m-Mode Analysis Imaging with the Owens Valley LWA Michael Eastwood - - PowerPoint PPT Presentation

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m-Mode Analysis Imaging with the Owens Valley LWA Michael Eastwood - - PowerPoint PPT Presentation

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m-Mode Analysis Imaging with the Owens Valley LWA Michael Eastwood California Institute of Technology CALIM2016 October 10, 2016 M. Eastwood m-Mode Analysis Imaging 1 / 24 Caltech Harvard/SAO Gregg Hallinan Lincoln Greenhill

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SLIDE 1

m-Mode Analysis Imaging with the Owens Valley LWA

Michael Eastwood

California Institute of Technology CALIM2016 – October 10, 2016 1 / 24

  • M. Eastwood – m-Mode Analysis Imaging
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SLIDE 2

Caltech

Gregg Hallinan Sandy Weinreb Stephen Bourke → Chalmers Jake Hartman → Google Harish Vedantham Kate Clark Marin Anderson Ryan Monroe David Wang

OVRO

Dave Woody James Lamb OVRO staff

Harvard/SAO

Lincoln Greenhill Jonathon Kocz → JPL Ben Barsdell → NVIDIA Danny Price → Berkeley Hugh Garsden

JPL

Larry D’Addario Joe Lazio and the rest of the LWA team

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SLIDE 3

Introduction

Foregrounds in 21 cm Cosmology

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SLIDE 4

Introduction

Foreground Leakage is a Problem

z ∼ 8.4

Ali et al. (2015) 4 / 24

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SLIDE 5

Introduction

The 408 MHz Haslam Map

Our understanding of the VHF sky is an extrapolation of this map.

Haslam et al. (1981, 1982) 5 / 24

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SLIDE 6

The Owens Valley LWA

The Owens Valley LWA (OVRO LWA)

  • Dark ages and the cosmic dawn
  • Radio transients
  • Extra-solar space weather
  • Monitoring of the Sun and Jupiter
  • Ionospheric studies

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SLIDE 7

The Owens Valley LWA

OVRO LWA Details

  • 288 crossed-dipole antennas

(expanding to 352)

  • 1.5 km maximum baseline

(expanding to 2.5 km)

  • 512-input LEDA correlator
  • 24.7 MHz to 82.3 MHz

instantaneous

  • 5 antennas have

noise-switched front ends

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SLIDE 8

The Owens Valley LWA

OVRO LWA Data Reduction Pipeline

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  • M. Eastwood – m-Mode Analysis Imaging
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SLIDE 9

The Owens Valley LWA

TTCal Details

  • Calibration routine developed for the OVRO LWA
  • Standard tool for OVRO LWA data reduction
  • Gain calibration
  • Polarization calibration
  • Direction-dependent calibration
  • Point sources, Gaussians, shapelets, disks, near-field

sources

  • Open source license (GPLv3+)
  • https://github.com/mweastwood/TTCal.jl

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  • M. Eastwood – m-Mode Analysis Imaging
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SLIDE 10

The Owens Valley LWA

WSClean Snapshot Image

OVRO LWA snapshot image provided courtesy of Marin Anderson 10 / 24

  • M. Eastwood – m-Mode Analysis Imaging
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SLIDE 11

The Owens Valley LWA

BPJSpec Details

  • m-mode analysis implementation
  • All-sky images
  • Foreground filtering
  • Power spectrum estimation
  • Open source license (GPLv3+)
  • https://github.com/mweastwood/BPJSpec.jl

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SLIDE 12

m-Mode Analysis

Introduction to m-Mode Analysis

A new analysis framework for CHIME-like telescopes.

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  • M. Eastwood – m-Mode Analysis Imaging
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SLIDE 13

m-Mode Analysis

m-Mode Analysis Fundamentals

visibility =

  • (sky brightness) × (beam) × (fringe pattern) dΩ

For a telescope that does not steer its beam, visibilities are a periodic function of the sidereal time. visibility sidereal time Fourier transform − − − − − − − − − − − − − − − − − − − − − − → m-mode     . . . m-modes . . .     =     ... transfer matrix ...         . . . alm . . .    

Shaw et al. (2014, 2015) 13 / 24

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SLIDE 14

m-Mode Analysis

The Fundamental Equation

v = B B Ba + noise

v is the vector of m-modes. This is what is measured by the interferometer. B B B is the transfer matrix. It describes the response of the interferometer to the sky. This matrix is block diagonal. a is the vector of spherical harmonic coefficients (for the sky brightness).

Shaw et al. (2014, 2015) 14 / 24

  • M. Eastwood – m-Mode Analysis Imaging
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SLIDE 15

m-Mode Analysis

m-Mode Analysis Imaging

Goal: Estimate a given the observations v Least squares minimization ˆ a = argmin v − Ba2 = (B B B∗B B B)−1B B B∗v Problem: B B B∗B B B is singular!

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SLIDE 16

m-Mode Analysis

Regularizing the Problem

Goal: Estimate a given the observations v, but unmeasured modes should be set to zero. Least squares with Tikhonov regularization ˆ a = argmin

  • v − Ba2 + λa2

= (B B B∗B B B + λI I I)−1B B B∗v Problem: How do we choose λ? (come talk to me!)

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SLIDE 17

m-Mode Analysis

Advantages of m-Mode Analysis

  • Exactly incorporates wide-field effects
  • Automatic deconvolution of large-scales
  • Uses spherical harmonic basis functions instead of pixels
  • Uses standard matrix algebra (BLAS, LAPACK)
  • Block diagonal → big computational savings

(over a naive linear algebra approach)

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SLIDE 18

m-Mode Analysis

Disadvantages of m-Mode Analysis

  • Only applicable to telescopes that do not steer their beam
  • Requires data from a full sidereal day
  • Requires explicit computation of the transfer matrix
  • The transfer matrix can be very large

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  • M. Eastwood – m-Mode Analysis Imaging
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SLIDE 19

m-Mode Analysis

m-Mode Analysis at the OVRO LWA

  • Transfer matrix = 500 GB per frequency channel
  • Computations distributed across 160 workers
  • 100 hours of integration time
  • 10 arcminute resolution in the output maps (l ≤ 1000)
  • 8 maps evenly spaced between 36.528 MHz and 72.152

MHz (each 24 kHz bandwidth)

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SLIDE 20

m-Mode Analysis

m-Mode Analysis Map at 41.760 MHz

CAUTION – very preliminary

Eastwood et al. (in prep.) 20 / 24

  • M. Eastwood – m-Mode Analysis Imaging
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SLIDE 21

m-Mode Analysis

m-Mode Analysis Map at 57.456 MHz

CAUTION – very preliminary

Eastwood et al. (in prep.) 21 / 24

  • M. Eastwood – m-Mode Analysis Imaging
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SLIDE 22

m-Mode Analysis

m-Mode Analysis Map at 73.152 MHz

CAUTION – very preliminary

Eastwood et al. (in prep.) 22 / 24

  • M. Eastwood – m-Mode Analysis Imaging
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SLIDE 23

m-Mode Analysis

Combined m-Mode Analysis Map

CAUTION – very preliminary

Eastwood et al. (in prep.) 23 / 24

  • M. Eastwood – m-Mode Analysis Imaging
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SLIDE 24

m-Mode Analysis

Summary

  • First demonstration of m-mode analysis imaging
  • (Preliminary) maps with 10 arcminute resolution
  • 8 maps evenly spaced between 36.528 MHz and 72.152

MHz (each 24 kHz bandwidth) Come talk to me about:

  • 21 cm cosmology
  • Foregrounds in 21 cm cosmology
  • m-mode analysis
  • Calibration, source removal, and peeling

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SLIDE 25

Backup Slides

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SLIDE 26

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SLIDE 27

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SLIDE 28

m-Mode Analysis

Scale Map of the Universe

Last Scattering Surface 14000 Mpc 14 Gyr 28 / 34

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SLIDE 29

m-Mode Analysis

Scale Map of the Universe

2dF 28 / 34

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SLIDE 30

m-Mode Analysis

Scale Map of the Universe

Hubble Ultra Deep Field 28 / 34

  • M. Eastwood – m-Mode Analysis Imaging
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SLIDE 31

m-Mode Analysis

Scale Map of the Universe

LWA PAPER CHIME 28 / 34

  • M. Eastwood – m-Mode Analysis Imaging
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SLIDE 32

m-Mode Analysis

Hyperfine Structure

  • Proton and electron spins symmetric or antisymmetric
  • Magnetic dipole transition → very weak
  • Optically thin tracer of HI

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  • M. Eastwood – m-Mode Analysis Imaging
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SLIDE 33

m-Mode Analysis

Radiative Transfer

∆TB ∼ 27xHI(1 + δ) Tspin − TCMB(z) Tspin

  • mK

Pritchard & Loeb (2012) 30 / 34

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SLIDE 34

m-Mode Analysis

Cooling

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SLIDE 35

m-Mode Analysis

Temperature History

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SLIDE 36

m-Mode Analysis

Temperature History

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SLIDE 37

m-Mode Analysis

Temperature History

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SLIDE 38

m-Mode Analysis

The 21 cm Signal

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SLIDE 39

m-Mode Analysis

Picking the Regularization Parameter

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SLIDE 40

m-Mode Analysis

Picking the Regularization Parameter

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