Atmospheric Phase Characteristics of

ALMA Long BaselineSatoki Matsushita (ASIAA)

Y. Asaki, E.B. Fomalont, K.-I. Morita, D. Barkats, R.E. Hills, R. Kawabe, L.T. Maud,B. Nikolic, R.P.J. Tilanus, C. Vlahakis, & N.D. Whyborn

Based on

Matsushita et al. 2017, PASP, 129, 035004

History of ALMALong Baseline Tests

600 m Baseline Test (2010/2011)

Submillimeter Array (SMA)

2.0 km Baseline Test (2012)

600 m Test (2010/2011)

2.0 km Test(2012)

Submillimeter Array (SMA)

3.0 km Baseline Test (2013)

600 m Test (2010/2011)

2.0 km Test (2012) 3.0 km Test (2013)

Submillimeter Array (SMA)

15 km Baseline Test (2014)

600 m Test(2010/2011)

2.0 km Test (2012) 3.0 km Test (2013)

SubmillimeterArray (SMA)

APEX

ASTE

Phase Fluctuations atLong Baselines

Without Atmosphere

With Atmosphere

Water Vapor

With Atmosphere

Taking Out the Phase Fluctuations

• 183 GHz Water Vapor Radiometer (WVR) Phase Correction Method.

• Fast Switching Phase Correction Method.

• Band-to-Band Phase Correction Method.

• Paired Antenna Phase Correction Method.

Improvement by WVR Phase Correction

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Raw

/WV

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PWV [mm]

Band 3(BL<1km)Band 6(BL<1km)Band 7(BL<1km)Band 8(BL<1km)Band 3(BL>1km)Band 6(BL>1km)Band 7(BL>1km)Band 8(BL>1km)

• WVR phase correction often works well whenPWV > 1 mm.– PWV > 1 mm:

Improvement = 2.8 +- 0.9

– PWV < 1 mm:Improvement = 1.5 +- 0.3

• No difference in baseline length (BL).– BL < 1 km:

Improvement = 2.3 +- 0.9

– BL > 1 km:Improvement = 2.0 +- 0.7

• No difference in Bands.

Blue: Baseline Length < 1 kmRed: Baseline Length > 1 km

Spatial Structure Function (SSF)• Spatial Structure Function (SSF):

RMS phase fluctuation as a function of baseline length.

[RMS phase] = 𝑃ℎ𝑎𝑠𝑒(𝑥) − 𝑃ℎ𝑎𝑠𝑒(𝑥 − 𝑑) 2

(namely, the phasedifference at thebaseline length of 𝑑).

100 m 1 km 10 km

1 mm~ 100o @ Band 3

100 mm~ 10o @ Band 3

Band 3, PWV = 1.5 mm

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Blue: Raw dataRed: WVR corrected data

Baseline Length [m]

a Possible to revealstatistically the sizedistribution of watervapor clumps in theatmosphere.

– 3-D Kolmogorovturbulence:

slope = 0.83– 2-D Kolmogorov

turbulence:slope = 0.33

SSF Slopes at Short Baseline Lengths

• At short baselines (< 500 m), SSF slopes are almost constant under whatever conditions:– Before WVR: 0.65 +- 0.06

– After WVR: 0.62 +- 0.09

• 50% quartile slope for the 3-year 11.2 GHz Radio Seeing Monitor data: 0.63(Butler et al. 2001).– Raw data we took seem typical

phase fluctuation condition at the ALMA site.

SSF Slopes at Short Baseline Lengths • Typically, there is a turn-over around 1 km.

• Increase of phase fluctuation at longer baselines is small. a Good news for longer baseline interferometry.

100 m 1 km 10 km

1 mm~ 100o @ Band 3

100 mm~ 10o @ Band 3

Band 3, PWV = 1.5 mm

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Blue: Raw dataRed: WVR corrected data

Baseline Length [m]

• In general, overall structure of SSF does not change much before and after the WVR phase correction.

What is the Cause of Phase Fluctuation?• SSFs with turn-over

– Turn-over is always around ~1 km.a Turbulent constituent with the scale height of ~1 km.aWater vapor.

• But after the WVR phase correction, SSFs are still very similar feature.a Not enough WVR phase

correction?

WVR scaling factoroptimization will improvethe WVR phase correction(Maud et al. 2017, A&A, 605, 121)

Band 3, PWV = 1.5 mm

Blue: Raw dataRed: WVR corrected data

SSF Slopes at Long Baseline Lengths

• At long baselines (> 1 km), SSF slope tends to be smaller, but more scattered:– Before WVR: 0.22 +- 0.15– After WVR: 0.29 +- 0.13

• Some data have the slopes larger than 0.5, which suggesting that the slopes do not change from short to long baselines.– This case is rare.– Sometimes shows up when

PWV is low (i.e., WVR phase correction does not work well).

– Some data turned to be this case after the WVR correction.

100 m 1 km 10 km

1 mm~ 100o @ Band 3

100 mm~ 10o @ Band 3

Band 6, PWV = 0.5 mm

RM

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[m

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Blue: Raw dataRed: WVR corrected data

Baseline Length [m]

What is the Cause of Phase Fluctuation?• SSFs without any turn-over (i.e., a constant slope)

– This SSF shows up when• PWV is low (i.e., WVR phase correction does not work well).

• After WVR phase correction.

a Highly possible phasefluctuation caused bynon-water-vaporcomponent.

• Scale height higher than the longest baseline length of ~10 km.

a Dry air component(N2 and/or O2) orwater ice?

100 m 1 km 10 km

1 mm~ 100o @ Band 3

100 mm~ 10o @ Band 3

Band 6, PWV = 0.5 mm

RM

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th L

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[m

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n] Blue: Raw data

Red: WVR corrected data

Baseline Length [m]

RMS Path Length at 10 km Baseline• Estimate the rms path length at the baseline length of 10 km.

– log10(rms path length)= [long baseline slope] x [baseline length]

+ [long baseline constant]

• Higher PWV data have larger rms path length at 10 km.• Even when PWV < 1 mm and after WVR phase correction,

mean rms path length is ~200 mm.

a Peak-to-peakphase fluctuationis ~2p or more for600 – 1000 GHz(300 – 500 mm).

a Need band-to-bandand/or fastswitching phasecalibration.

RMS Path Length at >>10 km Baseline

• Most of the case, SSF slope will be flat or close to flat.

a RMS phase fluctuation is expected to be similar as~10 km baseline even at >> 10 km baselines.

a Possible to perform >> 10 km baseline observationswith combining several phase correction methods.

• Unknown point is the non-water-vapor component.

– How long the constant slope continues?a Typically, N2 or O2 scale height is ~8 km, so that if it is dry

air component, then phase fluctuation is expected to beconstant at >> 10 km baselines.

Summary• Water Vapor Radiometer (WVR) phase correction works well,

especially when PWV > 1 mm.

• Spatial Structure Function (SSF; rms phase vs baseline length)

– Often has turnover around 1 km baseline length, and the slope will be shallower at longer baselines.• RMS phase increase at longer baseline is slower.

• Cause of the phase fluctuation is water vapor.

– When WVR phase correction does not work (PWV < 1 mm) or after WVR phase correction, a constant slope SSF sometimes show up.• RMS phase keep increasing as a function of baseline length.

• Cause of the phase fluctuation may be dry air (N2 or O2) or water ice.

• Longer baseline (>> 10 km) is promising if combine with other phase correction methods.

Matsushita et al. 2017, PASP, 129, 035004