Prospects for submillimeter VLBI of black hole photon rings with a stratospheric balloon-borne telescope

Introduction

Balloon-borne telescopes operate at float altitudes of 35–40 km, above more than 99.5% of the Earth’s atmosphere, and can therefore observe at submillimeter and far-infrared wavelengths. Such telescopes could serve as mobile outrigger stations for ground-VLBI arrays, giving higher angular resolution by permitting observations at frequencies that are not accessible from most ground sites [39] (Figure 1). Two pathfinder experiments are attempting to demonstrate that balloon telescopes can be used as VLBI stations. The BVEX (the Balloon-borne VLBI Experiment) is a 0.9 m telescope at 22 GHz, with the first balloon-to-ground fringe detection as its primary goal. It flies on a Centre National d’Études Spatiales (CNES) gondola launched through the Canadian Space Agency (CSA) STRATOS program. The first BVEX flight launched from Timmins, Ontario, in 2025 August, but was unable to take VLBI data because damage to the launch balloon meant that the experiment could not ascend to an altitude where the telescope could be pointed [3, 46]. Another balloon VLBI effort is the 20 GHz system of A. Doi et al. [14], which JAXA flew as a technology test to a 26 km float on 2026 June 14 ([26]).

A black hole surrounded by optically thin emission produces a stack of lensed sub-images, the direct $n=0 image and a series of thinner photon rings with $n \ge1$ [32]. Two measurements of the $n=1$ ring are within reach of ground arrays that include a balloon. The first is its diameter, which tracks the mass-to-distance ratio with only a weak dependence on the emitting plasma [32]. The Event Horizon Telescope (EHT) images of M87* and Sgr A* [15, 18] are dominated by the direct emission, which blends with the ring at 230 GHz resolution [32]. The second measurement needs no image, because beyond a transition baseline, which we call the polarimetric transition, the $n=1$ ring dominates the polarized visibility and shifts the phase of an interferometric polarization quotient [38].

Unlike a balloon, space VLBI, such as the proposed Black Hole Explorer (BHEX; [29]), lengthens the baselines beyond the Earth’s diameter. At higher frequency the emission near the black hole is also more optically thin [20], and the interstellar scattering toward Sgr A* decreases as the square of the wavelength [31]. A fixed baseline between the Atacama Large Millimeter/submillimeter Array (ALMA) and a balloon is longer in wavelengths at higher frequency. A longer flight mostly repeats the same baselines rather than lengthening them, since a balloon launched from Wanaka, New Zealand, circles the Earth about once every 7–10 days.

On a given physical baseline, a higher observing frequency increases the photon ring contribution to the visibilities. A higher frequency also lowers the signal-to-noise ratio, because the long-baseline signals are much fainter and the system noise is higher, both from the receivers and from the emission of the more opaque atmosphere above the ground stations. At 345 GHz and below, fringes are easy to detect but the photon ring contributes little structure on the available Earth-size baselines. At 690 GHz the ring dominates the long-baseline visibilities [32], but fringe detection is limited by sensitivity.

Longer integrations improve sensitivity only while the phase stays coherent. EHT stations at 230 GHz integrate coherently for about 10 s [16 c]. Frequency phase transfer (FPT) can extend this coherence time by measuring the phase in a simultaneously observed lower-frequency reference band and applying it, scaled by the frequency ratio, to the science band [40, 41]. Using an 86 GHz reference, FPT has extended the coherence at 215 and 258 GHz

on Earth-size baselines [28, 48].

This paper investigates what a submillimeter successor to the balloon VLBI pathfinders described above could add to the ground-VLBI arrays of the next decade. We forecast how far balloon stations could improve the ability of these arrays to constrain models of the photon ring emission. We generate synthetic observations with historical weather using versions of ngets im [39] and eht-imaging modified to support balloon stations. Section 2 describes the balloon platform, the ground arrays, and the simulation pipeline. Section 3 tests fringe detection on the single ALMA–balloon baseline and the coverage of the full arrays with FPT. Section 4 provides estimated reconstruction uncertainties for a geometric parametrization of the photon ring at 345 and 460 GHz, based on a Fisher analysis with ngEHTforecast¹. Section 5 discusses the polarimetric regime, the limitations, and the outlook, and Section 6 presents our conclusions. A companion paper (F. M. Thiel et al. [45]) uses the same modified software at 86 and 230 GHz, where balloon baselines from Kiruna, Sweden, fill short $(u,v)$ spacings and improve images of the extended jet of M87$^{*}$. That paper addresses dense $(u,v)$ coverage at millimeter wavelengths, while this one focuses on the detectability of the photon ring at submillimeter wavelengths.

Observing Platforms and Synthetic Observations

submm-BVEX: A Stratospheric VLBI Station

This paper forecasts a submillimeter successor to the 0.9 m, 22 GHz BVEX pathfinder introduced in § 1. We call the successor submm-BVEX to distinguish it from the pathfinder, and for this study we assume it to be a 2.5 m dish that operates at 35–40 km above sea level.

The residual atmosphere at the float altitudes for the balloon is thin enough that we can assume no atmospheric contribution at all, so opacity, sky brightness, and wind loading do not enter the balloon SEFD (system equivalent flux density). At a 38 km float altitude the MERRA-2 zonal-average profiles for the latitude bands of Wanaka (averaged over March to May) and Kiruna (averaged over June to August) predict a 0.16–0.17 $\mu\mathrm{m}$ water vapor column, compared to a typical 1 mm column at ALMA. The transmission spectrum is essentially identical from different stratospheric locations, varying only in the cores of narrow atmospheric lines. The SEFD for the balloon telescope is set by the dish diameter, the receiver temperature and sideband configuration, and the aperture efficiency.

We assume the submm-BVEX receiver temperatures listed in Table 1, each tied to demonstrated or funded hardware in its note e. Every parameter we assume for submm-BVEX is a design target, including these receiver temperatures, since no submillimeter hardware has yet been built for BVEX. We note, however, that superconducting heterodyne receivers have previously flown on balloons. For example, TELIS carried a 480–650 GHz superconductor–insulator–superconductor (SIS) receiver, with a pre-flight DSB noise temperature as low as 120 K, in a liquid-helium cryostat on a 2009 Kiruna flight (G. de Lange et al. 2010). We assume a nominal aperture efficiency of 0.70, which our assumed 10 $\mu\mathrm{m}$ rms surface accuracy reduces to 0.69, 0.67, and 0.64 at 345, 460, and 690 GHz, respectively. We also assume no efficiency loss due to pointing errors, since the sub-arcsecond gondola pointing of SuperBIT (A. S. Gill et al. [23]) is well within the roughly 40″ beam FWHM of a 2.5 m dish at 690 GHz. With these values, the projected balloon antenna SEFD is about 45 kJy at 345 GHz, 113 kJy at 460 GHz, and 197 kJy at 690 GHz.

Station	Band 8 (460 GHz)		Band 9 (690 GHz)		References
	$T_{\mathrm{R}}$ (K)	sideband	$T_{\mathrm{R}}$ (K)	sideband
ALMA	$120^{a}$	2SB (SSR $\approx0.1$)	80	DSB (SSR = 1)	J. Carpenter et al. [8]; A. M. Baryshev et al. [4]
APEX	150	2SB (SSR $\approx0.1$)	$225^{b}$	2SB (SSR $\approx0.1$)	APEX Observatory [1]; APEX Observatory [2]
JCMT	$200^{c}$	2SB	150	2SB	D. Bintley et al. [6]
GLTS	$200^{c}$	2SB	$150^{d}$	2SB	D. Bintley et al. [6]
submm-BVEX$^{e}$	120	2SB (SSR $\approx0.1$)	110	DSB (SSR = 1)	this work (§ 2.1)

Notes: 2SB and DSB are two-sideband and double-sideband receivers; SSR is the sideband separation ratio, and $T_{\mathrm{sys}}$ scales as $(1 + \mathrm{SSR})$ (D. W. Pesce et al. [39]). We assume that ALMA is operated in phased-array mode and that all stations record 32 GHz in both bands. The JCMT is 15 m and the GLTS 12 m (omitted for Sgr A$^{*}$).

In terms of observation bandwidth, we assume 16 GHz at 230 and 345 GHz, the bandwidth per polarization of the reference array of the next-generation EHT (ngEHT; S. S. Doeleman et al. [13]), 8 GHz in each of two sidebands, and 32 GHz at 460 and 690 GHz, with submm-BVEX recording the same bandwidth as its ground-station partners. In every campaign we assume that all stations simultaneously record 230 GHz at the science bandwidth to enable FPT, as described in § 2.3. The 32 GHz bandwidth is the goal of the ALMA Wideband Sensitivity Upgrade (WSU; J. Carpenter et al. [8]). Assuming two-bit sampling and two polarizations, 32 GHz of recorded bandwidth is a data rate of 256 Gbit s$^{-1}$, about thirty times the 8.2 Gbit s$^{-1}$ of the pathfinder BVEX backend (M. Bagchi et al. [3]).

The frequency standard for submm-BVEX is assumed to be an oven-controlled crystal oscillator (OCXO), since mass and power rule out a hydrogen maser on a balloon. For ground–ground baselines we assume coherent integrations of 10 s, which is standard EHT practice at 230 GHz (Event Horizon Telescope Collaboration [16]). On ground–balloon baselines we assume 5 s, with the balloon coherence time set by the clock stability and position-tracking precision rather than by the atmosphere. We apply both values at every observing frequency. The $\lambda/2\pi$ position-tracking requirement that F. M. Thiel et al. [46] set for BVEX at 22 GHz becomes about 100 $\mu\mathrm{m}$ at 460 GHz. A 5 s coherence at 460 GHz requires a fractional frequency stability near $7 \times10^{-14}$ over the integration. An oscillator that meets this requirement at 460 GHz supports only about 3.3 s at 690 GHz, so the 5 s we assume there is optimistic by a factor of 1.5, which is the ratio of the two frequencies. Single-baseline detections must therefore be achieved within a few seconds, and longer integrations require the FPT of § 2.3.

The balloon trajectory is set by the launch site and the stratospheric winds, which at float altitude blow mainly along lines of constant latitude and carry a balloon east–west around its launch site. Balloon telescopes cannot currently be steered. Launch sites are few, so a balloon team must pick a location that will optimize

the $(u,v)$ coverage on event-horizon scales. We choose for each source a single-baseline launch site from which the balloon and ALMA can see the source together for several hours per day. For M87$^{*}$ (+12.4° declination) we use a flight from Kiruna, Sweden (lat = +67°), for which both the balloon telescope and ALMA can see the source about 6 hours per day. For Sgr A$^{*}$ (−29° declination) we use a flight from Wanaka, New Zealand (lat = −45°), along which ALMA and submm-BVEX can both see Sgr A$^{*}$ for 4.8 hours per day in April. The ten-day, two-balloon campaigns of both sources use two launches from Wanaka on its recorded 39 d trajectory (§ 3.2). Figure 2 shows the two recorded trajecto-

ries as well as the locations of the ground VLBI stations with which they can potentially correlate.

Ground Arrays at 345, 460, and 690 GHz

At 345 GHz the benchmark is the 14-station 345 GHz configuration of ngEHTsim (D. W. Pesce et al. [39]), based on the ngEHT reference array (S. S. Doeleman et al. [13]), with science goals set out in M. D. Johnson et al. [30]. We treat this array as the future ground array, and investigate how balloon telescopes could add to it. The South Pole Telescope (SPT) never sees M87$^{*}$ and the Greenland Telescope never sees Sgr A$^{*}$, so each source is observed by 13 of the 14 stations. At the three new sites (San Pedro Mártir Observatory in Mexico, Teide Observatory in the Canary Islands, and Las Campanas Observatory in Chile) we assume 10 m dishes, the ngehtsim default for a new site.

At 460 GHz no comparable array forecasts exist, so we choose the sites whose atmospheric conditions allow VLBI at these frequencies. For ground-based stations in our 460 and 690 GHz simulations, we include ALMA, the Atacama Pathfinder Experiment (APEX), the James Clerk Maxwell Telescope (JCMT), and the Greenland Telescope at Summit Camp (GLTS). These sites are few, with ALMA and APEX co-located, so long 460 GHz ground baselines are scarce. System temperatures and SEFDs are calculated following the methodology of D. W. Pesce et al. [39], from the receiver temperatures, bandwidths, and sideband types listed in Table 1. Our simulated 690 GHz array consists of the same four stations with Band 9 (690 GHz) receivers.

Generation of Synthetic Observations

Each forecast starts by generating a synthetic observation using ngehtsim, following the methodology of D. W. Pesce et al. [39]. For each ground site and observing day the code reconstructs the atmospheric opacity and brightness temperature from historical weather data. It calculates the station SEFD from the dish diameter, aperture efficiency, receiver temperature, and the calculated atmospheric opacity, and it draws per-baseline thermal noise from the radiometer equation. The code evaluates the opacity and sky brightness at the center of the recorded band. At 460 GHz the 32 GHz band (444–476 GHz) contains the 448 GHz water line (Figure 1). We therefore calculated a band-averaged ground-station SEFD outside the simulation, weighting each frequency channel by its inverse noise variance, so the transparent part of the band dominates and the opaque line core adds little. The band average raises the thermal noise by a factor of about 1.5 on ALMA–balloon baselines and 1.6 on ground–ground baselines. At 345 and 690 GHz the ALMA–balloon noise changes by less than 3%. We keep the band-center values in the simulations and give the band-averaged results alongside them at 460 GHz.

Neither ngehtsim nor the underlying eht-imaging library ([10, 9]) supports balloon stations, so we modified both software packages. In our version the recorded flight trajectory (time, latitude, longitude, and altitude) is interpolated to each timestamp and converted to Earth-centered coordinates before the $(u,v)$ calculation, so the synthetic baselines follow the actual motion of the balloon telescope. The modified code also bypasses the atmospheric opacity, sky brightness, and wind-loading terms for balloon stations and applies separate coherence times to ground–ground and ground–balloon baselines in the fringe-detection and FPT analysis described below. These modifications, developed jointly for this project and the millimeter balloon-VLBI analysis presented in F. M. Thiel et al. [45], allow balloon station forecasts to be generated by the same software as the forecasts for ground stations.

The input source intensity models (Figure 3) are the geometric models (D. W. Pesce et al. [39], see their Appendix F), sampled at the observed $(u,v)$ points. Each model is a pair of concentric rings with a diameter of 42 $\mu$as for M87* and 52 $\mu$as for Sgr A*. A wide ring represents the direct emission and carries 90% of the flux, and a thin ring represents the photon ring and carries 10%. The M87* model is the same at every frequency we simulate (345, 460, and 690 GHz, and the 230 GHz FPT reference). The Sgr A* model has an elongation of 1.2 and is scattered at each frequency with the screen described in M. D. Johnson et al. [31].

The simulated observing campaigns take place in April, when the EHT typically observes and balloon launches take place from Wanaka, NZ. The ten-day campaigns use the reconstructed weather of 2020 April 15–24, while the Monte Carlo single-baseline detectability analysis of § 3.1 draws atmospheric opacities for each day from the April weather of 2012 to 2022. The weather in ngehtsim is a daily average of the MERRA-2 reanalysis, which is sampled every 3 hours ([39]), so it is constant within each simulated day.

Our simulations reach integration times longer than the coherence times of § 2.1 by using FPT. FPT is the first of the two calibration steps of source-frequency phase referencing ([40, 41]). M. J. Rioja et al. [41] and S. Issaoun et al. [27] proposed it for the ngEHT bands up to 345 GHz, and we also apply it at 460 and 690 GHz. The phase of a 230 GHz reference fringe observed at the same time is solved every 5 s on ground–balloon and every 10 s on ground–ground baselines, and the successive solutions are joined into a continuous phase solution (phase connection). That phase is multiplied by the frequency ratio and subtracted from the higher-frequency band phase, and the phase-corrected data are integrated over 300 s. We call each coherently averaged 5 or 10 s data point an integration and a 300 s block of integrations a scan. Coherent averaging sums the complex visibilities, so the noise falls as the square root of the averaging time, but only while the phase is stable. Incoherent averaging sums the visibility amplitudes or powers, which needs no phase stability but lowers the noise more slowly. The simulation keeps a scan when its 230 GHz reference fringe reaches a signal-to-noise ratio of 5 in one integration. The simulation then treats the 300 s average of the phase-corrected science-band data as coherent. In § 3.2 we test this assumption. An FPT-corrected

VLBI system could allow far longer scans than 300 s; we chose 300 s as a compromise between integration depth and the known intra-scan variability of Sgr A∗ ([19]). FPT sets a receiver requirement at both ends of the baseline, since the balloon and every ground station must simultaneously record the reference band and the science band. ALMA and APEX currently cannot record a 230 GHz reference simultaneously with a submillimeter band. FPT has not yet been demonstrated for a balloon telescope, but could be demonstrated by mm-BVEX, a planned millimeter successor to BVEX ([45]).

Figure 4 shows the resulting $(u,v)$ coverage predicted for the ten-day two-balloon campaigns at 345 and 460 GHz. At 345 GHz the balloons add tracks at and beyond the longest ngEHT ground baselines, and at 460 GHz, where the ground sites are few, they provide most of the long-baseline coverage.

Fringe Detectability and Baseline Coverage

Single-baseline detectability on ALMA–submm-BVEX

We first ask whether a fringe can be detected on ALMA–submm-BVEX, the balloon baseline with the lowest thermal noise in the array, since ALMA has by far the lowest SEFD of any station. We use a minimal set of assumptions: no FPT, no fringe grouping (in which fringe solutions on the strong baselines to a station are used to calibrate its weaker baselines), and no coherent or incoherent averaging across integrations. Every integration is assessed based on its thermal noise $\sigma$, calculated from the radiometer equation for the weather drawn in the Monte Carlo described below. We count an integration as detected only if the observed visibility amplitude is $> 3\sigma$ and the noiseless model visibility amplitude, sampled at the same $(u,v)$ point, also exceeds $3\sigma$. The latter requirement is included because the amplitude of a pure-noise sample is Rayleigh distributed, so a $3\sigma$ amplitude cut alone passes noise 1.1% of the time, which would result in multiple false detections per day at our sampling rate. We call this two-condition test the detection rule. A search for a fringe by varying the delay and rate requires a signal-to-noise ratio near 5 to 7 [7]. Incoherent averaging of the integrations in a scan can reach this level if each integration has a signal-to-noise ratio of about 1 or more and the scan holds a few tens of integrations [42]. Once the fringe search has found the delay and rate, tracking the fringe phase requires a detection above $3\sigma$ within one integration. We apply the $3\sigma$ detection rule to each integration without incoherent averaging over a scan, so the fractions of integrations detected that are presented in this subsection are conservative.

We assume the telescope and receiver configuration for submm-BVEX described in § 2.1, a 2.5 m dish with the per-band receiver temperatures and recorded bandwidths listed in Table 1, combined with a phased ALMA [24], which we take to be equivalent to a 75 m single-dish aperture following D. W. Pesce et al. [39]. We simulate observations for each source for one 24-hour day, sampling every 63 s (a 3 s integration followed by a 60 s gap), and derive the noise at 10 and 20 s from the 3 s schedule by the radiometer scaling $\sigma\propto1/\sqrt{t_{\mathrm{int}}}$. This gives 336 scheduled integrations per day for M87*, where ALMA is paired with a balloon on the Kiruna trajectory, and 274 for Sgr A*, where ALMA is paired with a balloon on the Wanaka trajectory; in both cases the balloon follows the first 24 hours of its recorded flight. Every fraction in this subsection is a fraction of these scheduled integrations. We use a Monte Carlo that draws the ALMA opacity and sky temperature calculated from a random day in April in a random year between 2012 and 2022, with the source elevation profile and $(u,v)$ track of 2020 April 15 held fixed. Each draw gives the baseline noise versus time for one day. We use 100 draws at 460 and 690 GHz and 20 draws at 230 and 345 GHz, where the noise varies less with weather (by a factor of 1.2–1.6 between the 16th and 84th percentile draws, against 4–9 at 460 and 690 GHz). The 10 and 20 s integrations exceed the roughly 5 s coherence time that we expect submm-BVEX’s OCXO and position tracking precision to support, but we include them to show how the noise scales with integration time. Table 2 lists, for each source, frequency, and integration time, the median daily detection fraction and the percentage of April days sampled that have ten or more integration detections. In the 230 GHz reference band M87$^{*}$ is detected on every 10 s integration and Sgr A$^{*}$ on about half, so the fringe detection at the reference band needed for FPT is present on the ALMA–balloon baseline. At 345 GHz both sources are detected on more than half of their 10 s integrations. At 230 and 345 GHz the Wanaka trajectory samples the scattered Sgr A$^{*}$ image at 6–11 G$\lambda$, where the visibility amplitude is only a few times the 10 s noise. Sgr A$^{*}$ at 460 GHz is at threshold, and its detections fall on the shorter baselines of the trajectory, 12.1–13.9 G$\lambda$, where the visibility amplitude is higher. Since we only simulate the trajectory for the first day of the balloon flight, the baseline variation is mostly due to Earth-rotation aperture synthesis. With the ground-station noise averaged over the recorded band (see § 2.3), ten or more 20 s detections occur at 460 GHz on about half of the sampled April days. The ALMA–balloon baseline at 460 GHz runs from 12.0 to 14.2 G$\lambda$ in this 24-hour simulation, so these detections lie beyond the 12 G$\lambda$ polarimetric transition of Sgr A$^{*}$ discussed in § 3.2. M87$^{*}$ at 460 GHz is not detected in any of the 100 April weather draws, because its median visibility amplitude of 14 mJy lies below the 21 mJy median 10 s baseline noise. At 690 GHz neither source is detected at any integration time. Launching in June to August, the driest months at the Chilean sites, would raise the median daily Sgr A$^{*}$ fraction at 460 GHz for 10 s integrations (band-center noise) from 15% to 24%, but balloon launches do not take place from Wanaka during those months.

Source, $\nu$ (GHz)	\multicolumn{2}{c}{$t_{\mathrm{int}} = 10$ s}	\multicolumn{2}{c}{$t_{\mathrm{int}} = 20$ s}
	median	days $> 10$	median	days $> 10$
M87$^{*}$, 230	100%	100%	100%	100%
M87$^{*}$, 345	73%	100%	98%	100%
M87$^{*}$, 460	0%	0%	0%	0%
M87$^{*}$, 690	0%	0%	0%	0%
Sgr A$^{*}$, 230	51%	100%	68%	100%
Sgr A$^{*}$, 345	56%	100%	76%	100%
Sgr A$^{*}$, 460	15%	58%	35%	72%
Sgr A$^{*}$, 460$^{a}$	0%	21%	9%	55%
Sgr A$^{*}$, 690	0%	0%	0%	0%

The thermal noise for a baseline will decrease as the dish diameter increases, or as the integration time–frequency bandwidth product increases, as shown in Figure 5. Table 3 lists the integration time required to achieve a $>3\sigma$ detection of Sgr A$^{*}$ at 460 GHz in median weather conditions for different combinations of dish diameters and frequency bandwidths. At the fiducial 32 GHz bandwidth and 2.5 m dish diameter we would require an approximately 20 s integration, which is why Sgr A$^{*}$ at 460 GHz is at threshold at 10–20 s. Doubling the bandwidth halves the required integration time. A 6 m dish would require 3.4 s at the fiducial bandwidth; this would be inside the expected OCXO coherence time with no FPT needed at all. M87$^{*}$ at 460 GHz would require about 200 s integration assuming a 2.5 m dish, beyond the OCXO coherence but potentially achievable with a 300 s scan if FPT can be used. With the band-averaged noise these requirements become 7.7 s for the 6 m dish, beyond the OCXO coherence, and about 470 s for M87$^{*}$, longer than one scan. At 690 GHz the M87$^{*}$ requirement exceeds a single 300 s scan at every diameter from 2 to 6 m. Sgr A$^{*}$ would require about 440 s with a 2.5 m dish, 304 s with a 3 m dish, just beyond a single scan, and 76 s with a 6 m dish.

Bandwidth	$D = 2$ m	$D = 2.5$ m	$D = 3$ m	$D = 6$ m
16 GHz	61.9 s	39.6 s	27.5 s	6.9 s
32 GHz (fiducial)	31.0 s	19.8 s	13.8 s	3.4 s
64 GHz	15.5 s	9.9 s	6.9 s	1.7 s

Full-array coverage with frequency phase transfer

Figure 6 classifies every 300 s phase-transferred scan of the ten-day two-balloon campaigns on the full arrays with the detection rule. Of the scheduled M87$^{*}$ scans, 62%, 27%, and 15% are detected at 345, 460, and 690 GHz, and of the Sgr A$^{*}$ scans 68%, 53%, and 33% are detected.

The two-balloon campaigns are two launches from Wanaka staggered by 16 d. We tested offsets from 2 to 28 d, and 16 d is the offset for which the largest fraction of the scheduled 460 GHz balloon scans lies beyond the polarimetric transition (D. C. M. Palumbo et al. [38]). Wanaka superpressure balloon flights, in which a sealed balloon holds a fixed volume and floats at nearly constant altitude for weeks, launch in March–May. SuperBIT launched there on 2023 April 16 (A. S. Gill et al. [23]), inside the April window we simulate, which is also when the EHT observes. An Antarctic long-duration flight would give the longest daily Sgr A* track, about 11.5 hours with ALMA, but its December–January launch opportunities (D. D. Gregory [25]; C. P. Geach et al. [21]) place Sgr A* near the Sun. In January the Chilean weather is also at its worst, and the median 10 s noise on the ALMA–submm-BVEX baseline at 460 GHz is 115 mJy compared to 17.5 mJy in April, so we did not simulate that flight trajectory.

The polarimetric transition indicated with a dashed vertical line in Figure 6 is the baseline beyond which the $n=1$ ring dominates the polarized visibility, about 15 Gλ for M87* and 12 Gλ for Sgr A* in the 230–690 GHz simulations of D. C. M. Palumbo et al. [38]. The transition moves inward with frequency (their Figures 2 and 3). For Sgr A* the 12 Gλ value is quoted at 345 GHz, so we can conservatively take the transition to be at 12 Gλ at 460 and 690 GHz. For M87* the 15 Gλ value is calculated near 690 GHz (their Figure 4). In the Stokes-I distribution the photon ring dominates the total intensity on baselines longer than about 20 Gλ (M. D. Johnson et al. [29]), which we call the Stokes-I transition scale. We use these same published values for the 460 and 690 GHz simulations.

For Sgr A* the balloon stations extend the longest detected baseline. At 460 GHz the ground array alone reaches 14.5 Gλ and the submm-BVEX stations extend that to 16.3 Gλ. At 690 GHz the ground detections are only on the 2.6 km ALMA–APEX baseline, apart from a few ALMA–JCMT scans (0.2% of the scheduled scans); ALMA–APEX is the baseline of the first 690 GHz VLBI fringe detection (M.-T. Chen et al. [11]). The balloon baselines provide the rest of the long-baseline coverage out to 23.3 Gλ. At 460 GHz, 41% of the ALMA–balloon scans of the Sgr A* campaign that pass the 230 GHz reference requirement (the calibratable scans) lie beyond the polarimetric transition. Of the scheduled scans, 7.6% at 460 GHz and 2.3% at 690 GHz are detected beyond the transition, most of them on balloon baselines. Raising the detection threshold from 3σ to 5σ keeps about three quarters of these balloon detections at 460 GHz and a third at 690 GHz.

The simulations treat each phase-transferred scan as perfectly coherent, so we also test the effect of an error in the transferred phase. The simulation requires a reference fringe signal-to-noise ratio of 5, which gives a thermal phase error of about 0.2 rad per solution. We test a larger residual reference phase error of 0.3 rad at 230 GHz, which corresponds to a signal-to-noise ratio of about 3, for which the frequency ratio scales the error to 0.6 rad at 460 GHz and 0.9 rad at 690 GHz. This error lowers the coherent visibility amplitude of a scan by a factor of $e^{-\phi^2/2}$ for a phase error $\phi$, which is 0.84 at 460 GHz and 0.67 at 690 GHz, and we apply the detection rule again to the lowered amplitudes. With this error, 93% and 38% of the balloon detections beyond the transition remain. The 690 GHz detections beyond the transition therefore require FPT that stays coherent at three times the reference frequency. Only 1% of the scheduled Sgr A* scans at 690 GHz are detected beyond the Stokes-I transition scale, which remains a target best suited for space VLBI (M. D. Johnson et al. [29]). For M87* at 460 GHz the two Wanaka-launched balloon stations add $(u,v)$ coverage but do not extend the longest detected baseline. The ALMA–balloon baseline to M87* from Wanaka has a median length of 7.2 G$\lambda$ at 460 GHz, so the longest detected baseline stays the 14.7 G$\lambda$ ground baseline there and no M87* detection lies beyond the 15 G$\lambda$ polarimetric transition. At 690 GHz the only M87* ground detections are on ALMA–APEX, so the balloon baselines, detected out to 10.9 G$\lambda$, set the longest detected baseline.

Photon Ring Forecasts

Ring model and Fisher forecast

We next test the ability of a ground plus balloon array to constrain parameters in a photon ring model. For this analysis we use a simple geometrical model of a double thick $m$-ring, which differs from the source images of Figure 3. The direct $n=0$ image, formed by photons that complete less than half an orbit around the black hole, is the 5-parameter asymmetric thick $m$-ring of M. D. Johnson et al. [32]: an infinitesimal ring of diameter $d_0$ and total flux $F_0$, modulated by an $m=1$ azimuthal Fourier mode with amplitude $|\beta_1|$ and phase $\arg\beta_1$ and convolved with a Gaussian of FWHM $w_0$. We also include an $n=1$ ring as a second concentric $m$-ring tied to the first by five parameters: the flux ratio $f_1$, the fractional diameter offset, the width ratio $f_w$, the asymmetry-amplitude ratio, and the asymmetry-phase offset. The width uses the P. Tiede et al. [47] reparametrization $w_1=f_w w_0$ with $f_w \in(0,1)$ (their $\epsilon_1$), which enforces a thinner $n=1$ ring, so the model cannot describe the same image with the two rings exchanged.

The M87* truth follows P. Tiede et al. [47] (their Section 2 and Eqs. 5–7), with the $n=1$ ring tied to the $n=0$ ring by the $e^{-\pi}$ demagnification of a $\gamma=\pi$ Lyapunov exponent (M. D. Johnson et al. [32]); the asymmetry amplitude of 0.4 (0.15 there) and the absence of the ellipticity they include are our choices. The Sgr A* truth scales the angular sizes by the ratio of gravitational radii, 24/19. The asymmetry ratio is 1 and the asymmetry-phase offset 0 (aligned rings).

The forecasts use ngEHTforecast, evaluated at the truth of Table 4, on the complex visibilities of every calibratable 300 s scan of the ten-day campaigns, that is, every scan whose 230 GHz reference reaches a signal-to-noise ratio of 5 in one integration. The Fisher matrix is built from the derivatives of the model visibilities with respect to the parameters, weighted by the thermal noise, and its inverse gives the parameter uncertainties. The scans with a low signal-to-noise ratio that fail the detection rule therefore contribute little. Note that the forecast baselines extend beyond the longest detected ones of § 3.2, because the forecasts include these scans. In addition, the Fisher forecasts and the detection fractions of § 3 use different source models, so they are not directly comparable. Per-station, per-scan complex gains are marginalized analytically, with $F_0$ fixed (so there are nine free parameters), 10% amplitude gains, and unconstrained phase gains, which matches the gains injected into the synthetic data.

Parameter	M87*	Sgr A*
$F_0$ (Jy)	0.600	2.500
$d_0$, $w_0$ ($\mu$as)	45.0, 18.0	56.84, 22.74
$|\beta_1|$, $\arg\beta_1$	0.4, $-\pi/2$	0.3, $-\pi/2$
$d_1$, $w_1$ ($\mu$as)	38.30, 0.778	48.38, 0.983
$f_1=f_w$	$e^{-\pi}=0.0432$	$e^{-\pi}$

We report the marginalized uncertainties on the $n=1$ ring diameter $d_1$ and width $w_1$ and the signal-to-noise ratio on the flux ratio $f_1$, in the parametrization of P. Tiede et al. [47]. We also fitted a single and a double $m$-ring to synthetic data generated from the double $m$-ring (self-fits). These self-fits distinguish a single ring from a double ring for both M87* and Sgr A* at 345 and 460 GHz.

Forecast Results at 345 and 460 GHz

The results of our Fisher forecasts are shown in Figure 7. At 345 GHz the ground array sets the constraint and the balloons barely change it. Adding two balloons changes $\sigma(d_1)$ from 0.029 to 0.027 $\mu$as for M87* and from 0.0080 to 0.0064 $\mu$as for Sgr A*, while $\sigma(w_1)$ changes from 1.18 to 1.11 $\mu$as for M87* and from 0.20 to 0.15 $\mu$as for Sgr A*. The 345 GHz constraint is set by the sensitivity of a 13-station array, so a balloon adds longbaseline coverage there but improves the ring-geometry precision by only 6 to 25%.

At 460 GHz the ground array gives no constraint. For M87* this four-station array returns a formal $\sigma(d_0)$ of 98 $\mu$as, larger than the ring, and for Sgr A* the Fisher matrix of the three-station array is ill-conditioned (condition number $2.4 \times10^{14}$), so it gives no usable uncertainties. ALMA and APEX are 2.6 km apart on the same plateau, so the Sgr A* array provides one short spacing and a single long-baseline direction toward Hawaii, from which nine free parameters cannot be constrained. One balloon makes the constraint possible, with $\sigma(d_1) = 0.36$ $\mu$as for M87* and 0.20 $\mu$as for Sgr A*. A second, staggered launch improves it to 0.33 $\mu$as for M87* and 0.12 $\mu$as for Sgr A*, and for Sgr A* the signal-to-noise ratio on the flux ratio, SNR($f_1$), rises from 14 with one balloon to 24 with two (from 7 to 8 for M87*). We therefore conclude that balloon baselines are necessary for 460 GHz constraints but would add little additional information to the much larger 345 GHz ground array.

For the ring geometry, the 460 GHz forecasts do not improve on the 345 GHz forecasts. The best 460 GHz balloon campaign gives $\sigma(d_1)$ of 0.33 $\mu$as for M87* and 0.12 $\mu$as for Sgr A*, against 0.029 and 0.0080 $\mu$as for the 345 GHz ground array alone, a factor of 11 to 15 worse, and $\sigma(w_1)$ is worse by a factor of about 4 to 5. At 460 GHz the constraint comes from three or four ground stations plus balloons instead of 13 ground stations. Averaging the ground-station noise over the 460 GHz band (§ 2.3) would raise the 460 GHz uncertainties by a further factor of about 1.5. We do not present ring-geometry forecast results for 690 GHz, where the balloon detections beyond the transition depend on FPT that stays coherent at three times the reference frequency. Without balloons the 690 GHz double $m$-ring Fisher matrix is singular for Sgr A* and ill-conditioned for M87*.

Discussion

Access to the Polarimetric Photon Ring Regime

Beyond the transition baseline the $n=1$ ring shifts the phase of the interferometric polarization quotient of D. C. M. Palumbo et al. [38]. The quotient removes most station-gain terms and cancels the diffractive scattering of Sgr A*, and it can be averaged coherently across epochs. For Sgr A* interstellar scattering permits the measurement at 345 GHz and above [38]. For M87* the transition is near 15 G$\lambda$, which lies beyond the 9.8 G$\lambda$ Earth diameter at 230 GHz, so at that frequency the measurement needs space VLBI [38], such as BHEX [29]. At 345 GHz the longest M87* detection in Figure 6 is at 13.1 G$\lambda$, short of the transition. The best target to resolve the polarimetric transition is therefore Sgr A*, and Figure 6 shows that both the ground–balloon and the ground–ground baselines can exceed the 12 G$\lambda$ transition at 345 GHz, while at 460 GHz most detections beyond the polarimetric transition are on balloon baselines. We note that balloon telescopes improve the long-baseline coverage by being able to observe at higher frequencies than most ground site locations, rather than by adding baselines longer than the Earth’s diameter. For Sgr A* in the two-balloon Wanaka campaign, 41% of the calibratable ALMA–balloon scans at 460 GHz lie beyond the 12 Gλ transition (§ 3.2), and 61% at 690 GHz.

The published requirements for measuring the $n=1$ phase of the polarization quotient in a single observation are a maximum per-visibility thermal noise of about 2 mJy for the M87* linear-polarization (LP) signature at 460–690 GHz and about 10 mJy for Sgr A* (D. C. M. Palumbo et al. [38]). The circular-polarization (CP) requirement for M87* at 230 GHz is more stringent still, below 1 mJy (A. Tamar & D. C. M. Palumbo [44]). Figure 8 shows the integration time at which our simulated thermal noise on the ALMA–balloon scans beyond the transition reaches those thresholds.

For Sgr A* the requirement is 44 s at 460 GHz, which is less than our assumed length of a phase-transferred scan (300 s), and 745 s at 690 GHz, about two and a half scans. ALMA–JCMT, the more sensitive of the two ground baselines beyond the transition at 460 GHz (the other is APEX–JCMT, which has nearly the same length), requires about 2900 s to reach the 10 mJy sensitivity needed to detect the polarimetric transition. With the band-averaged noise at 460 GHz, the 44 s requirement rises to about 100 s, which is still less than our assumed scan length. At 345 GHz the ngEHT ground array reaches the 12 Gλ transition by itself, and its baseline from the Submillimeter Telescope (SMT) to the SPT reaches the LP threshold in 154 s.

For M87*, 19% of the calibratable ALMA–submm-BVEX scans over the 3.6 days of the recorded Kiruna flight lie beyond the transition at 460 GHz. On the scans beyond the transition, the requirement is 30 min at 460 GHz and 54 h at 690 GHz. In the two-balloon Wanaka campaign no ALMA–balloon scan of M87* reaches the transition at 460 GHz, and the most sensitive ground–balloon baseline beyond it would require more than a hundred 300 s scans. The CP signal, which needs a noise below 1 mJy, is out of reach for a 2.5 m dish, since the median thermal noise of two averaged 300 s scans beyond the transition is 2.7–3.5 mJy at 460 GHz and 11–36 mJy at 690 GHz. We have not simulated the polarized signal, so we compare the thermal noise with published thresholds rather than make a polarimetric forecast, which is beyond the scope of this paper. Nevertheless, we find that balloon telescopes can provide baselines that probe the scales beyond the polarimetric transition, where the $n=1$ ring of Sgr A* dominates the polarized visibility, especially the ALMA–submm-BVEX baselines at 460 GHz, and possibly at 690 GHz if the scans can be coherently averaged.

Limitations

In our simulations we assume a roughly 5 s balloon coherence time, limited by the OCXO timing stability and position tracking system precision, and phase-connected 230 GHz reference solutions. The simulation treats every 300 s phase-transferred average as coherent. The reference 230 GHz frequency band is recorded at the science bandwidth. We also find that detections beyond the polarimetric transition baseline at 690 GHz will depend on whether we can coherently average the 5 s integrations over a 300 s scan (§ 3.2).

Our atmospheric opacity calculations for the ground stations assume that the opacity at the center of the band applies across the entire band. This assumption underestimates the opacity in the 460 GHz band, and consequently underestimates the thermal noise by a factor of about 1.5, because the band contains the 448 GHz water line (§ 2.3). In future forecasting work we could mitigate this higher ground-station noise by either increasing the central frequency of the band or tuning the two sidebands of the 2SB receivers to two 16 GHz windows with better atmospheric transmission properties.

The Fisher forecasts presented in this paper marginalize over a 10% amplitude and a free phase gain per station and scan, and non-closing errors such as bandpass mismatch and polarization leakage are not included in our analysis. The Fisher truth includes no interstellar scattering, whereas the Sgr A$^{*}$ model images used for the simulations of § 3 do include scattering. Finally, the analysis assumes that the sources do not change over the ten-day campaign. This is not true for Sgr A$^{*}$, which varies on timescales of minutes ([19]), so the forecasts overstate what a single Sgr A$^{*}$ epoch gives.

In contrast, the analysis of § 3.1 treats one baseline with no FPT, fringe grouping, or averaging across integrations, which gives a conservative lower bound on whether fringes can be detected on the ALMA–submm-BVEX baseline, the balloon baseline with the lowest thermal noise. With a 2.5 m balloon telescope paired with ALMA, both sources are detected on more than half of their 10 s integrations at 345 GHz, and Sgr A$^{*}$ at 460 GHz is at the detection threshold.

We note that the 460 GHz receivers at the JCMT and the GLTS, the 690 GHz receiver at the GLTS, and every submm-BVEX parameter are targets rather than fielded hardware.

Outlook

Here we discuss what would need to be done for submillimeter balloon VLBI to be feasible. Constraining the photon ring of Sgr A$^{*}$ at 460 GHz would require a 2.5 m balloon telescope with dual-polarization receivers, 32 GHz of recorded bandwidth, and FPT from a simultaneously observed 230 GHz band. ALMA would also need to observe the 230 and 460 GHz bands at the same time. This capability is not part of the WSU ([8]).

ALMA is currently increasing its recorded bandwidth through the WSU. A further doubling to 64 GHz, beyond the WSU goal of 32 GHz, would halve the 32 GHz integration times in Table 3 and bring the Sgr A$^{*}$ 460 GHz requirement for the 2.5 m dish to about 10 s. The other upgrade is dish diameter. The 2.5 m BLAST-TNG primary is among the largest mirrors flown on a balloon ([33]), and 2.5–3 m is the largest telescope size that can be launched in the near term. A 6 m dish (the last column of Table 3) brings the Sgr A$^{*}$ 460 GHz requirement to 3.4 s, inside the expected balloon–station coherence time. With the band-averaged noise the requirement becomes 7.7 s, longer than that coherence, and a dish that size is beyond what a balloon can lift today.

BHEX targets orbital baselines beyond the Stokes-I transition scale ([29] (A. Lupascu et al. 2024)), whereas a balloon reaches the polarimetric regime of Sgr A$^{*}$ at 460 and 690 GHz, at shorter baselines. Balloon stations could also add baselines to BHEX in its own observing bands, and we leave this to a future paper.

Conclusions

In this paper we present forecasts for a submillimeter successor experiment to the Balloon-borne VLBI Experiment (BVEX). We assume a 2.5 m telescope at 35–40 km that has effectively no atmospheric contribution to its noise, so it can observe at 460 and 690 GHz from any latitude or longitude. Ground VLBI at those frequencies is confined to a few dry sites, and balloon-borne VLBI stations can improve the $(u,v)$ coverage at these frequencies, where a fixed baseline is longer in wavelengths.

The pathways we identify for balloon telescopes to help ground-based arrays constrain photon ring models differ between 345, 460, and 690 GHz. For all submillimeter bands we assume simultaneous observations at 230 GHz as an FPT reference band, to obtain longer coherence times in the higher-frequency science bands. On the single ALMA–balloon baseline the 230 GHz reference fringe is detected on every 10 s integration for M87$^{*}$ and on about half for Sgr A$^{*}$, whose scattered image has a visibility amplitude only a few times the noise on this baseline. At 345 GHz the ngEHT ground array primarily sets the ring-geometry precision, though two balloons add baselines at and beyond the longest ngEHT spacings and improve that precision by 6 to 25%. At 460 GHz, Sgr A$^{*}$ is near the detection threshold on the ALMA–submm-BVEX baseline, with ten or more 20 s detections on about half of April days for a 2.5 m dish at the WSU goal bandwidth, while M87$^{*}$ would require FPT to make significant detections. A 460 GHz ring-geometry constraint exists only with balloons, though it would be less precise than the constraint from the 345 GHz ground array alone because of the smaller number of VLBI stations. At 690 GHz neither source is detected on the single baseline at any balloon telescope diameter up to 6 m or bandwidth up to 64 GHz without FPT.

The most interesting potential science case for submillimeter balloon VLBI is the polarimetric photon ring regime. The single-baseline Sgr A* detections at 460 GHz lie beyond the polarimetric transition of D. C. M. Palumbo et al. [38]. With FPT, most of the Sgr A* detections beyond the transition at 460 GHz are on balloon baselines, and the ground array reaches the transition there only on the baselines from ALMA and APEX to the JCMT. At 690 GHz such detections would require FPT that stays coherent at three times the reference frequency. No M87* detection on the balloon baselines from Wanaka reaches the transition baseline length in our forecasts. For Sgr A* the thermal noise on the ALMA–balloon scans beyond the transition meets the published linear-polarization threshold within one 300 s scan at 460 GHz.

The steps toward a submillimeter balloon VLBI experiment are a 32 GHz bandwidth backend, the submillimeter receivers of Table 1, simultaneous recording of the 230 GHz reference at every station, and multilaunch campaigns from one site. After balloon-borne VLBI is demonstrated, a next step toward such an experiment could be a demonstration of FPT applied to balloon VLBI observations at lower frequencies (e.g., 22 and 88 GHz).

Acknowledgments

The authors would like to thank the Centre National d’Études Spatiales (CNES) for providing GPS data of the 2024 TRANSAT flight from Kiruna used for the analysis in this paper through collaboration with the Canadian Space Agency (CSA).

MB, FMT and LMF would like to acknowledge the support from the Canadian Space Agency (CSA) Flights and Fieldwork for the Advancement of Science and Technology (FAST) grants (21FAQUEA18 and 25FAQUB72) as well as the support from the NSERC Collaborative Research and Training Experience (CREATE) Radio Astronomy-Driven Education and Training Excellence (RADEATE) program (CREATE 596358-2025). This research was also supported by the Canada Foundation for Innovation (CFI) John R. Evans Leaders Fund (JELF Project Number 43766), the Natural Sciences and Engineering Research Council (NSERC) Discovery Grant RGPIN/06266-2020 (LMF), and a Queen’s University Research Initiation Grant.

Software: ngehtsim ([39]), eht-imaging ([10, 9]), am ([37]), ngEHTforecast (https://github.com/aeb/ngEHTforecast). This work uses versions of ngehtsim and eht-imaging modified to support balloon stations (§ 2.3).