We apply here the Time Dependent Convection (TDC) treatment presented in our earlier paper in this series to the study of δ  Sct and γ  Dor pulsating stars. Stabilization of the δ  Sct p-modes at the red edge of the Instability Strip (IS) and the driving of the γ  Dor g-modes are explained by our models. Theoretical IS obtained with different values of the Mixing Length (ML) parameter α are compared to observations and a good agreement is obtained for α between 1.8 and 2. The influence of each term of our TDC treatment (perturbation of convective flux, turbulent pressure, and turbulent kinetic energy dissipation) on the eigenfrequencies and on the driving and damping mechanisms is investigated. Finally, we show that our TDC models predict the likely existence of hybrid stars with both δ  Sct p-modes and γ  Dor g-modes oscillations.

/pdf/convection-pulsation-coupling-ii-excitation-and-4t0ih9hofj.pdf

Convection-pulsation coupling - II. Excitation and stabilization mechanisms in $\delta$ Sct and $\gamma$ Dor stars

We present an extensive and up-to-date catalog of Galactic β Cephei stars. This catalog is intended to give a comprehensive overview of observational characteristics of all known β Cephei stars, covering information until 2004 June. Ninety-three stars could be confirmed to be β Cephei stars. We use data from more than 250 papers published over the last nearly 100 years, and we provide over 45 notes on individual stars. For some stars we reanalyzed published data or conducted our own analyses. Sixty-one stars were rejected from the final β Cephei list, and 77 stars are suspected to be β Cephei stars. A list of critically selected pulsation frequencies for confirmed β Cephei stars is also presented.     We analyze the β Cephei stars as a group, such as the distributions of their spectral types, projected rotational velocities, radial velocities, pulsation periods, and Galactic coordinates. We confirm that the majority of the β Cephei stars are multiperiodic pulsators. We show that, besides two exceptions, the β Cephei stars with high pulsation amplitudes are slow rotators. Those higher amplitude stars have angular rotational velocities in the same range as the high-amplitude δ Scuti stars (Prot 3 days).     We construct a theoretical HR diagram that suggests that almost all 93 β Cephei stars are main-sequence objects. We discuss the observational boundaries of β Cephei pulsation and the physical parameters of the stars. We corroborate that the excited pulsation modes are near to the radial fundamental mode in frequency and we show that the mass distribution of the stars peaks at 12 M⊙. We point out that the theoretical instability strip of the β Cephei stars is filled neither at the cool nor at the hot end and attempt to explain this observation.

https://iopscience.iop.org/article/10.1086/429408/pdf

Catalog of Galactic β Cephei Stars

New theoretical instability strips for δ  Sct and γ Dor stars are presented. These results have been obtained taking into account the perturbation of the convective flux following the treatment of Gabriel ([CITE]). For the first time, the red edge of the δ  Sct instability strip for non-radial modes is obtained. The influence of this time-dependent convection (TDC) on the driving of the γ Dor gravity modes is investigated. The results obtained for different values of the mixing-length parameter α are compared for the γ Dor models. A good agreement with observations is found for models with α between 1.8 and 2.0.

/pdf/theoretical-instability-strips-for-delta-scuti-and-gamma-3w3cb59x0y.pdf

Theoretical instability strips for $\delta$ Scuti and $\gamma$ Doradus stars

We investigate the early-time light-curves of a large sample of 223 type II supernovae (SNe) from the Sloan Digital Sky Survey and the Supernova Legacy Survey. Having a cadence of a few days and sufficient non-detections prior to explosion, we constrain rise-times, i.e. the durations from estimated first to maximum light, as a function of effective wavelength. At restframe g ′ -band (λeff = 4722u we find a distribution of fast rise-times with median of (7.5±0.3) days. Comparing these durations with analytical shock models of Rabinak & Waxman (2013); Nakar & Sari (2010) and hydrodynamical models of Tominaga et al. (2009), which are mostly sensitive to progenitor radius at these epochs, we find a median characteristic radius of less than 400 solar radii. The inferred radii are on average much smaller than the radii obtained for observed red supergiants (RSG). Investigating the post-maximum slopes as a function of effective wavelength in the light of theoretical models, we find that massive hydrogen envelopes are still needed to explain the plateaus of SNe II. We therefore argue that the SN II rise-times we observe are either a) the shock cooling resulting from the core collapse of RSG with small and dense envelopes, or b) the delayed and prolonged shock breakout of the collapse of a RSG with an extended atmosphere or embedded within pre-SN circumstellar material.

The rise-time of Type II supernovae

By using a non-local and time-dependent convection theory, we have calculated radial and low-degree non-radial oscillations for stellar evolutionary models with M = 1.4-3.0 M-circle dot. The results of our study predict theoretical instability strips for delta Scuti and gamma Doradus stars, which overlap with each other. The strip of gamma Doradus is slightly redder in colour than that of delta Scuti. We have paid great attention to the excitation and stabilization mechanisms for these two types of oscillations, and we conclude that radiative K mechanism plays a major role in the excitation of warm delta Scuti and gamma Doradus stars, while the coupling between convection and oscillations is responsible for excitation and stabilization in cool stars. Generally speaking, turbulent pressure is an excitation of oscillations, especially in cool delta Scuti and gamma Doradus stars and all cool Cepheid- and Mira-like stars. Turbulent thermal convection, on the other hand, is a damping mechanism against oscillations that actually plays the major role in giving rise to the red edge of the instability strip. Our study shows that oscillations of delta Scuti and gamma Doradus stars are both due to the combination of kappa mechanism and the coupling between convection and oscillations, and they belong to the same class of variables at the low-luminosity part of the Cepheid instability strip. Within the delta Scuti-gamma Doradus instability strip, most of the pulsating variables are very likely hybrids that are excited in both p and g modes.

Turbulent convection and pulsation stability of stars - II. Theoretical instability strip for δ Scuti and γ Doradus stars

The delta Scuti star catalogue is used to derive the observational locations of such stars on the HR diagram. The theoretical and observational instability strips are compared to check the theoretical red edge obtained by considering non-local time-dependent convection theory. The observational instability strip almost overlaps with the theoretical one, but the observed blue and red envelopes are hotter than the theoretical edges. The distribution of delta Scuti stars in the pulsation strip is not uniform.

On the Red Edge of the δ Scuti Instability Strip

We present a study of the beta Cephei instability strip based on a sample of 49 stars of this type. After deriving their effective temperatures and luminosities from their observed (B - V), (U - B) colors and parallaxes we find their positions in the HR diagram to be mostly confined to the main sequence, and their masses to lie between 7M(circle dot) and 30 M-circle dot. Their distribution on the HR diagram matches well with our previous theoretical instability strip which has an upper bound in the luminosity and rather tight boundaries in the effective temperature.

Statistics of the Instability Strip of Cephei Stars

In this paper, we investigate the problem of supersonic convection caused by the application of the usual Mixing Length Theory (MLT), and give a modification to the original expression of the MLT. In the case of the usual MLT, a zone of supersonic convection exists when the stellar model goes into yellow-red supergiant phase. When the modification is applied, the models of late type supergiants possess shallower convective envelopes for a given temperature compared with the normal formalism of the MLT. Therefore the stellar models made with our new formalism move to lower effective temperature by 100-400 K depending on the luminosity of the star. Such a modification does not affect the convective envelope structure of lower luminosity late type stars, as both expressions of the MLT give the same result. in these stars.

https://iopscience.iop.org/article/10.1088/1009-9271/1/1/50/pdf

Da-Run Xiong

Papers

On the Red Edge of the δ Scuti Instability Strip

Statistics of the Instability Strip of Cephei Stars

A note on the mixing length theory and massive star evolution