BHEX Mini

BHEX Mini

Direct Imaging Black Holes from LEO

Ref Bari | 06/22 Update

Antenna

Antenna

Receiver

Cryocooler

Solar Panels

Ultra-Stable Oscillator

Digital Backend

Downlink

Terminal

Original Analog Radio Signal

Sample the Signal every Unit Interval

f_s\geq 2f

Nyquist-Shannon Sampling Theorem

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

Reconstruct the original signal

Key Equations

\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}

Key Equations

\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\%

Key Equations

\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

Key Equations

\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}

Key Equations

\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

Physics

Engineering

Funding

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 & #2Ā 

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 & #2Ā 
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Decreased signal loss from LEO:

Decreased radiation environment in LEO vs. MEO

Phy

  • What are BHEX Mini's primary science objectives?
  • To what extent can BHEX Mini achieve its objectives?
  • SWaPC Requirements for Instrumentation
  • Write Grant Proposals for Nelson Grants
  • Write Abstract for SpaceCom 2026
  • Write De-scoped BHEX Mini #1 & #2Ā 
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Decreased signal loss from LEO:

Decreased radiation environment in LEO vs. MEO

  • What kind of targets can we observe with this angular resolution?

Phy

  • What are BHEX Mini's primary science objectives?
  • To what extent can BHEX Mini achieve its objectives?
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

  • What kind of targets can we observe with this angular resolution?
  • SWaPC Requirements for Instrumentation
  • Write Grant Proposals for Nelson Grants
  • Write Abstract for SpaceCom 2026
  • Write De-scoped BHEX Mini #1 & #2Ā 

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Decreased signal loss from LEO:

Decreased radiation environment in LEO vs. MEO

  • What horizon-scale structure can we observe on long baselines?
  • What extended structure can we probe on our shorter baseline?

Phy

  • What are BHEX Mini's primary science objectives?
  • To what extent can BHEX Mini achieve its objectives?
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

  • What kind of targets can we observe with this angular resolution?
  • SWaPC Requirements for Instrumentation

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}
  • What horizon-scale structure can we observe on long baselines?
  • What extended structure can we probe on our shorter baseline?
  • What is the integration time for BHEX Mini on the (u,v) plane?
  • Could that possibly enable direct imaging of dynamic accretion disk around Sgr A*? (i.e., creating a movie of a black hole!)

Fund

  • Write Grant Proposals for Nelson Grants
  • Write Abstract for SpaceCom 2026
  • Write De-scoped BHEX Mini #1 & #2Ā 
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Decreased signal loss from LEO:

Decreased radiation environment in LEO vs. MEO

Decreased radiation environment in LEO vs. MEO

Phy

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

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}
  • What is the integration time for BHEX Mini on the (u,v) plane?
  • Could that possibly enable direct imaging of dynamic accretion disk around Sgr A*? (i.e., creating a movie of a black hole!)

Fund

  • Write Grant Proposals for Nelson Grants
  • Write Abstract for SpaceCom 2026
  • Write De-scoped BHEX Mini #1 & #2Ā 
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Decreased signal loss from LEO:

Decreased radiation environment in LEO vs. MEO

Decreased radiation environment in LEO vs. MEO

Phy

  • What are BHEX Mini's primary science objectives?
  • To what extent can BHEX Mini achieve its objectives?
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

  • What kind of targets can we observe with this angular resolution?
  • SWaPC Requirements for Instrumentation

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}
  • What horizon-scale structure can we observe on long baselines?
  • What extended structure can we probe on our shorter baseline?
  • Can BHEX Mini enable imaging of dynamic accretion disk structure around Sgr A*?
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Decreased signal loss from LEO:

  • What is BHEX Mini's duty cycle? (i.e., how long will it be able to observe a radio target during one orbital period?)
  • How much data will BHEX Mini collect over one orbit?

Decreased radiation environment in LEO vs. MEO

Phy

  • What are BHEX Mini's primary science objectives?
  • To what extent can BHEX Mini achieve its objectives?
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

  • What kind of targets can we observe with this angular resolution?
  • SWaPC Requirements for Instrumentation

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}
  • What horizon-scale structure can we observe on long baselines?
  • What extended structure can we probe on our shorter baseline?
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Decreased signal loss from LEO:

  • What is BHEX Mini's duty cycle? (i.e., how long will it be able to observe a radio target during one orbital period?)
  • How much data will BHEX Mini collect over one orbit?

Decreased radiation environment in LEO vs. MEO

  • How much less radiation (i.e., dosage per orbital period) will BHEX Mini in LEO have than BHEX in MEO?
  • How much does that save us in mass? (i.e., because we don't have to radiation-harden our instrumentation)
  • Can BHEX Mini enable imaging of dynamic accretion disk structure around Sgr A*?

Phy

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

Challenges of Low-Earth Orbit at 86 GHz

  • Virtually no ground station coverage due to high orbital velocity
  • Cannot resolve Photon Ring at 86 GHz at LEO
  • Space-Ground VLBI will be difficult due to atmospheric decoherence
  • Interstellar medium scattering (ISM) is Ā  Ā  Ā  Ā  Ā  Ā  and significant for Sgr A* Ā  Ā Ā 
    • Prevents horizon-scale imaging forĀ 
    • At 86 GHz, BHEX Mini hasĀ 
I\propto \lambda^2
\lambda>2mm
\lambda=3.3mm

Phy

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

BHEX Mini Science Objectives (Safety)

  • Supplement (u,v)Ā coverage of Sgr A*/M87 at 86 GHz

BHEX Mini Science Objectives (Match)

  • 86 GHz VLBI survey of AGN Targets with d~2.5m antenna
  • Achieve Space-Space VLBI for the first time

BHEX Mini Science Objectives (Reach)

  • Enable imaging of dynamical accretion disk phenomenon
    • This would enable the first constraints on spin of Sgr A*Ā 
  • Enable multi-messenger astronomy of binary black hole targets
    • In conjunction with LIGO, LISA, or Einstein Telescope

Eng

  • SWaPC Requirements for Instrumentation

Fund

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

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 & #2Ā 

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 & #2Ā 

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 & #2Ā 

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 & #2Ā 

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 & #2Ā 

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 & #2Ā 

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 & #2Ā 

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 & #2Ā 

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 & #2Ā 

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 & #2Ā 

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 & #2Ā 
  • What material will we create the BHEX Mini antenna out of?
    • ā€‹This will determine the SWaPC requirements for the antenna
  • What are state-of-the-art antenna designs with the least areal density?
  • Deployable vs. fixed antenna designs?
    • ā€‹Model surface accuracy of antenna
    • Model aperture efficiency of antenna
  • Phased array antenna design?

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 & #2Ā 

LT-RSP2 Cryocooler

Raytheon long life cryocoolers for future space missions (T. Conrad et. al., Cryogenics 2017)

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 & #2Ā 

Stirling Cryocooler

Development of Advanced Two-Stage Stirling Cryocooler for Next Space Missions (Y. Sato et. al., Cryocoolers 15, 2009)

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 & #2Ā 

Stirling Cryocooler

Development of Advanced Two-Stage Stirling Cryocooler for Next Space Missions (Y. Sato et. al., Cryocoolers 15, 2009)

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 & #2Ā 

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 & #2Ā 

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 & #2Ā 

Phase Coherence for BHEX Mini

Phase Coherence for BHEX Mini

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

Phase Error

Phase Coherence for BHEX Mini

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

Observing Frequency

Phase Coherence for BHEX Mini

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

Timing Jitter

Phase Coherence for BHEX Mini

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

Allan Deviation

\sigma_t = \sigma_f \cdot \Delta t

Phase Coherence for BHEX Mini

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

Integration Time

\sigma_t = \sigma_f \cdot \Delta t

Phase Coherence for BHEX Mini

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

Integration Time

\sigma_t = \sigma_f \cdot \Delta t
\sigma_f = 5\cdot 10^{-11}

Phase Coherence for BHEX Mini

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

Phase Coherence for BHEX Mini

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

Phase Coherence for BHEX Mini

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

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 & #2Ā 

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 & #2Ā 

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 & #2Ā 

Coherence Loss for BHEX Mini

L = 1-\exp\left(-2\pi^{2}f^{2}t^{2}\sigma_y^{2}\right)

Coherence Loss

Coherence Loss for BHEX Mini

Observing Frequency

L = 1-\exp\left(-2\pi^{2}f^{2}t^{2}\sigma_y^{2}\right)

Coherence Loss for BHEX Mini

Integration Time

L = 1-\exp\left(-2\pi^{2}f^{2}t^{2}\sigma_y^{2}\right)

Allan Deviation

L = 1-\exp\left(-2\pi^{2}f^{2}t^{2}\sigma_y^{2}\right)

Coherence Loss for BHEX Mini

Allan Deviation

f=86 \text{ GHz}, t=10s, \sigma_y = 5\cdot 10^{-11}

ABRACON SMD OCXO

L = 1-\exp\left(-2\pi^{2}f^{2}t^{2}\sigma_y^{2}\right)
L = 1-\exp\left(-2\pi^{2}f^{2}t^{2}\sigma_y^{2}\right)

Coherence Loss for BHEX Mini

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)

Coherence Loss for BHEX Mini

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}

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 & #2Ā 
  • Plot of Power v. Mass for selected USOs
    • ā€‹This will determine SWaPC requirements
  • Plot of Visibility SNR for USOs/OCXOs

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 & #2Ā 

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 & #2Ā 

BHEX Mini Next Steps

Phy

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

BHEX Mini Science Objectives (Safety)

  • Supplement (u,v)Ā coverage of Sgr A*/M87 at 86 GHz

BHEX Mini Science Objectives (Match)

  • 86 GHz VLBI survey of AGN Targets with d~2.5m antenna
  • Achieve Space-Space VLBI for the first time

BHEX Mini Science Objectives (Reach)

  • Enable imaging of dynamical accretion disk phenomenon
    • This would enable the first constraints on spin of Sgr A*Ā 
  • Enable multi-messenger astronomy of binary black hole targets
    • In conjunction with LIGO, LISA, or Einstein Telescope

Todd Ely

Joseph Lazio

Eric Burt

Ben Hudson

Luke Anderson

Rick Fleeter

BHEX Mini Proposal Feedback

Todd Ely

BHEX Mini Proposal Feedback

Todd Ely

TLDR: It will be tough to fit an highly accurate clock on a small satellite

BHEX Mini Proposal Feedback

TLDR: It will be tough to fit an highly accurate clock on a small satellite

Eric Burt

  1. šŸŽÆ Primary Science Objectives
  2. šŸ”­ SWAPC Requirements
  3. šŸ“» Antenna Dimensions
  4. šŸ§Š Cryocooler Requirements
  5. šŸ•°ļø Frequency Reference System
  6. šŸ•’Ā BHEX Mini Timeline
  7. šŸ’°Funding Deadlines

BHEX Mini

\text{MEO} (20000 \text{ km})
\text{LEO} (400 \text{ km})
\textbf{BHEX}
\textbf{BHEX Mini}

Metrics and motivations for Earthā€“space VLBI: Time-resolving Sgr A* with the Event Horizon Telescope (Palumbo et. al., ApJ 2019)

BHEX Mini

BHEX Mini Orbit

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

20,000\text{ km}
12000\text{ km}
400\text{ km}
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

12,000 \text{ km}
400\text{ km}
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

Michael Johnson et. al., BHEX Team, 2024

T_{orb}=90 \text{ min}
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}

Mid-Range Science Objectives for the Event Horizon Telescope (EHT Collaboration, 2024)

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

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}

Less power required for data downlink from LEO than MEO:

R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}

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)
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}

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)
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}

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)
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}

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)
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}

Antenna Efficiency: How efficient are

both the space and ground antennas?

R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}

Noise Temperature: Background noise

of (similar to thermal noise) of receiver; Lower T means higher SNR.

R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}

Bandwidth: How "wide" the signal is in frequency space. A high frequency bandwidth is good (except possibly for thermal noise*!)

R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}

Bits per photon: How many bits each photon is encoded by (i.e., 1 bit or 2 bit)

R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}

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

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
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}

Distance: How much distance did the signal travel through free space? (LEO vs. 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
22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

Decreased signal loss from LEO:

22\mu as<\theta_{\text{BHEX-Mini}} < 1800 \mu as

Sub-milli arcsecond angular resolution:

BHEX Mini Unique Advantages

5.6 G \lambda < b_{s s}<9.3 G \lambda
0.11 G \lambda < b_{s g}<3.5 G \lambda

Dual short and long baseline lengths:

Rapid coverage of (u,v)Ā plane:

T_{orb}=90 \text{ min}
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right)

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
R_{\max } \approx \frac{P_t G_t G_r \eta}{k T_b B}\left(N_{\bmod }\right), G_r=\eta\left(\frac{\pi D}{\lambda}\right)^2
  1. šŸŽÆ Primary Science Objectives
  2. šŸ”­ SWAPC Requirements
  3. šŸ“» Antenna Dimensions
  4. šŸ§Š Cryocooler Requirements
  5. šŸ•°ļø Frequency Reference System
  6. šŸ•’Ā BHEX Mini Timeline
  7. šŸ’°Funding Deadlines

BHEX Mini

šŸŽÆ Primary Science Objectives

Original Mission

Descoped Mission

Descope Mission #2

šŸŽÆ Primary Science Objectives

OG

  • 86 GHz VLBI survey of AGN Targets with d~2.5m antenna
  • Supplement (u,v)Ā coverage of Sgr A*/M87 at 86 GHz
  • Achieve first Space-Space VLBI

Descoped Mission

Descope Mission #2

šŸŽÆ Primary Science Objectives

OG

  • 86 GHz VLBI survey of AGN Targets with d~2.5m antenna
  • Supplement (u,v)Ā coverage of Sgr A*/M87 at 86 GHz
  • Achieve first Space-Space VLBI

DS1

  • d~2m antenna cooled down to sub-25K temperatures
  • No Frequency Phase Transfer from 86 to 230 GHz
  • ABRACON OCXO for Frequency Reference System

Descope Mission #2

šŸŽÆ Primary Science Objectives

OG

  • 86 GHz VLBI survey of AGN Targets with d~2.5m antenna
  • Supplement (u,v)Ā coverage of Sgr A*/M87 at 86 GHz
  • Achieve first Space-Space VLBI

DS1

  • d~2m antenna cooled down to sub-25K temperatures
  • No Frequency Phase Transfer from 86 to 230 GHz
  • ABRACON OCXO for Frequency Reference System

DS2

  • 3 GHz VLBI survey of AGN targets
  • No Space-Space VLBI with BHEX
  • Ground-Space VLBI restricted to f~3 GHz ground stations

šŸŽÆ Primary Science Objectives

10 \text{ GHz}
47 \text{ GHz}
220 \text{ GHz}
1100 \text{ GHz}
\text{BHEX}
\text{BHEX Mini}
\text{EHT}
  1. šŸŽÆ Primary Science Objectives
  2. šŸ”­ SWAPC Requirements
  3. šŸ“» Antenna Dimensions
  4. šŸ§Š Cryocooler Requirements
  5. šŸ•°ļø Frequency Reference System
  6. šŸ•’Ā BHEX Mini Timeline
  7. šŸ’°Funding Deadlines

BHEX Mini

šŸ”­ SWAPC Requirements

Antenna

Cryocooler

Frequency Reference System

šŸ”­ SWAPC Requirements

Antenna

  • Antenna Diameter:Ā 
  • Primary Receiver Temperature:
  • Antenna Areal Density:Ā 
2.2< d < 2.5m
T_r \sim 20^{\circ}K
2<\sigma<5 \text{ kg}/\text{m}^2

Cryocooler

Frequency Reference System

šŸ”­ SWAPC Requirements

Antenna

RSP2

  • Raytheon RSP2:Ā Sterling-PTĀ Hybrid (450W Input)
  • Stage 1 (Sterling): 6W at 60K
  • Stage 2 (Pulse Tube): 2.1W at 20KĀ 
  • Antenna Diameter:Ā 
  • Primary Receiver Temperature:
  • Antenna Areal Density:Ā 
2.2< d < 2.5m
T_r \sim 20^{\circ}K
2<\sigma<5 \text{ kg}/\text{m}^2

Frequency Reference System

šŸ”­ SWAPC Requirements

Antenna

RSP2

  • Raytheon RSP2:Ā Sterling-PTĀ Hybrid (450W Input)
  • Stage 1 (Sterling): 6W at 60K
  • Stage 2 (Pulse Tube): 2.1W at 20KĀ 

USO

  • LISA USO:Ā 
  • RK409 Rakon USO:
  • O-CS41 ABRACON OCXO:
  • Antenna Diameter:Ā 
  • Primary Receiver Temperature:
  • Antenna Areal Density:Ā 
2.2< d < 2.5m
T_r \sim 20^{\circ}K
2<\sigma<5 \text{ kg}/\text{m}^2
\sigma_y = 8\cdot 10^{-15} (t=10s)
\sigma_y = 1\cdot 10^{-12} (t=10s)
\sigma_y = 2\cdot 10^{-12}(t=1s)

šŸ”­ SWAPC Requirements

Antenna

RSP2

  • Raytheon RSP2:Ā Sterling-PTĀ Hybrid
  • Stage 1 (Sterling): 6W at 60K
  • Stage 2 (Pulse Tube): 2.1W at 20KĀ 

USO

  • LISA USO:Ā 
  • RK409 Rakon USO:
  • O-CS41 ABRACON OCXO:
  • Antenna Diameter:Ā 
  • Primary Receiver Temperature:
  • Antenna Areal Density:Ā 
2.2< d < 2.5m
T_r \sim 20^{\circ}K
2<\sigma<5 \text{ kg}/\text{m}^2
\sigma_y = 8\cdot 10^{-15}
\sigma_y = 1\cdot 10^{-12}
\sigma_y = 2\cdot 10^{-12}
  1. šŸŽÆ Primary Science Objectives
  2. šŸ”­ SWAPC Requirements
  3. šŸ“» Antenna Dimensions
  4. šŸ§Š Cryocooler Requirements
  5. šŸ•°ļø Frequency Reference System
  6. šŸ•’Ā BHEX Mini Timeline
  7. šŸ’°Funding Deadlines

BHEX Mini

šŸ“» Antenna Dimensions

3C 84

NRAO 530

NGC 1052

BL Lac

3C 273

šŸ“» Antenna Dimensions

3C 84

NRAO 530

NGC 1052

BL Lac

3C 273

šŸ“» Antenna Dimensions

3C 84: Nucleus of galaxy NGC 1275 (22 GHz)

NRAO 530

NGC 1052

BL Lac

3C 273

šŸ“» Antenna Dimensions

3C 84

NRAO 530: Quasar 230 GHz, 20 Ī¼as (EHT)

NGC 1052

BL Lac

3C 273

šŸ“» Antenna Dimensions

3C 84

NRAO 530

NGC 1052:Ā Bright Elliptical Galaxy (65 mln lys)

BL Lac

3C 273

šŸ“» Antenna Dimensions

3C 84

NRAO 530

NGC 1052

BL Lac

3C 279:Ā An 'optically violent' variable quasar

Gamma Ray Image

šŸ“» Antenna Dimensions

3C 84

NRAO 530

NGC 1052

BL Lac

3C 273

šŸ“» Antenna Dimensions

šŸ“» Antenna Dimensions

šŸ“» Antenna Dimensions

šŸ“» Antenna Dimensions

šŸ“» Antenna Dimensions

šŸ“» Antenna Dimensions

  1. šŸŽÆ Primary Science Objectives
  2. šŸ”­ SWAPC Requirements
  3. šŸ“» Antenna Dimensions
  4. šŸ§Š Cryocooler Requirements
  5. šŸ•°ļø Frequency Reference System
  6. šŸ•’Ā BHEX Mini Timeline
  7. šŸ’°Funding Deadlines

BHEX Mini

šŸ§Š Cryocooler Requirements

LT-RSP2 Cryocooler

Raytheon long life cryocoolers for future space missions (T. Conrad et. al., Cryogenics 2017)

šŸ§Š Cryocooler Requirements

Stirling Cryocooler

Development of Advanced Two-Stage Stirling Cryocooler for Next Space Missions (Y. Sato et. al., Cryocoolers 15, 2009)

šŸ§Š Cryocooler Requirements

Stirling Cryocooler

Development of Advanced Two-Stage Stirling Cryocooler for Next Space Missions (Y. Sato et. al., Cryocoolers 15, 2009)

šŸ§Š Cryocooler Requirements

Stirling Cryocooler

Development of Advanced Two-Stage Stirling Cryocooler for Next Space Missions (Y. Sato et. al., Cryocoolers 15, 2009)

Phase Coherence for BHEX Mini

Phase Coherence for BHEX Mini

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

Phase Error

Phase Coherence for BHEX Mini

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

Observing Frequency

Phase Coherence for BHEX Mini

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

Timing Jitter

Phase Coherence for BHEX Mini

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

Allan Deviation

\sigma_t = \sigma_f \cdot \Delta t

Phase Coherence for BHEX Mini

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

Integration Time

\sigma_t = \sigma_f \cdot \Delta t

Phase Coherence for BHEX Mini

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

Integration Time

\sigma_t = \sigma_f \cdot \Delta t
\sigma_f = 5\cdot 10^{-11}

Phase Coherence for BHEX Mini

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

Phase Coherence for BHEX Mini

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

Phase Coherence for BHEX Mini

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

Phase Coherence for BHEX Mini

Coherence Loss for BHEX Mini

L = 1-\exp\left(-2\pi^{2}f^{2}t^{2}\sigma_y^{2}\right)

Coherence Loss

Coherence Loss for BHEX Mini

Observing Frequency

L = 1-\exp\left(-2\pi^{2}f^{2}t^{2}\sigma_y^{2}\right)

Coherence Loss for BHEX Mini

Integration Time

L = 1-\exp\left(-2\pi^{2}f^{2}t^{2}\sigma_y^{2}\right)

Allan Deviation

L = 1-\exp\left(-2\pi^{2}f^{2}t^{2}\sigma_y^{2}\right)

Coherence Loss for BHEX Mini

Allan Deviation

f=86 \text{ GHz}, t=10s, \sigma_y = 5\cdot 10^{-11}

ABRACON SMD OCXO

L = 1-\exp\left(-2\pi^{2}f^{2}t^{2}\sigma_y^{2}\right)
L = 1-\exp\left(-2\pi^{2}f^{2}t^{2}\sigma_y^{2}\right)

Coherence Loss for BHEX Mini

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)

Coherence Loss for BHEX Mini

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}

Antenna Diameter for BHEX Mini

šŸ•’ Prospective Timeline

June

July

August

September

šŸ•’ Prospective Timeline

June

July

August

September

  • NASA NIAC 2025 Phase I Step I
  • SpaceCom Conference 2026
  • Brown Nelson + Hazeltine Grants
  • Antenna Focus
    • Nacer Chahat
    • Emmanuel Decrossas

šŸ•’ Prospective Timeline

June

July

August

September

  • Cryocooler Focus
    • Lucas Anderson
    • Katelyn Boushon
  • NSF Foundational Research in Robotics Grant (FRR)
  • Fall Walls Foundation Selections
  • NASA NIAC 2025 Phase I Step I
  • SpaceCom Conference 2026
  • Brown Nelson + Hazeltine Grants
  • Antenna Focus
    • Nacer Chahat
    • Emmanuel Decrossas

šŸ•’ Prospective Timeline

June

July

Aug

September

  • Cryocooler Focus
    • Lucas Anderson
    • Katelyn Boushon
  • NSF Foundational Research in Robotics Grant (FRR)
  • Fall Walls Foundation Selections
  • Brown University Co-LabĀ 
  • NASA NIAC Phase I Round I Step B Selections Announced
  • Solar Panel Focus
    • DCubed Inc.
    • DHV Tech
  • NASA NIAC 2025 Phase I Step I
  • SpaceCom Conference 2026
  • Brown Nelson + Hazeltine Grants
  • Antenna Focus
    • Nacer Chahat
    • Emmanuel Decrossas

šŸ•’ Prospective Timeline

June

July

Aug

Sep

  • Cryocooler Focus
    • Lucas Anderson
    • Katelyn Boushon
  • NSF Foundational Research in Robotics Grant (FRR)
  • Fall Walls Foundation Selections
  • Brown University Co-LabĀ 
  • NASA NIAC Phase I Round I Step B Selections Announced
  • Solar Panel Focus
    • DCubed Inc.
    • DHV Tech
  • NSF Advanced Technologies and Instrumentation for the Astronomical Sciences (ATI)Ā 
  • Data Downlink Focus
    • MIT Lincoln Labs
    • ALICE/CLICK Teams
  • NASA NIAC 2025 Phase I Step I
  • SpaceCom Conference 2026
  • Brown Nelson + Hazeltine Grants
  • Antenna Focus
    • Nacer Chahat
    • Emmanuel Decrossas

šŸ•’ Prospective Timeline

Antenna

šŸ•’ Prospective Timeline

Cryocooler

šŸ•’ Prospective Timeline

Solar Panels

šŸ•’ Prospective Timeline

Orbital Parameters

šŸ•’ Prospective Timeline

Data Downlink

šŸ•’ Prospective Timeline

Systems Integration

  1. šŸ•’ Prospective Timeline
  2. šŸ’°Funding Deadlines
  3. šŸŽÆ Primary Science Objectives
  4. šŸ”­ Antenna Requirements
  5. šŸ§  Ideas!

BHEX Mini

šŸ’°Funding Oppurtunities

June

$3,000

šŸ’°Funding Oppurtunities

July

NASA NIAC Phase I

$175,000

$3,000

$175,000

šŸ’°Funding Oppurtunities

Sep

NASA NIAC Phase I

$175,000

$3,000

$250,000

šŸ’°Funding Oppurtunities

NASA NIAC Phase I

Oct

$175,000

$3,000

$250,000

šŸ’°Funding Oppurtunities

  1. šŸ•’ Prospective Timeline
  2. šŸ’°Funding Deadlines
  3. šŸŽÆ Primary Science Objectives
  4. šŸ”­ Antenna Requirements
  5. šŸ§  Ideas!

BHEX Mini

\textbf{Primary Science Objective: }\text{Resolve extended black hole structure}
\text{Image black hole accretion disk at low frequency}
\text{Increase number of short Space-Ground baselines}
\text{Achieve first Space-Space VLBI}

šŸŽÆ Mission Statement

10 \text{ GHz}
47 \text{ GHz}
220 \text{ GHz}
1100 \text{ GHz}

šŸŽÆ Mission Statement

10 \text{ GHz}
47 \text{ GHz}
220 \text{ GHz}
1100 \text{ GHz}
\text{BHEX}
\text{BHEX Mini}
\text{EHT}

šŸŽÆ Mission Statement

\textbf{BHEX Mini}
\text{PR: 86 GHz}
\textbf{BHEX}
\text{PR: 230-345 GHz}\\ \text{SR: 86-120 GHz}
  1. šŸ•’ Prospective Timeline
  2. šŸ’°Funding Deadlines
  3. šŸŽÆ Primary Science Objectives
  4. šŸ”­ Antenna Requirements
  5. šŸ§  Ideas!

BHEX Mini

D
D\sim2 m
T\sim20^{\circ}K

SecondaryĀ 

Science Targets

Gaussian Source Approximation

Visibility Amplitudes

Thermal Noise Constraints

\sigma_{GS}=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_{\mathrm{G}} \mathrm{SEFD}_{\mathrm{S}}}{2 \Delta \nu \Delta t}}

SEFD Constraint

\sigma_{GS}=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_{\mathrm{G}} \mathrm{SEFD}_{\mathrm{S}}}{2 \Delta \nu \Delta t}}
\mathrm{SEFD}_S=\frac{2 k_{\mathrm{B}} T_{\mathrm{sys}}^*}{\eta_{\mathrm{A}} A}

Constraints

T,A
\sigma_{GS}=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_{\mathrm{G}} \mathrm{SEFD}_{\mathrm{S}}}{2 \Delta \nu \Delta t}}
\mathrm{SEFD}_S=\frac{2 k_{\mathrm{B}} T_{\mathrm{sys}}^*}{\eta_{\mathrm{A}} A}

Ā 

Parameter Space

\sigma, T,A
\sigma_{GS}=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_{\mathrm{G}} \mathrm{SEFD}_{\mathrm{S}}}{2 \Delta \nu \Delta t}}
D
\mathrm{SEFD}_S=\frac{2 k_{\mathrm{B}} T_{\mathrm{sys}}^*}{\eta_{\mathrm{A}} A}

Antenna Diameter + Temperature!

Visibility Amplitudes

Visibility Amplitudes

Visibility Amplitudes

Visibility Amplitudes

Visibility Amplitudes

Delta

Visibility Amplitudes

Delta

Visibility Amplitudes

Delta

Visibility Amplitudes

Delta

Visibility Amplitudes

Delta

V(b) = S\cdot \exp(-\pi^2 b^2\theta^2/4\ln 2)
V(b) = S\cdot \exp(-\pi^2 b^2\theta^2/4\ln 2)
\sigma_{SS}<\frac{|V_{SS}|}{SNR}, \sigma_{SG}<\frac{|V_{SG}|}{SNR}
\sigma_{SS}<\frac{|V_{SS}|}{SNR}, \sigma_{SG}<\frac{|V_{SG}|}{SNR}

BHEX Mini

  1. šŸ•’ Prospective Timeline
  2. šŸ’°Funding Deadlines
  3. šŸŽÆ Primary Science Objectives
  4. šŸ”­ Antenna Requirements
  5. šŸ§  Introduction to (u,v)Ā Plane

šŸ§  The (u,v)Ā Plane

šŸ§  The (u,v)Ā Plane

šŸ§  The (u,v)Ā Plane

šŸ§  The (u,v)Ā Plane

šŸ§  The (u,v)Ā Plane

šŸ§  The (u,v)Ā Plane

šŸ§  The (u,v)Ā Plane

šŸ§  The (u,v)Ā Plane

Goal:

I(l,m)

šŸ§  The (u,v)Ā Plane

I(l,m)

Intensity of a certain part of the sky/

sky brightness pattern

Goal: Measure

šŸ§  The (u,v)Ā Plane

Goal: Measure

I(l,m)

Coordinates in the sky

šŸ§  The (u,v)Ā Plane

Now we add the effects of the radio interferometer ...

I(l,m)

Coordinates in the sky

šŸ§  The (u,v)Ā Plane

Now we add the effects of the radio interferometer ...

I(l,m)

Multiplicative envelope:

comes from size of antennas

A(l,m)

šŸ§  The (u,v)Ā Plane

Now we add the effects of the radio interferometer ...

I(l,m)

Simulates interference pattern

A(l,m)
e^{-2\pi i (ul+vm)}

šŸ§  The (u,v)Ā Plane

Now we add the effects of the radio interferometer ...

I(l,m)

(u,v): Baseline vector

u: East-west baseline distance

v: North-south baseline distance

A(l,m)
e^{-2\pi i (ul+vm)}
\vec{b}=(u,v)

šŸ§  The (u,v)Ā Plane

Take all the signals from the sky and add them up ...

I(l,m)
A(l,m)
e^{-2\pi i (ul+vm)}
\int
dl dm
V(u,v)=

šŸ§  The (u,v)Ā Plane

Take all the signals from the sky and add them up ...

I(l,m)
A(l,m)
e^{-2\pi i (ul+vm)}
\int
dl dm
V(u,v)=

Visibility Function

šŸ§  The (u,v)Ā Plane

Take all the signals from the sky and add them up ...

I(l,m)
A(l,m)
e^{-2\pi i (ul+vm)}
\int
dl dm
V(u,v)=

Multiplicative Envelope

šŸ§  The (u,v)Ā Plane

Take all the signals from the sky and add them up ...

I(l,m)
A(l,m)
e^{-2\pi i (ul+vm)}
\int
dl dm
V(u,v)=

Sky Intensity/Brightness

šŸ§  The (u,v)Ā Plane

Take all the signals from the sky and add them up ...

I(l,m)
A(l,m)
e^{-2\pi i (ul+vm)}
\int
dl dm
V(u,v)=

Interferometric Pattern

\vec{b}=(u,v)

šŸ§  The (u,v)Ā Plane

It's a Fourier Transformation!

I(l,m)
A(l,m)
e^{-2\pi i (ul+vm)}
\int
dl dm
V(u,v)=

One pair of antennas measures one singleĀ point on the (u,v) plane: one fourier mode!

šŸ§  The (u,v)Ā Plane

It's a Fourier Transformation!

I(l,m)
A(l,m)
e^{-2\pi i (ul+vm)}
\int
dl dm
V(u,v)=

What we want

šŸ§  The (u,v)Ā Plane

It's a Fourier Transformation!

I(l,m)
A(l,m)
e^{-2\pi i (ul+vm)}
\int
dl dm
V(u,v)=

What we getĀ :(

šŸ§  The (u,v)Ā Plane

It's a Fourier Transformation!

Fill up the (u,v) plane

and then fourier transform back to the real image!

šŸ§  The (u,v)Ā Plane

It's a Fourier Transformation!

Fill up the (u,v) plane

and then fourier transform back to the real image!

šŸ§  The (u,v)Ā Plane

But how do you fill up the (u,v) plane?

šŸ§  The (u,v)Ā Plane

But how do you fill up the (u,v) plane?

  1. Use an array of antennas!
N \text{ antennas} = \frac{N(N-1)}{2} \text{ baselines}

šŸ§  The (u,v)Ā Plane

  1. Use an array of antennas!
N \text{ antennas} = \frac{N(N-1)}{2} \text{ baselines}

šŸ§  The (u,v)Ā Plane

  1. Use an array of antennas!
4 \text{ antennas} = \frac{4(3)}{2}=6 \text{ baselines}

šŸ§  The (u,v)Ā Plane

But how do you fill up the (u,v) plane?

  1. Use an array of antennas!
N \text{ antennas} = \frac{N(N-1)}{2} \text{ baselines}

2. Earth Rotation Aperture Synthesis

\vec{u} = \frac{\vec{b}\cdot \hat{s}}{\lambda}

šŸ§  The (u,v)Ā Plane

2. Earth Rotation Aperture Synthesis

\vec{u} = \frac{\vec{b}\cdot \hat{s}}{\lambda}
\vec{b}\cdot \hat{s}