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Xuening Bai
AST 542 Observational Seminar May 4, 2011
Radio Interferometry
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Outline
Single-dish radio telescope
Two-element interferometer
Interferometer arrays and aperture synthesis
Very-long base line interferometry
Interferometry at millimeter wavelength
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Brief history of astronomical interferometry
1920: Michelson stellar interferometer
1946: First astronomical observations with a two-element radio interferometer
1962: Earth-rotation synthesis
1967: Very-long baseline interferometry
1974: Nobel prize to Martin Ryle and Antony Hewish
1980-1990s: mm/sub-mm wavelength instruments
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Single-dish Radio Telescope
Primary parabolic surface (dish)
Secondary reflector
Feed
25m radio telescope at Urumqi, China
Receivers
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Heterodyne Receiver
Incoming signal is generally very weak: pre-amplify. Convert high-frequency signal to intermediate-frequency. Receiver cooled to reduce noise. Spectrum: multi-channel / autocorrelation spectrometer.
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Measurement: noise and sensitivity
Spatial resolution:
Calibration: resistive load at fixed T
System noise:
Sensitivity:
∆S =2kTsys
Aeff
√BT
Tsys = Tatm + Tbg + Tsl + Tloss
θ =1.22λ
D≈ 4.2 λ/cm
D/10m
Sources of noise
Tsys TaIn general,
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Need for better resolution: interferometry
Cyg A Cas A
(Ryle, 1950)
Primary beam + interference
Filled-aperture telescope limited to ~100m With interferometers, resolution , with B (baseline) up
to , improvements by factors of thousands. ∼ λ/B
R⊕
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Two-element interferometer Assumptions: Monochromatic point source with two identical antennas.
Rxy(τ) = x(t)y(t − τ)
Cross-correlation:
Rxy(s) = A(s)F cos(2πbλ · s)
Sxy(ν) = X(ν)Y ∗(ν)
Cross-spectrum power density:
S gives the fringe amplitude and phase.
Sxy(s) = A(s)Fν exp (i2πbλ · s)
bλ ≡ b/λ
τg = b · s/c
Fringe pattern changes as the Earth rotates
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Effect of finite bandwidth
interferometer response attenuated
Solution: add time delay to compensate for phase difference
τi = τgτg = b · s/c
Pxy(τg) = ν0+B/2
ν0−B/2A(ν, s)Fν exp(−i2πντg)dν
≈ A(ν0, s)Fν0 exp (−i2πν0τg)sinc(Bτg)
Sxy(ν0, s)
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Effect of finite source size
Sxy(ν0, s0) ≈
4πA(s0 + σ)Bν0(s0 + σ) exp[i2πν0(τg − τi)]sinc[B(τg − τi)]dΩ
Vij ≡
A(σ)Bν(σ) exp (2πibij,λ · σ)dΩFringe visibility:
τg − τi = bij · σ/c
small
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u-v plane
Vij ≡
A(σ)Bν(σ) exp (2πibij,λ · σ)dΩ
bij,λ = ueu + vev + wew
σ = xeu + yev
V (u, v) =A(x, y)Bν(x, y) exp [i2π(ux + vy)]dxdy
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General properties
Sxy(ν0, s0) ≈
4πA(s0 + σ)Bν0(s0 + σ) exp[i2πν0(τg − τi)]sinc[B(τg − τi)]dΩ
Vij ≡
A(σ)Bν(σ) exp (2πibij,λ · σ)dΩ
τg − τi = bij · σ/c
small
Interferometers have the same field of view as individual antennas.
Bandwidth has to be narrow in high-resolution observations.
Visibility is zero if surface brightness is constant.
Recall:
∆ν
ν0 θres
θfov
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Practical interferometers
Different antennas have different effective areas, etc.
Local oscillators must be coherent
A(σ)→ Aeff(σ) ≡
A1(σ)A2(σ)
Extra phase difference raised from individual receivers
Geometric time delay
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Interferometer arrays
N antennas => N(N-1)/2 pairs of baselines
Each interferometer pair makes a curve on the u-v plane, as the Earth rotates
Resolution: ~ λ / longest baseline
Field of view: same as individual antennas
Sensitivity: lowered by the beam dilution factor ~(L/D)2
Capability relies on receivers and electronics
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Very Large Array
Located on the plains of San Agustin in West-Central New Mexico
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EVLA: basic facts
27 independent antennas of 25m each
Distributed in Y-shape along railroad tracks
Configurations A-D, with baseline of 36 km – 1 km
Upgraded with state of the art receivers and electronics recently
Frequency accessibility: 1.0-50 GHz, 8 GHz bandwidth (maximum)
Spectral resolution up to 1 Hz
Angular resolution up to 20 mas at 10 GHz
Point-source sensitivity better than 1 micro-Jy at 2-40 GHz
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u-v plane coverage by the VLA
uv-plane coverage PSF
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Aperture synthesis
Lots of Fourier components are missing
Synchronization of clocks Phase error from the atmosphere
and individual receivers Voltage gains from the antennas
are different
Goal: construct images from partial coverage in the u-v plane
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Calibration
Flagging: check for “bad baselines” for removal.
Phase and flux calibrators: nearby strong point radio sources
Closure relation for phase calibration
Closure relation of fringe amplitude (for gain calibration)
More antennas => Better calibration
Intense computation is involved.
φijk ≡ φij + φjk + φki
Aijkl ≡|Vij ||Vkl||Vik||Vjl|
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Image cleaning
dirty beam after being CLEANed
Involves CLEAN, hybrid-mapping, and self-calibration, computationally intensive.
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Very-long baseline interferometry
Signal recorded by tapes/disks and brought together for correlation
European VLBI Network space VLBI
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Very-long baseline array (VLBA)
NRAO facility of 10 radio-telescopes, 25m each. Located from Hawaii to Virgin Islands, baseline >5000 miles
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Famous results from VLBA
water maser surrounding the SMBH of NGC 4258 => SMBH mass ~3.6×107M
(Miyoshi et al. 1995)
resolving the jet-launching region of M87
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Millimeter interferometory
Frequency is high: signal processing is more demanding
Small dishes are used: reduced sensitivity
Strong emission from water vapor and oxygen: reduced sensitivity
Atmospheric effect: phase correction is difficult
Water vapor content rapidly varying: phase stability issues
Submillimeter array at Mauna Kea
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Hughes et al. 2009
Example from the sub-millimeter array Image Visibility
A spatially resolved inner hole in the disk around GM Aurigae
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Atacama Large Millimeter/sub-mm Array
Location: Chajnantor plain, Chile (altitude ~5000m)
Almost completed
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ALMA: bands and atmospheric transmission
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ALMA: Basic Facts
Arrays: 50 Antennas of 12m each
Wavelength: 0.4-3mm (84-720 GHz)
FWHM of the primary beam: 21” (at 300 GHz)
Baseline: 125m – 16 km
Spatial resolution: 4.8”-37 mas (at 110 GHz)
Spectral resolution: 3.8 kHz – 2GHz (0.01 km/s at best!)
Sensitivity: ~mJy for 60s integration
Science: high-z universe, star/planet formation, …
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Summary
Radio telescopes use heterodyne receivers
Observable from two-element interferometer: fringe visibility
u-v plane: Fourier counterpart of the sky
Interferometers make use of the Earth rotation to achieve large coverage in the u-v plane
Aperture synthesis: image reconstruction from the u-v plane
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