Frequency Standard Contributions to Limitations on the Signal-to-Noise Ratio in Very Long Baseline Interferometric (VLBI) Observations

Abstract

Since its observation in 2019, the first image of a super-massive black hole using Very Long Baseline Interferometry (VLBI) with an Earth-scale baseline has generated much scientific and public interest, including the possible extension of the baseline into space to obtain higher image resolution. Operating one or more VLBI nodes in space will require the use of frequency standards that are space qualified, greatly reducing the number of options available. The coherence function C(T) is the metric usually used to determine the viability of a frequency standard. Here we show that C(T) is a useful but not sufficient metric for gauging frequency standard performance in VLBI and instead derive an expression for the clock-limited VLBI visibility S/N. We evaluate this expression for real frequency standards and find only the Ultra-Stable Oscillator (USO) and hydrogen maser to be viable for upcoming high-frequency VLBI with the USO only useful for very limited integration times (30s at 90 GHz, 10s at 230 GHz, 5s at 345 GHz, and not viable at 630 GHz). The maser extends these, but may have prohivitive size for a space mission. We also evaluate emerging frequency standard technologies and find the Optical Local Oscillator portion of optical clocks to be very promising (conservatively >100s at 90 GHz, 60s at 230 GHz, 40s at 345 GHz, and 22s at 630 GHz) when accounting for both performance and potential operation in space.