V. Rudenko (SAI MSU), N. Bartel (York U.), L. Gurvits (JIVE), K. Belousov (ASC), M. Bietenholz (HartRAO), A. Biriukov (ASC), W. Cannon (York U.),

G. Cimo’ (JIVE), A. Fionov (SAI MSU), A. Gusev (SAI MSU), C. Gwinn (UCSB), D. Duev (JIVE), M. Johnson (UCSB), V. Kauts (ASC), G. Kopelyansky (ASC),

A. Kovalenko (PRAO), V. Kulagin (SAI MSU), D. Litvinov (SAI MSU), G. Molera (JIVE), S. Pogrebenko (JIVE), N. Porayko (SAI MSU),

S. Sazankov (ASC), A. Skripkin (Comcon), V. Soglasnov (ASC), K. Sokolovsky (ASC)

Probing the Gravitational Redshift Effect with the RadioAstron satellite

Astro Space Center of the Lebedev Physical Institute (Russia)Lavochkin Scientific and Production Association (Russia)

Sternberg Astronomical Institute (Russia)Keldysh Institute for Applied Mathematics (Russia)

York University (Canada)Joint Institute for VLBI in Europe (the Netherlands)

University of California in Santa-Barbara (USA)Hartebeesthoek Radio Observatory (South Africa)

Rencontre de Moriond, 21–28 March 2015

• Einstein obtained the gravitational redshift formula in 1906 considering the equivalence of homogeneous gravity field and inertia (accelerated reference system)

• a test of the grav. redshift effect is a test of the EP : measurement of the free fall acceleration of a photon

• RS astro test with Sirius B (W. Adams, 1925): light from massive stars arrives with decreased frequency

2// c

2cRGMstar

EP – fundamental basis of GR

GR postulates equivalence of gravity and inertia

• UFF – for test bodies ( ~ 10-12 – 10-13 )

• UGR – for photons ( ~ 10-4 )

• LLI – for physical laws ( ~ 10-4 )

PPN parameters

curvature – 1 ~ 10-5 light-time delaylight deflection

nonlinearity – 1 ~ 10-4 perihelion shiftred shift in 2nd order

h~104kmf/f=/~gh/c2~10-9

vmin~ 6 cm/s

f/f)H10-13

±0,01%

GP-A , 1976

(P/Q) – 2 (R/S)•

•[1+(N/M)2 ] -1/2 0

Online compensation

- Doppler shift

- atmospheric shift

Gravitational red shift experiment with SRT “Radioastron”

increase sensitivity due to the measurement repetition

10^{-4} 10^{-5}

Moon highly evolving orbit

Period: 8 – 10 day

GRS modulation: 0.4∙10-10 – 5.8∙10-10

280,000 – 350,000 km

1,000 – 80,000 km

6.8∙10 -10

9.4∙10 -11 – 6.4∙10 -10

RadioAstron orbit

Orbit determination accuracy

Position: 100 m radio, 10 cm SLR

Velocity: 1 mm/s

Radio links:8.4 GHz down (tone)15 GHz down (data)7.2 GHz up (tone)S-band T&C

Green Bank tracking station (USA)

Pushchino tracking station (Russia)

Effelsberg (Germany) Yebes (Spain)

Svetloe (Russia) GBT (USA)

VCH-1010 Hydrogen maser frequency standard of the space radio telescope “RadioAstron”

log y()

log

Allan deviation: stochastic and systematic

VCH-1010 (RadioAstron) vs. VLG-10 (GP-A)

Averaging time , s

FREQUENCY METHOD: CLOCK MOTION

meteo data + model

,

orbit

1st-order Doppler effect8.4 GHz link

Date (January 2014)

1st-order Dopplergeocentric distance

Distance, 103

km

Gravitational redshift and 2nd-order Doppler effect8.4 GHz link

Date (January 2014)

2nd-order Dopplergeocentric distance gravitational redshift

Distance, 103

km

GRAVITATIONAL REDSHIFT EXPERIMENT WITH THE SRT “RADIOASTRON”

Contributions to the total frequency shift of the 8.4 GHz signal. Puschino TS, Oct 2012

GRAVITATIONAL REDSHIFT EXPERIMENT WITH THE SRT “RADIOASTRON”

AGREEMENT BETWEEN THEORY AND EXPERIMENT: 3%

Residual frequency of the 8.4 GHz signal. Puschino TS, Oct 2012

geocentric distanceresidual frequency

Date (October)

Dista

nce, 103

km

Gravity Probe A (1976)

RadioAstron radio links operating modes

1-way “H-Maser” mode 2-way “Coherent” mode

RadioAstron radio links operating modes

Mixed “Semi-Coherent” mode

Biriukov et al. 2014, Astron. Rep. 58, N.11, p. 783

softwareprocessing

Spectrum of the 15 GHz signal, transmitted data is noise-like

SRT RADIOASTRON ON-BOARD HARDWARE SYNCHRONIZATION: “SEMI-COHERENT” MODE

Frequency, Hz

“Semi-Coherent” + “Test-2” incompatibility with astronomy

Spectrum of the 15 GHz signal “Test-2” mode

SRT RADIOASTRON ON-BOARD HARDWARE SYNCHRONIZATION:“SEMI-COHERENT” MODE

2015/02/15 Onsala, 8.4 GHz, 2-wayRecorded signal spectrum

Frequency, Hz

2015/02/15 Onsala, 8.4 GHz, 2-waySignal phase

Session time, s

Frequency, Hz

2015/02/15 Onsala, 8.4 GHz, 2-wayStopped-phase signal spectrum

f 0.001 Hz

SRT RADIOASTRON ON-BOARD HARDWARE SYNCHRONIZATION: “SEMI-COHERENT” MODE

Select components of the 15 GHz signal spectrum31 Aug 2014, Puschino TS, 08:20:00 UTC, mode: “Test-2” 18 MHz

Number of observing telescopes near perigee in 2016

~10 experiments at <10,000 km distance and

Number of observing telescopes near perigee in 2016

Experiment accuracy

Signal frequency instability at 1000 s 1 10–14 to 2 10–14 *)

Systematic errors:

space and ground clock drift over 1 experiment

uncertainties due to orbit determination errors

2 10–15

2 10–15

U/c2 variation 2 10–10 to 4 10–10

Experiment accuracy

(15 sessions 1+1 hr, 2 telescopes on average)

2 10–5

*) Work in progress

GRAVITATIONAL REDSHIFT TESTS

MissionLaunch/

statusFrequency standard

Achieved/planned accuracy

Gravity Probe A1976

completedH-maser 1.4∙10-4

RadioAstron2011

activeH-maser 2∙10-5

ACES 2016Cs-fountain +

H-maser2∙10-6

STE-Quest ≥ 2026 ? 2∙10-8

Thanks for attention