An Inverse Compton Scattering Origin of X-ray Flares from Sgr A*

Abstract

The X-ray and near-IR emission from Sgr A* is dominated by flaring, while a
quiescent component dominates the emission at radio and sub-mm wavelengths. The
spectral energy distribution of the quiescent emission from Sgr A* peaks at
sub-mm wavelengths and is modeled as synchrotron radiation from a thermal
population of electrons in the accretion flow, with electron temperatures
ranging up to $\sim 5-20$\,MeV. Here we investigate the mechanism by which
X-ray flare emission is produced through the interaction of the quiescent and
flaring components of Sgr A*. The X-ray flare emission has been interpreted as
inverse Compton, self-synchrotron-Compton, or synchrotron emission. We present
results of simultaneous X-ray and near-IR observations and show evidence that
X-ray peak flare emission lags behind near-IR flare emission with a time delay
ranging from a few to tens of minutes. Our Inverse Compton scattering modeling
places constraints on the electron density and temperature distributions of the
accretion flow and on the locations where flares are produced. In the context
of this model, the strong X-ray counterparts to near-IR flares arising from the
inner disk should show no significant time delay, whereas near-IR flares in the
outer disk should show a broadened and delayed X-ray flare.

Full text

The Astronomical Journal, 144:1 (10pp), 2012 July doi:10.1088/0004-6256/144/1/1
C
2012. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
AN INVERSE COMPTON SCATTERING ORIGIN OF X-RAY FLARES FROM Sgr A*
F. Yusef-Zadeh1, M. Wardle2, K. Dodds-Eden3,C.O.Heinke
4, S. Gillessen3,
R. Genzel3, H. Bushouse5, N. Grosso6, and D. Porquet6
1Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA
2Department of Physics and Astronomy, Macquarie University, Sydney NSW 2109, Australia
3Max Planck Institut f¨
ur Extraterrestrische Physik, Postfach 1312, D-85741 Garching, Germany
4Department of Physics, University of Alberta, 4-183 CCIS, Edmonton, AB T6G 2E1, Canada
5Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
6Observatoire astronomique de Strasbourg, Universit´
e de Strasbourg, CNRS, INSU, 11 rue de l’Universit´
e, 67000 Strasbourg, France
Received 2011 December 25; accepted 2012 March 4; published 2012 May 21
ABSTRACT
The X-ray and near-IR emission from Sgr A* is dominated by flaring, while a quiescent component dominates
the emission at radio and submillimeter (sub-mm) wavelengths. The spectral energy distribution of the quiescent
emission from Sgr A* peaks at sub-mm wavelengths and is modeled as synchrotron radiation from a thermal
population of electrons in the accretion flow, with electron temperatures ranging up to ∼5–20 MeV. Here, we
investigate the mechanism by which X-ray flare emission is produced through the interaction of the quiescent and
flaring components of Sgr A*. The X-ray flare emission has been interpreted as inverse Compton, self-synchrotron
Compton, or synchrotron emission. We present results of simultaneous X-ray and near-IR observations and show
evidence that X-ray peak flare emission lags behind near-IR flare emission with a time delay ranging from a
few to tens of minutes. Our inverse Compton scattering modeling places constraints on the electron density and
temperature distributions of the accretion flow and on the locations where flares are produced. In the context of this
model, the strong X-ray counterparts to near-IR flares arising from the inner disk should show no significant time
delay, whereas near-IR flares in the outer disk should show a broadened and delayed X-ray flare.
Key words: black hole physics – Galaxy: center – infrared: general – ISM: clouds – ISM: general – X-rays: general
Online-only material: color figures
1. INTRODUCTION
Observations of stellar orbits in the proximity of the enigmatic
radio source Sgr A*, located at the dynamical center of our
galaxy, have shown compelling evidence that it is associated
witha4×106Mblack hole (Ghez et al. 2005; Gillessen et al.
2009; Reid & Brunthaler 2004). The extremely high spatial
resolution made possible by its relative proximity provides the
best laboratory for studying the properties of low-luminosity
accreting black holes; 1 corresponds to 0.039 pc at the Galactic
center distance of 8 kpc (Reid 1993). The emission from Sgr A*
is assumed to be produced from radiatively inefficient accretion
flow as well as outflows. The bulk of the continuum flux from
Sgr A* is considered to be generated in an accretion disk, where
identifying the source of variable continuum emission becomes
essential for our understanding of the launching and transport
of energy in the nuclei of galaxies.
The emission from Sgr A* consists of both quiescent and
variable components. The strongest variable component is
detected as flares at near-IR and X-ray wavelengths (Baganoff
et al. 2003; Genzel et al. 2003; Goldwurm et al. 2003; Eckart
et al. 2006; Yusef-Zadeh et al. 2006a; Hornstein et al. 2007;
Porquet et al. 2008; Dodds-Eden et al. 2009; Sabha et al.
2010;Trapetal.2011), whereas only moderate flux variation
is found at radio and submillimeter (sub-mm) wavelengths
(Falcke et al. 1998; Zhao et al. 2001; Herrnstein et al. 2004;
Miyazaki et al. 2004; Yusef-Zadeh et al. 2006b; Marrone et al.
2008). The spectral energy distribution (SED) of the quiescent
component peaks at sub-mm wavelengths and is identified in
radio, millimeter, and sub-mm wavelengths (see Genzel et al.
2010, and references therein). This emission is thought to be
produced by synchrotron radiation from a thermal population of
electrons with kT ∼10–30 MeV participating in an accretion
flow. A variety of models have been proposed to explain the
quiescent emission from Sgr A* by fitting its SED, including
a thin accretion disk, a disk and jet, an outflow, an advection-
dominated accretion flow, a radiatively inefficient accretion flow,
and advection-dominated inflow/outflow solutions (Blandford
& Begelman 1999; Melia & Falcke 2001; Yuan et al. 2003;
Liu et al. 2004; Genzel et al. 2010, and references cited
therein). Unlike the quiescent component, which originates over
a wide range of physical conditions and length scales of the
accretion flow, flares are localized, allowing emission models
to be directly tested with observations. As a supermassive black
hole candidate, Sgr A* presents an unparalleled opportunity to
closely study the process by which gas is captured, accreted,
or ejected, by characterizing the emission variability over
timescales of minutes to months. Because the timescale for
variability is proportional to the mass of the black hole, this
corresponds to variability on timescales 100 times longer than
that of more massive black holes in the nuclei of other galaxies.
Studying near-IR emission from Sgr A* is crucial to track the
acceleration of energetic particles as well as the accretion flow.
Near-IR flares are produced by synchrotron radiation from a
transient population of accelerated electrons. The near-IR emis-
sion is dominated by flaring activity that occurs a few times
per day, with a small fraction of events showing simultaneous
X-ray flares. The X-ray flare mechanism has been interpreted
as either inverse Compton scattering (ICS), self-synchrotron
Compton (SSC), or synchrotron emission (Markoff et al. 2001;
Liu & Melia 2002; Yuan et al. 2004; Yusef-Zadeh et al. 2006a;
Eckart et al. 2009; Marrone et al. 2008; Dodds-Eden et al.
2009). The X-ray synchrotron mechanism implies that the ac-
celeration mechanism must continuously resupply the 100 GeV
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The Astronomical Journal, 144:1 (10pp), 2012 July Yusef-Zadeh et al.
electrons for the 30 minute duration of the observed flares, be-
cause the synchrotron loss time of the ∼100 GeV electrons that
are responsible for the synchrotron emission is ∼30 s. The syn-
chrotron self-Compton model requires that the local magnetic
field be extremely large or that the number density of electrons
is high. This is necessary to avoid overproducing the near-IR
synchrotron emission from the large number of energetic elec-
trons that are required to upscatter infrared photons into the
X-ray band (Dodds-Eden et al. 2009; Marrone et al. 2008;
Sabha et al. 2010; Trap et al 2011). The typical parame-
ters of the magnetic field—B∼1–10 G or electron density
ne∼109cm−3—correspond to an energy density in the accel-
erated electrons a thousand times larger than that in the magnetic
field. It is then difficult to understand how these particles are
accelerated and confined.
In the case of X-ray emission produced by ICS, two possibili-
ties have been explored. First, sub-mm photons arising from the
quiescent component of Sgr A* may be upscattered by the tran-
sient electron population that is producing the IR synchrotron
emission during IR flares (Yusef-Zadeh et al. 2006a). Alterna-
tively, near-IR photons emitted during the flare may be upscat-
tered by the mildly relativistic ∼20 MeV electrons responsible
for the quiescent radio–submm emission (Yusef-Zadeh et al.
2006a,2008,2009). If the sub-mm emission region were opti-
cally thin, this would produce a similar X-ray luminosity as the
upscattering of sub-mm seed photons. However, because the
sub-mm source is optically thick below ∼1000 GHz, the ob-
served sub-mm flux is produced by a fraction of the underlying
electrons. The exact frequency at which the quiescent emission
becomes optically thick is unknown. However, sub-mm mea-
surements between 230 and 690 GHz (Marrone et al. 2006)
indicate a flattening of the spectral index and thus a deviation
from the rising spectrum observed at lower frequencies (An et al.
2005). The emission region is optically thin to near-IR photons,
so all of these electrons are available to upscatter near-IR seed
photons to X-ray energies (Yusef-Zadeh et al. 2009). The ICS
luminosity produced through this scenario compares favorably
with the observed near-IR and X-ray luminosities (Yusef-Zadeh
et al. 2009). This is the model on which we will focus, as de-
scribed below.
One of the predictions of the ICS model, in which near-IR
photons are upscattered by ∼10–30 MeV electrons, is a time
delay between the peaks of the near-IR and X-ray flares (Yusef-
Zadeh et al. 2009; Dodds-Eden et al. 2009). Wardle (2011)
provided the theoretical framework for the X-ray echo picture
of the ICS. We present evidence for a time delay between the
peaks of X-ray and near-IR flare emission based on seven new
and archival observations. These measurements provide support
for X-ray production via ICS of IR flare photons by relativistic
electrons of the accretion flow. The cross-correlation profiles of
the peaks are generally skewed toward positive time lags, but
show maximum likelihood values that have low signal-to-noise
(S/N), due to the limited number of detections of simultaneous
X-ray and near-IR flares.
2. OBSERVATIONS
2.1. X-Rays
X-ray observations used in this study come from the
Chandra observatory. Data obtained on 2004 July 6–7 and 2005
July 30 consist of 50.2 and 46 kilosecond (ks) observations,
respectively, (ObsIDs 4683,5953), which were described pre-
viously by Eckart et al. (2006) and Muno et al. (2005). Data
obtained in 2008 (not previously reported) consist of six 28 ks
observations, starting May 5, May 6, May 10, May 11, July 25,
and July 26 (ObsIDs 9169, 9170, 9171, 9172, 9174, 9173, re-
spectively), scheduled to match nighttime IR observations in
Chile (see below). All observations placed Sgr A* at the ACIS-I
aim point and took data in FAINT mode.
We checked for any time intervals of strong background
flaring (none were found) and then reprocessed the data using
CIAO 4.3.7This involved applying corrections to the energy
scales to compensate for time-dependent gain changes and
charge-transfer inefficiency, removing pixel randomization and
improving spatial resolution, as well as creating an updated bad
pixel map. We filtered the data for “bad” grades and status.
We extracted light curves (in spacecraft TT time) from a 1
circular region around the position of Sgr A*, in the 1.5–8 keV
energy range, using Gehrels (1986) errors. We converted the
time stamps to UTC time following the prescription by A. Rots.8
The baseline quiescent X-ray emission from Sgr A* is spatially
extended (Baganoff et al. 2003), but we see no variations in
other local background emission. We tested several choices of
binning the data for comparison to other wavelengths, settling
on 1500 s binning for the 2008 data, 300 s binning for the
major flare on 2004 July 6–7, and 600 s binning for the flare
on 2005 July 30. Using the absorbed thermal plasma model
of Baganoff et al., the ratio of 1.5–8 keV counts to 2–10 keV
unabsorbed flux is 8 ×10−11 erg cm−2s−1per count/s. Recent
measurements indicate a distance of 8.3 kpc to Sgr A* (Gillessen
et al. 2009), but we assume a distance of 8 kpc, which gives
LX(2–10)=6×1035 erg s−1per count s−1, or a typical quiescent
luminosity of 3×1033 erg s−1, in agreement with Baganoff et al.
(2003).
We used Kolmogorov–Smirnov (K-S) tests (using the lcstats
FTOOL9) on the 2008 Chandra light curves (binned to 32.41 s)
to search for evidence of variability. We find evidence for
variability in three of the 2008 observations, while another
three show no evidence of variability. ObsIDs 9169, 9172,
and 9173 give K-S probabilities of a constant light curve of
5×10−6,2×10−4, and 1 ×10−8, respectively, while the
remaining observations give K-S probabilities greater than 5%.
This significantly strengthens the evidence of variability from
Sgr A* at very low levels, as Baganoff et al. (2003) reported a
much larger K-S probability of constancy of 7 ×10−3during
quiescence. Given that the quiescent X-ray emission arises from
much larger scales, presumably due to Bondi–Hoyle accretion
(Baganoff et al. 2003), we suggest that the X-ray variability
noted here is due to low-level flare emission superimposed on the
steady quiescent emission. Alternatively, the X-ray variability
on hourly timescales could arise from coronally active stars
producing giant flares (Sazonov et al. 2012).
2.2. Near-IR
For the near-IR observations we use archival data taken with
the Very Large Telescope (VLT) and Hubble Space Telescope
(HST). The near-IR data taken in 2004, 2005, and 2008 were
observed with the near-IR adaptive optics (AO) assisted imager
NACO at the VLT (Lenzen et al. 2003; Rousset et al. 2003).
We used Ks-band 13 milliarcsecond (mas) pixel imaging data
from 2004 (nights of July 6–7) and 2005 (night of July 30–31)
first presented by Eckart et al. (2006,2008), and Ks-band
7For example, http://cxc.harvard.edu/ciao/threads/createL2/
8http://cxc.harvard.edu/contrib/arots/time/time_tutorial.html/
9http://heasarc.gsfc.nasa.gov/lheasoft/ftools/xronos.html
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The Astronomical Journal, 144:1 (10pp), 2012 July Yusef-Zadeh et al.
13 mas pixel polarimetric imaging data from 2008 (nights
of May 4/5, 5/6, 9/10, 10/11 and July 25/26, 26/27) first
presented in Dodds-Eden et al. (2011). We did not apply any data
quality cut for the latter observations, except for the elimination
of 11 images from 2008 July 25, due to a bad AO correction
(quadfoils, or a “waffle” pattern).
We used both aperture photometry and point-spread function
(PSF) photometry methods to produce light curves, both carried
out in the way described in Dodds-Eden et al. (2011). In par-
ticular we note that, for the purposes of that paper, the aperture
method used two small apertures, one centered on the position
of Sgr A* and the other on the star S17 (confused with Sgr A*
in 2006–2008), in order to measure their combined flux. Since
S17 was further from Sgr A* in 2004 and the combined mea-
surement of the flux is not important for the purposes of this
paper, the use of the above method unnecessarily decreases the
S/N. As a result, for the near-IR/X-ray comparison we supple-
mented the data set with higher S/N light curves obtained from
PSF photometry, though the data were sparsely sampled. We
provide the light curve of S17 in the 2008 data set and the light
curve of the comparison star S7 for the 2004 and 2005 data sets.
The stellar background is estimated to be 3.4±0.2 mJy in 2008
(Dodds-Eden et al. 2011).
Near-IR HST observations used in this study are NICMOS
archival data obtained on 2007 April 4 as part of a larger Sgr A*
monitoring campaign. Full observational details have been
presented in Yusef-Zadeh et al. (2009). Briefly, the exposures
used NICMOS camera 1, which has a pixel scale of 0.
043, and
the medium-band filters F170M and F145M, which have central
wavelengths of 1.71 and 1.45 μm, respectively, and FWHMs of
0.2 μm. Individual exposures had a duration of 144 s, with
non-destructive detector readouts occurring every 16 s. We
averaged the readouts to sampling intervals of 64 and 128 s
in the 1.71 and 1.45 μm bands, respectively, to obtain adequate
S/N. Aperture photometry was performed on Sgr A* in each
sampling interval, using an aperture diameter of 3 pixels in order
to limit contamination by nearby stars.
All of the near-IR measurements presented here have been
corrected for reddening using extinction values of Aλ=2.42
(2.2 μm), 4.34 (1.71 μm), and 6.07 (1.45 μm) from Fritz et al.
(2011).
3. RESULTS
The middle two panels of Figure 1show the light curves
from the archival Ks-band and X-ray observations of Sgr A*
that were taken on 2005 July 30. The near-IR light curve of the
comparison star S7 is shown in the top panel. The X-ray and
near-IR light curves of Sgr A* were sampled at intervals of 200
and 600 s, respectively. These measurements, first reported in
Eckart et al. (2008), indicate a flare with a peak X-ray luminosity
of 8×1033 erg s−1. The bottom panel shows the cross-correlation
of these light curves. The cross-correlation analysis uses the
Z-transformed discrete correlation function (ZDCF) algorithm
(Alexander 1997). The ZDC function is an improved solution
to the problem of investigating correlation in unevenly sampled
light curves. Maximum likelihood values as well as 1σand 2σ
confidence intervals around those values are estimated using the
start time of each bin. This analysis finds that the X-ray peak
lags the near-IR peak in Figure 1by ∼8.0 (+10, −10.1) and
8.0 (+20.2, −17.9) minutes for 1σand 2σmaximum likelihood
values, respectively. We varied the sampling interval in the near-
IR and X-ray data between 1.5 and 10 minutes, but the maximum
likelihood lag value remained the same. Eckart et al. (2008)
Figure 1. Light curve of the comparison star S7 is shown in the top panel
with a time sampling of 65 s. Two middle panels show the light curves of
Ks-band (2.2 μm) and X-ray (2–8 keV) data taken simultaneously by the VLT
and Chandra on 2005 July 30 (Eckart et al. 2008). The time sampling for the
X-ray and near-IR data is 600 and 200 s, respectively. The cross-correlation
of the light curves and the corresponding 2σmaximum likelihood values are
shown in the bottom panel. The 1σerror bar is given in Table 2.Abaselevel
of 4.2 mJy have been subtracted from the light curve of Sgr A* (Dodds-Eden
et al. 2011).
(A color version of this figure is available in the online journal.)
compared the X-ray and near-IR flare emission and found that
the peaks are coincident within ±7 minutes.
The aperture photometry technique that was used to reanalyze
the near-IR VLT data from 2004 produced a light curve that
is quite similar to that published by Eckart et al. (2006), who
deconvolved their images. The only difference is that the present
analysis uses data extending up to 4 hr UT on July 7, which is
longer than that of Eckart et al. (2006). The bottom three panels
of Figure 2show the cross-correlation of these near-IR and X-ray
data with a maximum likelihood lag of 7.0 (+1.3, −1.1) minutes
and (+7.5, −6.9) minutes with 1σand 2σerrors, respectively.
The lag is larger than zero at the 1σlevel. The near-IR light curve
of the comparison star S7 is shown in the top panel. The light
curve of S7 is constant and supports the variable emission from
Sgr A* between 3 and 4h UT. The sampling of the near-IR data
reduced using PSF photometry is much more sparse than the
aperture photometry data. The 1σcross-correlation peak using
the PSF photometry showed a time lag 7.7 (+2.9, −3.4) minutes
within the error bars of that reduced by aperture photometry.
Eckart et al. (2006) also cross-correlated their data and showed
no time delay within 10 minutes.
Next we examined the X-ray and near-IR light curves ob-
tained on 2007 April 4 using XMM and VLT observations
(flare 2 in Porquet et al. 2008; Dodds-Eden et al. 2009).
These data contain the second brightest X-ray flare (flare 2 in
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The Astronomical Journal, 144:1 (10pp), 2012 July Yusef-Zadeh et al.
Figure 2. Top panel shows K-band (2.2 μm) VLT data of the comparison star
on S7 with a time sampling of 45 s and Sgr A* on 2004 July 6/7, while the
third panel shows simultaneous Chandra X-ray (2–8 keV) data (Eckart et al.
2006). The middle two panels show the light curves of K-band (2.2 μm) and
X-ray (2–8 keV) data taken simultaneously by the VLT and Chandra on 2004
July 6/7 (Eckart et al. 2006). The time sampling for the X-ray and near-IR data
on Sgr A* are 300 and 140 s, respectively. The cross-correlation of the light
curves is plotted in the bottom panel. For the 2004 light curve determined from
aperture photometry the stellar background estimate is 5.3±0.2 mJy which has
been subtracted. For the light curve determined from PSF photometry (separated
from S17 and S19 and free from any contribution from the seeing halo of S2)
the specific amount of faint stellar contribution is not clear, but small, <1mJy.
A maximum likelihood value with 2σerror bars are shown in the bottom panel.
The 1σerror bar is given in Table 2.
(A color version of this figure is available in the online journal.)
Porquet et al. 2008) coincident with one of the strongest near-IR
flares that has ever been detected. The cross-correlation of the
X-ray and near-IR data for this bright flare shows a 1σmaxi-
mum likelihood time delay of −0.5 (+7.0, −6.5) minutes, which
is consistent with zero time delay (Dodds-Eden et al. 2009;
Yusef-Zadeh et al. 2009). The peak luminosity of the brightest
flare is 24.6×1034 erg s−1(Porquet et al. 2008). Two other
moderate X-ray flares (flares 4 and 5) were detected on 2004
April 4 following the bright X-ray flare. X-ray flares 4 and 5,
with peak luminosities of ∼6×1034 and ∼8.9×1034 erg s−1,
respectively, are covered in the near-IR 1.71 and 1.45 μm
NICMOS data. The cross-correlations of the X-ray and near-
IR light curves for flares 4 and 5 are presented in Figures 3(a)–
(d). The NICMOS observations alternated between the 1.71 and
1.45 μm bands every 6 minutes. In all of the four cases studied,
the maximum likelihood values of flares 4 and 5 show positive
lags ranging between 5 and 10 minutes. Similar to the other
cases analyzed here, the peaks of the cross-correlations are all
skewed toward positive time lags.
Finally, we compared near-IR (VLT) and X-ray data taken
in 2008 May and July. Figure 4shows the light curves from
the two different days of observations. These X-ray flares are
an order of magnitude less luminous than those detected in
earlier observations. We have carried out K-S tests indicating
the reality of these low-level X-ray visibilities (Section 2.1).
The cross-correlations of the light curves from these two days
give maximum likelihood lags of 19 (+6.8, −2.4) and 14.6 (5.6,
−2.9) minutes with 2σerror bars. Figure 4also shows the cross-
correlation of X-ray with near-IR light curves derived from PSF
photometry. The resulting time delays of 26.5 (+19, −29) and
16.6 (14.8, −11.8) minutes are well within the error bars of
the aperture photometry data. To provide additional support for
the reality of the variability of Sgr A*, Figure 5compares the
light curves of Sgr A* and S17 using the 2008 May 5 and 2008
July 26 observations, which are based on PSF photometry. In
these data, where Sgr A* and S17 are separated from each other,
each source is detected independently.
Although most of the individual cross-correlation results that
are presented here have low S/N, the 1σmaximum likelihood
peaks in eight different measurements show a tendency for
X-ray emission to lag near-IR emission rather than lead. The
cross-correlation gives maximum likelihood near-IR-to-X-ray
lag values that are systematically higher than zero. The strongest
simultaneous near-IR and X-ray flares (Flare 2 in Porquet et al.
2008) do not show any time delay, whereas the faintest X-ray
flares seem to show the longest time delays.
4. SSC MODELS
Several alternative models for the relationship between near-
IR and X-ray flares have been proposed. Synchrotron emission
from a high-energy tail of the accelerated electron population
responsible for the near-IR flaring may be responsible for the
observed X-ray flaring (Dodds-Eden et al. 2009,2010). SSC
models, in which the same population of electrons produce
the near-IR synchrotron emission and upscatter lower-energy
synchrotron photons, require an unrealistically compact, and
hence over-pressured, source region (Dodds-Eden et al. 2009)
or a very weak magnetic field or a high electron density to
avoid overproducing the IR synchrotron emission (Marrone
et al. 2008; Sabha et al. 2010;Trapetal.2011).
In SSC models the observed ratio of the X-ray and IR
fluxes demands a certain Thomson optical depth in relativistic
electrons. SSC flare models (Marrone et al 2008; Sabha et al.
2010;Trapetal.2011) adopt source region radii R of order Rs.
The requisite electron densities then imply a particular magnetic
field strength, so that the synchrotron emission from the electron
population matches the observed near-IR flaring. These SSC
models have electron energy densities ranging between 103and
2×105times the magnetic energy density. Because electron
acceleration mechanisms invoke magnetic fields, the energy
density in the field should be comparable to or greater than
the energy density of the accelerated particles. Thus, scaling
the SSC models to equipartition fields by reducing the electron
density while increasing the magnetic field to keep the product
neB[(p+1)/2] and hence the near-IR synchrotron flux fixed, one
finds that a reduction in electron density by a factor of 40 or
more is required. Thus, SSC contributes at most 1/40 of the
observed X-ray flux in such a model.
Alternatively, one can attempt to construct SSC models in
which the field is in equipartition by reducing the source
size R, while keeping the products neB[(p+1)/2]R3and neR
fixed to preserve the synchrotron and SSC fluxes, respectively.
Equipartition between the relativistic electrons and magnetic
field is attained when Ris reduced by a factor of a thousand
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The Astronomical Journal, 144:1 (10pp), 2012 July Yusef-Zadeh et al.
(a) (b)
(c) (d)
Figure 3. (a) The light curves of flare 4 of 2007 April 4 in near-IR (1.70 μm) and X-ray (2–10 keV) are taken by HST/NICMOS, and XMM-Newton/EPIC, with a
time sampling of 64 and 300 s, respectively. (b) Same as (a) except that the 1.45 μm are sampled at 144 s interval to improve the S/N. (c) Same as (a) except that the
light curves of flare 5 are displayed at 1.70 μm. (d) Same as (c) except that the light curves of flare 5 are displayed at 1.45 μm. The cross-correlation and the maximum
likelihood values with 2σerror bars are shown in bottom panels. The 1σerror bars for flares 4 and 5 at 1.70 μmaregiveninTable2.
(A color version of this figure is available in the online journal.)
5

The Astronomical Journal, 144:1 (10pp), 2012 July Yusef-Zadeh et al.
(a) (b)
(c) (d)
Figure 4. (a) Using the aperture photometry technique, the top two panels show the light curves of Ks-band (2.2 μm) and X-ray (2–8 keV) data taken simultaneously
with VLT and Chandra on 2008 May 5. The sampling interval for X-ray and near-IR data are 25 and ∼2 minutes, respectively. The cross-correlation of the light
curves is plotted in the bottom panel. (b) Similar to (a) except that the data were taken on 2008, July 26+27. (c) Similar to (a) except the light curve of Sgr A* is
calibrated using PSF photometry technique. (d) Similar to (b) except the light curve of Sgr A* is calibrated using PSF photometry technique. The cross-correlation
and the maximum likelihood values with 2σerror bars are shown in bottom panels. The 1σerror bars for aperture photometric data are given in Table 2.
(A color version of this figure is available in the online journal.)
6

The Astronomical Journal, 144:1 (10pp), 2012 July Yusef-Zadeh et al.
(a) (b)
Figure 5. (a) The panels show the light curves of PSF photometrically reduced Sgr A* and S17 at 2.2 μm on 2008 May 5. (b) Similar to (a) except that the data were
taken on 2008, July 26+27. A base level of 3.6 mJy has been subtracted.
(A color version of this figure is available in the online journal.)
or more, with corresponding field strength in the 104–105G
range, which is orders of magnitude more than what is reason-
able.
5. X-RAY ECHO DUE TO ICS
Here we focus on an inverse Compton scenario for the
X-ray flares, suggested by Yusef-Zadeh et al. (2009) and
outlined in more detail by Wardle (2011). In this model, near-IR
flare photons are upscattered to X-ray energies by the thermal
electrons (kTe∼10 MeV) in the accretion flow. This process
dominates the alternative inverse Compton pathway, in which
the nonthermal energetic electrons responsible for the near-IR
synchrotron emission upscatter sub-millimeter photons emitted
by the thermal electrons in the accretion flow into the X-ray
band (Rybicki & Lightman 1986, chapter 7.5). This alternative
ICS pathway is less effective because the accretion flow is
optically thick in the submillimeter, so that the ratio between
sub-mm photons and the thermal electrons producing them is
reduced by a factor of the optical depth. Then the upscattering of
near-IR photons proportionately produces more emission than
would be inferred by implicitly assuming that the submillimeter
synchrotron flux is optically thin (e.g., Dodds-Eden et al.
2009). In this process, the second-order scattering echo can
also produce MeV γ-ray emission with a luminosity Lγthat is
lower than that of X-rays LXby a factor of a few (i.e., Lγ/LX∼
LX/LNIR).
One significant difference of the ICS picture from the syn-
chrotron and SSC pictures is that the longer path from the
near-IR source to the observer taken by an upscattered photon
detected in the X-ray compared to the straight-line path taken by
a photon received in the near-IR introduces a time delay between
flaring in the near-IR and X-rays. In addition, because scattering
occurs from a range of locations within the accretion flow, with a
corresponding range of time delays, the reflection signal tends to
be broadened compared to the near-IR seed photon light curve.
While there is some evidence of systematic delays between the
near-IR and X-ray flaring, the X-ray flares appear to generally
have a narrow FWHM compared to their corresponding near-IR
flares.
5.1. Modeling
To explore whether this model can plausibly explain the X-ray
flaring, we compute the X-ray “echoes” of the observed near-IR
flares to compare with our simultaneous X-ray observations. We
make a number of simplifying assumptions, none of which are
severe. We assume that the observed near-IR flare comes from
a point located in the accretion flow with a power-law spectrum
and Gaussian light curve, Sν(t)∝ν−0.5exp(−(t−t0)2/2σ2).
Because the X-ray flares are narrower than the near-IR we have
assumed that the FWHM of the near-IR flaring narrows as λ0.5
below 2.2 μm. The physical justification is that the synchrotron
loss timescale scales as λ0.5and becomes comparable with the
observed FWHM at about 2 μm. The energy of an upscattered
photon with initial energy hνIR isassumedtobe(4/3)γ2hνIR
where γis the electron Lorentz factor. Because the upscattered
photon energies are much lower than the electron rest energy,
the scattering occurs in the Thompson regime. Assuming
isotropic upscattering, the total production rate of upscattered
photons per unit volume is nIRneσTc, where nIR and neare the
7

The Astronomical Journal, 144:1 (10pp), 2012 July Yusef-Zadeh et al.
Tab l e 1
Model Parameters for Flare Events
Flare kT a
0nb
0rc
(MeV) (cm−3)(cm)
2004 Jul 7 9 2.9×1081.0×1013
2005 Jul 30 20 2.3×1071.0×1013
2007 Apr 4 flare 2 7 2.1×1084.0×1012
2007 Apr 4 flare 4 5 7.9×1081.0×1013
Notes.
aAccretion flow temperature profile Te(r)=T0(r/r0)−1where r0=2×
1012 cm.
bDensity profile ne(r, z)=n0(r/r0)0.75 exp(−2z2/r2).
cRadial location of near-IR flare in equatorial plane (Rs≈1.2×1012 cm for
MBH =4×106M).
number densities of infrared photons and relativistic electrons,
respectively. We ignore relativistic effects such as the Doppler
boosting associated with the bulk motion of the accretion flow,
because the corresponding Lorentz factor is small compared to
that of the individual electrons. We also ignore the time delay,
gravitational redshift and lensing effects of the Kerr metric,
which only become important close to the event horizon in
highly inclined systems.
The electron density and temperature profiles in the accretion
flow are assumed to be steady, axisymmetric power laws in
cylindrical radius r, with ne∝r−0.75 and Te∝r−1and
the density truncated within 2 Rsand beyond 20 Rs.The
accretion flow is assumed to be confined to a thick disk
with scale height/radius (h/r )=0.5. The electron population
is characterized by an approximate relativistic Maxwellian
f(x)=1/2x2exp(−x), where x=E/(kTe), which is a
good approximation for kTe>
∼2 MeV. The adopted profiles
are within the typical ranges considered in analytic estimates
(e.g., Loeb & Waxman 2007), semi-analytic models for the
accretion flow (e.g., Yuan et al. 2003), and MHD simulations
(e.g., Mo´
scibrodzka et al. 2009).
The remaining parameters specify the flare location relative to
the line of sight and relative to the accretion flow: the inclination
iof the disk to the line of sight, and the flare location (r, φ, z)in
the natural cylindrical coordinate system. The low optical depth
of the accretion flow to near-IR photons means that the results
are insensitive to the inclination iand the azimuthal angle φ
between the flare location and the poloidal plane containing the
line of sight and the z-axis. We therefore fix these at typical
values i=45◦and φ=90◦, respectively. Similarly, the results
are insensitive to the height zof the near-IR flare for z<
∼r,so
we simply assume that the flare occurs in the disk midplane, i.e.,
that z=0.
The free parameters are the electron density n0and tempera-
ture T0at the fiducial radius 2 ×1012 cm, and the radial location
of the flare, r. The noisiness of the observed light curves preclude
formal fitting, so for each near-IR/X-ray flare combination we
adjust these parameters by hand to approximately match the
X-ray light curve. Reasonable matches to the observed X-ray
profile are obtained with flares occurring at r∼10Rs, and elec-
tron densities ∼107.5–108.5cm−3and temperatures ∼5–20 MeV,
as listed in Table 1.
In the context of the ICS picture, we fit a sample of light curves
that have good time coverage in near-IR and X-ray wavelengths
in order to illustrate the point that this model can potentially be
a powerful tool to quantify the physical characteristics of the
accretion flow. The light curves presented in Figures 1and 2
are modeled following the second brightest X-ray flare that has
ever been recorded on 2007 April 4 (Porquet et al. 2008). The
light curves of the moderate flare that followed this bright flare
(flare 2) is presented in Figure 3. The time delays of the peak
emission shown in Figures 1,2, and 3are 8, 7, and 8 minutes,
respectively, whereas the bright flare on 2007 April 4 showed a
time delay consistent with zero. Given the limited simultaneous
time coverage of the flares shown in Figures 3and 4, we focus
only on modeling these four flares. Figure 6shows the observed
and modeled light curves for the simultaneous near-IR and X-ray
flares that occurred on 2005 July 30, 2004 July 6/7, and 2007
April 4 (the main flare and flare 4). Parameters of the fit for
each of the four examples are shown in Table 1. Substructures
corresponding to two weak flares in Figure 6(a) are also modeled
with the same parameters as the main flare, as listed in Table 1.A
baseline level has been subtracted from the near-IR light curves
before constructing the theoretical light curves. If we restrict the
evaluation of χ2to just the flare part of the X-ray light curve,
χ2/df is between 3 and 4. The reason is that there is often point-
to-point variability in the light curve that throws points well
away from the smooth “prediction”. In addition, the near-IR light
curve in Figure 6(c) shows substructures that could be arising
from different flares, which would have different time delays in
the context of ICS. Thus we have not formally fit the light curves
as our models are illustrative only. Given these limitations, we
obtain reasonable parameters from the theoretical X-ray light
curves, which are superimposed on the observed light curves in
Figure 6.
In each case a Gaussian form of the near-IR light curve has
been adopted to represent the observed (extinction-corrected)
near-IR flare at 3.8 μm, 2.2 μm, and 1.7 μm. However, in our
models, the X-ray flare arises from scattered optical photons.
We assume the peak flux of the synchrotron flare (emitting at
near-IR to optical) scales as ν−0.5with frequency. Because
the X-ray flare is narrower than the near-IR we have assumed
that the FWHM is constant below 2.2 μm and narrows as λ0.5
shortward of this. Reasonable matches to the observed X-ray
profile are obtained with the flare occurring at the inner edge
of the density profile and electron densities, as their estimated
values are given in Table 1. The FWHM assumption requires
both the rise and the decay timescale of the flare to be faster at
optical frequencies than at near-IR. For the decay timescale, this
is a natural result of synchrotron cooling (the synchrotron loss
timescale scales as ν−0.5). The rise timescale depends on the
acceleration mechanism. While the acceleration mechanism of
flare production is not understood, it is plausible that optically
emitting electrons are produced later than IR emitting electrons
(Kusunose & Takahara 2011).
Another issue involves the prediction that the spectral index
between X-rays and near-IR/optical emission be identical in the
context of ICS with the assumption that the electron distribution
has a single power-law spectrum. It is, however, possible that
the energy spectrum of electrons has a broken power law, thus
producing a different spectral index in near-IR and X-rays. The
mismatch in spectral index is in fact noted for the bright X-ray
flare coincident with a strong near-IR flare of 2007 April 4
(Dodds-Eden et al. 2009). Although these authors discuss the
difference in the spectral index using a synchrotron mechanism,
the broken power law of NIR emitting electrons with a steeper
spectral index shortward of 3.8 μm was also argued in the ICS
scenario (Yusef-Zadeh et al. 2009).
Although the spectral index measurements in X-ray and
near-IR cannot distinguish between the synchrotron and ICS
8

The Astronomical Journal, 144:1 (10pp), 2012 July Yusef-Zadeh et al.
0
2
4
6
8
Sν 2.2µm (mJy)
02468
0.0
0.5
1.0
1.5
2.0
UT (hours)
LX (2–8 keV) (1034 erg/s)
2005 Jul 30
0
2
4
6
8
Sν 2.2µm (mJy)
02468
0
2
4
6
UT (hours)
2004 Jul 07
LX (2–8 keV) (1034 erg/s)
0
10
20
30
Sν 3.8µm (mJy)
45678
0
1
2
3
4
UT (hours)
LX (2–10 keV) (1035 erg/s)
2007 Apr 04
0
2
4
Sν 1.7µm (mJy)
12 13 14 15 16
0.5
1
UT (hours)
LX (2–10 keV) (1035 erg/s)
2007 Apr 04 4A
(a) (b)
(c) (d)
Figure 6. Adopted near-IR light curves and the corresponding ICS produced X-ray light curves (solid lines) superimposed on the near-IR and X-ray flares observedon
2005 July 30 (a), 2004 July 7 (b), and two flares on 2007, April 4 ((c) and (d)), respectively. Near-IR flare data are an input to the ICS model. The X-ray and near-IR
flare of 2005 July 30 and 2004 July 7 are taken from Eckart et al. (2006,2008) whereas the 2007, April 4 data are taken from Porquet et al. (2008) and Dodds-Eden
et al. (2009). The ICS model parameters are listed in Table 1. Two weak flares before and after the main flare in the 2005 data in (a) have also been modeled. A possible
second flare of the 2004 data near 4h UT, as shown in Figure 2, has not been modeled in (b).
(A color version of this figure is available in the online journal.)
models for the production of X-rays, it is predicted that the ratio
of near-IR to X-ray flare emission can increase with increasing
time delay in the ICS scenario. This is because bright X-ray
flares are generated in the inner disk where the time delay is
expected to be small. Although the available data are limited
to test this aspect of the proposed model, we note a trend that
is consistent with this expectation. Table 2shows the ratio of
2.2 μm peak flux (mJy) to peak X-ray luminosity (1035 erg s−1)
for seven different measurements. The 1σerror bars of the
maximum likelihood values are given in Column 7. The smallest
to largest flux ratios, as shown in Column 6 of Table 2, support
the trend that near-IR/X-ray flux ratios increase with the time
9

The Astronomical Journal, 144:1 (10pp), 2012 July Yusef-Zadeh et al.
Tab l e 2
Flux Ratios versus Time Delay
Flare IR X-Ray IR Peak X-Ray Peak Peak Ratio Time Delay
Backg. Backg. (mJy) (1 ×1035 erg s−1)IR/X-Ray (minutes) 1σ
2007 Apr 4 flare 2 5.0 0.2 16.5 4.8 3.4 −0.5 (+7, −6.5)
2007 Apr 4 flare 5 −0.2 0.2 2.63 1.23 2.1 5.0 (+1.9, −1.5)
2007 Apr 4 flare 4 −0.2 0.2 4.67 1.22 3.8 5.0 (+1, −1.4)
2004 Jul 7 1.5 0.03 6 0.39 15.5 7 (+1.3 −1.2)
2005 Jul 30 0.0 0.002 5.9 0.13 45.4 8 (+10, −10.1)
2008 Jul 26+27 5.5 0.003 3.7 0.05 68.5 14.6 (+5.6, −7.4)
2008 May 5 6 0.003 2.74 0.021 130.0 19 (+6.8, −2.4)
delay, as expected in the context of the ICS model. For the near-
IR observations on 2007 April 4 obtained at 3.8 and 1.7 μm,
we convert the peak flux to 2.2 μm using the spectral index
of −0.7, where Sν∝ν−0.7, before we estimate the flux ratio.
Future simultaneous measurements of X-ray and near-IR flares
should examine the correlation of the peak near-IR to X-ray flux
as a function of increasing observed time delay.
In summary, we have presented cross-correlations of simul-
taneous X-ray and near-IR flare light curves from Sgr A* and
found a time lag of the X-ray peak flare emission with respect
to the near-IR. Such an X-ray echo provides support for ICS of
near-IR flare photons by ∼5–20 MeV electrons. A fraction of
near-IR flare photons must upscatter from the accretion flow into
the X-ray band. This can be significant for plausible accretion
models, and therefore may explain the observed X-ray flares, or
at least place significant constraints on the accretion flow. Future
cross-correlations based on more continuous near-IR and X-ray
observations should give us better S/N in the maximum likeli-
hood values of the time lag. In the context of the ICS model,
future measurements will place better constraints on the density
and temperature profiles of the accretion flow and the location
of near-IR flares.
This work is partially supported by grants AST-0807400
from the National Science Foundation and DP0986386 from the
Australian Research Council. C.O.H. is supported by NSERC
and an Ingenuity New Faculty Award.
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