Two first-order phase transitions in hybrid compact stars: Higher-order multiplet stars, reaction modes, and intermediate conversion speeds

We study compact stars with hybrid equations of state consisting a nuclear outer region and two nested quark phases, each separated from the lower density phase by strong first-order transition. The stability these models is determined calculating their radial oscillation modes different conversion rates between adjacent phases hence junction conditions for at separation interface them. In case when timescale transition faster than period oscillations, we recover traditional criterion implying that $\ensuremath{\partial}M/\ensuremath{\partial}{\ensuremath{\rho}}_{c}>0$ on stable branch(es), where $M$ mass ${\ensuremath{\rho}}_{c}$ central density. opposite limit slow conversion, find stellar multiplets beyond triplets are usual plus slow-conversion (denoted $s$) $\ensuremath{\partial}M/\ensuremath{\partial}{\ensuremath{\rho}}_{c}<0$ stabilized due to an alternative condition fluid displacement field reflecting rate conversion. also properties reaction mode, mode only exists rapid (abbreviated $r$) transitions, in either transitions or alternating first time. implications examined, generally being found provide similar those rate.