Advancing fundamental physics with the Laser Astrometric Test of Relativity

The Laser Astrometric Test of Relativity (LATOR) is an experiment designed to test the metric nature of gravitation—a fundamental postulate of the Einstein’s general theory of relativity. The key element of LATOR is a geometric redundancy provided by the long-baseline optical interferometry and interplanetary laser ranging. By using a combination of independent time-series of gravitational deflection of light in the immediate proximity to the Sun, along with measurements of the Shapiro time delay on interplanetary scales (to a precision respectively better than 0.1 picoradians and 1 cm), LATOR will significantly improve our knowledge of relativistic gravity and cosmology. The primary mission objective is i) to measure the key post-Newtonian Eddington parameter γ with accuracy of a part in 10⁹. $\frac{1}{2}(1-\gamma)$ is a direct measure for presence of a new interaction in gravitational theory, and, in its search, LATOR goes a factor 30,000 beyond the present best result, Cassini’s 2003 test. Other mission objectives include: ii) first measurement of gravity’s non-linear effects on light to ～0.01% accuracy; including both the traditional Eddington β parameter and also the spatial metric’s 2nd order potential contribution (never measured before); iii) direct measurement of the solar quadrupole moment J ₂ (currently unavailable) to accuracy of a part in 200 of its expected size of ??10^???7; iv) direct measurement of the “frame-dragging” effect on light due to the Sun’s rotational gravitomagnetic field, to 0.1% accuracy. LATOR’s primary measurement pushes to unprecedented accuracy the search for cosmologically relevant scalar-tensor theories of gravity by looking for a remnant scalar field in today’s solar system. We discuss the science objectives of the mission, its technology, mission and optical designs, as well as expected performance of this experiment. LATOR will lead to very robust advances in the tests of fundamental physics: this mission could discover a violation or extension of general relativity and/or reveal the presence of an additional long range interaction in the physical law. There are no analogs to LATOR; it is unique and is a natural culmination of solar system gravity experiments.     

Relativistic gravitational deflection of light and its impact on the modeling accuracy for the Space Interferometry Mission

We study the impact of relativistic gravitational deflection of light on the accuracy of future Space Interferometry Mission (SIM). We estimate the deflection angles caused by the monopole, quadrupole and octupole components of gravitational fields for a number of celestial bodies in the solar system. We observe that, in many cases, the magnitude of the corresponding effects is significantly larger than the 1 μas accuracy expected from SIM. This fact argues for the development of a relativistic observational model for the mission that would account for the influence of both static and time-varying effects of gravity on light propagation. Results presented here are different from the ones obtained elsewhere by the fact that we specifically account for the differential nature of the future SIM astrometric measurements. We also obtain an estimate for the accuracy of possible determination of the Eddington’s parameter γ via SIM global astrometric campaign; we conclude that accuracy of ∼7 × 10⁻⁶ is achievable via measurements of deflection of light by solar gravity. The article was translated by the authors.     

The onset of General Relativity: gravitationally redshifted emission lines

We study and quantify gravitational redshift by means of relativistic ray tracing simulations of emission lines. The emitter model is based on thin, Keplerian rotating rings in the equatorial plane of a rotating black hole. Emission lines are characterised by a generalized fully relativistic Doppler factor or redshift associated with the line core. Two modes of gravitational redshift, shift and distortion, become stronger with the emitting region closer to the Kerr black hole. Shifts of the line cores reveal an effect at levels of 0.0015 to 60% at gravitational radii ranging from 10⁵ to 2. The corresponding Doppler factors range from 0.999985 to 0.4048. Line shape distortion by strong gravity, i.e. very skewed and asymmetric lines occur at radii smaller than roughly ten gravitational radii. Gravitational redshift decreases with distance to the black hole but remains finite due to the asymptotical flatness of black hole space–time. The onset of gravitational redshift can be tested observationally with sufficient spectral resolution. Assuming a resolving power of ∼100000, yielding a resolution of ≈0.1 Å for optical and near‐infrared broad emission lines, the gravitational redshift can be probed out to approximately 75000 gravitational radii. In general, gravitational redshift is an indicator of black hole mass and spin as well as for the inclination angle of the emitter, e.g. an accretion disk. We suggest to do multi‐wavelength observations because all redshifted features should point towards the same central mass. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Interaction of relativistic dust grains with the solar radiation field

The effects of the solar radiation field on the propagation of relativistic dust grains are evaluated. It is concluded that relativistic iron grains with energies 10¹⁹ eV will melt in the solar radiation field before they reach the Earth's orbit around the Sun. However iron grains with lower energies will reach the Earth's orbit but grains travelling from the direction of the Sun will melt. This directional anisotropy or fingerprint may be used to search for relativistic dust grains in the primary cosmic rays. The fact that no significant solar system anisotropy has been detected places constraints on the hypothesis that the initiating particles of the extensive air showers are relativistic iron grains.     

Some Aspects of Relativistic Astrometry from Within the Solar System

In this article we outline the structure of a general relativistic astrometric model which has been developed to deduce the position and proper motion of stars from 1 µarcsecond optical observations made by an astrometric satellite orbiting around the Sun. The basic assumption of our model is that the Solar System is the only source of gravity, hence we show how we modeled the satellite observations in a many-body perturbative approach limiting ourselves to the order of accuracy of (v/c)². The microarcsecond observing scenario outlined is that for the GAIA astrometric mission.     

Galactic Sun's motion in the cold dark matter,MOdified Newtonian Dynamics and modified gravity scenarios

We numerically integrate the equations of motion of the Sun in Galactocentric Cartesian rectangular coordinates for –4.5 Gyr ≤ t ≤ 0 in Newtonian mechanics with two different models for the Cold Dark Matter (CDM) halo, in MOdified Newtonian Dynamics (MOND) and in MOdified Gravity (MOG) without resorting to CDM. The initial conditions used come from the latest kinematical determination of the 3D Sun's motion in the Milky Way (MW) by assuming for the rotation speed of the Local Standard of Rest (LSR) the recent value Θ₀ = 268 km s^–1 and the IAU recommended value Θ₀ = 220 km s^–1; the Sun is assumed located at 8.5 kpc from the Galactic Center (GC). For Θ₀ = 268 km s^–1 the birth of the Sun, 4.5 Gyr ago, would have occurred at large Galactocentric distances (12–27 kpc depending on the model used), while for Θ₀ = 220 km s^–1 it would have occurred at about 8.8–9.3 kpc for almost all the models used. The integrated trajectories are far from being circular, especially for Θ₀ = 268 km s^–1, and differ each other with the CDM models yielding the widest spatial extensions for the Sun's orbital path (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Imaging magnetographs for high‐resolution solar observations in the visible and near‐infrared wavelength region

The Coudé feed of the vacuum telescope (aperture D = 65 cm) at the Big Bear Solar Observatory (BBSO) is currently completely remodelled to accommodate a correlation tracker and a high‐order Adaptive Optics (AO) system. The AO system serves two imaging magnetograph systems located at a new optical laboratory on the observatory's 2^nd floor. The InfraRed Imaging Magnetograph (IRIM) is an innovative magnetograph system for near‐infrared (NIR) observations in the wavelength region from 1.0 μm to 1.6 μm. The Visible‐light Imaging Magnetograph (VIM) is basically a twin of IRIM for observations in the wavelength range from 550 nm to 700 nm. Both instruments were designed for high spatial and high temporal observations of the solar photosphere and chromosphere. Real‐time data processing is an integral part of the instruments and will enhance BBSO's capabilities in monitoring solar activity and predicting and forecasting space weather.     

Gregor@night: The future high‐resolution stellar spectrograph for the GREGOR solar telescope

We describe the future night‐time spectrograph for the GREGOR solar telescope and present its science core projects. The spectrograph provides a 3‐pixel resolution of up to R = 87 000 in 45 échelle orders covering the wavelength range 390‐900 nm with three grating settings. An iodine cell can be used for high‐precision radial velocity work in the 500‐630 nm range. The operation of the spectrograph and the telescope will be fully automated without the presence of humans during night‐time and will be based on the successful STELLA control system. Future upgrades include a second optical camera for even higher spectral resolution, a Stokes‐V polarimeter and a link to the laser‐frequency comb at the Vacuum Tower Telescope. The night‐time core projects are a study of the angular‐momentum evolution of “The Sun in Time” and a continuation of our long‐term Doppler imaging of active stars (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

SUMER - Solar Ultraviolet Measurements of Emitted Radiation

The instrument SUMER - Solar Ultraviolet Measurements of Emitted Radiation is designed to investigate structures and associated dynamical processes occurring in the solar atmosphere, from the chromosphere through the transition region to the inner corona, over a temperature range from 10⁴ to 2 × 10⁶ K and above. These observations will permit detailed spectroscopic diagnostics of plasma densities and temperatures in many solar features, and will support penetrating studies of underlying physical processes, including plasma flows, turbulence and wave motions, diffusion transport processes, events associated with solar magnetic activity, atmospheric heating, and solar wind acceleration in the inner corona. Specifically, SUMER will measure profiles and intensities of EUV lines; determine Doppler shifts and line broadenings with high accuracy; provide stigmatic images of the Sun in the EUV with high spatial, spectral, and temporal resolution; and obtain monochromatic maps of the full Sun and the inner corona or selected areas thereof. SUMER will be flown on the Solar and Heliospheric Observatory (SOHO), scheduled for launch in November, 1995. This paper has been written to familiarize solar physicists with SUMER and to demonstrate some command procedures for achieving certain scientific observations.     

A solar super‐flare as cause for the 14C variation in AD 774/5?

We present further considerations regarding the strong ¹⁴C variation in AD 774/5. For its cause, either a solar super‐flare or a short gamma‐ray burst were suggested. We show that all kinds of stellar or neutron star flares would be too weak for the observed energy input at Earth in AD 774/5. Even though Maehara et al. (2012) present two super‐flares with ∼10³⁵ erg of presumably solar‐type stars, we would like to caution: These two stars are poorly studied and may well be close binaries, and/or having a M‐type dwarf companion, and/or may be much younger and/or much more magnetic than the Sun – in any such case, they might not be true solar analog stars. From the frequency of large stellar flares averaged over all stellar activity phases (maybe obtained only during grand activity maxima), one can derive (a limit of) the probability for a large solar flare at a random time of normal activity: We find the probability for one flare within 3000 years to be possibly as low as 0.3 to 0.008 considering the full 1σ error range. Given the energy estimate in Miyake et al. (2012) for the AD 774/5 event, it would need to be ∼2000 stronger than the Carrington event as solar super‐flare. If the AD 774/5 event as solar flare would be beamed (to an angle of only ∼24°), 100 times lower energy would be needed. A new AD 774/5 energy estimate by Usoskin et al. (2013) with a different carbon cycle model, yielding 4 ot 6 time lower ¹⁴C production, predicts 4–6 times less energy. If both reductions are applied, the AD 774/5 event would need to be only ∼4 times stronger than the Carrington event in 1859 (if both had similar spectra). However, neither ¹⁴C nor ¹⁰Be peaks were found around AD 1859. Hence, the AD 774/5 event (as solar flare) either was not beamed that strongly, and/or it would have been much more than 4‐6 times stronger than Carrington, and/or the lower energy estimate (Usoskin et al. 2013) is not correct, and/or such solar flares cannot form (enough) ¹⁴C and ¹⁰Be. The 1956 solar energetic particle event was followed by a small decrease in directly observed cosmic rays. We conclude that large solar super‐flares remain very unlikely as the cause for the ¹⁴C increase in AD 774/5. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Plane of polarization rotation induced by a non-Minkowskian spacetime

Fermat's principle has been used to derive expressions for the curvature and torsion of the path of the electromagnetic radiation in a medium of refractive indexn (= function of space coordinates). Levi-Civita's notion of parallelism further, in conjunction with Brill's results (cf. reference in text) have enabled the derivation (1) of Einstein's formula for the deflection of light, and (2) an expression for the rotation of the plane of polarization, an entirely general relativistic effect, unaccountable in Newtonian physics. Finally, the idea is put forward that the observed rotation of polarization in pulsars might be a purely general relativistic effect due to the non-Minkowskian geometry around them.     

Effect of the stellar inclination angle upon theoretical errors of l = 1 p‐mode parameters

The asteroseismic observations provided by current and future missions like CoRoT or Kepler will have a quality closer to those obtained for the Sun. In this context, tools and methods developed for helioseismology can be applied to other stars. In this paper, we focus on solar‐like oscillations of stars with an unknown rotation axis inclination and study, by means of maximum‐likelihood estimation, the errors on the determination of l = 1 p‐mode parameters. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Diamagnetic pumping near the base of a stellar convection zone

The property of inhomogeneous turbulence in conducting fluids to expel large‐scale magnetic fields in the direction of decreasing turbulence intensity is shown as important for the magnetic field dynamics near the base of a stellar convection zone. The downward diamagnetic pumping confines a fossil internal magnetic field in the radiative core so that the field geometry is appropriate for formation of the solar tachocline. For the stars of solar age, the diamagnetic confinement is efficient only if the ratio of turbulent magnetic diffusivity η_T of the convection zone to the (microscopic or turbulent) diffusivity η_in of the radiative interior is η_T/η_in ≥ 10⁵. Confinement in younger stars requires larger η_T/η_in. The observation of persistent magnetic structures on young solar‐type stars can thus provide evidence for the nonexistence of tachoclines in stellar interiors and on the level of turbulence in radiative cores. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Why Newtonian gravity is reliable in large-scale cosmological simulations

Until now, it has been common to use Newtonian gravity to study the non-linear clustering properties of large-scale structures. Without confirmation from Einstein's theory, however, it has been unclear whether we can rely on the analysis (e.g. near the horizon scale). In this work we will provide confirmation of the use of Newtonian gravity in cosmology, based on the relativistic analysis of weakly non-linear situations to third order in perturbations. We will show that, except for the gravitational-wave contribution, the relativistic zero-pressure fluid equations perturbed to second order in a flat Friedmann background coincide exactly with the Newtonian results. We will also present the pure relativistic correction terms appearing in the third order. The third-order correction terms show that these terms are the linear-order curvature perturbation times the second-order relativistic/Newtonian terms. Thus, the pure general relativistic corrections in the third order are independent of the horizon scale and are small when considering the large-scale structure of the Universe because of the low-level temperature anisotropy of the cosmic microwave background radiation. Since we include the cosmological constant, our results are relevant to currently favoured cosmology. As we prove that the Newtonian hydrodynamic equations are valid in all cosmological scales to second order, and that the third-order correction terms are small, our result has the important practical implication that one can now use the large-scale Newtonian numerical simulation more reliably as the simulation scale approaches and even goes beyond the horizon. In a complementary situation, where the system is weakly relativistic (i.e. far inside the horizon) but fully non-linear, we can employ the post-Newtonian approximation. We also show that in large-scale structures, the post-Newtonian effects are quite small.     

Advancing tests of relativistic gravity via laser ranging to Phobos

Phobos Laser Ranging (PLR) is a concept for a space mission designed to advance tests of relativistic gravity in the solar system. PLR’s primary objective is to measure the curvature of space around the Sun, represented by the Eddington parameter γ, with an accuracy of two parts in 10⁷, thereby improving today’s best result by two orders of magnitude. Other mission goals include measurements of the time-rate-of-change of the gravitational constant, G and of the gravitational inverse square law at 1.5-AU distances—with up to two orders-of-magnitude improvement for each. The science parameters will be estimated using laser ranging measurements of the distance between an Earth station and an active laser transponder on Phobos capable of reaching mm-level range resolution. A transponder on Phobos sending 0.25-mJ, 10-ps pulses at 1 kHz, and receiving asynchronous 1-kHz pulses from earth via a 12-cm aperture will permit links that even at maximum range will exceed a photon per second. A total measurement precision of 50 ps demands a few hundred photons to average to 1-mm (3.3 ps) range precision. Existing satellite laser ranging (SLR) facilities—with appropriate augmentation—may be able to participate in PLR. Since Phobos’ orbital period is about 8 h, each observatory is guaranteed visibility of the Phobos instrument every Earth day. Given the current technology readiness level, PLR could be started in 2011 for launch in 2016 for 3 yr of science operations. We discuss the PLR’s science objectives, instrument, and mission design. We also present the details of science simulations performed to support the mission’s primary objectives.     

A diffraction limit on the gravitational lens effect

The focussing of gravitational radiation by the interior and exterior gravitational field of a Newtonian gravitational lens is considered. A graphical method for determining the caustic structure of a Newtonian gravitational lens is presented and the caustic structure of a solar type gravitational lens is discussed. Estimates of the amplitude magnification in the caustic region indicate that waves with frequencies less than a critical cutoff frequency ω _c are not amplified significantly. For a lens of massM this cutoff frequency is ω _c ≈(10^-1πM)^-1; for the Sun ω _c ≈10⁴s^-1. Work supported in part by National Science Foundation Grant PHY78-05368.     

Solar dynamo models with α ‐effect and turbulent pumping from local 3D convection calculations

Results from kinematic solar dynamo models employing α ‐effect and turbulent pumping from local convection calculations are presented. We estimate the magnitude of these effects to be around 2–3 m s^–1, having scaled the local quantities with the convective velocity at the bottom of the convection zone from a solar mixing‐length model. Rotation profile of the Sun as obtained from helioseismology is applied in the models; we also investigate the effects of the observed surface shear layer on the dynamo solutions. With these choices of the small‐ and large‐scale velocity fields, we obtain estimate of the ratio of the two induction effects, C _α /C _Ω ≈ 10^–3, which we keep fixed in all models. We also include a one‐cell meridional circulation pattern having a magnitude of 10–20 m s^–1 near the surface and 1–2 m s^–1 at the bottom of the convection zone. The model essentially represents a distributed turbulent dynamo, as the α ‐effect is nonzero throughout the convection zone, although it concentrates near the bottom of the convection zone obtaining a maximum around 30° of latitude. Turbulent pumping of the mean fields is predominantly down‐ and equatorward. The anisotropies in the turbulent diffusivity are neglected apart from the fact that the diffusivity is significantly reduced in the overshoot region. We find that, when all these effects are included in the model, it is possible to correctly reproduce many features of the solar activity cycle, namely the correct equatorward migration at low latitudes and the polar branch at high latitudes, and the observed negative sign of B _r B _ϕ . Although the activity clearly shifts towards the equator in comparison to previous models due to the combined action of the α ‐effect peaking at midlatitudes, meridional circulation and latitudinal pumping, most of the activity still occurs at too high latitudes (between 5° … 60°). Other problems include the relatively narrow parameter space within which the preferred solution is dipolar (A0), and the somewhat too short cycle lengths of the solar‐type solutions. The role of the surface shear layer is found to be important only in the case where the α ‐effect has an appreciable magnitude near the surface. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Speckle spectro‐polarimetry of magnetic structures

Two‐dimensional spectrograms were obtained with the Vacuum Tower Telescope, Tenerife, in order to study small‐scale structures and faculae on the Sun. Using the speckle reconstruction method, we obtain high‐resolution images and wavelength scans. Magnetic fields can be studied from Stokes V profiles, and velocity maps are gained by the Doppler shift of the center of gravity of Stokes I. Here some results about small‐scale structures and their magnetic fields are shown.     

Differential rotation and meridional flow of Arcturus

The spectroscopic variability of Arcturus hints at cyclic activity cycle and differential rotation. This could provide a test of current theoretical models of solar and stellar dynamos. To examine the applicability of current models of the flux transport dynamo to Arcturus, we compute a mean‐field model for its internal rotation, meridional flow, and convective heat transport in the convective envelope. We then compare the conditions for dynamo action with those on the Sun. We find solar‐type surface rotation with about 1/10th of the shear found on the solar surface. The rotation rate increases monotonically with depth at all latitudes throughout the whole convection zone. In the lower part of the convection zone the horizontal shear vanishes and there is a strong radial gradient. The surface meridional flow has maximum speed of 170 m/s and is directed towards the equator at high and towards the poles at low latitudes. Turbulent magnetic diffusivity is of the order 10¹⁵–10¹⁶ cm²/s. The conditions on Arcturus are not favorable for a circulation‐dominated dynamo (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic Flux Imbalance of the Solar and Heliospheric Magnetic Fields

A comparative analysis of solar and heliospheric magnetic fields in terms of their cumulative sums reveals cyclic and long-term changes that appear as a magnetic flux imbalance and alternations of dominant magnetic polarities. The global magnetic flux imbalance of the Sun manifests itself in the solar mean magnetic field (SMMF) signal. The north – south asymmetry of solar activity and the quadrupole mode of the solar magnetic field contribute the most to the observed magnetic flux imbalance. The polarity asymmetry exhibits the Hale magnetic cycle in both the radial and azimuthal components of the interplanetary magnetic field (IMF). Analysis of the cumulative sums of the IMF components clearly reveals cyclic changes in the IMF geometry. The accumulated deviations in the IMF spiral angle from its nominal value also demonstrate long-term changes resulting from a slow increase of the solar wind speed over 1965 – 2006. A predominance of the positive IMF B _z with a significant linear trend in its cumulative signal is interpreted as a manifestation of the relic magnetic field of the Sun. Long-term changes in the IMF B _z are revealed. They demonstrate decadal changes owing to the 11/22-year solar cycle. Long-duration time intervals with a dominant negative B _z component were found in temporal patterns of the cumulative sum of the IMF B _z .