Determination of frame-dragging using Earth gravity models from CHAMP and GRACE

Using the new generation Earth’s gravity field models EIGEN-2S, GGM01S and EIGEN-GRACE02S generated by the space missions CHAMP and GRACE, we have obtained an accurate measurement of the Lense–Thirring effect with the LAGEOS and LAGEOS II satellites analyzing about 10 years of data with the EIGEN-2S and GGM01S models and about 11 years of data with EIGEN-GRACE02S. This new analysis is in agreement with our previous measurements of the Lense–Thirring effect using the LAGEOS satellites and obtained with the JGM-3 and EGM96 Earth’s models. However, the new determinations are more accurate and, especially, more robust than our previous measurements. In the present analysis we are only using the nodal rates of the two satellites, making no use of the perigee rate, as in our previous analyses. The perigee is affected by a number of non-gravitational perturbations difficult to be modelled and whose impact in the total error budget is not easy to assess. Using the EIGEN-2S model, we obtain a total error budget between 18% and 36% of the Lense–Thirring effect due to all the error sources. Specifically, by using EIGEN-2S, we obtain: μ = 0.85, with a total error between ±0.18 and ±0.36, with GGM01S we get μ = 1.06 with a total error between ±0.19 and ±0.24 and with EIGEN-GRACE02S we obtain μ = 0.99, with a total error between ±0.05 and ±0.1, i.e., between 5% and 10% of the general relativistic predicted value of the Lense–Thirring effect. In addition to the analyses using EIGEN-2S, GGM01S and EIGEN-GRACE02S without the use of the perigee, we have also performed an analysis using the older model EGM96 with our previous method of combining the nodes of the LAGEOS satellites with the perigee of LAGEOS II. However, this analysis was performed over a period of about 10 years, i.e. about 2.5 times longer than any our previous analysis. The result using EGM96 over this longer period of observation agrees with our previous results over much shorter periods and with the EIGEN-2S, GGM01S and EIGEN-GRACE02S measurements of μ. In addition to the accurate determination of frame-dragging and in agreement with our previous analyses of the orbits of the LAGEOS satellites, we have observed, since 1998, an anomalous change in the Earth quadrupole coefficient, J₂ which agrees with recent findings of other authors. This anomalous variation of J₂ is accurately observed both on the node of LAGEOS and LAGEOS II and it is independent of the model used, i.e., it is observed by using the model EGM96 or by using EIGEN-2S, GGM01S or EIGEN-GRACE02S. However, this anomalous variation of the Earth quadrupole coefficient does not affect at all our determination of the Lense–Thirring effect thanks to the total elimination of the J₂-induced errors with our especially devised estimation technique.     

The impact of the new Earth gravity models on the measurement of the Lense–Thirring effect with a new satellite

In this paper we investigate the opportunities offered by the new Earth gravity models from the dedicated CHAMP and, especially, GRACE missions to the project of measuring the general relativistic Lense–Thirring effect with a new Earth’s artificial satellite. It turns out that it would be possible to abandon the stringent, and expensive, requirements on the orbital geometry of the originally prosed LARES mission (same semimajor axis a = 12,270 km of the existing LAGEOS and inclination i = 70°) by inserting the new spacecraft in a relatively low, and cheaper, orbit (a = 7500–8000 km, i  70°) and suitably combining its node Ω with those of LAGEOS and LAGEOS II in order to cancel out the first two even zonal harmonic coefficients of the multipolar expansion of the terrestrial gravitational potential J₂, J₄ along with their temporal variations , . The total systematic error due to the mismodelling in the remaining even zonal harmonics would amount to 1% and would be insensitive to departures of the inclination from the originally proposed value of many degrees. No semisecular long-period perturbations would be introduced because the period of the node, which is also the period of the solar K₁ tidal perturbation, would amount to 10² days. Since the coefficient of the node of the new satellite would be smaller than 0.1 for such low altitudes, the impact of the non-gravitational perturbations of it on the proposed combination would be negligible. Then, a particular financial and technological effort for suitably building the satellite in order to minimize the non-conservative accelerations would be unnecessary.     

Constraining the power spectrum using clusters

We analyze an extended redshift sample of Abell/ACO clusters and compare the results with those coming from numerical simulations of the cluster distribution, based on the truncated Zel'dovich approximation (TZA), for a list of eleven dark matter (DM) models. For each model we run several realizations, so that we generate a set of 48 independent mock Abell/ACO cluster samples per model, on which we estimate cosmic variance effects. Other than the standard CDM model, we consider (a) Ω₀ = 1 CDM models based on lowering the Hubble parameter and/or on tilting the primordial spectrum; (b) Ω₀ = 1 Cold + Hot DM models with 0.1 ≤Ω_ν ≤0.5; (c) low-density flat ΛCDM models with 0.3 ≤Ω₀ ≤0.5. We compare real and simulated cluster distributions by analysing correlation statistics, the probability density function, and supercluster properties from percolation analysis. We introduce a generalized definition of the spectrum shape parameter Γ in terms of σ₂₅/σ₈, where σ_ris the rms fluctuation amplitude within a sphere of radius r. As a general result, we find that the distribution of galaxy clusters provides a constraint only on the shape of the power spectrum, but not on its amplitude: a shape parameter 0.18 Γ 0.25 and an effective spectral index at the 20 h⁻¹ Mpc scale −1.1 n_eff −0.9 are required by the Abell/ACO data. In order to obtain complementary constraints on the spectrum amplitude, we consider the cluster abundance as estimated using the Press-Schechter approach, whose reliability is explicitly tested against N-body simulations. By combining results from the analysis of the distribution and the abundance of clusters we conclude that, of the cosmological models considered here, the only viable models are either Cold + Hot DM ones with 0.2 Ω_ν 0.3, better if shared between two massive ν species, and ΛCDM ones with 0.3 Ω₀0.5.     

Separation of gamma and hadron initiated air showers with energies between 20 and 500 TeV

The discrimination between air showers initiated by γ rays and by hadrons is one of the fundamental problems in experimental cosmic-ray physics. The physics of this ‘γ/hadron separation’ is discussed in this paper. We restrict ourselves to the energy range from about 20 to 500 TeV, and take only the information contained in the lateral Čerenkov light distribution and the number of electrons at the detector level into consideration. An understanding of the differences between air showers generated by γ rays and those due to hadrons leads us to formulate suitable observables for the separation process. Angle integrating Čerenkov arrays (AICA) offer a promising new approach to ground-based γ-ray astronomy in the energy region from about 20 to 500 TeV. In order to establish this technique, an efficient suppression of the overwhelming hadronic background radiation is required. As an example for our general discussion, we present one method for γ/hadron separation in AICAs called ‘LES’. It is based on the simultaneous determination of the shower size and some characteristic parameters of the lateral distribution of the Čerenkov light. The potential inherent within this technique is demonstrated in quantitative detail for the existing ‘AIROBICC’ AICA. We also propose an objective measure of the intrinsic sensitivity of a detection scheme in ground-based γ-ray astronomy, the ‘reduced quality factor’. It is shown that AICAs may reach a sensitivity to γ-ray point sources in the high VHE range similar to that of the Čerenkov-telescope imaging technique in the low VHE region.     

Discussion of trignometric parallaxes determined along right ascension and declination

We discuss the data of trignometric parallaxes determined along and δ published by the US Naval Observatory and Van Vleck Observatory. We found that the absolute difference δπ = π_x−π_y shows a very similar periodic variation with for both observations. This variation is shown to be due to errors in π_y and to be related to the current practice of maximising the parallax factor for parallax determination in right ascension. Therefore, if possible, we should increase observations where the parallax factor in declination is maximised.     

Thermal emission at radio frequencies from supernova remnants and a modified theoretical Σ–D relation

In this paper, we discuss known discrepancies between theoretically derived and empirically measured relations between the radio surface brightness Σ and the diameter D of supernova remnants (SNRs): these relations are commonly known as the Σ–D relations. We argue that these discrepancies may be at least partially explained by taking into account thermal emission at radio frequencies from SNRs at particular evolutionary stages and located in particular environments. The major contributions of this paper may be summarized as follows: (i) we consider thermal emission at radio frequencies from SNRs in the following scenarios: a relatively young SNR evolving in a dense molecular cloud environment (n  100–1000 cm⁻³) and an extremely evolved SNR expanding in a dense warm medium (n  1–10 cm⁻³). Both of these SNRs are assumed to be in the adiabatic phase of evolution. We develop models of the radio emission from both of these types of SNRs and each of these models demonstrate that through the thermal bremsstrahlung process significant thermal emission at radio frequencies is expected from both types of SNR. Based on a literature search, we claim that thermal absorption or emission at radio frequencies has been detected for one evolved Galactic SNR and four young Galactic SNRs with similar properties to our modelled evolved and young SNRs. (ii) We construct artificial radio spectra for both of these two types of SNRs: in particular, we discuss our simulated spectrum for the evolved Galactic SNR OA 184. By including thermal emission in our simulated spectra, we obtain different slopes in Σ–D relations: these new slopes are in closer agreement to empirically obtained relations than the theoretically derived relations which do not take thermal emission into account. (iii) Lastly, we present an additional modification to the theoretical Σ–D relation for SNRs in the adiabatic expansion phase. This modification is based on the convolution of the synchrotron emissivity with the emissivity derived in this paper for thermal bremsstrahlung emission from an ionized gas cloud (that is, a theoretical construct of an SNR).     

The equilibrium configuration of rapid rotating compact stars and some gravitational effects

In this paper, the equilibrium configurations of rapid rotating compact stars and some gravitational effects are studied within the general relativity by use of the Harrison-Wheeler equation of state and by the self-consistent field method. Numerical calculations show that the equilibrium configuration of a rotating star is a spheroid. For large spin velocities, say, ω > 3.0 × 10² sec⁻¹ the eccentricity and mass increase very rapidly as the angular velocity increases, for the critical angular velocity of the rotating star, the eccentricity is about 0.7, the increase in mass is about 10–35%. The difference of the gravitational redshifts at the surface of the star caused by rotation, and the difference of the light bending when the beam moves in the direction of rotation or in the opposite direction are obvious.     

Application of the complete linearization method to the analysis of solar prominence emission spectrum

We analysed the emission spectra of solar prominences using the complete linearization method [5] and found simultaneously the optical depth at the line centre τ₀, the doppler width of the line Δλ_D and the damping width a. The results show 1) that the complete linearization method has a larger radius of convergence, 2) that we must consider the variation of the source function with depth, when determining τ₀, and 3) that the calculated values of the damping constant for the H, Hβ of hydrogen and H and K lines of Calcium are all much greater than the theoretical values from doppler broadening and radiation damping, showing that other mechanisms besides these two also contribute to the broadening of prominence lines.     

The anisotropy of the diffuse cosmic X-ray background

From the new data of the 2–60 keV diffuse X-ray background from HEAO-1 A2, model galactic component is subtracted to give the cosmic component. The greater intensity in the northern galactic hemipshere is shown to be probably due to the motion of the Sun relative to the background (the Compton-Getting effect). The derived degree of anisotropy is δ = (0.45 ± 0.18)% and the velocity is V = (397 ± 159) km/s. These values are consistent with the known anisotropy in the microwave background.     

Density profiles of dark matter halos with anisotropic velocity tensors

We present density profiles, that are solutions of the spherical Jeans equation, derived under the following two assumptions: (i) the coarse grained phase-density follows a power-law of radius, ρ/σ³ ∝ r⁻, and (ii) the velocity anisotropy parameter is given by the relation β_a(r)=β₁+2β₂ (r/r_*)/[1+(r/r_*)²] where β₁, β₂ are parameters and r_* equals twice the virial radius, r_vir, of the system. These assumptions are well motivated by the results of N-body simulations. Density profiles have increasing logarithmic slopes γ, defined by γ=−d ln ρ/d ln r. The values of γ at r=10^−2.5r_vir, a distance where the systems could be resolved by large N-body simulations, lie in the range 1.0–1.6. These inner values of γ increase for increasing β₁ and for increasing concentration of the system. On the other hand, slopes at r=r_vir lie in the range 2.42–3.82. A model density profile that fits well the results at radial distances between 10⁻³r_vir and r_vir and connects kinematic and structural characteristics of spherical systems is described.     

Constraining cosmological models with cluster power spectra

Using extensive N-body simulations we estimate redshift space power spectra of clusters of galaxies for different cosmological models (SCDM, TCDM, CHDM, ΛCDM, OCDM, BSI, τCDM) and compare the results with observational data for Abell–ACO clusters. Our mock samples of galaxy clusters have the same geometry and selection functions as the observational sample which contains 417 clusters of galaxies in a double cone of galactic latitude |b|>30° up to a depth of 240 h⁻¹ Mpc. The power spectrum has been estimated for wave numbers k in the range 0.03k0.2 h Mpc⁻¹. For k>k_max0.05 h Mpc⁻¹ the power spectrum of the Abell–ACO clusters has a power-law shape, P(k)∝kⁿ, with n≈−1.9, while it changes sharply to a positive slope at k<k_max. By comparison with the mock catalogues SCDM, TCDM (n=0.9), and also OCDM with Ω₀=0.35 are rejected. Better agreement with observation can be found for the ΛCDM model with Ω₀=0.35 and h=0.7 and the CHDM model with two degenerate neutrinos and Ω_HDM=0.2 as well as for a CDM model with broken scale invariance (BSI) and the τCDM model. As for the peak in the Abell–ACO cluster power spectrum, we find that it does not represent a very unusual finding within the set of mock samples extracted from our simulations.     

On the use of Ajisai and Jason-1 satellites for tests of general relativity

In this paper we analyze in detail some aspects of the proposed use of Ajisai and Jason-1, together with the LAGEOS satellites, to measure the general relativistic Lense–Thirring effect in the gravitational field of the Earth. A linear combination of the nodes of such satellites is the proposed observable. The systematic error due to the mismodelling in the uncancelled even zonal harmonics would be ∼1% according to the latest present-day CHAMP/GRACE-based Earth gravity models. In regard to the non-gravitational perturbations especially affecting Jason-1, only relatively high-frequency harmonic perturbations should occur: neither semisecular nor secular bias of non-gravitational origin should affect the proposed combination: their maximum impact is evaluated to ∼4% over 2 years. Our estimation of the root-sum-square total error is about 4–5% over at least 3 years of data analysis required to average out the uncancelled tidal perturbations.     

Possible Effect of the Earth’s Inertial Induction on the Orbital Decay of LAGEOS

The theory of velocity dependent inertial induction, based upon extended Mach’s principle, has been able to generate many interesting results related to celestial mechanics and cosmological problems. Because of the extremely minute magnitude of the effect its presence can be detected through the motion of accurately observed bodies like Earth satellites. LAGEOS I and II are medium altitude satellites with nearly circular orbits. The motions of these satellites are accurately recorded and the past data of a few decades help to test many theories including the general theory of relativity. Therefore, it is hoped that the effect of the Earth’s inertial induction can have any detectable effect on the motion of these satellites. It is established that the semi-major axis of LAGEOS I is decreasing at the rate of 1.3 mm/d. As the atmospheric drag is negligible at that altitude, a proper explanation of the secular change has been wanting, and, therefore, this paper examines the effect of the Earth’s inertial induction effect on LAGEOS I. Past researches have established that Yarkovsky thermal drag, charged and neutral particle drag might be the possible mechanisms for this orbital decay. Inertial induction is found to generate a perturbing force that results in 0.33 mm/d decay of the semi major axis. Some other changes are also predicted and the phenomenon also helps to explain the observed changes in the orbits of a few other satellites. The results indicate the feasibility of the theory of inertial induction i.e. the dynamic gravitation phenomenon of the Earth on its satellites as a possible partial cause for orbital decay.     

Gamma–hadron separation methods for the VERITAS array of four imaging atmospheric Cherenkov telescopes

Ground-based arrays of imaging atmospheric Cherenkov telescopes have emerged as the most sensitive γ-ray detectors in the energy range of about 100 GeV and above. The strengths of these arrays are a very large effective collection area on the order of 10⁵ m², combined with excellent single photon angular and energy resolutions. The sensitivity of such detectors is limited by statistical fluctuations in the number of Cosmic-ray initiated air showers that resemble γ-ray air showers in many ways. In this paper, we study the performance of simple event reconstruction methods when applied to simulated data of the Very Energetic Radiation Imaging Telescope Array System (VERITAS) experiment. We review methods for reconstructing the arrival direction and the energy of the primary photons, and examine means to improve on their performance. For a software threshold energy of 300 GeV (100 GeV), the methods achieve point source angular and energy resolutions of σ_63% = 0.1° (0.2°) and σ_68% = 15% (22%), respectively. The main emphasis of the paper is the discussion of γ–hadron separation methods for the VERITAS experiment. We find that the information from several methods can be combined based on a likelihood ratio approach and the resulting algorithm achieves a γ–hadron suppression with a quality factor that is substantially higher than that achieved with the standard methods used so far.     

The cosmic ray primary composition in the “knee” region through the EAS electromagnetic and muon measurements at EAS-TOP

The evolution of the cosmic ray primary composition in the energy range 10⁶–10⁷ GeV (i.e. the “knee” region) is studied by means of the e.m. and muon data of the Extensive Air Shower EAS-TOP array (Campo Imperatore, National Gran Sasso Laboratories). The measurement is performed through: (a) the correlated muon number (N_μ) and shower size (N_e) spectra, and (b) the evolution of the average muon numbers and their distributions as a function of the shower size. From analysis (a) the dominance of helium primaries at the knee, and therefore the possibility that the knee itself is due to a break in their energy spectrum (at E_k^He=(3.5±0.3)×10⁶ GeV) are deduced. Concerning analysis (b), the measurement accuracies allow the classification in terms of three mass groups: light (p,He), intermediate (CNO), and heavy (Fe). At primary energies E₀≈10⁶ GeV the results are consistent with the extrapolations of the data from direct experiments. In the knee region the obtained evolution of the energy spectra leads to: (i) an average steep spectrum of the light mass group (γ_p,He>3.1), (ii) a spectrum of the intermediate mass group harder than the one of the light component (γ_CNO2.75, possibly bending at E_k^CNO≈(6–7)×10⁶ GeV), (iii) a constant slope for the spectrum of the heavy primaries (γ_Fe2.3–2.7) consistent with the direct measurements. In the investigated energy range, the average primary mass increases from lnA=1.6–1.9 at E₀1.5×10⁶ GeV to lnA=2.8–3.1 at E₀1.5×10⁷ GeV. The result supports the standard acceleration and propagation models of galactic cosmic rays that predict rigidity dependent cut-offs for the primary spectra of the different nuclei. The uncertainties connected to the hadronic interaction model (QGSJET in CORSIKA) used for the interpretation are discussed.     

Magnetospheric plasma discontinuity by the geostationary version of the differential phase method during storms

It is shown that the dynamics of the plasmapause, the plasmasphere plasma tails, the plasma sheet and the magnetosheath boundaries of the geomagnetosphere may be investigated by means of the geostationary version of the differential phase method, by which a signal transmitted from a sounding station (a geostationary satellite) and received by a response station on the Earth may be transformed, allowing the sign of the frequency shift and of the phase lag to be changed. Information on the location, the motion of the magnetospheric plasma discontinuities and the concentration drop at their boundaries may be obtained from measurements carried out on board the geostationary satellite of the phase difference of the sounding and response signals ΔΦ, the time of its increase Δt and the phase difference change rate (fast beating frequency Δƒ = ΔΦ/2π Δt). The establishment of communication between appropriately spaced ground stations and a satellite with a quasi-polar orbit allows the midlatitude plasmapause dynamics, and those of the ionosphere trough, polar cusp boundaries and of polar cap inhomogeneities to be studied. Equipment with a stability of 10⁻¹¹–10⁻¹² is needed for the most dynamical events (for ΔΦ= 10⁻⁴ tens of rad. and for Δƒ= 10⁻⁵ tens of Hz) occurring in the radio path during storms.     

An embedded exponentially fitted Runge–Kutta–Nyström method for the numerical solution of orbital problems

A new embedded pair of explicit exponentially fitted Runge–Kutta–Nyström methods is constructed. The methods integrate exactly systems of differential equations whose solutions are linear combinations of the functions from the set {exp(μt), exp(−μt)} (). The pair has four stages and algebraic orders five and three. An application to some well-known orbital problem shows that the new pair is very competitive when it is compared with high-quality codes proposed in the scientific literature.     

A revaluation of the rotational speed of the upper atmosphere

In this paper the rotational speed of the upper atmosphere, mainly at heights of 200–300 km, is evaluated from the changes in the orbital inclinations of thirteen satellites. The values obtained represent the mean rotational speed over the latitudes covered by the satellites, at dates between late 1962 and early 1966, i.e. when solar activity was low.

If the angular velocity of the atmosphere is taken as Λ times that of the Earth, the values of Λ found are mostly between 1.0 and 1.6 with estimated S.D. between 0.1 and 0.25. If we exclude two values at heights above 300 km and one anomalous value, the mean of the remaining ten values of Λ obtained is 1.27, with r.m.s. scatter 0.18: this would correspond to an average west-to-east wind of about 100 m/sec in mid-latitudes.