BHEX Mini

BHEX Mini

Direct Imaging Black Holes from LEO

Ref Bari | 06/24 Update

Goal

Goal

Goal

The Atmospheric Window

Radio Telescope

VLBI: Very Long Baseline Interferometry

šŸ§  The (u,v)Ā Plane

šŸ§  The (u,v)Ā Plane

Visibility Amplitudes

šŸ§  The (u,v)Ā Plane

(u,v)Ā Plane

šŸ§  The (u,v)Ā Plane

Reconstructed Image

šŸ§  The (u,v)Ā Plane

Visibility Amplitudes

šŸ§  The (u,v)Ā Plane

(u,v)Ā Plane

šŸ§  The (u,v)Ā Plane

Reconstructed Image

šŸ§  The (u,v)Ā Plane

Visibility Amplitudes

What's the structure of my radio target?

Big Idea: Different structures have different interferometric signatures!

šŸ§  The (u,v)Ā Plane

(u,v) Coverage

Can I resolve my target?

Big Idea: More coverage of the (u,v) plane means a better picture of the radio target!

šŸ§  The (u,v)Ā Plane

Reconstructed Image

What does my target look like?

Big Idea: Taking the fourier transform of the (u,v) plane results in the actual image!

šŸ§  The (u,v)Ā Plane

Visibility Amplitudes

šŸ§  The (u,v)Ā Plane

Visibility Amplitudes

šŸ§  The (u,v)Ā Plane

Visibility Amplitudes

šŸ§  The (u,v)Ā Plane

Visibility Amplitudes

šŸ§  The (u,v)Ā Plane

Visibility Amplitudes

Delta

šŸ§  The (u,v)Ā Plane

Visibility Amplitudes

šŸ§  The (u,v)Ā Plane

Visibility Amplitudes

šŸ§  The (u,v)Ā Plane

Visibility Amplitudes

šŸ§  The (u,v)Ā Plane

light bucket!

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

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

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

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

What we want

šŸ§  The (u,v)Ā Plane

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

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}

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}

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}

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

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}

3. Use multi-frequency observations!

u (G\lambda)
v (G\lambda)
u (G\lambda)
v (G\lambda)
\text{Black Hole Shadow } (\sim 25G\lambda)
u (G\lambda)
v (G\lambda)
\text{Black Hole Shadow } (\sim 25G\lambda)
\text{Accretion Disk } (\sim 10G \lambda)
u (G\lambda)
v (G\lambda)
\text{Black Hole Shadow } (\sim 25G\lambda)
\text{Accretion Disk } (\sim 10G \lambda)
\text{Large-Scale Jets } (\sim 5 G\lambda)
u (G\lambda)
v (G\lambda)
\text{Black Hole Shadow } (\sim 25G\lambda, 10-40 \mu as)
\text{Accretion Disk } (\sim 10G \lambda, 40-100 \mu as)
\text{Large-Scale Jets } (\sim 5 G\lambda, 100-500 \mu as)
u (G\lambda)
v (G\lambda)
345 \text{ GHz (BHEX)}
230 \text{ GHz (EHT)}
86 \text{ GHz (BHEX Mini)}
\text{Black Hole Shadow } (\sim 25G\lambda, 10-40 \mu as)
\text{Accretion Disk } (\sim 10G \lambda, 40-100 \mu as)
\text{Large-Scale Jets } (\sim 5 G\lambda, 100-500 \mu as)