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However, when we first observed this field with MMT, we found no obvious host galaxy, down to a magnitude of about 26 mag. Our curiosity drove us to obtain a much deeper image: a 3-hr integration with the 10-m GTC telescope on La Palma, which reached a limiting magnitude of roughly 28 mag. This is pretty much the deepest optical image that can currently be obtained from the surface of the Earth!
The ultra-deep optical image revealed a faint source, exactly at the radio-derived position of FRB 20190208A. Based on the dispersion measure (DM) of the bursts, we estimate that the redshift range of the source is about z = 0.1 - 0.8, depending on how much DM is contained in the host galaxy. This means that FRB 20190208A's host galaxy is at least a factor of a few less luminous than all other known FRB hosts, and potentially even >10x less luminous.
What is an FRB doing in such a puny dwarf galaxy? It's possible that the low-metallicity that is typically associated with dwarf galaxies is the reason: low-metallicity environments allow for the formation of exceptionally massive stars, which may create extremely magnetised and rapidly spinning neutron stars when they go supernova. This possibility is also supported by a couple other repeating FRBs that are known to be hosted in dwarf galaxies, and which are associated with persistent radio emission that may indicate a hyper-luminous nebula surrounding the burst engine. To better establish the properties of the host galaxy, we're going to need the power of JWST, and we've applied for follow-up observations to do so.