# PHANGS-JWST First Results: A combined HST and JWST analysis of the nuclear
star cluster in NGC 628

Nils Hoyer Donostia International Physics Center, Paseo Manuel de Lardizabal
4, E-20118 Donostia-San Sebastián, Spain  Max-Planck-Institut für Astronomie,
Königstuhl 17, D-69117 Heidelberg, Germany  Universität Heidelberg,
Seminarstrasse 2, D-69117 Heidelberg, Germany  Francesca Pinna Max-Planck-
Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany  Albrecht
W. H. Kamlah Astronomisches Rechen-Institut, Zentrum für Astronomie,
Mönchhofstrasse 12-14, D-69120 Heidelberg, Germany  Max-Planck-Institut für
Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany  Francisco Nogueras-
Lara Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg,
Germany  Anja Feldmeier-Krause Max-Planck-Institut für Astronomie, Königstuhl
17, D-69117 Heidelberg, Germany  Nadine Neumayer Max-Planck-Institut für
Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany  Mattia C. Sormani
Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische
Astrophysik, Albert-Ueberle-Strasse 2, D-69120 Heidelberg, Germany  Médéric
Boquien Centro de Astronomía (CITEVA), Universidad de Antofagasta, Avenida
Angamos 601, Antofagasta, Chile  Eric Emsellem European Southern Observatory,
Karl-Schwarzschild-Strasse 2, D-85748 Garching, Germany  Univ Lyon, Univ
Lyon1, ENS de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574,
F-69230 Saint-Genis-Laval France  Anil C. Seth Department of Physics and
Astronomy, University of Utah, Salt Lake City, UT 84112, USA  Ralf S. Klessen
Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische
Astrophysik, Albert-Ueberle-Strasse 2, D-69120 Heidelberg, Germany
Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches
Rechnen, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany  Thomas G.
Williams Sub-department of Astrophysics, Department of Physics, University of
Oxford, Keble Road, Oxford OX1 3RH, UK  Max-Planck-Institut für Astronomie,
Königstuhl 17, D-69117 Heidelberg, Germany  Eva Schinnerer Max-Planck-Institut
für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany  Ashley. T. Barnes
Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71,
D-53121, Bonn, Germany  Adam K. Leroy Department of Astronomy, The Ohio State
University, 140 West 18th Avenue, Columbus, Ohio 43210, USA  Silvia Bonoli
Donostia International Physics Center, Paseo Manuel de Lardizabal 4, E-20118
Donostia-San Sebastián, Spain  IKERBASQUE, Basque Foundation for Science,
E-48013 Bilbao, Spain  J. M. Diederik Kruijssen Cosmic Origins Of Life (COOL)
Research DAO, coolresearch.io  Justus Neumann Max-Planck-Institut für
Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany  Patricia Sánchez-
Blázquez Departamento de Física de la Tierra y Astrofísica, Universidad
Complutense de Madrid, E-28040 Madrid, Spain  Instituto de Física de
Partículas y del Cosmos (IPARCOS), Universidad Complutense de Madrid, E-28040
Madrid, Spain  Daniel A. Dale Department of Physics and Astronomy, University
of Wyoming, Laramie, WY 82071, USA  Elizabeth J. Watkins Astronomisches
Rechen-Institut, Zentrum für Astronomie, Mönchhofstrasse 12-14, D-69120
Heidelberg, Germany  David A. Thilker Department of Physics and Astronomy, The
Johns Hopkins University, Baltimore, MD 21218, USA  Erik Rosolowsky Department
of Physics, University of Alberta, Edmonton, Alberta, T6G 2E1, Canada  Frank
Bigiel Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71,
D-53121 Bonn, Germany  Kathryn Grasha Research School of Astronomy and
Astrophysics, Australian National University, Canberra, ACT 2611, Australia
ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D),
Australia  Oleg V. Egorov Astronomisches Rechen-Institut, Zentrum für
Astronomie, Mönchhofstrasse 12-14, D-69120 Heidelberg, Germany  Daizhong Liu
Max-Planck-Institut für Extraterrestrische Physik (MPE), Giessenbachstrasse 1,
D-85748 Garching, Germany  Karin M. Sandstrom Department of Physics,
University of California, San Diego, 9500 Gilman Drive, San Diego, CA 92093,
USA  Kirsten L. Larson AURA for the European Space Agency (ESA), Space
Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
Guillermo A. Blanc The Observatories of the Carnegie Institution for Science,
813 Santa Barbara St., Pasadena, CA, USA  Departamento de Astronomía,
Universidad de Chile, Camino del Observatorio 1515, Las Condes, Santiago,
Chile  Hamid Hassani Department of Physics, University of Alberta, Edmonton,
Alberta, T6G 2E1, Canada

(Received XXX; Revised YYY; Accepted ZZZ)

###### Abstract

We combine archival HST and new JWST imaging data, covering the ultraviolet to
mid-infrared regime, to morphologically analyze the nuclear star cluster (NSC)
of NGC 628, a grand-design spiral galaxy. The cluster is located in a
$$200\text{\,}\mathrm{pc}$\times$400\text{\,}\mathrm{pc}$$ cavity, lacking
both dust and gas. We find roughly constant values for the effective radius
($r_{\mathrm{eff}}\sim$5\text{\,}\mathrm{pc}$$) and ellipticity
($\epsilon\sim$0.05$$), while the Sérsic index ($n$) and position angle (PA)
drop from $n\sim$3$$ to $\sim$2$$ and
$\mathrm{\textit{PA}}\sim$130\text{\,}\mathrm{\SIUnitSymbolDegree}$$ to
$90\text{\,}\mathrm{\SIUnitSymbolDegree}$, respectively. In the mid-infrared,
$r_{\mathrm{eff}}\sim$12\text{\,}\mathrm{pc}$$, $\epsilon\sim$0.4$$, and
$n\sim$1$$-$1.5$, with the same
$\mathrm{\textit{PA}}\sim$90\text{\,}\mathrm{\SIUnitSymbolDegree}$$. The NSC
has a stellar mass of
$\log_{10}\,(M_{\star}^{\mathrm{nsc}}\,/\,$\mathrm{M_{\odot}}$)=$7.06$\pm$0.31$$,
as derived through $\mathrm{\textit{B}}-\mathrm{\textit{V}}$, confirmed when
using multi-wavelength data, and in agreement with the literature value.
Fitting the spectral energy distribution, excluding the mid-infrared data,
yields a main stellar population’s age of $($8$\pm$3$)\,$\mathrm{Gyr}$$ with a
metallicity of $Z=$0.012$\pm$0.006$$. There is no indication of any
significant star formation over the last few $\mathrm{Gyr}$. Whether gas and
dust were dynamically kept out or evacuated from the central cavity remains
unclear. The best-fit suggests an excess of flux in the mid-infrared bands,
with further indications that the center of the mid-infrared structure is
displaced with respect to the optical centre of the NSC. We discuss five
potential scenarios, none of them fully explaining both the observed
photometry and structure.

galaxies: disk galaxies (391)—star clusters: globular clusters (656)—space
observatories: hubble space telescope (761), james webb space telescope (2291)

††journal: ApJL††facilities: HST(STIS), JWST(STIS) ††software: Astropy (The
Astropy Collaboration et al., 2013, 2018), AplPy (Robitaille & Bressert, 2012;
Robitaille, 2019), dustmaps (Green, 2018), Imfit (Erwin, 2015), Matplotlib
(Hunter, 2007), NumPy (Harris et al., 2020), Photutils (Bradley et al., 2020)
TinyTim (Krist, 1993, 1995), WebbPSF (Perrin et al., 2012, 2014)

##  1 Introduction

Nuclear star clusters (NSCs) are massive and compact stellar systems in
galactic nuclei. The effective radii range from a few to tens of parsecs. Such
radii are typical of globular clusters and ultra-compact dwarfs (e.g. Georgiev
& Böker, 2014; Norris et al., 2014; Pechetti et al., 2020). Stellar masses may
reach up to ${10}^{9}\text{\,}\mathrm{M_{\odot}}$ (e.g. Georgiev et al.,
2016), which, in combination with the small effective radii, lead to core-
densities that can approach
$\lesssim${10}^{8}\text{\,}\mathrm{M_{\odot}}\text{\,}{\mathrm{pc}}^{-3}$$
(e.g. Stone et al., 2017) effectively making NSCs the densest stellar systems
known (see Neumayer et al., 2020, for a review).

The formation and growth of NSCs depends on host galaxy mass (Fahrion et al.,
2021), and potentially morphological type (Pinna et al., 2021). Two main
scenarios have been proposed in the literature: dissipationless globular
cluster (GC) migration dominates in the dwarf galaxy regime
($M_{\star}^{\mathrm{gal}}<${10}^{9}\text{\,}\mathrm{M_{\odot}}$$; Tremaine et
al., 1975; Capuzzo-Dolcetta, 1993; Agarwal & Milosavljević, 2011; Hartmann et
al., 2011; Arca Sedda & Capuzzo-Dolcetta, 2014; Antonini et al., 2015; Fahrion
et al., 2020, 2022a, 2022b) and in-situ star formation in more massive
galaxies (Milosavljević, 2004; Bekki et al., 2006; Bekki, 2007; Turner et al.,
2012; Sánchez-Janssen et al., 2019a; Neumayer et al., 2020). The latter
scenario requires gas inflow, which may be caused by non-axisymmetric
potentials (for example bars, Shlosman et al., 1990), dynamical friction of
star-forming clumps (e.g. Bekki et al., 2006; Bekki, 2007), supernova driven
turbulence (e.g. Sormani et al., 2020; Tress et al., 2020), or rotational
instabilities of the disk (Milosavljević, 2004). Once the gas settles at the
center of the cluster and cools off, star formation begins, leading to the
observation of young stellar populations (e.g. Walcher et al., 2006; Rossa et
al., 2006; Seth et al., 2008; Kacharov et al., 2018; Hannah et al., 2021;
Fahrion et al., 2021) and structural variations, such as a wavelength-
dependent effective radius (Georgiev & Böker, 2014; Carson et al., 2015).
Young stellar populations were also directly observed in various nuclei,
including the Milky Way’s NSC (e.g. Seth et al., 2006, 2008; Do et al., 2009;
Genzel et al., 2010; Carson et al., 2015; Feldmeier-Krause et al., 2015;
Kacharov et al., 2018; Nguyen et al., 2019; Hannah et al., 2021; Henshaw et
al., 2022). A combination of both GC migration and in-situ star formation is
also possible if the infalling GC keeps a gas reservoir and continues star
formation during inspiral (Guillard et al., 2016). Corroborated by scaling
relations between cluster properties and their host galaxies (e.g. Ferrarese
et al., 2006; Seth et al., 2008; Erwin & Gadotti, 2012; Scott & Graham, 2013;
Ordenes-Briceño et al., 2018; Sánchez-Janssen et al., 2019b), studying nuclear
clusters in detail reveals both their formation history as well as that of
their host galaxy. Drawing this connection in NGC 628 is one of the goals of
this work.

NSCs appear frequently, albeit not ubiquitously, at galaxy masses of
${10}^{9}$-${10}^{10}\text{\,}\mathrm{M_{\odot}}$ in various environments
(Côté et al., 2006; Turner et al., 2012; Baldassare et al., 2014; den Brok et
al., 2014; Neumayer et al., 2020; Hoyer et al., 2021). While this fraction
decreases towards higher galaxy masses, there are indications that it drops at
a slower rate for late-type galaxies compared to early-types (Neumayer et al.,
2020; Hoyer et al., 2021). A majority of NSCs in high-mass galaxies were
discovered in spiral galaxies (e.g. Carollo & Stiavelli, 1998; Böker et al.,
2002), likely due to high central luminosities of massive elliptical galaxies.

One example for a nucleated, massive
($M_{\star}^{\mathrm{gal}}\sim$2\text{\times}{10}^{10}\text{\,}\mathrm{M_{\odot}}$$;
Leroy et al., 2021) galaxy is NGC 628 (M 74), the object of this study. The
NSC was analyzed previously by Georgiev & Böker (2014, hereafter GB14) using
Hubble Space Telescope (HST) WFPC2 imaging data, but no in-depth analysis of
all available high-resolution data has been performed yet. With the advent of
the James Webb Space Telescope (JWST) earlier this year, we aim to study the
NSC of NGC 628 across the optical and infrared regimes, analyzing both its
structural and photometric properties.

This grand-design spiral galaxy is located at a distance of $d=$9.84$\pm
0.63\,$\mathrm{Mpc}$$ (Anand et al., 2021, and also McQuinn et al., 2017) at
the edge of the Local Volume ($\lesssim$11\text{\,}\mathrm{Mpc}$$). Both its
relatively isolated position (.g. Briggs et al., 1980) and nearly face-on
orientation ($i\sim$8.9\text{\,}\mathrm{\SIUnitSymbolDegree}$$; Lang et al.,
2020) make the galaxy an optimal test-case for detailed studies of galactic
disks, and star- and cluster-formation in massive late-types (see e.g.
Elmegreen & Elmegreen, 1984; Condon, 1987; Grasha et al., 2015; Adamo et al.,
2017; Mulcahy et al., 2017; Kreckel et al., 2018; Sun et al., 2018; Vílchez et
al., 2019; Schinnerer et al., 2019; Zaragoza-Cardiel et al., 2019; Chevance et
al., 2020; Yadav et al., 2021).

Figure 1 shows an overview of the innermost
$$20\text{\,}\arcsec$\times$20\text{\,}\arcsec$$ (approximately
$$950\text{\,}\mathrm{pc}$\times$950\text{\,}\mathrm{pc}$$) of NGC 628.
Corroborated by AstroSat UV, MUSE H$\alpha$ (Emsellem et al., 2022), and ALMA
CO maps (Leroy et al., 2021), the HST and JWST data reveal a spheroidal
component, dust and gas reservoirs along prominent spiral arm structures, and
star-forming regions. Instead of continued spiral arms down to the smallest
scales, a central cavity of approximately
$$200\text{\,}\mathrm{pc}$\times$400\text{\,}\mathrm{pc}$$ lacking both gas
and dust is present. The NSC of NGC 628 appears as a prominent bright source
in the center of the galaxy.

Secular evolution plays a key role in the history of NGC 628, as indicated by
the presence of a circum-nuclear region of star formation with radius
$\sim$25\text{\,}\arcsec$$ ($\sim$1.2\text{\,}\mathrm{kpc}$$) (Sánchez et al.,
2011). While the formation of such a region can be related to the presence of
a bar (Piner et al., 1995; Sakamoto et al., 1999; Sheth et al., 2005; Fathi et
al., 2007; Sormani et al., 2015; Spinoso et al., 2017; Bittner et al., 2020),
as argued to be present in NGC 628 by Seigar (2002) and Sánchez-Blázquez et
al. (2014), more recent work finds that NGC 628 does not contain an obvious
bar (Querejeta et al., 2021), despite an observed metallicity gradient, which
is related to mixing of gas induced by a bar-structure in other late-type
galaxies (Martin, 1995; Friedli & Benz, 1995; Dutil & Roy, 1999; Scarano &
Lépine, 2013). If not by a bar, the presence of a circum-nuclear region of
star formation may also be caused by past minor mergers, as speculated for
other unbarred late-types by Sil’chenko & Moiseev (2006). Indeed, dwarf
galaxies are known to exist around NGC 628 (Davis et al., 2021). It is also
plausible that the galaxy hosted a bar in the past, which was destroyed by
minor mergers (Cavanagh et al., 2022).

The large, approximately
$$200\text{\,}\mathrm{pc}$\times$400\text{\,}\mathrm{pc}$$ large, central
cavity remains challenging to explain. Currently, it is unclear whether inflow
of gas and dust is prohibited dynamically, or whether the material has been
expelled by star formation, supernovae, or a previously accreting massive
black hole. As motivated above, the NSC properties may give inform us on the
evolution of NGC 628, if studied in detail. Therefore, one of the goals of
this study is to relate the NSC properties to the evolution of its host
galaxy.

In this work, we combine archival HST and newly obtained JWST imaging data to
study the NSC of NGC 628 in great detail. Our data extend from the ultraviolet
to the mid-infrared regime (see Figure 2 and Table 1) and are of high-enough
resolution to resolve the cluster at all wavelengths. This study presents the
first analysis of an NSC with JWST data and highlights the telescope’s
scientific value for studies of galactic nuclei in the local Universe. Using
the available data, we derive photometric and structural parameters for all
bands, and model the spectral energy distribution of the NSC.

We introduce the data from both space telescopes in Section 2 and briefly
discuss the data processing pipelines as well as the generation of synthetic
point spread functions. Image analysis is described in Section 3 and the main
analysis steps are detailed in Section 4. The results of the study are
discussed in Section 5. We conclude in Section 6.

Figure 1: Overview of the nuclear region of NGC 628 in different bands. Each
panel gives the central $$20\text{\,}\arcsec$\times$20\text{\,}\arcsec$$
(approximately $$950\text{\,}\mathrm{pc}$\times$950\text{\,}\mathrm{pc}$$) of
the galaxy, centered on the nuclear star cluster. North is up and East is to
the left. Color correlates with intensity. The first row gives three color-
images using HST and JWST bands, highlighting star-formation by using the
continuum-subtracted HST ACS F658N (H$\alpha$) filter. Dust lanes, where star
formation occurs, are clearly visible in the first and third panel, while only
stellar emission is shown in the second panel. The squared box of side length
$5.5\text{\,}\arcsec$ in the third panel shows the region we considered for
the fit of the NSC. The second row highlights other available data sets,
namely the AstroSat ultraviolet emission, MUSE H$\alpha$, and ALMA CO. The
first two panels trace again star formation whereas the third panel shows the
location of the molecular gas. Note the absence of star formation and gas in
the immediate vicinity of the nuclear star cluster, which is marked with a
white cross. The third and fourth rows show the HST data, increasing in
wavelength. Star forming regions, identified in the HST WFC3 F275W, become
hidden behind dust filaments in other bands. The sixth panel, showing the HST
ACS F814W data, mainly shows stellar emission. We show the newly obtained JWST
NIRCam (fifth) and MIRI (sixth) in the last two rows, again in increasing
wavelength from the near-infrared to the mid-infrared. The NIRCam data
highlights the stellar emission while the MIRI data shows both stellar and
dust emission. As for the molecular gas (ALMA CO, second row), a central
cavity exists and dust is present in the spiral arms of NGC 628.  Figure 2:
Transmission of the HST and JWST bands used in this work.

##  2 Data

Our analysis is based on archival HST ACS & WFC3 taken from the Hubble Legacy
Archive111https://hla.stsci.edu/ and recently obtained JWST NIRCam & MIRI
imaging data (project ID 02107, PI J. Lee; see Lee et al., subm., this issue).
A brief overview of the available data is given in Table 1 and Figure 2. In
the next three subsections we briefly describe the data processing for each
instrument, followed by the generation of point spread functions.

Table 1: Data used in this work.  Instrument | Channel | Filter | PropID | $t_{\mathrm{exp}}$ | pixel scaleaaOriginal pixel values, which remained unchanged during data processing.
---|---|---|---|---|---
|  |  |  | [$\mathrm{s}$] | [$\mathrm{arcsec}\text{\,}{\mathrm{pixel}}^{-1}$]
HST | WFC3 | F275W | 13364 | $4962.00$ | $0.040$
HST | WFC3 | F336W | 13364 | $4962.00$ | $0.040$
HST | ACS | F435W | 10402 | $2716.00$ | $0.050$
HST | ACS | F555W | 10402 | $1716.00$ | $0.050$
HST | ACS | F658N | 10402 | $2844.00$ | $0.050$
HST | ACS | F814W | 10402 | $1844.00$ | $0.050$
JWST | NIRCam | F200W | 02107 | $9620.16$ | $0.031$
JWST | NIRCam | F300M | 02107 | $773.048$ | $0.063$
JWST | NIRCam | F335M | 02107 | $773.048$ | $0.063$
JWST | NIRCam | F360M | 02107 | $858.944$ | $0.063$
JWST | MIRI | F770W | 02107 | $266.40$ | $0.110$
JWST | MIRI | F1000W | 02107 | $366.30$ | $0.110$
JWST | MIRI | F1130W | 02107 | $932.412$ | $0.110$
JWST | MIRI | F2100W | 02107 | $965.712$ | $0.110$

###  2.1 Hubble Space Telescope

We obtain all available flat-fielded single exposures from the HLA to combine
them into a single master frame. As a first step, the world coordinate systems
of the ACS & WFC3 received updates using the latest reference files. These
updated files were fed to AstroDrizzle (Fruchter et al., 2010; Gonzaga et al.,
2012, see also Fruchter & Hook, 1997 for the drizzle algorithm), which
combines them into a master science product given user-specified settings. As
tested and justified in other work (Hoyer et al., 2022, subm.), we chose a
pixel fraction of $0.75$ but keep the pixel scale at their original
resolutions (see Table 1).222The pixel fraction controls how individual
exposures are added: a value of zero corresponds to pure interlacing whereas a
value of one results in a “shift-and-add” style of pixel values. No additional
sky subtraction was performed as we account for background flux from the
galaxy with a Sérsic profile (Sérsic, 1968) and a plane offset.

###  2.2 James Webb Space Telescope

As part of the “Physics at High Angular resolution in Nearby GalaxieS”
(PHANGS) JWST cycle 1 treasury program, NGC 628 was observed in various NIRCam
and MIRI bands on July 17, 2022 (see Table 1, and also Lee et al., subm., this
issue). Data reduction and co-addition were carried out using a custom data
reduction pipeline, which among other things, improves the astrometric
solutions and zero point offsets compared to the publicly available data
products. More specifically, the world coordinate system (WCS) was updated to
match the one from the HST and Gaia, and overall background level were
calibrated against e.g. IRAC4 $8\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
WISE3 $12\text{\,}\mathrm{\SIUnitSymbolMicro m}$ fluxes (Leroy et al., subm.,
this issue). More detail of the customized version of the data reduction
pipeline will be presented in Lee et al., subm. (this issue).

###  2.3 Point spread functions

For all bands, we used artificially generated point spread functions (PSFs)
instead of determining them from non-saturated stars in the images. The main
reason for this choice was that no star is unaffected by dust and falls close
to the location of the NSC (see Figure 1). Especially the latter condition is
important for HST data as the PSF is known to vary significantly across the
whole chip.

Following the approach by Hoyer et al. (2022, subm.), PSFs were generated
using TinyTim (Krist, 1993, 1995) for HST bands. To minimize systematic
differences in data processing, we did not directly use the resulting PSF from
TinyTim for deriving the structural properties. Instead, we copied all input
science frames and set their first header extension (science data) to zero. We
then generated PSFs at the location of the NSC on each individual exposure and
placed them into the previously normalized frames, taking into account the
orientation of the original science images. Afterwards, we repeated the
AstroDrizzle processing for the normalized frames in the same way as for the
science data. The final PSF was extracted from the output of AstroDrizzle. In
comparison to a PSF from TinyTim, the core of the extracted PSF is slightly
more extended due to the drizzling process. Taking this effect into account is
important for deriving accurate effective radii, as detailed in Hoyer et al.
(2022, subm.).

Generation of PSFs for JWST bands was performed with WebbPSF (Perrin et al.,
2012, 2014). To generate a star at the location of the NSC, we first generated
a grid of 36 PSFs for the detector elements where the position of the NSC
falls upon. The PSF for the position of the NSC was evaluated based on
interpolation of generated PSFs using WebbPSF. This step is crucial as the PSF
of JWST varies in both the spatial and temporal dimension (Nardiello et al.,
2022). By default, and in agreement with our choice for the TinyTim-based
PSFs, we chose a G2V star as the stellar template. As explored in Hoyer et al.
(2022, subm.), the choice of stellar type plays little to no role on the fit
results for HST data and we assume the same for JWST data.

##  3 Image fitting

###  3.1 Approach and model function

Focusing on the center of NGC 628, we extracted a square region of side length
$5.5\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ (equivalent to
$\sim$260\text{\,}\mathrm{pc}$$) centered on the NSC to avoid the more dust-
and gas-rich spiral structure, as shown in the first row, right panel of
Figure 1. Previous investigations used various model functions to describe the
light distribution of NSCs, including King profiles (see King, 1962 for the
original definition; e.g. Matthews et al., 1999; Seth et al., 2006; Georgiev
et al., 2009b; Georgiev & Böker, 2014), Gaussian profiles (e.g. Carollo et
al., 1997, 2002; Barth et al., 2009; den Brok et al., 2014), Nuker profiles
(see Lauer et al., 2005 for a definition, e.g. Carollo & Stiavelli, 1998;
Böker et al., 1999, 2002; Butler & Martínez-Delgado, 2005), Sérsic profiles
(e.g. Côté et al., 2006; Baldassare et al., 2014; Carson et al., 2015;
Spengler et al., 2017; Pechetti et al., 2020), or point sources (e.g.
Ferrarese et al., 2020; Poulain et al., 2021; Zanatta et al., 2021; Carlsten
et al., 2022). Here we use the Sérsic profile of the form

$I(r)=I_{\mathrm{eff}}\,\exp\bigg{\\{}-b_{n}\,\bigg{[}\bigg{(}\frac{r}{r_{\mathrm{eff}}}\bigg{)}^{1/n}-1\bigg{]}\bigg{\\}}\;,$
(1)

where $r$ is the radius, $r_{\mathrm{eff}}$ the half-light or effective
radius, $I_{\mathrm{eff}}$ the intensity at $r_{\mathrm{eff}}$, and $n$ the
Sérsic index. The parameter $b_{n}$ solves the equation
$\Gamma(2n)=2\gamma(2n,\,b_{n})$ where $\gamma(a,x)$ is the incomplete and
$\Gamma(x)$ the complete Gamma function. For $n\in($0.5$,\,$10$)$,
$b_{n}=$1.9992$n-$0.3271$$ is a good approximation (Capaccioli, 1989, but see
also Graham & Driver, 2005 for a general overview).

The background flux from the host galaxy and the sky was modeled with another
Sérsic profile and a plane offset. From our fits (see below), we found that in
all bands $I_{\mathrm{eff}}^{\mathrm{gal}}\ll
I_{\mathrm{eff}}^{\mathrm{nsc}}$, $r_{\mathrm{eff}}^{\mathrm{gal}}\gg
r_{\mathrm{eff}}^{\mathrm{nsc}}$, and $n^{\mathrm{gal}}\lesssim 1$, such that
the profile of the host galaxy becomes flat in the very center, thus
justifying the choice of models. As we describe in Appendix A, two Sérsic
profiles describe the NSC worse than a single profile.

To fit the data, we convolved the profiles with the previously generated
synthetic PSF at the position of the NSC (see Section 2.3). The fit itself was
performed with Imfit (Erwin, 2015), a specialized program to fit astronomical
images. For the minimization technique, we chose the Differential Evolution
solver with Latin hypercube sampling. In comparison with other available
options, the solver does not rely on initial parameter values but randomly
selects parameter values between user-specified boundaries (see Storn & Price,
1997, for details). We list the boundaries for the parameters of the Sérsic
profile used for the NSC in Table 2. By default, Imfit evaluates the goodness
of the fit with standard $\chi^{2}$ statistics.

Unless specified, Imfit assumes Poissonian statistics of the input data to
generate a noise map. We take this approach for all but the JWST MIRI data
where noise maps were generated by the previously mentioned custom data
calibration pipeline. The noise maps for the MIRI bands were determined from
uncertainties of the input data, the read noise and the flat fields, weighted
by the fractional contribution to each pixel. As a result, compared to the
standard noise map generated by Imfit, the MIRI noise maps give lower values
for the nucleus itself, but higher values for the faint emission by the
background galaxy.

In Figures 3 and 4 we show the data, best-fit two-component models, and the
residuals for the HST ACS & WFC3, JWST NIRCam, and MIRI data, respectively.
For the JWST MIRI F2100W all attempts failed to find a stable fit. Instead, to
get an estimate for the apparent magnitude, we fit a Sérsic profile excluding
PSF convolution.

Table 2: Sérsic parameters and their boundary values used to fit the data with Imfit. The same values are used for all HST and JWST bands.  Parameter | Boundary | Unit | Description
---|---|---|---
$x_{0}$ | $[$45$,\,$55$]$ | $\mathrm{pixel}$ | NSC position
$y_{0}$ | $[$45$,\,$55$]$ | $\mathrm{pixel}$ | NSC position
PA |  $[$-359.99$,\,$359.99$]$aaTo prevent the fit from running into boundaries at $0\text{\,}\mathrm{\SIUnitSymbolDegree}$, the lower boundary was changed to negative values. In the case that the best-fit position angle was negative, $180\text{\,}\mathrm{\SIUnitSymbolDegree}$ (or $360\text{\,}\mathrm{\SIUnitSymbolDegree}$) was added.  | $\deg$ | Position angle
$\epsilon$ | $[$0.00$,\,$0.99$]$ | – | Ellipticity
$n$ | $[$0.00$,\,$5.00$]$ | – | Sérsic index
$r_{\mathrm{eff}}$ | $[$0.00$,\,$10.00$]$ | $\mathrm{pixel}$ | Effective radius
$I_{\mathrm{eff}}$ |  $[$0.00$,\,I_{\mathrm{max}}]$bb$I_{\mathrm{max}}$ is the peak of the intensity of the NSC.  | counts | Intensity at $r_{\mathrm{eff}}$
Figure 3: Overview of the central
$$5.5\text{\,}\arcsec$\times$5.5\text{\,}\arcsec$$
($$1\text{\,}\arcsec$\approx$47\text{\,}\mathrm{pc}$$) of NGC 628 in six
different Hubble Space Telescope bands. North is up and East is left. Top row:
Data products as used for fitting. Middle row: Model images of the best fit
using one Sérsic profile for the nuclear star cluster, an additional Sérsic
profile for the background, and a plane offset. Bottom row: Residual map,
$\mathrm{Data}-\mathrm{Model}$. The gray scale of the maps are logarithmic and
vary from $5\text{\times}{10}^{-3}$ to $5\text{\times}{10}^{2}$ times the mean
of the residuals.  Figure 4: Overview of the same central region as in Figure
3 but for available JWST NIRCam and MIRI data. For the F2100W, no fit was
possible including PSF convolution. The model shown here is a pure Sérsic
profile without PSF convolution to determine the apparent magnitude of the
source. For the MIRI data, we adjust the gray scales to $0.99$ and $1.01$
times the mean.

###  3.2 Uncertainties

We determined uncertainties by repeating the fit $500$ times using
bootstrapping. During each iteration of bootstrapping, Imfit generates a new
data array where indices of pixels are randomly sampled. During re-sampling,
the pixel values of the input data as well as their location are not
considered. The quoted best-fit parameters equal the median value of the
parameter distribution and the uncertainties give the $$1$\sigma$ interval.

For some physical parameters, such as the determination of NSC mass (see
Section 4.3) or the transformation of the effective radius to parsec, the
bootstrapping uncertainties were propagated forward. Based on the assumption
that the underlying probability distributions are Gaussians, we used the
Gaussian error propagation.

The uncertainty of the zero point magnitudes for the HST bands is of the order
$\mathcal{O}($10$^{$-3$})$ and can be neglected. However, recent analyses of
early JWST data revealed that there exist issues with the flux calibration. As
detailed below, these issues persist and remain significant

For the JWST NIRCam data, the uncertainty on the flux calibration can be as
high as $0.2\text{\,}\mathrm{mag}$ (Boyer et al., 2022), depending on the band
and detector. Most recent analyses in the community try to solve this issue by
introducing multiplicative correction factors for the data.333See, for
example, https://github.com/gbrammer/grizli/pull/107. We corrected the
determined fluxes by the mean multiplicative correction factor of G. Brammer
and I. Labbe presented in Brammer (2022), $0.7845$. The correction factors are
presented for the F090W, F115W, F150W, and F200W, that is, only the last band
overlaps between the filter sets. To remain consistent between all four NIRCam
bands, we did not change the value of the apparent magnitude, but determine
the uncertainty from the multiplicative correction factor itself. The final
uncertainty on the magnitude was then determined through Gaussian error
propagation of this systematic uncertainty and the statistical uncertainty
obtained from the fit. For the other three NIRCam bands, we assumed that the
correction factor equals $0.8$, resulting in an uncertainty of
$\sim$0.24\text{\,}\mathrm{mag}$$. As for the F200W, we combined this value
with the statistical uncertainty from bootstrapping for the final uncertainty.

For the JWST MIRI data, the background level was, as described in Section 2.2,
adjusted by comparing the F770W flux to the IRAC4
$8\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and WISE3
$12\text{\,}\mathrm{\SIUnitSymbolMicro m}$ bands. The estimated uncertainty on
its value is $\pm$0.1\text{\,}\mathrm{mag}$$ (Leroy et al., subm., this
issue).

As pointed out in Section 2.3, we did not check the influence the calibration
and co-addition of the data have on the synthetic PSF generated by WebbPSF.
Hoyer et al. (2022, subm.) found for the HST data that the co-addition of
single exposures results in a slight broadening of the core of the PSF,
introducing a systematic overestimation of the NSCs size. To repeat this
experiment for the JWST data, we focused on the NIRCam F200W band and repeated
the fit introducing an additional jitter in the form of a Gaussian function
convolved with the synthetic PSF. In WebbPSF, we increased the jitter by
factors of two and five and repeated the fits using the new PSFs. The result
was that the structural parameters, as well as magnitude and color, remained
well within the $$1$\sigma$ distribution of the original fits. Therefore, we
conclude that our results are reliable given the presented uncertainties.

##  4 Analysis

###  4.1 Photometry

Integrating Equation 1 with an assumed ellipticity ($\epsilon$) yields the
luminosity ($L$; photon count per energy band and time) as

$L=$2$\pi\,($1$-\epsilon)\,I_{\mathrm{eff}}\,r_{\mathrm{eff}}^{$2$}\,\frac{n\mathrm{e}^{b_{n}}}{(b_{n})^{$2$n}}\,\Gamma($2$n)\;.$
(2)

We use the equation

$\displaystyle\mathrm{ZP}_{\mathrm{AB}}=$
$\displaystyle$-2.5$\,\log_{10}\,(\,\mathrm{PHOTFLAM}\,)$
$\displaystyle$-5$\,\log_{10}\,(\,\mathrm{PHOTPLAM}\,)$
$\displaystyle$-2.408$\;,$ (3)

to calculate the zero point magnitudes for HST ACS / WFC3 bands. The values of
PHOTFLAM and PHOTPLAM are given in the header extensions of the fits
files.444We find the following zero point magnitudes for the HST bands:
$\mathrm{ZP}_{\mathrm{\textit{F275W}}}=$24.159\text{\,}\mathrm{mag}$$,
$\mathit{ZP}_{\mathrm{\textit{F336W}}}=$24.689\text{\,}\mathrm{mag}$$,
$\mathit{ZP}_{\mathrm{\textit{F435W}}}=$25.677\text{\,}\mathrm{mag}$$,
$\mathit{ZP}_{\mathrm{\textit{F555W}}}=$25.722\text{\,}\mathrm{mag}$$,
$\mathrm{ZP}_{\mathrm{\textit{F658N}}}=$22.760\text{\,}\mathrm{mag}$$, and
$\mathrm{ZP}_{\mathrm{\textit{F814W}}}=$25.950\text{\,}\mathrm{mag}$$.

Pixel values in JWST data products have the unit
$\mathrm{MJy}\text{\,}{\mathrm{sr}}^{-1}$, which we convert to $\mathrm{Jy}$
by using Equation 2 and the pixel-to-steradian conversion factor PIXAR_SR from
the header extension. The zero point magnitude is then derived using

$\mathrm{ZP}_{\mathrm{AB}}=$-2.5$\,\log_{10}\,(L)+$8.9$\;.$ (4)

Foreground extinction is taken into account by using the re-calibrated version
of the Schlegel et al. (1998) extinction maps (Schlafly & Finkbeiner, 2011)
and assuming $R_{V}=$3.1$$ (Fitzpatrick, 1999). Due to the apparent lack of
dust in the center of NGC 628, we do not attempt to correct for intrinsic
extinction. For the HST bands, we derive
$A(\lambda)\,/\,A(\mathrm{\textit{V}})$ with the model from O’Donnell (1994),
which is based on Cardelli et al. (1989).

Figure 5 shows spectral flux densities as well as the extinction-corrected
apparent magnitudes of the NSC in the AB-magnitude system. The NSC is faintest
in the ultraviolet regime and becomes brighter towards the near-infrared. The
brightest magnitude is reached at $2\text{\,}\mathrm{\SIUnitSymbolMicro m}$
after which the nucleus becomes fainter again.

To compare to the values by GB14, we transform our magnitudes from the AB- to
the Vega-magnitude system using the approach outlined in Sirianni et al.
(2005) and applied in Pechetti et al. (2020) for NSCs. We find
$\mathrm{\textit{V}}_{0}=($17.85$\pm$0.04$)\,$\mathrm{mag}$$ and
$\mathrm{\textit{I}}_{0}=($16.69$\pm$0.05$)\,$\mathrm{mag}$$. GB14 present
$\mathrm{\textit{V}}_{0}=($17.88$\pm$0.01$)\,$\mathrm{mag}$$ and
$\mathrm{\textit{I}}_{0}=($16.57$\pm$0.01$)\,$\mathrm{mag}$$. While the
$V$-band magnitudes agree with each other, we find a significant difference in
the I-band. The different magnitude is most likely related to the extracted
structural parameters (cf. Section 4.4).

###  4.2 SED modeling

The combined HST and JWST data cover the ultraviolet to mid-infrared spectrum
and enable the study of the spectral energy distribution (SED) in detail. To
extract basic parameters describing the stellar population, we set up a model
assuming a delayed star formation history, two commonly used different initial
mass functions (Chabrier, 2003; Salpeter, 1955), and the Bruzual & Charlot
(2003) single stellar population model.

The fits were executed using CIGALE, a Python code for modeling the SEDs of
galaxies (see Boquien et al., 2019, and Burgarella et al., 2005; Noll et al.,
2009; Yang et al., 2020, 2022), which has successfully been applied to star
clusters (e.g. Fensch et al., 2019; Turner et al., 2021). The program allows
to adjust various physical properties such as the age of the stellar
populations or their metallicity. We test various parameter values, as
detailed in Table 3, to find the best possible fit to the data, as evaluated
by Bayesian statistics.

Table 3: Parameters values for the spectral energy distribution fits. The values remain unchanged between runs including and excluding the MIRI data.  Parameter | Unit | Values | Best-fit | Notes
---|---|---|---|---
|  |  | Incl. MIRI | Excl. MIRI |
Star formation history
tau_main | [$\mathrm{Myr}$] |  $1$, $10$, $100$, $1000$, $2000$, $3000$ | $$500$\pm$500$$ | $$220$^{+380}_{-220}$ | e-folding time of the main stellar population
age_main | [$\mathrm{Gyr}$] |  $3$, $4$, $5$, $6$, $7$, $8$, $9$, $10$, $11$, $12$, $13$ | $$8$\pm$2$$ | $$8$\pm$3$$ | Age of the main stellar population
tau_burst | [$\mathrm{Myr}$] |  $10$, $20$, $50$, $100$ | $$57$\pm$33$$ | $$57$\pm$33$$ | Time of the late starburst
age_burst | [$\mathrm{Myr}$] |  $10$, $20$, $50$, $100$ | $$27$\pm$17$$ | $$27$\pm$17$$ | Age of the late burst
f_burst | – |  $0.0$, $0.1$, $0.2$, $0.5$ | $$0$\pm$0$$ | $$0$\pm$0$$ | Mass fraction of the late burst
Simple stellar population
imf | – |  $0$, $1$ | $1$ | $1$ | Initial mass function (Salpeter, 1955, Chabrier, 2003)
metallicity | – |  $0.004$, $0.008$, $0.02$, $0.05$ | $$0.027$\pm$0.013$$ | $$0.012$\pm$0.006$$ | Metallicity of the stellar population

The fit was performed twice, excluding the MIRI data in one run. We do this to
test their influence to the fit result and disentangle emission from low-mass
stars and dust. The addition of a dust emission model yielded worse fits, as
evaluated by both the reduced $\chi^{2}$ and Bayesian statistics, which is why
we do not include it in the presented results. We discuss this issue in more
detail in Section 5.

For the fit including the MIRI data, we find that the mass-weighted age of the
main stellar population is $($8$\pm$2$)\,$\mathrm{Gyr}$$ with a metallicity of
$Z=$0.03$\pm$0.01$$, slightly more metal-rich than the Sun (Asplund et al.,
2009). The e-folding time of the main stellar population is
$($500$\pm$500$)\,$\mathrm{Myr}$$ and the mass fraction of the late burst is
consistent with zero. The fit preferred a Chabrier (2003)-type initial mass
function over a Salpeter (1955) one.

For the fit excluding the MIRI data, we find a mass-weighted age of the main
stellar population of $($8$\pm$3$)\,$\mathrm{Gyr}$$ with a metallicity of
$Z=$0.012$\pm$0.006$$. The e-folding time was determined to be
$$220$_{$-220$}^{$380$}\,$\mathrm{Myr}$$ and the mass fraction of the late
burst is comparable to zero. The fit again preferred a Chabrier (2003)-type
initial mass function.

According to the reduced $\chi^{2}$ statistics, the fit excluding the MIRI
data performed better than the one including them. The results of both fits
are consistent with each other, indicating the presence of a
$8\text{\,}\mathrm{Gyr}$ old stellar population with metallicity $Z\sim$0.02$$
and no presence of a young stellar population. We discuss the results obtained
for the mass of the stellar population in the next section.

Figure 5: Spectral flux density ($S_{\nu}$, left axis) and AB magnitude
($m_{\mathrm{AB}}$, right axis) versus wavelength ($\lambda$). Different
instruments are highlighted with marker symbols and colors. Red pentagons give
the results by Georgiev & Böker (2014) in the Vega-magnitude system.
Uncertainties are indicated with shaded areas. Two gray lines show the
spectral energy distribution fits to the data including (dashed line) and
excluding (solid line) the JWST MIRI data. The goodness of the fits is given
by reduced $\chi^{2}$ values in the panel. For both fits, we use the Bruzual &
Charlot (2003) stellar population model and a delayed star formation history.
The fit prefers a Chabrier (2003) initial mass function over the prescription
by Salpeter (1955). Both fits indicate the presence of a
$8\text{\,}\mathrm{Gyr}$ old stellar population with metallicity $Z\sim 0.02$.
No younger stellar population could be detected.

###  4.3 Stellar mass

We determine the stellar mass of the NSC in three different ways: (1) we use
$\mathrm{\textit{B}}-\mathrm{\textit{V}}$ color and its mass-to-light scaling
relations, (2) we combine the apparent magnitude in the F200W (roughly K-band)
with a constant mass-to-light ratio ranging between $0.5$ and $0.6$ (in solar
units), and (3) we extrapolate a stellar mass from SED fitting. The resulting
mass estimates and the literature value from Georgiev et al. (2016) are
presented in Table 4.

Following Hoyer et al. (2021), we use four different
$\mathrm{\textit{B}}-\mathrm{\textit{V}}$ color relations and the V-band
luminosity to obtain a stellar mass-to-light ratio. The original relations
were published by Bell et al. (2003); Portinari et al. (2004); Zibetti et al.
(2009); Into & Portinari (2013) but we adopt the revised parameters from
McGaugh & Schombert (2014), which ensures consistency between the relations.
An extended discussion and the assumptions made are detailed in Hoyer et al.
(2021).

First, the HST ACS F435W and F555W magnitudes were converted to the Johnson-
Cousin system (B\- and V-band, respectively) using Equation $12$ and Table
$22$ from Sirianni et al. (2005). Absolute magnitudes were derived using the
distance estimate of the galaxy and the absolute magnitude of the Sun
(Willmer, 2018).555See http://mips.as.arizona.edu/~cnaw/sun.html for an
overview. The uncertainty on the values is assumed to be
$0.04\text{\,}\mathrm{mag}$.

After transforming the HST magnitudes to the Johnson-Cousin system and using
magnitudes in the Vega-system, we find
$\mathrm{\textit{B}}_{0}=($18.59$\pm$0.03$)\,$\mathrm{mag}$$ and
$\mathrm{\textit{V}}_{0}=($17.86$\pm$0.04$)\,$\mathrm{mag}$$ with a color
$(\mathrm{\textit{B}}-\mathrm{\textit{V}})_{0}=($0.73$\pm$0.05$)\,$\mathrm{mag}$$,
which roughly matches the color of a G8V-type star
($\mathrm{\textit{B}}-\mathrm{\textit{V}}\sim 0.75$) and is consistent with
the results from the SED fits. From the four scaling relations, we determine
individual masses and combine them into one using the weighted average. The
resulting mass estimate is
$\log_{10}\,(M_{\star}^{\mathrm{nsc}}\,/\,$\mathrm{M_{\odot}}$)=$7.06$\pm$0.31$$.
The uncertainty budget is dominated by the uncertainty assumed for the mass-
to-light ratio, $0.3\text{\,}\mathrm{dex}$ (Roediger & Courteau, 2015).

An alternative approach is to use the magnitude in the K-band. McGaugh &
Schombert (2014) found that a constant mass-to-light ratio of $\sim$0.6$$ can
be used to estimate stellar masses as the near-infrared luminosity is only
weakly dependent on color. While we do not directly have a K-band magnitude,
we estimate the mass using the F200W band from JWST, centered on
$2\text{\,}\mathrm{\SIUnitSymbolMicro m}$. The K-band overlaps with the F200W
band such that we can use the mass estimate as a benchmark for the other mass
estimates.

Using the same four references as for the approach using the
$\mathrm{\textit{B}}-\mathrm{\textit{V}}$ color (Bell et al., 2003; Portinari
et al., 2004; Zibetti et al., 2009; Into & Portinari, 2013) and their re-
calibrated values from McGaugh & Schombert (2014), we find a stellar mass of
$\log_{10}\,(M_{\star}^{\mathrm{nsc}}\,/\,$\mathrm{M_{\odot}}$)=$7.2$\pm$1.1$$.
The uncertainty is much larger than for the mass determined from the
$\mathrm{\textit{B}}-\mathrm{\textit{V}}$ relation due to the uncertainty on
the zero point of the NIRCam data.

From the SED fitting in the previous section, the mass of the star cluster was
determined as well. In the fit including the MIRI data, we find
$\log_{10}\,(M_{\star,\,1}^{\mathrm{nsc}}\,/\,$\mathrm{M_{\odot}}$)=$7.17$\pm$0.10$$.
In the fit excluding the MIRI data, we find
$\log_{10}\,(M_{\star,\,2}^{\mathrm{nsc}}\,/\,$\mathrm{M_{\odot}}$)=$7.11$\pm$0.10$$.
As stated above, no young stellar population was found.

The mass of the NSC was previously determined by Georgiev et al. (2016) based
on the analysis of GB14. To obtain stellar masses, the authors use stellar
population models from Bruzual & Charlot (2003) with solar metallicity and an
initial mass function of the type presented in Kroupa (2001). The reported
mass for the NSC of NGC 628 is
$\log_{10}\,(M_{\star}^{\mathrm{nsc}}\,/\,$\mathrm{M_{\odot}}$)=$7.05$\pm$0.21$$,
which agrees within the uncertainty with our mass estimates.

Overall, we find agreement between all approaches finding that the NSC has a
stellar mass of $\sim${10}^{7}\text{\,}\mathrm{M_{\odot}}$$. In the following,
we use the mass value
$\log_{10}\,(M_{\star}^{\mathrm{nsc}}\,/\,$\mathrm{M_{\odot}}$)=$7.06$\pm$0.31$$.

Table 4: Determined nuclear star cluster mass as well as the literature value.  Method | Logarithmic stellar mass
---|---
| [$\mathrm{M_{\odot}}$]
$\mathrm{\textit{B}}-\mathrm{\textit{V}}$ | $$7.06$\pm$0.31$$
K-band |  $$7.2$\pm$1.1$$aaThe large uncertainty compared to the other values is caused by the high uncertainty on the zero point values for NIRCam data.
SED (incl. MIRI) | $$7.17$\pm$0.10$$
SED (excl. MIRI) | $$7.11$\pm$0.10$$
Georgiev et al. (2016) | $$7.05$\pm$0.21$$

###  4.4 Structure

Figure 6 shows the effective radius, ellipticity, Sérsic index, and position
angle versus wavelength (from Section 3). We also add the literature values by
GB14.

In panel A, we show the effective radius versus wavelength. It remains roughly
constant at $\sim$5\text{\,}\mathrm{pc}$$ in the ultraviolet and optical
regime, but starts to slightly increase towards $\sim$6\text{\,}\mathrm{pc}$$
at $3.6\text{\,}\mathrm{\SIUnitSymbolMicro m}$. This trend continues into the
mid-infrared where $r_{\mathrm{eff}}\sim$12\text{\,}\mathrm{pc}$$.

GB14 find different effective radii ranging from $\sim$2\text{\,}\mathrm{pc}$$
to $\sim$3.5\text{\,}\mathrm{pc}$$. They modeled the NSC light distribution by
convolving a TinyTim-generated PSF with King profiles of different
concentration parameters (ratio of the tidal to core radius: $5$, $15$, $30$,
and $100$). Using ISHAPE (Larsen, 1999), they fit the data and used the best-
fit model, according to $\chi^{2}$ residuals to derive the effective radius of
the cluster. In their fits, a concentration parameter of $100$ gave the best
results. The final value for the effective radius was obtained by taking the
geometric mean of the full-width-half-maximum along the semi-minor and major
axes and using a transformation factor from ISHAPE’s manual.

In the ultraviolet and optical regime, the ellipticity is $\sim$0.05$$ (panel
B in Figure 6). It remains in this range at
$2\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
$3\text{\,}\mathrm{\SIUnitSymbolMicro m}$, but starts to increase to
$\sim$0.1$$ at $3.6\text{\,}\mathrm{\SIUnitSymbolMicro m}$. At even longer
wavelengths, the ellipticity increases to $\sim$0.4$$ and is significantly
different from the other wavelength regimes. Our measurements in the optical
are consistent with the ones presented by GB14, but are smaller than the
typical ellipticity for other NSCs in the same mass range
($\epsilon\gtrsim$0.1$$, e.g. Seth et al., 2006; Carson et al., 2015; Spengler
et al., 2017; Hoyer et al., 2022, subm.).

The Sérsic index (panel C) appears to vary with wavelength. In the ultraviolet
and optical regime, we find $n\sim$3$$, but in the near-infrared the value
drops to $\sim$2$$. At the longest wavelengths, the value drops to
$\sim$1.5$$, but is also consistent with an exponential profile ($n=$1$$).
GB14 used a King profile to approximate the light distribution and no
comparison can be made.

The position angle of the NSC (panel D) starts at
$\sim$130\text{\,}\mathrm{\SIUnitSymbolDegree}$$ in the ultraviolet regime.
Starting in the optical regime, the position angle drops to
$\sim$100\text{\,}\mathrm{\SIUnitSymbolDegree}$$ and shows a mild anti-
correlation with wavelength, dropping further to
$\sim$90\text{\,}\mathrm{\SIUnitSymbolDegree}$$ in the mid-infrared. Only the
data point from the HST WFPC2 PC F606W band by GB14 is consistent with our
results. The other two data points are significantly elevated to
$\sim$135\text{\,}\mathrm{\SIUnitSymbolDegree}$$ and
$\sim$160\text{\,}\mathrm{\SIUnitSymbolDegree}$$.

Figure 6: Structural properties of the nucleus of NGC 628: effective radius
(panel A), ellipticity (panel B), Sérsic index (panel C), and position angle
(panel D) versus wavelength. Marker symbols and colors highlight different
instruments. Uncertainties are shown with shaded areas. Red pentagons show
literature values from Georgiev & Böker (2014).

###  4.5 Astrometric offset

From the previous section it is apparent that the nucleus shows an evolution
with wavelength, especially towards the mid-infrared regime. Here we
investigate the variability of the central position of the emission in
different bands.

In Figure 7 we show the emission in the JWST MIRI F2100W band (gray scale and
white contour lines) and overlay the emission from the HST WFC3 F275W band.
The WCS of each band were taken from the bands header files. We find that
there exists an offset between the centers of the emission, separated by
$\sim$0.2\text{\,}\arcsec$$, which approximates to
$\sim$9.5\text{\,}\mathrm{pc}$$ at the distance to the galaxy.

To test whether the offset persists in other bands, we perform the following
experiment: we determine the angular coordinates for other bands based on the
central position of the Sérsic profile fit to the light distribution. Figure 8
presents the resulting angular separation using the HST WFC3 F275W band as
reference. We find that the angular separation is of the order of
$\lesssim$0.1\text{\,}\mathrm{\SIUnitSymbolArcsecond}$$
($\lesssim$5\text{\,}\mathrm{pc}$$) in the optical, which is comparable to the
effective radius of the cluster. In the infrared the separation drops to
$\lesssim$0.06\text{\,}\mathrm{\SIUnitSymbolArcsecond}$$ but increases up to
$0.21\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ in the mid-infrared regime.

Depending on the band used as reference, the angular separation can become
insignificant. For example, while using the F200W as reference, the offsets in
the MIRI bands are still significant, whereas they become insignificant,
except for the F1000W, when using the F335M as reference. This behavior could
point towards issues with the calibration of the WCS’: while we calibrated all
HST data with the most recent WCS solutions from MAST, no reliable solutions
exist so far for the JWST data. The PHANGS-internal versions of the data were
calibrated in the following way: The NIRCam data was calibrated using HST and
Gaia astrometric solutions using asymptotic giant branch stars. Furthermore,
the direction of the separation is the same in the MIRI bands, towards the
North-West (as seen in Figure 7).

Compared to the HST data, the NIRCam calibration should yield “accurate”
astrometric values (see below). The MIRI data are astrometrically aligned to
the F335M image by cross-correlating the images and solving for relative
offsets. However, due to variations in the polycyclic aromatic hydrocarbons
emission structure between different bands and the lack of point-like emission
in the MIRI bands, the astrometric calibration is less certain.

To further quantify the offsets and benchmark the values, we compute the
angular separation of (a) a star outside the central cavity, (b) multiple
stars less than $1\text{\,}\arcsec$ South of the NSC within the cavity, and
(c) a GC about $10\text{\,}\arcsec$ South-West from the NSC. The star outside
the cavity has Gaia EDR3 designation 2589386446469602688, is non-saturated in
all but the HST ACS F435W, F555W, and F814W bands and lies about
$60\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ South-East of the NSC. For the
star outside the cavity and the GC, we fit the light distribution with a two-
dimensional Gaussian function, which yields the position of the center of the
sources, which we deem accurate within $0.5\text{\,}\mathrm{pixel}$. For the
other stars close to the NSC, we extract the position manually.

In Figure 8 we show the offset of the star outside the cavity and the GC in
addition to the offsets for the NSC. If we use the HST WFC3 F275W data as
reference, the offsets are significant in both the NIRCam and MIRI data. The
same result is found if we use the F200W as reference. However, the offsets
become insignificant in all except two bands (F200W & F1000W) if we use the
F335M data as reference. With the currently available WCS calibrations, while
there are hints of an astrometric offset, we cannot conclude whether they are
significant.

Figure 7: Main panel: Central
$$5.5\text{\,}\mathrm{\SIUnitSymbolArcsecond}$\times$5.5\text{\,}\mathrm{\SIUnitSymbolArcsecond}$$
of NGC 628 in the JWST MIRI F2100W. A darker shade and white contours show
high flux in the F2100W. Red contours highlight the HST WFC3 F275W emission.
Both maps are matched based on the most up-to-date world coordinate solutions.
Inset panel: Zoom into the nucleus of NGC 628. The white and red contours
highlight again the emission in the F2100W and F275W, respectively. The offset
between the centers of the contours measures approximately
$0.2\text{\,}\mathrm{\SIUnitSymbolArcsecond}$.  Figure 8: Angular separation
($\theta$) versus wavelength ($\lambda$) of the nuclear star cluster position
with respect to the HST WFC3 F275W. Different instruments are highlighted with
different marker symbols and colors. Crosses show the angular separation of a
star with Gaia EDR3 designation 2589386446469602688. The vertical length of
the cross give $0.5\text{\,}\mathrm{pixel}$, which we assume as an upper limit
on extracting the position of the star. Data points above the crosses indicate
that either the world coordinate system is offset, or the center of the
nucleus is offset compared to the HST WFC3 F275W. In some bands (for example
the HST ACS F814W), the star is saturated and no central position could be
determined. The separations for a globular cluster, located
$\sim$10\text{\,}\arcsec$$ South-West of the nucleus is shown with black
hexagons. The offsets agree with the offsets of the star in the NIRCam data.

##  5 Discussion

One of the most striking features of the JWST observations of the center of
NGC 628 is that the prominent NSC sits in a nuclear stellar component that is
devoid of gas and dust. It appears that both gas and dust have been evacuated
from the central cavity. The mechanism that created this cavity is not
obvious. There are no young stars that could have blown out the gas recently.
Alternatively, the central cavity could have been created by consumption of
the gas in the last star formation event, and the re-supply of gas is hindered
by a potential bar resonance, in case a bar is (or previously was) present.
666As mentioned in the introduction, Querejeta et al. (2021) find that NGC 628
hosts no bar.

###  5.1 Nuclear star cluster properties

We show the mass ratio (NSC mass divided by host galaxy mass) in the left
panel of Figure 9 where the NSC of NGC 628 is highlighted with a blue cross.
Data from the Local Volume (a field environment with distance
$\lesssim$11\text{\,}\mathrm{Mpc}$$; Seth et al., 2006; Georgiev et al.,
2009a; Graham & Spitler, 2009; Baldassare et al., 2014; Schödel et al., 2014a;
Calzetti et al., 2015; Carson et al., 2015; Crnojević et al., 2016; Nguyen et
al., 2017; Baumgardt & Hilker, 2018; Nguyen et al., 2018; Bellazzini et al.,
2020; Pechetti et al., 2020) are added for comparison. Dwarfs around massive
field galaxies and Virgo cluster members are taken from Carlsten et al. (2022)
and Sánchez-Janssen et al. (2019a), respectively. 777Although not considered
here, data for nucleated dwarf galaxies in the Fornax galaxy cluster is
presented by Muñoz et al. (2015); Eigenthaler et al. (2018); Venhola et al.
(2018); Ordenes-Briceño et al. (2018); Su et al. (2021). Data for other
massive late-type galaxies in the field are taken from GB14. The NSC of NGC
628 follows the overall trend in that the NSC mass becomes insignificant
compared to the host galaxy. However, other late-types of the same host galaxy
mass typically host more massive NSCs.

The effective radius of the NSC in NGC 628 also compares well to those of
other NSCs in late-type galaxies (in the F814W band; middle panel in Figure
9). Finally, the ellipticity in the F814W band is smaller than the typical
value in other late-types (right panel). This figure shows there exists no
apparent correlation with the inclination of the host.

Figure 9: Left panel: Mass ratio of nuclear star cluster (NSC) and host galaxy
stellar mass ($M_{\star}^{\mathrm{nsc}}/M_{\star}^{\mathrm{gal}}$) versus
galaxy stellar mass. The NSC of NGC 628 is highlighted with a blue cross.
Other data sets from the Local Volume (a field environment with a distance
$\lesssim$11\text{\,}\mathrm{Mpc}$$; green diamonds; Seth et al., 2006;
Georgiev et al., 2009a; Graham & Spitler, 2009; Baldassare et al., 2014;
Schödel et al., 2014a; Calzetti et al., 2015; Carson et al., 2015; Crnojević
et al., 2016; Nguyen et al., 2017; Baumgardt & Hilker, 2018; Nguyen et al.,
2018; Bellazzini et al., 2020; Pechetti et al., 2020), the Virgo galaxy
cluster (orange squares; Sánchez-Janssen et al., 2019a), dwarfs around massive
field galaxies (green triangles; Carlsten et al., 2022), and massive field
galaxies (gray circles; Georgiev & Böker, 2014) show the general distribution
of NSCs. The Milky Way NSC is highlighted with a blue plus-sign. In comparison
to other massive field late-type galaxies, the NSC of NGC 628 appears under-
massive. Middle panel: Effective radius ($r_{\mathrm{eff}}$) in the F814W
versus NSC stellar mass. The markers and colors of the data points are the
same as in the left panel. Dashed lines give the mean density of clusters.
Right panel: Ellipticity ($\epsilon$) versus NSC stellar mass. We show the
data by Georgiev & Böker (2014) and color-code them by the host galaxy
inclination. There exists no apparent correlation between ellipticity, mass,
or inclination. For NGC 628, the inclination has a value of
$i\sim$8.9\text{\,}\mathrm{\SIUnitSymbolDegree}$$ (Lang et al., 2020).

Since the mass of the NSC is smaller than most other masses of such a cluster
at $M_{\star}^{\mathrm{gal}}\sim${10}^{10}\text{\,}\mathrm{M_{\odot}}$$ and
assuming that stars formed in-situ should dominate the mass budget, we
speculate that the NSC had a quiet evolution and that, compared to other NSCs,
only little mass formed in-situ over the last few $\mathrm{Gyr}$. This
speculation is corroborated by our results in Sections 4.1, 4.2, and 4.4: the
effective radius shows no wavelength dependence from the ultraviolet to the
near-infrared regime, staying roughly constant at $5\text{\,}\mathrm{pc}$. The
color of the NSC was determined to be
$\mathrm{\textit{B}}-\mathrm{\textit{V}}=($0.73$\pm$0.05$)\,$\mathrm{mag}$$,
which compares to a star of G8V-class. Finally, the resulting best-fit SED
model indicate that all stellar mass is assembled in an “old” stellar
population, with the mass of the “young” stellar population being consistent
with zero. As indicated by the fit, “old” refers to an age of
$8\text{\,}\mathrm{Gyr}$. If true, this could also mean that the cavity has
existed for a few $\mathrm{Gyr}$ and that any massive black hole in the center
of NGC 628 did not grow significantly via gas accretion over the same time
period. So far, no reliable black hole mass measurement is available (see also
Section 5.3.1 below).

The SED fit also indicates that the metallicity of the NSC is $Z\sim$0.02$$,
which is comparable to NSCs in similar mass galaxies (Koleva et al., 2009;
Paudel et al., 2011; Spengler et al., 2017; Kacharov et al., 2018; Neumayer et
al., 2020), and also the Milky Way NSC (Do et al., 2015; Feldmeier-Krause et
al., 2017a). In combination with the age estimate of the stellar population,
this reveals that the NSC formed in a dense environment where rapid enrichment
took place. Such conditions could take place either during the formation of
the galaxy itself or during a past merger event.

As mentioned above, while in-situ star formation is expected to contribute a
significant mass fraction to the NSC, as measured in other galaxies, our
results indicate that no in-situ star formation occurred over the last few
$\mathrm{Gyr}$. This means that, since the formation of the NSC, either no or
very little amount of gas fell towards the center or that star formation was
inefficient. One possibility is that the shape of the gravitational potential
limits the amount of inflow. Indeed, it is well known that in a viscous
accretion disk, the amount of inward mass transport depends on the amount of
shear (e.g. Shakura & Sunyaev, 1973; Lynden-Bell & Pringle, 1974). One way to
limit the inflow of gas is to have a low shear, meaning that the rotation
curve is close to solid body rotation (e.g. Lesch et al., 1990; Krumholz &
Kruijssen, 2015). Note, however, that it is still unclear what mechanism
drives the ISM turbulence responsible for creating the required viscosity
(e.g. Klessen & Glover, 2016; Sormani & Li, 2020). Alternatively, it could be
that the in-flow is irregular and triggered by mergers or interactions with
satellite galaxies (e.g. Storchi-Bergmann & Schnorr-Müller, 2019). Multiple
dwarfs are known to reside around NGC 628 (Davis et al., 2021) and numerous
accretion events occurred in the galaxy’s history (Kamphuis & Briggs, 1992).

###  5.2 Comparison with the Milky Way

The obtained NSC size using near-infrared data seems to be very similar to the
Milky Way’s (MWNSC) with an effective radius of $\sim$5\text{\,}\mathrm{pc}$$
(e.g. Fritz et al., 2016; Gallego-Cano et al., 2020). However, the MWNSC also
presents a similar size when analyzed with Spitzer/IRAC mid-infrared data
(Schödel et al., 2014b; Gallego-Cano et al., 2020), which is in contrast to
the significantly larger effective radius we obtained for the NSC of NGC 628
from MIRI mid-infrared data. In addition, the mass estimates compare, with the
MWNSC having a mass of
$\sim$2\text{\times}{10}^{7}\text{\,}\mathrm{M_{\odot}}$$ (Launhardt et al.,
2002; Schödel et al., 2014a; Feldmeier-Krause et al., 2017b).

The predominantly old ($\sim$8\text{\,}\mathrm{Gyr}$$) and metal-rich
($Z\sim$0.02$$) population detected in NGC 628’s NSC is also in agreement with
the results obtained for the MWNSC (e.g. Feldmeier-Krause et al., 2017a;
Schödel et al., 2020; Nogueras-Lara, 2022), though recent work suggested a
younger age for the MWNSC of $\sim$5\text{\,}\mathrm{Gyr}$$ (Chen et al.
subm.). However, the MWNSC also shows recent star formation activity, about
$6\text{\,}\mathrm{Myr}$ ago (Paumard et al., 2006), which is not present in
NGC 628’s NSC, according to the best-fit SED model.

Overall, we find that little to no star formation occurred in the last few
$\mathrm{Gyr}$ in NGC 628’s center. This results in an under-massive NSC,
compared to other similar-mass late-type galaxies, a likely under-massive
central black hole, if present, and that the central cavity spanning
approximately $$200\text{\,}\mathrm{pc}$\times$400\text{\,}\mathrm{pc}$$
existed for a similar period.

###  5.3 Nature of the emission in the mid-infrared

While an old ($8\text{\,}\mathrm{Gyr}$) population with metallicity
$Z\sim$0.02$$ accounts for the emission in the ultraviolet to near-infrared
regime, we found an excess of emission in the mid-infrared bands (cf. Figure
5), which cannot be explained by that same population. In addition, the
effective radius and ellipticity do not change with wavelength until the mid-
infrared regime, the Sérsic index shows a weak wavelength dependence, and the
position angle does not change significantly between the near- and mid-
infrared (cf. Figure 6). We speculate about the nature of the emission in the
following sections.

####  5.3.1 Active galactic nucleus contribution

One possibility is that the emission in the mid-infrared bands is caused by an
active galactic nucleus (AGN) once X-ray photons are absorbed by dust, which
re-emits the radiation at longer wavelengths.

The presence of a massive black hole in NGC 628 is still disputed: Dong & De
Robertis (2006) use the black hole mass versus bulge
$\mathrm{\textit{K}}_{\mathrm{\textit{S}}}$-magnitude relation to find
$\log_{10}\,(M_{\mathrm{BH}}\,/\,$\mathrm{M_{\odot}}$)\sim$6.7$$ but such a
relation assumes that the bulge did not significantly grow through secular
processes, which is believed to be the case for NGC 628. She et al. (2017)
found an X-ray excess in the galaxy’s center, which they attribute to the
presence of an AGN with a black hole mass of
$\log_{10}\,(M_{\mathrm{BH}}\,/\,$\mathrm{M_{\odot}}$)\sim$6.0$$. The X-ray
luminosity was determined to be
$\log_{10}\,(L_{2\textrm{-}$10\text{\,}\mathrm{keV}$}\,/\,$\mathrm{W}$)=$31.15$^{+$0.32$}_{$-0.19$}$,
as determined through the hardness ratios of soft-, medium-, and hard X-ray
bands.

We determine the spectral flux density of the emission in the mid-infrared by
using this luminosity and the scaling relation by Asmus et al. (2015), which
connects the X-ray luminosity of an AGN to the mid-infrared luminosity at
$12\text{\,}\mathrm{\SIUnitSymbolMicro m}$. The result is
$S_{\nu}^{\mathrm{BH}}\sim$1.9\text{\times}{10}^{-4}\text{\,}\mathrm{mJy}$$.
We compare this value to the difference between the observed emission and the
model flux excluding the MIRI data in the
$11.3\text{\,}\mathrm{\SIUnitSymbolMicro m}$ band. The difference equals
$\Delta S_{\nu}^{$11.3\text{\,}\mathrm{\SIUnitSymbolMicro
m}$}\sim$0.06\text{\,}\mathrm{mJy}$$, far exceeding the expected flux density
of an AGN. Therefore, while the X-ray excess measured by She et al. (2017)
originating from a possible AGN could contribute to the mid-infrared emission,
it cannot fully explain it by itself. Furthermore, little to no dust is
present in the NSC, making this scenario unlikely.

####  5.3.2 Infalling star cluster

A possible scenario, which could perhaps explain the offset in Figure 7, if
real, is that we see the NSC and an in-falling star cluster, where the latter
could be in a late stage of tidal disruption by the more massive NSC. Such a
scenario for the build-up of NSCs has been proposed for a few decades
(Tremaine et al., 1975) and is sometimes referred to as the “dry-merger”
scenario (e.g. Arca Sedda & Gualandris, 2018) with ample observational and
theoretical evidence in both the Galactic but also extragalactic NSCs (e.g.
Antonini, 2013, 2014; Arca-Sedda & Capuzzo-Dolcetta, 2017; Fahrion et al.,
2020; Feldmeier-Krause et al., 2020).

The proposed scenario could occur as follows: the star cluster would form
outside the nuclear region and spiral inwards. During this time, the star
cluster can be considered self-gravitating, which implies that it evolved
predominantly due to its internal collisional dynamics. During the infall of
the cluster, it will experience gravothermal-gravogyro contraction and core-
collapse (e.g. Kamlah et al., 2022), mass segregate, and form a subsystem of
black holes in its center, or even an intermediate-mass black hole, if the
star cluster is massive enough. The most-massive stars accumulate in the star
cluster’s center and lower-mass stars occupy the halo of the star cluster.
Some of these low-mass stars will be stripped by the tidal field of the
surrounding field or may be ejected through dynamical interactions, while the
star cluster approaches the NSC. Some of the stripped or ejected stars might
be visible as asymptotic giant branch (AGB) stars (see also Section 5.3.3)
with their strong, dust-driven stellar winds (see Decin, 2021, and sources
therein) in the near- to mid-infrared bands as single sources scattered around
the NSC (see Figure 4).

From $N$-body simulations by Arca Sedda & Gualandris (2018), modeling the
MWNSC and an infalling star cluster, we know what the infall, merger, and
merger product phases look like in spatial coordinates (Figure 2 in Arca Sedda
& Gualandris, 2018 and Figure 1 in Arca Sedda et al., 2020). If the infalling
star cluster has already crossed the effective radius of the NSC, after which
the star cluster becomes entirely tidally disrupted and cannot be considered a
self-gravitating system anymore (Arca Sedda et al., 2020), the simulation
snapshots could explain the potential astrometric offset. The star cluster’s
core would eventually fall into the core of the NSC and the remaining halo
stars would tidally disperse. Among these would be AGB stars that may partly
be responsible for the astrometric offset shown in Figure 7 and contribute to
the elliptical increase in panel B of Figure 6 (see also Section 5.3.3 below).

One counter-argument is that it is unlikely to witness such an event: Arca
Sedda (2020) simulated the infall of a star cluster on an NSC whose properties
mimic the ones of the Milky Way NSC. They find that the star clusters enters a
region $10\text{\,}\mathrm{pc}$ around the center of the NSC after
$60\text{\,}\mathrm{Myr}$ and that the cluster is not a self-gravitating
system anymore after another $1\text{\,}\mathrm{Myr}$. Note that the bulge
component in their simulation is likely more massive than the bulge-component
of NGC 628 and that the time scale for in-spiral will be longer. Nevertheless,
the time scale will be short compared to the age of the cluster,
$\sim$8\text{\,}\mathrm{Gyr}$$.

####  5.3.3 Dust from AGB stars

While on the AGB, the outer layers of a star expand drastically leading to a
circum-stellar envelope, which leads to an enrichment of the interstellar
medium, contributing to the mass budget for future star formation (e.g. Loup
et al., 1997; van Loon et al., 1998). Material from the stellar winds can
produce dust, which cools off and becomes visible in the mid-infrared regime.
Note that the dust would reside “close” to the star (at a few hundred stellar
radii for a temperature of $\sim$100\text{\,}\mathrm{K}$$; Decin, 2021), thus
not obscuring the emission of other stars in the NSC, which is why we observe
no dust obscuration in the ultraviolet and optical regime. Here we explore
whether AGB stars can account for the emission in the MIRI bands (cf. Figure
5).

We first determine the residual flux, which is not accounted for by the SED
model excluding the data. The residual values are $\Delta S_{\nu}=$ $0.096$,
$0.062$, $0.049$, and $0.014\text{\,}\mathrm{mJy}$ in the F770W, F1000W,
F1130W, F2100W, respectively. Next, we generate absolute magnitudes of AGB
stars using PARSEC tracks (Bressan et al., 2012), with
$60\text{\,}\mathrm{\char 37\relax}$ Silicate and $40\text{\,}\mathrm{\char
37\relax}$ AlOx for M-type stars, and $85\text{\,}\mathrm{\char 37\relax}$ AMC
and $15\text{\,}\mathrm{\char 37\relax}$ SiC for C-type stars (Groenewegen,
2006), long-period variabilities from Trabucchi et al. (2021), a log-normal
Chabrier (2003) initial mass function, and a metallicity of $Z=$0.012$$.888The
models were calculated by http://stev.oapd.inaf.it/cgi-bin/cmd_3.6, Bressan et
al., 2012; Chen et al., 2014, 2015; Tang et al., 2014; Marigo et al., 2017;
Pastorelli et al., 2019, 2020. The last two settings equal the results found
from SED fitting. We then convert the absolute magnitudes to spectral flux
densities using the distance estimate to NGC 628 and Vega- to AB-magnitude
conversion factors for the Sun (Willmer, 2018).

First, we limit the AGB model stars to reside within the $1\sigma$ interval of
the measured colors.999We use the six colors
$\mathrm{\textit{F770W}}-\mathrm{\textit{F1000W}}$,
$\mathrm{\textit{F770W}}-\mathrm{\textit{F1130W}}$,
$\mathrm{\textit{F770W}}-\mathrm{\textit{F2100W}}$,
$\mathrm{\textit{F1000W}}-\mathrm{\textit{F1130W}}$,
$\mathrm{\textit{F1000W}}-\mathrm{\textit{F2100W}}$, and
$\mathrm{\textit{F1130W}}-\mathrm{\textit{F2100W}}$. Afterwards, we determine
how many AGB stars are required to account for the residual emission in the
MIRI bands and multiply that number by the mass of the stars. Figure 10 shows
the logarithmic mass fraction of AGB stars compared to the total NSC mass
versus the mass of the individual AGB stars. The data are color-coded by the
age of the AGB stars. We find that both a few young and many old AGB stars
could be responsible for the emission in the mid-infrared.

Figure 10: Logarithmic fraction of the number of AGB stars multiplied by their
mass and divided by the total nuclear star cluster mass ($\log_{10}\,f$)
versus AGB star mass. Each data point is color-coded according to the age of
the star. Note that all AGB stars are younger than the main stellar population
of the NSC, as identified by fitting the spectral energy distribution.

However, all model AGB stars that satisfy the color-cuts are younger than
$5\text{\,}\mathrm{Gyr}$, which gives the lower uncertainty on the age of the
main stellar population of the NSC. Therefore, if AGB stars are responsible
for the emission in the MIRI data, there must have been star formation in-situ
after the initial formation of the NSC.

In case the AGB stars are old, meaning that many AGB stars are required to
account for the emission in the mid-infrared, it remains unclear why both the
effective radius and ellipticity change significantly, as the cluster with the
AGB star should have relaxed between their formation and today. In contrast,
only few massive and young AGB stars are required to account for the mid-
infrared emission, which could explain the increased effective radius and
ellipticity, if they formed outside the center of the NSC. However, this would
require in-flow of gas in the past few $\mathrm{Myr}$ but we cannot detect the
presence of a young stellar population in the NSC. Therefore, it remains
challenging to explain both the structural and photometric parameters using
only AGB stars.

####  5.3.4 A circum-nuclear gaseous disk

Another possibility is that the infrared emission originates from a circum-
nuclear gaseous disk or ring with a radius of a few pc, similar to the one
present in the MW. Indeed, the MW hosts a clumpy, asymmetric, inhomogeneous,
and kinematically disturbed concentration of molecular/ionized gas at
$R\lesssim$5\text{\,}\mathrm{pc}$$ known as the circum-nuclear disk (e.g. Lau
et al., 2013; Hsieh et al., 2021). The MW circum-nuclear disk occupies similar
radii to its NSC, has a total mass of
$M_{\mathrm{gas}}^{\mathrm{disk}}\simeq${10}^{4}$$-${10}^{5}\text{\,}\mathrm{M_{\odot}}$
and it is probably a transient structure (on a timescale of few
$\mathrm{Myr}$) originating from a series of randomly oriented in-flow events
(Requena-Torres et al., 2012). By analogy, we could hypothezise that NGC 628
hosts a similar gaseous structure and that this is producing the observed mid-
infrared emission. While the emission from the gas disk could explain the
observed photometry, it is unclear why we do not detect a “young” (formed in
the last few $\mathrm{Gyr}$) stellar population in the NSC. While the ALMA CO
band does not show significant emission in NGC 628’s center (see Figure 1),
this may be related to the sensitivity of the ALMA measurements and could not
exclude a low-mass disk: in the the PHANGS–ALMA v4p0 “broad” CO (2-1) map, the
intensity measurement at the position of the NSC is
$I_{(\mathrm{CO})2-1}=(-0.27\pm$1.30$)$\mathrm{K}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$.
Given the beam size ($\theta=$1.12\text{\,}\arcsec$$) and distance to the
target, translating this value to a $$3$\sigma$ upper limit yields to the CO
(2-1) luminosity yields
$\log_{10}\,L_{(\mathrm{CO})2-1}\,/\,$\mathrm{K}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{pc}}^{2}$<4.1$.
For a standard Milky Way CO to H2 conversion factor and CO (2–1) to CO (1–0)
line ratio appropriate for NGC 628 (Bolatto et al., 2013; den Brok et al.,
2021), this luminosity limit corresponds to an upper mass limit of
$\log_{10}\,M_{\mathrm{H}_{2}}\,/\,$\mathrm{M_{\odot}}$<4.9$. In comparison,
the circum-nuclear disk of the Milky Way has a mass of
$M_{\mathrm{gas}}\sim$1.2\text{\times}{10}^{4}\text{\,}\mathrm{M_{\odot}}$$
(Requena-Torres et al., 2012).

####  5.3.5 Background galaxy

It is also plausible that the emission in the MIRI data originates from a
background galaxy, which happens to be aligned with the NSC along the line of
sight. Although an alignment of the order
$0.1\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ is unlikely, we investigate this
scenario further based on the photometry found in the MIRI data.

Hassani et al. (subm., this issue) investigate the properties of compact
sources at $21\text{\,}\mathrm{\SIUnitSymbolMicro m}$ for all four PHANGS–JWST
targets for which data are available. Using a dendogram-based algorithm, they
find $1271$ compact sources of which $115$ are classified as “potential
background sources” (or HZ). This classification was performed using flux
density ratios between MIRI bands (their Equations 1 and 2). The MIRI
structure coinciding with the NSC of NGC 628 was also classified as a
potential background object.

A search in the NASA Extragalactic Database101010https://ned.ipac.caltech.edu/
revealed that the $114$ sources were previously detected by the WISE / ALLWISE
mission (Wright et al., 2010; Cutri et al., 2013) and all objects were
classified as “infrared sources”. While these sources show a galaxy-like
morphology at $2\text{\,}\mathrm{\SIUnitSymbolMicro m}$, their detailed
properties remain unclear at this point.

To compare to the other potential background objects, we select the measured
spectral flux densities for the MIRI bands and subtract the extrapolated
emission from the NSC using the SED fit excluding the MIRI data (solid line in
Figure 5). While the flux density values compare to other potential background
sources, their evolution with wavelength does not: none of the $114$
identified potential background objects follow a similar trend in that the
flux densities decrease with increasing wavelength.

Therefore, if the other $114$ sources are background galaxies, the differences
in the evolution of flux densities with wavelength suggest that the MIRI
emission coinciding with the NSC of NGC 628 is not related to a background
galaxy. Such a scenario becomes more unlikely if we combine it with the
probability of alignment with the NSC along the line of sight.

##  6 Conclusions

In this work we analysed the nuclear star cluster (NSC) of NGC 628, a nearby
late-type spiral galaxy, with archival Hubble Space Telescope (HST) ACS & WFC3
and newly obtained James Webb Space Telescope (JWST) NIRCam & MIRI data. The
combined data cover the ultraviolet to mid-infrared wavelength, enabling an
unprecedented analysis of an extragalactic NSC. Our findings can be summarized
as follows:

  1. 1.

Combining the $\mathrm{\textit{B}}-\mathrm{\textit{V}}$ color with various
mass-to-light relations results in an NSC stellar mass of
$\log_{10}\,(M_{\star}^{\mathrm{nsc}}\,/\,$\mathrm{M_{\odot}}$)=$7.06$\pm$0.31$$.
We compare this number to an estimate derived using the K-band magnitude
(resulting in $$7.2$\pm$1.1$$) and the results from fitting the spectral
energy distribution (SED; resulting in $\sim$7.1$$). These values are
consistent with the literature value of $$7.05$\pm$0.21$$ (Georgiev et al.,
2016).

  2. 2.

The effective radius and ellipticity of the NSC are
$\sim$5\text{\,}\mathrm{pc}$$ and $\sim$0.05$$, respectively, across the
ultraviolet, optical, and near-infrared regime. At the same time the Sérsic
index drops from $\sim$3$$ to $\sim$2$$ and the position angle drops from
$\sim$130\text{\,}\mathrm{\SIUnitSymbolDegree}$$ to
$\sim$90$$-$100\text{\,}\mathrm{\SIUnitSymbolDegree}$. These values supersede
literature values, which varied significantly across neighboring bands
(Georgiev & Böker, 2014).

  3. 3.

In the mid-infrared bands, the effective radius and ellipticity increase to
$\sim$12\text{\,}\mathrm{pc}$$ and $\sim$0.4$$, respectively. The Sérsic index
drops further to $\sim$1.5$$ while being consistent with an exponential
profile, and the position angle remains unchanged compared to the near-
infrared.

  4. 4.

We fit the SED from the ultraviolet to the near-infrared with a total of ten
data points to find an old stellar population of $($8$\pm$3$)$\mathrm{Gyr}$$
with a metallicity of $Z=$0.012$\pm$0.006$$. The fit indicates that no younger
stellar population is present.

  5. 5.

Fitting the SED with the inclusion of the MIRI data yields an overall worse
fit, as evaluated by $\chi^{2}$ statistics. Nevertheless, the age and
metallicity of the main stellar population remain unchanged within the
uncertainties. The differences in both fits to the SED indicate that the MIRI
data do not trace the stellar population found in the lower wavelength
regimes.

  6. 6.

We find different angular separations between the center of the NSC in
different bands, being most significant in the mid-infrared data. However,
depending on the band from which the world coordinate system is taken as
reference, the separations become less significant. This could hint at
persistent calibration issues with the world coordinate systems of individual
bands.

The color, age, and metallicity of the main stellar population of NGC 628’s
NSC indicate that no star formation has taken place in the previous few
$\mathrm{Gyr}$ in its center. This is caused either by a dynamical mechanism
preventing gas and dust inflow, or by feedback from the center. The lack of a
young stellar population hints that the central cavity, which lacks both gas
and dust and has a size of approximately
$$200\text{\,}\mathrm{pc}$\times$400\text{\,}\mathrm{pc}$$ around the NSC, has
existed for the last few $\mathrm{Gyr}$ as well. The reason for the lack of
recent in-situ star formation and origin of the central cavity remains
unknown.

The nature of the emission in the mid-infrared bands remains a mystery as
well. From our SED fits it is clear that the old stellar population of the NSC
cannot completely explain the emission in JWST’s MIRI bands. We discussed five
different mechanisms, which may cause the emission: (1) contribution from a
central active galactic nucleus, (2) an infalling star cluster, (3) dust from
asymptotic giant branch (AGB) stars, (4) the presence of a circum-nuclear
disk, and (5) alignment with a background galaxy.

The AGB scenario could explain the observed photometry. However, we find that
the AGB stars whose colors fit the measurements are younger than the main
stellar population. From a comparison to model AGB stars, we find that either
a large number of old or a small number of young stars are required. While the
first scenario cannot explain the wavelength dependence of the structural
parameters, the latter scenario requires recent (a few $\mathrm{Myr}$ ago) in-
falling gas, however, no stellar population younger than
$5\text{\,}\mathrm{Gyr}$ was detected from SED fitting. In conclusion, none of
the four discussed scenarios can fully explain both the structural and
photometric measurements.

Our analysis highlights the potential JWST data has for exploring galactic
nuclei in the nearby Universe. An ongoing analysis of the stellar population
using PHANGS–MUSE data can improve the situation, albeit it cannot resolve the
NSC. To solve the riddle of the nucleus of NGC 628 at long wavelengths, we
will propose high-resolution spectroscopic observations, ideally Integral
Field Unit spectroscopic data with JWST, to determine the kinematic properties
of the NSC and its direct surroundings. In addition to the nature of the
structure in the mid-infrared bands, these data will constrain further the
presence of a young stellar population, the kinematic signature compared to
the cluster, and help to constrain the presence of a black hole in NGC 628 as
there is currently no available robust mass measurement or upper limit.

## Acknowledgments

This research is based on observations made with the NASA/ESA Hubble Space
Telescope obtained from the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS 5–26555. These observations are associated with
program 15654. This work is based on observations made with the NASA/ESA/CSA
JWST. The data were obtained from the Mikulski Archive for Space Telescopes at
the Space Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127.
The observations are associated with JWST program 02107. This research has
made use of the Spanish Virtual Observatory (https://svo.cab.inta-csic.es)
project funded by MCIN/AEI/10.13039/501100011033/ through grant
PID2020-112949GB-I00.

NH and AWHK are fellows of the International Max Planck Research School for
Astronomy and Cosmic Physics at the University of Heidelberg (IMPRS-HD) and
acknowledge their support. NH acknowledges support from Thomas Müller
(HdA/MPIA) for support with generating part of Figure 1, and Katja Fahrion and
Torsten Böker for useful discussions. ATB and FB would like to acknowledge
funding from the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme (grant agreement
No.726384/Empire). EJW acknowledges the funding provided by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID
138713538 – SFB 881 (“The Milky Way System”, subproject P1) TGW and JN
acknowledge funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (grant
agreement No. 694343). JMDK gratefully acknowledges funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme via the ERC Starting Grant MUSTANG (grant agreement
number 714907). COOL Research DAO is a Decentralized Autonomous Organization
supporting research in astrophysics aimed at uncovering our cosmic origins.
RSK acknowledges funding from the European Research Council via the ERC
Synergy Grant “ECOGAL” (project ID 855130), from the Deutsche
Forschungsgemeinschaft (DFG) via the Collaborative Research Center “The Milky
Way System” (SFB 881 – funding ID 138713538 – subprojects A1, B1, B2 and B8)
and from the Heidelberg Cluster of Excellence (EXC 2181 - 390900948)
“STRUCTURES”, funded by the German Excellence Strategy. RSK also thanks the
German Ministry for Economic Affairs and Climate Action for funding in the
project “MAINN” (funding ID 50OO2206). ER acknowledges the support of the
Natural Sciences and Engineering Research Council of Canada (NSERC), funding
reference number RGPIN-2022-03499. MB acknowledges support from FONDECYT
regular grant 1211000 and by the ANID BASAL project FB210003. KG is supported
by the Australian Research Council through the Discovery Early Career
Researcher Award (DECRA) Fellowship DE220100766 funded by the Australian
Government. KG is supported by the Australian Research Council Centre of
Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through
project number CE170100013. F. N.-L. gratefully acknowledges the sponsorship
provided by the Federal Ministry for Education and Research of Germany through
the Alexander von Humboldt Foundation. PSB acknowledges financial support from
the MCIN/AEI/10.13039/501100011033 under the grant PID2019-107427GB-C31 AKL
gratefully acknowledges support by grants 1653300 and 2205628 from the
National Science Foundation, by award JWST-GO-02107.009-A, and by a Humboldt
Research Award from the Alexander von Humboldt Foundation. G.A.B. acknowledges
the support from ANID Basal project FB210003.

## Data Availability

The data underlying this article are publicly available at the Milkulski
Archive for Space Telescopes (MAST)111111https://archive.stsci.edu/. The
specific observations analyzed can be accessed via
http://dx.doi.org/10.17909/t9-r08f-dq31 (catalog doi:10.17909/t9-r08f-dq31)
and http://dx.doi.org/10.17909/9bdf-jn24 (catalog doi:10.17909/9bdf-jn24).

##  Appendix A Number of Sérsic profiles

The description of the projected light distribution of NSCs is often
approximated by a single simple analytic function such as a Sérsic profile,
with few exceptions (Nguyen et al., 2018; Pechetti et al., 2022). With
increasing spatial resolution at all wavelength ranges, accurate descriptions
of the light distribution of NSCs may warrant multiple profiles. The NSC of
NGC 628 was analyzed previously by Georgiev & Böker (2014) and modeled with a
single King profile, but the goodness of the fit was not indicated.

Here we explore whether adding a second Sérsic profile improves the fit
compared to a single Sérsic profile. The goodness of the two fits may not be
compared via the standard $\chi^{2}$ statistics, as different number of free
parameters are at play. To compensate for the increased number of free
parameters $k$, a penalty is introduced by adding a term linear in $k$ to the
standard $\chi^{2}$ evaluation. We use the Bayesian Information Criteria (BIC,
Schwarz, 1978), defined as

$\mathrm{BIC}=-2\ln\,\mathcal{L}+k\ln\,N\;,$ (A1)

where $\mathcal{L}$ is the likelihood value and $N$ the total number of data
points. Model ($A$) is generally preferred over model ($B$) if
$\Delta\mathrm{BIC}=\mathrm{BIC}_{B}-\mathrm{BIC}_{A}>0$, but note that the
BIC is a heuristic approach and includes approximations.

We highlight the results for the single (labeled “A”) and double Sérsic
profile (labeled “B”) fits for the NSC in Table 5. The $F2100W$ is excluded
from the list as the fit with two profiles for the NSC did not converge under
any circumstance.

The conclusion from this experiment is that a single Sérsic profile is
preferred over fitting two Sérsic profiles for the NSC.

Table 5: Differences in the Bayesian Information Criteria ($\Delta\mathrm{BIC}$) between two ($A$) and a single Sérsic profile ($B$) for the NSC of NGC 628.  Band | $\mathrm{BIC}_{(A)}$ | $\mathrm{BIC}_{(B)}$ | $\Delta\mathrm{BIC}$ | $\frac{\mathrm{BIC}_{(A)}}{\mathrm{BIC}_{(B)}}$
---|---|---|---|---
$F275W$ | $269$ | $203$ | $66$ | $1.33$
$F336W$ | $225$ | $156$ | $69$ | $1.44$
$F435W$ | $234$ | $155$ | $79$ | $1.51$
$F555W$ | $227$ | $162$ | $65$ | $1.40$
$F658N$ | $216$ | $150$ | $66$ | $1.44$
$F814W$ | $284$ | $222$ | $62$ | $1.28$
$F200W$ | $14\,191$ | $14\,121$ | $70$ | $1.00$
$F300M$ | $940$ | $870$ | $70$ | $1.08$
$F335M$ | $1167$ | $1047$ | $120$ | $1.11$
$F360M$ | $1133$ | $1105$ | $27$ | $1.03$
$F770W$ | $421$ | $343$ | $78$ | $1.23$
$F1000W$ | DNFaaThe fit failed to terminate or parameter values ran into boundary conditions in all attempts.  | $382$ | – | –
$F1130W$ | DNFaaThe fit failed to terminate or parameter values ran into boundary conditions in all attempts.  | $482$ | – | –
$F2100W$ | DNFaaThe fit failed to terminate or parameter values ran into boundary conditions in all attempts.  | DNFaaThe fit failed to terminate or parameter values ran into boundary conditions in all attempts.  | – | –

##  Appendix B Data table

In Table 6 we present the best-fit parameters using a single Sérsic profile.

Table 6: Best-fit parameter estimates for the nuclear star cluster of NGC 628 using a single Sérsic profile. The parameter values and their uncertainties were determined via $500$ bootstrap iterations, where the best-fit value gives the median and the uncertainties the $1\sigma$ interval.  Band | RA | DEC | PA | $\epsilon$ | $n$ | $r_{\mathrm{eff}}$ |  $m_{0}$aaApparent magnitude in the AB-magnitude system. The values are corrected for extinction.
---|---|---|---|---|---|---|---
| [hms] | [dms] | [deg] |  |  | [$\mathrm{arcsec}$] | [$\mathrm{pc}$]bbUncertainties were determined based on the assumption that the parameter distribution is Gaussian. | [$\mathrm{mag}$]
F275W | 01:36:41.742 | +15:47:01.167 | $139^{+16}_{-25}$ | $0.13^{+0.03}_{-0.12}$ | $3.5^{+1.0}_{-1.5}$ | $0.17^{+0.03}_{-0.14}$ | $8.2^{+6.7}_{-6.7}$ | $21.38^{+0.31}_{-0.16}$
F336W | 01:36:41.742 | +15:47:01.173 | $125.1^{+5.5}_{-5.7}$ | $0.056^{+0.009}_{-0.010}$ | $2.07^{+0.10}_{-0.11}$ | $0.099^{+0.002}_{-0.002}$ | $4.74^{+0.09}_{-0.09}$ | $20.18^{+0.02}_{-0.02}$
F435W | 01:36:41.743 | +15:47:01.174 | $106.8^{+5.7}_{-6.1}$ | $0.066^{+0.013}_{-0.014}$ | $3.01^{+0.19}_{-0.18}$ | $0.107^{+0.003}_{-0.003}$ | $5.10^{+0.14}_{-0.14}$ | $18.54^{+0.02}_{-0.02}$
F555W | 01:36:41.738 | +15:47:01.216 | $89^{+29}_{-23}$ | $0.020^{+0.011}_{-0.015}$ | $2.51^{+0.20}_{-0.29}$ | $0.103^{+0.003}_{-0.003}$ | $4.91^{+0.14}_{-0.14}$ | $17.89^{+0.04}_{-0.02}$
F658N | 01:36:41.736 | +15:47:01.186 | $105^{+11}_{-10}$ | $0.049^{+0.020}_{-0.018}$ | $2.91^{+0.21}_{-0.31}$ | $0.103^{+0.003}_{-0.005}$ | $4.91^{+0.22}_{-0.22}$ | $17.45^{+0.04}_{-0.02}$
F814W | 01:36:41.738 | +15:47:01.227 | $118.6^{+7.1}_{-7.2}$ | $0.066^{+0.015}_{-0.014}$ | $3.21^{+0.28}_{-0.43}$ | $0.113^{+0.004}_{-0.005}$ | $5.39^{+0.24}_{-0.24}$ | $17.12^{+0.04}_{-0.03}$
F200W | 01:36:41.741 | +15:47:01.133 | $81^{+12}_{-12}$ | $0.036^{+0.013}_{-0.013}$ | $2.26^{+0.15}_{-0.02}$ | $0.111^{+0.004}_{-0.004}$ | $5.31^{+0.21}_{-0.21}$ | $16.54^{+0.27}_{-0.27}$
F300M | 01:36:41.738 | +15:47:01.177 | $96^{+12}_{-10}$ | $0.053^{+0.022}_{-0.023}$ | $2.21^{+0.23}_{-0.37}$ | $0.122^{+0.006}_{-0.007}$ | $5.81^{+0.35}_{-0.35}$ | $17.41^{+0.25}_{-0.25}$
F335M | 01:36:41.737 | +15:47:01.219 | $103^{+11}_{-3}$ | $0.074^{+0.027}_{-0.032}$ | $2.12^{+0.21}_{-0.28}$ | $0.122^{+0.008}_{-0.010}$ | $5.80^{+0.47}_{-0.47}$ | $17.54^{+0.25}_{-0.25}$
F360M | 01:36:41.741 | +15:47:01.223 | $95.6^{+7.2}_{-5.8}$ | $0.099^{+0.029}_{-0.033}$ | $1.88^{+0.18}_{-0.21}$ | $0.129^{+0.007}_{-0.008}$ | $6.16^{+0.38}_{-0.38}$ | $17.65^{+0.25}_{-0.25}$
F770W | 01:36:41.733 | +15:47:01.294 | $86.6^{+4.3}_{-4.5}$ | $0.296^{+0.034}_{-0.033}$ | $0.63^{+0.08}_{-0.08}$ | $0.173^{+0.007}_{-0.007}$ | $8.25^{+0.36}_{-0.36}$ | $18.53^{+0.02}_{-0.02}$
F1000W | 01:36:41.733 | +15:47:01.245 | $93.2^{+5.0}_{-5.6}$ | $0.395^{+0.083}_{-0.045}$ | $1.45^{+0.71}_{-0.64}$ | $0.250^{+0.015}_{-0.022}$ | $11.9^{+1.0}_{-1.0}$ | $18.78^{+0.15}_{-0.15}$
F1300W | 01:36:41.733 | +15:47:01.247 | $93.1^{+5.0}_{-3.9}$ | $0.393^{+0.071}_{-0.045}$ | $1,46^{+0.63}_{-0.40}$ | $0.251^{+0.009}_{-0.015}$ | $11.99^{+0.72}_{-0.72}$ | $18.82^{+0.08}_{-0.08}$
F2100WccNo fit to the data succeeded if PSF convolution was enabled. To determine the central position of the NSC and the magnitude, the data were fit without PSF convolution. | 01:36:41.728 | +15:47:01.231 | – | – | – | – | – | $19.51^{+0.68}_{-0.68}$

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