Technical Considerations on VLBI Astrometry with FAST Zhihan Qian（钱志瀚） and Bo Zhang（张波） Shanghai Astronomical Observatory, CAS Outline Existing VLBI stations in China (CVN) The sensitivity of CVN with FAST at L—band Requirements of accuracy of FAST station positions for VLBI astrometry Determination of reference point of FAST Phase—referencing for relative astrometry with FAST Suggestions on FAST VLBI Astrometry in early stage 2015/7/29-31 FAST2015

Exisiting VLBI Stations in China Diameter (m) Coordinates Band Tianma 65 31 06N 121 08 E L, S/X, C, X/Ka, Ku, K, Q Sheshan 25 121 12 E L, S/X, C, K Miyun 50 40 33N 116 09 E S/X Kunming 40 25 02N 102 48 E Urumqi 43 28N 87 11 E L, S/X, C, K, Q * S/X is common band 2015/7/29-31 FAST2015

Exisiting VLBI stations and FAST in China 北京密云 上海天马 2015/7/29-31 FAST2015 FAST

L-band only SH(25) UR(25) 3249km 2645km TM(65) 1525km FAST(300) 北京 密云 上海 佘山 2645km TM(65) 1525km 昆明 FAST(300) FAST2015

Sensitivities of baselines of CVN with FAST at L-band Antenna parameters Sensitivities of baselines Antenna Diameter (m) Tsys (K)  SEFD (Jy) FAST 300m 25K 0.5 1.95 TM 65m 0.6 34.7 UR 25m 234 Baseline Bandwidth Smin (t=10min) Smin (t=4hr) FAST——TM 300MHz 14Jy 2.8Jy FAST——UR 36Jy 7.3Jy TM——UR 150Jy 31Jy * Smin=1 2015/7/29-31 FAST2015

Comparison of baseline sensitivity and observed source number Baseline Length Relative Smin Relative Observed Source Number TMUR 3249km 1 FASTUR 2645km 0.23 8.9 FASTTM 1525km 0.09 35 2015/7/29-31 FAST2015

Baseline resolution(=18cm) Baseline Length SNR , (as) TMUR 3249km 10 182 FASTUR 2645km 43 52 FASTTM 1525km 111 35 Sc=0.3 mJy ; t=4hr 2015/7/29-31 FAST2015

Using HSA: Arecibo, VLBA, GBT, Effelsberg. Importance of high sensitivity & high precision astrometry A sample: VLBI Resolution of Pleiades Distance Controversy Using HSA: Arecibo, VLBA, GBT, Effelsberg. From: Carl Melis et al, 2014 2015/7/29-31 FAST2015

Astrometric errors caused by baseline errors Absolute astrometry: Let: B=1.0 cm, B=1500 km; =0.0014(1.4 mas) Relative astrometry: Let: B=1.0 cm, Δ=3; =0.000073(73 as) Δ=1; =0.000024(24 as) 2015/7/29-31 FAST2015

Requirements of baseline victor accuracy of TM-FAST for relative astrometry FAST is suitable for relative astrometry Sources of baseline errors Station position errors EOP (Earth Orientation Parameter) errors Model errors of Earth solid tides and ocean tides Model errors of water and atmosphere loading, and so on Sources of station position errors Stability of reference point of antenna Measurement errors of reference point Requirements of TM—FAST baseline accuracy If Δ3, 1.00 mas; B137 cm 0.10 mas; B13.7 cm 0.01 mas; B1.37 cm 2015/7/29-31 FAST2015

Reference Point of FAST Definition: “O” is the reference point of FAST. Measurement: Firstly, to measure the positions of feed and illuminated reflector in a local geodetic reference frame; Secondly, to derive the positions of reference point “O” in a local geodetic reference frame; Finally, to transfer positions of “O” into International VLBI reference frame. From: FAST Project Documents 2015/7/29-31 FAST2015

VLBI PhaseReferencing Observing methods: Simultaneously observing reference and target sources In-beam (2.5 for FAST at =18cm) Using a nearby small antenna to observe reference sources Alternately observing reference and target sources (It is not suitable for FAST) 2015/7/29-31 FAST2015

Using two antennas in FAST site for phase-referencing observations To construct a new antenna (12m or larger) nearby FAST for the observations of the reference sources (as well for the geodetic VLBI observations); To observe the target sources by FAST; Recently, there are a new 65m antenna and a old 25m antenna separated about 6km in Sheshan area, Shanghai. Therefore, it is possible to do VLBI phase-referencing observations using 4-antenna mode if there is an another antenna nearby FAST. 2015/7/29-31 FAST2015

4Antenna Interferometer (FASTTM baseline) for VLBI phase-referencing observations 北京 密云 上海 佘山 1525 昆明 FAST2015

Conclusions The VLBI astrometry plays an important role for the astronomical research. The CVN including FAST will become a very powerful VLBI network around the world. The sensitivity of CVN will reach dozens Jy with enough SNR for VLBI astrometry. The requirements of the accuracy for the FAST reference point should be less than 10cm in order to obtain better than 0.1 mas accuracy of the positions of target sources in the early stage. It is very useful to construct a small antenna nearby the FAST for VLBI phase-referencing observations. (See Arecibo Online News, June 28, 2010) The suggestions on the FAST VLBI astrometry in the early stage: Pulsar VLBI astrometry, especially, for the new pulsars discovered by FAST pulsar survey. Detection of extra-solar planets by VLBI astrometry. 2015/7/29-31 FAST2015

To detect the wobble of the parent star for estimation of the orbit and the mass of extra-solar planet 2015/7/29-31 FAST2015

Thank you for your attention 2015/7/29-31 FAST2015