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Reverse shock of the Fermi bubbles explains their origin
Yutaka Fujita1?
1Department of Physics, Graduate School of Science, Tokyo Metropolitan University,
1-1 Minami-Osawa, Hachioji-shi, Tokyo 192-0397, Japan
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
The Fermi bubbles are large gamma-ray-emitting structures. They are symmetric about the Galactic Centre (GC),
and their creation is therefore attributed to intensive energy injection at the GC. In this study, we focus on the
X-ray gas structures associated with the bubbles. We show that a combination of the density, temperature, and
shock age profiles of the X-ray gas can be used to distinguish the energy injection mechanisms. By comparing the
results of numerical simulations with observations, we indicate that the bubbles were created by a fast wind from the
GC because it generates a strong reverse shock and reproduces the observed temperature peak there. On the other
hand, instantaneous energy injection at the GC cannot reproduce the temperature profile. The wind had a speed of
∼1000 km s−1, and blew for ∼107yr. Because the mass flux of the wind is large, the entrainment of interstellar
gas by wide-angle outflows from the black hole is required. Thus, the wind may be the same as active galactic nuclei
outflows often observed in other galaxies and thought to regulate the growth of galaxies and their central black holes.
Key words: ISM: jets and outflows – Galaxy: centre – Galaxy: halo
1 INTRODUCTION
The Fermi bubbles are large gamma-ray-emitting structures
extending ∼ ±50◦above and below the Galactic Centre
(Dobler et al. 2010;Su et al. 2010), and related structures
have been discovered based on X-ray (Keshet & Gurwich
2018) and radio observations (Finkbeiner 2004;Dobler &
Finkbeiner 2008;Planck Collaboration 2013). However, the
origin of the Fermi bubbles, for example, the instantaneous
explosive activity of a central supermassive black hole (Sagit-
tarius A∗;Guo & Mathews 2012;Fujita et al. 2013,2014;
Mondal et al. 2022;Yang et al. 2022), winds from the black
hole (Zubovas & Nayakshin 2012;Mou et al. 2014,2015), a
starburst (Carretti et al. 2013;Lacki 2014;Sarkar et al. 2015),
or steady star-formation activity (Crocker & Aharonian 2011;
Crocker 2012), has been debated.
Peculiar X-ray structures were recognised in the direction
of the Galactic Centre (GC) even before the discovery of
Fermi bubbles in gamma rays. In particular, the regions cor-
responding to high X-ray and radio wave intensities are called
the North Polar Spur and Loop I (Snowden et al. 1995). There
has been discussion on whether their origin is from a nearby
supernova remnant or galactic-scale structures located near
the GC (Salter 1983;Sofue 2000). However, recent eROSITA
telescope observations have shown that these X-ray struc-
tures are part of a larger structure encompassing the Fermi
bubbles, which means that their association with the galac-
tic structure and Fermi bubbles has been confirmed (Predehl
et al. 2020). Consequently, the properties of the X-ray struc-
?E-mail: y-fujita@tmu.ac.jp
tures are related to the formation process of the Fermi bub-
bles. Previous studies have mainly focused on the morphology
of X-ray structures that reflect gas density distributions (e.g.
Yang et al. 2022). By contrast, in this study, we demonstrate
that the combined analysis of the density, temperature, and
shock age profiles of the gases based on X-rays is a power-
ful tool for distinguishing the energy-injection mechanisms of
the Fermi bubbles. Importantly, this helps us understand the
origin of the Fermi bubbles. Here, the shock age is defined as
the time elapsed since the passing of a shock wave through a
gas element.
The paper is organized as follows. In Section 2, we explain
our models and numerical setup. In section 3, we compare
our simulation results with observations, and show that the
Fermi bubbles should have been created by a fast wind. In
section 4, we discuss the origin of the wind based on the
parameters derived in Section 3. The conclusion of this paper
is presented in Section 5.
2 MODELS
To study the dependence of the X-ray gas profiles on different
energy-injection mechanisms at the GC, we performed one-
dimensional Lagrangian hydrodynamic simulations of shock
propagation from the GC (Bodenheimer et al. 2007), re-
garding the Fermi bubbles as a single bubble. The one-
dimensionality of the code enables unknown parameters to
be specified by performing ∼104simulations and comparing
the results with observations. Because the actual Fermi bub-
bles are not spherically symmetric, we adopted the volume-
averaged radius (r∼4kpc) as the typical radius of the bub-
©2022 The Authors
arXiv:2208.01654v1 [astro-ph.HE] 2 Aug 2022
2Yutaka Fujita
bles (Crocker et al. 2015). Radiative cooling is ignored be-
cause the densities of the ejecta and halo gas are low. The
code allows us to explicitly determine the shock age by mea-
suring the time elapsed since shock passage at each gas el-
ement. The position of the shock wave can be identified by
searching for the position where the flow converges.
2.1 Galaxy model
The gravitational potential is given by
Φ = Φhalo + Φdisk + Φbulge ,(1)
where
Φhalo(r) = v2
halo ln(r2+d2
h)(2)
is the halo potential,
Φdisk(r) = −GMdisk
a+√r2+b2(3)
is the potential known as the Miyamoto-Nagai disk, Gis the
gravitational constant (Miyamoto & Nagai 1975), and
Φbulge(r) = −GMbulge
r+db
(4)
is the potential, known as the Hernquist stellar bulge. The
adopted values are vhalo = 131.5kms−1,dh= 12 kpc, Mdisk =
1011 M,a= 6.5kpc, b= 0.26 kpc, Mbulge = 3.4×1010 M,
and db= 0.7kpc (Yang et al. 2012;Fujita et al. 2014). The
influence of gravity was minor because supersonic flows were
considered.
2.2 Energy injection
We considered two energy-injection types. One is the wind
type, in which a constant wind blows from the GC for a
period of 0< t < t0, where t=t0is the current time. Specif-
ically, the wind blows into the galactic halo, and two shock
waves are formed. One is the forward shock, which propa-
gates in the galactic halo gas, and the other is the reverse
shock, which propagates in the wind gas (Fig. 1). In this con-
text, the wind gas can be regarded as ejecta from the GC. A
contact discontinuity or boundary between the halo gas and
ejecta exists between the two shocks. As for the wind type,
we considered two models. One is the wind-K model, in which
we assumed that the wind is cold at the boundary and that
the thermal energy can be ignored. Another is the wind-T
model, in which the wind gas has a large thermal energy
The other energy-injection type is the explosion type, for
which energy is instantaneously injected into the GC at t= 0
as a single explosion. We also consider two models for this
type. In the explosion-K model, the energy is given as the
kinetic energy of the ejecta. Another one is the explosion-T
model, in which the explosion energy is given as the thermal
energy of the ejecta. As in the wind type, the forward shock
is formed in the halo gas, the reverse shock is formed in the
ejecta, and there is contact discontinuity between the two
shocks.
At t= 0, the halo gas is in hydrostatic equilibrium and is
isothermal (T= 0.2keV; Yoshino et al. 2009). We set the in-
ner boundary at rin = 1 (wind models) or 0.5 kpc (explosion
models), and the outer boundary at rout = 15 kpc from the
GC. The results were insensitive to the boundary positions
Forward shock
Reverse shock
Halo gas
Contact discontinuity
Galactic
Centre
(Fermi
bubbles)
×
Ejecta
Down
Up
Down
Up
Figure 1. Schematic of the structures surrounding the Fermi bub-
bles. Cyan and green areas are filled with halo gas and ejecta (wind
gas), respectively. The contact discontinuity (red solid line) is the
boundary between the two gases. The forward and reverse shocks
are shown by the black dotted lines; the upstream side and the
downstream side of each shock are indicated by “Up” and “Down,”
respectively. Regions heated by the forward and reverse shocks are
shown in dark colours. The gamma-ray emitting Fermi bubbles
correspond to the region inside the reverse shock (light green).
when the wind or explosion conditions were the same. The
initial halo gas density at r=rin is treated as a parameter
(ρ1). In the wind models, we injected the wind (ejecta) gas
at r=rin with velocity uw1 and density ρw1. The thermal
energy of the wind at the boundary is assumed to be negli-
gible. In the wind-T model, the wind gas has thermal energy
of 3.1keV per particle r=rin. Because the temperature is
much higher than that of the halo gas (T= 0.2keV), it may
not be realistic for the wind gas to have a thermal energy
of this level. In other words, even if the actual wind has a
thermal energy, it should be much smaller.
In the explosion-K model, the energy of the ejecta (Eexp)
is given in the form of kinetic energy. The ejecta of a mass of
Mej with kinetic energy of Eexp is uniformly distributed at
rin = 0.5< r < 1kpc at t= 0, The velocity of the ejecta is
given such that it increases linearly at 0.5< r < 1kpc. The
initial thermal energy of the ejecta was zero. In the explosion-
T model, the ejecta of a mass of Mej with thermal energy of
Eexp is uniformly distributed at 0.5< r < 1kpc at t= 0,
and the ejecta is initially at rest.
3 RESULTS
We compared the simulation results with the observed pro-
files recently obtained by reanalysing the data from the
Suzaku satellite, which has a high sensitivity to diffuse X-ray
emissions (Yamamoto et al. 2022). Contrary to previous stud-
MNRAS 000,1–6(2022)
Reverse shock of the Fermi bubbles 3
Table 1. Best-fit parameters.
Models t0uw1 ρw1/mp1Mej Eexp ρ1/mp1χ2/dof
(yr) (km s−1) (cm−3) (M) (erg) (cm−3)
wind-K 9.0×1061.1×1039.3×10−3... ... 0.024 51.7/56
wind-T 9.1×1061.7×1025.3×10−2... ... 0.017 55.8/55
explosion-K 6.5×106... ... 3.9×1073.0×1056 0.027 190.0/54
explosion-T 5.7×106... ... 4.2×1076.7×1056 0.032 242.3/56
1mpis the proton mass.
(a)
RS
CD
FS
RS
CD
FS
(b)
Figure 2. The gas profiles for (a) wind-K model, and (b) wind-T model. The panels are electron density (top), temperature (upper
middle), shock age (lower middle), and velocity (bottom) at t=t0(current time). The simulation results are shown by the dotted lines,
and the observations are shown by the dots (Yamamoto et al. 2022). For the latter, the errors are 1σ, and the angular size is transformed
into the radius, assuming that the distance to the GC is 8 kpc. The colours correspond to those in Fig. 1. The boundaries are the reverse
shock (RS), the contact discontinuity (CD), and the forward shock (FS).
ies (Kataoka et al. 2013;LaRocca et al. 2020), a collisional
ionisation equilibrium state is not assumed in this analysis
because the gas density associated with the Fermi bubbles is
low. In the analysis, the shock age is estimated from the de-
gree of non-equilibrium ionisation because the gas (plasma) is
forced out of equilibrium by the passage of a shock and then
gradually regains equilibrium. The profiles were derived for a
part of the X-ray bright regions surrounding the Fermi bub-
bles (North Polar Spur/Loop I). The observed temperature
increases toward the inner (r∼4kpc) and outer (∼6.5kpc)
edges of the structure, while the density and shock age peak
around the middle (Figs. 2and 3). Here, we assumed that
the distance to the GC is 8 kpc.
To best reproduce the observed profiles (density, temper-
ature, and shock age), four simulation parameters were ad-
justed. For the wind models, the parameters were the current
time t0, wind velocity (uw1), wind density (ρ1), and initial
density of the halo gas (ρ1) at r= 1 kpc from the GC. The
explosion model includes t0, total ejecta mass (Mej ), total
explosion energy (Eexp), and ρ1. We performed ∼104sim-
ulations for each model to determine the parameters that
reproduced the observed profiles. We choose only the simula-
MNRAS 000,1–6(2022)
4Yutaka Fujita
(a)
RS
CD
FS
(b)
RS
CD
FS
Figure 3. Same as Fig. 2but for (a) explosion-K model, and (b) explosion-T model.
tion results in which the reverse shock is at r= 4.0±0.2kpc,
and the forward shock is at 6.5±0.2kpc at t=t0. These
radii are the boundaries of the observed bright X-ray struc-
tures. We simultaneously fitted the simulated profiles to the
observed profiles for the density, temperature, and shock age.
The fits were performed in logarithmic parameter spaces. The
best-fit parameters, the associated χ2values, and the degree
of freedom (dof) are shown in Table 1. The simulation re-
sults with the best fit parameters are presented in Figs 2
and 3. Although the density and shock age profiles are simi-
lar among the two wind and explosion-T models, the temper-
ature and velocity profiles are intrinsically different. While
the wind models reproduce all observed density, tempera-
ture, and shock age profiles, the explosion models does not
reproduce the temperature profile. In the explosion-K model
(Fig. 3a), the sharp density peak between the reverse shock
and contact discontinuity is inconsistent with the observa-
tions. The peak height of the density is ∼0.06 cm−3.
In the wind models (Fig. 2), the forward and reverse shocks
initially formed at the contact discontinuity, where the shock
age is the largest. Subsequently, the gas on the downstream
sides of both shocks was considerably heated. Currently, the
inner temperature peak (r∼4kpc) corresponds to the re-
verse shock, and the outer peak (r∼6.4kpc) corresponds to
the forward shock. In the wind-K model, the reverse shock
is powered by a fast wind blowing from the GC. The wind
velocity is almost constant on the upstream side of the re-
vised shock (uw∼1100 km s−1at r < 4kpc; bottom of
Fig. 2a). This large wind velocity results in a drastic velocity
decrease to uw∼500 km s−1at the reverse shock, thereby
converting the large kinetic energy into thermal energy and
creating a sharp temperature peak. The contact discontinu-
ity between the wind gas (ejecta) and halo gas is at the peak
of the density and shock age profiles and at the trough of
the temperature profile. The wind-T model shows a similar
behaviour (Fig. 2b). In this model, although the wind ve-
locity at r=rin kpc (uw1 ) is only 170 km s−1(Table 1), it
increased to ∼1000 km s−1slightly upstream of the reverse
shock (r.4kpc; Fig. 2b), which is comparable to that in the
wind-K model (Fig. 2a). By contrast, for the explosion models
(Fig. 3), a prominent temperature peak is not observed at the
reverse shock (r∼3.8kpc), although a minor temperature
increase exists there. According to this model, the ejecta ex-
panded after the explosion. However, the expansion rate has
decreased substantially over the last t0∼6×106yr (Ta-
ble 1), and the velocity peak at the reverse shock is at most
comparable to that at the forward shock. Thus, the velocity
decrease at the reverse shock is moderate, which results in less
thermal energy creation and no temperature peak. Therefore,
the temperature profile is not consistent with observations.
The value of χ2/dof of the wind-K model is close to one
(Table 1), which means that this model successfully repro-
MNRAS 000,1–6(2022)
Reverse shock of the Fermi bubbles 5
duced the observations. The value of χ2/dof of the wind-T
model is almost the same as that of the wind-K model, which
means that the influence of thermal energy is minor. On the
other hand, the values of χ2/dof of the explosion models are
much larger than one (Table 1), and they are inconsistent
with the observations. The success of the wind model implies
that the duration of the GC activities (∼107years) was nei-
ther instantaneous nor extremely long (say ∼109years).
4 DISCUSSION
The wind power and mass flux obtained above offer clues
regarding the origin of the Fermi bubbles. The best-fit wind-
K model indicates that the energy injection rate is Lw=
1.4×1042 erg s−1. Given the mass of the supermassive black
hole in the GC (∼4×106M;Boehle et al. 2016;Gillessen
et al. 2017), Lwis much smaller than the theoretical maxi-
mum rate given by the Eddington limit(∼5×1044 erg s−1).
Thus, the black hole can provide sufficient power to propagate
the wind. This is in contrast to the explosion model, in which
the energy input must be instantaneous and as powerful as
the Eddington limit. The best-fit wind model also indicated
that the mass flux is ˙
M= 3.4Myr−1. The large flux sug-
gests that the wind is not directly produced near the black
hole but is formed as light energetic outflows from the black
hole entraining the surrounding interstellar gas. For example,
because the black hole in the GC is surrounded by a massive
molecular cloud (∼3×107M) called the central molecular
zone (Molinari et al. 2011), a fraction of the cold gas may
be blown out and become the wind. The cold (∼10–100 K)
gas outflow observed around the GC (Di Teodoro et al. 2020)
may be remnants of the windblown cold gas. The existence of
high-velocity, low-metallicity clouds may indicate that even
clouds in the halo have been blown away (Ashley et al. 2022,
see also Fox et al. 2015;Bordoloi et al. 2017;Karim et al.
2018;Ashley et al. 2020). In addition, warm (∼103–105K)
and hot (&106K) interstellar gases around the GC may be
accelerated. Notably, outflows of warm and hot gases have
been observed around the GC (McClure-Griffiths et al. 2013;
Fox et al. 2015;Nakashima et al. 2019;Ponti et al. 2019).
These multiphase gases may have mixed, becoming the wind
blowing into the Fermi bubbles. To entrain a large amount of
gas ( ˙
M= 3.4Myr−1), the initial gas flows generated near
the black hole should have wide opening angles, say ∼60–
100◦, and large cross-sectional areas. Therefore, they are un-
likely to be thin jets. This type and scale of outflows are often
observed around active galactic nuclei (AGN) in other galax-
ies (Tombesi et al. 2013,2014;Laha et al. 2021). Thus, the
formation of the wind and the process of mass loading around
the GC may be similar to those of AGN outflows (King &
Pounds 2015). The current level of activity of Sagittarius A∗
is much lower than Lw, suggesting that the activity ceased
only recently or fluctuated on a time scale much shorter than
the wind period of ∼107years (Koyama et al. 1996;Totani
2006). If the activity ceases, the mass flux of the wind should
decrease near the GC. On the other hand, the star forma-
tion activity and associated supernova explosions around the
GC are unlikely to be the energy sources of the fast wind and
Fermi bubbles. This is because the star formation rate around
the GC has been only ∼0.1Myr−1for the past &106years
(Yusef-Zadeh et al. 2009;Immer et al. 2012), which suggests
that the power provided by the activity is only ∼1040 erg s−1
(Crocker et al. 2015).
The AGN outflows in other galaxies are thought to reg-
ulate the growth of the galaxies and black holes (King &
Pounds 2015); therefore, it may be natural that the same
phenomenon occurs in the Milky Way Galaxy. If the wind
blowing into the Fermi bubbles is the same as the AGN out-
flows, the proximity of the GC can allow us to closely study
the nature of the AGN outflows. Moreover, the temperature
and shock age of the gas associated with the Fermi bubbles
will soon be measured more precisely with the X-Ray Imaging
and Spectroscopy Mission (XRISM) satellite with an excep-
tional energy resolution (Tashiro et al. 2020). The XRISM
satellite can also directly measure X-ray gas velocity for the
first time. The velocity gradient in the high-density region
(r∼4–6.5 kpc) is particularly useful because the gradient dif-
fers between the wind and explosion models (Figs. 2and 3).
Observations of the gas velocity around the GC could also
be helpful in understanding the mass loading process of the
wind.
5 CONCLUSION
We have studied the properties of the X-ray gas structures
around the Fermi bubbles. Using numerical simulations, we
showed that a combination of the density, temperature, and
shock age profiles can be a useful tool to identify the energy
injection mechanism at the GC. By comparing the results of
numerical simulations with observations, we found that the
Fermi bubbles were most likely to be created by a fast wind
from the GC, which had a speed of ∼1000 km s−1, and blew
for ∼107yr. The wind generates a strong reverse shock and
reproduces a sharp temperature increase as is observed. On
the other hand, models in which energy was instantaneously
injected cannot reproduce the observed temperature profile.
Considering the power of the wind, the energy source seems
to be Sagittarius A∗, and not star formation activities. Since
the mass flux of the wind is large, interstellar gas might have
been entrained by the wind. For the entrainment, the initial
outflows launched in the vicinity of the black hole should
have a large opening angle and they are not likely to be thin
jets. The outflows may be the same as AGN outflows that
are often observed in other galaxies.
ACKNOWLEDGEMENTS
Y.F. was supported by JSPS KAKENHI 20H00181,
22H00158, 22H01268.
DATA AVAILABILITY
The data generated from computations are reported in the
paper and any additional data will be made available upon
reasonable request to the corresponding author.
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