Radiative Zone Research Articles

Local direct numerical simulations of turbulent mixing in stellar radiative zones

One of the key issues of stellar evolution theory is the influence of the transport processes related to rotationally driven macroscopic motions on the internal structure and the evolution of stars. Turbulent mixing of chemical elements due to differential rotation in stellar radiative zones is currently taken into account in many stellar evolution codes through transport coefficients firstly derived by Zahn (1992, A&A, 265, 115). The purpose of our work is to constrain one of these coefficients, the radial diffusion coefficient driven by radial differential rotation through local direct numerical simulations of steady homogeneous stably stratified sheared turbulence, and to compare the results with phenomenological models. In particular, we have determined the dependence of the turbulent diffusion coefficient on thermal diffusivity and chemical stratification.

Seismic diagnostics for transport of angular momentum in stars

Rotational splittings are currently measured for several main sequence stars and a large number of red giants with the space mission Kepler. This will provide stringent constraints on rotation profiles. Our aim is to obtain seismic constraints on the internal transport and surface loss of angular momentum of oscillating solar-like stars. To this end, we study the evolution of rotational splittings from the pre-main sequence to the red-giant branch for stochastically excited oscillation modes. We modified the evolutionary code CESAM2K to take rotationally induced transport in radiative zones into account. Linear rotational splittings were computed for a sequence of $1.3 M_{\odot}$ models. Rotation profiles were derived from our evolutionary models and eigenfunctions from linear adiabatic oscillation calculations. We find that transport by meridional circulation and shear turbulence yields far too high a core rotation rate for red-giant models compared with recent seismic observations. We discuss several uncertainties in the physical description of stars that could have an impact on the rotation profiles. For instance, we find that the Goldreich-Schubert-Fricke instability does not extract enough angular momentum from the core to account for the discrepancy. In contrast, an increase of the horizontal turbulent viscosity by 2 orders of magnitude is able to significantly decrease the central rotation rate on the red-giant branch. Our results indicate that it is possible that the prescription for the horizontal turbulent viscosity largely underestimates its actual value or else a mechanism not included in current stellar models of low mass stars is needed to slow down the rotation in the radiative core of red-giant stars.

A numerical magnetohydrodynamic scheme using the hydrostatic approximation

In gravitationally stratified fluids, length scales are normally much greater in the horizontal direction than in the vertical one. When modelling these fluids it can be advantageous to use the hydrostatic approximation, which filters out vertically propagating sound waves and thus allows a greater timestep. We briefly review this approximation, which is commonplace in atmospheric physics, and compare it to other approximations used in astrophysics such as Boussinesq and anelastic, finding that it should be the best approximation to use in context such as radiative stellar zones, compact objects, stellar or planetary atmospheres and other contexts. We describe a finite-difference numerical scheme which uses this approximation, which includes magnetic fields.

An analysis of apparent r-mode oscillations in solar activity, the solar diameter, the solar neutrino flux, and nuclear decay rates, with implications concerning the Sun’s internal structure and rotation, and neutrino processes

This article presents a comparative analysis of solar activity data, Mt Wilson diameter data, Super-Kamiokande solar neutrino data, and nuclear decay data acquired at the Lomonosov Moscow State University (LMSU). We propose that salient periodicities in all of these datasets may be attributed to r-mode oscillations. Periodicities in the solar activity data and in Super-Kamiokande solar neutrino data may be attributed to r-mode oscillations in the known tachocline, with normalized radius in the range 0.66–0.74, where the sidereal rotation rate is in the range 13.7–14.6year−1. We propose that periodicities in the Mt Wilson and LMSU data may be attributed to similar r-mode oscillations where the sidereal rotation rate is approximately 12.0year−1, which we attribute to a hypothetical “inner” tachocline separating a slowly rotating core from the radiative zone. We also discuss the possible role of the Resonant Spin Flavor Precession (RSFP) process, which leads to estimates of the neutrino magnetic moment and of the magnetic field strength in or near the solar core.

THE RESPONSE OF GIANT STARS TO DYNAMICAL-TIMESCALE MASS LOSS

We study the response of giant stars to mass loss. One-dimensional simulations of red and asymptotic giant branch stars with mass loss rates from $10^{-3}$ up to a few \msun/yr show in no case any significant radius increase. The largest radius increase of 0.2% was found in the case with the lowest mass loss rate. For dynamical-timescale mass loss rates, that may be encountered during a common envelope phase, the evolution is not adiabatic. The superadiabatic outer layer of the giant's envelope has a local thermal timescale comparable to the dynamical timescale. Therefore, this layer has enough time to readjust thermally. Moreover, the giant star is driven out of hydrostatic equilibrium and evolves dynamically. In these cases no increase of the stellar radius with respect to its initial value is found. If the mass loss rate is high enough, the superadiabaticity of the outer layer is lost progressively and a radiative zone forms due to a combination of thermal and dynamical readjustment. Conditions for unstable mass transfer based on adiabatic mass loss models that predict a significant radius increase, may need to be re-evaluated.

The stability of stratified, rotating systems and the generation of vorticity in the Sun

We examine the linear behavior of three-dimensional Lagrangian displacements in a stratified, shearing background. The isentropic and iso-rotation surfaces of the equilibrium flow are assumed to be axisymmetric, but otherwise fully two-dimensional. Three-dimensional magnetic fields are included in the perturbation equations; however the equilibrium is assumed to be well-described by purely hydrodynamic forces. The model, in principle very general, is used to study the behavior of fluid displacements in an environment resembling the solar convection zone. Some very suggestive results emerge. All but high-latitude displacements align themselves with the observed surfaces of constant angular velocity. The tendency for the angular velocity to remain constant with depth in the bulk of the convective zone, together with other critical features of the rotation profile, emerge from little more than a visual inspection of the governing equation. In the absence of a background axial angular velocity gradient, displacements exhibit no poleward bias, suggesting that solar convection "plays-off" of prexisting shear rather than creates it. We argue that baroclinic vorticity of precisely the right order is generated at the radiative/convective zone boundary due to centrifugal distortion of equipotential surfaces that is not precisely followed by isothermal surfaces. If so, many features of the Sun's internal rotation become more clear, including: i) the general appearance of the tachocline; ii) the extension of differential rotation well into the radiative zone; iii) the abrupt change of morphology of convective zone isorotation surfaces; and iv) the inability of current numerical simulations to reproduce the solar rotation profile without imposed entropy boundary conditions.

CONVECTION AND DIFFERENTIAL ROTATION IN F-TYPE STARS

Differential rotation is a common feature of main-sequence spectral F-type stars. In seeking to make contact with observations and to provide a self-consistent picture of how differential rotation is achieved in the interiors of these stars, we use the three-dimensional anelastic spherical harmonic (ASH) code to simulate global-scale turbulent flows in 1.2 and 1.3 $M_\odot$ F-type stars at varying rotation rates. The simulations are carried out in spherical shells that encompass most of the convection zone and a portion of the stably stratified radiative zone below it, allowing us to explore the effects of overshooting convection. We examine the scaling of the mean flows and thermal state with rotation rate and mass and link these scalings to fundamental parameters of the simulations. Indeed, we find that the differential rotation becomes much stronger with more rapid rotation and larger mass, scaling as $\Delta\Omega$ $\alpha$ $M^{3.9}$$\Omega_0^{0.6}$. Accompanying the growing differential rotation is a significant latitudinal temperature contrast, with amplitudes of 1000 K or higher in the most rapidly rotating cases. This contrast in turn scales with mass and rotation rate as $\Delta$$T$ $\alpha$ $M^{6.4}$$\Omega_0^{1.6}$. On the other hand, the meridional circulations become much weaker with more rapid rotation and with higher mass, with their kinetic energy decreasing as KE$_{MC}$ $\alpha$ $M^{-1.2}$$\Omega_0^{-0.8}$. Additionally, three of our simulations exhibit a global-scale shear instability within their stable regions that persists for the duration of the simulations. The flow structures associated with the instabilities have a direct coupling to and impact on the flows within the convection zone.

Terahertz spectroscopy of the reactive and radiative near-field zones of split ring resonator

A terahertz microscope has been used to excite and observe the resonant modes of a single split ring resonator in the reactive and radiative near-field zones. The two lowest resonant modes of an isolated split ring resonator with their corresponding radiation patterns are reported; they showed good agreement to simulations. The passage from the reactive to radiative near-field zone is also discussed. Further, our result introduced a novel technique to perform terahertz time-domain spectroscopy of samples a few tens of micrometers in size by measuring the in-plane radiative near-field zone.

CRITICAL FIELDS AND GROWTH RATES OF THE TAYLER INSTABILITY AS PROBED BY A COLUMNAR GALLIUM EXPERIMENT

Many astrophysical phenomena (such as the slow rotation of neutron stars or the rigid rotation of the solar core) can be explained by the action of the Tayler instability of toroidal magnetic fields in the radiative zones of stars. In order to place the theory of this instability on a safe fundament it has been realized in a laboratory experiment measuring the critical field strength, the growth rates as well as the shape of the supercritical modes. A strong electrical current flows through a liquid-metal confined in a resting columnar container with an insulating outer cylinder. As the very small magnetic Prandtl number of the gallium-indium-tin alloy does not influence the critical Hartmann number of the field amplitudes, the electric currents for marginal instability can also be computed with direct numerical simulations. The results of this theoretical concept are confirmed by the experiment. Also the predicted growth rates of the order of minutes for the nonaxisymmetric perturbations are certified by the measurements. That they do not directly depend on the size of the experiment is shown as a consequence of the weakness of the applied fields and the absence of rotation.

Stellar evolution of massive stars with a radiative α-Ω dynamo

Models of rotationally-driven dynamos in stellar radiative zones have suggested that magnetohydrodynamic transport of angular momentum and chemical composition can dominate over the otherwise purely hydrodynamic processes. A proper consideration of the interaction between rotation and magnetic fields is therefore essential. Previous studies have focused on a magnetic model where the magnetic field strength is derived as a function of the stellar structure and angular momentum distribution. We have adapted our one-dimensional stellar rotation code, RoSE, to model the poloidal and toroidal magnetic field strengths with a pair of time-dependent advection-diffusion equations coupled to the equations for the evolution of the angular momentum distribution and stellar structure. This produces a much more complete, though still reasonably simple, model for the magnetic field evolution. Our model reproduces well observed surface nitrogen enrichment of massive stars in the Large Magellanic Cloud. In particular it reproduces a population of slowly-rotating nitrogen-enriched stars that cannot be explained by rotational mixing alone alongside the traditional rotationlly-enriched stars. The model further predicts a strong mass-dependency for the dynamo-driven field. Above a threshold mass, the strength of the magnetic dynamo decreases abruptly and so we predict that more massive stars are much less likely to support a dynamo-driven field than less massive stars.

The Dynamics of the Solar Radiative Zone

The dynamics of the solar radiative interior are still poorly constrained by comparison to the convective zone. This disparity is even more marked when we attempt to derive meaningful temporal variations. Many data sets contain a small number of modes that are sensitive to the inner layers of the Sun, but we found that the estimates of their uncertainties are often inaccurate. As a result, these data sets allow us to obtain, at best, a low resolution estimate of the solar core rotation rate down to approximately 0.2R. We present inferences based on mode determination resulting from an alternate peak-fitting methodology aimed at increasing the amount of observed modes that are sensitive to the radiative zone, while special care was taken in the determination of their uncertainties. This methodology has been applied to MDI and GONG data, for the whole Solar Cycle 23, and to the newly available HMI data. The numerical inversions of all these data sets result in the best inferences to date of the rotation in the radiative region. These results and the method used to obtain them are discussed. The resulting profiles are shown and analyzed, and the significance of the detected changes discussed.

A NEW TWIST IN THE EVOLUTION OF LOW-MASS STARS

We show that the evolutionary track of a low-mass red giant should make an extended zigzag on the Hertzsprung-Russel diagram just after the bump luminosity, if fast internal rotation and enhanced extra mixing in the radiative zone bring the temperature gradient close to the adiabatic one. This can explain both the location and peculiar surface chemical composition of Li-rich K giants studied by Kumar, Reddy, & Lambert (2011). We also discuss a striking resemblance between the photometric and composition peculiarities of these stars and giant components of RS CVn binaries. We demonstrate that the observationally constrained values of the temperature gradient in the Li-rich K giants agree with the required rate of extra mixing only if the turbulence which is believed to be responsible for this extra mixing is highly anisotropic, with its associated transport coefficients in the horizontal direction strongly dominating over those in the vertical direction.

An3He-DRIVEN INSTABILITY NEAR THE FULLY CONVECTIVE BOUNDARY

We report on the discovery of an instability in low mass stars just above the threshold ($\sim 0.35 \textrm{M}_{\odot}$) where they are expected to be fully convective on the main sequence. Non-equilibrium He3 burning creates a convective core, which is separated from a deep convective envelope by a small radiative zone. The steady increase in central He3 causes the core to grow until it touches the surface convection zone, which triggers fully convective episodes in what we call the "convective kissing instability". These episodes lower the central abundance and cause the star to return to a state in which is has a separate convective core and envelope. These periodic events eventually cease when the He3 abundance throughout the star is sufficiently high that the star is fully convective, and remains so for the rest of its main sequence lifetime. The episodes correspond to few percent changes in radius and luminosity, over Myr to Gyr timescales. We discuss the physics of the instability, as well as prospects for detecting its signatures in open clusters and wide binaries. Secondary stars in cataclysmic variables (CVs) will pass through this mass range, and this instability could be related to the observed paucity of such systems for periods between two and three hours. We demonstrate that the instability can be generated for CV secondaries with mass-loss rates of interest for such systems, and discuss potential implications.

ASTEROSEISMOLOGY OF THE NEARBY SN II PROGENITOR RIGEL. II. ϵ-MECHANISM TRIGGERING GRAVITY-MODE PULSATIONS?

The cores of luminous B and A-type (BA) supergiant stars are the seeds of later core collapse supernovae. Thus, constraining the near-core conditions in this class of stars can place tighter constraints on the size, mass and chemical composition of supernova remnants. Asteroseismology of these massive stars is one possible approach into such investigations. Recently, Moravveji et al. (2012, hereafter Paper I) extracted 19 significant frequencies from a 6-year radial velocity monitoring or Rigel (\beta Ori, B8 Ia). The periods they determined broadly range from 1.22 to 74.74 days. Based on our differentially rotating stellar structure and evolution model, Rigel, at it's current evolutionary state, is undergoing core He burning and shell H burning. Linear fully non-adiabatic non-radial stability analyses result in the excitation of a dense spectrum of non-radial gravity-dominated mixed modes. The fundamental radial mode (\ell=0) and its overtones are all stable. When the hydrogen burning shell is located even partially in the radiative zone, a favorable condition for destabilization of g-modes through the so-called \epsilon-mechanism becomes viable. Only those g-modes that have high relative amplitudes in the hydrogen burning (radiative) zone can survive the strong radiative damping. From the entire observed range of variability periods of Rigel (found in Paper I), and based on our model, only those modes with periods ranging between 21 to 127 days can be theoretically explained by the \epsilon-mechanism. The origin of the short-period variations (found in Paper I) still remain unexplained. Because Rigel is similar to other massive BA supergiants, we believe that the \epsilon-mechanism may be able to explain the long-period variations in \alpha Cygni class of pulsating stars.

Power spectrum analysis of LMSU (Lomonosov Moscow State University) nuclear decay-rate data: Further indication of r-mode oscillations in an inner solar tachocline

This article presents a power-spectrum analysis of 2350 measurements of the 90Sr-90Y decay process acquired over the interval August 4 2002 to February 6 2009 at the Lomonosov Moscow State University. As we have found for other long sequences of decay measurements, the power spectrum is dominated by a very strong annual oscillation. However, we also find a set of low-frequency peaks, ranging from 0.26 to 3.98year−1, which are very similar to an array of peaks in a power spectrum formed from Mt Wilson diameter measurements. The Mt Wilson measurements have been interpreted in terms of r-mode oscillations in a region where the sidereal rotation frequency is 12.08year−1. We find that the LMSU measurements may also be attributed to the same type of r-mode oscillations in a solar region with the same sidereal rotation frequency. We propose that these oscillations occur in an inner tachocline that separates the radiative zone from a more slowly rotating solar core.

Impact of rotation and disc lifetime on pre-main sequence lithium depletion of solar-type stars

Aims: We study the influence of rotation and disc lifetime on lithium depletion of pre-main sequence (PMS) solar-type stars. Methods: The impact of rotational mixing and of the hydrostatic effects of rotation on lithium abundances are investigated by computing non-rotating and rotating PMS models that include a comprehensive treatment of shellular rotation. The influence of the disc lifetime is then studied by comparing the lithium content of PMS rotating models experiencing different durations of the disc-locking phase between 3 and 9 Myr. Results: The surface lithium abundance at the end of the PMS is decreased when rotational effects are included. During the beginning of the lithium depletion phase, only hydrostatic effects of rotation are at work. This results in a decrease in the lithium depletion rate for rotating models compared to non-rotating ones. When the convective envelope recedes from the stellar centre, rotational mixing begins to play an important role due to differential rotation near the bottom of the convective envelope. This mixing results in a decrease in the surface lithium abundance with a limited contribution from hydrostatic effects of rotation, which favours lithium depletion during the second part of the PMS evolution. The impact of rotation on PMS lithium depletion is also found to be sensitive to the duration of the disc-locking phase. When the disc lifetime increases, the PMS lithium abundance of a solar-type star decreases owing to the higher efficiency of rotational mixing in the radiative zone. A relationship between the surface rotation and lithium abundance at the end of the PMS is then obtained: slow rotators on the zero-age main sequence are predicted to be more lithium-depleted than fast rotators due to the increase in the disc lifetime.

Dynamical tides in compact white dwarf binaries: tidal synchronization and dissipation

In compact white dwarf (WD) binary systems (with periods ranging from minutes to hours), dynamical tides involving the excitation and dissipation of gravity waves play a dominant role in determining the physical conditions (such as rotation rate and temperature) of the WDs prior to mass transfer or binary merger. We calculate the amplitude of the tidally excited gravity waves as a function of the tidal forcing frequency ω= 2(Ω−Ωs) (where Ω is the orbital frequency and Ωs is the spin frequency) for several realistic carbon–oxygen WD models, under the assumption that the outgoing propagating waves are efficiently dissipated in the outer layer of the star by non-linear effects or radiative damping. Unlike main-sequence stars with distinct radiative and convection zones, the mechanism of wave excitation in WDs is more complex due to the sharp features associated with composition changes inside the WD. In our WD models, the gravity waves are launched just below the helium–carbon boundary and propagate outwards. We find that the tidal torque on the WD and the related tidal energy transfer rate, ⁠, depend on ω in an erratic way, with varying by orders of magnitude over small frequency ranges. On average, scales approximately as Ω5ω5 for a large range of tidal frequencies. We also study the effects of dynamical tides on the long-term evolution of WD binaries prior to mass transfer or merger. Above a critical orbital frequency Ωc, corresponding to an orbital period of the order of 1h (depending on WD models), dynamical tides efficiently drive Ωs towards Ω, although a small, almost constant degree of synchronization (Ω−Ωs∼ constant) is maintained even at the smallest binary periods. While the orbital decay is always dominated by gravitational radiation, the tidal energy transfer can induce a significant phase error in the low-frequency gravitational waveforms, detectable by the planned Laser Interferometer Space Antenna project. Tidal dissipation may also lead to significant heating of the WD envelope and brightening of the system long before binary merger.

Seismology of Sun and stars and related opacity laboratory measurements

CNES, ESA and NASA have invested in helioseismic and asteroseismic disciplines for 2 decades with SoHO (1995–2015), COROT (2006–2013), KEPLER (2009–2014), PICARD (2010–2013) and SDO (2010–2015). These missions focus on the stellar internal dynamics and their influence of neighboring planets. Progress along this path requires that the microscopic physics is well under control, but several seismic probes indicate some discrepancies which justify new investigations of the energy transport in radiative zones of the Sun and massive stars, despite strong efforts dedicated to reaction rates, screening, equation of state and opacity coefficients between 1990 and 2000. We describe here how the OPAC consortium tackles the complex problem of photon absorption by matter both theoretically and experimentally, by using high energy laser facilities. These studies might be also useful for other disciplines like fusion for energy and X-ray spectroscopy astronomy.

Magnetic confinement of the solar tachocline: The oblique dipole

Abstract3D MHD global solar simulations coupling the turbulent convective zone and the radiative zone have been carried out. Essential features of the Sun such as differential rotation, meridional circulation and internal waves excitation are recovered. These realistic models are used to test the possibility of having the solar tachocline confined by a primordial inner magnetic field. We find that the initially confined magnetic fields we consider open into the convective envelope. Angular momentum is transported across the two zones by magnetic torques and stresses, establishing the so‐called Ferarro's law of isorotation. In the parameter space studied, the confinement of the magnetic field by meridional circulation penetration fails, also implying the failure of the tachocline confinement by the magnetic field. Three‐dimensional convective motions are proven responsible for the lack of magnetic field confinement. Those results are robust for the different magnetic field topologies considered, i.e. aligned or oblique dipole (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Further Evidence Suggestive of a Solar Influence on Nuclear Decay Rates

Recent analyses of nuclear decay data show evidence of variations suggestive of a solar influence. Analyses of datasets acquired at the Brookhaven National Laboratory (BNL) and at the Physikalisch-Technische Bundesanstalt (PTB) both show evidence of an annual periodicity and of periodicities with sidereal frequencies in the neighborhood of 12.25 year^{-1} (at a significance level that we have estimated to be 10^{-17}). It is notable that this implied rotation rate is lower than that attributed to the solar radiative zone, suggestive of a slowly rotating solar core. This leads us to hypothesize that there may be an "inner tachocline" separating the core from the radiative zone, analogous to the "outer tachocline" that separates the radiative zone from the convection zone. The Rieger periodicity (which has a period of about 154 days, corresponding to a frequency of 2.37 year^{-1}) may be attributed to an r-mode oscillation with spherical-harmonic indices l=3, m=1, located in the outer tachocline. This suggests that we may test the hypothesis of a solar influence on nuclear decay rates by searching BNL and PTB data for evidence of a "Rieger-like" r-mode oscillation, with l=3, m=1, in the inner tachocline. The appropriate search band for such an oscillation is estimated to be 2.00-2.28 year^{-1}. We find, in both datasets, strong evidence of a periodicity at 2.11 year^{-1}. We estimate that the probability of obtaining these results by chance is 10^{-12}.