Radial and Nonradial Oscillation Modes in Rapidly Rotating Stars

Radial and nonradial oscillations offer the opportunity to investigate the interior properties of stars. We use 2D stellar models and a 2D finite difference integration of the linearized pulsation equations to calculate non-radial oscillations. This approach allows us to directly calculate the pulsation modes for a distorted rotating star without treating the rotation as a perturbation. We are also able to express the finite difference solution in the horizontal direction as a sum of multiple spherical harmonics for any given mode. Using these methods, we have investigated the effects of increasing rotation and the number of spherical harmonics on the calculated eigenfrequencies and eigenfunctions and compared the results to perturbation theory. In slowly rotating stars, current methods work well, and we show that the eigenfunction can be accurately modelled using 2nd order perturbation theory and a single spherical harmonic. We use 10 Msun models with velocities ranging from 0 to 420 km/s (0.89 Omega_c) and examine low order p modes. We find that one spherical harmonic remains reasonable up to a rotation rate around 300km s^{-1} (0.69 Omega_c) for the radial fundamental mode, but can fail at rotation rates as low as 90 km/s (0.23 Omega_c) for the 2H mode or l = 2 p_2 mode, based on the eigenfrequencies alone. Depending on the mode in question, a single spherical harmonic may fail at lower rotation rates if the shape of the eigenfunction is taken into consideration. Perturbation theory, in contrast, remains valid up to relatively high rotation rates for most modes. We find the lowest failure surface equatorial velocity is 120 km/s (0.30 Omega_c) for the l = 2 p_2 mode, but failure velocities between 240 and 300 km/s (0.58-0.69 Omega_c)are more typical.Comment: accepted for publication in Ap

The Structure of Close Binaries in Two Dimensions

The structure and evolution of close binary stars has been studied using the two-dimensional (2D) stellar structure algorithm developed by Deupree (1995). We have calculated a series of solar composition stellar evolution sequences of binary models, where the mass of the 2D model is 8Msun with a point-mass 5Msun companion. We have also studied the structure of the companion in 2D, by considering the zero-age main-sequence (ZAMS) structure of a 5Msun model with an 8Msun point-mass companion. In all cases the binary orbit was assumed to be circular and co-rotating with the rotation rate of the stars. We considered binary models with three different initial separations, a = 10, 14 and 20Rsun. These models were evolved through central hydrogen burning or until the more massive star expanded to fill its critical potential surface or Roche lobe. The calculations show that evolution of the deep interior quantities is only slightly modified from those of single star evolution. Describing the model surface as a Roche equipotential is also satisfactory until very close to the time of Roche lobe overflow, when the self gravity of the model about to lose mass develops a noticeable aspherical component and the surface time scale becomes sufficiently short that it is conceivable that the actual surface is not an equipotential.Comment: 22 pages, 10 figures, accepted by Ap

LACHESIS -- An instrumentation system for obtaining containment and environmental data

The instrumentation system developed to obtain containment and environmental data in the LYNER complex is presented. The primary purpose of this report is to familiarize potential operators of the system with the details of its use. The instrumentation system has three major hardware modules: (1) the sensor power source, amplifier, and signal conditioner module, (2) the digitizers, and (3) the computer controller. Each of these is described with emphasis on the steps required to make that component perform effectively. In addition the roles of activities of other people besides the Los Alamos shot engineer who are required to ensure the success of the system are outlined

CCD Photometry of Galactic Globular Clusters. IV. The NGC 1851 RR Lyraes

The variable star population of the galactic globular cluster NGC 1851 (C0512-400) has been studied by CCD photometry, from observations made in the B, V, and I bands during 1993-4. Light curves are presented for 29 variables, seven of which are new discoveries. The behavior of the RR lyraes in the period-temperature diagram appears normal when compared to clusters which bracket the NGC 1851 metallicity. Reddening and metallicity are re-evaluated, with no compelling evidence to change from accepted values. Photometry for stars within an annulus with radii 80 and 260 arcsec agrees to better than 0.02 mag in all colors with extensive earlier photometry, to at least V = 18.5. Instability strip boundary positions for several clusters shows a trend for the red boundary to move to redder colors as the metallicity increases.Comment: 29 pages, 9 figures, accepted by A.

Pulsation modes in rapidly rotating stellar models based on the Self-Consistent Field method

Context: New observational means such as the space missions CoRoT and Kepler and ground-based networks are and will be collecting stellar pulsation data with unprecedented accuracy. A significant fraction of the stars in which pulsations are observed are rotating rapidly. Aims: Our aim is to characterise pulsation modes in rapidly rotating stellar models so as to be able to interpret asteroseismic data from such stars. Methods: The pulsation code developed in Ligni\`eres et al. (2006) and Reese et al. (2006) is applied to stellar models based on the self-consistent field (SCF) method (Jackson et al. 2004, 2005, MacGregor et al. 2007). Results: Pulsation modes in SCF models follow a similar behaviour to those in uniformly rotating polytropic models, provided that the rotation profile is not too differential. Pulsation modes fall into different categories, the three main ones being island, chaotic, and whispering gallery modes, which are rotating counterparts to modes with low, medium, and high l-|m| values, respectively. The frequencies of the island modes follow an asymptotic pattern quite similar to what was found for polytropic models. Extending this asymptotic formula to higher azimuthal orders reveals more subtle behaviour as a function of m and provides a first estimate of the average advection of pulsation modes by rotation. Further calculations based on a variational principle confirm this estimate and provide rotation kernels that could be used in inversion methods. When the rotation profile becomes highly differential, it becomes more and more difficult to find island and whispering gallery modes at low azimuthal orders. At high azimuthal orders, whispering gallery modes, and in some cases island modes, reappear.Comment: 16 pages, 11 figures, accepted for publication in A&

Recent Advances in Modeling Stellar Interiors

Advances in stellar interior modeling are being driven by new data from large-scale surveys and high-precision photometric and spectroscopic observations. Here we focus on single stars in normal evolutionary phases; we will not discuss the many advances in modeling star formation, interacting binaries, supernovae, or neutron stars. We review briefly: 1) updates to input physics of stellar models; 2) progress in two and three-dimensional evolution and hydrodynamic models; 3) insights from oscillation data used to infer stellar interior structure and validate model predictions (asteroseismology). We close by highlighting a few outstanding problems, e.g., the driving mechanisms for hybrid gamma Dor/delta Sct star pulsations, the cause of giant eruptions seen in luminous blue variables such as eta Car and P Cyg, and the solar abundance problem.Comment: Proceedings for invited talk at conference High Energy Density Laboratory Astrophysics 2010, Caltech, March 2010, submitted for special issue of Astrophysics and Space Science; 7 pages; 5 figure

Effects of Uniform and Differential Rotation on Stellar Pulsations

We have investigated the effects of uniform rotation and a specific model for differential rotation on the pulsation frequencies of 10 \Msun\ stellar models. Uniform rotation decreases the frequencies for all modes. Differential rotation does not appear to have a significant effect on the frequencies, except for the most extreme differentially rotating models. In all cases, the large and small separations show the effects of rotation at lower velocities than do the individual frequencies. Unfortunately, to a certain extent, differential rotation mimics the effects o f more rapid rotation, and only the presence of some specific observed frequencies with well identified modes will be able to uniquely constrain the internal rotation of pulsating stars.Comment: 33 pages, 16 figures. Accepted for publication in Ap

Calibrating the Mixing Length Parameter for a Red Giant Envelope

Two-dimensional hydrodynamical simulations were made to calibrate the mixing length parameter for modeling red giant's convective envelope. As was briefly reported in Asida & Tuchman (97), a comparison of simulations starting with models integrated with different values of the mixing length parameter, has been made. In this paper more results are presented, including tests of the spatial resolution and Large Eddy Simulation terms used by the numerical code. The consistent value of the mixing length parameter was found to be 1.4, for a red giant of mass 1.2 solar-mass, core mass of 0.96 solar-mass, luminosity of 200 solar-luminosities, and metallicity Z=0.001.Comment: 18 pages, 1 table, 13 figures. Accepted for publication in Ap.

Vertical abundance stratification in the blue horizontal branch star HD135485

It is commonly believed that the observed overabundances of many chemical species relative to the expected cluster metallicity in blue horizontal branch (BHB) stars appear as a result of atomic diffusion in the photosphere. The slow rotation of BHB stars (with T_eff > 11,500K), typically v sin{i} < 10 km/s, is consistent with this idea. In this work we search for observational evidence of vertical chemical stratification in the atmosphere of HD135485. If this evidence exists, it will demonstrate the importance of atomic diffusion processes in the atmospheres of BHB stars. We undertake an extensive abundance stratification analysis of the atmosphere of HD135485, based on recently acquired high resolution and S/N CFHT ESPaDOnS spectra and a McDonald-CE spectrum. Our numerical simulations show that nitrogen and sulfur reveal signatures of vertical abundance stratification in the stellar atmosphere. It appears that the abundances of these elements increase toward the upper atmosphere. This fact cannot be explained by the influence of microturbulent velocity, because oxygen, carbon, neon, argon, titanium and chromium do not show similar behavior and their abundances remain constant throughout the atmosphere. It seems that the iron abundance may increase marginally toward the lower atmosphere. This is the first demonstration of vertical abundance stratification of metals in a BHB star.Comment: 8 pages, 5 figures, accepted to A&

Towards a new generation of multi-dimensional stellar evolution models: development of an implicit hydrodynamic code

This paper describes the first steps of development of a new multidimensional time implicit code devoted to the study of hydrodynamical processes in stellar interiors. The code solves the hydrodynamical equations in spherical geometry and is based on the finite volume method. Radiation transport is taken into account within the diffusion approximation. Realistic equation of state and opacities are implemented, allowing the study of a wide range of problems characteristic of stellar interiors. We describe in details the numerical method and various standard tests performed to validate the method. We present preliminary results devoted to the description of stellar convection. We first perform a local simulation of convection in the surface layers of a A-type star model. This simulation is used to test the ability of the code to address stellar conditions and to validate our results, since they can be compared to similar previous simulations based on explicit codes. We then present a global simulation of turbulent convective motions in a cold giant envelope, covering 80% in radius of the stellar structure. Although our implicit scheme is unconditionally stable, we show that in practice there is a limitation on the time step which prevent the flow to move over several cells during a time step. Nevertheless, in the cold giant model we reach a hydro CFL number of 100. We also show that we are able to address flows with a wide range of Mach numbers (10^-3 < Ms< 0.5), which is impossible with an anelastic approach. Our first developments are meant to demonstrate that the use of an implicit scheme applied to a stellar evolution context is perfectly thinkable and to provide useful guidelines to optimise the development of an implicit multi-D hydrodynamical code.Comment: 21 pages, 18 figures, accepted for publication in A&