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Register a new userThe traditional approximation of rotation for rapidly rotating stars and planets. I. The impact of strong deformation
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The Traditional Approximation of Rotation (TAR) is a treatment of the hydrodynamic equations of rotating and stably stratified fluids in which the action of the Coriolis acceleration along the direction of the entropy and chemical stratifications is neglected because it is weak in comparison with the buoyancy force. The dependent variables in the equations for the dynamics of gravito-inertial waves (GIWs) then become separable into radial and horizontal parts as in the non-rotating case. The TAR is built on the assumptions that the star is spherical (i.e. its centrifugal deformation is neglected) and uniformly rotating. We study the feasibility of carrying out a generalisation of the TAR to account for the centrifugal acceleration in the case of strongly deformed uniformly and rapidly rotating stars (and planets), and to identify the validity domain of this approximation. We built analytically a complete formalism that allows the study of the dynamics of GIWs in spheroidal coordinates which take into account the flattening of rapidly rotating stars by assuming the hierarchies of frequencies adopted within the TAR in the spherical case and by deriving a generalised Laplace tidal equation for the horizontal eigenfunctions of the GIWs and their asymptotic wave periods, which can be used to probe the structure and dynamics of rotating deformed stars with asteroseismology. Using 2D ESTER stellar models, we determine the validity domain of the generalised TAR as a function of the rotation rate of the star normalised by its critical angular velocity and its pseudo-radius. This generalisation allows us to study the signature of the centrifugal effects on GIWs in rapidly rotating deformed stars. We found that the effects of the centrifugal acceleration in rapidly rotating early-type stars on GIWs are theoretically detectable in modern space photometry using observations from Kepler.
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We continue our studies on stellar latitudinal differential rotation. The presented work is a sequel of the work of Reiners et al. who studied the spectral line broadening profile of hundreds of stars of spectral types A through G at high rotational speed (vsini > 12 km/s). While most stars were found to be rigid rotators, only a few tens show the signatures of differential rotation. The present work comprises the rotational study of some 180 additional stars. The overall broadening profile is derived according to Reiners et al. from hundreds of spectral lines by least-squares deconvolution, reducing spectral noise to a minimum. Projected rotational velocities vsini are measured for about 120 of the sample stars. Differential rotation produces a cuspy line shape which is best measured in inverse wavelength space by the first two zeros of its Fourier transform. Rigid and differential rotation can be distinguished for more than 50 rapid rotators (vsini > 12 km/s) among the sample stars from the available spectra. Ten stars with significant differential rotation rates of 10-54 % are identified, which add to the few known rapid differential rotators. Differential rotation measurements of 6 % and less for four of our targets are probably spurious and below the detection limit. Including these objects, the line shapes of more than 40 stars are consistent with rigid rotation.
We measure the bulk system parameters of the seismically active, rapidly-rotating $delta$-Scuti KOI-976 and constrain the orbit geometry of its transiting binary companion using a combined approach of asteroseismology and gravity-darkening light curve analysis. KOI-976 is a $1.62pm0.2~mathrm{M_odot}$ star with a measured $vsin(i)$ of $120pm2$ km/s and seismically-induced variable signal that varies by $sim$ 0.6% of the stars total photometric brightness. We take advantage of the stars oblate shape and seismic activity to perform three measurements of its obliquity angle relative to the plane of the sky. We first apply rotational splitting theory to the stars variable signal observed in short-cadence emph{Kepler} photometry to constrain KOI-976s obliquity angle, and then subtract off variability from that dataset using the linear algorithm for significance reduction software {tt LASR}. We perform gravity-darkened fits to emph{Kepler} variability-subtracted short-cadence photometry and to emph{Keplers} phase-folded long-cadence photometry to obtain two more measurements of the stars obliquity. We find that the binary system transits in a grazing configuration with measured obliquity values of $36^circpm17^circ$, $46^circpm16^circ$, and $43^circpm20^circ$ respectively for the three measurements. We perform these analyses as a way to demonstrate overcoming the challenges high-mass stars can present to transit light curve fitting and to prepare for the large number of exoplanets emph{TESS} will discover orbiting A/F stars.
We consider a universal relation between moment of inertia and quadrupole moment of arbitrarily fast rotating neutron stars. Recent studies suggest that this relation breaks down for fast rotation. We find that it is still universal among various suggested equations of state for constant values of certain dimensionless parameters characterizing the magnitude of rotation. One of these parameters includes the neutron star radius, leading to a new universal relation expressing the radius through the mass, frequency, and spin parameter. This can become a powerful tool for radius measurements.
A new two dimensional non-perturbative code to compute accurate oscillation modes of rapidly rotating stars is presented. The 2D calculations fully take into account the centrifugal distorsion of the star while the non perturbative method includes the full influence of the Coriolis acceleration. This 2D non-perturbative code is used to study pulsational spectra of highly distorted evolved models of stars. 2D models of stars are obtained by a self consistent method which distorts spherically averaged stellar models a posteriori. We are also able to compute gravito-acoustic modes for the first time in rapidly rotating stars. We present the dynamics of pulsation modes in such models, and show regularities in their frequency spectra.
The understanding of the rotational evolution of early-type stars is deeply related to that of anisotropic mass and angular momentum loss. In this paper, we aim to clarify the rotational evolution of rapidly rotating early-type stars along the main sequence (MS). We have used the 2D ESTER code to compute and evolve isolated rapidly rotating early-type stellar models along the MS, with and without anisotropic mass loss. We show that stars with $Z=0.02$ and masses between $5$ and $7~M_odot$ reach criticality during the main sequence provided their initial angular velocity is larger than 50% of the Keplerian one. More massive stars are subject to radiation-driven winds and to an associated loss of mass and angular momentum. We find that this angular momentum extraction from the outer layers can prevent massive stars from reaching critical rotation and greatly reduce the degree of criticality at the end of the MS. Our model includes the so-called bi-stability jump of the $dot{M}-T_{rm eff}$ relation of 1D-models. This discontinuity now shows up in the latitude variations of the mass-flux surface density, endowing rotating massive stars with either a single-wind regime (no discontinuity) or a two-wind regime (a discontinuity). In the two-winds-regime, mass loss and angular momentum loss are strongly increased at low latitudes inducing a faster slow-down of the rotation. However, predicting the rotational fate of a massive star is difficult, mainly because of the non-linearity of the phenomena involved and their strong dependence on uncertain prescriptions. Moreover, the very existence of the bi-stability jump in mass-loss rate remains to be substantiated by observations.
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