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1.
We present the results of the reduction of our photometric and spectroscopic observations for the eclipsing binary SZ Cam performed with the telescopes at the Astronomical Observatory of the Ural Federal University and the Special Astrophysical Observatory of the Russian Academy of Sciences in 1996–2014. Based on an 11-year-long photometric monitoring of SZ Cam, we have obtained new elements of its photometric orbit and parameters of its components. We have detected low-amplitude periodic light variations in SZ Cam that are possibly related to the ellipsoidal shape of the components of the spectroscopic binary third body. Based on published data and our new spectroscopy, we have found new values for the mass ratio, q = 0.72 ± 0.01, and parameters of the radial velocity curves of the components, V 0 = ?3.6 ± 1.7 km s?1, K 1 = 190.2 ± 1.9 km s?1, and K 2 = 263.0 ± 2.4 km s?1. The component masses have been estimated to be M 1 = 16.1 M ⊙ and M 2 = 11.6 M ⊙. We have obtained new light elements and parameters of the radial velocity curves for the third body, V 0 3b = 4.2 ± 0.6 km s?1 and K 1 3b = 26.6 ± 0.8 km s?1. We have improved the period of the relative orbit of SZ Cam and the third body, P orb = 55.6 ± 1.5 yr.  相似文献   

2.
Speckle interferometric binary system HD375; Is it a sub-giant binary?   总被引：1，自引：0，他引：1  
Atmospheric modeling is used to build synthetic spectral energy distributions (SEDs) for the individual components of the speckle interferometric binary system HD375. These synthetic SEDs are combined together for the entire system and compared with its observed SED in an iterative procedure to achieve the best fit. Kurucz blanketed models and the measurements of magnitude differences were used to build these SEDs. The input physical parameters for building these best fitted synthetic SEDs represent adequately enough properties of the system. These parameters are: T eff a = 6100 ± 50 K, T eff b = 5940 ± 50 K, log g a = 4.01 ± 0.10, log g b = 3.98 ± 0.10, R a = 1.93 ± 0.20R ⊙, R b = 1.83 ± 0.20R ⊙, M v a = 3 · m 26 ± 0.40, M v b = 3 · m 51 ± 0.50, L a = 4.63 ± 0.80 L ⊙, and L b = 3.74 ± 0.70 L ⊙, in accordance with the new estimated parallax π = 12.02 ± 0.60 mas. A modified orbit of the system is built and compared with earlier orbits, and the masses of the two components are calculated as M a = 1.35M ⊙ and M b = 1.25M ⊙. Based on the estimated physical and geometrical parameters of the system, which are confirmed by synthetic photometry, we suggest that the two components are evolved subgiant (F8.5 IV and G0 IV) stars with the age of 3.5 Gyr, formed by fragmentation.  相似文献   

3.
We have performed hydrodynamic calculations of the radial pulsations of helium stars with masses 10M⊙ ≤ M ≤ 50M⊙, luminosity-to-mass ratios 5 × 103L⊙/M⊙ ≤ L/M ≤ 2.5 × 104L⊙/M⊙, and effective temperatures 2 × 104 K ≤ Teff ≤ 105 K for helium and heavy-element mass fractions of Y=0.98 and Z=0.02, respectively. We show that the high-temperature boundary of the instability region for radial pulsations at L/M ? 104L⊙/M⊙ extends to Teff≈105 K. The amplitude of the velocity variations for outer layers is several hundred km s?1, while the brightness variations in the B band of the UBV photometric system are within the range from several hundredths to half a magnitude. At constant luminosity-to-mass ratio, the radial pulsation period is determined only by the effective temperature of the star. In the ranges of luminosity-to-mass ratios 104L⊙/M⊙ ≤ L/M ≤ 2 × 104L⊙/M⊙ and effective temperatures 5 × 104 K ≤ Teff ≤ 9 × 104 K, the periods of the radial modes are within 6 min ?Π?103 min.  相似文献   

4.
We report the results of our optical speckle interferometric observations of the nearby triple system GJ 795 performed with the 6 m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences with diffraction-limited angular resolution. The three components of the system were optically resolved for the first time. Position measurements allowed us to determine the elements of the inner orbit of the triple system. We use the measured magnitude differences to estimate the absolute magnitudes and spectral types of the components of the triple: M V Aa =7.31±0.08, M V Ab =8.66±0.10, M V B =8.42±0.10, Sp Aa≈K5, Sp Ab≈K9, Sp B ≈K8. The total mass of the system is equal to ΣM AB =1.69±0.27M ⊙. We show GJ795 to be a hierarchical triple system which satisfies the empirical stability criteria.  相似文献   

5.
A series of highly accurate photoelectric observations of the eclipsing binary MZ Lac was obtained with a 48-cm AZT-14 reflector at the Tien-Shan High-Altitude Station of the Sternberg Astronomical Institute from 1985 to 2004 to study its apsidal motion. We constructed a consistent system of physical and geometrical parameters of the components and the binary’s orbit: we determined their masses (M1 = 1.50M⊙, M2 = 1.29M⊙), radii (R1 = 1.86R⊙, R2 = 1.35R⊙), luminosities (L1 = 0.79L⊙, L2 = 0.45L⊙), surface gravities (logg1 = 4.06, logg2 = 4.27), age (t = 1.9 × 109 yr), and the distance to the binary (d = 510 pc). The binary exhibits apsidal motion with the period Uobs = 480 ± 40 yr, while its theoretically expected value is Uth = 450 ± 40 yr. Spectroscopic studies of MZ Lac and calculations of the absolute parameters of the components are required to test our conclusions.  相似文献   

6.
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   

7.
We present the results of our hydrodynamic calculations of radial pulsations in helium stars with masses 1 M⊙ ≤ M ≤ 10 M⊙, luminosity-to-mass ratios 1 × 103L⊙/M⊙ ≤ L/M ≤ 2 × 104L⊙/M⊙, and effective temperatures 2 × 104 K ≤ Teff ≤ 105 K for mass fractions of helium Y=0.98 and heavy elements Z=0.02. We show that the lower boundary of the pulsation-instability region corresponds to L/M ～ 103L⊙/M⊙ and that the instability region for L/M ? 5 × 103L⊙/M⊙ is bounded by effective temperatures Teff ? 3 × 104 K. As the luminosity rises, the instability boundary moves into the left part of the Hertzsprung-Russell diagram and radial pulsations can arise in stars with effective temperatures Teff ? 105 K at L/M ? 7 × 103L⊙/M⊙. The velocity amplitude for the outer boundary of the hydrodynamic model increases with L/M and lies within the range 200 ? ΔU ? 700 km s?1 for the models under consideration. The periodic shock waves that accompany radial pulsations cause a significant change of the gas-density distribution in the stellar atmosphere, which is described by a dynamic scale height comparable to the stellar radius. The dynamic instability boundary that corresponds to the separation of the outer stellar atmospheric layers at a superparabolic velocity is roughly determined by a luminosity-to-mass ratio L/M ～ 3 × 104L⊙/M⊙.  相似文献   

8.
We have selected and analyzed a sample of OB stars with known line-of-sight velocities determined through ground-based observations and with trigonometric parallaxes and propermotions from the Gaia DR2 catalogue. Some of the stars in our sample have distance estimates made from calcium lines. A direct comparison with the trigonometric distance scale has shown that the calcium distance scale should be reduced by 13%. The following parameters of the Galactic rotation curve have been determined from 495 OB stars with relative parallax errors less than 30%: (U, V,W)⊙ = (8.16, 11.19, 8.55)± (0.48, 0.56, 0.48) km s?1, Ω0 = 28.92 ± 0.39 km s?1 kpc?1, Ω'0 = ?4.087 ± 0.083 km s?1 kpc?2, and Ω″ 0 = 0.703 ± 0.067 km s?1 kpc?3, where the circular velocity of the local standard of rest is V0 = 231 ± 5 km s?1 (for the adopted R0 = 8.0 ± 0.15 kpc). The parameters of the Galactic spiral density wave have been found from the series of radial, VR, residual tangential, ΔVcirc, and vertical, W, velocities of OB stars by applying a periodogram analysis. The amplitudes of the radial, tangential, and vertical velocity perturbations are fR = 7.1± 0.3 km s?1, fθ = 6.5 ± 0.4 km s?1, and fW = 4.8± 0.8 km s?1, respectively; the perturbation wavelengths are λR = 3.3 ± 0.1 kpc, λθ = 2.3 ± 0.2 kpc, and λW = 2.6 ± 0.5 kpc; and the Sun’s radial phase in the spiral density wave is (χ⊙)R = ?135? ± 5?, (χ⊙)θ = ?123? ± 8?, and (χ⊙)W = ?132? ± 21? for the adopted four-armed spiral pattern.  相似文献   

9.
Long-term photometric and spectroscopic observations of the yellow symbiotic star LT Del are analyzed. UBV light curves are presented. Based on the observations of 20 cycles, we have refined the orbital period of the star, P = 476 · d 0 ± 1 · d 0. The brightness has been found to be unstable at some orbital phases with an amplitude up to 0 · m 3. We have measured the fluxes in hydrogen and helium emission lines and in continuum and investigated their relationship to the orbital period. The fluxes in hydrogen and HeI lines follow the UBV light curves in phase; the He II 4686 Å flux does not depend on the phase and is constant within the accuracy of our measurements. The intensity ratio of the 4686 Å andHβ lines changes from 0.2 to 0.9 over the period. We interpret the spectroscopic observations based on the hypothesis of heating and ionization of the stellar wind from a cool component by high-frequency radiation from a hot star with a temperature of 105 K. We have estimated the spectral type of the cool star from our photometry and its continuum energy distribution as a bright K2–4 red giant branch halo star. The bolometric luminosity and mass loss rate have been estimated for the K component to be L bol ～ 700L ⊙ and \(\dot{M}\) ～ 10?8 M ⊙ yr?1, respectively.  相似文献   

10.
HD 10009 is a spectroscopic and speckle interferometric binary with almost identical solar-type components. It was studied via speckle interferometry using the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences and had its spectrophotometry performed in the 3500–9600 Å wavelength interval with the 2-m telescope of the Terskol Branch of the Institute of Astronomy of the Russian Academy of Sciences. A detailed analysis of the atmosphere of the primary component (component 1) of the binary yielded the abundances of some of the elements. The luminosities and temperatures of the components are found to be L 1= 2.9 L ⊙, L 2= 1.0 L ⊙ and T eff1=6017 K, T eff2=5930 K, respectively. The iron abundance is [Fe]=?0.27±0.05. Our results make it possible to assess the evolutionary status of the system. The binary is 7.9 Gyr old and the primary component is close to become a red giant, whereas the secondary component is still in the hydrogen-burning stage near the main sequence.  相似文献   

11.
Open star clusters from the MWSC (Milky Way Star Clusters) catalogue have been used to determine the Galactic rotation parameters. The circular rotation velocity of the solar neighborhood around the Galactic center has been found from data on more than 2000 clusters of various ages to be V 0 = 236 ± 6 km s?1 for the adopted Galactocentric distance of the Sun R 0 = 8.3 ± 0.2 kpc. The derived angular velocity parameters are Ω 0 = 28.48 ± 0.36 km s?1 kpc?1, Ω’0 = ?3.50 ± 0.08 km s?1 kpc?2, and Ω″0 = 0.331 ± 0.037 km s?1 kpc?3. The influence of the spiral density wave has been detected only in the sample of clusters younger than 50 Myr. For these clusters the amplitudes of the tangential and radial velocity perturbations are f θ = 5.6 ± 1.6 km s?1 and f R = 7.7 ± 1.4 km s?1, respectively; the perturbation wavelengths are λ θ = 2.6 ± 0.5 kpc (i θ = ?11? ± 2?) and λ R = 2.1 ± 0.5 kpc (i R = ?9? ± 2?) for the adopted four-armed model (m = 4). The Sun’s phase in the spiral density wave is (χ⊙)θ = ?62? ± 9? and (χ⊙)R = ?85? ± 10? from the residual tangential and radial velocities, respectively.  相似文献   

12.
We present the results of the study of the eclipsing polar CRTS CSS081231 J071126+440405. Photometric observations allowed us to refine the orbital period of the system \(P_ \circ = 0_ \cdot ^d 0.08137673\). Considerable changes in the appearance of the object’s spectra have occurred over the period of September 20–21, 2001: the slope of the continuum changed from “red” to “blue”, and the variability of the line profiles over the duration of the orbital period has also changed. Doppler maps have shown a shift of the emission line-forming region along the accretion stream closer to the white dwarf. We measured the duration of the eclipse of the system and imposed constraints on the inclination angle \(78_ \cdot ^ \circ 7 < i < 79_ \cdot ^ \circ 3\). The derived radial velocity amplitude was used to obtain the basic parameters of the system: M1 = 0.86 ± 0.08M⊙, M2 = 0.18 ± 0.02 M⊙, q = 0.21 ± 0.01, RL2 = 0.20 ± 0.03 R⊙, A = 0.80 ± 0.03 R⊙. The spectra of the object exhibit cyclotron harmonics. Their comparison with model spectra allowed us to determine the parameters of the accretion column: B = 31–34 MG, Te = 10–12 keV, θ = 80–90°, and Λ = 105.  相似文献   

13.
Based on observations of SN 1999em, we determined the physical parameters of this supernova using hydrodynamic calculations including nonequilibrium radiative transfer. Taking the distance to SN 1999em estimated by the expanding photosphere method (EPM) to be D = 7.5 Mpc, we found the parameters of the presupernova: radius R = 450R⊙, mass M = 15M⊙, and explosion energy E = 7 × 1050 erg. For the distance D = 12 Mpc determined from Cepheids, R, M, and E must be increased to the following values: R = 1000R⊙, M = 18M⊙, and E = 1051 erg. We show that one cannot restrict oneself to using the simple analytical formulas relating the supernova and presupernova parameters to obtain reliable parameters for type-IIP presupernovae.  相似文献   

14.
Highly accurate W BV R photometric measurements of the eclipsing binary HP Aur were performed in 2002–2003 with the 48-cm AZT-14 reflector at the Tien-Shan High-Altitude Observatory to determine the rate of apsidal motion. A consistent system of physical and geometrical parameters of the components and the binary as a whole has been constructed for the first time by analyzing these new measurements together with other published data: we determined their radii (R1 = 1.05R⊙, R2 = 0.82R⊙) and luminosities (L1 = 1.10L⊙, L2 = 0.46L⊙), spectral types (G2V + G8V) and surface gravities (log g1 = 4.38, log g2 = 4.51), age (t = 9.5 × 109 yr), and the distance to the binary (d = 197 pc). We detected an ultraviolet excess in the spectra of both components, \(\Delta (W - B) \simeq - 0\mathop .\limits^m 25\), that is probably attributable to a metal deficiency in the atmospheres of these stars. In this system of two solar-type stars, we found a third body with the mass M3 sin i 3 3 = 0.17M⊙ that revolved with the period P3 = 13.7 yr around the eclipsing binary in a highly eccentric elliptical orbit: e3 = 0.70 and A3 sin i3 ? 7 AU. The orbit of the eclipsing binary itself was shown to be also elliptical, but with a low eccentricity (e = 0.0025(5)), while apsidal motion with a period Uobs > 80 yr was observed at a theoretically expected period Uth ≈ 92 yr. At least 20 to 30 more years of photoelectric measurements of this star will be required to reliably determine Uobs.  相似文献   

15.
This paper is a continuation of our recent paper devoted to refining the parameters of threecomponent (bulge, disk, halo) axisymmetric model Galactic gravitational potentials differing by the expression for the dark matter halo using the velocities of distant objects. In all models the bulge and disk potentials are described by the Miyamoto–Nagai expressions. In our previous paper we used the Allen–Santillán (I), Wilkinson–Evans (II), and Navarro–Frenk–White (III) models to describe the halo. In this paper we use a spherical logarithmic Binney potential (model IV), a Plummer sphere (model V), and a Hernquist potential (model VI) 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 the listed models, which are employed most commonly at present. The model rotation curves are 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 = 77M ⊙pc?2 acting perpendicularly to the Galactic plane. The Galactic mass within spheres of radius 50 and 200 kpc are shown to be, respectively, M 50 = (0.409 ± 0.020) × 1012 M ⊙ and M 200 = (1.395 ± 0.082) × 1012 M ⊙ in model IV, M 50 = (0.417 ± 0.034) × 1012 M ⊙ and M 200 = (0.469 ± 0.038) × 1012 M ⊙in model V, and M 50 = (0.417 ± 0.032) × 1012 M ⊙ and M 200 = (0.641 ± 0.049)× 1012 M ⊙ in model VI. Model VI looks best among the three models considered here from the viewpoint of the achieved accuracy of fitting the model rotation curves to the measurements. This model is close to the Navarro–Frenk–White model III refined and considered best in our previous paper, which is shown using the integration of the orbits of two globular clusters, Lynga 7 and NGC 5053, as an example.  相似文献   

16.
Data on HII regions, molecular clouds, and methanol masers have been used to estimate the Sun’s distance from the symmetry plane z ⊙ and the vertical disk scale height h. Kinematic distance estimates are available for all objects in these samples. The Local-arm (Orion-arm) objects are shown to affect noticeably the pattern of the z distribution. The deviations from the distribution symmetry are particularly pronounced for the sample of masers with measured trigonometric parallaxes, where the fraction of Local-arm masers is large. The situation with the sample of HII regions in the solar neighborhood is similar. We have concluded that it is better to exclude the Local arm from consideration. Based on the model of a self-gravitating isothermal disk, we have obtained the following estimates from objects located in the inner region of the Galaxy (R ≤ R 0): z ⊙ = ?5.7 ± 0.5 pc and h 2 = 24.1 ± 0.9 pc from the sample of 639 methanol masers, z ⊙ = ?7.6±0.4 pc and h 2 = 28.6±0.5 pc from 878HII regions, z ⊙ = ?10.1 ± 0.5 pc and h 2 = 28.2 ± 0.6 pc from 538 giant molecular clouds.  相似文献   

17.
Based on a one-dimensional hydrodynamic model, we investigate carbon burning in a thermonuclear type-Ia supernova in the approximation of unsteady convection. The relatively broad range of convective parameters, 1×10?3≤αc≤2×10?3, in which delayed detonation from the edge takes place was found to be preserved only for cases with a low boundary temperature at the presupernova stage, T b (PS) = 6.4 × 106 K, and with a high envelope mass, mex ? 2 × 10?3M⊙. In cases with a more realistic temperature, T b (PS) = 2 × 108 K, which corresponds to helium burning in the shell source, and with a lower mass mex, delayed detonation from the edge takes place only at αc = 2 × 10?3, while at αc = 1 × 10?3, numerous model pulsations occur during t?500 s. Artificial viscosity is shown to give a determining contribution to the increase in entropy in outer model shells, which is caused by the generation of weak shock waves during pulsations. We also show that the entropies calculated by two independent methods are equal.  相似文献   

18.
We investigate the variation of the fraction of galaxies with suppressed star formation (MK < ?21 . m 5) and early-type galaxies (fracE) of the “red sequence” along the projected radius in six galaxy clusters:Coma (A1656), A1139, and A1314 in the Leo supercluster region (z ≈ 0.037) and A2040, A2052, A2107 in the Hercules supercluster region (z ≈ 0.036). According to SDSS (DR10) data, fracE is the highest in the central regions of galaxy clusters and it is, on the average, equal to 0.62 ± 0.03, whereas in the 2–3R/R200c interval and beyond the Rsp ≈ 0.95 ± 0.04 R200m radius that we inferred from the observed profile fracE is minimal and equal to 0.25 ± 0.02. This value coincides with the estimate fracE = 0.24 ± 0.01 that we inferred for field galaxies located between the Hercules and Leo superclusters at the same redshifts. We show that the fraction of galaxies with suppressed star formation decreases continuously with cluster radius from 0.87 ± 0.02 in central regions down to 0.43 ± 0.03 in the 2–3 R/R200c interval and beyond Rsp, but remains, on the average, higher than 26% than the corresponding fraction for field objects. This decrease is especially conspicuous in the galaxy mass interval log M* [M⊙] = 9.5–10. We found that galaxies with ongoing star formation have average clustercentric distances 1.5–2.5 R/R200c and that their radial-velocity dispersions are higher than those of galaxies with suppressed star formation.  相似文献   

19.
The evolution of a Population-I star with an initial mass M ZAMS = 60 M ⊙ has been calculated. At the stage when a red giant turns into an early-type helium star, the vast bulk of the stellar mass is concentrated in a compact core surrounded by an extended envelope that is unstable with respect to radial oscillations. The range of effective temperatures within which the instability arises extends to T eff ? 105 K. For the models corresponding to the Wolf-Rayet evolutionary stage (5 × 104 K ≤ T eff ≤ 1.05 × 105 K), hydrodynamic calculations of self-exciting radial stellar pulsations have been performed. The pulsational instability develops in a time interval comparable to the dynamic timescale. Once the amplitude has ceased to grow, the pulsational motions are nonlinear traveling waves propagating from the core boundary to the stellar surface. The velocity amplitude of the outer layers is 500 km s?1 < ΔU < 103 km s?1, depending on the effective temperature. During the evolution of a helium star, the mean ratio of the maximum expansion velocity of the outer layers to the local escape velocity decreases and lies within the range 0.25 < U max/v esc < 0.6 for the models considered. The nonlinearity of the stellar pulsations is responsible for the increase in the mean radius \(\bar r\) of the Lagrangian layers compared to the equilibrium radius r eq. The effect of the increase in mean radius decreases with rising effective temperature from\(\bar r\)/r ～ 10 at T eff = 7 × 104 K to \(\bar r\)/r ≈ 2 at T eff = 105 K. The radial pulsation periods for the models considered lie within the range 0.1 day ≤ Π ≤ 1.6 day and the amplitude of the bolometric magnitude variations does not exceed 0 . m 2.  相似文献   

20.
We measured the radial velocity of the star θ1 Ori D from IUE spectra and used published observations. Based on these data, we determined the period of its radial-velocity variations, P=20.2675±0.0010 days, constructed the phase radial-velocity curve, and solved it by least squares. The spectroscopic orbital elements were found to be the following: the epoch of periastron passage Ep=JD 2430826.6±0.1, the system's center-of-mass velocity /Gg=32.4±1.0 km s?1, K=14.3±1.5 km s?1, Ω=3.3±0.1 rad, e=0.68±0.09, a1 sin i = 3 × 1010 km, and f1 = 0.0025M⊙. Twice the period, P=40.528±0.002 days, is also consistent with the observations.  相似文献   

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