Inversion of satellite gradiometry data using statistically modified integral formulas for local gravity field recovery

The satellite gravity gradiometric data can be used directly to recover the gravity anomaly at sea level using inversion of integral formulas. This approach suffers by the spatial truncation errors of the integrals, but these errors can be reduced by modifying the formulas. It allows us to consider smaller coverage of the satellite data over the region of recovery. In this study, we consider the second-order radial derivative (SORD) of disturbing potential (T_rr) and determine the gravity anomaly with a resolution of 1° × 1° at sea level by inverting the statistically modified version of SORD of extended Stokes’ formula. Also we investigate the effect of the spatial truncation error on the quality of inversion considering noise of T_rr. The numerical investigations show satisfactory results when the area of T_rr coverage is the same with that of the gravity anomaly and the integral formula is modified by the biased least-squares modification. The error of recovery will be about 6 mGal after removing the regularization bias in the presence of 1 mE noise in T_rr measured on the orbit.     

Comparative evaluation of five global gravity models over a part of the Bay of Bengal

Several global gravity models (GGMs) are freely available in the public domain, which can be utilised to study the earth's gravity field in almost every part of the globe. The present study compared the free-air gravity anomalies calculated from the five GGMs EGM2008, EIGEN6C4, GECO, XGM2019e_2159, and SGG-UGM-2 archived by the International Centre for Global Earth Models (ICGEM) with respect to shipborne gravity in the Bay of Bengal. The average correlation coefficient and covariance are ～ 96 % and ～ 450mGal². The mean difference between the shipborne and the modelled gravity is ? 5 mGal. Relatively higher amplitude gravity differences observed at the continental-oceanic transition, the 85°E and Ninetyeast ridges, and the western basin are possibly due to high gradient, dominant density contrasts, and rugged topography. The average standard deviation and root-mean-square-error (RMSE) of the differences are ～ 6.5 mGal and ～ 7.5 mGal. A significantly lower standard deviation and RMSE found for the models generated at higher degree/order compared to lower degree/order is due to diminishing omission error of the GGMs with increasing degrees of truncation. The spectral analysis and coherence estimation of the modelled gravity demonstrate excellent correspondence for anomalies wider than ～ 25 km. The agreement between anomaly amplitudes and shapes and calculated statistics indicates that the accuracy and resolution of the modelled gravity data are certainly good enough for regional-scale studies aiming to map Moho topography and mantle structures. However, the delineation of shorter wavelength features originating from the shallow-level basement/sedimentary might be uncertain and requires further validations. The present study confirms that all five models show promising results in terms of their accuracy and resolution. Moreover, the SGG-UGM-2 and XGM2019e_2159 models compare favourably with respect to the GECO, EIGEN6C4 and EGM2008 models in the Bay of Bengal.     

Electrostatic gravity gradiometer design for the future mission

Satellite gravity gradiometry has been applied in GOCE mission to obtain higher harmonics of the Earth’s gravity mapping. In-orbit results showed that the precision of GOCE gradiometry achieved a level of 10–20 mE/Hz^1/2 in the bandwidth of 38–100 mHz, and the major error source came from the intrinsic noise of the core sensor electrostatic accelerometer. Two schemes for improving sensitivity of such accelerometer are presented by optimizing the parameters to reduce the dynamic range and choosing the heavier proof mass to suppress the thermal noise limited by the discharging gold wire. As a result, an accelerometer with a better resolution of 6.6×$6.6\times$10⁻¹³ m/s²/Hz^1/2 could be developed, and then a precision of 3 mE/Hz^1/2, corresponding to a spatial resolution of about 78 km half wavelength, is achievable for the future satellite gradiometric mission.     

The effect of spatial truncation error on integral inversion of satellite gravity gradiometry data

The satellite gravity gradiometry (SGG) data can be used for local modelling of the Earth’s gravity field. In this study, the SGG data in the local north-oriented and orbital frames are inverted to the gravity anomaly at sea level using the second-order partial derivatives of the extended Stokes formula. The emphasis is on the spatial truncation error and the kernel behaviour of the integral formulas in the aforementioned frames. The paper will show that only the diagonal elements of gravitational tensor at satellite level are suitable for recovering the gravity anomaly at sea level. Numerical studies show that the gravity anomaly can be recovered in Fennoscandia with an accuracy of about 6 mGal directly from on-orbit SGG data.     

Investigation of ionospheric irregularities and scintillation using TEC at high latitude

The occurrence of ionospheric irregularities at high latitudes, with dimensions of several kms down to decameter scale size shows strong correlation with geomagnetic disturbance, season and solar activity. Transionospheric radio waves propagating through these irregularities experience rapid random fluctuations in phase and/or amplitude of the signal at the receiver, termed scintillation, which can degrade GNSS services. Thus, investigation and prediction of this scintillation effect is very important. To investigate such scintillation effects, a GISTM (GPS Ionospheric Scintillation and TEC Monitoring) NovAtel dual frequency (L1/L2) GPS receiver has been installed at Trondheim, Norway (63.41°$63.41°$ N, 10.4°$10.4°$ E), capable of collecting scintillation indices at a 1 min rate as well as the raw data (phase and intensity) of the satellite signals at a 50 Hz sampling rate and TEC (Total Electron Content) at a 1 Hz rate. Many researchers have reported that both phase and amplitude scintillation is closely associated with TEC fluctuations or associated with a significant developing enhancement or depletion in the TEC. In this study, a novel analogous phase index is developed which provides samples at a 1 min rate. Generally the scintillation indices can help in estimating the irregularity scintillation effect at a one minute rate, but such procedures are time consuming if DFTs of the phase and/or amplitude at a 50 Hz data are required. In this study, instead, this analogous phase index is estimated from 1 Hz rate TEC values obtained from the raw signals and is then compared for weak, moderate and strong scintillation at Trondheim for one year of data collected from the installed GPS receiver. The spectral index of the irregularities (that is the inverse power law of their spatial spectrum) is determined from the resultant phase scintillation psd. The correlations of the scintillation indices and spectral indices with the analogous phase index have been investigated under different geomagnetic conditions (represented by the Kp index) and an approximate linear correlation of phase scintillation with the analogous phase index was found. Then a principal advantage of this index is that it achieves this correlation without requiring a high sampling data rate and the need for DFTs. Thus, the index seems a good candidate for developing a simple means of ionospheric scintillation prediction which could also be utilized in the development of alerts using regional mappings.     

Generation of vertical–horizontal and horizontal–horizontal gravity gradients using stochastically modified integral estimators

The Earth’s gravity field modelling is an ill-posed problem having a sensitive solution to the error of data. Satellite gravity gradiometry (SGG) is a space technique to measure the second-order derivatives of geopotential for modelling this field, but the measurements should be validated prior to use. The existing terrestrial gravity anomalies and Earth gravity models can be used for this purpose. In this paper, the second-order vertical–horizontal (VH) and horizontal–horizontal (HH) derivatives of the extended Stokes formula in the local north-oriented frame are modified using biased, unbiased and optimum types of least-squares modification. These modified integral estimators are used to generate the VH and HH gradients at 250 km level for validation purpose of the SGG data. It is shown that, unlike the integral estimator for generating the second-order radial derivative of geopotential, the system of equations from which the modification parameters are obtained is unstable for all types of modification, with large cap size and high degree, and regularization is strongly required for solving the system. Numerical studies in Fennoscandia show that the SGG data can be estimated with an accuracy of 1 mE using an integral estimator modified by a biased type least-squares modification. In this case an integration cap size of 2.5° and a degree of modification of 100 for integrating 30′ × 30′ gravity anomalies are required.     

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.     

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.     

Moderate geomagnetic storms of January 22–25, 2012 and their influences on the wave components in ionosphere and upper stratosphere-mesosphere regions

Moderate geomagnetic storms occurred during January 22–25, 2012 period. The geomagnetic storms are characterized by different indices and parameters. The SYM-H value on January 22 increased abruptly to 67 nT at sudden storm commencement (SSC), followed by a sharp decrease to −87 nT. A second SSC on January 24 followed by a shock on January 25 was also observed. These SSCs before the main storms and the short recovery periods imply the geomagnetic storms are CME  -driven. The sudden jump of solar wind dynamic pressure and IMF _Bz$B_z$ are also consistent with occurrence of CMEs. This is also reflected in the change in total electron content (TEC) during the storm relative to quiet days globally. The response of the ionospheric to geomagnetic storms can also be detected from wave components that account for the majority of TEC variance during the period. The dominant coherent modes of TEC variability are diurnal and semidiurnal signals which account upto 83% and 30% of the total TEC variance over fairly exclusive ionospheric regions respectively. Comparison of TEC anomalies attributed to diurnal (DW1) and semidiurnal (SW2) tides, as well as stationary planetary waves (SPW1) at 12 UTC shows enhancement in the positive anomalies following the storm. Moreover, the impact of the geomagnetic storms are distinctly marked in the daily time series of amplitudes of DW1, SW2 and SPW1. The abrupt changes in amplitudes of DW1 (5 TECU) and SW2 (2 TECU) are observed within 20°S–20°N latitude band and along 20°N respectively while that of SPW1 is about 3 TECU. Coherent oscillation with a period of 2.4 days between interplanetary magnetic field and TEC was detected during the storm. This oscillation is also detected in the amplitudes of DW1 over EIA regions in both hemispheres. Eventhough upward coupling of quasi two day wave (QTDWs) of the same periodicity, known to have caused such oscillation, are detected in both ionosphere and upper stratosphere, this one can likely be attributed to the geomagnetic storm as it happens after the storm commencement. Moreover, further analysis has indicated that QTDWs in the ionosphere are strengthened as a result of coherent oscillation of interplanetary magnetic field with the same frequency as QTDWs. On the otherhand, occurrences of minor SSW and geomagnetic storms in quick succession complicated clear demarcation of attribution of the respective events to variability of QTDWs amplitudes over upper stratosphere.     

Cramér-rao lower bound for pulsar rotation parameters estimation with X-ray pulsar observation data

In this paper, the Cramér-Rao Lower Bound (CRLB) for estimating the rotation parameters of pulsars using X-ray pulsar observation data is deduced, and the calculation equation is presented. In order to verify the correctness of the deduced equation, we use the X-ray pulsar observation data to estimate pulsar rotation parameters, and obtain the root mean square error (RMSE) of the estimated pulsar rotation parameters through conducting repeated experiments. The experimental results suggest that when the observation time increases, the RMSE gradually approaches the estimated CRLB, and that when the observation time is 2.4 × 10⁶ s, the error between the RMSE of pulsar frequency estimation and the CRLB stays at 10^?11 order of magnitude. This verifies that the CRLB expression deduced in this paper is the theoretical lower bound for estimating pulsar rotation parameters. The deduced CRLB in this paper helps determine the minimum variance estimator for pulsar rotation parameter estimation using X-ray pulsar data, providing a benchmark for the comparison between the minimum variance estimator and other estimators.     

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.     

An estimation of Envisat’s rotational state accounting for the precession of its rotational axis caused by gravity-gradient torque

The rotational state of Envisat is re-estimated using the specular glint times in optical observation data obtained from 2013 to 2015. The model is simplified to a uniaxial symmetric model with the first order variation of its angular momentum subject to a gravity-gradient torque causing precession around the normal of the orbital plane. The sense of Envisat’s rotation can be derived from observational data, and is found to be opposite to the sense of its orbital motion. The rotational period is estimated to be $(120.674\pm 0.068)·\exp \left((4.5095\pm 0.0096)\times {10}^{-4}·t\right)\text{s}$, where t is measured in days from the beginning of 2013. The standard deviation is 0.760?s, making this the best fit obtained for Envisat in the literature to date. The results demonstrate that the angle between the angular momentum vector and the negative normal of the orbital plane librates around a mean value of $8.53°\pm 0.42°$ with an amplitude from about $0.7°$ (in 2013) to $0.5°$ (in 2015), with the libration period equal to the precession period of the angular momentum, from about 4.8?days (in 2013) to 3.4?days (in 2015). The ratio of the minimum to maximum principal moments of inertia is estimated to be $0.0818\pm 0.0011$, and the initial longitude of the angular momentum in the orbital coordinate system is $40.5°\pm 9.3°$. The direction of the rotation axis derived from our results at September 23, 2013, UTC 20:57 is similar to the results obtained from satellite laser ranging data but about $20°$ closer to the negative normal of the orbital plane.     

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.     

Pioneer 10 Doppler data analysis: Disentangling periodic and secular anomalies

This paper reports the results of an analysis of the Doppler tracking data of Pioneer probes which did show an anomalous behaviour. A software has been developed for the sake of performing a data analysis as independent as possible from that of Anderson et al. [Anderson, J., Laing, P.A., Lau, E.L., Liu, A.S., Nieto, M.M., Turyshev, S.G. Study of the anomalous acceleration of Pioneer 10 and 11. Phys. Rev. D 65, 082004, 2002], using the same data set. A first output of this new analysis is a confirmation of the existence of a secular anomaly with an amplitude about 0.8 nm s⁻² compatible with that reported by Anderson et al. A second output is the study of periodic variations of the anomaly, which we characterize as functions of the azimuthal angle φ$\phi$ defined by the directions Sun–Earth Antenna and Sun-Pioneer. An improved fit is obtained with periodic variations written as the sum of a secular acceleration and two sinusoids of the angles φ$\phi$ and 2φ$2\phi$. The tests which have been performed for assessing the robustness of these results are presented.     

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.