Convection in the atmospheres and envelopes of Pre-Main Sequence stars

Abstract

The ${T}_{\rm eff}$ location of Pre-Main Sequence (PMS) evolutionary tracks depends on the treatment of over-adiabaticity (D'Antona & Mazzitelli [CITE], [CITE]). Since the convection penetrates into the stellar atmosphere, also the treatment of convection in the modeling of stellar atmospheres will affect the location of the Hayashi tracks. In this paper we present new non-grey PMS tracks for ${T}_{\rm eff}$ $>4000$ K. We compute several grids of evolutionary tracks varying: i) the treatment of convection: either the Mixing Length Theory (MLT) or Canuto et al. ([CITE], CGM) formulation of a Full Spectrum of Turbulence; ii) the atmospheric boundary conditions: we use the new Vienna grids of ATLAS9 atmospheres (Heiter et al. [CITE]), which were computed using either MLT (with $\alpha=\Lambda/H_{\rm p}=0.5$) or CGM treatments. For comparison, we also compute grids of models with the NextGen (Allard & Hauschildt [CITE], AH97) atmosphere models, and a 1 ${M}_{\odot}$ grey MLT evolutionary track using the α calibration based on 2D-hydrodynamical models (Ludwig et al. [CITE]). These different grids of models allow us to analyze the effects of convection modeling on the non-grey PMS evolutionary tracks. We disentangle the effect of the wavelength dependent opacity on a self-consistent treatment of convection in the atmosphere from the role of the convection model itself in the atmosphere and in the interior. While for some parts of the HR diagram (e.g., A stars) a low efficiency of atmospheric convection is clearly indicated by the data, for others the evidence is conflicting, showing the weaknesses of all the presently adopted local convection models. Nevertheless, the assumption of a low photospheric efficiency permits us to reproduce a larger amount of data and we have hence restricted our study to this case and draw the following conclusions for it: i) in spite of the solar calibration, if MLT convection is adopted a large uncertainty results in the shape and location of PMS tracks, and the MLT calibration loses sense. ii) As long as the model of convection is not the same in the interior and in the atmosphere, the optical depth at which we take the boundary conditions is an additional parameter of the models. iii) Furthermore, very different sub-atmospheric structures are obtained (for MS and PMS stellar models) depending not only on the treatment of convection, but also on the optical depth at which the boundary conditions are taken. iv) The comparison between NextGen based models and ATLAS9 based models shows that in the ${T}_{\rm eff}$ domain they have in common (4000–10 000 K) the improved opacities in NextGen atmosphere models have no relevant role on the PMS location, this being determined mainly by the treatment of the over-adiabatic convection. v) In the framework of standard stellar modeling (i.e., non-magnetic, non-rotating, spherical models), the comparison between theoretical models and observational data in very young binary systems indicates that, for both treatments of convection (MLT and CGM) and for any of the atmosphere grids (including those based on the 2D-hydrodynamical atmosphere models), the same assumption for convection cannot be used in PMS and MS: either the models fit the MS – and the Sun in particular – or they fit the PMS. Convection in the PMS phase appears to be less efficient than what is necessary to fit the Sun.