On the proper use of the Schwarzschild and Ledoux criteria in stellar evolution computations

The era of detailed asteroseismic analyses opened by space missions such as CoRoT and $\textit{Kepler}$ 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 zones 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 $\textit{within the convective zone}$, the mass where the radiative luminosity is equal to the total one. We then discuss two misuses of the boundary condition and the way they affect stellar modeling and stellar evolution. The first one consists in applying the neutrality condition for convective instability on the $\textit{radiative}$ 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 \textit{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 boundaries. The specific problem of a convective shell is discussed and some remarks concerning overshooting are given.Comment: 14 pages, 10 figures, to appear in A&

The Stability of Massive Main Sequence Stars as a Function of Metallicity

We investigate the pulsational stability of massive (M >~ 120 Msun) main sequence stars of a range of metallicities, including primordial, Population III stars. We include a formulation of convective damping motivated by numerical simulations of the interaction between convection and periodic shear flows. We find that convective viscosity is likely strong enough to stabilize radial pulsations whenever nuclear-burning (the epsilon-mechanism) is the dominant source of driving. This suggests that massive main sequence stars with Z <~ 2 x 10^-3 are pulsationally stable and are unlikely to experience pulsation-driven mass loss on the main sequence. These conclusions are, however, sensitive to the form of the convective viscosity and highlight the need for further high-resolution simulations of the convection-oscillation interaction. For more metal-rich stars (Z >~ 2 x 10^-3), the dominant pulsational driving arises due to the kappa-mechanism arising from the iron-bump in opacity and is strong enough to overcome convective damping. Our results highlight that even for oscillations with periods a few orders of magnitude shorter than the outer convective turnover time, the "frozen-in" approximation for the convection-oscillation interaction is inappropriate, and convective damping should be taken into account when assessing mode stability.Comment: 8 pages, 6 figures; accepted to MNRA

Variability of stellar granulation and convective blueshift with spectral type and magnetic activity. I. K and G main sequence stars

In solar-type stars, the attenuation of convective blueshift by stellar magnetic activity dominates the RV variations over the low amplitude signal induced by low mass planets. Models of stars that differ from the Sun will require a good knowledge of the attenuation of the convective blueshift to estimate its impact on the variations. It is therefore crucial to precisely determine not only the amplitude of the convective blueshift for different types of stars, but also the dependence of this convective blueshift on magnetic activity, as these are key factors in our model producing the RV. We studied a sample of main sequence stars with spectral types from G0 to K2 and focused on their temporally averaged properties: the activity level and a criterion allowing to characterise the amplitude of the convective blueshift. We find the differential velocity shifts of spectral lines due to convection to depend on the spectral type, the wavelength (this dependence is correlated with the Teff and activity level), and on the activity level. This allows us to quantify the dependence of granulation properties on magnetic activity for stars other than the Sun. The attenuation factor of the convective blueshift appears to be constant over the considered range of spectral types. We derive a convective blueshift which decreases towards lower temperatures, with a trend in close agreement with models for Teff lower than 5800 K, but with a significantly larger global amplitude. We finally compare the observed RV variation amplitudes with those that could be derived from our convective blueshift using a simple law and find a general agreement on the amplitude. Our results are consistent with previous results and provide, for the first time, an estimation of the convective blueshift as a function of Teff, magnetic activity, and wavelength, over a large sample of G and K main sequence stars

Convective injection and photochemical decay of peroxides in the tropical upper troposphere: Methyl iodide as a tracer of marine convection

The convective injection and subsequent fate of the peroxides H2O2 and CH3OOH in the upper troposphere is investigated using aircraft observations from the NASA Pacific Exploratory Mission-Tropics A (PEM-Tropics A) over the South Pacific up to 12 km altitude. Fresh convective outflow is identified by high CH3I concentrations; CH3I is an excellent tracer of marine convection because of its relatively uniform marine boundary layer concentration, relatively well-defined atmospheric lifetime against photolysis, and high sensitivity of measurement. We find that mixing ratios of CH3OOH in convective outflow at 8-12 km altitude are enhanced on average by a factor of 6 relative to background, while mixing ratios of H2O2 are enhanced by less than a factor of 2. The scavenging efficiency of H2O2 in the precipitation associated with deep convection is estimated to be 55-70%. Scavenging of CH3OOH is negligible. Photolysis of convected peroxides is a major source of the HOx radical family (OH + peroxy radicals) in convective outflow. The timescale for decay of the convective enhancement of peroxides in the upper troposphere is determined using CH3I as a chemical clock and is interpreted using photochemical model calculations. Decline of CH3OOH takes place on a timescale of a 1-2 days, but the resulting HOx converts to H2O2, so H2O2 mixing ratios show no decline for ∼5 days following a convective event. The perturbation to HOx at 8-12 km altitude from deep convective injection of peroxides decays on a timescale of 2-3 days for the PEM-Tropics A conditions. Copyright 1999 by the American Geophysical Union

Ledoux's convection criterion in evolution and asteroseismology of massive stars

Saio et al. (2006) have shown that the presence of an intermediate convective zone (ICZ) in post-main sequence models could prevent the propagation of g-modes in the radiative interior and hence avoid the corresponding radiative damping. The development of such a convective region highly depends on the structure of the star in the mu-gradient region surrounding the convective core during the main sequence phase. In particular,the development of this ICZ depends on physical processes such as mass loss, overshooting (Chiosi & Maeder 1986, Chiosi et al. 1992, see also Godart et al., these proceedings) and convective instability criterion (Schwarzschild's or Ledoux's criteria). In this paper we study the consequences of adopting the Ledoux's criterion on the evolution of the convective regions in massive stars (15 and 20 Msun), and on the pulsation spectrum of these new B-type variables (also called SPBsg).Comment: Contribution to the Proceedings of the 38th LIAC/HELAS-ESTA/BAG, 2008 Accepted for publication in CoAs

Modeling the Rise of Fibril Magnetic Fields in Fully Convective Stars

Many fully convective stars exhibit a wide variety of surface magnetism, including starspots and chromospheric activity. The manner by which bundles of magnetic field traverse portions of the convection zone to emerge at the stellar surface is not especially well understood. In the Solar context, some insight into this process has been gleaned by regarding the magnetism as consisting partly of idealized thin flux tubes (TFT). Here, we present the results of a large set of TFT simulations in a rotating spherical domain of convective flows representative of a 0.3 solar-mass, main-sequence star. This is the first study to investigate how individual flux tubes in such a star might rise under the combined influence of buoyancy, convection, and differential rotation. A time-dependent hydrodynamic convective flow field, taken from separate 3D simulations calculated with the anelastic equations, impacts the flux tube as it rises. Convective motions modulate the shape of the initially buoyant flux ring, promoting localized rising loops. Flux tubes in fully convective stars have a tendency to rise nearly parallel to the rotation axis. However, the presence of strong differential rotation allows some initially low latitude flux tubes of moderate strength to develop rising loops that emerge in the near-equatorial region. Magnetic pumping suppresses the global rise of the flux tube most efficiently in the deeper interior and at lower latitudes. The results of these simulations aim to provide a link between dynamo-generated magnetic fields, fluid motions, and observations of starspots for fully convective stars.Comment: 20 pages, 15 figures, accepted to Astrophysical Journa

Preventing blow up by convective terms in dissipative PDEs

We study the impact of the convective terms on the global solvability or finite time blow up of solutions of dissipative PDEs. We consider the model examples of 1D Burger's type equations, convective Cahn-Hilliard equation, generalized Kuramoto-Sivashinsky equation and KdV type equations, we establish the following common scenario: adding sufficiently strong (in comparison with the destabilizing nonlinearity) convective terms to equation prevents the solutions from blowing up in finite time and makes the considered system globally well-posed and dissipative and for weak enough convective terms the finite time blow up may occur similarly to the case when the equation does not involve convective term. This kind of result has been previously known for the case of Burger's type equations and has been strongly based on maximum principle. In contrast to this, our results are based on the weighted energy estimates which do not require the maximum principle for the considered problem