PHASE REFERENCED MAPPING
AND
DIFFERENTIAL ASTROMETRY:
APPLICATIONS
JON MARCAIDE
26 Sept 2001
Castel San Pietro Terme
Very Long Baseline Interferometry (VLBI)
s

B
 = B·s / c
Phase referenced map:
I(x,y) =∫∫V(u,v) e-i 2 (ux + vy) du dv
V(u,v) e-iA-B
Marcaide & Shapiro, Ap.J. 276, 56-59 (1984)
Phase-reference mapping:
Differential phase:
A-B = A-B(str) + A-B(pos) + A-B(ins) +A-B(atm)
Phase referenced map:
I(x,y) =∫∫V(u,v) e-i 2 (ux + vy) du dv
V(u,v) e-iA-B
Marcaide & Shapiro, A.J. 88, 1134-1137
(1983)
Differential astrometry vs phase reference
Alternating observation:
A(t1)
B(t2)
A(t3)
B(t4)
A(t5)
B(t6) ...
Analysis:
A(t1;res) = A(t1;obs)  A(t1;thr)
B(t2;res) = B(t2;obs)  B(t2;thr)
A-B(t’1;res) = A(t1;res)  B(t2;res)
A-B(res) = A-B(res; str) + A-B(res; pos)
+A-B(res; ins) +A-B(res; atm)
Phase-reference mapping:
Differential phase:
A-B(res) = A-B(res; str) + A-B(res; pos) + A-B(res; ins) +A-B(res; atm)
0
Phase referenced map:
I(x,y) =∫∫V(u,v) e-i 2 (ux + vy) du dv
V(u,v) e-iA-B(res)
0
Differential astrometry:
A-B(res) = A-B(res; str) + A-B(res; pos) + A-B(res; ins) +A-B(res; atm)
0
WLSF
Residuals
(30º a 7mm)
Technique
• Walter Alef (1989), Very Long Baseline
Interferometry: Techniques and
Applications, M. Felli & R.E. Spencer, Eds.
NATO ASI Series, Kluwer C283
• Phil Diamond, idem
• Thompson, Moran & Swenson (1986)
“Inteferometry and Synthesis in Radio
Astronomy”, p. 384
PRECISION DIFFERENTIAL ASTROMETRY
• For a long time: Standard frequencies: 8.4 & 2.3 GHz
• Difficulty in reference point definition:
“-arcsec astrometry vs. m-arcsec resolution images”
• Examples: 4C39.25, 1928+738....
4C39.25
1928+738
A hybrid approach
Observations of the pair 0735+178 / 0748+128
Combination of :
1) Differential astrometry @ 8.4 GHz
2) Simultaneous maps @ 43GHz
The idea is to interpret the 8.4GHz astrometry with the help of the
43GHz maps.
0735+178
3.6cm
0735+178
3.6cm
0735+178
3.6cm
0735+178
7mm
3.6cm
Differential astrometry @ 7mm
Advantages:
•
•
•
Easier identification of the reference point
Reference point closer to central engine (assumed stationary)
Ionospheric contribution 25 times smaller than @ 3.6cm
Disadvantages:
•
•
Tropospheric water vapor contribution larger
Phase cycle duration: 23ps (5 times shorter than @ 3.6cm)
¿Are the Earth Orientation models precise enough to predict the
interferometric phase to a small fraction of 23ps?
Astrometry @ 7mm
Observation cycle vs weather
Observation cycle (switching time) is VERY dependent on
weather
Observation cycle vs weather
Observation cycle vs weather
1928+738 / 2007+777 @ 7mm
1928+738 / 2007+777 @ 7mm
Rate residuals
1928+738 / 2007+777
Rate residuals
7mm
1928+738 / 2007+777
7mm
Astrometric model:
• IERS Standard
•Ionosphere (IONEX)
•Troposphere (nodes)
r.m.s.  30º
Differenced phase delay
residual
( 2 ps)
Important for phase
reference mapping
Beyond Earth limitations:
SPACE VLBI
V.S.O.P.
VLBI
Space
Observatory
Program
Astrometry with VSOP
Halca limitations for astrometry:
HALCA (Highly Advanced Laboratory for
Communication and Astronomy)
 Short memory span to manoever the antenna
(Difficulty for alternating observations of sources)
 Large fractional errors in the space baselines:
()    B/B
B  50-100m (JPL)
This implies that for source pairs with   1º, ()  10 mas
However, how about observing two sources simultaneously?
Astrometry with VSOP
VLBA + HALCA observations of the pair of quasars
1342+662 / 1342+663 @ 6cm
1342+662 / 1342+663 with separation  = 4‘ have been observed
simultaneously by HALCA y VLBA
1342+662 / 1342+663
Maps of 1342+662 and 1342+663
1342+662
1342+663
Phase reference analysis of 1342+662
A-B(res) = A-B(res; str) + A-B(res; pos) + A-B(res; ins) +A-B(res; atm)
I(x,y) =∫∫V(u,v) e-i 2 (ux + vy) du dv
Phase reference analysis of 1342+662
Phase reference analysis of 1342+662
Astrometric information:
 = -0.5 mas
 = 1.5 mas
Phases of 1342+662 referenced to 1342+663
Phases of 1342+662 referenced to 1342+663
B HALCA ~
10 m
Phase-referenced maps of 1342+662
Only VLBA
VLBA +HALCA
Only HALCA
Space astrometry with VSOP
Scatter of position of maximum in maps: 50 as
B HALCA ~
3m
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