Ground-based optical atomic clocks as a tool to monitor vertical surface motion (2015)
Ruxandra Bondarescu, Andreas Schärer, Andrew Lundgren, György Hetényi, Nicolas Houlié, Philippe Jetzer and Mihai Bondarescu
Geophys. J. Int. (September, 2015) 202 (3): 1770-1774.
According to general relativity, a clock experiencing a shift in the gravitational potential ΔU will measure a frequency change given by Δf/f ≈ ΔU/c^2. The best clocks are optical clocks. After about 7 hr of integration they reach stabilities of Δf/f ∼ 10^−18 and can be used to detect changes in the gravitational potential that correspond to vertical displacements of the centimetre level. At this level of performance, ground-based atomic clock networks emerge as a tool that is complementary to existing technology for monitoring a wide range of geophysical processes by directly measuring changes in the gravitational potential. Vertical changes of the clock's position due to magmatic, post-seismic or tidal deformations can result in measurable variations in the clock tick rate. We illustrate the geopotential change arising due to an inflating magma chamber using the Mogi model and apply it to the Etna volcano. Its effect on an observer on the Earth's surface can be divided into two different terms: one purely due to uplift (free-air gradient) and one due to the redistribution of matter. Thus, with the centimetre-level precision of current clocks it is already possible to monitor volcanoes. The matter redistribution term is estimated to be 3 orders of magnitude smaller than the uplift term. Additionally, clocks can be compared over distances of thousands of kilometres over short periods of time, which improves our ability to monitor periodic effects with long wavelength like the solid Earth tide.Link to (free) ArXiV version and published GJI version.
Testing scalar-tensor theories and parametrized post-Newtonian parameters in Earth orbit (2014)
Andreas Schärer, Raymond Angélil, Ruxandra Bondarescu, Philippe Jetzer, and Andrew Lundgren
Phys. Rev. D 90, 123005 – Published 4 December 2014
We compute the parametrized post-Newtonian (PPN) parameters γ and β for general scalar-tensor theories in the Einstein frame, which we compare to the existing PPN formulation in the Jordan frame for alternative theories of gravity. This computation is important for scalar-tensor theories that are expressed in the Einstein frame, such as chameleon and symmetron theories, which can incorporate hiding mechanisms that predict environment-dependent PPN parameters. We introduce a general formalism for scalar-tensor theories and constrain it using the limit on γ given by the Cassini experiment. In particular, we discuss massive Brans-Dicke scalar fields for extended sources. Next, using a recently proposed Earth satellite experiment, in which atomic clocks are used for spacecraft tracking, we compute the observable perturbations in the redshift induced by PPN parameters deviating from their general relativistic values. Our estimates suggest that |γ−1|∼|β−1|∼10^−6 may be detectable by a satellite that carries a clock with fractional frequency uncertainty Δf/f∼10^−16 in an eccentric orbit around the Earth. Such space experiments are within reach of existing atomic clock technology. We discuss further the requirements necessary for such a mission to detect deviations from Einstein relativity.
Spacecraft Clocks and Relativity: Prospects for Future Satellite Missions (2014)
Raymond Angélil, Prasenjit Saha, Ruxandra Bondarescu, Philippe Jetzer, Andreas Schärer, and Andrew Lundgren
Phys. Rev. D 89, 064067 – Published 31 March 2014
The successful miniaturization of extremely accurate atomic clocks invites prospects for satellite missions to perform precise timing experiments. This will allow effects predicted by general relativity to be detected in Earth’s gravitational field. In this paper we introduce a convenient formalism for studying these effects, and compute the fractional timing differences generated by them for the orbit of a satellite capable of accurate time transfer to a terrestrial receiving station on Earth, as proposed by planned missions. We find that (1) Schwarzschild perturbations will be measurable through their effects both on the orbit and on the signal propagation, (2) frame-dragging of the orbit will be readily measurable, and (3) in optimistic scenarios, the spin-squared metric effects may be measurable for the first time ever. Our estimates suggest that a clock with a fractional timing inaccuracy of 10−16 on a highly eccentric Earth orbit will measure all these effects, while for a low Earth circular orbit like that of the Atomic Clock Ensemble in Space mission, detection will be more challenging.