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Register a new userTurbulent convection and pulsation stability of stars - I. Basic equations for calculations of stellar structure and oscillations
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Starting from hydrodynamic equations, we have established a set of hydrodynamic equations for average flow and a set of dynamic equations of auto- and cross-correlations of turbulent velocity and temperature fluctuations, following the classic Reynolds treatment of turbulence. The combination of the two sets of equations leads to a complete and self-consistent mathematical expressions ready for the calculations of stellar structure and oscillations. In this paper, non-locality and anisotropy of turbulent convection are concisely presented, together with defining and calibrating of the three convection parameters ($c_1$, $c_2$ and $c_3$) included in the algorithm. With the non-local theory of convection, the structure of the convective envelope and the major characteristics of non-adiabatic linear oscillations are demonstrated by numerical solutions. Great effort has been exercised to the choice of convection parameters and pulsation instabilities of the models, the results of which show that within large ranges of all three parameters ($c_1$, $c_2$ and $c_3$) the main properties of pulsation stability keep unchanged.
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We have computed linear non-adiabatic oscillations of luminous red giants using a non-local and anisotropic time-dependent theory of convection. The results show that low-order radial modes can be self-excited. Their excitation is the result of radiation and the coupling between convection and oscillations. Turbulent pressure has important effects on the excitation of oscillations in red variables.
By using a non-local and time-dependent convection theory, we have calculated radial and low-degree non-radial oscillations for stellar evolutionary models with $M=1.4$--3.0,$mathrm{M}_odot$. The results of our study predict theoretical instability strips for $delta$ Scuti and $gamma$ Doradus stars, which overlap with each other. The strip of $gamma$ Doradus is slightly redder in colour than that of $delta$ Scuti. We have paid great attention to the excitation and stabilization mechanisms for these two types of oscillations, and we conclude that radiative $kappa$ mechanism plays a major role in the excitation of warm $delta$ Scuti and $gamma$ Doradus stars, while the coupling between convection and oscillations is responsible for excitation and stabilization in cool stars. Generally speaking, turbulent pressure is an excitation of oscillations, especially in cool $delta$ Scuti and $gamma$ Doradus stars and all cool Cepheid- and Mira-like stars. Turbulent thermal convection, on the other hand, is a damping mechanism against oscillations that actually plays the major role in giving rise to the red edge of the instability strip. Our study shows that oscillations of $delta$ Scuti and $gamma$ Doradus stars are both due to the combination of $kappa$ mechanism and the coupling between convection and oscillations, and they belong to the same class of variables at the low-luminosity part of the Cepheid instability strip. Within the $delta$ Scuti--$gamma$ Doradus instability strip, most of the pulsating variables are very likely hybrids that are excited in both p and g modes.
Within the framework of non-local time-dependent stellar convection theory, we study in detail the effect of turbulent anisotropy on stellar pulsation stability. The results show that anisotropy has no substantial influence on pulsation stability of g modes and low-order (radial order $n_mathrm{r}<5$) p modes. The effect of turbulent anisotropy increases as the radial order increases. When turbulent anisotropy is neglected, most of high-order ($n_mathrm{r}>5$) p modes of all low-temperature stars become unstable. Fortunately, within a wide range of the anisotropic parameter $c_3$, stellar pulsation stability is not sensitive to the specific value of $c_3$. Therefore it is safe to say that calibration errors of the convective parameter $c_3$ do not cause any uncertainty in the calculation of stellar pulsation stability.
The ANTARES code has been designed for simulation of astrophysical flows in a variety of situations, in particular in the context of stellar physics. Here, we describe extensions as necessary to model the interaction of pulsation and convection in classical pulsating stars. These extensions encomprise the introduction of a spherical grid, movable in the radial direction, specific forms of grid-refinement and considerations regarding radiative transfer. We then present the basic parameters of the cepheid we study more closely. For that star we provide a short discussion of patterns of the H+HeI and the HeII convection zones and the interaction with pulsation seen in the pdV work or atmospheric structures.
We present a statistical analysis of turbulent convection in stars within our Reynolds-Averaged Navier Stokes (RANS) framework in spherical geometry which we derived from first principles. The primary results reported in this document include: (1) an extensive set of mean-field equations for compressible, multi-species hydrodynamics, and (2) corresponding mean-field data computed from various simulation models. Some supplementary scale analysis data is also presented. The simulation data which is presented includes: (1) shell convection during oxygen burning in a 23 solar mass supernova progenitor, (2) envelope convection in a 5 solar mass red giant, (3) shell convection during the helium flash, and (4) a hydrogen injection flash in a 1.25 solar mass star. These simulations have been partially described previously in Meakin [2006], Meakin and Arnett [2007a,b, 2010], Arnett et al. [2009, 2010], Viallet et al. [2011, 2013a,b] and Mocak et al. [2009, 2011]. New data is also included in this document with several new domain and resolution configurations as well as some variations in the physical model such as convection zone depth and driving source term. The long term goal of this work is to aid in the development of more sophisticated models for treating hydrodynamic phenomena (e.g., turbulent convection) in the field of stellar evolution by providing a direct link between 3D simulation data and the mean fields which are modeled by 1D stellar evolution codes. As such, this data can be used to test previously proposed turbulence models found in the literature and sometimes used in stellar modeling. This data can also serve to test basic physical principles for model building and inspire new prescriptions for use in 1D evolution codes.
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