Theory of stellar convection: Removing the Mixing-Length Parameter

Abstract

Stellar convection is customarily described by Mixing-Length Theory, which makes use of the mixing-length scale to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to suggest that the mixing-length parameter is the same in all stars and at all evolutionary phases. The aim of this study is to present a new theory of stellar convection that does not require the mixing length parameter. We present a self-consistent analytical formulation of stellar convection that determines the properties of stellar convection as a function of the physical behaviour of the convective elements themselves and of the surrounding medium. This new theory is formulated starting from a conventional solution of the Navier-Stokes/Euler equations, i.e. the Bernoulli equation for a perfect fluid, but expressed in a non-inertial reference frame co-moving with the convective elements. In our formalism the motion of stellar convective cells inside convectively-unstable layers is fully determined by a new system of equations for convection in a non-local and time-dependent formalism. We obtain an analytical, non-local, time-dependent sub-sonic solution for the convective energy transport that does not depend on any free parameter. The theory is suitable for the outer convective zones of solar type stars and stars of all mass on the main sequence band. The predictions of the new theory are compared with those from the standard mixing-length paradigm for the most accurate calibrator, the Sun, with very satisfactory results.

arXiv commentAccepted 2014 September 12

References in corpus (12)

• Scaled solar tracks and isochrones in a large region of the Z-Y plane I. From the ZAMS to the TP-AGB end for 0.15 - 2.5 Mo stars
• Turbulent Convection in Stellar Interiors. I. Hydrodynamic Simulation
• Preparing for an Explosion: Hydrodynamic Instabilities and Turbulence in Presupernovae
• Scaled solar tracks and isochrones in a large region of the Z-Y plane. II. From 2.5 to 20 solar masses
• Calibrating Convective properties of Solar-like Stars in the Kepler Field of View
• Turbulent Cells in Stars: I. Fluctuations in Kinetic Energy and Luminosity
• Testing intermediate-age stellar evolution models with VLT photometry of LMC clusters. III. Padova results
• Convective envelopes in rotating OB stars
• How to define the boundaries of a convective zone and how extended is overshooting?
• Variation of Stellar Envelope Convection and Overshoot with Metallicity
• Tidal Effects on the Spatial Structure of the Local Group
• Dissipative phenomena in extended-bodies interactions I: Methods Dwarf galaxies of the Local Group and their synthetic CMDs

Cited by in corpus (7)

• Sub-Inertial Gravity Modes in the B8V Star KIC 7760680 Reveal Moderate Core Overshooting and Low Vertical Diffusive Mixing
• Beyond Mixing-length Theory: a step toward 321D
• Stellar models with mixing length and T(tau) relations calibrated on 3D convection simulations
• Confronting uncertainties in stellar physics II. exploring differences in main-sequence stellar evolution tracks
• Theory of stellar convection II: first stellar models
• On the relevance of bubbles and potential flows for stellar convection
• Environmental effects on star formation in dwarf galaxies and star clusters