INTRODUCTION

The Black Hole Explorer (BHEX) mission concept aims to image the sharp "photon ring" signature around black holes resulting from strongly lensed photon trajectories in extreme gravity, see Figure 1. 1 Measuring the size and shape of the photon ring would enable a direct measurement of a black hole's spin for two horizon-scale targets: M87 * and Sgr A * . BHEX will join an existing ground network of radio observatories through very long baseline interferometry (VLBI). With an extension to space, BHEX will provide unprecedented high resolution studies of active galactic nuclei (AGN) jets and a growing population of supermassive black holes in low accretion states.

The BHEX science goals hinge on building sensitivity from high recording bandwidths and optimal atmospheric conditions at the ground very-long-baseline-interferometric (VLBI) stations co-observing with the satellite. Weather considerations also need to be taken into account when developing the downlink network receiving the signal from the satellite. The high bandwidth requirements for BHEX necessitate a downlink infrastructure with optical communications, which have demonstrated higher bandwidth rates than radio-frequency methods commonly used in past space-VLBI experiments.

The operations concept for BHEX essentially involves a three-part "hybrid observatory 2 " (see Figure 2): satellite operations of the space-based component, coordinated operations of the ground-based VLBI network, and coordinated operations of the ground-based downlink terminals.

Figure 1: The BHEX Mission Concept. Black hole images display distinctive, universal features such as a sharp "photon ring" that is produced from light that has orbited the black hole before escaping. By extending the EHT into space, BHEX will be the first mission to make precise measurements of this striking, untested prediction from general relativity, enabling the first direct measurement of a supermassive black hole's spin. Reproduced from [1].

MISSION CONCEPT

BHEX is a space-based component of a space-ground interferometer with a 3.5-meter antenna at medium Earth orbit. The satellite will be equipped with a coherent dual-polarization dual-band receiver system covering 80-106 GHz and 240-320 GHz frequency ranges, see Table 1. 3,4 The receiver system will allow simultaneous dualband observations, leveraging frequency phase transfer techniques and phase stability at the lower frequency band to build sensitivity at the higher frequency band. The total downlink bandwidth from the satellite will be 64 Gb/s. 5 The BHEX orbit will be a 12-hour circular orbit at medium-earth-orbit distances (∼20000 km). This orbit is optimized to obtain circular coverage for M87 * , focused on multi-directional sampling of the n = 1 photon ring signal, while appearing elliptical toward Sgr A * , focusing on north-south detections of the n = 1 photon ring where scattering is least affecting. 6 Figure 3 shows the BHEX (u, v) coverage expected for M87 * and a diagram for the orbit.

• Exploration Mode: this portion of the satellite time will include three partner ground stations, of which two will be of 25 m or larger diameter to ensure the sensitivity requirements are met. The exploration mode targets visibility domain studies of AGN, transients, and other bright radio sources with flexible scheduling.

An additional science observing mode, the "single-dish" mode, will be available for science that does not require a ground VLBI component. This mode will still require coordination of the optical downlink, likely at lower data rates.

GROUND FACILITIES

The BHEX ground operations involve the simultaneous coordination of both VLBI radio observatories and optical downlink terminals. Suitability of individual sites depends on various factors:

• telescope location and mutual visibility with BHEX

• local weather trends (cloud cover, optical depth, atmospheric stability)

• telescope sensitivity (aperture size, design, instrumentation)

• telescope compatibility (downlink/VLBI equipment, availability)

In the following sections, we discuss the properties of various VLBI and optical stations under consideration for the BHEX ground operations.

VLBI stations

The sensitivity of continuum VLBI observations depends on the properties of both ends of a particular telescope pair. Assuming a characteristic system-equivalent flux density (SEFD) of ∼ 20, 000 Jy for BHEX at 240 GHz, an RMS thermal noise σ G-S of ∼ 5 mJy is targeted to reach the sensitivity requirement for photon ring detection. The ground-space baseline sensitivity would then be:

SEFD S 20,000 Jy

where ∆ν is the averaged bandwidth (single polarization), ∆t is the integration time, and η Q ≤ 1 is a factor that accounts for quantization of the electric field (for BHEX baselines we have η Q = 0.75).

BHEX will leverage established (sub)millimeter observatories currently observing as part of the EHT. Based on EHT observations, large sensitive apertures, such as the LMT, ALMA, and the IRAM 30-m and NOEMA telescopes, achieve SEFDs on the ground below 1000 Jy. 7,8 Observing with one or two large dishes can successfully anchor BHEX to a wider network of smaller dishes filling the coverage for high-fidelity imaging.

We performed a weather study of potential anchor stations for VLBI science using 44 years of aggregated weather data from the MERRA-2 database. We identified four potential stations that have the receiver range and sensitivity to anchor BHEX to a ground array: the LMT in Mexico, the SMA in Hawaii, the IRAM 30-m telescope in Spain, and ALMA in Chile. All four telescopes operate at the frequencies targeted by BHEX, and are positioned at some of the best (sub)millimeter sites in the world. Of those, we identified ALMA as the best observatory to anchor Sgr A * photon ring science in the June-August months, and the other three telescopes as most suitable for M87 * , see Figure 6. The SMA is able to support observations of both targets throughout the year due to the high quality of the Mauna Kea site.

Additionally, we identified the Haystack 37-m telescope and the Greenbank Telescope as potential anchors for BHEX at the secondary frequency (80-100 GHz). These large sensitive dishes are not at prime sites for higher frequency science, but we can leverage their sensitivity in the secondary receiver range to anchor BHEX to the ground and make use of frequency phase transfer techniques to build sensitivity at the higher frequencies. Both Haystack and GBT would be suitable for M87 * science in the January-March periods, see Figure 7. payload, however in order to preserve signal quality, an adaptive optics (AO) system is needed on the ground terminal. In addition, the telescope must support daytime observing to ensure complete downlink coverage and must be compatible with an 8-micron single-mode fiber to couple to the downlink receiver. Ground station sites must have a favorable weather conditions with minimal cloud coverage to maximize orbital coverage. These considerations guide the selection of ground stations most compatible with the BHEX mission's requirements.

It is ideal to partner with sites that operate exclusively for downlink to eliminate the need for modifications, and down-select within proximity to our radio telescopes for the coordination of data transfer. A number of facilities stand out while assessing possible terminals.

The optical station Low Cost Optical Terminal (LCOT) managed by NASA Goddard is specifically designed to support laser communication, offering features we seek in our terminal sites for Sgr A * detection window. The NICT ground terminals consist of four 1-2 meter telescopes to be distributed throughout different locations in Japan, ensuring at least one terminal can operate optimally under varying atmospheric conditions. 18 The Optical Ground Station-2 located in Haleakala, Hawai'i, offers optimal weather conditions, ideal for the photon ring campaigns of both targets. Despite its 0.6 meter aperture, its strategic location and design for laser communications make it an important asset for mission operations.

Additionally, there are several other optical telescope facilities that, although they were not originally designed for laser downlink, have had collaboration in other laser communication projects, therefore they could be modified to meet our requirements, see Table 2. For instance, the Lowell Observatory in Perth is equipped with a 0.6meter telescope, the ESO facility in Chile features a 2.2-meter telescope, and the Aristarchos 2.3-meter aperture telescope is located in Greece. These sites hold great potential due to their large apertures and clear skies. Many of these telescopes were also suggested because they are compatible with the observing campaign for our second target, Sgr A * . The Sgr A * campaign benefits by having a significantly wider range of location terminals specifically designed for laser communication. In order to facilitate a 12-hour circular orbit in medium-Earth orbit, we down-selected four optical terminals among multiple locations. Reaching a balanced site distribution is essential to maintain complete coverage throughout the orbit. By covering a specific percentage of the orbit, each ground terminal will shorten the downlink path and lower the transmission latency. This is essential for obtaining real-time observations. A set of simulations were conducted to generate (u, v) coverage expected for photon ring target observations, to show a representation of the predicted coverage pattern of the data downlink from BHEX. We take into account the elevation for each terminal and a 15-degree telescope tilt cut-off. In this setting, the selected stations covering a full 24-hour downlink were in La Silla, Chile, Perth, Australia, Haleakala, Hawaii, and Achaea, Greece. The orbit coverage of each terminal is shown in Figure 8. For both M87 * and Sgr A * , a subset of downlink terminal sites were determined, most of which track the satellite during the local night, see Figure 9. The ESO telescope in Chile demonstrated the most extensive coverage, as shown by the (u, v) plots in Figure 10. The terminal