Low-Frequency, All-Sky Imaging with the PAPER Array Using AIPY

Transcription

1 Low-Frequency, All-Sky Imaging with the PAPER Array Using AIPY A. Parsons 1, D. Backer 1, G. Foster 1, R. Bradley 2,4, C. Parashare 2, N. Gugliucci 2, E. Mastrantonio 4, J. Aguirre 3, D. Jacobs 3, C. Carilli 5, A. Datta 5, M. Lynch 6, D. Herne 6, T. Colegate 6 1 U. of California, Berkeley, 2 U. of Virginia, 3 U. of Pennsylvania, 4 NRAO, Charlottesville, 5 NRAO, Socorro, 6 Curtin U., Perth, Australia

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3 The PAPER Architecture Non-tracking Crossed Dipoles Wide Bandwidth ( MHz)! Movable (unburied TV cable)! Smooth Beam Flexible FPGA-based Packetized Correlator Full-Stokes Large # Ants (scalable)! Wide Band (up to 200 MHz)! 2048 Channel Polyphase Filter Banks 4-bit Cross-Multipliers AIPY: Model-based Imaging/Calibration Bootstrap Imaging/Calibration W Projection, Multi-frequency Synthesis Python-Based, Ties in MIRIAD, HEALPIX Measurement Equation-based Parameter Fit

4 PAPER Antennas/Analog Electronics Developed by the Charlottesville (NRAO,UVA) Team! Smooth beam (spatially and spectrally)! Gain sensitive to ambient temperature

5 PAPER/CASPER Packetized Correlator Two Dual 500 Msps ADCs + IBOB Berkeley Wireless Research Center's BEE2

6 Two Calibration/Imaging Paths... Parameter Space: Bootstrap: Direct, fast, imperfect Sometimes you can't get started because you can't get started Don Backer AIPY: Astronomical Interferometry in Python Model-Fit: Clean, correct, expensive an open-source toolkit ta low-frequency interferometry

7 What AIPY Is (and Isn't)! AIPY is:! A module adding tools for interferometry to Python (not visa versa)!! An amalgam of pure-python and wrappers around C++ and Fortran! Object-Oriented! A collection of low- to mid-level operations (you write the program)!! A toolkit (i.e. a grocery store, not a restaurant)!! In beta release (frequent updates/bug-fixes/changes)! AIPY isn't:! A solution (it just helps you find it)!! A one-stop shop (it makes use of other open-source projects)!! A replacement for other interferometry packages! Wedded to a file format (but only MIRIAD-UV, FITS currently supported)! Philosophical Pedantry:! Follow the (abbreviated) Zen of Python:! Explicit is better than implicit! Simple is better than complex! Complex is better than complicated! Special cases aren't special enough to break the rules! Practicality beats purity! There should be one (and preferably only one) obvious way to do it, although that way may not be obvious at first unless you're Dutch! Now is better than never! In the face of ambiguity, refuse the temptation to guess! Don't handicap the programmer; allow them all the rope they want! Don't hide data; return it (or at least grant access) at every turn

8 The Toolbox MODULES: ant/sim/fit const coord deconv healpix img loc map miriad optimize src ----3rd party---- ephem pyfits numpy pylab/matplotlib geometry, phase / gain, amplitude / parameter fitting physical constants coordinate transforms (eq, ec, ga, precession, etc.)! deconvolution (clean, lsq, mem, anneal)! wrapper around healpix C++ (Max-Planck-Institut)! imaging (gridding/weighting, W projection, beam calc)! machinery for importing user-defined AntennaArrays generation of all-sky maps, faceting interface to MIRIAD files parameter fitting, optimization code lists of known sources and parameters astrometry (relied upon heavily)! reading/writing FITS files numerical python (fundamental to everything)! plotting, map projection and example scripts for: manipulating/visualizing MIRIAD files, flagging RFI, filtering out crosstalk, fitting parameters, simulating arrays, making/viewing all-sky maps, phasing to/filtering out sources, imaging, etc.

9 Building a Simulator AntennaArray! set_jultime(...)!! gen_phs(...)!! gen_uvw(...)!! sim(...)! Antenna! x,y,z! dly,off! bp_r,bp_i Beam! response(...)!! <coeffs> Antenna! x,y,z! dly,off! bp_r,bp_i RadioFixedBody! compute(...)!! ra,dec! str,index! angsize SrcCatalog! compute(...)!! get_crd(...)! YourModule.py! get_aa(...)!! get_catalog(...)! RadioSpecial! compute(...)!! str,index! angsize

10 PAPER Deployments PGB: PAPER, Green Bank! PGB-4: , ants w/o flaps, 1 brd correlator! PGB-8: , upgraded ants, packet correlator! PGB-16: 2008-?, testing & characterization! Prototype facility for PWA deployments PWA: PAPER, Western Australia! PWA-4: 2007, ants w/o flaps, 1 brd correlator! (PWA-32): 2009, ants w/ flaps, packet correlat! (PWA-128): 2010?! Low-RFI, full-capability facility 38:25:59.24 N -79:51:02.1 W Green Bank, WV -26:44:12.74 S 116:39:59.33 E Boolardy, WA

11 Antenna Configuration! Inner circle is PWA-4 configuration! Outer circle is PGB-8 configuration! Shaded circles have radius = 10x elevation (dark is negative)!

12 Sample Data: 1 Day, 1 Baseline, PGB Phase Amplitude (log)! Fringes (Cas,Cyg,Sun)! Crosstalk Intermittent TX Beating sources Satellite TX TV/Aircraft

13 1-D Delay Imaging XRFI:! Remove model sky! Statistical thresholding! Manual flagging DELAY TF:! ifft of passband! Convolved by delay beam 1D CLEAN:! Compensate for holes in passband! Retain passband shape for self-cal

14 Delay/Delay-Rate Transform! 1 hour of data with Cas A, Cyg A, Tau A! Phase to a source (here, Cas A)!! FFT of frequency axis = Delay Image! FFT of time axis = Delay/Delay-Rate! Cas A is confined to a region near origin! PSF determined by bandpass + time var! Can recover bandpass + beam functions

15 Delay/Delay-Rate Transform! Two sources can show up at same delay for a given baseline! Over a time interval (say, 1 hr), can be differentiated by fringe rates (see below)!! To prevent excessive blurring (changing fringe rate w/ time) best to phase to source before filtering! Clean delay axis before ifft of time axis! Clean fringe rate axis to account for flagging of entire integrations! Top to bottom: 3 baseline orientations! Left to right: delay bins, delay-rate bins, and com filter bins! DDR filters have 2 lobes of response: one that tr your source, one that sweeps across the sky

16 Recovering Bandpass and Beam Kernels from DDR Transform! Top plot:! '+' = uncleaned bandpass recovered! heavy dots = cleaned bandpass! light dots = autocorr for comparison! Bottom plot:! '+' = uncleaned delay image! line = cleaned delay image! Cas A response versus time, Cyg A removed MHz (top) and 165 MHz (bottom)!! '+' = beam response recovered using delay fi! dots = beam response recovered using DDR! lines = prediction of beam model

17 Modeling Beam of Dipole + Flaps 138 MHz 156 MHz 174 MHz 40dB zenith to horizon, 60 degree FWHM Smooth spatially and vs. frequency

18 Model Beam vs. Source Strengths Black: response toward Cas A Blue: response toward Cyg A Cyan: response toward Tau A Green: response toward Vir A Red: response toward Sun

19 Imaging with Non-Tracking Beams Only possible to weight for one track through primary beam! Dirty beam weighted for phase center imperfectly deconvolves away from center! Can evade problem with snapshot imaging! Position-Dependent Weighting in Data Dirty Beam with Incorrect Weighting

20 MHz PWA-4/PGB-8! Scale: log(jy/beam)!! black->cyan = -1 to 1! yellow >= 2, red >= 3! Equatorial Mollweide Projection, RA=0 on right! Confusion at 80mJy/beam RMS at positive dec! Sun at (1:10,+7:27), removed with DDR filter! Cyg,Cas,Vir,Tau peeled with ionospheric-dependent solutions. Using: 8 Antennas at pos dec, 4 at negative 3 days of data, 14s integrations W projected, ~15 deg phase centers

21 ! 1 day of 8-element single polarization data! Spans to MHz! Model subtraction of Cyg,Cas,Vir,Crab! Fit for ionospheric defraction! Delay/F subtraction of Sun! Map has constant flux scale! Changing noise level due to beam response 150 MHz PGB-8

22 PGB-8 Thermal Noise Map RMS Noise Map, log10(jy/bm)! Integrations added with alternating signs T sys = 250K # FoV = strradians $ 0 = MHz %$ = 35.2 MHz # bm = 2.2e-5 strradians N ant = 8 antennas & int = 3 day observing = 3.5 hrs/pointing RA,DEC = 12:00, 40:00 < "T > = 625 mk (10 mjy/bm)!

23 Tsys (and predicted synchrotron)! Thermal noise (3 day integration)! PGB-8 System Temperature Tsky (confusion + synchrotron)! Tsky Thermal noise Using RMS pixel values from 4 patches near RA=12:00,DEC=40:00 as a function of frequency, we determine a perceived Tsky and thermal noise level. Backing out integration, this gives us Tsys

24 Power Spectra and Foregrounds Beware the Jabberwock, my son! The jaws that bite, the claws that catch! -Lewis Carrol (1872)! Galactic Synchrotron Confusion Noise Galactic Free-Free 21 cm EoR (z=9.5)! Extragalactic Free-Free 21 cm EoR (z=9.5)! Power spectra at 146.6, 155.7, 164.5, and MHz (top to bottom w/ error bars), from 4 fields near RA=12:00,DEC=40:00. Point source dominated, starting to see synchrotron at lower frequencies, wavemodes CMB Background

25 Summary!16 antennas deployed in PGB, 32 in PWA this fall!analog system working well, going into production!packetized Correlator enabling build-out in staged deployments! Working on QADC to lower digitizing cost, reducing to 100 MHz BW! Lowering integration time to ~8s!AIPY-based processing pipeline maturing! Available at Working on cluster/parallel computing!ionospheric refraction noticeable in data, compensated per source!have a confusion/synchrotron-limited map (8.4K), ready for next tier of foreground removal!thermal noise in map (600 mk) continuing to integrate down!source removal currently limited by primary beam model! Using satellites to characterize per-antenna beam shapes!have not started investigating polarization or galactic synchrotron

26 Confusion Noise Need to balance array configuration between resolving and removing confusing sources (long baselines), and optimizing for a power spectrum detection (concentrated core). Below, a map with n sources removed (left) and with the top 5 sources removed (right), with corresponding pixel histogra

27 Ionosphere Time scale: 10s Length scale: few km Refraction scale: few ar Pushes up data rates, need for instantaneous UV coverage (snapshot imaging)! Avoid dawn/dusk when ionosphere is highly variable Affects degree to which confusion noise can be suppressed

28 Ionosphere Time scale: 10s Length scale: few km Refraction scale: few ar Pushes up data rates, need for instantaneous UV coverage (snapshot imaging)! Avoid dawn/dusk when ionosphere is highly variable Affects degree to which confusion noise can be suppressed Black: Cas A, Magenta: Cyg A, 3 days of data, nighttime is shaded

29 38:25: :51:02.1 W Green Bank, W

30 38:25: :51:02.1 W Green Bank, W

31 -26:44: :39:59.33 Boolardy, W

32 -26:44: :39:59.33 Boolardy, W

33 Radio Frequency Interference Solution 1: Discretion is the better part of valor (run away)! Solution 2: Statistical thresholding of raw data Solution 3: Manually flag contaminated channels Solution 4: Delay/Delay-Rate Filtering Solution 5: Statistical thresholding after model subtraction Boolardy, Australia Site Characterization Blue:Peak, Green:Average, Red:Minimum Light: PWA, 3 days of data Dark: PGB, 3 days of data

34 Interferometry Fundamentals Our Parameterized Measurement Equation: Flat Field (Small Angle) Approximation:! (u,v) coordinates represent the Fourier transform of the angular sky coordinates (l,m)!! Angular power spectrum directly measured in UV (visibility) domain! Inverse 2D FFT of gridded UV visibilities yields dirty image (convolved with synthesized PSF)!! Synthesized PSF is inverse 2D FFT of visibility weights

35 Comparing with Other Experiments MWA PAPER LOFAR 21CMA Advantages/Philosophies:! Hands on: collect data early, address problems as they are encountered in data! Flexibility to adapt to new theory and new knowledge about foregrounds! Optimize smoothness of parameter space to allow faster, more precise fitting! Wide simultaneous bandwidth, full correlation of large numbers of antennas! Both fully functional prototype environment and low RFI location Disadvantages:! Collecting area! Simulation Unsure:! Spectral resolution vs. bandwidth! Group size

36 Sky-Vis Relationships Sky Vis ø(vis)! Implications for measuring PS Actual Field of view (FoV) determines coherence regi in visibility domain. Signal strength depends o FoV Primary Beam For incoherent signal summation, scaling of SNR # samples depends on SNR samples: Restricted Visibilities

37 Sample UV Optimized for 3 Scales Nested Triangular Configuration with Outlying Calibrators UV coverage Dirty

38 Slices Through Image Virgo A Galactic Plane/Her A Confusion Sun Confusion 2008 May 13 Harvard-Smithsonian: 21cm Cosmology

39 Power Spectra What an interferometer measures: Related measures used in literature:

40 Sensitivity in Visibility Domain Tsky ~ 160K #beam ~ 60 deg x 60 deg %$ ~ 5 MHz #patch ~ 10 deg x 10 deg Nsamples ~ 81 baselines &s ~ 40 min (varies with patch size and baseline orientation)! To hit SNR~1 in a UV pixel: ' ~ 2 months for 0.5 mk Minimum to constrain cosmic variance: - 3 sigma detection ~ 9 pixels around circle. - Using nested triangles with 3x3 antennas at each virtex, ~ 64 antennas (being clever). - Want to sample multiple rings to select for shape of power spectrum, so more like 128 antennas. - Need calibrator/imaging antennas, so more like 160 antennas. BUT... ** UV pixel sampled is frequency dependent, undermining ability to subtract foregrounds.!^ v

41 What we can learn in first experiments:! Time of EoR degenerately constrains What We Can Learn! Dark Energy/Dark Matter (time for structure to collapse) + star formation rate! Confirm inside-out structure formation! X-ray heating by first quasars What we can learn with SKA-class study:! Matter power spectrum through Dark Ages! Constrains dark energy, dark matter (growth factor in collapse)!! Constrains time of radiation-matter equality (transfer function)!! Geometry of Reionization! Star formation! Galaxy formation! Supermassive black hole formation! Feedback of reionization on structure formation Richest of all datasets

42 Evolution of Perturbations Matter-Radiation Equality Recombination Interaction Distance Scale (log)! Density Perturbation (log)! Inflationary Radiation Dominated Matter Dominated... Time (log)!

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44 Simulated Power Spectra

45 21 cm Spin Temp Wouthuysen Field Effect

46 Bounds on EoR (6<z EoR <12)! Gunn-Peterson Absorption in high-z galaxies, (Becker, Fan)! CMB Polarization from Thompson Scattering (Page, Spergel)!

47 Raw Sensitivity in Image Domain Tsys = Tsky + Trx ~ 170K + 110K %$ ~ 1 MHz N ~ 256 Aeff ~ 2 #obs ~ 1 to 0.1 degrees For necessary sensitivity: ' ~ 1 month for 1 mk at 1 degree (l ~ 100)! or more likely: ' ~ 10 yrs for 1 mk at 0.1 degree (l ~ 1000)! Have added flaps to! increase collecting area! reduce sky temp! suppress sidelobes of sources! supress RF Galactic Synchrotron Confusion Noise Galactic Free-Free Extragalactic Free-Free 21 cm EoR (z=9.5)! CMB Background

48 Challenge: Starting from Scratch Sometimes you can't get started because you can't get started Don Backer The Problem:! Self-calibration needs single-source data! Source isolation requires calibration! Parameter fitting needs a good starting guess! How do we get to first base? Bootstrapping:! Direct, imperfect, iterative! Do not rely (excessively) on priors! Take advantage of wide bandwidth! Address degeneracies one at a time

49 Polarized Galactic Synchrotron 150 MHz Power Spectrum Predicted from Komolgorov Turbulence Faraday Rotation Screen:! Smooth with frequency, but improperly calibrated line polarization can produce frequency-dependent structu! Smooth power spectrum can allow further rejection.! Need a factor of 1000 suppression 325 MHz Measured Polarizati