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Register a new userRapid Rotation and Nonradial Pulsations: Kappa-Mechanism Excitation of G-Modes in B Stars
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Several classes of stars (most notably O and B main-sequence stars, as well as accreting white dwarfs and neutron stars) rotate quite rapidly, at spin frequencies greater than the typical g-mode frequencies. We discuss how rapid rotation modifies the $kappa$-mechanism excitation and observability of g-mode oscillations. We find that, by affecting the timescale match between the mode period and the thermal time at the driving zone, rapid rotation stabilizes some of the g-modes that are excited in a non-rotating star, and, conversely, excites g-modes that are damped in absence of rotation. The fluid velocities and temperature perturbations are strongly concentrated near the equator for most g-modes in rapidly rotating stars, which means that a favorable viewing angle may be required to observe the pulsations. Moreover, the stability of modes of the same $l$ but different $m$ is affected differently by rotation. We illustrate this by considering g-modes in Slowly Pulsating B-type stars as a function of the rotation rate.
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For the first time nonradial oscillations of superfluid nonrotating stars are self-consistently studied at finite stellar temperatures. We apply a realistic equation of state and realistic density dependent model of critical temperature of neutron and proton superfluidity. In particular, we discuss three-layer configurations of a star with no neutron superfluidity at the centre and in the outer region of the core but with superfluid intermediate region. We show, that oscillation spectra contain a set of modes whose frequencies can be very sensitive to temperature variations. Fast temporal evolution of the pulsation spectrum in the course of neutron star cooling is also analysed.
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.
Detection of solar gravity modes remains a major challenge to our understanding of the innerparts of the Sun. Their frequencies would enable the derivation of constraints on the core physical properties while their amplitudes can put severe constraints on the properties of the inner convective region. Our purpose is to determine accurate theoretical amplitudes of solar g modes and estimate the SOHO observation duration for an unambiguous detection. We investigate the stochastic excitation of modes by turbulent convection as well as their damping. Input from a 3D global simulation of the solar convective zone is used for the kinetic turbulent energy spectrum. Damping is computed using a parametric description of the nonlocal time-dependent convection-pulsation interaction. We then provide a theoretical estimation of the intrinsic, as well as apparent, surface velocity. Asymptotic g-mode velocity amplitudes are found to be orders of magnitude higher than previous works. Using a 3D numerical simulation, from the ASH code, we attribute this to the temporal-correlation between the modes and the turbulent eddies which is found to follow a Lorentzian law rather than a Gaussian one as previously used. We also find that damping rates of asymptotic gravity modes are dominated by radiative losses, with a typical life-time of $3 times 10^5$ years for the $ell=1$ mode at $ u=60 mu$Hz. The maximum velocity in the considered frequency range (10-100 $mu$Hz) is obtained for the $ell=1$ mode at $ u=60 mu$Hz and for the $ell=2$ at $ u=100 mu$Hz. Due to uncertainties in the modeling, amplitudes at maximum i.e. for $ell=1$ at 60 $mu$Hz can range from 3 to 6 mm s$^{-1}$.
We present the identification of very low frequency g modes in the asymptotic regime and two important parameters that have long been waited for: the core rotation rate, and the asymptotic equidistant period spacing of these g modes. The GOLF instrument on board the SOHO space observatory has provided two decades of full-disk helioseismic data. In the present study, we search for possible collective frequency modulations that are produced by periodic changes in the deep solar structure. Such modulations provide access to only very low frequency g modes, thus allowing statistical methods to take advantage of their asymptotic properties. For oscillatory periods in the range between 9 and nearly 48 hours, almost 100 g modes of spherical harmonic degree 1 and more than 100 g modes of degree 2 are predicted. They are not observed individually, but when combined, they unambiguouslyprovide their asymptotic period equidistance and rotational splittings, in excellent agreement with the requirements of the asymptotic approximations. Previously, p-mode helioseismology allowed the g-mode period equidistance parameter $P_0$ to be bracketed inside a narrow range, between approximately 34 and 35 minutes. Here, $P_0$ is measured to be 34 min 01 s, with a 1 s uncertainty. The previously unknown g-mode splittings have now been measured from a non-synodic reference with very high accuracy, and they imply a mean weighted rotation of 1277 $pm$ 10 nHz (9-day period) of their kernels, resulting in a rapid rotation frequency of 1644 $pm$ 23 nHz (period of one week) of the solar core itself, which is a factor 3.8 $pm$ 0.1 faster than the rotation of the radiative envelope. The g modes are known to be the keys to a better understanding of the structure and dynamics of the solar core. Their detection with these precise parameters will certainly stimulate a new era of research in this field.
We use the traditional approximation to describe oscillations with frequencies comparable to the angular rotation rate. Validity of this approximation in application to main-sequence B stars is discussed. Numerical results regarding mode stability and visibility are presented for a model of the Be star HD 163868. For this object, Walker et al.(2005) detected a record number of mode frequencies using data from the small space telescope MOST. Our interpretation of these data differs from that of Walker et al. In particular, we interpret peaks in the lowest frequency range as retrograde g modes. We find instability in a large number of modes that remain undetectable because of unfavourable aspect and/or effect of cancellation. There is no clear preference to excitation of prograde modes.
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