RELATIVE ASTROMETRY AND PHASE REFERENCING. Ed Fomalont National Radio Astronomy Observatory Charlottesville, VA USA. OUTLINE. 1. Group Delays and Phase Delays Comparison and Accuracies VLBA Relative Astrometry with Phase Delay
National Radio Astronomy Observatory
Charlottesville, VA USA
--For any Source-Baseline-Frequency for a scan of ~2 min
Residual Phase Fr(n)
Fr (n) = (Total phase -2pn (Model delay)): Modulo 360o
Residual Group Delay Gr
Gr =DFr / 2pDn = Total group delay – Model delay
--Both Fr andGr are functions of astrometric/geodetic offsets
Analysis programs determine these offsets
Fr is ambiguous, only defined between -0.5, 0.5 fringe.
Need accurate model delay (<20 psec at 8 GHz)
about 0.5 cm!!
Gr is well-defined even with a relatively poor Model delay
Can be used directly to determine astrometric/geodetic prop.
Relative Accuracy (at 8 GHz):
Residual Phase Fr accuracy = (50/SNR) psec
Residual Group Delay Gr accuracy = (50/SNR) (Dn / n) psec
Delay scatter is about 20 psec,
Hence, Group Delay is as ‘good’ as phase for SNR >50. Not
limited by SNR, but by intrinsic delay scatter.
Phase needed for Imaging:
Residual closure phases provide an image by Fourier Transform
Non-closing Group delays cannot easily obtain source image
By fast switching between close-by sources:
(VERA observed two sources simultaneously)
--Temporal model delay errors are removed to first order.
--Effect of angular dependent model errors are decreased by source
separation in radians (2o separation = 1/25 decrease).
--Tropospheric unmodeled delay scatter between close sources
becomes < 1 psec, no ambiguity in the differential phase delay.
--Main contribution of residual phase-delay difference are position
offsets. Achieved accuracies are 0.05 mas for VLBA, EVN, VERA.
Fast switching among many close sources:
--The angular model delay errors from nearly all effects produce a
phase-gradient in the source region (including some software bugs).
(We do not care about distinguishing among the various effects.)
--Potential accuracy is <0.02 mas for VLBA even for 50 mJy sources.
The Solar Deflection Experiment of October 2005
Example of Multi-source Phase Referencing
Kopeikin (Missouri), Lanyi (JPL), Fomalont (NRAO)
--J1246, J1248 and J1304 (~0.2 Jy) are used as calibrators for 3C279.
--Observe at 15, 23, 43 GHz to remove coronal bending.
Cannot observe at these frequencies simultaneously!
--Observations on Oct 1, 18 (far from sun)
--Observations on Oct 5-6-7-9-10-11 to measure gravitational bending
Cycle between frequencies every
Derive position for 3C279 from group
Remove frequency dependent
coronal position change.
Determine g, gravitational bending
Observation switching within
3C279 ~ 10 Jy. Good SNR
Other cals, ~0.2 Jy okay for
phase, but not group delay
PHASE FITTING AT 15 GHz
Residual phase after fit
+3C279;+J1304;+J1256; + J1258
Use a ‘mini-solve to determine better
source positions and linear phase
gradient in sky. Phase gradient is
caused by the sum of many
effects but dominated by the error
in the zenith path delay.
Result of best fit to source positions
And phase gradient. What remains
is the residual temporal clock
error. Relative position error
About 0.03 msec. (Structure effect
has been removedl)
OCTOBER 1, 2005
15 GHz phase for 13-min period 43 GHz phases for 20-min period
+3C279;+J1304;+J1256; + J1258
Rms scatter for 3C279 at 4000 km is about 3 psec = 0.03 mas
3C279 at 15 GHz on Oct 10 (1.2o from sun)
Derived position of 3C279
(GR bending of ~150 mas removed)
Disagreement of phase positions (using
an image), with the group delay
position is 0.5 mas. Origin in yet
unknown. Phase cal?, source
SUMMARY FOR RELATIVE ASTROMETRIC ACCURACY
Source Evolution with Time (G127, Geldzahler and Fomalont)
Motivation: G127 is a compact 0.5 Jy radio source near the center of a
40’ SNR. Is it the relic of the original star?
Experiment goal: Determine the parallax and proper motion. SNR
distance is ~ 10 kpc, so should be detectable.
Observations: Five 10-hour VLBA observations at 8.4 GHz at
a six month-intervals with maximum east/west parallax signal.
Technique: Phase reference of G127 with a nearby 60 mJy
calibrator only 0.8o away. By the way, weaker calibrations may be
more stable calibrators with less structure than stronger calibrators.
Results: Image and Position of Peak of G127 wrt calibrator.
Source is variable (30%) and
minor structure changes occur,
although dominated by a core
with 50% of the flux density.
Is the peak of the bright
component the stationary
point of G127?
MODELING THE BRIGHT COMPONENT
Make image of the source for each epoch.
Little obvious change between epochs
10% weak and very slightly smaller
in size in second epoch. Steeper gradient on
Determine inner structure of bright radio
component using a physically realistic mode.
Unresolved radio core plus extended
inner jet in direction of more extended structure
Best fit of two components shown. Algorithm
in difmap to fit observed u-v data directly to
model. Approximate positional accuracy is
1.0 mas / SNR; diameter limit is
1.0 mas / SQRT(SNR)
Now have position of ‘true’ radio core wrt
peak intensity of main component.
Does this improve the experiment accuracy?
Resultant Motion of G127 with Time
Position of G127 with respect
to the reference quasar is
more stable when the position
of the unresolved fitted core is
taken as the stationary point,
compared with the peak of the
bright radio component.
Also, a 0.068 mas shift in position.
Incidently, no significant proper
motion and a parallax < 0.04 mas
Distance > 25 kpc.
3C279 Frequency Dependence
Oct 1, 2005
(0,0) is location
of fringe fit phase
15 GHz 23 GHz 43 GHz
Oct 18, 2005
x=+76, y=+127 x= -5, y=+6 x= -18, y=+32 Core Location(mas)
3.5 of 15 Jy 5.5 of 14 Jy 6.0 of 12 Jy
DETERMINATION OF TRUE RADIO CORE (STATIONARY POINT?)
For observations with reasonably high signal-to-noise and a radio structure
which conforms to the general physical model of quasars,
Position of the true radio core may be obtained to 0.1 mas with
respect to the entire source radio extent.
Astrometry Using ALMA
ALMA on its own is a good astrometric/geodetic array!
Size=15 km, Freq=300 GHz 15 mas fringe = 3 psec
4 dual-pol IF’s of 2 GHz each; maximum spanned BW = 25 GHz
58 12-m telescopes and 7 7-m telescopes
Troposphere at 5000 m at Atacama is extremely good.
Must do astrometry/geodesy to Calibrate:
Antenna location needed to 0.06 mm accuracy!
20 deg phase at 300 GHz 0.02 psec accuracy
WVR (Oxygen line at 360 GHz) to measure wv
Accurate tropospheric parameter measurements
Probably use group delays from observations.
Typical calibrator targets:
Quasars. Very variable, but probably very compact
Position nearly coincides with optical object
Many stars available.
Many planets, asteroids easily detectable.
VLBI with ALMA.
Main difficulty is phasing up array. Need not do entire array