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تسجيل مستخدم جديدThe Cluster Ages Experiment (CASE). VIII. Age and Distance of the Globular Cluster 47 Tuc from the Analysis of Two Detached Eclipsing Binaries
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We use photometric and spectroscopic observations of the eclipsing binary E32 in the globular cluster 47 Tuc to derive the masses, radii, and luminosities of the component stars. The system has an orbital period of 40.9 d, a markedly eccentric orbit with e = 0.24, and is shown to be a member of or a recent escaper from the cluster. We obtain Mp = 0.862(5) Msun , Rp = 1.183(3) Rsun , Lp = 1.65(5) Lsun for the primary and Ms = 0.827(5) Msun , Rs = 1.004(4) Rsun , Ls = 1.14(4) Lsun for the secondary. Based on these data and on an earlier analysis of the binary V69 in 47 Tuc we measure the distance to the cluster from the distance moduli of the component stars, and, independently, from a color - surface brightness calibration. We obtain 4.55(3) and 4.50(7) kpc, respectively - values compatible within 1 sigma with recent estimates based on Gaia DR2 parallaxes. By comparing the M - R diagram of the two binaries and the color-magnitude diagram of 47 Tuc to Dartmouth model isochrones we estimate the age of the cluster to be 12.0 pm 0.5 Gyr, and the helium abundance of the cluster to be Y approx 0.25.
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We use photometric and spectroscopic observations of the eclipsing binary V69-47 Tuc to derive the masses, radii, and luminosities of the component stars. Based on measured systemic velocity, distance, and proper motion, the system is a member of the
globular cluster 47 Tuc. The system has an orbital period of 29.5 d and the orbit is slightly eccentric with e=0.056. We obtain Mp=0.8762 +- 0.0048 M(Sun), Rp=1.3148 +-0.0051 R(Sun), Lp=1.94 +- 0.21 L(Sun) for the primary and Ms=0.8588 +- 0.0060 M(Sun), Rs=1.1616 +- 0.0062 R(Sun), Ls=1.53 +- 0.17 L(Sun) for the secondary. These components of V69 are the first Population II stars with masses and radii derived directly and with an accuracy of better than 1%. We measure an apparent distance modulus of (m-M)v=13.35 +- 0.08 to V69. We compare the absolute parameters of V69 with five sets of stellar evolution models and estimate the age of V69 using mass-luminosity-age, mass-radius-age, and turnoff mass - age relations. The masses, radii, and luminosities of the component stars are determined well enough that the measurement of ages is dominated by systematic differences between the evolutionary models, in particular, the adopted helium abundance. By comparing the observations to Dartmouth model isochrones we estimate the age of V69 to be 11.25 +- 0.21(random) +- 0.85(systematic) Gyr assuming [Fe/H]=-0.70, [alpha/Fe]=0.4, and Y=0.255. The determination of the distance to V69, and hence to 47Tuc, can be further improved when infrared eclipse photometry is obtained for the variable.
We use photometric and spectroscopic observations of the detached eclipsing binaries V40 and V41 in the globular cluster NGC 6362 to derive masses, radii, and luminosities of the component stars. The orbital periods of these systems are 5.30 and 17.8
9 d, respectively. The measured masses of the primary and secondary components ($M_p$, $M_s$) are (0.8337$pm$0.0063, 0.7947$pm$0.0048) M$_odot$ for V40 and (0.8215$pm$0.0058, 0.7280$pm$0.0047) M$_odot$ for V41. The measured radii ($R_p$, $R_s$) are (1.3253$pm$0.0075, 0.997$pm$0.013) R$_odot$ for V40 and (1.0739$pm$0.0048, 0.7307$pm$0.0046) R$_odot$ for V41. Based on the derived luminosities, we find that the distance modulus of the cluster is 14.74$pm$0.04 mag -- in good agreement with 14.72 mag obtained from CMD fitting. We compare the absolute parameters of component stars with theoretical isochrones in mass-radius and mass-luminosity diagrams. For assumed abundances [Fe/H] = -1.07, [$alpha$/Fe] = 0.4, and Y = 0.25 we find the most probable age of V40 to be 11.7$pm$0.2 Gyr, compatible with the age of the cluster derived from CMD fitting (12.5$pm$0.5 Gyr). V41 seems to be markedly younger than V40. If independently confirmed, this result will suggest that V41 belongs to the younger of the two stellar populations recently discovered in NGC 6362. The orbits of both systems are eccentric. Given the orbital period and age of V40, its orbit should have been tidally circularized some $sim$7 Gyr ago. The observed eccentricity is most likely the result of a relatively recent close stellar encounter.
We use photometric and spectroscopic observations of the eclipsing binaries V65, V66 and V69 in the field of the globular cluster M4 to derive masses, radii, and luminosities of their components. The orbital periods of these systems are 2.29, 8.11 an
d 48.19 d, respectively. The measured masses of the primary and secondary components (Mp and Ms) are 0.8035+-0.0086 and 0.6050+-0.0044 Msun for V65, 0.7842+-0.0045 and 0.7443+-0.0042 Msun for V66, and 0.7665+-0.0053 and 0.7278+-0.0048 Msun for V69. The measured radii (Rp and Rs) are 1.147+_0.010 and 0.6110+-0.0092 Rsun for V66, 0.9347+_0.0048 and 0.8298+-0.0053 Rsun for V66, and 0.8655+-0.0097 and 0.8074+-0.0080 Rsun for V69. The orbits of V65 and V66 are circular, whereas that of V69 has an eccentricity of 0.38. Based on systemic velocities and relative proper motions, we show that all the three systems are members of the cluster. We find that the distance to M4 is 1.82+-0.04 kpc - in good agreement with recent estimates based on entirely different methods. We compare the absolute parameters of V66 and V69 with two sets of theoretical isochrones in mass-radius and mass-luminosity diagrams, and for an assumed [Fe/H] = -1.20, [alpha/Fe] = 0.4, and Y = 0.25 we find the most probable age of M4 to be between 11.2 and 11.3 Gyr. CMD-fitting with the same parameters yields an age close to, or slightly in excess of, 12 Gyr. However, considering the sources of uncertainty involved in CMD fitting, these two methods of age determination are not discrepant. Age and distance determinations can be further improved when infrared eclipse photometry is obtained.
We use photometric and spectroscopic observations of the eclipsing binary OGLEGC-228 (V228) to derive the masses, radii, and luminosities of the component stars. Based on measured systemic velocity, proper motion and distance, the system is a blue st
raggler member of the globular cluster 47 Tuc. Our analysis shows that V228 is a semi-detached Algol. We obtain M=1.512 +/- 0.022 Msun, R=1.357 +/- 0.019 Rsun, L=7.02 +/- 0.050 Lsun for the hotter and more luminous primary component and M=0.200 +/- 0.007 Msun, R=1.238 +/- 0.013 Rsun, L=1.57 +/- 0.09 Lsun for the Roche lobe filling secondary.
We present the first detailed analysis of the detached eclipsing binary V15 in the super-metal rich open cluster NGC 6253. We obtain the following absolute parameters: M_p=1.303+-0.006 Msun, R_p=1.71+-0.03 Rsun, L_p=2.98+-0.10 Lsun for the primary, a
nd M_s=1.225+-0.006 Msun, R_s=1.44+-0.02 Rsun, L_s=2.13+-0.06 Lsun for the secondary. Based on Dartmouth isochrones, the age of NGC 6253 is estimated to be 3.80 - 4.25 Gyr from the mass-radius diagram and 3.9 - 4.6 Gyr from color-magnitude diagram (CMD) fitting. Both of these estimates are significantly higher than those reported so far. The derived apparent distance modulus of 11.65 mag agrees well with the range of 10.9 - 12.2 mag derived by other authors; however our estimated reddening (0.113 mag) is lower than the lowest published value (0.15 mag). We confirm earlier observations that model atmospheres are not accurate enough to account for the whole CMD of the cluster, with the largest discrepancies appearing on the subgiant and giant branches. Although age estimation from the mass-radius diagram is a relatively safe, distance- and reddening-independent procedure, our results should be verified by photometric and spectroscopic observations of additional detached eclipsing binaries which we have discovered, at least two of which are proper-motion members of NGC 6253.
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