###### Abstract

Hot gas around a supermassive black hole (SMBH) should be captured within the
gravitational “sphere of influence”, characterized by the Bondi radius. Deep
Chandra observations have spatially resolved the Bondi radii of at least five
nearby SMBHs. Contrary to earlier hot accretion models that predicted a steep
temperature increase within the Bondi radius, none of the resolved temperature
profiles exhibit such an increase. The temperature inside the Bondi radius
appears to be complex, indicative of a multi-temperature phase of hot gas with
a cooler component at about 0.2–0.3 keV. The density profiles within the Bondi
regions are shallow, suggesting the presence of strong outflows. These
findings might be explained by recent realistic numerical simulations that
suggest that large-scale accretion inside the Bondi radius can be chaotic,
with cooler gas raining down in some directions and hotter gas outflowing in
others. With an angular resolution similar to Chandra and a significantly
larger collecting area, AXIS will collect enough photons to map the emerging
accretion flow within and around the “sphere of influence” of a sample of
active galactic nuclei (AGNs). AXIS will reveal transitions in the inflow that
ultimately fuels the AGN, as well as outflows that provide feedback to the
environment. _This White Paper is part of a series commissioned for the AXIS
Probe Concept Mission; additional AXIS White Papers can be found at theAXIS
website with a mission overview here_.

xx 1 5 Prospects for AGN Studies with AXIS: AGN Fueling – Resolving Hot Gas
inside Bondi Radius of SMBHs Ka-Wah Wong 1, Helen Russell 2, Jimmy Irwin 3,
Nico Cappelluti 4 and Adi Foord 5 Ka-Wah Wong, Helen Russell, Jimmy Irwin,
Nico Cappelluti and Adi Foord

###### Contents

  1. 1 Introduction
  2. 2 Current status in resolving the hot gas within the Bondi radius of SMBHs
  3. 3 Prospects for Bondi radius studies with AXIS

###### List of Figures

  1. 1 Resolved Bondi regions with Chandra
  2. 2 Multiphase gas inside Bondi radius
  3. 3 Sample of supermassive black holes for AXIS

##  1 Introduction

Supermassive black holes (SMBHs) are ubiquitous in the centers of galaxies
(Ho, 2008). Accretion processes determine the growth of SMBHs and feedback
mechanisms play a critical role in the evolution of their host galaxies
(Fabian, 2012; McNamara & Nulsen, 2007). Understanding how SMBHs are fueled
from the surroundings and how matter and energy are transported back to the
environment is important for understanding the cosmic ecosystem.

Immersed in the diffused hot gas of the host galaxy, the gravitational
potential of the black hole dominates the thermal energy of the hot gas inside
the “sphere of influence,” which is defined by the characteristic Bondi
radius, $R_{B}=2GM_{\rm BH}/c_{s}^{2}$, where $M_{\rm BH}$ is the mass of the
black hole and $c_{s}$ is the sound speed of the gas at a distance far away
from the black hole (Bondi, 1952). Although the Bondi accretion model is
likely an oversimplification of actual accretion processes, it provides a
baseline for theoretical and observational comparisons of different accretion
models. Moreover, the inferred Bondi accretion rate is of great interest for a
wide range of applications, such as the possible correlation between Bondi
accretion rate and AGN feedback power (e.g., Allen et al., 2006; Russell et
al., 2013), and the accretion rate and feedback efficiency used for
cosmological simulations (e.g., Pillepich et al., 2018). More importantly,
direct study of the hot gas within and around the Bondi “sphere of influence”
is crucial for understanding the accretion processes that begin when the gas
begins to be captured by the gravitational pull of the black hole (see, e.g.,
Brighenti & Mathews, 1999; Quataert & Narayan, 2000; Baganoff et al., 2003;
Garcia et al., 2010).

Unlike the most powerful AGNs or quasars radiating at about 10% Eddington
luminosity ($L_{\rm Edd}$), which are very rare in the SMBH population, most
of the SMBHs are low-luminosity AGNs (LLAGNs) radiating at $\ll L_{\rm Edd}$.
At most about a few percent of the SMBHs are shining at $\sim 10^{-5}L_{\rm
Edd}$, while most of the SMBHs are much quieter ($\sim 10^{-8}L_{\rm Edd}$)
(Ho, 2008). It is widely believed that those AGNs radiating at
$\sim$$10\%L_{\rm Edd}$ are accreting close to the Eddington rate of
${\dot{M}}_{\rm Edd}$ in a cold accretion mode, with the classical optically
thick and geometrically thin alpha-disk where most of the radiation is coming
from the disk region close to the SMBHs. For accretion rates
$<0.01{\dot{M}}_{\rm Edd}$, the accretion is believed to be operating in the
hot accretion mode, where the accretion flow is optically thin and
geometrically thick (e.g., Figure 13 in Ho, 2008). However, it is not simply
that they are starved for gas to explain such low luminosity.

Extensive theoretical work has been conducted to understand why LLAGNs are
under-luminous. It has been suggested that during the hot accretion process,
most of the energy in the gas is carried by the ions and is advected into the
black hole before it has a chance to radiate much energy (advection-dominated
accretion flows, or ADAFs; Ichimaru (1977); Rees et al. (1982); Narayan & Yi
(1994)). It is also possible that matter passing through the Bondi region does
not reach the event horizon of the black hole, but either circulates in
convective eddies (convective dominated advection flows or CDAFs; Narayan et
al. (2000); Quataert & Gruzinov (2000); Abramowicz et al. (2002), or some of
the gas actually escapes the potential of the black hole in an outflow (such
as advection-dominated inflow-outflow solutions or ADIOS; Blandford & Begelman
(1999); Begelman (2012)), or variations on these themes. These models can
collectively be classified as radiatively inefficiently accretion flow (RIAF)
models. A more comprehensive review of these hot accretion models, with more
detailed numerical simulations, can be found in Yuan & Narayan (2014).

To test and distinguish these RIAF models, one might compare the predictions
with the X-ray properties of the hot gas flowing into the Bondi region.
Notably, all of these early hot-accretion models predict a temperature
increase towards the center due to the gravitational influence of the black
holes. However, the density slope of hot gas inside the Bondi radius strongly
depends on the specific RIAF models. A direct measurement of the temperature
and density profile of the hot X-ray emitting gas both inside and around the
Bondi radius is key to understanding and constraining the RIAF models. Yet,
observational constraints have proven to be challenging due to the small
angular scale of the Bondi radius of black holes. Even for the closest SMBHs,
the angular sizes of the Bondi radii are on the order of a few arcseconds or
less (Figure 1 below).

Figure 1: LLAGNs and their host galaxies with Bondi regions spatially resolved
with Chandra. From upper left to lower right: (a) Sgr A∗ (Wang et al., 2013),
(b) NGC 3115 (Wong et al., 2011, 2014), (c) M87 (Russell et al., 2015, 2018),
(d) NGC 1600 (Runge & Walker, 2021), and (e) M84 (Bambic et al., 2023). In the
first two panels, X-ray emission is shown in blue, and is also visible in the
insets (image credits: NASA/CXC/SAO). The remaining panels are X-ray images.

Figure 2: (a) A megasecond Chandra image of NGC 3115 inside the Bondi radius
of about 5 arcsec (circle) (Wong et al., 2014). Different colors represent
different intensity levels, with the brightest region at the center. (b)
Multiphase inflow-outflow simulation of a LLAGN overlaid on the Chandra image
[Qiu et al. in preparation]. The infalling directions (shown in blue) are
cooler, while the outflow directions (shown in orange) are hotter. The
simulation is not specifically tailored to NGC 3115, but is shown here to
illustrate the potential of using AXIS temperature maps to test the multiphase
model. (c) Temperature profiles of NGC 3115 featuring a hotter component of
about 1 keV and a cooler component of about 0.3 keV inside about 3 arcsec
using a two-component model (Wong et al., 2014). Different colors represent
different radial binning schemes. A single temperature model fit would give a
drop in temperature toward the center (see Figure 3 in Wong et al., 2014).

##  2 Current status in resolving the hot gas within the Bondi radius of SMBHs

Thanks to the sub-arcsec resolution of Chandra, a few of the Bondi regions
have finally been resolved and studied in detail (Baganoff et al., 2003;
Bambic et al., 2023; Runge & Walker, 2021; Russell et al., 2015, 2018; Wang et
al., 2013; Wong et al., 2014, 2011). Figure 1 shows the X-ray images of these
Bondi regions; all of these regions belong to LLAGNs and are believed to be
undergoing hot accretion. Although two of these systems were the targets of
Chandra visionary projects (Sgr A∗ and NGC 3115, Wang et al., 2013; Wong et
al., 2014, 2011), the angular resolution, spectral capabilities, and photon
statistics were just barely adequate for the task, resulting in data that
necessitate further study. In Sgr A∗, the flat density profile of the gas
inflow implies the presence of an outflow that expels more than 99% of the
matter initially captured at the Bondi radius (Wang et al., 2013). NGC 3115
has one of the largest Bondi regions in angular scale, approximately 2.4–4.8
arcsec (Wong et al., 2014, 2011). Hot gas inside the Bondi region of NGC 3115
has been clearly resolved, providing the sharpest view of the accretion flow
to date (Figure 2). A flattening of the density profile within the Bondi
radius of NGC 3115 also indicates the presence of an outflow. The measured
density profile and inferred outflow have provided important constraints for
modeling the full spectral energy distributions (SED) of RIAF modes (e.g.,
Nemmen et al., 2014; Broderick et al., 2016; Feng et al., 2016; Almeida et
al., 2018; Ma et al., 2019).

One of the most surprising results regarding NGC 3115 is the absence of a gas
temperature increase towards the center (right panel in Figure 2). This
finding is in sharp contrast to all the earlier RIAF models. The temperature
inside the Bondi radius appears to be complex, indicative of a multi-
temperature phase of hot gas. More specifically, the X-ray spectrum inside the
Bondi radius includes a hotter gas component ($\sim$ 1 keV) and a cooler one
($\sim$ 0.3 keV). The gas may be cooling out of the X-ray hot phase and
feeding the rotating gas disk, rather than free falling onto the black hole.
Indeed, more realistic numerical simulations suggest that the large-scale
accretion inside the Bondi radius can be more chaotic (e.g., Prasad et al.,
2017), with cooler gas raining down in some directions and hotter gas
outflowing in the others (e.g., Gaspari et al., 2013, 2015). Additional
physical factors such as conduction, stellar feedback, viscosity, and galactic
potential have also been investigated to explain the observed temperature and
density measurements (e.g., Shcherbakov et al., 2014; Yao & Gan, 2020; Sun &
Yang, 2021; Almeida & Nemmen, 2020).

M87 also has one of the largest Bondi radii ($\sim$5 arcsec; Russell et al.,
2015, 2018). It is the most gas rich system among those with resolved Bondi
radii, providing us with very high photon statistics to study the hot gas
spectrum in more detail. Consistent with the results of NGC 3115, there is
also no evidence for the expected temperature increase within the Bondi
radius. This suggests that the hot gas structure is not dictated by the SMBH’s
potential and, together with the shallow density profile, indicates that the
classical Bondi or ADAF formalism with pure accretion may not be applicable.
In stark contradiction to most theoretical calculations, these observations
suggest that the gas flows within the Bondi radius are a complex mixture of
inflow fueling the black hole and powerful outflows.

The evidence of hot gas existing in multi-temperature phase is very strong in
M87, with the possibility of a mini cooling flow of temperature down to
$\sim$0.2 keV inside the smallest radius resolved by Chandra (Russell et al.,
2018). It is possible that the gas can further cool down to lower temperature
but was not detected with Chandra due to the limitation of its soft response.
With high sensitive of AXIS in soft X-rays (Reynolds et al., 2023), it will be
able search for even cooler gas structure inside Bondi radii of M87 and other
LLAGNs.

Recently, the Bondi regions of two additional LLAGNs, NGC 1600 and M84, have
been resolved by Chandra (Bambic et al., 2023; Runge & Walker, 2021). The
results are very consistent with previous studies. Notably, neither displays
the temperature increase toward the center that is predicted by earlier RIAF
models. Both exhibit fairly flat density profiles, which is more consistent
with significant gas outflow. Multi-temperature hot gas has also been
significantly detected in NGC 1600. However, there is no evidence of multi-
temperature gas in M84, perhaps due to its more uniform temperature or the
presence of cooler gas below 0.2 keV that could not be detected with Chandra.
In any case, multi-temperature seems to be quite typical inside the Bondi
radius of SMBHs. A more detailed spectral analysis of the multi-temperature
phase would require significantly higher photon statistics.

Figure 3: (a) Distribution of the sizes of the Bondi radius111It should be
noted that the concept of Bondi radius is not well defined in a realistic
system due to the multi-temperature nature of the hot gas and the non-trivial
outer boundary condition. Nevertheless, we can still estimate the size of the
Bondi radius observationally to characterize the rough size of the accretion
region. However, the sizes shown here are only approximate, as we assume the
hot gas temperature to be 0.5 keV, which underestimates the Bondi radii for
cooler systems.for a sample of supermassive black holes. The vertical line
separates samples that can be resolved with AXIS’s current best estimate HPD
of 1.2 arcsec, illustrating its ability to measure the Bondi radius in a
significant number of sources. Exposure times required for at least 3000
counts in the soft band 0.5-1keV, with the exception of Sgr A∗ where the
estimation was based on hard flux (highlighted in red) due to high absorption
in soft X-rays. The total number of counts across the full energy range would
be significantly higher. (b) Simulated AXIS spectrum of M87 with 100 ks
exposure for a region with the size of AXIS’s half power diameter (HPD). AXIS
will collect a total of $\sim$10,000 photon counts in 0.3–10 keV (including
the thermal gas emission and the non-thermal emissions from the AGN and the
jet), while Chandra can only collect for about 170 counts in 0.5–7 keV with
the same exposure. This allows for a very high spatial resolution temperature
map to study multi-temperature gas inside the Bondi radius of M87 in great
detail.

##  3 Prospects for Bondi radius studies with AXIS

Although the current studies were somewhat limited by photon statistics, they
have supported the idea that LLAGNs are generally associated with strong
outflow, and in the most extreme cases, take the form of realistic jets (e.g.,
M87). The connection between hot accretion flows and outflow/jets has been
extensively discussed in Yuan & Narayan (2014). A more detailed study of hot
gas inside and near the Bondi radius of SMBHs, using the finest spatial
resolution, will be crucial for understanding both the accretion mechanism and
feedback process.

With the current baseline spatial resolution of 1.5 arcsec and the current
best estimate of 1.2 arcsec (Half Power Diameter, HPD), AXIS will have a
resolution very similar to Chandra but with a significantly larger effective
area for collecting photons. This will enable us to resolve and map the
emerging hot accretion flow within and around the Bondi radius of about 8
nearby AGNs (Figure 1). AXIS will reveal transitions in the inflow that
ultimately fuels the AGN and outflows along the jet-axis that limit the
accretion rate.

With the estimated exposures listed in Figure 1, AXIS will be able to collect
at least 3000 gas counts in the soft band (0.5–1 keV) within $R_{B}$, enabling
us to measure density and temperature with less than a 10% uncertainty. The
total number of counts across the full energy range would be significantly
higher. Multi-temperature gas with a cooler component has been detected in
three LLAGNs, which has provided important constraints on theoretical models
of the accretion flow and feedback models. The larger sample with higher
photon statistics will allow us to search for multi-temperature signature,
which appears to be common. The sample also contains a range of
AGN/outflow/jet activities (e.g., from NGC 3115 with no AGN activity, to NGC
1600 with moderate activity, to M87 with a relativistic jet), allowing us to
study accretion and outflow in a diverse population of systems and to search
for a correlation with jet power.

The best targets with the largest Bondi radii, such as NGC 3115 and M87, will
be resolved into many more regions, allowing a more detailed comparison with
numerical simulations that predict cooler gas in the accretion directions and
hotter gas in the outflow directions (e.g., Figure 2). Hot gas around and
beyond the Bondi regions will also be mapped with the highest possible
resolutions, allowing us to understand the interplay between large-scale
accretion and feedback to the environment. This can also be done for those
LLAGNs with Bondi radii just a bit too small to be resolved, significantly
increasing the sample size.

The gas structure on these scales is key to understanding the following
questions: How are AGNs fueled? How can an AGN respond to the large-scale
cooling rate? How and why do AGNs evolve from a quasar-era peak to local
quiescence? To answer these bigger questions, deep Chandra observations have
already resolved Bondi radius in a handful of nearby LLAGNs, suggesting strong
outflows expelling most of the gas in all systems and rapidly cooling inflow
in M87. The next step is to test whether these processes are sufficient to
power the AGN in nearby systems and whether there is a correlation with jet
power. With the decreased soft response, such studies are now beyond the
capabilities of Chandra. AXIS would be an excellent choice to carry forward
this research. The science addressed by AXIS also directly ties to the
Astro2020 Decadal Survey’s theme of the Cosmic Ecosystem in Stellar and Black
Hole Feedback, which seeks to understand “how the energy from the black hole
couples to the surrounding gas” (National Academies of Sciences, 2021).

###### Acknowledgements.

We kindly acknowledge the AXIS team for their outstanding scientific and
technical work over the past year. This work is the result of several months
of discussion in the AXIS-AGN and AXIS-GALAXY SWGs. KW acknowledges support
from SUNY Brockport.

## References:

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## References

  * Abramowicz et al. (2002) Abramowicz, M. A., Igumenshchev, I. V., Quataert, E., & Narayan, R. 2002, ApJ, 565, 1101
  * Allen et al. (2006) Allen, S. W., Dunn, R. J. H., Fabian, A. C., Taylor, G. B., & Reynolds, C. S. 2006, MNRAS, 372, 21
  * Almeida & Nemmen (2020) Almeida, I., & Nemmen, R. 2020, MNRAS, 492, 2553
  * Almeida et al. (2018) Almeida, I., Nemmen, R., Wong, K.-W., Wu, Q., & Irwin, J. A. 2018, MNRAS, 475, 5398
  * Baganoff et al. (2003) Baganoff, F. K., Maeda, Y., Morris, M., et al. 2003, ApJ, 591, 891
  * Bambic et al. (2023) Bambic, C. J., Russell, H. R., Reynolds, C. S., et al. 2023, MNRAS, 522, 4374
  * Begelman (2012) Begelman, M. C. 2012, MNRAS, 420, 2912
  * Blandford & Begelman (1999) Blandford, R. D., & Begelman, M. C. 1999, MNRAS, 303, L1
  * Bondi (1952) Bondi, H. 1952, MNRAS, 112, 195
  * Brighenti & Mathews (1999) Brighenti, F., & Mathews, W. G. 1999, ApJ, 527, L89
  * Broderick et al. (2016) Broderick, A. E., Fish, V. L., Johnson, M. D., et al. 2016, ApJ, 820, 137
  * Fabian (2012) Fabian, A. C. 2012, ARA&A, 50, 455
  * Feng et al. (2016) Feng, J., Wu, Q., & Lu, R.-S. 2016, ApJ, 830, 6
  * Garcia et al. (2010) Garcia, M. R., Hextall, R., Baganoff, F. K., et al. 2010, ApJ, 710, 755
  * Gaspari et al. (2015) Gaspari, M., Brighenti, F., & Temi, P. 2015, A&A, 579, A62
  * Gaspari et al. (2013) Gaspari, M., Ruszkowski, M., & Oh, S. P. 2013, MNRAS, 432, 3401
  * Ho (2008) Ho, L. C. 2008, ARA&A, 46, 475
  * Ichimaru (1977) Ichimaru, S. 1977, ApJ, 214, 840
  * Ma et al. (2019) Ma, R.-Y., Roberts, S. R., Li, Y.-P., & Wang, Q. D. 2019, MNRAS, 483, 5614
  * McNamara & Nulsen (2007) McNamara, B. R., & Nulsen, P. E. J. 2007, ARA&A, 45, 117
  * Narayan et al. (2000) Narayan, R., Igumenshchev, I. V., & Abramowicz, M. A. 2000, ApJ, 539, 798
  * Narayan & Yi (1994) Narayan, R., & Yi, I. 1994, ApJ, 428, L13
  * National Academies of Sciences (2021) National Academies of Sciences, Engineering, M. 2021, Pathways to Discovery in Astronomy and Astrophysics for the 2020s (Washington, DC: The National Academies Press)
  * Nemmen et al. (2014) Nemmen, R. S., Storchi-Bergmann, T., & Eracleous, M. 2014, MNRAS, 438, 2804
  * Pillepich et al. (2018) Pillepich, A., Springel, V., Nelson, D., et al. 2018, MNRAS, 473, 4077
  * Prasad et al. (2017) Prasad, D., Sharma, P., & Babul, A. 2017, MNRAS, 471, 1531
  * Quataert & Gruzinov (2000) Quataert, E., & Gruzinov, A. 2000, ApJ, 539, 809
  * Quataert & Narayan (2000) Quataert, E., & Narayan, R. 2000, ApJ, 528, 236
  * Rees et al. (1982) Rees, M. J., Begelman, M. C., Blandford, R. D., & Phinney, E. S. 1982, Nature, 295, 17
  * Reynolds et al. (2023) Reynolds, C. S., Kara, E. A., Mushotzky, R. F., et al. 2023, arXiv e-prints, arXiv:2311.00780
  * Runge & Walker (2021) Runge, J., & Walker, S. A. 2021, MNRAS, 502, 5487
  * Russell et al. (2015) Russell, H. R., Fabian, A. C., McNamara, B. R., & Broderick, A. E. 2015, MNRAS, 451, 588
  * Russell et al. (2018) Russell, H. R., Fabian, A. C., McNamara, B. R., et al. 2018, MNRAS, 477, 3583
  * Russell et al. (2013) Russell, H. R., McNamara, B. R., Edge, A. C., et al. 2013, MNRAS, 432, 530
  * Shcherbakov et al. (2014) Shcherbakov, R. V., Wong, K.-W., Irwin, J. A., & Reynolds, C. S. 2014, ApJ, 782, 103
  * Sun & Yang (2021) Sun, H.-W., & Yang, X.-H. 2021, MNRAS, 505, 4129
  * Wang et al. (2013) Wang, Q. D., Nowak, M. A., Markoff, S. B., et al. 2013, Science, 341, 981
  * Wong et al. (2014) Wong, K.-W., Irwin, J. A., Shcherbakov, R. V., et al. 2014, ApJ, 780, 9
  * Wong et al. (2011) Wong, K.-W., Irwin, J. A., Yukita, M., et al. 2011, ApJ, 736, L23
  * Yao & Gan (2020) Yao, Z., & Gan, Z. 2020, MNRAS, 492, 444
  * Yuan & Narayan (2014) Yuan, F., & Narayan, R. 2014, ARA&A, 52, 529