High-spectral-resolution Observations of the Optical Filamentary Nebula Surrounding NGC 1275

We present new high-spectral-resolution observations (R = λ/Δλ = 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 with a field of view of 11′×11′ , encapsulating the entire filamentary structure of ionized gas despite its large size of 80 kpc × 50 kpc. Here, we present renewed fluxes, velocities, and velocity dispersion maps that show in great detail the kinematics of the optical nebula at [S ii] λ6716, [S ii] λ6731, [N ii] λ6584, Hα (6563 Å), and [N ii] λ6548. These maps reveal the existence of a bright flattened disk-shaped structure in the core extending to r ∼10 kpc and dominated by a chaotic velocity field. This structure is located in the wake of X-ray cavities and characterized by a high mean velocity dispersion of 134 km s−1. The disk-shaped structure is surrounded by an extended array of filaments spread out to r ∼ 50 kpc that are 10 times fainter in flux, remarkably quiescent, and have a uniform mean velocity dispersion of 44 km s−1. This stability is puzzling given that the cluster core exhibits several energetic phenomena. Based on these results, we argue that there are two mechanisms that 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 spreading throughout the core.

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 ∼ 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 (∼ 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 Hα 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 × 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 (∼ 8200 km/s) associated with a forefront spiral galaxy falling onto NGC 1275 (Yu et al. 2015), and a low-velocity (LV) structure (∼ 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 highresolution imaging, integral field, and long-slit spectroscopy (WIYN & KPNO).These observations brought forth the first velocity map of the central ∼ 45 arcsec (∼ 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 arcmin × 11 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 ≳ 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 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 kpc arcmin −1 .This z also corresponds to a luminosity distance of 75.5 Mpc, assuming H 0 = 69.6 km s −1 Mpc −1 , Ω M = 0.286 and Ω vac = 0.714  (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).

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]λ6717 and [S ii]λ6731 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.

Weighted Voronoi Tessellation -WVT
From a preliminary analysis of the high-spectral resolution data of NGC 1275, we noticed that the signalto-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 Hα 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 × 10 −17 erg s −1 cm −2 after the fitting to our final maps to properly eliminate

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.nddatapackage 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.interpolatepackage, 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.

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(Rhea et al. ,b, 2021a,b) ,b) 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.htmlfor 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.minimizefunction from the scipy package.
This function uses the Sequential Least Squares Programming (SLSQP) optimization algorithm.Since SITELLE's Instrumental Spectra Function (ISFsee 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]λ6716, [S ii]λ6731, [N ii]λ6584, Hα(6563 Å), and [N ii]λ6548, where we separated the fitting procedure by first considering the SNR of the Hα 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 Hα 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.

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 threedimensional structure of the filaments is currently un-known, 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 ∼ 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 ∼ 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.
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 ∼ 2.6 kpc from the center of the galaxy.There was also evidence of a small number (∼ 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 multiplecomponent analysis of the few localized regions with overlapping filaments, as well as of the core, will be performed in the future.

[SII] Emission Lines Fitting
Regarding the detection and fitting of the [S ii]λ6716 and [S ii]λ6731 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).How-ever, 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]λ6716 and [S ii]λ6731 doublet SNR, which are fainter than the [N ii]λ6583, Hα(6563 Å), and [N ii]λ6548 lines.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 ∼ 80 km/s.However, with a high-spectral resolution of R = 7000, the lower velocity dispersion value that can be determined is of ∼ 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.

Emission Line Intensity Ratios and Flux Maps
First, the Hα averaged flux map visible in the upper plot of Figure 6 shows a disk-shaped structure in the central region with a size of ∼ 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 Hα fluxes, but most of them have a homogeneous lower flux.
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]λ6583/Hα 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 Hα flux ≫ [N ii]λ6583 flux), photons from young stars can be the ionizing source, while for a higher ratio (meaning Hα flux ≤ [N ii]λ6583 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]λ6716 by Hα(6563 Å) can be used as a confirmation value for various ionization mechanisms.Here, to   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]λ6583/Hα 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 : 03:19:48.16and 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 ± 0.5 to 0.6 ± 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 lowspectral 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. 2010Canning et al. , 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]λ6548 / Hα 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]λ6548 / Hα emission line ratio would be close to ∼ 0.3.However, if we consider the ratio of [S ii]/Hα, displayed in the bottom left plot of Figure 10, we can see that the outer filaments show higher ratios above ∼ 1, nevertheless, various behavior are observed for different filaments.In the case of ionization by cosmic rays, the ratio of [S ii]/Hα 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]/Hα ratio values above ∼ 2.0.Nevertheless, in the bottom right plot of Figure 10, we produced the mean and ensemble fit results of the [S ii]λ6716/Hα ratio across annuli containing 1500 pixels each, we can see that most mean values are constrained between ∼ 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)

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 Xrays (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).
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 ∼ 4 × 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 Hα, as well as the Xray emission between 0.5 and 2.0 keV.The X-ray image shown in Figure 11 was obtained by combining several Chandra observations between 0.5 and 2.0 keV and correcting the exposure of the background subtracted image.The exposure time is comprised between 800 ks and 1 Ms.Our new observations with SITELLE as seen in Figure 11 also show that the Hα flux contours spatially correlate with the CO(2-1) molecular gas as seen by Lim et al. (2008), especially in the case of the leftside 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 Hα 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 struc-ture (∼ 1 × 10 −17 erg s −1 cm −2 Å−1 flux) as opposed to the outer filaments (∼ 1 × 10 −18 erg s −1 cm −2 Å−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 ∼ 0.06, most of the filaments would be undetectable leaving only the central bright region surrounded by unresolved features (see Fig. 16 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 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.

Velocity Dispersion Structure
Previous observations of the filamentary nebula surrounding NGC 1275 with slit spectroscopy or IFU in- struments demonstrated that the velocity dispersion of the ionised optical gas was higher in the central region near the AGN (∼ 150 km/s) while diminishing gradually to lower values (∼ 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 ∼ 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 1×10 −17 erg s −1 cm −2 Å−1 , the mean velocity dispersion of the central disk-shaped structure is ∼ 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 (∼ 134 km/s) and the lower dispersion of the outer filaments (∼ 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 ∼ 44 km/s, as indicated by the Hα velocity dis-persion 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 Hα filaments.For each output, we make a line-ofsight velocity dispersion map of the Hα gas (with temperatures of ∼ 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 1σ 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.
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 Hα.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 ∼ 350 km/s) which quickly falls to lower values for the outer filaments (∼ 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 andRussell et al. 2019).

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 ∼ 4 × 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 lay-ers 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 (∼ 4×10 7 K, see Hitomi Collaboration et al. 2016), while the cold molecular gas found all throughout the filaments has a much lower temperature (∼ 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(Fabian et al. , 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 (∼ 30 km/s.).These simulations results could potentially prove insightful in regards of the observed mean velocity dispersion value of ∼ 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 ve-locity 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 ∼ 30 − 100 M ⊙ .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.

Velocity Structure
Now focusing on the analysis of the velocity structure obtained with the new SITELLE observations, we find a very similar Hα 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 consider-  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 blueshifted 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 Hα emission shows a similar velocity structure for the central disk-shaped structure (see Figure 15 and Figure 2 of Lim et al. 2008).
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 perpendicu-lar 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 ∼ −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.• We detected a central disk-shaped structure displaying higher averaged flux (∼ 1 × 10 −17 − 2 × 10 −16 erg.s −1 .cm−2 .Å−1 ) and velocity dispersion (∼ 134 km/s) than the rest of the filaments which is also spatially correlated with a diskshaped 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.
• 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 mech-anisms 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.

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 1 :
Figure 1: The complete field of view (11' × 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 Hα filaments in red.The white square denotes the Horseshoe filament.

Figure 2 :
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.

Figure 3 :
Figure 3: Example of a weighted Voronoi tesselation performed by LUCI to produce the resulting Hα 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 :
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.

Figure 6 :
Figure 6: Top : Hα averaged flux map of the filaments in NGC 1275.Bottom left : Hα velocity map of the filaments in NGC 1275.Bottom right : Hα velocity dispersion map of the filaments in NGC 1275.

Figure 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 ∼ 5 pixels.
3. RESULTS AND DISCUSSION3.1.Comparison with Previous SITELLE ObservationsPrevious SITELLE R=1800 observations of the filamentary nebula surrounding NGC 1275 were already analyzed byGendron-Marsolais et al. (2018) and revealed several key features of the velocity structure.

Figure 8 :
Figure 8: Upper left: [S ii]λ6716 flux map of the filaments in NGC 1275.Upper right: [S ii]λ6731 flux map.Bottom left: [S ii]λ6716 velocity map.Bottom right: [S ii]λ6716 velocity dispersion map.The velocity and velocity dispersion of [S ii]λ6731 are the same as the ones for the [S ii]λ6716 line since these parameters were tied when fitting the doublet.produce the ratio map of [S ii]λ6716 by Hα(6563 Å), we specifically applied the fitting procedure for the Hα 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 Hα Figure 10 upper-left map shows that the central region of the structure displays a ratio of [N ii]λ6583/Hα

Figure 9 :
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 Hα 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.

Figure 10 :
Figure 10: Upper left: [N ii]λ6583 by Hα ratio map.Upper right: Mean (in red) and ensemble fits (in blue) across annuli containing 1500 pixels for the [N ii]λ6583 by Hα 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]λ6716 by Hα ratio map.Bottom right: Mean (in red) and ensemble fits (in blue) across annuli containing 1500 pixels for the [S ii]λ6716 by Hα ratio.The error bars for the ensemble fit have been plotted but are too small to see compared to the data scale.

Figure 11 :
Figure 11: Left: Chandra 0.5 -2.0 keV observations of NGC 1275.The magenta contours show the Hα filaments as observed with SITELLE at high-spectral resolution at a flux level stating at 1 × 10 −18 erg s −1 cm −2 Å−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 Hα flux cut-off of 1 × 10 −17 erg s −1 cm −2 Å−1 .
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 Hα nebula surrounding it.Recent ALMA observations of NGC 1275 by Nagai et al. (

Figure 12 :
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: Hα 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: Hα 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: Hα velocity map as obtained with SITELLE data at high spectral resolution overplotted with contours of Herschel velocity between 50 to 350 km/s.

Figure 13 :
Figure 13: Left: Hα velocity dispersion map.Right: Mean (in purple) and ensemble fits (in green) across annuli containing 1500 pixels for the Hα 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 1σ scatter is shown though the orange shaded area.

Figure 14 :
Figure 14: Left: Hα velocity map.Right: Mean (in red) and ensemble fits (in blue) across annuli containing 1500 pixels for the Hα velocity.The error bars for the ensemble fit have been plotted but are too small to see compared to the data scale.ingsimilar velocity intervals as Figure5inMittal et al. (2012), we can clearly see that the south-western filaments kinematics (see top-right plot of Figure12) 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 Figure12).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 Figure12).Lim et al. (2008) also obtained a velocity map of the central molecular gas disk, which showed mostly blueshifted 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 byLim et al. (2008) instead of the adopted z = 0.017284.After this correction, the Hα emission shows a similar velocity structure for the central disk-shaped structure (see Figure15and Figure2ofLim et al. 2008).The detection of similar disk-shaped structures can also be found in simulation works such as those done byLi & 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 perpendicu-

Figure 15 :
Figure 15: Velocity map in Hα 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.
analysis of new high-spectral resolution observations with SITELLE and obtained new flux, velocity, and velocity dispersion maps of [S ii]λ6716, [S ii]λ6731, [N ii]λ6584, Hα(6563 Å), and [N ii]λ6548 emission lines for the filamentary nebula surrounding NGC 1275, the brightest cluster galaxy of the Perseus cluster.

Figure 16 :
Figure16: 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.

Figure 18 :
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.