Gradient Of Mean Molecular Weight Research Articles

Compositional turbulence and layering in the gaseous envelopes of forming planets

ABSTRACT Differential settling and growth of dust grains impact the structure of the radiative envelopes of gaseous planets during formation. Sufficiently rapid dust growth can result in envelopes with substantially reduced opacities for radiation transport, thereby facilitating planet formation. We revisit the problem and establish that dust settling and grain growth also lead to outer planetary envelopes that are prone to compositional instabilities, by virtue of their inverted mean-molecular weight gradients. Under a variety of conditions, we find that the radiative envelopes of forming planets experience compositional turbulence driven by a semi-transparent version of the thermohaline instability (’fingering convection’). The standard double-diffusive thermohaline theory does not apply here and is replaced by a simplified first-principle treatment for the semitransparent regime of interest. The compositional turbulence seems efficient at mixing dust in the radiative envelopes of planets forming at super-au distances (say 5 au) from a Sun-like star, but not so at sub-au distances (say 0.2 au). We also address the possibility of compositional layering in this context. Distinct turbulent regimes for planetary envelopes growing at sub-au versus super-au distances could leave an imprint on the final planets formed.

The importance of silicate vapour in determining the structure, radii, and envelope mass fractions of sub-Neptunes

ABSTRACT Substantial silicate vapour is expected to be in chemical equilibrium at temperature conditions typical of the silicate–atmosphere interface of sub-Neptune planets, which can exceed 5000 K. Previous models of the atmospheric structure and evolution of these exoplanets, which have been used to constrain their atmospheric mass fractions, have neglected this compositional coupling. In this work, we show that silicate vapour in a hydrogen-dominated atmosphere acts as a condensable species, decreasing in abundance with altitude. The resultant mean molecular weight gradient inhibits convection at temperatures above ∼4000 K, inducing a near-surface radiative layer. This radiative layer decreases the planet’s total radius compared to a planet with the same base temperature and a convective, pure H/He atmosphere. Therefore, we expect silicate vapour to have major effects on the inferred envelope mass fraction and thermal evolution of sub-Neptune planets. We demonstrate that differences in radii, and hence in inferred atmospheric masses, are largest for planets which have larger masses, equilibrium temperatures, and atmospheric mass fractions. The effects are largest for younger planets but differences can persist on gigayear time-scales for some sub-Neptunes. For a 10 M⊕ planet with Teq = 1000 K and an age of ∼300 Myr, an observed radius consistent with an atmospheric mass fraction of 10 per cent when accounting for silicate vapour would be misinterpreted as indicating an atmospheric mass fraction of 2 per cent if an H/He-only atmosphere were assumed. The presence of silicate vapour in the atmosphere is also expected to have important implications for the accretion and loss of primordial hydrogen atmospheres.

The Evolution of Massive Close Binaries: Anomalous Relationship between Nitrogen Abundances and Rotational Velocities

Abstract The combined effects of rotation and mass accretion on the evolution of binary systems are investigated in this work. Rotational binaries provide us with a promising channel that could explain the abnormal phenomenon of the nitrogen abundances in Groups 1 and 2 of the Galactic Hunter diagram. Group 1 contains fast-rotating but nitrogen-unenriched stars, whereas Group 2 includes apparently slowly rotating but nitrogen-enhanced stars. The donor star suffers from heavy mass loss that progressively exposes deep layers of nitrogen and corresponding angular momentum loss that can efficiently spin the star down. Rapid-rotation stars without nitrogen enrichment may be related to mass gainers that had accreted little matter from a close companion and then been spun up to rapid rotation. Nitrogen enrichment of mass gainers can be greatly suppressed by low accreting efficiency, which is induced by critical rotation, thermohaline mixing, and the gradient of mean molecular weight. Nitrogen enrichment due to mass accretion appears to be more efficient than that due to rotational mixing, because there exist thermohaline instabilities during Roche lobe overflow. The mixing in the enlarged convective core reduces carbon and nitrogen abundances but increases oxygen abundances in mass gainers. This process significantly triggers CNO cycling but does not support CN cycling. The orbital separation can be widened because of the nonconservative mass transfer, and this process gives rise to weak tidal torques. Therefore, invoking binaries has the potential to simultaneously explain the observed stars in Groups 1 and 2 of the Galactic Hunter diagram.

Semi-convective layer formation

Semi-convective mixing, as an example of double-diffusive convection, is of general importance in multi-component fluid mixing processes. In astrophysics it occurs when the mean molecular weight gradient caused by a mixture of light material on top of heavier one counteracts the convective instability caused by a temperature gradient. Direct numerical simulations of double-diffusive fluid flows in a realistic stellar or planetary parameter space are currently non-feasible. Hence, a model describing incompressible semi-convection was developed, which allows to investigate semi-convective layer formation. A detailed parameter study with varying Rayleigh number and stability parameter has been performed for the giant planet case. We conclude that semi-convective layering may not play that important role as suggested in earlier works for the planetary case.

Condensation-inhibited convection in hydrogen-rich atmospheres

In an atmosphere, a cloud condensation region is characterized by a strong vertical gradient in the abundance of the related condensing species. On Earth, the ensuing gradient of mean molecular weight has relatively few dynamical consequences because N2is heavier than water vapor, so that only the release of latent heat significantly impacts convection. On the contrary, in a hydrogen dominated atmosphere (e.g., giant planets), all condensing species are significantly heavier than the background gas. This can stabilize the atmosphere against convection near a cloud deck if the enrichment in the given species exceeds a critical threshold. This raises two questions. What is transporting energy in such a stabilized layer, and how affected can the thermal profile of giant planets be? To answer these questions, we first carry out a linear analysis of the convective and double-diffusive instabilities in a condensable medium showing that an efficient condensation can suppress double-diffusive convection. This suggests that a stable radiative layer can form near a cloud condensation level, leading to an increase in the temperature of the deep adiabat. Then, we investigate the impact of the condensation of the most abundant species (water) with a steady-state atmosphere model. Compared to standard models, the temperature increase can reach several hundred degrees at the quenching depth of key chemical tracers. Overall, this effect could have many implications for our understanding of the dynamical and chemical state of the atmosphere of giant planets, for their future observations (withJunofor example), and for their internal evolution.

Numerical tests of rotational mixing in massive stars with the new population synthesis code BONNFIRES

We use our new population synthesis code BONNFIRES to test how surface abundances predicted by rotating stellar models depend on the numerical treatment of rotational mixing, such as spatial resolution, temporal resolution and computation of mean molecular weight gradients. We find that even with identical numerical prescriptions for calculating the rotational mixing coefficients in the diffusion equation, different timesteps lead to a deviation of the coefficients and hence surface abundances. We find the surface abundances vary by 10-100% between the model sequences with short timestep of 0.001Myr to model sequences with longer timesteps. Model sequences with stronger surface nitrogen enrichment also have longer main-sequence lifetimes because more hydrogen is mixed to the burning cores. The deviations in main-sequence lifetimes can be as large as 20%. Mathematically speaking, no numerical scheme can give a perfect solution unless infinitesimally small timesteps are used. However, we find that the surface abundances eventually converge within 10% between modelling sequences with sufficiently small timesteps below 0.1Myr. The efficiency of rotational mixing depends on the implemented numerical scheme and critically on the computation of the mean molecular weight gradient. A smoothing function for the mean molecular weight gradient results in stronger rotational mixing. If the discretization scheme or the computational recipe for calculating the mean molecular weight gradient is altered, re-calibration of mixing parameters may be required to fit observations. If we are to properly understand the fundamental physics of rotation in stars, it is crucial that we minimize the uncertainty introduced into stellar evolution models when numerically approximating rotational mixing processes.

ASTEROSEISMIC ANALYSIS OF THECoRoTTARGET HD 49933

The frequency ratios and of HD 49933 exhibit an increase at high frequencies. This behavior also exists in the ratios of other stars, which is considered to result from the low signal-to-noise ratio and the larger line width at the high-frequency end and could not be predicted by stellar models in previous work. Our calculations show that the behavior not only can be reproduced by stellar models, but can be predicted by asymptotic formulas of the ratios. The frequency ratios of the Sun, too, can be reproduced well by the asymptotic formulas. The increased behavior derives from the fact that the gradient of mean molecular weight at the bottom of the radiative region hinders the propagation of p-modes, while the hindrance does not exist in the convective core. This behavior should exist in the ratios of stars with a large convective core. The characteristic of the ratios at high frequencies provides a strict constraint on stellar models and aids in determining the size of the convective core and the extent of overshooting. Observational constraints point to a star with $M=1.28\pm0.01 M_{\odot}$, $R=1.458\pm0.005 R_{\odot}$, $t=1.83\pm0.1$ Gyr, $r_{cc}=0.16\pm0.02 R_{\odot}$, $\alpha=1.85\pm0.05$, and $\delta_{ov}=0.6\pm0.2$ for HD 49933.

IMPLICATIONS OF RAPID CORE ROTATION IN RED GIANTS FOR INTERNAL ANGULAR MOMENTUM TRANSPORT IN STARS

Core rotation rates have been measured for red giant stars using asteroseismology. This data, along with helioseismic measurements and open cluster spin down studies, provide powerful clues about the nature and timescale for internal angular momentum transport in stars. We focus on two cases: the metal poor red giant KIC 7341231 ("Otto") and intermediate mass core helium burning stars. For both we examine limiting case studies for angular momentum coupling between cores and envelopes under the assumption of rigid rotation on the main sequence. We discuss the expected pattern of core rotation as a function of mass and radius. In the case of Otto, strong post-main-sequence coupling is ruled out and the measured core rotation rate is in the range of 23 to 33 times the surface value expected from standard spin down models. The minimum coupling time scale (.17 to .45 Gyr) is significantly longer than that inferred for young open cluster stars. This implies ineffective internal angular momentum transport in early first ascent giants. By contrast, the core rotation rates of evolved secondary clump stars are found to be consistent with strong coupling given their rapid main sequence rotation. An extrapolation to the white dwarf regime predicts rotation periods between 330 and .0052 days depending on mass and decoupling time. We identify two key ingredients that explain these features: the presence of a convective core and inefficient angular momentum transport in the presence of larger mean molecular weight gradients. Observational tests that can disentangle these effects are discussed.

THE STABILITY OF WEAKLY COLLISIONAL PLASMAS WITH THERMAL AND COMPOSITION GRADIENTS

Over the last decade, substantial efforts have been devoted to understanding the stability properties, transport phenomena, and long-term evolution of weakly-collisional, magnetized plasmas which are stratified in temperature. These studies have improved our understanding of the physics governing the intra-cluster medium (ICM), but assumed that ICM is a homogeneous. This, however, might not be a good approximation if heavy elements sediment in the inner region of the galaxy cluster. In this paper, we analyze the stability of a weakly-collisional, magnetized plane-parallel atmosphere which is stratified in both temperature and composition. This allows us to discuss for the first time the dynamics of weakly-collisional environments where heat conduction, momentum transport, and ion-diffusion are anisotropic with respect to the direction of the magnetic field. We show that, depending on the relative signs and magnitudes of the gradients in the temperature and the mean molecular weight, the plasma can be subject to a wide variety of unstable modes which include modifications to the magnetothermal instability (MTI), the heat-flux-driven buoyancy instability (HBI), and overstable gravity modes previously studied in homogeneous media. We discuss the astrophysical implications of our findings for a representative galaxy cluster where helium has sedimented. Our findings suggest that the core insulation that results from the magnetic field configurations that arise as a natural consequence of the HBI, which would be MTI stable in a homogeneous medium, could be alleviated if the mean molecular weight gradient is steep enough, i.e., $(\nabla \mu)/\mu > (\nabla T)/T$. This study constitutes a first step toward understanding the interaction between magnetic turbulence and the diffusion of heavy elements in the ICM. (abridged)

The impact of helium on thermosphere mass density response to geomagnetic activity during the recent solar minimum

High‐resolution mass density observations inferred from accelerometer measurements on the CHAMP and GRACE satellites are employed to investigate the thermosphere mass density response with latitude and altitude to geomagnetic activity during the recent solar minimum. Coplanar orbital periods in February 2007 and December 2008 revealed the altitude and latitude response in thermosphere mass density for their respective winter hemispheres was influenced by the relative amount of helium and oxygen present. The CHAMP‐to‐GRACE (C/G) mass density ratio depends on two terms; the first proportional to the ratio of the mean molecular weight to temperature and the second proportional to the vertical gradient of the logarithmic mean molecular weight. For the relative levels of helium and oxygen in February 2007, the winter hemisphere C/G mass density response to geomagnetic activity, although similar to the summer hemisphere, was caused predominantly by changes in the vertical gradient of the logarithmic mean molecular weight. In December 2008, the significant presence of helium caused the mean molecular weight changes to exceed temperature changes in the winter hemisphere leading to an increase in the C/G ratio with increasing geomagnetic activity, in opposition to the decrease observed in the summer hemisphere that was caused primarily by temperature changes. The observed behavior is indicative of composition effects influencing the mass density response and the dynamic action of the oxygen to helium transition region in both latitude and altitude will lead to complex behaviors in the mass density at GRACE altitudes throughout the extended solar minimum from 2007 to 2010.

A search for a new class of pulsating DA white dwarf stars in the DB gap

While white dwarf stars are classified into many subgroups based on the appearance of hydrogen, helium, carbon, oxygen and other spectral lines – or even pure continuum with no lines in the case of the DC stars – the vast majority fall into two major subgroups: those with hydrogen atmospheres (the DA white dwarfs), and those with helium atmospheres (the DO and DB white dwarfs). Remarkably, in the range 45 000 ≥Teff≥ 30 000 K there are only a few white dwarfs with helium atmospheres to be found – the vast majority are DAs in this temperature range – although white dwarfs with helium atmospheres are found at both hotter (DO) and cooler (DB) effective temperatures. This dearth of helium atmosphere white dwarfs in this temperature range is known as the ‘DB gap’ and is understood in terms convective mixing of the outer atmospheres at the hot and cool ends of the gap, while radiative stability allows the lighter hydrogen to float to the top in the DB gap, so the stars are seen to be DA hydrogen atmosphere white dwarfs. Asteroseismology is an important tool for probing stellar interiors, and white dwarf stars are the most successfully studied group using this technique. In a stability analysis of the stars in the DB gap, Shibahashi has recently predicted the existence of a new class of pulsating white dwarf stars. He finds from models that DA white dwarfs near the red edge of the DB gap have convectively stable outer atmospheres because of a steep mean molecular weight gradient, yet nevertheless have a superadiabatic layer that renders them pulsationally unstable due to radiative heat exchange. There have been very few observational tests for pulsation among stars of this type. We have initiated a survey to search for the predicted pulsators and report here our first observations of five stars with the South African Astronomical Observatory 1.9-m telescope and University of Cape Town CCD photometer, and two stars with the William Herschel Telescope 4.2-m telescope and the ULTRACAM photometer. We have two detections at formal significance levels greater then 4σ; the rest are null results with upper limits of about 6–8 mmag with the 1.9-m telescope and about 3 mmag with the 4.2-m telescope. The two formally significant detections need confirmation, but the cases for them are good. Should they be confirmed, a new class of pulsating white dwarfs will become available for asteroseismic investigation, providing new insight into white dwarfs in general and into the DB gap in particular.

What Prevents Internal Gravity Waves from Disturbing the Solar Uniform Rotation?

Internal gravity waves (IGWs) are naturally produced by convection in stellar envelopes, and they could be an important mechanism for transporting angular momentum in the radiative interiors of stars. Prior work has established that they could operate over a short enough timescale to explain the internal solar rotation as a function of depth. We demonstrate that the natural action of IGWs is to produce large-scale oscillations in the solar rotation as a function of depth, which is in marked contrast to the nearly uniform rotation in the outer radiative envelope of the Sun. An additional angular momentum transport mechanism is therefore required, and neither molecular nor shear-induced turbulent viscosity is sufficient to smooth out the profile. Magnetic processes, such as the Tayler-Spruit dynamo, could flatten the rotation profile. We therefore conclude that IGWs must operate in conjunction with magnetic angular momentum transport processes if they operate at all. Furthermore, both classes of mechanisms must be inhibited to some degree by mean molecular weight gradients in order to explain the recent evidence for a rapidly rotating embedded core in the Sun, should it be confirmed by a further analysis of solar g-mode oscillations.

AmFm Stars as a Test of Rotational Mixing Models

Stellar evolution models have been calculated for stars of 1.7-2.5 M☉ with both the Geneva-Toulouse and Montreal codes. In the Geneva-Toulouse code, the internal evolution of angular momentum is calculated self-consistently along with the transport of a few species. In the Montreal code, the transport of 24 species is treated in detail, taking into account radiative accelerations, thermal diffusion, and gravitational settling, along with the turbulent diffusion coefficients calculated in the Geneva-Toulouse code. It is verified that the two codes lead to very similar internal structure for a given mass. The calculated surface abundances are compared to abundance anomalies observed on AmFm stars. It is found that with approximately the same parameters as used for other types of stars, the Geneva-Toulouse code leads to turbulent transport coefficients that produce abundance anomalies consistent with the observed ones for HD 73045, HD 23610, and Sirius. Taking into account the effect of the anisotropy of turbulence on vertical transport plays an important role, although the level of anisotropy in stellar envelopes is very uncertain; this effect is usually neglected in calculations. The stabilizing effect of the mean molecular weight gradient can also be important. The current level of accuracy of observed abundances only permits to choose within a one-parameter family of models. To distinguish between turbulent models with different interior profiles, an accuracy of 0.03 dex is required of abundance determinations, a level of accuracy that is not currently achieved. It is also shown that taking into account the pre-main-sequence evolution of the rotation profile leads to an important reduction in the Ω dependence of turbulent transport for slow rotators.

Which massive stars are gamma-ray burst progenitors?

The collapsar model for gamma-ray bursts requires three essential ingredients: a massive core, removal of the hydrogen envelope, and enough angular momentum in the core. We study current massive star evolution models of solar metallicity to determine which massive star physics is capable of producing these ingredients. In particular, we investigate the role of hydrodynamic and magnetic internal angular momentum transport and binary mass and angular momentum transfer. We follow the evolution of rotating single stars and of binary systems that include rotational processes for both stars. Neglecting magnetic fields, we show that the cores of massive single stars can maintain a high specific angular momentum when evolved with the assumption that mean molecular weight gradients suppress rotational mixing processes. In binary systems that undergo mass transfer during core hydrogen burning the mass receiving star accretes large amounts of high angular momentum material, leading to a spin-up of the core. We find, however, that this merely compensates for the tidal angular momentum loss due to spin-orbit coupling, which leads to synchronous rotation before the mass transfer event. Therefore the resulting cores do not rotate faster than in single stars. We also present models that include magnetic fields generated by differential rotation and we consider the internal angular momentum transport by magnetic torques. We investigate the capability of magnetic torques to efficiently pump angular momentum into the cores of accreting stars. Despite our finding that this mechanism works, the magnetic coupling of core and envelope after the accreting star ends core hydrogen burning leads to slower rotation than in the non-magnetic case.

Evolution of Rotating AGB Stars and the s-Process Nucleosynthesis

AbstractWe present new results on the evolution and nucleosynthesis in rotating AGB stars. We analyse the role of the gradient of mean molecular weight in the mixing process and show that neglecting this component induces a potentially strong third dredge-up. We also quantify the impact of rotation on the structure and conclude that the effects of rotation (1) mainly concern the inner, fast rotating regions of the stars and (2) are relatively weak as long as rotational mixing does not induce a deep third dredge-up. We also focus our investigations on the s-process nucleosynthesis and show that rotational mixing tends to inhibit the production of s-elements. This results from the contamination of the 13C-rich layers responsible for the neutron production by the poisonous 14N. Our calculations also indicate that the distribution of s-process elements depends sensitively on the magnitude of the diffusion coefficient. These results suggest that rotational mixing is not the main mechanism responsible for the production of s-elements in AGB stars, but that it can influence, and in particular reduce, the final enrichment in s-elements.

On the possibility of partial matter mixing in rotating massive stars

The principal role of strong horizontal diffusion in overcoming the inhibiting effect of mean molecular weight gradient and in producing partial matter mixing between convective core and radiative envelope of a rotating star, is shown.

The Stratification of Jupiter's Troposphere at the Galileo Probe Entry Site

Galileo Probe Atmospheric Structure Investigation (ASI) pressure and temperature sensor data acquired during the parachute descent phase have been used to derive the static stability structure of Jupiter's troposphere at pressure levels of 0.5–22 bars using three techniques. The first approach utilizes both the p-sensor and T-sensor data, but since the p-sensor's zero offset was significantly affected by the thermal anomaly in the probe, two other approaches using only T-sensor data have also been developed. By making the physically reasonable assumptions of equilibrium descent for the probe and hydrostatic balance of the atmosphere, an algorithm for deriving the background static stability from T-sensor measurements alone is developed. Regions with static stability 0.1–0.2 K km −1 are found at 0.5–1.7 bars, 3–8.5 bars, and 14–20 bars. Between these layers, regions of weaker static stability are present. Mean molecular weight gradients due to the vertical variation of water vapor abundance near the 11-bar pressure level appear to stabilize the atmosphere at this level. Oscillatory structures with vertical wavelength ∼15–30 km and amplitude ∼0.1–0.2 K are observed in the T-sensor data. For pressure <2 bars, these eddies are well above the noise level of the measurements and are consistent with the predictions of linear gravity wave theory for a wave with horizontal phase speed c x =160 m s −1 with respect to System III propagating through the static stability derived from the T-sensor data alone. They provide quantitative confirmation of the static stability derived from T-sensor data in the troposphere where p<2 bars. The observed static stability structure shows an inverse correlation with the regions of wind shear observed by the Doppler Wind Experiment: regions of highest shear in the horizontal wind appear to be associated with regions of lowest static stability. The particulate population detected by other experiments on the probe shows some correlation with the uppermost layer of static stability, suggesting enhanced solar energy deposition at these levels may play a role in producing the positive static stability.

Numerical Prediction of Diffusion Flames Using Multicomponent Diffusion and the Accuracy Evaluation.

Numerical computations are made of axisymmetric laminar jet H2 diffusion flames, taking account of multicomponent diffusion and detailed chemical kinetics. Availability of multicomponent diffusion calculation is investigated by comparison between the computational results with exact multicomponent diffusion coefficients or effective binary diffusivity and experimental results. The effect of thermal diffusion is also investigated. Computational results with exact method are close to experimental results for major species. Consideration of thermal diffusion improves the accuracy of the prediction. When fuel is H2 diluted with N2, mass flux of major species calculated with effective binary diffusivity agrees with that with exact multicomponent diffusion coefficient except for N2 and the results of concentration agree with experimental results. In the pure H2 diffusion flame, concen-tration and mass flux of N2 and H2O obtained by the numerical method with effective binary diffusivity disagree with that by exact method or experimental results. Excessive diffusion of H2 is caused by the assumption that spatial gradient of mean molecular weight is neglected.

The Importance of Realistic Starting Models for Hydrodynamic Simulations of Stellar Collisions

We demonstrate the necessity of using realistic stellar models taken from stellar evolution codes, as opposed to polytropes, for starting models in smoothed particle hydrodynamics calculations of collisions between main sequence stars. Evolved stars have mean molecular weight gradients, which affect their entropy profiles and therefore affect how they react during a collision. The structure of stellar collision products of polytrope parent stars is significantly different from that of collision products of realistic parent models. These differences strongly affect the future evolution of the collision products, particularly products of collisions between unequal mass stars which have undergone significant chemical evolution. The use of polytropes as parent star models is likely to result in qualitatively mistaken results for the structure of the collision product.

Stellar models with microscopic diffusion and rotational mixing. 1: Application to the Sun

The Yale stellar evolution code has been modified to include the combined effects of diffusion and rotational mixing on H-1, H-4, and the trace elements He, Li-6, Li-7, and Be-9. The interaction between rotational mixing and diffusion is studied by calculating a number of calibrated solar models. The rotational mixing inhibits the diffusion in the outer parts of the models, leading to a decrease in the envelope diffusion by 25%-50%. Conversely, diffusion leads to gradients in mean molecular weight which can inhibit the rotational mixing. The degree to which gradients in mean molecular weight inhibit the rotational mixing is somewhat uncertain. A comparison with the observed solar oblateness suggests that gradients in the mean molecular weight play a smaller role in inhibiting the rotational mixing than previously believed. This is reinforced by the fact that the model with the standard value for the inhibiting effect of mean molecular weight on the rotational mixing depletes no Li on the main sequence. This is clear in contrast to the observations. A reduction in the inhibiting effect of mean molecular weight gradients by a factor of 10 loads to noticeable main-sequence Li depletion.