VLBI - techniques p2

Very big data rates (432 TB per day, 4320TB per session), so discarded basebnd data after correlation (Store and distribute correlated data products)

Clocks and timing

All interferometry relies on accurate alignment of signal

To track delay/phase errors to transfer from reference to target, the data recorder time signal must be stable during the cycle time

Nominally need <10 deg waveront phase error in 1000s at 10GHz

This means clock stability of 10/(360x1000x10e9) ~ 2e10-15

Clock differences between station = delay/rate

We need a hydrogen maser at each VLBI antenna

Connected interferometers can use one central clock as a single standard

Correlator delay model

All Radio astronomy correlators use a delay model to correct data:

Accounts for e.g. Earth rotation, the delay on a single baseline towards a sky target chages with time

To track a source in VBI, we need to mode the decay changes

The "delay model" calculates the delay between two telescopes at a particular time to get fringes in a specific direction

Tota delay = geometry + Earth rotation (+tides etc) + clocks + electronics + troposphere + ionosphere + special and general relativity.

Typically schedule periodic observations of a bright fringe finder source where fringes can be found in correlator

good but not perfect

Atmosphere is hard to predict in detail

Calibration work is needed to correct errors after correlation

Use simple point like sources to solve for errors

Transfer correction to the unknown target image

Flux calibration

Short Baseline

Long

Problem

Solution

Antenna gains fluctuate with time (e.g. temperature)

So: How bright is my target source

Also observe a source with known flux density (power)

Compare with "known answer" gain factor

Scale target with the same gain factor

All standard 'stable calibrators' are resolved - can't give reliable gain factor

Remaining compact source are more variable = not good flux calibrators

Before VBI observation: meaure with single dish:

During observations

Antenna gain as a function of altitude "gain curve"

The power of a "noise diode" in the antenna " noise diode profile"

An absolute flux density source "absolute gain factor"

Combine 1,2,3 noise dioe can be used a flux density reference

Fire noise diode periodically and log received power

After observation

Compare noise diode power with known reference values

Derive corrections as function of time (altitude)

Scale correlated target visabilities with noise diode corrections

Typically applied by a Tsys table which comes with data

Fringe fitting delay/rate corrections

Delays close to 0, ok for bright sources, but for faint sources not ok

Largely due to clock problems at the different location - you have clock drift that maybe small but can amount to a problem

Other interferometers only have one clock

Also chages of baseline geometry

Tidal effects (more relevent for larger arrays

Or antenna positions

Or even in connected arrays (stretching of cable

Some atmospheric affects

AIPS - Global fringe fitting

Use all baselines to jointly estimate the antenna phase, delay and rate relative to a reference antenna

Solves the baselines phase error equation, with one of the antennas set to the reference antenna

Delay, rate and phase residuals for reference antenna are set to 0

Hence only measures difference, not absolute errors

Assumes calibrator is a bright point source at phase centre

Similar to self-calibration as source structure is part of the model

Implimented in AIPS (older radio astronomy package - still used for VLBI a lot) but soon to be implemented in CASA

Phase referencing

Similar to what we have seen for our secondary phase calibrator, just need to be close

Fringe fitting requires observations of a bright, compact source -> e.g. phase cal

Cycle time shorter than atmospheric variations

Obtain fringe fitting solutions for phase, delay and rate but applying fringe fitting to calibrator and applying to target

Issues:

High frequencies - wet troposphere and few calibrators

Low frequency - ionosphere

Closure phase

All antennas have different random phase fluctuation -> atmosphere

Closure phase = sum of simultaneously observed phases of a source on 3 baselines forming a triangle

Independent of station based phase errors

Phase errors due to atmospheric variations are cancelled

Fringe fitting (and self-cal) uses this triangle to solve for the residual phases, rates and delay