Evidence for a giant companion orbiting Tabby's star
KIC 8462852, also known as Tabby's star, shows deep, irregular flux variations up to 20 per cent in its Kepler light curve. These unusual events show no apparent periodicity. Multi-wavelength observations show the dips are consistent with transiting dust, although its origin remains uncertain. The leading explanation is that dust may originate from a family of exocomets or planetesimal fragments. TESS data reveal a unique, symmetric transit event consistent with a planet or brown dwarf. This would support the theory that incoming exocometary bodies may result from orbital perturbations by a planet. The analysis of the TESS and, archival and newly obtained radial velocity (RV) data, suggests that a companion could orbit around Tabby's star with a period of at least ~1030 d. When combined with the constraints imposed by Kepler and other photometric surveys, we find only five orbital period windows are possible. We conduct observations to follow-up the first two windows, significantly reducing the allowed ranges. Fitting the TESS transit using exocometary models produces a poor fit or the need of physically unrealistic parameters, favouring the giant companion hypothesis. A 2.3 $\sigma$ detection of $M=9.4^{+4.9}_{-4.1}$ M$_{\mathrm{Jup}}$ (3$\sigma$ upper limit < 28.0 M$_{\mathrm{Jup}}$) at the transit orbital period provides tentative evidence of the companion, but more RV observations are required. Along with the radius $R=1.7\pm0.1$ R$_{\mathrm{Jup}}$, the companion would lie in the giant planet-brown dwarf regime. In the future Gaia DR4 astrometry will reveal the nature of this object.