Mitigating the Counterpart Selection Effect for Standard Sirens

The disagreement in the Hubble constant measured by different cosmological probes highlights the need for a better understanding of the observations or new physics. The standard siren method, a novel approach using gravitational-wave observations to determine the distance to binary mergers, has great potential to provide an independent measurement of the Hubble constant and shed light on the tension in the next few years. To realize this goal, we must thoroughly understand the sources of potential systematic bias of standard sirens. Among the known sources of systematic uncertainties, selection effects originating from electromagnetic counterpart observations of gravitational-wave sources may dominate the measurements with percent-level bias and no method to mitigate this effect is currently established. In this Letter, we develop a new formalism to mitigate the counterpart selection effect. We show that our formalism can reduce the systematic uncertainty of standard siren Hubble constant measurement to less than the statistical uncertainty with a simulated population of 200 observations ($\lesssim 1\%$) for a realistic electromagnetic emission model. We conclude with how to apply our formalism to different electromagnetic emissions and observing scenarios.

Figure 1

Maximum observable luminosity distance as a function of the binary inclination angle for the two kilonova models and different telescope configurations (listed in Table 1) we consider. The gray crosses mark the inclination angle and luminosity distance of our simulated BNS detections. We also give an example of the function [Eq. (4)] we used to parametrize the shape of curves in this figure (cyan line, ${\beta }_1=450$, ${\beta }_2=100$ in this example).

Figure 2

The median and symmetric 68% credible interval for $H_0$ inferred using 200 simulated BNS detections. The horizontal axis labels the telescope configurations (cf. Table 1) and kilonova models (cf. Fig. 1). Selection effect (orange). When $H_0$ inference ignores the presence of counterpart selection effect. Mitigation (green). $H_0$ inference using the formalism we present in Eq. (2). For comparison, we also show the $H_0$ inferred when all counterparts are captured and there is no counterpart selection effect (blue). The horizontal dashed line denotes the $H_0$ we picked for the simulations.