*7.2. Performance Predictions*

Generally, the coming decade looks promising. In the ∼10–1000 keV energy range a number of new detailed measurements are foreseen, which should be capable of resolving the current differences in PD reported by different groups. This is illustrated in Figure 18, which shows the yearly number of measurements capable of excluding a non-polarized flux as a function of the true polarization degree of GRBs for three different instruments, GAP, POLAR, and POLAR-2. For this figure, the instrument response of POLAR, as used in the POLAR analysis, was used as well as that for POLAR-2 in combination with the Fermi-GBM GRB catalog. For GAP, for which the response is not available, the numbers were produced by scaling the POLAR numbers based on the performance of GAP and

POLAR for respectively detected GRBs, again in combination with the Fermi-GBM GRB catalog. It should be noted that for GAP, for which the detailed response is not known, a fixed *M*<sup>100</sup> was used, which, given its design, should be close to the truth.

**Figure 18.** The rate of measurements capable of excluding a non-polarized flux, for different confidence levels, as a function of the true polarization degree (PD) of GRBs for three different instruments, GAP, POLAR, and POLAR-2. Although exact numbers are not available it can be assumed that LEAP will be capable of similar rates as POLAR-2, albeit slightly lower.

It can be seen that with GAP excluding a non-polarized flux was possible for a handful of GRBs per year only in cases where the true PD of the emission is relatively high. For POLAR, the situation improves and, as was the case, with less than a year of data it was able to claim exclusion of polarization levels above ≈50%. It could not, however, effectively probe polarization levels below 30% with a high confidence. With POLAR-2, this region will be probed within a few months, while with 1 year of data it will be capable of determining whether GRB emission is polarized to levels as low as 10%. To illustrate the type of GRBs that can be probed with the different instruments, Figure 19 shows the mean MDP for the three different instruments as a function of the GRB fluence for both short (1 s observed duration) and long (100 s observed duration) GRBs. As an illustration, the fluence of the short and very weak GRB 170817A as well as the long and very bright GRB 190114C are added. It should be noted that the energy ranges used for the different instruments differs, and the energy range of 50–300 keV was used for GAP, 50–500 keV for POLAR and 20–500 keV for POLAR-2. Although no detailed response is available, the performance of LEAP is foreseen to be similar to that of POLAR-2 with a typical effective area ∼30% smaller than that of POLAR-2. A launch of LEAP would therefore further improve the situation, not only regarding the statistics but more importantly regarding the systematics. As for Daksha, not enough details on the instrument are available to make any clear predictions, while the SPHiNX performance would be similar to that of POLAR.

It is evident that the next generation of polarimeters will be capable of almost probing GRBs with fluences as weak as GRB 170817A, a GRB which was hard to even detect with both Fermi-GBM and INTEGRAL-SPI but was important due to its association with a gravitational wave signal [12]. Additionally, for very bright GRBs such as 190114C, which was observed at TeV energies [280,318], highly detailed polarization measurements will become possible, indicating that fine time or energy binning will become an available tool to study such GRBs. It should again be stressed that the mean MDP is simply a figure of merit and that the estimates given here are not exact, as the details will depend not only on the fluence and length of the GRBs but also on its energy spectrum, incoming angle, and position of the polarimeter along its orbit. Additionally, systematic errors, which can be significant, are not taken into account in an MDP calculation. The predictions should therefore be taken only to give an indication of the advancement in the field as well as the possibilities during the coming decade.

**Figure 19.** The mean minimal detectable polarization for 99% confidence level (MDP averaged over PA) as a function of the fluence in the 10–1000 keV energy band for GAP, POLAR, and POLAR-2 for both short (1 s observed duration) and long (100 s observed duration) GRBs. Short GRBs with a fluence above 10−<sup>6</sup> erg/cm<sup>2</sup> occur at a rate of approximately 10 per year on the full sky, whereas, for long GRBs, the rate is about 200 per year. For POLAR-2, the MDP for 5*σ* confidence is added as well, using a dotted line. The fluences of two well-known GRBs, the weak and short 170817A and the long and bright 190114C, were added as an illustration.

Apart from an improvement in the Compton scattering regime, the first polarization measurements of the prompt emission at MeV energies can be expected towards the end of this decade. There still remains an additional need for energy-dependent polarization measurements. Whereas the eXTP instrument can probe the polarization at keV energies, it is unlikely to detect the prompt emission due to its narrow field of view. An instrument such as the LPD would, especially when placed closed to POLAR-2, allow to provide an energy range of 2–800 keV for many GRBs per year. This would allow to study a potential change in PD in the 10–50 keV energy range, as proposed in some photospheric emission models [232]. In addition, if either COSI or AMEGO will be launched, detailed energyresolved studies will become possible for bright GRBs in the 2 keV to 5 MeV energy range, thereby fully probing the prompt emission over several orders of magnitude in energy.
