###### Abstract

The nature and origin of supermassive black holes (SMBHs) remain an open
matter of debate within the scientific community. While various theoretical
scenarios have been proposed, each with specific observational signatures, the
lack of sufficiently sensitive X-ray observations hinders the progress of
observational tests. In this white paper, we present how AXIS will contribute
to solving this issue. With an angular resolution of 1.5′′ on-axis and minimal
off-axis degradation, we have designed a deep survey capable of reaching flux
limits in the [0.5-2] keV range of approximately 2$\times$10-18 erg s-1 cm-2
over an area of 0.13 deg2 in approximately 7 million seconds (7 Ms).
Furthermore, we have planned an intermediate depth survey covering
approximately 2 deg2 and reaching flux limits of about 2$\times$10-17 erg s-1
cm-2 in order to detect a significant number of SMBHs with X-ray luminosities
(LX) of approximately 1042 erg s-1 up to z$\sim$10\. These observations will
enable AXIS to detect SMBHs with masses smaller than 105 M⊙, assuming
Eddington-limited accretion and a typical bolometric correction for Type II
AGN. AXIS will provide valuable information on the seeding and population
synthesis models of SMBH, allowing for more accurate constraints on their
initial mass function (IMF) and accretion history from z$\sim$0-10. To
accomplish this, AXIS will leverage the unique synergy of survey telescopes
such as JWST, Roman, Euclid, LSST, and the new generation of 30m class
telescopes. These instruments will provide optical identification and redshift
measurements, while AXIS will discover the smoking gun of nuclear activity,
particularly in the case of highly obscured AGN or peculiar UV spectra as
predicted and recently observed in the early Universe. _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 Surveying the onset and evolution of supermassive black holes at high-z
with AXIS Nico Cappelluti 1, Adi Foord 2 Stefano Marchesi 3,4,5, Fabio Pacucci
6,7, Angelo Ricarte 7,6, Melanie Habouzit 10,11, Fabio Vito5, Meredith
Powell2, Michael Koss8, Richard Mushotzky9, and the AXIS AGN-SWG Firstname
Lastname, Firstname Lastname and Firstname Lastname

###### Contents

  1. 1 Introduction
  2. 2 The Role of X-ray surveys in understanding the nature and the evolution of SMBHs.
    1. 2.1 Obscuration as a challenge to understand SMBH growth
    2. 2.2 High angular resolution X-ray surveys to unveil the elusive nature of High-z AGN.
    3. 2.3 The power of combining AXIS and JWST surveys
    4. 2.4 SMBH and host galaxy coevolution over cosmic time with AXIS
  3. 3 AXIS Pillar 1: Determining the Nature of SMBH Seeds with AXIS at z = 6-10 XLF
    1. 3.1 Accretion mode and signatures of the first SMBHs
  4. 4 Assembly of black holes with large-scale structures as traced by high-z AGN clustering
  5. 5 AXIS Survey of The First AGN
    1. 5.1 The AXIS wedding Cake Survey
    2. 5.2 Synergies
      1. 5.2.1 Optical Identifications
      2. 5.2.2 Photometric and Spectroscopic Redshifts
    3. 5.3 Stacking Analysis of JWST detected high-z galaxies
  6. 6 Conclusions

###### List of Figures

  1. 1 Evolution Tracks for Black Hole Seeds
  2. 2 Comparison of AXIS and Chandra Angular Resolution
  3. 3 AXIS Simulated X-ray Spectrum of High-z Highly Obscured AGN
  4. 4 The z$>$6 XLF of Light and Heavy Seeds AGN with AXIS Surveys
  5. 5 AXIS Survey Sensitivity

##  1 Introduction

The origin of the very first supermassive black holes (SMBHs) in the Universe
remains an open puzzle in astrophysics, attracting significant theoretical
attention for the past two decades. The scarcity of observational data to
address this question has added to its intrigue. Furthermore, the detection of
numerous quasars powered by SMBHs that accrete matter at both high and low
redshifts has underscored the importance of understanding their origins. It is
predicted that the remnants of the first stars would have given rise to a
population of relatively light black hole (BH) seeds during the early cosmic
epochs. However, the key question remains: What is the actual mass of these
remnants?

The reason for this puzzle is the detection of SMBHs with masses exceeding 109
M⊙ at redshifts (z) around 7 [see e.g. 32, 5, 58] and preliminary Chandra and
JWST evidence of 107 M⊙ SMBHs up to z$\sim$10 [8, 30]. These observations have
raised an intriguing paradox. The conventional mechanisms for stellar remnants
to grow into such massive SMBHs within the limited available time seem
inadequate. This inconsistency has spurred the investigation of alternative
explanations, including the presence of heavy seeds like Direct Collapse Black
Holes [DCBH, see e.g. 28, 7], remnants of relatively massive but lighter
Population III stars (POPIII), or from BH mergers in compact clusters, or
collapse of very massive stars formed through mergers of stars[57].

DCBHs are hypothesized to originate directly from the collapse of primordial
gas clouds, bypassing the conventional process of star formation. These unique
entities, formed with substantial masses from the outset, offer a compelling
explanation for the swift growth of SMBHs observed during the early stages of
cosmic history.

Figure 1: Evolution tracks for black hole seeds (light and heavy), assuming
Eddington-limited growth. The heavy seeds range between $10^{4}$ and
$10^{6}\,\rm M_{\odot}$ in initial mass, while the light seeds range between
$10$ and $100$. Seeding occurs at a typical redshift of $z\sim 25$ [6]. The
black points show the masses and redshifts of known $z>6$ quasars [18, 27,
30]. The X-ray bolometric correction is assumed to be 10%. AXIS will be able
to detect all black holes within the green-shaded area.

Likewise, remnants of POPIII stars, which are believed to have formed in
environments lacking heavy elements, may retain significant masses as they
undergo stellar evolution. Although these remnants are lighter than DCBHs,
they still have the potential to act as seeds for the subsequent growth into
supermassive entities.

In recent times, the notion of Primordial Black Holes [see e.g., 24, 11, 10]
has regained prominence as another plausible solution to the enigma of the
formation of SMBH. PBHs are black holes that might have emerged directly from
the extreme density fluctuations present in the early universe right after
inflation. If PBHs exist, they could offer a plentiful supply of massive
seeds, facilitating the rapid growth of SMBHs within the observable timespan.

The resurrection of the PBH concept, along with the consideration of DCBHs and
remnants of POPIII stars, underscores the capacity for alternative mechanisms
to explain the early formation and growth of SMBHs. These ideas challenge the
traditional paradigm and call for further theoretical investigations,
observational constraints, and potential detection methods to gain deeper
insights into the enigma surrounding the origins of supermassive black holes
in the cosmos.

In Fig. 1, we present the growth of two hypothetical SMBHs that are seeded
either from a "light" M$\sim$10-100 M⊙seed or from a "heavy" M$\sim$104-6
M⊙seed, in comparison with a collection of quasar detections at z$>$6\. The
plot is compared with the sensitivity limit of a 7 Ms AXIS observation (see
below). Assuming an indicative seed collapse at z=25, the heavy seeds are
capable of producing the observed high-redshift SMBH masses without requiring
prolonged periods of super-Eddington accretion. In contrast, if SMBHs
originated solely from light seeds, an extended phase of sustained super-
Eddington growth would be necessary. However, in the case of PBHs, these
assumptions are relaxed due to the considerably longer time available for
black hole growth or, as suggested by certain models [19, 11], the possibility
of PBHs forming with very large masses at the $e^{+}e^{-}$ annihilation phase
transition, a few seconds after the Big-Bang.

The presence of X-ray emission is widely considered to be a definitive
indicator of the existence of an actively growing supermassive black hole
(SMBH) in a galaxy, observed as an Active Galactic Nucleus (AGN). Current,
highly sensitive X-ray telescopes such as Chandra and XMM-Newton have played a
crucial role in advancing our understanding of the growth and evolution of
AGNs up to redshifts of z$\sim$4-5. Surveys conducted with Chandra have
achieved deep [0.5-2] keV flux measurements on the order of 10-17 erg s-1
cm-2, although limited to relatively small fields spanning a few square
arcminutes. This limitation is due to the rapid degradation of the Point
Spread Function (PSF) with increasing off-axis angles and the presence of
strong vignetting. On the other hand, XMM-Newton offers a more stable but
larger PSF, but having an angular resolution typically exceeding 5′′ on-axis
limiting its sensitivity due to source confusion. Moreover, Chandra’s
performance degradation has prevented it from reaching much deeper fluxes than
what it has already obtained in the CDFS [29] with a reasonable time
investment; therefore, the discovery space in the limiting flux-area space has
stalled over the last decade.

With a proposed on-axis angular resolution of 1.5′′ and an averaged Point
Spread Function (PSF) Half Energy Width (HEW) of 1.6′′ , coupled with an
effective area of 4200 cm2 at 1 keV, 830 cm2 at 6 keV, and a 24′ diameter
active field of view (i.e. $\sim$0.13 deg2), AXIS [44] is poised to be a
cutting-edge "X-ray survey machine" for the next decade. Benefitting from the
low background provided by its low Earth orbit, AXIS will surpass Chandra by
achieving depths that are one order of magnitude greater over a high-angular-
resolution area that is at least 10 times larger. The net result is an
effective grasp (number of detected sources per unit area) of the faintest
fluxes that is at least 2 (3) orders of magnitude better than that of Chandra
(XMM-Newton).

In Fig. 2, we present a simulated deep survey conducted by AXIS, allowing for
a comparison of its imaging capabilities with those of Chandra.

In this paper, we present how the proposed AXIS probe will revolutionize the
field of high-z X-ray surveys and the quest to understand the nature and
growth of SMBHs.

Figure 2:  The large image on the left displays a simulated AXIS deep 7 Ms
field. The two top right panels provide a zoomed-in view of the green area,
showcasing a comparison of the on-axis performances between AXIS and Chandra.
Within this area, an extended source has been included in the simulation to
demonstrate how AXIS can readily detect point sources embedded within diffuse
emission. The central and bottom right panels depict the yellow and red areas,
respectively. The performance of AXIS optics exhibits minimal degradation in
angular resolution even at large off-axis angles, whereas Chandra’s point
spread function (PSF) and effective area experience substantial degradation.
AXIS’s performance remains largely unaffected by the off-axis angle.

##  2 The Role of X-ray surveys in understanding the nature and the evolution
of SMBHs.

X-ray surveys have brought about a revolutionary understanding of the
evolution of supermassive black holes (SMBHs). It is now evident that in the
redshift range of approximately z$\sim$0-5, we observe a phenomenon known as
"downsizing." This implies that the highest density and volume emissivity of
the most rapidly growing, luminous, and massive SMBHs occur earlier in cosmic
time (around z=3-4) compared to the less luminous, slowly growing, or less
massive active SMBHs that dominate the Universe at z=0-1.

###  2.1 Obscuration as a challenge to understand SMBH growth

This downsizing trend is probably influenced by a combination of factors.
According to the unified model of AGN, the accretion process is frequently
concealed by a cold absorber, such as the torus or interstellar material. The
intense radiation from luminous quasars can rapidly dissociate molecules,
allowing radiation to escape rapidly. Conversely, if a SMBH accretes at a low
rate or has a lower mass, the process is prolonged, and the line of sight
remains obstructed for an extended period, delaying the clearing of the
absorber.

The observed downsizing phenomenon could be attributed to the presence of cold
absorbers, the ionizing radiation from luminous quasars, and the rate of
accretion and mass of the SMBHs themselves. Understanding these mechanisms is
crucial to unraveling the intricate processes that govern the growth and
evolution of SMBH populations throughout cosmic history.

Indeed, recent studies have revealed an intriguing trend with regard to
obscured quasars, indicating an increasing fraction of them with redshift. In
particular, most (over 75%) of the quasars at z$>$3-4 exhibit significant
obscuration due to absorbing material with column densities N${}_{H}>$1023
[e.g., 40]. These findings highlight the prevalence of heavily obscured
sources at higher redshifts which are very difficult to detect with restframe
optical or UV observations.

###  2.2 High angular resolution X-ray surveys to unveil the elusive nature of
High-z AGN.

Preliminary results from early observations with the James Webb Space
Telescope (JWST) [59] have provided valuable insights into the nature of
obscured sources. Specifically, at z=5, the number of type II sources is
estimated to be at least three times higher than previously inferred from
observations conducted by the Chandra X-ray Observatory [53]. This discrepancy
can be attributed to two primary factors.

First, the volume covered by high-resolution Chandra observations is
relatively limited, effectively constrained to the inner few on-axis
arcminutes of the survey. Consequently, these observations do not capture the
rarer, more luminous sources, potentially leading to underestimated numbers.

Secondly, these highly obscured sources are predicted to be inherently faint
in X-ray emission, with [0.5-2] keV flux levels below the detection threshold
of approximately 1-5$\times 10^{-17}$ erg s-1 cm-2. As a result, they may go
undetected in the Chandra deep X-ray surveys, further contributing to the
underestimation of their abundance.

Taken together, these factors highlight the necessity of combining
observations from different wavelengths, such as infrared (e.g., JWST) and
X-ray (e.g., Chandra or future missions like AXIS), to obtain a comprehensive
understanding of obscured sources. By leveraging the capabilities of both
telescopes, we can overcome the limitations imposed by the small volume probed
by Chandra and the faintness of highly obscured sources, thus providing a more
accurate and complete picture of the population of obscured quasars across
cosmic history.

At the same time, distinguishing highly obscured AGNs from normal star-forming
galaxies based solely on Near-Mid Infrared observations is indeed challenging,
if not virtually impossible. This difficulty arises due to the presence of
highly degenerate features shared by both star formation processes (such as
dust and narrow spectral lines) and obscured AGNs.

This similarity in features makes it extremely challenging to untangle the
true nature of a given source using only infrared observations.

To overcome this challenge and gain a more accurate understanding, a multi-
wavelength approach is crucial. Combining observations from different spectral
ranges, such as X-ray, optical, and infrared, allows for a more comprehensive
analysis. X-ray surveys, such as those conducted by Chandra or future missions
like AXIS, provide valuable information about the presence of AGN activity
through the detection of X-ray emissions associated with the accretion onto
supermassive black holes.

Furthermore, optical observations can provide insight into the presence of
broad emission lines and other AGN signatures. By integrating data from
multiple wavelengths with Near-Mid Infrared observations, a more thorough
examination of sources can be achieved, leading to more accurate
classification and differentiation between highly obscured AGNs and normal
star-forming galaxies.

Indeed, a commonly employed technique for selecting AGNs involves the use of
rest-frame (observed NIR at high-z) optical spectroscopy, typically employing
the BPT diagram. However, early results from JWST indicate that this approach
may not be as effective at high redshifts, as the spectra of AGNs at these
cosmic epochs differ from those commonly observed in the local Universe.

For example, a recent study by [30] presents the case of an AGN at
z$\sim$10.6, where an unusually bright Ne [IV] line is observed. This emission
line is atypical for AGNs [50], highlighting the distinct nature of high-
redshift AGN spectra. Additionally, a recent survey of high-redshift broad-
line AGNs using JWST has revealed a lack of [NII] emission [23]. As a
consequence, these AGNs fall within the parameter space characterized by high
[OIII]/H${\beta}$ ratios and low [NII]/H${\alpha}$ ratios, similar to galaxies
at z$\gtrsim$4 without broad-line emission. This finding suggests that the low
metallicity of their host galaxies prevents their differentiation from regular
star-forming galaxies using the BPT diagram.

However, it is worth noting that at higher luminosities, this phenomenon seems
to be less pronounced. Hence, low-mass SMBHs (on the order of 106-7 M⊙)
growing in low-metallicity, high-column-density galaxies necessitate
confirmation in the X-ray band to be definitively labeled as AGNs. X-ray
observations, such as those conducted by AXIS, can play a crucial role in
confirming the presence of AGN activity in these sources.

###  2.3 The power of combining AXIS and JWST surveys

Therefore, the distinctive spectroscopic features observed in high-redshift
AGNs, coupled with their occurrence in low-metallicity environments, pose
challenges for their identification using traditional methods such as the BPT
diagram. Complementary observations in the X-ray band are essential for
providing definitive confirmation of AGN activity in these specific scenarios.

Indeed, the combination of JWST and AXIS is of utmost importance in
comprehending the nature of galaxies hosting the first AGNs, as well as the
coevolution of supermassive black holes (SMBHs) and galaxies.

Soft X-ray surveys play a crucial role in this endeavor, as obscured AGNs,
including Compton-thick sources, exhibit peak emissivity in the 10-20 keV
energy range. At redshifts z$>$6, this peak is shifted into the [0.5-2] keV
energy range, precisely where focusing X-ray telescopes like AXIS possess
their maximum effective area, as depicted in Figure 3.

This advantageous alignment allows AXIS to detect sources that JWST may not be
able to identify as AGNs because of the relatively unbiased nature of X-ray
selection. By conducting soft X-ray surveys, AXIS can identify and
characterize obscured AGNs even in cases where they may be missed or
misclassified based on other observational criteria. This unbiased selection
is essential for a comprehensive understanding of the AGN population and its
connection to the early Universe.

The synergistic combination of JWST and an X-ray telescope like AXIS enables a
holistic view of galaxy evolution, shedding light on the intricate interplay
between SMBHs and their host galaxies. By harnessing the power of multi-
wavelength observations, we can explore the coevolutionary processes that
shape these systems throughout cosmic history.

To study SMBHs at redshifts z=6-10, it is crucial to have an observatory
capable of detecting sources with intrinsic X-ray luminosities L${}_{X}>$1042
erg s-1 , and log N(H)>23 as most of the accretion in this epoch is expected
to be obscured. The X-ray luminosities of highly obscured, Eddington limited,
M$\gtrsim$7$\times$105 M⊙, sources correspond to fluxes of approximately
1-4$\times$10-18 erg s-1 cm-2in the [0.5-2] keV energy band. Such sensitivity
levels are necessary to probe the presence and properties of rapidly growing
BHs in the high-reshift universe.

AXIS, with its designed capabilities and sensitivity, is precisely tailored to
achieve these required limits. Combined with the survey strategy outlined
below, AXIS has the potential to serendipitously detect hundreds of SMBHs at
redshifts z=6-10 and even extend the search to z$\sim$12 in the case of
pointed observations targeting pre-selected objects.

###  2.4 SMBH and host galaxy coevolution over cosmic time with AXIS

The combination of AXIS’s sensitivity to faint X-ray sources and its survey
strategy will significantly advance our understanding of the early Universe,
shedding light on the formation and evolution of SMBHs during these cosmic
epochs. By enabling the detection of a large number of SMBHs at high
redshifts, AXIS will contribute to our knowledge of the coevolution of
galaxies and their central supermassive black holes and its early onset,
providing crucial insights into the early stages of cosmic structure
formation.

Figure 3:  Simulation of a 7 Ms observation of a Compton Thick AGN with an
intrinsic luminosity of LX=2$\times$1044 erg s-1 at redshifts around 6 and 8.
AXIS will detect hundreds of counts, enabling the measurement of column
density (NH) at a significance level of 5$\sigma$. The continuous lines
represent the best fits obtained using the XSPEC MyTorus model. This level of
statistical accuracy is comparable to that achieved by NuSTAR in studying
Compton Thick AGN in the local Universe.

Studying the growth of supermassive black holes (SMBHs) from the earliest
epochs of the universe with redshifts greater than 6, through to the peak of
star formation at redshifts 1-2, is crucial for unraveling the intertwined
evolution of SMBHs and galaxies. During this period, most stars in the
universe formed, making it a pivotal phase in cosmic history.

Recent advances in our understanding of active galactic nuclei (AGNs) have
revealed that they are not constant sources of light. Instead, they exhibit
variability in their Eddington ratios on relatively short timescales,
typically less than 105-6 years [25]. As a result, it is essential to explore
the full range of accretion rates and luminosities across the entire cosmic
timeline in order to comprehensively characterize the AGN population.

Additionally, based on new JWST data of galactic systems in the redshift range
$z=4-7$, with both SMBH and stellar mass measurements available, [38] recently
found that SMBH masses are $10-100$ times higher than what the host’s stellar
mass would suggest, based on the local scaling relations. This study indicates
a significant number of yet-to-be-detected SMBHs in current JWST surveys. They
are still undetected because (i) they may be inactive (i.e., duty cycles
$1\%-10\%$), (ii) the host overshines the AGN, or (iii) the AGN is obscured
and not immediately recognizable by line diagnostics. Next-generation X-ray
missions, such as AXIS, could then play a fundamental role in uncovering this,
thus far, hidden population of sources.

This approach has been successfully implemented by [3, 4] at redshift
z$\sim$0, and future studies extending this methodology to higher redshifts
will be crucial for obtaining a complete understanding of SMBH growth and its
coevolution with host galaxies. By investigating the interaction between the
growth of large-scale structures and the accretion rates on SMBHs, profound
advances can be made in our understanding of the AGN-galaxy coevolution [e.g.,
43, 42].

By examining the intricate relationship between SMBH growth, star formation,
and structure formation across different cosmic epochs, we can gain
transformative insights into the processes that govern the coevolution of AGNs
and their host galaxies. This comprehensive understanding will contribute to
our broader knowledge of galaxy evolution and the formation of the cosmic
structures that we observe today.

##  3 AXIS Pillar 1: Determining the Nature of SMBH Seeds with AXIS at z =
6-10 XLF

The growth of SMBHs by accretion and mergers gradually erases seeding
information. However, the closer to the seeding epoch that we can probe AGN,
the closer we get to their initial masses and host galaxy relationships. The
epoch of $z\gtrsim 7$ is a special time: only at these extreme redshifts do
quasars require seeds to have grown continuously near the Eddington limit to
acquire their observed masses. This places interesting joint constraints on
the astrophysics of SMBH seeding and accretion, which grow more and more
informative as redshift increases.

Using a semi-analytical model (SAM) that integrated the SMBH assembly from
$z=20$ to $z=0$, Ricarte & Natarajan [45] simultaneously studied gravitational
wave signals, luminosity functions, and occupation fractions to search for
signatures that could be used to discriminate seeding models. This model
contrasted rare and “heavy” seeds from direct collapse with abundant and low-
mass light seeds from the remnants of Population III stars. Using empirical
relations, these seeds grow at a rate capped at the Eddington limit with a
duty cycle modulated by major halo mergers. Interestingly, the luminosity
functions of these two cases are identical for $z\lesssim 8$and down to
L${}_{X}\sim$1042 erg s-1 , where AGN behavior was determined almost entirely
by SMBH-galaxy co-evolution. However, the two cases diverge at higher
redshift, nearer to the seeding epoch, where the Eddington limit leads to very
different high-to-moderate luminosity functions. We note that there are three
major factors that determine the luminosity function at this epoch: BH masses,
occupation fractions, and accretion rates. In combination with other
facilities, AXIS will enable us to disentangle these effects.

In Figure 4, we plot the source counts predicted from Ricarte & Natarajan [45]
SAM (heavy seeds in red, light seeds in blue). We add in orange a compilation
of LF obtained from the large-scale cosmological hydrodynamical simulations of
the field [22]. The scatter at fixed Lx reflects the impact of different
seeding, BH growth, and feedback modeling in these simulations.111Values are
collected in Habouzit et al. in prep. from Horizon-AGN [15], Illustris [20],
EAGLE [49], TNG100 and TNG300 [41], SIMBA [14], and Astrid [34]. The points
with errorbars represent the combination of the proposed “Deep” and
“Intermediate” survey strategies, assuming the SAM points as true. SAM
bolometric luminosity functions have been converted to 2-10 keV assuming
bolometric corrections of Duras et al. [16] for Type II AGN and have been
additionally suppressed by an ad hoc factor of 10, assuming an extreme
Compton-thick fraction. Despite all being calibrated to eventually yield the
correct local scaling relations between SMBH mass and galaxy mass, the
cosmological simulations span a wide range, implying that additional
constraints at this epoch would help constrain the astrophysics of this epoch.
As discussed above, the two SAM curves begin to diverge at $z\gtrsim 8$, due
to the assumed Eddington limit. Since heavy seeds were initialized at higher
masses, they are able to produce AGN with higher luminosity at high redshifts
than their light seed counterparts. A measurement of the evolution of the
luminosity function during this epoch would place interesting joint
constraints on seeding and accretion. The main goal of AXIS will be to
unambiguously detect SMBH at z$>$7 to derive the XLF to inform and constrain
seeding models. This will only be possible by performing an X-ray survey with
AXIS in the region where NIR measurements with JWST and/or Roman exist or
follow-ups are possible to properly characterize the host galaxies.

So far extrapolations from population synthesis models differ of up to two
orders of magnitude from theoretical models, but even the deepest Chandra
surveys are not able to discriminate among them at $z\gtrsim 6$. In fact,
regardless of the assumed model, $<<1$ AGN is expected to be detected with
Chandra at $z>6$ with flux $<10^{-17}\,\mathrm{erg/,cm^{-2}\,s^{-1}}$, since
only $\approx 10\,\mathrm{arcmin^{2}}$ in the 7 Ms Chandra Deep Field-South
are sensitive to such emission level.

###  3.1 Accretion mode and signatures of the first SMBHs

To date, we detected more than $300$ quasars at $z>5.9$, with tens of them
already characterized by mass estimates [18]. Several confirmed detections at
$z>7$, including some recent striking observations of candidate AGN by JWST at
$z\sim$6-12 [27, 30, 26], provide us with a test bed for our models of black
hole growth.

Seeds, light and heavy, are predicted to form in the redshift range $z\sim
20-30$ [6]. Because the detection redshifts of quasars are increasing, the
time between seed formation and SMBH detection is decreasing [see, e.g. 17,
18]. The decreasing time between seeding and detection shrinks the parameter
space of seed properties [36]: initial mass, average Eddington ratio, duty
cycle, and radiative efficiency. Consequently, detecting SMBHs at very high
redshift allows us to pinpoint the properties of black hole seeds in the most
efficient way. For example, detecting a SMBH with mass $\sim
10^{10}\,M_{\odot}$ by $z\sim 9$ would exclude the entire parameter space
available for light seeds and dramatically reduce the one for heavy seeds
[36]. The detection of a more moderate case (e.g., GNz11, if confirmed, a
$\sim 10^{7}\,M_{\odot}$ at $z\sim 10$) would still provide important
constraints on the seeding mechanisms, especially if the (instantaneous)
Eddington ratio is constrained. For example, [36] shows that, in this case,
the marginal distributions for the seed mass for eight quasars already
detected at $z>7$ can already be constrained down to 2 orders of magnitude in
mass. Modeling of some of these quasars already shows a preference for heavy
seeding scenarios.

Detecting accreting SMBHs at $z>7-8$ is one of the main goals of AXIS. With
its surveys, AXIS will be able to detect low-luminosity AGN up to the highest
redshifts probed spectroscopically with JWST (see Fig. 1). By detecting X-ray
emission from these sources, a first estimate of their black hole mass will be
available, assuming accretion at the Eddington rate. This first analysis can
be complemented by follow-up observations with JWST, either with photometry
or, for sources that are sufficiently bright, with spectroscopy. This
additional information will constrain the mass and the redshift of the source.
Hence, improved modeling with those as priors will further pinpoint the
initial seed mass and the average growth rate (i.e., sub-Eddington vs. super-
Eddington) to a precision that is unreachable today with current facilities.

In the electromagnetic realm, signatures of heavy vs. light seeding can be
grouped into two categories: seed-related and host-related. Seed-related
signatures are generated from the black hole itself. Early studies (see, e.g.,
[35, 51, 46]) show that heavy seeding will lead to steep, red infrared spectra
and a bell-shaped X-ray emission peaked at $\sim 1$ keV rest-frame. While
current X-ray facilities, such as Chandra, are able to detect extremely
massive, unobscured seeds, next-generation facilities are urgently needed to
detect broader, fainter, and obscured populations. With a peak emission, at
$\sim 1$ keV, 1-2 orders of magnitude fainter, obscured populations of seeds
will remain unobserved until next-generation instruments are operative [39].
AXIS will thus play a crucial role in detecting the Compton-thick population
of heavy black hole seeds. The obscured fraction of seeds is expected to
represent the norm at such high redshifts [37].

Host-related signatures, such as the black hole-to-stellar mass ratio, are
essential in discriminating between light- and heavy-seeding models. In the
heavy seed case, the ratio is expected to remain of order unity for several
Myrs after the seeding process (see, e.g., [52]). On the contrary, in the
light seeding case, the ratio is expected to be much lower and progressively
stabilize around the local ratio of $\sim 10^{-4}$ over some Gyrs. Assuming
typical effective radii nowadays detected for $z\sim 10$ hosts, JWST will be
able to detect their infrared light and constrain their stellar mass [33, 1].
As X-ray observations are crucial both for studying the spectral energy
distribution of the X-ray emission and for estimating the mass of the SMBH,
AXIS will become the facility of reference to investigate both populations of
black hole seeds.

The X-ray spectra of AGN are also a direct tool for studying the accretion
mechanism and the properties of the accretion discs. In the redshift range
$0<z<6$ [56] reports a lack of substantial evolution of the inner accretion-
disk and hot-corona structure in QSOs. Surprisingly, recent results from [60]
show that a sample of very luminous broad-line AGN z$>$6 presents an unusually
steep X-ray spectrum with spectral index $\Gamma\sim$2.4 compared to average
$\Gamma\sim$1.9 observed at z$<6$. This points to a different physics of the
disc and the corona of the AGN at high-z which, combined with the peculiar
requirements of fast growth of the SMBH at high makes the study of the physics
of accretion at that epoch even more intriguing. AXIS will be able to study
the spectra of hundreds of AGN at z$>$6 allowing the study of accretion
physics over a much wider range of luminosities and accretion rates. Another
suggestion of [60], which cannot be currently tested because of the low count
statistics, is that these sources could instead present an unusual extremely
low-energy cutoff and a typical $\Gamma$=1.9 spectral index. AXIS with its
very large effective area will be able to produce much better spectra than
XMM-Newton at high-z and further test the accretion physics of AGN in the
early Universe.

Figure 4: The expected source counts from both semi-analytical models (SAMs)
and cosmological simulations are shown in the figure. The red and blue curves
represent heavy and light seeding scenarios, respectively, from the SAM
developed by Ricarte & Natarajan [45] (see text for more details). These
curves diverge at redshifts above 9, highlighting the different predictions
for these scenarios. The cosmological simulations compiled by Habouzit et al.
[22] exhibit a wide range of luminosity functions, underscoring the need for
additional high-redshift constraints to better constrain the models.
Additionally, at redshift 6, the 3$\sigma$ upper uncertainty on the number
counts from the X-ray luminosity function by Vito et al. [54] is shown for
reference. This uncertainty is extrapolated from observational evidence at
redshift 4, providing additional context for the expected source counts at
high redshifts.

##  4 Assembly of black holes with large-scale structures as traced by high-z
AGN clustering

A complementary way to study the growth of supermassive black holes is by
connecting them to their larger-scale dark matter environments, probed by the
spatial clustering of AGN. Together with the luminosity function, AGN
clustering constrains the relationship between black holes and their host dark
matter halos and infers any preferred cosmic environments for AGN activity.
Since the growth and evolution of halos is well understood, clustering can be
used to statistically connect SMBHs to their progenitors in the earlier
universe, which would infer how certain populations evolve over time.

The area and depth of the intermediate AXIS survey (with redshift measurements
from future multiwavelength facilities; see Section 5.2.2) would allow the
uncertainties of AGN clustering at $z\sim 3$ to be at the 10% level or better
on both the large and small scales ($0.1-10$ Mpc/h). This is an order-of-
magnitude better than the Athena ESA concept mission, and unfeasible with
current instruments. Cross-correlations with galaxies at intermediate
redshifts ($z\sim 1.5$) are predicted to provide uncertainties less than 5%.
The unprecedented clustering statistics at these epochs (especially on 1-halo
scales; $<1$ Mpc/h) would allow for measurements in several bins of AGN
luminosity, which would provide powerful constraints on AGN fueling and
feedback mechanisms at the peak of SMBH growth (e.g., determining whether or
not the majority of AGN are triggered by galaxy mergers, as well as
constraining the environmental dependence of the distribution of Eddington
ratios).

Finally, JWST will dramatically improve the characterization of the close
environments around high redshift ($z>6$) AGN, via observations of galaxy
fields around AXIS AGN of varying luminosities. This will determine whether or
not high-z AGNs reside in overdensities for a wide range of accretion rates
and mass scales. Although theory predicts that the most massive black holes at
high redshift reside in the progenitors of today’s massive clusters,
observations have so far led to conflicting conclusions, most likely due to
the limited HST sensitivity. JWST will detect high-z galaxies much more
efficiently, and together with the wide range of AGN luminosities from the
AXIS surveys, this long-standing problem will be solved.

Moreover, the clustering statistics of over-(or under-)massive SMBHs at high-z
will shed light on their seeding mechanisms, as those that originated from
DCBHs are predicted to be significantly more clustered than SMBHs formed via
other mechanisms. This is because the Lyman-Werner radiation from one DMBH
would likely trigger additional DCBHs within the same region, resulting in
highly clustered AGN statistics in the early universe. Therefore, the
clustering amplitudes of AXIS AGN will provide powerful additional constraints
on such SMBH formation models.

##  5 AXIS Survey of The First AGN

Surveys with the AXIS probe have been first simulated and discussed in
Marchesi et al. [31], to which we refer for a more detailed explanation of the
simulations. Both the Marchesi et al. [31] simulations and the ones used to
obtain the numbers reported in this paper have been performed using the Monte
Carlo code Simulation of X-ray Telescopes [hereafter SIXTE, 13]. This software
allows one to simulate an observation with an X-ray telescope by creating a
photon list, which includes the arrival time, energy, and position of each
photon based on the simulated telescope setup (i.e., effective area, field of
view, point spread function, vignetting, read-out properties, redistribution
matrix). In doing so, SIXTE generates an impact list that contains the energy
and arrival time of each photon, as well as its position on the detector. The
final event file is obtained from this intermediate list, reprocessed to take
into account the simulated detector read-out properties and redistribution
matrix file.

The input catalog we used for our simulations is based on the Gilli et al.
[21] AGN population synthesis model. AGN have been simulated down to a 0.5–2
keV luminosity L0.5-2=1040 erg s-1 and up to redshift $z=$3\. The mocks have
been checked to ensure the correct reproduction of the trends with luminosity,
redshift, and column density of the AGN densities as a function of luminosity,
redshift, and column density, and are in close agreement with the
observational evidence at all fluxes sampled by current X-ray surveys. In the
high-redshift regime (i.e., at $z>$3, where the AGN space density starts
declining), we use a separate mock catalog, built from the Vito et al. [54]
$z>$3 AGN luminosity function, which nicely describes the observational
evidence from the deepest X-ray surveys currently available up to redshift
$z\sim$5 [e.g., 55]. Finally, neither AGN nor host galaxy clustering are
included in the mock generation. The catalogs we used are available online at
http://cxb.oas.inaf.it/mock.html in FITS format and ready to be used within
SIXTE.

###  5.1 The AXIS wedding Cake Survey

Following a standard approach extensively used in past X-ray surveys, AXIS
plans to use a so-called “Wedding cake” strategy to perform its extragalactic
surveys, as follows.

  1. 1.

A deep, pencil-beam survey, that is, a 7 Ms observation of a single AXIS
pointing ($\sim$0.13 deg2).

  2. 2.

An intermediate–area, and intermediate–depth survey, which would cover 2 deg2
with an uniform, 360 ks exposure, for an overall time request of 6 Ms.

  3. 3.

Finally, while no wide–area survey is currently planned, it would be possible
to obtain an AXIS Serendipitous field by combining Guest Observer
observations. Assuming 20 Ms of GO non-Galactic plane time, with a median of
50 ks per pointing, it would be possible to cover 50 deg2 with a sensitivity
$\sim$10-16 erg s-1 cm-2.

We report in Table 1 a summary of the properties of these surveys: the number
of detections and flux limits have been obtained from end-to-end simulations
with the SIXTE tool described in the previous section. Note that in this
table, we report only the expected number of sources at z$<$6, as the model
used to generate the mocks employs a simple power-law extrapolation of
z$\sim$3-4 XLF. In the AXIS Deep Field, the 3 $\sigma$ upper boundary of the
Vito et al. [54] XLF predicts that one should detect $\sim$25 AGN in the
redshift range $z$=[6–7]; in the Intermediate Field, instead, in the same
redshift range one should detect $\sim$80 sources. In the same redshift range,
the SAM heavy seed scenario predicts $\sim$120 detections in the Deep Field
and $\sim$240 in the Intermediate Field, while the SAM light seed scenario 120
detections in the Deep Field and $\sim$230 in the Intermediate one. At higher
redshifts, as shown in Figure 4, the two SAM models diverge more
significantly, and the expected number of AXIS detections is much larger. For
example, at $z$=9 the SAM Heavy seed scenario predicts 10–12 detections in the
two AXIS fields, while the SAM Light seed scenario predicts only 1–2
detections.

Survey | Area | Tile exposure | Total exposure | Flux limit (0.5–2 keV) | Number of AGN detections
---|---|---|---|---|---
| deg2 | ks | Ms | erg s-1 cm-2 |
|  |  |  | 1 % | 20 % | 80 % |
Deep | 0.13 | 5800 | 7 | 4.5$\times$10-19 | 1.9$\times$10-18 | 4.3$\times$10-18 | 2800
Intermediate | 2 | 360 | 6 | 4.5$\times$10-18 | 1.1$\times$10-17 | 2.6$\times$10-17 | 21000

Table 1: Properties of three reference AXIS surveys simulated in this work.
The flux limits are calculated at 1 %, 20 %, and 80 % of the covered field,
and correspond to the fluxes at which which 1 %, 20 %, and 80 % of the input
sources are detected. The number of detections is computed in the 0.5–7 keV
band.  Figure 5:  The figure displays the 0.5–2,keV area-flux curves for the
AXIS Deep, Intermediate, and Wide Serendipitous surveys, as outlined in this
paper. The plotted lines represent the sensitivity curves of the surveys in
the 0.5–2,keV range, covering an area range of 20% to 80% of the survey
coverage. The light blue and pink areas indicate the parameter space covered
by the SAM heavy- and light-black hole (BH) seed models, respectively. These
areas represent the predicted range of AGN detections in the redshift ranges
of $z=[8-9]$ and $z=[9-10]$, assuming the detection of 10 AGN in each range.
As discussed in the text, the AXIS Deep and Intermediate surveys have the
potential to detect a sufficient number of sources at $z\sim 8-10$, resulting
in a significant reduction in the prediction range of the current SAM models.
For comparison, the figure also includes a yellow area representing the
parameter space covered by current X-ray surveys using Chandra, XMM-Newton,
and eROSITA. This provides context for the coverage and capabilities of these
existing surveys compared to the proposed AXIS surveys.

###  5.2 Synergies

AXIS is proposed to fly during an unprecedented epoch for extragalactic
surveys. In the early 2030s, NASA and ESA will boast an exceptional fleet of
survey satellites, while powerful ground-based telescopes will observe the
first light of the universe. JWST, having completed its first decade of
operation, will have already amassed a wealth of near-infrared to mid-infrared
photometric and spectroscopic data from various deep survey fields. Roman and
Euclid, covering a significant portion of the extragalactic sky in the visible
and near-infrared bands, will contribute to the comprehensive view of the
universe. Meanwhile, LSST-Rubin will observe the extragalactic sky with high
cadence, capturing transient and variable phenomena, while the ELT (Extremely
Large Telescope) will make its debut as a cutting-edge 30-meter class
telescope. Additionally, the SKA (Square Kilometre Array) will provide a
groundbreaking perspective of the radio sky.

Within this vibrant observational landscape, AXIS will serve as the ideal
X-ray counterpart, completing the panchromatic view of the extragalactic
universe. By harnessing its capabilities in X-ray observations, AXIS will play
a vital role in unequivocally detecting accreting objects, such as AGN and
other X-ray-emitting sources. Its synergistic partnership with the
aforementioned observatories and telescopes will allow for a comprehensive
understanding of the properties, dynamics, and coevolution of objects across
the electromagnetic spectrum. This collaborative effort will significantly
advance our understanding of the extragalactic universe and provide a holistic
view of the diverse phenomena that shape our cosmic landscape.

####  5.2.1 Optical Identifications

While X-ray emission serves as a clear indicator of accretion in galaxies, a
mere detection is not sufficient to obtain informative insights. However, due
to the high angular resolution of AXIS, we will have the ability to achieve
optical identification for more than 95% of the detected sources, as estimated
by the COSMOS-Legacy survey [12]. To accomplish this, we will rely on NIR
source catalogs from observatories such as HST, Subaru, JWST, Roman, Euclid,
and potentially the ELT.

Optical identification involves more than just positional cross-matching, as
obtaining precise source centroids is crucial. It also requires leveraging
prior knowledge of the colors and magnitude distribution of potential
counterparts. To facilitate these complex optical identifications, various
tools have been developed, including LYR and N-WAY. These tools use well-
tested Bayesian approaches to efficiently perform the intricate process of
optical identification [48, 40, 9].

By combining the X-ray detections from AXIS with accurate optical
identifications, we can establish robust associations between the X-ray
sources and their optical counterparts. This multi-wavelength approach not
only provides valuable information about the nature of the accreting objects,
but also enables detailed studies of their properties, including redshifts,
spectral features, and host galaxy characteristics. The combination of X-ray
and optical data, supported by advanced identification techniques, will
significantly enhance our understanding of the connection between accretion
processes and the larger astrophysical context.

####  5.2.2 Photometric and Spectroscopic Redshifts

To accurately measure the luminosity function of high-redshift AGNs, obtaining
their redshift information is of fundamental importance. The survey fields
targeted by AXIS will be strategically chosen in highly investigated areas of
the sky, including regions such as COSMOS, Chandra Deep Fields, JWST deep
Fields, and areas covered by either Roman or Euclid, or both.

The counterparts of high-redshift AGNs are expected to be extremely faint,
with magnitudes on the order of m${}_{AB-3.6\mu m}\sim$26-29. Preliminary
results from JWST indicate that the NIR magnitudes of the first AGN candidates
identified at redshifts z$\sim$7-10 fall within the range of 25-26. By cross-
matching these sources with AXIS data, they can be easily identified,
especially considering that the typical flux limit of deep JWST surveys is
around 29 (AB mag). In cases where optical identifications are available,
spectroscopic redshifts can be obtained either from previous JWST measurements
or through follow-up observations using JWST-NIRSPEC for fainter sources.
Spectroscopic campaigns will also be initiated using 10m and 30m class
telescopes such as Keck MOSFIRE, Subaru PFS, or the ELT. Additionally, grism
spectroscopic campaigns conducted by Roman and Euclid will provide valuable
sources of redshifts for the brightest sources with redshifts z$<$6-8.

Spectra play a crucial role in determining the masses of black holes, which is
essential for understanding the distributions of Eddington rates and tracking
the evolution of the M${}_{BH}-\sigma$ relation. By obtaining spectroscopic
information, AXIS, in conjunction with other observatories and telescopes,
will contribute to advancing our knowledge of the masses of black holes in
high-redshift AGNs. This, in turn, will enable detailed investigations into
the accretion processes and the relationships between black hole masses and
the properties of their host galaxies.

To assemble an even larger sample of redshift measurements, photometric
redshifts (Photo-z) will be relied upon. Photo-z has become a well-established
technique to determine the redshifts of AGNs [47, 2]. The abundant amount of
ancillary photometric data available from NIR surveys will enable precise
measurements of Photo-z. Using this photometric information, we can obtain
high-quality estimates of redshifts for almost all sources detected in the
survey.

The Photo-z measurements can be effectively employed in determining the X-ray
luminosity function (XLF). The sources can be distributed across the redshift
range based on their associated probability density functions, allowing for a
comprehensive determination of the XLF [e.g., 2]. This approach enables us to
derive statistical information about the AGN population and its evolution over
cosmic time.

As a valuable by-product of this work, we will obtain measurements of the
Spectral Energy Distribution (SED) for all sources. The SEDs provide crucial
insights into the host properties of AGNs, including stellar mass, gas mass,
extinction, and indirectly the black hole mass and Eddington rates. By
analyzing the SEDs, we can gain a deeper understanding of the physical
characteristics and compositions of the host galaxies, shedding light on the
intricate interplay between the central supermassive black hole and its
environment.

Through the utilization of photometric redshifts and the comprehensive
analysis of SEDs, AXIS will significantly contribute to the study of AGN
populations, their properties, and their coevolution with host galaxies. This
approach will provide valuable information to advance our understanding of the
growth and dynamics of supermassive black holes across cosmic time.

###  5.3 Stacking Analysis of JWST detected high-z galaxies

The strategic stacking of X-ray images at locations of known galaxies offers a
remarkable increase in sensitivity. This approach provides a powerful means to
investigate the average properties of a population that may otherwise be
challenging to study individually. An illustrative example of the efficacy of
this technique was demonstrated by [55], who stacked X-ray signals from HST-
selected massive galaxies at redshifts of 4-5 using the 7 Ms CDFS (Chandra
Deep Field South). Using this method, they achieved effective exposure times
of approximately 109 s, exceeding Chandra’s capabilities, and successfully
detected the cumulative X-ray signal up to redshifts around 5.

Considering a short AXIS exposure of 50 ks in regions covered by JWST,
assuming a magnitude limit of 28th at 7 $\mu$m, it is estimated that the
expected source density would be on the order of 20000 deg-2. If 1% of these
sources are AGN, statistically significant fluxes on the order of
5$\times$10-19 erg s-1 cm-2can be achieved. At a redshift of approximately 4,
this corresponds to luminosities of around 1041 erg s-1 . In the deep fields,
AXIS will reach even deeper flux levels, although the scaling with exposure
time is not linear because of the transition from being photon-limited to
being background-limited at such depths. This capability will enable AXIS to
study populations of very faint sources detected by JWST, extending
investigations to redshifts well beyond 10.

By employing the stacking technique and leveraging the synergistic
observations with JWST, AXIS will significantly contribute to our
understanding of the high-redshift universe and the properties of faint AGN
populations. This combined effort will push the boundaries of knowledge,
enabling investigations into the early stages of galaxy and black hole
formation and evolution.

##  6 Conclusions

In this white paper, we have thoroughly explored the necessity and potential
of AXIS in investigating the early accretion of supermassive black holes
(SMBHs) in the universe. Specifically:

  * •

AXIS will measure the X-ray Luminosity Function (XLF) of AGN up to redshifts
around 10, providing crucial insights into their evolution over cosmic time
with its deep and intermediate surveys in combination with ancillary
information from JWST, Roman, Euclid, LSST-Rubin, and the ELT. With the XLF,
AXIS will inform and constrain models of SMBH seeding, potentially helping to
distinguish between scenarios where they grow from light or heavy seeds.

  * •

AXIS will significantly expand the current flux-area parameter space of X-ray
surveys, covering a range of 0.13-2.5 deg2, and reaching much fainter fluxes.
This, coupled with the constant Point Spread Function (PSF) across the field
of view, will result in a leap forward in survey grasp, achieving a two-order-
of-magnitude improvement compared to Chandra.

  * •

AXIS will play a crucial role in determining the nature of high-redshift
galaxies observed by JWST that exhibit characteristics typical of star-forming
galaxies (SFGs), aiding in their classification as AGN in particular in the
case of highly obscured and low-metallicity sources.

  * •

The excellent angular resolution of AXIS will facilitate clear identification
of X-ray sources with NIR detections, enabling comprehensive studies of their
Spectral Energy Distributions (SEDs) and spectral features.

  * •

With access to a wealth of ancillary data, AXIS will enable the study of the
onset and evolution of galaxy-SMBH coevolution.

  * •

The high source surface density observed by AXIS will allow for the
characterization of the coevolution of early AGN with their environments
through clustering studies. It will also enable investigations into the
environment of individual high-redshift quasars.

  * •

Leveraging the low background and exceptional angular resolution, stacking
AXIS images at the positions of very faint JWST sources will facilitate the
study and constraint of the AGN population, potentially extending to redshifts
beyond 10 and probing low-luminosity (black hole mass) sources at lower
redshifts.

This white paper, along with the entire series, emphasizes the crucial and
unparalleled importance of adopting a high-angular-resolution X-ray telescope
such as AXIS as a key instrument for studying the Universe in the early 2030s.
AXIS, a remarkable X-ray survey machine building upon the legacy of Chandra,
will surpass the achievements of its predecessor and push the boundaries of
black hole exploration into new and uncharted territories.

###### Acknowledgements.

We kindly acknowledge the entire AXIS team for outstanding scientific and
technical work. This work is the result of several months of discussion in the
AXIS-AGN SWG. NC thanks the University of Miami for support during the
proposal and this paper writing phase. no multiple yes

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11institutetext: Colorado State University, Fort Collins CO 80523, USA

# Automated Code Extraction from Discussion Board Text Dataset

Sina Mahdipour Saravani 11 0000-0003-4285-1439 Sadaf Ghaffari 11
0000-0002-2413-5829 Yanye Luther 11 0000-0002-0995-3356 James Folkestad 11
0000-0003-0301-8364 Marcia Moraes 11 0000-0002-9652-3011 {sinamps,
sadaf.ghaffari, yanye.luther, james.folkestad<EMAIL_ADDRESS>
###### Abstract

This study introduces and investigates the capabilities of three different
text mining approaches, namely Latent Semantic Analysis, Latent Dirichlet
Analysis, and Clustering Word Vectors, for automating code extraction from a
relatively small discussion board dataset. We compare the outputs of each
algorithm with a previous dataset that was manually coded by two human raters.
The results show that even with a relatively small dataset, automated
approaches can be an asset to course instructors by extracting some of the
discussion codes, which can be used in Epistemic Network Analysis.

###### Keywords:

Code extraction Topic modeling Unsupervised learningAutomated topic
extraction.

##  1 Introduction

Epistemic Network Analysis (ENA) has been used as an analysis technique in
several different domains such as health care [29], educational games [4], and
online discussion [22]. Recently, some researchers started to use ENA as a
learning analytics visualization to support participatory Quantitative
Ethnography (QE) [28] and instructor’s assessment of student’s participation
in online discussions [18]. In that work, researchers presented the use of ENA
as a tool to visualize connections among the codes that were discussed in the
online discussion boards to assist instructors in assessing those discussions.
Two human annotators manually coded the text data.

Based on the study presented in [18], we submitted a project proposal to our
university’s teaching innovation grant to examine the use of ENA as a
visualization tool. One feedback provided by the reviewers was that
instructors would not have time to be involved in the coding process, even if
that process used nCoder [15]. The reviewers pointed out that they would like
to have access to the visualization but not have the “burden” to build the
codes. However, they would be willing to provide keywords that should be
present in the codes. Considering that feedback, we decided to apply text
mining and Natural Language Processing (NLP) algorithms to automate the
extraction of codes from data and use the keywords that were provided by the
instructors as guiding input to the algorithms. NLP has been applied to
various applications [9, 30] and has improved drastically with deep learning
[23, 24, 25], motivating us to exploit it in this educational application.

We developed three text mining systems based on Latent Semantic Analysis,
Latent Dirichlet Analysis, and Clustering Word Vectors to examine their
capabilities for this task and determine the one that produced the best
results. We compared the codes that were previously manually coded and
validated by human coders in [18] with the outputs from the automated systems.

Previous work [1] on comparing coding from human raters and automatic
algorithms found that the topic modeling algorithm was only compared with
human coders for broad topics and that additional domain knowledge is
necessary to identify more fine-grained topics. Similarly, another work [5]
examined how keywords from codes manually extracted were presented in topics
generated from topic modeling. It found that top keywords of a single topic
often contain words from multiple manual codes. Contrarily, words from manual
codes appear as high-probability keywords in multiple topics. It is important
to notice that both studies used large datasets to run their topic modelling
algorithms. Our study is different in the sense that we have a relatively
small dataset (section 1.2). We will consider the findings from both previous
works and will discuss how those are present in our work.

In this paper, we present a set of potential solutions to automatically
extract codes from discussion data. We also propose detailed modifications to
previously incorporated methods as a way to overcome the limitation of working
with a small dataset. This is a challenging problem since there is no accurate
mapping between this task and the well-defined tasks in Natural Language
Processing (NLP) and Information Retrieval. This results in a lack of solid
prior studies on the topic. We demonstrate that even with a small dataset,
automated approaches can be an asset to course instructors by extracting some
of the discussion codes. Further, instructors can provide input to the
algorithms to guide them towards better results.

###  1.1 Research Questions

Considering the particularity of our study regarding the use of a small
dataset, we aim to answer the following research questions:

  * •

RQ1: Are Latent Semantic Analysis, Latent Dirichlet Analysis, and Clustering
Word Vectors algorithms able to extract the codes previously coded by [18]?

  * •

RQ2: What are the limitations of each algorithm?

###  1.2 Dataset

Our dataset consisted of online discussion data from seven semesters (Fall
2017, Fall 2018, Fall 2019, Spring 2020, Fall 2020, Spring 2021, Fall 2021)
from an online class for organizational leaders as part of a Masters of
Education program at a Research 1 land-grant university. The dataset has 2648
postings. This dataset was provided to us by Moraes and colleagues [18]. The
codebook established after meeting with Moraes and colleagues consists of the
“a priori” codes presented in Table 1.

Table 1: Codebook Code Name |  Definition |  Kappa
---|---|---
Retrieval practice, Spacing out practice, Interleaving |  Retrieval practice is the act of recalling facts or concepts or events from memory. The use of retrieval practice as a learning tool is known also as testing effect or retrieval-practice effect. Spacing out practice allows people to a little forgetting that helps their process of consolidation (in which memory traces are strengthened, given meaning, and connected to prior knowledge). Interleaving the practice of two or more concepts or skills help develop the ability to discriminate later between different kinds of problems and select the better solution. |  0.85
Elaboration |  Elaboration is the process of giving new material meaning by expressing it in your own words and making connections with your prior knowledge. The more connections you create, the easy will be to remember it in the future. |  0.79
Illusion of mastery |  Researches have pointed out that students usually have a misunderstanding about how learning occurs and engage with learning strategies that are not beneficial for their long-term retention, such as rereading the material several times and cramming before exams. When we got familiar with some content due to fluency in reading it, we create an illusion of mastering that content. |  0.89
Effortful learning |  Learning is deeper and more durable when it is effortful, meaning that efforts, short-terms impediments (desirable difficulties), learning from mistakes, and trying to solve some problem before knowing the correct answer makes for stronger learning. |  0.85
Get beyond learning styles |  There is no empirical evidence of the validity of learning styles theory in education. Researchers found that when instructional style matches the nature of the content, all learners learn better, regardless of their learning styles. |  0.86

##  2 Related Work

Previous works such as [5] in the context of topic modelling mostly deal with
using nCoder. Although nCoder is a popular learning analytic platform used to
develop a coding scheme, it is not fully automated. In other words, it
requires human in the loop to read through the text and validate if the coding
is appropriate. nCoder+ [6] is another work in the direction of nCoder. This
work specifically discusses an improvement to nCoder through semantic
component addition to the nCoder process. This paper contributes to finding
false negatives in the current nCoder version. Furthermore, as mentioned by
authors of nCoder+, the idea is just a prototype and is not a public tool yet.
A very recent work by Cai et. al [5] centers around nCoder as well. They
investigate how close human created codewords are to topic models in large
text documents. They also discuss whether the top keywords in topics match
human codewords. There are distinct aspects between our work and others.
First, we mainly take advantage of NLP approaches and compare three different
unsupervised learning techniques to automate the topic extraction in our
relatively small text documents. Second, we utilize coherence analysis as a
way to determine the optimal number of topics in our text discussion data.
Interestingly, in the context of our data, the established number of topics is
same as our acquired ground truth information from course instructors. In
Section 3, we provide the details of our techniques for topic extraction.

##  3 Methods

For mining topics from our textual data, we begin our analysis with applying
Latent Semantic Analysis (LSA) [13] to our discussion data. We then present
two methods for automatic code extraction from text data. The first method
follows the efforts of previous researchers and is based on Latent Dirichlet
Allocation (LDA) topic modeling [2]. The second method uses K-means [14] to
cluster word embeddings. Both of these methods provide a way for the expert
user to guide the automated learning process. Further details are provided in
the following sub-sections.

###  3.1 Shared Preprocessing for All Algorithms

Preprocessing is highly important in NLP tasks that are based on the bag of
words modeling of the text where the order of words in the sentences is
ignored and a sentence is considered a bag of its words. Since our target task
entails the retrieval of codes – in contrast with classification tasks like
[25] – and the best outcome is to retrieve each of them in a uniform written
form, such preprocessing steps are critical for better performance. Stop
words, for example, do not carry any information that is useful for our task.
Named-entity categories such as the name of authors and dates are also not
relevant to the codes. We performed the following preprocessing steps that
improved our experimental results. All of these steps, except the last one,
are also applied in the word embedding method. The term document refers to a
post in our online discussion board dataset.

  * •

Tokenization. We use the simple_preprocess from GENSIM [20] to tokenize the
text using a regular expression from Python regex package.

  * •

Lowercasing. We lowercase all words for uniformity and normalization of
various writing styles and arbitrary capitalization.

  * •

Stop word removal. Stop words do not contribute to codes and their removal
would allow the algorithms to focus on useful words.

  * •

Applying minimum word length. We assume that words with a length less than 3
characters in the English language do not contain useful information.

  * •

Irrelevant text removal. We remove non-breaking space (NBSP), roman numerals,
numbers, and URLs using regular expressions since these components do not
contribute to the codes.

  * •

Named-entity removal. Names of the students, authors, or books are not
relevant to codes. After preliminary experiments, we concluded that they
confuse the algorithms. We use SpaCy [12] to remove all tokens that are
recognized as the name of a person or a work of art.

  * •

In-document frequency filtering. Words that very rarely appear or are very
frequent are not likely to be codes. We removed words that occur only in one
single document. We also removed words that occur in more than 10% of the
documents.

  * •

Generating bigrams and trigrams. Since we are interested in code terms that
contain more than one word – e.g. the code term “interleaved practice” – we
extend the list of tokens in each document with its bigrams and trigrams:
consecutive two and three words [8].

In our second proposed method, clustering word vectors: fastText + K-means, we
do not consider bigrams and trigrams due to the lack of a natural operator to
represent two or three single word vectors as a single vector of the same
dimension. We leave further explorations of this path to future work.

###  3.2 Code Extraction Algorithms

One potential solution to the problem of code extraction, following the
related work [5], involves using topic modeling algorithms. Another potential
solution involves using word embedding vectors and clustering algorithms. We
present a brief introduction to these algorithms and explain how we use them
to discover the different topics of discussion in the class. Further, we
provide qualitative comparisons between them for our objective.

####  3.2.1 Latent Semantic Analysis (LSA)

is a technique discovering statistical co-occurrences of words which appear
together and provide further insights to the topic of words and documents. In
this approach, a term-document matrix is formed from documents. The rows, in
this matrix, are individual words and columns are documents. Specifically, the
entries in a term-document matrix contain the frequency which a term occurs in
a document. Singular Value Decomposition (SVD) is applied to the Term-Document
matrix. As a result of applying SVD, we get the best k-dimensional
approximation to the term-document matrix. The similarities among the entities
in the lower dimension space are computed.

####  3.2.2 Latent Dirichlet Analysis (LDA)

is a generative probabilistic model in the context of NLP which represents
documents over latent topics. These topics are each a distribution over words.
The main assumption in topic modeling is that documents discuss the same topic
if they use the same or similar set of words. Topics in LDA act as a hidden
intermediate level between documents and words. This provides a path to
dimensionality reduction, where a large matrix of association between all
documents and words is broken into two matrices: one between documents and
latent topics, and one between the latent topics and words [10, 26]. Being
built upon the probabilistic latent semantic indexing (pLSI [11], LDA
overcomes some of the shortcomings of pLSI. The pLSI has no natural way to
assign a topic probability to an unseen document since it only learns a topic-
document distribution for documents it has seen in its training. This is due
to the use of a distribution that is indexed by training documents. Growth of
pLSI’s number of parameters with the number of documents also makes it prone
to overfitting. Both of these limitations are resolved in LDA by using a
parameterized hidden random variable as a topic-document distribution which is
not explicitly linked to training documents.

LDA and the task of topic modeling for automated code extraction benefits from
the separation of documents. The separation of documents is actually inherent
in our target task. We intend to i) know what codes are covered in each
discussion post, i.e. in each document, and ii) extract all codes that have
appeared in all discussions. Hence, the separation of documents provides
useful information for our objective.

After preprocessing, we create a LDA topic model over our aforementioned
dataset (Sec. 1.2). We experiment with three variations: without bigrams and
trigrams, with bigrams and trigrams, and with bigrams and trigrams where prior
topic-word distribution is modified. The first two variations are self-
explanatory. The third variation introduces the notion of a human user
providing some codes or keywords in an input file to the program that are
likely to be discussed in the course. We assume a constant topic for all
keywords that are provided in a single line in the input file. For all
keywords in a line, we assign a higher probability of belonging to that
arbitrary constant topic compared to all other words in the dataset. We
currently use a hyperparameter value (keywords_total_probability) to divide
over the number of keywords and assign it to each of them. Thus, the
probability for each keyword-topic pair is:

$p(k_{t},t)=\frac{\textit{keywords\\_total\\_probability}}{n_{k_{t}}}.$ (1)

For the rest of the words, the probability for that topic is the following
uniform value,

$p(w,t)=\frac{(1-\textit{keywords\\_total\\_probability})}{(n_{w}-n_{k_{t}})},$
(2)

where $n_{w}$ is the number of words in the whole dataset and $n_{k_{t}}$ is
the number keywords that user has provided for the arbitrary topic t. $k_{t}$
is a provided keyword for topic $t$.

In case there are topics that the user has not provided any keywords for, the
word-topic probability is

$p(w,t)=\frac{1}{n_{w}}.$ (3)

Although our experiments had a limited volume of data, this mechanism does not
provide a significant improvement but provides a natural way to optionally use
human expert knowledge in the code extraction process using LDA. We implement
this mechanism using the eta parameter of GENSIM’s LDA implementation.

####  3.2.3 Clustering Word Vectors: fastText + K-means

is another method which we present here as a potential solution to the code
extraction problem. This approach is based on the idea of clustering
algorithms. Although the code retrieval process is not evident, we propose a
heuristic for that. The first requirement for clustering is representing the
words in vectors. However, bag of words modelling is not sufficient here, as
the clustering algorithm, being an unsupervised algorithm, only captures the
already-present distinguishing characteristics of data rather than learning
new features. Hence, the word vectors need to carry useful information for the
latter use of the clustering algorithm. Exploiting the syntactic and semantic
information contained in pre-trained word embedding vectors, which have
successfully improved the accuracy on many NLP tasks [16, 3, 19, 7], is a
natural choice. To further handle out-of-vocabulary words that have not been
observed in the pre-training process, we use fastText [3] word embeddings,
which is a character-level word representation model. This ensures that even
uncommon words that are discussed in a specific expert course would have
appropriate vector embeddings. After preprocessing, we convert all of the
words in the dataset to their embedding vectors. Unfortunately, in this step,
we lose the information about which documents each word appeared in, which is
a limitation of this approach. Next, we use the K-means clustering algorithm
[14] to create groups of semantically and syntactically relevant words.

Word embedding models are pre-trained on huge amounts of digital text to learn
the co-occurrence statistics of words. This pre-training objective results in
a projection of syntactically and semantically relevant words to a close
proximity in the resulting vector space. Furthermore, these word vectors have
an interesting behaviour against addition and subtraction operators where they
prove capable of learning some relationships among words. For example, the
arithmetic operation Paris - France + Italy equals Rome [16].

For the retrieval of words that represent each cluster, we utilize cluster
centroids. We find the five closest word vectors to the center of each cluster
and retrieve their words as the extracted codes. The closeness measure is the
cosine similarity function. While this mechanism extracts interesting words,
it has some limitations. The distance from cluster centroids does not
necessarily imply irrelevance. Some code words may be closely related to two
topics and far from the center of both associated cluster; hence, they would
not be retrieved in either of the clusters. On the other hand, there is no
reason to believe that the code words would appear in the center of the
clusters.

For an analogous use of human expert input, the program accepts the same
aforementioned keywords file. Here the input keywords, if present, are used to
initialize the K-means cluster centroids. First, all words in a single line of
the keywords file, which are assumed to represent one code, are converted to
their respective fastText word embeddings. Then they are averaged and used as
the initial center for one arbitrary cluster. During the training process of
K-means, they are updated to fit the dataset. Generally, K-means algorithm
without specific initialization is run multiple times with random
initialization to find the best final convergence. However, since we
specifically initialize all or some of the centroids using the keywords file,
this variation of our implementation would execute K-means only once. In this
case, it is reasonable to expect the code words to appear at the center of the
clusters. This mitigates the aforementioned concern about the centers being
ill-defined in terms of representing the actual codes, and further provides
more computational efficiency by avoiding redundancy [24, 23].

The most important limitation of this approach is that the information about
document boundaries and what words are contained is what documents are lost.
While benefiting from the knowledge that is transferred from the pre-training
of the word embedding model, this method treats the whole dataset merely as a
dictionary of words.

##  4 Experimental Results

In order to answer the research questions we posed, we conducted experiments
with the three aforementioned algorithms. To extract the topics from our
discussion data, we were interested to find the optimal number of topics for
our approach. Therefore, we conducted a topic coherence analysis [21] to
achieve our aim. Given that text mining algorithms are in the category of
unsupervised learning approaches, coherence analysis is considered an
important measure as it gives structure to inherently unstructured textual
data. Furthermore, it assesses the topics’ quality and the coherence of words
within each topic or cluster. The results in Table 2 indicate the optimal
number of clusters is five. Therefore, we present ten words from each of the
five topics for respective algorithms. The extracted topics from the Latent
Semantic Analysis, Latent Dirichlet Allocation, and Clustering Word Vectors
algorithms are demonstrated in Tables 3, 4, and 5 respectively.

Table 2: Coherence Score for Various Number of Topics. No. Clusters |  Coherence Score
---|---
2 |  0.2851
3 |  0.2915
4 |  0.2944
5 |  0.5017
6 |  0.3776
7 |  0.4071
8 |  0.4067
9 |  0.3427
10 |  0.3773
Table 3: Extracted Topics from Latent Semantic Analysis

Topic 0 |  Topic 1 |  Topic 2 |  Topic 3 |  Topic 4
---|---|---|---|---
learn |  practice |  practice |  memory |  memory
practice |  learn |  forget |  forget |  difficulty
author |  mass |  mass |  train |  desire
think |  author |  lecture |  difficulty |  train
memory |  time |  inform |  practice |  example
time |  memory |  think |  desire |  story
wait |  retrieve |  learn |  example |  mindset
inform |  forget |  understand |  mass |  deliberation
knowledge |  like |  surgeon |  learner |  growth
skill |  train |  solution |  help |  plf*

  * •

∗Stands for Parachute Landing Fall.

Table 4: Extracted Topics from Latent Dirichlet Allocation Topic 0 | Topic 1 | Topic 2 | Topic 3 | Topic 4
---|---|---|---|---
lecture | desire | dylexia | confidence | mass
solution | desire_difficuty | learn_style | feedback | mass_practice
classroom | plf | individual | calibration | interleaving_practice
surgeon | resonate | learn_differ | confidence_memory | space_retrieval
acquire | parachute | disable | accuracy | tend
instruct | fall | intelligent | peer | day
learn_learn | land | prefer | answer | long_term
impact | jump | support | event | week
demand | parachute_land | dyslex | state | myth
lecture_classroom | land_fall | focus | calibration_learn | practice_space
Table 5: Extracted Topics from fastText + K-means Topic 0 | Topic 1 | Topic 2 | Topic 3 | Topic 4
---|---|---|---|---
aspects | teacher | merely | pull | just
concepts | girl | simply | off | even
strategies | college | seemingly | down | know
perception | american | consequently | sticking-out | think
knowledge | school | ostensibly | underneath | going
understanding | juniour | essentially | divits | get
implications | teacher | evidently | loose | thought
analysis | baylee | being | stick | really
approach | mom | therefore | rope | come
methodology | student | rather | sideways | but

To answer RQ1 and RQ2, we presented these results to Moraes and colleagues.
Through qualitative analysis they determined that the outputs from LSA and LDA
could extract some of the codes previously coded, but Clustering Word Vectors
did not capture any code. They mentioned that the best code words are captured
by the presented LDA algorithm where 4 of the 5 codes from the manual
annotation have been extracted. In Table 4, Topic 1 code words were related to
_Effortful learning_ code, Topic 2 code words were related to _Get beyond
learning styles_ , Topic 3 code words were related to _Illusion of mastery_ ,
and Topic 4 code words were related to _Retrieval practice_ , _Spacing out
practice_ , and _Interleaving_. Only Topic 0 did not represent any one of the
codes. It is important to note that the _Elaboration_ code, not present in any
topic, had the lowest kappa between the two human coders (Table 1), meaning
that even between human raters it wasn’t an easy code to agree upon. Our
results corroborate what was found in [1], as the topic modeling algorithm
could only find broad topics. Assess whether that is enough, in terms of
accurately predicting codes in the remaining of our dataset, is something that
still needs to be examined.

Our LSA results present the same limitations found by [5] work. As we can
observe in Table 3, extracted code words of a single topic often contain words
from multiple manual codes and words from manual codes appear as keywords in
multiple topics.

Analyzing the extracted topics from the fastText + K-means algorithm, Topic 2,
Topic 3, and Topic 4 in Table 5 are not actual codes. Topic 2 seems to contain
only adverbs. As we expected and discussed this in Section 3.2, the pre-
training process of the word embedding models (fastText) causes the vector
space to have syntactically similar words positioned in a close proximity –
the semantic closeness is not the only positioning objective of the pre-
training process. As a result, the clustering algorithm (K-means) groups such
words in a cluster. This is undesirable for the purpose of extracting codes.
We discuss a potential solution to this problem in Section 5.

##  5 Conclusion and Future Directions

The goal of this study is to investigate the capabilities of Latent Semantic
Analysis, Latent Dirichlet Analysis, and Clustering Word Vectors to
automatically extract codes from a relatively small discussion dataset. As
previously stated, this is a challenging problem due to a lack of solid prior
studies on the topic.

As observed in the experiments, LDA was the best approach and further
examinations will be done in order to assess the prediction capabilities for
the remaining dataset. The use of non-contextualized word embeddings, such as
fastText (the third presented method (clustering word vectors)) results in
some clusters containing only syntactically relevant words – Topic 2 in Table
5. However, syntactic similarity of words may not be necessarily useful in our
target task of extracting codes because of the pre-training objective of the
word embedding model. One possible solution is to use recent contextualized
word embeddings such as BERT [7] as a substitute. Their word representation
vectors are much richer in linguistic information and have been pre-trained to
attend to important tokens in a text [27]. Such models also open up
opportunities to keep the word-document information, as they are designed to
use the context to generate the word vectors. However, due to their dynamic
nature, the retrieval process is not trivial.

Another possible solution is exploiting the LDA2Vec model for code extraction.
As mentioned in Section 3.2, both the topic modeling and the clustering word
embeddings have their advantages and disadvantages. To gain benefits from
both, we intend to conduct experiments with LDA2Vec. Many advances in NLP
focus on improving machines in processing text, while LDA2Vec aims to
automatically extract information that is useful to from a large volume of
text [17]. The LDA2Vec model is a modified version of the skip-gram word2vec
model, where in addition to the pivot word vector a document vector is also
exploited to predict the context, a modified architecture and pre-training
objective. This makes LDA2Vec capable of capturing document-related
information as well as word information. Since word vectors, document vectors,
and topics are learned at the same time, they would be linked to each other
and contain inherent information about the others.

Despite the limitations presented in this study which corroborates the
findings of previous works [1, 5], we demonstrate that even with a relatively
small dataset, automated approaches can be an asset to course instructors. Our
intention is to incentivize further discussions on how text mining algorithms
can be used to extract codes, even from relatively small datasets.

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