Galileo gravitational Redshift test with Eccentric satellites (GREAT)

Galileo gravitational Redshift test with Eccentric satellites (GREAT) P. DELVA and N. PUCHADES SYRTE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, LNE ACES Workshop Fundamental and applied science with clocks and cold atoms in space University Zurich, Switzerland, June 29 30, 2017 Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 1 / 25

Outline 1 Galileo satellites 201 and 202 2 Gravitational redshift test 3 Data analysis Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 2 / 25

Galileo satellites 201 and 202 Outline 1 Galileo satellites 201 and 202 2 Gravitational redshift test 3 Data analysis Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 3 / 25

Galileo satellites 201 and 202 The Galileo system 24 satellites + 6 spares in medium Earth orbit on three orbital planes [actually 18]; A global network of sensor stations receiving information from the Galileo satellites; Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 4 / 25

Galileo satellites 201 and 202 The Galileo system 24 satellites + 6 spares in medium Earth orbit on three orbital planes [actually 18]; A global network of sensor stations receiving information from the Galileo satellites; The control centres computing information and synchronising the time signal of the satellites; Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 4 / 25

Galileo satellites 201 and 202 The story of Galileo satellites 201 & 202 Galileo satellites 201 & 202 were launched with a Soyuz rocket on 22 august 2014 on the wrong orbit due to a technical problem Launch failure was due to a temporary interruption of the joint hydrazine propellant supply to the thrusters, caused by freezing of the hydrazine, which resulted from the proximity of hydrazine and cold helium feed lines. Paco me DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 5 / 25

Galileo satellites 201 and 202 Galileo satellites 201&202 orbit Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 6 / 25

Gravitational redshift test Outline 1 Galileo satellites 201 and 202 2 Gravitational redshift test 3 Data analysis Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 7 / 25

Gravitational redshift test Gravity Probe A (GP-A) (1976) Test of the gravitational redshift on a single parabola [Vessot and Levine, 1979, Vessot et al., 1980, Vessot, 1989] Continuous two-way microwave link between a spaceborne hydrogen maser clock and ground hydrogen masers Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 8 / 25

Gravitational redshift test Gravity Probe A (GP-A) (1976) Test of the gravitational redshift on a single parabola [Vessot and Levine, 1979, Vessot et al., 1980, Vessot, 1989] Continuous two-way microwave link between a spaceborne hydrogen maser clock and ground hydrogen masers Frequency shift verified to 7 10 5 Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 8 / 25

Gravitational redshift test Gravity Probe A (GP-A) (1976) Test of the gravitational redshift on a single parabola [Vessot and Levine, 1979, Vessot et al., 1980, Vessot, 1989] Continuous two-way microwave link between a spaceborne hydrogen maser clock and ground hydrogen masers Frequency shift verified to 7 10 5 Gravitational redshift verified to 1.4 10 4 Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 8 / 25

Gravitational redshift test TOPEX/POSEIDON Relativity Experiment (1995) N. Ashby, Living Rev. Rel. (2003) RMS deviation between theory and experiment is 2.2% Evidence of systematic bias during some particular passes Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 9 / 25

Gravitational redshift test Why Galileo 201 & 202 are perfect candidates? An elliptic orbit induces a periodic modulation of the clock bias at orbital frequency ( τ(t) = 1 3Gm ) 2ac 2 t 2 Gma c 2 e sin E(t) + Cste 0.4 0.3 0.2 0.1 Very good stability of the on-board atomic clocks test of the variation of the redshift 0-0.1-0.2-0.3-0.4 Jul 31 Aug 01 Aug 02 Aug 03 Aug 04 2015 Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 10 / 25

Gravitational redshift test Why Galileo 201 & 202 are perfect candidates? An elliptic orbit induces a periodic modulation of the clock bias at orbital frequency ( τ(t) = 1 3Gm ) 2ac 2 t 2 Gma c 2 e sin E(t) + Cste 0.4 0.3 0.2 0.1 0-0.1-0.2 Very good stability of the on-board atomic clocks test of the variation of the redshift Satellite life-time accumulate the relativistic effect on the long term -0.3-0.4 Jul 31 Aug 01 Aug 02 Aug 03 Aug 04 2015 Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 10 / 25

Gravitational redshift test Why Galileo 201 & 202 are perfect candidates? An elliptic orbit induces a periodic modulation of the clock bias at orbital frequency ( τ(t) = 1 3Gm ) 2ac 2 t 2 Gma c 2 e sin E(t) + Cste 0.4 0.3 0.2 0.1 0-0.1-0.2-0.3-0.4 Jul 31 Aug 01 Aug 02 Aug 03 Aug 04 2015 Very good stability of the on-board atomic clocks test of the variation of the redshift Satellite life-time accumulate the relativistic effect on the long term Visibility the satellite are permanently monitored by several ground receivers Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 10 / 25

Gravitational redshift test Galileo gravitational Redshift test with Eccentric satellites Two parallel studies funded by ESA: SYRTE/Observatoire de Paris and ZARM/University of Bremen Improvement of the orbit/clock solution by ESA/ESOC using enhanced models Improvement of Solar Radiation Pressure (SRP) modelling with finite element method Dedicated Laser ranging campaign launched with ILRS community to disentangle clock and orbit radial errors Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 11 / 25

Gravitational redshift test Galileo gravitational Redshift test with Eccentric satellites Two parallel studies funded by ESA: SYRTE/Observatoire de Paris and ZARM/University of Bremen Improvement of the orbit/clock solution by ESA/ESOC using enhanced models Improvement of Solar Radiation Pressure (SRP) modelling with finite element method Dedicated Laser ranging campaign launched with ILRS community to disentangle clock and orbit radial errors Processing more data from the 2 Galileo eccentric satellites (GAL-201 & 202) so to further improve the statistics Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 11 / 25

Data analysis Outline 1 Galileo satellites 201 and 202 2 Gravitational redshift test 3 Data analysis Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 12 / 25

Data analysis Flowchart for the time approach Satellite orbits (sp3 files) Clock Bias (clk files) SLR residuals (res files) Coordinate to proper time transformation Pre-processing Model of systematics Theoretical clock bias Corrected clock bias Clock bias systematics Test of gravitational redshift Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 13 / 25

Data analysis Data availability GAL-201 sp3 time: 618.00 days clk time: 615.86 days GAL-202 sp3 time: 592.00 days clk time: 590.99 days Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 14 / 25

Data analysis Transformation from ITRS to ITRF: GAL-201 Use of SOFA routines Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 15 / 25

Data analysis Theoretical clock bias: contributions (GAL-201) 0.4 0.2 2 10-5 0.3 0.15 1.5 0.2 0.1 1 0.1 0.05 0.5 0 0 0-0.1-0.05-0.5-0.2-0.1-1 -0.3-0.15-1.5-0.4 Jul 31 Aug 01 Aug 02 Aug 03 Aug 04 2015-0.2 Jul 31 Aug 01 Aug 02 Aug 03 Aug 04 2015-2 Jul 31 Aug 01 Aug 02 Aug 03 Aug 04 2015 x = [ 1 GM rc 2 v 2 2c 2 GMR2 0 J 2 ( 1 3 cos 2 2r 3 c 2 θ ) ] dt; Note: for a keplerian orbit, gravitational (GM) and velocity contributions are equal for the periodic part. Here the maximum difference is 20 ps. Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 16 / 25

Data analysis Clock bias drift: GAL-201 10 1.5 8 1 6 0.5 4 0 2-0.5 0-1 -2 Jul 2014 Jan 2015 Jul 2015 Jan 2016 Jul 2016 Jan 2017 Jul 2017-1.5 Jul 2014 Jan 2015 Jul 2015 Jan 2016 Jul 2016 Jan 2017 Jul 2017 The clock bias drift is 34 µs.d 1 ( 3.9 10 10 ). Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 17 / 25

Data analysis Systematic effects in clock residuals 0.3 5 4 0.2 3 0.1 2 1 0 0-0.1-1 -2-0.2-3 -4 Jul 2014 Jan 2015 Jul 2015 Jan 2016 Jul 2016 Jan 2017 Jul 2017-0.3 Aug 01 Aug 02 Aug 03 Aug 04 Aug 05 Aug 06 Aug 07 2015 We remove one linear fit per day: x= X i ( 1 for day i fi (t)(ai + bi t), fi (t) = 0 otherwise Paco me DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 18 / 25

Data analysis Fit of the GR deviation model 0.3 5 Data minus daily linear fits Fitted GR deviation Data minus daily linear fits Fitted GR deviation 4 0.2 3 0.1 2 1 0 0-0.1-1 -2-0.2-3 -4 Jul 2014 Jan 2015 Jul 2015 Jan 2016 Jul 2016 Jan 2017 Jul 2017 x= X i -0.3 Aug 01 Aug 02 Aug 03 Aug 04 Aug 05 Aug 06 Aug 07 2015 Z GM GMR02 J2 2 fi (t)(ai + bi t) + α 1 3 cos θ dt 2 rc 2r 3 c 2 Paco me DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 19 / 25

Data analysis Systematic errors [Delva et al., 2015] 1 Effects acting on the frequency of the reference ground clock can be safely neglected 2 Effects on the links (mismodeling of atmospheric delays, variations of receiver/antenna delays, multipath effects, etc...) very likely to be uncorrelated with the looked for signal, averages with the number of ground stations 3 Effects acting directly on the frequency of the space clock (temperature and magnetic field variations on board the Galileo satellites) 4 Orbit modelling errors (e.g. mismodeling of Solar Radiation Pressure) are strongly correlated to the clock solution Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 20 / 25

Data analysis Systematic errors [Delva et al., 2015] 1 Effects acting on the frequency of the reference ground clock can be safely neglected 2 Effects on the links (mismodeling of atmospheric delays, variations of receiver/antenna delays, multipath effects, etc...) very likely to be uncorrelated with the looked for signal, averages with the number of ground stations 3 Effects acting directly on the frequency of the space clock (temperature and magnetic field variations on board the Galileo satellites) 4 Orbit modelling errors (e.g. mismodeling of Solar Radiation Pressure) are strongly correlated to the clock solution Condidering systematic errors, simulations have shown that Galileo 5 and 6 can improve on the GP-A (1976) limit on the gravitational redshift test, down to an accuracy of (3 4) 10 5 with at least one year of data. Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 20 / 25

Data analysis Systematic effects in clock residuals Orbital frequency: 1.855 d 1 ( 13 hours period) July 2016: Change of clock from PHM B to PHM A... Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 21 / 25

Data analysis Systematic effects in clock residuals: PHM B Orbital frequency: 1.855 d 1 ( 13 hours period) β = 0 in June 2015 figure from Steigenberger et al, AdSR 55, 2015. Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 22 / 25

Data analysis Conclusion Opportunity to improve gravitational redshift constraint thanks to the launch failure of Galileo satellites 201 and 202 Two ESA GREAT projects: SYRTE and ZARM Without taking into account systematics, current constraint is around the level of Gravity Probe A Investigation of systematic effects is on-going: dedicated one-year ILRS/SLR campaign Other fundamental tests using atomic clocks [Delva et al., 2017] Test of Special Relativity Using a Fiber Network of Optical Clocks, Phys. Rev. L, 118(22) [Pihan-Le Bars et al., 2017] Lorentz-Symmetry Test at Planck-Scale Suppression with Nucleons in a Spin-Polarized 133 Cs Cold Atom Clock, Phys. Rev. D, 95(7) [Hees et al., 2016] Searching for an Oscillating Massive Scalar Field as a Dark Matter Candidate Using Atomic Hyperfine Frequency Comparisons, Phys. Rev. L, 117(6) Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 23 / 25

Data analysis Literature I Delva, P., Hees, A., Bertone, S., Richard, E., and Wolf, P. (2015). Test of the gravitational redshift with stable clocks in eccentric orbits: Application to Galileo satellites 5 and 6. Class. Quantum Grav., 32(23):232003. Delva, P., Lodewyck, J., Bilicki, S., Bookjans, E., Vallet, G., Le Targat, R., Pottie, P.-E., Guerlin, C., Meynadier, F., Le Poncin-Lafitte, C., Lopez, O., Amy-Klein, A., Lee, W.-K., Quintin, N., Lisdat, C., Al-Masoudi, A., Dörscher, S., Grebing, C., Grosche, G., Kuhl, A., Raupach, S., Sterr, U., Hill, I. R., Hobson, R., Bowden, W., Kronjäger, J., Marra, G., Rolland, A., Baynes, F. N., Margolis, H. S., and Gill, P. (2017). Test of Special Relativity Using a Fiber Network of Optical Clocks. Physical Review Letters, 118(22):221102. Hees, A., Guéna, J., Abgrall, M., Bize, S., and Wolf, P. (2016). Searching for an Oscillating Massive Scalar Field as a Dark Matter Candidate Using Atomic Hyperfine Frequency Comparisons. Physical Review Letters, 117(6):061301. Pihan-Le Bars, H., Guerlin, C., Lasseri, R.-D., Ebran, J.-P., Bailey, Q. G., Bize, S., Khan, E., and Wolf, P. (2017). Lorentz-symmetry test at Planck-scale suppression with nucleons in a spin-polarized 133 Cs cold atom clock. Phys. Rev. D, 95(7):075026. Vessot, R. F. C. (1989). Clocks and spaceborne tests of relativistic gravitation. Advances in Space Research, 9:21 28. Vessot, R. F. C. and Levine, M. W. (1979). A test of the equivalence principle using a space-borne clock. General Relativity and Gravitation, 10:181 204. Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 24 / 25

Data analysis Literature II Vessot, R. F. C., Levine, M. W., Mattison, E. M., Blomberg, E. L., Hoffman, T. E., Nystrom, G. U., Farrel, B. F., Decher, R., Eby, P. B., and Baugher, C. R. (1980). Test of relativistic gravitation with a space-borne hydrogen maser. Phys. Rev. Lett., 45:2081 2084. Pacôme DELVA (SYRTE/Obs.Paris) GREAT 2017 ACES Workshop 25 / 25