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Nature Astronomy
nature astronomy
https://doi.org/10.1038/s41550-024-02238-3
Artice
Orbital polarimetric tomography of a
flare near the Sagittarius A
*
supermassive
black hole
Aviad Levis
1
, Andrew A. Chael
2
, Katherine L. Bouman
1
,
Maciek Wielgus
3
& Pratul P. Srinivasan
4
The interaction between the supermassive black hole at the centre of the
Milky Way, Sagittarius A
*
, and its accretion disk occasionally produces
high-energy flares seen in X-ray, infrared and radio. One proposed
mechanism that produces flares is the formation of compact, bright
regions that appear within the accretion disk and close to the event horizon.
Understanding these flares provides a window into accretion processes.
Although sophisticated simulations predict the formation of these flares,
their structure has yet to be recovered by observations. Here we show a
three-dimensional reconstruction of an emission flare recovered from
Atacama Large Millimeter/Submillimeter Array light curves observed on
11 April 2017. Our recovery shows compact, bright regions at a distance
of roughly six times the event horizon. Moreover, it suggests a clockwise
rotation in a low-inclination orbital plane, consistent with prior studies
by GRAVITY and the Event Horizon Telescope. To recover this emission
structure, we solve an ill-posed tomography problem by integrating a neural
three-dimensional representation with a gravitational model for black holes.
Although the recovery is subject to, and sometimes sensitive to, the model
assumptions, under physically motivated choices, our results are stable and
our approach is successful on simulated data.
The compact region around the Galactic Centre supermassive black
hole Sagittarius (Sgr) A
*
is a unique environment where the magnetized
turbulent flow of an accretion disk is subject to extreme gravitational
physics. The dynamical evolution of this complex system occasionally
leads to the production of energetic flares
1
seen in X-ray
2
, infrared
3
and
radio
4
. The physical nature, structure, origin, formation and even
-
tual dissipation of flares are topics of active research
3
,
5
8
key to our
understanding of accretion flows around black holes. One proposed
explanation for Sgr A
*
flares is the formation of compact bright regions
caused by hot pockets of lower-density plasma within the accretion
disk, which are rapidly energized (for example, through magnetic
reconnection
9
). These ‘bubbles’, ‘hotspots’ or ‘flux tubes’ observed in
numerical simulations (for example, ref.
10
) are hypothesized to form
in orbit close to the innermost stable circular orbit (ISCO) of Sgr A
*
. The
association of flares with orbiting hotspots close to the event hori
-
zon is consistent with near-infrared detections made by the GRAVITY
Collaboration
11
,
12
and radio observations of the Atacama Large
Millimeter/Submillimeter Array (ALMA)
13
.
The context for this work is set by the first images
14
of Sgr A
*
revealed by the Event Horizon Telescope (EHT) collaboration. The
images, reconstructed from very-long-baseline interferometry obser
-
vations from 6–7 April 2017, show a ring-like structure with a central
brightness depression—a strong suggestion that the source is indeed
a supermassive black hole
15
. Even in its quiescent state, imaged by EHT
Received: 8 September 2023
Accepted: 5 March 2024
Published online: xx xx xxxx
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1
California Institute of Technology, Pasadena, CA, USA.
2
Princeton University, Princeton, NJ, USA.
3
Max-Planck-Institut für Radioastronomie, Bonn,
Germany.
4
Google Research, San Francisco, CA, USA.
e-mail:
aviad.levis@gmail.com
Nature Astronomy
Artice
https://doi.org/10.1038/s41550-024-02238-3
partially depolarized in an image-average sense
13
. In contrast, compact
bright sources, such as a putative hotspot, are characterized by a large
fractional LP and fast evolution on dynamical timescales
13
,
23
, hence
allowing separation of the flare component from the background
accretion. In Supplementary Information Section 2.2, we quantita
-
tively assess the effect of the background accretion disk on simulated
reconstruction results.
Results
On 11 April 2017, ALMA observed Sgr A
*
at ~230 GHz as part of a larger
EHT campaign (Fig.
2
, top). The radio observations directly followed a
flare seen in the X-ray. The LP, measured by ALMA-only light curves
4
,
13
as a complex time series
Q
(
t
) + i
U
(
t
), appears to evolve in a structured,
periodic manner suggesting a compact emission structure in orbit.
The work of ref.
13
hypothesizes a simple bright spot (that is, idealized
point-source
24
or spherical Gaussian
25
) at radius (
r
) ≈ 11
M
(where
M
is the
black-hole mass; 2
M
is the Schwarzschild radius); however, a rigorous
data fitting was not performed. Furthermore, the proposed parametric
model is limited and does not explain all the data features. The orbital
polarimetric tomography approach that we propose enables a rigorous
data fitting and recovery of flexible 3D distributions of the emitting
matter, relaxing the assumption of a fixed orbiting feature enforced
by prior studies
11
,
13
,
26
. This opens a new window into understanding the
spatial structure and location of flares relative to the event horizon.
Our model, detailed in Methods, is able to fit the ALMA light curve
data very accurately (Fig.
2
, bottom). The optimization procedure
simultaneously constrains the inclination angle of the observer and
estimates a 3D distribution of the emitting matter associated with this
flaring event, starting from 9:20 UT (~30 min after the peak of the X-ray
flare
13
). Despite the fact that ALMA observations are unresolved (effec
-
tively a single pixel with time-dependent complex LP information) at
the horizon scale, our analysis suggests some interesting insights:
Low inclination angles (
θ
o
< 18°, Fig.
1a
, red) are preferred by the
validation-
χ
2
(Methods). Although the methodology is different,
this result is broadly consistent with EHT findings from 6–7 April
27
,
which favoured low inclination angles of ~30° by comparing recov
-
ered images with general relativistic (GR) magnetohydrodynamic
simulations. The fiducial model of ref.
13
corresponded to an
inclination angle of ~22°. Low inclination was also favoured in the
analysis of the GRAVITY infrared flares
11
,
12
,
23
.
The recovered 3D emission has two compact bright regions at
r
≈ 11
M
and 13
M
(Fig.
1b
). The location (radius and azimuthal
position) of the bright region is consistent with the qualitative
analysis of refs.
13
,
26
.
on 6–7 April, Sgr A
*
has shown considerable structural variability
16
. On
11 April 2017, Sgr A
*
was observed by ALMA directly after a high-energy
flare seen in X-ray. The ALMA light curves exhibit an even higher degree
of variability than 6–7 April
4
,
17
, including distinct coherent patterns in
the linear polarization
13
with variability on the scale of an orbit. The
presence of synchrotron-radiating matter very close to the horizon of
Sgr A
*
could potentially give rise to bright three-dimensional (3D) struc
-
tures that orbit and evolve within the accretion disk. In this work, we
present a 3D recovery of emission in orbit around Sgr A
*
, reconstructed
from ALMA light curves observed on 11 April 2017 (Fig.
1
).
To achieve this 3D reconstruction, we developed a new computa
-
tional approach that we call orbital polarimetric tomography. In con-
trast to prior work by refs.
11
,
13
, which employed a strongly constrained
parametric hotspot model with only a handful of parameters to tune
and interpret the observations, the goal of this work is to recover the
complex 3D structure of flares as they orbit and evolve in the accretion
disk around Sgr A
*
.
Tackling this inverse problem necessitates a change from typical
tomography, wherein 3D recovery is enabled by multiple viewpoints.
Instead, the tomography setting we propose relies on observing a
structure in orbit, travelling through curved space-time, from a fixed
viewpoint. As it orbits the black hole, the emission structure is observed
(projected) along different curved ray paths. These observations of the
evolving structure over time effectively replace the observations from
multiple viewpoints required in traditional tomography. Our approach
builds upon prior work on dynamical imaging and 3D tomography in
curved space-time, which showed promising results in simulated future
EHT observations
18
20
.
Similar to the computational images recovered by EHT
16
, our
approach solves an underconstrained inverse problem to fit a model to
the data. Nevertheless, ALMA observations do not resolve event horizon
scales (~10
5
lower resolution), which makes the tomography problem we
propose particularly challenging. To put it differently, we seek to recover
an evolving 3D structure from a single-pixel observation over time. To
solve this challenging task, we integrate the emerging approach of neural
3D representations
20
,
21
, which has an implicit regularization that favours
smooth structures
22
with physics constraints (details in Methods). The
robustness of the results thus relies on the validity of the constraints
imposed by the gravitational and synchrotron emission models.
We take advantage of the very high signal-to-noise and cadence
of the ALMA dataset
4
, as well as the linear polarization information
13
.
The choice to only fit the linear polarization (LP) light curves reflects
the uncertainty associated with the unpolarized intensity of the back
-
ground accretion disk. Although the total intensity light curve is domi
-
nated by the accretion disk, such extended emission structures are
1.5
12
20
40
60
Inclination (deg)
Spin
80
0
0.2
0.4
0.6
1.0
0.8
1.0
log
χ
2
3D recovery (
θ
o
= 12°)
0.5
–20
–20
–20
0
0
20
20
0
20
x
(
M
)
–20
0
20
x
(
M
)
11
M
13
M
y
(
M
)
z
(
M
)
Validation-
χ
2
(
θ
o
|
a
= 0)
Validation-
χ
2
(
a
|
θ
o
= 12°)
0
a
b
Fig. 1 | A 3D recovery of a Sgr A
*
flare observed by ALMA on 11 April 2017.
a
, The
validation-
χ
2
, a robust data-fitting metric (Methods), indicates a preference of
low inclination angles,
θ
o
< 18°, with a local minimum around
θ
o
= 12° (red curve).
For each inclination, the 3D recovery is run with five random initializations,
producing a spread that indicates recovery stability. The blue curve indicates
that the analysis is largely insensitive to the black-hole spin.
b
, A recovered 3D
volume visualized from two view angles in intrinsic (flat space) coordinates
(the event horizon illustrated for size comparison). The recovery shows two
emission regions (blue arrows) at radii of 11–13
M
(approximately six times the
Schwarzschild radius).