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1.
Hidden Mass in the Asteroid Belt   总被引：1，自引：0，他引：1  
The total mass of the asteroid belt is estimated from an analysis of the motions of the major planets by processing high precision measurements of ranging to the landers Viking-1, Viking-2, and Pathfinder (1976-1997). Modeling of the perturbing accelerations of the major planets accounts for individual contributions of 300 minor planets; the total contribution of all remaining small asteroids is modeled as an acceleration caused by a solid ring in the ecliptic plane. Mass Mring of the ring and its radius R are considered as solve-for parameters. Masses of the 300 perturbing asteroids have been derived from their published radii based mainly on measured fluxes of radiation, making use of the corresponding densities. This set of asteroids is grouped into three classes in accordance with physical properties and then corrections to the mean density for each class are estimated in the process of treating the observations. In this way an improved system of masses of the perturbing asteroids has been derived.The estimate Mring≈(5±1)×10−10M⊙ is obtained (M⊙ is the solar mass) whose value is about one mass of Ceres. For the mean radius of the ring we have R≈2.80 AU with 3% uncertainty. Then the total mass Mbelt of the main asteroid belt (including the 300 asteroids mentioned above) may be derived: Mbelt≈(18±2)×10−10M⊙. The value Mbelt includes masses of the asteroids which are already discovered, and the total mass of a large number of small asteroids—most of which cannot be observed from the Earth. The second component Mring is the hidden mass in the asteroid belt as evaluated from its dynamical impact onto the motion of the major planets.Two parameters of a theoretical distribution of the number of asteroids over their masses are evaluated by fitting to the improved set of masses of the 300 asteroids (assuming that there is no observational selection effect in this set). This distribution is extrapolated to the whole interval of asteroid masses and as a result the independent estimate Mbelt≈18×10−10M⊙ is obtained which is in excellent agreement with the dynamical finding given above.These results make it possible to predict the total number of minor planets in any unit interval of absolute magnitude H. Such predictions are compared with the observed distribution; the comparison shows that at present only about 10% of the asteroids with absolute magnitude H<14 have been discovered (according to the derived distribution, about 130,000 such asteroids are expected to exist).  相似文献   

2.
It is shown here that Newton’s gravity law can be derived from the uncertainty principle. The idea is that as the distance between two bodies in mutual orbit decreases, their uncertainty of position decreases, so their momentum and hence the force on them must increase to satisfy the uncertainty principle. When this result is summed over all the possible interactions between the Planck masses in the two bodies, Newton’s gravity law is obtained. This model predicts that masses less than the Planck mass will be unaffected by gravity and so it may be tested by looking for an abrupt decrease in the density of space dust, for masses above the Planck mass.  相似文献   

3.
An inequality that allows the minimum sum of the component masses for a binary, M0, to be determined was derived from simple geometric considerations. This quantity satisfies the observed orbital motion according to Newton's law with a known parallax. The M0 value can be calculated if the apparent-motion parameters for the components, including the curvature of the observed short orbital arc, were determined from observations. We estimated M0 for 14 Pulkovo program stars for which the apparent orbital arc covered with observations was no less than 10°. We compare M0 with the masses estimated from the mass-luminosity relation. A significant mass excess was found for the star ADS 10329.  相似文献   

4.
The temperatures, radii, and masses of 81 He-rich white dwarfs are calculated from photometric data. It is shown that, on the average, they are less massive than DA white dwarfs: 70% of He-rich white dwarfs have masses<0.55M ⊙. Space density and birth-rate for different mass groups of H-rich and He-rich white dwarfs are obtained. Birth-rate is 1×10?12 pc?3 yr?1 and 1.5×10?12pc?3yr?1 for He-rich and H-rich white dwarfs, respectively. The mean mass of nascent white dwarfs is about 0.55M ⊙. It is shown thatV Tand its dispersion σ are correlated with the mass of white dwars, and from this progenitors' masses — of different mass groups of white dwarfs are estimated.  相似文献   

5.
Evolutionary tracks from the zero age main sequence to the asymptotic giant branch were computed for stars with initial masses 2 M ⊙ ≤ M ZAMS ≤ 5 M ⊙ and metallicity Z = 0.02. Some models of evolutionary sequences were used as initial conditions for equations of radiation hydrodynamics and turbulent convection describing radial stellar pulsations. The early asymptotic giant branch stars are shown to pulsate in the fundamental mode with periods 30 day ? Π ? 400day. The rate of period change gradually increases as the star evolves but is too small to be detected (Π?/Π < 10?5 yr?1). Pulsation properties of thermally pulsing AGB stars are investigated on time intervals comprising 17 thermal pulses for evolutionary sequences with initial masses M ZAMS = 2 M ⊙ and 3 M ⊙ and 6 thermal pulses for M ZAMS = 4 M ⊙ and 5 M ⊙. Stars with initial masses M ZAMS ≤ 3 M ⊙ pulsate either in the fundamental mode or in the first overtone, whereas more massive red giants (M ZAMS ≥ 4 M ⊙) pulsate in the fundamental mode with periods Π ? 103 day. Most rapid pulsation period change with rate ?0.02 yr?1 ? Π?/Π ? ?0.01 yr?1 occurs during decrease of the surface luminosity after the maximum of the luminosity in the helium shell source. The rate of subsequent increase of the period is Π?/Π ? 5 × 10?3 yr?1.  相似文献   

6.
We analytically generalize the well-known solution of steady supersonic spherically symmetric gas accretion onto a star (Bondi 1952) for an iron atmosphere with completely degenerate electrons with an arbitrary degree of relativity. This solution is used for typical physical conditions in the vicinity of protoneutron stars produced by gravitational collapse with masses M 0=(1.4?1.8)M ⊙ and over a wide range of nonzero “iron gas” densities at infinity, ρ∞=(104?5×106)g cm?3. Under these conditions, we determine all accretion parameters, including the accretion rate, whose value is ～(10?50)M ⊙s?1 at M 0=1.8M ⊙ (it is a factor of 1.7 lower for M 0=1.4M ⊙, because the accretion rate is exactly ∝M 0 2 ). We take into account the effect of accreting-gas rotation in a quasi-one-dimensional approximation, which has generally proved to be marginal with respect to the accretion rate.  相似文献   

7.
Population synthesis is used to model the number of neutron stars in globular clusters that are observed as low-mass X-ray sources and millisecond radio pulsars. The dynamical interactions between binary and single stars in a cluster are assumed to take place only with a continuously replenished “background” of single stars whose properties keep track of the variations in parameters of the cluster as a whole and the evolution of single stars. We use the hypothesis that the neutron stars forming in binary systems from components with initial masses of ～8–12 M ⊙ during the collapse of degenerate O-Ne-Mg cores through electron captures do not acquire a high space velocity. The remaining neutron stars (from single stars with masses >8 M ⊙ or from binary components with masses >12 M ⊙) are assumed to be born with high space velocities. According to this hypothesis, a sizeable fraction of the forming neutron stars remain in globular clusters (about 1000 stars in a cluster with a mass of 5 × 105 M ⊙). The number of millisecond radio pulsars forming in such a cluster in the case of accretion-driven spinup in binary systems is found to be ～10, in agreement with observations. Our modeling also reproduces the observed shape of the X-ray luminosity function for accreting neutron stars in binary systems with normal and degenerate components and the distribution of spin periods for millisecond pulsars.  相似文献   

8.
We consider a cosmological model in which part of the Universe, Ωh～10?5, is in the form of primordial black holes with masses of ～ 105 M ⊙. These primordial black holes were the centers for growing protogalaxies, which experienced multiple mergers with ordinary galaxies and with each other. The galaxy formation is accompanied by the merging and growth of central black holes in the galactic nuclei. We show that the recently discovered correlations between central black hole masses and galactic bulge parameters naturally arise in this scenario.  相似文献   

9.
The results of investigations of a number of eclipsing Wolf-Rayet binaries are presented. The ‘core’ radiuses, the ‘core’ temperatures and masses of WR stars in the eclipsing WR+OB binary systems V 444 Cyg, CX Cep, CQ Cep, and CV Ser are obtained (see Table I). The results obtained from the light curves analysis of the V 444 Cyg in the range λλ2460 Å-3.5μ give strong evidence for the Beals (1944) model of WR phenomenon. The chromospheric-coronal effects in the WN5 extended atmosphere are not observed up to a distance ofr?20R ⊙. In the Hertzsprung—Russell diagram all the WR stars lie on the left side from the main sequence between the main sequence and the sequence of uniform helium stars (see Figure 9). Their locations are close to those of the helium remnants formed as a result of mass exchange in massive close binary systems. The period variations in the systems V 444 Cyg and CQ Cep have been discovered and a reliable value of the mass loss rateM=10?5 M ⊙yr?1 is obtained, for the two WR stars. The results of the photometric and spectroscopic investigations of the WR stars with low mass companions (post X-ray binary stage?) are presented too (see Table II). The masses of the companions are (1–2)M ⊙, their optical luminosity is ～1036, erg s?1 which implies that these companions cannot be the normal stars. It is possible that these companions are neutron stars accreting from the stellar wind of the WR stars. Low values of the X-ray luminosities of such WR stars with low mass companions imply that the accretion of matter in such systems is distinct from the accretion process in classical X-ray binary systems. It is noted also that the parameters of low massive companions coupled with WR stars are close to those of helium stars.  相似文献   

10.
The fast spinning B-star Regulus has recently been found to be orbited by a fainter companion in a close circular path with orbital period P b=40.11(2) d. Being its equatorial radius R e 32% larger than the polar one R p, Regulus possesses a remarkable quadrupole mass moment Q. We investigate the effects of Q on the orbital period P b of its companion in order to see if they are measurable, given the present-day level of accuracy in measuring P b. Conversely, we will look for deviations from the third Kepler law, attributed to the quadrupole mass moment Q of Regulus, to constrain the ratio γ=m/M of the system’s masses. The impact of Q on the orbital period is analytically worked out with a straightforward perturbative approach. The resulting correction P Q is compared to other competing dynamical effects. P Q and the Keplerian period P Kep are expressed in terms of the phenomenologically determined system’s parameters; γ is treated as an unknown. P Q is compared to the observational accuracy in measuring the orbital period δ P b=0.02 d and to the systematic uncertainty δ(P Kep) due to the errors in the system’s parameters entering it. The discrepancy ΔP=|P b?P Kep| is examined in order to see for which values of γ it becomes statistically significant. The physical meaning of the obtained range of values for γ is discussed in terms of Q. P Q is larger than δ P b but still smaller than the systematic uncertainty in P Kep by two orders of magnitude. The major sources of bias are the velocity semiamplitude K of the motion of the primary and its mass M. Assuming edge-on configuration, i.e. i=90 deg, if γ?0.096 Q would be positive, i.e. Regulus would be prolate, contrary to the observations. If γ?0.078 Q would be negative, but its magnitude would be one-two orders of magnitude larger than the approximate estimate Q≈M(R p 2 ?R e 2 )=?2.4±0.5×1049 kg?m2. Regulus is the first extrasolar binary system in which the orbital effects of the asphericity of the primary are larger than the observational sensitivity; moreover, no other competing aliasing orbital effects are present. Thus, it is desirable that it will become the object of future intensive observational campaigns in order to reduce the systematic uncertainty due to the system’s parameters below the measurability threshold.  相似文献   

11.
《Planetary and Space Science》1999,47(10-11):1183-1200
Interior models of Jupiter and Saturn are calculated and compared in the framework of the three-layer assumption, which rely on the perception that both planets consist of three globally homogeneous regions: a dense core, a metallic hydrogen envelope, and a molecular hydrogen envelope. Within this framework, constraints on the core mass and abundance of heavy elements (i.e. elements other than hydrogen and helium) are given by accounting for uncertainties on the measured gravitational moments, surface temperature, surface helium abundance, and on the inferred protosolar helium abundance, equations of state, temperature profile and solid/differential interior rotation. Results obtained solely from static models matching the measured gravitational fields indicate that the mass of Jupiter’s dense core is less than 14 M⊕ (Earth masses), but that models with no core are possible given the current uncertainties on the hydrogen–helium equation of state. Similarly, Saturn’s core mass is less than 22 M⊕ but no lower limit can be inferred. The total mass of heavy elements (including that in the core) is constrained to lie between 11 and 42 M⊕ in Jupiter, and between 19 and 31 M⊕ in Saturn. The enrichment in heavy elements of their molecular envelopes is 1–6.5, and 0.5–12 times the solar value, respectively. Additional constraints from evolution models accounting for the progressive differentiation of helium (Hubbard WB, Guillot T, Marley MS, Burrows A, Lunine JI, Saumon D, 1999. Comparative evolution of Jupiter and Saturn. Planet. Space Sci. 47, 1175–1182) are used to obtain tighter, albeit less robust, constraints. The resulting core masses are then expected to be in the range 0–10 M⊕, and 6–17 M⊕ for Jupiter and Saturn, respectively. Furthermore, it is shown that Saturn’s atmospheric helium mass mixing ratio, as derived from Voyager, Y=0.06±0.05, is probably too low. Static and evolution models favor a value of Y=0.11−0.25. Using, Y=0.16±0.05, Saturn’s molecular region is found to be enriched in heavy elements by 3.5 to 10 times the solar value, in relatively good agreement with the measured methane abundance. Finally, in all cases, the gravitational moment J6 of models matching all the constraints are found to lie between 0.35 and 0.38×10−4 for Jupiter, and between 0.90 and 0.98×10−4 for Saturn, assuming solid rotation. For comparison, the uncertainties on the measured J6 are about 10 times larger. More accurate measurements of J6 (as expected from the Cassini orbiter for Saturn) will therefore permit to test the validity of interior models calculations and the magnitude of differential rotation in the planetary interior.  相似文献   

12.
We succeeded in separating the absorption lines of both the primary C1 and the secondary C2 component in the spectra of the young massive binary θ 1 OriC (O6Vp + B0V, mass sum 44 ± 7M ⊙), obtained during the period from November 1995 to February 2013 with different telescopes. These observations allowed us to derive, for the first time, the radial velocities of both components. The orbitalmotion of the secondary star is traced through its weak (the line depth is approximately 0.01–0.02) absorption lines of CII, NII, OII, Si III, which are broadened by fast rotation of the star. Silicon absorptions Si III λλ 4553, 4568, and 4575 are better suited for radial velocity measurements than the other lines. From the velocity curves, we obtained the systemic velocity of the system, γ = 31 ±2 kms?1, and semi-amplitudes of the C1 and C2 velocities: K 1 = 15 ± 2 kms?1, K 2 = 43 ± 3 kms?1. This leads to individual component masses of M 1 = 33 ± 5 M ⊙ and M 2 = 11 ± 5 M ⊙, based on the adopted mass sum. At present, the combined spectroscopic-interferometric orbital solution cannot be obtained because of the large scatter of velocity measurements caused by chaotic line shifts in the spectrum of the primary star and by the weakness of wide absorptions from the secondary. New spectroscopy with a resolution of R ≥ 30000 and S/N ratio over 200 performed in the period close to the periastron passage in the second half of 2013, as well as additional long-baseline interferometry, will be decisive in refining the parameters of θ 1 OriC. We expect that as a result of this campaign, masses and luminosities of the components will be determined with an accuracy of 2–3%.  相似文献   

13.
The results of calculations of graphite grain formation in the atmospheres of R CrB stars are given. The parameters for the models wereM=1M ⊙,M bol=?6 mag. The effective temperature ranged from 5300K to 8300K. The chemical composition corresponded to the hydrogen-deficient carbon rich mixture:X=0,Y=0.9,Z c=0.1. The results obtained show the existence of a critical mass loss rate which is ranged fromM *≈10?6 M ⊙yr?1 forT eff=5300 K toM *≈10?5 M ⊙ yr?1 forT eff=8300 K. As soon as the rate of mass loss exceedsM * by 3–5 times the degree of condensation of carbon changes from 0 to 0.7. The finite radii of grains are about from 0.01 μm to 0.6 μm depending on the density near the condensation point, the velocity of matter outflow, and the stellar effective temperature. The duration of grain growth should amount to some dozens of days. It is supposed that the most probable explanation of dust-shell formation around R CrB stars is graphite condensation behind a shock wave arising from nonlinear stellar pulsation.  相似文献   

14.
We show that hydrostatically equilibrium models for the thin photospheres of helium stars based on new opacities κR (OPAL and OP) can be constructed only for masses M<5M ⊙. The parameter Г=κL/4πGMc, defined as the ratio of light pressure to gravity, exceeds a critical value of 1.0 for larger masses, which must result in mass outflow under light pressure. This mass limit matches the observed lower limit for the masses of Wolf-Rayet stars (M WR>5M ⊙)), which is an additional argument that the Wolf-Rayet stellar cores are actually helium stars. By solving the equation of radiative transfer in extended atmospheres, we construct a semiempirical model for a WN5 star (M WN5=10M ⊙)) with a helium core and an expanding envelope, whose physical and geometric parameters are known mainly from light-curve solution for the eclipsing binary V444 Cyg (WN5+06): outflow rate $\dot M \approx 1.0 \times 10^{ - 5} M_ \odot yr^{ - 1} $ , terminal velocity V ∞≈2000 km s?1, and expanding-envelope optical depth τenv≈25. The temperature at the outer boundary of the photosphere of a helium star surrounded by such an envelope is approximately 130 kK higher than that in the absence of an envelope, being T ph≈240 kK. Because of the high temperatures, the absorption coefficients at the corresponding photospheric levels are smaller than those in models with no envelope; therefore, the photosphere turns out to be in hydrostatic equilibrium and stable against light pressure (Гmax≈0.9). As a way out of this conflicting situation (an expanding envelope together with a hydrostatically equilibrium photosphere), we propose a model of discrete mass outflow, which is also supported by the observed cloudy structure of the envelopes in this type of stars. To quantitatively estimate parameters of the nonuniform outflow model requires detailed gas-dynamical calculations.  相似文献   

15.
In this article the charged analogues of recently derived Buchdahl’s type fluid spheres have been obtained by considering a particular form of electric field intensity. In this process, Einstein–Maxwell field equations yield eight different classes of solutions, joining smoothly with the exterior Reissner–Nordstrom metric at the pressure free intersurface. Out of the eight solutions only seven could be utilized to represent superdense star models with ultrahigh surface density of the order 2×1014 gm cm−3. The maximum masses of the star models were found to be 8.223931MΘ and 8.460857MΘ subject to strong and weak energy conditions, respectively, which are much higher than the maximum masses 3.82MΘ and 4.57MΘ allowed in the neutral cases. The velocity of sound seen to be less than that of light throughout the star models.  相似文献   

16.
Ravit Helled  Gerald Schubert 《Icarus》2008,198(1):156-162
Sedimentation rates of silicate grains in gas giant protoplanets formed by disk instability are calculated for protoplanetary masses between 1 MSaturn to 10 MJupiter. Giant protoplanets with masses of 5 MJupiter or larger are found to be too hot for grain sedimentation to form a silicate core. Smaller protoplanets are cold enough to allow grain settling and core formation. Grain sedimentation and core formation occur in the low mass protoplanets because of their slow contraction rate and low internal temperature. It is predicted that massive giant planets will not have cores, while smaller planets will have small rocky cores whose masses depend on the planetary mass, the amount of solids within the body, and the disk environment. The protoplanets are found to be too hot to allow the existence of icy grains, and therefore the cores are predicted not to contain any ices. It is suggested that the atmospheres of low mass giant planets are depleted in refractory elements compared with the atmospheres of more massive planets. These predictions provide a test of the disk instability model of gas giant planet formation. The core masses of Jupiter and Saturn were found to be ∼0.25 M⊕ and ∼0.5 M⊕, respectively. The core masses of Jupiter and Saturn can be substantially larger if planetesimal accretion is included. The final core mass will depend on planetesimal size, the time at which planetesimals are formed, and the size distribution of the material added to the protoplanet. Jupiter's core mass can vary from 2 to 12 M⊕. Saturn's core mass is found to be ∼8 M⊕.  相似文献   

17.
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18.
Supermassive black holes, with masses of 106 M to more than 109 M, are among the most spectacular objects in the Universe, and are laboratories for physics in extreme conditions. The primary goal of ARISE (Advanced Radio Interferometry between Space and Earth) is to use the technique of Space VLBI to increase our understanding of black holes and their environments, by imaging the havoc produced in the near vicinity of the black holes by their enormous gravitational fields. The mission will be based on a 25-meter space-borne radio telescope operating at frequencies between 8 and 86 GHz, roughly equivalent to an orbiting element of the Very Long Baseline Array. In an elliptical orbit with an apogee height of 40 000–100 000 km, ARISE will provide a resolution of 15 microarcsecond or better, 5–10 times better than that achievable on the ground. At frequencies of 43 and 86 GHz, the resolution of light weeks to light months in distant quasars will complement the gamma-ray and X-ray observations of high-energy photons, which come from the same regions near the massive black holes. At 22 GHz, ARISE will image the H2O maser disks in active galaxies more than 15 Mpc from Earth, probing accretion physics and giving accurate measurements of black-hole masses. ARISE also will study gravitational lenses at resolutions of tens of microarcseconds, yielding important information on the dark-matter distribution and on the possible existence of compact objects with masses of 103 M to 106 M.  相似文献   

19.
The stars in the Main Sequence are seen as a hierarchy of objects with different massesM and effective dynamical radiiR eff=R/α given by the stellar radii and the coefficients for the inner structure of the stars. As seen in a previous work (Paper I), during the lifetime in the Main SequenceR eff(t) remains a near invariant when compared to the variation in the time ofR(t) and α(t). With such an effectiveR eff one obtains the amounts of actionA c(M), the effective densities ρeff(M)=ρ(M)α3(M), the densities of action and of energy (or mean presures in the stellar interior)a c(M),e c(M), and the potential energiesE p(M). The amounts of action areA c∝M k withk≈1.87 for the M stars,k≈5/3 for the KGF stars, andk≈1.83 for the A and earlier stars, representing very simples conditions for the other dynamical parameters. For instancek≈5/3 means a near invariant effective density αeff for the KGF stars, while for such stars the mean densities and coefficients α present the strongest variations with masses ρ(M)∝M ?1.81, α(M)∝M0.6. The cases for the M stars (e c(M)∝M ?1) and for the A and earlier stars (betweena c(M)=constant and αeff(M)∝M ?1) and also discussed. These conditions for the earlier stars also represent reasonable mean values for the whole stellar hierarchy in the range of masses 0.2M ⊙≤M≤25M ⊙. With all this, one can build ‘dynamical’ HR diagrams withA c(M), Ep(M), αeff M ?p , etc., whose characteristics are analogous to these in the photometrical HR diagram. A comparison is made betweenA c(M) from the models here and the HR diagram with the best known stars of luminosity classes IV, V, and white dwarfs. The comparison of the potential energiesE p(M)∝M ?p according to the stellar models used here and the observed frequency function ψ(M∝M ?q (number of stars in a given interval of masses) from different authors suggests the possibility that the productE p(M)ψ(M) is a constant, but this must be confirmed with further studies of the function ψ(M) and its fine structure. There are analogies between the formulation used here for the stellar hierarchy and other physical processes, for instance, in modified forms of the Kolmogorov law of turbulence and in the formulation used for the hierarchy of molecular clouds in gravitational equilibrium. Besides, the function of actionA c(M) for the stars has analogous properties to the relations of angular momenta and massesJ(M) for different types of objects. The cosmological implications of all this are discussed.  相似文献   

20.
The grid of evolutionary tracks of population II stars with initial masses 0.81 M⊙ ≤ MZAMS ≤ 0.85 M⊙ and chemical composition of the globular cluster M3 is computed. Selected models of horizontal branch stars were used as initial conditions for solution of the equations of radiation hydrodynamics and time–dependent convection describing radial stellar oscillations. The boundaries of the instability strip on the Herztsprung–Russel diagram were determined using ≈100 hydrodynamic models of RR Lyr pulsating variables. For each evolutionary track crossing the instability strip the pulsation period was determined as a function of evolutinary time. The rate of period change of most variables is shown to range within ?0.02 ≤ \(\dot{\Pi}\) ≤ 0.05 day/106 yr. Theoretical estimate of the mean period change rate obtained by the population synthesis method is 〈\(\dot{\Pi}\)〉 = 6.0 × 10?3 day/106 yr and agrees well with observations of RR Lyr variables of the globular cluster M3.  相似文献   

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