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. 2003 Belkacem et al. 2008 … • 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. 2004 a,b) • The lower part and the red-side of HRD: convection! Eggen 1977 MACHO: Pulsating AGBs Wood 2000 OGLE: OSARGs & Mira Soszynski et al. 2004 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=0.6-3.0M; o Linear non-adiabatic modes: radial P0-P39; nonradial l=1-4, P0-P39 and for the Sun l=1-25, G4P39 are calculated; 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. 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-P5 Stability analysis for P16-P25 Calculations are made for models selected along the track of a 1 solar mass star Solid symbols: stable modes (η<0); Open symbols: unstable modes (η>0) Amplitude Growth Rate (AGR) η=-2πωi/ωr ω=ωr+iωi 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 !