Second post-Newtonian approximation of scalar-tensor theory of gravity

Deep space laser ranging missions like ASTROD I (Single-Spacecraft Astrodynamical Space Test of Relativity using Optical Devices) and ASTROD, together with astrometry missions like GAIA and LATOR will be able to test relativistic gravity to an unprecedented level of accuracy. More precisely, these missions will enable us to test relativistic gravity to 10^-7–10^-9${10}^{-7}''–''{10}^{-9}$ of the size of relativistic (post-Newtonian) effects, and will require second post-Newtonian approximation of relevant theories of gravity. The first post-Newtonian approximation is valid to 10^-6${10}^{-6}$ and the second post-Newtonian approximation is valid to 10^-12${10}^{-12}$ in terms of post-Newtonian effects in the solar system. The scalar-tensor theory is widely discussed and used in tests of relativistic gravity, especially after the interests in inflation models and in dark energy models. In the Lagrangian, intermediate-range gravity term has a similar form as cosmological term. Here we present the full second post-Newtonian approximation of the scalar-tensor theory including viable examples of intermediate-range gravity. We use Chandrasekhar’s approach to derive the metric coefficients and the equation of the hydrodynamics governing a perfect fluid in the second post-Newtonian approximation in scalar-tensor theory; all terms inclusive of O(c^-4)$\mathrm{O}(c^{-4})$ are retained consistently in the equations of motion.     

Ion and electron superdiffusive transport in the interplanetary space

We study the propagation of energetic particles, accelerated by interplanetary shock waves, upstream of the shock. By using the appropriate propagator, we show that in the case of superdiffusive transport, the time profile of particles accelerated at a traveling planar shock is a power-law with slope 0<γ<1$0<\gamma <1$, at variance with the exponential profile obtained for normal diffusion. By analyzing data sets of interplanetary shocks in the solar wind observed by the Ulysses and the Voyager 2 spacecraft, we find that the time profiles of energetic electrons correspond to power-laws, with slopes γ?0.30–0.98$\gamma ?0.30''–''0.98$, implying a mean square displacement 〈Δx²〉∝t^α$〈\mathrm{\Delta }{x}^2〉\propto t^{\alpha }$, with α=2-γ>1$\alpha =2-\gamma >1$, i.e., superdiffusion. In addition, the propagation of ions is also superdiffusive, with α=1.07–1.13$\alpha =1.07''–''1.13$.     

Validation of the in-flight calibration procedures for the MICROSCOPE space mission

The MICROSCOPE space mission aims to test the Equivalence Principle with an accuracy of 10^-15${10}^{-15}$. The drag-free micro-satellite will orbit around the Earth and embark a differential electrostatic accelerometer including two cylindrical test masses submitted to the same gravitational field and made of different materials. The experience consists in testing the equality of the electrostatic acceleration applied to the masses to maintain them relatively motionless. The accuracy of the measurements exploited for the test of the Equivalence Principle is limited by our a priori knowledge of several physical parameters of the instrument. These parameters are partially estimated on-ground, but with an insufficient accuracy, and an in-orbit calibration is therefore required to correct the measurements. The calibration procedures have been defined and their analytical performances have been evaluated. In addition, a simulator software including the dynamics model of the instrument, the satellite drag-free system and the perturbing environment has been developed to numerically validate the analytical results. After an overall presentation of the MICROSCOPE mission, this paper will describe the calibration procedures and focus on the simulator. Such an in-flight calibration is mandatory for similar space missions taking advantage of a drag-free system.     

A model study of the negative chlorine ion chemistry in the Earth’s mesosphere

An ion chemistry model is used to investigate the negative chlorine ion chemistry of the mesosphere for quiet ionospheric conditions. Model results are presented for high latitudes in February as well as for the equator in Summer. For nighttime, Cl^-${\text{Cl}}^{-}$, Cl^-${\text{Cl}}^{-}$(HCl), and NO₃⁻(HCl) are the most abundant chlorine anions in the mesosphere. The concentration of ClO₃⁻ depends significantly on its stability against collision-induced dissociation. In contrast to previous model predictions, the abundance of Cl^-(_H2O)${\text{Cl}}^{-}({\mathrm{H}}_2\mathrm{O})$ is small. For daytime, photoelectron detachment and photodissociation have pronounced impact on the negative chlorine ion chemistry in the mesosphere. The abundance of all anion cluster is considerably smaller than at night. While Cl^-${\text{Cl}}^{-}$ decreases in the upper mesosphere, its abundance increases at lower altitudes.     

The ultraviolet view of the Magellanic Clouds from GALEX: A first look at the LMC source catalog

The Galaxy Evolution Exporer (GALEX) has performed unprecedented imaging surveys of the Magellanic Clouds (MC) and their surrounding areas including the Magellanic Bridge (MB) in near-UV (NUV, 1771-2831 Å) and far-UV (FUV, 1344-1786 Å) bands at 5^″$5^{″}$ resolution. Substantially more area was covered in the NUV than FUV, particularly in the bright central regions, because of the GALEX FUV detector failure. The 5σ$\sigma$ depth of the NUV imaging varies between 20.8 and 22.7 (ABmag). Such imaging provides the first sensitive view of the entire content of hot stars in the Magellanic System, revealing the presence of young populations even in sites with extremely low star-formation rate surface density like the MB, owing to high sensitivity of the UV data to hot stars and the dark sky at these wavelengths.     

Medium resolution near-infrared spectra of the host galaxies of nearby quasars

We present medium resolution near-infrared host galaxy spectra of low redshift quasars, PG 0844+349$0844+349$ (z = 0.064), PG 1226+023$1226+023$ (z = 0.158), and PG 1426+015$1426+015$ (z = 0.086). The observations were done by using the Infrared Camera and Spectrograph (IRCS) at the Subaru 8.2 m telescope. The full width at half maximum of the point spread function was about 0.3 arcsec by operations of an adaptive optics system, which can effectively resolve the quasar spectra from the host galaxy spectra. We spent up to several hours per target and developed data reduction methods to reduce the systematic noises of the telluric emissions and absorptions. From the obtained spectra, we identified absorption features of Mg I (1.503 μm), Si I (1.589 μm) and CO (6-3) (1.619 μm), and measured the velocity dispersions of PG 0844+349$0844+349$ to be 132 ± 110 km s⁻¹ and PG 1426+015$1426+015$ to be 264 ± 215 km s⁻¹. By using an _MBH–σ$M_{\text{BH}}''–''\sigma$ relation of elliptical galaxies, we derived the black hole (BH) mass of PG 0844+349$0844+349$, log(_MBH/_M⊙)=7.7±5.5$\log (M_{\text{BH}}/M_{\odot })=7.7\pm 5.5$ and PG 1426+015,log(_MBH/_M⊙)=9.0±7.5$1426+015\text{,}\log (M_{\text{BH}}/M_{\odot })=9.0\pm 7.5$. These values are consistent with the BH mass values from broad emission lines with an assumption of a virial factor of 5.5.     

Space debris: Assessing risk and responsibility

We model the orbital debris environment by a set of differential equations with parameter values that capture many of the complexities of existing three-dimensional simulation models. We compute the probability that a spacecraft gets destroyed in a collision during its operational lifetime, and then define the sustainable risk level as the maximum of this probability over all future time. Focusing on the 900- to 1000-km altitude region, which is the most congested portion of low Earth orbit, we find that – despite the initial rise in the level of fragments – the sustainable risk remains below 10^-3${10}^{-3}$ if there is high (>98%) compliance to the existing 25-year postmission deorbiting guideline. We quantify the damage (via the number of future destroyed operational spacecraft) generated by past and future space activities. We estimate that the 2007 FengYun 1C antisatellite weapon test represents ≈1%$\approx 1\%$ of the legacy damage due to space objects having a characteristic size of ?10$?10$ cm, and causes the same damage as failing to deorbit 2.6 spacecraft after their operational life. Although the political and economic issues are daunting, these damage estimates can be used to help determine one-time legacy fees and fees on future activities (including deorbit noncompliance), which can deter future debris generation, compensate operational spacecraft that are destroyed in future collisions, and partially fund research and development into space debris mitigation technologies. Our results need to be confirmed with a high-fidelity three-dimensional model before they can provide the basis for any major decisions made by the space community.     

Anomalies in radiation-collisional kinetics of Rydberg atoms induced by the effects of dynamical chaos and the double Stark resonance

Radiative and collisional constants of excited atoms contain the matrix elements of the dipole transitions and when they are blocked one can expect occurring a number of interesting phenomena in radiation-collisional kinetics. In recent astrophysical studies of IR emission spectra it was revealed a gap in the radiation emitted by Rydberg atoms (RA  ) with values of the principal quantum number of n≈10$n\approx 10$. Under the presence of external electric fields a rearrangement of RA emission spectra is possible to associate with manifestations of the Stark effect. The threshold for electric field ionization of RA   is E≈3·10⁴$E\approx 3·{10}^4$ V/cm for states with n>10$n>10$. This means that the emission of RA   with n≥10$n\ge 10$ is effectively blocked for such fields. In the region of lower electric field intensities the double Stark resonance (or Förster resonance) becomes a key player. On this basis it is established the fact that the static magnetic or electric fields may strongly affect the radiative constants of optical transitions in the vicinity of the Föster resonance resulting, for instance, in an order of magnitude reduction of the intensity in some lines. Then, it is shown in this work that in the atmospheres of celestial objects lifetimes of comparatively long-lived RA states and intensities of corresponding radiative transitions can be associated with the effects of dynamic chaos via collisional ionization. The Föster resonance allows us to manipulate the random walk of the Rydberg electron (RE) in the manifold of quantum levels and hence change the excitation energies of RA, which lead to anomalies in the IR spectra.     

Dynamics of the plasma sheet in the magnetotail: Interrelation of turbulent flows and thin current sheet structures

Dynamics of the magnetotail involves elementary processes of magnetic field merging (reconnection layer formation) occurring on medium spatial scales. Every such process features two different stages, a fast one and a subsequent slower one. The corresponding short time scale _T1$T_1$ is associated with disturbances propagating in the tail lobes. The longer time scale _T2$T_2$ is associated with plasma motions in the plasma sheet. A disturbance appearing in the magnetotail on the time scale _T1$T_1$ results in a loss of equilibrium in the plasma sheet. By means of theoretical argument and numerical simulation, it is shown that the relaxation process which follows on the time scale _T2$T_2$, produces extremely thin embedded current sheets, along with generation of fast plasma flows. The process provides an effective mechanism for transformation of magnetic energy accumulated in the magnetotail, into energy of plasma flows. The fast flows may drive turbulent motions on shorter spatial scales. In their turn, those motions can locally produce very thin current sheets; after that, nonlinear tearing process leads to generation of neutral lines, and reconnection. The latter produces new fast disturbances on the time scale _T1$T_1$ closing the feedback loop.     

On the effects of each term of the geopotential perturbation along the time I: Quasi-circular orbits

This paper provides a useful new method to determine minimum and maximum range of values for the degree and order of the geopotential coefficients required for simulations of orbits of satellites around the Earth. The method consists in a time integration of the perturbing acceleration coming from each harmonic of the geopotential during a time interval T. More precisely, this integral represents the total velocity contribution of a specific harmonic during the period T  . Therefore, for a pre-fixed minimum contribution, for instance 1×10^-8$1\times {10}^{-8}$ m/s during the period of time T, any harmonic whose contribution is below this value can, safely, be neglected. This fact includes some constraints in the degree and order of the terms which are present in the geopotential formula, saving computational efforts compared to the integration of the full model. The advantage of this method is the consideration of other perturbations in the dynamics (we consider the perturbations of the Sun, the Moon, and the direct solar radiation pressure with eclipses), since these forces affect the value of the perturbation of the geopotential, because these perturbations depend on the trajectory of the spacecraft, that is dependent on the dynamical model used. In this paper, we work with quasi-circular orbits and we present several simulations showing the bounds for the maximum degree and order (M) that should be used in the geopotential for different situations, e. g., for a satellite near 500 km of altitude (like the GRACE satellites at the beginning of their mission) we found 35?M?198$35?M?198$ for T=1$T=1$ day. We analyzed the individual contribution of the second order harmonic (_J2$J_2$) and we use its behavior as a parameter to determine the lower limit of the number of terms of the geopotential model. In order to test the accuracy of our truncated model, we calculate the mean squared error between this truncated model and the “full” model, using the CBERS (China-Brazil Earth Resources Satellite) satellite in this test.