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Register a new userCalculation of the Masses of the Binary Star HD 93205 by Application of the Theory of the Apsidal Motion
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Added by
Aldo Marcelo Serenelli
Publication date
2001
fields
Physics
and research's language is
English
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We present a method to calculate masses for components of both eclipsing and non-eclipsing binary systems as long as their apsidal motion rates are available. The method is based on the fact that the equation that gives the rate of apsidal motion is a supplementary equation that allows the computation of the masses of the components, if the radii and the internal structure constants of them can be obtained from theoretical models. For this reason the use of this equation makes the method presented here model dependent. We apply this method to calculate the mass of the components of the non-eclipsing massive binary system HD 93205 (O3V+O8V), which is suspected to be a very young system. To this end, we computed a grid of evolutionary models covering the mass range of interest, and taking the mass of the primary (M_1) as the only independent variable, we solve the equation of apsidal motion for M_1 as a function of the age of the system. The mass of the primary we find ranges from M_1= 60+-19 msun for ZAMS models, which sets an upper limit for M_1, down to M_1= 40+-9 msun for an age of 2 Myr. Accordingly, the upper limit derived for the mass of the secondary (M_2= Q M_1) is M_2= 25 msun is in very good agreement with the masses derived for other O8V stars occurring in eclipsing binaries.
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Apsidal motion in massive eccentric binaries offers precious information about the internal structure of the stars. This is especially true for twin binaries consisting of two nearly identical stars. We make use of the tidally induced apsidal motion in the twin binary HD152248 to infer constraints on the internal structure of the O7.5 III-II stars composing this system. We build stellar evolution models with the code Cles assuming different prescriptions for the internal mixing occurring inside the stars. We identify the models that best reproduce the observationally determined present-day properties of the components of HD152248, as well as their $k_2$, and the apsidal motion rate of the system. We analyse the impact of some poorly constrained input parameters, including overshooting, turbulent diffusion, and metallicity. We further build single and binary GENEC models that account for stellar rotation to investigate the impacts of binarity and rotation. We discuss some effects that could bias our interpretation of the apsidal motion in terms of the internal structure constant. Reproducing the observed $k_2$ value and rate of apsidal motion simultaneously with the other stellar parameters requires a significant amount of internal mixing or enhanced mass-loss. The results suggest that a single-star evolution model is sufficient to describe the physics inside this binary system. Qualitatively, the high turbulent diffusion required to reproduce the observations could be partly attributed to stellar rotation. Higher-order terms in the apsidal motion are negligible. Only a very severe misalignment of the rotation axes could significantly impact the rate of apsidal motion, but such a high misalignment is highly unlikely in such a binary system. We infer an age estimate of $5.15pm0.13$ Myr for the binary and initial masses of $32.8pm0.6$ M$_odot$ for both stars.
Orbital, spin and astrometric parameters of the millisecond pulsar PSR J0621+1002 have been determined through six years of timing observations at three radio telescopes. The chief result is a measurement of the rate of periastron advance, omega_dot = 0.0116 +/- 0.0008 deg/yr. Interpreted as a general relativistic effect, this implies the sum of the pulsar mass, m_1, and the companion mass, m_2, to be M = m_1 + m_2 = 2.81 +/- 0.30 msun. The Keplerian parameters rule out certain combinations of m_1 and m_2, as does the non-detection of Shapiro delay in the pulse arrival times. These constraints, together with the assumption that the companion is a white dwarf, lead to the 68% confidence maximum likelihood values of m_1 = 1.70(+0.32 -0.29) msun and m_2 =0.97(+0.27 - 0.15) msun and to the 95% confidence maximum likelihood values of m_1 = 1.70(+0.59 -0.63) msun and m_2 = 0.97(+0.43 -0.24) msun. The other major finding is that the pulsar experiences dramatic variability in its dispersion measure (DM), with gradients as steep as 0.013 pc cm^{-3} / yr. A structure function analysis of the DM variations uncovers spatial fluctuations in the interstellar electron density that cannot be fit to a single power law, unlike the Kolmogorov turbulent spectrum that has been seen in the direction of other pulsars. Other results from the timing analysis include the first measurements of the pulsars proper motion, mu = 3.5 +/- 0.3 mas / yr, and of its spin-down rate, dP/dt = 4.7 x 10^{-20}, which, when corrected for kinematic biases and combined with the pulse period, P = 28.8 ms, gives a characteristic age of 1.1 x 10^{10} yr and a surface magnetic field strength of 1.2 x 10^{9} G.
The eccentric massive binary HD152248 (also known as V1007 Sco), which hosts two O7.5 III-II(f) stars, is the most emblematic eclipsing O-star binary in the very young and rich open cluster NGC6231. Its properties render the system an interesting target for studying tidally induced apsidal motion. Measuring the rate of apsidal motion in such a binary system gives insight into the internal structure and evolutionary state of the stars composing it. A large set of optical spectra was used to reconstruct the spectra of the individual binary components and establish their radial velocities using a disentangling code. Radial velocities measured over seven decades were used to establish the rate of apsidal motion. We furthermore analysed the reconstructed spectra with the CMFGEN model atmosphere code to determine stellar and wind properties of the system. Optical photometry was analysed with the Nightfall binary star code. A complete photometric and radial velocity model was constructed in PHOEBE 2 to determine robust uncertainties. We find a rate of apsidal motion of $(1.843^{+0.064}_{-0.083})deg$ yr$^{-1}$. The photometric data indicate an orbital inclination of $(67.6^{+0.2}_{-0.1})deg$ and Roche-lobe filling factors of both stars of about 0.86. Absolute masses of $29.5^{+0.5}_{-0.4}$M$_odot$ and mean stellar radii of $15.07^{+0.08}_{-0.12}$R$_odot$ are derived for both stars. We infer an observational value for the internal structure constant of both stars of $0.0010pm0.0001$. Our in-depth analysis of the massive binary HD152248 and the redetermination of its fundamental parameters can serve as a basis for the construction of stellar evolution models to determine theoretical rates of apsidal motion to be compared with the observational one. In addition, the system hosts two twin stars, which offers a unique opportunity to obtain direct insight into the internal structure of the stars.
Massive binary systems are important laboratories in which to probe the properties of massive stars and stellar physics in general. In this context, we analysed optical spectroscopy and photometry of the eccentric short-period early-type binary HD 152218 in the young open cluster NGC 6231. We reconstructed the spectra of the individual stars using a separating code. The individual spectra were then compared with synthetic spectra obtained with the CMFGEN model atmosphere code. We furthermore analysed the light curve of the binary and used it to constrain the orbital inclination and to derive absolute masses of 19.8 +/- 1.5 and 15.0 +/- 1.1 solar masses. Combining radial velocity measurements from over 60 years, we show that the system displays apsidal motion at a rate of (2.04^{+.23}_{-.24}) degree/year. Solving the Clairaut-Radau equation, we used stellar evolution models, obtained with the CLES code, to compute the internal structure constants and to evaluate the theoretically predicted rate of apsidal motion as a function of stellar age and primary mass. In this way, we determine an age of 5.8 +/- 0.6 Myr for HD 152218, which is towards the higher end of, but compatible with, the range of ages of the massive star population of NGC 6231 as determined from isochrone fitting.
We perform numerical simulations to explore the dynamical evolution of the HD 82943 planetary system. By simulating diverse planetary configurations, we find two mechanisms of stabilizing the system: the 2:1 mean motion resonance between the two planets can act as the first mechanism for all stable orbits. The second mechanism is a dynamical antialignment of the apsidal lines of the orbiting planets, which implies that the difference of the periastron longitudes $theta_{3}$ librates about $180^{circ}$ in the simulations. We also use a semi-analytical model to explain the numerical results for the system under study.
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