First mid-infrared detection and modeling of a flare from Sgr A*

Draft version January 14, 2025
Typeset using L
A
TEX twocolumn style in AASTeX631
First mid-infrared detection and modeling of a flare from Sgr A*
Sebastiano D. von Fellenberg,1
Tamojeet Roychowdhury,1, 2
Joseph M. Michail,3, ∗
Zach Sumners,4, 5
Grace Sanger-Johnson,6
Giovanni G. Fazio,3
Daryl Haggard,4
Joseph L. Hora,3
Alexander Philippov,7
Bart Ripperda,8, 9, 10, 11
Howard A. Smith,3
S. P. Willner,3
Gunther Witzel,1
Shuo Zhang,6
Eric E. Becklin,12
Geoffrey C. Bower,13
Sunil Chandra,14
Tuan Do,12
Macarena Garcia Marin,15
Mark A. Gurwell,3
Nicole M. Ford,4, 5
Kazuhiro Hada,16
Sera Markoff,17, 18
Mark R. Morris,12
Joey Neilsen,19
Nadeen B. Sabha,20
and Braden Seefeldt-Gail8, 9, 21
1Max Planck Institute for Radio Astronomy, Bonn & 53121, Germany
2Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
3Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138-1516; USA
4McGill University, Montreal QC H3A 0G4, Canada
5Trottier Space Institute, 3550 Rue University, Montréal, Québec, H3A 2A7, Canada
6Michigan State University, Department of Physics and Astronomy, East Lansing, MI 48824, USA
7University of Maryland, College Park, MD 20742, USA.
8Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada.
9Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada.
10Department of Physics, University of Toronto, 60 St. George Street, Toronto, ON M5S 1A7, Canada.
11Perimeter Institute for Theoretical Physics,
31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada.
12Department of Physics & Astronomy, University of California, Los Angeles, 90095-1547, USA
13Academia Sinica Institute of Astronomy and Astrophysics, 645 N. A’ohoku Pl., Hilo, HI 96720, USA
14Physical Research Laboratory, Navrangpura, Ahmedabad, 380009
15European Space Agency (ESA), ESA Office, Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
16Graduate School of Science, Nagoya City University, Yamanohata 1, Mizuho-cho, Mizuho-ku, Nagoya, 467-8501, Aichi, Japan
17Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
18Gravitation and Astroparticle Physics Amsterdam Institute, University of Amsterdam, Science Park 904, 1098 XH 195 196 Amsterdam,
The Netherlands
19Villanova University Department of Physics, 800 E. Lancaster Ave., Villanova PA, 19085, USA
20Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
21Dunlap Institute for Astronomy & Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada
ABSTRACT
The time-variable emission from the accretion flow of Sgr A*, the supermassive black hole at the
Galactic Center, has long been examined in the radio-to-mm, near-infrared (NIR), and X-ray regimes
of the electromagnetic spectrum. However, until now, sensitivity and angular resolution have been
insufficient in the crucial mid-infrared (MIR) regime. The MIRI instrument on JWST has changed
that, and we report the first MIR detection of Sgr A*. The detection was during a flare that lasted
about 40 minutes, a duration similar to NIR and X-ray flares, and the source’s spectral index steep-
ened as the flare ended. The steepening suggests that synchrotron cooling is an important process for
Sgr A*’s variability and implies magnetic fields strengths ∼40–70 Gauss in the emission zone. Obser-
vations at 1.3 mm with the Submillimeter Array revealed a counterpart flare lagging the MIR flare
by ≈10 minutes. The observations can be self-consistently explained as synchrotron radiation from
a single population of gradually cooling high-energy electrons accelerated through (a combination of)
magnetic reconnection and/or magnetized turbulence.
Corresponding author: Sebastiano D. von Fellenberg
sfellenberg@mpifr-bonn.mpg.de
1. INTRODUCTION
∗ NSF Astronomy and Astrophysics Postdoctoral Fellow
arXiv:2501.07415v1
[astro-ph.HE]
13
Jan
2025

2
Sgr A* is the source of electromagnetic radiation asso-
ciated with the Milky Way Galaxy’s central supermas-
sive black hole. Of particular interest is its near-infrared
and X-ray emission, which show variable emission with
sporadic bright peaks in the light curve, phenomenolog-
ically called “flares” (Baganoff et al. 2001; Genzel et al.
2003; Ghez et al. 2004). Despite decades of research,
the mechanism(s) behind these flares and their connec-
tion to Sgr A*’s less-variable radio emission is not fully
understood. Generally accepted to be caused by some
energetic electron-acceleration event, plausible scenar-
ios range from fluctuations in accretion rate and tur-
bulence heating to magnetic reconnection (Yuan et al.
2004, 2009; Ball et al. 2016; Dexter et al. 2020; Ripperda
et al. 2020).
A crucial missing observational link has been obser-
vations of flares in the mid-infrared (MIR), which has
been the major gap between the near-infrared (NIR) and
(sub-)millimeter regimes (Schödel et al. 2011a). The
circumnuclear disk associated with Sgr A* was origi-
nally studied with ground-based MIR observations in
the 1970’s, especially in the 12.8 µm [Ne II] line (e.g.,
Wollman et al. 1976). Lacy et al. (1980) modeled the
[Ne II] line shapes and argued for the presence of a
∼3 × 106
M⊙ point mass. However, these first MIR
observations had limited the available spectral windows
and lacked the high angular resolution and sensitivity
now available with the James Webb Space Telescope
(JWST). More recently, observations with the VISIR in-
strument (Lagage et al. 2004) at the Paranal observatory
have provided stringent constraint on the flux density of
Sgr A* at 8.6 µm using a filter centered on the Paschen
α line (Schödel et al. 2011b; Haubois et al. 2012; Dinh
et al. 2024). These ground-based observations, however,
lacked the temporal stability to detect Sgr A*’s variable
flux in differential light curves and provide upper lim-
its 20 − 50 mJy, depending on the choice of extinction
correction.
The temporal evolution, and possible flux dependence
of Sgr A* NIR spectral index, has been subject of inten-
sive research. Evidence points towards a canonical index
of ≈ +0.5 (νLν) during bright flares (Hornstein et al.
2007; Dodds-Eden et al. 2010; Ponti et al. 2017; GRAV-
ITY Collaboration et al. 2021), with tentative evidence
for negative indices at lower flux states and low level
spectral index variations (Gillessen et al. 2006; Witzel
et al. 2014, 2018).
2. OBSERVATIONS AND DATA REDUCTION
2.1. JWST MIRI/MRS
The JWST observations were obtained on 2024 April
6 UT with the MIRI Medium Resolution Spectrome-
ter (MRS) as part of Cycle 2 (Program ID 4572, PI
D. Haggard merged with Program ID 3324, co-PIs: J.
Hora, D. Haggard, G. Witzel). The MRS observes in
four non-contiguous wavelength bands, in this case cov-
ering a spectral range 4.9 to 20.1 µm in four bands sep-
arated by three gaps.1
The observations used the inte-
gral field unit, which observes a 3.
′′
2×3.
′′
7 field of view
(FoV) in Channel 1 (the shortest-wavelength band) and
successively larger FoVs in the longer-wavelength chan-
nels. Pixel sizes are 0.
′′
196 in Channels 1 and 2, 0.
′′
245 in
Channel 3, and 0.
′′
273 in Channel 4. The spectral reso-
lution is ∼3500–1700, but for present purposes, the full
spectrum in each channel was averaged to a single value
representing flux densities at 5.3, 8.1, 12.5, and 19.3 µm.
This paper analyzed a part of the light curve from
10:39:35 UT to 12:37:09 UT. Time at the solar-system
barycenter was 243 seconds later.2
The MRS data used
here were taken in a single exposure of 85 integrations.
This exposure was divided into five segments, the first
four consisting of 18 integrations and the last one hav-
ing 13 integrations. We calibrated the MIRI data using
the default JWST pipeline (Bushouse et al. 2024) ver-
sion 1.16.0 in context of pmap jwst-1242 starting with
the Level 2 data products downloaded from the MAST
archive. To use the integration-level data (86.04-second
cadence), we exported each level 2 segment into its in-
dividual integrations. The integrations were converted
into 85 flux-calibrated 3D data cubes using the pipeline
routine calwebb spec3, which uses the drizzle algo-
rithm (Smith et al. 2007; Law et al. 2023) to create an
optimum data cube (R.A./Decl./wavelength) from the
2D image on the MRS detector. In each of the 85 data
cubes, we masked wavelengths affected by emission lines,
and the remaining flux densities in each of the four MRS
wavelength bands were averaged. This gave light curves
at four wavelengths with 85 data points each. Images in
the four MRS channels are shown in Figure 1.
The calibration was refined by computing reference
light curves from all pixels that showed a median flux
level within 10% of the median flux in the Sgr A* pixel
(within 15% for channel 4, where fewer than 10 pixels
were within 10%) and ≥3 pixels away from the Sgr A*
pixel so as to remain outside its PSF. A detailed discus-
sion of the reduction and lightcurve extraction are given
in Appendix A.
1 https://jwst-docs.stsci.edu/jwst-mid-infrared-instrument/
miri-observing-modes/miri-medium-resolution-spectroscopy#
gsc.tab=0
2 Keyword bartdelt in the processed Level 3 file header.

3
3
0
3
Dec.
offset
[as]
A) B)
3 0 3
R.A. offset [as]
3
0
3
Dec.
offset
[as]
C)
3 0 3
R.A. offset [as]
D)
Figure 1. Mid infrared images of the Galactic Center with
JWST. The color insets show JWST 5.3 µm (A), 8.1 µm
(B), 12.5 µm (C), and 19.3 µm (D) observations. The
JWST/MIRI images are superposed on the L′
(NIR 3.8 µm)
stellar-background image from the Keck Observatory (Hora
et al. 2014). The image scale is labeled in arcseconds with
Sgr A* at the origin. North is up, east to the left.
The data show characteristics of the known systemat-
ics of the MIRI/MRS system,3
including fringing in the
spectra as well as a quasi-periodic modulation in the
spectra due to the MRS undersampling of the point-
spread function. Both effects introduce errors in the
observed flux density as a function of wavelength, but
these are constant and therefore cancel in the normal-
ized light curves. However, both effects can affect the
light curve if the pupil illumination changes, i.e., if point-
ing errors occur. During the observed flare, the point-
ing was stable, and the effect was negligible. Neverthe-
less, we mitigated the effect of fringing by using the
pipeline routine fit residual fringes 1d. The rec-
ommended strategy for mitigating the PSF undersam-
pling is to use a larger flux extraction aperture. How-
ever, in our case, sampling more than one pixel in-
creased the noise in the reference light curves (Hora
et al. 2014 found the same result in IRAC data). There-
fore, we derived the Sgr A* light curves from a single
pixel. To convert the pixel value of surface brightness
in MJy/sr to the total flux of a point source at that
location in mJy, we multiply the pixel value by the en-
circled energy ratio assuming a Gaussian point spread
3 https://jwst-docs.stsci.edu/known-issues-with-jwst-data/
miri-known-issues/miri-mrs-known-issues#gsc.tab=0
functions for each channel given in the JWST MIRI doc-
umentation (fch1 = 2.74 × 10−3
; fch2 = 4.40 × 10−3
;
fch3 = 7.66 × 10−3
; fch4 = 19.84 × 10−3
).
We estimate a False Alarm Rate (FAR) for detecting
a (stochastic) change in spectral index with comparable
significance in our reference light curves by computing
10,000 bootstrapped sets of CH1 to Ch4 reference light
curves. We fit the spectral index for each set for all
light curve points. We create 190,000 such spectral index
measurements. We find 2418 measurements significantly
different from zero at 1σ, 2 at 2σ. Since our signal is
significant at < 4σ, the FAR < 190,000−1
.
2.2. SMA 220 GHz Observations
The SMA observation of Sgr A* (project code 2023B-
S017, P.I. H. Smith) began on-source at 11:44 UT and
ended at 15:43 UT. These times were corrected to TDB
using astropy times and EarthLocation sites, which gave
a correction of +172 seconds. The SMA was in the
extended configuration with a central tuning of 220.1
GHz, split into upper and lower sidebands consisting of
six contiguous spectral windows. Each spectral window
had 2.288 GHz bandwidth in 4096 spectral channels. We
manually calibrated the total intensity (Stokes I) data in
CASA (version 5.6.2-3, McMullin et al. 2007) following
standard interferometric calibration. Before calibration,
we flagged channels showing RFI spikes on each base-
line and kept only the inner 95% of channels in each
spectral window. 3C 279 was used as the bandpass cal-
ibrator, and Ceres set the absolute flux level. We used
the JPL/Horizons model of Ceres (Butler 2012) and
transferred the solutions to the three gain calibrators:
J1751+096, J1733−130, and J1924−292. We solved for
scan-averaged gain solutions on these calibrators and
applied them to Sgr A*.
We split the calibrated Sgr A* visibilities for point-
source self-calibration on all baselines and exported the
self-calibrated data and the gain calibrator visibilities
into AIPS for light-curve extraction. We used the AIPS
task dftpl to extract light curves in the upper and lower
sidebands at 60-second binning on projected baselines
≥30 kλ to suppress any potential contamination by the
surrounding extended emission. To obtain a realistic
estimate of the measurement uncertainty, we calculated
the RMS of all calibrator light curves.
2.3. Chandra X-ray Observations
The Chandra observation of Sgr A* (Program
25700310, PI D. Haggard, ObsID 28230) was taken in
FAINT mode using a 1/8 subarray on the ACIS-S3 chip
for a total exposure time of 25.09 ks. The small subar-
ray and shorter frame rate decrease photon pileup during

4
A)
3.75
4.00 B)
0 50
Time [min]
0.0
1.2
norm.
Flux
C)
0
3
5.3 m
0
3
8.1 m
0 50
Time [min]
0
3
12.5 m
0 50
Time [min]
0
3
19.3 m
Observed
flux
density
[mJy]
[Jy]
Figure 2. Images and light curves of Sgr A* observed on 2024-04-06. Panel A (top) shows 8.1 µm residual images
after subtracting a constant image shown by the grey contour lines. Each image shows ∼20 minutes of averaged data before
(left), during (middle), and after (right) the flare. North is up, and east is to the left. Panels B show light curves of Sgr A*
at 1.3 mm (top left and right duplicated) and the four MIRI spectral channels with wavelengths as labeled. Flux densities are
as observed, i.e., calibrated but with no extinction correction. t = 0 marks the beginning of the flare as we define it, and all
times have been corrected to the barycentric reference frame. Panel C shows normalized light curves of the four MIRI bands to
demonstrate the change in spectral index.
flares. The Chandra observation times were barycenter-
corrected using the axbary method from the CIAO
v4.16 software package. The script calculates the cor-
rection using the ICRS reference system and applies the
value to the TIME column in the observation’s event file.
This was performed immediately after recalibration so
adjustments were carried downstream and applied to the
resulting analysis such as lightcurve extraction. In this
observation, the median Chandra barycenter correction
was +172 seconds.
Chandra data reduction followed Boyce et al. (2022)
and used the CIAO v4.16 software package. We first re-
processed the level 2 event file with the latest calibration
using the chandra repro script (CALDB v4.11.2) and
then applied the barycentric correction. We extracted a
300 s-binned 2–8 keV background-subtracted light curve
within a circular 1.
′′
25 radius region centered on Sgr A*
and a circular background annulus of inner radius 14′′
and outer radius 20′′
(Figure 3). The small extraction
region decreases background events and X-ray emission
from nearby sources. While severe pileup was mitigated
by the observing setup, we applied the pileup correc-
tion method of Bouffard et al. (2019) to compensate for
any remaining effects. We searched for X-ray flares us-
ing the Bayesian Blocks algorithm (Scargle et al. 2013)
but did not observe any flares in the Chandra exposure.
Sgr A*’s average X-ray flux during the entire observation
was 0.005 counts s−1
corresponding to 2.9 × 10−13
ergs
cm−2
s−1
(Figure 3).
2.4. NuSTAR X-ray Observations

5
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7
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0
0
0
8
:
0
0
0
9
:
0
0
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0
:
0
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1
:
0
0
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2
:
0
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3
:
0
0
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4
:
0
0
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5
:
0
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6
:
0
0
April 6, 2024 (UTC)
3.5
3.8
4.1
4.4
4.7
5.0
5.3
5.6
5.9
6.2
6.5
SMA
Flux
(Jy)
SMA
2.5
2.1
1.7
1.3
0.9
0.5
0.1
0.3
0.7
1.1
1.5
NuSTAR
Rate
(counts/s)
NuSTAR
0.150
0.125
0.100
0.075
0.050
0.025
0.000
0.025
0.050
0.075
0.100
Chandra
Rate
(counts/s)
Chandra
6
4
2
0
2
4
6
8
10
12
14
JWST
Flux
(mJy)
JWST
Figure 3. Full multi-wavelength Sgr A* light curves on 2024 April 6. From bottom to top: the green curve shows the
average of the SMA upper (230 GHz) and lower (210 GHz) sidebands. The superposed yellow to red curves show the observed
flux densities in JWST/MIRI channels 1 to 4, respectively. The blue curve shows the Chandra 2–8 keV light curve (corrected
for background and pileup) with 300 s binning, and the horizontal dark blue line shows the median of the entire Chandra
observation. The purple curve shows the NuSTAR 3–30 keV light curve with 300 s binning. The dark purple overlay is the
average during the observation period. Each light curve has its own ordinate as labeled, and times are UTC at the Solar System
barycenter. No X-ray flares were detected by either Chandra or NuSTAR. The grey region highlights the MIR flare interval
seen by JWST.
NuSTAR X-ray observations on 2024 April 6 were col-
lected as part of the Sgr A* multi-wavelength campaign
((Program 9041, PI S. Zhang, ObsID 30902013004).
We reduced the NuSTAR data using NuSTAR-DAS
(v.2.1.1) and HEASOFT (v.6.32) to extract 3–30 keV
barycenter-corrected (∼ +172 seconds) light curves from
a 30′′
region at the position of Sgr A* with 300 s bin-
ning (Figure 3). Following Zhang et al. (2017), we also
ran a Bayesian Blocks search for flares in the NuSTAR
lightcurves but did not detect any X-ray flares. The
combined Focal Plane Module (FPMA+FPMB) count
rate from the source region in 3–30 keV was 1.1 counts
s−1
corresponding to an observed flux of 9.6×10−12
ergs
cm−2
s−1
. The emission is background dominated, with
Sgr A* contributing ∼5% of the total signal.
3. RESULTS
The MIR light curves (Figure 2) revealed a bright flare
seen in all four bands and lasting about 50 minutes, sim-
ilar to the duration of NIR flares (e.g., von Fellenberg
et al. 2023, 2024). No variability was observed at X-
ray wavelengths. NIR flares without X-ray emission are
common (e.g., Boyce et al. 2019), and it is not surpris-
ing to see the same occurrence for a MIR flare. The
SMA began observing Sgr A* about 10-minutes into the
MIR flare and saw the 1.3 mm flux density increase by
∼0.3 Jy compared to its initial value ((Figure 2 and S4).
The discussion below argues that the mm-wave increase
was most likely connected to the MIR flare.
Due to the bright, surrounding thermal dust MIR
emission in the Galactic Center, Sgr A* in its quiescent
state is not detectable; only its variable emission is de-

6
tected in the difference images (Figure 2). In addition,
because the strong (about 3 magnitudes at 10 µm; e.g.,
Fritz et al. 2011) dust extinction varies both spectrally
and spatially, the MIR extinction to Sgr A* is uncer-
tain, complicating the derivation of an absolute flux-
calibrated spectrum of Sgr A* and making it prone to
systematic biases. To mitigate this problem, we adopted
a spectro-differential approach: we normalized the four
MIR light curves between their median flux levels and
the bright flux levels at one moment near the beginning
of the flare. The resulting normalized spectral energy
distribution (SED) is independent of the wavelength-
dependent extinction and the unknown static flux sub-
tracted from each light curve. While this prevents abso-
lute spectral-index measurements, it is a robust way to
measure the relative light curves and the time evolution
of the spectral index.
The MIR flare can be divided into three phases (Fig-
ure 4): 1) a fast rise (≈10 minutes), 2) a falling-and-
rising phase (≈20 minutes), and 3) a fast decay of the
flux density at the end (≈10 minutes). The light curves
of the flare in MIRI’s four bands were not the same
(Figure 5), and Sgr A*’s spectral index α (defined by
Fν(t) ∝ να(t0)+∆α(t)
) changed systematically during the
flare. During the first phase, there was no measurable
change in spectral index, ∆α ≈ 0. During the second
phase, the spectrum reddened by ∆α ≈ −0.4±0.1. This
slope remained similar until the flare ended. This is the
first measurement of a significant change in spectral in-
dex during a bright phase of a Sgr A* flare.
4. FLARE MODELING
4.1. Description of Model
A simple flare model can explain the temporal evo-
lution of Sgr A*’s spectral index. Details of the model
are given in Appendix C. Our model assumes a particle
acceleration event where electrons are continuously in-
jected into an emission region of constant size with the
injection rate following a Gaussian profile. The mag-
netic field in the emission region is assumed constant.
The injected electrons have a power-law energy distri-
bution dN/dE ∝ γ−p
for γ ∈ [γmin, γmax], where dN
is the number density of electrons in an energy range
dE, γ is the electron Lorentz factor, and p is a free pa-
rameter. During and after the injection event, the elec-
tron energy distribution evolves by electron-synchrotron
cooling (e.g., Dodds-Eden et al. 2010), where the syn-
chrotron cooling time scale is given by:
tsync(B, ν) ≈ 8

B
30 G
−3/2 ν
1014 Hz
−1/2
minutes ,
(1)
for a fiducial magnetic field strength B = 30 G. The
model includes Doppler boosting and de-boosting from
a circular orbit of the emission region around the cen-
tral black hole as well as a gravitational-redshift term.
The amplitude of these effects depends on the observer
angle ϕinc, the radial separation of the emitting region
from the black hole Rorb, and the initial angular posi-
tion of the emitting region Ω0. Gravitational lensing
was ignored in our model, a valid assumption if the
orbit is viewed at inclination ϕinc ≲ 50◦
and the mo-
tion is mostly in the plane of the accretion flow (e.g.,
GRAVITY Collaboration et al. 2020a). The inclusion
of Doppler boosting is motivated by the GRAVITY ob-
servation of low-inclination orbital motion (GRAVITY
Collaboration et al. 2018, 2020a, 2023), the EHT im-
age of the black-hole shadow (Event Horizon Telescope
Collaboration et al. 2022a,b,c,d,e,f), and the mm obser-
vations in the context of the EHT observations (Wielgus
et al. 2022a), all of which suggest that Doppler boosting
must be an important contributor to the overall vari-
ability (von Fellenberg et al. 2023, 2024).
According to the model, in the first phase of the flare
the fast, achromatic rise in flux is caused by the grow-
ing number of injected electrons together with Doppler
boosting. In the second phase, the reddening of the
spectral index by ∆α ≈ −0.4 arises from synchrotron
cooling of high-energy electrons to lower energies. The
decrease and subsequent increase in flux is explained by
Doppler de-boosting first and then boosting that occurs
one orbit after the initial injection. In the third phase,
the initial decline comes from efficient cooling, and the
decline speeds up as Doppler de-boosting sets in. The
change in spectral index and the fast decay at the end
of the flare constrain the total duration of the electron
acceleration event. While we do not know the intrin-
sic injection profile, a Gaussian profile fits the observed
flare shape when allowing for Doppler boosting due to
orbital motion. The best-fit injection timescale has a
Gaussian root-variance width σ = 11.7+0.2
−0.2 minutes.
Doppler deboosting alone cannot explain the flare’s
fast decay. Assuming an orbiting hot-spot model, where
there is no net outflow and/or expansion of the emis-
sion region, the flare’s fast decay requires the removal
of emitting electrons either by particle escape or by
efficient electron cooling through the emission of syn-
chrotron radiation. Particle escape is unlikely because
MIR-emitting electrons have a gyroradius smaller than
the Schwarzschild radius and, therefore, should be con-
fined in the turbulent emission region (Lemoine 2023;
Kempski et al. 2023). However, particles can cool ef-
ficiently on timescales of ≈5 minutes within the emit-
ting region provided the magnetic field is high, B ≈ 40–

7
0.2
0.4
F
220GHz
[Jy]
A)
0 10 20 30 40 50 60
Time [min]
0
1
JWST
norm.
flux
B)
Phase 1 Phase 2 Phase 3
5.3 m
8.1 m
12.5 m
19.8 m
Figure 4. Observed light curves with model fit. Points
show the observed data, and solid lines show the predictions
of the simple model described in the text. (A) 220 GHz
data. (B) MIR data. The four yellow-to-red lines show the
best-fit model predictions for each channel as labeled. The
black dashed line shows the modeled Doppler boosting and
de-boosting due to the orbital motion of the emission region.
The dotted line shows the modeled Gaussian injection curve
of power-law electrons. The flare phases described in the
text are indicated at bottom.
70 G (Equation 1) for MIR-emitting (νJWST ≈ (1.5–6)×
1013
Hz) electrons.
Depending on the underlying model assumptions, the
best fit magnetic field strength (B ≈ 40–70 G) required
for synchrotron cooling in the flare emission zone is
slightly higher than the ∼30 G typically suggested (e.g.,
Dodds-Eden et al. 2010; Ponti et al. 2017; GRAVITY
Collaboration et al. 2021). However, the higher field
strength is consistent with those earlier modeling re-
sults. Previous ground and space observations lacked
the sensitivity and spectral range to measure the spec-
tral evolution during flares, and absent spectral infor-
mation, the magnetic field strength is largely degener-
ate with the size of the emission region and the particle
number density within it (e.g., GRAVITY Collaboration
et al. 2021).
A strong prediction of the model is that as the elec-
trons cool to lower energies, they must emit synchrotron
radiation at lower frequencies. If γmin = 10 and the total
electron number density in the emitting region ne ≈ 1–
10 × 106
cm−3
, the model produces mm flux in the
range of the observed values while at the same time
fitting the observed MIR flare (Figure 4). This result
is a lower limit for the total number density, consistent
with canonically quoted accretion-flow densities ∼106
–
107
cm−3
(e.g., Gillessen et al. 2019). Thus, synchrotron
cooling is a plausible mechanism to explain the observed
0
1
Norm.
flux
A)
0 10 20 30 40 50 60
Time [min]
0.0
0.5
B)
0.4 0.2 0.0
Figure 5. Evolution of the spectral index during the
flare. Panel A) shows the normalized MIR light curves, and
panel B) shows the change in the best-fit spectral index. The
colors indicate the spectral index with blue colors ∆α ≈ 0.0,
and red colors ∆α ≈ −0.4.
∆F1.3 mm ∼ 0.3 Jy increase in mm flux density. How-
ever, the MIR data alone do not require a low γmin. If
γmin ≳ 10, then the total mm flux is too low. The model
also does not inherently require the electron numbers to
be that high. If ne 1×105
cm−3
, the model’s mm flux
density would be 0.05 Jy, too small to be discernible
in the mm light curve. Such models fit the MIR light
curve, but the observed mm variability would have to be
explained by an independent process, and the observed
mm rise would be just a coincidence. Because Sgr A*’s
mm emission is constantly variable (e.g., Event Hori-
zon Telescope Collaboration et al. 2022e), with observed
flux densities ranging from ∼2–6 Jy, a by-chance associ-
ation is tenable, and the observed variability amplitude
of 0.3 Jy is consistent with the measured variability am-
plitude at 230 GHz (e.g., Dexter et al. 2014). Never-
theless, the model’s ability to produce detectable mm
flux, assuming canonical accretion-flow parameters, fa-
vors a causal connection between the MIR and mm-flux
density.
While the simple one-zone model has no specific sce-
nario of electron acceleration, it reflects several aspects
of electron acceleration in turbulence in a magnetized
region in the accretion flow, e.g., in flux tubes in accre-
tion disks (Porth et al. 2021; Ripperda et al. 2022; Zh-
dankin et al. 2023; Grigorian Dexter 2024). In such
a model, an eruption of magnetic flux from the black
hole’s event horizon produces an orbiting low-density
cavity in the accretion flow, where the typical proton
magnetization is of order σp = B2
/(4πnpmpc2
) ∼ 0.1–
1 (e.g., Dexter et al. 2020; Porth et al. 2021; Ripperda

8
et al. 2022; Najafi-Ziyazi et al. 2024; Grigorian Dexter
2024). Due to Rayleigh–Taylor instability, these cavities
are quickly protruded by streams of plasma from the
surrounding accretion flow. Subsequently, reconnection
within the protrusions can efficiently accelerate electrons
to Lorentz factors capable of producing IR synchrotron
emission (Zhdankin et al. 2023). In contrast to sporadic
magnetic reconnection events, the Rayleigh–Taylor in-
stability can continuously drive turbulence in the cavity,
energizing electrons for as long as the cavity exists.
The number density of electrons in the non-thermal
component and the magnetic field strength set an
upper limit on the electron magnetization σe =
B2
/(4πnemec2
) ≈ 40 for an emitting region of size
Rflare = 1 RS. Because the amount of synchrotron
flux produced by the flare depends on the size of the
emission region and the particle density, changing the
size changes the electron magnetization σe. We derive
the posterior distribution of σe assuming that the cavity
sizes range from Rflare ∈ [0.8RS, 2.3RS] (i.e., a flat Rflare
prior), based on typical sizes of orbiting low-density
magnetic flux tubes in GRMHD simulations (Porth et al.
2021; Dexter et al. 2020; Ripperda et al. 2022). The
derived posterior distributions imply σe 10 with an
inter-quartile range IQR ≈ 140 (25%), 380 (50%), 920
(75%). Accounting for the higher proton mass, the pro-
ton magnetization σp 0.006, IQR ≈ 0.1 (25%), 0.2
(50%), 0.5 (75%). Values of σp ≳ 0.1 are consistent
with the proton magnetization found in magnetized cav-
ities in GRMHD simulations (Ripperda et al. 2022), and
with magnetic reconnection in the turbulent cavity as
an electron acceleration mechanism. Within the cavity,
we expect reconnection with a significant component of
the magnetic field orthogonal to the reconnecting field
(the so-called “guide” field). Under these conditions, re-
connection is expected to quickly accelerate electrons to
Lorentz factors γ ∼ σe (e.g., Comisso 2024). This pop-
ulation of electrons would be able to emit at infrared
wavelengths (Zhdankin et al. 2023).
4.2. Model Results
The synchrotron model predicts flux densities at all
wavelengths from mm to X-ray, though by construction
it predicts zero X-ray emission. (If an X-ray flare had
been observed, a higher γmax would have predicted X-
ray emission, but we have not explored whether this
would fit historically observed X-ray flares.) At mm
wavelengths, an extra model component is needed to
account for synchrotron emission by low-energy, ther-
mal electrons. We did not model this component but
included a constant offset in the model fit. Because we
set the lowest point in the mm-light curve to 0.1 Jy, this
offset is ≈0.1 Jy.
The synchrotron model describes the following char-
acteristics of the data:
1. The rising phase of the flare, where injected elec-
trons and Doppler boosting cause a rapid rise of
MIR flux.
2. The falling-and-rising phase in the middle, where
the Doppler de-boosting decreases the observed
flux of the still-increasing intrinsic emission.
3. The spectral-index change during the falling-and-
rising phase of the flare, caused by high-energy
electron cooling.
4. The rapid decay of the emission at the end of
the flare, explained by continued electron cooling
along with the decrease in electron-injection rate.
One thing the simplest model cannot explain is the
fast double-peak clearly seen in bands 1, 2, and 3 at the
beginning of the flare (t ≈ 10–20 minutes). To avoid
biasing the fit by this double peak feature, we increased
the error bars for two data points at t = 25.5 minutes
and t = 28.5 minutes by a factor of 3 in channels 1
and 2. This fast double-peak could be explained by a
more complex (double) injection profile or by variation
in the magnetic-field strength. Section C.2.2 demon-
strates the former by including a second Gaussian injec-
tion event to describe the fast double-peak at the be-
ginning of the flare. As noted above, when taking into
account the theoretical uncertainty in electron temper-
ature and magnetic to electron pressure ratio, the es-
timated magnetic field strength from the flaring region
is consistent with the range of magnetic field strengths
inferred based on EHT observations (i.e., Event Horizon
Telescope Collaboration et al. 2022e).
5. CONCLUSIONS
All in all, the new MIR observations suggest that
Sgr A*’s MIR emission comes from synchrotron emis-
sion by a cooling population of electrons. The parti-
cle acceleration could come from a combination of mag-
netic reconnection and magnetized turbulence. In ad-
dition, our observations indicate that variable emission
immediately following high-energy flares can be caused
by non-thermal processes. This underlines the impor-
tance of including non-thermal processes even for mod-
eling lower-energy radio emissions. A complete physical
model will need to include both global accretion-disk dy-
namics, which can provide particle acceleration sites, as
well as microscopic energization processes and their role

9
in powering the observed radiation (e.g., Galishnikova
et al. 2023; Zhdankin et al. 2023).
We thank Charles Gammie and Michi Bauboeck for
their comments and discussion on the manuscript. This
research was supported by the International Space Sci-
ence Institute (ISSI) in Bern, through ISSI International
Team project #24-610, and we thank Mark Sargent and
his team for their generous hospitality. This work is
based on observations made with the NASA/ESA/CSA
James Webb Space Telescope. The data were obtained
from the Mikulski Archive for Space Telescopes at the
Space Telescope Science Institute, which is operated
by the Association of Universities for Research in As-
tronomy, Inc., under NASA contract NAS 5-03127 for
JWST. These observations are associated with program
#4572. The Submillimeter Array is a joint project be-
tween the Smithsonian Astrophysical Observatory and
the Academia Sinica Institute of Astronomy and Astro-
physics and is funded by the Smithsonian Institution
and the Academia Sinica. We recognize that Maunakea
is a culturally important site for the indigenous Hawai-
ian people; we are privileged to study the cosmos from
its summit. This research has made use of data ob-
tained from the Chandra Data Archive provided by the
Chandra X-ray Center (CXC).
DH, RZS, NMF acknowledge support from the Cana-
dian Space Agency (23JWGO2A01), the Natural Sci-
ences and Engineering Research Council of Canada
(NSERC) Discovery Grant program, the Canada Re-
search Chairs (CRC) program, the Fondes de Recherche
Nature et Technologies (FRQNT) Centre de recherche
en astrophysique du Québec, and the Trottier Space In-
stitute at McGill. NMF acknowledges funding from the
FRQNT Doctoral Research Scholarship.
Support for program #4572 was provided by NASA
through a grant from the Space Telescope Science Insti-
tute, which is operated by the Association of Universities
for Research in Astronomy, Inc., under NASA contract
NAS 5-03127.
AP is supported by a grant from the Simons Foun-
dation (MP-SCMPS-00001470). A.P. additionally ac-
knowledges support by NASA grant 80NSSC22K1054.
BR, BSG are supported by the Natural Sciences
Engineering Research Council of Canada (NSERC),
the Canadian Space Agency (23JWGO2A01), and by
a grant from the Simons Foundation (MP-SCMPS-
00001470). BR acknowledges a guest researcher posi-
tion at the Flatiron Institute, supported by the Simons
Foundation.
SZ And GS acknowledge funding support from the
NASA grant #80NSSC23K1604. We thank the NuS-
TAR team for their efforts with the observation schedul-
ing. This research has made use of software provided by
the High Energy Astrophysics Science Archive Research
Center (HEASARC), which is a service of the Astro-
physics Science Division at NASA/GSFC.
JM is supported by an NSF Astronomy and As-
trophysics Postdoctoral Fellowship under award AST-
2401752. This research was supported in part through
the computational resources and staff contributions pro-
vided for the Quest high-performance computing facility
at Northwestern University, which is jointly supported
by the Office of the Provost, the Office for Research, and
Northwestern University Information Technology.
TR acknowledges funding support from the Deutscher
Akademischer Austauschdienst (DAAD) Working In-
ternships in Science and Engineering (WISE) program.
The observations are available at the Mikulski Archive
for Space Telescopes (https://mast.stsci.edu/) under
proposal IDs 4572 for JWST and at the Chandra Data
Archive (https://cxc.harvard.edu/cda/) proposal num-
ber 25700310 for Chandra. The source code used for the
flare model is available at https://github.com/ydallilar/
flaremodel.
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12
APPENDIX
A. MIRI/MRS REDUCTION DETAILS
The calibration was refined by computing reference light curves from all pixels that showed a median flux level within
10% of the median flux in the Sgr A* pixel (within 15% for channel 4, where fewer than 10 pixels were within 10%) and
≥3 pixels away from the Sgr A* pixel so as to remain outside its PSF. Figure A1 shows the reference-pixel locations.
The only systematic effect within the exposure was a linear drift of the pixel zeropoints. We corrected that by fitting a
linear function to each reference pixel’s light curve, averaging the slopes, and subtracting the corresponding flux from
the Sgr A* pixel flux of each point in the Sgr A* light curves. Figure A2 shows the de-trending result, and Table A1
gives the measured slopes along with the RMS of the reference-pixel light curves and the flux offset subtracted from
the Sgr A* data. Figure A3 shows the light curves of Sgr A* and the reference pixels after correction for the average
slope but not each pixel’s median. This shows that the linear drift does not depend on the absolute flux values, i.e.,
it was a zeropoint drift rather than a gain drift. In order to estimate the systematic uncertainty introduced by the
drift correction, we generated bootstrapped surrogates of the reference pixels and calculated the drift correction for
each bootstrapped sample. We then calculated the RMS of the resulting light curves and took the maximum RMS
value as the uncertainty reported in Table A1. Because these uncertainties are small with respect to the photometric
uncertainty, we ignore this source of systematic uncertainty.
0 20
0
10
20
30
Channel-1
0 20
0
10
20
30
Channel-2
0 20
0
10
20
30
Channel-3
0 10 20
0
10
20
Channel-4
104
105
104
105
Flux
Density
(MJy/Sr)
105 105
106
Flux
Density
(MJy/Sr)
Figure A1. Median images of the Galactic Center in channels 1, 2, 3, and 4. The location of Sgr A* is marked with
the square box, and the locations of the reference pixels used to estimate the noise in the image are marked by white dots. Axis
labels are in pixel number with pixel angular sizes given in the text. The flux-density scale is in MJy/sr.
To extract Sgr A*’s flux density, we created median-subtracted data cubes. In the data cubes, Sgr A* is detected
against the temporally constant background. We determined the pixel position of Sgr A* by fitting a circular Gaussian.
The flux was measured using this single pixel. The flux density was normalized as
Fnorm(t) =
F(t) − Fmed
F(t0) − Fmed
, (A1)

13
0 30 60
0
4 A)
0 30 60
B)
11:00 12:00
0
4 C)
11:00 12:00
D)
Time in UTC (hh:mm) barycentre-corrected on 6 Apr 2024
Median-subtracted
flux
density
(mJy)
Time in minutes
Figure A2. Comparison of Sgr A* and reference-pixel light curves. Panels show the median-subtracted light curves
of the Sgr A* pixel (color) and reference pixels (grey) in channels 1, 2, 3, and 4 (panels A, B, C and D respectively). The black
lines show the best linear fit to each reference-pixel trend. Table A1 gives the line slopes. Times are shown in UTC at the Solar
System barycenter on the lower abscissa and relative to the adopted T = 0 on the upper abscissa.
0 30 60
23
26
0 30 60
90
100
11:00 12:00
360
400
11:00 12:00
1000
1200
Time in UTC (hh:mm) barycentre-corrected on 6 Apr 2024
Detrended
flux
density
(mJy)
Time in minutes
Figure A3. Light curves of reference pixels compared with the Sgr A* pixel. Grey curves in each panel (channels
1, 2, 3, 4 in panels A, B, C, D respectively) show the reference-pixel light curves after removing the linear slope but without
subtracting each pixel’s median value. Colored lines show the same for the Sgr A* pixel.
where Fmed stands for the median flux of each light curve 34 minutes before the flare. We chose t0 = 12.49 minutes.
We estimated the uncertainty in the Sgr A* flux-density measurements by computing the standard deviation of the
temporal variability in the reference-pixel light curves. These are then propagated to the normalized light curve via
Gaussian error propagation. In order to assess the impact of uncertainty of the flux by which we normalize the data,

14
0.50
0.25
0.00
0.25
0.50
0.75
1.00
1.25
1.50 Detector Extraction
40 20 0 20 40 60 80
0.50
0.25
0.00
0.25
0.50
0.75
1.00
1.25
1.50
40 20 0 20 40 60 80
Normalized
Flux
Time [minutes]
Figure A4. Background-subtracted, detrended light curves extracted from 2D detector frames compared to
cub-extracted light curves. The colored light curves are the light curves used in the analysis of this paper. The black lines
are the corresponding lines extracted from the 2D IFU detector, extracted from the detector slice corresponding to the Sgr A*
spaxel in the 3D cube. Both light curves have been normalized using Eq. C9.
Table A1. Subtracted median flux densities, RMS values, and drift models
Channel Median flux density [mJy] RMS [mJy] Drift [10−3
mJy/h] Drift error [10−3
mJy/h]
Channel 1 23.54 0.035 13.4 1.6
Channel 2 92.67 0.097 98.1 7.4
Channel 3 379.55 0.309 6.9 58.9
Channel 4 1100.1 0.540 811.5 77.3
we compute 100 simulated normalization fluxes based on its error bar. The change in the spectral index is derived by
fitting a power-law two the for channels, once for the real data with propagated uncertainties, and once for the set
of 100 simulated normalized light curves. The change in the spectral index was determined by averaging the spectral
index before and after the change, which gives a ∆α = 0.36, the RMS based of the fitted and simulated error bar is
0.06, which we round to ∆α = 0.4 ± 0.1. Table A1 gives the results for each channel.
The pipeline-constructed 3D cubes use a complex algorithm (see Law et al. 2023) to assign the intensities measured
on the 2D MRS detector to the corresponding spectral pixels (spaxels) in the 3D cubes. We verified that this procedure
does not introduce photometric biases by measuring the light curves directly on the 2D detector pixels that correspond
to Sgr A*’s position at each wavelength. The resulting detrended light curves are shown in Figure A4. These light
curves have the same features as the light curves extracted from the 3D cubes and in particular show the same change
in Sgr A*’s spectral index.

15
B. COMPARISON TO PREVIOUS MIR MEASUREMENTS
The VISIR instrument at the VLT offers high sensitivity imaging at mid-infrared wavelengths, and in particular a
filter centered on the PAH1 feature at 8.6µm. Three works obtained flux limits with this instrument, Schödel et al.
(2011b) who studied the mean emission of Sgr A* and obtained a 3σ flux density limit of f3σ;mean = 13.3 mJy, or
58.0 mJy if an extinction value of A8.6µm = 1.6 (Fritz et al. 2011) is applied. Haubois et al. (2012) obtained MIR
observation during a bright NIR flare and obtained a 3σ flux limit of 5.1 mJy, or 22.4 mJy if extinction correction is
applied. The last work, Dinh et al. (2024), focuses on compact objects and temperature maps of the central region and
does not report a MIR flux density limit for Sgr A*. Applying the same spectral selection as the PAH1 of VISIR, we
obtain a PAH1 light curve, which we can directly compare against these observations. We obtain a peak flux density
of 1.96 mJy of the flare, corresponding to a de-extincted flux density of 8.6 mJy. We caution that the existing MIR
extinction correction provided by Fritz et al. (2011) are based on much smaller aperture ISO/SWS observations (Lutz
et al. 1996). The GC extinction is highly variable (e.g., Fritz et al. 2011; Haggard et al. 2024). Thus, the previously
derived extinction laws may not be directly applicable for high spatial resolution JWST observations. Most segments
of the light curve are variable and seem to show intrinsic variation of Sgr A*. However, a detailed study of the MIR
flux distribution is beyond the scope of this work. A conservative estimate on the lower limit of Sgr A*’s flux density
can be obtained with the RMS values of the measurement uncertainty (Table A1).
C. FLARE MODELING
The accretion flow of Sgr A* is likely in a magnetically arrested state (Bisnovatyi-Kogan Ruzmaikin 1974, 1976;
Narayan et al. 2003), based on EHT and GRAVITY observations (Event Horizon Telescope Collaboration et al. 2022e;
GRAVITY Collaboration et al. 2020b; Event Horizon Telescope Collaboration et al. 2024) and simulations of the wind-
fed accretion onto the Galactic center (Ressler et al. 2020, 2023). In this scenario, a large amount of magnetic flux is
accreted onto the black hole with the infalling gas. The flux on the horizon can then become strong enough to repel
the accreting plasma in a flux eruption (Igumenshchev et al. 2003; Igumenshchev 2008; Tchekhovskoy et al. 2011). The
ejection of flux occurs through the process of magnetic reconnection, which can potentially power high-energy flares
from the region near the event horizon (Ripperda et al. 2020, 2022). The energies of particles and photons powered
by the flare depend on the typical magnetization of the plasma near the event horizon (Crinquand et al. 2022), which
is largely unconstrained for Sgr A*. The reconnection event produces a flux tube of vertical field (i.e., it transforms
toroidal field into poloidal field) that can push away the accretion flow. Low-density plasma from the magnetospheric
region feeding the reconnection layer will heat up due to the reconnection and populate the flux tube. Once the flux
tube is ejected from the black hole magnetosphere, it orbits in the accretion disk (Porth et al. 2019; Dexter et al. 2020).
It is protruded by Rayleigh–Taylor plumes due to the inward pointing gravity and the density contrast with the disk
(Ripperda et al. 2022; Zhdankin et al. 2023). These Rayleigh–Taylor instabilities can accelerate the electrons in the
flux tube to energies capable of powering infrared emission (Zhdankin et al. 2023). The Rayleigh–Taylor instabilities
can also drive turbulence inside the cavity (Stone Gardiner 2007; Zhdankin et al. 2023) that can trap accelerated
electrons (Kempski et al. 2023; Lemoine 2023).
The general idea of particle energization due to turbulence and reconnection in a magnetized and orbiting cavity
motivated us to model the flare spectrum as arising from a spherical, orbiting, one-zone emission region with a
constant magnetic field B and constant radius Rflare. A total of Ne electrons are injected into the region with a
Gaussian temporal profile
Qinj(t) =
Ne
σ
√
2π
exp[−(t − tmax)2
/σ2
] . (C2)
The electrons’ energy distribution is a power law given by:
dN
dγ
=
−p − 1
γmin

γ
γmin
−p
: γmin ≤ γ ≤ γmax (C3)
= 0 : γ γmin ∨ γ γmax . (C4)
Here γmin and γmax are the minimum and maximum electron Lorentz factors. In the model, electrons cool continuously
through their synchrotron emission with a cooling timescale given by Equation 1. The electron energy distribution as
a function of time is given by the continuity equation
∂Ne(γ, t)
∂t
= Qinj −
∂(γ̇Ne)
∂γ
. (C5)

16
No particle escape term (Blumenthal Gould 1970; Dodds-Eden et al. 2011) is included in the model as motivated
by the long confinement timescale (Kempski et al. 2023; Lemoine 2023)
τconf ∝
rg
c

rg
rLarmor
1/3
(C6)
and absence of substantial outflows from the flux tube region as motivated by GRMHD simulations (Ripperda et al.
2022). We solved Equation C5 numerically and computed the resulting synchrotron emission from the emission region
for each time step using the code flaremodel (Dallilar et al. 2022).
Once the intrinsic emission is known, the model accounts for Doppler boosting by computing the Doppler factor
Dboost(Rflare, ϕ, Ω) =
1
γ(1 − β cos ϕ cos Ω)
× Dgrav(Rflare) , (C7)
where β = 2πRflare(4π2
R3
flare)
−0.5
, ϕ is the observer inclination angle, Ω is the angular position (“longitude”) of
the emission region in its circular orbit, and Rflare is in units of gravitational radii. In addition, we included the
gravitational redshift Dgrav(Rflare) = (1 − 1/Rflare)
−0.5
in the Doppler factor D = Dboost × Dgrav and computed the
observed flux as
F′
model(ν) = D3
× Fmodel(ν/D) . (C8)
The resulting boosted light curve shows a sinusoidal modulation. Other than the gravitational redshift, we have ignored
general relativistic effects. The model MIR light curves were normalized identically as the JWST measurements.
The model was fit using the MCMC code emcee (Foreman-Mackey et al. 2013) using a χ2
likelihood that included
χ2
from all four MIRI channels and from the SMA light curve. We used a standard setup of 32 “walkers” and started
the sampling chain at a region visually perceived as a good fit. The chain ran for 1000 steps, but we discarded the
first 500 steps and used only every fifteenth sample to minimize correlation in the sampling. The fit converged well,
and Figure C2 shows the posterior corner plots. Table C1 shows the derived median and the 16% and 84% quantiles
for the model’s free parameters.
C.1. Magnetic field strength in the accretion disk—comparison to Event Horizon Telescope modeling
Modeling of the Event Horizon Telescope (EHT) observations allows to infer the magnetic field strength in the
accretion disk of Sgr A*. Such a calculation often invokes a one-zone model that assumes the emission comes from
a uniform sphere with radius Rflare = 5GM/c2
(Event Horizon Telescope Collaboration et al. 2022e). The sphere is
filled with a collisionless plasma and a uniform magnetic field oriented to θ = π/3 with respect to the line-of-sight.
The observed specific flux from this sphere is given as
Fν =
4
3
πr3
D2
jν, (C9)
where D is the distance to Sgr A* (8.127 kpc), and the specific volumetric synchrotron emission coefficient is taken
from Equation (72) of Leung et al. (2011):
jν = ne
√
2πe2
νs
3cK2(1/Θe)

ν
νs
1/2
+ 211/12

ν
νs
1/6
#2
exp −

ν
νs
1/3
!
,
which assumes a thermal distribution of electrons. Here, K2 is a modified Bessel function of the second kind, νs =
2νcΘ2
e sin(θ)/9, where νc = eB/(2πmec) is the cyclotron frequency, and Θe = kBTe/(mec2
) is the dimensionless electron
temperature.
The plasma β parameter is used to compare the magnetic and gas pressure:
β =
8πkB(neTe + niTi)
B2
(C10)
where Te and Ti are the electron and ion temperatures, respectively. If the plasma is fully ionized, the number density
of ions and electrons should be equal (ne = ni). Additionally, due to the collisionless nature of the plasma, the ions and

17
electrons can have differential heating, leading to a non-unity value for the ion–electron temperature ratio R = Ti/Te.
These assumptions lead to an equation for the electron number density:
ne = β
B2
8π
R
kB(R + 1)Ti
. (C11)
The specific flux can be expressed in terms of only a few parameters by substituting ne from Equation (C11)
and jν from Equation (C.1) into Equation (C9). Assuming the ion temperature is a third of the virial temperature
(Ti = GMmp/(9kBr) = 2.4 × 1011
K) and Fν = 2.4 Jy from the 2017 ALMA campaign (Wielgus et al. 2022b), we
are left with Rflare, β, and B as free parameters. We estimated the range of magnetic field strengths based on this
one-zone model for a reasonable range of parameters by numerically solving for B while varying β ∈ [0.1, 10] and
Rflare ∈ [1, 10]. Figure C1 shows that this results in a range of B ∈ [12, 85] which clearly includes both EHT’s result
of B = 30 G (Event Horizon Telescope Collaboration et al. 2022e) as well as the fiducial magnetic field strength based
on the MIR flare model, B = 45 G. MAD simulations support β values on the order 0.1 in the the inner accretion
region, where we expect the emission to originate (Ressler et al. 2020, 2023; Ripperda et al. 2022; Salas et al. 2024;
Galishnikova et al. 2024). Figure C1 indicates that the larger magnetic field strengths estimated based on the MIR
flare are within the range predicted based on the EHT observed submm emission.
C.2. Model fits and parameter posteriors
Certain parameters are only poorly constrained by the light curve data, and we had to fix them to reasonable
fiducial values. One parameter is γmin, which we set to 10. This corresponds to the typically quoted energy of the
ambient thermal electrons responsible for the bulk of the mm emission (e.g., von Fellenberg et al. 2018). The Chandra
X-ray observations constrain γmax: depending on γmax and the power-law slope p, the model could produce significant
synchrotron flux at X-ray energies. The absence of the X-ray emission during the flare constrains γmax, and we set
γmax = 3 × 104
. Similarly, the normalization of the flux density leaves p unconstrained. We therefore set p = 2, which
gives the canonically observed NIR spectral slope Fν,NIR ∝ ν−0.5
(e.g., Hornstein et al. 2007).
C.2.1. Single Injection Event
Table C1 reports the model’s posterior parameters. The best-fit model has a reduced χ2
= 3.5. Because the light
curve shows small but highly significant variations that the simple model cannot capture, we rescaled the error bars
to obtain χ2
r = 1. This required rescaling factors fCH1 = 3.47, fCH2 = 1.35, fCH3 = 0.75, fCH4 = 0.7, f220GHz = 1.3.
Unless otherwise stated, we adopted those rescaling factors for all fits described below. The best-fit model has a
magnetic field strength B = 44+5
−6 G and log(ne) = 6.9+0.3
−0.2, resulting in σe ≈ 10–50.
Changing p to p = 3 leaves Ω0, σ, tmax, and Rflare unchanged, but the magnetic field strength increases to 52+4
−5 G
and the electron density to 107.1
cm−3
, resulting in very similar σe ∼ 20. The difference in χ2
is negligible (∆χ2
= 0.1,
see Table C1).
In the absence of astrometric or polarimetric measurements of the flare, the orbital parameters of the flare are poorly
constrained. In particular, the inclination, which causes stronger or weaker magnification, is largely degenerate with
the strength of the intrinsic emission. For the fit reported in Table C1, both the inclination and the orbital radius
are free parameters. The best-fit value of the inclination is ϕ = 25◦
± 2◦
and of orbital radius is Rflare ∼ 6.6 RS.
These values are consistent with observations by GRAVITY and ALMA and with the statistics of the NIR light curve
(GRAVITY Collaboration et al. 2023; Wielgus et al. 2022a; von Fellenberg et al. 2024).
The electron magnetization σe depends on the magnetic field strength and the particle density. Because the lumi-
nosity of the flare depends on the size of the emission zone, L ∝ neR3
, the magnetization is not directly constrained.
In order to estimate the range of allowed electron magnetization, we adopted a flat prior distribution of allow emission
regions Rflare ∈ [0.7RS, 2.3RS], motivated by the typical flux tube sizes in GRMHD simulations Ripperda et al. (2022).
For numerical reasons, we fixed the model parameters, which show only weak correlations with the magnetic field
strength, and the electron density, ϕ, Rflare, and the submm offset o. In order to compute the posterior distribution
of the magnetization, we used dynesty (Skilling 2004, 2006). This fit derives a median posterior magnetic field
strength of 46+7
6 G and log(ne) = 5.6+1.1
−0.7 (Table C1). The posterior distribution is shown in Figure C3. The median
magnetization is ∼350 with lower and upper quartiles at (110, 810). This range depends on the prior width chosen for
the flare emission-region size Rflare.

18
C.2.2. Double Injection Event
The observed flare shows a secondary peak at t ≈ 20 minutes. The baseline model does not explain this peak, but
several scenarios could explain it. Examples include a variation in the magnetic field strength or a deviation from
a purely Gaussian injection profile. We modeled the latter scenario by adding a secondary Gaussian injection event,
slightly improving the fit (∆χ2
= −0.5). Table C2 gives the fit posterior values. The magnetic field strength is slightly
higher (∼62 G) with correspondingly lower log(ne) ∼ 6.0, leading to σe ≈ 420 for Rflare = 1 RS. Allowing for a
secondary injection event is not the only explanation that could model the second peak in the light curve. Plausible
alternatives include a variable magnetic field, a shorter orbital period for a spinning black hole, or a variable emission
radius.
C.2.3. Fit without sub-mm contribution
We explored the possibility that the mm increase is by chance and unrelated to the observed MIR variability by
fixing the electron number density to ne = 105.5
cm−3
. The resulting best fit, reported in Table C1, is largely consistent
with the fit reported in Table C1. However, the magnetic field is slightly lower, B ≈ 38 G. Based on the requirement
to not produce submm flux, σe 280.
C.3. Summary of fit results
Depending on the choices of the model parameters, the electron magnetization is constrained to be within B ≈ 40–
70 G and log(ne) ≈ 106
–107
, resulting in σe ≈ 10–900 if the submm variability is considered to be causally connected to
the MIR variability. If this is not the case, i.e., the submm variability is generated by a separate process, the submm flux
produced by the MIR flare has to be lower than the measurement uncertainty in the submm measurement. Assuming
γmin ≡ 10, this places a constraint on electron density and, given σe ∝ n−1
e , σe ≥ 300. The statistical uncertainty on
the model parameters is smaller than the differences between the models, indicating a large theoretical uncertainty
due to the simplicity of the model. We therefore caution that a more rigorous treatment of the electron injection or a
different treatment of the relativistic modulation of the light curve may alter the values.
Figure C1. Distribution of model magnetic field values as β and Ti/Te are varied. The green line shows all parameter
combinations that result in a 45 G magnetic field, while the red cross indicates EHT’s magnetic field value for their chosen
parameters of β = 1 and Ti/Te = 3.

19
= 220.58+8.71
9.02
1
5
.
0
1
6
.
5
1
8
.
0
1
9
.
5
= 16.76+1.21
1.28
1
2
1
5
1
8
2
1
2
4
t
max
tmax = 20.85+2.10
2.36
3
2
4
0
4
8
5
6
B
B = 43.91+6.07
5.18
6
.
4
6
.
8
7
.
2
7
.
6
log(ne)
log(ne) = 6.90+0.31
0.17
1
4
1
6
1
8
2
0
2
2
= 17.00+1.83
1.24
5
.
8
5
6
.
0
0
6
.
1
5
6
.
3
0
6
.
4
5
R
orb.
Rorb. = 6.16+0.13
0.12
1
9
5
2
1
0
2
2
5
2
4
0
0
.
0
0
0
.
0
3
0
.
0
6
0
.
0
9
o
1
5
.
0
1
6
.
5
1
8
.
0
1
9
.
5
1
2
1
5
1
8
2
1
2
4
tmax
3
2
4
0
4
8
5
6
B
6
.
4
6
.
8
7
.
2
7
.
6
log(ne)
1
4
1
6
1
8
2
0
2
2
5
.
8
5
6
.
0
0
6
.
1
5
6
.
3
0
6
.
4
5
Rorb.
0
.
0
0
0
.
0
3
0
.
0
6
0
.
0
9
o
o = 0.04+0.03
0.03
Figure C2. Posterior of the MCMC chain. Columns left to right show the starting angular position of the emitting
region (Ω0), the width of the Gaussian electron-injection pulse (σ), the time of the maximum electron injection rate (tmax),
the magnetic-field strength (B), the total number of injected electrons (log(Ne)), the flux density of the constant 220 GHz
component (ϕ in mJy), and the orbit radius of the emitting region in units of the Schwarzschild radius (Rflare/RS). Histograms
above or to the right of each column show the probability distribution for the corresponding parameter, and each parameter’s
median value and uncertainty (16% and 84% range) are shown above its histogram plot.
101 102 103
e
Density
10 2 10 1 100
p
Figure C3. Posteriors of the electron magnetization σe (left) and proton magnetization σp (right) of the flare.
The thick vertical lines indicate the median values, and the dashed lines mark the quartiles.

20
Table C1. Model Posteriors
Model Posterior p Rflare Ω0 σ tmax log(ne) B ϕ Rorb χ2
red.
Type [RS] [◦
] [minutes] [cm−3
] [G] [◦
] [RS]
Best Fit 2.0 1.0 205+5
−5 16.5+0.6
−0.6 19.6+0.7
−0.7 6.7+0.1
−0.1 39+2
−3 20+1
−1 6.0+0.1
−0.1 3.5
2.0 1.0 221+9
−9 16.7+1.3
−1.3 20.9+2.1
−2.4 6.9+0.3
−0.2 44+5
−6 17+2
−2 6.2+0.1
−0.1 ≡ 1.0
Two Electron-Injection Phases:
First 2.0 1.0 217+9
−8 16.1+1.8
−1.1 25.1+0.5
−0.6 6.0+0.1
−0.1
Second 2.0 1.0 1.7+0.4
−0.7 24.7+0.2
−0.2 5.3+0.1
−0.1
Different Electron
Power-law
Distribution Slope
3.0 1.0 254+7
−4 12.3+0.2
−0.2 25.1+0.7
−0.6 7.1+0.3
−0.6 52+5
−5 30 6.6+0.1
−0.1 1.2
Free Emission
Zone Radius
2.0 ∈[0.8, 2.3] 252+5
−4 14.4+0.6
−0.6 21.8+1.6
−2.2. 5.8+1.1
−0.7 47+7
−7 20 6.2 · · ·
No mm Flare 2.0 1.0 188+9
−11 21.4+1.9
−1.9 15.9+2.9
−3.6 5 38+4
−4 14+1
−1 5.8+0.1
−0.2 0.9
Table C2. Model Posteriors with Two Electron-Injection Phasesa
Ω0 σ1 tmax1 log(ne1 ) σ2 tmax2 log(ne2 ) B o R χ2
red
[◦
] [min] [min] [min] [min] [G] [Jy] [Rg]
217+9
−8 16.1+1.8
−1.1 25.1+0.5
−0.6 6.0+0.1
−0.1 1.7+0.4
−0.7 24.7+0.2
−0.2 5.3+0.1
−0.1 62+3
−3 0.2+0.1
−0.1 6.2+0.1
−0.1 2.6
afor a p = 2, i = 30◦
, and Rflare = 1.0RS model.

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