D. R. Xiong

Non‐adiabatic oscillations of red giants

Using our non-local time-dependent theory of convection, the linear non-adiabatic oscillations of 10 evolutionary model series with masses of 1-3 M-circle dot are calculated. The results show that there is a red giant instability strip in the lower temperature side of the Hertzsprung-Russell diagram which goes along the sequences of the red giant branch and the asymptotic giant branch. For red giants of lower luminosities, pulsation instability is found at high order overtones; the lower order modes from the fundamental to the second overtone are stable. Towards higher luminosity and lower effective temperature, instability moves to lower order modes, and the amplitude growth rate of oscillations also grows. At the high luminosity end of the strip, the fundamental and the first overtone become unstable, while all the modes above the fourth order become stable. The excitation mechanisms have been studied in detail. It is found that turbulent pressure plays a key role for excitation of red variables. The frozen convection approximation is unavailable for the low temperature stars with extended convective envelopes. In any case, this approximation can explain neither the red edge of the Cepheid instability strip, nor the blue edge of the pulsating red giant instability strip. An analytic expression of a pulsation constant as a function of stellar mass, luminosity and effective temperature is presented from this work.

How to define the boundaries of a convective zone, and how extended is overshooting ?

In non-local convection theory, convection extends without limit and therefore an apparent boundary cannot be defined clearly, as in local theory. From the requirement that a similar structure for both local and non-local models has the same depth of convection zone, and taking into account the driving mechanism of turbulent convection, we argue that a proper definition of the boundary of a convective zone should be the place where the convective energy flux (i.e. the correlation of turbulent velocity and temperature) changes its sign. Therefore, it is a convectively unstable region when the flux is positive, and it is a convective overshooting zone when the flux becomes negative. The physical picture of the overshooting zone drawn by the usual non-local mixing-length theory is incorrect. In fact, convection is already subadiabatic (del < del(ad)) long before reaching the unstable boundary, while in the overshooting zone below the convective zone, convection is subadiabatic and superradiative (del(rad) < del < del(ad)). The transition between the adiabatic and radiative temperature gradients is continuous and smooth instead of being a sudden switch. In the unstable zone, the temperature gradient approaches a radiative temperature gradient rather than an adiabatic temperature gradient. We would like to note again that the overshooting distance is different for different physical quantities. In an overshooting zone at deep stellar interiors, the e-folding lengths of turbulent velocity and temperature are about 0.3H(P), whereas that of the velocity-temperature correlation is much shorter, about 0.09H(P). The overshooting distance in the context of stellar evolution, measured by the extent of the mixing of stellar matter, should be more extended. It is estimated to be as large as 0.25-1.7H(P) depending on the evolutionary time-scale. The larger the overshooting distance, the longer the time-scales. This is because of the participation of the extended overshooting tail in the mixing process.

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

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 - I. Basic equations for calculations of stellar structure and oscillations

Starting from hydrodynamic equations, we have established a set of hydrodynamic equations for average flow and a set of dynamic equations of auto- and cross-correlations of turbulent velocity and temperature fluctuations, following the classic Reynolds treatment of turbulence. The combination of the two sets of equations leads to a complete and self-consistent mathematical expressions ready for the calculations of stellar structure and oscillations. In this paper, non-locality and anisotropy of turbulent convection are concisely presented, together with defining and calibrating of the three convection parameters (c(1), c(2) and c(3)) included in the algorithm. With the non-local theory of convection, the structure of the convective envelope and the major characteristics of non-adiabatic linear oscillations are demonstrated by numerical solutions. Great effort has been exercised to the choice of convection parameters and pulsation instabilities of the models, the results of which show that within large ranges of all three parameters (c(1), c(2) and c(3)) the main properties of pulsation stability keep unchanged.

The physical properties of Fermi TeV BL Lac objects’ jets

We investigate the physical properties of \textit{Fermi} TeV BL Lac objects jets by modeling the quasi-simultaneous spectral energy distribution of 29 \textit{Fermi} TeV BL Lacs in the frame of a one-zone leptonic synchrotron self-Compton model. Our main results are the following: (i) There is a negative correlation between

Multicolor Optical Monitoring of the Quasar 3C 273 from 2005 to 2016

B

Curvature of the spectral energy distribution, the inverse Compton component and the jet in Fermi 2LAC blazars

and

MULTI-COLOR OPTICAL MONITORING OF MRK 501 FROM 2010 TO 2015

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Turbulent convection and pulsation stability of stars – III. Non-adiabatic oscillations of red giants

in our sample, which suggests that

Optical multi-color monitoring of OJ 287 from 2006 to 2012

B