The Eddington Mission

The Eddington mission was given full approval by the European Space Agencyon the 23rd May 2002, as part of the new `Cosmic Vision' Science programme, with launch scheduled for 2007/8. Its twin scienceobjectives are asteroseismology and planet finding.In its current design it consists of 4 × 60 cm folded Schmidt telescopes, eachwith 6° × 6° field of view and its own CCD array camera.The current observing plan is to spend 2 years primarily devoted to asteroseismologywith 1–3 months on different target fields monitoring up to 50,000 stars per field,and 3 years continuously on asingle target field monitoring upwards of 100,000 stars as required for planetsearching. The asteroseismic goal is to be able to detect oscillationsfrequencies with a precision 0.1–0.3 Hz.     

The Eddington Mission

The Eddington mission was given full approval by the European Space Agency on the 23rd May 2002, with launch scheduled for 2007/8. Its science objectives are stellar evolution and asteroseismology, and planet finding. In its current design it consists of 4 × 60 cm folded Schmidt telescopes, each with 6^o × 6^o field of view and its own CCD array camera. Eddington will spend 2 years primarily devoted to asteroseismology with 1–3 months on different target fields monitoring up to 50,000 stars per field, and 3 years continuously on a single field monitoring upwards of 100,000 stars for planet searching. The asteroseismic goal is to be able to detect oscillations frequencies of stars with a precision 0.1–0.3 μHz, to probe their interior structure and the study the physical processes that govern their evolution. This revised version was published online in August 2006 with corrections to the Cover Date.     

The range of validity of the two-body approximation in models of terrestrial planet accumulation: I. Gravitational perturbations

Gravitational perturbations in semimajor axis, eccentricity, and inclination resulting from close planetesimal encounters (near 1 AU) out to 10 Tisserand sphere of influence radii were calculated by two- and three-dimensional numerical integration. These are compared with the results of treating the encounter as a two-body problem, as is customary in Monte Carlo calculations of orbital evolution and in numerical and analytical studies of planetary accumulation. It is found that for values of $\text{(}\text{V}\text{V}{}_{\mathrm{e}}\text{) ? 0.35 (V =}\text{relative velocity}\text{, V}{}_{\mathrm{e}}\text{=}\text{escape velocity of largest body}\text{)}$, the two-body body approximation fails to describe the outcome of individual encounters. In this low-velocity region, the two-body “gravitational focusing” cross section is no longer valid; “anomalous gravitational focusing” often leads to bodies on distant unperturbed trajectories becoming close encounters and vice versa. In spite of these differences, average perturbations given by the two-body approximation are valid within a factor of 2 when $\text{V}\text{V}{}_{\mathrm{e}}\text{> 0.07}$. In this same velocity range the “Arnold extrapolation,” whereby a few very close encounters are used to estimate the effect of many more distant encounters, is found to be a useful approximation.     

The range of validity of the two-body approximation in models of terrestrial planet accumulation: II. Gravitational cross sections and runaway accretion

The validity of the two-body approximation in calculating encounters between planetesimals has been evaluated as a function of the ratio of unperturbed planetesimal velocity (with respect to a circular orbit) to mutual escape velocity when their surfaces are in contact (V/V_e). Impact rates as a function of V/V_e are calculated to within ～20% by numerical integration of the equations of motion. It is found that when V/V_e > 0.4, the two-body approximation is a good one. At low velocities (V/V_e < 0.1) two-body “collision-course” trajectories fail to lead to impacts. On the other hand, at these low velocities many impacts result from encounter trajectories with unperturbed separation distances far beyond the two-body gravitational radius. These two effects tend to cancel, and the resulting impact rates remain within a factor of ～3 of the two-body value in spite of these major differences in the nature of the impact trajectories. Therefore, on the average, the two-body approximation is useful well below the value of V/V_e for which it fails to describe individual encounters, and the required corrections are not large. As a consequence of this “anomalous gravitational focusing” planetesimals will continue to interact even when their orbits are noncrossing. This reduces the difficulty with premature isolation of planetesimal embryos during accumulation. Quantitatively, when 0.06 ? V/V_e ? 0.2, the impact rate varies approximately with the fifth power of the radius of the larger body, and is about a factor of 3 above that predicted using the conventional two-body gravitational cross-section formula. At lower values of V/V_e , the impact rate increases less rapidly. Finally, at the lowest values of V/V_e (<.02), the impact rate increases only in proportion to the geometric cross section, as a consequence of the swarm being essentially two dimensional for large unperturbed encounter distances. The gravitational enhancement in effective cross section is thereby limited to a value of about 3000. This leads to an optimal size for growth of planetesimals from a swarm of given eccentricity, and places a limit on the extent of runaway accretion.     

The Eddington Ratio of H 2 O Maser Host AGN

The Eddington ratio λ was derived for the entire maser host AGN sample, based on the intrinsic X-ray luminosity, the X-ray bolometric correction C _X and the mass of central black hole. Further the [O III] bolometric correction C _{[O III]} was estimated for our sample. Possible relations were also investigated between the maser luminosity and the bolometric luminosity – the Eddington ratio.     

On the validity of application of the radial approximation for the photospheric field

The radiality approximation, introduced by Wang and Sheeley (1992), is rather frequently used to calculate – within the current-free approximation – the magnetic structure of the solar corona. In this paper it is shown that the data that are used as observational evidence of the `radiality' contradict neither the `radiality' nor the `non-radiality' of the measured magnetic field, while to ascertain the true character requires quantifying the standard deviation of the transverse component of the field. On the basis of a statistical processing of daily magnetograms, a method is suggested for quantifying the measure of non-radiality of the observed field. For Stanford magnetograms (Fei 5250) and NSO/Kitt Peak magnetograms (Fei 8688) it is shown that the measures of non-radiality corresponding to them are equal in magnitude and not small. The only difference between the two lines of measurement is the presence of a small mean azimuthal field in the line of Fei 5250, which may be interpreted as an indication of the non-potentiality at the level of measurement lying in deeper layers. Nevertheless, such a non-potentiality does not lead to magnetic field radialization.The final conclusion of this paper: the observational data indicate an essential non-radiality of the magnetic field at the level of measurements and, hence, the classical interpretation of magnetic measurements for extrapolating the magnetic field to the corona is preferred.     

Black hole transients and the Eddington limit

I show that the Eddington limit implies a critical orbital period P _crit(BH)≃2 d beyond which black hole LMXBs cannot appear as persistent systems. The unusual behaviour of GRO J1655–40 may result from its location close to this critical period.     

The solution topology of the Eddington quartic-like equationY=αX 4+X−1

The root structure of the Eddington quartic equation is examined in a general manner. The complex and real root topology is annotated, and an explicit expression for the real positive root is derived.     

活动星系核中黑洞质量和吸积率分布研究

红移、中心黑洞质量和吸积率是活动星系核演化的重要参数.利用反响映射法计算了172个类星体和Seyfert星系样本的中心黑洞质量,并分析了中心黑洞的质量、红移、爱丁顿吸积率的分布,进而验证了从类星体过渡到Seyfert星系的演化.     

The anticorrelation between the hard X-ray photon index and the Eddington ratio in low-luminosity active galactic nuclei

We find a significant anticorrelation between the hard X-ray photon index Γ and the Eddington ratio   L _bol/ L _Edd  for a sample of low-ionization nuclear emission-line regions and local Seyfert galaxies, compiled from literature with Chandra or XMM–Newton observations. This result is in contrast with the positive correlation found in luminous active galactic nuclei (AGN), while it is similar to that of X-ray binaries (XRBs) in the low/hard state. Our result is qualitatively consistent with the spectra produced from advection-dominated accretion flows (ADAFs). It implies that the X-ray emission of low-luminosity active galactic nuclei (LLAGN) may originate from the Comptonization process in ADAF, and the accretion process in LLAGN may be similar to that of XRBs in the low/hard state, which is different from that in luminous AGN.     

The polarization-free approximation

The development of effective iterative methods capable of accurately solving NLTE Stokes transfer problems is of considerable importance for the investigation of solar and stellar magnetic fields. After briefly indicating the iterative approach which is being presently pursued for the exact solution of such problems, the particular regime where polarization signals can only be due to the Zeeman effect is considered in some detail. By means of NLTE Stokes transfer calculations for a two-level atomic model it is first shown that the currently-used field-free approximation (Rees, 1969) cannot be safely applied in the presence of magnetic field gradients. Such gradients lead to changes in the shape and width of the line profiles and they can produce non-negligible effects on the atomic level populations and line source functions. A new approximate method is then proposed, which does not require the actual solution of the Stokes vector transfer equation and is practically as fast as the field-free one. This polarization-free approximation provides a fairly good account of the effects of homogeneous and inhomogeneous magnetic fields on the statistical equilibrium and is very easy to implement in any existing non-magnetic, multi-level transfer code.On leave from the Dipartimento di Astronomia e Scienza dello Spazio, Università di Firenze, Largo E. Fermi 5, I-50125 Firenze, Italia     

The WKB approximation and the plasma ring of Jupiter

In this note we study the behaviour of hydromagnetic oscillations along the field lines of Jupiter's magnetosphere crossing the Io plasma ring. We compare the shape and period of these oscillations, as found by a direct numerical calculation, with those obtained with the WKB method, in order to show the unaccuracy of this approximation.     

The validity of the continuum limit in the gravitational N-body problem

This paper attempts to give quantitative as well as qualitative answers to the question of the analogy between smooth potentials and N-body systems. A number of simulations were performed in both integrable and nonintegrable smooth environments and their frozen N-body analogues, and comparisons were made using a number of different tools. The comparisons took place on both statistical and pointwise levels. The results of this study suggest that microscopic chaos associated with discreteness effects is always present in N-body configurations. This chaos is different from the macroscopic chaos which is associated with the bulk potential and persists even for very large N. Although the Lyapunov exponents of orbits evolving in N-body environments do not decrease as N increases, comparisons associated with the statistical properties, as well as with the power spectra of the orbits, affirm the existence of the continuum limit.     

The waiting point approximation inr-process calculations

The steady flow approximation to ther-process has been used to evaluate the validity of the waiting point assumption (that, for a given charge numberZ, neutron captures become balanced by neutron photodisintegrations) under a variety of conditions. The criterion for the accuracy of the approximation for any set of nuclei with the same value ofZ is that the ratio of the total rate of neutron photodisintegration in those nuclei to the total rate of neutron captures should be close to unity. We have failed to find any set of conditions involving neutron production by helium thermonuclear reactions (at temperatures up to 10⁹ K) for which the waiting point approximation is useful for all values ofZ, and we recommend that all suchr-process calculations not use this approximation. At higher temperatures, such as those characteristic of explosive carbon burning (2×10⁹ K), the waiting point approximation is much better.