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Register a new userThe interior angular momentum of core hydrogen burning stars from gravity-mode oscillations
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A major uncertainty in the theory of stellar evolution is the angular momentum distribution inside stars and its change during stellar life. We compose a sample of 67 stars in the core-hydrogen burning phase with a $log,g$ value from high-resolution spectroscopy, as well as an asteroseismic estimate of the near-core rotation rate derived from gravity-mode oscillations detected in space photometry. This assembly includes 8 B-type stars and 59 AF-type stars, covering a mass range from 1.4 to 5,M$_odot$, i.e., it concerns intermediate-mass stars born with a well-developed convective core. The sample covers projected surface rotation velocities $vsin,i in[9,242],$km,s$^{-1}$ and core rotation rates up to $26mu$Hz, which corresponds to 50% of the critical rotation frequency. We find deviations from rigid rotation to be moderate in the single stars of this sample. We place the near-core rotation rates in an evolutionary context and find that the core rotation must drop drastically before or during the short phase between the end of the core-hydrogen burning and the onset of core-helium burning. We compute the spin parameter, which is the ratio of twice the rotation rate to the mode frequency (also known as the inverse Rossby number), for 1682 gravity modes and find the majority (95%) to occur in the sub-inertial regime. The ten stars with Rossby modes have spin parameters between 14 and 30, while the gravito-inertial modes cover the range from 1 to 15.
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We propose a methodological framework to perform forward asteroseismic modeling of stars with a convective core, based on gravity-mode oscillations. These probe the near-core region in the deep stellar interior. The modeling relies on a set of observed high-precision oscillation frequencies of low-degree coherent gravity modes with long lifetimes and their observational uncertainties. Identification of the mode degree and azimuthal order is assumed to be achieved from rotational splitting and/or from period spacing patterns. This paper has two major outcomes. The first is a comprehensive list and discussion of the major uncertainties of theoretically predicted gravity-mode oscillation frequencies based on linear pulsation theory, caused by fixing choices of the input physics for evolutionary models. Guided by a hierarchy among these uncertainties of theoretical frequencies, we subsequently provide a global methodological scheme to achieve forward asteroseismic modeling. We properly take into account correlations amongst the free parameters included in stellar models. Aside from the stellar mass, metalicity and age, the major parameters to be estimated are the near-core rotation rate, the amount of convective core overshooting, and the level of chemical mixing in the radiative zones. This modeling scheme allows for maximum likelihood estimation of the stellar parameters for fixed input physics of the equilibrium models, followed by stellar model selection considering various choices of the input physics. Our approach uses the Mahalanobis distance instead of the often used $chi^2$ statistic and includes heteroscedasticity. It provides estimation of the unknown variance of the theoretically predicted oscillation frequencies.
We present numerical simulations of internal gravity waves (IGW) in a star with a convective core and extended radiative envelope. We report on amplitudes, spectra, dissipation and consequent angular momentum transport by such waves. We find that these waves are generated efficiently and transport angular momentum on short timescales over large distances. We show that, as in the Earths atmosphere, IGW drive equatorial flows which change magnitude and direction on short timescales. These results have profound consequences for the observational inferences of massive stars, as well as their long term angular momentum evolution. We suggest IGW angular momentum transport may explain many observational mysteries, such as: the misalignment of hot Jupiters around hot stars, the Be class of stars, Ni enrichment anomalies in massive stars and the non-synchronous orbits of interacting binaries.
CONTEXT. Gamma Doradus stars (hereafter gamma Dor stars) are known to exhibit gravity- and/or gravito-intertial modes that probe the inner stellar region near the convective core boundary. The non-equidistant spacing of the pulsation periods is an observational signature of the stars evolution and current internal structure and is heavily influenced by rotation. AIMS. We aim to constrain the near-core rotation rates for a sample of gamma Dor stars, for which we have detected period spacing patterns. METHODS. We combined the asymptotic period spacing with the traditional approximation of stellar pulsation to fit the observed period spacing patterns using chi-squared optimisation. The method was applied to the observed period spacing patterns of a sample of stars and used for ensemble modelling. RESULTS. For the majority of stars with an observed period spacing pattern we successfully determined the rotation rates and the asymptotic period spacing values, though the uncertainty margins on the latter were typically large. This also resulted directly in the identification of the modes corresponding with the detected pulsation frequencies, which for most stars were prograde dipole gravity and gravito-inertial modes. The majority of the observed retrograde modes were found to be Rossby modes. We further discuss the limitations of the method due to the neglect of the centrifugal force and the incomplete treatment of the Coriolis force. CONCLUSION. Despite its current limitations, the proposed methodology was successful to derive the rotation rates and to identify the modes from the observed period spacing patterns. It forms the first step towards detailed seismic modelling based on observed period spacing patterns of moderately to rapidly rotating gamma Dor stars.
Red giants are evolved stars that have exhausted the supply of hydrogen in their cores and instead burn hydrogen in a surrounding shell. Once a red giant is sufficiently evolved, the helium in the core also undergoes fusion. Outstanding issues in our understanding of red giants include uncertainties in the amount of mass lost at the surface before helium ignition and the amount of internal mixing from rotation and other processes. Progress is hampered by our inability to distinguish between red giants burning helium in the core and those still only burning hydrogen in a shell. Asteroseismology offers a way forward, being a powerful tool for probing the internal structures of stars using their natural oscillation frequencies. Here we report observations of gravity-mode period spacings in red giants that permit a distinction between evolutionary stages to be made. We use high-precision photometry obtained with the Kepler spacecraft over more than a year to measure oscillations in several hundred red giants. We find many stars whose dipole modes show sequences with approximately regular period spacings. These stars fall into two clear groups, allowing us to distinguish unambiguously between hydrogen-shell-burning stars (period spacing mostly about 50 seconds) and those that are also burning helium (period spacing about 100 to 300 seconds).
Analyses of large spectroscopic surveys of early-type stars in the LMC have found an excess of nitrogen enriched B-type targets with a vsini<40 km/s compared with the predictions of single star evolutionary models incorporating rotational mixing. By contrast the number of such targets with 40<vsini<80 km/s were consistent with such models. We have undertaken a similar analysis for 61 B-type similar targets, towards the young cluster, NGC 346 in the Small Magellanic Cloud (SMC). Approximately 65% could have nitrogen enhancements of less than 0.3 dex, consistent with them having experienced only small amounts of mixing due to their low rotational velocities. However as with the previous LMC surveys, an excess of stars with low projected rotational velocities, vsini<40 km/s and significant nitrogen enrichments is found. This is estimated to be approximately 5% of the total population of apparently single B-type stars or 40% of all stars with current rotational velocities of less than 40 km/s. For all three surveys, the presence of undetected binaries and other uncertainties imply that these percentages might be underestimated and indeed it is possible that all single stars with current rotational velocities of less than 40 km/s are nitrogen enriched. Possible explanations incorporate the effects of magnetic fields, via either a stellar merger followed by magnetic breaking or the evolution of a single star with a large magnetic field. Both mechanisms are compatible with the observed frequency of nitrogen-enriched stars in the Magellanic Clouds. Differences in the properties of the nitrogen-enriched stars compared with the remainder of the sample would be consistent with the former mechanism. For the latter, a qualitative comparison with evolutionary models incorporating magnetic fields is encouraging in terms of the amount of nitrogen enrichment and its presence in stars near the ZAMS.
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