###### Abstract

Stellar and black hole feedback heat and disperse surrounding cold gas clouds,
launching gas flows off circumnuclear and galactic disks and producing a
dynamic interstellar medium. On large scales bordering the cosmic web,
feedback drives enriched gas out of galaxies and groups, seeding the
intergalactic medium with heavy elements. In this way, feedback shapes galaxy
evolution by shutting down star formation and ultimately curtailing the growth
of structure after the peak at redshift $2-3$. To understand the complex
interplay between gravity and feedback, we must resolve both the key physics
within galaxies and map the impact of these processes over large scales, out
into the cosmic web. The Advanced X-ray Imaging Satellite (AXIS) is a proposed
X-ray probe mission for the 2030s with arcsecond spatial resolution, large
effective area, and low background. AXIS will untangle the interactions of
winds, radiation, jets, and supernovae with the surrounding ISM across the
wide range of mass scales and large volumes driving galaxy evolution and trace
the establishment of feedback back to the main event at cosmic noon. _This
White Paper is part of a series commissioned for the AXIS Probe mission
concept; additional AXIS White Papers can be found at theAXIS website with a
mission overview here_.

xx 1 5 figuret The evolution of galaxies and clusters at high spatial
resolution with AXIS H. R. Russell1, L. A. Lopez2, S. W. Allen3,4,5, G.
Chartas6, P. P. Choudhury7,8, R. A. Dupke9,10, A. C. Fabian7, A. M. Flores3,4,
K. Garofali11, E. Hodges-Kluck11, M. J. Koss12, L. Lanz13, B. D. Lehmer14,
J.-T. Li15, W. P. Maksym16, A. B. Mantz4, M. McDonald17,18, E. D. Miller18, R.
F. Mushotzky19, Y. Qiu20, C. S. Reynolds19,21, F. Tombesi22, P. Tozzi23, A.
Trindade-Falcão16, S. A. Walker24, K.-W. Wong25, M. Yukita11 and C. Zhang26 H.
R. Russell, L. A. Lopez, S. W. Allen, G. Chartas, P. P. Choudhury, R. A.
Dupke, A. C. Fabian, A. M. Flores, K. Garofali, E. Hodges-Kluck, M. J. Koss,
L. Lanz, B. D. Lehmer, J.-T. Li, W. P. Maksym, A. B. Mantz, M. McDonald, E. D.
Miller, R. F. Mushotzky, Y. Qiu, C. S. Reynolds, F. Tombesi, P. Tozzi, A.
Trindade-Falcão, S. A. Walker, K. W. Wong, M. Yukita and C. Zhang

###### Contents

  1. 1 Introduction
  2. 2 Stellar Feedback in Nearby Galaxies
  3. 3 Black hole feedback: quasar mode
    1. 3.1 Quasar-mode feedback in nearby galaxies
    2. 3.2 Quasar feedback at high cosmological redshifts
  4. 4 Black hole feedback: radio mode
    1. 4.1 Radio-mode feedback in galaxies
    2. 4.2 Feedback in galaxy clusters
    3. 4.3 Hidden cooling flows in clusters
    4. 4.4 Inverse Compton Ghosts in the deep X-ray Sky
  5. 5 The integrated history of feedback with high-z clusters
    1. 5.1 Radio-mode feedback in high-z clusters
    2. 5.2 Metallicity evolution
  6. 6 The circumgalactic medium and connections to the cosmic web
    1. 6.1 Connections to the cosmic web
    2. 6.2 Inflows and outflows from galaxy clusters
    3. 6.3 Microphysics of the intracluster and circumgalactic medium
  7. 7 Formation and evolution of large-scale structure
    1. 7.1 IGM heating by early X-ray sources
    2. 7.2 Protocluster structure
  8. 8 Conclusions

###### List of Figures

  1. 1 AXIS simulation of stellar feedback in M83
  2. 2 Composite image and AXIS simulation of Mrk573
  3. 3 A partial X-ray Einstein ring and simulated AXIS spectrum for PG1115+080
  4. 4 The distribution of lens image separations compared to the AXIS half-power diameter
  5. 5 The AXIS view of Atlas3D galaxies and simulated spectra for NGC 1266
  6. 6 A Chandra image and an AXIS simulation of AGN feedback in NGC 5813
  7. 7 A Chandra image and AXIS simulations of AGN feedback in the Perseus cluster
  8. 8 Chandra images and AXIS simulations of strong absorption at the center of the Centaurus cluster
  9. 9 An HST image of dusty filaments in the Centaurus cluster and an AXIS simulation of a hidden cooling flow spectrum.
  10. 10 A Chandra image and a simulated AXIS spectrum of the inverse Compton ghost HDF 130
  11. 11 SZ cluster detections as a function of redshift
  12. 12 AXIS observations of X-ray cavities at high redshift
  13. 13 The forecasted improvement in metallicity constraints for cluster outskirts with AXIS.
  14. 14 AXIS observations of the outskirts of clusters and the cosmic web
  15. 15 Structure in the outskirts of clusters
  16. 16 Electron-ion equilibration behind shock fronts with AXIS
  17. 17 Fluctuations in emission-weighted density and temperature in a 3D hydrodynamic simulation of galaxy cluster
  18. 18 Chandra and simulated AXIS spectra of the Spiderweb galaxy

##  1 Introduction

Galaxies form and evolve through a vigorous cosmic struggle. The inexorable
pull of gravity drives the assembly of galaxies by drawing primordial gas into
dark matter halos and collapsing cold clouds into stars. At most twenty
percent of baryons are converted into stars [e.g. Wechsler & Tinker, 2018].
This inexplicable inefficiency across the galaxy mass scale is the result of
high-energy processes around stars and supermassive black holes. Stellar
feedback, via stellar winds and supernovae, heats and disperses cold gas
clouds and collectively inflates large gas bubbles that lift hot gas and
metals into galactic halos [for reviews, see Veilleux et al., 2005; Heckman &
Thompson, 2017]. In massive galaxies, more powerful feedback from active
galactic nuclei (AGN), in the form of radiation, winds and relativistic jets,
drives large outflows, suppresses cooling of hot atmospheres, and produces a
correlative slowing of black hole activity Fabian (2012). Feedback indelibly
shapes galaxy evolution on all scales of the galaxy mass function, back to the
peak of galaxy growth at $z\sim 2$ and beyond.

X-ray observations reveal the key interactions on all spatial scales: the
acceleration of winds and jets close to black holes, the impact zones where
stellar winds, supernovae, AGN winds, and jets meet the ISM, and the
distribution of energy and metal-rich gas across galaxy halos. Arcsecond
spatial resolution is essential for disentangling the complex interactions of
winds, radiation, jets, and supernovae with the surrounding gas. However, only
when combined with high throughput can the key scales of individual HII
regions, star clusters, wind shocks, and jet-blown bubbles be reached across
the galaxy population, tracing the establishment of feedback back to the main
event at cosmic noon. AXIS now capitalizes on the key technological advance of
precision-focusing with light-weight X-ray mirrors to deliver $1.5\rm\;arcsec$
spatial resolution on-axis, $1.6\rm\;arcsec$ on average across the
$24\rm\;arcmin$ field of view, and a factor of $\sim 10$ increase in
collecting area over existing facilities Reynolds et al. (2023). AXIS will
answer major questions on feedback including:

  * •

How do star-forming structures shape the ISM? What are the conditions for
breakout or outflow?

  * •

How do AGN winds and jets inject energy and drive outflows in individual
galaxies?

  * •

How and when did AGN feedback begin to shape the evolution of galaxy clusters
and groups?

  * •

How and when did the hot and diffuse universe become enriched with heavy
elements?

Furthermore, in combination with the low particle background of a low-
inclination low Earth orbit, AXIS will unveil the faint and diffuse X-ray
universe: the remarkable interconnected gas flows that comprise the cosmic
web, giant filaments that feed cluster assembly, and the missing baryons in
the circumgalactic medium [CGM, see e.g., Walker et al., 2019b].

In this white paper, we discuss how AXIS will transform our understanding of
all aspects of feedback in galaxies, a main science driver of the mission, and
we present the far wider impact that AXIS will precipitate across all areas of
galaxy formation and evolution, which will be realized in the $>70\%$ of
general observer time.

##  2 Stellar Feedback in Nearby Galaxies

(Contributed by L. A. Lopez, M. Yukita, E. Hodges-Kluck and K. Garofali)

Figure 1: AXIS $300\rm\;ks$ simulation of the soft-band ($0.3-2\rm\;keV$)
image of the spiral galaxy M83. X-ray binaries and diffuse hot gas are
apparent, occupying the star-forming regions and inflating bubbles through the
collective influence of supernovae and stellar winds. With AXIS sensitivity
and spatial resolution, spectro-imaging analyses across arcsecond
($10-30\rm\;pc$) scales are possible. Right: A sharp, sensitive survey will
definitively measure the luminosity function of $>5000$ star clusters down to
below the “knee" in the H$\alpha$ luminosity function. Chandra is not able to
achieve these depths in multiple Ms even with capabilities at launch.

Over the past decade, observational and theoretical investigations have
revealed that the large-scale behavior of galaxies (e.g., the shape and
structure of galaxies, the rate and efficiency of star formation) emerge from
local phenomena, particularly stellar feedback Hopkins et al. (2014). The
injection of energy and momentum by stars has a profound influence on their
surroundings. For example, stellar winds and supernovae from massive star
clusters inflate bubbles that disrupt natal clouds Chevance et al. (2020),
triggering star formation on their periphery and dispersing gas and metals
that become fodder for the next generation of stars (Krumholz et al., 2019).
Collections of these bubbles build on each other, and in the extreme cases of
starburst galaxies, form superheated gas that can drive galactic winds that
eject much of the ISM gas into galactic halos Veilleux et al. (2005).

Stellar feedback is often cited as one of the biggest uncertainties in star
and galaxy formation [e.g., Dobbs et al., 2014; Hopkins et al., 2014],
stemming from the need to constrain how the energy and momentum of star
clusters is partitioned and couples to the ISM. Feedback operates through
several channels (e.g., photoionization, radiation, stellar winds, supernovae,
cosmic rays), and their effectiveness and impact vary, depending on star
cluster mass, age, metallicity, and environment. An accurate energetics
inventory that measures feedback efficiency is crucial to understand galactic
ecosystems. This endeavor necessitates a multiwavelength perspective to
connect cluster stars (UV, optical, and infrared) to HII regions (X-ray, UV,
and optical) and the surrounding ISM (mm, radio, and infrared).

X-ray observations are a critical missing piece and are essential to
quantitatively measure the energetics because they trace the internal energy
remaining in the hot gas. How and where this energy is lost remains an open
question [e.g., Rosen et al., 2014; Lancaster et al., 2021]. However, HII
regions have sizes of $1-200\rm\;pc$ and typical luminosities of $L_{\rm
X}=10^{32}-10^{37}\hbox{$\rm\;erg\rm\;s^{-1}\,$}$, largely inaccessible by
modern X-ray facilities even in the Local Group. To date, only the brightest
($>10^{37}\hbox{$\rm\;erg\rm\;s^{-1}\,$}$) tens of sources in the Local Group
have been studied because Chandra lacks the sensitivity to detect fainter
sources and XMM-Newton cannot resolve them spatially.

AXIS’s high spatial resolution and large, soft X-ray collecting area will
enable the first representative inventory of the X-ray properties of
individual star-forming regions ($1-10\rm\;arcsec$ scales) in nearby
($<7\rm\;Mpc$) galaxies (e.g., Fig. 1). AXIS will measure the X-ray signatures
(e.g., temperature, density, luminosity) of $>5000$ star clusters down to
$L_{\rm X}\sim 10^{34}\hbox{$\rm\;erg\rm\;s^{-1}\,$}$ in these galaxies,
sufficient to detect the X-ray counterparts of star cluster populations and to
produce the first-ever X-ray luminosity function of this population. Nearby
targets offer a wide range in parameter space to quantify feedback efficiency
via, for example, the outflow mass-loading factor and the stellar winds and
supernovae thermalization efficiency constrained from the hot gas properties.
These properties will be determined as a function of cluster mass, age,
metallicity, galactocentric radius, and star cluster concentration, which are
necessary inputs to test star and galaxy formation models.

X-rays are a longstanding missing piece in the puzzle of stellar feedback and
its role in galactic ecosystems. By measuring the internal energy of a vast
range of star clusters in nearby galaxies for the first time as part of the
core science program, AXIS will finally provide the long-sought quantification
of how hot gas from stellar winds and supernovae, X-ray binaries, and cosmic
rays regulate star formation and shape galaxies.

##  3 Black hole feedback: quasar mode

###  3.1 Quasar-mode feedback in nearby galaxies

(Contributed by A. Trindade-Falcão, H.R. Russell, F. Tombesi and W.P. Maksym)

Figure 2: Composite image of the Seyfert galaxy Mrk573 comprising a PSF-
deconvolved Chandra image, radio VLA $6\rm\;cm$ emission from the radio jets
and HST [O iii] emission Paggi et al. (2012). Simulated AXIS spectrum
($150\rm\;ks$) for the region shown. The best-fit model has one thermal
component (purple line) and two photoionization components (blue and orange
lines). The total model is shown by the red line.

Even though the central SMBH has a mass of only $\sim 0.1\%$ of its host
galaxy, the enormous radiative and mechanical energy released as it grows (and
shines as an AGN) can slow or completely suspend the entire galaxy’s growth
[for a review see Fabian, 2012]. Now included as standard physics in
simulations of structure formation, this mechanism may be able to transform
gas-rich, star-forming progenitors into ‘red and dead’ ellipticals and imprint
the observed strong correlation between black hole mass and galaxy bulge
velocity dispersion Magorrian et al. (1998); Bower et al. (2006); Croton et
al. (2006). The majority of black hole growth occurs during phases of high-
accretion radiative/quasar mode where intense radiation and high velocity
winds off the accretion disk heat, ionize, and expel gas from the surrounding
ISM Silk & Rees (1998); Fabian (1999); King (2003); Murray et al. (2005).
However, estimates of the energy and momentum input vary widely, and the
necessary coupling to kpc-scale cold gas clouds is still far from being fully
understood.

Spatially-resolved spectroscopy on scales of hundreds of parsecs (arcsec
scales) is required to resolve the intricate structure of shocks, and
ionization cones, to map the resulting transitions in the hot gas properties,
and thereby to measure the energy transmitted to the surrounding ISM. With an
order of magnitude increase in soft X-ray effective area, AXIS will
dramatically extend our reach beyond the few brightest, most massive systems
to cover extensive samples of individual galaxies in the local universe and to
develop physical models for the unresolved quasar feedback at the peak epochs
of galaxy and black hole growth at much higher cosmological redshifts (z$>$2).

AXIS observations of nearby Seyferts will map the impact zones where winds
from the luminous AGN first meet the ISM (Fig. 2). Outflow velocities at
hundreds of parsec scales are typically $\sim
1000\hbox{$\rm\;km\rm\;s^{-1}\,$}$, for which the characteristic interaction
energies are $1\rm\;keV$ and require X-ray observations. Soft X-ray bright
knots and arcs result from a complex mixture of photoionization and thermal
shock emission [e.g., Fabbiano et al., 2018; Maksym et al., 2019; Trindade
Falcao et al., 2023], which AXIS will disentangle with multi-component
spectral models on arcsec scales and measurements of multiple high-ionization
species to break degeneracies. With its unprecedented large effective area,
AXIS will detect very low surface brightness components to test complex shock
heating models, such as "slow cooling" where the gas is strongly heated,
cannot cool efficiently, and produces disconnected arcs of X-ray emission as
the energy is dissipated far beyond the deceleration point [e.g., Fornasini et
al., 2022]. AXIS could rapidly observe large samples in the GO phase and cover
a wide range of AGN luminosities, accretion rates, and galaxy masses. AXIS
will then quantify the thermal power injected into the ISM as a fraction of
the AGN bolometric luminosity and test different feedback models. Strong
coupling of the radiative energy would imply so-called simple AGN feedback,
where a supersonic pressure or momentum-driven outflow off the accretion disk
propagates to large scales. Weaker coupling would instead signify a two-stage
mechanism where radiative pressure drives a weak wind in the hot ISM and
secondary effects, such as the radiative effects of dust absorption and
ionization, act on cold gas at large scales King & Pounds (2015).

###  3.2 Quasar feedback at high cosmological redshifts

(Contributed by G. Chartas)

Figure 3: Left: A deconvolved Chandra image obtained by stacking all available
observations of PG1115+080 (total exposure time of $173\rm\;ks$). A partial
X-ray Einstein ring is resolved between lensed images. Center: The stacked
$173\rm\;ks$ Chandra spectrum extracted from the regions (left) covering the
partial X-ray Einstein ring. A model that includes a plane-parallel shock
plasma component plus a power-law component is shown in red. The spectrum can
be equivalently fit by only a power-law model (blue). Right: A simulated
$173\rm\;ks$ unfolded AXIS spectrum of the partial X-ray Einstein ring clearly
resolves the shocked plasma component (blue) from the power-law component
(red).

The observed evolution of the stellar mass of galaxies [e.g., Madau &
Dickinson, 2014a] indicates that approximately 75% of the stellar mass had
already formed before $z\sim 1.3$. It is therefore important to determine the
energetics and morphology of multi-phase outflows/winds at high redshift, near
the peak of AGN and star formation activity. One prediction of numerical
models of ultrafast outflows (UFOs) is that they interact with the ISM,
producing shocks and extended X-ray emission at the shock front [e.g.,
Faucher-Giguère & Quataert, 2012; Zubovas & King, 2012]. The extent of the
shocked ISM gas is predicted to be of the order of $\sim 0.1-1\rm\;kpc$. At
$z=2$ , this corresponds to a range of angular sizes of $0.01-0.1\rm\;arcsec$
that cannot be resolved by any current X-ray telescope. A direct detection of
the interaction of a small-scale UFO originating at $10$-$100$ $r_{\rm g}$,
where $r_{\rm g}$ = G$M_{\rm BH}$/c2, with kpc-scale gas would provide
confirmation that UFOs transfer a significant amount of their energy to the
host galaxy and are thus an important component of galaxy feedback.

When gravitationally lensed, a compact quasar source forms multiple images
whilst any extended emission around the quasar forms a ring (aka Einstein
ring) that connects the individual images. A technique that has been
successfully employed to resolve extended optical and IR emission around
quasars involves lens modeling the Einstein rings of gravitationally lensed
quasars. Finding lensed extended emission is easier than finding unlensed
extended emission because the lens magnification enormously reduces the
contrast between the extended emission and the central quasar Kochanek et al.
(2001). The detections of X-ray Einstein rings associated with UFOs in distant
lensed quasars are rare due to their X-ray weakness and the limited number of
known lensed quasars with relativistic outflows Chartas et al. (2021). The
detection of both the UFO from the spectra of the lensed images and the
extended emission from the shock can only be accomplished with an X-ray
telescope with a PSF of the order of 1 arcsec (required to resolve the lensed
images and Einstein ring) and an effective area of about $>$ 10 times Chandra
(required to obtain high signal-to-noise UFO and shocked ISM spectra). AXIS is
the only proposed X-ray probe mission that meets these requirements.

A hint of the detection of both a UFO and an Einstein ring is provided in
Chandra observations of the lensed quasar PG 1115+080 Chartas et al. (2023).
PG 1115+080 is a quadruply lensed quasar containing a powerful UFO ($v\sim
0.4$c). Our preliminary spatial analysis of the available Chandra observations
of PG1115+080 shows hints of a partial X-ray Einstein ring. In Fig. 3, we show
the deconvolved Chandra image obtained by stacking all available Chandra
observations (total exposure time of $173\rm\;ks$). The extended emission
forming a partial Einstein ring is visible in both the stacked observation and
in a single $30\rm\;ks$ observation of PG115+080. The Chandra spectrum of the
partial Einstein ring is also shown in Fig. 3. An acceptable spectral model
includes a plane-parallel shock plasma model and an absorbed power-law model.
Due to the low signal-to-noise ratio, however, a model that only includes an
absorbed power law also provides a satisfactory fit to the data. We simulated
an AXIS spectrum with a matching exposure time ($173\rm\;ks$) using the best-
fit model to the Chandra spectrum of the partial Einstein ring (Fig. 3). The
simulated AXIS observation of PG1115+080 shows that we will unambiguously
detect the presence of shocked emission from the interaction of the UFO with
the ISM.

Figure 4: The distribution of lens image separations for three different lens
types: galaxy, group, and cluster-scales, predicted by a halo model. The total
distribution is shown by the thick line. The vertical lines represent the
current best estimate half-power diameters of AXIS and Athena.

There is an important synergy between AXIS and other multi-wavelength
observatories that will improve our understanding of galaxy feedback through
multi-phase winds. Spectra and images from mm observatories (e.g., ALMA) will
be used to determine the properties of the macro-scale winds. Numerical models
of UFOs [e.g., Faucher-Giguère & Quataert, 2012; Zubovas & King, 2012] predict
that they drive powerful winds that heat and expel cold gas from the galaxy on
larger scales. At present, there are few examples where the momentum flux of
the AGN wind can be linked to a large-scale molecular outflow, but a
combination of AXIS and ALMA can increase the sample and allow us to test
models of this process. The Vera C. Rubin Observatory is predicted to discover
$>10,000$ gravitationally lensed quasars, most of which will be resolved with
AXIS [Oguri, 2006, see Fig. 4]. The planned observing window of AXIS ($\sim
2032-2037$) will overlap with the multi-band photometric optical surveys of
Rubin ($\sim 2024-2034$), GAIA and EUCLID. The eROSITA all-sky survey will
provide the X-ray fluxes of the lensed quasars discovered by Rubin and other
surveys (J-PAS, Pan-STARRS1, DESI legacy, and Dark Energy Survey) but cannot
resolve the lensed images or extended emission. AXIS will target lensed
systems that are X-ray bright enough and detect UFOs and Einstein rings.

AXIS observations of a sample of high-$z$ lensed quasars will allow us to
study both the central drivers of galaxy growth at the smallest scales
($1-100r_{\rm g}$) and the interaction of the winds with the ISM at mesoscale
($\sim\rm\;pc-\rm\;kpc$).

##  4 Black hole feedback: radio mode

###  4.1 Radio-mode feedback in galaxies

(Contributed by L. Lanz and H.R. Russell)

Figure 5: Left: X-ray flux vs. gas temperature for galaxies in the ATLAS3D
sample Cappellari et al. (2011) with Chandra observations Kim & Fabbiano
(2015). AXIS exposure times to obtain $>10,000$ counts from the diffuse gas
are shown for representative targets. Note that, given the low temperatures of
these hot atmospheres, $10\rm\;ks$ with AXIS is equivalent to $250\rm\;ks$
with Chandra at launch and $2.5\rm\;Ms$ currently. Uncertainties on Chandra’s
global temperature measurements are not shown for clarity, but are typically
$15-80\%$. Galaxies with and without detected nuclear radio emission are shown
by the red and black points, respectively Nyland et al. (2016). The
temperature components of the Milky Way’s circumgalactic medium are shown for
reference [e.g. Das et al., 2019]. Right: Chandra (upper) and simulated AXIS
spectra (lower) of NGC 1266, a post-starburst lenticular with a 6′′ multiphase
nuclear outflow, showing the degradation of Chandra’s soft response and the
benefit of AXIS’ high effective area. More than twice as many photons were
collected in less than 1/7th of the exposure time.  Figure 6: Left and center:
Chandra (at launch) and AXIS simulated images of AGN feedback in NGC 5813
($100\rm\;ks$) with spatial binning for 1500 counts per region. Color bars are
matched and units are $\rm\thinspace counts\hbox{$\rm\;arcsec^{-2}\,$}$. The
radio jet has carved out large cavities in the galaxy’s hot atmosphere, which
are visible in the AXIS simulation as depressions in X-ray surface brightness.
With 1500 counts per region, AXIS will map the gas properties on these spatial
scales to an accuracy of e.g. a few percent in temperature. The spatial bins
were generated with the contour binning algorithm and group pixels with
similar surface brightness Sanders (2006). All panels cover the same field of
view. Right: Simulated temperature map in keV for a $100\rm\;ks$ AXIS
observation, which probes the thermodynamic properties on the scales of the
bubble rims, shocks, and cool gas plumes Randall et al. (2011, 2015).

Powerful radio jets are a means by which AGN exert influence on their host
galaxies, but how they are able to provide steady, distributed, and self-
regulated heating to galaxy and cluster environments is still not well
understood [see, e.g., Fabian, 2012; McNamara & Nulsen, 2012 for reviews].
Mechanical- or radio-mode feedback typically occurs when accretion is
happening at low rates ($\lesssim 1\%$ of the Eddington rate), enabling this
mode to be active for longer periods than intense quasar mode feedback (see
section 3.1). Radio-mode AGN have primarily been studied in massive systems,
where they must efficiently couple to their surrounding hot X-ray atmospheres
to suppress cooling and maintain low levels of star formation at late times.
The physical processes by which the energy and momentum are transferred to
cooling and star-forming gas, distributed on galaxy scales, and how these
mechanisms scale with host mass remain unknown.

Spatially-resolved spectroscopy with high angular resolution is critical for
resolving and characterizing extended diffuse emission and differentiating
between feedback from nuclear star clusters and star formation and feedback
from the AGN including via small-scale jets. As jets encounter the ISM, they
can shock some of this gas to a range of temperatures, producing emission in
the mid-infrared [e.g., Ogle et al., 2014] and X-ray bands [e.g., Lanz et al.,
2015]. AXIS’s high throughput coupled to arcsecond spatial resolution will be
key in resolving the structure and properties of the hot gas for comparison
with warm gas mid-IR and near-IR tracers mapped by JWST and Roman, enabling us
to trace the processes by which energy is deposited into the ISM from radio
jets. Fig. 5 shows a comparison of Chandra observations from Cycle 11 and
Cycle 18 with an AXIS spectrum of the same outflow region in NGC 1266. The
typical temperature of galactic hot atmospheres lies below $1\rm\;keV$ and the
dramatic loss of Chandra ACIS soft response (currently only
$8\hbox{$\rm\;cm^{2}\,$}$ at $0.5\rm\;keV$) has long placed these targets out
of reach [e.g., Werner et al. 2019]. With an effective area more than 400
times Chandra ACIS at $0.5\rm\;keV$, AXIS will allow detailed studies of the
mechanical processes by which AGN impart energy to their host galaxies and
crucially widen our view from individual investigations of only the brightest
sources to statistically important samples.

On larger scales of a few to tens of kpc (arcsec to tens of arcsec), jets
inflate huge bubbles of radio-emitting plasma and couple very efficiently to
the volume-filling hot CGM [e.g., McNamara et al., 2000; Fabian et al., 2000;
Churazov et al., 2001; McNamara & Nulsen, 2007]. Our current understanding is
almost entirely shaped by deep Chandra observations of the nearest, richest
cluster atmospheres [e.g., Perseus, Fabian et al., 2006; M87, Forman et al.,
2007a; Centaurus, Sanders et al., 2016; Abell 2052, Blanton et al., 2011].
Although remarkable, these systems are clearly unrepresentative of the wider
galaxy population driving the slowdown in star formation at low redshift.
Chandra observations of the brightest ellipticals indicate analogous jet
interactions with the galaxy’s hot atmosphere Allen et al. (2006); Nulsen et
al. (2009); Panagoulia et al. (2014) but have been severely limited by the
loss of ACIS’s effective area at low energies. AXIS’s expansive soft response
will enable Perseus-like studies for numerous systems in the nearby universe
to determine if feedback stabilizes cooling in all nearby massive galaxies,
whether cluster processes scale down, and what the dominant mechanism is
distributing and dissipating energy throughout the galaxy’s hot atmosphere.
Fig. 5 (left) shows all galaxies in the ATLAS3D sample with Chandra
observations Kim & Fabbiano (2015) measuring the global properties of the hot
atmosphere. With at least 10,000 counts per target in a large sample with
AXIS, we will identify cavities, measure the gas properties in radial profiles
and calculate the energy input by the AGN. AXIS observations of massive
ellipticals (Fig. 6) will uncover additional pairs of relic bubbles from
previous AGN outbursts to reveal the history of AGN activity, whether bubbles
break up, merge or pile up at large radius, trace metal-rich, low entropy gas
flows, and determine the implications for the distribution of the energy input
by jets. In this way, for the first time, AXIS will reveal how feedback
operates across the whole gamut of hot atmospheres from L* galaxies at
$10^{12}\hbox{$\rm\thinspace M_{\odot}$}$ to the richest clusters above
$10^{15}\hbox{$\rm\thinspace M_{\odot}$}$.

###  4.2 Feedback in galaxy clusters

(Contributed by Y. Qiu)

Figure 7: Left: Chandra image of the Perseus cluster ($100\rm\;ks$ at launch)
with spatial binning for 7500 counts per region (color bar units counts
arcsec-2). Center: AXIS simulated image of the Perseus cluster ($100\rm\;ks$)
also binned for 7500 counts per region. Right: AXIS simulated spectra for the
region shown with a radius of $2.5\rm\;arcsec$ (factor of 10 reduction in
spatial bin size compared to Chandra). The total spectrum and model are shown
in black, and the intrinsic emission from a region of the soft X-ray filament
[shown center, projected emission subtracted with a neighboring off-filament
region, Fabian et al., 2011] is shown in purple.

AGN feedback reaches far beyond the SMBH’s sphere of influence to interact
with the multiphase medium in and around galaxies. In galaxy clusters, where
there is a concentration of hot gas pulled in by the dark matter halo, AGN
feedback acts against gravity to shape the structure of the X-ray-emitting
intracluster medium (ICM). Direct imaging of the ICM with X-ray facilities has
proven fruitful in detecting imprints of AGN activity. For example, Chandra
has detected the innermost cavities inflated by radio jets in numerous rich
clusters and shown that the energy required to inflate them is sufficient to
suppress cooling of the cluster atmospheres Bîrzan et al. (2004); McNamara &
Nulsen (2007). However, the physical mechanisms by which the jets heat the ICM
or the residual gas cooling fuels the AGN remain unknown. Very deep Chandra
observations of a few of the nearest clusters, such as Perseus, reveal highly
structured networks of soft X-ray filaments, weak shocks, sound waves,
turbulence and numerous pairs of outer bubbles [e.g., Fabian et al., 2003].
AXIS’s angular resolution, soft response, and wide field of view are therefore
essential to understand how the distribution, multi-temperature thermal state,
and metallicity evolution of the plasma are influenced by AGN feedback in a
wide range of clusters.

The cooling of the ICM in cool-core clusters is inextricably linked with AGN
feedback [e.g., Li et al., 2015; Qiu et al., 2019b, a]. How the plasma cools
and forms (sometimes star-forming) cold filaments is still a highly debated
topic, including theoretical models such as plasma thermal instability, uplift
of low-entropy gas by AGN-driven bubbles, as well as radiatively cooling AGN-
driven outflows Pizzolato & Soker (2005); Gaspari et al. (2012); Li & Bryan
(2014); McNamara et al. (2016); Voit et al. (2017); Qiu et al. (2020, 2021).
AXIS’s soft response and spatial resolution are perfect for tracing the lowest
energy plasma out of which these filaments form (Fig. 7), potentially
unveiling the fueling of the central AGN and the growth of the stellar
component. When combined with optical and radio observations (such as SITELLE,
MUSE, and ALMA) that capture the velocity distribution and turbulent
structures of the cold gas Li et al. (2020); Hu et al. (2022); Zhang et al.
(2022), AXIS will enable a comprehensive account for the continuous
thermodynamical evolution of the plasma, and further reveal the role AGNs play
in tightly controlling the growth of these elliptical galaxies.

Figure 8: Left: Ratio of soft ($0.5-0.7\rm\;keV$) and mid-band
($0.8-1.1\rm\;keV$) Chandra images ($280\rm\;ks$ taken $2000-2004$) showing
regions of strong absorption in the center of the Centaurus cluster. Center:
$100\rm\;ks$ Chandra soft band counts image binned for $>100$ counts per pixel
in regions of interest. Right: Same as center but for $100\rm\;ks$ with AXIS.
Substantial expansion of the soft response with AXIS ensures over an order of
magnitude improvement in resolution.

Figure 9: Left: HST H$\alpha$ image of the core of the nearby Centaurus
Cluster around its Brightest Cluster Galaxy NGC 4696 Fabian et al. (2016).
Note the dusty filaments and emission clouds, all of which will absorb soft
X-rays originating from this region. Right: Simulated $100\rm\;ks$ AXIS
spectrum of the inner arcmin diameter of NGC 4696. The green line shows a
$15\hbox{$\hbox{$\rm\thinspace M_{\odot}$}\rm\;yr^{-1}\,$}$ cooling flow, the
red line similar but with a total intrinsic absorption of $1.6\times
10^{22}\hbox{$\rm\;cm^{-2}\,$}$ included to match the XMM RGS result Fabian et
al. (2022). The AXIS spectrum will vary between the green to below the red
line depending on the absorption along a specific sightline, as in left.

In the absence of AGN feedback, the properties of the ICM, such as temperature
and density distribution, are determined primarily by the underlying gravity
Voit et al. (2005). Detecting and characterizing property modifications
associated with activities of the AGN are therefore crucial in understanding
how feedback energy is delivered to the surrounding medium. Measurements of
shocks, cavities, and turbulence [e.g., Bîrzan et al., 2004; Forman et al.,
2007b; Zhuravleva et al., 2014] in the plasma all require a large collecting
area with arcsecond resolution. AXIS’s advancement over existing X-ray imaging
telescopes enables the detection of these features beyond the central tens of
kpc. The combination of spatial resolution (providing detailed maps of the
density and temperature structure) with velocity structure from future X-ray
calorimeters (such as XRISM, HUBS, and Athena) is key to understanding how
energy is transmitted to the ICM and distributed throughout the cluster core.

###  4.3 Hidden cooling flows in clusters

(Contributed by A.C. Fabian)

The radiative cooling time at the center of the hot atmospheres of massive
galaxies, groups and clusters can drop below $10\rm\;Myr$. The observed mass
cooling rate of this gas is very low and drops to near zero as the gas
temperature falls below $0.4\rm\;keV$ Peterson et al. (2001); Sanders et al.
(2008). Either AGN feedback is very tightly balanced, as discussed in sections
4.1 and 4.2, or the soft X-ray emission from cooling is somehow hidden from
view, which is considered here. The gas in the centers of cool core clusters,
groups, and elliptical galaxies is then cooling at significant rates of order
100, 10 and $1\hbox{$\hbox{$\rm\thinspace M_{\odot}$}\rm\;yr^{-1}\,$}$,
respectively. As the gas cools below $1\rm\;keV$ in the central kpcs it
becomes entwined with the gas that has already cooled. It is hidden from
direct detection by photoelectric absorption in the cold gas, as revealed by a
recent analysis of XMM-Newton RGS spectra Fabian et al. (2022, 2023a).

The fate of the rapidly accumulating cold gas is unknown, but the observed
metallicity peaks at about $10\rm\;kpc$ radius in nearby clusters indicate
slow outflows of enriched gas from their centers. Some gas may, however,
become ultra-cool at close to $3\rm\;K$, fragment and form low mass stars
Fabian et al. (2022). Some low-mass stars may be swallowed whole by the
central black hole while emitting little radiation Fabian et al. (2023b).

The high angular resolution and soft response of AXIS will enable detailed
spatial (Fig. 8) and spectral (Fig. 9) mapping of these important regions,
uncovering the workings of the innermost parts of the most massive galaxies in
the Universe.

###  4.4 Inverse Compton Ghosts in the deep X-ray Sky

(Contributed by A.C. Fabian)

Figure 10: Left: The extended X-ray emission around HDF 130 at $z=1.99$ Fabian
et al. (2009). It is an inverse Compton ghost of a giant radio source in the
Chandra Deep Field North ($2\rm\;Ms$). The Chandra spectrum for HDF 130 can be
equivalently fit by power-law and thermal models. Right: Simulated AXIS
spectrum of HDF 130 in a $300\rm\;ks$ pointing from the AXIS Wide Survey. The
AXIS simulated background (soft and non-X-ray background) and the best-fit
power-law model with $\Gamma=2.65\pm 0.05$ and $\chi^{2}=80$ for 89 degrees of
freedom (compared to $\chi^{2}=111$ for 89 degrees of freedom for a thermal
model) are also shown.

Powerful jetted AGN feedback from isolated galaxies leads to giant double-
lobed sources in the radio band. The energetic electrons in the lobes lose
energy to inverse Compton scattering of the microwave background, the energy
density $\epsilon_{\rm cmb}$ of which grows with redshift $z$ as $(1+z)^{4}$.
The lifetime of an electron of Lorentz factor $\gamma$ scales as
$1/(\gamma\epsilon_{\rm cmb})$. Consequently, when the jets switch off, the
radio emission, requiring $\gamma\sim 10^{4}-10^{5}$, dies away faster than
the inverse Compton X-ray emission, which requires $\gamma\sim 10^{3}$. This
results in a double-lobed inverse Compton ghost appearing in the soft X-ray
band (its spectrum is likely steep). A candidate ghost was found in the
$2\rm\;Ms$ Chandra Deep Field North, centered on the massive galaxy HDF 130 at
$z=1.99$ [Fig. 10, see Fabian et al., 2009]. The lack of any such ghosts in
the deeper Chandra Deep Field South is likely due to the lack of sensitivity
to soft X-rays that had developed due to the buildup of obscuring matter in
the optical blocking filter on Chandra’s ACIS detector. Such sources may have
a higher space density than clusters at $z>2$ and $L_{\rm
X}>10^{44}\hbox{$\rm\;erg\rm\;s^{-1}\,$}$.

Several other examples of jets with X-ray but not radio emission have been
reported from Chandra observations Mocz et al. (2011a). AXIS should detect
many more with its capability to map faint X-ray emission. The distribution
with redshift and luminosity will provide a valuable guide to the importance
and evolution of jetted feedback in isolated galaxies Mocz et al. (2011b,
2013).

##  5 The integrated history of feedback with high-z clusters

###  5.1 Radio-mode feedback in high-z clusters

(Contributed by S.W. Allen, A.B. Mantz and M. McDonald)

Figure 11:  The number of SZ cluster detections expected as a function of
redshift from Stage 3 SZ surveys and the proposed CMB-S4 project [adapted from
Mantz et al., 2019]. Blue to red shading shows the transition to the $z>1.5$
regime, for which high spatial resolution and throughput are key requirements
for extracting information about halo centers, relative masses, dynamical
states, internal structure, and galaxy/AGN populations. Figure 12: Left:
Chandra observation of the X-ray cavities in RBS 797. Two cavities are visible
$\sim 30\rm\;kpc$ to the E and W of the AGN and are each $\sim 30\rm\;kpc$
across [e.g., Ubertosi et al., 2021]. Center and right: Chandra and AXIS
simulations of RBS 797 scaled for a mass of $M_{500}=5\times
10^{14}\hbox{$\rm\thinspace M_{\odot}$}$ at $z=1.5$ (applying cosmological
dimming, reducing angular size, etc.). AXIS will extend measurements of AGN
feedback in these environments into the high redshift regime for the first
time.

Galaxy clusters are the pinnacle of hierarchical structure formation. As the
most massive and largest virialized structures in the Universe, clusters
provide unique, high density environments within which to study the physics of
galaxy evolution Allen et al. (2011); Kravtsov & Borgani (2012). Their deep
gravitational potentials preserve the integrated history of generations of
star formation and AGN feedback in the thermodynamic properties McDonald et
al. (2017); Sanders et al. (2018); Ghirardini et al. (2021). Powerful new
surveys at millimeter (e.g., South Pole Telescope, Atacama Cosmology
Telescope, Simons Observatory and CMB-S4), optical/near-IR (eg. Rubin, Roman,
Euclid) and soft X-ray wavelengths (eROSITA) are now set to expand, by orders
of magnitude, the size of cluster catalogs (Fig. 11). Critically, the new
millimeter and optical/near-IR surveys will also reach much further in
redshift, back to the epoch when these massive, virialized structures first
formed. High-spatial-resolution X-ray follow-up observations of high redshift
clusters will unfurl the complex interplay between gravity, star formation and
AGN feedback over their full history. However, such measurements lie beyond
the reach of existing facilities: detailed studies with Chandra and XMM-Newton
are restricted to $z<1$, with only a handful of low S/N measurements for a few
extreme systems that extend to $z\sim 1.5$. With its combination of high
spatial resolution, expansive soft X-ray response, low instrumental
background, and wide field of view, AXIS will transform our understanding of
high redshift clusters, allowing us to observe their complete formation
history, including the period of ‘cosmic noon’ ($z\sim 2-3$), when AGN and
stellar activity within them peaked.

AXIS guaranteed time observations will target the most massive, most luminous
X-ray clusters discovered at redshifts $1.5<z<3$, resolving the AGN within
them and measuring the density and temperature of the ICM, to a precision of
better than 5% on spatial scales as small as $20\rm\;kpc$. Such measurements,
which also provide determinations of the pressure and entropy structure of the
ICM, will reveal the evolving and cumulative impact of AGN feedback on its
environments. For brighter targets, AXIS will also determine the instantaneous
impact of this feedback manifested, for example, by AGN-blown cavities
inflated in the surrounding X-ray gas. Such cavities are routinely observed at
low-to-intermediate redshifts with Chandra and XMM-Newton, providing powerful
insights into the physics of AGN feedback. High spatial resolution is
critical; at redshifts $z>1.5$, these cavities are expected to typically
subtend only a few arcsec (Fig. 12). AXIS will extend these measurements, for
the first time, into the high-redshift regime.

###  5.2 Metallicity evolution

(Contributed by A.M. Flores, A.B. Mantz and S.W. Allen)

Figure 13: The forecasted improvement in metallicity constraints for cluster
outskirts with AXIS. Current measurements (dark blue points) provide
relatively weak constraints on how rapidly enrichment may have advanced in
dense cluster environments, remaining consistent with even non-evolving
metallicity (light blue band). The addition of 3 Ms of targeted AXIS data at
$1.5<z<3$ will provide tight constraints on the rate of enrichment at early
times, easily distinguishing between models where the enrichment in dense
cluster environments tracks the star formation rate in the field (red points
and band), and models where the enrichment of denser environments proceeds
faster (dotted and dash-dotted lines). $t_{\mathrm{AGN}}$ labels refer to the
age of the Universe when the rate of ICM enrichment is most rapid in each
model.

Measurements of cluster metallicity encode the entire history of star
formation and AGN activity within cluster volumes, up to the redshift of
observation, providing unique insights into the enrichment history of the
Universe. Metallicity distributions in clusters have been well characterized
for nearby systems [Werner et al., 2013; Urban et al., 2017] and for
statistical ensembles out to z$\sim$1.5 McDonald et al. (2016); Flores et al.
(2021). These reveal a remarkable universality from system to system and
region to region within clusters Werner et al. (2013); Urban et al. (2017),
which requires that AGN feedback played a profound role in redistributing
metals throughout the Universe at early times Biffi et al. (2017, 2018);
Vogelsberger et al. (2018). However, current X-ray flagship observatories lack
the capability to perform such measurements at the redshifts most critical for
evolutionary studies, $1.5<z<3.0$, when star formation and AGN activity in the
Universe peaked.

In order to probe high redshifts, including the period of cosmic noon
($2<z<3$), where we expect these processes to have been most prolific, we
require spatially resolved X-ray measurements of clusters at these redshifts.
As discussed in section 5.1, Sunyaev-Zel’dovich (SZ) surveys, from SPT, ACT,
the Simons Observatory and CMB-S4, will soon unveil, for the first time, the
most massive, virialized systems at these redshifts, which will be prime
targets for X-ray followup with AXIS. Despite being the most massive
structures in the Universe, most of the extended emission from clusters at
these redshifts is concentrated within regions less than an arcminute in size
($\sim$r500). To simultaneously explore the physics of ongoing feedback within
cluster cores, and the low surface brightness emission from cluster outskirts,
while excising the emission from contaminating point sources, we require an
instrument combining high sensitivity, high spatial resolution, and low
particle background contamination. Only AXIS provides this combination.

The proposed $3\rm\;Ms$ AXIS observing program for 30 clusters at $1.5<z<3$
will transform our understanding of metal enrichment at high z, providing
precise measurements for individual systems and tracing the evolutionary
history of cluster enrichment as a whole. In combination with $>20\rm\;Ms$ of
existing X-ray observations from Suzaku, Chandra, and XMM-Newton at lower
redshifts, the new AXIS measurements will provide the first meaningful
constraints on the enrichment of the ICM at early times. The data will
distinguish, to high precision, models in which enrichment in clusters tracks
the star formation rate in the field, from models in which enrichment in the
densest environments proceeds at an accelerated pace [as hinted at by recent
studies with HST, Willis et al., 2020, and JWST, Tacchella et al., 2023].

Fig. 13 shows the existing constraints on the metallicity of cluster outskirts
($0.3<r/r_{500}<1.0$) from Suzaku, Chandra and XMM-Newton, binned in redshift,
and the predicted measurements from 3 Ms of AXIS data (100 ks for each of 30
clusters, divided equally among redshifts 1.5, 2.0 and 3.0). The baseline
model assumed in the AXIS simulations (dashed line) is one where the
enrichment of the ICM follows the same functional form as the cumulative star
formation in field galaxies Madau & Dickinson (2014b), i.e. metals are
produced (and immediately dispersed) in cluster environments at the same rate,
per unit mass, as in the field. An additional free parameter then allows the
enrichment of cluster environments to be slowed or sped up relative to the
field; slowing could result from the AGN feedback being delayed relative to
star formation, while speedups may follow if star formation in the densest
environments proceeds earlier than in the field. Although current data already
disfavor significantly delayed enrichment in cluster environments, they remain
consistent with arbitrarily rapid enrichment at early times, including models
with approximately constant metallicity at all observable redshifts. In
contrast, the addition of AXIS measurements will provide tight constraints, at
the $<10\%$ level, on the rate of enrichment at early times, and a new anchor
for studies of star formation and metal enrichment at high redshifts.

##  6 The circumgalactic medium and connections to the cosmic web

###  6.1 Connections to the cosmic web

(Contributed by S.A. Walker and K.-W. Wong)

Figure 14: Left: Hydrodynamical cosmological simulation of large-scale
structure formation, showing that galaxy clusters reside at the nodes of IGM
filaments Dolag et al. (2006). With Chandra and XMM-Newton, only the central
regions of clusters can be explored in detail (inner white circle). To begin
exploring large-scale structure in its entirety (outer white contours)
requires at least a factor of 50 improvement in sensitivity to low surface
brightness extended emission. AXIS will achieve this increase in sensitivity
through a combination of a high effective area and a low and stable particle
background. Right: Simulated X-ray mosaic of the RomulusC cluster Tremmel et
al. (2019), a low mass (1014 M⊙) cluster at $z=0.05$, comparing 100 ks deep
coverage from Chandra (top) and AXIS (bottom). The mock Chandra simulation
includes background point sources from the cosmic X-ray background. Due to the
high background and small collecting areas of current X-ray telescopes, we are
only able to see the brightest X-ray emission in the cluster cores. The bulk
of the ICM in the outskirts beyond the virial radius (dashed white circle),
and the IGM filaments that connect clusters together remain hidden from view.
Figure adapted from Walker et al. (2019b).

The cosmic web forms the backbone of gas flows on cosmological scales. In the
local universe, around half of all baryons are expected to lie in the Warm-Hot
Intergalactic Medium (WHIM), $10^{5}<T<10^{7}\rm\;K$. The hottest part of the
WHIM, ($10^{6}<T<10^{7}\rm\;K$), can be revealed in the soft X-ray band [see
Reiprich et al., 2013; Walker & Lau, 2022 for a review]. However, due to its
very low density, it is very faint in X-ray emission (see Fig. 14). Only with
a combination of a large effective area and low background can we observe the
cosmic web in emission in X-rays. By combining with X-ray and UV absorption
line studies from future missions, AXIS will enable a complete census of the
baryons and metals in the local universe for the first time Richter et al.
(2008). Cosmological simulations provide predictions for the distribution of
metals in the cosmic web and how this distribution depends on AGN feedback
over time. AXIS will test these models by charting the distribution of metals
in the cluster outskirts and in the WHIM filaments. AXIS will also detect the
missing baryons in the CGM around galaxies.

By measuring gas densities and temperatures in the outskirts of galaxy
clusters, we will be able to measure the hydrostatic masses of clusters.
Simulations predict that the contribution from non-thermal pressure support
should increase in the outskirts, reaching a level of $10\%-30\%$ of the total
pressure, and by providing extra support against gravity. Comparing
hydrostatic masses with gravitational lensing masses from Euclid and Roman
will allow powerful constraints on the levels of non-thermal pressure support
in the outskirts of clusters, where they interface with the cosmic web [for a
review see Walker et al., 2019a].

AXIS’s high spatial resolution, along with its large effective area and low
background compared to Chandra, would allow it to directly resolve and remove
small-scale gas clumps and measure diffuse emission out to $\sim$$2r_{200}$
(corresponding to around 2 Mpc for low mass clusters and 5 Mpc for the most
massive clusters). Gas clumping is believed to be due to infalling gas
substructures. Simulations indicate that the level of gas clumping should
increase dramatically in the (1–2)$r_{200}$ region of clusters, where the
infalling clumps have not yet been entirely ram-pressure stripped by the ICM
(Nagai & Lau, 2011; Roncarelli et al., 2013; Vazza et al., 2013). If not
resolved, clumping will bias gas profile measurements by overestimating the
gas density and the gas mass fraction and underestimating the gas temperature,
leading to biases in hydrostatic mass estimates (Simionescu et al., 2011;
Towler et al., 2023). Detecting and resolving gas clumps, which are associated
with infalling galaxies in the outskirts of clusters, is also crucial to gain
insight into the stripping of their CGM through their interactions with the
ICM (Cen et al., 2014). Removing gas clumps would be critical in order to
provide the strongest constraints on electron-ion equilibration and non-
equilibrium ionization models in the outskirts of clusters [see section 6.3
and e.g., Wong & Sarazin, 2009a; Wong et al., 2011; Akamatsu et al., 2011;
Avestruz et al., 2015; Andreon et al., 2023]. Current X-ray telescopes are
unable to resolve faint gas clumps that contribute to the bulk of the clumping
(Fig. 14, right), and their physical properties are almost completely
unexplored.

###  6.2 Inflows and outflows from galaxy clusters

(Contributed by C. Zhang)

Galaxy clusters are assembled through smooth accretion and occasional mergers
of small structures (e.g., galaxies, groups) from the cosmic web (see Kravtsov
& Borgani, 2012; Vikhlinin et al., 2014, for reviews). The newly-accreted IGM
(a.k.a., inflows) is heated by accretion shocks at the boundary of the ICM and
piles up in the cluster outskirts (Bertschinger, 1985). Mergers, on the other
hand, not only stir cluster cores, but also drive outflows that can
significantly expand the hot atmosphere (Zhang et al., 2020b). It is crucial
to study these inflow and outflow processes, not only to gain a deeper
understanding of the hierarchical structure formation theory but also to
leverage galaxy clusters as powerful tools to investigate cosmology and plasma
physics.

Sharp gaseous structures, including shocks and contact discontinuities [for a
review, see, e.g., Markevitch & Vikhlinin, 2007], provide rich information on
inflows and outflows of the ICM, e.g., their formation mechanisms, energy
transportation, and dissipation. Current X-ray detections, performed by, e.g.,
Chandra and XMM-Newton, are typically limited to within $R_{500}$. Fig. 15
illustrates a general picture of gaseous structures in the cluster outskirts,
highlighting the significance of resolving discontinuities outside $R_{500}$
to understand the dynamics of galaxy clusters. Bow shocks formed ahead of
infalling subhalos eventually detach from subhalos themselves after the
primary core passages, occurring typically between $R_{500}$ and $R_{200}$,
and propagate all the way to the cluster peripheries (Zhang et al., 2019,
2021a). The collisionless nature of these “runaway” shocks makes them ideal
targets to characterize the electron-ion non-equilibrium and constrain the
plasma physics of the ICM. Given the typical merger rate of galaxy clusters
(e.g., Fakhouri et al., 2010) and a combination of high spatial resolution and
large effective area, AXIS is expected to detect a large number of such
shocks. Together with radio surveys, we will be able to connect X-ray shocks
with large-scale radio relics and understand how shocks with moderate Mach
numbers accelerate electrons (see Bykov et al., 2019; van Weeren et al., 2019,
for reviews).

Figure 15: A sketch summarizing how mergers and smooth accretion shape the
outskirts of galaxy clusters [see also Fig. 1 in Zhang et al., 2020a]. Three
green circles depict matter distributions within the cluster radius $R_{500}$,
$R_{200}$, and external shock radius $R_{\rm sh}$, respectively. An infalling
subcluster (blue) moves in the main cluster along the trajectory shown as the
dotted black line. The red arcs illustrate merger shocks, which experience a
transition from bow shocks to runaway shocks (Zhang et al., 2019). The latter
associate with radio relics in the cluster peripheries. The Coma cluster
provides a beautiful example supporting this scenario [figure adapted from
Churazov et al., 2021; see also Lyskova et al., 2019]. The long-lived runaway
shocks eventually overtake the accretion shock and shape the new boundary of
the ICM (i.e., a merger-accelerated accretion shock or MA-shock). In this
process, Mpc-scale contact discontinuities (CD) are formed near $R_{\rm vir}$
[blue dashed line in the sketch; see Zhang et al., 2020a]. One such candidate
has been tentatively identified in the Perseus cluster [Gaussian gradient
magnitude filtered map in red over the XMM-Newton mosaic in blue; figure
adapted from Walker et al., 2022]. AXIS will dramatically advance our ability
to measure sharp gaseous structures (e.g., runaway shocks, contact
discontinuities) in the cluster outskirts, essential to understand the
assembly history of galaxy clusters.

The evolution of runaway shocks largely depends on the steepness of the gas
density radial profiles for the diffuse ICM (Zhang et al., 2019). AXIS will
provide an unprecedented measurement out to $2R_{200}$ by carefully excluding
contributions from cold gas clumps (e.g., Fig. 14). This is essential to
understand the evolution of merger-driven outflows, e.g., fate of runaway
shocks, and how dramatically they can perturb/re-distribute matter and energy
in the cluster outskirts.

Current theoretical studies predict that runaway shocks can be long-lived and
eventually overtake accretion shocks and shape a new boundary of the ICM [i.e.
merger-accelerated accretion shock fronts or MA-shocks; see Zhang et al.,
2020b, 2021b], leading to a significant radial offset between the ICM and
dark-matter halo boundaries. This is one of the most prominent effects caused
by merger-driven outflows. Cosmological simulations show that the boundaries
of the ICM (e.g., accretion shock fronts) are up to $5-6R_{200}$ in the non-
filamentary directions (e.g., Lau et al., 2015; Aung et al., 2021). Detecting
the Mpc-scale contact discontinuity near the virial radius formed together
with the MA-shock can provide a direct evidence of the merger-driven outflow
and how it breaks ICM self-similarity in the cluster outskirts (Zhang et al.,
2020a). One such candidate has been tentatively identified in the Perseus
cluster from deep XMM-Newton observations [see Fig. 15 and also Walker et al.,
2022]. AXIS will not only provide detailed structures of the discontinuity
interfaces (e.g., instabilities, mixing), but also extend the sample size,
allowing a systematic study of the gas dynamics in the cluster outskirts.

Last but not least, along filamentary directions, gas dynamics can be very
different from the other diffuse directions, due to the anisotropy of the mass
accretion rate (Zhang et al., 2021b; Vurm et al., 2023). Deeply-penetrated
filaments in the intracluster medium have been measured in cosmological
simulations (e.g., Zinger et al., 2016) and result in accretion shocks near
and even within $R_{200}$. AXIS will be able to detect these innermost
accretion shocks and characterize their role in thermalizing IGM and quenching
infalling galaxies along the filaments.

Figure 16: Left: Chandra image of the merging galaxy cluster Abell 2146
Russell et al. (2022). Right: Projected electron temperature profiles
extracted for the sector across the bow shock front at a radius of $\sim
150\rm\;arcsec$ (shown on the left). The electrons are not directly heated by
the shock front and instead come back into thermal equilibrium with the shock-
heated ions behind the shock. The expectation for the collisional heating
timescale is shown by the blue line. However, systematic uncertainties
increasingly dominate with distance behind the shock (shown by the low
temperatures at radii $<130\rm\;arcsec$ compared to the collisional model).
AXIS will resolve the critical region of the postshock gas (between the dashed
lines) where equilibration models can be effectively distinguished.

###  6.3 Microphysics of the intracluster and circumgalactic medium

(Contributed by P.P. Choudhury and C.S. Reynolds)

The ICM and CGM are massive reservoirs of dilute, optically thin, weakly
collisional (electrons and ions not necessarily in thermal equilibrium by
Coulomb collisions), magnetized (with thermal to magnetic pressure $>100$) and
hot ($\sim 10^{5}-10^{7}\rm\;K$) plasmas which are ideal testbeds for
microphysical transport processes [e.g., Helander & Sigmar, 2005; Schekochihin
et al., 2009]. Since AXIS will allow the census and mapping of hot plasma out
to the cluster/halo virial radius (see section 6.1), energy transport across
large volumes of these astrophysical environments can be studied. Cosmological
hydrodynamic galaxy formation simulations apply phenomenological “sub-grid"
prescriptions [e.g., Vogelsberger et al., 2013; Crain et al., 2015] for AGN
feedback at galactic scale. These models are not informed by the underlying
physical transport and thermalization mechanisms. Thus, there is no good way
to constrain how the diffuse plasma is heated and maintained despite an
overall consensus on the source of energy. Moreover, this limits our
understanding of how much multiphase gas forms in the ICM/CGM - a key unknown
of AGN feedback models (sections 4.1 and 4.2). Although the magnetic field
permeating the diffuse plasma is weak, its dynamical role is highlighted in
fully collisionless models of the plasma [e.g., Komarov et al., 2016] and more
recently in magnetohydrodynamics Drake et al. (2021). In the presence of
typical magnetic fields and large-scale gradients of macroscopic variables
(like density, temperature, etc.), a host of microinstabilities are generated
at the electron/ion Larmor scale. These instabilities (e.g.,
whistlers/mirror/firehose) can grow to large amplitudes and scatter off
electrons in the nonlinear stage to alter transport properties in weakly
magnetized plasma [e.g., Schekochihin et al., 2008]. While the impact of this
phenomenon at global scale is not widely explored [but see Berlok et al.,
2021; Beckmann et al., 2022] even in theoretical/computational research due to
the large separation of scales, the consequences for AGN energy transport can
be profound. The other aspect of energetics that is not explored sufficiently
is the dissipation mechanism (kinetic to thermal energy conversion).
Dissipation is crucial to combat the rapid cooling via free-free emission,
especially in clusters. Overall, it is invaluable to experimentally measure
these key plasma properties like electron-ion equilibration, energy transport,
dissipation, role of magnetic field, etc to prescribe accurate “sub-grid"
computational models.

AXIS will be instrumental in analysing shock discontinuity and contact
discontinuity [in terms of electron temperature and density; see Markevitch &
Vikhlinin, 2007] to assess the impact of plasma physics at macroscopic scales.
First, the ratio of electron to ion temperature [e.g., Wong & Sarazin, 2009b]
behind the shock front is dependent on the Coulomb collisional timescale and
plasma turbulence (which can transfer energy between the species). Very deep
Chandra observations of a few of the brightest merger shocks have not produced
a consensus on the equilibration timescale and mechanism from the electron
temperature structure [Fig. 16, see Markevitch, 2006; Wang et al., 2018;
Russell et al., 2022]. AXIS’s large effective area will allow us to map the
detailed temperature structure in the key region close to the shock front
where equilibration models can be effectively distinguished. Secondly, the
contact discontinuity (“cold front") will be smeared if the Kelvin-Helmholtz
instability is strong at the interface (not viscous). Weakly compressible wave
features will be sharp if energy transport and viscous dissipation processes
are inefficient in cluster plasma (Fig. 17). Moreover, an assessment of the
survival timescale of jet-inflated bubbles can probe the levels of viscosity.
Third, the electron temperature gradient maps can provide information on
electron-dominated conduction [Ettori & Fabian, 2000], especially across shock
fronts. Smaller gradients and/or an electron temperature precursor (electron
temperature gradually increases from pre-shock to post-shock region) near a
shock discontinuity will imply efficient transport. These investigations can
be enabled via AXIS’s combination of high spatial resolution and large
effective area to obtain high signal-to-noise data on the scale of the
electron mean-free path.

Figure 17: Fluctuations in emission-weighted density (left) and temperature
(right) on a given plane in a 3D hydrodynamic simulation of galaxy cluster
Choudhury & Reynolds (2022). The central turbulent region is volume-filling
and contributes dominantly to isobaric fluctuations. The correlation of the
compressible fluctuations are highlighted in the zoom-in. If transport and
dissipation are inefficient in cluster plasma, these features can be sharp.
AXIS can verify the presence/absence of such spatially concentrated
compressible features. This simulation incorporates idealized isotropic AGN
feedback with injection frequency motivated by bubble dynamics in clusters.

##  7 Formation and evolution of large-scale structure

###  7.1 IGM heating by early X-ray sources

(Contributed by K. Garofali and B. D Lehmer)

Current and upcoming facilities are primed to peer back to the earliest cosmic
epochs. JWST is now observing galaxies during the epoch of reionization (EoR),
and $21\rm\;cm$ interferometers such as the Hydrogen Epoch of Reionziation
(HERA) array will soon be sensitive to signals as far back as $z\sim 27$
(Abdurashidova et al., 2022). The cosmic $21\rm\;cm$ signal is a window into
the ionization state and thermal history of the intergalactic medium (IGM),
which is sensitive to the high-energy (UV–to–X-ray) photons from the first
galaxies (e.g., McQuinn, 2016). In particular, the X-ray emission from the
first galaxies can both ionize and heat the neutral IGM, given X-ray photons’
longer mean free path. However, the timing of X-ray heating in the early
Universe depends critically on assumptions about the sources of high-energy
photons in early galaxies (e.g., Mesinger et al., 2013).

Recent theoretical models (e.g., Fragos et al., 2013; Madau & Fragos, 2017)
predict that compact luminous accreting stellar mass objects (i.e. X-ray
binaries, XRBs) would have dominated the X-ray emissivity at redshifts $z>5$,
leading to an epoch of heating (EoH) that precedes the EoR. However,
predictions for X-ray heating at $z>10$ from star-forming galaxies are based
on extrapolations of X-ray emissivity trends that are constrained only at
$z<3$, a regime where galaxies with actively accreting central engines
dominate X-ray emissivity. For XRB emission from star-forming galaxies, the
deepest existing survey fields yield direct detections in the hundreds of
galaxies out to $z\sim 1$, with further measurements of XRB radiative power
only out to $z\sim 3$ using high signal-to-noise stacks (Lehmer et al., 2016).
Therefore, we currently lack direct measurements of when XRBs begin to
dominate the X-ray emissivity, limiting our understanding of the role of XRB
feedback during key epochs in cosmic history, such as the EoH. AXIS, with its
broad bandpass, high spatial resolution that is well matched to current and
future facilities at other wavelengths, stable PSF across the FOV, and high
effective area, will directly measure the X-ray emission from star-forming
galaxies out to $z\sim 6-8$. With the nominal AXIS deep survey field,
detections of XRB emission from star-forming galaxies will number in the
thousands per redshift bin, providing a direct measurement of the redshift
evolution of XRB emissivity. In this way, AXIS will bridge the gap between
locally measured XRB power output and upcoming indirect measurements of X-ray
emission from the first galaxies at $z>10$ from $21\rm\;cm$ interferometers.

###  7.2 Protocluster structure

(Contributed by P. Tozzi)

The large-scale environment is expected to have a major influence on galaxy
evolution, particularly in so-called protoclusters (Overzier, 2016). These are
defined as overdense regions on scales of several physical Mpc at $z>2$ and
are destined to evolve into galaxy clusters with masses in the range
$10^{14}-10^{15}M_{\odot}$ by $z=0$ (Chiang et al., 2013). Gravitational
processes, coupled with the larger availability of diffuse gas at higher
densities and a high merger rate are expected to drive enhanced star formation
and a higher AGN duty cycle in protocluster galaxies, significantly affecting
their evolution. In addition, according to the hierarchical model of structure
formation, a few halos may be already virialized within the protocluster,
heating the diffuse baryons and lighting up the proto-intra-cluster medium
(proto-ICM) in emission in the X-ray band.

Many of these aspects were recently highlighted in a deep Chandra observation
of the archetypal Spiderweb protocluster (Tozzi et al., 2022a), where a high
AGN fraction of $25\pm 5$% (corresponding to an enhancement of $\sim 6$ with
respect to the COSMOS field) has been measured in members with
${\log}(M_{*})>10.5$. The current measurement of the X-ray AGN fraction in
protoclusters provides a confusing picture (see Vito et al., 2020; Polletta et
al., 2021; Tozzi et al., 2022a), presumably obscured by the diversity of
large-scale structure investigated so far. With AXIS, we will routinely probe
luminosities below $L_{[2-10\rm\;keV]}10^{43}\hbox{$\rm\;erg\rm\;s^{-1}\,$}$
and measure intrinsic absorption, iron line properties, and spectral slope in
most of the protocluster AGN. AXIS will thereby reveal whether the X-ray
nuclear emission is triggered by mergers, gas infall, or secular processes,
and ultimately constrain the AGN duty cycle as a function of local
overdensity, redshift and stellar mass of the host. In addition, the
interactions of X-ray-emitting AGN and the warm diffuse baryons across the
entire proto-ICM may explain the presence of large Ly$\alpha$ emission-line
nebulae extending across several hundreds of kpc that have been recently
discovered at high-z with integral-field unit spectrographs (Cantalupo et al.,
2014; Arrigoni Battaia et al., 2018).

Figure 18: Left: the Chandra spectrum (unfolded) of the thermal emission from
the Spiderweb Galaxy halo within $12\rm\;arcsec$ removing the AGN and jets,
from the entire exposure of $715\rm\;ks$. Solid lines show the best fit
obtained with a thermal mekal model plus the AGN contamination. Right: the
unfolded spectrum of this target from a simulated $200\rm\;ks$ AXIS
observation at the aimpoint. To account for the larger PSF, the AGN
contamination is twice that of the Chandra spectrum.

Another key scientific topic is the formation and evolution of the proto-ICM.
Thanks to Chandra, a roughly spherical ICM halo with $kT\sim 2\rm\;keV$ has
been found around the Spiderweb Galaxy (see Fig. 13 in Tozzi et al., 2022b),
clearly showing that all unresolved and diffuse components can be identified
and characterized with $\sim$ arcsec angular resolution, even in the most
complex case where thermal and non-thermal emission largely overlap due to the
presence of a bright radio galaxy. Coupling high angular resolution to the
large effective area of AXIS, particularly at soft energies, will
revolutionize protocluster studies in every aspect. In medium-deep exposures
(of the order of $200-300\rm\;ks$) with AXIS, the combination of imaging and
spectral analysis will allow us to measure the chemical enrichment of the
proto-ICM, the presence of temperature gradients, and possibly cooling flows
(that can host much larger mass deposition rates compared to those at low
redshifts), and the presence of cavities carved within the proto-ICM by
mechanical feedback. In Fig. 18, we compare the Chandra spectrum of the
Spiderweb to that expected from a $200\rm\;ks$ exposure with AXIS at the
aimpoint, finding that we can measure the average proto-ICM temperature with
an accuracy of $0.1\rm\;keV$ and the proto-ICM chemical abundance with an
uncertainty of 20% for a reference case with an average temperature below 2
keV and an average metallicity of $0.3Z_{\odot}$ at $z\sim 2$.

Many other fields of investigation are made possible by AXIS. The spectral
characterization of the nonthermal, diffuse X-ray emission from radio jets due
to inverse Compton scattering onto the photons of the cosmic microwave
background (and possibly local IR photons), allows us to directly constrain
the magnetic fields and pressure around the jets, shedding light on the
interactions between the relativistic electrons and the diffuse ICM (see
Carilli et al., 2022; Anderson et al., 2022). In addition, with AXIS’s high
spatial resolution, it will be possible to investigate the X-ray emission from
star formation in a single, strong starburst, and as an average across
protocluster galaxies. Considering that a star formation rate of
$100\hbox{$\hbox{$\rm\thinspace M_{\odot}$}\rm\;yr^{-1}\,$}$ corresponds to
$\sim 3\times 10^{-17}\hbox{$\rm\;erg\rm\;cm^{-2}\rm\;s^{-1}\,$}$ at $z=2.5$,
and that the cumulative SFR integrated over the protocluster members can
amount to several thousands, the X-ray emission from star formation can be
detected through stacking down to an average level of few
$\hbox{$\rm\thinspace M_{\odot}$}\rm\;yr^{-1}\,$ over a population of $\sim
100$ protocluster members. In this way, AXIS will map the SFR from the central
regions to the outskirts and constrain the triggering mechanisms of star
formation episodes in protoclusters (see Chiang et al., 2017). Finally, the
hot ICM in virialized halos at temperatures above $1\rm\;keV$ can be
serendipitously detected at any distance, considering that the typical surface
brightness of virialized halos does not decrease significantly with redshift
(Churazov et al., 2015). For the faintest halos, for which an X-ray spectral
analysis is not viable, it is possible to recover the temperature and the
entropy profiles by exploiting the complementarity of SZ and X-ray
observations, as demonstrated in the Spiderweb protocluster (Di Mascolo et
al., 2023, Lepore et al. in preparation).

The study of the formation, evolution, and physical properties of
protoclusters is one of the most vibrant fields in modern astrophysics and is
rapidly advancing with new state-of-the-art instrumentation, such as JWST,
ALMA, and MUSE@VLT. Furthermore, future survey missions, such as Euclid and
the Vera Rubin Observatory, will prioritize the study of protoclusters. In the
near future, these facilities will boost the number of known and well
characterized protoclusters, providing a large sample of large scale
overdensities across different epochs, with vastly different properties.

##  8 Conclusions

AXIS will be a powerful community-based X-ray observatory for the 2030s. The
unparalleled combination of arcsecond spatial resolution, high throughput, and
wide field of view will allow AXIS to capture the complete picture of feedback
from the impact zones, where stellar winds, AGN winds, and radio jets collide
with the ISM, to the widespread distribution of energy and metal-rich gas
across galaxy and cluster halos. AXIS’s low instrumental background and wide
field of view will finally permit a dramatic emergence of the cosmic web as a
vast network of soft X-ray filaments, reveal the establishment of feedback in
clusters at cosmic noon, and show us the structure of the first groups and
clusters at high redshift. AXIS’s primary science goals on galaxy evolution
and feedback address the science questions asked by the Astro2020 Decadal
‘Cosmic Ecosystems’ priority area and, as such, will have a wide-ranging
impact on the whole astronomical community. From radio jets (ngVLA, SKA) and
the multi-phase gas flows driven by feedback in galaxies and clusters
(ELT/TMT, JWST, ALMA) to the detection of massive clusters at high redshift
(CMB-S4, Simons Observatory, Rubin, Roman and Euclid), AXIS has synergies with
essentially every planned observatory for the 2030s. Companion white papers on
topics including stellar physics and exoplanets, compact object populations
and supernova remnants, transients and multi-messenger astronomy, and the
evolution of AGN demonstrate the breadth of discoveries that the AXIS probe
mission will deliver for the entire astronomical community (see the AXIS
website).

###### Acknowledgements.

We thank everyone who has contributed to the development of the AXIS Probe
mission concept. HRR acknowledges support from an STFC Ernest Rutherford
Fellowship and an Anne McLaren Fellowship from the University of Nottingham.
LAL acknowledges support by the Heising-Simons Foundation and the Simons
Foundation. This work was performed in part at the Simons Foundation Flatiron
Institute’s Center for Computational Astrophysics during LAL’s time as an IDEA
Scholar.

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