Here we present a new method of simultaneously reconstructing interferometric images at multiple frequencies along with their spectral index maps. In addition, combining information from data obtained at multiple frequencies is a powerful tool for interferometric image reconstruction, since gaps in spatial scales in single-frequency observations can be filled in with information from other frequencies. Resolved spectral index maps in the near-horizon and jet-launching regions of these supermassive black hole sources can constrain properties of the emitting plasma that are degenerate in single-frequency images. At these frequencies, both Sgr A* and M87* transition from optically thin to optically thick. Observations with the next-generation Event Horizon Telescope (ngEHT) will have significantly improved Fourier plane coverage and will be conducted at multiple frequency bands (86, 230, and 345 GHz), each with a wide bandwidth. The Event Horizon Telescope (EHT) has produced images of the plasma flow around the supermassive black holes in Sgr A* and M87* with a resolution comparable to the projected size of their event horizons. LST and AtLAST will be a key element enabling transformative science cases with next-generation millimeter/submillimeter VLBI arrays. In addition to ngEHT, its unique location in Chile will substantially improve angular resolutions of the planned Next Generation Very Large Array in North America or any future global millimeter VLBI arrays if combined. A large aperture of 50 m that is co-located with two existing EHT stations, the Atacama Large Millimeter/Submillimeter Array (ALMA) and the Atacama Pathfinder Experiment (APEX) Telescope in the excellent observing site of the Chajnantor Plateau, will offer excellent capabilities for highly sensitive, multi-frequency, and time-agile millimeter very long baseline interferometry (VLBI) observations with accurate data calibration relevant to key science cases of ngEHT. Both are designed to have a 50-meter diameter and operate at the planned ngEHT frequency bands of 86, 230 and 345 GHz. Here, we introduce two projects for planned next generation large radio telescopes in the 2030s on the Chajnantor Plateau in the Atacama desert in northern Chile, the Large Submillimeter Telescope (LST) and the Atacama Large Aperture Submillimeter Telescope (AtLAST). A key technical component of ngEHT is the utilization of large aperture telescopes to anchor the entire array, allowing the connection of less sensitive stations through highly sensitive fringe detections to form a dense network across the planet. The proposed next generation Event Horizon Telescope (ngEHT) concept envisions the imaging of various astronomical sources on scales of microarcseconds in unprecedented detail with at least two orders of magnitude improvement in the image dynamic ranges by extending the Event Horizon Telescope (EHT). We test and characterize the performance of an improved LMT joining future ngEHT observations through simulated observations of Sgr A* and M 87. These include the commissioning of a simultaneous 230 + 345 GHz dual-frequency, dual-polarization heterodyne receiver, improved real-time surface measurement and setting, and improvements to thermal stability, which should enable expanded daytime operation. In this work, we detail current and planned future upgrades to the LMT that will directly impact its Very Large Baseline Interferometry (VLBI) performance for the EHT and ngEHT. The Large Millimeter Telescope (LMT) is the largest sub-mm single dish telescope in the world at 50 m in diameter, and both its sensitivity and central location within the EHT array make it a key anchor station for the other telescopes. The next-generation Event Horizon Telescope (ngEHT) is a project that plans to double the number of telescopes in the VLBI array and extend observations to dual-frequency 230 + 345 GHz, improving total and snapshot coverage, as well as observational agility. These tantalizing early results motivate an expansion of the array, its instrumental capabilities, and dedicated long-term observations to resolve and track faint dynamical features in the black hole jet and accretion flow. The landmark black hole images recently taken by the Event Horizon Telescope (EHT) have allowed the detailed study of the immediate surroundings of supermassive black holes (SMBHs) via direct imaging.
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