PHASE REFERENCED MAPPING PHASE REFERENCED MAPPING ANDAND

DIFFERENTIAL ASTROMETRY:DIFFERENTIAL ASTROMETRY:

APPLICATIONSAPPLICATIONS

JON MARCAIDE26 Sept 2001

Castel San Pietro Terme

Very Long Baseline Interferometry (VLBI)Very Long Baseline Interferometry (VLBI)

B

s = B·s / c

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-iA-B

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-iA-B

Marcaide & Shapiro, A.J. 88, 1134-1137 (1983)

Differential astrometry vs phase referenceDifferential astrometry vs phase reference

Alternating observation:  

A(t1) A(t3) A(t5) B(t2) B(t4) 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 0 Phase referenced map:

I(x,y) =∫∫V(u,v) e-i 2 (ux + vy) du dv

V(u,v) e-iA-B(res)

Differential astrometry: 

A-B(res) = A-B(res; str) + A-B(res; pos) + A-B(res; ins) +A-B(res; atm)

 

0 WLSFResiduals

(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 ASTROMETRYPRECISION 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....

4C39.254C39.25

1928+7381928+738

A hybrid approachA 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+1780735+178

3.6cm3.6cm

0735+1780735+178

3.6cm3.6cm

0735+1780735+178

3.6cm3.6cm

0735+1780735+178

3.6cm3.6cm7mm7mm

Differential astrometry @ Differential astrometry @ 7mm7mm

 

 

 

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 @ Astrometry @ 7mm7mmObservation cycle vs weatherObservation cycle vs weather

 

 

  Observation cycle (switching time) is VERY dependent on weather

Observation cycle vs weatherObservation cycle vs weather

Observation cycle vs weatherObservation cycle vs weather

1928+738 / 2007+777 @ 1928+738 / 2007+777 @ 7mm 7mm

1928+738 / 2007+777 @ 1928+738 / 2007+777 @ 7mm 7mm

Rate residualsRate residuals

Rate residualsRate residuals

1928+738 / 2007+777 1928+738 / 2007+777 7mm 7mm

1928+738 / 2007+777 1928+738 / 2007+777 7mm 7mm

Differenced phase delay Differenced phase delay residualresidual

Astrometric model:

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

r.m.s. r.m.s. 30º ( 30º ( 2 ps) 2 ps)

Important for phase reference mapping

Beyond Earth limitations:Beyond Earth limitations:

SPACE VLBISPACE VLBI

VLBI VLBI

Space Space Observatory Observatory ProgramProgram

V.S.O.P.V.S.O.P.

Astrometry with VSOPAstrometry 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 VSOPAstrometry 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 1342+662 / 1342+663

Maps of 1342+662 and 1342+663 Maps of 1342+662 and 1342+663

1342+662

1342+663

Phase reference analysis of 1342+662 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

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+663Phases of 1342+662 referenced to 1342+663

Phases of 1342+662 referenced to 1342+663Phases of 1342+662 referenced to 1342+663

B HALCA ~ 10 m

Phase-referenced maps of 1342+662 Phase-referenced maps of 1342+662

VLBA +HALCA

Only HALCA

Only VLBA

Space astrometry with VSOPSpace astrometry with VSOP

 

 

   

 

Scatter of position of maximum in maps: 50 as

B HALCA ~ 3 m

Exoplanet search