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PHASE REFERENCED MAPPING AND DIFFERENTIAL
ASTROMETRY APPLICATIONS
JON MARCAIDE 26 Sept 2001 Castel San Pietro Terme
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Very Long Baseline Interferometry (VLBI)
s
?
? Bs / c
B
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Marcaide Shapiro, Ap.J. 276, 56-59 (1984)
Phase referenced map I(x,y) ??V(u,v) e-i 2?
(ux vy) du dv
?V(u,v)? e-i?A-B
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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
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Marcaide Shapiro, A.J. 88, 1134-1137 (1983)
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Differential astrometry vs phase reference
Alternating observation     ?A(t1)
?A(t3) ?A(t5)
?B(t2) ?B(t4) ?B(t6)
...
Analysis   ?A(t1res) ?A(t1obs) ?
?A(t1thr) ?B(t2res) ?B(t2obs) ? ?B(t2thr)
  ?A-B(t1res) ?A(t1res) ? ?B(t2res)
  ?A-B(res) ?A-B(res str) ?A-B(res pos)
?A-B(res ins) ?A-B(res
atm)
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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 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)
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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)
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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

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• 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, 1928738....

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4C39.25
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1928738
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A hybrid approach
Observations of the pair 0735178 /
0748128 Combination of 1) Differential
astrometry _at_ 8.4 GHz 2) Simultaneous maps _at_
43GHz The idea is to interpret the 8.4GHz
astrometry with the help of the 43GHz maps.
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0735178
?3.6cm
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0735178
?3.6cm
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0735178
?3.6cm
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0735178
?3.6cm
?7mm
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Differential astrometry _at_ ?7mm

•  
• Advantages
•   Easier identification of the reference point
•   Reference point closer to central engine
  (assumed stationary)
• Ionospheric contribution 25 times smaller than
  _at_ ?3.6cm
• Disadvantages
•    Tropospheric water vapor contribution larger
•    Phase cycle duration 23ps (5 times shorter
  than _at_ ?3.6cm)
•  
• Are the Earth Orientation models precise enough
  to predict the interferometric phase to a small
  fraction of 23ps?
•  
•  
•  

 
 
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Astrometry _at_ ?7mm Observation cycle vs weather
 
 
  Observation cycle (switching time) is VERY
dependent on weather
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Observation cycle vs weather
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Observation cycle vs weather
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Observation cycle vs weather
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1928738 / 2007777 _at_ ?7mm
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1928738 / 2007777 _at_ ?7mm
Rate residuals
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1928738 / 2007777 ?7mm
Rate residuals
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1928738 / 2007777 ?7mm

• Astrometric model
• IERS Standard
• Ionosphere (IONEX)
• Troposphere (nodes)

r.m.s. ? 30º (? 2 ps) Important for phase
reference mapping
Differenced phase delay residual
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A2
B
B
A2
C
A1
C
A1
HST image
Quadruple Gravitational Lenses MGJ04140534 Ros
et al., AA (2000)
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Beyond Earth limitations SPACE VLBI
V.S.O.P.
VLBI Space Observatory Program
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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? 
 
 
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Astrometry with VSOP
 
 
  VLBA HALCA observations of the pair of
quasars 1342662 / 1342663 _at_ ?6cm 1342662 /
1342663 with separation ?? 4 have been
observed simultaneously by HALCA y VLBA
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1342662 / 1342663
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Maps of 1342662 and 1342663
1342662
1342663
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Phase reference analysis of 1342662
?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
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Phase reference analysis of 1342662
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Phase reference analysis of 1342662
Astrometric information ?? -0.5 mas ?? 1.5
mas
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Phases of 1342662 referenced to 1342663
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Phases of 1342662 referenced to 1342663
?B HALCA 10 m
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Phase-referenced maps of 1342662
Only VLBA
VLBA HALCA
Only HALCA
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Space astrometry with VSOP
     
  Scatter of position of maximum in maps 50
?as ?B HALCA 3 m
 
 
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Exoplanet search
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