11institutetext: Instituto de Astrofísica de Canarias (IAC), La Laguna, 38205,
Spain 11email<EMAIL_ADDRESS>22institutetext: Departamento de
Astrofísica, Universidad de La Laguna (ULL), E-38200, La Laguna, Spain
33institutetext: School of Physics, University of New South Wales, Sydney, NSW
2052, Australia 44institutetext: Australian Research Council Centre of
Excellence for All-Sky Astrophysics in 3 Dimensions (ASTRO 3D), Stromlo, ACT
2611, Australia 55institutetext: Centro de Estudios de Física del Cosmos de
Aragón (CEFCA), Plaza San Juan 1, 44001, Teruel, Spain 66institutetext: School
of Physics $\&$ Astronomy, Monash University, Clayton, VIC 3800, Australia
77institutetext: NASA Ames Research Center, Moffett Field, CA 94035, USA
88institutetext: Bay Area Environmental Research Institute, Moffett Field,
California 94035, USA 99institutetext: Kavli Institute for Particle
Astrophysics & Cosmology (KIPAC), Stanford University, Stanford, CA 94305, USA
1010institutetext: Kapteyn Astronomical Institute, University of Groningen,
Landleven 12, 9747 AD Groningen, The Netherlands

# The truncation of the disk of NGC 4565:

Detected up to $z=4$ kpc, with star formation, and affected by the warp

Cristina Martínez-Lombilla 11223344 Raúl Infante-Sainz 112255 Felipe Jiménez-
Ibarra 6633 Johan H. Knapen 1122 Ignacio Trujillo 1122 Sébastien Comerón 2211
Alejandro S. Borlaff 778899 Javier Román 11221010

(Received XXX; accepted XX)

###### Abstract

Context. The hierarchical model of galaxy formation suggests that galaxies are
continuously growing. However, our position inside the Milky Way prevents us
from studying the disk edge. Truncations are low surface brightness features
located in the disk outskirts of external galaxies. They indicate where the
disk brightness abruptly drops and their location is thought to change
dynamically. In previous analyses of Milky Way-like galaxies, truncations were
detected up to 3 kpc above the mid-plane but whether they remain present
beyond that height remains unclear.

Aims. Our goal is to determine whether truncations can be detected above 3 kpc
height in the Milky Way-like galaxy NGC 4565, thus establishing the actual
disk thickness. We also aim to study how the truncation relates to disk
properties such as star formation activity or the warp.

Methods. We perform a vertical study of the disk of NGC 4565 edge in
unprecedented detail. We explore the truncation radius at different heights
above/below the disk mid-plane ($0<z<8$ kpc) and at different wavelengths. We
use new ultra-deep optical data ($\mu_{g,\rm{lim}}=30.5$ mag arcsec-2;
$3\sigma$ within $10\times 10$ arcsec2 boxes) in the $g$, $r$ and $i$ broad
bands, along with near- and far-ultraviolet, H$\alpha$, and H i observations.

Results. We detect the truncation up to 4 kpc in the $g$, $r$ and $i$ ultra-
deep bands which is 1 kpc higher than in any previous study for any galaxy.
The radial position of the truncation remains constant up to 3 kpc while
higher up it is located at a smaller radius. This result is independent of the
wavelength but is affected by the presence of the warp.

Conclusions. We propose an inside-out growth scenario for the formation of the
disk of NGC 4565. Our results point towards the truncation feature being
linked to a star-forming threshold and to the onset of the disk warp.

###### Key Words.:

Galaxies: individual: NGC 4565 – Galaxies: evolution – Galaxies: structure –
Galaxies: star formation – Techniques: image processing – Techniques:
photometric

##  1 Introduction

Over several decades, the analysis of internal secular processes, star
formation history, and the interstellar medium (e.g. Kormendy & Kennicutt,
2004) has enabled significant advances in our understanding of the evolution
of galaxies within their optical radius. In contrast, our knowledge of the
outskirts of galaxies —the so-called low surface brightness (LSB) science— has
come from a recent set of observational studies and theories that have
provided precise details on the hierarchical nature of cosmological structure
formation (e.g. Martínez-Delgado et al., 2009; Kim et al., 2012; Duc et al.,
2015; Mihos et al., 2017; Kaviraj et al., 2017; Kado-Fong et al., 2018;
Zaritsky et al., 2019; Iodice et al., 2019a; Montes & Trujillo, 2019; Trujillo
et al., 2021; Montes, 2022; Saifollahi et al., 2022).

One aspect of this advance relates to galaxy disk truncations, which
constitute a well-defined and abrupt drop in the surface brightness typically
observed at radial distances of $\sim$4 times the exponential scale length of
the inner disk (van der Kruit, 1979; van der Kruit & Searle, 1981a, b). These
truncations are found in three quarters of the thin disks in spiral galaxies
(van der Kruit & Freeman, 2011; Comerón et al., 2012). However, the nature of
disk truncations remains unclear and different scenarios have been proposed to
explain their origin. Some researchers explain the truncation as the location
of those stars having the largest angular momentum at the moment of the
protogalaxy collapse (van der Kruit, 1987), while others have suggested that
truncations are associated with a threshold in star formation (Kennicutt,
1989; Bakos et al., 2008; Roškar et al., 2008a, b; Martínez-Lombilla et al.,
2019; Díaz-García et al., 2022).

The location of the truncations at the edge of disks and therefore within the
LSB regime (i.e. $\mu_{V}>24$ mag arcsec-2) makes these features difficult to
detect at large heights above the mid-plane. In consequence, the truncations
have historically been considered a property of the galactic mid-plane.
However Martínez-Lombilla et al. (2019, hereafter ML19) studied the
truncations of two edge-on nearby galaxies, NGC 4565 and NGC 5907, in a wide
wavelength range from the near ultraviolet (NUV) to the near-infrared (NIR) at
different altitudes above/below the galaxies disk mid-plane. They found that
the radial location of the truncation is independent of both wavelength and
altitude above the galaxies’ mid-plane. The truncation was detected as high as
3 kpc height above the galaxies mid-plane. In addition, ML19 associated the
truncation location with a star formation threshold. At the location of the
truncation, they obtained a face-on deprojected stellar mass density of 1–2 M⊙
pc-2, very close to the critical gas density necessary to transform gas into
stars ($\sim 3-10\leavevmode\nobreak\ M_{\odot}$ pc-2), indicating an
efficiency of $\sim$30 percent in transforming gas into stars. Independently,
Gilhuly et al. (2020) confirmed the existence of such a star formation
threshold in NGC 4565 although they proposed an accretion-based build-up of
the outer disk. Recently, Díaz-García et al. (2022) analysed the disk of UGC
7321, a well-studied edge-on, low-mass, diffuse, isolated, bulgeless, and
ultra-thin galaxy. They reported the discovery of a truncation at and above
the mid-plane ($\sim 0.5$ kpc height, i.e., where $90\%$ of the light comes
from the thick disk) at all the probed wavelength ranges, from FUV to NIR.
This truncation was also found to be linked to a star formation threshold.

Based on the above results, Trujillo et al. (2020) proposed a physically
motivated galaxy size indicator based on the location of the gas density for
star formation threshold. As a proxy to identify this position, Trujillo et
al. (2020) suggested using 1 M⊙ pc-2. This stellar mass density value refers
to the region where the gas density threshold for star formation in galaxies
is found theoretically (see e.g. Schaye, 2004). Chamba et al. (2022) has
explored at which stellar mass density value the truncation is found for a
large number of galaxies. They found that 1 M⊙ pc-2 is a good approximation
for galaxies changing several orders of magnitude in mass.

In this work, we present a follow-up study to ML19 in which we analyse the
vertical structure of the disk of the edge-on Milky Way-like galaxy NGC 4565.
Due to the limited depth of the data and image quality limitations, ML19 did
not find the altitude above the galactic mid-plane at which the truncation
disappears. Thus, an evaluation of the consequences that the vertical extent
of the truncation could have on the structure and origin of the galaxy disk
components is missing. In this study, we aim to address the issue using new
ultra-deep optical data from the 4.2 m William Hershel Telescope (WHT,
$\mu_{g,\rm{lim}}=30.5$ mag arcsec-2; $3\sigma$ within $10\times 10$ arcsec2
boxes) in the $g$, $r$ and $i$ broad bands. We perform an unprecedented deep
vertical analysis of the light and colour distribution of its disk. Our goal
is to firmly establish the location of the truncation at any altitude and give
a vertical extent of the thin and thick disks of NGC 4565. Based on those
results we discuss the origin of the two disk components. In addition, we
broaden the study with H$\alpha$ and H i data, which allows us to analyse the
stellar population and star formation rate (SFR) at the truncation and beyond.

NGC 4565 is a barred edge-on spiral galaxy with a similar mass to that of the
Milky Way ($88.5\pm 0.5$ deg of inclination to the line-of-sight according to
ML19, and $v_{\rm{rot}}=243.6\pm 4.7$ km/s from Makarov et al. 2014). In terms
of its mass assembly history, recent studies suggest that NGC 4565 has not
experienced a strong interaction (Gilhuly et al., 2020; Mosenkov et al., 2020)
that disturbs the disk structure. Gilhuly et al. (2020) proposed a tidal
ribbon event to explain the fan-like structure in the northwest part of the
outer disk. The physical properties of NGC 4565 and the absence of evidence of
a major disruption event guarantee a reliable comparison of the vertical
properties of the disk of NGC 4565 to that of the Milky Way. In addition, the
combination of its nearby location in the Coma I Group (Gregory & Thompson
1977; $\sim 13$ Mpc distance), and the size of its disk ($R\sim 30$ kpc; e.g.,
ML19, Gilhuly et al. 2020), sets NGC 4565 as the galaxy of this kind with the
most extended apparent size on the sky. This means that NGC 4565 provides the
best spatial resolution ($\sim 65$ pc/arcsec) for a detailed study of a
galaxy’s vertical disk structure.

We have detected the highest truncation in a galaxy disk up to date. We
measured the disk truncation up to 4 kpc above/below the NGC 4565 mid-plane,
with a mean radial truncation position of $25.9\leavevmode\nobreak\
\pm\leavevmode\nobreak\ 0.4$ kpc for the three $g$, $r$ and $i$ bands. This
truncation feature is also found in the H$\alpha$ image at the galaxy mid-
plane and in H i data up to $\sim 1.5-2$ kpc height. Also, a colour analysis
allowed us to measure the threshold of star formation associated with the
truncation and the blue stellar populations of the disk warp. The results from
the analysis of the truncation and the vertical disk structure of the edge-on
Milky Way-like galaxy NGC 4565 are presented in this paper as follows. In
Section 2, we describe the data in each wavelength range; we then explain the
methods used to extract the information from that data in Section 3, giving
details of key processes such as the mask construction, sky subtraction, PSF
modelling, profile extraction, how we estimated the truncation radius and the
star formation rates. The main results on the truncation radius and how they
compare with previous works are presented in Section 4. We then discuss the
implications of these results regarding the star formation activity at the
edge of the disk in Section 5, the actual vertical extent of the disk in
Section 6, and what is the role of the warp in the truncation location in this
Milky Way-like galaxy in Section 7. Finally, we draw our conclusions in
Section 8. All magnitudes are provided in the AB system.

##  2 Data

We present an ultra-deep photometric study of the vertical structure of the
disk of the edge-on galaxy NGC 4565 (see Fig. 1). NGC 4565 is a well-known
nearby galaxy whose structural component parameters make it a suitable
analogue of our Milky Way (Bland-Hawthorn & Gerhard, 2016; Kormendy & Bender,
2019).

In this work, we used the same physical parameters for NGC 4565 as in ML19
(see their Table 1). The analysis was mainly performed in the optical
wavelength range, including ultra-deep broad-band data in $g$, $r$, and $i$
filters, and an extra image in a narrow H$\alpha$ filter. We also used far-
and near-ultraviolet (FUV and NUV respectively), as well as H i data to
extract additional and complementary properties. In the following sections, we
explain how each type of data was obtained.

Figure 1: NGC 4565 images in the wavelength ranges studied in this work with
our custom-made mask in shaded black. From top to bottom: coaddition of the
optical $g$, $r$, and $i$ band images using our observed data at WHT; NUV
image from GALEX; FUV image from GALEX; H$\alpha$ narrow-band image from
observation at INT; and H i integrated intensity map from VLA. The radial
location of the disk edge of NGC 4565 is almost the same in all wavelength
ranges. Figure 2: Same that Fig. 1 but showing the bins of the extracted
profiles. The bins extracted over the galaxy mid-plane are indicated in red
while the ones above/below the disk mid-plane are shown in black. The readers
checking the digital version of the paper can zoom in on the image to see even
the smallest bin separately.

###  2.1 New WHT ultra-deep broad-band optical data

We obtained the ultra-deep imaging data at the 4.2 m William Herschel
Telescope (WHT; La Palma, Spain). The images were obtained with the Physics of
the Accelerating Universe Camera (PAUCam; Padilla et al., 2019) in three
broad-band filters $g$, $r$, and $i$, with a total amount of time observed in
each of them of 4.8, 3.1, and 4.4 hours, respectively. The large field of view
of PAUCam ($\sim$1 $\times$ 1 deg2) allows us to observe the target but also
its surroundings making it possible to perform an exquisite data reduction and
sky background treatment. The images have a pixel size of 0.253 arcsec, this
is, a resolution of 16 pc pix-1 considering that the distance to the galaxy is
13.14 Mpc (distance obtained from the average of all calculated distances to
NGC 4565 since 2010 in the NASA$/$IPAC Extragalactic
Database111http://ned.ipac.caltech.edu/, NED). We also observed very bright
stars to construct an extended point spread function (PSF) and correct the
scattered light field (see Sect. 3.3).

We designed an observational strategy and data reduction optimised to detect
and preserve the low surface brightness structures around our target. When
observing, we followed a dithering pattern with large steps (of the order of
the size of the galaxy) combined with different rotation positions of the
camera. This allows to correct systematic effects introduced by the
instrument/telescope system and to perform a night sky flat-fielding
correction procedure (see e.g., Trujillo & Fliri, 2016; Montes et al., 2020).

We briefly summarise the processing of the raw data. We obtained individual
images with an exposure time of 200 seconds each. The PAUCam consists of 14
CCDs, with 4 channels for each CCD. Due to the illumination effects on the
more external CCDs, we decided to use only the 8 central CCDs with the best
illumination quality. Each channel was bias-corrected and flat-fielded. The
master flat field images were obtained from the science images themselves. The
methodology was to mask all sources on each individual image using NoiseChisel
(Akhlaghi & Ichikawa, 2015; Akhlaghi, 2019), normalise those images, and
combine them to obtain the master flat field image. To subtract the sky
background we masked all the signal pixels detected by NoiseChisel and
computed a very smooth surface model to the remaining background pixels. We
then subtracted a 3-$\sigma$-clipped median value of the sky model from the
science images. This procedure ensures the correction of systematics and the
sky background while preserving the low surface brightness structures. Further
details will be provided in Infante-Sainz et al. (in prep.).

After the correction of the systematic effects, we used the
Astrometry222http://Astrometry.net software (Lang et al., 2010) to produce a
first-order astrometric solution that was later improved with SCAMP (Bertin,
2006). Relative astrometry techniques are very difficult to implement in
images with large dithering steps and, at the same time, obtaining an accurate
astrometric solution is key in low surface brightness studies as small offsets
in the alignment of the images will introduce a loss of signal-to-noise ratio
(S/N) in the final stacked image.

The next step is the co-addition of all the aligned images to increase the S/N
of the final very deep images of NGC 4565. We used a 3$\sigma$-clipped median
to generate a final image per filter. Finally, the photometric calibration was
done using SDSS DR12 (Alam et al., 2015).

The final images of NGC 4565 have a limiting surface brightness of 30.5, 29.9,
and 29.3 mag arcsec-2 ($3\sigma$; $10\times 10$ arcsec2) for the $g$, $r$, and
$i$ filters, respectively. They were calculated using NoiseChisel (Akhlaghi &
Ichikawa, 2015; Akhlaghi, 2019) and following the procedure in Borlaff et al.
(2019) and in Román et al. (2020). This is, obtaining the standard deviation
of the images where all the sources are masked (see Sect. 3.1) and applying
this method in each band. These surface brightness limits are, $\sim$3 mag
arcsec-2 deeper than in ML19. The zero point value to convert between
instrumental magnitudes and calibrated magnitudes is fixed to 22.5 mag for the
three bands.

###  2.2 INT narrow-band H$\alpha$ data

We took narrow-band images of the galaxy NGC 4565 using the Wide Field Camera
(WFC), an optical mosaic camera located at the prime focus of the 2.5 m Isaac
Newton Telescope (INT; La Palma, Spain). We used the narrow filter H$\alpha$
6568/95 centred at 6567.98 ${\rm{\AA}}$ with a FWHM 95.63 ${\rm{\AA}}$ (and a
transmission $>80\%$). We also got images in the $R$ broad-band filter to
subtract the contribution of the continuum in the narrow-band images. The WFC
has a pixel size of 0.33 arcsec and a field of view of 34 $\times$ 34 arcmin2,
wide enough to cover our target diameter of 16.6 $\pm$ 0.1 arcmin at the
isophotal level 25 mag arcsec-2 (value for the $B$ band corrected for galactic
extinction; HyperLeda, Makarov et al., 2014).

We performed a basic data reduction of both the H$\alpha$ and $R$ images using
THELI333https://www.astro.uni-bonn.de/theli (Erben et al., 2005; Schirmer,
2013), a software to automatically reduce astronomical images. Once the images
were completely reduced, we subtracted the sky background from all the images
in both filters. To do that, we adjusted a 2D polynomial function to a version
of the images where all the sources were completely masked.

Then, we aligned and combined all the H$\alpha$ images weighted by their
exposure time into a final mosaic with the median value of each pixel obtained
after applying a 3$\sigma$-clipping rejection algorithm. The total observing
time on the source with the narrow-band filter was 16991.86 s. In the same
way, we got the $R$ broad-band mosaic, with a total exposure time of 3010.88
s.

Finally, we subtracted the continuum contribution to the H$\alpha$ flux. The
$R$-band continuum images were scaled and subtracted from the H$\alpha$ filter
image using a scaling factor of $R$/H$\alpha=0.0675$. We refer the reader to
Knapen et al. (2004) for further details about the method used to calculate
this scale factor of the continuum image. There are strong light gradients in
the observed data that could not be properly subtracted, particularly in the
innermost $\sim 4$ kpc.

The continuum-subtracted image was photometrically calibrated using public
available SDSS DR12 data (Alam et al., 2015), and found that the calibrated
zero point of the continuum-subtracted H$\alpha$ mosaic is $5.9\times
10^{-16}$ erg s-1 cm-2. The final image is shown in the second to last panel
in Fig. 1.

###  2.3 VLA H i data

H i integrated intensity maps of NGC 4565 were provided by Yim et al. (2014).
Yim’s team obtained the raw data from the Very Large Array (VLA) archive,
available at the National Radio Astronomy
Observatory444https://science.nrao.edu/facilities/vla/archive/index (NRAO).
Then, they reduced them using the CASA (Common Astronomy Software
Applications) software package (McMullin et al., 2007) which was built for
reprocessing the whole data set in a uniform procedure. We refer the reader to
Yim et al. (2014) for a more detailed description of the data acquisition and
reduction process.

In Table 1 we list the observing parameters and in the bottom panel of Fig. 1
we show the H i integrated intensity maps of NGC 4565 in units of Jy beam-1 km
s-1. The one-sided warp of NGC 4565, noted in previous studies (e.g., Rupen,
1991; Oosterloo et al., 2007; Zschaechner et al., 2012; Radburn-Smith et al.,
2014; Yim et al., 2014; Das et al., 2020; Gilhuly et al., 2020) and in our
optical data (see Sect. 2.1) is evident. We visually identified the H i warp
onset radius at $\sim 26-27$ kpc.

Table 1: NGC 4565 VLA H i observing parameters. $\theta$ and $\Delta v$ are the angular and velocity resolutions, respectively. Parameter | NGC 4565
---|---
Array configuration | BCD
$\theta$ [arcsec]2 | 6.26 $\times$ 5.59
$\Delta v$ [km s-1] | 20
Total flux [Jy km s-1] | 274
Channel noise [K] | 2.73
Velocity range [km s-1] | 970-1490

###  2.4 GALEX ultraviolet data

We use the deepest available data from the Galaxy Evolution Explorer (GALEX,
Martin et al., 2005; Morrissey et al., 2007). GALEX images have a circular
field of view (FOV) of 1.2 degrees, a pixel size of 1.5 arcsec, and a spatial
resolution (FWHM) of 4.2 arcsec and 5.3 arcsec in the FUV and NUV channels,
respectively. The effective wavelengths are 1516 ${\rm{\AA}}$ (FUV) and
2267$\leavevmode\nobreak\ {\rm{\AA}}$ (NUV). The FUV image has an exposure
time of 1693.05 seconds and GALEX zero point magnitude $m_{0,\rm{FUV}}=18.82$
mag. In the case of the NUV data we use the same image as in ML19 with a long
exposure time of 12050.15 seconds, which allows for a surface brightness limit
of $\mu_{AB}\sim 30.5$ mag arcsec-2 (1$\sigma$), and $m_{0,\rm{NUV}}=20.08$
mag. The second and third panels in Fig. 1 show the NUV and FUV images,
respectively.

##  3 Methods

As mentioned in the Introduction (Sect. 1), this work is a follow-up study of
ML19. Here we used deeper images of NGC 4565 data and a wider wavelength range
to answer the open questions from our previous work. These are: 1) what is the
altitude above the galaxy mid-plane where the truncation disappears?; and 2)
what is the amount of stars that are being formed at the very edge of the disk
of NGC 4565 –this is, the specific star formation rate (SFR)?

Thus, most of the techniques applied in this study were previously developed
as a semi-automatic code optimised for LSB data as described in ML19 (see
their Sect. 3). The following sections will only detail the changes with
respect to the previous work.

###  3.1 Mask

The aim of the mask is to cover the flux from all the sources other than our
target. However, this is a complicated task when working with data that reach
LSB levels such as ours, where we detect structures at $\mu_{g}\gtrsim 30$ mag
arcsec-2. At these depths, even the light from very faint objects in the
surroundings of NGC 4565 could contribute to the measured galaxy flux. Thus, a
dedicated mask is key to obtaining reliable surface brightness measurements.

There are two main differences relative to the masking procedure of ML19. The
first is that here we used Python-based routines only as they are built from
modular and object-oriented scripts, that allow for easy implementation of
modifications and improvements. In particular, we used the tools provided by
Photutils (Bradley et al., 2020) to detect astronomical sources using image
segmentation. The second difference is the two-step approach using a
“hot+cold” combined mask (Rix et al., 2004) as in e.g., Montes & Trujillo
(2018), Montes et al. (2020), or Martínez-Lombilla et al. (2023). We first
obtain a “cold” mask optimised to detect bright and extended sources. Then,
over an image –masked with the “cold” mask– we get a “hot” mask that accounts
for faint and small objects. In order to smooth the noise and maximise the
sensitivity of the algorithm, the images were filtered with 2D circular
Gaussian kernels (FWHM sizes of $\sim$1.3 arcsec and $\sim$0.8 arcsec for the
“cold” and “hot” masks respectively), prior to thresholding. The detection
threshold is 1.1$\sigma$ above the background.

Once the “hot+cold” combined masks were finished, the visual check of the
extent of the masks is done accordingly to ML19 (see their Sect. 3.1). The aim
of this last step is to make sure the masks are covering all undesirable flux.
In the case of the NUV data, we directly used the mask obtained in ML19.

###  3.2 Sky background treatment

Figure 3: Local sky correction for the $g$ broad-band image. We show the outer
parts of the profiles in detail ($R>450$ arcsec) along both sides of the
galaxy disk. The profile extracted from the right side of the disk of NGC 4565
is in blue, and the one from the left side is in orange. Left panel: Measured
sky profiles. The vertical red dashed line indicates the radial distance from
which we measured the mean sky value, the horizontal green dashed line is
located at the measured mean sky level and the black dotted line shows the
zero counts level. Right panel: Sky-subtracted profiles, this is, the result
of subtracting the mean sky value from the profiles on the left panel. The
mean profile of the whole disk is in red solid line. The profiles are slightly
corrected for over- and under-subtracted areas around our target.

We used co-added sky-rectified versions of all our images in which in general,
a non-aggressive sky subtraction strategy had been done (see Sect. 2). In
addition, we performed a second-order (also non-aggressive) local background
subtraction. This is, we evaluated the sky covering only our region of
interest in the outermost parts of the disk of NGC 4565. Following the
procedures in Pohlen & Trujillo (2006) and in ML19 (see details in their Sect.
3.2), we measured the mean background levels well beyond the disk edges
through very extended radial surface brightness profiles. We consider as the
sky the flattest part of the outermost region of the extended profiles
($R\gtrsim 700$ arcsec). We measured the mean values in counts of that sky
region using a $3\sigma$-clipping rejection algorithm. We then subtracted the
mean sky from the corresponding image. This local second-order background
evaluation allows us to identify clearly where the surface brightness profiles
of the disk of NGC 4565 reach the sky limit and in consequence, the location
where the sky background starts to be dominant in the profiles. An example of
the extracted profiles for our $g$ broad-band optical data is shown in Fig. 3.

###  3.3 PSF correction in WHT broad-band optical data

The PSF characterises how the light coming from a point source is affected by
the combination of the telescope, the instrument, the detector, and the
atmosphere, and measures the extent of the scattered light (e.g. Michard,
2002; Slater et al., 2009; Sandin, 2015; Trujillo & Fliri, 2016; Infante-Sainz
et al., 2020). Moreover, the outer wings of the PSF of bright stars can add
some flux to the outer parts of extended objects or in low surface brightness
objects around them. Thus, properties of thick disks, stellar haloes, and
faint outskirts of galactic disks can be severely influenced by the wings of
the PSF (e.g. Zibetti et al., 2004; de Jong, 2008; Sandin, 2014, 2015;
Trujillo & Fliri, 2016; Peters et al., 2017; Comerón et al., 2018; Martínez-
Lombilla & Knapen, 2019). For these reasons, is crucial to model not only the
PSF of relatively faint and well-resolved stars but to construct our own very
extended PSF that reaches the whole extent of those wings.

We built three extended (R $\sim$ 20 arcmin) PSF models for each of the $g$,
$r$, and $i$ filters of the PAUCam at the WHT telescope. Following the
methodology outlined in Román et al. (2020) and Infante-Sainz et al. (2020),
we combined three very bright stars (saturated) with magnitudes 2.57, 4.82 and
5.84 mag ($G$-band from Gaia EDR3, Gaia Collaboration et al., 2021), and 50
fainter stars of 11 and 13 mag. The resulting PSFs have full-width-at-half-
maximum (FWHM) values of 0.8 arcsec in each of the $g$, $r$, and $i$ bands. We
fit and subtracted all stars in the field-of-view of the camera brighter than
$G=16$ mag, according to the Gaia EDR3 catalogue, in order to minimise
contamination in our photometry. To do so, we followed the steps in Sect. 3.2
of Infante-Sainz et al. (2020). These scattered light-subtracted images were
the ones used in the following analysis in this work.

The extraordinary depth of the images as well as the extended PSFs
characterisation allowed us to perform a detailed and reliable study of the
outermost parts of the disk of NGC 4565, including colour and stellar
population analyses above/below the mid-plane.

As explained above, the physical properties derived from the outskirts of a
galactic disk can be strongly affected by scattered light. Besides this, that
PSF effect has been proven to be more dramatic in edge-on than in face-on
galaxies, also affecting their outer colours (e.g., de Jong, 2008; Sandin,
2014, 2015). The strength of the PSF effect is also highly correlated with the
depth of the images (e.g., Trujillo & Fliri, 2016; Comerón et al., 2018;
Martínez-Lombilla & Knapen, 2019). In consequence, it is not only necessary to
correct the scattered light field due to the bright stars, but also to the
scattered light from the galaxy itself. Thus, NGC 4565 has also to be modelled
and corrected.

Interestingly, ML19 found that the effect of the PSF only slightly influenced
the radial flux distribution and the slope of the surface brightness profiles
of the edge-on galaxies NGC 4565 and NGC 5907. Also, in the same work they
verified that the radial position of the galaxy truncations was not affected
by the PSF (see their Sect. 4.3 and Figures 1 and 4). Borlaff et al. (2017)
reported a similar result in a study of the disk breaks in a sample of Type-
III S0 and E/S0 galaxies at $0.2<z<0.6$. They found that the PSF tends to
increase the scale lengths of the inner and outer disk profiles, but it does
not significantly affect either the central surface brightness values of the
inner and outer disks or the break location. However, Martínez-Lombilla &
Knapen (2019) showed that a careful PSF treatment is absolutely indispensable
for deep imaging of extended objects because if the PSF effect is not
accounted for, flux and mass measurements of the outskirts of disks of edge-on
galaxies can be overestimated when reaching surface brightness values of
$\sim$28 mag arcsec-2 or deeper. In particular, they found that the mass of a
thick disk can be overestimated by a factor of 1.5–2 in low-mass sources
($\sim 10^{9}M_{\sun}$) and of 2.5–4 in intermediate- to high-mass galaxies
($>10^{10}M_{\sun}$). Previous works such as Comerón et al. (2018) did not
find this mass excess because they only reached surface brightness levels of
$\sim$26 mag arcsec-2. Although the sample of five galaxies of Martínez-
Lombilla & Knapen (2019) is small, it is worth checking whether the PSF is now
affecting the location of the truncation in our ultra-deep WHT optical images,
especially in the highest (and faintest) parts of the disk of NGC 4565.

We had the scattered light-subtracted images of WHT optical data in the $g$,
$r$, and $i$ broad bands in which the light of the foreground stars had been
corrected. However, it is still necessary to model the effect of the PSF over
the galaxy itself. To do that, we use imfit555Precompiled binaries,
documentation, and full source code (released under the GNU Public License)
are available at the following website:
https://www.mpe.mpg.de/~erwin/code/imfit/ (Erwin, 2015), which allows us to
model the intrinsic light distribution of NGC 4565 and convolve it with the
image of the extended PSF. Then, the PSF-convolved model of the galaxy is
fitted to the observed data. In this way, a new image of the source is built
as the result of the PSF-deconvolved model of NGC 4565 plus the PSF-convolved
fitting residuals. These residuals consider all the non-symmetric features,
such as the spiral arms, that the model cannot properly fit. A comprehensive
overview of the steps, assumptions, and optimization algorithms used in this
2D deconvolution process have already been addressed in previous works (e.g.
Trujillo & Fliri, 2016; Peters et al., 2017; Martínez-Lombilla & Knapen,
2019).

To model NGC 4565 we had to use four galaxy components, as indicated by its
morphology (Buta et al., 2015): a bulge using an elliptical 2D Sérsic function
with generalised ellipses (“boxy” to “disky” shapes) for the isophotes instead
of pure ellipses (Athanassoula et al., 1990); a bar represented by a 2D Sérsic
function (Sersic, 1968); a disk truncated at the same distance as the data
represented with a 3D broken exponential disk function; and finally, a halo
component with a purely exponential function (for more details about the
analytical functions, see Erwin, 2015).

An example of the final 2D deconvolved model of NGC 4565 and its components is
shown in Fig. 18 (Appendix B). We see that the PSF is clearly affecting the
outermost regions of the disk of NGC 4565 as the width of the galaxy changes
after the deconvolution process. This is an effect clearly visible due to the
extraordinary depth of our images. By using the scattered light-corrected
images and these 2D PSF-deconvolved models of the galaxy, we are in the
position to obtain reliable photometry which impacts the subsequent analysis
of the physical properties of the outskirts regions in NGC 4565. We,
therefore, use the images of the 2D PSF-deconvolved models of the galaxy for
further analysis in this work. Hereafter, we refer to the 2D PSF-deconvolved
model of the galaxy in each of the bands as “the galaxy model”.

###  3.4 Profile extraction

####  3.4.1 Broad-band optical profiles

Our goal is to measure the height above the mid-plane where the disk
truncation disappears. For that, we need to extract radial surface brightness
profiles (RSBP) at different altitudes with the best possible vertical
resolution and up to the highest regions that the S/N of our images allows. A
galaxy RSBP can be extracted by calculating the fluxes through a slit with a
given width along the radial axis. In general, we followed the method
explained in ML19 (see details in their Sect. 3.3) over the galaxy models
(details in Sect. 3.3). However, the depth of our new data allowed us to
implement some statistical improvements as well as a slightly different slit
configuration. These changes are described below:

  * •

For each bin, we calculated the surface brightness by applying the Galactic
absorption coefficient correction at each wavelength from the NED (Schlafly &
Finkbeiner, 2011). For simplicity, we applied the same correction coefficient
throughout the whole galaxy ($A_{g}=0.051$, $A_{r}=0.035$, and $A_{i}=0.026$
mag). Each resulting surface brightness value was obtained by calculating the
3$\sigma$-clipping median of the given set of pixels.

  * •

We increased the number of bins to 180 of each RSBP due to higher S/N of the
images (in ML19 there were 150 bins in each RSBP). The radial spacing between
bins remains evenly spaced on a radial logarithmic scale.

  * •

The uncertainties for each bin were defined as in ML19 but this time the $RMS$
quantity was determined over 25000 well-distributed and different background
regions of $\sim 10\times 10$ arcsec2 in the masked image.

  * •

The new ultra-deep optical data from the WHT allowed us to reach higher
altitudes above and below the NGC 4565 mid-plane. Thus, the widths and
vertical locations of the shifted RSBP are slightly different from the ML19
configuration. Now, the boxes with 0.5 kpc height reach up to 4 kpc. Then we
have two steps of 1.0 kpc at 5.0 and 6.0 kpc in height, and one last step of
1.5 kpc at an 8.0 kpc altitude. In this way, we reach the same external
regions as in ML19 but with better spatial resolution and higher S/N allowed
by our data.

  * •

Our technique provides reliable RSBPs down to $\mu_{g}=$ 30.5 mag arcsec-2
($3\sigma$; $10\times 10$ arcsec2).

The size and location of all the apertures and their corresponding bins for
the broad-band optical profiles are shown in the first panel of Fig. 2.

####  3.4.2 H$\alpha$ profiles

The H$\alpha$ stacked and continuum-subtracted image needs a different
treatment in terms of galactic extinction correction. For this narrow filter,
it is also required to remove possible contributions to the total flux from
other emission lines. In order to extract RSBPs in H$\alpha$ we undertook the
following steps:

  * •

To correct for total absorption for the galaxy, we needed to determine the
contribution from both, the foreground Galactic absorption in the $R$ band,
$A(R)$, and the internal absorption of NGC 4565 in the H$\alpha$ narrow
filter, $A(\rm{H}\alpha)$. Thus, the total absorption in magnitude units can
be obtained as the sum of them: $A_{T}=A(R)+A(\rm{H}\alpha)$. For $A(R)$, we
used the value given by the NED (from Schlafly & Finkbeiner, 2011). In the
case of $A(\rm{H}\alpha)$, several solutions have been proposed in the
literature (e.g., Kennicutt & Kent, 1983; Niklas et al., 1997; Helmboldt et
al., 2004; James et al., 2005). In this work we took the approach of Sánchez-
Gallego et al. (2012, see their Sect. 5.7) where $A(\rm{H}\alpha)$ = 0.3 when
$M_{B}\leavevmode\nobreak\ \leq-16$ (the absolute B-band magnitude of NGC 4565
is -21.44 $\pm$ 0.24; HyperLeda, Makarov et al., 2014).

  * •

As our narrow-band filter is wider than 35-40 ${\rm{\AA}}$, we also applied
the statistical correction to the H$\alpha$ fluxes for [N ii] forbidden lines
contamination at $\lambda$6548, 6584 ${\rm{\AA}}$. We estimated this
contribution using the expression from Kennicutt et al. (2008):
$\rm{log([{N\textsc{ii}}]/H\alpha)}$ = 0.54 if $M_{B}\leq$-21. As the FWHM of
the H$\alpha$ 6568/95 filter is 95.63 ${\rm{\AA}}$ there is no need to correct
the [N ii]/H$\alpha$ ratio for the transmission profile of the filter
(Sánchez-Gallego et al., 2012).

  * •

After all the above corrections, we extracted one RSBP along the galaxy mid-
plane in a region of 1 kpc width in physical flux units (see the second to
last panel in Fig. 2). This was the best spatial resolution and the higher
height we could reach with the current data. However, the measured flux in the
inner galaxy disk ($\lesssim 4$ kpc) is slightly overestimated as we could not
properly subtract the sky emission and the continuum due to strong light
gradients in the observed data.

####  3.4.3 H i profiles

We extracted RSBPs from the H i data as shown in the bottom panel of Fig. 2.
One profile was extracted along the galaxy mid-plane and the rest at four
altitudes above/below it: at 0.5, 1.5, 3, and 5 kpc. The profiles have an
increasing width from 0.5 kpc to 2 kpc the higher the position above/below the
galaxy mid-plane. However, due to the nature of these data, the procedure is
slightly different from the one explained above for the data in other
wavelength ranges.

Our VLA zeroth-moment intensity maps are in Jy beam-1 km s-1 units but we need
to extract a surface mass density profile, this is, in units of M⊙ pc-2. To do
that, we first converted the value of each bin of the RSBP from flux density
per area in Jy beam-1 to brightness temperature in K, by specifying the beam
area. We used the Rayleigh-Jeans equivalent temperature as it shows a linear
relation between flux and temperature. This equivalence is usually known as
“Antenna Gain” as the flux density sensitivity at a given frequency is related
to the aperture size, while the telescope brightness sensitivity is not. Thus,
the Rayleigh-Jeans relation is only dependent on the aperture size. For a more
comprehensive explanation, see equations 8.16 and 8.19 in Wilson et al.
(2009).

The derived values in K km s-1 were converted to H i surface mass densities
using the optically thin approximation from Hunter et al. (2012):

$N{\rm(HI)\,\,[atoms\,cm^{-2}]}=1.823\times
10^{18}I{\rm{}_{HI}\,\,[K\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}]}\,.$ (1)

This, together with the mass of the H i atom value and the corresponding unit
adjustments, returns the surface mass density values in M⊙ pc-2. The
uncertainties for each bin of the profiles reflect the standard deviation of
the fluxes within each bin. These surface mass density measurements are not
corrected for the inclination of the galaxy. The H i profiles are shown in
Fig. 14.

####  3.4.4 UV profiles

The NUV data has poorer spatial resolution and S/N than optical. For this band
we enlarged the height of the uppermost bins to increase the S/N (see the
second panel in Fig. 2). We extracted only 3 profiles, at the mid-plane (of 1
kpc width), at 1.5, and 5 kpc above and below it (the latter two of 2 kpc
width). There are two main reasons why we adopted this criterion: first, the
NUV data has already been studied in ( ML19, ); and second, because we only
use the NUV image to compare the profiles at three particular vertical
locations in Sect. 4.1.

The FUV data is used for qualitative comparison purposes on the disk light
emission in different regions. Therefore, we only extracted one RSBP along the
galaxy mid-plane in a region of 1 kpc width.

###  3.5 Truncation position

Once we extracted all the RSBPs at all the different highs above and below the
galaxy mid-plane and in all the wavelengths, the last step of the process was
to determine the position of the truncation in the radial axis. We define the
truncation as the sharp edge in the disk of a highly-inclined galaxy (although
some works have been able to detect truncations in face-on galaxies; e.g.,
Martín-Navarro et al., 2012; Peters et al., 2017; Trujillo et al., 2021). This
sharp edge is seen in a RSBP as the change in the slope, mimicking a type II
break but in the galaxy disk edge. In consequence, the regions before and
after the truncation can be modelled with straight lines of different slopes.

We developed a routine to detect the truncation. This routine fits two
exponential functions to the $g$, $r$, $i$ and H i RSBPs to fit the regions of
the disk inside and outside the truncation. When working in logarithmic scales
of flux units, these functions are seen as lines that intersect at a given
point. That point is considered as the truncation radial location. The fitting
of exponential functions is restricted to either the inner or the outer part
of the disk. Those boundaries are estimated by a visual inspection using an
interactive interface of the routine. However, with the aim of reaching
unbiased results, we carried out a fitting procedure afterwards based on
Sequential Least Squares Programming (SLSQP) optimisation algorithm and least
squares statistic. These algorithms perform a broken linear fit of the two
lines and find the intersection point if any. This fitting procedure is
combined with an iterative 3$\sigma$-clipping outlier removal technique in
which, given a maximum number of iterations (3 in our case), outliers are
removed and the fitting is performed for each iteration until no new outliers
are found or the maximum number of iterations is reached. In addition, the
routine performs a Bootstrap re-sampling over 100 fitting points subsets of
each of the two lines in each RSBP. Bootstrap re-sampling is a method that
estimates the variability of our results by making a more detailed analysis of
the parameter distributions. The combined set of bootstrapped parameter values
can be used to estimate confidence intervals, and consequently, to discern
between the multiple good solutions.

The derived truncation radii, obtained as the location where both lines
intersect, are almost always in agreement with those derived by eye. We
computed the errors as the standard deviation of the determination of the
truncation position distribution for a given band and height.

###  3.6 Star formation rate (SFR)

H$\alpha$ is one of the preferred tracers of star formation as it is a strong
emission line with a short timescale ($\lesssim 10$ Myr, Hao et al. 2011),
relatively easy to observe, and with a good spatial resolution. However, this
narrow wavelength range also presents many uncertainties and difficulties due
to extinction, [N ii] contamination, diffuse/absorbed fractions, or
sensitivity to the upper initial mass function (IMF) slope in the very upper
mass range. So, in order for H$\alpha$ to be a precise tracer of the SFR one
must take into account extinction. Moreover, when using narrow-band filters
around H$\alpha$ to measure the luminosity of the line, it is required to
consider the contamination of the H$\alpha$ flux by the neighbouring [N ii]
$\lambda$ 6548 and 6584 lines. These two corrections were addressed in this
work (see Sect. 3.4.2).

The SFR can be obtained from the measured H$\alpha$ fluxes. We applied the
following relation between the H$\alpha$ line intensity and the SFR from
Kennicutt et al. (2009):

${\rm SFR[M_{\odot}\,yr^{-1}]}=5.5\times 10^{-42}{L(\rm{H}\alpha)}\,\,,$ (2)

with $L$(H$\alpha$) being the luminosity, determined as follows:

${L(\rm{H}\alpha)[erg\,s^{-1}]}=4\pi D(3.086\times
10^{24})^{2}{F_{\rm{H}\alpha}}\,\,,$ (3)

where $D$ is the distance to the galaxy in Mpc and $F_{\rm H\alpha}$ is the
flux in H$\alpha$ corrected by absorption and [N ii] contamination. For the
estimation of this SFR conversion factor, we assumed a “Kroupa” IMF (Kroupa &
Weidner, 2003).

##  4 Disk truncation radius results and comparison with previous works

In the following sections, we highlight the main outcomes derived after
applying the methods described in Sect. 3 and how these findings fit within
the current context of the field. We have used the deepest available data of
the edge-on Milky Way-like galaxy NGC 4565 in a broad wavelength range, to
measure the disk truncation radius at different heights above/below the mid-
plane. To do that, we have extracted multiple radial surface brightness
profiles of the disk of NGC 4565 as shown in Fig. 2. Then, we modelled those
profiles and fitted the truncation location (see Sect. 3.5). In the following
sections, we detail the results derived in this work and compare them with
previous relevant studies.

Figure 4: Truncation radius measured from the RSBP along the disk mid-plane
(i.e. 0 kpc), and at different heights above/below the NGC 4565 mid-plane (the
horizontal axis is scaled so as to show the region around the truncation). The
shaded regions denote the standard deviations of the corresponding
distribution of truncation positions. The vertical dashed lines represent the
mean values of the corresponding truncation radius. Top: broad-band optical
data values in comparison with the corresponding models. Centre: truncation
radii for the disk quadrant with warp (north quadrant or upper right in Fig.
6) for the three $g$, $r$, and $i$ bands. Bottom: same as in the centre panel
but for a disk quadrant with no warp feature (west quadrant or lower right in
Fig. 6). In this work we detected truncations up to 4 kpc above/below the
galaxy mid-plane, that is, 1 kpc higher than in ML19. The presence of a warp
clearly affects the radial location of the truncation feature.

###  4.1 Truncation detected up to 4 kpc above/below the NGC 4565 mid-plane

We obtained a mean radial truncation position of 25.9 $\pm$ 0.4 kpc for the
three $g$, $r$, and $i$ bands and for all the altitudes above/below the galaxy
mid-plane, up to 4 kpc. Beyond this height, the truncation is not detected.
These findings are shown in the top panel of Fig. 4, where we put together the
values of the radial truncation positions obtained from the RSBPs of the
galaxy models and those of the optical broad-bands (see Sect. 3.5). The full
set of RSBPs above/below the galaxy mid-plane are shown in the Appendix A
while in Table 2 are the values of the corresponding scale lengths before and
after the truncation obtained in the fittings of the profile. In Figs. 11, 12,
13, and 14 we have the RSBPs extracted from the observed data, while Figs. 15,
16 and 17 show the ones extracted from the models of NGC 4565. As mentioned in
Sect. 3.3, we are going to use the optical data from the latter for further
results and discussion. The error bars in the profiles account for the
uncertainties in the source detection, the detector noise, and the sky
fluctuations.

The lower S/N of the data in ML19, limited their measurements of any reliable
radial position of the truncation of the disk above 3 kpc in height. However,
in this work we are confidently detecting the truncation up to 4 kpc in the
ultra-deep optical data, this is, at 1 kpc higher locations than in any
previous study for any studied galaxy. These high-altitude off-plane
truncation detections are shown in detail in Fig 5. Beyond 4 kpc the
truncation is not detected while the uncertainties of the surface brightness
measurements are smaller than the fluctuations of the profiles. This
guarantees that the data provides enough S/N at high altitudes above the
galaxy mid-plane, ensuring the non-detection of the truncation beyond 4 kpc.

Figure 5: Detail of the two linear fits (transparent straight lines) before and after the truncation radius. These lines fit the radial surface brightness profiles extracted at 3, 3.5 and 4 kpc height above/below the galaxy mid-plane (columns) for each ultra-deep $g$ (blue), $r$ (green), and $i$ (red) band (rows). The surface brightness profiles are those from the PSF-deconvolved models of NGC 4565 shown in Figs. 15, 16, and 17. In each panel, the intersection radius between the two lines provide the truncation radius of the corresponding profile, which is indicated with a dashed vertical line. The truncation radius value is indicated in the top right corner. Figure 6:  NGC 4565 radial surface brightness profiles in the $r$-band for the four disk quadrants and at four different heights above/below the mid-plane as indicated in the bottom panel (i.e. at 1, 2, 3, and 4 kpc height). The vertical dashed lines are placed at the mean truncation radius of each quadrant. The standard deviation of the truncation position distribution is represented with shaded grey regions. In each panel, the upper-right insets with the image of NGC 4565 show two colour-shaded regions that indicate the quadrants where the RSBPs were extracted and colour-coded accordingly. The vertical development of the truncation radius is sharper on the northwest side (right; in red) of the disk while the southeast side (left; in blue) shows two breaks along the radial distribution. The first break is at a radius of $\sim 17$ kpc while the second break corresponds to the truncation. Nonetheless, the truncation radius remains similar within the uncertainties for the three quadrants without a strong warp feature. Table 2: Scale lengths in kiloparsecs of the profile fits on both sides of the truncation for NGC 4565 in the ultra-deep $g$, $r$, and $i$ bands and for H i data. For each height $\mid z\mid$ and each wavelength, we give the numerical value of the exponential fit before and after the truncation radius ($h_{\rm bef}$ and $h_{\rm aft}$). | $g$ | $r$ | $i$ | H i
---|---|---|---|---
$\mid z\mid$ | $h_{\rm bef}$ | $h_{\rm aft}$ | $h_{\rm bef}$ | $h_{\rm aft}$ | $h_{\rm bef}$ | $h_{\rm aft}$ | $h_{\rm bef}$ | $h_{\rm aft}$
0.0 | $8.6\pm 0.3$ | $1.6\pm 0.2$ | $7.3\pm 0.3$ | $1.6\pm 0.1$ | $5.9\pm 0.2$ | $1.8\pm 0.1$ | $17.7\pm 0.7$ | $9.0\pm 0.9$
0.5 | $10.2\pm 0.4$ | $1.6\pm 0.2$ | $7.9\pm 0.3$ | $1.7\pm 0.2$ | $7.1\pm 0.2$ | $1.7\pm 0.2$ | $28.8\pm 0.8$ | $11.3\pm 1.1$
1.0 | $9.1\pm 0.1$ | $2.0\pm 0.2$ | $7.1\pm 0.2$ | $2.1\pm 0.2$ | $6.7\pm 0.3$ | $2.0\pm 0.2$ | $-$ | $-$
1.5 | $7.3\pm 0.3$ | $2.7\pm 0.2$ | $5.8\pm 0.2$ | $3.0\pm 0.3$ | $6.7\pm 0.2$ | $2.5\pm 0.2$ | $21.7\pm 1.2$ | $7.0\pm 1.4$
2.0 | $7.4\pm 0.3$ | $3.5\pm 0.2$ | $7.0\pm 0.2$ | $3.7\pm 0.2$ | $7.2\pm 0.2$ | $3.0\pm 0.3$ | $-$ | $-$
2.5 | $8.8\pm 0.3$ | $3.9\pm 0.3$ | $8.4\pm 0.2$ | $4.1\pm 0.2$ | $8.6\pm 0.3$ | $3.3\pm 0.2$ | $-$ | $-$
3.0 | $10.1\pm 0.3$ | $4.8\pm 0.3$ | $10.0\pm 0.2$ | $4.7\pm 0.2$ | $9.5\pm 0.2$ | $3.8\pm 0.3$ | $-$ | $-$
3.5 | $11.0\pm 0.4$ | $6.0\pm 0.3$ | $10.9\pm 0.3$ | $5.8\pm 0.3$ | $10.2\pm 0.3$ | $4.9\pm 0.3$ | $-$ | $-$
4.0 | $11.6\pm 0.4$ | $6.4\pm 0.4$ | $11.5\pm 0.3$ | $6.5\pm 0.3$ | $11.2\pm 0.4$ | $5.2\pm 0.3$ | $-$ | $-$

The location of the radial position of the truncation remains constant up to 3
kpc, in agreement with ML19. Further up, we have two more detections at 3.5
and 4 kpc but they are located at an inner radius (see Fig. 4). In other
words, we see a shift in the radial location of the truncation towards the
centre of the galaxy above 3 kpc. Then, the higher the altitude, the closer to
the galactic centre. This shift is contributing to the differences with
previous studies when obtaining the mean radial position of the truncation. In
this work, the mean truncation radius in the optical broad bands is 25.9 $\pm$
0.4 kpc, a slightly smaller distance than the 26.4 $\pm$ 0.4 kpc obtained by
ML19 (see their Sect. 4.4), but in agreement within errors. However, if we do
not take into account the two higher detections at 3.5 and 4 kpc in our
estimation of the mean location of the truncation, we got a value of 26.1
$\pm$ 0.2 kpc. This is a similar result to what was found before by ML19.

Some other works have also found this independence on the location of the
truncation with high above/below the galaxy mid-plane in edge-on disk galaxies
(de Jong et al., 2007; Comerón et al., 2012, 2018). However, none of them have
reached our combination of high spatial resolution, high altitude in the disk,
and ultra-deep imaging. In the case of Comerón et al. (2012, 2018), they also
studied the vertical light distribution of the disk of NGC 4565, between
$\sim$2.7–7 kpc above the galaxy mid-plane. They found the truncation radius
located at 27.5 $\pm$ 0.8 kpc up to a high of 3 kpc using lower spatial
resolution data. They did not detect any evidence of truncation at large
heights.

We also explored whether there is any significant difference in the position
of the truncation depending on the disk quadrant. To do that, we extracted
RSBPs from each disk quadrant at five different heights above/below the mid-
plane as shown in Fig. 6. The truncation is systematically sharper in the
right side of the disk (NW; red profiles in Fig. 6). Also, the surface
brightness of the truncation is slightly brighter ($\sim$0.3 mag arcsec-2) in
the right disk, although this could be expected from the fact that NGC 4565 is
not perfectly edge-on. The light profiles show different features depending on
the disk side. On the right side (NW), the profiles are composed of two
exponential light distributions that intersect at the truncation radius. On
the left side of the disk (SE), the light shows an additional break located at
$\sim 21$ kpc. This inner break is clearly visible in the mid-plane profile
but it gradually vanishes as height increases. The asymmetry in the disk of
NGC 4565 has been previously reported by Naeslund & Joersaeter (1997); Wu et
al. (2002) and Gilhuly et al. (2020). The latter authors associated the disk
asymmetry with a tidal ribbon produced by the fan-like feature located around
the northwest disk side.

From the aforementioned profiles, we measured the truncation radius for each
disk quadrant separately. Despite the disk light distribution asymmetry, the
truncation radius remains at the same location and almost constant within the
uncertainties for all the quadrants and heights above/below the mid-plane up
to where we have enough S/N, with the only exception of the quadrant with a
clear warp feature (north quadrant). This is shown in the central and bottom
panels in Fig. 4. When there is no warp, the truncation radius remains
constant. However, the truncation radius systematically increases with height
above the galaxy mid-plane in the presence of the warp. It seems as if the
truncation traces the warp feature, at least, up to 3 kpc height. The possible
role of the warp on the origin of the disk of NGC 4565 will be further
discussed in Sect. 7.

In a previous work, Gilhuly et al. (2020) reported the truncation location at
a smaller radius on the left (SE) side of the disk. However, we consider that
the truncation at a smaller radius in the SE side of the disk is an inner
break. Then, at $\leavevmode\nobreak\ 26$ kpc, we measure a second decline in
the light distribution that coincides with the truncation radius on the right
side of the disk. The higher spatial resolution and depth of our data in
comparison with that in Gilhuly et al. (2020) allowed us to distinguish both
disk features.

###  4.2 Truncation radius remains independent of the wavelength

Figure 7: NGC 4565 radial surface brightness profiles in all the wavelength
ranges used in this work, from FUV to H i. The right y-axis is in surface mass
density units to account for the H i data. Each panel shows the RSBP at the
indicated height above/below the mid-plane. In the cases of FUV and H$\alpha$
we only extracted profiles in the mid-plane (see Sect. 3.4.2). The NUV
profiles are those from ML19. The vertical dashed lines indicate the mean
radius of the truncation in the broad-band optical data as obtained from the
data points in the top panel of Fig 4. The shaded grey regions are the
standard deviation of the truncation radius distribution. The truncation
feature is present in all wavelengths at the same radius until it completely
vanishes beyond 4 kpc height.

The radial position of the NGC 4565 truncation is the same, within errors, for
our full wide wavelength range, independently of the height above/below NGC
4565 mid-plane. We find the same results when measuring the truncation radius
in each disk quadrant separately. This is illustrated in Fig. 7 and also in
Fig. 4 for the optical $g$, $r$, and $i$ bands only. For any given altitude,
the radial location of the truncation is not systematically either closer or
further from the galaxy centre in any of the filters. This result confirms our
expectations as previous studies of NGC 4565 found this independence on the
radial location of the truncation. Gilhuly et al. (2020) extracted RSBPs in
$g$ and $r$ band with the same outcome, so as ML19, in a wide wavelength
range, from NUV to near-infrared ($3.6\,\mu$m).

There is an evident sharp decline in the brightness of the H$\alpha$ emission
around the truncation region in the mid-plane. We also detect such a decline
in surface mass density in H i gas component around the truncation that
gradually vanishes with height to then completely disappears beyond 3 kpc
above/below the galaxy mid-plane. We detect the radius of truncation feature
in the H i gas at $24.0\pm 1.2$, $24.5\pm 1.2$ and $27.4\pm 1.6$ kpc for the
mid-plane, 0.5 and 1.5 kpc height respectively (see the whole set of H i RSBPs
in Fig. 14). Similar trend is shown in both FUV and NUV data (see Fig. 7). It
is clear that the disk truncation in the FUV, H$\alpha$ and H i data is also
detected although it is affected by the lower spatial resolution and/or depth
(as previously explained in Sects. 2.4, 3.4.2 and 3.4.3). These findings
extend the independence of the location of the truncation in the Milky Way-
like galaxy NGC 4565 towards a wider wavelength range, from FUV to H i, in all
measured wavelengths (i.e., FUV, NUV, $g$, $r$, $i$, H$\alpha$, $3.6\,\mu$m,
and H i).

Our findings are in good agreement with Díaz-García et al. (2022). They
extracted light profiles of the disk of UGC 7321 from FUV, optical ($grz$
combined mean), and NIR ($3.6\,\mu$m) images. They reported the discovery of a
truncation at and above the mid-plane at all the probed wavelength ranges.
This is particularly interesting due to the pristine nature of UGC 7321, a
well-studied edge-on, low-mass, diffuse, isolated, bulgeless, and ultra-thin
galaxy. As suggested by Díaz-García et al. (2022), this supports that disks
and truncations can form via internal mechanisms alone.

###  4.3 PSF affects the outskirts of the disk of NGC 4565 but not the
truncation radius

To ensure that our truncation measurements were not affected by the PSF, we
fitted analytical 2D models convolved with the PSF to the ultra-deep optical
broad-band data (see Sect. 3.3). From these models, we built the galaxy PSF
deconvolved models, which are an approximation to the observed images, but
without the PSF effects and with the noise and intrinsic asymmetries of the
galaxy such as the warp. We refer to those models as the “galaxy models”.

The PSF affects the light distribution in the outermost regions of the disk of
NGC 4565 as there is more flux in the observed data than in the galaxy models
as it has also previously reported in ML19. Despite that, the truncation
radius remains the same within the uncertainties when accounting for the PSF.

To prove the above, we extracted a full set of RSBPs from the final models of
NGC 4565 in the optical broad-bands (Figs. 15, 16 and 17). From these
profiles, we determined the radial positions of the truncation at each height
above/below the NGC 4565 mid-plane as described in Sect. 3.5. We did the same
for the corresponding RSBPs extracted from the observed data from Figs. 11, 12
and 13. We show all those radial positions of the truncation in the top panel
of Fig. 4. As previously stated, there are no systematic trends or behaviour
between both sets of data.

Our galaxy model, shown in Fig. 18, is able to properly reproduce and recover
the light in the outskirts of the galaxy up to $\sim$ 1000 arcsec (i.e. $\sim$
60 kpc). This is shown in the profiles and also in the images below, where the
combination of the four galaxy components (i.e. bulge, bar, disk and halo)
successfully mimics the shape of NGC 4565. The residuals basically account for
the dusty regions surrounding the galaxy mid-plane and some asymmetries such
as the disk warp, both impossible to reproduce with the available analytical
functions in the software (see details in Sect. 3.3). Gilhuly et al. (2020)
also obtained a model of NGC 4565 but using just two components: a 3D broken
exponential disk and a 2D Sérsic function. By comparing both approaches, their
model underestimates the light in the outer parts of the disk by up to a 21
$\%$ in $g$-band (Gilhuly et al., 2020, see caveats of the model in their
Sect. 4.2). Nevertheless, both works agree in the fact that there is no
significant variation in the radial location of the truncation between the
observed data and the models (note that Gilhuly et al., 2020, extracted an
azimuthally averaged profile, that is, from elliptical isophotes).

Regarding the shape of the RSBPs in the truncation region, the truncation
always shows the sharpest decline in the mid-plane of the galaxy and becomes
less prominent at large heights in both the galaxy models and the observed
data. However, the truncation feature remains clear at higher altitudes
above/below mid-plane in the models than in the observed data, for the three
bands. This is showed in detail in the figures of the Appendix A (Figs. 11,
12, 13, 15, 16 and 17).

##  5 Star formation activity at the edge of the disk

Figure 8: SFR per radial parsec as a function of the disk radius in NGC 4565
obtained from the H$\alpha$ data. The vertical dashed line indicates the mean
radius of the truncation in the broad-band optical data at 25.9 $\pm$ 0.4 kpc,
and the shaded grey region is the uncertainty of the mean estimation. The
radial bins are logarithmically spaced so the innermost bins are smaller that
those in the outer parts of the disk. For the first time, we measure that NGC
4565 is forming stars at the truncation radius at a rate of $3.5\times
10^{-6}\pm 5\times 10^{-6}$ M⊙/yr/pc, or a total of $0.011\pm 0.002$ M⊙/yr
within the bin.

We found, for the first time, that quiescent NGC 4565 galaxy is forming
$0.011\pm 0.002$ solar masses of stars per year at the truncation radius, at a
rate of $3.5\times 10^{-6}\pm 5\times 10^{-6}$ M⊙/yr/pc. The SFR values per
parsec at the galaxy mid-plane as a function of the radial distance are shown
in Fig. 8 as a radial SFR profile extracted from the continuum-subtracted
H$\alpha$ imaging (see Sect. 3.6). This allows us to investigate the star
formation activity in the vicinity and beyond the truncation radius of NGC
4565.

We verified the drop-off in SFR at the disk truncation. Right before the
truncation and three more times throughout the galaxy disk, there are peaks of
SFR with values of $\sim 1\times 10^{-5}$ M⊙/yr/pc, located at radii 10.4,
16.6, 19.3 and 24.4 kpc. After the truncation, the SFR decreases until it is
completely quenched at radius of $\sim$ 28 kpc.

The total SFR in the disk is 0.63 $\pm$ 0.01 M⊙ yr-1 while the median SFR is
0.02 $\pm$ 0.01 M⊙ yr-1. To get these values we avoided the more active inner
4 kpc in radius that is also the region where we could not properly subtract
the sky emission and the continuum due to light gradients in the observed data
so the flux is overestimated. NGC 4565 is a widely studied quiescent nearby
late-type spiral galaxy with both a low SFR and SFR surface density. In
comparison with previous works, Heald et al. (2012) determined a total SFR of
0.67 $\pm$ 0.10 M⊙ yr-1 (among the lowest in their HALOGAS sample), while
Wiegert et al. (2015) obtained a value of 0.73 $\pm$ 0.02 M⊙ yr-1. These total
SFR values are smaller to ours if we consider the whole disk. However, our
measurements in the innermost disk region are probably overestimated and, on
the other side, Heald et al. (2012) and Wiegert et al. (2015) considered
smaller distances to NGC 4565 than in our work.

Figure 9: $g$-$r$ colour radial profile at six different heights above/below
the NGC 4565 mid-plane up to 4 kpc but excluding the mid-plane. Solid pink
lines are the profiles from the disk region affected by a warp (north
quadrant) while the green ones indicate the profiles of the region of the disk
with no warp feature (west quadrant). The vertical shaded pink area highlights
the warp region. The colour profiles show two moving U-shape features,
characteristic of a star formation threshold. The first U-shape is at the
truncation radius and close to the mid-plane, while the second traces the warp
beyond $R\sim 38$ kpc and above 1.5 kpc height.

We detect a clear characteristic U-shaped age gradient up to 2 kpc in height
around the location of the truncation in all the optical and NUV colour
profiles allowed by our data. The $g$-$r$ colour radial profiles (Fig. 9) show
the most prominent U-shape feature in optical wavelength allowing also for
high S/N beyond the truncation. The U-shape is clearly detected up to 1 kpc in
height and then slowly disappears when moving to larger heights. In Fig. 9, we
show a colour profile for the region of the disk with a warp (the upper-right
disk; red region in the inset of the top panel in Fig. 6) and a region less
affected by the warp (the lower-right disk; red region in the inset of the
bottom panel in Fig. 6). The potential role of the warp in the truncation
properties will be further discussed in Sect. 7.

The bluest colour (i.e., the youngest stellar population) is 0.23 $\pm$ 0.02
at a radius of 27 kpc in the $g$-$r$ colour radial profiles. Beyond the
truncation, the colour reddens again. In the case of the $g$-$i$ colour
profile, a less prominent minimum of age is located at a radius of 27 kpc with
a colour value of 0.43 $\pm$ 0.02. Finally, in the $r$-$i$ colour, the U-shape
feature shows just a hint of its presence in the profiles extracted in the
galactic plane and at 0.5 kpc high. Again, we found the minimum colour value
(i.e., age) of 0.20 $\pm$ 0.02 at a radius of 27 kpc.

It is important to note that the mid-plane regions of the disk of NGC 4565 are
strongly affected by dust which could influence our measured colours. However,
by comparing the light distribution in NUV, optical, and NIR regimes, ML19
found that extinction is mostly limited to the inner areas and there is almost
no dust extinction at the location of the truncation and beyond.

This U-shape feature in the colour profiles has originally been found in
observations of type II breaks (see e.g. Azzollini et al., 2008; Bakos et al.,
2008) at lower radial distances. However, recent works have related the
U-shape with the truncation location. The first detection of this feature was
by ML19, who found it in the Milky Way-like galaxies NGC 5907 and NGC 4565
(for this galaxy later confirmed by Gilhuly et al., 2020). Díaz-García et al.
(2022) observed the U-shape at the truncation location of the low-mass ultra-
thin galaxy UGC 7321 for both the thin and thick disc. In addition, Chamba et
al. (2022) measured a characteristic U-shape from $g$-$r$ colour profiles in a
broad variety of galaxy types (dwarfs to ellipticals) and stellar masses
($10^{7}$ M${}_{\sun}<M_{*}<10^{12}$ M☉).

Theoretical studies on the origin of type II breaks in galaxy disks by Roškar
et al. (2008a) predict that if breaks and truncations share the same formation
process, this would be the result of a radially declining SFR. In that
scenario, the minimum stellar age value would be at the location of the
truncation or break, combined with radial migration further out, producing the
U-shape in the radial colour profiles. As reported above, we find a U-shape in
our colour profiles (see Fig. 9). Also, these theoretical predictions are in
good agreement with our results shown in Fig. 8, where the SFR decreases just
before reaching the truncation radius.

The star formation threshold linked to the U-shape in the colour profiles
(Fig. 9) traces, on the one hand, the youngest stellar population at the
truncation location and, on the other hand, a likely radial migration of stars
towards the outer regions associated with the redder colours beyond the
truncation radius (see related discussion in ML19 and Díaz-García et al.,
2022). The lack of H$\alpha$ emission beyond the truncation (see Fig. 1)
supports this scenario as it is indicative of a death of recent star formation
($<10$ Myr). However, there is FUV emission beyond the truncation, tracing
past star formation of several tens to 100 Myr ago (Kennicutt, 1998). The NUV
flux traces a slightly older population of stars formed $\lesssim 300$ Myr ago
(Kennicutt, 1998) and reaches higher altitudes above/below the galaxy mid-
plane than both H$\alpha$ and FUV. The NUV emission extents up to similar
radial distances beyond the truncation than the FUV. We suggest the outward
radial migration of stars from the star-forming threshold at the truncation
radius to the outer disk as the main mechanism populating the external disk.
The young stars then become visible in FUV and NUV wavelengths. Thus, the
further from the truncation radius, the older the stellar population. In
summary, our observational measurements are consistent with a common origin
for breaks and truncations.

##  6 Vertical extent of the disk and its origin

In ML19, we found that at the truncation could be observed up to a height of
$\sim 2.9$ kpc. This agrees with our results of a coherent disk structure up
to 3 kpc as the truncation is located at a constant radius of 26.1 $\pm$ 0.2
kpc. However, the extra truncation detections in this work that extend this
feature up to 4 kpc from the mid-plane suggest different possible scenarios
for the disk vertical structure.

If the truncation in the mid-plane is a phenomenon associated to the end of
the star formation in the disk and the truncation is moving with time to
further distances, then one should expect the radial position of the
truncations above/below the mid-plane to be located at smaller radial
distances. This is supported by the fact that stars in galactic disks are
subject to migrations in both the radial and vertical directions (see for
reviews Sellwood, 2014; Debattista et al., 2017). Our highest truncation
detections at 3.5 and 4 kpc height, which are at closer radial distances to
the centre of NGC 4565 (see top panel in Fig. 4), support this inside-out disk
growth scenario.

Assuming a similar physical origin for the truncation in both the galactic
plane and at higher altitudes (e.g., de Jong et al., 2007; Radburn-Smith et
al., 2012), the brightness of a thick disk component is still not enough to
outshine the truncation feature from the thin disk at $\sim 3-4$ kpc height.
There is also the possibility of a flared thin disk that dominates at large
heights in the outskirts of the galaxy. The ($g-r$) colour map in Fig. 10
shows evidence of a flare of the younger (bluer) stellar populations in the
outer part of the thin disk ($R>15$ kpc). This flaring is more clear in the SE
side of the disk (left), where the warp is less prominent. Also, as NGC 4565
is not perfectly edge-on ($i=88.5\pm 0.5$ deg; ML19), the flare could be
partially blurred by the addition of light along the line of sight.

Numerical simulations suggest that flaring cannot be avoided due to a range of
different dynamical effects. The main disk flaring mechanism is probably
satellite–disk interactions (e.g., Kazantzidis et al., 2008; Villalobos &
Helmi, 2008; Bournaud et al., 2009; Qu et al., 2011), but mergers (Abadi et
al., 2003), misaligned gas infall (Scannapieco et al., 2009; Roškar et al.,
2010) and reorientation of the disk rotation axis (Aumer & White, 2013) can
produce disk flaring too. However, simulations by Minchev et al. (2015) led
them to propose that purely secular evolution, based in an inside-out growing
disks, also cause flared disks. The latter scenario satisfies both our
observational constraints and the environment conditions in NGC 4565.

From observations, Iodice et al. (2019b) found flared thin disks in three S0
edge-on galaxies within a dense environment in the Fornax cluster from
isophotal and colour analysis. Pinna et al. (2019a, b) supported these
findings with high-quality MUSE stellar kinematic data. Kasparova et al.
(2020), using deep long-slit spectroscopic data across the massive edge-on
galaxy NGC 7572, measured a flare in both the thin and thick disks with
similar radial disk scales. However, is important to consider that all these
galaxies are located in fairly dense environments, unlike the isolated Milky
Way-like galaxy NGC 4565, potentially affecting the formation process of the
flare. In the Milky Way, several authors have also reported flaring of younger
stellar populations (e.g., Feast et al., 2014; Kalberla et al., 2014; Carraro
et al., 2015; Ding et al., 2021; Chrobáková et al., 2022).

In terms of the stellar population ages in the NGC 4565 disk, we see that the
($g-r$) colour is clearly below 0.8 at the truncation/warp, while ($g-r$)
$\sim 1$ in the innermost parts (Fig. 10), reflecting a young population. The
individual light distribution of the galaxy in each wavelength (Fig. 1)
highlights a thin H$\alpha$ disk of stars born $\sim 10$ Myr ago. The FUV data
exhibit a rather thicker thin disk of $\sim 2$ kpc (accounting for inclination
effects), tracing star formation that occurred from several tens to $\sim 100$
Myr ago. The thin disk is even thicker in NUV data, which traces $<300$ Myr
populations (Kennicutt, 1998). However, we do not see star formation in the
thick disk. The H i gas is also concentrated within the thin disk area.

All these findings suggest that the disk of the Milky Way-like galaxy NGC 4565
has been formed mainly through internal processes. In particular, the thin
disk stars would be born in the galaxy mid-plane (up to $\sim 1$ kpc) and then
migrate along the vertical axis, supporting an inside-out and down-up growth
of the disk with an outer flare feature.

##  7 The role of the disk warp of NGC 4565 in the truncation radius

Figure 10: $g-r$ colour map of NGC 4565 with values indicated in the bottom
colour bar. The dashed black line shows the outermost H i isocontour. The warp
is traced with bluer colours in the off-plane regions along the upper-right
side of the disk. We can also see the bluer and little dust-affected regions
around the truncation ($R\sim 26$ kpc). Also, the H i emission follows the
optical light distribution.

We clearly see a warp in the disk of NGC 4565 (Fig. 1) and we report, for the
first time, the warp detection in FUV and NUV data. This warp in NGC 4565 has
been previously reported in optical and H i data (van der Kruit, 1979; Rupen,
1991; Naeslund & Joersaeter, 1997; Radburn-Smith et al., 2014; Yim et al.,
2014; Martínez-Lombilla et al., 2019; Gilhuly et al., 2020). However, our
ultra-deep data indicate a very prominent warp in the north side (upper-right
disk quadrant) with $\sim 6-7$ kpc length, while it is fainter and shorter in
the south edge. As we do not see the warp in H$\alpha$, this indicates that
there is recent ($\gtrsim 100$ Myr ago) but not ongoing star formation in this
disk structure. The warp also shows clear H i gas content. These measurements
are in agreement with the stellar populations of less than 600 Myr old
reported for the warp by Radburn-Smith et al. (2014).

The presence of the warp affects the truncation feature (see Sect. 4.1),
contrary to our findings in ML19. The extraordinary depth of the new optical
data allows us to measure a truncation radius that is systematically larger
the higher the detection above the NGC 4565 mid-plane (see central panel in
Fig. 4). Both the ($g-r$) colour profiles in Fig. 9 and the maps in Fig. 10,
highlight younger (bluer) stellar populations at the truncation radius in the
presence of the prominent warp. The H i map also reveals that the truncation
radii is related to the warp location. From Frig. 1 we can estimate the onset
of the warp in H i at $\sim 26-27$ kpc, coinciding in radius with the mean
radial truncation value in the optical bands (25.9 $\pm$ 0.4 kpc).

We measured a two moving U-shapes in the colour profiles (see Fig. 9) of the
disk quadrant with a warp. Such U-shapes are indicative of a threshold in star
formation. We find a first U-shape tracing the truncation at $R\sim 26$ kpc
(see Sect. 5) and a second one further outside and at higher altitudes off the
galaxy mid-plane following the warp beyond $R\sim 38$ kpc and above 1.5 kpc
height. To our knowledge, this is the first time such a feature has been
detected in a disk warp.

Truncations have previously been linked to the maximum angular momentum of the
protogalactic cloud (e.g., van der Kruit, 1987; Martín-Navarro et al., 2012),
but also to the presence of disk warps (van der Kruit, 1979; Naeslund &
Joersaeter, 1997) and to star forming thresholds (Kennicutt, 1989, ML19). We
find that the truncation of the Milky Way-like galaxy NGC 4565 is linked to
two of the above-mentioned mechanisms: a threshold in star formation and the
warp.

##  8 Conclusions

We perform a multi-wavelength vertical analysis of the disk of the edge-on
Milky Way-like galaxy NGC 4565 to establish the height up to where the
truncation is still present at the edge of the disk and how is it related with
disk properties such as the warp or the disk thickness. This is a follow-up
work of ML19 including a wider wavelength range and ultra-deep optical data
from the 4.2 m WHT. Our findings can be summarised in the following
statements:

  1. 1.

We obtain a mean radial truncation position of 25.9 $\pm$ 0.4 kpc for the $g$,
$r$, and $i$ bands up to a height of 4 kpc above/below the galaxy mid-plane.

  2. 2.

We confidently detect the truncation up to 4 kpc in the new ultra-deep optical
images, that is, at locations 1 kpc higher than in any previous work for any
studied galaxy. The location of the truncation radius remains constant up to a
height of 3 kpc, in agreement with ML19. Higher up, we report two more
detections at 3.5 and 4 kpc but they are located at an inner radius.

  3. 3.

The truncation is systematically sharper on the right side of the disk (NW).
Despite this, the truncation radius remains almost constant within the
uncertainties for all the disk quadrants and heights above/below the mid-plane
with the exception of the north quadrant, that is, the one with a clear warp.

  4. 4.

The radial position of the truncation is the same, within uncertainties, for
our full wide wavelength range, independently of the height above/below NGC
4565 mid-plane. Combining these results with those in ML19, we confirm that
the truncation radius is similar at all measured wavelength ranges from FUV to
H i.

  5. 5.

Despite the effect of PSF scattering in the light distribution of NGC 4565,
the radial position of the truncation remains unaffected (within
uncertainties).

  6. 6.

Our observational measurements on the colour profiles (U-shape feature), SFR
profile, and UV emission in the outer disk are in agreement with the predicted
common origin for breaks and truncations.

  7. 7.

We propose that the disk of NGC 4565 has been mainly formed through internal
processes. The stars were born in the galaxy mid-plane (up to $\sim 1$ kpc)
and then migrated vertically forming an outer flare. This supports an inside-
out growth mechanism of the disk.

  8. 8.

We report the first detection of the warp of NGC 4565 in FUV and NUV data.

  9. 9.

The onset radius of the disk warp in H i is located at $\sim 26-27$ kpc,
coinciding in radius with the truncation location in the optical bands.

  10. 10.

Our findings suggest that the truncation of the Milky Way-like galaxy NGC 4565
is linked to both a threshold in star formation and the presence of a warp.

This work highlights the connection between the truncation of the disk, the
star formation activity, and the onset of the warp of the nearby galaxy NGC
4565 using an unprecedentedly wide wavelength range and ultra-deep optical
data. Further analyses of large samples of edge-on galaxies, including studies
of the dependence of these connections with the redshift, are required to
understand the role of the truncations in galaxy disks.

###### Acknowledgements.

We acknowledge constructive remarks by an anonymous referee that help to
improve this paper. We thank Kijeong Yim for kindly sharing the VLA H i
reduced integrated maps with. CML thanks Sarah Brough and Simón Díaz-García
for useful discussions and support during the project. CML acknowledges the
support of the Australian Research Council Discovery Project DP190101943.
Parts of this research were supported by the Australian Research Council
Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D),
through project number CE170100013. RIS acknowledges the funding by the
Governments of Spain and Aragón through the Fondo de Inversiones de Teruel;
and the Spanish Ministry of Science, Innovation and Universities
(MCIU/AEI/FEDER, UE) with grant PGC2018-097585-B-C21. We acknowledge financial
support from the State Research Agency (AEI-MCINN) of the Spanish Ministry of
Science and Innovation under the grants PID2019-107427GB-C32 and ”The
structure and evolution of galaxies and their central regions” with reference
PID2019-105602GB-I00/10.13039/501100011033, from the ACIISI, Consejería de
Economía, Conocimiento y Empleo del Gobierno de Canarias and the European
Regional Development Fund (ERDF) under a grant with reference PROID2021010044,
and from IAC projects P/300624 and P/300724, financed by the Ministry of
Science and Innovation, through the State Budget and by the Canary Islands
Department of Economy, Knowledge and Employment, through the Regional Budget
of the Autonomous Community. SC acknowledges support from the Ramón y Cajal
programme funded by the Spanish Government (references RYC2020-030480-I), and
from the State Research Agency (AEI-MCINN) of the Spanish Ministry of Science
and Innovation under the grant “Thick discs, relics of the infancy of
galaxies” with reference PID2020-113213GA-I00. This research includes
computations using the computational cluster Katana supported by Research
Technology Services at UNSW Sydney. This research has made use of the SVO
Filter Profile Service (http://svo2.cab.inta-csic.es/theory/fps/) supported by
the Spanish MINECO through grant AYA2017-84089. This article is based on
observations made in the Observatorios de Canarias del IAC with the WHT and
INT operated on the island of La Palma by the Isaac Newton Group in the
Observatorio del Roque de los Muchachos. A.B. was supported by an appointment
to the NASA Postdoctoral Program at the NASA Ames Research Center,
administered by Oak Ridge Associated Universities under contract with NASA.
A.B. is supported by a NASA Astrophysics Data Analysis grant (22-ADAP22-0118),
program Hubble Archival Research project AR 17041, and Chandra Archival
Research project ID #24610329, provided by NASA through a grant from the Space
Telescope Science Institute and the Center for Astrophysics Harvard &
Smithsonian, operated by the Association of Universities for Research in
Astronomy, Inc., under NASA contract NAS 5-03127.

Facilities: William Herschel Telescope (WHT), Isaac Newton Telescope (INT),
Very Large Array (VLA), and Galaxy Evolution Explorer (GALEX), UNSW Katana
cluster (https://doi.org/10.26190/669x-a286).

Software: Astropy (The Astropy Collaboration et al. 2018), Photutils v0.7.2
(Bradley et al., 2020), Numpy (Oliphant, 2006), NoiseChisel (Akhlaghi &
Ichikawa, 2015; Akhlaghi, 2019), SExtractor v2.19.5 (Bertin & Arnouts, 1996),
SWarp v2.38.0 (Bertin et al., 2002), SCAMP v2.0.4 (Bertin, 2006), imfit
(Erwin, 2015), SAOImageDS9 (Joye & Mandel, 2003).

## References

  * Abadi et al. (2003) Abadi, M. G., Navarro, J. F., Steinmetz, M., & Eke, V. R. 2003, ApJ, 597, 21
  * Akhlaghi (2019) Akhlaghi, M. 2019, arXiv e-prints, arXiv:1909.11230
  * Akhlaghi & Ichikawa (2015) Akhlaghi, M. & Ichikawa, T. 2015, ApJS, 220, 1
  * Alam et al. (2015) Alam, S., Albareti, F. D., Prieto, C. A., et al. 2015, ApJS, 219, 12
  * Athanassoula et al. (1990) Athanassoula, E., Morin, S., Wozniak, H., et al. 1990, MNRAS, 245, 130
  * Aumer & White (2013) Aumer, M. & White, S. D. M. 2013, MNRAS, 428, 1055
  * Azzollini et al. (2008) Azzollini, R., Trujillo, I., & Beckman, J. E. 2008, ApJ, 679, L69
  * Bakos et al. (2008) Bakos, J., Trujillo, I., & Pohlen, M. 2008, ApJ, 683, L103
  * Bertin (2006) Bertin, E. 2006, in Astronomical Society of the Pacific Conference Series, Vol. 351, Astronomical Data Analysis Software and Systems XV, ed. C. Gabriel, C. Arviset, D. Ponz, & S. Enrique, 112
  * Bertin & Arnouts (1996) Bertin, E. & Arnouts, S. 1996, A&AS, 117, 393
  * Bertin et al. (2002) Bertin, E., Mellier, Y., Radovich, M., et al. 2002, in Astronomical Society of the Pacific Conference Series, Vol. 281, Astronomical Data Analysis Software and Systems XI, ed. D. A. Bohlender, D. Durand, & T. H. Handley, 228
  * Bland-Hawthorn & Gerhard (2016) Bland-Hawthorn, J. & Gerhard, O. 2016, ARA&A, 54, 529
  * Borlaff et al. (2017) Borlaff, A., Eliche-Moral, M. C., Beckman, J. E., et al. 2017, A&A, 604, A119
  * Borlaff et al. (2019) Borlaff, A., Trujillo, I., Román, J., et al. 2019, A&A, 621, A133
  * Bournaud et al. (2009) Bournaud, F., Elmegreen, B. G., & Martig, M. 2009, ApJ, 707, L1
  * Bradley et al. (2020) Bradley, L., Sipőcz, B., Robitaille, T., et al. 2020, astropy/photutils: 1.0.1
  * Buta et al. (2015) Buta, R. J., Sheth, K., Athanassoula, E., et al. 2015, ApJS, 217, 32
  * Carraro et al. (2015) Carraro, G., Vázquez, R. A., Costa, E., Ahumada, J. A., & Giorgi, E. E. 2015, AJ, 149, 12
  * Chamba et al. (2022) Chamba, N., Trujillo, I., & Knapen, J. H. 2022, A&A, 667, A87
  * Chrobáková et al. (2022) Chrobáková, Ž., Nagy, R., & López-Corredoira, M. 2022, A&A, 664, A58
  * Comerón et al. (2012) Comerón, S., Elmegreen, B. G., Salo, H., et al. 2012, ApJ, 759, 98
  * Comerón et al. (2018) Comerón, S., Salo, H., & Knapen, J. H. 2018, A&A, 610, A5
  * Das et al. (2020) Das, S., Sardone, A., Leroy, A. K., et al. 2020, ApJ, 898, 15
  * de Jong (2008) de Jong, R. S. 2008, MNRAS, 388, 1521
  * de Jong et al. (2007) de Jong, R. S., Seth, A. C., Radburn-Smith, D. J., et al. 2007, ApJ, 667, L49
  * Debattista et al. (2017) Debattista, V. P., Roškar, R., & Loebman, S. R. 2017, The Impact of Stellar Migration on Disk Outskirts, ed. G. d. P. Knapen, Lee (Astrophysics and Space Science Library, Springer International Publishing, Cham, Switzerland), 77–114
  * Díaz-García et al. (2022) Díaz-García, S., Comerón, S., Courteau, S., et al. 2022, A&A, 667, A109
  * Ding et al. (2021) Ding, P.-J., Xue, X.-X., Yang, C., et al. 2021, AJ, 162, 112
  * Duc et al. (2015) Duc, P.-A., Cuillandre, J.-C., Karabal, E., et al. 2015, MNRAS, 446, 120
  * Erben et al. (2005) Erben, T., Schirmer, M., Dietrich, J. P., et al. 2005, Astronomische Nachrichten, 326, 432
  * Erwin (2015) Erwin, P. 2015, ApJ, 799, 226
  * Feast et al. (2014) Feast, M. W., Menzies, J. W., Matsunaga, N., & Whitelock, P. A. 2014, Nature, 509, 342
  * Gaia Collaboration et al. (2021) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649, A1
  * Gilhuly et al. (2020) Gilhuly, C., Hendel, D., Merritt, A., et al. 2020, ApJ, 897, 108
  * Gregory & Thompson (1977) Gregory, S. A. & Thompson, L. A. 1977, ApJ, 213, 345
  * Hao et al. (2011) Hao, C.-N., Kennicutt, R. C., Johnson, B. D., et al. 2011, ApJ, 741, 124
  * Heald et al. (2012) Heald, G., Józsa, G., Serra, P., et al. 2012, A&A, 544, C1
  * Helmboldt et al. (2004) Helmboldt, J. F., Walterbos, R. A. M., Bothun, G. D., O’Neil, K., & de Blok, W. J. G. 2004, ApJ, 613, 914
  * Hunter et al. (2012) Hunter, D. A., Ficut-Vicas, D., Ashley, T., et al. 2012, AJ, 144, 134
  * Infante-Sainz et al. (2020) Infante-Sainz, R., Trujillo, I., & Román, J. 2020, MNRAS, 491, 5317
  * Iodice et al. (2019a) Iodice, E., Sarzi, M., Bittner, A., et al. 2019a, A&A, 627, A136
  * Iodice et al. (2019b) Iodice, E., Spavone, M., Capaccioli, M., et al. 2019b, A&A, 623, A1
  * James et al. (2005) James, P. A., Shane, N. S., Knapen, J. H., Etherton, J., & Percival, S. M. 2005, A&A, 429, 851
  * Joye & Mandel (2003) Joye, W. A. & Mandel, E. 2003, in Astronomical Society of the Pacific Conference Series, Vol. 295, Astronomical Data Analysis Software and Systems XII, ed. H. E. Payne, R. I. Jedrzejewski, & R. N. Hook, 489
  * Kado-Fong et al. (2018) Kado-Fong, E., Greene, J. E., Hendel, D., et al. 2018, ApJ, 866, 103
  * Kalberla et al. (2014) Kalberla, P. M. W., Kerp, J., Dedes, L., & Haud, U. 2014, ApJ, 794, 90
  * Kasparova et al. (2020) Kasparova, A. V., Katkov, I. Y., & Chilingarian, I. V. 2020, MNRAS, 493, 5464
  * Kaviraj et al. (2017) Kaviraj, S., Laigle, C., Kimm, T., et al. 2017, MNRAS, 467, 4739
  * Kazantzidis et al. (2008) Kazantzidis, S., Bullock, J. S., Zentner, A. R., Kravtsov, A. V., & Moustakas, L. A. 2008, ApJ, 688, 254
  * Kennicutt & Kent (1983) Kennicutt, R. C., J. & Kent, S. M. 1983, AJ, 88, 1094
  * Kennicutt (1998) Kennicutt, Robert C., J. 1998, ARA&A, 36, 189
  * Kennicutt et al. (2009) Kennicutt, Robert C., J., Hao, C.-N., Calzetti, D., et al. 2009, ApJ, 703, 1672
  * Kennicutt et al. (2008) Kennicutt, Robert C., J., Lee, J. C., Funes, J. G., et al. 2008, ApJS, 178, 247
  * Kennicutt (1989) Kennicutt, Jr., R. C. 1989, ApJ, 344, 685
  * Kim et al. (2012) Kim, T., Sheth, K., Hinz, J. L., et al. 2012, ApJ, 753, 43
  * Knapen et al. (2004) Knapen, J. H., Stedman, S., Bramich, D. M., Folkes, S. L., & Bradley, T. R. 2004, A&A, 426, 1135
  * Kormendy & Bender (2019) Kormendy, J. & Bender, R. 2019, ApJ, 872, 106
  * Kormendy & Kennicutt (2004) Kormendy, J. & Kennicutt, Jr., R. C. 2004, ARA&A, 42, 603
  * Kroupa & Weidner (2003) Kroupa, P. & Weidner, C. 2003, ApJ, 598, 1076
  * Lang et al. (2010) Lang, D., Hogg, D. W., Mierle, K., Blanton, M., & Roweis, S. 2010, AJ, 139, 1782
  * Makarov et al. (2014) Makarov, D., Prugniel, P., Terekhova, N., Courtois, H., & Vauglin, I. 2014, A&A, 570, A13
  * Martin et al. (2005) Martin, D. C., Fanson, J., Schiminovich, D., et al. 2005, ApJ, 619, L1
  * Martín-Navarro et al. (2012) Martín-Navarro, I., Bakos, J., Trujillo, I., et al. 2012, MNRAS, 427, 1102
  * Martínez-Delgado et al. (2009) Martínez-Delgado, D., Pohlen, M., Gabany, R. J., et al. 2009, ApJ, 692, 955
  * Martínez-Lombilla et al. (2023) Martínez-Lombilla, C., Brough, S., Montes, M., et al. 2023, MNRAS, 518, 1195
  * Martínez-Lombilla & Knapen (2019) Martínez-Lombilla, C. & Knapen, J. H. 2019, A&A, 629, A12
  * Martínez-Lombilla et al. (2019) Martínez-Lombilla, C., Trujillo, I., & Knapen, J. H. 2019, MNRAS, 483, 664
  * McMullin et al. (2007) McMullin, J. P., Waters, B., Schiebel, D., Young, W., & Golap, K. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 376, Astronomical Data Analysis Software and Systems XVI, ed. R. A. Shaw, F. Hill, & D. J. Bell, 127
  * Michard (2002) Michard, R. 2002, A&A, 384, 763
  * Mihos et al. (2017) Mihos, J. C., Harding, P., Feldmeier, J. J., et al. 2017, ApJ, 834, 16
  * Minchev et al. (2015) Minchev, I., Martig, M., Streich, D., et al. 2015, ApJ, 804, L9
  * Montes (2022) Montes, M. 2022, Nature Astronomy, 6, 308
  * Montes et al. (2020) Montes, M., Infante-Sainz, R., Madrigal-Aguado, A., et al. 2020, ApJ, 904, 114
  * Montes & Trujillo (2018) Montes, M. & Trujillo, I. 2018, MNRAS, 474, 917
  * Montes & Trujillo (2019) Montes, M. & Trujillo, I. 2019, MNRAS, 482, 2838
  * Morrissey et al. (2007) Morrissey, P., Conrow, T., Barlow, T. A., et al. 2007, ApJS, 173, 682
  * Mosenkov et al. (2020) Mosenkov, A., Rich, R. M., Koch, A., et al. 2020, MNRAS, 494, 1751
  * Naeslund & Joersaeter (1997) Naeslund, M. & Joersaeter, S. 1997, A&A, 325, 915
  * Niklas et al. (1997) Niklas, S., Klein, U., & Wielebinski, R. 1997, A&A, 322, 19
  * Oliphant (2006) Oliphant, T. E. 2006, All Faculty Publications, 278
  * Oosterloo et al. (2007) Oosterloo, T., Fraternali, F., & Sancisi, R. 2007, AJ, 134, 1019
  * Padilla et al. (2019) Padilla, C., Castander, F. J., Alarcón, A., et al. 2019, AJ, 157, 246
  * Peters et al. (2017) Peters, S. P. C., van der Kruit, P. C., Knapen, J. H., et al. 2017, MNRAS, 470, 427
  * Pinna et al. (2019a) Pinna, F., Falcón-Barroso, J., Martig, M., et al. 2019a, A&A, 625, A95
  * Pinna et al. (2019b) Pinna, F., Falcón-Barroso, J., Martig, M., et al. 2019b, A&A, 623, A19
  * Pohlen & Trujillo (2006) Pohlen, M. & Trujillo, I. 2006, A&A, 454, 759
  * Qu et al. (2011) Qu, Y., Matteo, P. D., Lehnert, M. D., & van Driel, W. 2011, A&A, 530, A10
  * Radburn-Smith et al. (2014) Radburn-Smith, D. J., de Jong, R. S., Streich, D., et al. 2014, ApJ, 780, 105
  * Radburn-Smith et al. (2012) Radburn-Smith, D. J., Roškar, R., Debattista, V. P., et al. 2012, ApJ, 753, 138
  * Rix et al. (2004) Rix, H.-W., Barden, M., Beckwith, S. V. W., et al. 2004, ApJS, 152, 163
  * Román et al. (2020) Román, J., Trujillo, I., & Montes, M. 2020, A&A, 644, A42
  * Roškar et al. (2010) Roškar, R., Debattista, V. P., Brooks, A. M., et al. 2010, MNRAS, 408, 783
  * Roškar et al. (2008a) Roškar, R., Debattista, V. P., Quinn, T. R., Stinson, G. S., & Wadsley, J. 2008a, ApJ, 684, L79
  * Roškar et al. (2008b) Roškar, R., Debattista, V. P., Stinson, G. S., et al. 2008b, ApJ, 675, L65
  * Rupen (1991) Rupen, M. P. 1991, AJ, 102, 48
  * Saifollahi et al. (2022) Saifollahi, T., Zaritsky, D., Trujillo, I., et al. 2022, MNRAS, 511, 4633
  * Sánchez-Gallego et al. (2012) Sánchez-Gallego, J. R., Knapen, J. H., Wilson, C. D., et al. 2012, MNRAS, 422, 3208
  * Sandin (2014) Sandin, C. 2014, A&A, 567, A97
  * Sandin (2015) Sandin, C. 2015, A&A, 567, A106
  * Scannapieco et al. (2009) Scannapieco, C., White, S. D. M., Springel, V., & Tissera, P. B. 2009, MNRAS, 396, 696
  * Schaye (2004) Schaye, J. 2004, ApJ, 609, 667
  * Schirmer (2013) Schirmer, M. 2013, ApJS, 209, 21
  * Schlafly & Finkbeiner (2011) Schlafly, E. F. & Finkbeiner, D. P. 2011, ApJ, 737, 103
  * Sellwood (2014) Sellwood, J. A. 2014, Reviews of Modern Physics, 86, 1
  * Sersic (1968) Sersic, J. L. 1968, Nature), 342–354
  * Slater et al. (2009) Slater, C. T., Harding, P., & Mihos, J. C. 2009, PASP, 121, 1267
  * Trujillo et al. (2020) Trujillo, I., Chamba, N., & Knapen, J. H. 2020, MNRAS, 493, 87
  * Trujillo et al. (2021) Trujillo, I., D’Onofrio, M., Zaritsky, D., et al. 2021, A&A, 654, A40
  * Trujillo & Fliri (2016) Trujillo, I. & Fliri, J. 2016, ApJ, 823, 123
  * van der Kruit (1979) van der Kruit, P. C. 1979, A&AS, 38, 15
  * van der Kruit (1987) van der Kruit, P. C. 1987, A&A, 173, 59
  * van der Kruit & Freeman (2011) van der Kruit, P. C. & Freeman, K. C. 2011, ARA&A, 49, 301
  * van der Kruit & Searle (1981a) van der Kruit, P. C. & Searle, L. 1981a, A&A, 95, 105
  * van der Kruit & Searle (1981b) van der Kruit, P. C. & Searle, L. 1981b, A&A, 95, 116
  * Villalobos & Helmi (2008) Villalobos, Á. & Helmi, A. 2008, MNRAS, 391, 1806
  * Wiegert et al. (2015) Wiegert, T., Irwin, J., Miskolczi, A., et al. 2015, AJ, 150, 81
  * Wilson et al. (2009) Wilson, C. D., Warren, B. E., Israel, F. P., et al. 2009, ApJ, 693, 1736
  * Wu et al. (2002) Wu, H., Burstein, D., Deng, Z., et al. 2002, AJ, 123, 1364
  * Yim et al. (2014) Yim, K., Wong, T., Xue, R., et al. 2014, AJ, 148, 127
  * Zaritsky et al. (2019) Zaritsky, D., Behroozi, P., Peeples, M. S., et al. 2019, BAAS, 51, 127
  * Zibetti et al. (2004) Zibetti, S., White, S. D. M., & Brinkmann, J. 2004, MNRAS, 347, 556
  * Zschaechner et al. (2012) Zschaechner, L. K., Rand, R. J., Heald, G. H., Gentile, G., & Józsa, G. 2012, ApJ, 760, 37

##  Appendix A Radial surface brightness profiles (RSBP)

In Figs. 11, 12, and 13, we plot all the RSBPs of the observed data at
different heights above/below the NGC 4565 mid-plane for the three ultra-deep
$g$, $r$, and $i$ bands, respectively. Then, we show the same but for the H i
surface mass density profiles in Fig. 14. The RSBPs of the corresponding
models in the $g$, $r$, and $i$ bands are shown in Figs. 15, 16, and 17
respectively.

Each figure shows the RSBP at all the different heights above/below the galaxy
mid-plane in a given band. In this way, we explicitly illustrate the
variations of the radial position of the truncation along the vertical axis as
well as the profiles where the truncation is not detected. The black line
always shows the mid-plane surface brightness profile. From top to bottom and
from left to right, the panels show in colour the surface brightness profile
at a given altitude above the galaxy mid-plane (indicated in the legend) and,
in light grey, the surface brightness profiles plotted in the previous panels.
When the truncation is detected by our algorithm, its radial position is also
indicated with a value in kpc in the bottom left corner of each panel with a
typical uncertainty of $2\%$ of the truncation radius value.

Figure 11: Vertical development of the radial surface brightness profiles in
the $g$ band for NGC 4565. The truncation radius is indicated for each panel.
In all the cases the uncertainties are of the order of $2\%$ of the truncation
radius value. The black line shows the mid-plane surface brightness profile.
From top to bottom and from left to right, the panels show in blue the surface
brightness profile at a given altitude above the galaxy mid-plane (indicated
in the legend) and, in light grey, the surface brightness profiles plotted in
the previous panels. Figure 12: Same than 11 but for $r$-band. Figure 13: Same
than 11 but for $i$-band. Figure 14: Same than 11 but in this case it is shown
the vertical development of the radial surface mass density profiles in M⊙
pc-2 extracted from the H i integrated maps. The vertical line indicates the
truncation radial position for each height above/below the galaxy mid-plane
and the light grey shaded region is the associated uncertainty. Figure 15:
Same than 11 but showing the vertical development of the radial surface
brightness profiles extracted from the model of NGC 4565 in the $g$ band. The
truncation radius is indicated for each panel. In all the cases the
uncertainties are of the order of $2\%$ of the truncation radius value. Figure
16: Same than 15 but for $r$-band. Figure 17: Same than 15 but for $i$-band.

##  Appendix B NGC 4565 model

Figure 18 shows the details of the analytical 2D model of NGC 4565 and its
components in comparison to the observed data in $r$-band. There is a good
agreement between the observed data and the model in both, the 1D profiles and
the 2D images. The results for the $g$ and $i$ band are similar. The full
details on how to obtain this model are in Sect. 3.3.

Figure 18: Top 4 panels: Radial (left) and vertical (right) surface brightness
profiles of the observed data and the 2D galaxy model in $r$-band, convolved
with the extended PSF (solid black line). We show the model galaxy components
colour coded as in the legend, along with the observed data (black points).
The two top panels show the central profiles in each case, while the other two
panels are the profiles shifted 1.5 kpc from the ones above. Bottom 3 panels:
Images of the NGC 4565 observed data in $r$-band (left), its model (centre)
obtained with imfit as explained in Sect. 3.3, and the associated residuals
(right). The model reproduces NGC 4565 and the residuals are minimal, just
accounting for the dusty regions surrounding the mid-plane and some
asymmetries.