Testing the bloated star hypothesis in the massive young stellar object IRAS 19520+2759 through optical and infrared variability

Using optical time series with Telescopi Joan Or\'o (TJO), Gaia, TESS, and NEOWISE archival data, we performed a variability study on the candidate bloated massive young stellar object (MYSO) IRAS 19520+2759. This is the first time that a bloated star candidate has been tested for the theoretically predicted periodic variability. The source is found to be variable at optical and mid-infrared wavelengths and classified as a long-period variable MYSO. The observed TJO data gives a period of the source of $\sim$ 270$\pm$40 days (in the Rc band) and $\sim$ 270$\pm$50 days (in the Ic band), which is very close to the value predicted by the theoretical Period-Luminosity relation for a bloated young star of $\sim 10^5 L\odot$. Additionally, a large period of $\sim$ 460$\pm$80 days (in the G band) and $\sim$ 440$\pm$70 (in the Rp band) is also visible in the Gaia light curve. The physical parameters of the source, such as mass, radius, and accretion rate, based on the theoretical predictions for the spherical accretion case and corresponding to a period of 270--460 days, are $\sim 24$--28$\,M\odot$, $\sim 650$--900$\,R\odot$ and $\sim (6$--$9)\times10^{-3}\,M\odot yr^{-1}$. However, these numbers are very sensitive to the effective temperatures assumed in the models. Additionally, these values strongly depend on the geometry of accretion and could significantly decrease for the case of a MYSO accreting through a disc. The observed periodic variability, the observed colour trend, and the nature of the variability are found to be consistent with the pulsational model for a bloated MYSO.