Non-linear excitation of low frequency modes by overstable convective modes in rotating stars

Abstract

We discuss non-linear excitation and amplitude saturation of $g$-modes, $r$-modes and overstable convective (OsC) modes in early type main sequence stars, taking account of the effects of three-mode couplings on amplitude evolutions. OsC modes are rotationally stabilized convective modes in the convective core and they resonantly excite low frequency $g$-modes to obtain large amplitudes in the envelope when the rotation rate of the core is larger than critical rates. We use, for a network of three-mode couplings, amplitude equations governing the time evolution of the mode amplitudes where each of three-mode couplings is assumed to occur between two stable modes and one unstable mode. Assuming that the unstable modes in the couplings are OsC modes in the core and the stable modes are $g$- and $r$-modes in the envelope, we integrate the amplitude equations to see how the $g$- and $r$-modes are non-linearly excited by the OsC modes and whether or not the amplitude evolutions tend toward a state of finite amplitudes. We find that the non-linear three-mode couplings do excite low frequency $g$- and $r$-modes but they are not necessarily effective to achieve amplitude saturation since the three-mode couplings between the OsC modes with large growth rates and $g$- and $r$-modes with small damping rates tend to destabilize amplitude evolutions.

arXiv comment14 pages, 13 figures, accepted for publication in MNRAS

References in corpus (24)

• Probing the interior physics of stars through asteroseismology
• Angular Momentum Transport in Stellar Interiors
• Saturation of the R-mode Instability
• Nonlinear mode coupling in rotating stars and the r-mode instability in neutron stars
• Theory and evidence of global Rossby waves in upper main-sequence stars: r-mode oscillations in many Kepler stars
• On the sensitivity of gravito-inertial modes to differential rotation in intermediate-mass main-sequence stars
• Nonlinear Tides in Close Binary Systems
• Non-Linear Evolution of the r-Modes in Neutron Stars
• Gravity-Modes in ZZ Ceti Stars: IV. Amplitude Saturation by Parametric Instability
• Nonlinear Damping of Oscillations in Tidal-Capture Binaries
• Rotation of the convective core in $\gamma$ Dor stars measured by dips in period spacings of g modes coupled with inertial modes
• First evidence of inertial modes in $\gamma$ Doradus stars: The core rotation revealed
• Rotational modulation in TESS B stars
• CoRoT's view on variable B8/9 stars: spots versus pulsations: Evidence for differential rotation in HD 174648
• Nonlinear Development of the R Mode Instability and the Maximum Rotation Rate of Neutron Stars
• Pulsation among TESS A and B stars and the Maia variables
• A Nonlinear Coupling Network to Simulate the Development of the r-mode Instablility in Neutron Stars II. Dynamics
• Numerical evolutions of nonlinear r-modes in neutron stars
• Rotating Convective Core Excites Non-Radial Pulsations to Cause Rotational Modulations in Early-Type Stars
• Amplitudes of low frequency modes in rotating B type stars
• Overstable Convective Modes in Rotating Early Type Stars
• Spectroscopy of hot Gamma Doradus and A-F hybrid Kepler candidates close to the hot border of the Delta Scuti instability strip
• Overstable Convective Modes of Rotating Hot Jupiters
• Stellar rotation rates in Kepler eccentric (heartbeat) binaries obtained from r-mode signatures

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