On the excitation mechanism of Solar 5-min & solar-like oscillations of stars Licai Deng (NAOC) Darun Xiong (PMO)

contents Background Our theoretical approach The numerical models Solar 5-min, solar-like and Mira-like oscillations Main results and conclusions

Background The most popular theory: Turbulent stochastic excitation (TSE) mechanism Goldreich & Keeley 1977a,b Samadi et al Belkacem et al … However, we think it is still not settled because convective zone can damp out solar oscillations Theoretically: Balmform 1992a,b Observationally: finite spectral lines of Solar oscillations (Libbrecht 1988)

Observational facts δ Scuti star strip (the red edge) Solar and solar-like oscillations; Mira-type and pulsating red variables located at the upper part of RGB and AGB (a series of early work by Eggen; Wood 2000, Soszynski et al a,b) The lower part and the red-side of HRD: convection!

OGLE: OSARGs & Mira Soszynski et al MACHO: Pulsating AGBs Wood 2000 Eggen 1977

Our results on Solar oscillations For stars with extended convective zone such the Sun, convection work not as damping only; it can be excitation in some cases; For the Sun and solar-like less luminous stars, the coupling between convection and oscillations (CCO) effectively damps F-modes and lower order P-modes, while excites intermediate- and high-order P-modes

Cont. As luminosity increases (along RGB), the most unstable mode shifts to lower orders; Our theory provides a consistent solution to: 1). The red edge of Cepheid instability strip; 2). Solar 5-min and solar-like oscillations; 3). Mira and Mira-like stars (Mira instability strip); We think there is no distinct natures in Mira-like and Solar-like oscillations: CCO  Mira-like CCO+TSE  Solar-like

The theoretical scheme Convection: Nonlocal- and time-dependent convection theory (Xiong 1989, Xiong Cheng & Deng 1997) Oscillations: Xiong & Deng 2007

Numerical results Solar 5-min oscillations; Evolutionary models of stars with non-local convection; Linear non-adiabatic oscillations: o A series of model with Z=0.020, M= M  ; o Linear non-adiabatic modes: radial P0-P39; non- radial l =1-4, P0-P39 and for the Sun l =1-25, G4- P39 are calculated;

For Solar 5-min oscillations Modes with 3 ≤ Period ≤ 16 min are all unstable; all others outside this range: P 16 min P-, F- and G- (not incl. l = 1-5 P1-) modes are stable; The amplitude growth rate depends only on oscillation frequency, depend on l ; These predictions match observations very well.

Instability strips δ Scuti instability strip The red-edge of Cepheid instability strip (RR Lyr: Xiong, Cheng & Deng 1998; δ Scuti : Xiong & Deng 2001) Mira instability strip (LPV: Xiong, Deng & Cheng 1998; Xiong & Deng 2007) Solar-like oscillations in solar-like stars and low-luminosity red giants (Radial: Xiong, Cheng & Deng 2000, Non-radial: Xiong & Deng 2010)

Stability analysis for P0-P5Stability analysis for P16-P25

Solid symbols: stable modes ( η <0); Open symbols: unstable modes ( η >0) Calculations are made for models selected along the track of a 1 solar mass star Amplitude Growth Rate (AGR) η=-2πω i /ω r ω=ω r +iω i

The width of instability in Nr as a function of stellar luminosity

AGR as a function of luminosity for the most unstable modes [radial (red) and non-radial (blue, l =1)] in the models

Conclusion and discussions Both CCO and TSE play important roles in stellar oscillations; CCO is dominant for Mira type oscillations ; Solar-like oscillations are caused by CCO & TSE (TSE may dominate); There is no distinct difference in solar- and Mira-like oscillations: (L  unstable mode shift to lower order modes).

Thank you !