PHASE REFERENCED MAPPING AND DIFFERENTIAL ASTROMETRY: APPLICATIONS JON MARCAIDE 26 Sept 2001 Castel San Pietro Terme

Very Long Baseline Interferometry (VLBI) B s   = B·s / c

Marcaide & Shapiro, Ap.J. 276, (1984) Phase referenced map: I(x,y) =∫∫V(u,v) e -i 2  (ux + vy) du dv  V(u,v)  e-i  A-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-i  A-B

Marcaide & Shapiro, A.J. 88, (1983)

Differential astrometry vs phase reference Alternating observation:  A (t 1 )  A (t 3 )  A (t 5 )  B (t 2 )  B (t 4 )  B (t 6 )... Analysis:  A (t 1 ;res) =  A (t 1 ;obs)   A (t 1 ;thr)  B (t 2 ;res) =  B (t 2 ;obs)   B (t 2 ;thr)  A-B (t’ 1 ;res) =  A (t 1 ;res)   B (t 2 ;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-i  A-B(res)

Differential astrometry:  A-B (res) =  A-B (res; str) +  A-B (res; pos) +  A-B (res; ins) +  A-B (res; atm) 0WLSF 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,

4C C39.25

A hybrid approach Observations of the pair / Combination of : 1) Differential 8.4 GHz 2) Simultaneous 43GHz The idea is to interpret the 8.4GHz astrometry with the help of the 43GHz maps.

cm 3.6cm

cm 3.6cm

cm 3.6cm

cm 3.6cm 7mm 7mm

Differential 7mm Advantages: Easier identification of the reference point Reference point closer to central engine (assumed stationary) Ionospheric contribution 25 times smaller 3.6cm Disadvantages: Tropospheric water vapor contribution larger Phase cycle duration: 23ps (5 times shorter 3.6cm) ¿Are the Earth Orientation models precise enough to predict the interferometric phase to a small fraction of 23ps?

7mm Observation cycle vs weather Observation cycle (switching time) is VERY dependent on weather

Observation cycle vs weather

/ 7mm / 7mm

/ 7mm Rate residuals

/ mm

Differenced phase delay residual Differenced phase delay residual Astrometric model: IERS Standard Ionosphere (IONEX) Troposphere (nodes) r.m.s.  30º (  2 ps) Important for phase reference mapping

HST image A1 B A2 C B C A1 A2 Quadruple Gravitational Lenses: MGJ Ros et al., A&A (2000)

Beyond Earth limitations: SPACE VLBI SPACE VLBI VLBI Space Observatory Program V.S.O.P.

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  m (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 / 6cm / with separation  = 4‘ have been observed simultaneously by HALCA y VLBA

/

Maps of and

Phase reference analysis of Phase reference analysis of  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

Astrometric information:  = -0.5 mas  = 1.5 mas

Phases of referenced to

 B HALCA ~ 10 m

Phase-referenced maps of VLBA +HALCA Only HALCA Only VLBA

Space astrometry with VSOP Scatter of position of maximum in maps : 50  as  B HALCA ~ 3 m

Exoplanet search