21CMA/PAST data analysis

Ue-Li Pen 彭威礼Chris Hirata

Xiang-Ping Wu 武向平 , Jeff Peterson

Reionization

• First objects: • 21cm @ z>6• 50-200 Mhz• ΔT = 23 mK, ~0.3

mJy• Angular scale 5’<Θ<2

0’, freq res 500 khz

z=10 simulation, Furlanetto et al, 2004

Foreground: Synchrotron

408 MHz Haslam Much brighter than signal, but no spectral structure

Detectability

• Luminosity proportional to object volume: bigger structures easier to find

• Noise dominated by galaxy: T=300(f/150 Mhz)-2.5, higher frequency (lower redshift) much easier

• Mean emission very hard to discern (Gnedin and Shaver 2004).

• First targets: Stromgren spheres around bright quasars (Wyithe and Loeb 2004).

21CMA/PAST Site

21CMA/PAST Strategy

• Fast track to data: avoid custom design, off-the-shelf only.

• Use existing TV technology, commodity PC’s for correlations

• Learn as you build: fast turnaround, flexibility

Antenna Design

• Noise dominated by galaxy: Tgal=280 (150Mhz/f)2.5 K @ NCP

• sensitivity: 104 m2 effective area• Resolution: aperture synthesis， 80 elements,

3km baselines• Receiver noise: NF < 2 dB (T<200K)• Pointing at north celestial pole, elevation 43o

• simple， fast。 Currently 23 hexagonal pods, 12 correlating

Ulastai

Ustir station

42º 55’N 86º 45’ E

elev 2600m

Urumqi 150 km

Ground shield： 5000m 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, 10o FOV

3C061.1

NCP

CMB Analogy

• Searching for very low surface brightness sources

• Potentially severe foregrounds• Fully sampled u-v planes: different from CLEANing

• Statistics of noise and foregrounds can be described very accurately

• Large Field of view: planar assumption breaks. WMAP: 120 deg difference map

CMB map making

• Linear algebra approach to map making

• Used by most experiments, including WMAP, Planck, Boomerang, DASI, CBI

• Exactly solvable for Gaussian random fields

• Noise properties fully characterized

• Computationally expensive

• Fast workarounds: CG, multigrid, etc.

Data Flow

• raw time stream

• Optimal map construction to reduce data size: Deconvolution, Wiener, etc

• Foreground removal

• Noise covariance matrix

• Power spectrum

• Window functions

Analysis procedure

• Calibrate system from celestial sources

• Determine beam from sky

• Generalized BEAM contains all processes between source and data: ISM, ionosphere, antenna, polarization, transmission line, etc.

• Wiener filtered map

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)

Computational Complexity

• O(N3): not tractable for all sky, workable for small fields at low resolution, up to 105 pixels

• Accelerated plans in development: Conjugate gradient, multigrid (e.g. Pen 2004) as used in lensing and CMB analysis

Conclusions

• Linear map making theory well understood from CMB analysis, optimal algorithms for Gaussian fields, even full sky.

• Minimum signal-to-noise deconvolved foreground subtraction with Wiener filters, implementation on real data in progress