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
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
Visibility Amplitudes
š§ The (u,v)Ā Plane
(u,v)Ā Plane
š§ The (u,v)Ā Plane
Reconstructed Image
š§ The (u,v)Ā Plane
Visibility Amplitudes
š§ The (u,v)Ā Plane
(u,v)Ā Plane
š§ The (u,v)Ā Plane
Reconstructed Image
š§ The (u,v)Ā Plane
Visibility Amplitudes
What's the structure of my radio target?
Big Idea: Different structures have different interferometric signatures!
š§ 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!
š§ 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!
š§ The (u,v)Ā Plane
Visibility Amplitudes
š§ The (u,v)Ā Plane
Visibility Amplitudes
š§ The (u,v)Ā Plane
Visibility Amplitudes
š§ The (u,v)Ā Plane
Visibility Amplitudes
š§ The (u,v)Ā Plane
Visibility Amplitudes
Delta
š§ The (u,v)Ā Plane
Visibility Amplitudes
š§ The (u,v)Ā Plane
Visibility Amplitudes
š§ The (u,v)Ā Plane
Visibility Amplitudes
š§ The (u,v)Ā Plane
light bucket!
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
š§ The (u,v)Ā Plane
Goal:
I(l,m)
š§ 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
š§ 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 :(
š§ The (u,v)Ā Plane
I(l,m)
Intensity of a certain part of the sky/
sky brightness pattern
Goal: Measure
š§ The (u,v)Ā Plane
Goal: Measure
I(l,m)
Coordinates in the sky
š§ The (u,v)Ā Plane
Now we add the effects of the radio interferometer ...
I(l,m)
Coordinates in the sky
š§ 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)
š§ 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)}
š§ 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)
š§ 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)=
š§ 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
š§ 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
š§ 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
š§ 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)
š§ 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!
š§ 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
š§ 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 :(
š§ 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!
š§ 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!
š§ The (u,v)Ā Plane
But how do you fill up the (u,v) plane?
š§ The (u,v)Ā 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}
š§ The (u,v)Ā Plane
- Use an array of antennas!
N \text{ antennas} = \frac{N(N-1)}{2} \text{ baselines}
š§ The (u,v)Ā Plane
- Use an array of antennas!
4 \text{ antennas} = \frac{4(3)}{2}=6 \text{ baselines}
š§ The (u,v)Ā 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}
š§ The (u,v)Ā Plane
2. Earth Rotation Aperture Synthesis
\vec{u} = \frac{\vec{b}\cdot \hat{s}}{\lambda}
\vec{b}\cdot \hat{s}
š§ The (u,v)Ā Plane
2. Earth Rotation Aperture Synthesis
\vec{u} = \frac{\vec{b}\cdot \hat{s}}{\lambda}
\vec{b}\cdot \hat{s}
š§ The (u,v)Ā Plane
2. Earth Rotation Aperture Synthesis
\vec{u} = \frac{\vec{b}\cdot \hat{s}}{\lambda}
\vec{b}\cdot \hat{s}
š§ The (u,v)Ā 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}
š§ The (u,v)Ā 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}
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)
BHEX Mini | 06/24 Update
By Ref Bari
