Time-Resolving Sgr A* from LEO

Ref Bari (Brown University)

T-REX

T-REX

T-REX

T-REX

Optical Terminals

RF Tracking Stations

VLBI Ground Stations

\text{T-REX}

T-REX Data Center

% Gain Error

NRMSE

25%

50%

100%

0.5

Bispectrum

Cl Amplitude + Cl Phase

T-REX

SWaPC

Antenna

Cryocooler

Receiver

Oscillator

Backend

Downlink

Satellite Bus

Cost

Weight

Power

\$2-5 \text{Mln}

\$10 \text{mln}

\$1 \text{mln}

\$5 \text{mln}

\sim 25-50kg

5-7 kg

22 kg

1 kg

3 kg

10W

10-20W

\sim 10W

\sim 4W

1kW

\sim 4W

\sim \$30 \text{mln}

Component

T-REX

T-REX

600\text{km}

640\text{km}

620\text{km}

# LEO satellite altitudes [km] - triangular constellation
altitudes_km = [600.0, 620.0, 640.0]
sat_names = ["SAT1", "SAT2", "SAT3"]

# Common orbital elements
inc_deg = 85.0         
ecc = 0.0              
argp_deg = 0.0        

# RAAN spacing: 120° apart for triangle
raan_base_deg = 110.0
raan_offsets = [0.0, 120.0, 240.0]

T-REX

600\text{km}

640\text{km}

620\text{km}

# LEO satellite altitudes [km] - triangle
altitudes_km = [600.0, 620.0, 640.0]
sat_names = ["SAT1", "SAT2", "SAT3"]

# Common orbital elements
inc_deg = 85.0  # Inclination
ecc = 0.0       # Eccentricity
argp_deg = 0.0  # Arg of Perigee

# RAAN spacing: 120° apart for triangle
raan_base_deg = 110.0
raan_offsets = [0.0, 120.0, 240.0]

T-REX

6,000\text{km}

85^{\circ}

# LEO satellite altitudes [km] - triangle
altitudes_km = [600.0, 620.0, 640.0]
sat_names = ["SAT1", "SAT2", "SAT3"]

# Common orbital elements
inc_deg = 85.0  # Inclination
ecc = 0.0       # Eccentricity
argp_deg = 0.0  # Arg of Perigee

# RAAN spacing: 120° apart for triangle
raan_base_deg = 110.0
raan_offsets = [0.0, 120.0, 240.0]

T-REX

6,000\text{km}

# LEO satellite altitudes [km] - triangle
altitudes_km = [600.0, 620.0, 640.0]
sat_names = ["SAT1", "SAT2", "SAT3"]

# Common orbital elements
inc_deg = 85.0  # Inclination
ecc = 0.0       # Eccentricity
argp_deg = 0.0  # Arg of Perigee

# RAAN spacing: 120° apart for triangle
raan_base_deg = 110.0
raan_offsets = [0.0, 120.0, 240.0]

T-REX

6,000\text{km}

120^{\circ}

# LEO satellite altitudes [km] - triangle
altitudes_km = [600.0, 620.0, 640.0]
sat_names = ["SAT1", "SAT2", "SAT3"]

# Common orbital elements
inc_deg = 85.0  # Inclination
ecc = 0.0       # Eccentricity
argp_deg = 0.0  # Arg of Perigee

# RAAN spacing: 120° apart for triangle
raan_base_deg = 110.0
raan_offsets = [0.0, 120.0, 240.0]

T-REX

6,000\text{km}

# Sgr A* coordinates
ra_hr = 17 + 45/60 + 40.0383/3600       # 17h 45m 40.0383s
dec_deg = -(29 + 0/60 + 28.069/3600)    # -29° 00' 28.069"

# Observation setup
rf = 230e9  # Reference frequency [Hz] (230 GHz)
bw = 4e9    # Bandwidth [Hz]
mjd = 58211 # Modified Julian Date (April 2018)

# Scheduling
tint = 10.0    # Integration time [s]
tadv = 60.0    # Cadence between samples [s]
tstart = 0.0   # Start time [hr UTC]
tstop = 24.0   # Stop time [hr UTC]
elevmin = 15.0 # Min ground elevation [deg]

(\text{RA, DEC})

T-REX

# Sgr A* coordinates
ra_hr = 17 + 45/60 + 40.0383/3600       # 17h 45m 40.0383s
dec_deg = -(29 + 0/60 + 28.069/3600)    # -29° 00' 28.069"

# Observation setup
rf = 86e9  # Reference frequency [Hz]
bw = 8e9    # Bandwidth [Hz]
mjd = 26226 # Modified Julian Date

10 \text{ GHz}

47 \text{ GHz}

220 \text{ GHz}

1100 \text{ GHz}

T-REX

# Scheduling
tint = 10.0   # Integration time [s]
tadv = 60.0   # Cadence between samples [s]
tstart = 0.0  # Start time [hr UTC]
tstop = 24.0  # Stop time [hr UTC]
elevmin = 15  # Minimum elevation for ground stations [deg]

t_{\text{start}}=0

t_{\text{stop}}=24\text{ hr}

t_{\text{int}}=10s

\Delta t=60s

T-REX

# Scheduling
tint = 10.0   # Integration time [s]
tadv = 60.0   # Cadence between samples [s]
tstart = 0.0  # Start time [hr UTC]
tstop = 24.0  # Stop time [hr UTC]
elevmin = 15  # Minimum elevation for ground stations [deg]

t_{\text{start}}=0

t_{\text{stop}}=24\text{ hr}

t_{\text{int}}=10s

\Delta t=60s

T-REX

# Scheduling
tint = 10.0   # Integration time [s]
tadv = 60.0   # Cadence between samples [s]
tstart = 0.0  # Start time [hr UTC]
tstop = 24.0  # Stop time [hr UTC]
elevmin = 15  # Minimum elevation for ground stations [deg]

t_{\text{start}}=0

t_{\text{stop}}=24\text{ hr}

15^{\circ}

\Delta t=60s

T-REX

T-REX

# Generate observation with uv sampling (no visibilities yet)
obs0 = arr.obsdata(
    ra_hr, dec_deg, rf, bw,
    tint=tint, tadv=tadv, tstart=tstart, tstop=tstop,
    mjd=mjd, timetype='UTC', polrep='stokes',
    elevmin=elevmin, no_elevcut_space=True
)

T-REX

# Simple Gaussian source for debugging
total_flux = 2.0                           # Total flux [Jy]
fwhm_uas = 60.0                            # FWHM [μas]
fwhm_rad = fwhm_uas * eh.RADPERUAS         # FWHM [rad]

\mathcal{F}=2\text{ Jy}

\sim 60\mu as

T-REX

# Simple Ring source
total_flux = 2.0                   
fwhm_uas = 60.0                   
fwhm_rad = fwhm_uas * eh.RADPERUAS

T-REX

# SEFDs (System Equivalent Flux Density)
alma_sefd = 100.0      # ALMA SEFD
sat_sefd = 60000.0     # Space antennas

# Initialize empty array
arr = eh.array.Array(np.array([], dtype=ehc.DTARR))

# Add ALMA
arr = arr.add_site("ALMA", coords=(ALMA_x, ALMA_y, ALMA_z), sefd=alma_sefd)

# Add T-REX
for i, params in enumerate(orbital_params):
    # Phase the satellites in their orbits (spread by 1/3 of period)
    perigee_offset_days = i * params['period_days'] / 3.0

    arr = arr.add_satellite_elements(
        params['name'],
        perigee_mjd=mjd + tstart/24.0 + perigee_offset_days,
        period_days=params['period_days'],
        eccentricity=ecc,
        inclination=inc_deg,
        arg_perigee=argp_deg,
        long_ascending=params['raan_deg'],
        sefd=sat_sefd
    )

ALMA

T-REX

# SEFDs (System Equivalent Flux Density)
alma_sefd = 100.0      # ALMA SEFD
sat_sefd = 60000.0     # Space antennas

# Initialize empty array
arr = eh.array.Array(np.array([], dtype=ehc.DTARR))

# Add ALMA
arr = arr.add_site("ALMA", coords=(ALMA_x, ALMA_y, ALMA_z), sefd=alma_sefd)

# Add T-REX
for i, params in enumerate(orbital_params):
    # Phase the satellites in their orbits (spread by 1/3 of period)
    perigee_offset_days = i * params['period_days'] / 3.0

    arr = arr.add_satellite_elements(
        params['name'],
        perigee_mjd=mjd + tstart/24.0 + perigee_offset_days,
        period_days=params['period_days'],
        eccentricity=ecc,
        inclination=inc_deg,
        arg_perigee=argp_deg,
        long_ascending=params['raan_deg'],
        sefd=sat_sefd
    )

ALMA

T-REX

# Generate observation with uv sampling (no visibilities yet)
obs0 = arr.obsdata(
    ra_hr, dec_deg, rf, bw,
    tint=tint, tadv=tadv, tstart=tstart, tstop=tstop,
    mjd=mjd, timetype='UTC', polrep='stokes',
    elevmin=elevmin, no_elevcut_space=True
)

T-REX

T-REX

T-REX

T-REX

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

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

Satellite Bus Class

Bus Parameters

Bus Payload Capacity

T-REX Bus

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

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-REX Bus

SBC

ESPA-Grande
4-point mount launch vehicle interface
Compliant to SpaceX Rideshare

Energy Storage: 75 Ah
Orbital lifetime: LEO (>5 yrs)
Solar Array Power: 1876 W (50% sunlight for LEO ~ 1kW)

BPC

Standard rideshare payload capability: 250 kg
Pointing accuracy: 0.002 (1-sigma), 3 axes, 2 trackers
40.0" x 40.0" x 45.0" (objective)
Slew rate: 3.1 deg/sec

T-REX

Introduction
Science Traceability Matrix
Primary Science Objectives
SWaPC Requirements
NASA Mission Life Cycle
Work Breakdown Structure (WBS)
Critical Mission Parameters
Preliminary Concept of Operations
Expected Data Products
Funding & Timeline

T-REX

Introduction
Science Traceability Matrix
Primary Science Objectives
SWaPC Requirements
NASA Mission Life Cycle
Work Breakdown Structure (WBS)
Critical Mission Parameters
Preliminary Concept of Operations
Expected Data Products
Funding & Timeline

T-REX

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

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-REX

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

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

Introduction
Science Traceability Matrix
Primary Science Objectives
SWaPC Requirements
NASA Mission Life Cycle
Work Breakdown Structure (WBS)
Critical Mission Parameters
Preliminary Concept of Operations
Expected Data Products
Funding & Timeline

T-REX

Introduction
Science Traceability Matrix
Primary Science Objectives
SWaPC Requirements
NASA Mission Life Cycle
Work Breakdown Structure (WBS)
Critical Mission Parameters
Preliminary Concept of Operations
Expected Data Products
Funding & Timeline

T-REX

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

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-REX

Introduction
Science Traceability Matrix
Primary Science Objectives
SWaPC Requirements
NASA Mission Life Cycle
Work Breakdown Structure (WBS)
Critical Mission Parameters
Preliminary Concept of Operations
Expected Data Products
Funding & Timeline

T-REX

Introduction
Science Traceability Matrix
Primary Science Objectives
SWaPC Requirements
NASA Mission Life Cycle
Work Breakdown Structure (WBS)
Critical Mission Parameters
Preliminary Concept of Operations
Expected Data Products
Funding & Timeline

T-REX

Mission Parameters

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})\sim 20,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}

\theta_{\text{T-REX - EHT}} \sim 35 \mu as

\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}

\tau_{\text{Coherence, T-REX}}\lessapprox 2 \text{ min} \sim 120 s

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 66,000 \text{ Jy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

Introduction
Science Traceability Matrix
Primary Science Objectives
SWaPC Requirements
NASA Mission Life Cycle
Work Breakdown Structure (WBS)
Critical Mission Parameters
Preliminary Concept of Operations
Expected Data Products
Funding & Timeline

T-REX

Introduction
Science Traceability Matrix
Primary Science Objectives
SWaPC Requirements
NASA Mission Life Cycle
Work Breakdown Structure (WBS)
Critical Mission Parameters
Preliminary Concept of Operations
Expected Data Products
Funding & Timeline

T-REX

Introduction
Science Traceability Matrix
Primary Science Objectives
SWaPC Requirements
NASA Mission Life Cycle
Work Breakdown Structure (WBS)
Critical Mission Parameters
Preliminary Concept of Operations
Expected Data Products
Funding & Timeline

T-REX

Introduction
Science Traceability Matrix
Primary Science Objectives
SWaPC Requirements
NASA Mission Life Cycle
Work Breakdown Structure (WBS)
Critical Mission Parameters
Preliminary Concept of Operations
Expected Data Products
Funding & Timeline

T-REX

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

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-REX

T-REX

T-REX

f_{obs}

f_{obs}=86\text{ GHz}

T-REX

f_{obs}

f_{obs}=150\text{ GHz}

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

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

f_{obs}=86\text{ GHz}

5.6 G \lambda < b_{s s}<9.3 G \lambda

T-REX

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

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-REX

f_{obs}=150\text{ GHz}

Introduction
Science Traceability Matrix
Primary Science Objectives
SWaPC Requirements
NASA Mission Life Cycle
Work Breakdown Structure (WBS)
Critical Mission Parameters
Preliminary Concept of Operations
Expected Data Products
Funding & Timeline

T-REX

Introduction
Science Traceability Matrix
Primary Science Objectives
SWaPC Requirements
NASA Mission Life Cycle
Work Breakdown Structure (WBS)
Critical Mission Parameters
Preliminary Concept of Operations
Expected Data Products
Funding & Timeline

T-REX

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

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-REX

Oct

NASA NIAC Phase I
- Submitted: July 15
- Decision: Sep 6

$175,000

$60,000

Brown DSI Grant
- Submitted: Oct 15
- Decision: Dec 10

AAS Splinter Meeting
- Submitted: Sep 25
- Decision: Oct 30

CSA FAST Grant
- Submitted: Oct 26
- Decision: Dec 15

>$400,000

Introduction
What is a black hole?
How do you image a black hole?
How do you record a black hole?
T-REX Primary Science Objectives
T-REX (u,v) Coverage
T-REX Engineering Challenges
T-REX SWaPC Requirements
T-REX Concept of Operations
T-REX Timeline & Funding Deadlines

T-REX

T-REX

T-REX

Event Horizon

Singularity

T-REX

Event Horizon

Singularity

Photon Sphere

1.5R

T-REX

Event Horizon

Black Hole Shadow

1.5R

Photon Ring

2.6R_s

T-REX

Event Horizon

Black Hole Shadow

1.5R_s

Photon Ring

2.6R_s

Innermost Stable

Circular Orbit

3R_s

T-REX

ds^2 = -\left(1-\frac{2M}{R}\right)dt^2 + -\left(1-\frac{2M}{R}\right)^{-1}dr^2 + r^2 d\Omega^2

p^\mu p_\mu = -m^2 \to \left(\frac{dr}{d\tau}\right)^2=E^2-\left(1-\frac{2M}{r} \right)\left(1+ \frac{L^2}{r^2}\right)

Event Horizon

Photon Ring

Shadow

ISCO

T-REX

ds^2 = -\left(1-\frac{2M}{R}\right)dt^2 + -\left(1-\frac{2M}{R}\right)^{-1}dr^2 + r^2 d\Omega^2

p^\mu p_\mu = -m^2 \to \left(\frac{dr}{d\tau}\right)^2=E^2-\left(1-\frac{2M}{r} \right)\left(1+ \frac{L^2}{r^2}\right)

Event Horizon

Photon Ring

Shadow

ISCO

T-REX

ds^2 = -\left(1-\frac{2M}{R}\right)dt^2 + -\left(1-\frac{2M}{R}\right)^{-1}dr^2 + r^2 d\Omega^2

p^\mu p_\mu = -m^2 \to \left(\frac{dr}{d\tau}\right)^2=E^2-\left(1-\frac{2M}{r} \right)\left(1+ \frac{L^2}{r^2}\right)

Event Horizon

Photon Ring

Shadow

ISCO

Photon Ring

T-REX

ds^2 = -\left(1-\frac{2M}{R}\right)dt^2 + -\left(1-\frac{2M}{R}\right)^{-1}dr^2 + r^2 d\Omega^2

p^\mu p_\mu = -m^2 \to \left(\frac{dr}{d\tau}\right)^2=E^2-\left(1-\frac{2M}{r} \right)\left(\frac{L^2}{r^2}\right)

Event Horizon

Photon Ring

Shadow

ISCO

Photon Ring

T-REX

ds^2 = -\left(1-\frac{2M}{R}\right)dt^2 + -\left(1-\frac{2M}{R}\right)^{-1}dr^2 + r^2 d\Omega^2

p^\mu p_\mu = -m^2 \to \left(\frac{dr}{d\tau}\right)^2=E^2-\left(1-\frac{2M}{r} \right)\left(1+\frac{L^2}{r^2}\right)

Event Horizon

Photon Ring

Shadow

ISCO

T-REX

T-REX

T-REX

Introduction
What is a black hole?
How do you image a black hole?
How do you record a black hole?
T-REX Primary Science Objectives
T-REX (u,v) Coverage
T-REX Engineering Challenges
T-REX SWaPC Requirements
T-REX Concept of Operations
T-REX Timeline & Funding Deadlines

T-REX

M87

T-REX

SED, Sgr A*

The Supermassive Black Hole at the Galactic Center (Melia & Falcke, 2001)

T-REX

Spectral Energy Distribution (Sgr A*)

The Supermassive Black Hole at the Galactic Center (Melia & Falcke, 2001)

radio

infrared

T-REX

SED, Sgr A*

The Supermassive Black Hole at the Galactic Center (Melia & Falcke, 2001)

T-REX

SED, Sgr A*

The Supermassive Black Hole at the Galactic Center (Melia & Falcke, 2001)

\theta\sim \frac{\lambda}{D}

\sim 50\mu as

T-REX

\sim 50\mu as

T-REX

\sim 50\mu as

T-REX

SED, Sgr A*

The Supermassive Black Hole at the Galactic Center (Melia & Falcke, 2001)

\theta\sim \frac{\lambda}{D}

\sim 50\mu as

T-REX

T-REX

Knox et al., “Spatial coherence from ducks”, Physics Today, March 2010

T-REX

T-REX

T-REX

T-REX

T-REX

E_1

E_2

T-REX

V(r_1 ,r_2)=\langle E_1^*

E_2\rangle

T-REX

V(r_1 ,r_2)=\langle E_1^*

E_2\rangle

T-REX

V(r_1 ,r_2)=\langle E_1^*

E_2\rangle

T-REX

V(r_1 ,r_2)=\langle E_1^*

E_2\rangle

T-REX

V(r_1 ,r_2)=\langle E_1^*

E_2\rangle

E_1

E_2

T-REX

T-REX

T-REX

T-REX

T-REX

T-REX

T-REX

T-REX

T-REX

EHT

(2019)

Event Horizon Telescope (EHT)

BHEX

(2031)

Black Hole Explorer Satellite (BHEX) Mission

BHEX

Introduction
What is a black hole?
How do you image a black hole?
How do you record a black hole?
T-REX Primary Science Objectives
T-REX (u,v) Coverage
T-REX Engineering Challenges
T-REX SWaPC Requirements
T-REX Concept of Operations
T-REX Timeline & Funding Deadlines

T-REX

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

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-REX

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}

Time-scale of Sgr A* accretion disk: 4<T<30 minutes (0<J<1)
Time-scale of LEO Orbit: 90 minutes, with 22-minute (u,v) coverage

T-REX

Sub-milli arcsecond angular resolution:

Dual short and long baseline lengths

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-REX

\text{To time resolve Sgr A*, we must have} \\f_{coverage}>50\% \text{ in } t < T_{ISCO} \sim 30 \text{ min}

Introduction
What is a black hole?
How do you image a black hole?
How do you record a black hole?
T-REX Primary Science Objectives
T-REX (u,v) Coverage
T-REX Engineering Challenges
T-REX SWaPC Requirements
T-REX Concept of Operations
T-REX Timeline & Funding Deadlines

T-REX

T-REX

Capture Time-Resolved Videos of M87 & Sgr A*

Time-Resolve Binary Black Hole Systems

Conduct VLBI Survey of AGN targets at 86 GHz

T-REX

Capture Time-Resolved Videos of M87 & Sgr A*

Time-Resolve Binary Black Hole Systems

Conduct VLBI Survey of AGN targets at 86 GHz

T-REX

Supplement (u,v) coverage at 86 GHz

Enable parameter estimation of Sgr A*/M87

400\text{ km}

Capture Time-Resolved Videos of M87 & Sgr A*

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

T-REX

T-REX

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

T-REX

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

T-REX

T-REX

$$\alpha=-\frac{\xi}{\sin i}, \quad \beta= \pm \sqrt{\eta+a^2 \cos ^2 i-\xi^2 \cot ^2 i}$$

$$M=\frac{c^2 D}{G} \frac{\theta_{sh}}{\mathcal{F}(a, i)}$$

\xi=\xi(r, M, a), \, \, \, \, \eta=\eta(r, M, a)

T-REX

\dot{M} = -2\pi R \rho u_R

T(R) = 2\pi \nu \rho R^3 \frac{d\Omega}{dR}

\Omega(R) = \sqrt{\frac{GM}{R^3}}

T-REX

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}

Videos of M87 & Sgr A*

"The Black Hole Explorer: Motivation and Vision" Johnson et. al. arXiv 2024

T-REX

Capture Time-Resolved Videos of M87 & Sgr A*

Time-Resolve Binary Black Hole Systems

Conduct VLBI Survey of AGN targets at 86 GHz

T-REX

Time-Resolve Binary Black Hole Systems

T-REX

Time-Resolve Binary Black Hole Systems

T-REX

Time-Resolve Binary Black Hole Systems

T-REX

Capture Time-Resolved Videos of M87 & Sgr A*

Time-Resolve Binary Black Hole Systems

Conduct VLBI Survey of AGN targets at 86 GHz

T-REX

Conduct VLBI Survey of AGN targets at 86 GHz

"The Black Hole Explorer: Motivation and Vision" Johnson et. al. arXiv 2024

T-REX

Introduction
What is a black hole?
How do you image a black hole?
How do you record a black hole?
T-REX Primary Science Objectives
T-REX (u,v) Coverage
T-REX Engineering Challenges
T-REX SWaPC Requirements
T-REX Concept of Operations
T-REX Timeline & Funding Deadlines

T-REX

20000\text{ km}

400\text{ km}

\text{MEO Satellite}

\text{T-REX}

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

\text{T-REX}

\text{EHT}

\text{T-REX}

\text{EHT}

\text{LEO}

\text{MEO}

T-REX

\text{MEO Satellite}

M87

Sgr A*

10:15

11:00

8:00

Sgr A*

10:15

11:00

8:00

T-REX

a=13,000 \text{ km}

a=26,000 \text{ km}

a=6,000 \text{ km}

t_{\text{res}}\sim22.5 min

\theta_{\text{res}}\sim 35 \mu as

t_{\text{res}}\sim1 hr

\theta_{\text{res}}\sim 10 \mu as

t_{\text{res}}\sim3 hr

\theta_{\text{res}}\sim 6 \mu as

a=13,000 \text{ km}

a=26,000 \text{ km}

a=6,000 \text{ km}

t_{\text{res}}\sim22.5 min

\theta_{\text{res}}\sim 35 \mu as

t_{\text{res}}\sim1 hr

\theta_{\text{res}}\sim 10 \mu as

t_{\text{res}}\sim3 hr

\theta_{\text{res}}\sim 6 \mu as

a=13,000 \text{ km}

a=26,000 \text{ km}

a=6,000 \text{ km}

t_{\text{res}}\sim22.5 min

\theta_{\text{res}}\sim 35 \mu as

t_{\text{res}}\sim1 hr

\theta_{\text{res}}\sim 10 \mu as

t_{\text{res}}\sim3 hr

\theta_{\text{res}}\sim 6 \mu as

T-REX

T-REX

t=30\min

t=60\min

t=24 \text{ hr}

86 \text{ GHz}

230 \text{ GHz}

320 \text{ GHz}

"Imaging the event horizon of M87* from space on different timescales" Shlentsova et. al. ApJ 2024

Introduction
What is a black hole?
How do you image a black hole?
How do you record a black hole?
T-REX Primary Science Objectives
T-REX (u,v) Coverage
T-REX Engineering Challenges
T-REX SWaPC Requirements
T-REX Concept of Operations
T-REX Timeline & Funding Deadlines

T-REX

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

Decreased signal loss

Decreased radiation environment

Infrared Thermal Emissions

Limited Ground Coverage

Aggressive Slew Rate Required

Potential Reduced ISM Scattering

mm-wavelength angular resolution

Dual-baseline capability

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

Decreased signal loss

Decreased radiation environment

Infrared Thermal Emissions

Limited Ground Coverage

Aggressive Slew Rate Required

Potential Reduced ISM Scattering

mm-wavelength angular resolution

Dual-baseline capability

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

a=6,000 \text{ km}

\text{M}87

\text{Sgr} A^*

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

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

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

Decreased signal loss

Decreased radiation environment

Infrared Thermal Emissions

Limited Ground Coverage

Aggressive Slew Rate Required

Potential Reduced ISM Scattering

mm-wavelength angular resolution

Dual-baseline capability

T-REX

\text{T-REX}

\text{EHT}

Decreased signal loss

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

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

Decreased signal loss

Decreased radiation environment

Infrared Thermal Emissions

Limited Ground Coverage

Aggressive Slew Rate Required

Potential Reduced ISM Scattering

mm-wavelength angular resolution

Dual-baseline capability

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

Decreased signal loss

Decreased radiation environment

Infrared Thermal Emissions

Limited Ground Coverage

Aggressive Slew Rate Required

Potential Reduced ISM Scattering

mm-wavelength angular resolution

Dual-baseline capability

T-REX

\text{T-REX}

\text{EHT}

Potential Reduced ISM Scattering

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

T-REX

T-REX

\text{T-REX}

\text{EHT}

Potential Reduced ISM Scattering

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)

T-REX

\text{T-REX}

\text{EHT}

Potential Reduced ISM Scattering

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

Decreased signal loss

Decreased radiation environment

Infrared Thermal Emissions

Limited Ground Coverage

Aggressive Slew Rate Required

Potential Reduced ISM Scattering

mm-wavelength resolution

Dual-baseline capability

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

Decreased signal loss

Decreased radiation environment

Infrared Thermal Emissions

Limited Ground Coverage

Aggressive Slew Rate Required

Potential Reduced ISM Scattering

mm-wavelength resolution

32\mu as<\theta_{\text{T-REX}} < 1800 \mu as

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

Decreased signal loss

Decreased radiation environment

Infrared Thermal Emissions

Limited Ground Coverage

Aggressive Slew Rate Required

Potential Reduced ISM Scattering

mm-wavelength resolution

Dual-baseline capability

T-REX

\text{T-REX}

\text{EHT}

Dual-baseline capability

\text{BHEX}

Rapid coverage of (u,v) plane

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

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

T-REX

\text{T-REX}

\text{EHT}

Dual-baseline capability

\text{BHEX}

Decreased signal loss from LEO

Decreased radiation environment in LEO vs. MEO

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

T-REX

\text{T-REX}

\text{EHT}

Dual-baseline capability

\text{BHEX}

\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}

\sigma=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_1 \mathrm{SEFD}_2}{2 \Delta \nu \tau}}

\text{Coherence Time}

\text{Thermal Noise}

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

Decreased signal loss

Decreased radiation environment

Infrared Thermal Emissions

Limited Ground Coverage

Aggressive Slew Rate Required

Potential Reduced ISM Scattering

mm-wavelength resolution

Dual-baseline capability

T-REX

\text{T-REX}

\text{EHT}

Infrared Thermal Emissions

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

Decreased signal loss

Decreased radiation environment

Infrared Thermal Emissions

Limited Ground Coverage

Aggressive Slew Rate Required

Potential Reduced ISM Scattering

mm-wavelength resolution

Dual-baseline capability

T-REX

\text{T-REX}

\text{EHT}

Limited Ground Coverage

T-REX

\text{T-REX}

\text{EHT}

Limited Ground Coverage

T-REX

\text{T-REX}

\text{EHT}

Limited Ground Coverage

T-REX

\text{T-REX}

\text{EHT}

Rapid (u,v) coverage

Decreased signal loss

Decreased radiation environment

Infrared Thermal Emissions

Limited Ground Coverage

Aggressive Slew Rate Required

Potential Reduced ISM Scattering

mm-wavelength resolution

Dual-baseline capability

T-REX

\text{T-REX}

\text{EHT}

Aggressive Slew Rate Required

Introduction
What is a black hole?
How do you image a black hole?
How do you record a black hole?
T-REX Primary Science Objectives
T-REX (u,v) Coverage
T-REX Engineering Challenges
T-REX SWaPC Requirements
T-REX Concept of Operations
T-REX Timeline & Funding Deadlines

T-REX

T-REX SWaPC

Size

Weight

Power

Cost

\sim 2.5m

\sim 25-50kg

22 kg

300W

400mW @15^{\circ}K

\$10 \text{mln}

754 mm \times \\ 146 mm \times \\ 300 mm

\$2-5 \text{Mln}

\$4-11 \text{Mln}

10-20W

\text{(deployment)}

5-7 kg

\sim 10W

\sim \$ 1 \text{mln}

\sim0.02m^3

\sim 1 kg

\sim 3W

\sim \$1\text{mln}^*

60 mm\times \\60mm \times \\32 mm

1U (100 mm\times \\100 mm \times \\100 mm)

1.2 kg

100W\\\text{generated}

\sim \$100\text{k}

3U (300 mm\times \\300 mm \times \\300 mm)

100W

3 kg

\sim \$1\text{mln}^*

\sim 4W

\sim 1 kg^*

12 mm \times \\12 mm

\sim \$1\text{mln}^*

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

NASA Pioneers

Aspera

Pandora

StarBurst

PUEO

(Galaxy Evolution via UV)

(Exoplanet Explorer)

(Neutron Stars via Gamma Rays)

(Particle Physics via High-Energy Neutrinos)

Mission Parameters

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}

\theta_{\text{T-REX -BHEX}}\sim 35 \mu as

\theta_{\text{T-REX - EHT}} \sim 1800 \mu as

\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}

\tau_{\text{Coherence, T-REX}}\lessapprox 2 \text{ min} \sim 120 s

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

Systems Design

SEFD

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 100K

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 100K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 100K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\text{SEFD}_{\text{BHEX}}\sim 18,000 \text{ Jy}

\text{SEFD}_{\text{ALMA}}\sim 74 \text{ Jy}

\text{SEFD}_{\text{SMA}}\sim 6700 \text{ Jy}

\text{SEFD}_{\text{SMT}}\sim 10,500 \text{ Jy}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\sigma_{\text{T-REX - BHEX}}=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_{\mathrm{BHEX}} \mathrm{SEFD}_{\text{T-REX}}}{2 \Delta \nu \Delta t}}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\sigma_{\text{T-REX - BHEX}}=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_{\mathrm{BHEX}} \mathrm{SEFD}_{\text{T-REX}}}{2 \Delta \nu \Delta t}}

\sigma_{\text{T-REX - EHT}}=\frac{1}{\eta_{\mathrm{Q}}} \sqrt{\frac{\mathrm{SEFD}_{\mathrm{EHT}} \mathrm{SEFD}_{\text{T-REX}}}{2 \Delta \nu \Delta t}}

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\sigma_{\text{T-REX - BHEX}}=\frac{1}{0.75} \sqrt{\frac{(18,000 \text{ Jy})(32,000 \text{Jy})}{2 (32 \text{GHz}) (100s)}}

\sigma_{\text{T-REX - EHT}}=\frac{1}{0.75} \sqrt{\frac{(6000 \text{ Jy})(32,000 \text{Jy})}{2 (32 \text{GHz}) (10s)}}

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

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

\sigma_t = \sigma_f \cdot \Delta t

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

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

\sigma_t = \sigma_f \cdot \Delta t

\sigma_t = 8\cdot 10^{-15} (\text{LISA USO})

\Delta \phi = 2\pi \cdot (86\cdot 10^9 \text{ Hz}) \cdot 8\cdot 10^{-15}s\sim 10^{-3} \text{ rad}<1 \text{ rad}

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\Delta t = \text{10 s})

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\Delta t = \text{10 s})

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

L = 1-\exp\left[-2\pi^{2}(86\cdot 10^9)^{2}(10)^{2}(5\cdot 10^{-11})^{2}\right]\sim 1\%

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})=N_{\text {bits }} \times \Delta \nu \times 2_{\text {pol }} \times 2_{\text {Nyquist }}

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})=N_{\text {bits }} \times \Delta \nu \times 2_{\text {pol }} \times 2_{\text {Nyquist }}

\text{Rate}\times T_{orb} \times \text{Duty Cycle} = \text{Total Data (GB)}

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}

\theta_{S-S} \sim \frac{\lambda}{D}

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}

\theta_{S-S} \sim \frac{\lambda}{D}=\frac{3.5mm}{20,000 km}

\theta_{S-G} \sim \frac{\lambda}{D}=\frac{3.5mm}{400 km}

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

\theta_{\text{T-REX -BHEX}}\sim 35 \mu as

\theta_{\text{T-REX - EHT}} \sim 1800 \mu as

Systems Design

\sim85.3 kg

\sim 437 W

\sim \$25\text{ million}

N/A

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}

\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

\theta_{\text{T-REX -BHEX}}\sim 35 \mu as

\theta_{\text{T-REX - EHT}} \sim 1800 \mu as

Systems Design

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}

\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}

\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

\theta_{\text{T-REX -BHEX}}\sim 35 \mu as

\theta_{\text{T-REX - EHT}} \sim 1800 \mu as

Systems Design

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}

\theta_{\text{T-REX -BHEX}}\sim 35 \mu as

\theta_{\text{T-REX - EHT}} \sim 1800 \mu as

\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}

\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}

\omega=\frac{2\pi}{P} = \frac{2\pi}{1.5 \text{ hr}\cdot \frac{3600 s}{1 \text{hr}}}=1.16\times 10^{-3} rad/s

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

Systems Design

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}

\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}

\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}

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

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

\theta_{\text{T-REX -BHEX}}\sim 35 \mu as

\theta_{\text{T-REX - EHT}} \sim 1800 \mu as

Systems Design

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}

\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}

\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}

\theta_{FOV} = 180 \mu as

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

\theta_{\text{T-REX -BHEX}}\sim 35 \mu as

\theta_{\text{T-REX - EHT}} \sim 1800 \mu as

Systems Design

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}

\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}

\tau<\frac{1}{\omega D_\lambda \theta_{\mathrm{FOV}}}=\frac{1}{(1.16\times 10^{-3} \frac{rad}{s}) (3.5 G\lambda)(1.6\cdot 10^{-7}s)}

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\theta_{\text{T-REX -BHEX}}\sim 35 \mu as

\theta_{\text{T-REX - EHT}} \sim 1800 \mu as

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

Systems Design

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}

\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}

\tau_{\text{T-REX}}\lessapprox \frac{15G\lambda}{3.5 G\lambda}\lessapprox 4.2 \text{ min}, \tau_{\text{Coherence, T-REX}}\sim 275 s

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\theta_{\text{T-REX -BHEX}}\sim 35 \mu as

\theta_{\text{T-REX - EHT}} \sim 1800 \mu as

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

Systems Design

T^*_{sys} = [T_{rx}+\eta_{ff}T_{b, inc}](1+r)\sim 30K

T_{b,inc}=\frac{F_{tot}A_{eff}}{2k}\sim 3\cdot 10^{-3} K

T_{rx}=15K, \eta_{ff}=0.95, \eta_{A}=0.85, r= 1, F_{tot}\sim 2\pm 0.2 Jy

SEFD

USO

Data

\theta_{\text{Res}}

Orbit

\sigma_{\text{Noise}}

\tau_{\text{max}}

\Delta \phi = 4.3\cdot 10^{-3} \text{ rad } (\text{LISA USO})

L\sim 1\% \text{ (JUICE USO)}

\operatorname{Rate}(\mathrm{bps})\sim 8,750 \text{ GB }(T_{obs}=.5T_{orb}) \text{ over 1 orbit}

\text{Circular Highly-Inclined Polar LEO}, r\sim 400 km, e \sim 0, i>78^{\circ}

66.93s<\tau_{GS}<275s

\text{SEFD}_{\text{T-REX}}=\frac{2kT^*_{sys}}{\eta_A A}\sim 32,000 \text{ Jy}

\theta_{\text{T-REX -BHEX}}\sim 35 \mu as

\theta_{\text{T-REX - EHT}} \sim 1800 \mu as

\sigma_{\text{T-REX - BHEX}}\sim 12.65 \text{ mJy}

\sigma_{\text{T-REX - EHT}}\sim 40 \text{ mJy}

T-REX

T-REX

Antenna

T-REX

Antenna

T-REX

Antenna

T-REX

T-REX

Cryocooler

HiPTC Heat Intercepted Pulse Tube Cooler

T-REX

T-REX

Ultra-Stable Oscillator

T-REX

Ultra-Stable Oscillator

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

\sigma_t = \sigma_f \cdot \Delta t

Phase Error

T-REX

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}

T-REX

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}

T-REX

Digital Backend

T-REX

Original Analog Radio Signal

T-REX

Sample the Signal every Unit Interval

f_s\geq 2f

Nyquist-Shannon Sampling Theorem

T-REX

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

T-REX

Reconstruct the original signal

T-REX

T-REX

T-REX

Introduction
What is a black hole?
How do you image a black hole?
How do you record a black hole?
T-REX Primary Science Objectives
T-REX (u,v) Coverage
T-REX Engineering Challenges
T-REX SWaPC Requirements
T-REX Concept of Operations
T-REX Timeline & Funding Deadlines

T-REX

T-REX ConOps

Optical Terminals

RF Tracking Stations

VLBI Ground Stations

\text{T-REX}

T-REX Data Center

T-REX ConOps

Introduction
What is a black hole?
How do you image a black hole?
How do you record a black hole?
T-REX Primary Science Objectives
T-REX (u,v) Coverage
T-REX Engineering Challenges
T-REX SWaPC Requirements
T-REX Concept of Operations
T-REX Timeline & Funding Deadlines

T-REX

Email BHEX Team

Jan 2025

T-REX

Email BHEX Team

Jan 2025

T-REX

Email BHEX Team

Jan 2025

T-REX

Email BHEX Team

Jan 2025

Feb 2025

Literature Review

T-REX

Email BHEX Team

Jan 2025

Feb 2025

Mar 2025

Literature Review

Advised on BHEX Mini by Prof. Rick Fleeter
Submit to Rhode Island Space Grant

Rick Fleeter

T-REX

Email BHEX Team

Jan 2025

Feb 2025

Mar 2025

Literature Review

Apr 2025

Ivy Space Conference
Ben Hudson (BHEX, KISPE)
Luke Anderson (Orion Space Systems)

Ben Hudson

Luke Anderson

Advised on BHEX Mini by Prof. Rick Fleeter
Submit to Rhode Island Space Grant

T-REX

Email BHEX Team

Jan 2025

Feb 2025

Mar 2025

Literature Review

Apr 2025

May 2025

Ivy Space Conference
Ben Hudson (BHEX, KISPE)
Luke Anderson (Orion Space Systems)

Trained ~6 undergraduates to run simulations on BHEX Mini
Jeffrey Olson (Cryocooler Engineer, Lockheed Martin

Jeffrey Olson

Advised on BHEX Mini by Prof. Rick Fleeter
Submit to Rhode Island Space Grant

T-REX

Jun 2025

Jul 2025

Completed Antenna SWaPC Requirements
Obtained Preliminary Grant Funding from Nelson Center
Began correspondence with NASA JPL on Ultrastable Oscillators

Constrained BHEX Mini SWaPC Requirements
Approved by Brown Division of Research as PI for BHEX Mini
Submitted to NASA NIAC Phase I Solicitation
Accepted to SmallSat Europe 2026

Todd Ely

Joseph Lazio

Eric Burt

Email BHEX Team

Jan 2025

Feb 2025

Mar 2025

Literature Review

Apr 2025

May 2025

Jun 2025

Jul 2025

Ivy Space Conference
Ben Hudson (BHEX, KISPE)
Luke Anderson (Orion Space Systems)

Trained ~6 undergraduates to run simulations on BHEX Mini
Jeffrey Olson (Cryocooler Engineer, Lockheed Martin)
Rejected from RISG

Completed Antenna SWaPC Requirements
Obtained Preliminary Grant Funding from Nelson Center
Began correspondence with NASA JPL on Space-Space VLBI

Constrained BHEX Mini SWaPC Requirements
Approved by Brown Division of Research as PI for BHEX Mini
Submitted to NASA NIAC Phase I Solicitation
Accepted to SmallSat Europe 2026

Advised on BHEX Mini by Prof. Rick Fleeter
Submit to Rhode Island Space Grant

Feb 2025

Mar 2025

Literature Review

Apr 2025

May 2025

Jun 2025

Jul 2025

Ivy Space Conference
Ben Hudson (BHEX, KISPE)
Luke Anderson (Orion Space Systems)

Trained ~6 undergraduates to run simulations on BHEX Mini
Jeffrey Olson (Cryocooler Engineer, Lockheed Martin)
Rejected from RISG

Completed Antenna SWaPC Requirements
Obtained Preliminary Grant Funding from Nelson Center
Began correspondence with NASA JPL on Space-Space VLBI
Rejected from International Astronautical Congress

Constrained BHEX Mini SWaPC Requirements
Approved by Brown Division of Research as PI for BHEX Mini
Submitted to NASA NIAC Phase I Solicitation
Accepted to SmallSat Europe 2026

Advised on BHEX Mini by Prof. Rick Fleeter
Submit to Rhode Island Space Grant

Meeting with MIT Lincoln Labs (8/15)
Colloquium at Princeton IAS (9/04)
Michael Johnson Colloquium at Brown (PI, BHEX) (9/22)
Assemble Science/Engineering Leadership Team for NASA / CSA

Aug 2025

Sep 2025

Accepted as NASA NIAC Finalist
Accepted to 10th International VLBI Conference (Sweden)
Accepted to Gravitational Wave Conference (Georgia Tech)

💰Funding Deadlines

June

💰Funding Deadlines

$5,000

Brown Nelson Grants
- Submitted: June 30
- Decision: Sep 15

July

💰Funding Deadlines

$5,000

$175,000

Brown Nelson Grants
- Submitted: June 30
- Decision: Sep 15

NASA NIAC Phase I
- Submitted: July 15
- Decision: Sep 6

Aug

💰Funding Deadlines

$5,000

$175,000

>$4M

Brown Nelson Grants
- Submitted: June 30
- Decision: Sep 15

NASA NIAC Phase I
- Submitted: July 15
- Decision: Sep 6

Templeton Grant
- Submitted: Aug 15
- Decision: Oct 10

Sep

💰Funding Deadlines

$5,000

$175,000

>$4M

Brown Nelson Grants
- Submitted: June 30
- Decision: Sep 15

NASA NIAC Phase I
- Submitted: July 15
- Decision: Sep 6

Templeton Grant
- Submitted: Aug 15
- Decision: Oct 10

AAS Splinter Meeting
- Submitted: Sep 25
- Decision: Oct 30

Oct

💰Funding Deadlines

$5,000

NASA NIAC Phase I
- Submitted: July 15
- Decision: Sep 6

$175,000

Brown Nelson Grants
- Submitted: June 30
- Decision: Sep 15

>$4M

Templeton Grant
- Submitted: Aug 15
- Decision: Oct 10

AAS Abstracts
- Submitted: Sep 25
- Decision: Oct 30

CSA FAST Grant
- Submitted: Oct 26
- Decision: Dec 15

>$400,000

Introduction
What is a black hole?
How do you image a black hole?
How do you record a black hole?
T-REX Primary Science Objectives
T-REX (u,v) Coverage
T-REX Engineering Challenges
T-REX SWaPC Requirements
T-REX Concept of Operations
The Request

T-REX