International Journal of Modern Physics D

In this paper, we present an overview of ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) and ASTROD I mission concepts and studies. The missions employ deep-space laser ranging using drag-free spacecraft to map the gravitational field in the solar-system. The solar-system gravitational field is determined by three factors: the dynamic distribution of matter in the solar system; the dynamic distribution of matter outside the solar system (galactic, cosmological, etc.) and gravitational waves propagating through the solar system. Different relativistic theories of gravity make different predictions of the solar-system gravitational field. Hence, precise measurements of the solar-system gravitational field test these relativistic theories, in addition to gravitational wave observations, determination of the matter distribution in the solar-system and determination of the observable (testable) influence of our galaxy and cosmos. The tests and observations include: (i) a precise determination of the relativistic parameters β and γ with 3–5 orders of magnitude improvement over previous measurements; (ii) a 1–2 order of magnitude improvement in the measurement of G; (iii) a precise determination of any anomalous, constant acceleration A_a directed towards the Sun; (iv) a measurement of solar angular momentum via the Lense-Thirring effect; (v) the detection of solar g-mode oscillations via their changing gravity field, thus, providing a new eye to see inside the Sun; (vi) precise determination of the planetary orbit elements and masses; (vii) better determination of the orbits and masses of major asteroids; (viii) detection and observation of gravitational waves from massive black holes and galactic binary stars in the frequency range 50 μHz to 5 mHz; and (ix) exploring background gravitational waves. The baseline scheme of ASTROD is to have two spacecraft in separate solar orbits and one spacecraft near the Earth–Sun L1/L2 point carrying a payload of a proof mass, two telescopes, two 1–2 W lasers with spares, a clock and a drag-free system ranging coherently among one another using lasers. ASTROD I is a first step towards ASTROD. Its scheme is to have one spacecraft in a Venus-gravity-assisted solar orbit, ranging optically with ground stations with less ambitious, but still significant scientific goals.

The Astrodynamical Space Test of Relativity using Optical Devices (ASTROD) is a multi-purpose relativity mission concept. ASTROD's scientific goals are the measurement of relativistic and solar system parameters to unprecedented precision, and the detection and observation of low-frequency gravitational waves to frequencies down to 5 × 10^-6 Hz. To accomplish its goals, ASTROD will employ a constellation of drag-free satellites, aiming for a residual acceleration noise of (0.3-1) × 10^-15 m s^-2 Hz^-1/2 at 0.1 mHz. Noise sources and strategies for improving present acceleration noise levels are reported.

The electrostatic test mass charging in the ASTROD I (Astrodynamical Space Test of Relativity using Optical Devices I) mission can affect the quality of the science data due to spurious Coulomb and Lorentz forces. To estimate the size of the resultant disturbances, credible predictions of charging rates and the charging noise are required. Using the GEANT4 software toolkit, we present a detailed Monte Carlo simulation of ASTROD I test mass charging due to exposure of the spacecraft to galactic cosmic-ray (GCR) protons and alpha particles (³He, ⁴He) in the space environment. A positive charging rate of 33.3 e⁺/s at solar minimum is predicted. The predicted rate reduces by 50% at solar maximum. Based on this charging rate and factoring in the contribution of minor cosmic-ray components, we calculate the acceleration noise and stiffness associated with charging. We conclude that the acceleration noise arising from Coulomb and Lorentz effects are well below the ASTROD I acceleration noise limit at 0.1 mHz both at solar minimum and maximum. The magnitude of coherent Fourier components due to charging are also estimated.

An electrostatically controlled torsion pendulum has been constructed to investigate the performance of the ASTROD I inertial sensor on the ground. The twist motion of the pendulum is monitored by a capacitive transducer and controlled by an electrostatic actuator. The preliminary experimental results show that the torque resolution of the pendulum is 2 × 10^-12 N m Hz^-1/2 at 3 mHz. Further improvements under consideration for the inertial sensor are discussed.

We present an overview of charge management for LISA, including a review of the problems caused by test mass charging and development of the LISA Pathfinder charge management device.

On the basis of many coorbital phenomena in astronomy and spacecraft motion, a dynamics model is proposed in this paper — treating the coorbital restricted problem together with method for obtaining a general approximate solution. The design of the LISA spacecraft orbits is a special 2+3 coorbital restricted problem. The problem is analyzed in two steps. First, the motion of the barycenter of the three spacecraft is analyzed, which is a planar coorbital restricted three-body problem. And an approximate analytical solution of the radius and the argument of the center is obtained consequently. Secondly, the configuration of the three spacecraft with minimum arm-length variation is analyzed. The motion of a single spacecraft is a near-planar coorbital restricted three-body problem, allowing approximate analytical solutions for the orbit radius and the argument of a spacecraft. Thus approximative expressions for the arm-length are given.

The Laser Interferometer Space Antenna (LISA) mission is a joint ESA-NASA mission for detecting low-frequency gravitational waves in the frequency range from 0.1 mHz to 1 Hz, by using accurate distance measurements with laser interferometry between three spacecraft, which will be launched around 2015 and one year later reach their orbits around the Sun. In order to operate successfully, it is crucial for the constellation of the three spacecraft to have extremely high stability. In this paper, several problems of the orbit optimization of the LISA constellation are discussed by using numerical and analytical methods for satisfying the requirements of accuracy. On the basis of the coorbital restricted problem, analytical expressions of the heliocentric distance and the trailing angle to the Earth of the constellation's barycenter are deduced, with the result that the approximate analytical solution of first order will meet the accuracy requirement of the spacecraft orbit design. It is proved that there is a value of the inclination of the constellation plane that will make the variation of the arm-length a minimum. The principle for selecting the optimum starting elements of orbits at any epoch is proposed. The method and programming principles of finding the optimized orbits are also presented together with examples of the optimization design.

The new generation of optical time transfer will allow the synchronization of remote ultra stable clocks and the determination of their performances over intercontinental distances. The principle of T2L2 (Time Transfer by Laser Link) is based on the techniques of satellite laser ranging coupled with time-frequency metrology. It consists of synchronizing ground and space clocks using short laser pulses travelling between ground clocks and satellite equipment. The instrument will be integrated on the ocean altimetry satellite Jason-2 that is scheduled for launch in 2008. The experiment should enhance the performance of time transfer by one or two magnitudes compared to existing microwave techniques such as GPS and Two-Way Satellite Time and Frequency Transfer (TWSTFT).

It is well-known that gravitational lensing is a powerful tool in the investigation of the distribution of matter, including that of dark matter (DM). Typical angular distances between images and typical time scales depend on the gravitational lens masses. For the case of microlensing, angular distances between images or typical astrometric shifts are about 10^-5 - 10^-6 arcsec. Such an angular resolution will be reached with the space–ground VLBI interferometer, Radioastron. The basic targets for microlensing searches should be bright point-like radio sources at cosmological distances. In this case, an analysis of their variability and a solid determination of microlensing could lead to an estimation of their cosmological mass density. Moreover, one could not exclude the possibility that non-baryonic dark matter could also form microlenses if the corresponding optical depth were high enough. It is known that in gravitationally lensed systems the probability (the optical depth) of observing microlensing is relatively high. Therefore, for example, gravitationally lensed objects, like the CLASS gravitational lens B1600+434, appear to be most suitable to detect astrometric microlensing, since features of photometric microlensing have been detected in these objects. However, to directly resolve these images and to directly detect the apparent motion of the knots, the Radioastron sensitivity would have to be improved, since the estimated flux density is below the sensitivity threshold. Alternatively, they may be observed by increasing an integration time, assuming that a radio source has a typical core–jet structure and microlensing phenomena are caused by the superluminal apparent motions of knots. In the case of a confirmation (or a negation) of claims about microlensing in gravitational lens systems, one can speculate about the microlens contribution to the gravitational lens mass. Astrometric microlensing due Galactic MACHOs is not very important because of low optical depths and long typical time scales. Therefore, the launch of the space interferometer Radioastron will enable the investigation of microlensing in the radio band, giving rise to the possibility of not only resolving microimages but also of observing astrometric microlensing.

In addition to the well-known Møller frame (or Rindler frame), we may construct another frame to describe the uniformly accelerating system. In the new frame, all "static" (i.e. spatial coordinates keeping constant) observers have the same proper acceleration but each has his own horizon. In contrast, the proper acceleration of a static observer in the Møller frame (or Rindler frame) depends on his position, but the horizon is (static-) observer-independent. We argue that the new uniformly accelerating reference frame is more suitable than the Møller frame to describe the system in an accelerating spacecraft. It is possible to distinguish the Møller frame and the new frame by high-precision experiments (such as arrival-time- and/or redshift-measurements) in an accelerating spacecraft. When the non-relativistic limit is taken, the second law of mechanics and Schrödinger equation in the new uniformly accelerating frame are all different from those in the Møller frame. The effects on the equivalence principle are discussed. We argue that even when the space–time curvature is ignored, it is still possible in some sense to distinguish gravity from acceleration at the next leading order.

In this work, we determine the central black hole mass for a sample of blazars including 30 γ-ray loud blazars with available variability timescales. The γ-ray energy, the emission size and the property of a two-temperature accretion disk are used to determine the absorption depth. If we take the intrinsic γ-ray luminosity to be λ times the Eddington luminosity, i.e. , then we have following results: the masses of the black hole are in the range of 0.59 ~ 67.99 × 10⁷M_⊙(λ = 1.0) or 0.90 ~ 104.13 × 10⁷M_⊙(λ = 0.1). Blazars are also discussed.

Several large-scale gravitational wave (GW) interferometers have achieved long term operation at design sensitivity. Questions arise on how to best combine all available data from detectors of different sensitivities for detection, consistency check or veto, localization and waveform extraction. We show that these problems can be formulated using the singular value decomposition (SVD)¹ method. We present techniques based on the SVD method for (1) detection statistic, (2) stable solutions to waveforms, (3) null-stream construction for an arbitrary number of detectors, and (4) source localization for GWs of unknown waveforms.

In this paper we briefly present our work on relic gravitational waves (RGW) and the CMB polarization in the accelerating universe. The spectrum of RGW has been obtained, showing the influence of dark energy. Compared with those from non-accelerating models, the shape of the spectrum is approximately similar, nevertheless, the amplitude of RGW now acquires a suppressing factor of the ratio of matter over dark energy ∝ Ω_m/Ω_Λ ~ 0.4 over almost the whole range of frequencies. The RGW Spectrum is then used as the source to calculate the spectra of CMB polarization. By using two half-Gaussian functions as an approximation to the visibility function during the photon decoupling, both the "electric" and "magnetic" spectra have been analytically derived and they are quite close to those obtained numerically. Several physical elements that affect the spectra have been examined, such as the decoupling process, inflation, dark energy, the baryons, etc.