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Register a new userDifferential Rotation in a 3D Simulation of Oxygen Shell Burning
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We study differential rotation in late-stage shell convection in a 3D hydrodynamic simulation of a rapidly rotating $16M_odot$ helium star with a particular focus on the convective oxygen shell. We find that the oxygen shell develops a quasi-stationary pattern of differential rotation that is neither described by uniform angular velocity as assumed in current stellar evolution models of supernova progenitors, nor by uniform specific angular momentum. Instead, the oxygen shell develops a positive angular velocity gradient with faster rotation at the equator than at the pole by tens of percent. We show that the angular momentum transport inside the convection zone is not adequately captured by a diffusive mixing-length flux proportional to the angular velocity or angular momentum gradient. Zonal flow averages reveal stable large-scale meridional flow and an entropy deficit near the equator that mirrors the patterns in the angular velocity. The structure of the flow is reminiscent of simulations of stellar surface convection zones and the differential rotation of the Sun, suggesting that similar effects are involved; future simulations will need to address in more detail how the interplay of buoyancy, inertial forces, and turbulent stresses shapes differential rotation during late-stage convection in massive stars. Our findings may have implications for neutron star birth spin periods and supernova explosion scenarios that involve rapid core rotation. If convective regions develop positive angular velocity gradients, angular momentum could be shuffled out of the core region more efficiently, potentially making the formation of millisecond magnetars more difficult.
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It has been suggested based on analytic theory that even in non-rotating supernova progenitors stochastic spin-up by internal gravity waves (IGWs) during the late burning stages can impart enough angular momentum to the core to result in neutron star birth spin periods below 100ms, and a relatively firm upper limit of 500ms for the spin period. We here investigate this process using a 3D simulation of oxygen shell burning in a $3M_odot$ He star. Our model indicates that stochastic spin-up by IGWs is less efficient than previously thought. We find that the stochastic angular momentum flux carried by waves excited at the shell boundary is significantly smaller for a given convective luminosity and turnover time than would be expected from simple dimensional analysis. This can be explained by noting that the waves launched by overshooting convective plumes contain modes of opposite angular wave number with similar amplitudes, so that the net angular momentum of excited wave packets almost cancels. We find that the wave-mediated angular momentum flux from the oxygen shell follows a random walk, but again dimensional analysis overestimates the random walk amplitudes since the correlation time is only a fraction of the convective turnover time. Extrapolating our findings over the entire life time of the last burning stages prior to collapse, we predict that the core angular momentum from stochastic spin-up would translate into long birth spin periods of several seconds for low-mass progenitors and no less than 100ms even for high-mass progenitors.
We perform for the first time a 3D hydrodynamics simulation of the evolution of the last minutes pre-collapse of the oxygen shell of a fast-rotating massive star. This star has an initial mass of 38 M$_odot$, a metallicity of $sim$1/50 Z$_odot$, an initial rotational velocity of 600 km s$^{-1}$, and experiences chemically homogeneous evolution. It has a silicon- and oxygen-rich (Si/O) convective layer at (4.7-17)$times 10^{8}$ cm, where oxygen-shell burning takes place. The power spectrum analysis of the turbulent velocity indicates the dominance of the large-scale mode ($ell sim 3$), which has also been seen in non-rotating stars that have a wide Si/O layer. Spiral arm structures of density and silicon-enriched material produced by oxygen-shell burning appear in the equatorial plane of the Si/O shell. Non-axisymmetric, large-scale ($m le 3$) modes are dominant in these structures. The spiral arm structures have not been identified in previous non-rotating 3D pre-supernova models. Governed by such a convection pattern, the angle-averaged specific angular momentum becomes constant in the Si/O convective layer, which is not considered in spherically symmetrical stellar evolution models. Such spiral arms and constant specific angular momentum might affect the ensuing explosion or implosion of the star.
We perform two- (2D) and three-dimensional (3D) hydrodynamics simulations of convective oxygen shell-burning that takes place deep inside a massive progenitor star of a core-collapse supernova. Using one dimensional (1D) stellar evolution code, we first calculate the evolution of massive stars with an initial mass of 9-40 $M_odot$. Four different overshoot parameters are applied, and CO core mass trend similar to previous works is obtained in the 1D models. Selecting eleven 1D models that have a silicon and oxygen coexisting layer, we perform 2D hydrodynamics simulations of the evolution $sim$100 s until the onset of core-collapse. We find that convection with large-scale eddies and the turbulent Mach number $sim$0.1 is obtained in the models having a Si/O layer with a scale of 10$^8$ cm, whereas most models that have an extended O/Si layer up to a few $times 10^9$ cm exhibit lower turbulent velocity. Our results indicate that the supernova progenitors that possess a thick Si/O layer could provide a preferable condition for perturbation-aided explosions. We perform 3D simulation of a 25 $M_odot$ model, which exhibits large-scale convection in the 2D models. The 3D model develops large ($ell = 2$) convection similar to the 2D model, however, the turbulent velocity is lower. By estimating the neutrino emission properties of the 3D model, we point out that a time modulation of the event rates, if observed in KamLAND and Hyper-Kamiokande, would provide an important information about structural changes in the presupernova convective layer.
The carbon-oxygen white dwarf (CO WD) + He star channel is one of the promising ways for producing type Ia supernovae (SNe Ia) with short delay times. Recent studies found that carbon under the He-shell can be ignited if the mass-accretion rate of CO WD is higher than a critical rate (about 2 * 10^-6 Msun/yr), triggering an inwardly propagating carbon flame. Previous studies usually supposed that the off-centre carbon flame would reach the centre, resulting in the formation of an oxygen-neon (ONe) WD that will collapse into a neutron star. However, the process of off-centre carbon burning is not well studied. This may result in some uncertainties on the final fates of CO WDs. By employing MESA, we simulated the long-term evolution of off-centre carbon burning in He-accreting CO WDs. We found that the inwardly propagating carbon flame transforms the CO WDs into OSi cores directly but not ONe cores owing to the high temperature of the burning front. We suggest that the final fates of the CO WDs may be OSi WDs under the conditions of off-centre carbon burning, or explode as iron-core-collapse SNe if the mass-accretion continues. We also found that the mass-fractions of silicon in the OSi cores are sensitive to the mass-accretion rates.
The detection of mixed modes that are split by rotation in Kepler red giants has made it possible to probe the internal rotation profiles of these stars, which brings new constraints on the transport of angular momentum in stars. Mosser et al. (2012) have measured the rotation rates in the central regions of intermediate-mass core helium burning stars (secondary clump stars). Our aim was to exploit& the rotational splittings of mixed modes to estimate the amount of radial differential rotation in the interior of secondary clump stars using Kepler data, in order to place constraints on angular momentum transport in intermediate-mass stars. We selected a subsample of Kepler secondary clump stars with mixed modes that are clearly rotationally split. By applying a thorough statistical analysis, we showed that the splittings of both gravity-dominated modes (trapped in central regions) and p-dominated modes (trapped in the envelope) can be measured. We then used these splittings to estimate the amount of differential rotation by using inversion techniques and by applying a simplified approach based on asymptotic theory (Goupil et al. 2013). We obtained evidence for a weak radial differential rotation for six of the seven targets that were selected, with the central regions rotating $1.8pm0.3$ to $3.2pm1.0$ times faster than the envelope. The last target was found to be consistent with a solid-body rotation. This demonstrates that an efficient redistribution of angular momentum occurs after the end of the main sequence in the interior of intermediate-mass stars, either during the short-lived subgiant phase, or once He-burning has started in the core. In either case, this should bring constraints on the angular momentum transport mechanisms that are at work.
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