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Register a new userOn the relevance of bubbles and potential flows for stellar convection
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Added by
Marcelo Miguel Miller Bertolami
Publication date
2016
fields
Physics
and research's language is
English
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Recently Pasetto et al. have proposed a new method to derive a convection theory appropriate for the implementation in stellar evolution codes. Their approach is based on the simple physical picture of spherical bubbles moving within a potential flow in dynamically unstable regions, and a detailed computation of the bubble dynamics. Based on this approach the authors derive a new theory of convection which is claimed to be parameter free, non-local and time-dependent. This is a very strong claim, as such a theory is the holy grail of stellar physics. Unfortunately we have identified several distinct problems in the derivation which ultimately render their theory inapplicable to any physical regime. In addition we show that the framework of spherical bubbles in potential flows is unable to capture the essence of stellar convection, even when equations are derived correctly.
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Numerical simulations have by now revealed that the fine scale structure of the penumbra in general and the Evershed effect in particular is due to overturning convection, mainly confined to gaps with strongly reduced magnetic field strength. The Evershed flow is the radial component of the overturning convective flow visible at the surface. It is directed outwards -- away from the umbra -- because of the broken symmetry due to the inclined magnetic field. The dark penumbral filament cores visible at high resolution are caused by the cusps in the magnetic field that form above the gaps. Still remaining to be established are the details of what determines the average luminosity of penumbrae, the widths, lengths, and filling factors of penumbral filaments, and the amplitudes and filling factors of the Evershed flow. These are likely to depend at least partially also on numerical aspects such as limited resolution and model size, but mainly on physical properties that have not yet been adequately determined or calibrated, such as the plasma beta profile inside sunspots at depth and its horizontal profile, the entropy of ascending flows in the penumbra, etc.
We study the effects of rotation on the growth and saturation of the double-diffusive fingering (thermohaline) instability at low Prandtl number. Using direct numerical simulations, we estimate the compositional transport rates as a function of the relevant non-dimensional parameters - the Rossby number, inversely proportional to the rotation rate, and the density ratio which measures the relative thermal and compositional stratifications. Within our explored range of parameters, we generally find rotation to have little effect on vertical transport. However, we also present one exceptional case where a cyclonic large scale vortex (LSV) is observed at low density ratio and fairly low Rossby number. The LSV leads to significant enhancement in the fingering transport rates by concentrating compositionally dense downflows at its core. We argue that the formation of such LSVs could be relevant to solving the missing mixing problem in RGB stars.
We present here the first stellar models on the Hertzsprung-Russell diagram (HRD), in which convection is treated according to the novel scale-free convection theory (SFC theory) by Pasetto et al. (2014). The aim is to compare the results of the new theory with those from the classical, calibrated mixing-length (ML) theory to examine differences and similarities. We integrate the equations describing the structure of the atmosphere from the stellar surface down to a few percent of the stellar mass using both ML theory and SFC theory. The key temperature over pressure gradients, the energy fluxes, and the extension of the convective zones are compared in both theories. The analysis is first made for the Sun and then extended to other stars of different mass and evolutionary stage. The results are adequate: the SFC theory yields convective zones, temperature gradients of the ambient and of the convective element, and energy fluxes that are very similar to those derived from the calibrated MT theory for main sequence stars. We conclude that the old scale dependent ML theory can now be replaced with a self-consistent scale-free theory able to predict correct results, one which is simpler and more physically grounded than the ML theory. Fundamentally, the SFC theory offers a deeper insight of the underlying physics than numerical simulations.
A common feature of the X-ray bubbles observed in Chandra images of some cooling flow clusters is that they appear to be surrounded by bright, cool shells. Temperature maps of a few nearby luminous clusters reveal that the shells consist of the coolest gas in the clusters -- much cooler than the surrounding medium. Using simple models, we study the effects of this cool emission on the inferred cooling flow properties of clusters. We find that the introduction of bubbles into model clusters that do NOT have cooling flows results in temperature and surface brightness profiles that resemble those seen in nearby cooling flow clusters. They also approximately reproduce the recent XMM-Newton and Chandra observations of a high minimum temperature of 1-3 keV. Hence, bubbles, if present, must be taken into account when inferring the physical properties of the ICM. In the case of some clusters, bubbles may account entirely for these observed features, calling into question their designation as clusters with cooling flows. However, since not all nearby cooling flow clusters show bubble-like features, we suggest that there may be a diverse range of physical phenomena that give rise to the same observed features.
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.
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