# MULTIWAVELENGTH BULGE-DISK DECOMPOSITION FOR THE GALAXY M81 (NGC 3031).
I. MORPHOLOGY

Jun-Yu Gong  Center for Astrophysics, GuangZhou University, GuangZhou 510006,
People’s Republic of China  Department of Astronomy, School of Physics and
Materials Science, GuangZhou University, GuangZhou 510006, People’s Republic
of China  Ye-Wei Mao  Center for Astrophysics, GuangZhou University, GuangZhou
510006, People’s Republic of China  Department of Astronomy, School of Physics
and Materials Science, GuangZhou University, GuangZhou 510006, People’s
Republic of China  Hua Gao  Institute for Astronomy, University of Hawaii,
2680 Woodlawn Drive, Honolulu HI 96822, USA  Kavli Institute for the Physics
and Mathematics of the Universe (WPI), The University of Tokyo Institutes for
Advanced Study, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan  Si-
Yue Yu  Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn,
Germany

###### Abstract

A panchromatic investigation of morphology for the early-type spiral galaxy
M81 is presented in this paper. We perform bulge-disk decomposition in M81
images at a total of 20 wavebands from FUV to NIR obtained with _GALEX_ ,
_Swift_ , SDSS, WIYN, 2MASS, _WISE_ , and _Spitzer_. Morphological parameters
such as Sérsic index, effective radius, position angle, and axis ratio for the
bulge and the disk are thus derived at all the wavebands, which enables
quantifying the morphological K-correction for M81 and makes it possible to
reproduce images for the bulge and the disk in the galaxy at any waveband. The
morphology as a function of wavelength appears as a variable-slope trend of
the Sérsic index and the effective radius, in which the variations are steep
at UV–optical and shallow at optical–NIR bands; the position angle and the
axis ratio keep invariable at least at optical–NIR bands. It is worth noting
that, the Sérsic index for the bulge reaches $\sim 4$–$5$ at optical and NIR
bands, but drops to $\sim 1$ at UV bands. This difference brings forward a
caveat that, a classical bulge is likely misidentified for a pseudo-bulge or
no bulge at high redshifts where galaxies are observed through rest-frame UV
channels with optical telescopes. The next work of this series is planned to
study spatially resolved SEDs for the bulge and the disk, respectively, and
thereby explore stellar population properties and star formation/quenching
history for the the galaxy composed of the subsystems.

galaxies: bulges - galaxies: fundamental parameters (morphology) - galaxies:
individual (M81) - galaxies: spiral - galaxies: structure

††thanks: Humboldt Postdoctoral Fellow

##  1 INTRODUCTION

Stellar systems on a galactic scale can be classified into the two fundamental
shapes, elliptical/spheroidal and discoidal, according to their morphology.
The two different morphological types originate from different formation
mechanisms. Elliptical/spheroidal systems such as elliptical/spheroidal
galaxies or bulges in spiral/lenticular galaxies are considered to be formed
by rapid and violent processes (e.g., major mergers, Eggen et al., 1962;
Toomre, 1977; Dekel et al., 2009; Ceverino et al., 2010); disks in
spiral/lenticular galaxies are considered to be formed by slow and gentle
processes (e.g., secular evolution, Kormendy, 1979; Kormendy & Kennicutt,
2004).

For early-type spiral/lenticular galaxies, a combination of bulges and disks
complicates studies of these galaxies, since measurements of such galaxies as
a mixture of bulges and disks would lead to an average effect on results
(e.g., Mancini et al. 2019). Therefore, it is necessary to decompose the
galaxies and separate the different galactic structures so as to acquire
unbiased knowledge of their nature (Debattista et al. 2006; Kendall et al.
2008; Simard et al. 2011).

Radial profiles of surface brightness are an effective tool for distinguishing
between different structures in galaxies. For both of elliptical/spheroidal
and discoidal systems, the surface-brightness profiles can be fitted with the
Sérsic function (Sersic 1968). The equation of the Sérsic function is as
follows:

$\Sigma(r)=\Sigma(e)\exp\left[-\kappa\left(\left(\frac{r}{R_{e}}\right)^{\frac{1}{n}}-1\right)\right]~{},$
(1)

where $\Sigma(r)$ is the surface brightness at the radius $r$, $R_{e}$ is the
effective radius, $\Sigma(e)$ is the surface brightness at the effective
radius, $n$ is named as the Sérsic index , and $\kappa$ is a coefficient
correlated with Sérsic index $n$. The Sérsic index $n$ is the parameter
distinct between different types of systems. Empirical statistics have found
$n\sim 4$ for elliptical/spheroidal systems (i.e., the de Vaucouleurs law, de
Vaucouleurs 1948) and $n\sim 1$ for discoidal systems (i.e., the exponential
law, Freeman 1970). The Sérsic function has been widely applied to the
decomposition of galaxies and helped to comprehensively understand formation
and evolution of stellar systems on a galactic or subgalactic scale (Peng et
al., 2002; Gabor et al., 2009; Peng et al., 2010; van der Wel et al., 2012;
Erwin, 2015; Meert et al., 2015; Gao et al., 2018, 2019).

At present, most morphological studies of galaxies are conducted at a single
waveband (e.g., observed optical wavelength). In fact, the morphology of
galaxies has been found, by modern observations, to vary with wavelength. The
variation of morphology with wavelength, i.e., called the ”morphological
K-correction”, is mainly ascribed to differences in stellar populations or/and
dust attenuation (Bohlin et al. 1991; Giavalisco et al. 1996; Mager et al.
2018). The morphological K-correction is likely to induce deviation in the
single-band classification, and particularly has impact on studies of high-
redshift galaxies for which the number of observable wavebands is limited
(Kuchinski et al. 2000, 2001; Windhorst et al. 2002; Huertas-Company et al.
2009). Even worse, due to the limitations of observation conditions such as
the spatial resolution and the signal-to-noise ratio (S/N), there have not
been adequate studies that could quantitatively measure multiwavelength
morphological parameters, even for nearby galaxies (Vulcani et al. 2014; Mager
et al. 2018; Psychogyios et al. 2020).

Aimed at exploring multiwavelength morphology and quantifying the
morphological K-correction, in this paper, we present an investigation of the
nearby galaxy M81 (also named NGC 3031). M81 is an early-type spiral galaxy
(classified as the Hubble type SAab), with the distance $\sim 3.6$ Mpc (Madore
et al. 1993) and the angular size $\sim 26\arcmin.9\times 14\arcmin.1$ (Nilson
1973). The adjacency of M81 brings on inherently high spatial resolution. M81
hosts a prominent bulge embedded in the disk. Space and ground-based
telescopes have obtained superb data with nearly full wavelength coverage.
These conditions make M81 to be an ideal target for a multiwavelength
morphological study.

The remainder of this paper is structured as follows. In Section 2, we
describe the multiwavelength data, the relevant data processing; Section 3
presents the methodology for the decomposition; morphological parameters as a
function of wavelength are presented in Section 4; in Section 5, we discuss
some questions in the wavelength-dependent morphology and practical
applicability of our findings. Conclusions of this work are summarized in
Section 6. In this paper, we adopt 1 kpc arcmin-1 at the distance 3.6 Mpc for
M81.

##  2 MULTIWAVELENGTH DATA AND PRE-PROCESSING

Table 1: Basic Information about the Data Used in This Work

Telescope | Filter | Wavelength | FWHM | Pixel Scale | Reference
---|---|---|---|---|---
|  | (Å) | (arcsec) | (arcsec pixel-1) |
(1) | (2) | (3) | (4) | (5) | (6)
_GALEX_ | FUV | 1516 | 4.3 | 1.5 | (a)
_Swift_ | UVW2 | 1928 | 2.5 | 1.0 | (b)
_GALEX_ | NUV | 2267 | 5.3 | 1.5 | (a)
_Swift_ | UVW1 | 2600 | 2.5 | 1.0 | (b)
SDSS | u | 3551 | 1.3 | 0.396 | (c)
WIYN | B | 4331 | 2.7 | 0.603 | (d)
SDSS | g | 4686 | 1.3 | 0.396 | (c)
WIYN | V | 5500 | 3.0 | 0.603 | (d)
SDSS | r | 6166 | 1.3 | 0.396 | (c)
WIYN | R | 6425 | 2.0 | 0.775 | (d)
SDSS | i | 7480 | 1.3 | 0.396 | (c)
SDSS | z | 8932 | 1.3 | 0.396 | (c)
2MASS | J | 12000 | 2.0 | 1.0 | (e)
2MASS | H | 16000 | 2.0 | 1.0 | (e)
2MASS | Ks | 22000 | 2.0 | 1.0 | (e)
_WISE_ | W1 (3.4 $\mu$m) | 34000 | 6.1 | 1.375 | (f)
_Spitzer_ -IRAC | I1 (3.6 $\mu$m) | 36000 | 1.66 | 0.75 | (g)
_Spitzer_ -IRAC | I2 (4.5 $\mu$m) | 45000 | 1.72 | 0.75 | (g)
_WISE_ | W2 (4.6 $\mu$m) | 46000 | 6.4 | 1.375 | (f)
_Spitzer_ -IRAC | I3 (5.8 $\mu$m) | 58000 | 1.88 | 0.75 | (g)

  * •

Notes. — Columns: (1) the name of the telescope or survey, (2) the band/filter
name, (3) the central wavelength of the filter, (4) the full width at the half
maximum (FWHM) of the point-spread function (PSF), (5) angular scale of the
pixel width in the image, (6) reference.

  * •

Reference. (a) Morrissey et al. (2007); data are retrieved from _GALEX_ Guest
Investigator project (https://asd.gsfc.nasa.gov/archive/galex/) and _GALEX_
DR6 (http://www.galex.caltech.edu/researcher/data.html); (b) data are
retrieved from SkyView Virtual Observatory
(https://skyview.gsfc.nasa.gov/current/cgi/titlepage.pl); (c) Alam et al.
(2015); data are retrieved from SDSS DR12 (https://www.sdss3.org/dr12/); (d)
Cheng et al. (1997); Marcum et al. (2001); data are retrieved from NASA NED
(https://ned.ipac.caltech.edu); (e) Skrutskie et al. (2006); data are
retrieved from IRSA (https://irsa.ipac.caltech.edu/frontpage/); (f) Wright et
al. (2010); data are retrieved from IRSA; (g) IRAC 3.6 and 4.5 $\mu$m date are
retrieved from IRSA, the Spitzer Survey of Stellar Structure in Galaxies (S4G,
Sheth et al., 2010; Muñoz-Mateos et al., 2013; Querejeta et al., 2015);
IRAC-5.8 $\mu$m data are retrieved from IRSA, the Spitzer Infrared Nearby
Galaxies Survey (SINGS, Kennicutt et al., 2003).

This work is conducted on the basis of imaging data from FUV to NIR obtained
with space and ground-based telescopes/surveys, including _GALEX_ , _Swift_ ,
SDSS, WIYN, 2MASS, _WISE_ , and _Spitzer_. All of these data were retrieved
from their official websites. Table 1 lists basic information about the data
used in this work. Figure 1 shows an atlas of M81 imaged at 20 wavebands from
1516 Å to 5.8 $\mu$m. In this work, correction for the Milky Way (MW)
foreground extinction was performed with the Fitzpatrick (1999) extinction
curve, the V-band extinction $A(\mathrm{V})_{\mathrm{GAL}}$ = 0.220 mag
(Schlafly & Finkbeiner 2011), and the total-to-selective extinction ratio
$R_{\mathrm{V}}$ = 3.1.

Figure 1: Images at 20 bands for M81 covering the wavelength range from FUV to
NIR, obtained with space and ground-based telescopes. The physical scale is
the same in each of the images. The scale in the bottom-right corner indicates
the 5$\arcmin$ length. North is up and east is to the left.

Prior to bulge-disk decomposition of the galaxy, it is necessary to subtract
background in each of the images.111 For _Spitzer_ data, although constant
background had been officially subtracted before the images were uploaded to
the website, we still performed background subtraction for the purpose of
treating spatial variations in the background. In order to avoid contamination
from non-background sources, we at first performed object detection with a
$3\sigma$ threshold and masked them in the images.

The image background was modeled for subtraction through two steps. The first
step is the median-window approach to smoothing the source-masked images at
all of the wavebands (Mao et al. 2012, 2014). In the median-smoothed images,
we performed bi-cubic fitting as the second step of the reproduction, during
which the background model was interpolated into the masked regions. The
reproduced background was subtracted from the observed image at each waveband.
The uncertainty in the background is defined as the standard deviation in
background pixels in each of the background-subtracted images.

##  3 METHODOLOGY OF THE DECOMPOSITION

Bulge-disk decomposition was carried out in the background-subtracted images
by using the software GALFIT (Peng et al. 2002, 2010). Before the
decomposition, objects unrelated to the galaxy, such as foreground stars and
background galaxies, were identified and masked in the images. For each-band
image, we created a point-spread function (PSF) image from statistics of
isolated, unsaturated foreground stars, by fitting with an analytical function
(following the method in Anderson & King, 2000; Anderson, 2016).

Sigma images, recording total noise for the observed images, were also created
at all of the wavebands. The construction is formulated as follows (addressed
in Peng et al. 2002).

${\sigma_{e}^{2}}={\sigma_{P}^{2}}+{\sigma_{R}^{2}}~{},$ (2)

where $\sigma_{e}$ is the sigma image, $\sigma_{P}$ is Poisson noise, and
$\sigma_{R}$ is the CCD readout noise. $\sigma_{P}$ follows the Poisson
distribution. In order to calculate $\sigma_{P}$, we converted the units for
the original images without background subtraction into electronic counts by
multiplying the CCD Gain, and $\sigma_{P}$ was defined as the square root of
the electronic counts. All of the parameters in Equation (2) are in units of
electronic counts.

Since M81 hosts an AGN at its center (Filippenko & Sargent 1988), in order to
obtain accurate results, we took the AGN into account during the process of
the bulge-disk decomposition and hence adopted three components including the
bulge, the disk, and the AGN in the model. The Sérsic function was used for
fitting the bulge and the disk (Equation (1)), while the PSF was used for
fitting the AGN.222 The presence of AGNs will affect morphological estimation
of galaxies, if they are not separated from other components in models (Pović
et al. 2012; Kauffmann et al. 2003; Hopkins et al. 2009). There are six
parameters for each Sérsic component in the model, including the central
coordinate ($x$, $y$), the Sérsic index ($n$), the effective radius ($R_{e}$),
the axis ratio ($q$), the position angle (PA), and the brightness (or
magnitude $m_{b}$). Among these parameters, the central coordinate ($x$, $y$)
is set to be constant and equal to the galactic center in all of the images.

Uncertainties in the decomposition are dominated by the background
subtraction. Estimation of the uncertainties follows the method in Huang et
al. (2013); Gao & Ho (2017), which empirically estimates influences of the
background subtraction on all of the morphological parameters. For most of the
images, we manually add or subtract a constant background value to the
background-subtracted images, and then perform the decomposition again in the
processed images to obtain new output as the upper or lower limit on the
parameters. The upper and lower limits are taken as the uncertainties in the
parameters. For SDSS-u, -z, and 2MASS images with low S/N, this empirical
method may yield problematic results such as the Sérsic index over 20, because
low-brightness sources in these images are easily affected by any change in
the background. In order to ensure that the best-fit models after adjusting
the background are always physically meaningful, we fixed the effective radius
when calculating the uncertainty of the Sérsic index, and vice versa. The
uncertainties estimated in this case serve as lower limits only. This special
method is applied only as a backup when the empirical method fails.

##  4 RESULTS OF THE DECOMPOSITION

Figure 2: Morphological parameters, including the Sérsic index (the top-left
panel), the effective radius (the top-right panel), the axis ratio (the
bottom-left panel), and the position angle (the bottom-right panel), as a
function of wavelength for the bulge (red color) and the disk (blue color) in
M81. In each panel, points are connected by solid lines. In the bottom two
panels, dotted lines represent the mean values for the axis ratio (i.e., 0.70
and 0.50 for the bulge and the disk, respectively) and the position angle
(i.e., $-33^{\circ}.62$ and $-27^{\circ}.52$ for the bulge and the disk,
respectively) among the optical and NIR bands.

###  4.1 Morphology as a Function of Wavelength

Figure 3: The Sérsic index (top-left panel), the effective radius (top-right
panel), the flux (bottom-left panel), and the flux ratio (bottom-right panel)
as a function of wavelength for the bulge (red) and the disk (blue) in M81. In
each panel, the _Spitzer_ -IRAC 5.8 $\mu$m band is symbolized as the open
square. In the top panels, dot-dashed and dotted lines represent the best-fit
quadratic and piecewise linear curves, respectively, for the wavebands with
the _Spitzer_ -IRAC 5.8 $\mu$m excluded; in the bottom-left panel, dashed
lines are the best-fit model spectra of stellar population synthesis; in the
bottom-right panel, dashed lines connect data points. Black filled circles in
the bottom-left panel indicate the total flux of the galaxy. The flux ratio in
the bottom-right panel is defined as the ratio of the bulge (red) or the disk
(blue) to the total galaxy enclosed in the same aperture, as well as the ratio
of the bulge to the disk (green)

.

After separately performing the decomposition in each of the images, we obtain
morphological parameters including the Sérsic index $n$, the effective radius
$R_{e}$, the axis ratio $q$, and the position angle PA for the bulge and the
disk in M81 at all of the wavebands. Figure 2 shows the variations in the four
parameters with wavelength. We can see that the axis ratio and the position
angle are nearly constant except at UV bands. The deviation in the axis ratio
and the position angle is mainly caused by the bias of other substructures
such as spiral arms, particularly at the UV bands, as well as low S/N. In
order to reduce the error, we fix $q$ and PA into the mean values for the two
parameters in the optical and NIR range. The decomposition is then performed
again to specially obtain variations in the Sérsic index and the effective
radius with wavelength for the bulge and the disk. Products of the bulge-disk
decomposition, including observed, model, residual images, radial profiles of
surface brightness, and parameters at the 20 wavebands are presented in detail
in Appendix A. The goodness of the fit will be discussed in Section 5.

With the axis ratio and the position angle fixed, the Sérsic index and the
effective radius as a function of wavelength are displayed in Figure 3. We can
see that the bulge and the disk present distinct features in the wavelength-
dependent morphology. For the bulge, the Sérsic index varies remarkably with
wavelength from $1516$ Å (i.e., the _GALEX_ FUV band) and reaches a peak
around $n\sim 5$ at $\lambda\sim 1.2$–$2.2\,\mu$m (i.e., the 2MASS bands),
including an intensive increase from $\sim 1$ to $\sim 5$ with $\lambda$ from
$1516$ Å to $1.2\,\mu$m, and a moderate decrease from $\sim 5$ to $\sim 4$
with $\lambda$ from $2.2\,\mu$m to $4.6\,\mu$m. The effective radius is almost
around $80\arcsec$ except for the _GALEX_ and _Swift_ UV-band data which
exhibit an increasing trend from 12$\arcsec$ to 43$\arcsec$ with wavelength.
The disk appears with the Sérsic index slightly increasing from 0.15 to 0.67
in the wavelength range from 1516 Å (i.e., the _GALEX_ FUV band) to 4331 Å
(i.e., the WIYN B band), and nearly constant at $n\sim 1$ from 4686 Å (i.e.,
the SDSS g band) to $4.6\,\mu$m (i.e., the _WISE_ W2 band). The variation in
the effective radius emerges with a turning shape similar to that for the
bulge but in an opposite direction: including a decrease from $\sim
450\arcsec$ (at _GALEX_ FUV 1516 Å) to $\sim 200\arcsec$ (at 2MASS J
$1.2\,\mu$m) and a subsequent increase to $\sim 300\arcsec$ (at _WISE_ W2
$4.6\,\mu$m).

The wavelength distribution for each of the Sérsic index and the effective
radius is well fitted with a quadratic function and a piecewise linear
function with two slopes, respectively.333 The _Spitzer_ -IRAC 5.8 $\mu$m band
is excluded from the polynomial fitting, because there is a large deviation in
the decomposition at this band, which will be discussed in detail in Section
5. For the piecewise linear function, the turn point is set as a free
parameter in the fit. The extrema (or turn points) of these functions are
generally in the wavelength range $\sim 1.0$–$1.5\,\mu$m. The formulae of the
best-fit curves are listed as follows:

Figure 4: The Sérsic index (top row) and the effective radius (bottom row) as
a function of wavelength for the bulge (red filled circles) and the disk (blue
filled circles), fitted with piecewise linear (left column) and quadratic
(right column) curves. In each panel, black dashed and dot-dashed lines
represent the best-fit curves; gray solid lines represent fitting curves
obtained from 1000 bootstrap resampling iterations, which define the error
ranges for the fits.

$n_{\mathrm{~{}bulge}}=(-3.63_{~{}\pm 1.03})\log^{2}(\lambda)+(23.76_{~{}\pm
6.07})\log(\lambda)+(-34.22_{~{}\pm 8.66}),$ (3)

$n_{\mathrm{~{}disk}}=(-0.88_{~{}\pm 0.26})\log^{2}(\lambda)+(5.89_{~{}\pm
1.53})\log(\lambda)+(-8.61_{~{}\pm 2.18}),$ (4)

${R_{e}}_{\mathrm{,~{}bulge}}=(-86.94_{~{}\pm
33.73})\log^{2}(\lambda)+(547.7_{~{}\pm 202.22})\log(\lambda)+(-770.14_{~{}\pm
291.55}),$ (5)

${R_{e}}_{\mathrm{,~{}disk}}=(195.51_{~{}\pm
48.13})\log^{2}(\lambda)+(-1280.48_{~{}\pm
286.05})\log(\lambda)+(2318.48_{~{}\pm 410.24}),$ (6)

$n_{\mathrm{~{}bulge}}=\left\\{\begin{aligned} &(5.25_{~{}\pm
0.92})[\log(\lambda)-(3.00_{~{}\pm 0.18})]+(4.96_{~{}\pm
0.89}),&&\quad\lambda\leq(1000.00~{}_{\pm 1.51})\,\mathrm{nm}\\\
&(-1.11_{~{}\pm 2.64})[\log(\lambda)-(3.0_{~{}\pm 0.18})]+(4.96_{~{}\pm
0.89}),&&\quad\lambda>(1000.00_{~{}\pm 1.51})\,\mathrm{nm}\\\
\end{aligned}\right.,~{}$ (7)

$n_{\mathrm{~{}disk}}=\left\\{\begin{aligned} &(1.57_{~{}\pm
0.25})[\log(\lambda)-(2.87_{~{}\pm 0.10})]+(1.12_{~{}\pm
0.16}),&&\quad\lambda\leq(741.31_{~{}\pm 1.26})\,\mathrm{nm}\\\
&(-0.003_{~{}\pm 0.27})[\log(\lambda)-(2.87_{~{}\pm 0.10})]+(1.12_{~{}\pm
0.16}),&&\quad\lambda>(741.31_{~{}\pm 1.26})\,\mathrm{nm}\\\
\end{aligned}\right.,~{}$ (8)

${R_{e}}_{\mathrm{,~{}bulge}}=\left\\{\begin{aligned} &(188.80_{~{}\pm
50.40})[\log(\lambda)-(2.60_{~{}\pm 0.19})]+(82.38_{~{}\pm
19.32}),&&\quad\lambda\leq(398.11_{~{}\pm 1.55})\,\mathrm{nm}\\\
&(-3.52_{~{}\pm 50.37})[\log(\lambda)-(2.60_{~{}\pm 0.19})]+(82.38_{~{}\pm
19.32}),&&\quad\lambda>(398.11_{~{}\pm 1.55})\,\mathrm{nm}\\\
\end{aligned}\right.,~{}$ (9)

and

${R_{e}}_{\mathrm{,~{}disk}}=\left\\{\begin{aligned} &(-255.98_{~{}\pm
43.7})[\log(\lambda)-(3.16_{~{}\pm 0.12})]+(182.54_{~{}\pm
28.59}),&&\quad\lambda\leq(1445.44_{~{}\pm 1.32})\,\mathrm{nm}\\\
&(152.46_{~{}\pm 99.77})[\log(\lambda)-(3.16_{~{}\pm 0.12})]+(182.54_{~{}\pm
28.59}),&&\quad\lambda>(1445.44_{~{}\pm 1.32})\,\mathrm{nm}\\\
\end{aligned}\right.,~{}$ (10)

where $\lambda$ is the wavelength in units of nanometers (nm). Uncertainties
in the fitting functions are estimated by using the ”bootstrap resampling”
method (Dey et al. 2019). We artificially construct a sample containing 1000
mock galaxies randomly distributed within the error ranges for the M81 data at
the 20 wavebands, fit the wavelength-dependent morphology of each mock galaxy
in the same way, and hence obtain the best-fit curves for all of the mock
galaxies. The uncertainties in Equations 3–10 are defined as standard
deviation in the best-fit curves for the mock galaxies from that for M81. The
results of the ”bootstrap resampling” method are displayed in Figure 4.

###  4.2 Spectral Energy Distributions and Multiwavelength Flux Ratios

Spectral energy distributions (SEDs) and multiwavelength flux ratios to the
galaxy as a whole for the bulge and the disk are also displayed in Figure 3.
Integrated measurements of the bulge, the disk, and the galaxy as a whole were
performed by photometry with the same aperture. The aperture is an ellipse
centered at R.A. = 148∘.888, Dec. = 69∘.065, with the semi-major axis
$750\arcsec\times 450\arcsec$ and the position angle $-20^{\circ}$.
Uncertainties in the measurements are estimated as a quadratic sum of
calibration errors and background deviation. The flux ratio is defined as the
flux of the bulge or the disk (measured in the model image) divided by the
flux of the galaxy as a whole (measured in the observed image) at a certain
waveband. The WIYN fluxes are not included in the SEDs and the flux ratios,
because the field of view for the WIYN images is smaller than the photometric
aperture.

The observed SEDs for the bulge, the disk, and the galaxy as a whole were
fitted with model spectra of stellar population synthesis by using the CIGALE
software (Boquien et al. 2019). The initial guess of parameters is made in
accordance with those in Nersesian et al. (2019). In the SED fitting, we
designate the solar metallicity ($Z$ = 0.02, Kong et al. 2000) and the star
formation history in an e-folding form on the star formation timescale 2600
Myr which is the best-fit value for M81; stellar population age and
interstellar dust attenuation are variable parameters.

In the bottom-left panel of Figure 3, the best-fit model spectra indicate that
the mean age of stellar populations is 6 Gyr for the bulge, 2 Gyr for the
disk, and 2.5 Gyr for the galaxy as a whole. The color index NUV$-$r is $\sim
4.02$ mag for the whole galaxy, $\sim 3.54$ mag for the disk, and $\sim 6.98$
mag for the bulge, respectively. Containing the oldest stellar population in
the galaxy, the bulge is extremely red in color.

Figure 5: Comparisons between the same best-fit parameters in the images with
the original and reduced S/N. By adding different levels of Gaussian noise
with an mean value of zero, we unify all data into the same S/N as the _GALEX_
FUV band, which has the lowest S/N in all data. The left panel shows the
comparison of the Sérsic index $n$; the right panel shows the comparison of
the effective radius $R_{e}$. In each panel, symbols and lines are the same as
assigned in Figure 8.

The bottom-right panel of Figure 3 shows the bulge-to-galaxy and disk-to-
galaxy flux ratios as a function of wavelength. We can see that, at the UV
bands, the disk dominates the galaxy ($>$ 80% at Swift UVW2, GALEX NUV, and
Swift UVW1), while the bulge is quite trivial ($<$ 10% at GALEX FUV, Swift
UVW2, and GALEX NUV); at longer wavelengths, the flux for the disk declines
whereas that for the bulge rises, and the contributions of the bulge and the
disk to the galaxy get close and comparable at optical and NIR bands ($\sim
50$% at 3551–58000 Å).

##  5 DISCUSSION

In the above section, variations in a series of morphological parameters for
the bulge and the disk in M81 with wavelength are displayed as a result of the
structural decomposition by fitting the surface-brightness profiles. In
practice, goodness of the surface-brightness fit is related with several
factors such as S/N of the data, the presence of the spiral arms, and the
covariance between the parameters. The potential influences on the fit, as
well as implications of the results and comparisons with other studies, are
presented and discussed in this section.

###  5.1 Sensitivity to the Signal-to-Noise Ratio

Among the factors potentially affecting the surface-brightness fit, the noise
level for the data often dominates the reliability of the products. In this
work, the multiwavelength images with different S/N are analyzed. The
difference in S/N is likely to contribute a systematic trend to the resultant
wavelength-dependent morphology. For the purpose of discerning the suspected
imprint of S/N and eliminating its influence, we artificially impose noise on
the images to equalize S/N at all of the wavebands, and then perform the same
fit to compare the noisy results with the normal ones.

Figure 6: The same as Figure 3 but for all of the images with S/N reduced to
an equal level.

In accordance with the definition in Davari et al. (2014), S/N is calculated
as follow:

$\mathrm{\,S/N}=\frac{f}{\sqrt{f+A\sigma^{2}}}~{},$ (11)

where $f$ is the flux for the galaxy obtained with the aperture photometry,
$A$ is the area of the aperture, and $\sigma$ is the background uncertainty.
The noise imposed on each image is configured to have a Gaussian distribution
with a mean value of zero and different amounts of the standard deviation, so
as to align S/N to that in the _GALEX_ FUV image ($\sim 90$, the lowest S/N
among all of the data).444 In this step, we only add background noise and do
not change the flux for the source. The method for reducing S/N is addressed
in Lotz et al. (2008); Meert et al. (2013); Davari et al. (2014). The WIYN and
_Spitzer_ -IRAC 5.8 $\mu$m images are not included in this part of processing,
because the WIYN fields of view are small, and the 5.8 $\mu$m band is
contaminated by dust emission, which potentially results in an incorrect
measurement of S/N. As a consequence, there are 16 wavebands in total adopted
for the investigation with the equalized S/N. The imposition of the Gaussian
noise inevitably introduce extra uncertainties in the results. In order to
diminish the extra uncertainties, we carry out the alignment of S/N for 10
times and thereby create 10 images at each waveband; in each of the 10 images
at each waveband, the surface-brightness profile is fitted to obtain the
morphological parameters; the average of the 10 estimates is taken as the
final value for each parameter at each waveband. The parameters at the 16
wavebands with the equalized S/N are presented in Appendix B.

Figure 7: The same as Figure 4 but for the images with S/N reduced to an equal
level.

Figure 5 shows the comparisons in the best-fit parameters between the original
and processed S/N. We can see that the S/N alignment does not affect most of
the data points, but the Sérsic index $n$ for the bulge at some NIR bands
increases, albeit within the $3\sigma$ range. This behavior appears effective
in the relation of the parameter with wavelength, as shown in Figures 6 and 7.
We still adopt a quadratic curve and a two-slope piecewise linear curve to,
respectively, fit each of the parameter-wavelength relations. The formulae
with uncertainties in coefficients are listed as follows:

$n_{\mathrm{~{}bulge}}=(-3.45_{~{}\pm 1.50})\log^{2}(\lambda)+(22.94_{~{}\pm
8.48})\log(\lambda)+(-33.05_{~{}\pm 11.67}),$ (12)

$n_{\mathrm{~{}disk}}=(-0.93_{~{}\pm 0.31})\log^{2}(\lambda)+(6.19_{~{}\pm
1.81})\log(\lambda)+(-9.08_{~{}\pm 2.55}),$ (13)

${R_{e}}_{\mathrm{,~{}bulge}}=(-91.26_{~{}\pm
55.16})\log^{2}(\lambda)+(575.35_{~{}\pm
317.53})\log(\lambda)+(-806.12_{~{}\pm 440.99}),$ (14)

${R_{e}}_{\mathrm{,~{}disk}}=(198.33_{~{}\pm
46.68})\log^{2}(\lambda)+(-1302.23_{~{}\pm
276.36})\log(\lambda)+(2354.71_{~{}\pm 394.79}),$ (15)

$n_{\mathrm{~{}bulge}}=\left\\{\begin{aligned} &(6.53_{~{}\pm
1.47})[\log(\lambda)-(2.79_{~{}\pm 0.17})]+(4.59_{~{}\pm
0.81}),&&\quad\lambda\leq(616.59_{~{}\pm 1.48})\,\mathrm{nm}\\\ &(0.30_{~{}\pm
2.66})[\log(\lambda)-(2.79_{~{}\pm 0.17})]+(4.59_{~{}\pm
0.81}),&&\quad\lambda>(616.59_{~{}\pm 1.48})\,\mathrm{nm}\\\
\end{aligned}\right.,~{}$ (16)

$n_{\mathrm{~{}disk}}=\left\\{\begin{aligned} &(1.87_{~{}\pm
0.31})[\log(\lambda)-(2.79_{~{}\pm 0.09})]+(1.12_{~{}\pm
0.17}),&&\quad\lambda\leq(616.59_{~{}\pm 1.23})\,\mathrm{nm}\\\ &(0.05_{~{}\pm
0.28})[\log(\lambda)-(2.79_{~{}\pm 0.09})]+(1.12_{~{}\pm
0.17}),&&\quad\lambda>(616.59_{~{}\pm 1.23})\,\mathrm{nm}\\\
\end{aligned}\right.,~{}$ (17)

${R_{e}}_{\mathrm{,~{}bulge}}=\left\\{\begin{aligned} &(260.81_{~{}\pm
88.19})[\log(\lambda)-(2.55_{~{}\pm 0.19})]+(94.15_{~{}\pm
25.83}),&&\quad\lambda\leq(354.81_{~{}\pm 1.55})\,\mathrm{nm}\\\
&(-21.70_{~{}\pm 44.26})[\log(\lambda)-(2.55_{~{}\pm 0.19})]+(94.15_{~{}\pm
25.83}),&&\quad\lambda>(354.81_{~{}\pm 1.55})\,\mathrm{nm}\\\
\end{aligned}\right.,~{}$ (18)

and

${R_{e}}_{\mathrm{,~{}disk}}=\left\\{\begin{aligned} &(-262.32_{~{}\pm
41.73})[\log(\lambda)-(3.14_{~{}\pm 0.10})]+(183.17_{~{}\pm
22.19}),&&\quad\lambda\leq(1442.54_{~{}\pm 1.26})\,\mathrm{nm}\\\
&(134.34_{~{}\pm 77.55})[\log(\lambda)-(3.14_{~{}\pm 0.10})]+(183.17_{~{}\pm
22.19}),&&\quad\lambda>(1442.54_{~{}\pm 1.26})\,\mathrm{nm}\\\
\end{aligned}\right.,~{}$ (19)

where $\lambda$ is the wavelength in units of nanometers (nm). After reducing
S/N to an equal value for all of the images, the Sérsic index as a function of
wavelength for the bulge appears with no peak and is better fitted by a two-
slope piecewise linear curve. At the wavelength $\lambda\leq 6252$ Å according
to the two-slope piecewise linear curve (or shorter than SDSS r band according
to the data), it increases sharply with wavelength, while over the turn-point
wavelength, the trend becomes nearly flat. In contrast to the Sérsic index for
the bulge, the other parameters stay the same as before.

It should be noted that, the S/N equalization is conducted for the purpose of
inspecting the sensitivity to S/N; the result of this processing does not mean
that it is closer to the real nature than that of keeping S/N unchanged. An
increment of noise will cause a random change in brightness for galactic
pixels, which hence changes the Sérsic index for the bulge at the sensitive
wavebands by random amounts. That is the reason why we make 10 sets of
parameters and take the averages. However, there remains to be fluctuation in
the wavelength-dependent morphology due to the random effect, which can be
hardly eliminated outright. Notwithstanding, the result suffices to illustrate
the sensitivity of the wavelength-dependent morphology to S/N. According to
our analysis, the Sérsic index with a larger value, i.e., a surface-brightness
profile with higher concentration, is more delicate and susceptible to
background noise. As a consequence, most of the parameters are robust against
the change in background noise, but the Sérsic index for the bulge at the NIR
bands are affected. A larger amount of noise imposition tends to cause a
higher value for the Sérsic index. Nevertheless, the influence seems not too
disruptive; the difference is less than the uncertainty in the estimate, and
the change in the relation of the Sérsic index with wavelength for the bulge
is modest. In the wavelength range from optical to NIR, it would still be
arbitrary to claim a constant value for the Sérsic index, but it is convincing
that the variation in the Sérsic index (if any) is much shallower compared
with the sharp rise from FUV to optical bands. A more solid and general
conclusion will rest on studies of a large sample of galaxies.

Figure 8: Comparisons between the same best-fit parameters with the spiral
arms masked and unmasked. The left panel shows the comparison of the Sérsic
index $n$; the right panel shows the comparison of the effective radius
$R_{e}$. In each panel, red solid circles represent the bulge, and blue solid
circles represent the disk; black dotted line represents the line of unity
($y=x$), with green dotted lines enveloping the range of three times the
standard deviation ($y=x\pm 3\delta$, where $\delta$ is the standard deviation
in the data). Error bars are superimposed on the data points.

###  5.2 Impact of the Spiral Arms

In this work, we use two Sérsic components to reproduce the bulge and the disk
in M81, with the spiral arms left unfitted. Compared with the bulge and the
disk, the spiral arms are an asymmetric structure and hence not able to be
reproduced by a common model. In most of the residual images (see Figures
A1–A20 in Appendix A), particularly at short wavelengths, spiral shapes are
clearly seen. In this case, it is necessary to understand the impact of the
spiral arms on the morphological parameterization of the bulge and the disk.
With this in mind, we masked the spiral arms and then performed the fit for
comparison with the results of the spiral arms unmasked.555 The spiral arms
are defined in the residual images as the pixels with the brightness larger
than the 5$\sigma$ level.

Figure 8 shows the comparisons between the same best-fit parameters for the
spiral arms masked and unmasked. The differences, as seen from this figure,
are less than three times the standard deviation at all wavelengths, which
illustrates that the presence of the spiral arms has a very trivial impact on
the bulge-disk decomposition, and the two-Sérsic fit suffices to characterize
the morphology of the bulge and the disk in M81.

Independent evidence proving that modeling spiral arms are not crucial has
been provided by Gao & Ho (2017) through detailed morphological analysis of
six spiral galaxies. They have found that the presence of spiral arms has a
subtle impact on the parameterization of bulges; specifically in the Sérsic
index, it introduces an uncertainty of $\sim 10$% for unbarred galaxies and
$\sim 1$% for barred galaxies. In addition, Gong & Mao (2023) have elaborately
investigated the _Spitzer_ -IRAC 4.5 $\mu$ m image for M81 by adopting six
types of decompositions with the number of model components from 1 to 5. The
most complicated model contains a bulge (fitted with one Sérsic function), a
disk (fitted with one Sérsic function), a pair of outer spiral arms (fitted
with one coordinate-rotation truncated Sérsic function), a pair of inner
spiral arms (fitted with one coordinate-rotation truncated Sérsic function),
and a galactic nucleus (fitted with one PSF). This experiment that, as long as
both of the bulge and the disk are included in the model (i.e., with the two-
Sérsic functions),666For the galaxy M81, as well as any galaxy hosting an AGN,
a PSF for fitting the nucleus is also requisite. the results are relatively
stable.

Indeed, it would be ideal to take spiral arms as well as other substructures
(if any) into model components, but this would induce extra errors and consume
more time in the fit. In general cases, two Sérsic components are an optimal
mode for describing morphology of galaxies even if asymmetric substructures
such as spiral arms, bars, or rings exist, especially when studying a large
sample of galaxies.

###  5.3 Degeneracy in the Fit

Figure 9: The Sérsic index (left column) and the effective radius (right
column) as a function of wavelength for the bulge (red filled circles) and the
disk (blue filled circles) with original (top row) and reduced S/N (bottom
row). Dot-dashed and dotted lines represent the best-fit quadratic and
piecewise linear curves, respectively. The Sérsic index for the disk is fixed
into $n_{\mathrm{~{}disk}}=1$ (the exponential disk).

Degeneracy of free parameters seems always to be an intractable problem in any
kind of fits. In this work, we adopt two Sérsic components to fit the bulge
and the disk in M81, respectively, where the Sérsic index and the effective
radius are free parameters when fitting surface-brightness profiles. This part
of the discussion focuses on the degeneracy in the surface-brightness fit.

Figure 10: The same as Figure 9 but with the effective radius for the bulge
fixed to ${R_{e}}_{\mathrm{,~{}bulge}}=80\arcsec.71$ (the mean value at all of
the wavebands apart from the four UV bands). Figure 11: The same as Figure 9
but with the Sérsic index for the disk fixed to $n_{\mathrm{~{}disk}}=1$ (the
exponential disk) and the effective radius for the bulge fixed to
${R_{e}}_{\mathrm{,~{}bulge}}=80\arcsec.71$ (the mean value at all of the
wavebands apart from the four UV bands) at the same time.

With the Sérsic function adopted in the fit, the bulge and the disk share a
common space from the center to infinity, and thus the two components always
overlap with each other. From Figures 3, 4, 6, and 7, we can see that the
Sérsic index for the disk and the effective radius for the bulge appears
constant with wavelength except for the UV bands, where the parameters appear
to have lower values, which hints at possible degeneracy of the two components
at these bands. In order to eliminate the possibility, we fix the Sérsic index
for the disk into $n_{\mathrm{~{}disk}}=1$ (the exponential disk), the
effective radius for the bulge into the mean value of all of the wavebands
apart from UV (${R_{e}}_{\mathrm{,~{}bulge}}=80\arcsec.71$), and both at the
same time. The results are shown in Figures 9–11, respectively. These figures
illustrate that fixing the parameters has almost no effect on the fit but
cause a problematic estimate at the UV bands, which demonstrates that the
bulge and the disk are not heavily coupled but separable by the decomposition.

Figure 12: Variations in surface-brightness profiles for the artificially
generated bulge and disk in the wavelength range from _GALEX_ FUV to _WISE_
W2, by using Equations 3–6. The colored zones represent the coverage of these
multiwavelength profiles, and indicate the effect of the changes in the Sérsic
index and the effective radius on the profiles. The profiles are reproduced on
the assumption of a constant total magnitude for both of the bulge and disk.

For an individual component, since the Sérsic index and the effective radius
are free parameters, the two parameters are necessarily coupled, which appears
as comparative covariance between the two parameters, but the surface-
brightness profile generally keeps unchanged in shape. In order to inspect the
degeneracy, a series of models for the bulge and the disk with the same total
brightness are artificially generated by use of Equations 3–6 in the
wavelength range for our data. By following the approach in Kelvin et al.
(2012), in Figure 12 we show variations in surface-brightness profiles as the
Sérsic index and the effective radius jointly vary. In this figure, the
optical–NIR bands and UV bands are separately displayed to show the distinct
behaviors between the two wavelength parts. The ranges for the Sérsic index
and the effective radius are regulated in accordance with the results in
Figure 3. At the optical–NIR bands, the bulge model ranges 2.60–5.37 in the
Sérsic index and 49$\arcsec$.71–91$\arcsec$.87 in the effective radius; the
disk model ranges 0.51–1.19 in the Sérsic index and
222$\arcsec$.90–353$\arcsec$.31 in the effective radius. At the UV bands, the
bulge model ranges 0.65–2.26 in the Sérsic index and
10$\arcsec$.54–42$\arcsec$.89 in the effective radius; the disk model ranges
0.014–0.42 in the Sérsic index and 371$\arcsec$.06–453$\arcsec$.38 in the
effective radius.

It is obvious from Figure 12 that the bulge and the disk differ quite a lot in
surface-brightness profiles, which indicates a good separation between the two
components in the decomposition by the fit. For individual Sérsic components,
the surface-brightness profiles for the bulge at the optical–NIR bands and the
disk at the UV bands are relatively stable with a mild variation, as the
Sérsic index and the effective radius vary in a wide range, whereas the UV
bulge covers a vast area in the surface-brightness plane indicating an
enormous change in the profiles. These behaviors imply that covariance between
the Sérsic index and the effective radius exists in the optical–NIR bulge and
the UV disk, where, comparatively, changes in the two parameters are likely to
have no effect on the surface-brightness profiles. This prevents accurate
measurements of the galactic morphology by means of the surface-brightness
fits. By contrast, the UV bulge appears with the surface-brightness profile
depending more on the morphological parameters, and the surface-brightness
fits are an effective tool for determining the Sérsic index and the effective
radius.

###  5.4 Morphology of the Bulge

####  5.4.1 Multiwavelength Features

It is interesting for the bulge of M81 that the Sérsic index ($n$) varies
widely with wavelength, steeply from $n\sim 1$ to $n\sim 4$ in the UV–optical
range and shallowly between $n\sim 4$–$5$ at the optical–NIR bands. In general
cases, the Sérsic index is an identification of classical bulges or pseudo-
bulges. The Sérsic index equal to 2 is the usual line of demarcation between
classical bulges ($n>2$) and pseudo-bulges ($n\leq 2$, Fisher & Drory
2008).777 In addition to the Sérsic index, there are also some alternative
schemes, such as the Petrosian concentration index, the Kormendy relation, and
kinematic indices (i.e., rotation velocity and velocity dispersion), for
distinguishing between classical and pseudo-bulges (Gadotti 2009; Neumann et
al. 2017; Gao et al. 2020; Gao et al. 2022). We focus the Sérsic index in this
work. Readers are suggested to take multiple criteria for precise
classification of bulges. The wavelength-dependent $n$ manifests that the
bulge of M81 appears as a prominently classical bulge at the optical and NIR
bands but as a bulgeless system at the UV bands. This hints that if we observe
through UV channels, we are likely to mistake a classical bulge for a pseudo-
bulge or no bulge. In this case, it is possible for one galaxy to be
classified into different morphological types if observed at different
wavebands, particularly for early-type spiral galaxies of which the UV
morphology usually behaves like late types (Kuchinski et al. 2000).

The variation in the morphology of bulges with wavelength provides an
interpretation of the inconsistency between observations of high-redshift
galaxies and modeling of galaxy evolution. It has been reported that bulges
are predicted to have been formed at the redshift $z\sim 2$, but galaxies at
$z$ = 1–3 are found to be mainly dominated by disks (van Dokkum et al. 2013;
Bruce et al. 2014; Shibuya et al. 2015; Toft et al. 2017; Dimauro et al. 2019;
Tacchella et al. 2019; Hashemizadeh 2022). In practical terms, for high-
redshift galaxies, optical telescopes observe their rest-frame UV appearances.
However, according to the increasing trend of the Sérsic index with wavelength
discovered in this work, a classical bulge becomes identifiable (i.e., $n\sim
3$) at the wavelength $\lambda\sim 3551$ Å (at the SDSS u band), prominent
(i.e., $n\sim 4$) at $\lambda\sim 5500$ Å (at the WIYN V band), and possesses
the Sérsic index in a constant range (i.e., $n\sim 4$–$5$) from optical V to
NIR J, H, Ks, and longer bands. This is to say, if a galaxy with the inherent
morphology similar to M81 is located at the redshift $z=2$, then it will be
identified with the Sérsic index $n>3$ at the observed wavelength
$\lambda>1.0\,\mu$m (corresponding to the rest-frame wavelength $\lambda>3551$
Å) and $n>4$ at the observed wavelength $\lambda>1.6\,\mu$m (corresponding to
the rest-frame wavelength $\lambda>5500$ Å). In this case, morphological
classifications based on optical observations through $\lambda\leq 1.0\,\mu$m
can hardly identify the presence of classical bulges but likely mistake early-
type spiral galaxies for late-type ones at redshifts $z\geq 2$. For the
redshift $z\geq 3$, the identification of the classical bulge by using the
Sérsic index rests on observations beyond NIR J, H, Ks bands, for which
ground-based and last-generation space telescopes fail to achieve, whereas the
James Webb Space Telescope (_JWST_) meets the requirement and has great
potential to make significant discoveries on this topic (Ferreira et al.
2022).

The SED for the bulge (in the bottom-left panel of Figure 3) indicates that it
is an old system ($\sim 6$ Gyr). The aged stellar population radiates
dominantly at optical and NIR bands, but dimly at UV bands. Taking 100 Myr to
divide stellar populations into old ($\geq 100$ Myr) and young ($<100$ Myr)
groups by following Verstocken et al. (2020), the SED-fitting result shows
that the mass ratio of young stars in the bulge to the total stellar mass is
$4\times 10^{-5}$, while the luminosity ratio of young stars in the bulge to
the total stellar luminosity is $5\times 10^{-3}$. For the disk, the mass
ratio of young stars to the total stellar mass is $3\times 10^{-3}$, while the
luminosity ratio of young stars to the total stellar luminosity is 0.23. This
means that there are almost no young stars in the bulge, while the disk
inhabits both young and old stars.

Figure 13: Left panel: isophote for M81 in the SDSS-i band image on a
logarithmic scale, where the red ellipse marks a radial distance of
100$\arcsec$. Right panels: radial profiles of ellipticity (upper panel) and
position angle (lower panel) in the isophote. The red dotted line indicates a
radius of 100$\arcsec$.

####  5.4.2 Lack of Pseudo-bulge Features

It is worth noting that, classical bulges and pseudo-bulges are likely to
coexist in galaxies (Erwin et al. 2003; Athanassoula 2005; Fisher & Drory
2010; Luo et al. 2020; Yu et al. 2022). If a pseudo-bulge coexists with the
classical bulge in M81, then the variation in the morphology with wavelength
for the bulge is interpretable with the coexistence of a classical bulge (with
the Sérsic index $n\geq 3$, containing old stellar populations, dominating
optical and NIR bands) and a pseudo-bulge (with the Sérsic index $n\sim 1$,
containing younger stellar populations, dominating UV bands). In this case,
the low value for the Sérsic index at the UV bands would be an impact of the
pseudo-bulge. In this section, we examine the possibility of the presence of a
pseudo-bulge in M81.

The presence of a pseudo-bulge, overlapping with a classical bulge, is likely
to leave a signature in isophote for the galaxy (Erwin et al. 2015). By
inspecting the ellipticity and the position angle of the isophote, we are able
to suggest whether or not a pseudo-bulge coexists with the classical bulge. In
this work, the isophote is created in the SDSS-i band image, where the maximum
is the highest flux in the image, and the minimum is the $3\sigma$ background
deviation. There are 20 contours in total, on a logarithmic scale, in the
isophote. Figure 13 shows the result of the isophote and relevant analysis.

During the isophote inspection, we define the bulge-dominated area at radii
$\leq 100\arcsec$, and the disk-dominated area at radii $>100\arcsec$, since
at a radius of $\sim 100\arcsec$, the bulge and the disk are equal in surface
brightness in the SDSS-i image (as can be seen from Figure A11 in Appendix A).
The isophote map in Figure 13 exhibits that the shape of the contours for the
bulge-dominated area appears much rounder than that for the disk-dominated
area. The ellipticity of the isophote is in the range 0.18–0.38 for the bulge-
dominated area and 0.35–0.58 for the disk-dominated area.888 The hump feature
in the ellipticity profile around a radius of $\sim 16\arcsec$ in Figure 13 is
caused by small-scale structures inside the bulge (Elmegreen et al. 1995; Mao
et al., in preparation). The ellipticities for both of the bulge- and disk-
dominated areas are consistent with those for the bulge and disk models in the
morphological decomposition. In the ellipticity profiles, the bulge-dominated
area is systematically lower than the disk-dominated area. The low ellipticity
for the bulge-dominated area manifests absent of the pseudo-bulge. Otherwise,
if there is a pseudo-bulge, the bulge-dominated area (at least for its outer
part) in the isophote will have high ellipticity, even comparable with the
disk (Erwin et al. 2015).

In addition to the isophote analysis, a number of alternative diagnostics,
such as the Petrosian concentration index (Gadotti 2009; Neumann et al. 2017),
the Kormendy relation (Gao et al. 2020), and kinematic indices (i.e., rotation
velocity and velocity dispersion, Kormendy & Illingworth 1982), indicate the
presence of a classical bulge and no sign of a pseudo-bulge for M81 from other
points of view.999 On the basis of preliminary analysis of the imaging data at
SDSS-i band, we obtained the Petrosian concentration index and the Kormendy
relation for the bulge of M81, which shows that it lies in a typical range for
classical bulges; on the other hand, according to the spectroscopic data in
Kormendy & Illingworth (1982), the bulge in M81 appears with a rotation
velocity less than velocity dispersion, which is a typical behavior of a
classical bulge with no pseudo-bulge feature from a kinematic point of view.

The lack of pseudo-bulge features makes the nature of the exponential-like
distribution for the UV bulge (i.e., to be more precise, the compact
exponential UV component) questionable. The most likely reason is a
contribution of the disk to the central area. The bulge and the disk overlap
with each other. The relative intensity of the bulge to the disk varies with
wavelength, and at UV bands the disk dominates the galaxy in flux and
morphology. In this case, the prominent disk is likely to contribute to the
bulge component during the decomposition. From the SEDs for the bulge in
Figures 3 and 5, we can see a systematic offset of the data points toward
higher fluxes from the best-fit SEDs at the UV–optical bands. This illustrates
a flux excess for the bulge component, which is a probable aftermath of the
disk contribution. Nevertheless, we still cannot rule out the other
possibility that the compact exponential UV component is exactly the classical
bulge imaged through UV channels, even while accounting for the disk
contribution. Many studies have disclosed some old elliptical/spheroidal
systems with a considerable amount of UV emission (O’Connell et al. 1992;
Kuchinski et al. 2000; Marcum et al. 2001; Windhorst et al. 2002). Despite the
reason for the exponential UV component, it is most important that we are
quite likely to misidentify the morphological type of galaxies (i.e., to
mistake a classical bulge for a pseudo-bulge or a no-bulge system by observing
through UV channels), which often takes place in high-redshift studies.

Figure 14: Comparisons between the same best-fit parameters for the two Sérsic
components and the one-Sérsic bulge plus one-exponential (i.e., the Sérsic
index $n=1$) disk. The left panel shows the comparison between the Sérsic
index $n$; the right panel shows the comparison between the effective radius
$R_{e}$. In each panel, symbols and lines are the same as assigned in Figure
8.

###  5.5 The Morphology of the Disk

####  5.5.1 Exponential at Optical and NIR Bands

In many studies involved with morphology of galaxies, surface-brightness
profiles for galactic disks are commonly assumed with an exponential decline
(i.e., the Sérsic index $n=1$) for simplicity. By setting the Sérsic index for
the disk as a free parameter, our work shows that the parameter is almost
around $n=1$ in the wavelength range from optical to NIR (Table A2, Figures 3
and 5), which corroborates the exponential form for the disk profile. In
particular, when fixing $n=1$ for the disk at all wavebands (i.e., assuming an
exponential disk) with the bulge still left in a free Sérsic form, we find no
significant difference in the result, except for the UV bands.

Figure 14 shows comparisons between the same parameters for the one-Sérsic
plus one-exponential components and the two Sérsic components. After fixing
the Sérsic index for the disk into $n=1$, the Sérsic index for the bulge and
the effective radius for both components at most wavebands are almost
unchanged, but the effective radius for the disk at the four UV bands offsets
towards larger values. Due to the presence of the faint inner area plus the
bright spiral arms in outer regions at UV bands, the Sérsic index is small
($n$ = 0.1–0.3, i.e., the surface-brightness profile is flat). If the Sérsic
index is artificially increased (to $n=1$), then the effective radius will
increase at the same time, in order to preserve the shape of the surface-
brightness profile.

####  5.5.2 Flat at UV Bands

From Figure 3 and Table A2, we can see that, the disk at the UV bands appears
to be extremely flat, with the Sérsic index $n\sim 0.15$–0.33. This flatness
is attributed to a joint effect of the dim inner area and the bright spiral
arms of the galaxy at the UV bands. In this section, we inspect flux
contributions of the inner area and the spiral arms to the whole galaxy at all
of the wavebands, so as to infer the influence on the bulge-disk decomposition
as a function of wavelength. The approach and the result are displayed in
Figure 15.

Locations of the inner galactic area and the spiral arms are defined in the
FUV image. The inner area of the galaxy is enclosed in a manually determined
elliptical aperture (marked in red) with the center R.A. = 148∘.888 and Dec. =
69∘.065 (consistent with the galactic center), the semi-major axis
212$\arcsec$, the ellipticity 0.47, and the PA $-35^{\circ}$. The bulge-
dominated innermost core, defined by a smaller elliptical aperture (marked in
blue), is not included in the measurement of the inner area. The aperture
enclosing the core shares the center, the ellipticity, and the position angle
the same with the larger aperture, but the semi-major axis is equal to two
times the effective radius of the bulge at the FUV band. The spiral arms are
defined outside the inner area (red ellipse) and inside the aperture (yellow
ellipse) for measuring the whole galaxy, by a threshold of the flux higher
than 10 times the background uncertainty with more than 50 pixels. The spiral
arms are then segmented and loaded into a new image, as shown in the bottom-
left panel of Figure 15. This spiral-arm segmentation was applied to all of
the images.

Figure 15: Left: the observed FUV image for M81 with the inner part of the
galaxy marked as the area between the red and blue ellipses (the upper panel),
where the yellow ellipse represents the aperture employed for photometry of
the whole galaxy, and the spiral-arm image (the lower panel) segmented from
the above FUV image. Right: flux ratios of the spiral arms (purple) and the
inner area (pink) to the whole galaxy as a function of wavelength, with the
inner area to the spiral arms overplotted as well (green)

.

The right panel of Figure 15 shows the flux ratios of the inner area and the
spiral arms to the whole galaxy as a function of wavelength. From this
diagram, we can see that, at the UV bands, the inner area trivially
contributes $<20\%$ flux to the whole galaxy, whereas the spiral arms
predominantly account for $\sim 70\%$ and even more at the FUV band. The
situation is in contrast to that at the optical and NIR bands; more than half
of the integrated flux for the galaxy is contributed by the inner area, but
the percentage of the spiral arms drops to $\sim 30\%$. As a result, the
fitting of the radial surface-brightness profile for the disk inevitably
results in a dimmer inner part and a brighter outer part at the UV bands than
those at the optical and NIR bands, which causes the extreme flatness.

The high flux fraction of the spiral arms found in the UV images are
consistent with the picture of the density-wave theory (Lin & Shu 1964). The
spiral arms in M81 have been suggested to be a density-wave pattern (Kendall
et al. 2008; Feng et al. 2014; Wang et al. 2015). When gas clouds go across
spiral arms, this triggers large-scale shock, facilitating gravitational
collapse, and production of new stars in gas clouds (Roberts 1969; Seigar &
James 2002; Kendall et al. 2015; Yu & Ho 2018; Yu et al. 2021; Pettitt et al.
2020; Yu et al. 2022). The flux fraction of spiral arms decreases toward
longer wavelengths where the emission is dominated by old stars. Nevertheless,
the flux fraction slightly increases beyond 3 $\mu$m, probably caused by a
contribution of polycyclic aromatic hydrocarbon (PAH) emission along the
spiral arms (Querejeta et al. 2015).

Figure 16: The same as Figure 3, but the morphological parameters at the
Spitzer-IRAC 5.8 $\mu$m band are determined according to Equations (3)–(6), so
there is no error bar for the date points of $n$ and $R_{e}$ at this band.

###  5.6 Practical Applicability of the Wavelength-dependent Morphology

Figure 17: Results of the surface brightness fitting in the Spitzer-IRAC 5.8
$\mu$m image. The left panels show the observed (top panel), model (middle
panel), and residual (bottom panel) images. The top-right panel shows the
radial surface brightness profiles of the observed galaxy and all of the
components in the model, with the best-fit curves superimposed. The bottom-
right panel shows the comparison between the observed data and the model, and
the gray dotted line indicates the error. The legend is listed in the diagram.
During the decomposition, values for the Sérsic index and the effective radius
for the bulge and the disk in the model are determined according to Equations
3–6.

In the top panels of Figure 3, the data points for _Spitzer_ -IRAC 5.8 $\mu$m
deviate from the best-fit curves except for the Sérsic index for the bulge. We
find that the inner area of M81 at the Spitzer-IRAC 5.8 $\mu$m band contains
dust emission in addition to starlight, which is a main cause of the deviation
in the morphological parameters at this band. Through our inspection, the
distribution of the radiation of the internal dust is within 180$\arcsec$ of
the radius. These internal dust radiations mislead GALFIT into allocating this
part of light to the bulge model, which resulted in an overestimate of the
effective radius and the total flux of the bulge. Because more starlight is
allocated to the bulge, the brightness of the central area of the disk model
decreases, resulting in an underestimate of the Sérsic index for the disk, as
discussed in Section 5.5.

The wavelength-dependent morphology presented above provides a recipe for
determining morphological parameters at any bands without radial surface-
brightness fitting. For M81 at the Spitzer-IRAC 5.8 $\mu$m band, the radial
surface-brightness fitting is affected by the presence of dust emission; as a
consequence, the bulge-disk decomposition and the morphological estimate are
conducted with considerable uncertainties. Notwithstanding, by alternatively
using Equations 3–6, we are able to obtain the Sérsic index and the effective
radius for the bulge and the disk at 5.8 $\mu$m, and subsequently create model
images for the bulge and the disk at this band.

Figures 16 and 17 show results of the bulge-disk decomposition, with the
Sérsic index and the effective radius at 5.8 $\mu$m determined by using the
morphology-wavelength relation (i.e., Equations 3–6) rather than obtained by
fitting radial profiles of surface brightness. This is an examination of the
morphological estimate without radial surface-brightness fitting. We can see
that the newly created bulge and disk at 5.8 $\mu$m are well fitted with the
models in SEDs, but deviate from the main loci in flux ratios. The integrated
flux of the bulge decreases by 40.9%, while the disk increases by 27.8%. In
this case, the effect of the internal dust, which misled GALFIT into
allocating some part of the emission from the disk to the bulge, is
eliminated. Notwithstanding, the radial surface-brightness profiles for the
newly created model have no obvious changes from the previous ones.

The relationship of morphological parameters with wavelength found in this
work is usable for recovering galactic morphology at any band where bulge-disk
decomposition and morphological fitting are not able to be carried out due to
any reason. According to our results, in the most general case, there is a
simple approach to obtaining multiwavelength morphology of galaxies. In this
recipe, we suggest an initial estimate at the three characteristic wavebands
$\lambda_{\mathrm{1}}<3000$ Å, $\lambda_{\mathrm{2}}\sim 5500$–$6000$ Å, and
$\lambda_{\mathrm{3}}>1.0\,\mu$m (in the rest frame), and a subsequent
interpolation at any other certain wavebands.

On the other hand, the results in this work bring forward a caveat that
galaxies with classical bulges are likely misidentified for those with pseudo
or no bulges if they are studied at rest-frame UV bands. This seems especially
crucial for high-redshift galaxies, which are usually observed through rest-
frame UV channels with optical telescopes. Our study of M81 is an attempt at
quantifying morphological K-correction in a specific case. Studies of
additional galaxies of different types would be significant in acquiring
comprehensive knowledge about wavelength-dependent morphology of galaxies, of
which a wide range of applications can be made to a number of areas in
practice.

Figure 18: This figure presents the morphological parameters of the galaxy,
including the Sérsic index (top-left panel) and effective radius (top-right
panel) fitting based on the original S/N data, as well as the Sérsic index
(lower-left panel) and effective radius (lower-right panel) fitting based on
reduced S/N data. The black dots represent the fitting results for the
integrated galaxy, which is a combination of all substructures.

###  5.7 Comparison with Other Work

Most previous studies involving multiwavelength morphology of galaxies have
found very mild or even constant trends of the Sérsic index with wavelength.
In general cases, galaxies have been found to be more compact and smaller at
longer wavelengths. For early-type galaxies or classical bulges observed
through optical–NIR channels (approximately from u to Ks bands), the Sérsic
index increases with wavelength, but the variations are shallow or flat
($n\sim 3$–$4$, Kelvin et al. 2012; Vika et al. 2013; Vulcani et al. 2014;
Lange et al. 2015; Marian et al. 2018; Lima-Dias et al. 2021); in the same
wavelength range, late-type galaxies or disks appears invariable in
concentration level (commonly with the Sérsic index $n\sim 1$, Kelvin et al.
2012; Vulcani et al. 2014; Lumbreras-Calle et al. 2019; Lima-Dias et al.
2021). When observed at UV bands ($\lambda<3000$ Å), early-type galaxies or
classical bulges appear with lower values for the Sérsic index ($n\sim 2$–$3$,
Rampazzo et al. 2017; Leahy et al. 2023). Nonetheless, morphology of galaxies
and galactic subsystems at wavelength extending to FUV or beyond Ks bands has
not yet been well explored in combination with optical–NIR channels. By
collecting 20-band imaging data spanning from 1516 Å to 5.8 $\mu$m, our study
creates the widest wavelength window into quantitative galactic morphology to
date. According to our results, if the wavelength is confined in the
optical–NIR range, particularly 5500 Å–1.0 $\mu$m, then the morphology appears
to be virtually changeless with wavelength.

Most of the previous studies on this topic have measured galaxies as a mixture
of all substructures, while in this work we carry out the bulge-disk
decomposition and separately measure the individual substructures, which is an
important difference of our study from others. In order to examine the effect
of the bulge-disk or no decomposition on the resultant morphology as a
function of wavelength, we perform morphological measurement with no bulge-
disk decomposition, i.e., using a single Sérsic component (plus a PSF
component to fit the AGN in M81) to fit the surface-brightness profiles at all
wavebands. The results, with both original and equalized S/N, are displayed in
Figure 18. It is clearly displayed that, for the galaxy as a mixture with no
decomposition, the Sérsic index is dominated by the disk at the UV bands and
by the bulge at the optical–NIR bands; the effective radius is determined
solely by the disk, but decreases monotonically with wavelength; both trends
remain to be obvious but show large dispersion. By comparison between the
results of the two- and one-Sérsic fits, we find that the one-Sérsic fit
yields a roughly consistent estimate of the Sérsic index with that for the
bulge at optical and NIR bands, albeit an overestimates of the effective
radius. However, if the wavelength is confined to a narrow range, particularly
at $\lambda\leq 2\,\mu$m, the variation in morphology with wavelength appears
to be monotonic with large dispersion.

In practice, quite a large number of investigations have assumed constant
morphology at different wavelengths for simplicity (McDonald et al. 2011; Vika
et al. 2014; Kennedy et al. 2016; Buzzo et al. 2021). According to our work,
this assumption is generally safe at the rest-frame wavelength $\lambda\geq
5500$ Å, but it takes a high risk of overestimating the Sérsic index for both
of the bulge and the disk at shorter wavelengths, particularly when
$\lambda<3000$ Å (in the rest frame).

##  6 SUMMARY

In this work, we collect imaging data at 20 wavebands in total from FUV to NIR
obtained with space and ground-based telescopes/surveys, including _GALEX_ ,
_Swift_ , WIYN, SDSS, 2MASS, _WISE_ , and _Spitzer_ , to investigate
multiwavelength morphology of the nearby early-type spiral galaxy M81. By
fitting radial surface brightness in the images, we carry out bulge-disk
decomposition and derive a series of morphological parameters as a function of
wavelength. We find that, the Sérsic index for the bulge and the effective
radius for the disk are tightly correlated with wavelength, where the Sérsic
index for the bulge increases sharply from $n\sim 1$ to $n\sim 4$ from UV to
optical bands and varies smoothly between $n\sim 4$ and $5$ at the optical–NIR
bands, while the effective radius for the disk emerges with a similar
intensity of the variation but in an opposite direction.

It is worth noting that the bulge in M81 is classical in type, with the Sérsic
index $n\sim 4$–$5$ at optical and NIR bands, but it behaves like a pseudo-
bulge or no bulge at UV bands with $n\sim 1$. This hints that, observing
through UV channels, we are likely to mistake a classical bulge for a pseudo-
bulge or no bulge. It is particularly important for high-redshift galaxies, of
which morphology is usually studied at rest-frame UV bands. The relationship
of morphological parameters with wavelength discovered in this work provides
panchromatic insight into the morphological K-correction and is usable for
recovering the galactic morphology at any band where morphological
measurements are not able to be carried out.

Previous investigations on multi-band morphology of galaxies were often
confined in the optical range with no separation of substructures, and they
found a monotonic and smooth change, or even an invariable trend, in
morphology with wavelength. With data spanning a wider wavelength range
collected and the bulge-disk composition performed, the morphological
characteristics revealed in this work are more comprehensive and convincing.
On the basis of the multiwavelength morphology, we plan to study spatially
resolved SEDs for the bulge and the disk in M81 in the next work of this
series, aimed at exploring stellar population properties and star
formation/quenching history for the galaxy and the galactic subsystems.

## ACKNOWLEDGMENTS

We are extremely grateful to Luis C. Ho for constructive comments and
discussion. We appreciate the careful reading and the insightful comments
offered by the anonymous reviewer, which have helped us to improve the paper
significantly. This work is supported by the National Natural Science
Foundation of China (NSFC, Nos. U2031106 and U2031201). Jun-Yu Gong especially
thanks Luis C. Ho, Ming-Yang Zhuang, and Ruan-Cun Li for their help and
hospitality during the visit to the Kavli Institute for Astronomy and
Astrophysics at Peking University (KIAA-PKU). Si-Yue Yu acknowledges the
support of the Alexander von Humboldt Foundation. Kavli IPMU was established
by World Premier International Research Center Initiative (WPI), MEXT, Japan.

This research is based on observations made with the _Galaxy Evolution
Explorer_ , and data obtained from the Mikulski Archive for Space Telescopes
(MAST) at the Space Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy, Inc., under NASA
contract NAS 5-26555. This research has made use of data provided by the High
Energy Astrophysics Science Archive Research Center (HEASARC), which is a
service of the Astrophysics Science Division at NASA/GSFC. This research has
made use of data from SDSS-III, which is funded by the Alfred P. Sloan
Foundation, the Participating Institutions, the National Science Foundation,
and the U.S. Department of Energy Office of Science; the SDSS-III web site is
http://www.sdss3.org/; SDSS-III is managed by the Astrophysical Research
Consortium for the Participating Institutions of the SDSS-III Collaboration
including the University of Arizona, the Brazilian Participation Group,
Brookhaven National Laboratory, Carnegie Mellon University, University of
Florida, the French Participation Group, the German Participation Group,
Harvard University, the Instituto de Astrofisica de Canarias, the Michigan
State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence
Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max
Planck Institute for Extraterrestrial Physics, New Mexico State University,
New York University, Ohio State University, Pennsylvania State University,
University of Portsmouth, Princeton University, the Spanish Participation
Group, University of Tokyo, University of Utah, Vanderbilt University,
University of Virginia, University of Washington, and Yale University. This
research has made use of the NASA/IPAC Extragalactic Database (NED) which is
funded by the National Aeronautics and Space Administration and operated by
the California Institute of Technology. This research has made use of the
NASA/IPAC Infrared Science Archive (IRSA), which is funded by the National
Aeronautics and Space Administration and operated by the California Institute
of Technology. This research has also made use of the SAO/NASA’s Astrophysics
Data System (ADS) Bibliographic Services.

##  Appendix A Products of the Multiwavelength Bulge-Disk Decomposition for
M81

In this appendix, we present products of the Bulge-Disk decomposition at the
20 wavebands (the process of the decomposition is presented in Section 3 in
detail). Morphological and flux parameters for the bulge and the disk are
listed in Tables A1 and A2, respectively.

Figures A1–A20 show observed, modeled, and residual images, as well as radial
profiles of surface brightness for the bulge, the disk, and the whole galaxy,
at the 20 wavebands. The model is a sum of all morphological fitting
components in the decomposition at a certain waveband. For most of the
wavebands, the fitting components include the bulge, the disk, and the PSF
component (representing the AGN), while for SDSS-r, SDSS-i, WIYN-V, WIYN-R,
and Spitzer-IRAC 3.6 $\mu$m, the M81 center is affected by saturated pixels,
so that we do not take the PSF component into the decomposition. The residual
image is obtained by subtracting the model image from the observed image. The
radial profiles of surface brightness are produced by using the same method as
in Gao & Ho (2017). First, we need to obtain the ellipticity, the position
angle, and the central coordinates of M81. We separately carry out isophote
fitting for images of different bands, and we use the isophote for which
brightness reaches the background uncertainty as the aperture of that band. We
define the ellipticity, position angle and center coordinates of M81 as the
average of the aperture properties in each band. We create multiple ellipses
with the same central coordinates, axis ratio, and position angle as M81, but
with a regular change in size. The median flux for the area between two
adjacent ellipses is counted and converted into AB magnitude. When the median
flux at an outer area reaches the background uncertainty, we set the area as
the outermost part of the radial profiles. At a certain waveband, the
uncertainty in the radial profile is an orthogonal combination of the
background uncertainty, the calibration error, and the isophote fitting error.
We consider the error of isophote here because the ellipticity, the position
angle, and the central coordinates of M81 all come from the method of isophote
fitting.

A reduced chi square ($\chi^{2}_{\nu}$) is employed as a quantification of the
goodness of the fit and defined as follows:

$\chi_{\nu}^{2}=\frac{1}{N_{\mathrm{dof}}}\sum_{i=1}^{N_{\mathrm{data}}}\frac{\left(m_{\mathrm{data},i}-m_{\mathrm{model},i}\right)^{2}}{\sigma_{m,i}^{2}}~{},$
(A1)

where $N_{\mathrm{dof}}$ is the degrees of freedom; $N_{\mathrm{data}}$ is the
number of data points in the surface brightness profile; $m_{\mathrm{data}}$
and $m_{\mathrm{model}}$ represent the surface brightness (in units of
magnitude) for data and model at a certain radius, respectively; $\sigma_{m}$
is the error in the data.

Table A1: Multiwavelength Statistics of the Bulge as a Result of the
Decomposition

Telescope | Filter |  Wavelength (Å) |  Sérsic index ($n$) |  Effective radius ($R_{e}$) (arcsec) |  Flux denisity (mJy) |  Flux ratio (%)
---|---|---|---|---|---|---
_GALEX_ | FUV | 1516 |  0.92${}^{+0.01}_{-0.01}$ |  12.15${}^{+0.24}_{-0.09}$ |  0.75$\pm$0.02 |  0.53$\pm$0.02
_Swift_ | UVW2 | 1928 |  1.19${}^{+0.01}_{-0.01}$ |  22.99${}^{+0.17}_{-0.09}$ |  6.85$\pm$0.09 |  3.29$\pm$0.09
_GALEX_ | NUV | 2267 |  1.06${}^{+0.01}_{-0.01}$ |  23.66${}^{+0.08}_{-0.05}$ |  5.69$\pm$0.08 |  2.53$\pm$0.07
_Swift_ | UVW1 | 2600 |  1.66${}^{+0.04}_{-0.02}$ |  43.02${}^{+1.81}_{-1.07}$ |  37.84$\pm$0.51 |  10.73$\pm$0.29
SDSS | u | 3551 |  2.80${}^{+0.70}_{-0.70}$ |  82.40${}^{+45.94}_{-45.80}$ |  397.23$\pm$1.62 |  33.37$\pm$0.27
WIYN | B | 4331 |  3.14${}^{+0.57}_{-0.57}$ |  82.61${}^{+18.69}_{-18.70}$ | — | —
SDSS | g | 4686 |  3.36${}^{+0.48}_{-0.48}$ |  71.62${}^{+10.60}_{-10.60}$ |  1747.31$\pm$6.99 |  38.09$\pm$0.30
WIYN | V | 5500 |  3.94${}^{+0.71}_{-0.72}$ |  80.19${}^{+16.88}_{-16.89}$ | — | —
SDSS | r | 6166 |  3.92${}^{+0.75}_{-0.75}$ |  80.58${}^{+24.28}_{-24.46}$ |  3706.65$\pm$14.83 |  40.98$\pm$0.33
WIYN | R | 6425 |  3.84${}^{+0.62}_{-0.62}$ |  74.15${}^{+17.83}_{-17.84}$ | — | —
SDSS | i | 7480 |  3.80${}^{+1.38}_{-0.87}$ |  81.91${}^{+20.75}_{-24.98}$ |  5476.54$\pm$19.17 |  42.05$\pm$0.29
SDSS | z | 8932 |  4.78${}^{+1.35}_{-1.35}$ |  97.88${}^{+50.13}_{-50.13}$ |  7410.17$\pm$29.66 |  44.83$\pm$0.36
2MASS | J | 12000 |  4.91${}^{+1.33}_{-1.33}$ |  88.15${}^{+49.49}_{-48.49}$ |  9928.89$\pm$84.41 |  48.84$\pm$0.83
2MASS | H | 16000 |  4.52${}^{+1.54}_{-1.33}$ |  85.25${}^{+94.06}_{-49.90}$ |  12323.43$\pm$117.11 |  52.50$\pm$0.99
2MASS |  Ks | 22000 |  5.10${}^{+1.97}_{-1.66}$ |  83.86${}^{+97.06}_{-50.31}$ |  9284.47$\pm$88.25 |  47.18$\pm$0.90
_WISE_ |  W1 (3.4 $\mu$m) | 34000 |  3.87${}^{+0.64}_{-0.65}$ |  74.10${}^{+9.42}_{-9.42}$ |  4749.84$\pm$68.87 |  42.48$\pm$1.23
_Spitzer_ -IRAC |  I1 (3.6 $\mu$m) | 36000 |  4.10${}^{+1.04}_{-0.71}$ |  72.00${}^{+40.28}_{-39.53}$ |  4779.20$\pm$71.69 |  42.19$\pm$1.27
_Spitzer_ -IRAC |  I2 (4.5 $\mu$m) | 45000 |  4.84${}^{+0.80}_{-0.82}$ |  83.67${}^{+26.64}_{-27.30}$ |  2891.50$\pm$43.37 |  42.77$\pm$1.28
_WISE_ |  W2 (4.6 $\mu$m) | 46000 |  4.04${}^{+0.68}_{-0.68}$ |  72.23${}^{+11.14}_{-11.14}$ |  2600.69$\pm$44.21 |  40.76$\pm$1.38
_Spitzer_ -IRAC |  I3 (5.8 $\mu$m) | 58000 |  4.04${}^{+1.39}_{-1.14}$ |  124.79${}^{+61.10}_{-56.30}$ |  2549.24$\pm$53.24 |  44.20$\pm$1.34

  * •

Notes. — The columns from left to right represent the telescope name, the
filter name, the central wavelength for the filter, the Sérsic index, the
effective radius, the flux density, and the flux ratio.

Table A2: Multiwavelength Statistics of the Disk as a Result of the
Decomposition

Telescope | Filter |  Wavelength (Å) |  Sérsic index ($n$) |  Effective radius ($R_{e}$) (arcsec) |  Flux denisity (mJy) |  Flux ratio (%)
---|---|---|---|---|---|---
_GALEX_ | FUV | 1516 |  0.15${}^{+0.07}_{-0.03}$ |  442.01${}^{+24.62}_{-26.18}$ |  85.29$\pm$1.92 |  60.08$\pm$2.71
_Swift_ | UVW2 | 1928 |  0.29${}^{+0.03}_{-0.03}$ |  389.38${}^{+21.63}_{-19.20}$ |  176.80$\pm$2.39 |  84.87$\pm$2.29
_GALEX_ | NUV | 2267 |  0.20${}^{+0.01}_{-0.01}$ |  415.23${}^{+6.35}_{-5.65}$ |  202.47$\pm$2.73 |  90.21$\pm$2.44
_Swift_ | UVW1 | 2600 |  0.33${}^{+0.07}_{-0.05}$ |  361.72${}^{+29.48}_{-22.15}$ |  279.64$\pm$3.78 |  79.32$\pm$2.14
SDSS | u | 3551 |  0.42${}^{+0.03}_{-0.03}$ |  335.12${}^{+73.75}_{-73.53}$ |  606.29$\pm$2.44 |  50.94$\pm$0.41
WIYN | B | 4331 |  0.67${}^{+0.11}_{-0.12}$ |  309.56${}^{+38.59}_{-38.60}$ | — | —
SDSS | g | 4686 |  0.94${}^{+0.21}_{-0.20}$ |  296.86${}^{+35.59}_{-35.26}$ |  2735.09$\pm$10.94 |  59.62$\pm$0.48
WIYN | V | 5500 |  0.97${}^{+0.22}_{-0.16}$ |  272.53${}^{+21.10}_{-20.50}$ | — | —
SDSS | r | 6166 |  1.10${}^{+0.48}_{-0.36}$ |  278.13${}^{+68.45}_{-68.63}$ |  5244.50$\pm$20.98 |  57.99$\pm$0.46
WIYN | R | 6425 |  0.97${}^{+0.17}_{-0.17}$ |  281.13${}^{+34.88}_{-34.90}$ | — | —
SDSS | i | 7480 |  1.18${}^{+0.42}_{-0.24}$ |  273.86${}^{+68.45}_{-68.63}$ |  7532.75$\pm$26.37 |  57.84$\pm$0.40
SDSS | z | 8932 |  1.21${}^{+0.40}_{-0.37}$ |  244.20${}^{+62.18}_{-62.35}$ |  8918.78$\pm$35.69 |  53.96$\pm$0.43
2MASS | J | 12000 |  1.05${}^{+0.05}_{-0.05}$ |  194.65${}^{+34.94}_{-34.94}$ |  10512.44$\pm$89.37 |  51.71$\pm$0.88
2MASS | H | 16000 |  0.98${}^{+0.27}_{-0.30}$ |  191.40${}^{+44.45}_{-42.39}$ |  11252.15$\pm$106.94 |  47.94$\pm$0.91
2MASS |  Ks | 22000 |  1.10${}^{+0.29}_{-0.30}$ |  199.40${}^{+50.62}_{-50.37}$ |  10416.70$\pm$99.05 |  52.93$\pm$1.00
_WISE_ |  W1 (3.4 $\mu$m) | 34000 |  1.15${}^{+0.10}_{-0.10}$ |  258.56${}^{+2.72}_{-2.73}$ |  6279.24$\pm$91.05 |  56.15$\pm$1.62
_Spitzer_ -IRAC |  I1 (3.6 $\mu$m) | 36000 |  1.09${}^{+0.04}_{-0.08}$ |  247.47${}^{+4.15}_{-9.66}$ |  6349.69$\pm$95.25 |  56.06$\pm$1.68
_Spitzer_ -IRAC |  I2 (4.5 $\mu$m) | 45000 |  1.13${}^{+0.01}_{-0.09}$ |  236.58${}^{+10.82}_{-15.44}$ |  3773.05$\pm$56.60 |  55.81$\pm$1.67
_WISE_ |  W2 (4.6 $\mu$m) | 46000 |  1.18${}^{+0.12}_{-0.12}$ |  266.68${}^{+4.18}_{-4.17}$ |  3696.27$\pm$62.84 |  57.93$\pm$1.97
_Spitzer_ -IRAC |  I3 (5.8 $\mu$m) | 58000 |  0.50${}^{+0.41}_{-0.40}$ |  297.62${}^{+84.12}_{-84.60}$ |  4296.41$\pm$64.45 |  53.51$\pm$1.63

  * •

Notes. — This table is in the same format as Table A1

Figure A1: Results of the surface brightness fitting in the _GALEX_ FUV image.
The left panels show the observed (top panel), modeled (middle panel), and
residual (bottom panel) images. The top-right panels show the radial surface
brightness profiles of the observed galaxy and all of the components in the
model, with the best-fit curves superimposed. The bottom-right panel show the
comparison between the observed data and the model, and the gray dotted line
indicates the error. The legend is listed in the diagram. Figure A2: The same
as Figure A1 but in the _Swift_ UVW2 image. Figure A3: The same as Figure A1
but in the _GALEX_ NUV image. Figure A4: The same as Figure A1 but in the
_Swift_ UVW1 image. Figure A5: The same as Figure A1 but in the SDSS u image.
Figure A6: The same as Figure A1 but in the WIYN B image. Figure A7: The same
as Figure A1 but in the SDSS g image. Figure A8: The same as Figure A1 but in
the WIYN V image. Figure A9: The same as Figure A1 but in the SDSS r image.
Figure A10: The same as Figure A1 but in the WIYN R image. Figure A11: The
same as Figure A1 but in the SDSS i image. Figure A12: The same as Figure A1
but in the SDSS z image. Figure A13: The same as Figure A1 but in the 2MASS J
image. Figure A14: The same as Figure A1 but in the 2MASS H image. Figure A15:
The same as Figure A1 but in the 2MASS Ks image. Figure A16: The same as
Figure A1 but in the _WISE_ W1 image. Figure A17: The same as Figure A1 but in
the _Spitzer_ -IRAC I1 image. Figure A18: The same as Figure A1 but in the
_Spitzer_ -IRAC I2 image. Figure A19: The same as Figure A1 but in the _WISE_
W2 image. Figure A20: The same as Figure A1 but in the _Spitzer_ -IRAC I3
image.

##  Appendix B Products of the Multiwavelength Bulge-Disk Decomposition for
M81 with Equalized S/N

This appendix presents products of the multiwavelength bulge-disk
decomposition for M81 in the images with S/N reduced to an equal level,
corresponding to the description in Section 5.1. Morphological and flux
parameters for the bulge and the disk are listed in Tables B1 and B2,
respectively.

Table B1: Multiwavelength Statistics of the Bulge as a Result of the
Decomposition with the Equalized S/N

Telescope | Filter |  Wavelength (Å) |  Sérsic index ($n$) |  Effective radius ($R_{e}$) (arcsec) |  Flux denisity (mJy) |  Flux ratio (%)
---|---|---|---|---|---|---
_GALEX_ | FUV | 1516 |  0.97${}^{+0.21}_{-0.21}$ |  10.08${}^{+0.96}_{-0.96}$ |  0.68$\pm$0.02 |  0.48$\pm$0.02
_Swift_ | UVW2 | 1928 |  1.32${}^{+0.43}_{-0.43}$ |  25.24${}^{+10.36}_{-10.36}$ |  7.27$\pm$0.10 |  3.44$\pm$0.09
_GALEX_ | NUV | 2267 |  1.04${}^{+0.30}_{-0.30}$ |  24.23${}^{+2.34}_{-2.34}$ |  5.65$\pm$0.08 |  2.48$\pm$0.06
_Swift_ | UVW1 | 2600 |  1.93${}^{+0.23}_{-0.23}$ |  50.22${}^{+4.39}_{-4.39}$ |  42.68$\pm$0.58 |  12.03$\pm$0.32
SDSS | u | 3551 |  3.30${}^{+1.04}_{-1.04}$ |  109.13${}^{+75.69}_{-75.69}$ |  467.86$\pm$1.89 |  39.34$\pm$0.30
SDSS | g | 4686 |  3.86${}^{+0.48}_{-0.48}$ |  82.32${}^{+15.72}_{-15.72}$ |  1787.92$\pm$7.15 |  39.02$\pm$0.31
SDSS | r | 6166 |  4.55${}^{+1.14}_{-1.14}$ |  97.24${}^{+45.22}_{-45.22}$ |  3833.47$\pm$15.33 |  42.27$\pm$0.34
SDSS | i | 7480 |  4.40${}^{+1.38}_{-1.38}$ |  99.06${}^{+53.63}_{-53.63}$ |  5812.92$\pm$20.35 |  45.17$\pm$0.32
SDSS | z | 8932 |  4.85${}^{+1.35}_{-1.35}$ |  99.32${}^{+61.31}_{-61.31}$ |  7390.34$\pm$29.58 |  44.74$\pm$0.36
2MASS | J | 12000 |  4.87${}^{+1.35}_{-1.35}$ |  87.38${}^{+49.49}_{-49.49}$ |  9897.42$\pm$84.45 |  48.32$\pm$0.82
2MASS | H | 16000 |  4.49${}^{+1.54}_{-1.54}$ |  84.45${}^{+94.06}_{-94.06}$ |  12294.59$\pm$117.84 |  52.52$\pm$1.00
2MASS |  Ks | 22000 |  5.02${}^{+1.97}_{-1.97}$ |  81.25${}^{+97.06}_{-97.06}$ |  9157.23$\pm$87.04 |  46.34$\pm$0.88
_WISE_ |  W1 (3.4 $\mu$m) | 34000 |  4.21${}^{+1.33}_{-1.33}$ |  79.12${}^{+9.42}_{-9.42}$ |  4798.42$\pm$69.58 |  42.56$\pm$1.23
_Spitzer_ -IRAC |  I1 (3.6 $\mu$m) | 36000 |  4.91${}^{+1.04}_{-1.04}$ |  85.03${}^{+40.28}_{-40.28}$ |  4848.63$\pm$72.73 |  43.61$\pm$1.32
_Spitzer_ -IRAC |  I2 (4.5 $\mu$m) | 45 000 |  5.25${}^{+2.49}_{-2.49}$ |  95.50${}^{+71.90}_{-71.90}$ |  2964.83$\pm$44.47 |  43.97$\pm$1.32
_WISE_ |  W2 (4.6 $\mu$m) | 46000 |  4.78${}^{+0.83}_{-0.83}$ |  83.78${}^{+22.30}_{-22.30}$ |  2735.86$\pm$46.51 |  43.68$\pm$1.50

  * •

Notes. — This table is in the same format as Table A1.

Table B2: Multiwavelength Statistics of the Disk as the Result of the
Decomposition with the Equalized S/N

Telescope | Filter |  Wavelength (Å) |  Sérsic index ($n$) |  Effective radius ($R_{e}$) (arcsec) |  Flux denisity (mJy) |  Flux ratio (%)
---|---|---|---|---|---|---
_GALEX_ | FUV | 1516 |  0.15${}^{+0.07}_{-0.07}$ |  438.13${}^{+26.62}_{-26.62}$ |  104.95$\pm$2.36 |  74.01$\pm$2.91
_Swift_ | UVW2 | 1928 |  0.23${}^{+0.11}_{-0.11}$ |  390.81${}^{+37.82}_{-37.82}$ |  186.68$\pm$2.52 |  88.43$\pm$2.30
_GALEX_ | NUV | 2267 |  0.19${}^{+0.01}_{-0.01}$ |  415.40${}^{+6.35}_{-6.35}$ |  207.15$\pm$2.80 |  90.73$\pm$2.37
_Swift_ | UVW1 | 2600 |  0.29${}^{+0.07}_{-0.07}$ |  354.56${}^{+67.75}_{-67.75}$ |  289.71$\pm$3.91 |  81.64$\pm$2.14
SDSS | u | 3551 |  0.42${}^{+0.27}_{-0.27}$ |  354.56${}^{+67.95}_{-67.95}$ |  609.79$\pm$2.46 |  51.27$\pm$0.39
SDSS | g | 4686 |  1.08${}^{+0.21}_{-0.21}$ |  293.42${}^{+41.39}_{-41.39}$ |  2750.00$\pm$11.10 |  60.02$\pm$0.48
SDSS | r | 6166 |  1.20${}^{+0.48}_{-0.48}$ |  270.39${}^{+68.63}_{-68.63}$ |  5166.37$\pm$20.99 |  56.96$\pm$0.45
SDSS | i | 7480 |  1.21${}^{+0.42}_{-0.42}$ |  262.25${}^{+68.63}_{-68.63}$ |  7223.63$\pm$26.38 |  56.13$\pm$0.40
SDSS | z | 8932 |  1.21${}^{+0.40}_{-0.40}$ |  243.73${}^{+63.77}_{-63.77}$ |  9008.18$\pm$36.05 |  54.53$\pm$0.43
2MASS | J | 12000 |  1.04${}^{+0.14}_{-0.14}$ |  195.68${}^{+34.94}_{-34.94}$ |  10591.24$\pm$90.04 |  51.71$\pm$0.88
2MASS | H | 16000 |  0.97${}^{+0.30}_{-0.30}$ |  191.26${}^{+44.45}_{-42.39}$ |  11268.25$\pm$107.09 |  48.13$\pm$0.92
2MASS |  Ks | 22000 |  1.10${}^{+0.33}_{-0.30}$ |  200.45${}^{+39.08}_{-39.08}$ |  10547.83$\pm$100.24 |  53.88$\pm$1.01
_WISE_ |  W1 (3.4 $\mu$m) | 34000 |  1.20${}^{+0.12}_{-0.12}$ |  252.75${}^{+10.16}_{-10.16}$ |  6306.34$\pm$91.44 |  55.94$\pm$1.61
_Spitzer_ -IRAC |  I1 (3.6 $\mu$m) | 36000 |  1.19${}^{+0.08}_{-0.08}$ |  239.46${}^{+11.92}_{-11.92}$ |  6402.18$\pm$96.03 |  57.58$\pm$1.74
_Spitzer_ -IRAC |  I2 (4.5 $\mu$m) | 45000 |  1.13${}^{+0.31}_{-0.31}$ |  232.40${}^{+15.16}_{-15.16}$ |  3749.87$\pm$56.75 |  55.61$\pm$1.67
_WISE_ |  W2 (4.6 $\mu$m) | 46000 |  1.20${}^{+0.12}_{-0.12}$ |  258.38${}^{+9.97}_{-9.97}$ |  3596.17$\pm$62.88 |  57.42$\pm$1.97

  * •

Notes. — This table is in the same format as Table A1.

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