Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Oleg Titov (Geoscience Australia) Anastasiia Girdiuk (Institute of Applied Astronomy, RAS)

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Outline 1. Introduction – General Relativity in geodetic VLBI 2. Gravitational delay vs light deflection angle 3. Observational results 4. Extra deflection with VLBI 5. Conclusion

Introduction 1.Geodetic Very Long Baseline Interferometry (VLBI) measures the group delay with accuracy up to 30 ps; 2.General relativity is presented by the gravitational delay and a coordinate term in the geometric delay; 3.Gravitational delay caused by the Sun gravitational field is about 40 ns near the Sun and about 400 ps in opposite direction; Deflection of light induced by the Sun gravity field and measured with geodetic VLBI

Introduction 1.Geodetic Very Long Baseline Interferometry (VLBI) measures the group delay with accuracy up to 30 ps; 2.General relativity is presented by the gravitational delay and a coordinate term in the geometric delay; 3.Gravitational delay caused by the Sun gravitational field is about 40 ns near the Sun and about 400 ps in opposite direction; Deflection of light induced by the Sun gravity field and measured with geodetic VLBI

Introduction Deflection of light induced by the Sun gravity field and measured with geodetic VLBI

Introduction Deflection of light induced by the Sun gravity field and measured with geodetic VLBI

Light deflection angle vs gravitational delay Q – quasar, B – deflecting body (Sun) b Q B   s

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Light deflection angle vs gravitational delay Q – quasar, B – deflecting body (Sun)

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Difference between two models

Light deflection angle vs gravitational delay Deflection angle for arbitrary  … …now explicitly presented in the equation for the VLBI group delay Deflection of light induced by the Sun gravity field and measured with geodetic VLBI

Light deflection angle vs gravitational delay

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Observational results 1. Geodetic VLBI data from Gravitational delay and coordinate term in geometric delay were switched off for a set of selected radio sources 3. Equatorial coordinates of the selected radio sources were estimated as daily parameters for each 24-hour VLBI sessions 4. The estimated coordinates are converted to the deflection angle  and PPN parameter .

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Light deflection angle

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Light deflection angle

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Light deflection angle Minimum elongation 2 .6

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Light deflection angle vs elongation

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Light deflection angle vs elongation

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Light deflection angle vs elongation

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Light deflection angle vs elongation

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Light deflection angle vs elongation

New formula: benefits 1. Simple; 2. Consistent with the geometric part of group delay model; 3. Linked to the deflection angle directly; 4. Free off coordinate terms; 5. Partial derivate for  is optimal; 6. Allows more flexibility; 7. Looking good as an alternative option for IERS Conventions Deflection of light induced by the Sun gravity field and measured with geodetic VLBI

Outreach – “When GR works?” OpticalVLBI During Solar eclipseAny time (365 days, 24/7) Near the SunAny elongation angle Optical instrumentRadio telescopes Nice sunny dayAny weather condition ~1”.75 0”.001  1”

Observations If all the general relativity effects are switched off the VLBI group delay model, the light deflection angle will be observed at any moment and at any elongation of a radio sources to the Sun (the closer, the better). The old good time (before 2002) when the radio sources were observed close to the Sun (as close as 1 .5). The PPN parameter  was estimated very accurately (  0.001) from a standard 24-hour session, if the number of delays is  100. The accuracy would be about  , were a dedicated session for observation of a strong radio source within 3  arranged. Deflection of light induced by the Sun gravity field and measured with geodetic VLBI

The “minor” terms (  = 1) The minor terms are not negligible in the small angle approximation (   0) Deflection of light induced by the Sun gravity field and measured with geodetic VLBI

The “minor” terms Deflection of light induced by the Sun gravity field and measured with geodetic VLBI

The “minor” terms for the Sun The additional deflection angle is individual for all baselines R (km)  b=3000 kmb=10000 km 700,000 (grazing light, 0 .25) 1”.750” ”0125 0”.450” ” ”.220” ” ”.090” ” Deflection of light induced by the Sun gravity field and measured with geodetic VLBI

The “minor” terms for Jupiter R (km)  b=3000 kmb=10000 km 70,000 (grazing light, 20”)0”.0160” ” ,000 (1’)0”.00530” ” ,000 (2’)0”.00260” ” For grazing light Deflection of light induced by the Sun gravity field and measured with geodetic VLBI

The “minor” terms The additional deflection angle is individual for all baselines and could be detected with observations within 2  from the Sun and 2’ from Jupiter Total magnitude Deflection of light induced by the Sun gravity field and measured with geodetic VLBI

Additional angle and its geometric interpretation Q – apparent position; Q’ – true position; B – deflecting body, b Q B   Q’ 

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Additional angle may be observed Q – apparent position; Q’ – true position; B – deflecting body, Q Q’ B B b Traditional deflection angle (unobservable) Additional deflection angle (observable), if b/R ~ 0.1

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Close alignment of star and radio source Separation is less than 2”

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI Conclusion 1. General relativity effects in VLBI could be expressed in term of the light deflection angle  ; 2. The light deflection angle could be estimated for an arbitrary elongation from the Sun with high precision; 3. The equation for light deflection at arbitrary elongation was tested using a set of VLBI data; 4. The PPN parameter  was estimated for several 24-hour sessions with accuracy Additional deflection angle could be observed for a close approach to the Sun or Jupiter; 6. A dedicated observational programs for detection of the additional angle are required.

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