optimal map construction to reduce data size: Deconvolution, Wiener, e...
Analysis procedure <ul><li>Calibrate system from celestial sources </li></ul><ul><li>Determine beam from sky </li></ul><ul...
 
Same for polarization: consider all polarization to be noise, solve for I map. One needs to know the beam accurately!  Var...
Computational Complexity <ul><li>O(N 3 ): not tractable for all sky, workable for small fields at low resolution, up to 10...
Conclusions <ul><li>Linear map making theory well understood from CMB analysis, optimal algorithms for Gaussian fields, ev...
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  1. 1. 21CMA/ PAST data analysis Ue-Li Pen 彭威礼 Chris Hirata Xiang-Ping Wu 武向平 , Jeff Peterson
  2. 2. Reionization <ul><li>First objects: </li></ul><ul><li>21 cm @ z>6 </li></ul><ul><li>50-200 Mhz </li></ul><ul><li>Δ T = 23 mK, ~0.3 mJy </li></ul><ul><li>Angular scale 5’< Θ < 20 ’ , freq res 500 khz </li></ul>z=10 simulation, Furlanetto et al, 2004
  3. 3. Foreground: Synchrotron 408 MHz Haslam Much brighter than signal, but no spectral structure
  4. 4. Detectability <ul><li>Luminosity proportional to object volume: bigger structures easier to find </li></ul><ul><li>Noise dominated by galaxy: T=300(f/150 Mhz) -2.5 , higher frequency (lower redshift) much easier </li></ul><ul><li>Mean emission very hard to discern (Gnedin and Shaver 2004). </li></ul><ul><li>First targets: Stromgren spheres around bright quasars (Wyithe and Loeb 2004). </li></ul>
  5. 5. 21CMA/ PAST Site
  6. 6. 21CMA/ PAST Strategy <ul><li>Fast track to data: avoid custom design, off-the-shelf only. </li></ul><ul><li>Use existing TV technology, commodity PC’s for correlations </li></ul><ul><li>Learn as you build: fast turnaround, flexibility </li></ul>
  7. 7. Antenna Design <ul><li>Noise dominated by galaxy: T gal =280 (150Mhz/f) 2.5 K @ NCP </li></ul><ul><li>sensitivity : 10 4 m 2 effective area </li></ul><ul><li>Resolution: aperture synthesis , 80 elements , 3km baselines </li></ul><ul><li>Receiver noise: NF < 2 dB ( T <200K) </li></ul><ul><li>Pointing at north celestial pole, elevation 43 o </li></ul><ul><li>simple , fast 。 Currently 23 hexagonal pods , 12 correlating </li></ul>
  8. 8. Ulastai Ustir station 42º 55’ N 86º 45’ E elev 2600m Urumqi 150 km Ground shield : 5 000 m mountains on all sides
  9. 11. Software correlator
  10. 12. U-V map data Almost no interference, excellent u-v coverage
  11. 13. Protype data, Feb, 2005 12 working pods of 127 antenna each 100-200 Mhz, 10 o FOV 3C061.1 NCP
  12. 14. CMB Analogy <ul><li>Searching for very low surface brightness sources </li></ul><ul><li>Potentially severe foregrounds </li></ul><ul><li>Fully sampled u-v planes: different from CLEAN ing </li></ul><ul><li>Statistics of noise and foregrounds can be described very accurately </li></ul><ul><li>Large Field of view: planar assumption breaks. WMAP: 120 deg difference map </li></ul>
  13. 15. CMB map making <ul><li>Linear algebra approach to map making </li></ul><ul><li>Used by most experiments, including WMAP, Planck, Boomerang, DASI, CBI </li></ul><ul><li>Exactly solvable for Gaussian random fields </li></ul><ul><li>Noise properties fully characterized </li></ul><ul><li>Computationally expensive </li></ul><ul><li>Fast workarounds: CG, multigrid, etc. </li></ul>
  14. 16. Data Flow <ul><li>raw time stream </li></ul><ul><li>Optimal map construction to reduce data size: Deconvolution, Wiener, etc </li></ul><ul><li>Foreground removal </li></ul><ul><li>Noise covariance matrix </li></ul><ul><li>Power spectrum </li></ul><ul><li>Window functions </li></ul>
  15. 17. Analysis procedure <ul><li>Calibrate system from celestial sources </li></ul><ul><li>Determine beam from sky </li></ul><ul><li>Generalized BEAM contains all processes between source and data: ISM, ionosphere, antenna, polarization, transmission line, etc. </li></ul><ul><li>Wiener filtered map </li></ul>
  16. 19. Same for polarization: consider all polarization to be noise, solve for I map. One needs to know the beam accurately! Varies with time, frequency, position on sky, position of antenna, ionosphere, instrument. Calibration from bright point sources (Hirata)
  17. 20. Computational Complexity <ul><li>O(N 3 ): not tractable for all sky, workable for small fields at low resolution, up to 10 5 pixels </li></ul><ul><li>Accelerated plans in development: Conjugate gradient, multigrid (e.g. Pen 2004) as used in lensing and CMB analysis </li></ul>
  18. 21. Conclusions <ul><li>Linear map making theory well understood from CMB analysis, optimal algorithms for Gaussian fields, even full sky. </li></ul><ul><li>Minimum signal-to-noise deconvolved foreground subtraction with Wiener filters, implementation on real data in progress </li></ul>

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