Hydrodynamical stellar models including rotation, internal gravity waves and atomic diffusion. I. Formalism and tests on Pop I dwarfs

In this paper, we develop a formalism in order to incorporate the contribution of internal gravity waves to the transport of angular momentum and chemicals over long time-scales in stars. We show that the development of a double peaked shear layer acts as a filter for waves, and how the asymmetry of this filter produces momentum extraction from the core when it is rotating faster than the surface. Using only this filtered flux, it is possible to follow the contribution of internal waves over long (evolutionary) time-scales. We then present the evolution of the internal rotation profile using this formalism for stars which are spun down via magnetic torquing. We show that waves tend to slow down the core, creating a "slow" front that may then propagate from the core to the surface. Further spin down of the surface leads to the formation of a new front. Finally we show how this momentum transport reduces rotational mixing in a 1.2Msun, Z=0.02 model, leading to a surface lithium abundance in agreement with observations in the Hyades.Comment: 14 pages, accepted for publication in A&

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&

Angular momentum transport by internal gravity waves. IV - Wave generation by surface convection zone, from the pre-main sequence to the early-AGB in intermediate mass stars

This is the fourth in a series of papers that deal with angular momentum transport by internal gravity waves in stellar interiors. Here, we want to examine the potential role of waves in other evolutionary phases than the main sequence. We study the evolution of a 3Msun Population I model from the pre-main sequence to the early-AGB phase and examine whether waves can lead to angular momentum redistribution and/or element diffusion at the external convection zone boundary. We find that, although waves produced by the surface convection zone can be ignored safely for such a star during the main sequence, it is not the case for later evolutionary stages. In particular, angular momentum transport by internal waves could be quite important at the end of the sub-giant branch and during the early-AGB phase. Wave-induced mixing of chemicals is expected during the early-AGB phase.Comment: A&A in press; 11 figure

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&

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&

Impact of internal gravity waves on the rotation profile inside pre-main sequence low-mass stars

We study the impact of internal gravity waves (IGW), meridional circulation, shear turbulence, and stellar contraction on the internal rotation profile and surface velocity evolution of solar metallicity low-mass pre-main sequence stars. We compute a grid of rotating stellar evolution models with masses between 0.6 and 2.0Msun taking these processes into account for the transport of angular momentum, as soon as the radiative core appears and assuming no more disk-locking from that moment on.IGW generation along the PMS is computed taking Reynolds-stress and buoyancy into account in the bulk of the stellar convective envelope and convective core (when present). Redistribution of angular momentum within the radiative layers accounts for damping of prograde and retrograde IGW by thermal diffusivity and viscosity in corotation resonance. Over the whole mass range considered, IGW are found to be efficiently generated by the convective envelope and to slow down the stellar core early on the PMS. In stars more massive than ~ 1.6Msun, IGW produced by the convective core also contribute to angular momentum redistribution close to the ZAMS. Overall, IGW are found to significantly change the internal rotation profile of PMS low-mass stars.Comment: Accepted for publication in A&A (15 pages