Physical Implications of the Sub-threshold GRB GBM-190816 and its Associated Sub-threshold Gravitational Wave Event

The LIGO-Virgo and Fermi collaborations recently reported a possible joint detection of a sub-threshold gravitational wave (GW) event and a sub-threshold gamma-ray burst (GRB), GBM-190816, that occurred 1.57 s after the merger. We perform an independent analysis of the publicly available data and investigate the physical implications of this potential association. By carefully studying the following properties of GBM-190816 using Fermi/GBM data, including signal-to-noise ratio, duration, f-parameter, spectral properties, energetic properties, and its compliance with some GRB statistical correlations, we confirm that this event is likely a typical short GRB. Assuming its association with the sub-threshold GW event, the inferred luminosity is $1.47_{-1.04}^{+3.40} \times 10^{49}$ erg s$^{-1}$. Based on the available information of the sub-threshold GW event, we infer the mass ratio q of the compact binary as $q=2.26_{-1.43}^{+2.75}$ according to the reported range of luminosity distance. If the heavier compact object has a mass > 3 solar masses, q can be further constrained to $q=2.26_{-0.12}^{+2.75}$. The leading physical scenario invokes an NS-BH merger system with the NS tidally disrupted. Within this scenario, we constrain the physical properties of such a system to produce a GRB. The GW data may also allow an NS-BH system with no tidal disruption of the NS or a BH-BH merger. We apply the charged compact binary coalescence (cCBC) theory (for both a constant charge and an increasing charge for the merging members) to derive the model parameters to account for GBM-190816 and found that the required parameters are extreme. Finally, we argue that the fact that the observed GW-GRB delay time scale is comparable to that of GW170817/GRB 170817A suggests that the GW-GRB time delay of these two cases is mainly defined by the time scale for the jet to propagate to the GRB emission site.