BHEX Mini

Direct Imaging Black Holes from LEO

Ref Bari | Ben & Luke Update

BHEX Mini

Partner Satellite to BHEX

Stand-alone Satellite

Pathfinder Mission

BHEX Mini

Partner Satellite to BHEX

Stand-alone Satellite

Pathfinder Mission

Supplement (u,v) coverage at 86 GHz

Enable parameter estimation of Sgr A*/M87

Achieve Space-Space VLBI

20,200\text{ km}
400\text{ km}

BHEX Mini

Pathfinder Mission

Partner Satellite to BHEX

Stand-alone Satellite

Supplement (u,v) coverage at 86 GHz

Enable parameter estimation of Sgr A*/M87

Achieve Space-Space VLBI

Supplement (u,v) coverage at 86 GHz

Enable parameter estimation of Sgr A*/M87

Achieve Space-Space VLBI

Survey of >25 AGN+BH Targets @86 GHz

Enable Population Modeling of SMBHs

Enable real-time imaging of dynamical accretion disk around Sgr A*

Enable multi-messenger gravitational astronomy w/ LIGO + LISA

BHEX Mini

Partner Satellite to BHEX

Stand-alone Satellite

Pathfinder Mission

Supplement (u,v) coverage at 86 GHz

Enable parameter estimation of Sgr A*/M87

Achieve Space-Space VLBI

Supplement (u,v) coverage at 86 GHz

Enable parameter estimation of Sgr A*/M87

Achieve Space-Space VLBI

Survey of >25 AGN+BH Targets @86 GHz

Enable Population Modeling of SMBHs

Enable real-time imaging of dynamical accretion disk around Sgr A*

Enable multi-messenger gravitational astronomy w/ LIGO + LISA

Enable low-cost Space-Ground & Space-Space VLBI

BHEX Mini

Sub-milli arcsecond angular resolution

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

BHEX Mini

Sub-milli arcsecond angular resolution

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

Prospects of Detecting a Jet in Sagittarius A* with VLBI (Chavez et. al., ApJ 2024)

BHEX Mini

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
  • What kind of targets can we observe with this angular resolution?

BHEX Mini

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
  • What kind of targets can we observe with this angular resolution?
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
20,000\text{ km}
12000\text{ km}
400\text{ km}

BHEX Mini

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
  • What kind of targets can we observe with this angular resolution?
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
20,000\text{ km}
12000\text{ km}
400\text{ km}

Metrics and Motivations for Earth–Space VLBI: Time-resolving Sgr A* with the Event Horizon Telescope (Palumbo et. al., ApJ 2019)

BHEX Mini

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
  • What kind of targets can we observe with this angular resolution?
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
400\text{ km}

Metrics and Motivations for Earth–Space VLBI: Time-resolving Sgr A* with the Event Horizon Telescope (Palumbo et. al., ApJ 2019)

BHEX Mini

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
  • What kind of targets can we observe with this angular resolution?
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Multifrequency Black Hole Imaging for the Next-generation Event Horizon Telescope (Chael et. al., 2023, ApJ)

400\text{ km}

BHEX Mini

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
T_{orb}=90 \text{ min}
  • What is the integration time for BHEX Mini on the (u,v) plane?
  • Could BHEX Mini possibly enable direct imaging of dynamic accretion disk around Sgr A*? (i.e., creating a movie of a black hole!)

BHEX Mini

Sub-milli arcsecond angular resolution

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
T_{orb}=90 \text{ min}

BHEX Mini

Sub-milli arcsecond angular resolution

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
T_{orb}=90 \text{ min}
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Maximum data transmission rate (in bits per second); How fast can you send data from BHEX Mini to the earth?

R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

BHEX Mini

Sub-milli arcsecond angular resolution

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
T_{orb}=90 \text{ min}
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Power of Transmitted Signal: Strength of downlink signal in Watts (i.e., shouting louder to be heard further away!)

R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

BHEX Mini

Sub-milli arcsecond angular resolution

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
T_{orb}=90 \text{ min}
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Transmitter Gain: How well-focused your signal is when it leaves the satellite

(i.e., shouting into a megaphone instead of into the wind)

R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

BHEX Mini

Sub-milli arcsecond angular resolution

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
T_{orb}=90 \text{ min}
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Receiver Gain: How effectively the ground station collects and concentrates the incoming signal (i.e., ALMA's big dish listening to our incoming signal)

R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Received Power: How strong is the signal once it hits the ground receiver? (after traveling through empty space)

P_r = P_tG_tG_r \left( \frac{\lambda}{4\pi R}\right)^2 \cdot \eta

BHEX Mini

Sub-milli arcsecond angular resolution

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
T_{orb}=90 \text{ min}
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Receiver Gain: How effectively the ground station collects and concentrates the incoming signal (i.e., ALMA's big dish listening to our incoming signal)

R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Distance: How much distance did the signal travel through free space? (LEO vs. MEO!)

P_r = P_tG_tG_r \left( \frac{\lambda}{4\pi R}\right)^2 \cdot \eta

BHEX Mini

Sub-milli arcsecond angular resolution

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
T_{orb}=90 \text{ min}
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Receiver Gain: How effectively the ground station collects and concentrates the incoming signal (i.e., ALMA's big dish listening to our incoming signal)

R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)
  • Since BHEX Mini's laser downlink would suffer less signal loss from LEO than BHEX at MEO, can we transmit more data?
  • Can this be leveraged to use 2-bit quantization instead of 1-bit quantization?

BHEX Mini

Sub-milli arcsecond angular resolution

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased radiation environment in LEO vs. MEO

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
T_{orb}=90 \text{ min}

Sub-milli arcsecond angular resolution

Dual short and long baseline lengths

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as
5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda
T_{orb}=90 \text{ min}

Decreased ISM scattering at LEO than MEO

R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)
P_r = P_tG_tG_r \left( \frac{\lambda}{4\pi R}\right)^2 \cdot \eta

BHEX Mini

Decreased ISM scattering at LEO than MEO

Orbit design for mitigating interstellar scattering effects in Earth-space VLBI observations of Sgr A* (Aditya Tamar, Ben Hudson, Daniel C.M. Palumbo, A&A, 2025)

BHEX Mini

Decreased ISM scattering at LEO than MEO

V_{obs}(b) = S\cdot \exp\left(-\frac{\pi^2 b^2\theta^2}{4\ln 2}\right)\exp \left(-\frac{1}{2} C_\phi^2 b^\alpha r_F^{2-\alpha}\right)

Intrinsic Gaussian Source

b=\frac{\lambda}{D}\to \text{BHEX Mini: } 0.1G\lambda b_{sg}<3.5G\lambda
b=\frac{\lambda}{D}\to \text{BHEX:}\geq 20G\lambda

BHEX Mini

Decreased ISM scattering at LEO than MEO

V_{obs}(b) = S\cdot \exp\left(-\frac{\pi^2 b^2\theta^2}{4\ln 2}\right)\exp \left(-\frac{1}{2} C_\phi^2 b^\alpha r_F^{2-\alpha}\right)

ISM Scattering

C_{\phi}\propto \lambda^2 (\lambda_{\text{BHEX Mini}}=3.5 mm)
  • At MEO, BHEX is 20x the orbital altitude of BHEX Mini
  • BHEX observes at a f=320 GHz, 4x higher than BHEX Mini

BHEX Mini

Decreased ISM scattering at LEO than MEO

V_{ratio}(b) = \frac{e^{-b_{\text{BHEX-Mini}}^2} e^{-\lambda_{\text{BHEX-Mini}}^2 b^\alpha}}{e^{-b_{\text{BHEX}}^2} e^{-\lambda_{\text{BHEX}}^2 b^\alpha}}
\lambda_{\text{BHEX Mini}}=3.7\lambda_{\text{BHEX}}, b_{\text{BHEX Mini}} = \frac{1}{5}b_{\text{BHEX}}
\lambda_{\text{BHEX}}=1.33mm, b_{\text{BHEX Mini}} \sim 20G\lambda
V_{\text{BHEX-Mini}}\sim 10V_{\text{BHEX}}

BHEX Mini Visibility Amplitude Advantage

Regardless of Source Flux Density!

V_{obs}(b) = S\cdot \exp\left(-\frac{\pi^2 b^2\theta^2}{4\ln 2}\right)\exp \left(-\frac{1}{2} C_\phi^2 b^\alpha r_F^{2-\alpha}\right)

BHEX Mini

Decreased ISM scattering at LEO than MEO

BHEX Mini

BHEX Mini

Antenna

BHEX Mini

Receiver

BHEX Mini

Cryocooler

BHEX Mini

Solar Panels

BHEX Mini

Ultra-Stable Oscillator

BHEX Mini

Ultra-Stable Oscillator

\Delta \phi = 2\pi \cdot f \cdot \sigma_t
\sigma_t = \sigma_f \cdot \Delta t

Phase Error

BHEX Mini

Ultra-Stable Oscillator

\sigma_f = 5\cdot 10^{-11}, f_{obs}=86 \text{ GHz}
\Delta t = 1s:
\sigma_t = 5\cdot 10^{-11} \cdot 1s = 5\cdot 10^{-11} s
\Delta \phi = 2\pi \cdot (86\cdot 10^9 \text{ Hz}) \cdot 5\cdot 10^{-11} s=27.01 \text{ rad}
\Delta t = 10s:
\sigma_t = 5\cdot 10^{-11} \cdot 10s = 50\cdot 10^{-11} s
\Delta \phi = 2\pi \cdot (86\cdot 10^9 \text{ Hz}) \cdot 50\cdot 10^{-11} s=270.01 \text{ rad}
\Delta \phi<1 \text{ rad for Phase Coherence}

BHEX Mini

Ultra-Stable Oscillator

Allan Deviation

f=86 \text{ GHz}, t=10s, \sigma_y = 5\cdot 10^{-11}
L = 1-\exp\left[-2\pi^{2}(86\cdot 10^9)^{2}(10)^{2}(5\cdot 10^{-11})^{2}\right]

ABRACON SMD OCXO

L = 1-\exp\left(-2\pi^{2}f^{2}t^{2}\sigma_y^{2}\right)
L\sim 1\%<10\% \text{ required for Phase Coherence}

BHEX Mini

Digital Backend

BHEX Mini

Original Analog Radio Signal

BHEX Mini

Sample the Signal every Unit Interval

f_s\geq 2f

Nyquist-Shannon Sampling Theorem

BHEX Mini

Retain only the samples and record the sign of the voltage for each sample

BHEX Mini

Reconstruct the original signal

BHEX Mini

\eta_{Q}(N_{bit})\sim 1-\frac{\pi}{2}\cdot 2^{-2N_{bit}}
SNR = \eta_{corr}\times \frac{T_{source}}{T_{system}}\times \sqrt{\Delta \nu \cdot \tau}
\operatorname{Rate}(\mathrm{bps})=N_{\text {bits }} \times \Delta \nu \times 2_{\text {pol }} \times 2_{\text {Nyquist }}
\eta = \sqrt{\eta_1\eta_2}

BHEX Mini

\eta_{Q}(N_{bit})\sim 1-\frac{\pi}{2}\cdot 2^{-2N_{bit}}
SNR = \eta_{corr}\times \frac{T_{source}}{T_{system}}\times \sqrt{\Delta \nu \cdot \tau}
\operatorname{Rate}(\mathrm{bps})=N_{\text {bits }} \times \Delta \nu \times 2_{\text {pol }} \times 2_{\text {Nyquist }}
\eta = \sqrt{\eta_1\eta_2}

Quantization Efficiency: how much of the analog SNR is retained after digitization

\eta_{Q}(1)\sim 63\%
\eta_{Q}(2)\sim 88\%

BHEX Mini

\eta_{Q}(N_{bit})\sim 1-\frac{\pi}{2}\cdot 2^{-2N_{bit}}
SNR = \eta_{corr}\times \frac{T_{source}}{T_{system}}\times \sqrt{\Delta \nu \cdot \tau}
\operatorname{Rate}(\mathrm{bps})=N_{\text {bits }} \times \Delta \nu \times 2_{\text {pol }} \times 2_{\text {Nyquist }}
\eta = \sqrt{\eta_1\eta_2}

SNR: Signal to Noise Ratio

SNR = 0.88\times \frac{1K}{100K}\times \sqrt{32 \text{GHz} \cdot 10\text{s}}=4.98

BHEX Mini

\eta_{Q}(N_{bit})\sim 1-\frac{\pi}{2}\cdot 2^{-2N_{bit}}
SNR = \eta_{corr}\times \frac{T_{source}}{T_{system}}\times \sqrt{\Delta \nu \cdot \tau}
\operatorname{Rate}(\mathrm{bps})=N_{\text {bits }} \times \Delta \nu \times 2_{\text {pol }} \times 2_{\text {Nyquist }}
\eta = \sqrt{\eta_1\eta_2}

Data Generation Rate: In Bits per Second

\text{Rate} = (2+2)\times 32 \text{ GHz} \times 2 \cdot 2=512 \text{Gb/s}

BHEX Mini

\eta_{Q}(N_{bit})\sim 1-\frac{\pi}{2}\cdot 2^{-2N_{bit}}
SNR = \eta_{corr}\times \frac{T_{source}}{T_{system}}\times \sqrt{\Delta \nu \cdot \tau}
\operatorname{Rate}(\mathrm{bps})=N_{\text {bits }} \times \Delta \nu \times 2_{\text {pol }} \times 2_{\text {Nyquist }}
\eta = \sqrt{\eta_1\eta_2}

Cross-Correlation

BHEX Mini Next Steps

Phy

  • What are BHEX Mini's primary science objectives?
  • To what extent can BHEX Mini achieve its objectives?

Eng

  • SWaPC Requirements for Instrumentation

Fund

  • Write Grant Proposals for Nelson Grants
  • Write Abstract for SpaceCom 2026
  • Write De-scoped BHEX Mini #1 & #2