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1.
Two types of trial three-layer models have been constructed for the satellites Io and Europa. In the models of the first type (Io1 and E1), the cores are assumed to consist of eutectic Fe-FeS melt with the densities ρ 1 = 5.15 g cm?3 (Io1) and 5.2 g cm?3 (E1). In the models of the second type (Io3 and E3), the cores consist of FeS with an admixture of nickel and have the density ρ 1 = 4.6 g cm?3. The approach used here differs from that used previously both in chosen model chemical composition of these satellites and in boundary conditions imposed on the models. The most important question to be answered by modeling the internal structure of the Galilean satellites is that of the condensate composition at the formation epoch of Jupiter’s system. Jupiter’s core and the Galilean satellites were formed from the condensate. Ganymede and Callisto were formed fairly far from Jupiter in zones with temperatures below the water condensation temperature, water was entirely incorporated into their bodies, and their modeling showed the mass ratio of the icy (I) component to the rock (R) component in them to be I/R ~ 1. The R composition must be clarified by modeling Io and Europa. The models of the second type (Io3 and E3), in which the satellite cores consist of FeS, yield 25.2 (Io3) and 22.8 (E3) for the core masses (in weight %). In discussing the R composition, we note that, theoretically, the material of which the FeS+Ni core can consist in the R accounts for ~25.4% of the satellite mass. In this case, such an important parameter as the mantle silicate iron saturation is Fe# = 0.265. The Io3 and E3 models agree well with this theoretical prediction. The models of the first and second types differ markedly in core radius; thus, in principle, the R composition in the formation zone of Jupiter’s system can be clarified by geophysical studies. Another problem studied here is that of the error made in modeling Io and Europa using the Radau-Darvin formula when passing from the Love number k 2 to the nondimensional polar moment of inertia $\bar C$ . For Io, the Radau-Darvin formula underestimates the true value of $\bar C$ by one and a half units in the third decimal digit. For Europa, this effect is approximately a factor of 3 smaller, which roughly corresponds to a ratio of the small parameters for the satellites under consideration α Io/α Europa ~ 3.4. In modeling the internal structure of the satellites, the core radius depends strongly on both the mean moment of inertia I* and k 2. Therefore, the above discrepancy in $\bar C$ for Io is appreciable.  相似文献   

2.
We construct a theory of the equilibrium figure and gravitational field of the Galilean satellite Io to within terms of the second order in the small parameter α. We show that to describe all effects of the second approximation, the equation for the figure of the satellite must contain not only the components of the second spherical function, but also the components of the third and fourth spherical functions. The contribution of the third spherical function is determined by the Love number of the third order h3, whose model value is 1.6582. Measurements of the third-order gravitational moments could reveal the extent to which the hydrostatic equilibrium conditions are satisfied for Io. These conditions are J3=C32=0 and C31/C33=?6. We have calculated the corrections of the second order of smallness to the gravitational moments J2 and C22. We conclude that when modeling the internal structure of Io, it is better to use the observed value of k2 than the moment of inertia derived from k2. The corrections to the lengths of the semiaxes of the equilibrium figure of Io are all positive and equal to ~64.5, ~26, and ~14 m for the a, b, and c axes, respectively. Our theory allows the parameters of the figure and the fourth-order gravitational moments that differ from zero to be calculated. For the homogeneous model, their values are:\(s_4 = \frac{{885}}{{224}}\alpha ^2 ,s_{42} = - \frac{{75}}{{224}}\alpha ^2 ,s_{44} = \frac{{15}}{{896}}\alpha ^2 ,J_4 = - \frac{{885}}{{224}}\alpha ^2 ,C_{42} = \frac{{75}}{{224}}\alpha ^2 ,C_{44} = \frac{{15}}{{896}}\alpha ^2 \).  相似文献   

3.
We present the results of extensive numerical modeling of the Martian interior. Yoder et al. in 2003 reported a mean moment of inertia of Mars that was somewhat smaller than the previously used value and the Love number k2 obtained from observations of solar tides on Mars. These values of k2 and the mean moment of inertia impose a strong new constraint on the model of the planet. The models of the Martian interior are elastic, while k2 contains both elastic and inelastic components. We thoroughly examined the problem of partitioning the Love number k2 into elastic and inelastic components. The information necessary to construct models of the planet (observation data, choice of a chemical model, and the cosmogonic aspect of the problem) are discussed in the introduction. The model of the planet comprises four submodels—a model of the outer porous layer, a model of the consolidated crust, a model of the silicate mantle, and a core model. We estimated the possible content of hydrogen in the core of Mars. The following parameters were varied while constructing the models: the ferric number of the mantle (Fe#) and the sulfur and hydrogen content in the core. We used experimental data concerning the pressure and temperature dependence of elastic properties of minerals and the information about the behavior of Fe(γ-Fe ), FeS, FeH, and their mixtures at high P and T. The model density, pressure, temperature, and compressional and shear velocities are given as functions of the planetary radius. The trial model M13 has the following parameters: Fe#=0.20; 14 wt % of sulfur in the core; 50 mol % of hydrogen in the core; the core mass is 20.9 wt %; the core radius is 1699 km; the pressure at the mantle-core boundary is 20.4 GPa; the crust thickness is 50 km; Fe is 25.6 wt %; the Fe/Si weight ratio is 1.58, and there is no perovskite layer. The model gives a radius of the Martian core within 1600–1820 km while ≥30 mol % of hydrogen is incorporated into the core. When the inelasticity of the Martian interior is taken into account, the Love number k2 increases by several thousandths; therefore, the model radius of the planetary core increases as well. The prognostic value of the Chandler period of Mars is 199.5 days, including one day due to inelasticity. Finally, we calculated parameters of the equilibrium figure of Mars for the M13 model: J 2 0 = 1.82 × 10?3, J 4 0 = ?7.79 × 10?6, e c-m D = 1/242.3 (the dynamical flattening of the core-mantle boundary).  相似文献   

4.
A family of well behaved perfect fluid balls has been derived starting with the metric potential g 44=B(1+Cr 2) n for all positive integral values of n. For n≥4, the members of this family are seen to satisfy the various physical conditions e.g. c 2 ρp≥0,dp/dr<0,/dr<0, along with the velocity of sound \((\sqrt{dp/c^{2}d\rho} )< 1\) and the adiabatic index ((p+c 2 ρ)/p)(dp/(c 2 ))>1. Also the pressure, energy density, velocity of sound and ratio of pressure and energy density are of monotonically decreasing towards the pressure free interface (r=a). The fluid balls join smoothly with the Schwarzschild exterior model at r=a. The well behaved perfect fluid balls so obtained are utilised to construct the superdense star models with their surface density 2×1014  gm/cm3. We have found that the maximum mass of the fluid balls corresponding to various values of n are decreasing with the increasing values of n. Over all maximum mass for the whole family turns out to be 4.1848M Θ and the corresponding radius as 19.4144 km while the red shift at the centre and red shift at surface as Z 0=1.6459 and Z a =0.6538 respectively this all happens for n=4. It is interesting to note that for higher values of n viz n≥170, the physical data start merging with that of Kuchowicz superdense star models and hence the family of fluid models tends to the Kuchowicz fluid models as n→∞. Consequently the maximum mass of the family of solution can not be less than 1.6096 M Θ which is the maximum mass occupied by the Kuchowicz superdense ball. Hence each member of the family for n≥4 provides the astrophysical objects like White dwarfs, Quark star, typical neutron star.  相似文献   

5.
We consider a spherically symmetric general relativistic perfect fluid in its comoving frame. It is found that, by integrating the local energy momentum conservation equation, a general form of g 00 can be obtained. During this study, we get a cue that an adiabatically evolving uniform density isolated sphere having ρ(r,t)=ρ 0(t), should comprise “dust” having p 0(t)=0; as recently suggested by Durgapal and Fuloria (J. Mod. Phys. 1:143, 2010) In fact, we offer here an independent proof to this effect. But much more importantly, we find that for the homogeneous and isotropic Friedmann-Robertson-Walker (FRW) metric having p(r,t)=p 0(t) and ρ(r,t)=ρ 0(t), \(g_{00} = e^{-2p_{0}/(p_{0} +\rho_{0})}\). But in general relativity (GR), one can choose an arbitrary tt ?=f(t) without any loss of generality, and thus set g 00(t ?)=1. And since pressure is a scalar, this implies that p 0(t ?)=p 0(t)=0 in the Big-Bang model based on the FRW metric. This result gets confirmed by the fact the homogeneous dust metric having p(r,t)=p 0(t)=0 and ρ(r,t)=ρ 0(t) and the FRW metric are exactly identical. In other words, both the cases correspond to the same Einstein tensor \(G^{a}_{b}\) because they intrinsically have the same energy momentum tensor \(T^{a}_{b}=\operatorname {diag}[\rho_{0}(t), 0,0, 0]\).  相似文献   

6.
We investigated the two deepest absorption bands observed in the spectra of stars and protostars, the water-ice band with the center near 3.1 μm and the silicate band with the center near 9.7 μm, by using a core-mantle confocal spheroid model with various axial ratios and relative volumes of the core material. We considered the effect of grain size, shape, structure, chemical composition, and orientation on the central wavelengths of the two bands, their full widths at half maximum (FWHMs), the ratio of the optical depths at their centers, and the polarization. We found that the observed relationships between the FWHMs of the bands and the ratio of their optical depths at the band centers could be explained if we chose slightly oblate or prolate particles (a/b ? 2) of small sizes (rv ? 0.35 μm) with a silicate core and a thin ice mantle (Vcore/Vtotal ? 0.7).  相似文献   

7.
We present our B, V, Rc, and Ic observations of a \(3'.6 \times 3'\) field centered on the host galaxy of GRB 000926 (α2000.0=17h04m11s, \(\delta _{2000.0} = + 51^ \circ 47'9\mathop .\limits^{''} 8\)). The observations were carried out on the 6-m Special Astrophysical Observatory telescope using the SCORPIO instrument. The catalog of galaxies detected in this field includes 264 objects for which the signal-to-noise ratio is larger than 5 in each photometric band. The following limiting magnitudes in the catalog correspond to this limitation: 26.6 (B), 25.7 (V), 25.8 (R), and 24.5 (I). The differential galaxy counts are in good agreement with previously published CCD observations of deep fields. We estimated the photometric redshifts for all of the cataloged objects and studied the color variations of the galaxies with z. For luminous spiral galaxies with M(B)z~1.  相似文献   

8.
Speckle interferometric observations made with the 6 m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences in 2000 revealed the triple nature of the nearby (π Hip = 51.80 ± 1.74 mas) low-mass young (≈ 200 Myr) star GJ 900. The configuration of the triple system allowed it to be dynamically unstable. Differential photometry performed from 2000 through 2004 yielded I- and K-band absolute magnitudes and spectral types for the components to be I A =6.66±0.08, I B =9.15±0.11, I C =10.08±0.26, K A =4.84±0.08, K B =6.76±0.20, K C =7.39±0.31, Sp A ≈K5?K7, Sp B ≈M3?M4, Sp C ≈M5?M6. The “mass-luminosity” relation is used to estimate the individual masses of the components: M A ≈0.64M , M B ≈0.21M , M C ≈0.13M . From the observations of the components’ relative motion in the period 2000–2006, we conclude that GJ 900 is a hierarchical triple star with the possible orbital periods PA-BC≈80 yrs and PBC≈20 yrs. An analysis of the 2MASS images of the region around GJ 900 leads us to suggest that the system can include other very-low-mass components.  相似文献   

9.
The water ice and silicate dust bands centered at about 3 and 10 μm, respectively, are simultaneously observed in the spectra of several objects. So far the wavelength dependence of the polarization in both bands has been modeled using two-layer spheroids, with the shape of the silicate core being confocal to that of the ice mantle. We show that nonconfocality of the spheroidal core and mantle boundaries changes fundamentally the wavelength dependence of the polarization within the 10-μm silicate band and affects significantly the polarization within the 3-μm water ice band, while the extinction profiles of these bands remain essentially unchanged. Since the results have been obtained for a theoretical model, we discuss their applicability and significance for cosmic dust grains. Original Russian Text ? M.S. Prokopjeva, V.B. Il’in, 2007, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2007, Vol. 33, No. 10, pp. 784–791.  相似文献   

10.
Speckle-interferometric observations of FU Ori are performed with the 6-m telescope of the Special Astrophysical Observatory with 600/40 nm and 800/100 nm (central bandwidth/halfwidth) filters. The companion star FU Ori S that was recently discovered at λ >-1.25µm was recorded in observations with the λλ==800/100 nm filter. The positional parameters and magnitude difference of the companion in the filter considered are found to be θ = (163.9 ± 1.0)°, ρ = (0.493 ± 0.007)″, Δm = 3.96 ± 0.28. An analysis of the spectral energy distribution of the companion implies that for the extinction A V toward FU Ori to be greater than about 1.6 m , i.e., the minimum value required by the available models of the fuor, the spectral type of the companion star must be no later than K3. The reliability of this conclusion and the possible ways for obtaining more accurate estimates of A V are discussed.  相似文献   

11.
In this paper, we have investigated the plane symmetric space-time with wet dark fluid (WDF), which is a candidate for dark energy, in the framework of f (R,T) gravity Harko et al. 2011, Phys. Rev. D, 84, 024020), where R and T denote the Ricci scalar and the trace of the energy–momentum tensor respectively. We have used the equation of state in the form of WDF for the dark energy component of the Universe. It is modeled on the equation of state p = ω(ρ ? ρ ?). The exact solutions to the corresponding field equations are obtained for power-law and exponential volumetric expansion. The geometrical and physical parameters for both the models are studied. Also, we have discussed the well-known astrophysical phenomena, namely the look-back time, proper distance, the luminosity distance and angular diameter distance with red shift.  相似文献   

12.
Repeated spectroscopic observations made with the 6-m telescope of SAO RAS yielded new data on the radial-velocity variability of the anomalous yellow supergiant QY Sge. The strongest and most peculiar feature in its spectrum is the complex profile of NaI D lines, which contains a narrow and a very wide emission components. The wide emission component can be seen to extend from ?170 to +120 km/s, and at its central part it is cut by an absorption feature, which, in turn, is split into two subcomponents by a narrow (16 km/s at r=2.5) emission peak. An analysis of all the Vr values leads us to adopt for the star a systemic velocity of Vr=?21.1 km/s, which corresponds to the position of the narrow emission component of NaI. The locations of emission-line features of NaI D lines are invariable, which point to their formation in regions that are external to the supergiant’s photosphere. Differential line shifts of about 10 km/s are revealed. Emission in the Hα line is weaker than in NaI D lines, it fills the photospheric absorption almost completely. The absorption lines in the spectrum of QY Sge have a substantial width of FWHM ≈ 45 km/s. The method of model atmospheres is used to determine the following parameters: the effective temperature T eff =6250±150 K, surface gravity l g g=2.0±0.2, and microturbulence velocity ξ t =4.5±0.5 km/s. The chemical composition of the atmosphere differs only slightly from the solar composition: the metallicity of the star is found to be somewhat higher than the solar metallicity with an average overabundance of iron-peak elements of [Met/H]=+0.20. The star is found to be slightly overabundant in carbon and nitrogen, [C/Fe]=+0.25, [N/Fe]=+0.27. The α-process elements Mg, Si, and Ca are slightly overabundant, on the average by [α/H]=+0.12, and sulfur overabundance is higher, [S/α]=+0.29. The strong overabundance of sodium, [Na/Fe]=+0.75, is likely to be due to the dredge-up of the matter processed in the NeNa cycle. Heavy elements of the s-process are underabundant relative to the Sun. On the whole, the observed properties of QY Sge do not give grounds for including this star into the group of RCrB or RVTau-type objects.  相似文献   

13.
We consider an equation of state that leads to a first-order phase transition from the nucleon state to the quark state with a transition parameter λ>3/2 (λ=ρQ/(ρN+P0/c2)) in superdense nuclear matter. Our calculations of integrated parameters for superdense stars using this equation of state show that on the stable branch of the dependence of stellar mass on central pressure dM/dPc>0) in the range of low masses, a new local maximum with Mmax=0.082 and R=1251 km appears after the formation of a toothlike kink (M=0.08M, R=205 km) attributable to quark production. For such a star, the mass and radius of the quark core are Mcore=0.005M and Rcore=1.73 km, respectively. In the model under consideration, mass accretion can result in two successive transitions to a quark-core neutron star with energy release similar to a supernova explosion: initially, a low-mass star with a quark core is formed; the subsequent accretion leads to configurations with a radius of ~1000 km; and, finally, the second catastrophic restructuring gives rise to a star with a radius of ~100 km.  相似文献   

14.
Based on a self-consistent solution of the equations of gas dynamics, kinetics of hydrogen atomic level populations, and radiative transfer, we analyze the structure of a shock wave that propagates in a partially ionized hydrogen gas. We consider the radiative transfer at the frequencies of spectral lines by taking into account the effects of a moving medium in the observer's frame of reference. The flux in Balmer lines is shown to be formed behind the shock discontinuity at the initial hydrogen recombination stage. The Doppler shift of the emission-line profile is approximately one and a half times smaller than the gas flow velocity in the Balmer emission region, because the radiation field of the shock wave is anisotropic. At Mach numbers M1?10 and unperturbed gas densities σ1=10?10 g cm?3, the Doppler shift is approximately one third of the shock velocity U1. The FWHM of the emission-line profile δ ? is related to the shock velocity by δ ? k ? U1, where k ? = 1, 0.6, and 0.65 for the Hα, Hβ, and Hγ lines, respectively.  相似文献   

15.
We present a charged analogue of Pant et al. (2010, Astrophys. Space Sci., 330, 353) solution of the general relativistic field equations in isotropic coordinates by using simple form of electric intensity E that involve charge parameter K. Our solution is well behaved in all respects for all values of X lying in the range 0 <X≤ 0.11, K lying in the range 4 <K≤ 6.2 and Schwarzschild compactness parameter u lying in the range 0 <u≤ 0.247. Since our solution is well behaved for wide ranges of the parameters, we can model many different types of ultra-cold compact stars like quark stars and neutron stars. We have shown that corresponding to X = 0.077 and K = 6.13 for which u = 0.2051 and by assuming surface density ρ b =4.6888×1014 g cm ?3 the mass and radius are found to be 1.509M , 10.906 km respectively which match with the observed values of mass 1.51M and radius 10.90 km of the quark star XTE J1739-217. The well behaved class of relativistic stellar models obtained in this work might have astrophysical significance in the study of more realistic internal structures of compact stars.  相似文献   

16.
From December 2006 to January 2008, we performed 1699 BV I c observations for 46 low-amplitude Cepheids discovered in the course of the ASAS project using the 76-cm telescope of the South-African Astronomical Observatory (SAAO). We provide the tables of observations and V light and B-V and V-I c color curves. These new observations, along with data from the ASAS-3 catalog, have been used to improve the elements of the light variations. Our data allow the number of known Galactic low-amplitude Cepheids to be almost doubled. This makes it possible to increase the number of distance indicators suitable for studying the structure of the inner Galactic arms by almost 15%.  相似文献   

17.
More than 80 giant planets are known by mass and radius. Their interior structure in terms of core mass, number of layers, and composition however is still poorly known. An overview is presented about the core mass M core and envelope mass of metals M Z in Jupiter as predicted by various equations of state. It is argued that the uncertainty about the true H/He EOS in a pressure regime where the gravitational moments J 2 and J 4 are most sensitive, i.e. between 0.5 and 4 Mbar, is in part responsible for the broad range \(M_{\mathit{core}}=0{-}18\:M_{\oplus }\), \(M_{Z}=0{-}38\:M_{\oplus }\), and \(M_{\mathit{core}}+M_{Z}=14{-}38\:M_{\oplus }\) currently offered for Jupiter. We then compare the Jupiter models obtained when we only match J 2 with the range of solutions for the exoplanet \(\mathrm{GJ}\:436\mathrm{b}\), when we match an assumed tidal Love number k 2 value.  相似文献   

18.
The stellar population of the blue compact dwarf galaxy SBS 1415+437 is investigated using the archive database of the Hubble space telescope. The color index-magnitude diagram for stars reaches a magnitude of 29 m in the V and I bands. It comprises young main-sequence stars, blue and red supergiants, and the old population of red giant branch and asymptotic giant branch. The tip of the red giant branch αTRGB) was used to calculate the distance modulus, which turned out to be m ? M = 30.65 ± 0.08 m . The corresponding distance to the galaxy is D = 13.5 ± 1.0 Mpc. The youngest stars are distributed irregularly near the bright H II region in the southwest part of SBS 1415+437. The old population occupies a larger area, it is distributed more evenly and forms the galactic halo. The spatial distribution of young stars shows that the star formation in the galaxy spread in the direction from northeast to southwest over the last 5 × 107 yr with an average rate of 60 km/s. The TRGB of SBS 1415+437 was found to be appreciably shifted to the blue range: (V ? I) TRGB ≈ 1.30. The galaxy age turns out to be not smaller than the age of Galactic globular clusters (about 1010 yr), provided that the galaxy originally had a very low metallicity (our photometric estimate is [Fe/H] = ?2.4). If the metallicity of SBS 1415+437 changed almost not at all in the course of evolution and was equal to [Fe/H] = ?1.3 (as estimated from the emission lines of ionized gas), the galaxy age is no more than 2 × 109 yr.  相似文献   

19.
We present some results of the photometric analysis of the stellar population of the irregular dwarf galaxy KK 230 on the basis of the archive database of the Hubble space telescope. The color index-magnitude diagram for KK 230 gets to magnitude 27 m in the V and I bands, and it comprises stellar populations of various ages. The age of the youngest main-sequence stars is 3.2 × 107 yr. These stars are distributed along the north-south direction in the picture plane, and this fact can be linked to the observed kinematics of the neutral gas in the galaxy. Older blue and red supergiants are no less than 1.6 × 108 years old, and such an age implies that the star formation was episodic over the last several hundreds of millions of years. As judged from the position of the tip of the red giant branch, the distance modulus for KK 230 is m ? M = 26.5 m . The corresponding distance is D = 2 Mpc. Based on the average absolute magnitude M I,RC and color index (V ? I)I,RC of the red clump, we conclude that the majority of KK 230 stars have an age of no more than (2–3) × 109 yr, their metallicity being Z ≈ 0.0004.  相似文献   

20.
Three three-component (bulge, disk, halo) model Galactic gravitational potentials differing by the expression for the dark matter halo are considered. The central (bulge) and disk components are described by the Miyamoto–Nagai expressions. The Allen–Santillán (I), Wilkinson–Evans (II), and Navarro–Frenk–White (III) models are used to describe the halo. A set of present-day observational data in the range of Galactocentric distances R from 0 to 200 kpc is used to refine the parameters of thesemodels. For the Allen–Santillán model, a dimensionless coefficient γ has been included as a sought-for parameter for the first time. In the traditional and modified versions, γ = 2.0 and 6.3, respectively. Both versions are considered in this paper. The model rotation curves have been fitted to the observed velocities by taking into account the constraints on the local matter density ρ = 0.1 M pc?3 and the force K z =1.1/2πG = 77 M pc?2 acting perpendicularly to the Galactic plane. The Galactic mass within a sphere of radius 50 kpc, M G (R ≤ 50 kpc) ≈ (0.41 ± 0.12) × 1012 M , is shown to satisfy all three models. The differences between the models become increasingly significant with increasing radius R. In model I, the Galactic mass within a sphere of radius 200 kpc at γ = 2.0 turns out to be greatest among the models considered, M G (R ≤ 200 kpc) = (1.45 ±0.30)× 1012 M , M G (R ≤ 200 kpc) = (1.29± 0.14)× 1012 M at γ = 6.3, and the smallest value has been found in model II, M G (R ≤ 200 kpc) = (0.61 ± 0.12) × 1012 M . In our view, model III is the best one among those considered, because it ensures the smallest residual between the data and the constructed model rotation curve provided that the constraints on the local parameters hold with a high accuracy. Here, the Galactic mass is M G (R ≤ 200 kpc) = (0.75 ± 0.19) × 1012 M . A comparative analysis with the models by Irrgang et al. (2013), including those using the integration of orbits for the two globular clusters NGC 104 and NGC 1851 as an example, has been performed. The third model is shown to have subjected to a significant improvement.  相似文献   

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