Deflection of light induced by the sun gravity field and measured with geodetic vlbi
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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). Outline. 1. Introduction – General Relativity in geodetic VLBI 2. Gravitational delay vs light deflection angle

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

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Deflection of light induced by the sun gravity field and measured with geodetic vlbi

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

Oleg Titov (Geoscience Australia)

AnastasiiaGirdiuk (Institute of Applied Astronomy, RAS)


Outline

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

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


Introduction

Introduction

  • Geodetic Very Long Baseline Interferometry (VLBI) measures the group delay with accuracy up to 30 ps;

  • General relativity is presented by the gravitational delay and a coordinate term in the geometric delay;

  • 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


Introduction1

Introduction

  • Geodetic Very Long Baseline Interferometry (VLBI) measures the group delay with accuracy up to 30 ps;

  • General relativity is presented by the gravitational delay and a coordinate term in the geometric delay;

  • 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


Introduction2

Introduction

  • Effect of general relativity is split into two separate terms;

  • Gravitational delay is expressed as a function of the barycentric distances and . Geometric delay is a function of baseline length

  • Light deflection angle is not presented – no link to the optical astrometry.

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


Introduction3

Introduction

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


Light deflection angle vs gravitational delay

Light deflection angle vs gravitational delay

  • Q – quasar, B – deflecting body (Sun)

b

Q

s

B

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


Light deflection angle vs gravitational delay1

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


Deflection of light induced by the sun gravity field and measured with geodetic vlbi

Difference between two models

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


Deflection of light induced by the sun gravity field and measured with geodetic vlbi

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


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

Observational results

  • 1. Geodetic VLBI data from 1991-2001

  • 2. 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 1803 784

Light deflection angle 1803+784

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


Light deflection angle 1606 106

Light deflection angle 1606+106

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


Light deflection angle 1334 127

Light deflection angle 1334-127

  • Minimum elongation 2.6

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


Light deflection angle vs elongation 1606 106

Light deflection angle vs elongation 1606+106

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


Light deflection angle vs elongation 1606 1061

Light deflection angle vs elongation 1606+106

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


Light deflection angle vs elongation 1606 1062

Light deflection angle vs elongation 1606+106

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


Light deflection angle vs elongation 0229 131

Light deflection angle vs elongation 0229+131

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


Light deflection angle vs elongation 0229 1311

Light deflection angle vs elongation 0229+131

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


New formula b enefits

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

Outreach – “When GR works?”

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


Observations

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 0.0001, 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 ( = 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

The “minor” terms

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


The minor terms for the sun

The “minor” terms for the Sun

The additional deflection angle is individual for all baselines

For geodetic VLBI observation of the radio sources near the Solar limb

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


The minor terms for jupiter

The “minor” terms for Jupiter

Angular size

Mass g

=70.000 km

For grazing light

For geodetic VLBI observation of the radio sources near Jupiter

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


The minor terms1

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

Additional angle and its geometric interpretation

  • Q – apparent position;

  • Q’ – true position;

  • B – deflecting body,

Q



Q’

b

B

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


Additional angle may be observed

Additional angle may be observed

  • Q – apparent position;

  • Q’ – true position;

  • B – deflecting body,

Q

B

Q’

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 0758 737

Close alignment of star and radio source 0758-737

  • Separation is less than 2”

0758-737

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


Conclusion

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 0.001.

  • 5. 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.

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


Any questions

Any Questions?

  • Thank you for your attention

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