Abstract

Brightness distribution of variable stars was investigated based on good Hipparcos parallaxes of semiregular variables (SRVs) in the solar neighborhood, and it is shown that the order of the variability types Lb, SR, SRb, SRa, and Mira is, statistically, an order of increasing brightness along the red giant branch and asymptotic giant branch. In addition, it is also shown that the majority of Miras are above and majority of SRVs are below the tip of the red giant branch. The periods of SRVs that fall in Wood's sequence C (fundamental mode) of large Magellanic clouds were identified. Statistically, the order of SR, SRb, and Mira variables with increasing period and increasing absolute magnitude is the same in six infrared (IR) band wavelengths. The slope of the P-L relation for SR $+$ SRb variables in sequence C increases systematically with wavelength in the near IR. This indicates that circumstellar IR emission increases with increasing period from the shorter period SRVs to Miras, which is consistent with the high mass loss rate found in long period Miras. (J-K)-M$_{K}$ diagram suggests that the sequence Lb, SR, SRb, SRab (emission), and Mira may be an evolutionary sequence.

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