1. High-Precision Differential Astrometry Eduardo Ros (Max-Planck-Institut für Radioastronomie) June 11, 2003

2. High-Precision Differential Astrometry Introduction Technique Science Futurology

3. High precision & accuracy

4. Astrometric precision Theoretical precision for an interferometer: Lestrade et al. AJ, 99, 1663, 1990 RADIO l as ALMA: 100 l as ( k 0.87mm, D=10km, SNR=30) OPTICAL SATELLITES 4 l as SIM: 4 l as (pointed mode) 1 (10) l as GAIA: 1 (10) l as (V=5 (10), survey mode)

5. Astrometric observables Geometric delay: Interferometric response: Phase-delay (~0.02s) most precise, 2 o -ambiguous Group delay less precise, unambiguous Delay rate (~1.5 l s/s) less precise, unambiguous Total phase:

6. 0 IMAGE – phases interpolated from the strong source to the weak one Phase-reference mapping 0 Hybrid-mapping of the two sources 0 Solved – weighted least-squares fit + phase-connection Phase-delay astrometry A priori model + fitting

7. Different techniques Phase-reference mapping (Alef, IAU Symp. 129, 523, 1988) –Hybrid double mapping (Rioja & Porcas A&A, 355, 552, 2000) –Fast-frequency switching (Middelberg et al., 6 th EVN Symp., 61, 2002) Phase-delay astrometry/phase-connection (Shapiro et al. AJ, 84, 1459, 1979) –Sky-closure (Ros et al. A&A, 384, 381, 1999) –Bootstrapping (Ros et al., in preparation) Cluster-cluster (Counselman et al. Phys. Rev. Lett. 33, 1621, 1974) 1st switched map (0.5º separation): Alef, IAU Symp. 192, Reid & Moran (eds.), p. 523, 1988

8. Attacking the problem – the software CALC / SOLVK – geodetic community –Provides and solves for the geometrical model VLBI3 / ASPY – MIT, CfA, Granada, València, York –Phase-delay, fine tuning of all parameters in the geometrical model, phase-connection process needed MASTERFIT / MODEST – JPL –Group delay SPRINT – Paris, Bordeaux –Phase reference mapping AIPS – general –Work with residuals over the model, easy handle of ionosphere, phase-reference mapping

9. Phase-delay astrometry PairΔθ (º)δΔθ (μas) Refs. 3C345/NRAO5120.580Shapiro 1979, Bartel 1986 1038+528 A/B0.0094Marcaide 1983, 1994, Rioja 1996 PSR 0329+54/0355+50855000Bartel 1985 PSR 1133+16/1119+183440000Bartel 1985 4C39.25/0920+3900.7550Guirado 1995 1928+738/2007+7774.656Guirado 1995, 1998, 2000 3C395/3C3826350Lara 1996 M81/SN1993J0.0580Ebbers 1998, Bartel 2000 PSR B1257+12/1257+145/1252+1191.6-33400Nunes 1998 1803+784/1928+738/2007+7774.6-6.8150Ros 1999 IM Peg/2251+158/2250+1940.7-2.9200Lebach 1999 PSR B2021+51/2037+51/2019+510.6-2.3130Campbell 1996 1150+812/1803+78415750Pérez-Torres 2001 0735+178/0748+1266300Guirado, in prep. S5 Polar Cap Sample1.6-30<100Ros, Pérez-Torres, Guirado, in preparation

10. Recent technical achievements Ionospheric correction from GPS measurements (Ros et al. A&A, 356, 357, 2000; AIPS task TECOR) Extension of the phase-connection up to 15º (Pérez- Torres et al. A&A, 360, 161, 2000) Astrometry with VSOP (Porcas et al., VSOP Conf., 245, 2000; Guirado et al. A&A, 371, 766, 2001) Phase-connection at k 7mm (Guirado et al. A&A, 353, L37, 2000) Phase-referencing test at k 3mm (Porcas & Rioja, 6 th EVN Symp., 65, 2002) <10 l as precisions via multiple calibrators at k 3.6cm (Fomalont & Kopeikin, 6 th EVN Symp., 53, 2002)

11. Astrometry & Astrophysics International Celestial Reference Frame establishment (comparison with optical –GAIA, SIM– frames; optical/radio shifts?) Registration of young supernova remnants (Bartel et al., ApJ, 581, 404, 2002) Pulsars  Brisken’s review Galactic dynamics and the Galactic Center  Reid’s talk AGN studies (absolute kinematics, core stationarity, opacities) General relativity Flaring stars & X-ray binaries – search for exoplanets Gravitational l -lensing (Honma & Kurayama, ApJ, 568, 717, 2002)

12. Core stationarity in AGN jets Following the standard jet model, the t ~1 surface (core) is frequency-dependent – How stable is this position in time? 3C 345 is stable within 20 l as/yr in R.A. (Bartel et al., Nature, 319, 733, 1986) 1038+528 A/B, B stationary, frequency-dependent position (Marcaide & Shapiro, AJ, 88, 1183, 1983; ApJ, 276, 56, 1984) 3C 66B, 8.4/2.3 GHz shift, elliptical paths at both freqs. – double black hole (Sudou et al., Science, 300, 1263, 2003)  Sudou’s poster

13. ABCD Deciphering 4C 39.25 Guirado et al. AJ 110, 2586, 1995 B component l a =90±43 l as/yr l d =7±68 l as/yr A B C Fey et al. AJ 114, 2284, 1997

14. The Draco Triangle: 1803+784/1928+738/2007+777 Ros et al., A&A, 384, 381, 1999 Dynamical center to the north of the VLBI core

15. The S5 Polar Cap sample Studied at the MPIfR since the 1980s (Eckart et al., 1987, Witzel et al., 1988, etc.) Flat spectrum radio sources: 8 QSOs 5 BL-Lac objects Long-term astrometric program Bootstrapping techniques

16. Gravitational delay from Sun: 3C 279 occultation in Oct. 1987,  PPN = 0.9996±0.0017 (Lebach et al., Phys. Rev. Lett. 75, 1439, 1995) Speed of gravity: Jupiter conjunction with J0832+1835, Sep. 2002,  = –0.02±0.19, c grav = (1.06±0.21)c (Fomalont & Kopeikin, 2003, astro-ph/0302294)  Fomalont’s talk VLBI & Gravity Probe B, measurement of the frame dragging – test observations of IM Pegasi (HR 8703) w.r.t. 3C 454.3 & 2250+194 since 1997  Ransom’s talk, Lederman’s poster Radio flare Lebach et al. ApJ, 517, L43, 1999 General relativity

17. Maser astrometry OH (1.6 GHz) –Large shells at 1000 AU of the stars –Amplified star image (originated at the radial outflow from mass-losing stars), not for all stars  van Langevelde’s poster H 2 O (22 GHz  50 l as) –Scales of 100 AU, ring-like –Much brighter than OH –Galactic dynamics (VERA project  Kobayashi’s talk, Hachisuka, Honma, Mochizuki’s posters ), motions in the Local Group (  Brunthaler’s talk ) SiO (43 GHz  10 l as) –Close to star (10 AU); bright and abundant –Instable in position and variable in brightness

18. Radio stars – continuum observations Proper motions & parallax Astrometric link between HIPPARCOS and the ICRF using 11 radio stars – precision of 0.5mas in orientation, 0.3 mas/yr in rotation rate (Lestrade et al., A&A 304, 182, 1995; A&A 344, 1014, 1999) LSI 61303, Algol, UX Ari, HR 1099, HD 283447, HR 5110, r 2 CrB, Cyg X1, HD 199178, AR Lac, IM Peg

19. Radio Star Astrometry: Exoplanets Star at 50 pc μ=50 mas/yr M p =15 M j e=0.2 a=0.6 AU Wobble magnified 30  Perryman (2000)

20. AB Dor and its Very Low Mass Companion Guirado et al. ApJ, 490, 835, 1997 HIPPARCOS + VLBI 0.76 M  0.08-0.11 M 

21. Perryman, Rep. Prog. Phys. 63, 1209, 2000 Mass vs. separation Wobble limit: 10 l as@10pc Radial speed limit: 10 m/s Mass vs. separation VLBI

22. Search for planet-like objects with a small, sensitive array Project running at Effelsberg/Robledo/ Goldstone Single baseline is enough: ~1 mas astrometric resolution Search for companions in nearby M dwarfs Wolf47 Do Cep EV Lac AD Leo EQ PegB DT Vir Guirado et al., 6th EVN Symp., 255, 2002

23. Future – instrumentation Model improvements: polar motion, mapping functions, antenna positions, etc.  Petrov’s talk Atmosphere & ionosphere: WVR & GPS analysis, better mapping functions  Lestrade’s poster Speed-up correlation: eMERLIN, eVLA, eVLBI  Garrington’s talk – real-time VLBI ? Telescopes: –VERA (V LBI Exploration for Radio Astrometry)  Kobayashi’s talk, Honma’s poster –ALMA

24. A wish list for the SKA (i) Intercontinental baselines – highest accuracy Provide calibrators everywhere in the sky for differential astrometry High frequencies: sources more point-like for astrometry – 22 GHz would allow water maser observations Sites equally spread in both hemispheres – full- sky coverage More antennas at one site – cluster-cluster mode

25. A wish list for the SKA (ii) Multi-beam system solves the Φ-extrapolation problem (observing simultaneously target and reference) Different lines of sight: tomography of the atmosphere/ionosphere - removal of propagation medium biases On-the-fly mapping and phase-connection with multiple beams/wide fields improves the precision for real-time astrometry and geodesy

26. General astronomy and astronautics: need of a reference frame, applications in space navigation Geodesy: polar motion, Earth Orientation Parameters, crustal displacements, tides, etc. Atmospheric science: troposphere and ionosphere modeling Astrophysics: alignment of VLBI images jet physics in extra-galactic radio sources opacity and spectral studies (after rigorous registration of images) radio stars (search for planets, X-ray binaries), etc. VLBI Astrometry