Atmospheric phase correction for ALMA Alison Stirling John Richer Richard Hills University of Cambridge Mark Holdaway NRAO Tucson

ALMA Goal To achieve: Diffraction-limited operation at sub-mm wavelengths on baselines up to 14 km Atmospheric phase correction essential Corresponds to 0.01 arcsec resolution requirement To achieve at ALMA’s highest frequencies (~950 GHz), require phase errors < 50 microns on baselines of 14 km Typical atmospheric phase fluctuations at Chajnantor:  on 300m baselines at 25-75% level Corresponds to fluctuations of ~300-  at 14km

Atmospheric phase dependence Atmospheric phase fluctuations in sub-mm caused by variations in water vapour and air density

Phase correction strategy To use a combination of: Fast switching Measure phase from a nearby point source calibrator Measures total atmospheric phase Intermittent (every ~10s of seconds) Gives phase along a different line of sight Water vapour radiometry 183 GHz radiometers four channels Only sensitive to wet component Continuous, on source Two prototype WVRs built by Cambridge and Onsala now ready for testing

Correction Strategy Issues How often to switch to a calibrator? Time spent on calibrator? Angular distance to calibrator? Smoothing time for WVR brightness temperatures? Calculation of conversion factor for WVR?

Correction Strategy Answers depend in detail on atmospheric structure, e.g. –Ratio of wet to dry phase fluctuations –Phase structure function Also depends on –Instrumental noise (antenna and WVR) –Distribution and brightness of point source calibrators Aim of work: to simulate realistic atmospheric phase fluctuations for the Chajnantor site Day time:  m (on 300 m baselines) Night:  Need separate analysis for day and night time conditions

Met Office Large Eddy Model Solves Navier-Stokes equation on a grid Assumes a Kolmogorov energy cascade on sub-grid scales Models water vapour, temperature, pressure Two scenarios: –daytime -- convection from surface heating –night time -- wind shear induced turbulence

Daytime profiles

. Height / km Horizontal distance / km

Y / km X /km

Location of dry, wet and total refractive index fluctuations Significant anticorrelation between dry and wet Fluctuations at the temperature inversion.

Scalings for convection C Relate variances of temperature and water vapour to mean temperature and water vapour profiles Apply relationships to deduce variances of radiosonde profiles Use to estimate dry and wet phase fluctuations from profiles

Estimation of fluctuations from radiosonde profiles Solid = total, Dotted wet, Dashed = dry * = Interferometric measurements of total daytime rms phase (Evans et al, 2003) At 50% level: Dry: 200 microns Wet: 400 microns Total: 400 microns Independent confirmation of phase fluctuation amplitude Initial estimates of dry fluctuation component

Daytime structure function Solid = dry Dot dashed = wet Dotted = cross- correlation term Consistent with Kolmogorov spectrum on small scales

Nocturnal mean profiles Gradient of temperature profile opposite sign from water vapour profile

Evolution of night time fluctuations Height / km Horizontal distance / km

Location of dry, wet and total refractive index fluctuations Negative correlation between wet and dry fluctuations near ground

Nocturnal structure function Blue dashed = wet; black solid = dry r.m.s. wet fluctuations ~ 2 x r.m.s dry Exponent of wet: 1.0, dry: 0.8 Turn over around 800m (~ depth of layer)

Simulations of phase correction AIPS++ code written by Mark Holdaway Combines Mark’s fast switching simulator with our 3-D simulations of atmosphere WVR simulated using `am’ radiative transfer code to calculate brightness temperatures (Scott Paine)

Correction process: WVR

WVR: rms error

Conclusions Now have realisations of the atmosphere at Chajnantor for day and night conditions Dry and wet fluctuations have different distributions depending on time of day Have developed simulations of FS+WVR phase correction Future plans: –Investigate different phase correction strategies –Validation of the two ALMA prototype WVRs on SMA

Estimation of fluctuations from daytime radiosonde data

AIPS++ simulations (2) Simulations have two stages: –Observing run Raw visibility data (as a function of baseline and time) WVR data (as a function of antenna and time) Fast switching data (as a function of baseline and time) –Data reduction -- Phase correction tests Combine all three to correct for phase

AIPS++ simulations (3) Can change: –Number of antennas, geometry –Observing frequency –Calibrator and target angular coordinates and integration times –Wind speed, PWV –WVR thermal and 1/f noise –Antenna noise

Correction process: FS 2pt

Correction process: WVR

Correction process: FS 2pt interpolation

Angular distance to calibrator Target source: 60 degrees elevation Red: elevation Blue: azimuth Day Night Initial estimate: Maximum angular distance to calibrator = 0.5 degrees for both day and night Little directional difference

Fast switching: rms error