On the excitation mechanism ofSolar 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) 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)

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!

OGLE: OSARGs & Mira Soszynski et al. 2004

MACHO: Pulsating AGBsWood 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=0.6-3.0M;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 < 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

Solid symbols: stable modes (η<0);Open symbols: unstable modes (η>0)

Calculations are made formodels selected along thetrack of a 1 solar mass star

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 !