Pulsations, eruptions, and evolution of four yellow hypergiants

We aim to explore the variable photometric and stellar properties of four yellow hypergiants (YHGs), HR8752, HR 5171A, $\rho$ Cas, and HD 179821, and their pulsations of hundreds of days, and long-term variations (LTVs) of years. We tackled multi-colour and visual photometric data sets, looked for photometric indications betraying eruptions or enhanced mass-loss episodes, calculated stellar properties mainly using a published temperature calibration, and investigated the nature of LTVs and their influence on quasi-periods and stellar properties. The $BV$ photometry revealed a high-opacity layer in the atmospheres. When the temperature rises the mass loss increases as well, consequently, as the density of the high-opacity layer. As a result, the absorption in $B$ and $V$ grow. The absorption in $B$, presumably of the order of one to a few 0\fm1, is always higher than in $V$. This difference renders redder and variable $(B-V)$ colour indexes, but the absorption law is unknown. This property of YHGs is unpredictable and explains why spectroscopic temperatures are always higher than photometric ones. We propose shorter distances for $\rho$ Cas and HR 5171A than the accepted ones. Therefore, a correction to decrease the blue luminescence of HR 5171A by polycyclic aromatic hydrocarbon (PAH) molecules is necessary, and HR 5171A would no longer be a member of the cluster Gum48d. HR 5171A is only subject to one source of light variation, not by two as the literature suggests. Eruptive episodes of YHGs prefer relatively cool circumstances when a red evolutionary loop (RL) has shifted the star to the red on the HR diagram. After the eruption, a blue loop evolution (BL) is triggered lasting one to a few decades. The reddening episode of HR 5171A between 1960 and 1974 was most likely due to a red loop evolution, and the reddening after the 1975 eruption was likely due to a shell ejection.