Laser Interferometry for a future GRACE follow-on mission Marina Dehne, Felipe Guzmán Cervantes, Gerhard Heinzel and Karsten Danzmann

Introduction 1670 Isaac Newton with his Law of Gravitation questioned the pure spheric geometry of Earth: Flattening of the poles and enlargement of the Equator due to rotation → Spheroid Today: → Equatorial radius approx. 21 km larger than radius at the poles

Spheroid (reference ellipsoid) Gravitational acceleration g=9,81 ms-² Increase of 0,02 ms-² at poles Gravity at Equator g-ω2r=9,78 ms-² Gravity depends on latitude Units of gravity: Gal = 10-2 ms-2 or mGal = 10-5 ms-2

Geoid undulations Geoid: undulating equipotential surface that closely matches Mean Sea Level Geoid undulation: deviation between geoid and ellipsoid → ± 100 meters Geoid Ellipsoid Ocean topographic surface

Geoid undulations Geoid: undulating equipotential surface that closely matches Mean Sea Level Geoid undulation: deviation between geoid and ellipsoid → ± 100 meters mGal

Gravity anomalies Irregular mass distributions with different density distribution Effective gravity field differs from nominal gravity field: → Gravity anomalies: ± 500 mGal

Temporal changes of gravity field Gravity field changes in time → Possible explanations: Changes in distribution of Atmospheric masses Oceanic water masses Continental water masses (ground water) Ice masses in Antarctica and Greenland Solid earth (postglacial rebound)

Temporal changes of gravity field Effect on relevant climatic phenomena Investigations of Earth system dynamics Effects are small and hard to disentangle → High temporal and spatial resolution necessary, (long time span) CHAMP (2000), GRACE (2002) and GOCE (2008)

GRACE (Gravity Recovery And Climate Experiment) Satellite to satellite tracking (SST): Separation: 220 km Altitude: ~500 km (decline orbit) Measurement: microwaves in K-band Relative range Relative velocity (range rate)

GRACE (Gravity Recovery And Climate Experiment) Mission concept: Approaching a mass anomaly: satellite 1 accelerates Passing across a mass anomaly: satellite 1 slows down, satellite 2 accelerates By moving away from mass anomaly: satellite 2 slows down

Comparison between obtained accuracies 1cm@275km

Challenges for future gravity satellite missions We‘re at the very beginning! Sneeuw et al., 2005

Aim of GRACE follow-on mission Aim: temporal and spatial resolution enhancement, (long time scales) Improvement of measurement system → Laser interferometry → SSI (Satellite-to-Satellite-Interferometry) Lower altitude Improvement of „drag-free“ control systems Improvement of the data post-processing

GRACE follow-on mission Short separation between two satellites: e.g. 10 km Laser interferometer (SSI) → Benefit from LISA and LISA Pathfinder (LTP) Low Earth Orbit Significant drag → „drag-free“ technology of LISA Pathfinder

Interferometer concept Large dynamic range (several wavelengths) Baseline: heterodyne interferometer absolute heterodyne frequency larger than maximal Doppler shift → fhet= 500 kHz

Requirement I Distance fluctuations: Sensitivity with LTP better than 3 orders of magnitude (pm/√Hz) SSI requirements achievable!

Requirement II Already achieved at our labs! Laser frequency noise: Interferometer with unequal arms Pathlength difference corresponds to the armlength → ΔL = L = 10 km Laser frequency noise translates to interferometric phase noise For resolution of δL < 1 nm/√Hz between 10mHz and 100mHz (measured by M. Tröbs) Already achieved at our labs!

Interferometer with polarising optics Two possible ways to separate incoming and outgoing beams: non-polarising optics polarising optics Advantage of pol. optics: Freedom to choose LO-Level Utilization of all light for interference Possible disadvantages: Thermal stability of polarising optics

Polarising interferometer breadboarding Modulation bench: laser + 2 AOMs @ approx. 80 MHz fhet = 1,6 kHz Fiber coupling to optical bench Optical bench: 3 Mach-Zehnder interferometers (2 non-pol +1 pol)

Sensitivity limited by mechanical stability of current setup First results Sensitivity limited by mechanical stability of current setup Next step: bonding!

Bonded optical bench 4 interferometers: (3 non-polarising + 1 polarising)

Bonded optical bench 4 interferometers: (3 non-polarising + 1 polarising) Reference Interferometer

Bonded optical bench 4 interferometers: (3 non-polarising + 1 polarising) Non-polarising Interferometer

Bonded optical bench 4 interferometers: (3 non-polarising + 1 polarising) Polarising Interferometer

Bonded optical bench 4 interferometers: (3 non-polarising + 1 polarising) Interferometer for frequency stabilisation

Outlook: heterodyne interferometry 500 kHz/phasemeter Operate bonded optical bench with fhet = 500 kHz Phasemeter has been adapted already Phasemeter for variable frequencies Include Doppler shift in phasemeter processing (LISA-like PM)

Summary Measure the Earth’s gravitational field with much higher resolution Constellation of 2 satellites separated by 10 km in a Low-Earth-Orbit Measurement technique is heterodyne laser interferometry (benefit from LISA and LPF experience!). Breadboarding on possible optical configurations has started Investigations on interferometry with polarising components at mHz (also relevant for LISA)

Thank you for your attention! Albert Einstein Institute www.lisa.aei-hannover.de Hannover Max Planck Institute for Gravitational Physics Thank you for your attention!

Resolution of gravity anomalies CHAMP GRACE Gravity anomalies (mgal) derived from the EIGEN-CHAMP03S (left) and EIGEN-GRACE02S (right) models.