Sun's Gravitational Potential Research Articles

Improved Limits for Violations of Local Position Invariance from Atomic Clock Comparisons.

We compare two optical clocks based on the ^{2}S_{1/2}(F=0)→^{2}D_{3/2}(F=2) electric quadrupole (E2) and the ^{2}S_{1/2}(F=0)→^{2}F_{7/2}(F=3) electric octupole (E3) transition of ^{171}Yb^{+} and measure the frequency ratio ν_{E3}/ν_{E2}=0.932829404530965376(32), improving upon previous measurements by an order of magnitude. Using two caesium fountain clocks, we find ν_{E3}=642121496772645.10(8) Hz, the most accurate determination of an optical transition frequency to date. Repeated measurements of both quantities over several years are analyzed for potential violations of local position invariance. We improve by factors of about 20 and 2 the limits for fractional temporal variations of the fine structure constant α to 1.0(1.1)×10^{-18}/yr and of the proton-to-electron mass ratio μ to -8(36)×10^{-18}/yr. Using the annual variation of the Sun's gravitational potential at Earth Φ, we improve limits for a potential coupling of both constants to gravity, (c^{2}/α)(dα/dΦ)=14(11)×10^{-9} and (c^{2}/μ)(dμ/dΦ)=7(45)×10^{-8}.

Thermalization time scales for WIMP capture by the Sun in effective theories

I study the process of dark matter capture by the Sun, under the assumption of a Weakly Interacting Massive Particle (WIMP), in the framework of non-relativistic effective field theory. Hypothetically, WIMPs from the galactic halo can scatter against atomic nuclei in the solar interior, settle to thermal equilibrium with the solar core and annihilate to produce an observable flux of neutrinos. In particular, I examine the thermalization process using Monte-Carlo integration of WIMP trajectories. I consider WIMPs in a mass range of 10–1000 GeV and WIMP-nucleon interaction operators with different dependence on spin and transferred momentum. I find that the density profiles of captured WIMPs are in accordance with a thermal profile described by the Sun's gravitational potential and core temperature. Depending on the operator that governs the interaction, the majority of the thermalization time is spent in either the solar interior or exterior. If normalizing the WIMP-nuclei interaction strength to a specific capture rate, I find that the thermalization time differs at most by 3 orders of magnitude between operators. In most cases of interest, the thermalization time is many orders of magnitude shorter than the age of the solar system.

Is the effect of the Sun's gravitational potential on dark matter particles observable?

We consider the effect of the Sun's gravitational potential on the local phase space distribution of dark matter particles, focusing on its implication for the annual modulation signal in direct detection experiments. We perform a fit to the modulation signal observed in DAMA/LIBRA and show that the allowed region shrinks if Solar gravitational focusing (GF) is included compared to the one without GF. Furthermore, we consider a possible signal in a generic future direct detection experiment, irrespective of the DAMA/LIBRA signal. Even for scattering cross sections close to the current bound and a large exposure of a xenon target with 270 ton yr it will be hard to establish the presence of GF from data. In the region of dark matter masses below 40 GeV an annual modulation signal can be established for our assumed experimental setup, however GF is negligible for low masses. In the high mass region, where GF is more important, the significance of annual modulation itself is very low. We obtain similar results for lighter targets such as Ge and Ar. We comment also on inelastic scattering, noting that GF becomes somewhat more important for exothermic scattering compared to the elastic case.

Effect of Gravitational Focusing on Annual Modulation in Dark-Matter Direct-Detection Experiments

The scattering rate in dark-matter direct-detection experiments should modulate annually due to Earth's orbit around the Sun. The rate is typically thought to be extremized around June 1, when the relative velocity of Earth with respect to the dark-matter wind is maximal. We point out that gravitational focusing can alter this modulation phase. Unbound dark-matter particles are focused by the Sun's gravitational potential, affecting their phase-space density in the lab frame. Gravitational focusing can result in a significant overall shift in the annual-modulation phase, which is most relevant for dark matter with low scattering speeds. The induced phase shift for light O(10) GeV dark matter may also be significant, depending on the threshold energy of the experiment.

Testing antimatter gravity with muonium

The debate about how antimatter or different antimatter systems behave gravitationally will be ultimately decided by experiments measuring directly the acceleration of various antimatter probes in the gravitational field of the Earth or perhaps redshift effects in antimatter atoms caused by the annual variation of the Sun's gravitational potential at the location of the Earth. Muonium atoms may be used to probe the gravitational interaction of leptonic, second generation antimatter. We discuss the progress of our work towards enabling such experiments with muonium.

Testing Local Position Invariance with Four Cesium-Fountain Primary Frequency Standards and Four NIST Hydrogen Masers

We report the most sensitive tests to date of the assumption of local position invariance (LPI) underlying general relativity, based on a 7 yr comparison of cesium and hydrogen atomic clocks (frequency standards). The latest results place an upper limit that is over 20 times smaller than the previous most sensitive tests; this is consistent with the null shift predicted by LPI. The result is based on precise comparisons of frequencies of four hydrogen masers maintained by NIST, with four independent Cs fountain clocks--one at NIST and three in Europe--as the Sun's gravitational potential at Earth's surface varies due to Earth's orbital eccentricity.

Is it possible to measure the Lense-Thirring effect on the orbits of the planets in the gravitational field of the Sun?

Here we explore a novel approach in order to try to measure the post-Newtonian 1/c^2 Lense-Thirring secular effect induced by the gravitomagnetic field of the Sun on the planetary orbital motion. Due to the relative smallness of the solar angular momentum J and the large values of the planetary semimajor axes a, the gravitomagnetic precessions, which affect the nodes Omega and the perihelia omega and are proportional to J/a^3, are of the order of 10^-3 arcseconds per century only for, e.g., Mercury. This value lies just at the edge of the present-day observational sensitivity in reconstructing the planetary orbits, although future missions to Mercury like Messenger and BepiColombo could allow to increase it. The major problems come from the main sources of systematic errors. They are the aliasing classical precessions induced by the multipolar expansion of the Sun's gravitational potential and the classical secular N-body precessions which are of the same order of magnitude or much larger than the Lense-Thirring precessions of interest. This definitely rules out the possibility of analyzing only one orbital element of, e.g., Mercury. In order to circumvent these problems, we propose a suitable linear combination of the orbital residuals of the nodes of Mercury, Venus and Mars which is, by construction, independent of such classical secular precessions. A 1-sigma reasonable estimate of the obtainable accuracy yields a 36% error. Since the major role in the proposed combination is played by the Mercury's node, it could happen that the new, more accurate ephemerides available in future thanks to the Messenger and BepiColombo missions will offer an opportunity to improve the present unfavorable situation.

Solar Rotation Measurements at Mount Wilson over the Period 1990–1995

One of the most fundamental properties of the Sun is its rate of rotation. Kinetic energy of large-scale circulation might interact with rotation and cause the surface rate to vary throughout the solar cycle. The solar wind carries off angular momentum from the Sun, and the coupling between the outer and inner parts of the heliosphere might produce effects that are evident in the photosphere and chromosphere. The quadrapole moment of Sun's gravitational potential depends on the rotation rate. The interaction between rotation, convection, and solar magnetic fields forms the solar dynamo which governs the solar cycle of activity. Although the rate of solar rotation has been measured for decades, several key questions remain: What is the rotation rate, and what is the uncertainty in this value? Does the rotation rate depend on the solar cycle? Can the gradient of rotation rate as a function of distance from the solar center be detected within the solar atmosphere? The synoptic program of solar observations carried out at the 150 foot tower of the Mount Wilson Observatory has long been a source of measurements which address these questions. Improvements in the facilities of this program over the past decade have led to a reduction in the errors of measurement which now permit a new examination of these questions. Key improvements were: 12/81?installation of a fiber-optic image reformattor to select the spectral sampling of the absorption lines; 2/86?multiple daily observations were begun; 12/87?the Cr II line at ?5237.3 was added to the regular program of observation; 9/90?the grating mount and alignment system were replaced; 7/91?the polarization analysis optics were placed in a new alignment box and index matching fluid was introduced around the KDP variable retarder; 11/95?antireflection optics were installed for the KDP end windows to reduce interference fringes. Each of these changes resulted in a noticeable reduction in the rms error in the measured rotation rate which is now at the level of 7 m s-1. Within this error we find that there is no solar cycle variation in the rotation rate and the rate is the same for both ?5250 and ?5237. We find that the synodic rotation rate is 2.84 ? 0.01 ?rad s-1. This value agrees well with most recent determinations.