# A Dynamic Galaxy: Stellar Age Patterns Across the Disk of M101

Ray Garner, III  Department of Astronomy, Case Western Reserve University,
10900 Euclid Avenue, Cleveland, OH 44106, USA  Department of Physics and
Astronomy, Texas A&M University, 578 University Drive, College Station, TX,
77843, USA  J. Christopher Mihos  Department of Astronomy, Case Western
Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA  Paul
Harding  Department of Astronomy, Case Western Reserve University, 10900
Euclid Avenue, Cleveland, OH 44106, USA  Charles R. Garner, Jr  Rockdale
Magnet School for Science and Technology, 930 Rowland Road, Conyers, GA,
30012, USA

###### Abstract

Using deep, narrowband imaging of the nearby spiral galaxy M101, we present
stellar age information across the full extent of the disk of M101. Our
narrowband filters measure age-sensitive absorption features such as the
Balmer lines and the slope of the continuum between the Balmer break and
$4000\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ break. We interpret these
features in the context of inside-out galaxy formation theories and dynamical
models of spiral structure. We confirm the galaxy’s radial age gradient, with
the mean stellar age decreasing with radius. In the relatively undisturbed
main disk, we find that stellar ages get progressively older with distance
across a spiral arm, consistent with the large-scale shock scenario in a
quasi-steady spiral wave pattern. Unexpectedly, we find the same pattern
across spiral arms in the outer disk as well, beyond the corotation radius of
the main spiral pattern. We suggest that M101 has a dynamic, or transient,
spiral pattern with multiple pattern speeds joined together via mode coupling
to form coherent spiral structure. This scenario connects together the radial
age gradient inherent to inside-out galaxy formation with the across-arm age
gradients predicted by dynamic spiral arm theories across the full radial
extent of the galaxy.

††software: Astropy (Astropy Collaboration et al., 2013, 2018), Matplotlib
(Hunter, 2007), NumPy (Harris et al., 2020), cigale (Noll et al., 2009;
Boquien et al., 2019), SciPy (Virtanen et al., 2020), piecewise-regression
(Pilgrim, 2021), SAOImage ds9 (Joye & Mandel, 2003), Phyla/adjustText (Flyamer
et al., 2023)

patch/longtable=false possessive’s’s mfirst#1 ewshort=EW, long=equivalent
width 2massshort=2MASS, long=Two Micron All Sky Survey cigaleshort=cigale,
long=Code Investigating GALaxy Emission sfrshort=SFR, long=star formation rate
psfshort=PSF, long=point spread function agnshort=AGN, long=active galactic
nucleus, long-plural-form=active galactic nuclei XUVshort=XUV, long=extended-
UV sfeshort=SFE, long=star formation efficiency lsbshort=LSB, long=low surface
brightness ismshort=ISM, long=interstellar medium sdssshort=SDSS, long=Sloan
Digital Sky Survey cwrushort=CWRU, long=Case Western Reserve University
digshort=DIG, long=diffuse ionized gas ifsshort=IFS, long=integral field
spectroscopy imfshort=IMF, long=initial mass function sfhshort=SFH, long=star
formation history, long-plural-form=star formation histories igmshort=IGM,
long=intergalactic medium hstshort=_HST_ , long=_Hubble Space Telescope_
sedshort=SED, long=spectral energy distribution galexshort=_GALEX_ ,
long=_Galaxy Evolution Explorer_

##  1 Introduction

Spiral galaxies are believed to have formed “inside-out,” that is the inner
parts of galactic disks form first followed by the formation of their outer
regions (e.g. White & Frenk, 1991; Mo et al., 1998). One notable consequence
of inside-out formation is a radial variation in the star formation history,
and thus stellar ages, of a spiral galaxy. These have been primarily observed
as a color gradient in the disk, in that inner regions appear redder (older)
than the bluer (younger) outer regions (e.g. de Jong, 1996; Bell & de Jong,
2000; MacArthur et al., 2004). Complicating this picture are non-axisymmetric
structures in the disk, such as spiral arms, that both radially scatter stars
(e.g. Sellwood & Binney, 2002; Roškar et al., 2008a, b) and imprint azimuthal
variations in the stellar age distribution (e.g. Dixon, 1971; Dobbs & Pringle,
2010; Chandar et al., 2017).

Understanding the nature and creation mechanism of spiral structure in
galaxies is still a fundamental problem in astronomy. We lack a complete, and
widely accepted, theory for the origin of spiral patterns. Many spiral
galaxies have structure driven by non-axisymmetric effects, whether that be
caused by external interactions with a companion (Kormendy & Norman, 1979;
D’Onghia et al., 2016; Pettitt et al., 2016) or by internal responses to a
centrally rotating bar (Contopoulos & Papayannopoulos, 1980; Athanassoula,
1992). There is also the possibility that some spiral structure is self-
excited. Broadly speaking there are two possible mechanisms for self-
excitation. First, there is the “density wave theory” that argues spiral
structure is the result of a quasi-steady, global mode in the stellar disk
(Lin & Shu, 1964; Bertin et al., 1989). Second, there is the suggestion that
spiral structure is caused by transient and recurrent instabilities resulting
in “dynamic” spiral arms that appear and reappear in cycles (Toomre, 1964;
Sellwood & Carlberg, 1984; Elmegreen & Elmegreen, 1986; Sellwood & Kahn,
1991). We will refer the interested reader to any number of reviews on spiral
mechanisms for more detailed information (e.g. Dobbs & Baba, 2014; Shu, 2016;
Sellwood & Masters, 2022).

Figure 1: Schematic of the shock scenario posited by Roberts (1969). Stellar
age gradients across the spiral arms are indicated by arrows that go from blue
to red. The azimuthal age gradients are produced by stars born in the spiral
shock, where the shocked interstellar medium forms a dust lane, and later
drift away as they age. The direction of the gradients flips at the corotation
radius. Inside corotation, the gas and stars overtake the spiral pattern, and
outside corotation the spiral pattern overtakes the gas and stars.

Clearly there are multiple spiral pattern generation mechanisms and we must
turn to observations and simulations of spiral galaxies to inform us which is
the primary mechanism. However, as highlighted by Sellwood (2011), it is very
difficult to find observational tests to distinguish between these theoretical
models. As an example, in the standard density wave theory, spiral arms are
density waves moving with a constant pattern speed. Inside corotation (the
radius at which the angular speed of stars and gas equals the pattern speed),
material will rotate faster than the spiral pattern. When gas enters the
spiral pattern, it may experience a shock and collapse to form stars (Roberts
1969; Shu et al. 1972; see McKee & Ostriker 2007 and references therein for an
extensive discussion of the theory). As these stars age, they overtake the
more slowly rotating spiral pattern, drifting away from their birth sites and
creating an azimuthal age gradient across the spiral arm (Figure 1; also
Figure 1 in Martínez-García et al. 2009). We would then expect to find young
star clusters near the spiral arm along the leading edge and older stars
further along, approaching the trailing side of the next spiral arm. Outside
of corotation, the spiral pattern moves faster than the gas and the opposite
sequence occurs (Dixon, 1971).

Numerous simulations have been performed in recent years to test this theory.
For example, Dobbs & Pringle (2010) found that in galaxies with a constant
pattern speed, a clear age sequence across spiral arms from young to old stars
is expected. This pattern was absent in dynamic and tidally-disturbed
galaxies. Subsequent simulations with more advanced hydrodynamical modeling
have confirmed the case for the latter pair of spiral arm mechanisms (Wada et
al., 2011; Grand et al., 2012; D’Onghia et al., 2013; Baba et al., 2015, 2017;
Dobbs et al., 2017; Pettitt et al., 2017). Observationally, evidence of the
large-scale shock scenario is hard to come by except in a few cases. Martínez-
García et al. (2009) studied color gradients across the spiral arms of
thirteen spiral galaxies, ten of which had the expected color gradient. They
have since found color gradients for a few more galaxies (Martínez-García &
González-Lópezlira, 2011, 2015). Similarly, Sánchez-Gil et al. (2011) produced
age maps of six nearby galaxies using the H$\alpha$/FUV flux ratio, only two
of which (M74 and M100) presented an age gradient across spiral arms.
Investigating resolved stellar clusters in three galaxies, Abdeen et al.
(2022) found evidence of the expected age gradients in galaxies where others
have not. Simply put, with the exception of a handful of specific cases, there
is no clear systematic trend in the observations.

Some of the observational ambiguity likely comes from the wide use of
broadband colors to discern age gradients. The well-known age-metallicity
degeneracy (Worthey, 1994), which combined with the reddening effects of dust,
blurs the conclusions made with color gradients. Spectroscopy gives the
ability to break this degeneracy by resolving multiple age- and metallicity-
sensitive absorption features. However spectroscopy becomes prohibitively
expensive to measure the lsb outskirts of disk galaxies. For nearby galaxies
with large angular sizes—where we can resolve physically small scales—most
integral field units are also not large enough to cover the whole galaxy
without resource-intensive mosaicing techniques.

Another alternative to broadband photometry is narrowband photometry,
particularly observations targeting age-diagnostic absorption features like
the Balmer lines, the $4000\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ break, or
metallic lines such as Mg b. Pioneering narrowband work has been performed for
spiral galaxies (Beauchamp & Hardy, 1997; Mollá et al., 1999; Ryder et al.,
2005) and modern narrowband photometry can measure absorption line strengths
that are compatible with spectroscopy (Stothert et al., 2018; Angthopo et al.,
2020; Renard et al., 2022). Absorption line ew are largely insensitive to dust
effects (MacArthur, 2005) and, combined with stellar population synthesis
modeling, have been used to investigate luminosity-weighted stellar ages in
integrated stellar populations (e.g. Fisher et al., 1995; Ganda et al., 2007;
Sánchez-Blázquez et al., 2014a, b)

In an effort to study stellar ages and their connection to the nature of
spiral patterns, we have used cwru Burrell Schmidt 24/36-inch telescope and
its accompanying narrowband filters to image the nearby spiral galaxy M101
(NGC 5457). While these images targeting H$\alpha$, H$\beta$, [O
III]$\lambda\lambda$4959,5007 and [O II]$\lambda\lambda$3726,3729 have been
used to study the emission line properties of M101 and its group environment
(Watkins et al., 2017; Garner et al., 2021, 2022), these images also reveal
age-diagnostic absorption signatures in the stellar disk of M101 (Figure 2).
Thus, by measuring equivalent widths through our narrowband filters, we are
able to place constraints on the stellar ages throughout M101’s disk.

M101 was chosen for this survey because its nearby distance
($D=$6.9\text{\,}\mathrm{Mpc}$$; see Matheson et al. 2012 and references
therein) enables its properties to be studied in great detail at high spatial
resolution. Indeed, Lin et al. (2013) performed a pixel-based multiwavelength
sed fitting and broadly found that M101 supports the inside-out disk growth
scenario with detections of radial stellar age and metallicity gradients. The
disk of M101 also has a dynamic nature: it has strong morphological
asymmetries (e.g. Beale & Davies, 1969), complex H I kinematics (e.g. Waller
et al., 1997; Mihos et al., 2012; Xu et al., 2021), a Type I XUV disk (Thilker
et al. 2007), and faint tidal features to the northeast and east (Mihos et
al., 2013, 2018). These are all likely signatures of an interaction M101 had
with its most massive satellite NGC 5474 about $300\text{\,}\mathrm{Myr}$ ago
(Linden & Mihos, 2022). Thus M101 provides an interesting, albeit often
overlooked, testing ground for the varying roles of self-excited spiral
patterns and tidally-induced spiral patterns.

##  2 Narrowband Observations

The narrowband imaging data for this project was taken over four observing
seasons using cwru Astronomy’s 24/36-inch Burrell Schmidt telescope located at
Kitt Peak Observatory. Full details of our narrowband imaging techniques are
given in Watkins et al. (2017) and Garner et al. (2022). Quantitative
information about the narrowband filters and final imaging stacks for the
dataset is given in Table 2 of Garner et al. (2022). Briefly, we summarize our
observations here.

Our dataset consists of a set of narrow on-band filters
($\Delta\lambda\approx$ $80100\text{\,}\mathrm{\SIUnitSymbolAngstrom}$)
centered on the redshifted emission lines H$\alpha$$\lambda$6563,
H$\beta$$\lambda$4861, [O III]$\lambda\lambda$4959,5007, and [O
II]$\lambda\lambda$3727,3729. To measure the adjacent stellar continuum for
each line, we also observed M101 in narrow off-band filters shifted in
wavelength by $\approx$$100150\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ from
each on-band filter. The Burrell Schmidt images a $$$\times$$$ field of view
onto a $4096\times 4096$ back-illuminated CCD, yielding a pixel scale of
$1.45\text{\,}\mathrm{arcsec}\text{\,}{\mathrm{pixel}}^{-1}$. In each filter,
we took $5070$ $1200\text{\,}\mathrm{s}$ images of the galaxy, randomly
dithering the telescope by $1030\text{\,}\mathrm{arcmin}$ between exposures.
Both twilight flats and night sky flats were taken throughout each observing
run, as were images of spectrophotometric standards and bright stars to assist
with photometric calibration and scattered light modeling, respectively.

All observed images are treated to the data reduction procedures described by
Watkins et al. (2017) and Garner et al. (2022). Namely, the steps are as
follows: (1) subtractions of bias frame; (2) flat-field correction; (3)
removal of scattered light from bright stars following the technique of Slater
et al. (2009); (4) registration of stacked images; (5) flux calibration of the
stacked images. We flux calibrated the final image stacks using a variety of
techniques: (1) deriving a photometric solution from observations of Massey et
al. (1988) spectrophotometric standard stars, (2) measuring zeropoints from
$ugr$ magnitudes of the $\sim$150 stars in the M101 field from the sdss, and
(3), where possible, synthesizing narrowband magnitudes using sdss
spectroscopy of $\sim$100 point sources in the M101 field. These different
techniques yielded flux zeropoints that agreed to within
$\pm$$5\text{\,}\mathrm{\char 37\relax}$, which we take to be the absolute
flux uncertainties in the data.

Previously we used these narrowband images of M101 and its group environment
to investigate emission-line sources, whether those be in the intragroup
environment (Garner et al., 2021) or within the disk of M101 and its
satellites (Watkins et al., 2017; Garner et al., 2022). However the level of
precision and accuracy of our imaging and reduction techniques reveals
absorption signatures in the images, particularly in the H$\beta$ and [O II]
continuum-subtracted images. We focus on these two images out of our
narrowband dataset since our [O III] filters do not sample any strong stellar
absorption features and while trends in H$\alpha$ absorption are similar to
the H$\beta$ absorption, H$\alpha$ absorption is less sensitive to age than
H$\beta$ (e.g. González Delgado et al., 2005). Figure 2 shows the H$\beta$ and
[O II] continuum-subtracted images, and within the disk of M101 darker regions
are present. We stress that this is not incorrect off-band over-subtraction in
our data reduction techniques, but rather the presence of absorption
signatures caused by the underlying older stellar population.

Figure 2: (a) The continuum-subtracted H$\beta$ image. (b) The continuum-
subtracted [O II] image. Images are scaled in such a way that emission-line
objects are in white and absorption features are in black. Note the strong
absorption features in the disk of M101. The satellite galaxy NGC 5477 is
marked to the left and a scale bar is provided. The image measures
$$$\times$$$. North is up and east is to the left.

In order to focus only on features in the stellar continuum, we need to mask
both foreground stars and strong emission line H II regions in M101. We follow
the techniques described by Garner et al. (2022) to remove foreground Milky
Way stars from our images. We masked those stars in the Tycho-2 Catalog (Høg
et al., 2000) brighter than $B_{T}=12.5$. All of these stars lie projected
outside of the disk of M101. For fainter stars, we used the 2mass All-Sky
Catalog of Point Sources (Skrutskie et al., 2006). We aggressively mask these
stars using $None$ apertures (roughly three times the FWHM of the PSF of the
coadded image stacks). To mask H II regions, we used the segmentation map
produced by Garner et al. (2022) which used astropy’s PhotUtil package and its
segmentation module (Bradley et al., 2023) to identify bright H II regions
using the continuum-subtracted H$\alpha$ image. Finally, we also mask the
nearby satellite galaxy NGC 5477, visible in our images projected $None$ or
$44\text{\,}\mathrm{kpc}$ to the east.

We note that although we have masked the brightest portions of the strongly
emitting H II regions, there is still scattered emission and dig in our
images. Briefly, scattered emission refers to light from bright H II regions
scattered towards the observer by interstellar dust particles in M101’s disk
regardless of the ionization state of the gas (e.g. Brandt & Draine 2012 and
references therein), while the dig refers to the warm, low density, ionized
component of the ism (ism; see Haffner et al. 2009 and references therein).
The dig has a varying presence throughout a galaxy, and so we correct for the
dig using the approach of Vale Asari et al. (2019). They separate the dig from
normal star-forming regions on the basis of the measured H$\alpha$ ew. Thus
the required correction as prescribed by Equation 2 of Vale Asari et al.
(2019) is $\sim$$5\text{\,}\mathrm{\char 37\relax}$ in all of our narrowband
observations, which we apply to our data. There is no similar correction for
scattered light, but this will be strongest near H II regions which we have
aggressively masked.

Figure 3: The radial profiles of the median stellar ew measured through our
H$\beta$ and [O II] filters, $W_{\mathrm{H}\beta}$ and $W_{3746}$,
respectively. Radial bins have widths of $1\text{\,}\mathrm{kpc}$ ($None$).
The error bars indicate the quartile scatter of the ew measured in each radial
bin.

As an example of the extent and depth of our data, Figure 3 shows the binned
radial profiles of the median stellar ew (after masking H II regions) measured
through our H$\beta$ and [O II] filters, $W_{\mathrm{H}\beta}$ and $W_{3746}$,
respectively, out to $30\text{\,}\mathrm{kpc}$ ($None$).111We note that
$W_{3746}$ is named for the central wavelength of the on-band filter, not for
the equivalent width of any individual absorption line. Importantly, the error
bars are dominated by physical scatter in data rather than measurement error.
The H$\beta$ ew, $W_{\mathrm{H}\beta}$, shows a negative gradient out to
$R\sim$10\text{\,}\mathrm{kpc}$$, beyond which it flattens and the [O II] ew,
$W_{3746}$, shows a negative gradient out to $R\sim$5\text{\,}\mathrm{kpc}$$,
similarly flattening beyond this radius. Interpretation of these trends is
simplest for the $W_{\mathrm{H}\beta}$, with the presence of A-type stars
increasing with radius, subsequently deepening the H$\beta$ absorption line,
although the scatter at large radius might suggest the presence of younger
populations. However, the interpretation of the ew measured through the [O II]
filters is less straightforward and motivates more detailed spectral modeling.
Additionally, the large variance in ew in the outer disk motivates treating
the main and outer disks separately, where in the main disk we can explore any
trends with respect to morphological environments.

##  3 Defining Environments Within M101’s Disk

Our goal is to construct morphological, environmental masks to allow us to
study the stellar ages of different regions in M101’s disk. In order to
outline stellar structures, we utilize the broadband $B$ image of M101 (Mihos
et al., 2013). In the following, we define several basic environments that are
included in the masks: inner disk, spiral arms and interarm regions, and the
main and outer disks.

###  3.1 The Inner Disk

In traditional photometric decompositions of galaxies, the exponential disk is
usually distinguished from a central bulge component. Additionally, some
galaxies have unresolved or marginally resolved stellar structures that are
centrally concentrated. Some of these structures might be an unresolved
nuclear bar, a nuclear ring, or a nuclear disk. Finally, at small radii,
spiral arms and their interarm regions become increasingly hard to define in
an objective manner.

In the specific case of M101, its morphological classification is that of a
spiral galaxy without a large classical bulge (SAB(rs)c; Buta et al. 2015). It
is known to have a mildly star-forming pseudobulge (Fisher et al., 2009;
Fisher & Drory, 2010; Kormendy et al., 2010) with an effective radius of
$372\pm 436\text{\,}\mathrm{pc}$ ($$$\pm$$$; Fisher & Drory 2010). While other
studies have resolved and studied the stellar age of the pseudobulge and
surrounding region (Lin et al., 2013), since our focus is on the spiral arms
and interarm regions, we visually define an inner disk region of $None$
($4\text{\,}\mathrm{kpc}$). This encompasses the pseudobulge and the region
where the spiral arms become so tightly wrapped they are hard to define. We
note that this is much larger than what studies of morphological features have
considered to be the central region, often $<$$$ (Lin et al., 2013; Querejeta
et al., 2021).

###  3.2 Spiral Arms and Interarm Regions

In general, logarithmic spirals are good approximations to the shape of
galactic spiral arms (Seigar & James, 1998). Ubiquitous throughout nature,
logarithmic spirals are easy to mathematically define (see Section 2 of Davis
et al. 2017), but defining in a robust sense where spiral arms are in a galaxy
is more difficult. Over the years, numerous methods have been presented in the
literature to define spiral arms and estimate their pitch angles (see Hewitt &
Treuthardt 2020 and references therein). These methods, while useful for large
surveys due to their (semi-)automation, each come with their own issues. For
instance, some methods may not always trace real three- or four-armed spiral
patterns in galaxies, nor do they handle asymmetric arms well (Elmegreen et
al., 1992). These methods also generally only model one global pitch angle for
a galaxy, rather than accurately define a more complicated spiral pattern.

Since our focus is on M101 and its strongly asymmetric spiral pattern, we
forego these automated methods and instead adopt a different approach based on
the visual inspection of the spiral arms. This allows for multiple pitch
angles at different radii in M101, and takes into account that those pitch
angles will be asymmetrical with respect to the galaxy center. Thus we follow
a semi-automatic procedure developed by the S4G (Sheth et al., 2010) and
PHANGS (Lee et al., 2022) teams in Herrera-Endoqui et al. (2015) and Querejeta
et al. (2021), respectively. We briefly summarize those procedures and our
slight modifications here.

First we create an unsharp mask using the $B$-band image from Mihos et al.
(2013). This is done by convolving the image with a Gaussian kernel and then
dividing the original image with the smooth convolved image (Malin, 1977). The
width of the Gaussian kernel was chosen to be 30 pixels ($None$). This unsharp
mask highlights the spiral features in the disk of M101. Points along each
spiral arm are marked in SAOImage ds9 (Joye & Mandel, 2003) and their
coordinates are then transformed into logarithmic polar coordinates,
$(\ln(r),\theta)$, where true logarithmic spirals appear as straight lines.

Figure 4: An illustration of the steps of our spiral arm detection method. Top
left: the unsharp, masked $B$-band image. Points were marked on this image to
define the spiral arms. Top right: the unsharp, masked $B$-band image in log-
polar coordinates. The different colored points and lines show the spiral arm
segments that were fitted with different pitch angles. Bottom left: the masked
$B$-band image with the spiral arm segments overlaid on top. Bottom right: an
illustrative schematic of the morphological masks used. The black circle marks
the boundary between the main and outer disk at $None$
($14.4\text{\,}\mathrm{kpc}$). See text.

It is here that we deviate slightly from previous works. To allow for the
pitch angle to vary as a function of radius, we start by making a preliminary
visual estimate of the arm segments in log-polar coordinates. We then pass
these starting values into our code to refine the number of break points in
the data. The positions of those break points are estimated iteratively using
the break-fitting method outlined in Muggeo (2003) and implemented with the
Python package piecewise-regression (Pilgrim, 2021). The algorithm randomly
generates a series of break points and fits a model of a line with a term that
incorporates a change in gradient between some number of segments of a
piecewise function. Using ordinary linear regression and bootstrap resampling
(Wood, 2001), this process is iterated until the position of the break
converges. The results of this semi-automatic process are then projected back
into the plane of the sky.

We then need to define a width of each of our spiral arms. Since we want to
differentiate between the star-forming spiral arms and the less active
interarm regions, we use the continuum-subtracted H$\alpha$ image to
iteratively dilate the spiral arm until the measured H$\alpha$ flux within the
arm reaches an empirical threshold following the procedure outlined in
Querejeta et al. (2021). This process results in widths of
$2\text{\,}\mathrm{kpc}$ to $2.5\text{\,}\mathrm{kpc}$, encompassing most of
the H$\alpha$ emission that one would associate with an arm by eye.

Finally, we defined the interarm regions. For simplicity, the interarm regions
are simply any part of the galaxy not in the spiral arms or inner disk. This
does include the extreme outer disk of M101 where there are no spiral arms but
still low levels of star formation. Figure 4 shows the spiral arm and interarm
masks, as well as an illustration of the process described above.

###  3.3 Main and Outer Disks

In addition to the morphological masks described above, we also make a
distinction between the main and outer disks of M101. This is motivated by two
reasons. First, the outer disk of M101 has structures that are quite irregular
and likely tidally-induced in nature while the main disk is relatively
ordered. We would then expect the outer disk to be more disorganized in terms
of any stellar age gradients. Second, the high surface brightness main disk
has higher signal-to-noise than the outer disk, and, unlike the outer disk,
can be studied without the need for large-scale rebinning of the pixel data.
While both disk regions will be analyzed in similar ways, the low surface
brightness of the outer disk requires a different treatment to build up
signal.

Therefore we define a boundary of $None$ ($14.4\text{\,}\mathrm{kpc}$),
roughly three times the disk scale length (Mihos et al., 2013; Watkins et al.,
2017). We define the main disk to be inside this boundary, including the inner
disk and portions of the spiral arms and interarm regions. We define the outer
disk to be outside this boundary to a radius of $None$
($30.8\text{\,}\mathrm{kpc}$). The maximum radius was chosen to represent
where the sky noise starts to dominate in our images. This is also
approximately the outermost radius at which H II regions were detected in
Garner et al. (2022).

Finally, in order to maximize the signal-to-noise in our images, we create a
binned version of our narrowband images. Using the masked images, for studying
the main disk we bin the image into $9\times 9$ pixel ($$$\times$$$ or
$$450\text{\,}\mathrm{pc}$\times$450\text{\,}\mathrm{pc}$$) blocks,
calculating the median intensity of unmasked pixels in each block. In order to
quantify uncertainties for each of these blocks, we also calculate the
uncertainty estimate of the median (Rider, 1960; Williams, 2001),

$\sigma_{\text{median}}=\sigma_{\text{mean}}\sqrt{\frac{\pi}{2}}=\text{std}\sqrt{\frac{\pi}{2N}},$
(1)

where std is the standard deviation, $N$ is the number of pixels in a block,
and $\sigma_{\text{mean}}$ is the uncertainty in the mean. However, when
studying the outer disk, we bin over much larger scales described later in
Section 6. It is from these medianed blocks that we calculate fluxes and ew in
each of the environments described above. In order to further maximize the
signal-to-noise, in the main disk region we reject low signal-to-noise pixels
at a threshold that corresponds to a surface brightness of roughly
$\mu_{B}=$23.6\text{\,}\mathrm{mag}\text{\,}{\mathrm{arcsec}}^{-2}$$.

##  4 Inferring Ages with Absorption Lines

To connect our measured narrowband imaging to the underlying stellar
populations, we utilize the SED fitting and modeling cigale (cigale; Noll et
al. 2009; Boquien et al. 2019). To illustrate how our filters span various
spectral features, Figure 5 shows the sed of an instantaneous burst of star
formation with solar metallicity that evolves to late times as generated with
cigale. Two broad spectral features are covered by our filters: individual
Balmer lines in both the H$\beta$ and [O II] filters, and in the [O II] filter
the slope of the blue continuum between the Balmer break at
$3646\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ and the
$4000\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ break, produced primarily by A/F
and O/B stars, respectively. It is important to note that we cannot make a
standard $D_{4000}$ measurement as both of our [O II] filters are bluer than
the wavelengths typically used for the $D_{4000}$ measurement (Bruzual, 1983;
Balogh et al., 1999).

Figure 5: The spectral energy distribution of an instantaneous burst of star
formation at solar metallicity and with a Chabrier (2003) IMF, increasing in
age from top to bottom: $1\text{\,}\mathrm{Myr}$, $10\text{\,}\mathrm{Myr}$,
$100\text{\,}\mathrm{Myr}$, $400\text{\,}\mathrm{Myr}$,
$1\text{\,}\mathrm{Gyr}$, $4\text{\,}\mathrm{Gyr}$, and
$13\text{\,}\mathrm{Gyr}$. Left: the [O II] filter set. Right: the H$\beta$
filter set. In both panels, the on-band is darker than the off-band. sed
created with cigale (Noll et al., 2009; Boquien et al., 2019).

Our H$\beta$ filters are most sensitive to the strengths of their respective
Balmer lines, while our [O II] filters are sensitive to the strengths of the
higher-order Balmer lines, and the slope of the continuum between the Balmer
break and the $4000\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ break.
Fortuitously, the H$\beta$ filters are positioned in such a way that they
avoid measuring the nearby metallic lines, which reduces the chance of any
secondary metallicity effects in the Balmer lines. On the other hand, the [O
II] filters act as a sort of “pseudo-measurement” of the Balmer break and the
$4000\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ break, targeting no specific
feature but sensitive to all of them. This motivates the need for stellar
population modeling to understand how populations of different ages,
metallicities, dust absorption, etc., behave through our filters.

###  4.1 Stellar Population Parameters

In order to understand how the narrowband spectral features progress with age
and what stellar population parameters they are sensitive to, we created a
grid of model sfh using cigale. While cigale is most commonly used to fit the
observed multiwavelength sed of galaxies, we instead use cigale as a simple
spectral synthesis code to model the observed ew in each filter pair under a
variety of sfh. In this way, we can use our understanding of the models to
inform our understanding of the dataset. In the following, we describe the
parameters that we investigated. The input parameters and their values used
are listed in Table 1. cigale uses theoretical models to parameterize the flux
emitted and absorbed by the stars, gas, and dust in model galaxies and
produces a grid of model spectra that are then converted to sed. Boquien et
al. (2019) describes the input models in complete detail, and we briefly
review each chosen component and its contribution.

To build a model galaxy sed, we first need to define the properties of the
underlying stellar population in terms of an assumed stellar population
synthesis model, an imf, and sfh. We adopt here in all models the high-
resolution version of the Bruzual & Charlot (2003) stellar population
synthesis models. We also adopt the Chabrier (2003) imf with solar metallicity
($Z_{\odot}=0.02$). While M101’s average stellar metallicity is somewhat
subsolar ($Z=$0.5\pm 0.3\text{\,}\mathrm{\mbox{$Z_{\odot}$}}$$; Lin et al.
2013), the relative insensitivity of the line strengths to metallicity in our
filters make this a reasonable choice. However, we do investigate the effect
of subsolar ($Z=0.008$, $0.4Z_{\odot}$) and supersolar ($Z=0.05$,
$2.5Z_{\odot}$) metallicities on the generated models in the next section.

Table 1: Input Parameters for SED Model Grid  Parameter | Symbol | Range
---|---|---
IMF: Chabrier (2003) |  |
Metallicity | $Z$ |  $0.0080.020.05$
Redshift | $z$ |  $0.0008$
SFH: sfh2exp |  |
Age of main population | $t$ |  $0.010.020.030.040.050.060.070.080.090.010.010.010.010.010.010.010.010.010.010.020.020.020.020.020.020.020.020.020.020.030.030.030.030.030.030.030.030.030.030.040.040.040.040.040.040.040.040.040.040.050.050.050.050.050.050.050.050.050.05\text{\,}\mathrm{Gyr}$
$e$-folding timescale of main population | $\tau$ |  $0.10.30.512345100.10.10.1\text{\,}\mathrm{Gyr}$
Age of a recent burst | $t_{b}$ |  $1050100500\text{\,}\mathrm{Myr}$
$e$-folding timescale of recent burst | $\tau_{b}$ |  $50\text{\,}\mathrm{Myr}$
Burst fraction of total mass | $f_{b}$ |  $0.00.010.10.50.70.9$
Dust Attenuation: dustatt_modified_CF00 |  |
$V$-band attenuation in the ISM | $A_{V,\text{ISM}}$ |  $0.00.10.30.5$
Fraction of total effective optical depth contributed by ISM | $\mu$ |  $0.44$
Power law slope of dust attenuation in the ISM | $\delta_{\text{ISM}}$ |  $-0.7$
Power law slope of dust attenuation in the birth clouds | $\delta_{\text{BC}}$ |  $-1.3$

We model the sfh as one or two decaying exponentials (Figure 6). The first
exponential models the long-term star formation that has formed the underlying
stellar mass of the disk, while the optional second exponential models a more
recent burst of star formation as might be expected due to spiral arm passages
or tidal encounters. Both exponentials are parameterized by the $e$-folding
times of the old and young populations ($\tau$ and $\tau_{b}$, respectively),
the time since the beginning of each star formation model for the old and
young populations ($t$ and $t_{b}$, respectively), and the fraction of stars
formed in the second burst relative to the total mass of stars ever formed,
$f_{b}$. The standard values we take for the $e$-folding times are
$\tau=$30\text{\,}\mathrm{Gyr}$$ (i.e., mimicking a slowly declining star
formation rate) and $\tau_{b}=$100\text{\,}\mathrm{Myr}$$. For reference,
under exponential sfh models, typical $e$-folding timescales for spiral
galaxies range from $230\text{\,}\mathrm{Gyr}$ (Bolzonella et al., 2000).

Figure 6: Schematic of the modeled star-formation histories used. Red lines
and text show the main population while blue lines and text show the recent
burst population. The grids samples the labeled parameters (e.g., $t$,
$t_{b}$, $\tau$, and $\tau_{b}$) over reasonable ranges. See text.

Dust attenuation is handled following the Charlot & Fall (2000) model. This
model makes the distinction between the heavily-extinguished stellar birth
clouds and the less extinguished ambient ism. We vary the $V$-band attenuation
of the ambient ism which also proportionally varies the $V$-band attenuation
of the stellar birth clouds (see Equation 7 in Boquien et al. 2019). For
reference, Lin et al. (2013) derived an integrated, global extinction for M101
of $A_{V}=0.24$, although the central region is dustier, $A_{V}=0.41$ (see
also Boissier et al. 2004). For our study, since we are masking the dense
star-forming H II regions before analysis, we expect typical extinction values
for the regions we study to be significantly lower.

###  4.2 Diagnostic $W_{3746}$ vs. $W_{\mathrm{H}\beta}$ Plots

Using these models, we perform a few basic tests to investigate to which
parameters our narrowband filters are most sensitive. We calculate the ew in
our H$\beta$ and [O II] filters, $W_{\mathrm{H}\beta}$ and $W_{3746}$,
respectively, through all of the models.222We note again for clarity that
$W_{3746}$ does not refer to the equivalent width of an individual absorption
line; $3746$ refers only to the central wavelength of the filter. Then holding
all parameters constant, we vary each parameter and see how the ew vary as a
function of that parameter in our diagnostic $W_{3746}$ vs.
$W_{\mathrm{H}\beta}$ plots. Figure 7 shows these plots for four different
varying parameters: the $e$-folding timescale of the main population, $\tau$,
the metallicity, $Z$, the age of a recent burst, $t_{b}$, and the $V$-band
dust attenuation in the ism, $A_{V,\text{ISM}}$.

Figure 7: Models for $W_{3746}$ vs. $W_{\mathrm{H}\beta}$ under different
parameter assumptions using cigale. Strong absorption is to the bottom left in
each plot. All models assume a Chabrier (2003) imf. Colored points along each
track indicate the age of the population in $\mathrm{Myr}$. Top left: varying
the main population $\tau$, assuming solar metallicity and no recent burst.
Top right: varying the metallicity, assuming $\tau=$10\text{\,}\mathrm{Gyr}$$
and no recent burst. Bottom left: varying the burst age, assuming solar
metallicity, $\tau=$10\text{\,}\mathrm{Gyr}$$,
$\tau_{b}=$100\text{\,}\mathrm{Myr}$$ and $f_{b}=$1\text{\,}\mathrm{\char
37\relax}$$. Bottom right: varying the dust attenuation, assuming solar
metallicity, $\tau=$10\text{\,}\mathrm{Gyr}$$, and no recent burst.

Broadly speaking, in each plot as a function of age, $W_{\mathrm{H}\beta}$ and
$W_{3746}$ numerically decrease (stronger absorption in H$\beta$; less flux in
the [O II] on-band than the off-band) at very young ages,
$$10\text{\,}\mathrm{Myr}$\lesssim t\lesssim$600\text{\,}\mathrm{Myr}$$. When
the models reach $600\text{\,}\mathrm{Myr}$ ages, both ew measurements begin
to numerically increase again, with $W_{\mathrm{H}\beta}$ increasing at a
faster rate than $W_{3746}$. The age of $600\text{\,}\mathrm{Myr}$ is
approximately the lifetime of an A main-sequence star, for which the Balmer
absorption lines are strongest. Since our [O II] filters are heavily sensitive
to the higher-order Balmer lines, this produces a similar effect in
$W_{3746}$.

The top left plot of Figure 7 shows how these quantities vary as we allow the
$e$-folding timescale of the main population to change. We see that regardless
of the timescale, a young population will follow the same track in the
diagnostic plot until reaching an age of $600\text{\,}\mathrm{Myr}$. Shorter
star-formation timescales (i.e., short main bursts) that are not continually
replenishing their supply of A-type stars rapidly have their
$W_{\mathrm{H}\beta}$ diminish. Meanwhile, as the higher-order Balmer lines
give way to weak absorption lines in our [O II]-on band, molecular bands (such
as CN) contributed by the dominating presence of cooler stars create large
absorption features in our [O II]-off band, having the effect of creating
artificial “emission” in $W_{3746}$ (i.e., $W_{3746}>0$). In contrast, larger
$e$-folding timescales (more constant star formation) have more young stars at
late times, which result in more absorption in the Balmer lines, resulting in
more negative ew in both filters even at late times.

Adjusting the metallicity of the stellar populations (top right of Figure 7),
we see that the strengths of $W_{\mathrm{H}\beta}$ and $W_{3746}$ change in
well-understood ways (e.g. González Delgado et al., 1999, 2005). At ages
younger than $1\text{\,}\mathrm{Gyr}$, the strengths of the Balmer lines has
only a small dependence on metallicity caused by the dependence of stellar
evolution in the integrated light of a stellar population. Again, the stellar
metallicity of M101 is slightly subsolar (Lin et al., 2013), but the subsolar
and solar metallicity tracks greatly differ only for very young ages,
$\lesssim$100\text{\,}\mathrm{Myr}$$. At ages older than
$1\text{\,}\mathrm{Gyr}$, the Balmer line metallicity-dependence is stronger.
Again, in addition to the higher-order Balmer lines, the $W_{3746}$ measure
also feels the increasing effect of molecular bands at old ages which are
slightly elevated at higher metallicities.

Allowing for a recent burst of star formation (bottom left of Figure 7)
creates strong variations in the strengths of $W_{3746}$ and
$W_{\mathrm{H}\beta}$. In these models, the main population is always older
than the burst population. It is clear that very recent bursts dominate the
light from the old population and approach the characteristics of a population
dominated by younger stars. This is primarily attributed to the addition of
more A-type stars, deepening the Balmer lines, leading to stronger signatures
in $W_{3746}$ and $W_{\mathrm{H}\beta}$.

Finally, including the effects of dust attenuation in the ism can affect the
ew, particularly at young ages when stars are presumed to be in their birth
clouds (bottom right of Figure 7). The effect on $W_{\mathrm{H}\beta}$ is
strongest for young ages, where dust greatly weakens the strength of the
absorption line. In the models of Charlot & Fall (2000), young stars are
embedded in heavily-extinguished birth clouds in addition to the dust in the
ism leading to the absorption line weakening we see for young ages. Since all
Balmer lines are plagued by this effect to some degree, we see a similar but
smaller trend in $W_{3746}$. At old ages, the Balmer lines are slowly becoming
weaker while age-independent molecular bands start to contribute, keeping the
$W_{3746}$ relatively constant. Both of these trends are explored in more
detail by MacArthur (2005) in the context of the Lick indices and $D_{4000}$
measurements.

Briefly summarizing the models, we see that we are very sensitive to some
physical properties while being relatively insensitive to others. Among those
that we are most sensitive to are differences between $e$-folding timescales
of the main population and recent bursts of star formation. As we will discuss
in the next section, recent bursts may explain stellar populations that lie in
between the two “prongs” predicted by the main population. We are less
sensitive to the effects of metallicity and dust. Both are constrained by
previous measurements (Boissier et al., 2004; Lin et al., 2013), although dust
may have a similar scattering effect to a recent burst of star formation where
any local dustier regions might artificially weaken the absorption lines we
measure. Again, however, since we have masked the youngest, dustiest regions
of M101—the star-forming H II regions—these effects should be relatively
small.

##  5 The Stellar Ages of the Main Disk

In this section, we begin by comparing the stellar population models generated
with cigale to the binned data inside the main disk (including what we have
defined as the inner disk) to investigate any broad age trends present. Then,
we examine how the stellar population ages differ between different
environments, namely between the spiral arms and interarm regions. As a
reminder, we define the main disk of M101 to be those regions inside $None$
($14.4\text{\,}\mathrm{kpc}$) of the center (§3).

Figure 8 shows our diagnostic $W_{3746}$ v. $W_{\mathrm{H}\beta}$ plot for
those binned pixels in the main disk of M101 colored by radial distance from
the center. Also shown is the prediction from cigale models where different
star formation histories should fall on this plot. Here, the colored lines
show different sfh models assuming different $e$-folding times of the main
stellar population, ranging from $500\text{\,}\mathrm{Myr}$ in light orange to
$10\text{\,}\mathrm{Gyr}$ in red. Points along the tracks are labeled by the
age of each model along the track. These models also include the effects of
dust assuming an average value of $A_{V,\text{ISM}}=0.3$ (Lin et al., 2013).

Figure 8: $W_{3746}$ vs. $W_{\mathrm{H}\beta}$ for all medianed pixels in the
main disk of M101 ($R<$$$, $\sim$$15\text{\,}\mathrm{kpc}$). Left: Points are
colored by distance from the center of M101. Standard uncertainty shown in the
upper left. Overplotted are different models from cigale. Models assume a
Chabrier (2003) imf, solar metallicity, and $A_{V,\text{ISM}}=0.3$. Different
colored lines indicate different $\tau$ models:
$0.5\text{\,}\mathrm{Gyr}1\text{\,}\mathrm{Gyr}2\text{\,}\mathrm{Gyr}3\text{\,}\mathrm{Gyr}4\text{\,}\mathrm{Gyr}5\text{\,}\mathrm{Gyr}10\text{\,}\mathrm{Gyr}$.
Ages of the stellar populations are indicated on the plot. Right: Contours are
colored by distance from the center of M101: $R\leq$4\text{\,}\mathrm{kpc}$$
in red, $$4\text{\,}\mathrm{kpc}$<R\leq$8\text{\,}\mathrm{kpc}$$ in green, and
$$8\text{\,}\mathrm{kpc}$<R\leq$12\text{\,}\mathrm{kpc}$$ in blue.
Characteristic error bars are shown in the top left. Contours show the data
point density for different radial ranges, encompassing
$30\text{\,}\mathrm{\char 37\relax}$, $50\text{\,}\mathrm{\char 37\relax}$,
and $80\text{\,}\mathrm{\char 37\relax}$ of all data points in each range.

Comparing the data with the generated models generally shows that the inner
regions within a few $\mathrm{kpc}$ are consistent with an older stellar
population, while the mean age generally becomes younger at larger radii. This
is more easily seen in the right plot of Figure 8, where we plot three radial
ranges with density contours. Thus we see that those points at large radii are
truly younger with very little old populations mixed in, and vice versa for
the points at small radii. Thus, we recover a radial age gradient for the main
disk of M101.

We also see that the two “prongs” of the models can be loosely considered the
bounds of “reasonable” stellar populations. However, a small number of points
scatter well outside the model tracks: one plume at high $W_{3746}$ and
$W_{\mathrm{H}\beta}\sim$-5\text{\,}\mathrm{\SIUnitSymbolAngstrom}$$ and
another at high $W_{\mathrm{H}\beta}$ and
$W_{3746}\sim$-5\text{\,}\mathrm{\SIUnitSymbolAngstrom}$$, and a large
population of points between the two “prongs.” Investigating the locations of
the two plumes on our images shows that these are caused by either an unmasked
foreground star or scattered diffuse light from masked H II regions.

Most of the true scatter lies between the two “prongs” of the model. Returning
to Figure 7, we see the effects of a recent burst is to bend the older “prong”
inwards towards the younger “prong.” As mentioned before this can be
physically attributed to the addition of A-type stars, deepening the Balmer
absorption lines. The addition of O/B stars will also weaken the slope of the
blue continuum, increasing the value of $W_{3746}$ despite there also being a
host of A-type stars as well. Therefore, recent bursts will move stellar
populations slightly away from the bend in the “prongs” in our models.

There are also a large amount of points “in emission” in $W_{3746}$ in Figure
8. As mentioned previously (§4.2), this is not caused by any real emission
feature being measured, but rather flattening continuum levels in our [O II]
filters combined with molecular bands such as CN appearing in our [O II] off-
band filter, creating a false “emission” measurement. Recent bursts will bend
the older “prong” inwards towards being “in absorption” in $W_{3746}$ caused
by the presence of A-type stars. Given the globally constant and locally
stochastic star-forming nature of spiral galaxies, we then expect that pixels
dominated by old populations but with a somewhat recent burst (i.e.,
$t_{b}\sim$500\text{\,}\mathrm{Myr}$$) will populate this area characterized
by being “in emission” in $W_{3746}$.

###  5.1 Inner Disk vs. Arm vs. Interarm

We now turn our attention to how the different main disk environments (inner
disk, spiral arms, interarm) are spectrally distinct. Applying the masks
described in Section 3, Figure 9 shows how these environments distribute
themselves on our $W_{3746}$ v. $W_{\mathrm{H}\beta}$ plot. Here, each
environment is shown in a different color with density contours overlayed. The
inner disk has a tendency to separate itself from the more actively star-
forming spiral arms and interarm regions. Notably, there is also a distinct
offset between the centroids of the density distributions for the spiral arms
and interarm regions.

Figure 9: The $W_{3746}$ vs. $W_{\mathrm{H}\beta}$ for all pixels in the main
disk of M101 ($R<$$$, $\sim$$15\text{\,}\mathrm{kpc}$) distinguished by
environment: the inner disk in red, spiral arms in blue, and interarm regions
in green. Characteristic error bars are shown in the bottom right. Contours
show the data point density for different environments, encompassing
$30\text{\,}\mathrm{\char 37\relax}50\text{\,}\mathrm{\char
37\relax}80\text{\,}\mathrm{\char 37\relax}$ of all data points in each
category.

These differences, just as in Figure 8, can be broadly interpreted as age
differences: the inner disk has a stellar population that is older than that
in more actively star-forming arm and interarm regions. However, it is worth
mentioning that what we define to be the inner disk is much larger than is
traditional since we defined the inner disk based on the inability to discern
separate spiral arms. This might cause smaller changes in the stellar ages to
be unresolvable. For instance, Lin et al. (2013) found that the bulge of M101
($R\lesssim$$$) has a younger stellar age than the surrounding disk by
$\sim$$3\text{\,}\mathrm{Gyr}$ using pixel-based multiwavelength sed fitting.
Young bulges are found in numerous late-type galaxies (e.g. Ganda et al.,
2007; Peletier et al., 2007), and M101 does have a mildly star-forming
pseudobulge (Fisher et al., 2009; Fisher & Drory, 2010; Kormendy et al.,
2010). However, given the extensive network of H II regions in the inner
$\mathrm{kpc}$ of M101, this region is largely masked in our imaging and thus
not measured by our analysis.

Moving on to the spiral arms and interarm regions, the spiral arms are
dominated by a recently-formed young population while the interarm region is
slightly mixed in ages. The interarm has a sizable young population that
overlaps with the spiral arm distribution, but also stellar populations that
have an older mean age, more similar to the non-star-forming populations of
the inner disk. The observation that the interarm region has a mix of
different stellar populations prompts the question of if these populations are
spatially distinct.

To test this, we select two spectral regions on our diagnostic plot. We select
interarm points that are spectrally distinct from the majority of the arm
points, that is $$-5\text{\,}\mathrm{\SIUnitSymbolAngstrom}$\leq
W_{\mathrm{H}\beta}\leq$-4\text{\,}\mathrm{\SIUnitSymbolAngstrom}$$ and
$$-7\text{\,}\mathrm{\SIUnitSymbolAngstrom}$\leq
W_{3746}\leq$-5\text{\,}\mathrm{\SIUnitSymbolAngstrom}$$, and arm and interarm
points that are spectrally indistinguishable, that is
$$-7\text{\,}\mathrm{\SIUnitSymbolAngstrom}$\leq
W_{\mathrm{H}\beta}\leq$-6\text{\,}\mathrm{\SIUnitSymbolAngstrom}$$ and
$$-13\text{\,}\mathrm{\SIUnitSymbolAngstrom}$\leq
W_{3746}\leq$-10\text{\,}\mathrm{\SIUnitSymbolAngstrom}$$. These points are
located approximately where the densest contours lie in Figure 9. Thus, the
interarm region is split into “like-arm” interarm regions and “true” interarm
regions, defined by their spectral properties. Figure 10 shows the spatial
distribution of these spectrally-defined regions.

Figure 10: The spatial distribution of spectrally-selected regions (see text).
The points labeled “interarm” are those that are spectrally distinct from the
spiral arms, while those labeled “like-arm interarm” are those that are
spectrally indistinct from the spiral arms. Schematics of the spiral arms are
the light blue regions.

What is immediately apparent is that the “like-arm” interarm regions are
preferentially found on the outer edge of the spiral arm, while the “true”
interarm regions are found in the inner edge of the spiral arm. According to
our stellar population models, the spiral arm and “like-arm” interarm regions
have similar stellar ages, while the “true” interarm regions are older. Thus,
we observe a potential age gradient in the ages of stars across a spiral arm.
There are small areas of “like-arm” interarm regions that appear to be
continuations of a spiral arm, particular towards the inner disk. This feature
is likely caused by the difficulty of defining spiral arms in such a tightly-
wound environment.

Figure 11: The spectral characteristics of spatially-selected regions. Left:
three selected boxes in the main disk. Points are colored by their
$W_{\mathrm{H}\beta}$. Empty regions in the boxes are either caused by masked
H II regions or are below our S/N cut. Right: each box’s $W_{\mathrm{H}\beta}$
as a function of distance across a spiral arm. Negative distances are towards
the center of M101 and positive distances are away from the center of M101.
Binned medians are shown in red. In all three boxes, the $W_{\mathrm{H}\beta}$
is stronger on the outer edge of an arm ($1\lesssim X\lesssim 3$) than the
inside of the arm ($-3\lesssim X\lesssim-1$), indicative of the shift towards
younger populations ahead (moving out of) the arm.

While Figure 10 shows the spatial distribution of points selected by their
spectral characteristics, an alternative analysis is to look at the spectral
characteristics of points along a track cutting through the spiral arms. To
check this, in Figure 11 we select three rectangular regions extending from
outside the inner disk environment, extending through one spiral arm, and
ending about halfway to the next spiral arm (i.e., in the middle of an
interarm environment). Investigating the trend of $W_{\mathrm{H}\beta}$ with
distance across a spiral arm, we see the expected age characteristics: inside
the arm lies weak absorption produced by older stellar populations, while
moving outside the arm is associated with the strengthening absorption of
younger stellar populations. Clearly these conclusions are not only supported
by the sfh modeling as in Figure 10, but also supported observationally with
direct measurements of the age-sensitive $W_{\mathrm{H}\beta}$ as in Figure
11.

Interpreting these observed age trends in the context of spiral density waves
is relatively straightforward due to the ordered nature of the main disk of
M101. These age trend are well described by the large-scale shock scenario
(Roberts, 1969; Dixon, 1971), which predicts that inside of corotation, ages
should change along these cuts through the arm, in this case decreasing along
our chosen direction. Thus our observations give strong support for the
dynamical scenario where the main disk is characterized by a quasi-steady
global spiral wave. As mentioned in the Introduction, this age trend is often
hard to measure due to the use of broadband colors and the well-known age-
metallicity degeneracy. However, techniques that control for the reddening
effects of dust and metallicity, such as the optical/infrared photometric
index used by González & Graham (1996) and Martínez-García et al. (2009), have
started to reveal these age trends across spiral arms.

Similarly in our data, our ability to detect these age differences may be due
to the reduced sensitivity to dust and metallicity in our narrowband imaging
compared to broadband optical studies. As mentioned earlier (§4.2), $W_{3746}$
and $W_{\mathrm{H}\beta}$ have different responses to dust and metallicity:
$W_{\mathrm{H}\beta}$ is only sensitive to one Balmer line that strongly
weakens for older populations, while $W_{3746}$ is sensitive to many Balmer
lines and the shape of the blue continuum which strongly weakens for younger
populations. The combination of these two age indicators allows us to break
the degeneracies any one indicator might have (MacArthur, 2005).

##  6 The Stellar Ages of the Outer Disk

Studying the stellar component of galaxy outskirts is particularly
challenging. The surface brightness of the outer stellar component is usually
well below that of the night sky, requiring very deep and accurate photometry
to constrain the properties of the stellar populations (e.g. Mihos et al.,
2013; Watkins et al., 2016; Peters et al., 2017). In addition, the lsb outer
regions can be contaminated by background sources and instrumental scattered
light, complicating the measurement of photometric ew. To alleviate these
issues, in our analysis of the outer disk, we focus on a small sample of
relatively “clean” regions in the outer disk, and compare their properties and
distribution to the main disk. These regions were picked by eye, marking areas
that are free of contamination and have high enough surface brightness to be
well-detected in our narrowband imaging. Each region measures $40\times 40$
pixels ($$$\times$$$ or
$$2\text{\,}\mathrm{kpc}$\times$2\text{\,}\mathrm{kpc}$$), in which we measure
the median $W_{3746}$ and $W_{\mathrm{H}\beta}$.

Figure 12: Left: The median binned H$\beta$ off-band image of M101. H II
regions and foreground stars are masked. The red dashed circle marks the
main/outer disk distinction, $R=$$$. Selected regions in the outer disk are
marked by red boxes measuring $40\times 40$ pixels ($$$\times$$$ or
$$2\text{\,}\mathrm{kpc}$\times$2\text{\,}\mathrm{kpc}$$) and numbered. The
image measures $$$\times$$$ or
$$80\text{\,}\mathrm{kpc}$\times$80\text{\,}\mathrm{kpc}$$. North is up, east
to the left. Right: The selected regions’ distribution on the diagnostic plot.
Labels are carried over from the left panel. Colored points and text (lower
right) correspond to the different environments of the regions selected. The
colored contours correspond to the density distribution of different
environments in the main disk; same as Figure 9. Colored tracks and text
(upper left) correspond to different sfh with different $\tau$. Characteristic
error bars are shown in black at the bottom right.

Figure 12 shows the location of each region in the $9\times 9$ median H$\beta$
off-band image. Particular pairs of regions inside (‘a’) and outside (‘b’)
spiral arms are labeled. Regions 1-5 lie along the northeastern arm, chosen to
sample stellar populations in the direction of the NE Plume (Mihos et al.,
2013). Regions 6a and 6b sample either side of a star-forming region, and
regions 7a and 7b sample the edge of a short spiral arm to the northwest.
Other regions have been placed targeting interarm regions, star-forming
complexes, and the faint, outer reaches of the galaxy. In this way, we have
attempted to target different features in M101’s outer disk, while also
remaining azimuthally unbiased.

Figure 12 also shows these regions’ locations on the diagnostic $W_{3746}$ vs.
$W_{\mathrm{H}\beta}$ plot. Comparing these outer disk regions with the main
disk environments, we see that while there is overlap, many regions show
stronger absorption features in one or both of our filters than the main disk.
Notably many of these regions are those that are along the northeast arm.
Stronger absorption is indicative of a more dominant young population than
that in the main disk, suggesting recent star formation in these regions
perhaps as a result of the M101-NGC 5474 interaction. Similar studies using
broadband colors have also inferred younger ages in the outer disk (Bianchi et
al., 2005; Lin et al., 2013; Mihos et al., 2013).

Also shown in Figure 12 are three representative sfh tracks generated with
cigale. All assume a Chabrier (2003) imf, solar metallicity, and
$A_{V,\text{ISM}}=0.5$ and differ in the $e$-folding timescale, $\tau$, being
$100\text{\,}\mathrm{Myr}$, $300\text{\,}\mathrm{Myr}$, or
$30\text{\,}\mathrm{Gyr}$. These are single-exponential sfh meant to describe
the bulk of the stellar population, i.e., the
$\tau=$100\text{\,}\mathrm{Myr}$$ model approximates a stellar population that
had most of its star formation early and is fading out. The effect of a
shorter $\tau$, i.e., a “burstier” sfh, is to produce stronger absorption
lines at the turn-around age of $\sim$$600\text{\,}\mathrm{Myr}$. The
different tracks rejoin one another at late times (several $\mathrm{Gyr}$).

Comparing the selected outer disk regions with these sfh tracks, we see that
none of them appear consistent with the “burstiest” model, that with
$\tau=$100\text{\,}\mathrm{Myr}$$, suggesting a slightly more extended sfh.
Meanwhile many of the regions on the north and northeastern side of M101 are
consistent with young populations. For instance, several regions could be
young populations associated with a fading burst (among them regions 2a, 3a,
6a, 6b). Others might be young populations in a near-constant sfh or a fading
burst (among them regions 4a, 5a).

Interesting to note are the regions in the direction of the NE Plume beyond
the northeast arm (regions ‘a’ 1-5). These five regions form a tight cluster
of points in Figure 12, near the turn-around point in the sfh tracks. The fact
that they have strong absorption features through our filters suggests that
these are young ages, consistent with a recent (few hundred $\mathrm{Myr}$)
burst of star formation on top of a somewhat older but not dominant background
stellar population. This timescale is similar to that found by Mihos et al.
(2018) who used hst to study the discrete stellar populations in M101’s NE
Plume (at a slightly larger radius than probed here), finding evidence for
both an old population and a $\sim$$300\text{\,}\mathrm{Myr}$ starburst
population in the region. In our studies of the integrated light here, the
starburst population and older background populations combine to give an older
mean age ($500\text{\,}\mathrm{Myr}$-$1\text{\,}\mathrm{Gyr}$), but the
scattering of regions shows good agreement with the picture of a recent weak
starburst in this part of M101’s outer disk.

However, Figure 12 also shows other regions in M101’s outer disk which are
dominated by older populations. Some of these lie in interarm regions or to
the west of M101, a part that likely did not participate strongly in the
M101-NGC 5474 interaction (in the model of Linden & Mihos 2022, these regions
were on the opposite side from the companion at closest approach).
Interestingly, most of the selected regions on the inside of spiral arms
(labeled ‘b’ in Figure 12) have weaker absorption features, suggesting an
older mean age than their partners on the outside of the spiral arms. These
age patterns across the outer arms are similar to those seen in the main disk,
again indicative of the large-scale shock scenario. However, here we are
sampling regions well outside the corotation radius of the main disk (found to
be at $15.6\pm 2.2\text{\,}\mathrm{kpc}$; Roberts et al. 1975; Scarano &
Lépine 2013). Outside of corotation, we would expect the age gradients to be
flipped (older populations leading the arms and younger populations inside;
Roberts 1969; Dixon 1971). The fact that we observe no change in the
directionality of the age gradients in the outer arms hints at the possibility
of multiple pattern speeds in M101, which we explore below.

##  7 Multiple Pattern Speeds of M101?

In the past two sections, we have presented evidence of the large-scale shock
scenario in both the main and outer disks of M101. There exists age gradients
across the spiral arms of M101 going from primarily old populations on the
inner edge to younger populations along the outer edge of an arm. This
gradient is predicted by the large-scale shock scenario (Roberts, 1969; Dixon,
1971), but interestingly we see no reversal of the gradient outside M101’s
main corotation radius ($R\approx$15\text{\,}\mathrm{kpc}$$; Scarano & Lépine
2013) contrary to the expectation in the large-scale shock scenario.

Thus there are two possible responses: either star formation patterns in M101
are not governed by the large-scale shock scenario, or there exists multiple
pattern speeds, and thus multiple corotation radii, producing the trends we
observe. The large-scale shock scenario requires star formation to occur
preferentially in the spiral arms, producing age gradients across the arms
that flip direction inside and outside corotation. Conversely, if star
formation occurs stochastically throughout the disk regardless of the location
of the spiral arms, this could introduce spurious patterns in the age
distributions that are inconsistent with the large-scale shock scenario. While
some studies have questioned the importance of spiral arms in driving star
formation (Foyle et al., 2010, 2011; Ragan et al., 2018; Querejeta et al.,
2021), that does not appear to be the case in M101. Not only do we see here
the gradients predicted by large-scale shocks, studies of the galaxy’s massive
star populations show strongly enhanced star formation in the spiral arms (up
to 30 times more efficient than in the interarm regions; Cedrés et al. 2013).
This picture of spiral-driven star formation is echoed in studies of other
spiral galaxies (Vogel et al., 1988; Lord & Young, 1990; Knapen & Beckman,
1996), and thus, at least for M101, the large-scale shock scenario likely
still holds.

Instead, what is more probable is that M101 is a spiral galaxy with multiple
pattern speeds. The existence of multiple pattern speeds which dominate over
concentric radial ranges has been measured for M101 and other galaxies in the
past. Meidt et al. (2009) used H I and CO data cubes of M101 to measure these
pattern speeds and found at least three distinct speeds each with their own
corotation radius: an inner pattern within $6\text{\,}\mathrm{kpc}$, a second
extending from $613\text{\,}\mathrm{kpc}$, and a third from
$1320\text{\,}\mathrm{kpc}$. Each pattern has its own corotation radius:
$3.7\text{\,}\mathrm{kpc}9.8\text{\,}\mathrm{kpc}19.6\text{\,}\mathrm{kpc}$,
respectively. Using different methods, other studies have confirmed the
innermost pattern speed as well (Egusa et al., 2009; Cedrés et al., 2013).

The possible existence of three pattern speeds in M101 could explain the
recurrence of the same age trend in the outer disk as in the inner disk. At
any particular radii in M101, the gas and stars would always be inside of some
corotation radius, resulting in stellar populations that are primarily old
along the inner edge of a spiral arm and becoming younger across the arm
towards the outer edge. There would likely not be a flipping of this trend
until beyond the outermost pattern speed. The fact that we don’t see this flip
in the outer disk of M101 does suggest that the outermost pattern speed in
Meidt et al. (2009) does extend further than their cutoff of
$\sim$$20\text{\,}\mathrm{kpc}$, potentially to at least
$25.5\text{\,}\mathrm{kpc}$ (the galactocentric distance to region 1a in
Figure 12).

The adoption of multiple pattern speeds necessarily requires the adoption of
“dynamic” spiral arms (i.e., transient and recurrent spiral arms; e.g.
Sellwood & Carlberg 1984; Elmegreen & Elmegreen 1986; Sellwood 2011) as
opposed to quasi-static, long-lived spiral arms (e.g. Lin & Shu, 1964; Bertin
et al., 1989). In the former theory, spiral arms appear and reappear in
cycles, breaking up into smaller segments with sizes of a few $\mathrm{kpc}$,
then reconnecting by differential rotation to reform large-scale patterns
(Wada et al., 2011). Thus dynamic spiral arms can appear to be long-lived
visually, but change on short timescales.

A “dynamic” M101 naturally has consequences for its shape and spiral
structure. Multiple pattern speeds are linked and supported by “mode coupling”
(Sygnet et al. 1988; Masset & Tagger 1997; see Sellwood & Carlberg 2019 and
references therein for more recent discussions), wherein resonances of
different pattern speeds overlap, such as the corotation radius of an inner
pattern overlapping with the inner Lindblad resonance of an outer pattern.
This overlap causes energy and angular momentum to be transferred efficiently
to the outer disk, building up the spiral pattern at large radii (e.g. Masset
& Tagger, 1997; Rautiainen & Salo, 1999; Meidt et al., 2008a, b; Font et al.,
2014). A consequence of mode coupling noted in simulations is that galaxies
are stimulated to produce $m=1$ spiral waves (e.g. Sellwood & Sparke, 1988;
Rautiainen & Salo, 1999; Salo & Laurikainen, 2000), just as we see with the
large asymmetric spiral arm in M101. Notably, this might be a potential
solution to the problem Linden & Mihos (2022) faced in constraining the mass
of NGC 5474, having to adopt a mass ratio of one-eighth that of M101 leading
to a significantly higher circular velocity for the satellite than observed in
order to reproduce the asymmetry by interaction alone. If the disk of M101 was
already sensitive to producing $m=1$ modes, it could be quite responsive to
tidal forcing even with a lower mass for NGC 5474. Fully hydrodynamical
simulations of the M101-NGC 5474 interaction, building on the work of Linden &
Mihos (2022), will need to be performed to test this theory.

However, a “dynamic” M101 and our measurements of an age gradient across
spiral arms has consequences for computational studies of spiral structure in
disk galaxies. In contrast to the canonical density wave model for spiral
structure, many hydrodynamical simulations show spiral patterns forming as
shearing arms that co-rotate with the stars and gas (e.g. Dobbs & Pringle,
2010; Grand et al., 2012; Baba et al., 2015, 2017; Dobbs et al., 2017). This
co-rotation makes it such that molecular clouds, H II regions, and star
clusters do not easily move across and out of the spiral arms, predicting that
no age gradients should be seen across the arm, in contrast to what we observe
in M101. Other models, generate spiral structure via a force response to mass
clumps in the disk (D’Onghia et al. 2013; see also the introduction of
Sellwood & Carlberg 2019), which produce “wakes” that extend over a small
radial range and could produce the age gradients we see in M101. However,
these wakes do not extend over large radii and thus do not get far from
corotation. Such a model would thus predict much milder age gradients across
the arms, possibly at odds with the strong age gradients we see in M101.
However, we also note that most simulations of dynamic spiral arm mechanisms
produce relatively weak spiral structure (e.g. Dobbs & Pringle, 2010; Grand et
al., 2012; D’Onghia et al., 2013). These models may provide good descriptions
of “flocculent” spiral structure, but in stark contrast stands M101, a galaxy
with strong spiral arms that are dynamic in nature and also likely influenced
by M101’s recent interaction with NGC 5474. Clearly, new simulations of
dynamic spiral structure are needed that reproduce the strong spiral arms of
M101 while also resulting in age gradients observed across its spiral arms.

##  8 Conclusions

Using narrowband filters that measure the absorption line strengths of
H$\beta$ and higher order Balmer lines and metallic lines between the Balmer
break at $3646\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ and the
$4000\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ break, we have placed
constraints on the stellar ages throughout the disk of M101. We calibrate and
confirm the efficacy of this technique using the stellar population synthesis
code cigale (Noll et al., 2009; Boquien et al., 2019) to observe the effect of
stellar population parameters on equivalent widths measured through our
filters. Our narrowband imaging technique proves sensitive to the star
formation history of the stellar populations, and is only modestly sensitive
to other effects such as dust and metallicity. We divided M101 into several
different radial regions to study the mean population age and also examined
the differences between spiral arms and their interarm environments. We
confirm studies of the overall radial age gradient as well as shown new
evidence for spiral driven features in the spatial age distribution. We
interpret these results in the context of spiral arm dynamics and multiple
pattern speeds in the disk of M101. Our main conclusions are summarized below.

  1. 1.

In the main disk, we focused on the differences between morphological
features, i.e., spiral arms, interarm regions, and the inner disk. We confirm
previous studies showing a radial age gradient (Bianchi et al., 2005; Lin et
al., 2013), where the inner disk has populations older than those at larger
radii. Comparing spiral arms and interarm populations revealed a spread in the
mean ages of the interarm population, some similar to the young arms, and
others older and more akin to the inner disk. These “like-arm” interarm
regions are preferentially found on the outer edge of a spiral arm, while the
“true” interarm regions are found on the inner edge.

  2. 2.

We interpreted these spatial trends in the context of the “large-scale shock
scenario” (Roberts, 1969; Dixon, 1971) a consequence of quasi-steady, global
spiral density waves. Inside of corotation, gas clouds overtake the spiral arm
and form stars in H II regions. These stars drift outwards, creating a color
and age gradient across the spiral arms. Despite being historically hard to
measure observationally, this evolutionary path has been predicted in
simulations (e.g. Dobbs & Pringle, 2010), and is now clearly in evidence in
our narrowband imaging.

  3. 3.

To combat the low signal-to-noise in the diffuse outer disk, we selected a
number of “clean” regions where we can spatially bin over larger areas to
accurately measure stellar absorption signatures. Unexpectedly, we recovered a
similar age trend across the spiral arms in the outer disk as we had found in
the main disk, with younger populations along the outer edge and older
populations along the inner edge of spiral arms. The outer disk, while having
significantly younger populations than the main disk, did also contain some
old populations similar to the main disk.

  4. 4.

In terms of processes shaping the outer disk, the lack of a change in the
spiral arm age trends beyond the assumed corotation radius of M101 suggests
that there are multiple pattern speeds and thus multiple corotation radii in
M101. Other groups have found evidence for radially varying pattern speeds in
M101 and other galaxies (Meidt et al., 2009; Font et al., 2014), and our work
supports this conclusion.

Overall, our results are consistent with a picture where M101 is a “dynamic”
galaxy, one with transient and recurrent spiral arms. While still showing the
radial signs expected by inside-out galaxy formation, where the inner region
is older and the outer region is younger, the nature of the spiral pattern
does not conform to standard density wave theory as measured by stellar ages.
Instead, there may be multiple pattern speeds in M101 linked by mode coupling.
This allows resonances in the different spiral patterns to overlap, causing
energy and angular momentum to be transferred efficiently to the outer disk,
building up the spiral pattern and resulting in the one-armed spiral pattern
we see in M101. While this has promising answers for the trends in M101 seen
here and elsewhere, hydrodynamical modeling of M101 and its interaction
history needs to be performed to fully unravel these mysteries.

The authors would like to thank Aaron Watkins for his work in collecting the
H$\alpha$ image used for determining the widths of the spiral arms. We thank
Stacy McGaugh for helpful discussions and comments on this paper. We also
thank Charley Knox for his work supporting the Burrell Schmidt, and the Mt.
Cuba Astronomical Society for financial support for the project. We also thank
the anonymous referee for a detailed report that helped improve this paper.
R.G. was supported in part by a Towson Memorial Scholarship. R.G. would like
to thank StackOverflow user ImportanceOfBeingErnest for their Python code used
in drawing the spiral arm masks. This publication makes use of data products
from the Two Micron All Sky Survey, which is a joint project of the University
of Massachusetts and the Infrared Processing and Analysis Center/California
Institute of Technology, funded by the National Aeronautics and Space
Administration and the National Science Foundation. This research has made use
of the NASA/IPAC Extragalactic Database, which is funded by the National
Aeronautics and Space Administration and operated by the California Institute
of Technology. _Facility:_ CWRU:Schmidt

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