We have identified a first group of 33 new candidates for symbiotic stars (SySt) of the accreting-only variety among the 600,255 stars so far observed by the GALAH high-resolution spectroscopic survey of the Southern Hemisphere, more than doubling the number of those previously known. GALAH aims to high latitudes and this offers the possibility to sound the Galaxy for new SySt away from the usual Plane and Bulge hunting regions. In this paper we focus on SySt of the M spectral type, showing an Halpha emission with a peak in excess of 0.5 above the adjacent continuum level, and not affected by coherent radial pulsations. These constraints will be relaxed in future studies. The 33 new candidate SySt were subjected to a vast array of follow-up confirmatory observations (X-ray/UV observations with the Swift satellite, search for optical flickering, presence of a near-UV upturn in ground-based photometric and spectroscopic data, radial velocity changes suggestive of orbital motion, variability of the emission line profiles). According to Gaia eDR3 parallaxes, the new SySt are located at the tip of the Giant Branch, sharing the same distribution in M(Ks) of the well established SySt. The accretion luminosities of the new SySt are in the range 1-10 Lsun, corresponding to mass-accretion rates of 0.1-1x10(-9) Msun/yr for WDs of 1 Msun. The M giant of one of the new SySt presents a large Lithium over-abundance.
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