The origin of R CrA variability: A complex triple system hosting a disk

R~CrA is the brightest member of the Coronet star forming region and it is the closest Herbig AeBe star with a spectrum dominated by emission lines. Its luminosity has been monitored since the end of the 19th century, but the origin of its variability, which shows a stable period of $65.767\pm 0.007$~days, is still unknown. We studied photometric and spectroscopic data for this star to investigate the nature of the variability of R~CrA. We exploited the fact that near infrared luminosity of the Herbig AeBe stars is roughly proportional to the total luminosity of the stars to derive the absorption, and then mass and age of R~CrA. In addition, we model the periodic modulation of the light curve as due to partial attenuation of a central binary by a circumbinary disk. This model reproduces very well the observations. We found that the central object in R~CrA is a very young ($1.5\pm 1.5$~Myr), highly absorbed ($A_V=5.47\pm 0.4$~mag) binary; we obtain masses of $M_A=3.02\pm 0.43$~M$_\odot$ and $M_B=2.32\pm 0.35$~M$_\odot$ for the two components. We propose that the secular decrease of the R~CrA apparent luminosity is due to a progressive increase of the disk absorption. This might be related to precession of a slightly inclined disk caused by the recently discovered M-dwarf companion. Thus, R~CrA may be a triple system hosting a disk.