BHEX Mini
BHEX Mini
Direct Imaging Black Holes from LEO
Ref Bari | 06/17 Update
\text{MEO} (20000 \text{ km})
\text{LEO} (400 \text{ km})
\textbf{BHEX}
\textbf{BHEX Mini}
Metrics and motivations for Earth–space VLBI: Time-resolving Sgr A* with the Event Horizon Telescope (Palumbo et. al., ApJ 2019)
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
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
Todd Ely
Joseph Lazio
Eric Burt
Ben Hudson
Luke Anderson
Rick Fleeter
- 🎯 Primary Science Objectives
- 🔭 SWAPC Requirements
- 📻 Antenna Dimensions
- 🧊 Cryocooler Requirements
- 🕰️ Frequency Reference System
- 🕒 BHEX Mini Timeline
- 💰Funding Deadlines
BHEX Mini
- 🎯 Primary Science Objectives
- 🔭 SWAPC Requirements
- 📻 Antenna Dimensions
- 🧊 Cryocooler Requirements
- 🕰️ Frequency Reference System
- 🕒 BHEX Mini Timeline
- 💰Funding Deadlines
BHEX Mini
🎯 Primary Science Objectives
Original Mission
Descoped Mission
Descope Mission #2
🎯 Primary Science Objectives
OG
- 86 GHz VLBI survey of AGN Targets with d~2.5m antenna
- Supplement (u,v) coverage of Sgr A*/M87 at 86 GHz
- Achieve first Space-Space VLBI
Descoped Mission
Descope Mission #2
🎯 Primary Science Objectives
OG
- 86 GHz VLBI survey of AGN Targets with d~2.5m antenna
- Supplement (u,v) 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
🎯 Primary Science Objectives
OG
- 86 GHz VLBI survey of AGN Targets with d~2.5m antenna
- Supplement (u,v) 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
🎯 Primary Science Objectives
10 \text{ GHz}
47 \text{ GHz}
220 \text{ GHz}
1100 \text{ GHz}
\text{BHEX}
\text{BHEX Mini}
\text{EHT}
- 🎯 Primary Science Objectives
- 🔭 SWAPC Requirements
- 📻 Antenna Dimensions
- 🧊 Cryocooler Requirements
- 🕰️ Frequency Reference System
- 🕒 BHEX Mini Timeline
- 💰Funding Deadlines
BHEX Mini
🔭 SWAPC Requirements
Antenna
Cryocooler
Frequency Reference System
🔭 SWAPC Requirements
Antenna
- Antenna Diameter:
- Primary Receiver Temperature:
- Antenna Areal Density:
2.2< d < 2.5m
T_r \sim 20^{\circ}K
2<\sigma<5 \text{ kg}/\text{m}^2
Cryocooler
Frequency Reference System
🔭 SWAPC Requirements
Antenna
RSP2
- Raytheon RSP2: Sterling-PT Hybrid (450W Input)
- Stage 1 (Sterling): 6W at 60K
- Stage 2 (Pulse Tube): 2.1W at 20K
- Antenna Diameter:
- Primary Receiver Temperature:
- Antenna Areal Density:
2.2< d < 2.5m
T_r \sim 20^{\circ}K
2<\sigma<5 \text{ kg}/\text{m}^2
Frequency Reference System
🔭 SWAPC Requirements
Antenna
RSP2
- Raytheon RSP2: Sterling-PT Hybrid (450W Input)
- Stage 1 (Sterling): 6W at 60K
- Stage 2 (Pulse Tube): 2.1W at 20K
USO
- LISA USO:
- RK409 Rakon USO:
- O-CS41 ABRACON OCXO:
- Antenna Diameter:
- Primary Receiver Temperature:
- Antenna Areal Density:
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)
🔭 SWAPC Requirements
Antenna
RSP2
- Raytheon RSP2: Sterling-PT Hybrid
- Stage 1 (Sterling): 6W at 60K
- Stage 2 (Pulse Tube): 2.1W at 20K
USO
- LISA USO:
- RK409 Rakon USO:
- O-CS41 ABRACON OCXO:
- Antenna Diameter:
- Primary Receiver Temperature:
- Antenna Areal Density:
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}
- 🎯 Primary Science Objectives
- 🔭 SWAPC Requirements
- 📻 Antenna Dimensions
- 🧊 Cryocooler Requirements
- 🕰️ Frequency Reference System
- 🕒 BHEX Mini Timeline
- 💰Funding Deadlines
BHEX Mini
📻 Antenna Dimensions
3C 84
NRAO 530
NGC 1052
BL Lac
3C 273
📻 Antenna Dimensions
3C 84
NRAO 530
NGC 1052
BL Lac
3C 273
📻 Antenna Dimensions
3C 84: Nucleus of galaxy NGC 1275 (22 GHz)
NRAO 530
NGC 1052
BL Lac
3C 273
📻 Antenna Dimensions
3C 84
NRAO 530: Quasar 230 GHz, 20 μas (EHT)
NGC 1052
BL Lac
3C 273
📻 Antenna Dimensions
3C 84
NRAO 530
NGC 1052: Bright Elliptical Galaxy (65 mln lys)
BL Lac
3C 273
📻 Antenna Dimensions
3C 84
NRAO 530
NGC 1052
BL Lac
3C 279: An 'optically violent' variable quasar
Gamma Ray Image
📻 Antenna Dimensions
3C 84
NRAO 530
NGC 1052
BL Lac
3C 273
📻 Antenna Dimensions
📻 Antenna Dimensions
📻 Antenna Dimensions
📻 Antenna Dimensions
📻 Antenna Dimensions
📻 Antenna Dimensions
- 🎯 Primary Science Objectives
- 🔭 SWAPC Requirements
- 📻 Antenna Dimensions
- 🧊 Cryocooler Requirements
- 🕰️ Frequency Reference System
- 🕒 BHEX Mini Timeline
- 💰Funding Deadlines
BHEX Mini
🧊 Cryocooler Requirements
LT-RSP2 Cryocooler
Raytheon long life cryocoolers for future space missions (T. Conrad et. al., Cryogenics 2017)
🧊 Cryocooler Requirements
Stirling Cryocooler
Development of Advanced Two-Stage Stirling Cryocooler for Next Space Missions (Y. Sato et. al., Cryocoolers 15, 2009)
🧊 Cryocooler Requirements
Stirling Cryocooler
Development of Advanced Two-Stage Stirling Cryocooler for Next Space Missions (Y. Sato et. al., Cryocoolers 15, 2009)
🧊 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
🕒 Prospective Timeline
June
July
August
September
🕒 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
🕒 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
🕒 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-Lab
- 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
🕒 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-Lab
- 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)
-
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
🕒 Prospective Timeline
Antenna
🕒 Prospective Timeline
Cryocooler
🕒 Prospective Timeline
Solar Panels
🕒 Prospective Timeline
Orbital Parameters
🕒 Prospective Timeline
Data Downlink
🕒 Prospective Timeline
Systems Integration
- 🕒 Prospective Timeline
- 💰Funding Deadlines
- 🎯 Primary Science Objectives
- 🔭 Antenna Requirements
- 🧠 Ideas!
BHEX Mini
💰Funding Oppurtunities
June
$3,000
💰Funding Oppurtunities
July
$175,000
$3,000
$175,000
💰Funding Oppurtunities
Sep
$175,000
$3,000
$250,000
💰Funding Oppurtunities
Oct
$175,000
$3,000
$250,000
💰Funding Oppurtunities
- 🕒 Prospective Timeline
- 💰Funding Deadlines
- 🎯 Primary Science Objectives
- 🔭 Antenna Requirements
- 🧠 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}
🎯 Mission Statement
10 \text{ GHz}
47 \text{ GHz}
220 \text{ GHz}
1100 \text{ GHz}
🎯 Mission Statement
10 \text{ GHz}
47 \text{ GHz}
220 \text{ GHz}
1100 \text{ GHz}
\text{BHEX}
\text{BHEX Mini}
\text{EHT}
🎯 Mission Statement
\textbf{BHEX Mini}
\text{PR: 86 GHz}
\textbf{BHEX}
\text{PR: 230-345 GHz}\\ \text{SR: 86-120 GHz}
- 🕒 Prospective Timeline
- 💰Funding Deadlines
- 🎯 Primary Science Objectives
- 🔭 Antenna Requirements
- 🧠 Ideas!
BHEX Mini
D
D\sim2 m
T\sim20^{\circ}K
Secondary
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}
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
- 🕒 Prospective Timeline
- 💰Funding Deadlines
- 🎯 Primary Science Objectives
- 🔭 Antenna Requirements
- 🧠 Introduction to (u,v) Plane
🧠 The (u,v) Plane
🧠 The (u,v) Plane
🧠 The (u,v) Plane
🧠 The (u,v) Plane
🧠 The (u,v) Plane
🧠 The (u,v) Plane
🧠 The (u,v) Plane
🧠 The (u,v) Plane
Goal:
I(l,m)
🧠 The (u,v) Plane
I(l,m)
Intensity of a certain part of the sky/
sky brightness pattern
Goal: Measure
🧠 The (u,v) Plane
Goal: Measure
I(l,m)
Coordinates in the sky
🧠 The (u,v) Plane
Now we add the effects of the radio interferometer ...
I(l,m)
Coordinates in the sky
🧠 The (u,v) Plane
Now we add the effects of the radio interferometer ...
I(l,m)
Multiplicative envelope:
comes from size of antennas
A(l,m)
🧠 The (u,v) 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)}
🧠 The (u,v) 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)
🧠 The (u,v) 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)=
🧠 The (u,v) 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
🧠 The (u,v) 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
🧠 The (u,v) 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
🧠 The (u,v) 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)
🧠 The (u,v) 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 single point on the (u,v) plane: one fourier mode!
🧠 The (u,v) 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
🧠 The (u,v) 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 get :(
🧠 The (u,v) Plane
It's a Fourier Transformation!
Fill up the (u,v) plane
and then fourier transform back to the real image!
🧠 The (u,v) Plane
It's a Fourier Transformation!
Fill up the (u,v) plane
and then fourier transform back to the real image!
🧠 The (u,v) Plane
But how do you fill up the (u,v) plane?
🧠 The (u,v) Plane
But how do you fill up the (u,v) plane?
- Use an array of antennas!
N \text{ antennas} = \frac{N(N-1)}{2} \text{ baselines}
🧠 The (u,v) Plane
- Use an array of antennas!
N \text{ antennas} = \frac{N(N-1)}{2} \text{ baselines}
🧠 The (u,v) Plane
- Use an array of antennas!
4 \text{ antennas} = \frac{4(3)}{2}=6 \text{ baselines}
🧠 The (u,v) Plane
But how do you fill up the (u,v) plane?
- 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}
🧠 The (u,v) Plane
2. Earth Rotation Aperture Synthesis
\vec{u} = \frac{\vec{b}\cdot \hat{s}}{\lambda}
\vec{b}\cdot \hat{s}
BHEX Mini | Ben & Luke Meeting
By Ref Bari
