where is the luminosity distance and the Hubble flow velocity. The direct measurement of the Hubble constant, , is one the biggest questions in contemporary cosmology. As measurements have become more precise, a significant uncertainty in the measurement have emerged due to the discrepancy of the value from late and early universe measurements. The cosmic microwave background gives us an estimate of from the early universe which is in tension with late time measurements such as the standard candle Type Ia supernovae. Events producing gravitational waves (GWs) detectable by LIGO/Virgo have been proposed as promising independent measurements of . This is often called using GWs as ”standard sirens” and utilizes the fact that the GW amplitude strain, , is dependent on the luminosity distance . Furthermore, for GW binaries one measures an effective mass known as the chirp mass, , compromised of the two compact objects masses. Both the GW amplitude strain, , and the rate of change of the GW frequency, , are dependent on the chirp mass. Thus, the measurement of and provide an absolute measurement of .
The next puzzle piece is the redshift which can be obtained either from the electromagnetic (EM) counterpart and its host galaxy, so called ”bright sirens”, or from a statistical analysis of galaxy clustering, ”dark sirens”. is then obtained from Eq. (1) by the independent measurements of and . The benefit of the above procedure is that the value of is obtained without relying on the cosmic distance ladder or a specific cosmological model. The main uncertainty in measuring from GWs lies in the difficulty of constraining the inclination angle of the binary. The constraints on can be improved by taking advantage of the viewing-angle, , dependence on the EM signals. The authors of today’s paper review the current constraints on using gamma-ray-bursts (GRBs) and kilonova (KN) observables from the GW170817 event and comment on the ability and future of this technique to solve the Hubble tension.
Inclination constraints of GRBs
Gamma ray bursts launch relativistic jets from the compact object formed after a black hole-neutron star (BH-NS) or binary neutron star (BNS) merger. The interaction of the jet with the surrounding environment produces an ”afterglow” consisting of synchrotron radiation of the accelerated electrons from the shocked medium in the X-ray and radio wavelengths. For a certain value of the jet angle , the constraint on is improved by a factor of two from the GW-only analysis. Furthermore, a jet moving close to the speed of light may appear to move with superluminal speed i.e. ”chasing” the emitted radiation along the line-of-sight of the observer. Therefore, a measurement of the apparent velocity can constrain the − hence improving the constraint on . The superluminal motion of the jet associated with GW170817 in combination with the radio light-curves lead to an improvement of the degeneracy between and .
Inclination constraints from the kilonova
The kilonova event associated with BNS and BH-NS mergers is a thermal emission powered by the r-process in the neutron rich outflow of the merger. Because the outflows consists of different components with a variety of compositions and geometries the KN has a viewing angle dependence. This fact has been exploited in the case of GW170817 to put constraints on the inclination angle and thereby an improvement on the . One of the first analyses of this type is summarized by the pink curve in Figure 1 which lead to a 34% improvement on the uncertainties on compared to only GW data. In contrast, a more recent study reduced the errors in even further by the use of spectroscopy, which lead to an 54% improvement on the uncertainties on showcased by the orange curve in Fig. 1.
Figure 1: Constraints on from the BNS merger GW170817 using GW and EM data. The figure shows the marginalized 1D posterior density distributions for with the inferred values labeled in the legend. Color scheme: Constraints from the GRB170817A with (cyan) or without (light green, red) including jet superluminal motion. Constraints from the KN AT 2017gfo from model fitting with broad-band photometry (pink) and spectroscopy (orange). The black curve correspond to the inferred value from the original standard siren approach. The inferred value from Planck and SHOES are shown with the 1 interval in brown and green respectively. Figure 2 in the paper.
Summary and outlook
Gravitational wave events are promising standard sirens for measurements. In order to reach a ∼1% precision on one would need about 50 − 200 GW events with an EM counterpart. Today’s paper has shown the constraints may be improved sooner and with fewer events if one improves the constraint on the viewing angle using the GRB afterglow, superluminal motion and KN. Doing so would significantly reduce the degeneracy between the distance and inclination angle of the GW data and improve the accuracy of the inferred value.
Even so, in order to have sufficient accuracy on the inferred values from GW and EM events one still requires the systematics from the standard siren approach and the GRB/KN modeling to be under control. The systematic errors that may contribute include calibration errors that may affect the inferred value of . Further systematic uncertainties may arise from the models used to fit the GRB and KN data which may introduce a bias on the value.
In conclusion, the coming decade will provide an increase in GW detectors and sensitivity. This will enable us to provide an understanding of the systematic uncertainties and showcase the potential of the standard siren approach. The combined effort of the multi-messenger community will have the potential to provide precise and accurate values of the Hubble constant.
interval in brown and green respectively. Figure 2 in the paper.
