Abstract:Helio-seismological data suggest an overshooting (OV) extent of 0.07 H p (H p is the pressure scale height), while theoretical predictions from both models and numerical simulations yield values that are an order of magnitude higher. The reason identified by the authors of numerical simulations is the limited range of physical parameters allowed by the numerical simulations compared to the true solar values; specifically, the simulations are still too viscous. In the case of theoretical models, we discuss limi… Show more
“…Therefore, the fully mixed cores in late B-type stars require ∼16% increase in mass beyond their canonical boundary from the MLT. We argue that future, more advanced non-local timedependent theories of convection (Xiong 1979(Xiong , 1989Canuto 2011aCanuto , 2011bZhang & Li 2012b;Zhang 2013Zhang , 2016Arnett et al 2015) should closely reproduce our seismic Note. Uncertainties in the grid parameters are set by the minimum stepsize in Table 1 and given in parentheses, which is a lower limit of the true uncertainty.…”
Section: Best Asteroseismic Model Candidatessupporting
confidence: 57%
“…The non-local, time-dependent convective models (see, e.g., Xiong 1979Xiong , 1989Canuto 2011aCanuto , 2011bZhang & Li 2012b;Zhang 2013Zhang , 2016Pasetto et al 2014Pasetto et al , 2015Arnett et al 2015) may be able to provide better insight into the physical structure of the overshoot region, and allow us to improve the fit to the observed period spacing of g-mode pulsators. Therefore, the long series of dipole period spacing in KIC 7760680 and Star I provides two ideal tests for theories of convective and nonconvective heat, as well as chemical and angular momentum transport.…”
Section: Mode Trapping In the Deep Stellar Interiormentioning
Thus far, KIC 7760680 is the richest slowly pulsating B star, exhibiting 36 consecutive dipole (ℓ = 1) gravity (g-) modes. The monotonically decreasing period spacing of the series, in addition to the local dips in the pattern, confirm that KIC 7760680 is a moderate rotator with clear mode trapping in chemically inhomogeneous layers. We employ the traditional approximation of rotation to incorporate rotational effects on g-mode frequencies. Our detailed forward asteroseismic modeling of this g-mode series reveals that KIC 7760680 is a moderately rotating B star with mass ∼3.25 M e . By simultaneously matching the slope of the period spacing and the number of modes in the observed frequency range, we deduce that the equatorial rotation frequency of KIC 7760680 is 0.4805 day −1 , which is 26% of its Roche break up frequency. The relative deviation of the model frequencies and those observed is less than 1%. We succeed in tightly constraining the exponentially decaying convective core overshooting parameter to f ov ≈ 0.024 ± 0.001. This means that convective core overshooting can coexist with moderate rotation. Moreover, models with exponentially decaying overshoot from the core outperform those with the classical step-function overshoot. The best value for extra diffusive mixing in the radiatively stable envelope is confined to » D log 0.75 0.25 ext (with D ext in cm 2 s −1 ), which is notably smaller than theoretical predictions.
“…Therefore, the fully mixed cores in late B-type stars require ∼16% increase in mass beyond their canonical boundary from the MLT. We argue that future, more advanced non-local timedependent theories of convection (Xiong 1979(Xiong , 1989Canuto 2011aCanuto , 2011bZhang & Li 2012b;Zhang 2013Zhang , 2016Arnett et al 2015) should closely reproduce our seismic Note. Uncertainties in the grid parameters are set by the minimum stepsize in Table 1 and given in parentheses, which is a lower limit of the true uncertainty.…”
Section: Best Asteroseismic Model Candidatessupporting
confidence: 57%
“…The non-local, time-dependent convective models (see, e.g., Xiong 1979Xiong , 1989Canuto 2011aCanuto , 2011bZhang & Li 2012b;Zhang 2013Zhang , 2016Pasetto et al 2014Pasetto et al , 2015Arnett et al 2015) may be able to provide better insight into the physical structure of the overshoot region, and allow us to improve the fit to the observed period spacing of g-mode pulsators. Therefore, the long series of dipole period spacing in KIC 7760680 and Star I provides two ideal tests for theories of convective and nonconvective heat, as well as chemical and angular momentum transport.…”
Section: Mode Trapping In the Deep Stellar Interiormentioning
Thus far, KIC 7760680 is the richest slowly pulsating B star, exhibiting 36 consecutive dipole (ℓ = 1) gravity (g-) modes. The monotonically decreasing period spacing of the series, in addition to the local dips in the pattern, confirm that KIC 7760680 is a moderate rotator with clear mode trapping in chemically inhomogeneous layers. We employ the traditional approximation of rotation to incorporate rotational effects on g-mode frequencies. Our detailed forward asteroseismic modeling of this g-mode series reveals that KIC 7760680 is a moderately rotating B star with mass ∼3.25 M e . By simultaneously matching the slope of the period spacing and the number of modes in the observed frequency range, we deduce that the equatorial rotation frequency of KIC 7760680 is 0.4805 day −1 , which is 26% of its Roche break up frequency. The relative deviation of the model frequencies and those observed is less than 1%. We succeed in tightly constraining the exponentially decaying convective core overshooting parameter to f ov ≈ 0.024 ± 0.001. This means that convective core overshooting can coexist with moderate rotation. Moreover, models with exponentially decaying overshoot from the core outperform those with the classical step-function overshoot. The best value for extra diffusive mixing in the radiatively stable envelope is confined to » D log 0.75 0.25 ext (with D ext in cm 2 s −1 ), which is notably smaller than theoretical predictions.
“…The green lines show expected velocities in the convective regions, while the brown lines show the dramatically reduced velocities expected for thermohaline or semi-convective mixing. For a general hydrodynamic formulation that includes both thermohaline mixing and semi-convection we refer the reader to Spiegel (1972) and Grossman et al (1993), and the series of papers by Canuto (Canuto 2011a, 2011b, 2011c, 2011d, 2011e). Figure 11. These diagrams show the main stability criteria for stellar models, the expected kind of mixing, and typical velocities.…”
Section: Evolution and Nucleosynthesis Prior To The Asymptotic Giant mentioning
The chemical evolution of the Universe is governed by the chemical yields from stars, which in turn are determined primarily by the initial stellar mass. Even stars as low as 0.9 M can, at low metallicity, contribute to the chemical evolution of elements. Stars less massive than about 10 M experience recurrent mixing events that can significantly change the surface composition of the envelope, with observed enrichments in carbon, nitrogen, fluorine, and heavy elements synthesized by the slow neutron capture process (the s-process). Low-and intermediate-mass stars release their nucleosynthesis products through stellar outflows or winds, in contrast to massive stars that explode as core-collapse supernovae. Here we review the stellar evolution and nucleosynthesis for single stars up to ∼10 M from the main sequence through to the tip of the asymptotic giant branch (AGB). We include a discussion of the main uncertainties that affect theoretical calculations and review the latest observational data, which are used to constrain uncertain details of the stellar models. We finish with a review of the stellar yields available for stars less massive than about 10 M and discuss efforts by various groups to address these issues and provide homogeneous yields for low-and intermediate-mass stars covering a broad range of metallicities.
Keywords
“…Canuto (1999aCanuto ( , 2011d has suggested to replace the boundary condition (7) by the condition that the helium or hydrogen concentration flux is equal to zero, i.e., that ρY − → V = 0 (as usual Y is the helium mass abundance). This will indeed provide a more precise location of the boundary as convection will be very inefficient in the outer overshooting zone so that − → F C and − → F K will be almost zero over an extended region while the chemical composition is expected to vary quite rapidly near the surface.…”
Section: Definition Of a Convective Zone Boundary And Of The Correct mentioning
The era of detailed asteroseismic analyses opened by space missions such as CoRoT and Kepler has highlighted the need for stellar models devoid of numerical inaccuracies, in order to be able to diagnose which physical aspects are being ignored or poorly treated in standard stellar modeling. We tackle here the important problem of fixing convective zone boundaries in the frame of the local mixing length theory. First we show that the only correct way to locate a convective zone boundary is to find, at each iteration step, through interpolations or extrapolations from points within the convective zone, the mass where the radiative luminosity is equal to the total luminosity. We then discuss two misuses of the boundary condition and the ways they affect stellar modeling and stellar evolution. The first consists in applying the neutrality condition for convective instability on the radiative side of the convective boundary. The second way of misusing the boundary condition comes from the process of fixing the convective boundary through the search for a change of sign of a possibly discontinuous function. We show that these misuses can lead to completely wrong estimates of convective core sizes with important consequences for the following evolutionary phases. We point out the advantages of using a double mesh point at each convective zone boundary. The specific problem of a convective shell is discussed and some remarks concerning overshooting are given.
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