Angular momentum transport by internal gravity waves III - Wave excitation by core convection and the Coriolis effect

This is the third in a series of papers that deal with angular momentum transport by internal gravity waves. We concentrate on the waves excited by core convection in a 3Msun, Pop I main sequence star. Here, we want to examine the role of the Coriolis acceleration in the equations of motion that describe the behavior of waves and to evaluate its impact on angular momentum transport. We use the so-called traditional approximation of geophysics, which allows variable separation in radial and horizontal components. In the presence of rotation, the horizontal structure is described by Hough functions instead of spherical harmonics. The Coriolis acceleration has two main effects on waves. It transforms pure gravity waves into gravito-inertial waves that have a larger amplitude closer to the equator, and it introduces new waves whose restoring force is mainly the conservation of vorticity. Taking the Coriolis acceleration into account changes the subtle balance between prograde and retrograde waves in non-rotating stars. It also introduces new types of waves that are either purely prograde or retrograde. We show in this paper where the local deposition of angular momentum by such waves is important.Comment: 9 pages, 10 figures, accepted for publication by A&

Gyroscopic pumping of large-scale flows in stellar interiors, and application to Lithium Dip stars

The maintenance of large-scale differential rotation in stellar convective regions by rotationally influenced convective stresses also drives large-scale meridional flows by angular--momentum conservation. This process is an example of ``gyroscopic pumping'', and has recently been studied in detail in the solar context. An important question concerns the extent to which these gyroscopically pumped meridional flows penetrate into nearby stably stratified (radiative) regions, since they could potentially be an important source of non-local mixing. Here we present an extensive study of the gyroscopic pumping mechanism, using a combination of analytical calculations and numerical simulations both in Cartesian geometry and in spherical geometry. The various methods, when compared with one another, provide physical insight into the process itself, as well as increasingly sophisticated means of estimating the gyroscopic pumping rate. As an example of application, we investigate the effects of this large-scale mixing process on the surface abundances of the light elements Li and Be for stars in the mass range 1.3-1.5 solar masses (so-called ``Li-dip stars''). We find that gyroscopic pumping is a very efficient mechanism for circulating material between the surface and the deep interior, so much in fact that it over-estimates Li and Be depletion by orders of magnitude for stars on the hot side of the dip.However, when the diffusion of chemical species back into the surface convection zone is taken into account, a good fit with observed surface abundances of Li and Be as a function of stellar mass in the Hyades cluster can be found for reasonable choices of model parameters.Comment: Submitted to Ap

Compressive Pattern Matching on Multispectral Data

We introduce a new constrained minimization problem that performs template and pattern detection on a multispectral image in a compressive sensing context. We use an original minimization problem from Guo and Osher that uses $L_1$ minimization techniques to perform template detection in a multispectral image. We first adapt this minimization problem to work with compressive sensing data. Then we extend it to perform pattern detection using a formal transform called the spectralization along a pattern. That extension brings out the problem of measurement reconstruction. We introduce shifted measurements that allow us to reconstruct all the measurement with a small overhead and we give an optimality constraint for simple patterns. We present numerical results showing the performances of the original minimization problem and the compressed ones with different measurement rates and applied on remotely sensed data.Comment: Published in IEEE Transactions on Geoscience and Remote Sensin

Diagnoses to unravel secular hydrodynamical processes in rotating main sequence stars

(Abridged) We present a detailed analysis of the main physical processes responsible for the transport of angular momentum and chemical species in the radiative regions of rotating stars. We focus on cases where meridional circulation and shear-induced turbulence only are included in the simulations. Our analysis is based on a 2-D representation of the secular hydrodynamics, which is treated using expansions in spherical harmonics. We present a full reconstruction of the meridional circulation and of the associated fluctuations of temperature and mean molecular weight along with diagnosis for the transport of angular momentum, heat and chemicals. In the present paper these tools are used to validate the analysis of two main sequence stellar models of 1.5 and 20 Msun for which the hydrodynamics has been previously extensively studied in the literature. We obtain a clear visualization and a precise estimation of the different terms entering the angular momentum and heat transport equations in radiative zones. This enables us to corroborate the main results obtained over the past decade by Zahn, Maeder, and collaborators concerning the secular hydrodynamics of such objects. We focus on the meridional circulation driven by angular momentum losses and structural readjustements. We confirm quantitatively for the first time through detailed computations and separation of the various components that the advection of entropy by this circulation is very well balanced by the barotropic effects and the thermal relaxation during most of the main sequence evolution. This enables us to derive simplifications for the thermal relaxation on this phase. The meridional currents in turn advect heat and generate temperature fluctuations that induce differential rotation through thermal wind thus closing the transport loop.Comment: 16 pages, 18 figures. Accepted for publication in A&

Dissipation of a tide in a differentially rotating star

The orbital period of the binary pulsar PSR J0045-7319, which is located in our neighbouring galaxy the Small Magellanic Cloud (SMC), appears to be decreasing on a timescale of half a million year. This timescale is more than two orders of magnitude smaller than what is expected from the standard theory of tidal dissipation. Kumar and Quataert (1997a) proposed that this rapid evolution can be understood provided that the neutron star's companion, a main sequence B-star, has set up significant differential rotation. They showed that the spin synchronization time for the B-star is similar to the orbit circularization time, whereas the time to synchronize the surface rotation is much shorter, and thus significant differential rotation in the star is indeed expected. However, their calculation did not include the various processes that can redistribute angular momentum in the star, possibly forcing it into solid body rotation; in that case the dissipation of the tide would not be enhanced. The goal of this paper is to include the redistribution of angular momentum in the B-star due to meridional circulation and shear stresses and to calculate the resulting rotation profile as a function of time. We find that although angular momentum redistribution is important, the B-star continues to have sufficient differential rotation so that tidal waves are entirely absorbed as they arrive at the surface. The mechanism proposed by Kumar and Quataert to speed up the orbital evolution of the SMC binary pulsar should therefore work as suggested.Comment: 7 pages, LaTeX, 4 figures, Submitted to ApJ. Replaces astro-ph/9707309 (minor changes

Effects of rotational mixing on the asteroseismic properties of solar-type stars

The influence of rotational mixing on the evolution and asteroseismic properties of solar-type stars is studied. Rotational mixing changes the global properties of a solar-type star with a significant increase of the effective temperature resulting in a shift of the evolutionary track to the blue part of the HR diagram. These differences are related to changes of the chemical composition, because rotational mixing counteracts the effects of atomic diffusion leading to larger helium surface abundances for rotating models than for non-rotating ones. Higher values of the large frequency separation are then found for rotating models than for non-rotating ones at the same evolutionary stage, because the increase of the effective temperature leads to a smaller radius and hence to an increase of the stellar mean density. Rotational mixing also has a considerable impact on the structure and chemical composition of the central stellar layers by bringing fresh hydrogen fuel to the core, thereby enhancing the main-sequence lifetime. The increase of the central hydrogen abundance together with the change of the chemical profiles in the central layers result in a significant increase of the values of the small frequency separations and of the ratio of the small to large separations for models including shellular rotation. This increase is clearly seen for models with the same age sharing the same initial parameters except for the inclusion of rotation as well as for models with the same global stellar parameters and in particular the same location in the HR diagram. By computing rotating models of solar-type stars including the effects of a dynamo that possibly occurs in the radiative zone, we find that the efficiency of rotational mixing is strongly reduced when the effects of magnetic fields are taken into account, in contrast to what happens in massive stars.Comment: 11 pages, 15 figures, accepted for publication in A&

3He-Driven Mixing in Low-Mass Red Giants: Convective Instability in Radiative and Adiabatic Limits

We examine the stability and observational consequences of mixing induced by 3He burning in the envelopes of first ascent red giants. We demonstrate that there are two unstable modes: a rapid, nearly adiabatic mode that we cannot identify with an underlying physical mechanism, and a slow, nearly radiative mode that can be identified with thermohaline convection. We present observational constraints that make the operation of the rapid mode unlikely to occur in real stars. Thermohaline convection turns out to be fast enough only if fluid elements have finger-like structures with a length to diameter ratio l/d > 10. We identify some potentially serious obstacles for thermohaline convection as the predominant mixing mechanism for giants. We show that rotation-induced horizontal turbulent diffusion may suppress the 3He-driven thermohaline convection. Another potentially serious problem for it is to explain observational evidence of enhanced extra mixing. The 3He exhaustion in stars approaching the red giant branch (RGB) tip should make the 3He mixing inefficient on the asymptotic giant branch (AGB). In spite of this, there are observational data indicating the presence of extra mixing in low-mass AGB stars similar to that operating on the RGB. Overmixing may also occur in carbon-enhanced metal-poor stars.Comment: 25 pages, 6 figures, modified version, accepted by Ap

WIYN/Hydra Detection of Lithium Depletion in F Stars of the Young Open Cluster M35 and Implications for the Development of the Lithium Gap

We report discovery of significant depletion of Li on the surfaces of F dwarf stars in the 150-Myr-old open cluster M35, analagous to a feature in the 700-Myr-old Hyades cluster that has been referred to as the ``Li gap.'' We have caught the gap in the act of forming: using high resolution, high S/N, WIYN/Hydra observations, we detect Li in all but a few M35 F stars; the maximum depletion lies at least 0.6-0.8 dex below minimally depleted (or undepleted) stars. The M35 Li depletion region, a) is quite wide, with clear depletion seen from 6000K to 6700K or hotter; b) shows a significant dispersion in Li abundance at all T_eff, even with stars of the same T_eff; and c) contains undepleted stars (as well as depleted ones) in the (narrow) classical Hyades gap region, which itself shows no undepleted stars. All of these M35 Li depletion properties support rotationally-induced slow mixing as the primary physical mechanism that forms the gap, and argues against other proposed mechanisms, particularly diffusion and steady main sequence mass loss. When viewed in the context of the M35 Li depletion properties, the Hyades Li gap may well be wider than is usually recognized.Comment: 14 Pages, 3 figures. Accepted to ApJ Letter

On the Coupling between Helium Settling and Rotation-Induced Mixing in Stellar Radiative Zones: II- Application to light elements in population I main-sequence stars

In the two previous papers of this series, we have discussed the importance of t he $\mu$-gradients due to helium settling on rotation-induced mixing, first in a n approximate analytical way, second in a 2D numerical simulation. We have found that, for slowly rotating low mass stars, a process of ``creeping paralysis" in which the circulation and the diffusion are nearly frozen may take place below the convective zone. Here we apply this theory to the case of lithium and beryll ium in galactic clusters and specially the Hyades. We take into account the rota tional braking with rotation velocities adjusted to the present observations. We find that two different cells of meridional circulation appear on the hot side of the "lithium dip" and that the "creeping paralysis" process occurs, not dir ectly below the convective zone, but deeper inside the radiative zone, at the to p of the second cell. As a consequence, the two cells are disconnected, which ma y be the basic reason for the lithium increase with effective temperature on thi s side of the dip. On the cool side, there is just one cell of circulation and t he paralysis has not yet set down at the age of the Hyades; the same modelisatio n accounts nicely for the beryllium observations as well as for the lithium ones .Comment: 13 printed pages, 10 figures. ApJ, in press (April 20, 2003