An upper limit to the density inhomogeneity in the universe

An upper limit to the amplitude of the overall density fluctuation has been found by means of the gravitational lensing effect of the density inhomogeneity on the luminosities of quasars with larger redshifts. The observed differences of luminosities of quasars located at different directions are partially given by the lensing effect, therefore, a useful upper limit to the inhomogeneity can be derived if the luminosity distribution of quasars is uniform enough. We obtain that, in the case of the density parameter of the Universe =1, the overall matter should be less clustered than the luminous matter by a factor of at least 3. This result may not favour the biased dark matter scenario for the formation of large-scale structure in the Universe.     

On upper limits for gravitational radiation

A procedure with a Bayesan approach for calculating upper limits to gravitational wave bursts from coincidence experiments with multiple detectors is described, where the detection efficiency for small signals is taken into consideration. The Bayesan approach to the upper limit estimation is confronted with the unified approach for the case when no events are observed in presence of a non-zero background.     

Gravitationless black holes

A gravitationless black hole model is proposed in accord with a five-dimensional fully covariant Kaluza-Klein (K-K) theory with a scalar field, which unifies the four-dimensional Einsteinian general theory of relativity and Maxwellian electromagnetic theory. It is shown that a dense compact core of a star, when it collapses to a critical density, suddenly turns off or shields its gravitational field. The core, if its mass exceeds an upper limit, directly collapses into a black hole. Otherwise, the extremely large pressure, as the gravity is turned off, immediately stops the collapse and drives the mantle material of supernova moving outward, which leads to an impulsive explosion and forms a neutron star as a remnant. A neutron star can further evolve into a black hole when it accretes enough matter from a companion star such that the total mass exceeds a lower limit. The black hole in the K-K theory is gravitationless at the surface because the scalar field is infinitely strong, which varies the equivalent gravitational constant to zero. In general, a star, at the end of its evolution, is relatively harder to collapse into a gravitationless K-K black hole than a strong gravitational Schwarzschild black hole. This is consistent with the observation of some very massive stars to form neutron stars rather than expected black holes. In addition, the gravitationless K-K black hole should be easier to generate jets than a Schwarzschild black hole.     

A simple magnetostatic model of sunspots

An analytical solution is derived for the nonlinear magnetostatic balance between the Lorentz forces on one side and the pressure and gravitational forces induced by the magnetic inhibition of granular convection in a sunspot on the other. In order to exhibit the mathematical structure of the problem it has been reduced to the simplest case which still contains the basic physical features. Although the results of a model with a two-dimensional periodic magnetic field are not quantitatively comparable with sunspot observations the conclusion can be drawn that an upper limit on the size of sunspots exists. The results suggest that this upper limit is close to the size of observed large sunspots.     

Fluctations in the cosmic microwave background arising from low-frequency gravitational radiation

Intense low-frequency intergalactic gravitational radiation with wave lengths λ smaller than the HUBBLE distance λ_H ≌ 3000 (100/H₀) Mpc but not exceedingly small compared to λ_H. generates anisotropies in the microwave background radiation. One contribution results from the local wave field and produces mainly a quadrupole-type temperature variation on the sky. Available data on large-scale microwave fluctuations do not exclude appreciable amounts of gravitational background radiation in the Megaparsec wave band. A more sensitive test is provided by a second far-field contribution, which has a small angular scale. Its amplitude depends strongly on the ratio of the (present) rest mass density to the HUBBLE constant, if a cosmological origin of the blackbody radiation is assumed. In a low-density universe, pre-galactic COMPTON scattering of the blackbody radiation is not able to reduce the fluctuations caused by the low-frequency gravitational wave field. The recent small-scale data by PARIJSKIJ would allow only small amplitudes of gravitational waves with an energy density significantly below the critical cosmological density. On the other hand, in a high-density universe, the small angular scale fluctuation in the blackbody radiation is completely damped out, and a gravitational radiation cosmos reaching the critical density is admitted. Independent of the matter density, the data by PARIJSKIJ would confine gravitational background radiation to insignificant amplitudes if a discrete source model for the origin of the microwave background has to be assumed.     

A constraint on pre-Main-Sequence mass loss

The principal energy source of a pre-Main-Sequence (PMS) star is gravitational contraction. Mass ejection, regardless of its actual mechanism, in effect transfers gravitational potential energy from the entire star to the escaping matter. The virial theorem limits the efficiency of such a process. Theoretical PMS mass-radius relationships limit the total loss to a few tenths of the initial mass. The observed luminosities and estimated mass loss rates of T-Tauri stars are used to estimate the fraction of available energy expended on mass ejection. Actual losses appear to be much smaller than the theoretical limit in most cases. Only stars of emission line intensity classes 4 and 5 may be capable of significant mass loss.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

Detection of Extended Thermal Infrared Emission around the Vega-like Source HD 141569

We report the detection of extended IR emission at 10.8 and 18.2 μm around the Vega-like source HD 141569. Mid-IR imaging with OSCIR on Keck II shows emission from dust extending out to 100 AU from the B9.5 Ve star. Our modeling of the dust places an upper limit of approximately 2 μm on the diameter of the mid-IR-emitting particles if they are Mie spheres of astronomical silicates. Comparison of our mid-IR images to the near-IR (1.1 μm) NICMOS images of HD 141569 (Weinberger et al. 1999) shows that the mid-IR emission originates at smaller distances from the star than the scattered near-IR light, as also previously observed for the archetype Vega-like source beta Pictoris.     

On the mass and distance of the Quasi-Stellar Object 3C 273

For the QSO 3C 273 we derive, on the basis of two different theoretical models, expressions for a lower limit to the mass of the QSO, as a function of its distance. We conclude that an appreciable gravitational redshift component is consistent with the observational data only if the QSO mass is at least Galactic in magnitude. The setting of an independent upper limit to the QSO massM10¹⁰ M could indicate that the QSO redshift is predominantly cosmological in nature.     

The effect of gravitational and pressure torques on Titan's length-of-day variations

Cassini radar observations show that Titan's spin is slightly faster than synchronous spin. Angular momentum exchange between Titan's surface and the atmosphere over seasonal time scales corresponding to Saturn's orbital period of 29.5 year is the most likely cause of the observed non-synchronous rotation. We study the effect of Saturn's gravitational torque and torques between internal layers on the length-of-day (LOD) variations driven by the atmosphere. Because static tides deform Titan into an ellipsoid with the long axis approximately in the direction to Saturn, non-zero gravitational and pressure torques exist that can change the rotation rate of Titan. For the torque calculation, we estimate the flattening of Titan and its interior layers under the assumption of hydrostatic equilibrium. The gravitational forcing by Saturn, due to misalignment of the long axis of Titan with the line joining the mass centers of Titan and Saturn, reduces the LOD variations with respect to those for a spherical Titan by an order of magnitude. Internal gravitational and pressure coupling between the ice shell and the interior beneath a putative ocean tends to reduce any differential rotation between shell and interior and reduces further the LOD variations by a few times. For the current estimate of the atmospheric torque, we obtain LOD variations of a hydrostatic Titan that are more than 100 times smaller than the observations indicate when Titan has no ocean as well as when a subsurface ocean exists. Moreover, Saturn's torque causes the rotation to be slower than synchronous in contrast to the Cassini observations. The calculated LOD variations could be increased if the atmospheric torque is larger than predicted and or if fast viscous relaxation of the ice shell could reduce the gravitational coupling, but it remains to be studied if a two order of magnitude increase is possible and if these effects can explain the phase difference of the predicted rotation variations. Alternatively, the large differences with the observations may suggest that non-hydrostatic effects in Titan are important. In particular, we show that the amplitude and phase of the calculated rotation variations are similar to the observed values if non-hydrostatic effects could strongly reduce the equatorial flattening of the ice shell above an internal ocean.     

Measurement of the seismic attenuation performance of the VIRGO Superattenuator

The gravitational wave detector VIRGO aims at extending the detection band down to a few Hertz by isolating the mirrors of the interferometer from seismic noise. This result is achieved by hanging each mirror through an elastic suspension (Superattenuator), designed to filter mechanical vibrations in all the degrees of freedom. An experimental upper limit of the mirror residual seismic noise at a few Hertz is provided in this paper. This is lower than the thermal noise floor, expected to limit the antenna sensitivity in the low frequency range.     

Prompt Iron Enrichment, Two r-Process Components, and Abundances in Very Metal-Poor Stars

We compare the structure and substructure of dark matter halos in model universes dominated by collisional, strongly self-interacting dark matter (SIDM) and collisionless, weakly interacting dark matter (CDM). While SIDM virialized halos are more nearly spherical than CDM halos, they can be rotationally flattened by as much as 20% in their inner regions. Substructure halos suffer ram-pressure truncation and drag, which are more rapid and severe than their gravitational counterparts tidal stripping and dynamical friction. Lensing constraints on the size of galactic halos in clusters are a factor of 2 smaller than predicted by gravitational stripping, and the recent detection of tidal streams of stars escaping from the satellite galaxy Carina suggests that its tidal radius is close to its optical radius of a few hundred parsecs-an order of magnitude smaller than predicted by CDM models but consistent with SIDM models. The orbits of SIDM satellites suffer significant velocity bias, sigmaSIDM&solm0;sigmaCDM=0.85, and are more circular than CDM satellites, betaSIDM approximately 0.5, in agreement with the inferred orbits of the Galaxy's satellites. In the limit of a short mean free path, SIDM halos have singular isothermal density profiles; thus, in its simplest incarnation SIDM, is inconsistent with galactic rotation curves.     

On Einstein clusters as galactic dark matter haloes

We consider global and gravitational lensing properties of the recently suggested Einstein clusters of weakly interacting massive particles (WIMPs) as galactic dark matter haloes. Being tangential pressure dominated, Einstein clusters are strongly anisotropic systems which can describe any galactic rotation curve by specifying the anisotropy. Due to this property, Einstein clusters may be considered as dark matter candidates. We analyse the stability of the Einstein clusters against both radial and non-radial pulsations, and we show that the Einstein clusters are dynamically stable. With the use of the Buchdahl type inequalities for anisotropic bodies, we derive upper limits on the velocity of the particles defining the cluster. These limits are consistent with those obtained from stability considerations. The study of light deflection shows that the gravitational lensing effect is slightly smaller for the Einstein clusters as compared to the singular isothermal density sphere model for dark matter. Therefore, lensing observations may discriminate, at least, in principle, between Einstein cluster and the other dark matter models.     

Laser Interferometer Space Antenna double black holes: dynamics in gaseous nuclear discs

We study the inspiral of double black holes, with masses in the Laser Interferometer Space Antenna ( LISA ) window of detectability, orbiting inside a massive circumnuclear, rotationally supported gaseous disc. Using high-resolution smoothed particle hydrodynamics simulations, we follow the black hole dynamics in the early phase when gas-dynamical friction acts on the black holes individually, and continue our simulation until they form a close binary. We find that in the early sinking the black holes lose memory of their initial orbital eccentricity if they corotate with the gaseous disc. As a consequence, the massive black holes bind forming a binary with a low eccentricity, consistent with zero within our numerical resolution limit. The cause of circularization resides in the rotation present in the gaseous background where dynamical friction operates. Circularization may hinder gravitational waves from taking over and leading the binary to coalescence. In the case of counter-rotating orbits, the initial eccentricity (if present) does not decrease, and the black holes may bind forming an eccentric binary. When dynamical friction has subsided, for equal mass black holes and regardless their initial eccentricity, angular momentum loss, driven by the gravitational torque exerted on the binary by surrounding gas, is nevertheless observable down to the smallest scale probed (≃1 pc). In the case of unequal masses, dynamical friction remains efficient down to our resolution limit, and there is no sign of formation of any ellipsoidal gas distribution that may further harden the binary. During inspiral, gravitational capture of gas by the black holes occurs mainly along circular orbits; eccentric orbits imply high relative velocities and weak gravitational focusing. Thus, the active galactic nucleus activity may be excited during the black hole pairing process and double active nuclei may form when circularization is completed, on distance scales of tens of parsecs.     

The onset of General Relativity: gravitationally redshifted emission lines

We study and quantify gravitational redshift by means of relativistic ray tracing simulations of emission lines. The emitter model is based on thin, Keplerian rotating rings in the equatorial plane of a rotating black hole. Emission lines are characterised by a generalized fully relativistic Doppler factor or redshift associated with the line core. Two modes of gravitational redshift, shift and distortion, become stronger with the emitting region closer to the Kerr black hole. Shifts of the line cores reveal an effect at levels of 0.0015 to 60% at gravitational radii ranging from 10⁵ to 2. The corresponding Doppler factors range from 0.999985 to 0.4048. Line shape distortion by strong gravity, i.e. very skewed and asymmetric lines occur at radii smaller than roughly ten gravitational radii. Gravitational redshift decreases with distance to the black hole but remains finite due to the asymptotical flatness of black hole space–time. The onset of gravitational redshift can be tested observationally with sufficient spectral resolution. Assuming a resolving power of ∼100000, yielding a resolution of ≈0.1 Å for optical and near‐infrared broad emission lines, the gravitational redshift can be probed out to approximately 75000 gravitational radii. In general, gravitational redshift is an indicator of black hole mass and spin as well as for the inclination angle of the emitter, e.g. an accretion disk. We suggest to do multi‐wavelength observations because all redshifted features should point towards the same central mass. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Collisions in self-gravitating clouds of planetesimals

A theory of partially elastic collisions is constructed for frictionless planetesimals in an arbitrary gravitational field. The non-zero size of the particles and the influence of gravitational encounters are included. The equations for a self-gravitating rotationally symmetric disk or ring are written in an explicit form. Such systems turn out to be bimodal in the same sense as the Keplerian systems, i.e. there are two kinds of stable configurations which may co-exist in adjacent regions without disturbing the mechanical equilibrium. The transitions from one mode to another can also occur at essentially smaller values of the optical thickness than those previously found for Saturn's rings: in one of the numerically studied cases the transition from the dense to the rarefied mode occurred at the optical thickness 3×10^?5 while the reversed process corresponded to a higher value, 10^?2. The difference illustrates the dependence of the transition on its direction. The characteristic S shape which several authors have found for the relation between the viscosity and the optical thickness in Keplerian systems becomes more complicated if the contribution of self-gravitation increases. In some cases the stable solutions also imply a certain minimum value of the optical thickness.     

The propagation of gravity waves through a critical layer for conditions of moderate wind shear

Solutions of the linearised hydrodynamic equations for a viscous atmosphere using (i) a full-wave integration procedure and (ii) a simplified analytical approach are used to examine the attenuation of gravity waves passing through a critical layer, where the horizontal phase velocity is equal to that of the mean wind. Particular attenuation is paid to the variation of this attenuation with values of Richardson number, Ri, greater than unity. The two sets of results are in good agreement with the predictions of Booker and Bretherton (1967) for an inviscid fluid for values of Ri up to about 4. However, a marked discrepancy from these predicted values is found for larger values of Ri, the present results indicating substantially smaller attenuation. Further calculations suggest that the wave-amplitude attenuation factor predicted by the inviscid model is approached asymptotically in the limit of vanishingly small viscosity and thermal conductivity coefficients.The inclusion of viscosity and thermal conduction gives rise to three characteristic modes of propagation for each direction of energy flow, in place of the single mode occurring in the inviscid case. The importance of energy exchange between these modes in the propagation through the critical layer is demonstrated.     

Exponential metric fields

The Laser Interferometer Space Antenna (LISA) mission will use advanced technologies to achieve its science goals: the direct detection of gravitational waves, the observation of signals from compact (small and dense) stars as they spiral into black holes, the study of the role of massive black holes in galaxy evolution, the search for gravitational wave emission from the early Universe. The gravitational red-shift, the advance of the perihelion of Mercury, deflection of light and the time delay of radar signals are the classical tests in the first order of General Relativity (GR). However, LISA can possibly test Einstein’s theories in the second order and perhaps, it will show some particular feature of non-linearity of gravitational interaction. In the present work we are seeking a method to construct theoretical templates that limit in the first order the tensorial structure of some metric fields, thus the non-linear terms are given by exponential functions of gravitational strength. The Newtonian limit obtained here, in the first order, is equivalent to GR.     

The stress state of Venusian crust and variations of its thickness: Implication for tectonics and geodynamics

The data obtained for the heights of the relief and the external gravitational field of Venus for spherical harmonics with degree and order up to 18 allow one to start theoretical analysis of the crust-mantle boundary (Venusian Moho) and stress state of the planetary interior. We suppose that Venusian convection is confined by floating massive crust. Apparently the convection in the upper mantle of Venus is separated from that one in the lower mantle and its lateral scale must be essentially smaller than on Earth. So, the convection is reflected to a larger degree of the gravitational field of the planet than for Earth. The spherical harmonic expansion of the topography for Venus correlates with corresponding expansion of the non-equilibrium part of the gravitational potential for n = 3–18. At the same time the relief of Venus is significantly compensated. It is reasonable to suppose that the gravity field for these harmonics is due to crustal thickness variations and, probably, to variations of crustal density. Thus, in the proposed scheme the Moho's relief causes the partial isostatic compensation of the topography.All calculations are carried out for the series of realistic models of Venus taking into consideration an asthenosphere. The asthenosphere is modeled either by a weakened (shear modulus is reduced), or by a liquid inviscid layer. We also suppose that the asthenosphere extends from the base of crust to a depth of 418 km, and the density contrast across the Moho boundary is –0.4 g * cm^–3. If the actual density contrast across the Moho is less than the supposed one by some factor, then one must increase the amplitudes of the roots and inverse roots by the same factor. The results for the Moho's relief and stresses in the crust are presented for the case of the mean thickness of the crust of 50 km, which satisfies the probable upper (connected with phase transitions in waterless basalts) and lower (appearing in the framework of our interpretation) limits.On the whole, the crust-mantle boundary on Venus is evidently smooth, and the stress level in the crust is appreciably smaller than the crustal stresses on the Earth. The strong sensitivity of the stresses character to the parameters of the model of external layers of Venus together with geological data allow us to begin a preliminary investigation of the tectonical structure and geodynamics of the planet.'Geology and Tectonics of Venus', special issue edited by Alexander T. Basilevsky (USSR Acad. of Sci. Moscow), James W. Head (Brown University, Providence), Gordon H. Pettengill (MIT, Cambridge, Massachusetts) and R. S. Saunders (J.P.L., Pasadena).     

Implications from the motion of outer belt asteroids

A principal feature of the asteroidal distribution is the rapid truncation of its population outward from ～3.4 AU. This paper presents further evidence, based on the motion and distribution of certain minor planets with large semimajor axes, that this truncation cannot be strictly the result of gravitational perturbations of the major planets even acting over times of ～10⁹ years. The motion of other outer asteroids sets a probable upper limit of 0.081 on Jupiter's eccentricity.