Convective Overshooting in Extreme Horizontal-branch Stars Using MESA with the k-omega Model*

To explore overshoot mixing beyond the convective core in core helium-burning stars, we use the k−ω model, which is incorporated into the Modules of Experiments in Stellar Astrophysics to investigate overshoot mixing in the evolution of subdwarf B (sdB) stars. Our results show that the development of the convective core can be divided into three stages. The mass of the convective core increases monotonically when the radiative temperature gradient, ∇rad, monotonically decreases outwardly, and overshoot mixing presents an exponential decay similar to Herwig. The splitting of the convective core occurs repeatedly when the minimum value of ∇rad near the convective boundary is smaller than the adiabatic temperature gradient, ∇ad. The mass at the outer boundary of the convective shell M sc can exceed 0.2 M ⊙ after the central helium abundance drops to about Y c ≈ 0.45. It is close to the convective core masses derived by asteroseismology for younger models (0.22 to ∼0.28 M ⊙). In the final stage, “core breathing pulses” occurred two or three times. Helium was injected into the convective core by overshoot mixing and increased the lifetime of sdB stars. The mass of the mixed region M mixed can rise to 0.303 M ⊙ by the end. The oxygen content in the central core of our g-mode sdB models is about 80% by mass. The high amounts of oxygen deduced from asteroseismology may be evidence supporting the existence of core breathing pulses.

Convective core entrainment in 1D main sequence stellar models

3D hydrodynamics models of deep stellar convection exhibit turbulent entrainment at the convective-radiative boundary which follows the entrainment law, varying with boundary penetrability. We implement the entrainment law in the 1D Geneva stellar evolution code. We then calculate models between 1.5 and 60 M⊙ at solar metallicity (Z = 0.014) and compare them to previous generations of models and observations on the main sequence. The boundary penetrability, quantified by the bulk Richardson number, RiB, varies with mass and to a smaller extent with time. The variation of RiB with mass is due to the mass dependence of typical convective velocities in the core and hence the luminosity of the star. The chemical gradient above the convective core dominates the variation of RiB with time. An entrainment law method can therefore explain the apparent mass dependence of convective boundary mixing through RiB. New models including entrainment can better reproduce the mass dependence of the main sequence width using entrainment law parameters A ∼ 2 × 10−4 and n = 1. We compare these empirically constrained values to the results of 3D hydrodynamics simulations and discuss implications.

Rotation of the convective core in γ Dor stars measured by dips in period spacings of g modes coupled with inertial modes

The relation of period spacing (ΔP) versus period (P) of dipole prograde g modes is known to be useful to measure rotation rates in the g-mode cavity of rapidly rotating γ Dor and slowly pulsating B (SPB) stars. In a rapidly rotating star, an inertial mode in the convective core can resonantly couple with g modes propagative in the surrounding radiative region. The resonant coupling causes a dip in the P - ΔP relation, distinct from the modulations due to the chemical composition gradient. Such a resonance dip in ΔP of prograde dipole g modes appears around a frequency corresponding to a spin parameter 2frot(cc)/νco-rot ∼ 8 − 11 with frot(cc) being the rotation frequency of the convective core and νco-rot the pulsation frequency in the co-rotating frame. The spin parameter at the resonance depends somewhat on the extent of core overshooting, central hydrogen abundance, and other stellar parameters. We can fit the period at the observed dip with the prediction from prograde dipole g modes of a main-sequence model, allowing the convective core to rotate differentially from the surrounding g-mode cavity. We have performed such fittings for 16 selected γ Dor stars having well defined dips, and found that the majority of γ Dor stars we studied rotate nearly uniformly, while convective cores tend to rotate slightly faster than the g-mode cavity in less evolved stars.

Is there large convective-core overshooting in Kepler targets KIC 2837475 and 11081729?

ABSTRACT The ratio of small-to-large separations r010 has been widely used in helioseismology and asteroseismology to investigate the internal structure of a star, as it is approximately independent of the structure of the outer layers. Several studies have used this tool to constrain the convective-core overshooting of main-sequence stars (i.e. 0.0 ≤ δov ≤ 0.2). This is consistent with the generally accepted values. However, Yang et al. have proposed that there is large convective-core overshooting in the Kepler targets KIC 2837475 and 11081729: 1.2 ≤ δov ≤ 1.6 and 1.7 ≤ δov ≤ 1.8, respectively. These are much larger than the normal values. Thus, the aim of this study is to re-investigate the ratios of the two stars using a model-independent method with the latest p-mode observations. Our results indicate that there is no robustness for including such a large convective-core overshooting while modelling these two stars. In fact, this leads to over-fitting, and the observational constraints of r010 prefer models with a normal convective-core overshooting (i.e. 0.0 ≤ δov ≤ 0.2) as the candidates for the best-fitting model of KIC 2837475 and 11081729.

Rotating convective core excites non-radial pulsations to cause rotational modulations in early-type stars

ABSTRACT We discuss low-frequency g modes excited by resonant couplings with weakly unstable oscillatory convective modes in the rotating convective core in early-type main-sequence stars. Our non-adiabatic pulsation analyses including the effect of Coriolis force for $2\, \mathrm{ M}_\odot$ main-sequence models show that if the convective core rotates slightly faster than the surrounding radiative layers, g modes in the radiative envelope are excited by a resonance coupling. The frequency of the excited g mode in the inertial frame is close to |mΩc| with m and Ωc being the azimuthal order of the g mode and the rotation frequency of the convective core, respectively. These g-mode frequencies are consistent with those of photometric rotational modulations and harmonics observed in many early-type main-sequence stars. In other words, these g modes provide a non-magnetic explanation for the rotational light modulations detected in many early-type main-sequence stars.

3D Radiative Heating of Tropical Upper Tropospheric Cloud Systems derived from Synergistic A-Train Observations and Machine Learning

Upper Tropospheric (UT) cloud systems constructed from Atmospheric Infrared Sounder (AIRS) cloud data provide a horizontal emissivity structure, allowing to link convective core to anvil properties. By using machine learning techniques we composed a horizontally complete picture of the radiative heating rates deduced from CALIPSO lidar and CloudSat radar measurements, which are only available along narrow nadir tracks. To train the artificial neural networks, we combined the simultaneous AIRS, CALIPSO and CloudSat data with ERA-Interim meteorological reanalysis data in the tropics over a period of four years. Resulting non-linear regression models estimate the radiative heating rates as a function of about 40 cloud, atmospheric and surface properties, with a column-integrated mean absolute error (MAE) of 0.8 K/d (0.5 K/day) for cloudy scenes and 0.4 (0.3 K/day) for clear sky in the longwave (shortwave) spectral domain. Already about 20 basic input variables yield good results, with a 6 % (10 %) larger MAE. Developing separate models for (i) high opaque clouds, (ii) cirrus, (iii) mid- and low-level clouds and (iv) clear sky, independently over ocean and over land, lead to a small improvement, when considering the profile shapes. These models were then applied to the whole AIRS cloud dataset, combined with ERA-Interim, to build 3D radiative heating rate fields. Over the deep tropics, UT clouds have a net radiative heating effect of about 0.3 K/day throughout the troposphere from 250 hPa downward, with a broad maximum of about 0.4 K/d around 330 hPa, enhancing the column-integrated latent heating by about 25 %. This value is larger than earlier results of about 20 %. Above the height of 200 hPa, the LW cooling above convective cores and thick cirrus anvils is opposed by thin cirrus heating. Whereas in cooler regions low-level clouds also influence the net radiative heating profile, in warmer regions it is nearly completely driven by deep convective cloud systems. These mesoscale convective systems (MCS) are colder and include slightly more thin cirrus around their anvils than those in cooler regions. Hence, the MCSs over these warmer regions produce a vertically more extended heating by the thicker cirrus anvils and a heating of 0.7 K/d above the height of 200 hPa by the surrounding thin cirrus. The roughly estimated horizontal gradients between cirrus anvil and convective core as well as between surrounding thin cirrus and cirrus anvil seem to be slightly smaller in warmer regions, which can be explained by their larger coverage. The 15-year time series of the heating/cooling effects of MCSs are well related to the ENSO variation. While the coverage of all MCSs is relatively stable (or very slightly decreasing) with surface warming, with −1.3 ± 0.6 %/K, the coverage of cold MCSs relative to all MCSs significantly increases by +18 ± 5 %/K.