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A Second Kelvin-Helmholtz Timescale of Post Helium-Flash Evolution

I show that after the "helium flash" abruptly ends its first ascent red giant evolution, a solar-type star is powered primarily by gravitational contraction of its helium core, rather than by nuclear fusion. Because this energy is released in the core rather than the envelope, the overall structure of the star, and so its luminosity, is driven toward that of a red clump star from its initial position at the tip of the red giant branch (TRGB). This occurs on a first (and well recognized) Kelvin-Helmholtz timescale t_{KH,1} ~ E_env/L_TRGB ~ 1e4 yrs., where E_env is the thermal energy stored in the envelope and L_TRGB is the luminosity at the TRGB. However, once the star assumes the approximate structure of a clump star, it remains powered primarily by contraction for a {\it second} Kelvin-Helmholtz timescale t_{KH,2} ~ E_core/L_clump ~ 1e6 yrs, where E_core is the thermal energy stored in the core and L_clump is the luminosity of a clump star. It is this second Kelvin-Helmholtz timescale that determines the overall pace of the moderately violent processes by which the star returns to nuclear-power generation as a full-fledged clump star. The reservoir of gravitational energy acts as ultimate regulator, providing whatever supplemental energy is needed to power L_clump and occasionally absorbing the large momentary excesses from helium mini-flashes. As this reservoir is gradually exhausted, helium fusion approaches the level of steady-state clump stars.