Forecast of gravitationally lensed Type Ia supernovae time delay measurement by Muztage-Ata 1.93 m Synergy Telescope

Strong lensing time delay measurement is a promising method to address the Hubble tension, offering a completely independent approach compared with both the cosmic microwave background analysis and the local distance ladder. As a third-party examination of the Hubble tension, this method provides a unique perspective. Strongly lensed quasar (glQSO) systems have demonstrated significant potential in tackling this issue, achieving an impressive 2% accuracy level. However, advancing to 1% or sub-percent accuracy is challenging due to several intrinsic limitations of glQSOs. Fortunately, strongly lensed supernovae (glSNe) offer a more robust solution, thanks to their characteristic light curve, significant brightness variations, and additional advantages. The Muztagh-Ata 1.93 m Synergy Telescope (MOST) is an exceptional instrument for monitoring strong lensing time delays. In this study, we simulate the follow-up multi-band light curve monitoring for glSNe Ia systems, which are expected to be firstly discovered by the Chinese Survey Space Telescope (CSST). The simulation employs the W7 model, integrating strong lensing and microlensing effects. Our results show that with 300 s × 9 exposures in each epoch, 2 quadruple-image systems and 14 double-image systems are observable by MOST each year. MOST can achieve a signal-to-noise ratio (SNR) of approximately 50 for the brightest images of glSNe Ia, while even the faintest images maintain an SNR of at least 7. Using a standard SNe Ia light curve template for fitting, we measured the time delays. With a 2-d cadence, MOST achieves a relative time delay error of less than 4.9%, with the bias typically remaining below 0.57%. Finally, we performed a Hubble parameter estimation. For a typical glSNe Ia system, the H₀ error is about ±1.8 kms⁻¹ Mpc⁻¹. This result is comparable or even better than those from LSST. This study highlights the capability of MOST to significantly advance the precision of time delay measurements, offering a promising path toward resolving the Hubble tension.