Nithyanandan Thyagarajan (or just “Nithya”) Arizona State University Design Guidelines for EoR science with SKA-low and Efficient Scalability of Next-generation Low-frequency Radio Telescopes Nithyanandan Thyagarajan (or just “Nithya”) Arizona State University MWA+, HERA+

MWA Collaboration

HERA Collaboration

Why study the Epoch of Reionization? Formation of large scale structures and evolution of astrophysical objects need to be probed Neutral Hydrogen is a direct probe of the Reionization epoch Current instruments have enough sensitivity for statistical detection of HI from the EoR

Motivation for High Precision Modeling Thyagarajan et al. (2013) Beardsley et al. (2013) >10-sigma statistical detection expected with ~1000 hours data Currently heavily limited by foregrounds and instrument systematics (e.g. PAPER64 - Ali et al. 2015, Pober et al. 2015; MWA – Dillon et al. 2013)

The Foreground Problem Bright Foregrounds (but smooth) HI signal extremely faint (but not smooth) Parsons et al. (2012)

Fourier Space and Delay Spectrum Parsons et al. (2012)

Foreground “Wedge” and EoR window

Precision Radio Interferometry Simulations (PRISim) Objectives with PRISim: Comprehensive all-sky simulations (with good match to data) Role of Wide-field measurements Role of compact, diffuse foregrounds Role of instrument such as antenna aperture and its chromaticity Solutions to mitigate systematics

Model-Data Agree well

Impact of diffuse, compact emission – “Pitchfork” effect Diffuse Emission Point sources

Mitigation of systematics via Antenna Geometry (e.g. PAPER) (e.g. MWA) (e.g. HERA) Foreground spillover from Pitchfork drops significantly Thyagarajan et al. (2015a)

HERA Example HERA (Hydrogen Epoch of Reionization Array) B = 100MHz 1024 channels ~100 kHz channels 14m dishes FoV ~ 10 deg. at 150 MHz Compact hexagonal array

HERA HI/FG Sensitivity vs. Beam Chromaticity Thyagarajan et al. (2016), Accepted in ApJ Uniform Disk Airy Pattern Simulated Chromatic HERA beam Differences seen only due to spectral differences in Antenna beam Beam chromaticity worsens foreground contamination HERA is sensitive to EoR nevertheless

Design Specs on Reflections in Instrument Reflections are inevitable in electrical systems Reflections extend foregrounds and contamination in delay spectrum Require reflected foregrounds to be below HI signal levels HERA will aim for these specs Similar study is essential for SKA for guaranteeing success Thyagarajan et al. (2016), Accepted in ApJ

EoR Observing Window Efficiency 150 MHz subband (z=8.47) 170 MHz subband (z=7.36) All HERA baselines sensitive to EoR for most of observing window Robust to different models and redshifts HERA has extreme control over instrumental systematics and foreground contamination Working on SKA point of view

Summary Solutions to tackle systematics and the way forward for HERA and SKA-low: Critical to explore antenna apertures and spectral features in future designs HERA design robust to systematics - offers great promise for EoR detection SKA design under study PRISim – high precision simulations for wide-field radio interferometry – publicly available (https://github.com/nithyanandan/PRISim) Discovery of new instrument + foreground physics: Foregrounds through the instrument are not smooth Wide-field effects lead to pitchfork effect - diffuse emission near horizon even on long baselines Contamination significant from far away from primary field of view due to small but non-zero beam response Antenna beam chromaticity and reflections worsen contamination

E-field Parallel Imaging Correlator: An Ultra-efficient Architecture for Future Radio Interferometers Nithyanandan Thyagarajan (ASU, Tempe) Adam P. Beardsley (ASU, Tempe) Judd Bowman (ASU, Tempe) Miguel Morales (UW, Seattle)

Outline Motivations for Direct Imaging Modular Optimal Frequency Fourier Imaging (MOFF) – A generic direct imaging algorithm EPIC implementation of MOFF in software EPIC imaging in action Imaging performance of EPIC vs. FX EPIC calibration in action (Adam Beardsley) EPIC on future large-N dense array layouts Time-domain capability of EPIC Testing GPU-based EPIC on HERA

Motivations for Direct Imaging Technological Scientific EoR studies Transient studies, Inter-Planetary Scintillations, Ionospheric monitoring Large collecting areas require large-N arrays Cost of the correlator scales as N2 Require fast writeouts Fast writeouts under technical Thornton et al. (2013)

Concept of Direct Imaging Antennas placed on a grid and perform spatial FFT of antenna voltages on grid to get complex voltage images Square the transformed complex voltage image to obtain real-valued intensity images Current implementation: 8x8 array in Japan (Daishido et al. 2000) 4x8 BEST-2 array at Radiotelescopi de Medicina, Italy (Foster et al. 2014)

Need for generic direct imaging Hurdles with current implementations MOFF algorithm Morales (2011) Uniformly arranged arrays have poor point spread functions – thus not ideal for imaging Aliasing of objects from outside field of view Assumptions of identical antennas => poor calibration Calibration still requires antenna correlations Antennas need not be on a grid but still exploit FFT efficiency Can customize to science needs Accounts for non-identical antennas Calibration does not require forming visibilities Can handle complex imaging issues - w-projection, time-dependent wide-field refractions and scintillations Optimal images

Mathematical basis for MOFF Measured visibility is the spatial correlation of measured antenna E-fields Antenna power pattern is the correlation of individual voltage patterns Visibility measurement equation is separable into antenna measurement equations Allows application of “multiplication route” in multiplication-convolution theorem of Fourier Transform (while visibility imaging uses “convolution route”) FFT efficiency leveraged by gridding E-fields using antenna voltage illumination pattern

MOFF vs. FX FX MOFF Na2 (vs.) Ng log Ng Parallelization for efficiency – not production-level Na2 (vs.) Ng log Ng

Imaging with EPIC vs. FX Simulated Example: Nchan = 16 df = 100 kHz f0 = 150 MHz MWA core layout inside 150 m (51 antennas) Square antenna kernels

EPIC on actual LWA Data LWA1 TBN data with a total of 2s and 100 kHz Image obtained with 20 ms, 80 kHz Cyg A and Cas A prominently visible

Calibration *Need to apply calibration before gridding.

Calibration Problem E-field incident on ground related to sky by FT: Antenna integrates with voltage pattern: Further corruption modeled as complex gain and noise Goal is to solve for the gain factor

Calibration Requirements No visibilities MOFF algorithm mixes antenna signals ⇒ Must apply calibration at front end Scale <

Calibration Loop An iterative approach Scales O(N)

Math behind EPICal … Inspect this product Prime means current estimate and tracks the actual gain

Convergence of Antenna Gains Gain Amplitudes Gain Phase Errors Each iteration = 400 timestamps totaling 10 ms, No receiver noise, only sky noise Remind about phase wrap Initial dip in amplitude is overcompensating for initial high gains Nyquist timeseries length = 25 micro-seconds Gain update after 10 ms of integration

EPICal in action

Calibrating LWA data Same LWA data 150 channels ~ 29 kHz bandwidth Cal loop on 51.2 ms cadence total 1.5 s (30 cal. iterations) Model Cyg A and Cas A as point sources If you use the new plots from Evernote, 10 timestamps per cal update, 30 cal updates, total of 1.5s Get auto-subtraction term from Adam’s paper on github

Calibrating LWA data Gain Amplitudes Gain Phases Real data implies phases and gains converge to different values but are locked in Nyquist timeseries length = 5 micro-seconds Gain update after 51 ms of integration

Calibrating LWA data 55% increase in dynamic range Comment on image quality 55% increase in dynamic range

Implications from Scaling Relations EPIC FX Most expensive step – 2D spatial FFT at every ADC output cycle – O(Ng log Ng) For a given Ng, it does not depend on Na. e.g., dense layouts like HERA, LWA, CHIME Thus the array layout can get dense with no additional cost Most expensive step – FX operations on N2 pairs at every ADC output cycle – O(Na2) Accumulation in visibilities before imaging offers some advantage Advantage lost for large arrays requiring fast writeouts (due to fast transients, rapid fringe rate, ionospheric changes, etc.) Na2 (vs.) Ng log Ng

Current and future telescopes in MOFF-FX parameter space Top left is where MOFF is more efficient than FX Dashed line shows where expanded HERA will be Shaded area is where LWA will evolve to be Large-N dense layouts favor EPIC EPIC will benefit most of future instruments, definitely SKA MOFF (EPIC) FX

Current and future telescopes in MOFF-FX parameter space

Writeout rates for Transients Data rate (EPIC) GB/s Data rate (FX/XF) GB/s Data rate ~Ng for MOFF with EPIC Data rate ~Na2 for visibilities to be written out MOFF using EPIC lowers data rates significantly in modern/future telescopes MOFF with EPIC also yields calibrated images on short timescales Ideal for bright, fast (FRBs) and slow transients with large-N dense arrays Telescope Assumes writeout timescale of 10 ms

Planned EPIC demonstration Design a GPU-based EPIC and EPICal Design a GPU-based, image-based transient search backend Test machine set up at ASU to experiment the porting Cost-effective way to test it since we have already the hardware. Test machine set up at ASU to experiment the porting.

EPIC Summary EPIC is promising for most modern/future telescopes (SKA1, HERA, LWA, CHIME, MWA II core, etc.) EoR studies Large-N dense arrays for sensitivity to large scales Radio Transients & Inter-planetary Scintillation Fast writeouts Economic data rates Calibrated images at no additional cost EPIC paper - Thyagarajan et al. (2016) in review (arXiv:1510.08318) Highly parallelized EPIC implementation in Python publicly available - https://github.com/nithyanandan/EPIC/ Results of calibration (EPICal) studies by Beardsley et al.(2016) in review (arXiv:1603.02126)