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