**2. Multi-Messenger Astrophysics with Gamma-ray Bursts**

In 2015 the advanced GW interferometers LIGO and Virgo [6,7] have detected gravitational waves for the first time [8,9]. Nowadays, the GW transient source catalogs published by the LIGO/Virgo collaboration counts several dozens of GW source candidates [10,11], all identified as compact binary coalescences. Among these sources, two are consistent with being BNSs and one has been associated with a short GRB (GRB170817A) [2,3]. In contrast, no neutrino counterpart has been found associated with any bright GRBs, putting stringent constraints on neutrino production in relativistic jets associated with these events [12]. The nearby class of long GRBs with low-luminosity (LL-GRBs) as well as ultra-long duration have been suggested as more promising candidates with respect to the bright GRBs (see e.g., [13] and references therein). The key feature of THESEUS is to independently detect these electromagnetic counterparts at the time of neutrino events and to provide refined sky localizations to allow multi-wavelength prolonged follow-up with other facilities.

#### *2.1. GRB 170817*

The first multi-messenger observations of a GRB happened on 17 August 2017 when a short GRB (GRB170817A) was detected with *Fermi* [14] and *INTEGRAL* [15].

The sky position and burst trigger time resulted to be consistent with an independent detection of GW event (GW 170817) achieved with the advanced LIGO and Virgo network [3,16]. The observed gravitational waveform of GW 170817 was consistent with the one expected from a BNS. The association with GRB 170817A has a gaussian-equivalent significance of 5.3*σ* [3] and marks the first direct evidence of short GRB progenitor. This breakthrough result confirmed a wealth of indirect evidence gathered in almost 20 years of short GRB observations, for instance the lack of any association with core-collapse supernova (contrary to long GRBs) yet plausible evidence for kilonova emission in some cases the mixed-type nature of the host galaxies (early and late) and the GRB sites within the host galaxy (see e.g., [17] and references therein).

Another milestone reached with GRB 170817A was the first direct evidence of a narrow, relativistic expanding jet. Indeed, from both the prompt and afterglow emission properties, it was realized that this burst was observed with a non-null viewing angle with respect to the jet axis. This allowed imaging and monitoring in time of the orthogonal component of the jet with the superb spatial accuracy of the VLBI and the results were consistent with a

compact source moving at relativistic velocities [18]. This result in turn confirms that BNSs can produce ultra-relativistic jets.

A major advance was also achieved due to the fact that the gravitational waveform of compact binary coalescences encodes not only information on the masses, but also on the luminosity distance *DL*. Indeed, by combining the measured *D<sup>L</sup>* for GW170817 with the redshift measurement of the host galaxy NGC 4993, identified through the electromagnetic counterpart follow-up [2], it was possible to estimate the Universal expansion rate through the Hubble constant (*H*0) measurement [4]. Despite the large uncertainties obtained with this single measure, this result showed the feasibility of a new, independent method to measure *H*0, with strong implications for the current tension plaguing the outcomes from different probes used to measure this fundamental parameter (see [4] and references therein).
