# High-Spectral Resolution Observations of the Optical Filamentary Nebula in
NGC 1275

Benjamin Vigneron Département de Physique, Université de Montréal, Succ.
Centre-Ville, Montréal, Québec, H3C 3J7, Canada  Julie Hlavacek-Larrondo
Département de Physique, Université de Montréal, Succ. Centre-Ville, Montréal,
Québec, H3C 3J7, Canada  Centre de recherche en astrophysique du Québec (CRAQ)
Carter Lee Rhea Département de Physique, Université de Montréal, Succ. Centre-
Ville, Montréal, Québec, H3C 3J7, Canada  Centre de recherche en astrophysique
du Québec (CRAQ)  Marie-Lou Gendron-Marsolais Instituto de Astrofísica de
Andalucía, IAA-CSIC, Apartado 3004, 18080 Granada, España  Jeremy Lim
Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong
Jake Reinheimer  Department of Physics, University of North Texas, Denton, TX
76203, USA  Yuan Li Department of Physics, University of North Texas, Denton,
TX 76203, USA  Laurent Drissen Département de physique, de génie physique et
d’optique, Université Laval, Québec (QC), G1V 0A6, Canada  Centre de recherche
en astrophysique du Québec (CRAQ)  Department of Physics and Astronomy,
University of Hawai’i at Hilo, Hilo, HI 96720, USA  Canada-France-Hawaii
Telescope, 65-1238 Mamalahoa Hwy, Kamuela, Hawaii 96743, USA  Greg L. Bryan
Department of Astronomy, Columbia University, 550 West 120th Street, New York,
NY 10027, USA  Center for Computational Astrophysics, Flatiron Institute, 162
5th Avenue, New York, NY 10010, USA  Megan Donahue Department of Physics and
Astronomy, Michigan State University, East Lansing, MI 48824, USA  Alastair
Edge Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
Andrew Fabian Institute of Astronomy, University of Cambridge, Madingley Road,
Cambridge CB3 0HA, UK  Stephen Hamer Institute of Astronomy, University of
Cambridge, Madingley Road, Cambridge CB3 0HA, UK  Thomas Martin Département de
physique, de génie physique et d’optique, Université Laval, Québec (QC), G1V
0A6, Canada  Centre de recherche en astrophysique du Québec (CRAQ)  Michael
McDonald Kavli Institute for Astrophysics and Space Research, MIT, Cambridge,
MA 02139, USA  Brian McNamara  Department of Physics and Astronomy, University
of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada
Annabelle Richard-Lafferrière Institute of Astronomy, University of Cambridge,
Madingley Road, Cambridge CB1 0HA, UK  Laurie Rousseau-Nepton Canada-France-
Hawaii Telescope, 65-1238 Mamalahoa Hwy, Kamuela, Hawaii 96743, USA  G. Mark
Voit Department of Physics and Astronomy, Michigan State University, East
Lansing, MI 48824, USA  Tracy Webb Department of Physics, McGill Space
Institute, McGill University, 3600 rue University, Montreal H3A 2T8, Canada
Norbert Werner Department of Theoretical Physics and Astrophysics, Faculty of
Science, Masaryk University, Brno, Czech Republic

###### Abstract

We present new high-spectral resolution observations (R =
$\lambda/\Delta\lambda$ = 7000) of the filamentary nebula surrounding NGC
1275, the central galaxy of the Perseus cluster. These observations have been
obtained with SITELLE, an imaging Fourier transform spectrometer installed on
the Canada-France-Hawai Telescope (CFHT) with a field of view of
$11\text{arcmin}\times 11\text{arcmin}$ encapsulating the entire filamentary
structure of ionised gas despite its large size of $80\text{kpc}\times
50\text{kpc}$. Here, we present renewed flux, velocity and velocity dispersion
maps that show in great detail the kinematics of the optical nebula at [S
ii]$\lambda 6716$, [S ii]$\lambda 6731$, [N ii]$\lambda 6584$,
H$\alpha$(6563Å), and [N ii]$\lambda 6548$. These maps reveal the existence of
a bright flattened disk-shaped structure in the core extending to r $\sim 10$
kpc and dominated by a chaotic velocity field. This structure is located in
the wake of X-ray cavities and characterised by a high mean velocity
dispersion of $134$ km/s. The disk-shaped structure is surrounded by an
extended array of filaments spread out to $r\sim 50$ kpc that are 10 times
fainter in flux, remarkably quiescent and has a uniform mean velocity
dispersion of $44$ km/s. This stability is puzzling given that the cluster
core exhibits several energetic phenomena. Based on these results, we argue
that there are two mechanisms to form multiphase gas in clusters of galaxies:
a first triggered in the wake of X-ray cavities leading to more turbulent
multiphase gas and a second, distinct mechanism, that is gentle and leads to
large-scale multiphase gas spread throughout the core.

Galaxies: NGC 1275 - Galaxies: clusters: individual: Perseus cluster

††journal: ApJ††software: python (Van Rossum & Drake 2009), astropy
(Robitaille et al. 2013, Price-Whelan et al. 2018), numpy (Harris et al.
2020), scipy (Virtanen et al. 2020), matplotlib (Hunter 2007), LUCI (Rhea et
al. 2021a)

##  1 Introduction

Clusters of galaxies are extended structures hosting several hundred to
thousands of gravitationally bound galaxies (e.g. Bahcall 1977, Abell et al.
1989). They are mostly composed of dark matter while galaxies only represent a
very small fraction of the cluster’s mass (e.g. Sand et al. 2004, Voigt &
Fabian 2006). There is also a third component made of hot X-ray emitting gas
at temperatures of $\sim 10^{7}-10^{8}$ K that fills the space between the
galaxies and is known as the intra-cluster medium or ICM (e.g. Cavaliere et
al. 1971, Gursky et al. 1971, Hitomi Collaboration et al. 2016).

This ICM accounts for a substantial fraction of the mass of a cluster ($\sim
13\%$) and often leads clusters to being classified into two distinct
categories depending on their X-ray emission profiles: cool-core clusters with
a strongly peaked X-ray emission profile and non-cool core clusters with a
more diffuse and uniform X-ray emission profile (Million & Allen 2009, Hudson
et al. 2010). The central dominant galaxy located in the core, known as the
brightest cluster galaxy (BCG), often exhibits extended filamentary nebulae of
optical ionised gas in the case of cool-core clusters (Crawford et al. 1999,
McDonald et al. 2010). These filaments are composed of multiphase gas that
have high H$\alpha$ luminosities (e.g. Conselice et al. 2001) and are often
co-spatial with cold gas (e.g. Salomé et al. 2006), as well as soft X-ray gas.
The most extended filaments can be mostly devoid of star formation, which
excludes photoionization as a primary ionization mechanism (e.g. Kent &
Sargent 1979).

A promising explanation for the formation of the filamentary nebulae
surrounding BCGs resides in the precipitation limit hypothesis (e.g. Gaspari
et al. 2012, 2013, 2015, Voit & Donahue 2015; Voit et al. 2015, Li et al.
2015, Voit et al. 2017). Here, the constant cooling by emission of the ICM in
cool-core clusters should imply high star formation rates in the cores of
clusters. However, since there is limited evidence of correspondingly
extremely high star formation inside these galaxies, a mechanism is necessary
to stop the gas from cooling and falling in the potential well (e.g. Crawford
et al. 1999). In clusters of galaxies, the heating mechanism is thought to be
orchestrated by the supermassive black hole residing in the BCG. This
mechanism can be seen in action in radio bubbles generated by the central
black hole which carve out large X-ray cavities in the ICM, entailing shocks,
turbulence, and mixing (e.g. Graham et al. 2008, Randall et al. 2015,
Zhuravleva et al. 2014). This phenomenon will in turn bring enough energy to
limit the cooling of the ambient gas and therefore star formation in the
galaxy (Crawford et al. 1999, Best et al. 2007, Voit et al. 2008). However,
the mechanisms explaining how the AGN energy reheats the ICM remains a matter
of debate.

The precipitation limit hypothesis proposes that the heating process
associated with the activity of the AGN sets in motion flows, which in turn
encourage the hot surrounding medium to condense at higher altitudes. Hence,
the adiabatic uplift of material through radio bubbles promotes condensation
by reducing the ratio of cooling time to free-fall time in some locations.
This cycle is analogous to the precipitations occurring on Earth, where
raindrops are formed by the uplifting of gas higher in the atmosphere.
Moreover, simulations show that the rain of cold gas towards the center of the
galaxy will initially feed the central black hole and therefore the power of
the flows that it produces, enabling a self-regulated feedback loop (e.g. Voit
et al. 2017). This energy from the black hole will, in turn, heat the ambient
medium and increase the ratio of the cooling time to the free fall time so
that the precipitation will cease. The filamentary nebulae surrounding BCGs
have been interpreted as a tell-tale sign of this model and could therefore
offer the possibility to study this hypothesis.

Here, we target the filamentary nebula that surrounds NGC 1275, the BCG
located at the center of the Perseus cluster of galaxies. NGC 1275 has been
studied extensively at all wavelengths (see Forman et al. 1972, Fabian et al.
2011, Salomé et al. 2011, Lim et al. 2012, Nagai et al. 2019). The cluster
hosts several X-ray cavities that originate from multiple generations of radio
jets emitted from the active galactic nuclei (AGN) of NGC 1275 (Boehringer et
al. 1993, Fabian et al. 2000, Fabian et al. 2011, Gendron-Marsolais et al.
2018). These jets carve the neighbouring ICM, creating buoyantly rising radio-
emitting bubbles.

NGC 1275 also displays one of the largest filamentary nebulae known with a
size of about $80$ kpc $\times\text{}50$ kpc (e.g. McNamara et al. 1996,
Conselice et al. 2001, Hamer et al. 2016). Combined with the proximity of the
Perseus cluster, this makes NGC 1275 a target of choice for our understanding
of the formation and ionization mechanisms of filamentary nebulae in clusters.

The first observations of the filamentary nebula surrounding NGC 1275 by
Minkowski (1957), Lynds (1970), and Rubin et al. (1977) unveiled a high-
velocity (HV) feature ($\sim$ 8200 km/s) associated with a forefront spiral
galaxy falling onto NGC 1275 (Yu et al. 2015), and a low-velocity (LV)
structure ($\sim$ 5200 km/s) linked to NGC 1275. Hubble Space Telescope
observations of the low-velocity structure then revealed the filamentary
appearance of the ionised gas (Fabian et al. 2008), whereas soft X-ray
counterparts were discovered for certain bright filaments with the Chandra
X-Ray Observatory (Fabian et al. 2003). Moreover, cold molecular gas has been
associated with the emission of the filamentary nebula of NGC 1275 (Salomé et
al. 2006, Ho et al. 2009, Salomé et al. 2011, Mittal et al. 2012), and also
linked to a disk of emission near the galaxy (Lim et al. 2008).

Nevertheless, the first detailed observations of the nebula was performed by
Conselice et al. (2001) with high-resolution imaging, integral field, and
long-slit spectroscopy (WIYN & KPNO). These observations brought forth the
first velocity map of the central $\sim 45\text{arcsec}$ ($\sim 16.5$ kpc) of
the nebula. Observations from the Gemini Multi-Object Spectrograph along six
slits carefully positioned along certain filaments showed evidence of
outflowing gas and flow patterns (Hatch et al. 2006). In 2018, the filamentary
nebula was then imaged for the first time with SITELLE (Spectromètre Imageur à
Transformée de Fourier pour l’Etude en Long et en Large de raies d’Emission),
an imaging Fourier transform spectrometer (Drissen et al. 2019) installed at
the Canada-France-Hawaï Telescope (CFHT) that has an extremely large field of
view ($11\text{arcmin}\times 11\text{arcmin}$) capable of imaging the nebula
in its entirety (see Figure 1). Gendron-Marsolais et al. (2018) showed that
the velocity structure of the filaments appears to be generally devoid of
specific trends or rotation.

In this paper, we present new high-spectral resolution observations of the
filamentary nebula surrounding NGC 1275 obtained with SITELLE. The first
SITELLE observations presented in Gendron-Marsolais et al. (2018) revealed the
kinematics of the ionized nebula, but suffered from poor spectral resolution
(R = 1800) that could not spectroscopically resolve the filaments beyond a
projected radii of $r\gtrsim 10$ kpc centered on the AGN.

Here, the high-spectral resolution nature of the data at R = 7000 allows us to
deepen the scope of the study by performing a detailed analysis of the
kinematics of the nebula, in particular the velocity dispersion of the gas.
The analysis of the data revealed a central structure displaying higher mean
flux and velocity dispersion than the rest of the outer filaments. This disk-
shaped structure seems spatially correlated with a similar structure of cold
molecular gas, which will be detailed in later sections. This result appears
relevant when considering the clear kinematic correlations between the ionized
and molecular gas in the central region, as well as possibly far infrared (IR)
[CII] emission lines of the gas surrounding NGC 1275 as observed with Herschel
by Mittal et al. (2012).

In Section 2, we present the new SITELLE observations and the various
procedures used during the data analysis. In Section 3 we present and discuss
our results. Finally, a summary of our conclusions will be presented in
Section 4.

To directly compare our results to those of Gendron-Marsolais et al. (2018)
and the Hitomi Collaboration et al. (2018), we also adopt for NGC 1275 a
redshift of $z=0.017284$, which implies an angular scale of
$21.2\;\text{kpcarcmin}^{-1}$. This $z$ also corresponds to a luminosity
distance of $75.5$ Mpc, assuming $H_{0}=69.6\;\text{kms}^{-1}\text{Mpc}^{-1}$,
$\Omega_{M}=0.286$ and $\Omega_{vac}=0.714$

Figure 1: The complete field of view (11’ $\times$ 11’) of the SITELLE
observations of NGC 1275 with full-band SN3 filter (648-685 nm) at high-
spectral resolution (R = 7000). Here, we show the integrated flux images in
grayscale with the brightest H$\alpha$ filaments in red. The white square
denotes the Horseshoe filament.

##  2 Data Analysis

###  2.1 Observations with SITELLE

The filamentary nebula surrounding NGC 1275 was observed in February 2020 with
SITELLE during Queued Service Observations 20AD99 by PIs Hlavacek-Larrondo and
Rhea. SITELLE is a Fourier transform imaging spectrometer with an incredibly
large field of view of 11 arcmins by 11 arcmins and equipped with two E2V
detectors of 2048 × 2064 pixels, resulting in a spatial resolution of 0.321 ×
0.321 arcsecs. SITELLE was used with the SN3 filter for 4 hours (1710
exposures of 8.42s) including overheads, necessary to obtain a high-spectral
resolution of $R=7000$. This filter covers wavelengths from 648 nm to 685 nm.
These observations were centered on NGC 1275 with RA : 03:19:48.16 and DEC :
+41:30:42.1. Five emission lines are covered with the SN3 filter, namely : [S
ii]$\lambda 6716$, [S ii]$\lambda 6731$, [N ii]$\lambda 6584$,
H$\alpha$(6563Å), and [N ii]$\lambda 6548$. The oxygen emission lines [O
I]$\lambda 6300$ and [O I]$\lambda 6363$ cannot be observed in such a
configuration since they fall just outside of the spectral range of the SN3
filter (648-685 nm). The data reduction of SITELLE is performed at CFHT
through a dedicated pipeline: ORBS. We summarize the reduction process here.
The electronic bias and the flat-field curvature of the interferometric images
are first corrected. Images are then aligned to solve potential guiding
errors. Cosmic rays are detected through an algorithm comparing successive
images to determine if any abnormal flux increase can be observed for a given
pixel. These detections are corrected by an estimation of the given gaussian
flux of nearby pixels. Atmospheric variations are also taken into account and
corrected through a transmission function taken during the data acquisition.
The reduction pipeline then produces the Fourier transform of all the
interferograms contained within the data cube, which are then phase corrected.
Finally, wavelength and flux calibrations are performed to adequately record
the high-spectral resolution observations (Drissen et al. 2019).

###  2.2 Background Subtraction

After a careful evaluation of the high-spectral resolution data obtained from
SITELLE, it became clear that an important variability of the background
emission across the field-of-view is present in the spectra (see Appendix A).
This background emission is mainly produced by the galaxies present near the
filamentary nebula as well as the diffuse emission of other structures in the
field-of-view. Background subtraction is therefore needed to properly
disentangle this unwanted emission from the filament emission lines, however,
this procedure is not taken into account in the reduction pipeline. This step
must therefore be performed during the fitting procedure. The background
variability affects mainly the analysis of the [S ii]$\lambda 6717$ and [S
ii]$\lambda 6731$ emission lines, which are much fainter than the other
optical lines. To tackle this issue, we decided to divide the entire
filamentary nebula into nine regions as illustrated in Figure 2. For each of
these nine regions, we attributed a specific sky zone devoid of targeted
emission lines and located within the boundaries of that region. The red
circles shown in Figure 2 illustrate these 9 sky zones. The sky zone is then
used during the fitting procedure to perform the background subtraction for
each dedicated region. Once all the regions have been fitted properly (see
following sections), we can then create a mosaic of the flux, velocity, and
dispersion maps for the complete filamentary nebula. This procedure allows us
to counter the background variability by considering several background
regions instead of one to increase the reliability of our results. This
approach allowed us to validate results obtained while considering this
background variability. The development of a dedicated methodology to tackle
background variability in detail for SITELLE data will be part of a future
paper.

Figure 2: Mosaic map used during the analysis to tackle the background
variability issue. The blue squares represent the regions whose spectra are
fitted by LUCI, while the red circles denote the regions whose emission was
used for background subtraction. The grayscale background of the figure is the
deep image of the filaments surrounding NGC 1275 produced with LUCI.

###  2.3 Weighted Voronoi Tessellation - WVT

From a preliminary analysis of the high-spectral resolution data of NGC 1275,
we noticed that the signal-to-noise ratio (SNR) of the filamentary nebula was
relatively low compared to what was expected from the SITELLE Exposure Time
Calculator. Poor weather conditions during the data acquisition are considered
to be the main cause of a lower SNR (see Appendix B for an example of the SNR
map).

Thus, to tackle this issue, we decided to implement a weighted Voronoi
tessellation algorithm as a feature of the LUCI software using the following
tool https://github.com/XtraAstronomy/AstronomyTools (Rhea et al. 2020b). This
procedure creates bins of pixels whose SNR is defined by a threshold chosen by
the user. Therefore, regions with strong emission will be contained within
smaller bins, while noisier regions will be grouped into larger bins compared
to regions of interest such as filaments. This also leads to the presence of
bins containing a single pixel where the signal-to-noise ratio is already
high.

More specifically, we started by making a SNR map of the filamentary nebula by
only considering the H$\alpha$ emission line and [N ii] emission line doublet.
The SNR map is produced by determining the ratio of the maximum value of the
emission lines by the standard deviation of the spectra in a waveband devoid
of emission lines. The pixels are then aggregated to create the bins and reach
the SNR threshold established. In our case, we decided to fix the SNR level to
30 which is close to the estimated value of SNR = 35 for most of the filaments
that would have been obtained in ideal observing conditions with SITELLE. From
there, we established the number of bins defined by the algorithm and created
numpy files of pixels coordinates for each to be later used in the spectral
fitting procedure. The function wvt_fit_region of LUCI can be called to
produce the fitting of a specific region of the image which will be run
through the weighted Voronoi algorithm first.

One example of the WVT procedure can be seen in Figure 3 where the algorithm
has been applied to the horseshoe filament as shown in Figure 1. It
illustrates that the WVT code manages to improve the flux detection of the
base of the horseshoe compared to the background emission. However, the flux
of the filament’s upper region remains too low to be properly detected and
accounted for in the resulting flux map. We therefore applied a flux threshold
of $2\times 10^{-17}\text{ergs}^{-1}\text{cm}^{-2}$ after the fitting to our
final maps to properly eliminate unwanted bins of noisy data displaying higher
flux. A similar flux threshold was also applied in the analysis of low-
spectral resolution observations with SITELLE by Gendron-Marsolais et al.
(2018).

Figure 3: Example of a weighted Voronoi tesselation performed by LUCI to
produce the resulting H$\alpha$ flux map after fitting the spectra of the
horseshoe filament, whose general contour, taken from the mask displayed in
Figure 4, is superimposed on the figure as white contours. In this case, we
had chosen a SNR value equal to 30. Figure 4: Applied mask on the SITELLE data
of NGC 1275. White pixels are masked while black pixels are unmasked. The data
used to produce this mask comes from the high-spatial resolution images taken
by Conselice et al. (2001) with the WIYN telescope. Note that the field of
view is smaller than the field of view of the SITELLE observations, but covers
the filaments.

###  2.4 Masking Procedure

To help the fitting process, we decided to implement a masking procedure
designed to keep as much information about the filamentary nebula as
necessary. To implement this mask, we used the observational data presented by
Conselice et al. (2001) and produced by the WIYN 3.5m telescope. These deep
observations showed the filamentary nebula surrounding NGC 1275 with higher
signal-to-noise therefore, by using these observations as a basis for our
masking procedure, we can retain the necessary information for our fitting
results.

The procedure used to develop this mask was implemented as follows : first, a
threshold signal-to-noise value of 10 in the Conselice et al. (2001) WIYN data
was chosen in order to retain as much information regarding the filaments as
possible without keeping too many background pixels in the resulting image.

Secondly, for the mask to be used in conjunction with the LUCI software, some
groundwork was needed to perfectly match the size and position of the mask
with our SITELLE data according to the WCS coordinates of the latter. Indeed,
the WIYN observations did not have the same astrometry as our data, meaning
that they were not properly aligned. Moreover, the number of pixels in both
observations are not the same which required specific care to handle their
interpolation.

To solve this issue, we determined the number of pixels needed to cover the
entirety of the SITELLE field of view by considering the pixel dimensions of
both the SITELLE and WIYN instruments. Then, by knowing the position of the
central pixel of the SITELLE data cube using the declination and right
ascension, we were able to determine the corresponding pixel on the mask.
Thus, by knowing the number of pixels needed as well as the central pixel we
used the function Cutout2D from the astropy.nddata package to extend our mask
to fit the SITELLE field of view. We then interpolated the mask onto the
specific dimensions of the SITELLE observations using the function interp2d
from the scipy.interpolate package, therefore creating a fitted mask without
losing its nature despite having different dimensions originally.

Finally, to properly align the mask with the SITELLE data, we used the WCS
coordinates given within the SITELLE data cube to determine the position of 11
stars, which would then act as anchor points for the estimate_transform and
apply_transform functions of the astroalign package. By determining the
position of these stars within the newly produced mask, we matched their
positions to the ones of the SITELLE data and allow the overlapping of both
images.

###  2.5 Emission Line Fitting Procedure

After obtaining our mask to the SITELLE data cube, we were able to proceed to
the emission lines fitting part of the analysis. The recent software LUCI was
used to perform the fit (Rhea et al. 2020a, b, 2021a, 2021b) according to our
mosaic structure detailed previously. Since LUCI is a novel analysis software,
a summary of LUCI capabilities is described here but we invite the user to see
https://crhea93.github.io/LUCI/index.html for more details (Rhea et al.
2021a).

First, the spectra found in the data cube are normalized according to the
highest amplitude and a shift in wavelength is applied to properly center the
velocities between $-500$ and $500$ km/s. This constraint is necessary for the
following procedure that uses machine learning since it allows better prior
estimates for the fitting algorithm. This velocity range was chosen after a
visual inspection of the data and considering the previous work by Gendron-
Marsolais et al. (2018). These boundaries were given as training parameters
for the neural network to predict the velocity shift of the emission lines. To
efficiently fit a spectrum, the velocity and broadening prior information need
to be precise to facilitate the minimization algorithm at the heart of the
emission lines fitting and thus to accelerate the whole procedure (Zeidler et
al. 2019, Bittner et al. 2019). Therefore, a machine learning technique based
on a convolutional neural network (CNN) is used to properly determine these
priors.

From there, the values obtained through the CNN are passed as the line
position and broadening. The amplitude, however, is obtained from the height
of the shifted emission line. With these three values, the line can be
effectively fitted by LUCI with the scipy.optimize.minimize function from the
scipy package. This function uses the Sequential Least Squares Programming
(SLSQP) optimization algorithm. Since SITELLE’s Instrumental Spectra Function
(ISF - see Martin et al. 2016) is a sinc convolved with a gaussian resulting
from the velocity dispersion along the line of sight, we used the sincgauss
fitting model presented by LUCI. The results from this procedure are the
amplitude, velocity, and broadening of the five emission lines present in the
spectrum: [S ii]$\lambda 6716$, [S ii]$\lambda 6731$, [N ii]$\lambda 6584$,
H$\alpha$(6563Å), and [N ii]$\lambda 6548$, where we separated the fitting
procedure by first considering the SNR of the H$\alpha$ and [N ii] emission
lines to obtain their respective parameters. Then, we specifically considered
the [S ii] emission lines to derive their own parameters, which will be
detailed in Section 2.7.

Finally, to account for the location of Earth on its orbit at the time of
observations, a correction is applied to the velocity map. This correction is
determined with the heliocentric_correction function of the LUCI package, and
gives a velocity correction of $-27.5$ km/s.

Through this analysis, we adopted a redshift of $z=0.017284$ for NGC 1275,
which LUCI uses during the fitting procedure so that all calculations are done
in the rest frame of the object to properly determine the velocity, velocity
dispersion and flux parameters of the emission lines. An example of a fitted
spectrum using LUCI is displayed in Fig. 5. The resulting H$\alpha$ flux,
velocity and velocity dispersion maps are shown in Fig. 6.

Finally, through these steps, we explored the fitting of averaged spectra over
the bins produced by the WVT procedure to better understand the complex nature
of the ionised gas in these filaments and determine their most prominent
features as if no binning was applied.

Figure 5: Example of a fitted spectrum using LUCI for a small circular region
of $\sim 2.2$ pixels radius within the filamentary nebula surrounding NGC 1275
in the central western filaments (coordinates RA : 3:19:49.72, DEC :
+41:30:51).

Figure 6: Top : H$\alpha$ averaged flux map of the filaments in NGC 1275.
Bottom left : H$\alpha$ velocity map of the filaments in NGC 1275. Bottom
right : H$\alpha$ velocity dispersion map of the filaments in NGC 1275.

###  2.6 Multiple Emission Components

Due to the high-spectral resolution of our observations, we have to take into
account the possibility of resolving multiple velocity components that a
single bin can potentially contain due to the potential overlapping of
filaments (see Appendix C). Indeed, since the three-dimensional structure of
the filaments is currently unknown, it is impossible to decipher the possible
overlap of several filaments.

For the sake of clarity in our resulting maps, we decided to mask the main
sources of multiple emission components. Firstly, the high-velocity system,
associated with a forefront galaxy, has a velocity of $\sim 8200$ km/s. It can
thus be identified through its systemic velocity and ignored during the
fitting procedure by only considering the emission lines associated with the
filamentary nebula.

Moreover, broad, multiple component emission lines from the AGN are coupled
with the filament emission in the central $\sim 2.6$ kpc, thus, the resulting
fits produced by LUCI are poor when considering these specific regions. An
example of a spectra extracted from the central region close to the AGN is
displayed in Fig. 7.

Figure 7: Example spectrum extracted from the central region of the
filamentary nebula surrounding NGC 1275 centered on the AGN. Narrow emission
lines overlaid on a broad component are clearly seen. This region has a radius
of $\sim 5$ pixels.

The large broadening of the AGN’s emission overlapping with the filaments’
narrow emission impedes LUCI from properly fitting the central regions of the
filamentary nebula. Indeed, the fitting algorithm proves to be limited by the
presence of largely broadened and blended emission lines for which the machine
learning algorithm has not been trained on, therefore preventing it from
performing accurate fitting. Therefore, to facilitate the analysis, we decided
to mask the central region of emission coming from the AGN displaying broad
emission lines. To do so, we studied the emission line profiles with LUCI and
determined that the AGN spectral presence is confined within a radius of $\sim
2.6$ kpc from the center of the galaxy. There was also evidence of a small
number ($\sim 10$) of localized clumps detected over 1 to 5 pixels within the
central regions ($r<10$ kpc) that showed evidence of multiple components in
the emission lines. Similar clumps had already been detected in a previous
study by Hatch et al. (2006), where the authors mentioned the presence of
several regions displaying double-peaked emission lines.

Some of these regions appear as small knots or plumes displaying an extremely
low separation in velocity components, leading to slightly double-peaked
emission lines. However, we can also detect slightly larger regions displaying
several components in velocity and located near the eastern part of the
filamentary nebula below the high-velocity system. It is not yet clear if
these regions with multiple velocity components are due to the superposition
of filaments with Doppler-shifted velocities in the line of sight. Spectra of
specific regions displaying several emission lines components are presented in
Appendix C.

Here we focus only on the results from the fitting of a single component to
all bins. A dedicated multiple-component analysis of the few localized regions
with overlapping filaments, as well as of the core, will be performed in the
future.

###  2.7 [SII] Emission Lines Fitting

Regarding the detection and fitting of the [S ii]$\lambda 6716$ and [S
ii]$\lambda 6731$ emission lines, one of the main difficulties in their
analysis resides in the presence of strong sky lines at the same wavelengths
(see Appendix A). However, after applying our methodology to tackle the
background variability, we were able to detect these emission lines. To help
the fitting procedure, we made new WVT bins based on the [S ii]$\lambda 6716$
and [S ii]$\lambda 6731$ doublet SNR, which are fainter than the [N
ii]$\lambda 6583$, H$\alpha$(6563Å), and [N ii]$\lambda 6548$ lines.

The new larger bins thus created improved the detection of these fainter
emission lines. The resulting [S ii]$\lambda 6716$ and [S ii]$\lambda 6731$
flux maps, velocity and velocity dispersion maps are shown in Fig. 8. The
bottom left and right plots clearly show similar velocity and velocity
dispersion maps as H$\alpha$ seen in Fig. 6. A deeper analysis of the [S ii]
emission lines ratio, which are often used as an estimate of the gas density
compared to the density of the hot X-ray gas, will be presented in a future
article (Vigneron et al., in preparation).

Figure 8: Upper left: [S ii]$\lambda 6716$ flux map of the filaments in NGC
1275. Upper right: [S ii]$\lambda 6731$ flux map. Bottom left: [S ii]$\lambda
6716$ velocity map. Bottom right: [S ii]$\lambda 6716$ velocity dispersion
map. The velocity and velocity dispersion of [S ii]$\lambda 6731$ are the same
as the ones for the [S ii]$\lambda 6716$ line since these parameters were tied
when fitting the doublet.

##  3 Results and discussion

###  3.1 Comparison with Previous SITELLE Observations

Figure 9: Comparison of the spectra extracted from four regions denoted by the
letters A, B, C, and D for both low and high-spectral resolution. On the left
side, the high-spectral resolution H$\alpha$ averaged flux map is used to
display the region of emission while the right side showcases the differences
between low and high-resolution spectra.The white contours overlayed on the
left-hand flux map display the HVS structure situated in the forefront of the
filamentary nebula of NGC 1275.

Previous SITELLE R=1800 observations of the filamentary nebula surrounding NGC
1275 were already analyzed by Gendron-Marsolais et al. (2018) and revealed
several key features of the velocity structure.

Our new high-spectral resolution observations, however, presented new
challenges during the analysis step. Indeed, the spectra produced by SITELLE
uses a Fourier transformation based on a sinc function, which shows specific
lobes around the central peak. Since SITELLE instrumental function is a sinc
function convoluted with a gaussian resulting from the velocity dispersion
along the line of sight, a sincgauss model was specifically chosen during the
spectral fitting procedure with LUCI to properly take into account the
spectral information contained within the lobes

Moreover, the spectral resolution associated with the SITELLE observations
induce a minimum value of velocity dispersion that can be resolved clearly
(see Figure 3 in Rousseau-Nepton et al. 2019). Thus, when considering a small
spectral resolution of R = 1800 with the SITELLE instrument, as was the case
for the observations studied in Gendron-Marsolais et al. (2018), the lower
velocity dispersion bound that could be obtained was of $\sim 80$ km/s.
However, with a high-spectral resolution of R = 7000, the lower velocity
dispersion value that can be determined is of $\sim 15$ km/s, allowing us to
properly resolve the emission lines (see Figure 3 of Rousseau-Nepton et al.
2019). This result is visible in Figure 9 when comparing the spectra of the
same region at both low and high-spectral resolution. We can indeed observe
that the width of the emission lines is smaller than what was previously found
by Gendron-Marsolais et al. (2018) in region A, B and D. Region C is contained
within the central region and given its intrinsic large velocity dispersion,
the low-spectral resolution observations of SITELLE were capable of resolving
this structure.

For illustrative purposes, we also overplotted the contours of the HVS on the
left-hand map of Figure 9 These contours were created by forcing LUCI to
specifically fit the emission line from the HVS thus allowing us to isolate it
on a dedicated small region of the SITELLE data.

###  3.2 Emission Line Intensity Ratios and Flux Maps

First, the H$\alpha$ averaged flux map visible in the upper plot of Figure 6
shows a disk-shaped structure in the central region with a size of $\sim 22$
kpc by $5$ kpc displaying a flux an order of magnitude higher than the rest of
the filaments. The flux map from Gendron-Marsolais et al. (2018) hinted to
this structure, but the new data reveal it in much greater detail. The high
averaged flux of this disk-shaped structure is also associated with a large
velocity dispersion, which will be discussed in section 3.4. Beyond the disk-
shaped structure, localised parts of specific filaments display slightly
higher H$\alpha$ fluxes, but most of them have a homogeneous lower flux.

Figure 10: Upper left: [N ii]$\lambda 6583$ by H$\alpha$ ratio map. Upper
right: Mean (in red) and ensemble fits (in blue) across annuli containing 1500
pixels for the [N ii]$\lambda 6583$ by H$\alpha$ ratio. The error bars for the
ensemble fit have been plotted but are too small to see compared to the data
scale. Bottom left: [S ii]$\lambda 6716$ by H$\alpha$ ratio map. Bottom right:
Mean (in red) and ensemble fits (in blue) across annuli containing 1500 pixels
for the [S ii]$\lambda 6716$ by H$\alpha$ ratio. The error bars for the
ensemble fit have been plotted but are too small to see compared to the data
scale.

Emission line ratios can be of great interest when studying the ionization
properties of an emitting gas (see Kewley et al. 2019). In this regard, the [N
ii]$\lambda 6583$/H$\alpha$ ratio is of importance since it informs us of the
relative implication of soft versus hard sources of ionization. In the case of
a low ratio (meaning H$\alpha$ flux $\gg$ [N ii]$\lambda 6583$ flux), photons
from young stars can be the ionizing source, while for a higher ratio (meaning
H$\alpha$ flux $\leq$ [N ii]$\lambda 6583$ flux), a harder ionizing spectrum
(from an AGN, for example) or energetic ICM particles are needed to provide
additional heat (see Sanchez Almeida et al. 2012). Similarly, the ratio of [S
ii]$\lambda 6716$ by H$\alpha$(6563Å) can be used as a confirmation value for
various ionization mechanisms. Here, to produce the ratio map of [S
ii]$\lambda 6716$ by H$\alpha$(6563Å), we specifically applied the fitting
procedure for the H$\alpha$ emission line by considering the bins obtained
through the WVT algorithm which uses an SNR of 35 for the [S ii] doublet
(between wavelengths of 671,1 nm to 675,7 nm) thus creating bins of the exact
same size and position as the [S ii] doublet flux maps but fitting the
H$\alpha$ emission line at $\lambda=656$ nm. Afterwards, we can obtain the
ratio map by dividing both these flux maps therefore producing a flux ratio
map for both the emission lines with the exact same number of bins (see
bottom-left plot of Figure 10).

Figure 10 upper-left map shows that the central region of the structure
displays a ratio of [N ii]$\lambda 6583$/H$\alpha$ close to or slightly
superior to 1.0, while the extended filaments show a variety of smaller ratio
values between 0.5 to 1.0. This trend between central and extended filaments
can also be seen in the upper right plot of Figure 10, where we produced the
mean (i.e. taking the mean of the ratio values accross the annuli) and
ensemble fit results (i.e. extracting one combined spectra for the entirety of
the pixels inside the annulus and fitting it to obtain an ensemble ratio
value) for the [N ii]$\lambda 6583$/H$\alpha$ ratio across annuli containing
1500 pixels each, reproducing Gendron-Marsolais et al. (2018). However, in the
optics of emulating this methodology for high spectral resolution SITELLE
data, we noticed that ensemble spectra at high spectral resolution are
severely affected by the spatial distance between annuli pixels leading to
blended emission lines and to large offsets between the mean and ensemble
fits. We have decided to leave those results, but we are analyzing only the
mean fit results.

The center of each annuli is determined based on the WCS coordinates of the
central galaxy NGC 1275 given as RA : 03:19:48.16 and DEC : +41:30:42.1
through the literature (see Gaia Collaboration 2020) and observed in our
SITELLE data. The width of the annuli is determined according to the fixed
number of 1500 detected pixels they contain. Therefore, they vary between
widths of 7 to 10 pixels and up to 57 pixels for the outer filaments. Error
bars are also plotted for both methods and obtained through statistical
calculations for the mean, or through LUCI’s fitting procedure for the
ensemble fit. The error bars for the ensemble fit have also been plotted but
are too small to see compared to the data scale. This profile shows a decrease
in the mean values from the center (0 - 10 kpc) to the outer filaments (10 -
30 kpc) from $1.0\pm 0.5$ to $0.6\pm 0.5$, thus suggesting a gradual change or
variation of the ionisation mechanism. However, the ratio values appear more
chaotic than structured in the extended filaments which is reflected by a
fairly large standard deviation in the error bars of the mean profile (see
upper right plot of Figure 10).

Such radial trend is similar to what was previously found by Gendron-Marsolais
et al. (2018) with the low-spectral resolution SITELLE data (R=1800), but also
through slit spectroscopy (Hatch et al. 2006). The presence of star formation
has already been detected for specific southern and north-western regions of
the filamentary nebula (see Canning et al. 2010, 2014). However,
photoionization models predict a ratio that is highly dependent on
metallicity, with an upper limit of around 0.5 (Kewley et al. 2006), thus,
such a process could not explain the higher ratios found throughout the
southern filaments. In addition, we can also conclude that the central region,
near the AGN, is more likely to be ionised by its activity as well as
energetic particles since it displays higher ratios, while the outer filaments
could predominantly be ionized by energetic particles thus showing
intermediate [N ii]$\lambda 6548$ / H$\alpha$ emission line ratios.

Another possibility that is often presented as a mechanism to explain the
energetics and ionisation of the filaments is through collisional excitation
by energetic particles coming from the hot ICM (see Ferland et al. 2009). In
such circumstances, the [N ii]$\lambda 6548$ / H$\alpha$ emission line ratio
would be close to $\sim 0.3$. However, if we consider the ratio of [S
ii]/H$\alpha$, displayed in the bottom left plot of Figure 10, we can see that
the outer filaments show higher ratios above $\sim 1$, nevertheless, various
behavior are observed for different filaments. In the case of ionization by
cosmic rays, the ratio of [S ii]/H$\alpha$ is predicted to be at $1.4$
according to the cosmic ray heating model (see Table 5 of Ferland et al.
2009), which could be an argument in favor of the collisional ionisation model
for the outer filaments. However, the northern filaments as well as parts of
some other filaments show even higher [S ii]/H$\alpha$ ratio values above
$\sim 2.0$. Nevertheless, in the bottom right plot of Figure 10, we produced
the mean and ensemble fit results of the [S ii]$\lambda 6716$/H$\alpha$ ratio
across annuli containing 1500 pixels each, we can see that most mean values
are constrained between $\sim 0.5$ and $1.5$ which could argue in favor of an
ionization mechanism through cosmic rays, though it is not possible to offer
conclusive results with the emission lines at hand.

Using subsequent SITELLE observations with SN1 (365 - 385 nm) and SN2 (480 -
520 nm) filters of NGC1275 (PI: G.-Marsolais), that provides other emission
lines, we are currently pursuing a deeper analysis of the ionization
mechanisms at play in the filamentary nebula (Rhea et al. in preparation).
Similarly, the analysis of [S ii] emission lines and their ratios will be
explored in a future article (Vigneron et al. in preparation)

###  3.3 Central disk-shaped Structure

As we mentioned, the filamentary nebula seen in the optical is part of a
larger multiphase structure that correlates spatially with filament-like
structures seen in X-rays (Fabian et al. 2003, Walker et al. 2015) and
molecular gas structures (Salomé et al. 2008, Ho et al. 2009) Such multi-phase
filaments are at the heart of many models explaining the formation of such
structures. Indeed, it is argued that the black hole jets create expanding
bubbles, rising through and carving the ICM, while inducing turbulence, sound
waves and shocks (e.g. Dhawan et al. 1998, Falceta-Gonçalves et al. 2010).
This effect can be seen through the deformation of optical filaments taking
the shape of convection cells and their spatial correlation with the trailing
radio bubbles (Fabian et al. 2003; see also the horseshoe filament in left
plot of Fig 11).

Figure 11: Left: Chandra 0.5 - 1 keV observations of NGC 1275. The magenta
contours show  the H$\alpha$ filaments as observed with SITELLE at high-
spectral resolution at a flux level stating at $1\times
10^{-18}\text{ergs}^{-1}\text{cm}^{-2}\text{\AA}^{-1}$. The cyan contours
display the radio emission from 0.23 to 0.470 GHz as observed with the VLA
(Gendron-Marsolais et al. 2020) tracing the radio jets. The blue contours
represent the CO(2-1) central emission disk-shaped structure as observed with
the SMA (Lim et al. 2008). Right: Zoomed-in image of the left-side figure with
a H$\alpha$ flux cut-off of $1\times
10^{-17}\text{ergs}^{-1}\text{cm}^{-2}\text{\AA}^{-1}$.

Figure 12: Upper left: Herschel Infrared Space Observatory [CII] emission line
velocity map corrected for a redshift of z = 0.017284 (Mittal et al. 2012).
Upper right: H$\alpha$ velocity map as obtained with SITELLE data at high
spectral resolution overplotted with contours of Herschel velocity between
-350 to -50 km/s. Bottom left: H$\alpha$ velocity map as obtained with SITELLE
data at high spectral resolution overplotted with contours of Herschel
velocity between -50 to 50 km/s. Bottom right: H$\alpha$ velocity map as
obtained with SITELLE data at high spectral resolution overplotted with
contours of Herschel velocity between 50 to 350 km/s.

One model argues that the depletion of metals in the galaxy and the deformed
morphology of these filaments are explained by the rise of bubbles fueled by
the activity of the central supermassive black hole (e.g. McNamara & Nulsen
2007).

A second model demonstrates that the rising of radio bubbles through the ICM
can trigger local thermal instabilities in the X-ray emitting gas that would
lead to local cooling flows where the density of material would increase as a
consequence of cooling. Due to the intense gravitational potential of the BCG,
these filaments of cooler gas would fall onto the BCG, fueling the black hole
activity through this feedback cycle (e.g. Voit et al. 2017, Tremblay et al.
2018). This precipitation-based model would explain the observed multiphase
structure by the cooling of gas from X-ray temperatures at $\sim 4\times
10^{7}$K, down to cold molecular gas at $<10^{3}$K visible in radio (McNamara
et al. 2016, Dutta et al. 2022). Thus, the detection of a cold CO(2-1)
molecular gas structure close to the central region of the filaments in NGC
1275, as well as similar detections of correlated cold molecular gas in the
outer filaments (Salomé et al. 2011) offer a key argument regarding this
formation model. The strongly emitting central structure was detected and
studied by Lim et al. (2008) and is divided into three main filaments and
smaller clumps, all located near the central plane of the galaxy. They also
showed that this central disk spatially correlates with the optical filaments
seen in H$\alpha$, as well as the X-ray emission between 0.5 and 1 keV. Our
new observations with SITELLE as seen in Figure 11 also show that the
H$\alpha$ flux contours spatially correlate with the CO(2-1) molecular gas as
seen by Lim et al. (2008), especially in the case of the left-side filaments
of the central disk-shaped structure (see right panel of Figure 11), while
also located along the lower borders of an expanding radio-filled bubble as
observed by Gendron-Marsolais et al. (2020). This region seems to be directly
linked with the central disk that has higher averaged flux and velocity
dispersion as seen with the H$\alpha$ flux map shown in Figure 6.

Such contrast between central and extended flux is similar to what was
previously obtained by Salomé et al. (2011), where the detection of CO across
the filaments demonstrated that the central region has a flux around 10 times
higher than the emission found in the filaments. However, Lim et al. (2008)
clearly showed that this higher central flux emission is not only linked to
the AGN, but also to this bright and uniform disk-shaped feature. This result
proves insightful when considering the observations of BCGs by ALMA (Russell
et al. 2019) revealing mostly filamentary and disk-shaped structures around
these galaxies. Some of these features display rotation (e.g. Hamer et al.
2014), however, this doesn’t appear to be the case for the central disk-shaped
structure of NGC 1275 (see Lim et al. 2008), even though, closer observations
of the inner regions close to the central galaxy indicates rotation motions of
the gas (see Nagai et al. 2019, Riffel et al. 2020).

Decades of optical observations have revealed that NGC 1275 is surrounded by
an extended array of filaments spreading throughout the inner 100 kpc and are
the largest seen in any cluster (e.g. Conselice et al. 2001). However, we also
know that the Perseus cluster is one of the closest to us, therefore, in more
distant clusters, only the brightest filaments could potentially be seen.
Indeed, when considering our renewed observations of NGC 1275 with SITELLE, we
can observe a significantly brighter central disk-shaped structure ($\sim
1\times 10^{-17}\text{ergs}^{-1}\text{cm}^{-2}\text{\AA}^{-1}$ flux) as
opposed to the outer filaments ($\sim 1\times
10^{-18}\text{ergs}^{-1}\text{cm}^{-2}\text{\AA}^{-1}$ flux). Thus, more
distant clusters could also harbour extended array of filaments that our
current generation of telescopes are not able to detect. Simulations exploring
this idea have been developped for NGC 1275 by McDonald et al. (2010) and
revealed that by a redshift of $z\sim 0.06$, most of the filaments would be
undetectable leaving only the central bright region surrounded by unresolved
features (see Fig. 16 of McDonald et al. 2010). Similarly, recent observations
of the BCG of the Centaurus cluster by Fabian et al. (2016) revealed a faint
and diffuse H$\alpha$ nebula surrounding it.

Recent ALMA observations of NGC 1275 by Nagai et al. (2019) provided a
detection of a smaller portion of the central disk in CO(2-1) close to the
AGN, as well as HCN(3-2) and $\text{HCO}^{+}$(3-2) emission within a radius of
1.8 arcsec (0.658 kpc) around the AGN, revealing a rotating motion of the
emitting gas at this scale. Such detection is within the central region that
we have masked in our SITELLE fits due to the broad component being present as
mentionned in Section 2.6.

###  3.4 Velocity Dispersion Structure

Previous observations of the filamentary nebula surrounding NGC 1275 with slit
spectroscopy or IFU instruments demonstrated that the velocity dispersion of
the ionised optical gas was higher in the central region near the AGN ($\sim
150$ km/s) while diminishing gradually to lower values ($\sim 50$ km/s) in the
outer filaments (Hatch et al. 2006, Gendron-Marsolais et al. 2018). These
observations support the idea that the AGN activity was the source of a higher
level of agitation in the central region while other mechanisms such as the
turbulence and shocks induced by the trailing of ascending radio-filled
bubbles would induce a lower but non-negligible velocity dispersion in the
outskirts of the structure (Falceta-Gonçalves et al. 2010).

The new SITELLE observations at high-spectral resolution confirm that the
central disk-shaped structure with higher velocity dispersion is not due to
multiple velocity components based on visual inspection of the spectra.
Indeed, the regions displaying multiple velocity components are extremely
localized compared to the extended disk-shaped central structure visible in
Fig. 6. Beyond this disk-shaped structure, the velocity dispersion decreases
sharply and remains uniformly low throughout the rest of the filaments, out to
$r\sim 50$ kpc. The central velocity dispersion is almost two times higher in
the central disk-shaped structure than what previous low-spectral observations
showed (Gendron-Marsolais et al. 2018, see left plot of Fig. 13). When
considering only the central bright region by applying a more stringent flux
cut-off of $1\times 10^{-17}\text{ergs}^{-1}\text{cm}^{-2}\text{\AA}^{-1}$,
the mean velocity dispersion of the central disk-shaped structure is $\sim
134$ km/s. The disk-shaped structure seems specifically located at the
position of the central CO(2-1) disk of molecular gas and at the border of the
inflating radio bubble (see right side of Figure 11).

The most striking feature displayed in Fig. 13 is the lack of a smooth
gradient between the high dispersion of the central region ($\sim 134$ km/s)
and the lower dispersion of the outer filaments ($\sim 44$ km/s - see also the
right plot of Figure 13). For the gas in the central region, we could expect
to see a higher velocity dispersion since more gas is likely found near the
central regions, whereas for the outer filaments, we are viewing individual
filaments and therefore, we are probing more of a pencil beam view of the
kinematics in the outer filaments. However, the sharp contrast in velocity
dispersion from the central disk-shaped structure to the filaments beyond this
structure is puzzling. We also note that despite this expected overlap of gas
in the central region, few highly separated velocity component emission lines
are found in this region, which will be discussed in section 3.7.

If we consider the entire system of low dispersion filaments, it has a global
velocity dispersion much greater than $\sim 44$ km/s, as indicated by the
H$\alpha$ velocity dispersion map, even if the central region displaying
higher values is excluded. The uniformity in the (pencil beam) velocity
dispersion of the outer filaments might therefore be reflecting a different
physical process from the one responsible for the global velocity dispersion
of the filament system.

The global velocity dispersion is likely to be connected to motions of the hot
medium, while the pencil beam velocity dispersion of the ionized gas is more
likely to be connected to shearing motions at the interfaces between the
filaments and the hot medium, which we will investigate in section 3.5.

Thus, this result could also imply that two completely different mechanisms
might be at play to introduce such a clear differentiation in velocity
dispersion.

We also compare our result with simulations from Li et al. (2015) (see Figure
13). The brown line shows the average line-of-sight velocity dispersion as a
function of radius in simulated filaments from Li et al. (2015) that reproduce
the ones seen in NGC 1275. We first take the simulation outputs generated
every 10 Myr over a 300 Myr period when the simulated cluster most resembles
Perseus in the morphology and spatial distribution of the H$\alpha$ filaments.
For each output, we make a line-of-sight velocity dispersion map of the
H$\alpha$ gas (with temperatures of $\sim 10^{4}$ K) weighted by emissivity.
Then, the data is split into radial distance bins and averaged for each bin.
We then compute the time-averaged velocity dispersion profile and its
1$\sigma$ scatter (orange shaded area). We can thus see that the simulation
shows lower values of velocity dispersion further away from the central region
which is in accordance with our observational results. Overplotted in purple
and green are the mean and ensemble fits extracted from the annuli seen in the
left side of 13. These datapoints clearly show a drop in velocity dispersion
at a short radial distance away from the central region and matching the
simulated data. The outer filaments display stable low velocity dispersion in
agreement with simulated data.

Figure 13: Left: H$\alpha$ velocity dispersion map. Right: Mean (in purple)
and ensemble fits (in green) across annuli containing 1500 pixels for the
H$\alpha$ velocity dispersion. The error bars for the ensemble fit have been
plotted but are too small to see compared to the data scale. Simulation
results of the velocity dispersion in optical filaments of the Perseus
Cluster. The brown line shows the average line-of-sight velocity dispersion as
a function of radius in the simulated Perseus cluster from Li et al. (2015),
while the 1$\sigma$ scatter is shown though the orange shaded area.

An interesting similarity to our results can be observed in the study of Abell
2597 by Tremblay et al. (2018) as observed with MUSE and ALMA. This study also
demonstrated the presence of a spatial correlation between a central v-shaped
molecular gas structure and its optical emission counterpart in H$\alpha$.
Both of these structures were also found to be comoving and closely tracing
the wake of the X-ray cavities formed by the activity of the BCG’s AGN.
Moreover, when considering the velocity dispersion of the optical gas in Abell
2597 (see Figure 13 of Tremblay et al. 2018), a similar result can be observed
where the correlated emission region displays an extremely high velocity
dispersion (up to $\sim 350$ km/s) which quickly falls to lower values for the
outer filaments ($\sim 50$ km/s) can be seen.

Regarding the filament formation models that have been developed and detailed
previously, Tremblay et al. (2018) explore a unifying model involving chaotic
cold accretion, precipitation, and stimulated feedback through the description
of a galaxy-scaled ”fountain”. In this model, the central cold molecular gas
and optically emitting filaments would supply the accretion reservoir of the
AGN, thus fueling its activity. The jets it produces would then inflate radio
bubbles, buoyantly rising and carving the surrounding ICM, therefore creating
turbulence and thermal instabilities as well as uplifting ionised gas in their
trail (e.g. McNamara et al. 2016 and simulation works by Li & Bryan 2014). The
raised material would then precipitates back to the central potential well
thus sustaining the ”fountain”. Moreover, further thermal instabilities
generated by the turbulent AGN feedback would reinforce the precipitation of
colder gas in slightly denser parts of the ICM, thus facilitating the
formation of extended filamentary nebulae (e.g. Voit 2018, see also McNamara
et al. 2014 and Russell et al. 2019).

###  3.5 Extended Filaments and Turbulent Radiative Mixing Layers

We now investigate a possible formation scenario for the extended filaments
displaying lower velocity dispersion through turbulent radiative mixing
layers. This scenario involves the formation of filaments in situ instead of
beeing dragged out by the adiabatic rise of the radio bubbles carved by the
SMBH jets.

Turbulent mixing layers are frontier layers between gaseous materials at
different temperatures. Due to their extreme difference in internal energy,
the materials will interact and produce a layer of intermediate temperature
where turbulent motions are more prominent. This layer will thus produce
emission lines associated with the intermediate temperature and possibly
shield the inner colder layer from being completely mixed with the higher
temperature material. In the context of filaments in clusters, the hot
intracluster gas at $\sim 4\times 10^{7}$ K (Hitomi Collaboration et al. 2016)
acts as the warm layer while turbulent motions are thought to be due to the
AGN feedback processes and set a frontier layer between this medium and the
colder optically emitting filaments at $10^{4}$ K.

Previous works by Begelman & Fabian (1990) have highlighted the idea of
extended turbulent mixing layers in the intracluster medium. They discussed
that filamentary structures visible in the optical could form out of the
cooling flows of AGN through absorption of far UV emission of turbulent mixing
layers, which would then induce UV and optical emission by photoionization of
the colder gas. However, detections of embedded cold molecular gas all
throughout the filamentary nebula were made later by Salomé et al. (2006),
implying that turbulent radiative mixing layers could be created at the
boundaries between cold molecular gas and the surrounding hot ICM.

Indeed, the ICM of the Perseus cluster is known to have a high temperature
($\sim 4\times 10^{7}$ K, see Hitomi Collaboration et al. 2016), while the
cold molecular gas found all throughout the filaments has a much lower
temperature ($\sim 10-10^{3}$ K, e.g. Salomé et al. 2011). Thus, we might
wonder if the optical emission observed with the SITELLE data could be part of
a radiative turbulent mixing layer between the two media. The presence of a
turbulent mixing layer could then explain the intermediate temperature of the
optical gas.

We do know that the filaments are extremely thin and display a thread-like
structure (Fabian et al. 2008, 2016) which would be reminiscent of the shape
taken by turbulent mixing layers (see Abruzzo et al. 2022). With such a thin
structure, physically close filaments must be connected, leading to single
component emission lines (see Hatch et al. 2006). A higher spectral resolution
than $R=7000$ would be needed to explore in detail the possible multiple
components of their emission lines since none are detected within the outer
filaments after a spectral examination of the SITELLE data.

The velocity dispersion in mixing layers are increased by in situ turbulence
caused by the interaction between material at different temperatures. Recent
simulations (e.g. Ji et al. 2019, Fielding & Bryan 2022, Abruzzo et al. 2022)
show however that the turbulence of material inside the layer remains low
($\sim 30$ km/s.). These simulations results could potentially prove
insightful in regards of the observed mean velocity dispersion value of $\sim
44$ km/s, prevalent within the extended filamentary nebula surrounding NGC
1275.

Hence, when considering the structure of a turbulent mixing layer in
conjunction with our optically emitting extended filaments, it could mean that
the outer layer of turbulence between the cold molecular gas and the hot ICM
could be shielding the inner filaments and preventing them from having a
higher velocity dispersion, leading to a clear dichotomy between inner
filaments, disturbed by the formation and growth of radio bubbles, and outer
quiescent filaments. Therefore, the velocity dispersion in outer extended
filaments could be a proxy for turbulent radiative mixing layers.

Finally, recent works reported the discovery of hidden cooling flows in a
sample of nearby clusters of galaxies, including Perseus (see Fabian et al.
2022, Fabian et al. 2023a, Fabian et al. 2023b). Here, the authors argue that
AGN feedback may not be as efficient in heating the intracluster medium as
initially thought - instead, the intracluster medium would be allowed to cool,
explaining the substantial molecular gas reservoirs found in these systems.
They predict that these cooling flows are not seen at X-ray wavelengths
because they are being obscured by photoelectrically-absorbing cold clouds and
dust (e.g. White et al. 1991, Johnstone et al. 1992, Fabian et al. 1994) - if
this is the case, then the absorbed emission will re-emerge in far infrared.

Indeed, extreme cooling of the gaseous material surrounding BCGs could
prohibit them from being detected due to extremely low temperature and
emissivity (see Fabian et al. 2023a). According to these results cooling flows
of $\sim 30-100$ $M_{\odot}\text{.yr}^{-1}$ could therefore be present within
clusters such as the Perseus cluster of galaxies (Fabian et al. 2022).
Interestingly, it is suggested that these hidden cooling flows could have
internal structures resembling that of turbulent radiative mixing layers,
similar to those proposed here (see Begelman & Fabian 1990, Fabian et al.
2023a). Nevertheless, future observations of the ICM in clusters of galaxies
with upcoming X-ray telescopes such as XRISM will probe a variety of
transitions expected from such hidden cooling flows, providing further insight
into these flows and their connection to multiphase gas in clusters.

###  3.6 Velocity Structure

Figure 14: Left: H$\alpha$ velocity map. Right: Mean (in red) and ensemble
fits (in blue) across annuli containing 1500 pixels for the H$\alpha$
velocity. The error bars for the ensemble fit have been plotted but are too
small to see compared to the data scale.

Now focusing on the analysis of the velocity structure obtained with the new
SITELLE observations, we find a very similar H$\alpha$ velocity map as to what
was previously obtained by Gendron-Marsolais et al. (2018) at lower spectral
resolution observations (see Figure 5 of Gendron-Marsolais et al. 2018 and
left plot of Figure 14). This result strengthens previous conclusions
regarding the dynamics of the filamentary nebula. Moreover, when looking at
the mean and ensemble velocity fits across annuli containing 1500 pixels (see
right plot of Figure 14), there does not appear to be a specific radial
velocity trend throughout the filaments, which reinforces the idea of a
chaotic velocity structure.

Considering the Herschel infrared emission kinematics as studied by Mittal et
al. (2012) and displayed in the upper left panel of Figure 12, we can see that
similar velocity trends could also hint at a comoving nature of the gas in
various wavelengths. Indeed, when considering similar velocity intervals as
Figure 5 in Mittal et al. (2012), we can clearly see that the south-western
filaments kinematics (see top-right plot of Figure 12) display a similar trend
of negative velocities between $-350$ and $-50$ km/s with the spatially
correlated [CII] emission line kinematics (see top-left plot of Figure 12).
This trend is also visible for both intermediate velocity values between $-50$
and $50$ km/s as well as positive velocities between $50$ and $350$ km/s,
although less strikingly (see bottom plots of Figure 12).

Lim et al. (2008) also obtained a velocity map of the central molecular gas
disk, which showed mostly blue-shifted velocities and without sign of global
rotation. To compare directly the velocity maps obtained for the optical
emission to the molecular map, we shifted our map considering a redshift value
of $z=0.01756$ used by Lim et al. (2008) instead of the adopted $z=0.017284$.
After this correction, the H$\alpha$ emission shows a similar velocity
structure for the central disk-shaped structure (see Figure 15 and Figure 2 of
Lim et al. 2008).

Figure 15: Velocity map in H$\alpha$ and [N ii] of the central region of the
filamentary nebula shifted to a redshift of z=0.01756 in order to match the
study of Lim et al. (2008). The contours of the central disk observed in
CO(2-1) with the SMA by Lim et al. (2008) are superimposed in green. Figure
16: Velocity profiles of selected filaments in the nebula surrounding NGC 1275
(in km/s with the green lines showing a null velocity). For the first three
profiles, we show in blue the velocity of each pixel bin found in the region,
while the red points illustrates the mean taken in ten subregions of equal
widths. The velocity profile of the Horseshoe filament only displays the mean
velocity across 10 subregions.

The detection of similar disk-shaped structures can also be found in
simulation works such as those done by Li & Bryan (2014), where they exhibit
higher levels of flux and originate from the cooling of gas onto the black
hole’s potential well. However, the main difference to these simulations is
the fact that the central disk always displayed a rotating motion along the
plane perpendicular to the jets, which is not the case for our observations
where the motion seems more chaotic (see Figures 14 & 15). This difference
shows that these simulations seems to not be fully capturing the physical
processes at play in the formation and evolution of the filaments we are
observing in NGC 1275. Moreover, the presence of radio bubbles fueled by the
SMBH relativistic jets, which seem spatially linked to the presence of this
disk, was not considered in previous simulations until recently (see Yang et
al. 2019). However, these simulations incorporating the effect of expanding
radio bubbles do not yet study their impact on the velocity dispersion and
kinematics of the surrounding medium of the bubbles. This aspect of 3D
hydrodynamical simulations of AGN feedback still needs to be explored to
properly understand the prominent role of radio bubbles on their surrounding
environment.

In that sense, recent simulation works by Zhang et al. (2022) clearly show the
turbulence and eddy formation as well as the uplift of material in the wake of
rising radio bubbles. Though the simulation models only involve detached
bubbles approaching their terminal velocities, it is still of interest to see
that material close to the central region gets lifted upwards and acts as the
upper layer of the deformation close to the bubble’s lower boundary (see top
panels of Figure 4 from Zhang et al. 2022). Therefore, an argument could be
made that the central region or disk visible in our observations, displaying a
higher level of velocity dispersion as well as a clear spatial correlation to
cold molecular gas, could be lifted through the detachment and adiabatic rise
of the bubbles thereafter forming future filamentary structures around NGC
1275.

Thanks to the high-spatial and spectral resolution of SITELLE, we can also
study the velocity profiles of targeted filaments in their entirety. To do
this, we extracted the velocity measurements and means within 10 bins over
some specific filaments as in Gendron-Marsolais et al. (2018). Figure 16 shows
that the velocities of the outer filaments are significantly more
heterogeneous and chaotic, while the velocities of the central disk display
less variations. Its velocity profile could also hint at a potential rotation
pattern in the central radius of 2.5 kpc around the AGN, however, the error
bars prevent us from making a clear conclusion.

The northern filament displays a velocity profile ranging from slightly
positive to slightly negative values the further away from the base of the
filament, which would indicate stretching. Similar results were obtained both
with SITELLE (Gendron-Marsolais et al. 2018) and the Gemini Multi-Object
Spectrograph (Hatch et al. 2006). The southern filament mostly shows negative
velocities slightly decreasing then increasing along the filament, while the
central filament seems to display an inverse trend with mostly positive
velocity values. If we now bring our attention to the averaged velocity
profile of the Horseshoe filament, we can see that both its bases (first and
last datapoints of the lower left panel of Figure 16) seem to display an
average velocity closer to negative velocities of $\sim-25$ km/s while the tip
of the Horseshoe (represented by the fifth and sixth datapoints of the lower
left panel of Figure 16) also display a drop in averaged velocity closer to a
null velocity. On the other hand, the branches of the Horsehoe clearly display
positively increasing then decreasing averaged velocity values (as shown in
the lower left panel of Figure 16). This averaged velocity profile could
indicate that the branches of the Horsehoe filament might be stretching
horizontally as opposed to the bases and tip who seem to follow a trend of
displacement through the traction of a radio emitting bubble (see Hatch et al.
2006). However, the limited detection of the tip of the Horseshoe, as can be
seen on the right-hand side of Figure 16, prevents us from making affirmative
statements regarding these central bins of the Horseshoe averaged velocity
profile.

##  4 Conclusion

We performed the analysis of new high-spectral resolution observations with
SITELLE and obtained new flux, velocity, and velocity dispersion maps of [S
ii]$\lambda 6716$, [S ii]$\lambda 6731$, [N ii]$\lambda 6584$,
H$\alpha$(6563Å), and [N ii]$\lambda 6548$ emission lines for the filamentary
nebula surrounding NGC 1275, the brightest cluster galaxy of the Perseus
cluster.

  * •

We detected a central disk-shaped structure displaying higher averaged flux
($\sim 1\times 10^{-17}-2\times 10^{-16}$ erg.s-1.cm-2.$\AA^{-1}$) and
velocity dispersion ($\sim 134$ km/s) than the rest of the filaments which is
also spatially correlated with a disk-shaped structure as seen in CO(2-1)
associated with molecular gas. Both of these structures seem to spatially
correlate with the wake of the radio bubbles that have been inflated through
the relativistic jets of the supermassive black hole at the center of the
galaxy. However, this disk-shaped feature does not display a clear rotation
pattern which entails a definitive difference from similar structures obtained
through simulations.

  * •

The rest of the filamentary structure displays fainter flux measurement ($\sim
1\times 10^{-18}$ erg.s-1.cm-2.$\AA^{-1}$) as well as a much lower velocity
dispersion ($\sim 44$ km/s) across the outer filaments, thus implying a
potential more quiescent formation mechanism.

  * •

Thanks to our very high-spectral resolution, we also managed to detect regions
and knots displaying multiple emission line components. However, they are
extremely localized and only found in the central part of the filamentary
nebula within $r<10$ kpc. Nevertheless, a future study of these structures
could potentially help us to gain more insight into the three-dimensional
structure of the central filaments.

  * •

Regarding the formation model explored for this filamentary nebula, it seems
that a unifying model as explored by Tremblay et al. (2018) could potentially
explain the observed characteristics of the emitting gas observed flux and
velocity dispersion measurements obtained through the analysis of the SITELLE
observations of NGC 1275. Indeed, regarding the galaxy-scale fountain model
explored by Tremblay et al. (2018) we observe similar trends both in terms of
kinematics and velocity dispersion between NGC 1275 and Abell 2597. These
similarities are also seen in the comoving nature of filamentary nebulaes with
both cold molecular structures and surrounding gas. Therefore, a unifying
model of formation through the inflow of cold molecular clouds toward the AGN
could thus feed its accretion and drive the formation of radio bubbles. This
would in turn uplift multiphase material away from the BCG which could then
precipitate back as toward the AGN and supply the fountain, while turbulent
radiative mixing layers could form between the hot ICM and cold molecular gas.
However, contentious points still remain to be explored to properly comprehend
the mechanisms leading to the formation of such extended filamentary nebula.

Through our analysis of new high-spectral resolution observations of the
filamentary nebula surrounding NGC 1275, we reinforced the previous results
established by Gendron-Marsolais et al. (2018) and discovered new structures
in the optical emission of the filaments. However, these are the first results
obtained with this dataset and we expect to get more through an improved
analysis of the emission close to the AGN, a study of the SN1 and SN2 filters
of SITELLE, as well as the calculation of the velocity structure function with
these new maps. Finally, new X-ray observations with the XRISM space telescope
(XRISM Science Team 2020), the successor of Hitomi, will enable a breakthrough
in the study of AGN feedback. This study will offer a touchstone for the
analysis of renewed X-ray observations of NGC 1275.

The authors would like to thank the Canada-France-Hawaii Telescope (CFHT)
which is operated by the National Research Council (NRC) of Canada, the
Institut National des Sciences de l’Univers of the Centre National de la
Recherche Scientifique (CNRS) of France, and the University of Hawaii. The
observations at the CFHT were performed with care and respect from the summit
of Maunakea which is a significant cultural and historic site. B.V.
acknowledges financial support from the physics departement of the Université
de Montréal. J.H.-L. acknowledges support from NSERC via the Discovery grant
program, as well as the Canada Research Chair program. M.G.-M. acknowledges
financial support from the grant CEX2021-001131-S funded by MCIN/AEI/
10.13039/501100011033, from the coordination of the participation in SKA-
SPAIN, funded by the Ministry of Science and Innovation (MCIN). J.L.
acknowledges support from the Research Grants Council of Hong Kong through
grant 17300620. N.W. is supported by the GACR grant 21-13491X. Y.L.
acknowledges financial support from NSF grants AST-2107735 and AST-2219686,
NASA grant 80NSSC22K0668, and Chandra X-ray Observatory grant TM3-24005X.
L.R.-N. is grateful to the National Science foundation NSF - 2109124 and the
Natural Sciences and Engineering Research Council of Canada NSERC -
RGPIN-2023-03487 for their support. B.V. also personally acknowledges Pr.
Christopher Conselice for sharing observational data of NGC 1275 in the
optical, as well as Dr. Rupal Mittal for sharing Herschel kinematic data of
NGC 1275 in the infrared.

##  Appendix A Background Variability

In this section, we display two spectra extracted from background regions (see
Figure 17) which illustrate the clear variability in background sky emission
at high-spectral resolution.

Figure 17: Comparison of the spectra extracted from two background regions
denoted by the numbers 1 and 8 at high-spectral resolution. The main emission
lines positions are indicated by dotted lines. The gray shaded area represents
the location of the principal sky lines overlapping with the [S ii] emission
lines doublet.

##  Appendix B Signal-to-Noise Ratio

In this section, we present the signal-to-noise ratio map obtained with the
create_snr_map function of LUCI before applying the weighted Voronoi
tesselation binning. As can be seen in Figure 18, the overall signal-to-noise
ratio is low across the entire filamentary nebula and thus binning is
required.

Figure 18: Signal-to-noise ratio map in linear scale of the high-spectral
resolution observations of the filamentary nebula surrounding NGC 1275 with
SITELLE.

##  Appendix C Multiple Emission Line Components Spectra

In this section, we show a small number of spectra belonging to localized
region of the filamentary nebula and displaying multiple emission line
components. Their central respective coordinates are the following : RA :
3:19:48.165, DEC : +41:30:54.275 ; RA : 3:19:46.92, DEC : +41:30:51.703 ; RA :
3:19:46.623, DEC : +41:30:40.277

Figure 19: Spectra of localized regions of the filamentary nebula displaying
multiple components emission lines.

## References

  * Abell et al. (1989) Abell, G. O., Corwin, Jr., H. G., & Olowin, R. P. 1989, The Astrophysical Journal Supplement Series, 70, 1, doi: 10.1086/191333
  * Abruzzo et al. (2022) Abruzzo, M. W., Fielding, D. B., & Bryan, G. L. 2022, arXiv e-prints, arXiv:2210.15679, doi: 10.48550/arXiv.2210.15679
  * Bahcall (1977) Bahcall, N. A. 1977, In: Annual review of astronomy and astrophysics. Volume 15\. (A78-16576 04-90) Palo Alto, Calif., Annual Reviews, Inc., 1977, p. 505-540., 15, 505, doi: 10.1146/annurev.aa.15.090177.002445
  * Begelman & Fabian (1990) Begelman, M. C., & Fabian, A. 1990, Monthly Notices of the Royal Astronomical Society, 244, 26P
  * Best et al. (2007) Best, P. N., Von Der Linden, A., Kauffmann, G., Heckman, T. M., & Kaiser, C. R. 2007, Monthly Notices of the Royal Astronomical Society, 379, 894, doi: 10.1111/j.1365-2966.2007.11937.x
  * Bittner et al. (2019) Bittner, A., Falcón-Barroso, J., Nedelchev, B., et al. 2019, Astronomy & Astrophysics, Volume 628, id.A117, 14 pp., 628, A117, doi: 10.1051/0004-6361/201935829
  * Boehringer et al. (1993) Boehringer, H., Voges, W., Fabian, A. C., Edge, A. C., & Neumann, D. M. 1993, mnras, 264, L25, doi: 10.1093/mnras/264.1.L25
  * Canning et al. (2010) Canning, R., Fabian, A., Johnstone, R., et al. 2010, Monthly Notices of the Royal Astronomical Society, 405, 115
  * Canning et al. (2014) Canning, R. E. A., Ryon, J. E., Gallagher, J. S., et al. 2014, Monthly Notices of the Royal Astronomical Society, 444, 336, doi: 10.1093/mnras/stu1191
  * Cavaliere et al. (1971) Cavaliere, A. G., Gursky, H., & Tucker, W. H. 1971, Nature, 231, 437, doi: 10.1038/231437a0
  * Collaboration et al. (2018) Collaboration, H., Aharonian, F., Akamatsu, H., et al. 2018, Publications of the Astronomical Society of Japan, 70, doi: 10.1093/pasj/psx138
  * Conselice et al. (2001) Conselice, C. J., Gallagher III, J. S., & Wyse, R. F. 2001, The Astronomical Journal, 122, 2281
  * Crawford et al. (1999) Crawford, C. S., Allen, S. W., Ebeling, H., Edge, A. C., & Fabian, A. C. 1999, Monthly Notices of the Royal Astronomical Society, 306, 857, doi: 10.1046/j.1365-8711.1999.02583.x
  * Dhawan et al. (1998) Dhawan, V., Kellermann, K. I., & Romney, J. D. 1998, The Astrophysical Journal, 498, L111, doi: 10.1086/311313
  * Drissen et al. (2019) Drissen, L., Martin, T., Rousseau-Nepton, L., et al. 2019, mnras, 485, 3930, doi: 10.1093/mnras/stz627
  * Dutta et al. (2022) Dutta, A., Sharma, P., & Nelson, D. 2022, Monthly Notices of the Royal Astronomical Society, 510, 3561, doi: 10.1093/mnras/stab3653
  * Fabian et al. (2022) Fabian, A., Ferland, G., Sanders, J., et al. 2022, Monthly Notices of the Royal Astronomical Society, 515, 3336
  * Fabian et al. (2023a) Fabian, A., Sanders, J., Ferland, G., et al. 2023a, Monthly Notices of the Royal Astronomical Society, 521, 1794
  * Fabian et al. (2023b) —. 2023b, Monthly Notices of the Royal Astronomical Society, 524, 716
  * Fabian et al. (1994) Fabian, A., Tawara, Y., Bautz, M., & Arnaud, K. 1994, ASCA observations of cooling flows in clusters of galaxies, Tech. rep., SCAN-9410345
  * Fabian et al. (2008) Fabian, A. C., Johnstone, R. M., Sanders, J. S., et al. 2008, Nature, 454, 968, doi: 10.1038/nature07169
  * Fabian et al. (2003) Fabian, A. C., Sanders, J. S., Crawford, C. S., et al. 2003, Monthly Notices of the Royal Astronomical Society, 344, L48, doi: 10.1046/j.1365-8711.2003.06856.x
  * Fabian et al. (2000) Fabian, A. C., Sanders, J. S., Ettori, S., et al. 2000, Monthly Notices of the Royal Astronomical Society, 318, L65, doi: 10.1046/j.1365-8711.2000.03904.x
  * Fabian et al. (2011) Fabian, A. C., Sanders, J. S., Allen, S. W., et al. 2011, Monthly Notices of the Royal Astronomical Society, 418, 2154, doi: 10.1111/j.1365-2966.2011.19402.x
  * Fabian et al. (2016) Fabian, A. C., Walker, S. A., Russell, H. R., et al. 2016, mnras, 461, 922, doi: 10.1093/mnras/stw1350
  * Fabian et al. (2016) Fabian, A. C., Walker, S., Russell, H., et al. 2016, Monthly Notices of the Royal Astronomical Society, 461, 922
  * Falceta-Gonçalves et al. (2010) Falceta-Gonçalves, D., de Gouveia Dal Pino, E. M., Gallagher, J. S., & Lazarian, A. 2010, The Astrophysical Journal, 708, L57, doi: 10.1088/2041-8205/708/1/L57
  * Ferland et al. (2009) Ferland, G. J., Fabian, A. C., Hatch, N. A., et al. 2009, Monthly Notices of the Royal Astronomical Society, 392, 1475, doi: 10.1111/j.1365-2966.2008.14153.x
  * Fielding & Bryan (2022) Fielding, D. B., & Bryan, G. L. 2022, apj, 924, 82, doi: 10.3847/1538-4357/ac2f41
  * Forman et al. (1972) Forman, W., Kellogg, E., Gursky, H., Tananbaum, H., & Giacconi, R. 1972, The Astrophysical Journal, 178, 309, doi: 10.1086/151791
  * Gaia Collaboration (2020) Gaia Collaboration. 2020, VizieR Online Data Catalog, I/350, doi: 10.26093/cds/vizier.1350
  * Gaspari et al. (2015) Gaspari, M., Brighenti, F., & Temi, P. 2015, Astronomy & Astrophysics, 579, A62
  * Gaspari et al. (2013) Gaspari, M., Ruszkowski, M., & Oh, S. P. 2013, Monthly Notices of the Royal Astronomical Society, 432, 3401
  * Gaspari et al. (2012) Gaspari, M., Ruszkowski, M., & Sharma, P. 2012, The Astrophysical Journal, 746, 94
  * Gendron-Marsolais et al. (2018) Gendron-Marsolais, M., Hlavacek-Larrondo, J., Martin, T. B., et al. 2018, Monthly Notices of the Royal Astronomical Society, 479, L28, doi: 10.1093/mnrasl/sly084
  * Gendron-Marsolais et al. (2020) Gendron-Marsolais, M., Hlavacek-Larrondo, J., van Weeren, R. J., et al. 2020, Monthly Notices of the Royal Astronomical Society, 499, 5791, doi: 10.1093/mnras/staa2003
  * Graham et al. (2008) Graham, J., Fabian, A. C., & Sanders, J. S. 2008, Monthly Notices of the Royal Astronomical Society, 386, 278, doi: 10.1111/j.1365-2966.2008.13027.x
  * Gursky et al. (1971) Gursky, H., Kellogg, E. M., Leong, C., Tananbaum, H., & Giacconi, R. 1971, The Astrophysical Journal, 165, L43, doi: 10.1086/180713
  * Hamer et al. (2014) Hamer, S. L., Edge, A. C., Swinbank, A. M., et al. 2014, mnras, 437, 862, doi: 10.1093/mnras/stt1949
  * Hamer et al. (2016) Hamer, S. L., Edge, A. C., Swinbank, A. M., et al. 2016, Monthly Notices of the Royal Astronomical Society, 460, 1758, doi: 10.1093/mnras/stw1054
  * Harris et al. (2020) Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2
  * Hatch et al. (2006) Hatch, N. A., Crawford, C. S., Johnstone, R. M., & Fabian, A. C. 2006, Monthly Notices of the Royal Astronomical Society, 367, 433, doi: 10.1111/j.1365-2966.2006.09970.x
  * Hitomi Collaboration et al. (2016) Hitomi Collaboration, Aharonian, F., Akamatsu, H., et al. 2016, Nature, 535, 117, doi: 10.1038/nature18627
  * Ho et al. (2009) Ho, I. T., Lim, J., & Dinh-V-Trung. 2009, The Astrophysical Journal, 698, 1191, doi: 10.1088/0004-637X/698/2/1191
  * Ho et al. (2009) Ho, I. T., Lim, J., & Dinh-V-Trung. 2009, apj, 698, 1191, doi: 10.1088/0004-637X/698/2/1191
  * Hudson et al. (2010) Hudson, D. S., Mittal, R., Reiprich, T. H., et al. 2010, Astronomy & Astrophysics, 513, A37
  * Hunter (2007) Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, doi: 10.1109/MCSE.2007.55
  * Ji et al. (2019) Ji, S., Oh, S. P., & Masterson, P. 2019, Monthly Notices of the Royal Astronomical Society, 487, 737
  * Johnstone et al. (1992) Johnstone, R., Fabian, A., Edge, A., & Thomas, P. 1992, Monthly Notices of the Royal Astronomical Society, 255, 431
  * Kent & Sargent (1979) Kent, S. M., & Sargent, W. L. W. 1979, The Astrophysical Journal, 230, 667, doi: 10.1086/157125
  * Kewley et al. (2006) Kewley, L. J., Groves, B., Kauffmann, G., & Heckman, T. 2006, Monthly Notices of the Royal Astronomical Society, 372, 961, doi: 10.1111/j.1365-2966.2006.10859.x
  * Kewley et al. (2019) Kewley, L. J., Nicholls, D. C., & Sutherland, R. S. 2019, Annual Review of Astronomy and Astrophysics, 57, 511
  * Li & Bryan (2014) Li, Y., & Bryan, G. L. 2014, apj, 789, 153, doi: 10.1088/0004-637X/789/2/153
  * Li & Bryan (2014) Li, Y., & Bryan, G. L. 2014, The Astrophysical Journal, 789, 54, doi: 10.1088/0004-637X/789/1/54
  * Li et al. (2015) Li, Y., Bryan, G. L., Ruszkowski, M., et al. 2015, The Astrophysical Journal, 811, 73
  * Lim et al. (2008) Lim, J., Ao, Y., & Dinh-V-Trung. 2008, The Astrophysical Journal, 672, 252, doi: 10.1086/523664
  * Lim et al. (2012) Lim, J., Ohyama, Y., Yan, C.-H., Dinh-V-Trung, & Wang, S.-Y. 2012, The Astrophysical Journal, 744, 112, doi: 10.1088/0004-637X/744/2/112
  * Lynds (1970) Lynds, R. 1970, The Astrophysical Journal, 159
  * Martin et al. (2016) Martin, T. B., Prunet, S., & Drissen, L. 2016, Monthly Notices of the Royal Astronomical Society, 463, 4223, doi: 10.1093/mnras/stw2315
  * McDonald et al. (2010) McDonald, M., Veilleux, S., Rupke, D. S. N., & Mushotzky, R. 2010, The Astrophysical Journal, 721, 1262, doi: 10.1088/0004-637X/721/2/1262
  * McDonald et al. (2010) McDonald, M., Veilleux, S., Rupke, D. S. N., & Mushotzky, R. 2010, apj, 721, 1262, doi: 10.1088/0004-637X/721/2/1262
  * McNamara & Nulsen (2007) McNamara, B. R., & Nulsen, P. E. J. 2007, Annual Review of Astronomy & Astrophysics, vol. 45, Issue 1, pp.117-175, 45, 117, doi: 10.1146/annurev.astro.45.051806.110625
  * McNamara et al. (1996) McNamara, B. R., O’Connell, R. W., & Sarazin, C. L. 1996, The Astronomical Journal, 112, 91, doi: 10.1086/117991
  * McNamara et al. (2016) McNamara, B. R., Russell, H. R., Nulsen, P. E. J., et al. 2016, The Astrophysical Journal, 830, 79, doi: 10.3847/0004-637X/830/2/79
  * McNamara et al. (2014) McNamara, B. R., Russell, H. R., Nulsen, P. E. J., et al. 2014, ApJ, 785, 44, doi: 10.1088/0004-637X/785/1/44
  * Million & Allen (2009) Million, E., & Allen, S. 2009, Monthly Notices of the Royal Astronomical Society, 399, 1307
  * Minkowski (1957) Minkowski, R. 1957, 4, 107.  https://ui.adsabs.harvard.edu/abs/1957IAUS....4..107M
  * Mittal et al. (2012) Mittal, R., Oonk, J. R., Ferland, G. J., et al. 2012, Monthly Notices of the Royal Astronomical Society, 426, 2957
  * Nagai et al. (2019) Nagai, H., Onishi, K., Kawakatu, N., et al. 2019, The Astrophysical Journal, 883, 193, doi: 10.3847/1538-4357/ab3e6e
  * Price-Whelan et al. (2018) Price-Whelan, a. A. M., Sip\Hocz, B. M., Günther, H. M., et al. 2018, The Astronomical Journal, 156, 123, doi: 10.3847/1538-3881/aabc4f
  * Randall et al. (2015) Randall, S. W., Nulsen, P. E. J., Jones, C., et al. 2015, The Astrophysical Journal, 805, 112, doi: 10.1088/0004-637X/805/2/112
  * Rhea et al. (2020a) Rhea, C., Hlavacek-Larrondo, J., Perreault-Levasseur, L., Gendron-Marsolais, M.-L., & Kraft, R. 2020a, The Astronomical Journal, 160, 202, doi: 10.3847/1538-3881/abb468
  * Rhea et al. (2021a) Rhea, C., Hlavacek-Larrondo, J., Rousseau-Nepton, L., Vigneron, B., & Guité, L.-S. 2021a, Research Notes of the American Astronomical Society, 5, 208, doi: 10.3847/2515-5172/ac2517
  * Rhea et al. (2020b) Rhea, C., Rousseau-Nepton, L., Prunet, S., Hlavacek-Larrondo, J., & Fabbro, S. 2020b, The Astrophysical Journal, 901, 152, doi: 10.3847/1538-4357/abb0e3
  * Rhea et al. (2021b) Rhea, C., Rousseau-Nepton, L., Prunet, S., et al. 2021b, The Astrophysical Journal, 910, 129, doi: 10.3847/1538-4357/abe627
  * Riffel et al. (2020) Riffel, R. A., Storchi-Bergmann, T., Zakamska, N. L., & Riffel, R. 2020, mnras, 496, 4857, doi: 10.1093/mnras/staa1922
  * Robitaille et al. (2013) Robitaille, T. P., Tollerud, E. J., Greenfield, P., et al. 2013, Astronomy & Astrophysics, 558, A33, doi: 10.1051/0004-6361/201322068
  * Rousseau-Nepton et al. (2019) Rousseau-Nepton, L., Martin, R. P., Robert, C., et al. 2019, MNRAS, 489, 5530, doi: 10.1093/mnras/stz2455
  * Rubin et al. (1977) Rubin, V., Oort, J., Ford, W., & Peterson, C. 1977, Astrophysical Journal, 211, 693
  * Russell et al. (2019) Russell, H. R., McNamara, B. R., Fabian, A. C., et al. 2019, Monthly Notices of the Royal Astronomical Society, 490, 3025, doi: 10.1093/mnras/stz2719
  * Salomé et al. (2011) Salomé, P., Combes, F., Revaz, Y., et al. 2011, Astronomy & Astrophysics, Volume 531, id.A85, 8 pp., 531, A85, doi: 10.1051/0004-6361/200811333
  * Salomé et al. (2008) —. 2008, Astronomy and Astrophysics, Volume 484, Issue 2, 2008, pp.317-325, 484, 317, doi: 10.1051/0004-6361:200809493
  * Salomé et al. (2006) Salomé, P., Combes, F., Edge, A. C., et al. 2006, Astronomy and Astrophysics, Volume 454, Issue 2, August I 2006, pp.437-445, 454, 437, doi: 10.1051/0004-6361:20054745
  * Sanchez Almeida et al. (2012) Sanchez Almeida, J., Terlevich, R., Terlevich, E., Fernandes, R., & Morales-Luis, A. 2012, Astrophysical Journal, 756, doi: 10.1088/0004-637X/756/2/163
  * Sand et al. (2004) Sand, D. J., Treu, T., Smith, G. P., & Ellis, R. S. 2004, The Astrophysical Journal, 604, 88, doi: 10.1086/382146
  * Team (2020) Team, X. S. 2020, arXiv preprint arXiv:2003.04962
  * Tremblay et al. (2018) Tremblay, G. R., Combes, F., Oonk, J. B. R., et al. 2018, The Astrophysical Journal, 865, 13, doi: 10.3847/1538-4357/aad6dd
  * Van Rossum & Drake (2009) Van Rossum, G., & Drake, F. L. 2009, PYTHON 2.6 reference manual, CreateSpace
  * Virtanen et al. (2020) Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261, doi: 10.1038/s41592-019-0686-2
  * Voigt & Fabian (2006) Voigt, L. M., & Fabian, A. C. 2006, Monthly Notices of the Royal Astronomical Society, 368, 518, doi: 10.1111/j.1365-2966.2006.10199.x
  * Voit et al. (2015) Voit, G., Donahue, M., Bryan, G., & McDonald, M. 2015, Nature, 519, 203
  * Voit (2018) Voit, G. M. 2018, The Astrophysical Journal, 868, 102, doi: 10.3847/1538-4357/aae8e2
  * Voit et al. (2008) Voit, G. M., Cavagnolo, K. W., Donahue, M., et al. 2008, The Astrophysical Journal, 681, L5, doi: 10.1086/590344
  * Voit & Donahue (2015) Voit, G. M., & Donahue, M. 2015, The Astrophysical Journal Letters, 799, L1
  * Voit et al. (2017) Voit, G. M., Meece, G., Li, Y., et al. 2017, The Astrophysical Journal, 845, 80, doi: 10.3847/1538-4357/aa7d04
  * Walker et al. (2015) Walker, S. A., Kosec, P., Fabian, A. C., & Sanders, J. S. 2015, Monthly Notices of the Royal Astronomical Society, 453, 2480, doi: 10.1093/mnras/stv1829
  * White et al. (1991) White, D., Fabian, A., Johnstone, R., Mushotzky, R., & Arnaud, K. 1991, Monthly Notices of the Royal Astronomical Society, 252, 72
  * Yang et al. (2019) Yang, H.-Y. K., Gaspari, M., & Marlow, C. 2019, The Astrophysical Journal, 871, 6, doi: 10.3847/1538-4357/aaf4bd
  * Yu et al. (2015) Yu, A. P. Y., Lim, J., Ohyama, Y., Chan, J. C. C., & Broadhurst, T. 2015, apj, 814, 101, doi: 10.1088/0004-637X/814/2/101
  * Zeidler et al. (2019) Zeidler, P., Nota, A., Sabbi, E., et al. 2019, The Astronomical Journal, 158, 201, doi: 10.3847/1538-3881/ab44bb
  * Zhang et al. (2022) Zhang, C., Zhuravleva, I., Gendron-Marsolais, M.-L., et al. 2022, mnras, 517, 616, doi: 10.1093/mnras/stac2282
  * Zhuravleva et al. (2014) Zhuravleva, I., Churazov, E., Schekochihin, A. A., et al. 2014, Nature, 515, 85, doi: 10.1038/nature13830