# The Metallicity Dependence of PAH Emission in Galaxies I:
Insights from Deep Radial Spitzer Spectroscopy

Cory M. Whitcomb Ritter Astrophysical Research Center, Department of Physics &
Astronomy, University of Toledo, Toledo, OH 43606, USA  J.-D. T. Smith Ritter
Astrophysical Research Center, Department of Physics & Astronomy, University
of Toledo, Toledo, OH 43606, USA  Karin Sandstrom Department of Astronomy &
Astrophysics, University of California, San Diego, 9500 Gilman Drive, La
Jolla, CA 92093, USA  Carl A. Starkey Ritter Astrophysical Research Center,
Department of Physics & Astronomy, University of Toledo, Toledo, OH 43606, USA
The Ohio State University Wexner Medical Center, 460 W 12th Ave, Columbus, OH
43210, USA  Grant P. Donnelly Ritter Astrophysical Research Center, Department
of Physics & Astronomy, University of Toledo, Toledo, OH 43606, USA  Bruce T.
Draine Department of Astrophysical Sciences, Princeton University, Princeton,
NJ 08544, USA  Evan D. Skillman University of Minnesota, Minnesota Institute
for Astrophysics, School of Physics and Astronomy,
116 Church Street, S.E., Minneapolis, MN 55455, USA  Daniel A. Dale Department
of Physics and Astronomy, University of Wyoming, Laramie, WY 82071, USA  Lee
Armus IPAC, California Institute of Technology, 1200 E. California Boulevard,
Pasadena, CA 91125, USA  Brandon S. Hensley Jet Propulsion Laboratory,
California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, USA
Thomas S.-Y. Lai (賴劭愉) IPAC, California Institute of Technology, 1200 E.
California Boulevard, Pasadena, CA 91125, USA  Robert C. Kennicutt Steward
Observatory, University of Arizona, Tucson, AZ 85719, USA Cory M. Whitcomb
<EMAIL_ADDRESS>
###### Abstract

We use deep Spitzer mid-infrared spectroscopic maps of radial strips across
three nearby galaxies with well-studied metallicity gradients (M101, NGC 628,
and NGC 2403) to explore the physical origins of the observed deficit of
polycyclic aromatic hydrocarbons (PAHs) at sub-solar metallicity (i.e. the
PAH-metallicity relation or PZR). These maps allow us to trace the evolution
of all PAH features from 5–18 µm as metallicity decreases continuously from
solar ($Z_{\odot}$) to 0.2 $Z_{\odot}$. The total PAH to dust luminosity ratio
remains relatively constant until reaching a threshold of $\sim$$\frac{2}{3}$
$Z_{\odot}$, below which it declines smoothly but rapidly. The PZR has been
attributed to preferential destruction of the smallest grains in the hard
radiation environments found at low metallicity. In this scenario, a decrease
in emission from the shortest wavelength PAH features is expected. In
contrast, we find a steep decline in long wavelength power below $Z_{\odot}$,
especially in the 17 µm feature, with the shorter wavelength PAH bands
carrying an increasingly large fraction of power at low metallicity. We use
newly developed grain models to reproduce the observed PZR trends, including
these variations in fractional PAH feature strengths. The model that best
reproduces the data employs an evolving grain size distribution that shifts to
smaller sizes as metallicity declines. We interpret this as a result of
inhibited grain growth at low metallicity, suggesting continuous replenishment
in the interstellar medium is the dominant process shaping the PAH grain
population in galaxies.

Polycyclic aromatic hydrocarbons (1280), Metallicity (1031)

##  1 Introduction

The smallest carbonaceous dust grains in the interstellar medium emit bright,
broad vibrational features in the mid-infrared. These dust grains are commonly
believed to be polycyclic aromatic hydrocarbons (PAHs) composed of dozens to
thousands of aromatically-bonded carbon atoms (Tielens, 2008; Li, 2020). The
emission from these PAH features alone contributes over 10% of the total
infrared luminosity of star-forming galaxies (Smith et al., 2007).

Many previous studies across a wide variety of interstellar conditions have
found deficits in the fraction of PAH luminosity relative to total dust
continuum power at sub-solar metallicity, typically interpreted as a marked
change in the abundance of dust in the form of PAHs (e.g. Engelbracht et al.,
2005; Madden et al., 2006; Jackson et al., 2006; Draine et al., 2007; Smith et
al., 2007; Gordon et al., 2008; Muñoz-Mateos et al., 2009; Haynes et al.,
2010; Sandstrom et al., 2012; Lai et al., 2020; Aniano et al., 2020; Whitcomb
et al., 2020; Zang et al., 2022; Shivaei et al., 2024). Little is known about
the origins of this deficit. In the era of JWST it is crucial that we
understand this PAH-metallicity relation (PZR) in order to accurately
interpret PAH emission from local highly-resolved galaxies to systems at high
redshift where metallicities for a given stellar mass may be significantly
lower.

A common explanation for the PZR is that smaller PAHs are destroyed by high
energy photons in low metallicity regions (Madden et al., 2006; Gordon et al.,
2008; Egorov et al., 2023). At low metallicity, young stars are hotter and
less dust is present to attenuate their hard photons. The resulting
interstellar radiation fields (ISRFs) have a higher ratio of UV to optical
photons, increasing the stochastic heating rate and peak temperature of PAHs.
In general the heat capacity of dust grains is proportional to their volume,
so the smallest PAH molecules may begin to dissociate when they absorb photons
of sufficiently high energy (Guhathakurta & Draine, 1989; Le Page et al.,
2003; Duley, 2009; Draine et al., 2021).

In this paper we investigate the PZR using large, deep, Spitzer spectral maps
(5–18 µm) in radial strips across three nearby galaxies — M101, NGC 628, and
NGC 2403 — with well-studied abundance gradients obtained using auroral-line
based measurements (Kennicutt et al., 2003; Croxall et al., 2016; Berg et al.,
2013, 2015; Rogers et al., 2021). These mid-infrared (MIR) spectral mapping
datasets are some of the deepest ever observed with the Spitzer-InfraRed
Spectrograph (IRS), and extend up to $\sim$15 kpc from galaxy center, enabling
variations in the full PAH emission spectrum to be tracked, aside from the
weak 3.3 µm band. By studying how the PAH spectrum changes in strength and
shape as a function of radius within each galaxy, we can isolate the
variations that result primarily from the radial metallicity gradient. For the
first time, we model the recovered PZR trends using detailed physical models
of PAH emission in the context of varying incident radiation fields and
underlying grain size distributions (GSDs).

This paper is organized as follows. In § 2 we summarize the key physical
processes and potential explanations for the observed PZR trends. In § 3 we
describe our data, region definition criteria, and the resulting suite of data
products. In § 4 we describe details of the observed PZR trends. In § 5 we
introduce several physically-motivated model scenarios and test them against
the observations. In § 6 we discuss the physical implications of our results
and compare them with previous studies. In § 7 we outline our most significant
conclusions.

Figure 1: Three-color images for M101 (top), NGC 628 (left), and NGC 2403
(right). Red is MIPS 24 µm, green is IRAC 8 µm, and blue is IRAC 3.6 µm. All
images are convolved to match PACS 160 µm resolution, except those for NGC
2403 which are convolved to match SPIRE 350 µm resolution. The footprint of
the radial spectroscopic maps studied in this work are shown in cyan, and the
eight additional apertures for the Hii region maps in M101 are shown as black
squares.

##  2 Background and Definitions

As the gas-phase metal abundance of the interstellar medium (ISM) drops, the
dust-to-gas mass ratio decreases towards the background level set by stellar
production (Rémy-Ruyer et al., 2014), or lower in galaxies where grain
destruction is more efficient than grain growth (Aniano et al., 2020). The
resulting lack of dust opacity increases the average hardness $\langle
h\nu\rangle$ and intensity $U$ of the starlight incident on dust grains. Just
as important as the heating environment, the distribution of grain sizes plays
a key role in the emerging PAH spectrum.

Leading models suggest the distribution of grain sizes results from a complex
balance between many opposing forces: injection in carbon-rich AGB winds,
destruction in supernova shocks and ionized gas, fragmentation of larger
grains into smaller units, coagulation and accretion building grain mass in
dense clouds, etc. (Dwek & Scalo, 1980; Zhukovska et al., 2008; Draine, 2009;
Micelotta et al., 2010a; Galliano et al., 2018; Choban et al., 2022; Narayanan
et al., 2023; Choban et al., 2024). Many of these processes are sensitive to
metal abundance. For example, the timescale of gas-phase accretion onto grain
surfaces has a strong dependence on the free metal content of the ISM
(Zhukovska et al., 2008; Zhukovska & Henning, 2013).

One of the earliest Spitzer results on PAHs revealed a striking difference in
PAH emission between galaxies with solar metallicity and those below one-
quarter solar: over this range, PAH emission declines rapidly (Engelbracht et
al., 2005; O’Halloran et al., 2006; Smith et al., 2007; Hunt et al., 2010;
Rémy-Ruyer et al., 2015; Shivaei et al., 2017; Chastenet et al., 2019; Aniano
et al., 2020). It remains unclear whether the PAH abundance fraction relative
to the total dust mass – $q_{\rm{PAH}}$ – drops suddenly or smoothly as
metallicity decreases. Some studies find $q_{\rm{PAH}}$ remains constant at
about 4%, then drops suddenly to about 1% after a threshold at about 0.2 - 0.3
$Z_{\odot}$ (Draine et al., 2007; Chastenet et al., 2019; Shim et al., 2023).
Others find a continuous decrease in the PAH fraction as a function of
metallicity (Galliano et al., 2008; Rémy-Ruyer et al., 2015; Galliano et al.,
2018; Aniano et al., 2020).

It has been common to study the PZR using integrated galaxy measurements from
galaxies across a wide range of metallicity (Engelbracht et al., 2005; Draine
et al., 2007; Smith et al., 2007; Engelbracht et al., 2008; Hunt et al., 2010;
Shim et al., 2023). This method introduces complications because the radiation
environments and star formation histories vary between galaxies. In
comparison, within individual galaxies the main properties that vary with
radius on scales larger than 100 pc are the stellar density, stellar age, and
gas-phase metal abundance. As the density of stars decreases at larger radii,
the average intensity $U$ of the ISRF decreases as well. The average age of
stars and the ISM density also decrease at larger radii (García-Benito et al.,
2017; Dale et al., 2020), increasing the average hardness $\langle
h\nu\rangle$ of the ISRF.

The effect each of these properties of the radiation environment has on the
PAH spectrum can be explicitly modeled with the new suite of theoretical
spectra from Draine et al. (2021) (hereafter D21). The D21 models are based on
the simplifying assumption that PAHs can be idealized as nearly spherical
grains of pure graphite characterized by a single size parameter and a binary
ionization state. This is sufficient to produce MIR emission features that
match observations of galaxies. Other models use spectra of specific PAH
molecules from quantum-chemical calculations, however this is currently only
feasible for a small fraction of the PAH size distribution (Rigopoulou et al.,
2021). Since we are interested in exploring the spectrum produced by the full
range of PAH sizes exposed to various radiation environments, the D21 models
provide an excellent framework for comparison to the observations.

Resolved PZR studies probing the centers of individual star-forming spiral
galaxies using photometric tracers of PAH emission have been conducted with
JWST imaging. These have well-constrained metallicity gradients in the radial
direction, and the fraction $q_{\rm{PAH}}$ is found to decrease relatively
smoothly (Chastenet et al., 2023). Most previous studies on the PZR only make
use of photometric PAH tracers, primarily at 8 µm to study the strongest PAH
feature at 7.7 µm. This feature is primarily emitted by ionized PAHs with
$\sim 100$ carbon atoms ($N_{\rm C}$), resulting in the common explanation
that the smallest PAHs are being preferentially destroyed in low metallicity
environments. The full PAH spectrum has contributions from both ionized and
neutral grains with $\sim$20 – 106 $N_{\rm C}$. A full accounting of the
properties of the small grain population requires spectroscopic access to all
the main PAH emission bands.

In addition to changes in the overall PAH luminosity, we can track several key
variations in the PAH spectrum itself as metallicity decreases. Based on the
theoretical work of Li & Draine (2001); Draine & Li (2007); Draine et al.
(2021), each PAH feature traces a specific regime of the grain size and
ionization distributions of the local PAH population. In general, small PAHs
emit more efficiently at shorter wavelengths and large PAHs emit more
efficiently at longer wavelengths. Specifically, the approximate peaks are as
follows (Draine et al., 2021, see Figure 6): the 17 µm feature is emitted most
efficiently by PAHs with $\sim 2,000$ $N_{\rm C}$ with no ionization
preference, 11.3 µm by neutral PAHs with $\sim 400$ $N_{\rm C}$, 7.7 µm by
ionized PAHs with $\sim 100$ $N_{\rm C}$, and 6.2 µm by ionized PAHs with
$\sim 70$ $N_{\rm C}$. The final major PAH feature at 3.3 µm is emitted at
peak efficiency by neutral PAHs just above the minimum survivable PAH size
adopted in D21 of 27 $N_{\rm C}$. Since this work uses Spitzer spectroscopy
from 5–38 µm, we do not have 3.3 µm coverage. Instead we use the best fit
models to predict the metallicity trends in this final PAH feature.

Smith et al. (2007) found the ratio of the 17 to 11.3 µm features drops
significantly as metallicity declines. This was attributed to enhanced
formation of grains larger than $\sim 400$ $N_{\rm C}$ at higher
metallicities. Sandstrom et al. (2012) found a similar result: the 17 µm
feature is significantly weaker, but still detected, in low metallicity
regions of the Small Magellanic Cloud (SMC) compared to the higher metallicity
galaxies of the Spitzer Infrared Nearby Galaxies Survey (SINGS; Smith et al.,
2007). They found the 7.7 µm feature is also significantly weaker, and the 6.2
and 11.3 µm features carry an increased fraction of the PAH power. This
suggests PAHs in the low metallicity SMC are smaller and more neutral. Hunt et
al. (2010) found the fractional PAH power in the 8.6 µm and 11.3 µm features
is increased for low-metallicity blue compact dwarf galaxies compared to the
SINGS galaxies, while the 6.2 µm and 7.7 µm features remain constant. They
interpret this as evidence for an decrease in the PAH population smaller than
100 $N_{\rm C}$ in low metallicity galaxies compared to high metallicity
systems.

Studies of the PZR in galaxies have resulted in many different interpretations
and several questions remain unanswered. Some attribute the PAH deficit to
timing: a galaxy with low metallicity and a young stellar population simply
has not had enough time to build up a significant reservoir of PAHs yet
(Galliano et al., 2008). However, most agree that the relative PAH-to-dust
luminosity drops as a result of (or correlated with) the decreased gas-phase
metal abundance (O’Halloran et al., 2006; Draine et al., 2007; Gordon et al.,
2008; Hunt et al., 2010; Shivaei et al., 2017; Aniano et al., 2020; Shivaei et
al., 2024).

Table 1: Spitzer-IRS Observations Target Name | RA (J2000) | Dec (J2000) | AORID | Observation Date
---|---|---|---|---
M101-BG | 14h03m26.50s | +54d37m35.0s | 14800896 | 2006-01-20 16:42:25
M101_SLmap_01 | 14h03m01.90s | +54d17m01.0s | 14800128 | 2006-01-20 16:50:08
M101_SLmap_00 | 14h03m10.50s | +54d20m10.8s | 14799872 | 2006-01-21 02:57:54
M101_SLmap_02 | 14h02m53.30s | +54d13m51.2s | 14800384 | 2006-01-21 08:56:46
M101 - HalfStrip Offset | 14h03m01.90s | +54d17m01.0s | 14799616 | 2006-04-22 13:13:16
M101-BG | 14h03m26.50s | +54d37m35.0s | 14800640 | 2006-04-23 04:28:50
NGC628_SLmap_00 | 1h36m48.10s | +15d43m56.2s | 14802432 | 2006-01-24 14:12:51
NGC628_SLmap_01 | 1h36m43.30s | +15d46m14.4s | 14802688 | 2006-01-24 18:42:01
NGC628-BG | 1h36m54.13s | +15d37m59.0s | 14803200 | 2006-01-22 14:53:25
NGC628 - HalfStrip Offset | 1h36m45.70s | +15d45m05.3s | 14802944 | 2006-01-22 14:59:23
NGC628-BG | 1h36m54.13s | +15d37m59.0s | 14803456 | 2006-01-23 23:50:00
NGC2403-BG | 7h36m29.69s | +65d27m27.6s | 14802176 | 2006-03-10 13:23:20
NGC2403_SLmap_01 | 7h36m44.70s | +65d35m23.7s | 14801408 | 2006-03-10 13:31:00
NGC2403_SLmap_00 | 7h36m28.90s | +65d33m24.5s | 14801152 | 2006-03-10 18:00:20
NGC2403-BG | 7h36m29.69s | +65d27m27.6s | 14801920 | 2006-04-17 17:44:11
NGC2403 - HalfStrip Offset | 7h36m36.80s | +65d34m24.1s | 14801664 | 2006-04-17 17:50:06

Interpretation of the observed PZR trends is further complicated by the many
unknowns about how small grains are produced and survive in the ISM. It is
still unclear if the trends are a result of changes to the initial PAH GSD
from stellar injection or changes in formation and processing pathways in the
ISM. What the dominant sources of grains that emit as PAHs are and how their
formation mechanisms depend on metal content are areas of ongoing research
(Zhukovska et al., 2008; Galliano et al., 2018). It has been theorized that
the smallest dust grains should be more susceptible to destruction by ionizing
radiation in low metallicity environments due to their reduced heat capacities
(Micelotta et al., 2010a, b; Draine et al., 2021). A deficiency of PAH
emission has been observed in extreme environments such as Hii regions
(Cesarsky et al., 1996; Kassis et al., 2006; Povich et al., 2007; Gordon et
al., 2008; Chastenet et al., 2019; Egorov et al., 2023), likely due to strong
radiative processing. Therefore we expect in some cases it is possible for
PAHs to be destroyed while larger dust grains survive. It is likely that grain
formation and destruction processes shape the observed spectrum, and these may
be more or less dominant in different environments and galaxies.

##  3 Data

The primary data products used in this study are co-spatial Spitzer-IRS Short-
Low (SL1 7.5 – 14.7 µm, SL2 5.2 – 7.6 µm, and SL3 7.4 – 8.7 µm) and Long-Low
(LL1 20.6 – 38.4 µm and LL2 14.2 – 21.1 µm) spectroscopic maps. We extracted
spectra from these maps in $\sim$0.43 – 1.7 kpc apertures across three nearby
galaxies from the PAH-BIGMAP program 20518: M101 (NGC 5457), NGC 628, and NGC
2403. These maps extend radially outwards from the center of each galaxy at an
orientation designed to avoid bright Hii regions. We also include eight
Spitzer spectral observations of Hii regions in M101 from Gordon et al.
(2008), re-reduced in a consistent manner.

Figure 1 shows the position of each spectroscopic map on a three-color image
of each galaxy. These images are composed of IRAC 3.6 µm in blue, IRAC 8 µm in
green, and MIPS 24 µm in red (see § 3.2). Note the shift from green to red
with increasing radius in each galaxy. This suggests the PAH emission at 8 µm
is decreasing faster than the dust continuum emission at 24 µm.

Figure 2: Three-color images from slices of the Spitzer-IRS SL1 spectral cubes
for M101 (top), NGC 628 (left), and NGC 2403 (right). Red is the surface
brightness at the PAH 12.6 µm peak, green is at the PAH 11.3 µm peak, and blue
is at the PAH 7.7 µm peak. The apertures defined in § 3.3 are shown in cyan.

###  3.1 Spectroscopic Data Reduction

All spectral maps were reduced with CUBISM (Smith et al., 2007), using
background frames created from both the dedicated background spectra
associated with each observation set, as well as emission-free regions on the
outskirts of the radial strip maps. Automatic and by-eye pixel selection was
employed to remove bad pixels and mitigate striping in the final cube.

Slight mismatches in the surface brightness of aperture-matched spectra were
found in faint regions for sub-orders SL1, SL2, and SL3. These were determined
to arise at low surface brightness levels from light contamination which
varies spatially on the detector and over time. We corrected the effect with a
row-by-row box-car average of inter-order pixels across time-adjacent
background-subtracted detector images. This process is implemented with the
program sl_io_correct (Sandstrom et al.,
2012)111https://tir.astro.utoledo.edu/spitzer/io_correct/. Correction using
inter-order light results in a significant improvement in the flux agreement
between SL1, SL2, and SL3 intensities at the wavelengths where they overlap
for low surface brightness spectra.

The sub-orders of SL and LL were stitched by averaging the brightness at
wavelengths where they overlap. The combined LL spectrum was then scaled to
match the SL spectrum. This was done with a multiplicative factor or an
additive offset based on the brightness of the spectrum. After removing
backgrounds, residual baseline variations in dark regions of the cube remained
below 1 MJy/sr. For faint spectra (i.e. average brightness $<$0.75 MJy/sr), we
employed an additive offset to bring spectral segments into agreement. For
brighter spectra, we employ a multiplicative factor. We find this process
results in good agreement between SL and LL for all spectra in our sample and
all offsets and factors are small, typically $\sim$0.1 MJy/sr (additive) and
$\sim$1.1 (multiplicative).

###  3.2 Infrared Photometric Data

We also compiled infrared photometric data from 8 µm through 160 µm in order
to derive the total infrared (TIR) surface brightness in each of our
apertures. The 8 µm data from the Infrared Array Camera (IRAC), the 24 µm data
from the Multiband Imaging Photometer for Spitzer (MIPS), and the 70, 100, and
160 µm data from the Photodetector Array Camera and Spectrometer (PACS) of the
Herschel Space Observatory were retrieved from the Key Insights on Nearby
Galaxies: a Far-Infrared Survey with Herschel (KINGFISH, Kennicutt et al.,
2011) and NGC 2403 from the Very Nearby Galaxies Survey (VNGS, Bendo et al.,
2012). NGC 2403 was never observed with PACS 100 µm, so data at 250 µm from
the Spectral and Photometric Imaging Receiver (SPIRE) of Herschel were
included so the spectral energy distribution (SED) could be modeled. All
photometric data were convolved to the point-spread function (PSF) of the
lowest resolution images used for SED determination – PACS 160 µm, full-width
half-maximum (FWHM) 11$\farcs$2, and a Gaussian PSF with FWHM 25″ for NGC
2403.

###  3.3 Region Definition

The spectral cubes for M101 and NGC 628 were convolved to the resolution of
PACS 160 µm (11$\farcs$2) with kernels produced by the STINYTIM program
(Sandstrom et al., 2009). Since NGC 2403 has no PACS 100 µm data, it was
necessary to convolve the cubes to a lower resolution than SPIRE 250 µm (a
Gaussian of FWHM 25″). The convolution process (when the image is padded with
zeros) also dims the edges of each spectral cube where the convolution kernel
falls off the coverage footprint. We trimmed the edges of our spectral cube by
5″ on all sides to preserve as much area as possible while ensuring
appropriate data coverage. This 5″ is approximately the size of one pixel in
the LL cubes, and just less than two pixels in the SL cubes.

Extraction apertures were defined to span the entire overlap region between
the SL and LL footprints. We tiled each galaxy with rectangular apertures with
a minimum side length of the limiting PSF of the supplemental photometric data
(11$\farcs$2, 25″ for NGC 2403). An iterative algorithm was used to define
apertures based on the continuum brightness at MIPS 24 µm to ensure
sufficiently high signal-to-noise PAH detections. The final apertures are
shown in Figure 2. The initial apertures for this process were square and
spanned the width of each radial strip. If the average surface brightness of
the aperture was above 0.25 MJy/sr at MIPS 24 µm, then the square was split
into a vertical pair and a horizontal pair. Next, we checked whether the
vertical or horizontal pair was brighter. If the brightest pair was at least
10% brighter than the original square, or above 1 MJy/sr, then the algorithm
continued on the pair. The pair was then broken into two squares, and the same
process was repeated until the minimum size is reached.

From all radial strips there are a total of 160 regions that meet the minimum
continuum brightness threshold: 85 in M101, 64 in NGC 628, and 11 in NGC 2403.
Including the 8 Hii regions, a total of 168 regions with well-measured spectra
were analyzed.

###  3.4 MIR Spectral Fitting

The final extracted Spitzer spectra (5–38 µm) were fit with the IDL program
PAHFIT (Smith et al., 2007). From PAHFIT we obtained the integrated
intensities of all emission features and their propagated uncertainties. We do
not expect significant attenuation in spectra of the spiral galaxies in our
sample, so attenuation was not included in the fit. The sub-features of major
PAH complexes were combined with PAHFIT to produce combined power in the 7.7,
11.3, 12.6, and 17 µm bands. We further combined all PAH features (5–18 µm)
into $\Sigma$PAH using PAHFIT.

The Hii region spectral cubes are smaller and sparsely sampled by the slit, so
we did not convolve them to a common resolution. Instead, we scaled our
derived PAH luminosities in these apertures by the ratio between their average
native IRAC 8 µm photometry and their average IRAC 8 µm when convolved to PACS
160 µm resolution. The median ratio is 1.94, the mean is 1.86, and the
standard deviation is 0.25, so the PAH luminosity of each Hii region was
scaled down by about a factor of two, with no change in the band ratios.

Figure 3: Example IRS spectra from M101. The spectrum of the center (red),
threshold metallicity (green), and edge regions (blue) from the M101 radial
strip. Each spectrum is normalized by the surface brightness at 11.3 µm. The
PAHFIT result for each spectrum is shown in gray along with each component of
the fit: stellar continuum (cyan), dust continuum (orange), line emission
(black), and PAH emission (magenta). Note the relative shift in power from
long wavelength PAH features to short as metallicity drops from $Z_{\odot}$ to
0.4 $Z_{\odot}$.

Figure 4: (Top) PAH emission deficit at low metallicity. Ratio of all PAH
emission to all other dust emission ($\Sigma$PAH/TIR) as a function of
metallicity. The hexagons and their errorbars indicate the mean and standard
deviation in six bins of width 0.1 $Z_{\odot}$. The gray bin includes only the
points below 0.4 $Z_{\odot}$. The pink bin falls within the bulge radius of
M101 and indicates the mean after a correction for reddened ISRF is applied
(see § 4.1.1). The solid black lines indicate the median above
$Z_{\mathrm{th}}$ and a power law fit below. (Bottom) Correlation between
$\Sigma$PAH/TIR and modeled PAH mass abundance fraction ($q_{\rm{PAH}}$). The
dashed lines indicate the expected trend from D21 models for three incident
ISRFs with $U$=1: M31 bulge (red), mMMP (black), and a low-metallicity
starburst (cyan). The dotted cyan line indicates the low-metallicity spectrum
with $U$=100. The solid black line indicates a linear fit with intercept fixed
at zero. The hexagons indicate the mean and standard deviation in bins of
width 0.5% in $q_{\rm{PAH}}$. The gray bin includes only the points below
$q_{\rm{PAH}}$ = 1%.

###  3.5 Derived Quantities

From the photometric data we derived total infrared luminosity (3–1100µm, TIR)
for each region in M101 and NGC 628 using the calibration presented in
Galametz et al. (2013):

$\begin{split}\rm TIR&~{}=~{}2.051\times\nu
I_{\nu}(24\micron)\,+0.521\times\nu I_{\nu}(70\micron)~{}\\\
&~{}~{}\,+0.294\times\nu I_{\nu}(100\micron)+0.934\times\nu
I_{\nu}(160\micron)\end{split}$ (1)

where the constants were taken from their Table 3 and $I_{\nu}$ ($\lambda$) is
the surface brightness at $\lambda$ microns in MJy/sr.

There is no data at 100 µm for NGC 2403, so we used the calibration from
Galametz et al. (2013) that does not depend on this band:

$\begin{split}\rm TIR&~{}=~{}2.126\times\nu
I_{\nu}(24\micron)~{}+0.670\times\nu I_{\nu}(70\micron)\\\
&~{}~{}\,+1.134\times\nu I_{\nu}(160\micron)\end{split}$ (2)

where the notation is the same as Equation 1.

We determined metallicities (12 + [O/H]) for our extracted regions in M101,
NGC 628, and NGC 2403 using the radial gradient equations presented in Rogers
et al. (2021). We defined solar metallicity as $Z_{\odot}$ $\equiv$ 12 + [O/H]
= 8.69 (Asplund et al., 2009) and we assumed that O/H is a good tracer of the
abundance of all metal species. Skillman et al. (2020) found the relative C/O
abundance decreases radially in M101 by about 0.4 dex over two effective radii
(Re, see Table 2). Therefore there is likely even less carbon than expected
from a linear scaling with the oxygen abundance gradient of each galaxy. The
parameters of the metallicity gradient equation for each galaxy are shown in
Table 2, where the metallicity is largest at the center ($Z_{o}$) and
decreases with a constant slope ($m$) as a function of deprojected
galactocentric radius ($R$): $Z$ $=$ $Z_{o}$ $-~{}m~{}\times~{}(R/R_{\rm e})$.

We assumed metallicity is purely radial with no small scale or azimuthal
variations. Kreckel et al. (2019) found the metallicity of nearby spiral
galaxies varies by up to 0.05 dex on scales of 120 pc, but the radial
dependence dominates. This is comparable to the scatter in the metallicity
gradient fits employed here. Including a 0.05 dex uncertainty for all
metallicity values would not significantly alter the results of this work.

####  3.5.1 Dust and Galaxy Property Maps

The properties of dust and local environmental conditions can be derived from
infrared photometric data from IRAC 3.6 µm, IRAC 4.5 µm, IRAC 5.8 µm, IRAC 8
µm, MIPS 24 µm, PACS 70 µm, PACS 100 µm, and PACS 160 µm. This was done by
fitting the SED with the Draine & Li (2007) model using the methodology of
Aniano et al. (2020). NGC 2403 was not observed with PACS 100 µm so an
additional far-infrared band, SPIRE 250 µm was necessary to accurately fit the
SED model. The SED models produce resolved maps of quantities such as the
fraction of dust mass in the form of PAHs with $N_{\rm C}$ $<~{}10^{3}$
($q_{\rm{PAH}}$), and the mass-weighted average starlight energy density per
unit frequency that is illuminating the local dust ($\bar{U}$). We focus
primarily on the maps of these two quantities in this analysis. Values for
each region are extracted from these maps using the matched apertures defined
in § 3.3.

Table 2: Galaxy Information & Metallicity Gradients

Property | M101 | NGC 628 | NGC 2403
---|---|---|---
Central Abundance (12 + [O/H]) | 8.70 $\pm$ 0.04 | 8.65 $\pm$ 0.05 | 8.55 $\pm$ 0.04
Slope $m$ (dex/Re) | 0.17 $\pm$ 0.02 | 0.09 $\pm$ 0.03 | 0.09 $\pm$ 0.03
Re (arcsec) | 197.6 | 95.4 | 178.0
Distance (Mpc) | 7.4 | 7.2 | 3.2
Inclination ($\degree$) | 18 | 5 | 63
Position Angle ($\degree$) | 39 | 12 | 124

††footnotetext: Values adopted from Berg et al. (2020) and Rogers et al.
(2021).

##  4 Observational Results

Figure 3 shows three example spectra from the M101 radial strip. Comparing
them, we observe the 17 µm feature and the brightest feature at 7.7 µm are
significantly reduced at lower metallicity. The remaining PAH power is in the
11 µm complexes and the 6.2 µm feature which is brighter at 0.4 $Z_{\odot}$
than at $Z_{\odot}$.

###  4.1 PAH to Total Dust Emission Metallicity Relation

The ratio of all PAH emission ($\Sigma$PAH) to the total infrared brightness
(TIR) is shown in the top panel of Figure 4. $\Sigma$PAH/TIR rises from about
10% to 16% as metallicity decreases from $Z_{\odot}$ to $\sim\frac{2}{3}$
$Z_{\odot}$, then drops below 2% by $\sim\frac{1}{4}$ $Z_{\odot}$. We refer to
this threshold metallicity where the drop in $\Sigma$PAH/TIR occurs as
$Z_{\mathrm{th}}$ $\equiv$ 0.625 $Z_{\odot}$ (12 + [O/H] = 8.5). The best-fit
relation between $\Sigma$PAH/TIR and metallicity has the form:

$\rm\frac{\Sigma
PAH}{TIR}(\%)=\begin{cases}15.1~{}\pm~{}2.0&~{}~{}Z>Z_{\mathrm{th}}\\\
(15.1\pm~{}0.2)\left(\frac{Z}{~{}Z_{\rm
th}}\right)^{2.6~{}\pm~{}0.1}&~{}~{}Z\leq Z_{\mathrm{th}}\end{cases}$ (3)

where the fit at metallicities above $Z_{\mathrm{th}}$ is the uncertainty-
weighted median with bulge light correction applied (see § 4.1.1) and below
$Z_{\mathrm{th}}$ the fit is a power law. The value of $Z_{\mathrm{th}}$ is
determined by requiring the fit to be continuous at $Z_{\mathrm{th}}$ to
within 1$\sigma$. The Hii regions in the mid-disk are notably offset from the
overall trend; their $\Sigma$PAH/TIR is lower than expected based on their
metallicity.

The bottom panel of Figure 4 shows the strong correlation between
$\Sigma$PAH/TIR and $q_{\rm{PAH}}$, where the linear fit has the form:

$\begin{split}&\rm\frac{\Sigma
PAH}{TIR}=(3.69~{}\pm~{}0.02)\times\textit{q}_{PAH}\end{split}$ (4)

Also indicated in this figure is the expected $\Sigma$PAH/TIR for a given
$q_{\rm{PAH}}$ from the D21 models. We use their ‘standard’ GSD and re-scale
it such that the resulting integral for $N_{\rm C}$$~{}<~{}10^{3}$ gives a
desired $q_{\rm{PAH}}$. A spectrum is then produced from each GSD and
$\Sigma$PAH/TIR is calculated by PAHFIT and Equation 1. We leave $U$ fixed at
1 and repeat this using three different ISRFs to plot the three dashed lines:
the 10 Myr $Z_{\odot}$/20 SED from Eldridge et al. (2017), the solar
neighborhood mMMP SED from Mathis et al. (1983); Draine et al. (2021), and the
M31 bulge SED from Groves et al. (2012). An additional dotted line is also
shown where we have increased $U$ to 100 and used the 10 Myr $Z_{\odot}$/20
SED. These lines indicate the general effect that increasing the ISRF hardness
and intensity has on the PAH and dust luminosities.

####  4.1.1 Bulge ISRF Correction

Figure 5: $\bar{U}$ as a function of galactocentric radius. Values detected
below 3$\sigma$ are set to zero.

Following the work of Draine et al. (2014), we can interpret the decrease in
$\Sigma$PAH/TIR as metallicity increases from 0.9 $Z_{\odot}$ to $Z_{\odot}$
as a result of the increasing bulge fraction at low galactocentric radii in
M101. NGC 628 and NGC 2403 do not have significant bulges (Fisher & Drory,
2010). PAHs in the bulge are excited by an ISRF dominated by older stars, so
they emit less compared to PAHs in the disk where the ISRF is more dominated
by UV and optical photons from young stars. This effect is less significant
for larger dust grains, so $\Sigma$PAH/TIR drops as the bulge fraction
increases. The red dashed line in Figure 4 shows this using the D21 models: a
given $q_{\rm{PAH}}$ illuminated by the M31 bulge SED results in $\sim 50\%$
less $\Sigma$PAH/TIR than the same $q_{\rm{PAH}}$ illuminated by the solar
neighborhood mMMP SED.

Figure 5 shows the $\bar{U}$ values extracted from our apertures. Based on
this, the disk of M101 has $\bar{U}$ $\approx$ 1 and it begins to increase due
to the bulge component of the galaxy closer to the center. We consider the
bulge radius to be where $\bar{U}$ begins to increase above 1 (about
60$\arcsec$ from galaxy center, approximately where metallicity is 0.9
$Z_{\odot}$). Within this radius is also where the drop in $\Sigma$PAH/TIR and
$q_{\rm{PAH}}$ occurs for regions in M101.

We used the equations from Draine et al. (2014) to correct $q_{\rm{PAH}}$ by
accounting for the softer radiation field in the bulge of M101. Again using
the $\bar{U}$ maps we calculated $U_{bulge}$ for all regions within the bulge
radius as $U_{bulge}$ = $\bar{U}$ \- $U_{disk}$ with $U_{disk}$ = 1. However
we find that this shifts points within the bulge radius from 1% below the
median $q_{\rm{PAH}}$ between $Z_{\mathrm{th}}$ and 0.9 $Z_{\odot}$ (4%) to 1%
above the median. A correction that brings these points to share the median
can be obtained by a small modification to Equation 21 from Draine et al.
(2014). The parameter $A$ is tied to the hardness of the radiation field with
higher values corresponding to harder radiation. For instance the $A$ value
for the bulge of M31 is 1.95 and the value for the disk is 4.72. We find
changing only the value of $A_{bulge}$ from 1.95 to 3.85 brings the points in
the bulge radius to agree with the median of the points outside this radius
(and less than $Z_{\mathrm{th}}$) in both $\Sigma$PAH/TIR and $q_{\rm{PAH}}$.
This brings $A_{bulge}$ closer to $A_{disk}$ = 4.72. This change is reasonable
since M101 has a weak, actively star-forming bulge while the bulge of M31
considered in Draine et al. (2014) has over three times the metal abundance,
significantly more dust attenuation, and an older stellar population
dominating the ISRF.

###  4.2 PAH Band Ratios

Figure 6: As a function of metallicity: (top) PAH 11.3/17 µm ratio, (second)
PAH 7.7/11.3 µm ratio, (third) PAH 6.2/7.7 µm ratio, (bottom) PAH 6.2/17 µm
ratio. Hexagons indicate the mean and standard deviation in six bins with
width 0.1 $Z_{\odot}$. The vertical line indicates the threshold metallicity
$Z_{\mathrm{th}}$. Ratios detected below 3$\sigma$ are set to zero.

To better diagnose what is happening with the PAHs, we plot short-to-long
wavelength band ratios as a function of metallicity in Figure 6. The top panel
shows the ratio PAH 11.3/17 µm is constant until $Z_{\mathrm{th}}$, then it
rises steeply as metallicity drops. Since the 17µm feature originates from the
largest neutral and ionized PAHs, this could be evidence that the largest PAHs
($>~{}2,000~{}$$N_{\rm C}$) are preferentially depleted at low metallicity.
This rise could also be a result of increasing ISRF hardness as metallicity
decreases below $Z_{\mathrm{th}}$ causing a shift in PAH luminosity from
longer to shorter wavelength bands (Draine et al., 2021).

The second panel shows the ratio PAH 7.7/11.3 µm decreases away from the
threshold metallicity on either side. The 7.7 µm feature is emitted most by
ionized PAHs with $\sim 100$ $N_{\rm C}$ and the 11.3 µm feature is from
neutral PAHs with $\sim 400$ $N_{\rm C}$. As metallicity decreases from
$Z_{\odot}$ to $Z_{\mathrm{th}}$ the PAHs may be getting smaller or more
ionized, then below $Z_{\mathrm{th}}$ they may become larger or less ionized.
It is also possible that the harder ISRF at lower metallicity is raising the
fractional PAH luminosity at short wavelengths and resulting in an increase in
the PAH 7.7/11.3 µm ratio, however this could not explain why the ratio then
decreases below $Z_{\mathrm{th}}$.

The third panel shows the ratio PAH 6.2/7.7 µm is mostly constant from
$Z_{\odot}$ to $Z_{\mathrm{th}}$, then increases at lower metallicities. The
increase is steeper for the M101 strip regions than for those from NGC 2403
and the M101 Hii regions. The 6.2 µm feature is from ionized PAHs with $\sim
70$ $N_{\rm C}$ so the increase at low metallicity could be a result of PAHs
becoming smaller below $Z_{\mathrm{th}}$. It is also possible that the
increasing ISRF hardness is responsible for the increase in the PAH 6.2/7.7 µm
ratio.

The final panel shows the ratio PAH 6.2/17 µm rises steadily as metallicity
decreases. This again indicates that the PAHs are becoming smaller on average.
Alternatively the PAHs may remain the same and the ISRF hardness is
increasing, causing the PAHs to emit more at shorter wavelengths.

Overall the trends in these four PAH band ratios suggest the following. PAH
7.7/11.3 µm and PAH 6.2/17 µm rise between $Z_{\odot}$ and $Z_{\mathrm{th}}$
while PAH 6.2/7.7 µm and PAH 11.3/17 µm are constant. This suggests the effect
of increasing ISRF hardness is not significant at these metallicities, or else
all ratios would show a steady increase. The observed increase in PAH 6.2/17
µm by about an order of magnitude could be interpreted as an increase in the
amount of PAHs with $\sim 70$ $N_{\rm C}$ relative to PAHs with $\sim 2,000$
$N_{\rm C}$. Similarly, the observed increase in PAH 7.7/11.3 µm by about 40%
could be interpreted as an increase in the amount of PAHs with $\sim 100$
$N_{\rm C}$ relative to PAHs with $\sim 400$ $N_{\rm C}$.

It is also possible that the increase in PAH 7.7/11.3 µm is evidence of PAHs
becoming more ionized. This is the only ratio shown that is strongly dependent
on the ionization distribution of the PAHs. The ionization fraction of PAHs
depends on the conditions of the gas and the grain size, with smaller PAHs
being more neutral on average than larger PAHs (Draine et al., 2021). If PAHs
are becoming smaller then the overall fraction of neutral PAHs will increase
as well.

Below $Z_{\mathrm{th}}$, again all ratios except for PAH 7.7/11.3 µm show the
same trend of increasing with decreasing metallicity. The three ratios that
increase at low metallicity suggest PAHs overall are becoming smaller and/or
hotter. If changes in the radiation field hardness were the primary driver, we
would expect the PAH 7.7/11.3 µm ratio to also increase below
$Z_{\mathrm{th}}$. This is not what is observed, suggesting instead that there
are also changes in the PAH size distribution and overall ionization fraction.

Figure 7:  (Top) The observed metallicity effect on PAHs from the ratio of
each major PAH feature to total PAH luminosity. The gray vertical line
indicates the threshold metallicity $Z_{\mathrm{th}}$. (Bottom) Fractional
change in PAH/$\Sigma$PAH relative to the value at $Z_{\odot}$. Relative to
the total PAH luminosity, the power shifts to shorter wavelengths, then after
$Z_{\mathrm{th}}$ the 7.7 and 17 µm features decrease, the 11.3 µm feature is
unchanged, and the 6.2 µm feature increases.

The bottom panel of Figure 7 shows the differential change in each PAH feature
relative to the total PAH luminosity compared to the value at solar
metallicity. This figure shows the shifts in power among the PAH features. As
metallicity drops from $Z_{\odot}$ to $Z_{\mathrm{th}}$, the PAH power shifts
out of the longer wavelength features and into the short wavelength features.
When metallicity drops below about $Z_{\mathrm{th}}$ the power begins to shift
out of the 7.7 µm PAH feature and toward the 11-13 µm complexes. The most
dramatic changes are in the 6.2 µm and 17 µm feature. The 6.2 µm feature
increases about 60% from $Z_{\odot}$ to $\frac{1}{2}$ $Z_{\odot}$. The 17 µm
feature decreases about 75% over this same metallicity range.

##  5 Modeled PAH & Dust SED Analysis

Figure 8: Size distributions of PAH feature emitting grains. Shown are the
size distributions as described in Draine et al. (2021) with several values of
$a_{\rm 01}$. Note that changing $a_{\rm 01}$ shifts the location of the first
peak but the integral remains constant. The photo-destruction parameter
$a_{\mathrm{min}}$ is shown in red; below this value all PAHs are deleted from
the distribution without preserving the integral.

To interpret the changes in band ratios, we created models of PAHs with
various size distributions and illuminated by different radiation fields using
the theoretical PAH spectra from D21. By comparing the variations in
$q_{\rm{PAH}}$, $\Sigma$PAH/TIR, and PAH/$\Sigma$PAH we investigated what
changes in PAH size and ISRF can reproduce our observed trends. D21 produced
model PAH spectra based primarily on four input parameters: incident radiation
field spectrum, incident radiation intensity ($U$), PAH grain size
distribution, and a binary PAH ionization distribution (either neutral or
cationized). The standard grain size distribution is described in D21 as a
double-peaked log-normal distribution with peak locations characterized by
grain sizes $a_{\rm 01}$$=4$ Å and $a_{02}=30$ Å (see Figure 8). Based on the
agreement between the linear fit in the bottom panel of Figure 4 and the D21
model using the mMMP ISRF with $U~{}=~{}1$, we assumed these parameters are
constant in each of the scenarios described below other than the ISRF hardness
scenario. For simplicity, we used the standard ionization distribution as a
function of grain size. When we generated an infrared dust SED from the D21
models, we also included the emission from larger ‘astrodust’ grains in order
to get an accurate measure of TIR.

For each spectrum we generated from the D21 models, we measured all the PAH
features using PAHFIT (Smith et al., 2007) to be consistent with the PAH
feature strengths measured in the observed spectra. We used an updated version
of the PAHFIT model that includes the 3.3 µm PAH feature (Lai et al., 2020).
From the PAHFIT results we derived the sum of all PAH emission ($\Sigma$PAH)
as well as the ratio of every PAH band relative to $\Sigma$PAH
(PAH/$\Sigma$PAH). TIR was determined by integrating the generated spectrum
from 3 to 1,100 µm. $q_{\rm{PAH}}$ for every spectrum is calculated by the
ratio of PAH mass – from integration of the input GSD for grains with $N_{\rm
C}$ $<~{}10^{3}$ ($\sim 13.4\,\mathrm{\AA}$) – relative to the total astrodust
mass.

###  5.1 Model Scenarios

We considered three realistic scenarios that could reproduce the major
observed PZR trends: $q_{\rm{PAH}}$, $\Sigma$PAH/TIR, and the main
PAH/$\Sigma$PAH ratios, all as a function of metallicity. The ‘ISRF hardness’
model fixes the size distribution and varies the hardness of the incident ISRF
as metallicity decreases. The ‘photo-destruction’ model simulates bottom-up
destruction of PAHs by increasing the minimum grain size as metallicity
decreases. Finally, the ‘inhibited growth’ model mimics a reduced accretion
rate of carbon from the gas phase by decreasing the average PAH size and the
overall abundance of carbonaceous grains.

####  5.1.1 ISRF Hardness Model

Figure 9:  Fractional PAH power as a function of metallicity for the ISRF
hardness model (§5.1.1). The binned data from Figure 7 are shown. Also shown
is the model-predicted trend for the fractional change in the relative 3.3 µm
feature brightness (black line).

First, we test if changes in the incident ISRF SED alone can explain the
observed PZR trends. For this test we use the two ISRF hardness extremes: the
bulge SED of M31 and a 10 Myr $Z_{\odot}$/20 SED (low-Z). At high metallicity
(at galaxy center), we assume the ISRF is weighted as 1:0 M31:low-Z, and at
the lowest metallicity (at galaxy edge) we assume the weighting is 0:1
M31:low-Z with a linear interpolation between these extremes. The low-Z SED is
characteristic of significantly lower metallicity than we expect at the edges
of our three galaxies, and the M31 bulge SED is likewise significantly softer
than we expect in the centers of our galaxies. Therefore we expect that the
resulting changes to the PAH ratios from this ISRF hardness model represent an
upper bound and more realistically the radial change in radiation hardness for
our three galaxies will be smaller than suggested by this model.

Figure 9 shows the effect of changing the ISRF hardness on the ratios
PAH/$\Sigma$PAH. In the top panel, the ISRF hardness model produces the same
trends as the observations but the magnitude is insufficient. Since the ratios
from this model represent an upper bound, this indicates that the increased
radiation hardness at low metallicity may play a role in the observed PZR
trends, but the effect is not strong enough to be the primary driver.

This model is also incapable of producing the observed drop in $q_{\rm{PAH}}$
and $\Sigma$PAH/TIR as metallicity decreases below $Z_{\mathrm{th}}$. When
only the incident radiation field hardness is increased, PAHs of all sizes
emit more, so $\Sigma$PAH increases. Due to the difference in heat capacities
between PAHs and larger dust grains that emit mid- and far-IR continuum,
$\Sigma$PAH increases faster than TIR in harder radiation environments. Since
$q_{\rm{PAH}}$ is derived from the GSD and we do not change it in this
scenario, $q_{\rm{PAH}}$ remains constant regardless of the incident ISRF. In
practice $q_{\rm{PAH}}$ is often inferred from the 8 µm brightness and,
similar to $\Sigma$PAH/TIR, this increases faster than the total dust
luminosity as the incident radiation field becomes harder. Therefore changing
the ISRF hardness alone cannot explain all observed PZR trends.

####  5.1.2 Photo-Destruction Model

Figure 10: Grain photo-destruction model summary. Top-Left: the size
distribution of PAH-emitting grains varies as a function of metallicity, with
the lower size cutoff $a_{\mathrm{min}}$ increasing as metallicity drops below
a specific threshold, at a rate (top-right) which reproduces the
$q_{\rm{PAH}}$-$Z$ relationship. The dashed blue line indicates grains with
$N_{\rm C}$ = 103 so at this $a_{\mathrm{min}}$ $q_{\rm{PAH}}$ = 0. Bottom:
comparisons between six observed PZR trends (black) and the photo-destruction
model (red). The dashed vertical line indicates the threshold metallicity
below which $a_{\mathrm{min}}$ begins increasing. Seven metallicity bins
indicate the median of each trend in cyan, with detections below 3$\sigma$ set
to zero.

We simulate the effects of photo-destruction of small PAHs as the average
hardness of the radiation field increases inversely with metallicity by
imposing a sliding minimum grain size below which all PAHs are destroyed. In
this scenario, $q_{\rm{PAH}}$ and $\Sigma$PAH/TIR decrease because small PAHs
are removed from the population starting from the smallest grains up. We model
this with a minimum grain size cutoff, $a_{\mathrm{min}}$, which rises as
metallicity drops. The functional form of $\log(a_{\mathrm{min}}(Z))$ is a
power law, with index determined by minimizing $\chi^{2}$ between
$q_{\rm{PAH}}$ from the model GSDs and the observationally-determined
$q_{\rm{PAH}}$ values. The model is summarized in Figure 10. The best fit
correlation for $a_{\mathrm{min}}$($Z$) is:

$\log\left(\frac{a_{\mathrm{min}}}{4\rm\AA}\right)~{}=~{}\begin{cases}0&~{}~{}Z>Z_{\mathrm{th}}\\\
0.52\times\left[1-\left(\frac{Z}{~{}Z_{\mathrm{th}}}\right)^{3.2}\right]&~{}~{}Z\leq
Z_{\mathrm{th}}\end{cases}$ (5)

and is shown in the top right panel of Figure 10. We find this model can be
fit to the $q_{\rm{PAH}}$ trend and it coarsely reproduces the $\Sigma$PAH/TIR
decline. The resulting band ratio trends, however, are a poor match for the
observations. Since $q_{\rm{PAH}}$ is constant at metallicities higher than
$Z_{\mathrm{th}}$, the modeled band ratios likewise do not change. We found
this model does not explain many of the observed trends. The resulting shift
in the PAH band ratios with metallicity is for many features _opposite_ of the
observed trend, as can be expected for a scenario which preferentially weakens
short wavelength bands. For instance, the bottom panel of Figure 10 shows that
modeled PAH 6.2/$\Sigma$PAH decreases but the observed trend increases, and
PAH 17/$\Sigma$PAH increases dramatically in the model, while the observed
trend drops steeply. The model does reproduce the drop in the 7.7 µm feature
below $Z_{\mathrm{th}}$, however it does not explain the observed rise in this
feature from $Z_{\odot}$ to $Z_{\mathrm{th}}$. Even a combination of the
radiation hardness and photo-destruction models cannot produce the observed
shift of power from long to short wavelength PAH features, because the small
PAHs that emit most effectively at shorter wavelengths are being
preferentially destroyed faster than the radiation hardness is increasing.

Figure 11: Inhibited grain growth model summary. As in Fig. 10. Top-Left: GSDs
as a function of metallicity. Top-right: Mapping between average PAH size
$a_{\rm 01}$ (black) and GSD re-scale factor $B_{r}$ (pink) and metallicity
Bottom: comparisons between six observed PZR trends (black) and our best
inhibited growth model (red). Figure 12:  Fractional PAH power as a function
of metallicity for our best inhibited growth model (§5.1.3). The data bins
from Figure 7 are shown. The gray lines indicate extrapolations of the model
to lower metallicities than probed by our observations. Also shown is the
model-predicted trend for the fractional change in the relative 3.3 µm feature
brightness.

####  5.1.3 Inhibited Growth Model

We simulate the effects of inhibited PAH growth by reducing the abundance and
fiducial size of PAHs. The fiducial size parameter $a_{\rm 01}$ characterizes
the location of the first peak in the bi-modal log-normal GSD of carbonaceous
dust grains seen in Figure 8. To reproduce the observed $q_{\rm{PAH}}$, we
also use a multiplicative factor $B_{r}$ that re-scales the entire GSD as
metallicity falls.

The functional form of $a_{\rm 01}$($Z$) is assumed to be a power law: $a_{\rm
01}$ = 5Å ($Z$/$Z_{\odot}$)β, where the value of $a_{\rm 01}$ at $Z_{\odot}$
is chosen to match the ‘large’ end of sizes considered in Draine et al.
(2021), and $\beta~{}>~{}0$. We then explore the parameter space of $\beta\leq
6$ in steps of 0.5 by calculating the resulting $\chi^{2}$ between the the
model and 6 primary observed PZR trends (i.e. $q_{\rm{PAH}}$, $\Sigma$PAH/TIR,
PAH 6.2/$\Sigma$PAH, PAH 7.7/$\Sigma$PAH, PAH 11.3/$\Sigma$PAH, and PAH
17/$\Sigma$PAH). We assume a similar power-law form for $B_{r}$($Z$) but with
a different exponent, constrained by minimizing $\chi^{2}$ between the model
and $q_{\rm{PAH}}$ trends.

Figure 11 summarizes the inhibited growth model that most closely matches
observations. Since $q_{\rm{PAH}}$ is held constant as metallicity drops from
$Z_{\odot}$ to $Z_{\mathrm{th}}$, the amplitude of the GSD stays approximately
constant until metallicity drops below $Z_{\mathrm{th}}$. The best value for
$\beta$ is 1, with negligible improvements from increasing to 1.5 or 2; future
work with more data will allow us to better constrain this parameter.

Since $B_{r}$ is constrained based on the $q_{\rm{PAH}}$-metallicity trend,
the functional form of $B_{r}$ is equivalent to a fit to the $q_{\rm{PAH}}$
trend. Above $Z_{\mathrm{th}}$ $B_{r}$ increases slightly with metallicity to
keep $q_{\rm{PAH}}$ constant while $a_{\rm 01}$ shifts to larger sizes.
$q_{\rm{PAH}}$ has a small dependence on $a_{\rm 01}$ because it is defined as
the integral of the GSD for grains with $N_{\rm C}$ $<~{}10^{3}$, so as
$a_{\rm 01}$ is increased, more of the distribution falls above this range and
$q_{\rm{PAH}}$ decreases slightly. Below $Z_{\mathrm{th}}$ $q_{\rm{PAH}}$
decreases as a power law with index 2.1 and $B_{r}$ has this same relation
normalized to one at $Z_{\mathrm{th}}$.

With $a_{\rm 01}$ decreasing linearly as metallicity drops the relative
changes in each major PAH feature are reproduced to first order (see Figure 11
and Figure 12). Specifically: PAH 17/$\Sigma$PAH drops by 50% at 0.4
$Z_{\odot}$ relative to $Z_{\odot}$, PAH 11.3/$\Sigma$PAH drops by $\sim
20\%$, PAH 7.7/$\Sigma$PAH drops by $\sim 5\%$, and PAH 6.2/$\Sigma$PAH rises
by $\sim 50\%$. There are residual differences between the best model and the
observations. For example, it is not possible to match the strong increase in
PAH 6.2/$\Sigma$PAH of almost 75% between $Z_{\odot}$ and 0.4 $Z_{\odot}$ with
any value of $\beta$. Similarly we cannot reproduce the $\sim$30% drop in PAH
7.7/$\Sigma$PAH after a 10% rise from $Z_{\odot}$ to $Z_{\mathrm{th}}$. The
model does show this rise and fall in PAH 7.7/$\Sigma$PAH, but the amplitude
is much smaller. The photo-destruction model results in a better match for
this specific trend, but fails significantly for other bands.

The inhibited growth model does an excellent job reproducing the observed
trend between $\Sigma$PAH/TIR and metallicity. This trend is _not_ explicitly
fit; the modeled trend is a result of employing the factor $B_{r}$ to best
match the $q_{\rm{PAH}}$ trend and fitting $a_{\rm 01}$($Z$) to best match the
ratios PAH/$\Sigma$PAH. While $q_{\rm{PAH}}$ is constant as metallicity drops
from $Z_{\odot}$ to $Z_{\mathrm{th}}$, $\Sigma$PAH/TIR rises because the
average PAH size $a_{\rm 01}$ decreases, and smaller PAHs emit more per unit
mass (Draine et al., 2021). Below $Z_{\mathrm{th}}$, $q_{\rm{PAH}}$ begins to
drop as well and this causes $\Sigma$PAH/TIR to fall faster than the shifting
of $a_{\rm 01}$ causes it to rise.

##  6 Discussion

###  6.1 Inferences from Observational Trends

As metallicity decreases from $Z_{\odot}$ to $\frac{2}{3}$ $Z_{\odot}$
$\Sigma$PAH/TIR remains fairly constant at about 15% with a scatter of about
2% (see Figure 4). As metallicity decreases below $\frac{2}{3}$ $Z_{\odot}$
$\Sigma$PAH/TIR begins to drop following a power law of index 2.6. The slope
of this power law is steeper than observed in previous works. Rémy-Ruyer et
al. (2015) found a slope of about 1.3 between their $f_{\rm PAH}$ and oxygen
abundance for galaxies in the Dwarf Galaxy Survey (DGS) and part of the
KINGFISH sample (Madden et al., 2013; Kennicutt et al., 2011). The difference
may be a result of sample variations since Rémy-Ruyer et al. (2015) compares
photometric integrated galaxy measurements for the PAH fraction while in this
work we study the PAH fraction from spectroscopy within individual galaxies.
Future studies in this series with a significantly larger sample will allow us
to place better constraints on the power law index and scatter of the
$\Sigma$PAH/TIR-metallicity relationship.

Some of the Hii regions are notably offset from the overall $\Sigma$PAH/TIR
trend with metallicity. Since these regions have a lower $\Sigma$PAH/TIR than
their metallicity would otherwise imply, this may be evidence of a local PAH
luminosity deficit inside ionized gas within Hii regions. Previous works have
proposed that the hard radiation environment near young O and B stars destroys
small dust grains (Povich et al., 2007; Chastenet et al., 2019; Egorov et al.,
2023). In the UV-illuminated neutral and molecular gas of the photo-
dissociation region surrounding the Hii region, the small grains survive and
have a steady source of photons for excitation. At the $\sim\\!300$ pc scales
probed by the apertures used in this work, our Hii region pointings contain a
mix of both of these environments, resulting in a moderately lower
$\Sigma$PAH/TIR in some cases.

The modeled quantity $q_{\rm{PAH}}$ is typically derived from the brightness
at IRAC 8 µm which only traces the 7.7 µm PAH feature. In this work we have
found that the 7.7 µm PAH feature decreases significantly relative to
$\Sigma$PAH when metallicity falls below $Z_{\mathrm{th}}$, but this is not
the case for all PAH features. Specifically, the 6.2 µm feature decreases more
slowly and the 17 µm feature decreases faster as metallicity drops, implying
the situation is more complex than simply a decrease in $q_{\rm{PAH}}$. The
assumption that the 7.7 µm feature is representative of all PAH emission
underlies many past interpretations based on 8 µm photometry. The common
explanation for the decrease in 8 µm photometry in such studies is photo-
destruction of the smallest PAHs. However, our observations show an increase
of 6.2 µm/$\Sigma$PAH at low metallicity (see Figure 7). The 6.2 µm feature is
more dependent on the presence of small PAHs than 7.7 µm, so the increase in
6.2 µm/$\Sigma$PAH is evidence against this photo-destruction explanation for
the PZR trends.

The shift in power between PAH features provides a good diagnostic of what is
happening to the PAHs as metallicity changes. We observed a general trend of
power shifting from longer wavelength features to shorter wavelength features.
This occurs immediately as metallicity decreases below $Z_{\odot}$, despite
the fact that $q_{\rm{PAH}}$ and $\Sigma$PAH/TIR remain approximately constant
(with bulge ISRF correction applied, see § 4.1.1). Previous works have
observed similar trends. Smith et al. (2007) found the ratio PAH 11.3/17 µm
increases from $\sim$1.2 to $\sim$2.2 as metallicity decreases from 0.8
$Z_{\odot}$ to 0.45 $Z_{\odot}$. We find a more significant increase in PAH
11.3/17 µm over this range, from $\sim$1.5 to $\sim$10.1 (see top panel of
Figure 6). Note the average at 0.45 $Z_{\odot}$ is strongly affected by the
points from NGC 2403 while the points from M101 show a lower average of
$\sim$2.5 that is more in line with the Smith et al. (2007) result.

Another nearby low metallicity galaxy with extensive Spitzer-IRS spectroscopy
is the SMC ($\sim 0.2\,Z_{\odot}$; Toribio San Cipriano et al., 2017).
Measurements of the PAH fraction and band strengths in the SMC are in good
agreement with the trends predicted by our inhibited growth model at that
metallicity, and do not match predictions with the photo-destruction or ISRF
hardness models. In particular, $q_{\rm{PAH}}$ for the SMC is $\lesssim$ 1%
(Sandstrom et al., 2010; Chastenet et al., 2019). The band strengths in the
SMC show a similar shift of PAH power between features, namely higher PAH
6.2/$\Sigma$PAH and PAH 11.3/$\Sigma$PAH and lower PAH 7.7/$\Sigma$PAH
compared to higher metallicity regions (Sandstrom et al., 2012). The SMC
regions also showed notably low PAH 17/$\Sigma$PAH compared to the SINGS
average. These trends are all in line with a scenario where inhibited growth
leads to smaller PAHs and lower PAH fractions in the low metallicity SMC.

In addition to metallicity, many physical properties vary with radius in
spiral galaxies. Of relevance to PAH emission, changes in the radiation
environment including the intensity and average photon hardness are expected.
As found in Figure 5 and § 5.1.1, these properties are unlikely to drive the
observed trends. Other potentially radially-varying properties we do not model
that could affect PAH emission include the phase balance of dense and neutral
gas, gross differences in the optical properties of small carbon grains,
varying carbon depletion fractions, and the metal content of the gas that
exists in the dense phase.

Figure 13: Summary of observed and modeled PAH/$\Sigma$PAH differentials. Top:
Percent change in each major PAH feature relative to the sum of all PAH
emission, as metallicity decreases from $Z_{\odot}$ to $Z_{\mathrm{th}}$.
Observations are in black and the three models considered appear as colored
curves. Bottom: Same as above but for metallicity decreasing from
$Z_{\mathrm{th}}$ to 0.45 $Z_{\odot}$. Note that the models differ most in
their predictions for the 3.3 µm feature, not included in the current data
set.

###  6.2 Modeling Interpretation

We tested three physically-motivated explanations for the observed PZR trends
using D21 models: ISRF hardness, photo-destruction, and inhibited grain
growth. A summary of how each of these models compares to the observed PAH
band ratios is shown in Figure 13. The ISRF hardness model quantified the
effect of changing only the incident starlight spectrum with a fixed PAH
population. The photo-destruction model tested the most common explanation for
the PZR: selective destruction of small grains. The inhibited growth model
approximated the effects of reduced accretion of carbon onto grains by
decreasing the average size and overall abundance of PAHs.

The ISRF hardness model was intended to simulate a scenario where the PAH GSD
remains unchanged and the PZR trends arise purely a result of the increasing
radiation hardness as metallicity decreases. This model resulted in the
correct band ratio trends, but the magnitude of these trends is too low by a
factor of 2–3. Furthermore, the adopted model explores the _extremes_ of such
a hardness trend, varying the incident starlight spectrum from that of a 3
$Z_{\odot}$ old bulge down to a $Z_{\odot}$/20 starburst. We conclude that
starlight hardness alone cannot account for the varying shape of the PAH
spectrum, and that the small GSD must also be changing.

If, however, the ratio of far-UV-to-optical absorption cross sections of the
PAH grains were substantially increased, then such a model could better match
the observations as grain heating rate would exhibit increased sensitivity to
the starlight hardness. Donnelly et al. (2024) also concluded that such a
change in the relative absorption cross sections would result in better
agreement between the D21 models and PAH emission observed near a low-
luminosity active galactic nucleus. Regardless, the radiation hardness model
is not capable of reproducing the $q_{\rm{PAH}}$ and $\Sigma$PAH/TIR trends as
a function of metallicity. As the average exciting photon energy increases, it
is not possible for either $q_{\rm{PAH}}$ or $\Sigma$PAH/TIR to decrease. In
fact, without changes in the grain population, relative PAH power is expected
to _increase_ with hardness, as every PAH grain reaches higher stochastic
temperatures.

The photo-destruction scenario we modelled in § 5.1.2 is commonly invoked to
explain the deficit of PAH emission relative to total dust luminosity as a
function of decreasing metallicity (Madden et al., 2006; Gordon et al., 2008).
To reproduce the steep $q_{\rm{PAH}}$ decline, the photo-destruction model
requires increasing the grain cutoff size $a_{\mathrm{min}}$ up to $\sim$400
$N_{\rm C}$ to match the $q_{\rm{PAH}}$ drop from its $Z_{\odot}$ value of
$\sim$3.9% to below 0.5% at 0.2 $Z_{\odot}$. Based on theoretical work, it is
highly unlikely for a majority of PAHs smaller than 400 $N_{\rm C}$ to be
photo-dissociated in ISM at low metallicity. Guhathakurta & Draine (1989)
found that PAHs smaller than $\sim$ 23 $N_{\rm C}$ cannot survive in the ISM
under typical solar-neighborhood radiation conditions. In Guhathakurta &
Draine (1989) the significantly harder radiation field of a B type star is
considered and is found to increase the minimum grain size to
$a_{\mathrm{min}}$ $\sim$ 35 $N_{\rm C}$. This is an order of magnitude too
low to explain the observed trend in $q_{\rm{PAH}}$ with photo-destruction
alone.

Because of this and the strong disagreement in band ratio behavior, we
conclude that small grain photo-destruction likely does not play a dominant
role in the PZR. We do note that this is based on PAH emission trends at
wavelengths longer than 5 µm. It remains possible that a modest amount of
photo-destruction may affect the very smallest PAHs traced by the 3.3 µm
feature, which the photo-destruction model predicts will drop precipitously
towards low metallicity.

The model that best matches the observed PAH-metallicity trends simulates
inhibited grain growth. We implemented this scenario by shifting the average
PAH size smaller and reducing the total mass of all carbon grains as
metallicity decreases. If individual carbon atoms are accreted and grow on the
surfaces of larger grains (bottom-up formation), their reduced availability
and longer accretion timescales at lower metallicity could explain the overall
shift towards smaller grain sizes, although the increased intensity and
hardness of radiation could also play a role in inhibiting growth. Despite the
successes of the inhibited growth model, several trends in the observations
remain unaccounted for. These may be a result of simplifying assumptions in
the D21 models.

We have assumed that the radiation field intensity remains fixed at $U=1$.
This is the typical value of $U$ extracted from the SED modelling maps with
our matched apertures, and there is little effect on the shape or relative
strength of the PAH spectrum at such low intensities. On smaller scales (e.g.
approaching individual Hii regions), however, this assumption may break down
and larger values of $U$ that could lead to multi-photon heating may be
present.

Similarly, aside from the radiation hardness model, we have assumed the mMMP
radiation field of the solar neighborhood applies to all regions in each
galaxy. We have no direct measure of the shape of the incident SED that
illuminates the dust, but the radiation hardness model (§ 5.1.1) shows that
even shifting from an M31 bulge SED to a $Z_{\odot}$/20 10Myr SED cannot
reproduce the observed band ratio variations as a function of metallicity.
Since our data do not span such a wide range in metallicity, the local
radiation fields are unlikely to be changing this rapidly. However, previous
works have found evidence that band ratio variations are correlated with
radiation field hardness in nearby galaxies (Baron et al., 2024).

All three models assume unchanging vibrational properties of PAH grain
material; if the chemical structure of PAH grains change as metallicity
declines – for example, losing the ability to emit effectively at 17 µm– this
could offer an alternative explanation for the success of the inhibited growth
model.

Finally, we have also made the assumption that the ionization fraction as a
function of grain size remains fixed at the standard value. This was done
primarily to reduce the number of free parameters. However, the overall
success of our inhibited growth model implies the standard ionization fraction
as a function of size is reasonable. Since the ionization fraction is lower
for smaller grains and the average grain size in our inhibited growth model
decreases, the model naturally results in reduced effective ionization
fraction. This is consistent with the observations of the PAH 7.7/11.3 µm
ratio shown in Figure 6.

The strong agreement between the inhibited growth model and the observations
emphasizes the role of accretion and regrowth in maintaining the small grain
population in the ISM. At low metallicities, these processes become less
efficient as the carbon abundance and average size and number of large grains
drops (Zhukovska et al., 2008). This suggests that the majority of small
grains are formed by accretion in the denser phases of the ISM and are not
directly stellar in origin.

###  6.3 Future Work

The spectral coverage of Spitzer did not include the aromatic feature at 3.3
µm. Theoretical and laboratory results show this feature originates almost
exclusively from the smallest PAH molecules ($<$ 100 $N_{\rm C}$,
Maragkoudakis et al., 2020; Draine et al., 2021). If these small grains are
significantly affected by photo-destruction, we expect that the 3.3 µm
emission will become very weak at sufficiently low metallicity. And yet, the
low-metallicity galaxy IIZw40 ($\sim$20% $Z_{\odot}$) has been found to have a
relatively _high_ fractional 3.3µm luminosity ($\sim 3\%$, Lai et al., 2020).

We have also seen little evidence in this work that small PAHs are
preferentially destroyed at low metallicity. In fact, the success of our
inhibited growth model suggests that even as the total PAH grain population
drops in abundance, smaller PAHs _rise_ in relative importance. However, the
3.3 µm feature is far more sensitive to the abundance of PAHs with $N_{\rm C}$
$\ll\,100$ than the 6.2 or 7.7 µm features (Hensley & Draine, 2023), so our
conclusions in this work cannot rule out photo-destruction thresholds at
smaller grain sizes.

If our inhibited grain growth model holds true, we predict the 3.3 µm fraction
should carry a higher fraction of the total emission from PAH bands as
metallicity decreases. The best inhibited growth model suggests the 3.3 µm
feature contributes only 2% of all PAH band emission at solar metallicity, but
extrapolating to 0.2 $Z_{\odot}$ we predict 3.3 µm could contribute about 10%
of all remaining PAH band emission. As shown in Figure 13, the relative
behavior of the 3.3 µm PAH feature has the strongest variation between models.
Future studies on the PZR with 3.3 µm using JWST can disentangle which model
or combination of models applies to the smallest PAHs with $N_{\rm C}$
$\ll\,$100.

Figure 4 shows $\Sigma$PAH/TIR increases from 10% to 16% as metallicity drops
from $Z_{\odot}$ to $Z_{\mathrm{th}}$. We applied a correction for this in §
4.1.1 before performing the fit under the assumption that the ISRF is softer
in the central region of M101. However we also found our inhibited growth
model naturally results in an excellent match to the observed $\Sigma$PAH/TIR
trend as the average grain size shifts larger at higher metallicity. Future
work with high metallicity regions dominated by young stars can explore this
further and determine if the decrease in $\Sigma$PAH/TIR is a result of softer
radiation environment or grain growth in high metallicity ISM. If the trend is
truly metallicity dependent, this may suggest that the threshold metallicity
$\sim\\!\frac{2}{3}$ $Z_{\odot}$ forms a modest local maximum in PAH
brightness relative to all other dust.

The high luminosity of PAHs, dropping steeply and changing shape below
$\sim\\!\frac{2}{3}$ $Z_{\odot}$, may indicate that PAH emission could serve
as a powerful probe of metal content in galaxies. JWST has been able to
directly detect 3.3µm PAH emission at z $\sim$ 4.1 (Spilker et al., 2023), and
evidence from UV attenuation at z $\sim$ 7 may indicate the presence of large
quantities of carbonaceous grains at very early times (Witstok et al., 2023).
A future far-IR observatory with spectroscopic capabilities could offer an
effective way to recover dust conditions and metal content in the early
Universe (Moullet et al., 2023).

##  7 Conclusions

Spitzer-IRS spectroscopic radial strip maps across three nearby spiral
galaxies with well-characterized metallicity gradients were used to study the
deficit of PAH emission relative to total dust luminosity as metallicity
declines. We found $\Sigma$PAH/TIR remains relatively constant between
$Z_{\odot}$ and $\frac{2}{3}$ $Z_{\odot}$. Below this threshold,
$\Sigma$PAH/TIR drops smoothly and rapidly with metallicity. We studied how
the PAH emission spectrum changes in strength and form to diagnose the
physical origins of the PAH-metallicity relationship. Building on the latest
models from Draine et al. (2021), we reproduced these trends with a model of
declining grain size and overall abundance designed to simulate the effects of
inhibited PAH growth. The main findings of this work are:

  * •

PAH emission constitutes about 15% of all infrared emission in high
metallicity regions of normal star-forming galaxies. Below about $\frac{2}{3}$
$Z_{\odot}$, the power emitted in the PAH features begins to drop smoothly
with metallicity, approximately as a power law with slope $\sim$2.6.

  * •

As its overall luminosity declines with lower metallicity, PAH feature power
shifts toward shorter wavelengths, with the 17µm band declining particularly
rapidly. The dominant 7.7 µm band rises but then drops below the threshold
metallicity, potentially due to the competing effects of smaller average grain
size and the implicit changes in PAH ionization balance that naturally follow.

  * •

Models based on the commonly assumed scenario of small grain photo-destruction
– when tuned to match measured trends in $q_{\rm{PAH}}$ – fail to reproduce
observed changes in the PAH spectrum, predicting roughly the _opposite_ band
ratio trends as observed. We conclude that photo-destruction cannot be the
dominant effect driving the decline in PAH power at low metallicity.

  * •

Although the harder radiation at low metallicity does shift PAH power to
shorter wavelengths, the effects are modest, and modeling suggests the
observed trends cannot arise solely from this increased radiation field
hardness. Strong changes to the underlying carbonaceous grain size
distribution are needed to reproduce these trends.

  * •

A model of inhibited grain growth in which the average size of PAH grains
declines while the overall PAH abundance drops can explain most details of the
varying PAH spectrum towards low metallicity. This emphasizes the importance
of dust regrowth as grains cycle through dense phases of the ISM.

  * •

Our best inhibited growth model predicts the 3.3 µm PAH feature strength
relative to the total PAH luminosity will increase from 2% to 10% as
metallicity decreases from $Z_{\odot}$ to 0.2 $Z_{\odot}$, although moderate
levels of photo-destruction that do not substantially impact longer wavelength
bands could limit this value.

CW thanks the members of R. Chandar’s University of Toledo Paper Writing Class
(2022–2023) for constructive feedback. We thank K. Gordon, C. Engelbracht, E.
Tarantino, D. Narayanan, E. Peeters, L. Hunt, and A. Li for helpful
discussions over the years regarding the PAH-metallicity problem, and D. Berg
for insights on metallicity gradients and their measurement. JDS thanks the
Max Plank Institut für Astronomie for hosting numerous scientific visits which
contributed to the development of this work. We gratefully acknowledge support
from NASA ADAP grant 80NSSC21K0851. This work uses observations made with the
Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory,
California Institute of Technology, under a contract with NASA. This research
has made use of NASA’s Astrophysics Data System and Tiny-Tim/Spitzer,
developed by John Krist for the Spitzer Science Center. The Center is managed
by the California Institute of Technology under a contract with NASA. This
research was carried out in part at the Jet Propulsion Laboratory, California
Institute of Technology, under a contract with the National Aeronautics and
Space Administration.

## References

  * Aniano et al. (2020) Aniano, G., Draine, B. T., Hunt, L. K., et al. 2020, ApJ, 889, 150, doi: 10.3847/1538-4357/ab5fdb
  * Asplund et al. (2009) Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481, doi: 10.1146/annurev.astro.46.060407.145222
  * Baron et al. (2024) Baron, D., Sandstrom, K. M., Rosolowsky, E., et al. 2024, arXiv e-prints, arXiv:2402.04330, doi: 10.48550/arXiv.2402.04330
  * Bendo et al. (2012) Bendo, G. J., Boselli, A., Dariush, A., et al. 2012, MNRAS, 419, 1833, doi: 10.1111/j.1365-2966.2011.19735.x
  * Berg et al. (2020) Berg, D. A., Pogge, R. W., Skillman, E. D., et al. 2020, ApJ, 893, 96, doi: 10.3847/1538-4357/ab7eab
  * Berg et al. (2015) Berg, D. A., Skillman, E. D., Croxall, K. V., et al. 2015, ApJ, 806, 16, doi: 10.1088/0004-637X/806/1/16
  * Berg et al. (2013) Berg, D. A., Skillman, E. D., Garnett, D. R., et al. 2013, ApJ, 775, 128, doi: 10.1088/0004-637X/775/2/128
  * Cesarsky et al. (1996) Cesarsky, D., Lequeux, J., Abergel, A., et al. 1996, A&A, 315, L309
  * Chastenet et al. (2019) Chastenet, J., Sandstrom, K., Chiang, I.-D., et al. 2019, ApJ, 876, 62, doi: 10.3847/1538-4357/ab16cf
  * Chastenet et al. (2023) Chastenet, J., Sutter, J., Sandstrom, K., et al. 2023, ApJ, 944, L11, doi: 10.3847/2041-8213/acadd7
  * Choban et al. (2022) Choban, C. R., Kereš, D., Hopkins, P. F., et al. 2022, MNRAS, 514, 4506, doi: 10.1093/mnras/stac1542
  * Choban et al. (2024) Choban, C. R., Kereš, D., Sandstrom, K. M., et al. 2024, MNRAS, 529, 2356, doi: 10.1093/mnras/stae716
  * Croxall et al. (2016) Croxall, K. V., Pogge, R. W., Berg, D. A., Skillman, E. D., & Moustakas, J. 2016, ApJ, 830, 4, doi: 10.3847/0004-637X/830/1/4
  * Dale et al. (2020) Dale, D. A., Anderson, K. R., Bran, L. M., et al. 2020, AJ, 159, 195, doi: 10.3847/1538-3881/ab7eb2
  * Donnelly et al. (2024) Donnelly, G. P., Smith, J. D. T., Draine, B. T., et al. 2024, ApJ, 965, 75, doi: 10.3847/1538-4357/ad2169
  * Draine (2009) Draine, B. T. 2009, in Astronomical Society of the Pacific Conference Series, Vol. 414, Cosmic Dust - Near and Far, ed. T. Henning, E. Grün, & J. Steinacker, 453
  * Draine & Li (2007) Draine, B. T., & Li, A. 2007, ApJ, 657, 810, doi: 10.1086/511055
  * Draine et al. (2021) Draine, B. T., Li, A., Hensley, B. S., et al. 2021, ApJ, 917, 3, doi: 10.3847/1538-4357/abff51
  * Draine et al. (2007) Draine, B. T., Dale, D. A., Bendo, G., et al. 2007, ApJ, 663, 866, doi: 10.1086/518306
  * Draine et al. (2014) Draine, B. T., Aniano, G., Krause, O., et al. 2014, ApJ, 780, 172, doi: 10.1088/0004-637X/780/2/172
  * Duley (2009) Duley, W. W. 2009, ApJ, 705, 446, doi: 10.1088/0004-637X/705/1/446
  * Dwek & Scalo (1980) Dwek, E., & Scalo, J. M. 1980, ApJ, 239, 193, doi: 10.1086/158100
  * Egorov et al. (2023) Egorov, O. V., Kreckel, K., Sandstrom, K. M., et al. 2023, ApJ, 944, L16, doi: 10.3847/2041-8213/acac92
  * Eldridge et al. (2017) Eldridge, J. J., Stanway, E. R., Xiao, L., et al. 2017, PASA, 34, e058, doi: 10.1017/pasa.2017.51
  * Engelbracht et al. (2005) Engelbracht, C. W., Gordon, K. D., Rieke, G. H., et al. 2005, ApJ, 628, L29, doi: 10.1086/432613
  * Engelbracht et al. (2008) Engelbracht, C. W., Rieke, G. H., Gordon, K. D., et al. 2008, ApJ, 678, 804, doi: 10.1086/529513
  * Fisher & Drory (2010) Fisher, D. B., & Drory, N. 2010, ApJ, 716, 942, doi: 10.1088/0004-637X/716/2/942
  * Galametz et al. (2013) Galametz, M., Kennicutt, R. C., Calzetti, D., et al. 2013, MNRAS, 431, 1956, doi: 10.1093/mnras/stt313
  * Galliano et al. (2008) Galliano, F., Dwek, E., & Chanial, P. 2008, ApJ, 672, 214, doi: 10.1086/523621
  * Galliano et al. (2018) Galliano, F., Galametz, M., & Jones, A. P. 2018, ARA&A, 56, 673, doi: 10.1146/annurev-astro-081817-051900
  * García-Benito et al. (2017) García-Benito, R., González Delgado, R. M., Pérez, E., et al. 2017, A&A, 608, A27, doi: 10.1051/0004-6361/201731357
  * Gordon et al. (2008) Gordon, K. D., Engelbracht, C. W., Rieke, G. H., et al. 2008, ApJ, 682, 336, doi: 10.1086/589567
  * Groves et al. (2012) Groves, B., Krause, O., Sandstrom, K., et al. 2012, MNRAS, 426, 892, doi: 10.1111/j.1365-2966.2012.21696.x
  * Guhathakurta & Draine (1989) Guhathakurta, P., & Draine, B. T. 1989, ApJ, 345, 230, doi: 10.1086/167899
  * Haynes et al. (2010) Haynes, K., Cannon, J. M., Skillman, E. D., Jackson, D. C., & Gehrz, R. 2010, ApJ, 724, 215, doi: 10.1088/0004-637X/724/1/215
  * Hensley & Draine (2023) Hensley, B. S., & Draine, B. T. 2023, ApJ, 948, 55, doi: 10.3847/1538-4357/acc4c2
  * Hunt et al. (2010) Hunt, L. K., Thuan, T. X., Izotov, Y. I., & Sauvage, M. 2010, ApJ, 712, 164, doi: 10.1088/0004-637X/712/1/164
  * Jackson et al. (2006) Jackson, D. C., Cannon, J. M., Skillman, E. D., et al. 2006, ApJ, 646, 192, doi: 10.1086/504707
  * Kassis et al. (2006) Kassis, M., Adams, J. D., Campbell, M. F., et al. 2006, ApJ, 637, 823, doi: 10.1086/498404
  * Kennicutt et al. (2003) Kennicutt, Robert C., J., Bresolin, F., & Garnett, D. R. 2003, ApJ, 591, 801, doi: 10.1086/375398
  * Kennicutt et al. (2011) Kennicutt, R. C., Calzetti, D., Aniano, G., et al. 2011, PASP, 123, 1347, doi: 10.1086/663818
  * Kreckel et al. (2019) Kreckel, K., Ho, I. T., Blanc, G. A., et al. 2019, ApJ, 887, 80, doi: 10.3847/1538-4357/ab5115
  * Lai et al. (2020) Lai, T. S. Y., Smith, J. D. T., Baba, S., Spoon, H. W. W., & Imanishi, M. 2020, ApJ, 905, 55, doi: 10.3847/1538-4357/abc002
  * Le Page et al. (2003) Le Page, V., Snow, T. P., & Bierbaum, V. M. 2003, ApJ, 584, 316, doi: 10.1086/345595
  * Li (2020) Li, A. 2020, Nature Astronomy, 4, 339, doi: 10.1038/s41550-020-1051-1
  * Li & Draine (2001) Li, A., & Draine, B. T. 2001, ApJ, 554, 778, doi: 10.1086/323147
  * Madden et al. (2006) Madden, S. C., Galliano, F., Jones, A. P., & Sauvage, M. 2006, A&A, 446, 877, doi: 10.1051/0004-6361:20053890
  * Madden et al. (2013) Madden, S. C., Rémy-Ruyer, A., Galametz, M., et al. 2013, PASP, 125, 600, doi: 10.1086/671138
  * Maragkoudakis et al. (2020) Maragkoudakis, A., Peeters, E., & Ricca, A. 2020, MNRAS, 494, 642, doi: 10.1093/mnras/staa681
  * Mathis et al. (1983) Mathis, J. S., Mezger, P. G., & Panagia, N. 1983, A&A, 128, 212
  * Micelotta et al. (2010a) Micelotta, E. R., Jones, A. P., & Tielens, A. G. G. M. 2010a, A&A, 510, A36, doi: 10.1051/0004-6361/200911682
  * Micelotta et al. (2010b) —. 2010b, A&A, 510, A37, doi: 10.1051/0004-6361/200911683
  * Moullet et al. (2023) Moullet, A., Kataria, T., Lis, D., et al. 2023, arXiv e-prints, arXiv:2310.20572, doi: 10.48550/arXiv.2310.20572
  * Muñoz-Mateos et al. (2009) Muñoz-Mateos, J. C., Gil de Paz, A., Boissier, S., et al. 2009, ApJ, 701, 1965, doi: 10.1088/0004-637X/701/2/1965
  * Narayanan et al. (2023) Narayanan, D., Smith, J. D. T., Hensley, B. S., et al. 2023, ApJ, 951, 100, doi: 10.3847/1538-4357/accf8d
  * O’Halloran et al. (2006) O’Halloran, B., Satyapal, S., & Dudik, R. P. 2006, ApJ, 641, 795, doi: 10.1086/500529
  * Povich et al. (2007) Povich, M. S., Stone, J. M., Churchwell, E., et al. 2007, ApJ, 660, 346, doi: 10.1086/513073
  * Rémy-Ruyer et al. (2014) Rémy-Ruyer, A., Madden, S. C., Galliano, F., et al. 2014, A&A, 563, A31, doi: 10.1051/0004-6361/201322803
  * Rémy-Ruyer et al. (2015) —. 2015, A&A, 582, A121, doi: 10.1051/0004-6361/201526067
  * Rigopoulou et al. (2021) Rigopoulou, D., Barale, M., Clary, D. C., et al. 2021, MNRAS, 504, 5287, doi: 10.1093/mnras/stab959
  * Rogers et al. (2021) Rogers, N. S. J., Skillman, E. D., Pogge, R. W., et al. 2021, ApJ, 915, 21, doi: 10.3847/1538-4357/abf8b9
  * Sandstrom et al. (2010) Sandstrom, K. M., Bolatto, A. D., Draine, B. T., Bot, C., & Stanimirović, S. 2010, ApJ, 715, 701, doi: 10.1088/0004-637X/715/2/701
  * Sandstrom et al. (2009) Sandstrom, K. M., Bolatto, A. D., Stanimirović, S., van Loon, J. T., & Smith, J. D. T. 2009, ApJ, 696, 2138, doi: 10.1088/0004-637X/696/2/2138
  * Sandstrom et al. (2012) Sandstrom, K. M., Bolatto, A. D., Bot, C., et al. 2012, ApJ, 744, 20, doi: 10.1088/0004-637X/744/1/20
  * Shim et al. (2023) Shim, H., Hwang, H. S., Jeong, W.-S., et al. 2023, AJ, 165, 31, doi: 10.3847/1538-3881/aca09c
  * Shivaei et al. (2017) Shivaei, I., Reddy, N. A., Shapley, A. E., et al. 2017, ApJ, 837, 157, doi: 10.3847/1538-4357/aa619c
  * Shivaei et al. (2024) Shivaei, I., Alberts, S., Florian, M., et al. 2024, arXiv e-prints, arXiv:2402.07989, doi: 10.48550/arXiv.2402.07989
  * Skillman et al. (2020) Skillman, E. D., Berg, D. A., Pogge, R. W., et al. 2020, ApJ, 894, 138, doi: 10.3847/1538-4357/ab86ae
  * Smith et al. (2007) Smith, J. D. T., Draine, B. T., Dale, D. A., et al. 2007, ApJ, 656, 770, doi: 10.1086/510549
  * Spilker et al. (2023) Spilker, J. S., Phadke, K. A., Aravena, M., et al. 2023, Nature, 618, 708, doi: 10.1038/s41586-023-05998-6
  * Tielens (2008) Tielens, A. G. G. M. 2008, ARA&A, 46, 289, doi: 10.1146/annurev.astro.46.060407.145211
  * Toribio San Cipriano et al. (2017) Toribio San Cipriano, L., Domínguez-Guzmán, G., Esteban, C., et al. 2017, MNRAS, 467, 3759, doi: 10.1093/mnras/stx328
  * Whitcomb et al. (2020) Whitcomb, C. M., Sandstrom, K., Murphy, E. J., & Linden, S. 2020, ApJ, 901, 47, doi: 10.3847/1538-4357/abaef6
  * Witstok et al. (2023) Witstok, J., Shivaei, I., Smit, R., et al. 2023, Nature, 621, 267, doi: 10.1038/s41586-023-06413-w
  * Zang et al. (2022) Zang, R. X., Maragkoudakis, A., & Peeters, E. 2022, MNRAS, 511, 5142, doi: 10.1093/mnras/stac214
  * Zhukovska et al. (2008) Zhukovska, S., Gail, H. P., & Trieloff, M. 2008, A&A, 479, 453, doi: 10.1051/0004-6361:20077789
  * Zhukovska & Henning (2013) Zhukovska, S., & Henning, T. 2013, A&A, 555, A99, doi: 10.1051/0004-6361/201321368