The Potential of Continuous, Local Atomic Clock Measurements for Earthquake Prediction and Volcanology

Modern optical atomic clocks along with the optical fiber technology currently being developed can measure the geoid, which is the equipotential surface that extends the mean sea level on continents, to a precision that competes with existing technology. In this proceeding, we point out that atomic clocks have the potential to not only map the sea level surface on continents, but also look at variations of the geoid as a function of time with unprecedented timing resolution. The local time series of the geoid has a plethora of applications. These include potential improvement in the predictions of earthquakes and volcanoes, and closer monitoring of ground uplift in areas where hydraulic fracturing is performed.

Atomic clocks as a tool to monitor vertical surface motion

Atomic clock technology is advancing rapidly, now reaching stabilities of $Delta f/f sim 10^{-18}$, which corresponds to resolving $1$ cm in equivalent geoid height over an integration timescale of about 7 hours. At this level of performance, ground-based atomic clock networks emerge as a tool for monitoring a variety of geophysical processes by directly measuring changes in the gravitational potential. Vertical changes of the clocks position due to magmatic, volcanic, post-seismic or tidal deformations can result in measurable variations in the clock tick rate. As an example, we discuss the geopotential change arising due to an inflating point source (Mogi model), and apply it to the Etna volcano. Its effect on an observer on the Earths surface can be divided into two different terms: one purely due to uplift 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 2-3 orders of magnitude smaller than the uplift term, and should be resolvable when clocks improve their stability to the sub-millimetre level. Additionally, clocks can be compared over distances of thousands of kilometres on a short-term basis (e.g. hourly). These clock networks will improve our ability to monitor periodic effects with long-wavelength like the solid Earth tide.

The Physics of the Far Future

We observe the past and present of the universe, but can we predict the far future? Observations suggest that in thousands of billions of years from now most matter and radiation will be absorbed by the cosmological horizon. As it absorbs the contents of the universe, the cosmological horizon is pushed further and further away. In time, the universe asymptotes towards an equilibrium state of the gravitational field. Flat Minkowski space is the limit of this process. It is indistinguishable from a space with an extremely small cosmological constant (Lambda -> 0) and thus has divergent entropy.

Merging Gravitation with Thermodynamics to Understand Cosmology

We discuss the evolution of the universe in the context of the second law of thermodynamics from its early stages to the far future. Cosmological observations suggest that most matter and radiation will be absorbed by the cosmological horizon. On the local scale, the matter that is not ejected from our supercluster will collapse to a supermassive black hole and then slowly evaporate. The history of the universe is that of an approach to the equilibrium state of the gravitational field.

Geophysical applicability of atomic clocks: direct continental geoid mapping

The geoid is the true physical figure of the Earth, a particular equipotential surface of the gravity field of the Earth that accounts for the effect of all subsurface density variations. Its shape approximates best (in the sense of least squares) the mean level of oceans, but the geoid is more difficult to determine over continents. Satellite missions carry out distance measurements and derive the gravity field to provide geoid maps over the entire globe. However, they require calibration and extensive computations including integration, which is a non-unique operation. Here we propose a direct method and a new tool that directly measures geopotential differences on continents using atomic clocks. General Relativity Theory predicts constant clock rate at sea level, and faster (resp. slower) clock rate above (resp. below) sea level. The technology of atomic clocks is on the doorstep of reaching an accuracy level in clock rate that is equivalent to 1 cm in determining equipotential surface (including geoid) height. We discuss the value and future applicability of such measurements including direct geoid mapping on continents, and joint gravity and geopotential surveying to invert for subsurface density anomalies. Our synthetic calculations show that the geoid perturbation caused by a 1.5 km radius sphere with 20% density anomaly buried at 2 km depth in the crust of the Earth is already detectable by atomic clocks of achievable accuracy. Therefore atomic clock geopotential surveys, used together with relative gravity data to benefit from their different depth sensitivities, can become a useful tool in mapping density anomalies within the Earth.

Lukewarm dark matter: Bose condensation of ultralight particles

We discuss the thermal evolution and Bose-Einstein condensation of ultra-light dark matter particles at finite, realistic cosmological temperatures. We find that if these particles decouple from regular matter before Standard model particles annihilate, their temperature will be about 0.9 K. This temperature is substantially lower than the temperature of CMB neutrinos and thus Big Bang Nucleosynthesis remains unaffected. In addition the temperature is consistent with WMAP 7-year+BAO+H0 observations without fine-tuning. We focus on particles of mass of $msim 10^{-23}$ eV, which have Compton wavelengths of galactic scales. Agglomerations of these particles can form stable halos and naturally prohibit small scale structure. They avoid over-abundance of dwarf galaxies and may be favored by observations of dark matter distributions. We present numerical as well as approximate analytical solutions of the Friedmann-Klein-Gordon equations and study the cosmological evolution of this scalar field dark matter from the early universe to the era of matter domination. Today, the particles in the ground state mimic presureless matter, while the excited state particles are radiation like.

Spinning down newborn neutron stars: nonlinear development of the r-mode instability

We model the nonlinear saturation of the r-mode instability via three-mode couplings and the effects of the instability on the spin evolution of young neutron stars. We include one mode triplet consisting of the r-mode and two near resonant inertial modes that couple to it. We find that the spectrum of evolutions is more diverse than previously thought. The evolution of the star is dynamic and initially dominated by fast neutrino cooling. Nonlinear effects become important when the r-mode amplitude grows above its first parametric instability threshold. The balance between neutrino cooling and viscous heating plays an important role in the evolution. Depending on the initial r-mode amplitude, and on the strength of the viscosity and of the cooling this balance can occur at different temperatures. If thermal equilibrium occurs on the r-mode stability curve, where gravitational driving equals viscous damping, the evolution may be adequately described by a one-mode model. Otherwise, nonlinear effects are important and lead to various more complicated scenarios. Once thermal balance occurs, the star spins-down oscillating between thermal equilibrium states until the instability is no longer active. For lower viscosity we observe runaway behavior in which the r-mode amplitude passes several parametric instability thresholds. In this case more modes need to be included to model the evolution accurately. In the most optimistic case, we find that gravitational radiation from the r-mode instability in a very young, fast spinning neutron star within about 1 Mpc of Earth may be detectable by advanced LIGO for years, and perhaps decades, after formation. Details regarding the amplitude and duration of the emission depend on the internal dissipation of the modes of the star, which would be probed by such detections.

Spin Evolution of Accreting Neutron Stars: Nonlinear Development of the R-mode Instability

The nonlinear saturation of the r-mode instability and its effects on the spin evolution of Low Mass X-ray Binaries (LMXBs) are modeled using the triplet of modes at the lowest parametric instability threshold. We solve numerically the coupled equations for the three mode amplitudes in conjunction with the spin and temperature evolution equations. We observe that very quickly the mode amplitudes settle into quasi-stationary states. Once these states are reached, the mode amplitudes can be found algebraically and the system of equations is reduced from eight to two equations: spin and temperature evolution. Eventually, the system may reach thermal equilibrium and either (1) undergo a cyclic evolution with a frequency change of at most 10%, (2) evolve toward a full equilibrium state in which the accretion torque balances the gravitational radiation emission, or (3) enter a thermogravitational runaway on a very long timescale of about $10^6$ years. Alternatively, a faster thermal runaway (timescale of about 100 years) may occur. The sources of damping considered are shear viscosity, hyperon bulk viscosity and boundary layer viscosity. We vary proprieties of the star such as the hyperon superfluid transition temperature T_c, the fraction of the star that is above the threshold for direct URCA reactions, and slippage factor, and map the different scenarios we obtain to ranges of these parameters. For all our bound evolutions the r-mode amplitude remains small $sim 10^{-5}$. The spin frequency is limited by boundary layer viscosity to $ u_{max} sim 800 Hz [S_{ns}/(M_{1.4} R_6)]^{4/11} T_8^{-2/11}$. We find that for $ u > 700$ Hz the r-mode instability would be active for about 1 in 1000 LMXBs and that only the gravitational waves from LMXBs in the local group of galaxies could be detected by advanced LIGO interferometers.