On the excitation mechanism of Solar 5- min & solar-like oscillations of stars

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

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

3. Background • The most popular theory: Turbulent stochastic excitation (TSE) mechanismGoldreich & Keeley 1977a,bSamadi et al. 2003Belkacem et al. 2008 … • However, we think it is still not settled because convective zone can damp out solar oscillationsTheoretically: Balmform 1992a,bObservationally: finite spectral lines of Solar oscillations (Libbrecht 1988)

4. 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. 2004 a,b) • The lower part and the red-side of HRD: convection!

5. Eggen 1977 MACHO: Pulsating AGBs Wood 2000 OGLE: OSARGs & Mira Soszynski et al. 2004

6. 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

7. 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

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

10. Numerical results • Solar 5-min oscillations; • Evolutionary models of stars with non-local convection; • Linear non-adiabatic oscillations: • A series of model with Z=0.020, M=0.6-3.0M; • 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;

11. For Solar 5-min oscillations • Modes with 3 ≤ Period ≤ 16 min are all unstable; all others outside this range:P < 3 min (P-modes) &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.

12. 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)

13. Stability analysis for P0-P5 Stability analysis for P16-P25

14. Calculations are made formodels selected along thetrack of a 1 solar mass star Amplitude Growth Rate (AGR)η=-2πωi/ωrω=ωr+iωi Solid symbols: stable modes (η<0); Open symbols: unstable modes (η>0)

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

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

17. 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).

18. Thank you !