1. RELATIVE ASTROMETRY AND PHASE REFERENCING Ed Fomalont National Radio Astronomy Observatory Charlottesville, VA USA

2. OUTLINE 1. Group Delays and Phase Delays Comparison and Accuracies 2. VLBA Relative Astrometry with Phase Delay Many results: Solar bending of 3C279 in October 2005 Very accurate relative positions (0.02-0.05 mas) Group delays during unstable periods 3. Source Structure Problems A problem for relative and absolute astrometry at <0.1 mas level Source variations over time/frequency. Registration to 0.1 mas? 4. Combining Techniques Can phase delays be used? Stepwise approach? Imaging and position monitoring into a coherent picture. 5. Use of ALMA for Astrometry

3. Group versus Phase Delay (1) --For any Source-Baseline-Frequency for a scan of ~2 min Residual Phase  r (   r ( ) = (Total phase - 2  (Model delay)): Modulo 360 o Residual Group Delay G r G r =  r /  = Total group delay – Model delay --Both  r and G r are functions of astrometric/geodetic offsets Analysis programs determine these offsets  r is ambiguous, only defined between -0.5, 0.5 fringe. Need accurate model delay (<20 psec at 8 GHz) about 0.5 cm!! G r is well-defined even with a relatively poor Model delay Can be used directly to determine astrometric/geodetic prop.

4. Group versus Phase Delay (2) Relative Accuracy (at 8 GHz): Residual Phase  r accuracy = (50/SNR) psec Residual Group Delay G r accuracy = (50/SNR) (  ) psec Delay scatter is about 20 psec, Hence, Group Delay is as ‘good’ as phase for SNR >50. Not limited by SNR, but by intrinsic delay scatter. Phase needed for Imaging: Residual closure phases provide an image by Fourier Transform Non-closing Group delays cannot easily obtain source image

5. Relative Astrometry using Phases By fast switching between close-by sources: (VERA observed two sources simultaneously) -- Temporal model delay errors are removed to first order. --Effect of angular dependent model errors are decreased by source separation in radians (2 o separation = 1/25 decrease). --Tropospheric unmodeled delay scatter between close sources becomes < 1 psec, no ambiguity in the differential phase delay. --Main contribution of residual phase-delay difference are position offsets. Achieved accuracies are 0.05 mas for VLBA, EVN, VERA. Fast switching among many close sources: --The angular model delay errors from nearly all effects produce a phase-gradient in the source region (including some software bugs). (We do not care about distinguishing among the various effects.) --Potential accuracy is <0.02 mas for VLBA even for 50 mJy sources.

6. The Solar Deflection Experiment of October 2005 Example of Multi-source Phase Referencing Kopeikin (Missouri), Lanyi (JPL), Fomalont (NRAO) --J1246, J1248 and J1304 (~0.2 Jy) are used as calibrators for 3C279. --Observe at 15, 23, 43 GHz to remove coronal bending. Cannot observe at these frequencies simultaneously! --Observations on Oct 1, 18 (far from sun) --Observations on Oct 5-6-7-9-10-11 to measure gravitational bending. 3C273

7. Cycle between frequencies every 15 minutes. Derive position for 3C279 from group Remove frequency dependent coronal position change. Determine  gravitational bending Observation switching within each group. 3C279 ~ 10 Jy. Good SNR Other cals, ~0.2 Jy okay for phase, but not group delay

8. Observed phaseResidual phase after fit BR-OV 1050 km HN-OV 4600 km MK-OV 3900 km PT-OV 700 km + 3C279; + J1304; + J1256; + J1258 Use a ‘mini-solve to determine better source positions and linear phase gradient in sky. Phase gradient is caused by the sum of many effects but dominated by the error in the zenith path delay. Result of best fit to source positions And phase gradient. What remains is the residual temporal clock error. Relative position error About 0.03 msec. (Structure effect has been removedl) PHASE FITTING AT 15 GHz 60 psec

9. OCTOBER 1, 2005 15 GHz phase for 13-min period 43 GHz phases for 20-min period  13 minutes  + 3C279; + J1304; + J1256; + J1258 Rms scatter for 3C279 at 4000 km is about 3 psec = 0.03 mas 60 psec 20 psec

10. 3C279 at 15 GHz on Oct 10 (1.2 o from sun) Disagreement of phase positions (using an image), with the group delay position is 0.5 mas. Origin in yet unknown. Phase cal?, source structure? Derived position of 3C279 (GR bending of ~150 mas removed)

11. SUMMARY FOR RELATIVE ASTROMETRIC ACCURACY Weak calibrators (0.05 Jy) can be used. Only need 5-sigma detection in a coherence time Target positional accuracy about 0.05 mas with 2 o separation. VLBA, EVN and VERA general results. Multi-calibration sources can produce <0.02 mas accuracy. Weak, undetectable ‘group delay’ targets can be imaged. Useful for bright GAIA quasars that are faint radio sources. Use phase referencing to tie a 0.5 mJy radio star to ICRF grid to 0.1 mas. Techniques not useful for ‘normal’ astrometry/geodetic work BUT, A COMMON PROBLEM IS SOURCE STRUCTURE Becomes a serious source of error for position accuracy < 0.1 mas, regardless of the method.

12. Source Evolution with Time (G127, Geldzahler and Fomalont) Motivation: G127 is a compact 0.5 Jy radio source near the center of a 40’ SNR. Is it the relic of the original star? Experiment goal: Determine the parallax and proper motion. SNR distance is ~ 10 kpc, so should be detectable. Observations: Five 10-hour VLBA observations at 8.4 GHz at a six month-intervals with maximum east/west parallax signal. Technique: Phase reference of G127 with a nearby 60 mJy calibrator only 0.8 o away. By the way, weaker calibrations may be more stable calibrators with less structure than stronger calibrators. Results: Image and Position of Peak of G127 wrt calibrator. Source is variable (30%) and minor structure changes occur, although dominated by a core with 50% of the flux density. Is the peak of the bright component the stationary point of G127?

13. MODELING THE BRIGHT COMPONENT Make image of the source for each epoch. Little obvious change between epochs 10% weak and very slightly smaller in size in second epoch. Steeper gradient on east edge. Determine inner structure of bright radio component using a physically realistic mode. Unresolved radio core plus extended inner jet in direction of more extended structure Best fit of two components shown. Algorithm in difmap to fit observed u-v data directly to model. Approximate positional accuracy is 1.0 mas / SNR; diameter limit is 1.0 mas / SQRT(SNR) Now have position of ‘true’ radio core wrt peak intensity of main component. Does this improve the experiment accuracy?

14. Resultant Motion of G127 with Time Position of G127 with respect to the reference quasar is more stable when the position of the unresolved fitted core is taken as the stationary point, compared with the peak of the bright radio component. Also, a 0.068 mas shift in position. Incidently, no significant proper motion and a parallax < 0.04 mas (two-sigma) Distance > 25 kpc. Extragalactic.

15. 3C279 Frequency Dependence Core  x=+76, y=+127 x= -5, y=+6 x= -18, y=+32 Core Location (  as) 3.5 of 15 Jy 5.5 of 14 Jy 6.0 of 12 Jy (0,0) is location of fringe fit phase center. Oct 1, 2005 Oct 18, 2005 15 GHz 23 GHz 43 GHz -- x y

16. DETERMINATION OF TRUE RADIO CORE (STATIONARY POINT?) General Conclusion: For observations with reasonably high signal-to-noise and a radio structure which conforms to the general physical model of quasars, Position of the true radio core may be obtained to 0.1 mas with respect to the entire source radio extent.

17. COMBINING TECHNIQUES Use phase delays instead of group delays: Must decrease residual model errors – troposphere and instrumental. Better troposphere models, WVR corrections, ‘Petrachenko’ array Small scale phase referencing to global astrometry Multi-source (30) phase referencing at 8 GHz in 15 o radius including about ~8 ICRF sources. Will obtain <0.05 mas relative positions and images (and maybe core positions. Then, connect each region using normal astrometric procedures. Any gain in this? Monitoring of source images (phase) and position changes (group delay). To reach 0.05 mas level, need reasonable evolution of all sources. How to organized this effectively.

18. Astrometry Using ALMA ALMA on its own is a good astrometric/geodetic array! Specifications: Size=15 km, Freq=300 GHz  15 mas fringe = 3 psec 4 dual-pol IF’s of 2 GHz each; maximum spanned BW = 25 GHz 58 12-m telescopes and 7 7-m telescopes Troposphere at 5000 m at Atacama is extremely good. Must do astrometry/geodesy to Calibrate: Antenna location needed to 0.06 mm accuracy! 20 deg phase at 300 GHz  0.02 psec accuracy Developing: WVR (Oxygen line at 360 GHz) to measure wv Accurate tropospheric parameter measurements Probably use group delays from observations. Typical calibrator targets: Quasars. Very variable, but probably very compact Position nearly coincides with optical object Many stars available. Many planets, asteroids easily detectable. VLBI with ALMA. Main difficulty is phasing up array. Need not do entire array