Period distributions in pulsating and binary stars |
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Authors: | R J Quiroga J C Mello |
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Institution: | (1) Departmento de Fisica Universidade Federal de Minas Gerais, Belo Horizonte, Brazil |
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Abstract: | We analyze the hypothesis of quantization in bands for the angular momenta of binary systems and for the maount of actionA
c in stable and pulsating stars. This parameter isA
c=Mv
eff
R
eff, where the effective velocity corresponds to the kinetic energy in the stellar interior and the effective radius corresponds to the potential energyGM
2/R
eff. Analogous parameters can be defined for a pulsating star withm=M where is the rate of the massm participating in the oscillation to the total massM andv
osc,R
osc the effective velocity and oscillation radius.From an elementary dimensional analysis one has thetA
c (energy x time) (period)1/3 independently ifA
c corresponds to the angular momentum in a binary system, or to the oscillation in a pulsating star or the inner energy and its time-scaleP
eff in a stable star.From evolving stellar models one has that P
effP
eff(solar)1.22 hr a near-invariant for the Main Sequence and for the range of masses 0.6M
<M<1.6M
.With this one can give scalesn
k=kn
1 withk integers andn
1=(P/P
1)1/3 withP
1=P
eff1.22 hr. In these scales proportional toA
c, one sees that the periods in binary and pulsating stars are clustered in discrete unitsn
1,n
2,n
3, etc.This can be seen in pulsating Scuti, Cephei, RR Lyrae, W Virginis, Cephei, semi-regular variables, and Miras and in binary stars as cataclysmic binaries, W Ursa Majoris, Algols, and Lyrae with the corresponding subgroups in all these materials. Phase functions (n
k) in RR Lyrae and Cephei are also associated with discrete levelsn
k.the suggested scenario is that the potential energies and the amounts of actionE
p(t), Ac(t) are indeed time-dependent, but the stars remain more time in determinated most proble states. The Main Sequence itself is an example of this. These most probable states in binary systems, or pulsating or stable stars, must be associated with velocities sub-multiplesc/
F
, given by the velocity of light and the fine structure constant.Additional tests for such a hypothesis are suggested when the sufficient amount of observational data are available. They can made with oscillation velocities in pulsating stars and velocity differences of pairs of galaxies. |
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Keywords: | |
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