Observations of radio sources near the Sun · General Relativity 1. Eddington detected the...
Transcript of Observations of radio sources near the Sun · General Relativity 1. Eddington detected the...
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Observations of radio sources near the Sun
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EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
Einstein predicted the light deflection for the Solar gravitational
field on 1”.75 for the Solar radius R ~ 700.000 km (1915).
Rc
GM2
4 R
General Relativity
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General Relativity
1. Eddington detected the deflection in 1919;
Dyson, Eddington and Davidson (1920)
EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
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Equation for the light deflection at
arbitrary elongation (Shapiro, 1967)
2
22
ctg
rc
GM
Rc
GM
Rc
GM22
1(24
= 1 in General Relativity;
Parametrised Post-Newtonian (PPN) approximation (Will, 1973)
a constant parameter for all elongations θ
2
1(
2
222
ctg
rc
GMctg
rc
GM
Small angle approximation θ → 01
𝑟𝑐𝑡𝑔
𝜃
2=2
𝑅
α = 1”.75 for grazing light,
𝑅 = 𝑅⊙
EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
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Time delay vs light deflection
,ln
)1(3 srr
srr
22
11
c
GMgrav
))((1
1
2
)(1)(
1)(
2
)1(1
)(
2
22
2
2
2
2
wVs
sVVb
wVVsb
c
ccccrc
GM
c
geom
rc
GM
cc
GMcoordgravGR 23
)(1(ln
1( sb
srr
srr
22
11
𝜏𝐺𝑅 = 𝛼𝑏
𝑐𝑠𝑖𝑛𝜑𝑐𝑜𝑠𝐴 +⋯ 𝛼 =
1 + 𝛾 𝐺𝑀
𝑐2𝑟𝑐𝑡𝑔
𝜃
2
EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
Titov & Girdiuk A&A(2015)
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ICRF3 related problems
Light deflection in VLBI
elongation ( ), degrees
0 20 40 60 80 100 120 140 160 180
de
fle
ctio
n,
arc
se
c
0.0
0.1
0.2
0.3
0.4
0.5
arcsec
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
arc
se
c
0.0
0.1
0.2
0.3
0.4
0.5
2~
ctg
For a radio source within 1 from Sun
rrV
1~)(
cos1
sin22
Rc
GMShapiro, Science, (1967); Ward, ApJ, (1970)
EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
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Test of General Relativity with VLBI
1. The gravitational delay includes the PPN parameter gamma,
which is estimated using a large set of geodetic VLBI (since
1980s).
2. The current accuracy of the γ estimate is σ ≈ 2 × 10−4 ,
whereas numerous modifications of the theory of gravity
predict deviation from γ=1 at level of Δγ = 10−6 ÷ 10−7
3. From the “Cassini” experiment σ ≈ 2 × 10−5 (Bertotti et al.
2003)
EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
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Test of General Relativity with VLBI
From “Cassini” σ ~ 5102 Bertotti et al (2003)
EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
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Single VLBI experiment to estimate parameter γ
AUA020 - 1 May 2017 with 7 radio telescopes (Asia, Australia, South Africa,Europe), data correlated in Shanghai Astronomical Observatory
24-hour experiment
first 6 hours and the last hour
– standard geodetic schedule
17 hours – focusing on two
radio sources near the Sun
Experiment AUA020 - custom designed and scheduled (IVS OPC did notsupport the R&D proposal)
EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
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Two radio sources were observed within 1°-3° from the Sun during 17 hours
>1000 observations
452 obs of 0235+164
(from 1º.5 to 1º.15)
577 obs of 0229+131
(from 2º.2 to 2º.6)
Single VLBI experiment to estimate parameter γ
EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
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Solar corona electon density
First determination of both
power-law parameters N0 & β •2+ radio sources close to the Sun
needed
(Soja et al. EGU 2018)
EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
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Estimation of PPN parameter γ (ICRF2)
To find correction Δγ
AUA020 vs all other IVS
sessions
Estimation of Δγ ·10−4
0235+164 1.16 +/- 1.29
0229+131 0.32 +/- 2.83
In general relativity γ = 1
Both sources
Δγ = 0.89 (+/- 0.94) ·10−4, i. e.better than from a global
solution
EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
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Testing general relativity with geodetic VLBI
EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
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Estimation of PPN parameter γ (OCCAM vs SOLVE)
Estimation of Δγ ·10−4
OCCAM SOLVE
0235+164 1.64 +/- 1.29 1.85 +/- 1.48
0229+131 0.32 +/- 2.83 -6.84 +/- 2.53
Both sources 0.89 +/- 0.94 -0.26 +/- 1.09
New global solution done by Sebastien Lambert using VLBI data since 1979
(6301 sessions, 12.6 millions delays) provides σ = 0.92 ∙ 10−4 with AUA020
and σ = 0.97 ∙ 10−4 without AUA020
EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
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Single VLBI experiment AOV022
1 May 2018 with 9 radio telescopes (Asia, Australia, South Africa, Europe,NZ), data correlated in Shanghai Astronomical Observatory
0229+131, Ishioka - Kunming
MJD
58239.9 58240.0 58240.1 58240.2 58240.3 58240.4
cm
-10
-8
-6
-4
-2
0
2
4
6
0229+131, Kunming - Zelenchk
MJD
58240.10 58240.15 58240.20 58240.25 58240.30 58240.35 58240.40cm
-1
0
1
2
3
4
Post-fit residuals show a strong systematic depending on baseline.
Strong source structure effect – needs to be cleaned
EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
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Conclusion
1. VLBI observations at small elongation angles are important
2. Solar corona could be estimated if two radio sources are
measured at different elongation angles
3. AUA020 - formal accuracy of the PPN parameter γ is better
than 10−4
4. Estimate of γ is sensitive to the coordinates of the reference
radio sources
EVGA 2019, Las Palmas de Gran Canaria, Observations of radio sources near the Sun
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