<p>This talk will present the methods and procedures used to produce the first image of a black hole from the Event Horizon Telescope. It has been theorized for decades that a black hole will leave a "shadow" on a background of hot gas. Taking a picture of this black hole shadow could help to address a number of important scientific questions, both on the nature of black holes and the validity of general relativity.</p><p>Unfortunately, due to its small size, traditional imaging approaches require an Earth-sized radio telescope. In this talk, I discuss techniques we have developed to photograph a black hole using the Event Horizon Telescope, a network of telescopes scattered across the globe. Imaging a black hole’s structure with this computational telescope required us to reconstruct images from sparse measurements, heavily corrupted by atmospheric error. The resulting image is the distilled product of an observation campaign that collected approximately five petabytes of data over four evenings in 2017.</p>

1. Seeing the Unseen

2. The Black Hole Shadow in M87
Cover Pages April 11, 2019
Cover Pages Around The World
April 11, 2019

3. 200+ scientists from 59 institutes in 18 countries in
Europe, Asia, Africa, North and South America
The Event Horizon Telescope Collaboration

6. Black Hole Simulation
Black Hole
Shadowin New York
Grain of Sand

7. Angular Resolution
Wavelength
Telescope Size
How Big Must Our Telescope Be?
20 µas
1.3 mm
13 million meters
Simulation of M87 Ideal Image with
Earth-Sized Telescope

8. The Event Horizon Telescope (EHT)

9. Light From the Black Hole
Combines Light
Mirror

10. Light From the Black Hole

11. Light From the Black Hole
!y

13. Black Hole Image Frequency Measurements
North-SouthFrequency(v)
East West Frequency (u)
The Event Horizon Telescope (EHT)

14. Frequency Measurements
North-SouthFrequency(v)
East West Frequency (u)
The Event Horizon Telescope (EHT)

15. North-SouthFrequency(v)
East West Frequency (u)
MeasurementsFrequency Measurements
The Event Horizon Telescope (EHT)
Ae i
amplitude
phase

16. North-SouthFrequency(v)
East West Frequency (u)
MeasurementsFrequency Measurements
The Event Horizon Telescope (EHT)
D
C

17. yx
TrueImage
Sparse
Measurements
Solving for the Image
ALGORITHM
Reconstruction

18. yx
TrueImage
Sparse
Measurements
f-1
(y)Inverse Fourier
Transform
Reconstruction
Solving for the Image

19. yx
TrueImage
Solving for the Image
Sparse
Measurements
Inverse Fourier
Transform
Reconstruction
+
Noisy

20. / e i(⇥+ 1 2)V12
Atmospheric Error: Unknown Phase
/
TimeDelay
Atmospheric Noise
Frequency Measurement:
cos(!t + 2)cos(!t)cos(!t + ⇥)cos(!t + ⇥ + 1)
21
/ e i⇥V12
Corrupted
Measurement
Ideal
Measurement

21. Atmospheric Error: Amplitude Attenuation
Atmospheric Noise g1 g2
g2g1 V12V12 =
Ideal
Measurement
Corrupted
Measurement
Frequency Measurement:

22. Phase & Amplitude Error
Amplitude Errors Phase Error
e i( 1 2)g1 g2V12 V12=
Measured Ideal

23. Phase & Amplitude Error
Amplitude Errors Phase Error
e i( 1 2)g1 g2V12 V12=
3
3
33
Measured Ideal

24. Two Classes of Imaging Algorithms
Forward Modeling
(Regularized Maximum Likelihood)
Inverse Modeling
(CLEAN + Self-Calibration)

25. Two Classes of Imaging Algorithms
Forward Modeling
(Regularized Maximum Likelihood)
x
ˆx
yy
f-1
(y)f-1
(y)
+ guidance from
knowledgeable user
Standard
Self Calibration
Inverse Modeling
(CLEAN + Self-Calibration)

26. Two Classes of Imaging Algorithms
Forward Modeling
(Regularized Maximum Likelihood)
yx
f(x)-1
ˆy p(y|ˆx)
p(ˆx)
+
y
Amp
Error
Phase
Error
Thermal
Noise
Systematic
Errors
x
ˆx
yy
f-1
(y)
Inverse Modeling
(CLEAN + Self-Calibration)
f-1
(y)
+ guidance from
knowledgeable user
Standard
ˆIMAP = argmaxI [log P(D|I) + log P(I)]= argmaxx [log p(y|x) + log p(x)]ˆxSelf Calibration

27. How do we verify what we are
reconstructing is real?

28. The 4-Step Process to Making a Picture of a Black Hole
1. Synthetic Data Tests
2. Blind Imaging of M87 Data
3. Objectively Choosing Imaging Parameters
4. Validation of Images

29. Step 1: Synthetic Data Tests

30. Measurements
Imaging Challenge
“Hmm…What Do I See?”
1) Generate Measurements 2) Make Images
Panel of
Experts
3) Evaluate Quality
True Image
Method
1
Method
2
Method
3
Event Horizon Telescope
Imaging Challenges

31. True Image
Method 1 Method 2 Method 3 Method 4 Method 5
Blurred by 1/2 beam

32. True Image
Method 1 Method 2 Method 3 Method 4 Method 5
Blurred by 1/2 beam

33. Step 2: Blind Imaging of M87 Data

34. Step 2: Blind Imaging
Team
1 Team
4
Team
2
Team
3
Harvard-Smithsonian
University of Arizona
U. Concepcion
MIT Haystack
Radboud University
NAOJ
MPIfR
Boston University
IAA
Aalto
ASIAA
KASI
NAOJ
TheAmericasGlobal
Cross-AtlanticEastAsia

35. Team 1 – End of the First Day of Imaging M87

36. 1 month later…
7 weeks later…

37. Step 2: Blind Imaging
50 µas
Team 1 (RML)
0 5 10
Team 2 (RML)
0.0 2.5 5.0
Team 3 (CLEAN)
0 2 4
Team 4 (CLEAN)
0 2 4
Brightness Temperature (109
K)

39. Step 3: Objectively Choosing Parameters

40. Step 3: Imaging Pipelines
DIFMAP
(CLEAN + Self Calibration)
eht-imaging
(Regularized Max Likelihood)
SMILI
(Regularized Max Likelihood)
Compact Flux
Stop Condition
Weighting on ALMA
Mask Size
Data Weights
Compact Flux
Initial Gaussian Size
Systematic Error
Regularizes
MEM
TV
TSV
L1
Compact Flux
L1 Soft Mask Size
Systematic Error
Regularizes
TV
TSV
L1

41. FakeData
IMAGING
METHOD
disk
IMAGING
METHOD
disk
M87Data
Step 3: Training on a Disk
SYNTHETIC DATA
GENERATION

42. DIFMAP
April 5April 5April 5 April 6April 6April 6 April 10April 10April 10 April 11April 11April 11
50 µas
eht-imaging
FakeDataM87Data
IMAGING
METHOD
IMAGING
METHOD
SYNTHETIC DATA
GENERATION
Step 3: Training on Full Set

43. Step 3: Different Days and Imaging Pipelines
DIFMAP
April 5April 5April 5 April 6April 6April 6 April 10April 10April 10 April 11April 11April 11
50 µas
0
2
4
6
eht-imaging
0
2
4
6
8
10
BrightnessTemperature(109
K)
SMILI
0.0
2.5
5.0
7.5
ImagingPipeline Observing Day

44. Step 3: Blurred to Equivalent Resolution

45. Step 4: Validation

46. Step 4: Finding “Top Set” Parameters
DIFMAP
April 5April 5April 5 April 6April 6April 6 April 10April 10April 10 April 11April 11April 11
50 µas
eht-imaging
FakeDataM87Data
IMAGING
METHOD
IMAGING
METHOD
SYNTHETIC DATA
GENERATION

47. Step 4: eht-imaging Parameter Slice
0.01ALMA
50 µas Mask 60 µas Mask 70 µas Mask 80 µas Mask 100 µas Mask
0.1ALMA0.3ALMA0.5ALMA1.0ALMA
0 4 8
Brightness Temperature (109
K)
0.01ALMA
50 µas Mask 60 µas Mask 70 µas Mask 80 µas Mask 100 µas Mask
0.1ALMA0.3ALMA0.5ALMA1.0ALMA
0 4 8
Brightness Temperature (109
K)
TV0
MEM 0 MEM 1 MEM 10 MEM 100 MEM 1000
TV1TV10TV100TV1000
0 15 30
Brightness Temperature (109
K)
TV0
MEM 0 MEM 1 MEM 10 MEM 100 MEM 1000
TV1TV10TV100TV1000
0 8 16
Brightness Temperature (109
K)
Synthetic Data M87 Data
Top Set
Parameters

48. Step 4: Variance Over the Top Set
Mean Image Standard Deviation Fractional Standard Deviation

49. Did We Prove Einstein Was Right?
Short answer: No, but we didn’t prove he was wrong

50. Non-spinning Black Hole’s Event Horizon
Diameter = 2rs
rs =
2GM
c2
Photon Orbit
Diameter = 3rs
Schwarzschild Radius:

51. Non-spinning Black Hole (Schwarzschild)
Diameter = 5.2 rs
adapted from Michael Johnson
rs =
2GM
c2

52. Non-spinning Black Hole (Schwarzschild)
Diameter = 5.2 rs
Maximally-spinning Black Hole (Kerr)
Diameter = 4.8 rs
adapted from Michael Johnson
rs =
2GM
c2

53. Spinning Black Hole (Kerr)
Diameter = ( 4.8 – 5.2 ) rs
adapted from Michael Johnson
rs =
2GM
c2

54. M87 Mass from Stellar Dynamics
MBH = 6.6×109M⊙
M87 Mass from Gas Dynamics
MBH = 3.5×109M⊙
Spinning Black Hole (Kerr)
Diameter = ( 4.8 – 5.2 ) rs
adapted from Michael Johnson
Spinning Black Hole (Kerr)
Diameter = ( 4.8 – 5.2 ) rs
rs =
2GM
c2
[Walsh et al 2013] [Gebhardt et all 2011]

55. M87 Mass from Stellar Dynamics
MBH = 6.6×109M⊙
M87 Mass from Gas Dynamics
MBH = 3.5×109M⊙
Wormhole
Diameter = 2.7 rs
adapted from Michael Johnson
Spinning Black Hole (Kerr)
Diameter = ( 4.8 – 5.2 ) rs
Spinning Black Hole (Kerr)
Diameter = ( 4.8 – 5.2 ) rs
rs =
2GM
c2

56. M87 Mass from Stellar Dynamics
MBH = 6.6×109M⊙
M87 Mass from Gas Dynamics
MBH = 3.5×109M⊙
Wormhole
Diameter = 2.7 rs
Naked Singularity (Super-spinning)
Diameter = rs
adapted from Michael Johnson
Spinning Black Hole (Kerr)
Diameter = ( 4.8 – 5.2 ) rs
Spinning Black Hole (Kerr)
Diameter = ( 4.8 – 5.2 ) rs
rs =
2GM
c2

57. M87 Mass from Stellar Dynamics
MBH = 6.6×109M⊙
M87 Mass from Gas Dynamics
MBH = 3.5×109M⊙
adapted from Michael Johnson
Wormhole
Diameter = 2.7 rs
Naked Singularity (Super-spinning)
Diameter = rs
Spinning Black Hole (Kerr)
Diameter = ( 4.8 – 5.2 ) rs
Spinning Black Hole (Kerr)
Diameter = ( 4.8 – 5.2 ) rs
rs =
2GM
c2

58. Black Hole Simulation

59. April 5April 6April 10April 11

60. April 5April 6April 10April 11

61. Time Variability in M87
16 18 20
GMST (h)
0
50
100
ClosurePhase(deg)
ALMA-LMT-SMA
16 18 20
GMST (h)
0
100
200
300
ClosurePhase(deg)
LMT-SMA-SMT
April 6
April 11
Clear Signature of Evolution over the 5 day span

62. The “No Hair” Theorem
The spacetime surrounding a black hole can be fully characterized by three numbers:
Mass Angular Momentum (spin) Charge
Constant Mass
Image credit: Avery Broderic

63. The EHT’s Black Hole Targets
0.1 1 10 100
Shadow diameter (µas)
0.1
1
10
230GHzfluxdensity(Jy)
230GHznominalresolution(ground)
345GHznominalresolution(ground)
230GHznominalresolution(ground+GEO)
345GHznominalresolution(ground+GEO)
Sgr A*
M87
Cen A
3C273
OJ287
NGC 1052
IC 1459
M84
M81
IC 4296
NGC 4261
NGC 1399
M104
1010
M
108
M
106
M
Sagittarius A* (Sgr A*)
4 Million Solar Masses
Orbital Period: 4 – 30 minutes
M87
6.5 Billion Solar Masses
Orbital Period: 4 – 30 days
video credit: Hotoka Shiokawa, plot credit: Dom Pesce
Every 1 second in this simulation
corresponds to 3 minutes

64. Reconstructing a Video Over a Night
xN
…
…
MeasurementsMeasurementsMeasurementsMeasurements
y1 y2 y3 yN
x1 x2 x3 xN

65. Truth Video EHT Ground Sites
Video Reconstruction Simulation of Sagittarius A*

66. Adding Face-On Low Earth Orbiters
“Metrics and Motivations for Earth-Space VLBI: Time-Resolving Sgr A* with the Event Horizon Telescope”
Daniel Palumbo, Michael Johnson, Katie Bouman, Andrew Chael, Shep Doeleman

67. WavelengthLow Earth Orbiters: 90 minute period
EHT’s Current Ground Based Sites EHT’s Current Ground Based Sites
+ 1 Low-Earth Orbiter
Frequency MeasurementsFrequency Measurements
simulation credit: Daniel Palumbo

68. WavelengthLow Earth Orbiters: 90 minute period
EHT’s Current Ground Based Sites EHT’s Current Ground Based Sites
+ 4 Low-Earth Orbiter
Frequency Measurements Frequency Measurements
simulation credit: Daniel Palumbo

69. Truth Video EHT Ground Sites + 1 Orbiter + 4 Orbiters
Video Reconstruction Simulations of Sagittarius A*
simulation credit: Daniel Palumbo

70. Theoretical Simulation
& Computer Graphics
Reconstruction &
Inference
Algorithms
Instrumentation &
Observing Strategies

71. The night after revealing the first M87 pictures to one another!

72. Event Horizon Telescope Collaboration