# Sensitivity of JWST to eV-Scale Decaying Axion Dark Matter

Sandip Roy<EMAIL_ADDRESS>Department of Physics, Princeton
University, Princeton, NJ 08544, USA  Carlos Blanco
<EMAIL_ADDRESS>Department of Physics, Princeton University,
Princeton, NJ 08544, USA  Stockholm University and The Oskar Klein Centre for
Cosmoparticle Physics, Alba Nova, 10691 Stockholm, Sweden  Christopher Dessert
<EMAIL_ADDRESS>Center for Computational Astrophysics, Flatiron
Institute, New York, NY 10010, USA  Anirudh Prabhu<EMAIL_ADDRESS>Princeton Center for Theoretical Science, Princeton University, Princeton, NJ
08544, USA  Tea Temim<EMAIL_ADDRESS>Department of Astrophysical
Sciences, Princeton University, Princeton, NJ 08544, USA

###### Abstract

The recently-launched James Webb Space Telescope (JWST) can resolve eV-scale
emission lines arising from dark matter (DM) decay. We forecast the end-of-
mission sensitivity to the decay of axions, a leading DM candidate, in the
Milky Way using the blank-sky observations expected during standard
operations. Searching for unassociated emission lines will constrain axions in
the mass range $0.18$ eV to $2.6$ eV with axion-photon couplings
$g_{a\gamma\gamma}\gtrsim 5.5\times 10^{-12}$ GeV-1. In particular, these
results will constrain astrophobic QCD axions to masses $\lesssim$ 0.2 eV.

Introduction.— Pseudoscalar particles with feeble couplings to photons are
ubiquitous in beyond the Standard Model constructions and are natural dark
matter (DM) candidates. A famous example is the quantum chromodynamics (QCD)
axion, which was originally proposed to resolve the Strong CP problem Peccei
and Quinn (1977a, b); Weinberg (1978); Wilczek (1978). Similar pseudoscalar
axion-like particles (ALPs) arise independently in String Theory. For example,
in ten-dimensional superstring theory ALPs arise as Kaluza-Klein modes in the
compactification of $p$-form fields on 6-manifolds Svrcek and Witten (2006);
Arvanitaki  _et al._ (2010); Gendler  _et al._ (2023). The non-detection of
weak-scale dark matter (DM) candidates, strengthens the case that the missing
$\sim 85\%$ of the matter of the universe is comprised of axions and/or ALPs.
Therefore, the detection of pseudoscalars is pivotal if we hope to complete
our cosmological and particle physics models of the universe. Here, we
identify the recently launched James Webb Space Telescope (JWST) as a uniquely
well-suited instrument to look for the astrophysical photon signatures of
decaying axion and ALP DM. Note that for the remainder of this Letter, we
refer to both QCD axions and ALPs as axions.

Figure 1:  The expected 95% upper limits (dotted lines) on the axion-photon
coupling from an end-of-mission analysis of JWST observations. The solid green
(yellow) region encloses our projections at 1(2)-$\sigma$ containment. We show
in gray the existing constraints on axions Dolan  _et al._ (2022); Arik  _et
al._ (2009, 2014); Janish and Pinetti (2023); Todarello  _et al._ (2023).
Possible QCD axion models live in the transparent yellow region. In order to
consistently compare our projections with the recent JWST analysis Janish and
Pinetti (2023), we rescale their constraints according to the NFW profile
adopted in this work.

Axion cosmology is governed by the scale of symmetry breaking, $f_{a}$, that
leads to the axion as a Goldstone boson and that of non-perturbative effects,
$\Lambda$, that give the axion a periodic potential, such as
$V(a)=\Lambda^{4}\cos(a/f_{a})$, where $\Lambda^{4}=m_{a}^{2}f_{a}^{2}$. If
the symmetry is broken before inflation, the present-day axion abundance is
determined by the misalignment mechanism Irastorza and Redondo (2018),

$\displaystyle{\Omega_{a}\over\Omega_{\rm DM}}\approx\left({m_{a}\over{\rm
eV}}\right)^{1/2}\left({f_{a}\over 10^{11}\ {\rm
GeV}}\right)^{2}\left({a_{i}\over\pi f_{a}/\sqrt{3}}\right)^{2},$ (1)

where $a_{i}$ is the amplitude of the axion field at the time of symmetry
breaking. Therefore, axions with non-thermal misalignment production
mechanisms are consistent with a vast parameter space Arias  _et al._ (2012),
living anywhere in unexplored parameter space in Fig. 1, motivating searches
over a broad mass range. If the symmetry is broken after inflation ends, the
axion field takes on uncorrelated values in distinct Hubble patches, leading
to topological defects such as axion strings and domain walls that decay and
provide contributions to the axion DM abundance Benabou  _et al._ (2023). The
QCD axion lives on the narrow band with a linear relationship between the QCD
axion mass and its coupling to photons in Fig. 1. Then the axion mass and
potential are temperature-dependent, leading to a modification to Eq. (1) in
the pre-inflationary scenario Grilli di Cortona  _et al._ (2016). In the post-
inflationary scenario, recent cosmological simulations of the topological
defects find that the observed DM density is consistent with axion masses up
to $m_{a}\gtrsim$ meV Gorghetto  _et al._ (2021) (although, Refs. Buschmann
_et al._ (2020, 2022a) find masses in the range 40 $\mu$eV $\leq m_{a}\leq$
180 $\mu$eV).

In flavor-universal models, the QCD axion mass is constrained to be
$m_{a}\lesssim 0.02$ eV by anomalous cooling bounds from neutron stars
Buschmann  _et al._ (2022b) and supernovae Lella  _et al._ (2023). However,
cooling constraints can be relaxed for axions with nucleophobic couplings,
e.g. flavor non-universal scenarios Di Luzio  _et al._ (2018); Björkeroth  _et
al._ (2019); Badziak and Harigaya (2023), opening up the possibility of eV-
scale QCD axions. Indeed, there are many models in which the QCD axion DM mass
is in the range meV $\lesssim m_{a}\lesssim$ eV Co  _et al._ (2018); Caputo
and Reig (2019); Visinelli and Gondolo (2010); Co  _et al._ (2020); Cyncynates
and Thompson (2023).

Much of the effort to detect axions in the laboratory and in astrophysical
settings relies on the axion-photon interaction $\mathcal{L}\supset-
g_{a\gamma\gamma}a(x)F\tilde{F}/4$, where $a(x)$ is the axion field,
$g_{a\gamma\gamma}=C_{a\gamma\gamma}\alpha/2\pi f_{a}$ is the axion-photon
coupling constant, with $C_{a\gamma\gamma}$ an $\mathcal{O}(1)$ number, $F$
represents the electromagnetic field strength tensor, and $\tilde{F}$ is its
dual. In the mass range of interest, model-independent constraints on
$g_{a\gamma\gamma}$ come from the CAST helioscope experiment Arik  _et al._
(2009, 2014) and stellar evolution in globular clusters Dolan  _et al._
(2022). In addition, laboratory experiments have been proposed to probe the
same region of parameter space Armengaud  _et al._ (2019); Liu  _et al._
(2022); Baryakhtar  _et al._ (2018). Another powerful technique for detecting
axions is to look for their decay products. In particular, axions can decay
into photons with rate $\Gamma_{a}=g_{a\gamma\gamma}^{2}m_{a}^{3}/64\pi$
Barnett  _et al._ (1996). Searches for photons from decaying axions spans from
radio 111At low frequency the decay rate is Bose-enhanced relative to the
previously-quoted vacuum decay rate. to gamma rays Caputo  _et al._ (2019);
Chan (2021); Sun  _et al._ (2022); Todarello  _et al._ (2023); Grin  _et al._
(2007); Dessert  _et al._ (2020); Foster  _et al._ (2021); Calore  _et al._
(2023); DeRocco  _et al._ (2022); Blanco and Hooper (2019). Searching for
photons from decaying axion DM in the range meV $\lesssim m_{a}\lesssim$ eV
requires a highly sensitive infrared telescope, such as the JWST.

JWST represents a substantial leap in space-based imaging technology and is
the scientific successor to the Hubble Space Telescope. Designed for infrared
(IR) observation at the diffraction limit, JWST is capable of broad- and
narrow-band imagery and integral-field spectroscopy in the wavelength range of
$0.6\;\mu\text{m}\leq\lambda\leq 29\;\mu\text{m}$, which corresponds to photon
energies between about 0.05 and 2 eV Greenhouse (2016). JWST is equipped with
instruments that are uniquely suited for the search for IR-scale decaying DM,
namely, the Near-Infrared Spectrograph (NIRSpec) Integral Field Unit (IFU)
Jakobsen  _et al._ (2022), and the Mid-Infrared Instrument (MIRI) Medium
Resolution Spectrometer (MRS) Wells  _et al._ (2015).

In this Letter, we show that JWST will have leading sensitivity to eV-scale
axion decay at the end-of-mission. Because the Earth is embedded in the Milky
Way (MW) DM halo, every JWST observation ever taken is sensitive to axion
decay. A particularly efficient approach for DM decay searches is to analyze
blank-sky observations Dessert  _et al._ (2020); Foster  _et al._ (2021);
Dessert  _et al._ (2023a), which are observations of low-surface-brightness
locations in the sky. In the Mikulski Archive for Space Telescopes (MAST)
database MAS , we find 9.4 Ms of data usable for this purpose.

Figure 2:  _Left panel_ : $D_{\rm eff}$ in galactic coordinates at
$1{\,{\rm\mu m}}$, corresponding to $m_{a}=2.5{\,{\rm eV}}$. The grey dashed
lines delineate our ring edges and the dashed white lines are
$|b|=10^{\circ}$, below which we mask out in our analysis. _Right panel_ : The
angular-averaged $D_{\rm eff}$ at a wavelength of $1{\,{\rm\mu m}}$ (solid
line) and without any dust extinction (dotted line), avoiding the masked
galactic plane region. Lines of sight close to the galactic plane at
$\theta_{\rm GC}=0^{\circ}$ and $\theta_{\rm GC}=180^{\circ}$ experience the
strongest dust extinction. At wavelengths greater than $1{\,{\rm\mu m}}$, the
dust extinction decreases as shown in detail in the Supplemental Material.

Computing the Axion-Decay Photon Flux.— The expected flux density from axion
decays is expressed as Lisanti  _et al._ (2018)

$\dfrac{d\Phi}{d\lambda}(\lambda,l,b)=\dfrac{m_{a}}{2}\dfrac{\Gamma_{a}}{4\pi
m_{a}}\dfrac{dN_{\gamma}(l,b)}{d\lambda}D(l,b)$ (2)

where $d\Phi/d\lambda$ has units of [MJy/sr Hz/${\,{\rm\mu m}}$],
$dN_{\gamma}/d\lambda$ is the axion decay flux at Earth which depends on
galactic coordinates $(l,b)$ through Doppler broadening, shifting and dust
extinction, and the D-factor $D=\int_{\rm l.o.s.}ds\,\rho_{a}(ds,l,b)$ is the
integrated DM density along the line of sight (l.o.s.) in units of [eV/cm2].
Often the Doppler broadening and shifting of the DM particles can be ignored,
but JWST has $\mathcal{O}(0.1\%)$ energy resolution, meaning that it can
resolve emission lines produced by axion decay. Furthermore, lines of sight
near the Galactic plane (GP) can be attenuated due to extinction by
interstellar dust. Including all these effects, we have

$\dfrac{dN_{\gamma}}{d\lambda}=\dfrac{m_{a}}{2}\dfrac{\int_{\rm
l.o.s.}ds\exp(-\int_{0}^{s}ds^{\prime}n_{d}\sigma)\rho_{a}(s)f(v(\lambda);r)}{\int_{\rm
l.o.s.}ds\rho_{a}(s)}$ (3)

where $f(v(\lambda);r)$ is the isotropic DM velocity distribution in Dessert
_et al._ (2023a). That velocity is a function of the observed wavelength via
$|v(\lambda)|=2/(m_{a}\lambda(1-{\bf\hat{n}}\cdot{\bf v_{\odot}}))-1$, where
${\bf\hat{n}}$ is the direction along the line of sight and ${\bf v_{\odot}}$
is the velocity of the Sun with respect to the galaxy. The extinction is
provided by the exponential factor, where $n_{d}(s,l,b)$ is the dust density
and $\sigma(\lambda)$ is its cross-section with photons. Although some
3-dimensional models of the galactic dust distribution exist Green  _et al._
(2019), they are typically not reliable out to distances of order the Milky
Way scale radius, so in this work we conservatively model the extinction as if
all emission originated at infinity, so that
$\exp(-\int_{0}^{s}ds^{\prime}n_{d}\sigma)\to 10^{-0.44A_{\lambda}}$ where
$A_{\lambda}$ is the galactic extinction at wavelength $\lambda$. We use the
galactic dust models in Schlegel  _et al._ (1998); Schlafly and Finkbeiner
(2011) and the extinction curve from Gao  _et al._ (2013) to compute the
galactic extinction (for details, see the Supplemental Material (SM)). The
axion decays to a diphoton final state, meaning that $\int d\lambda
dN_{\gamma}/d\lambda=2\times 10^{-0.44A_{2/m_{a}}}$ and the total expected
flux simplifies to $\Phi=\Gamma_{a}D_{\rm eff}/4\pi$, where $D_{\rm eff}$ is
the D-factor times the attenuation due to dust. We compute the D-factor in the
Milky Way using a Navarro-Frenk-White (NFW) profile Navarro  _et al._ (1996,
1997) with DM density at Earth $\rho_{\rm Earth}=0.29$ GeV/cm3 and a scale
radius $r_{s}=19.1$ kpc, using recent results calibrated on Gaia DR2 data
Cautun  _et al._ (2020), along with a GC-Earth distance $d_{\rm Earth}=8.23$
kpc Leung  _et al._ (2022). $D_{\rm eff}$ at $1{\,{\rm\mu m}}$ (i.e.
$m_{a}=2.5{\,{\rm eV}}$) is shown in Fig. 2. With knowledge of the
astrophysical parameters, the axion DM decay flux is given by Grin  _et al._
(2007)

$\Phi(l,b)=1.0\times 10^{-9}\
\textrm{erg/cm}^{2}\textrm{/s/sr}\left(\dfrac{g_{a\gamma\gamma}}{10^{-11}\
\textrm{GeV}^{-1}}\right)^{2}\left(\dfrac{m_{a}}{1\
\textrm{eV}}\right)^{3}\left(\dfrac{D_{\textrm{eff}}}{10^{31}\
\textrm{eV}/{\rm cm}^{2}}\right)$ (4)

where the line wavelength $\lambda=2.5\ (1\ \textrm{eV}/m_{a})\ \mu$m,
corresponding to an energy $E_{\gamma}=m_{a}/2$. In particular, the MIRI MRS
filters are sensitive to axions with masses $0.089$ eV $\leq m_{a}\leq 0.506$
eV, while the NIRSPEC IFU filters are sensitive to $0.47$ eV $\leq m_{a}\leq
2.75$ eV, so that our projections cover unexplored parameter space over an
order of magnitude in axion mass.

In this work, we compute the expected sensitivity of JWST to axion decays in
the Milky Way halo. To this end we need to know the total exposure time usable
for blank-sky observations. Every IFU observation taken is useful, unless the
source is sufficiently extended such that emission will dominate the
observation. On the other hand, point sources can be removed via a spatial
mask. JWST’s lifetime is fuel-limited, and the telescope was designed to
operate for 10 years, but is expected to continue operating for about 20
years. Not all of this time will be spent observing the blank sky; in
particular, the observing efficiency is expected to be around 70% JWS . We pay
an additional penalty because only some fraction of this time will be spent
observing with the IFU modes. We compute the expected exposure time in each
instrument mode in a data-driven way by extrapolating the first $\sim$1.5
years of observations, taken between March 17, 2022 and Nov 6, 2023, to that
expected in 10 years of operation. We obtain the exposure times from the MAST
database. In this computation we exclude observations with extended sources
and observations within the GP mask, which collectively account for
approximately 30% of the total exposure time. However, we note that extended
source observations are typically accompanied by dedicated background
observations, so that this approach is extremely conservative. Our expected
exposure times are shown in Tab. 1. Given that the JWST IFU field of view
(FOV), $\mathcal{O}(10\ \textrm{arcsec}^{2})$ depending on the observing mode,
is only 1 part in $10^{11}$ of the full sky at any time, we need to know the
observing pattern. We assume that JWST observes isotropically across the full
sky. In reality this distribution is likely to be biased towards the Galactic
Center (GC) and Galactic Plane (GP), i.e. towards regions of larger signal.

We use the jwst_backgrounds 222https://jwst-docs.stsci.edu/jwst-other-
tools/jwst-backgrounds-tool tool developed by JWST to compute the background
contribution at a given point on the sky. The astrophysical background is
modeled with four components. The dominant contributions are the in-field
zodiacal light Kelsall  _et al._ (1998); Wright (1998); Gorjian  _et al._
(2000) and the in-field interstellar medium (ISM) emission Schlegel  _et al._
(1998). Zodiacal emission arises through the reflection of sunlight by dust in
our solar system and thus dominates the background at low ecliptic latitudes.
The ISM background is produced by dust emission within the Milky Way and thus
dominates at low galactic latitudes. Other background components include the
astrophysical and detector stray-light Lightsey and A. (2016); Wainscoat  _et
al._ (1992) and the thermal self-emission which dominate at wavelengths
$\gtrsim 20{\,{\rm\mu m}}$. For further details and a measurement of the
astrophysical background, see Rigby  _et al._ (2023).

Projecting JWST’s Sensitivity to Axion Decays.—Using the procedure developed
in Ref. Foster  _et al._ (2021), we bin the data in 30 concentric rings around
the GC of width $6^{\circ}$ and mask the GP up to $b\leq 10^{\circ}$ so that
the innermost and outermost rings are entirely masked. This mask is motivated
by that the dust extinction can be difficult to calculate in the GP due to a
larger variety of dust molecules Gao  _et al._ (2013), and we wish to remain
insensitive to such details. As we show in the SM, smaller masks actually
reduce $D_{\rm eff}$ near the GP, although we would gain $\sim$10% in exposure
time. We compute the expected exposure time in each JWST spectroscopic mode
and ring. Note that there are 12 MRS modes, but they are split into groups of
three by wavelength, and the entire group is observed simultaneously. There
are 8 NIRSpec filters over four wavelength bands. Each band is observed in
high and medium resolution. We do not consider the NIRSpec PRISM mode, which
has reduced spectral resolution.

The axion decay flux is modeled as in Eq. 2, where $D_{\rm eff}$ is computed
by averaging over each ring. In the course of this averaging, the line is
broadened beyond the intrinsic width of 220 km/s of Doppler broadening because
the Doppler shifting can change significantly over a ring. We could shift the
data to the galactic rest frame, but this introduces difficult-to-model bin-
to-bin correlations in the data Dessert  _et al._ (2023b). We compute the
root-mean-square Doppler shift in each ring and add it in quadrature to the
Doppler broadening to determine the observed width of the line $v_{\rm line}$.
For the innermost ring, nearly transverse to the solar motion, the width is
220 km/s; for the rings 90∘ from the GC the width increases to $\sim$275 km/s,
(for details, see SM).

MIRI MRS Grating | Short | Medium | Long
---|---|---|---
$t_{\rm exp}$ [Ms] | 12.5 | 12.4 | 12.5

NIRSpec | F070LP | F100LP | F170LP | F290LP | F070LP | F100LP | F170LP | F290LP
---|---|---|---|---|---|---|---|---
Filter | G140M | G140M | G235M | G395M | G140H | G140H | G235H | G395H
$t_{\rm exp}$ [ks] | 1.4 | 750 | 1060 | 1980 | 5.9 | 1300 | 6900 | 8070

Table 1:  The exposure times $t_{\rm exp}$ in [Ms] for MIRI and [ks] for
NIRSpec assumed in our projections for each observing mode.

To model the expected signal-to-noise ratio (SNR) for the axion decay, we use
the output of the JWST Exposure Time Calculator (ETC) ETC  in each analysis
ring assuming a fixed exposure time $t_{\textrm{exp}}$ and axion-photon
coupling $g_{a\gamma\gamma}$. This approach is agnostic to any particular
analysis strategy, such as parametric likelihood-based frequentist modeling as
in Ref. Dessert  _et al._ (2020) or nonparametric approaches such as Gaussian
Processes as in Frate  _et al._ (2017); Foster  _et al._ (2021), which should
be developed when performing analysis on real data. However, we verified on
simulated data that the parametric approach, where, e.g. , the signal line is
modeled along with a quadratic background model, returns results consistent
with that of the ETC. Note, however, that we have not included possible
systematics into this projection. For instance, we do not account for diffuse
astrophysical line emission. In the vicinity of bright astrophysical lines,
our limits may disappear; however, these lines exist over only a small
fraction of the parameter space. There are known possible spurious line
signals JWS : scattered light from a bright line emitters and the
12.2${\,{\rm\mu m}}$ MRS spectral leak. The former should affect only a few
individual observations, and particular wavelengths with less-understood
instrumental spectral features can be avoided, so we expect these issues to
have minimal impact on our results.

The ETC incorporates sky-dependent background models; we query the background
model at the point in the ring closest to the ecliptic plane where the
backgrounds are largest outside $|b|\leq 10^{\circ}$. We show the effects of
other choices in the SM. We query the ETC for each observing mode at an axion
mass such that the decay occurs in the mode’s wavelength range. The axion
signal in each ring is input as a spectral line positioned at a frequency
$m_{a}/2$ with the observed ring-dependent width. We use the scaling relation
in Eq. 5, verified empirically with the JWST ETC, to determine the SNR across
the entire filter bandwidth and repeat this process for each NIRSPEC and MIRI
filter of interest (where the $N_{a}$ and $N_{\rm bkg}$ represent the detector
counts for axions and background respectively, $\epsilon_{\lambda}$ represents
the wavelength-dependent filter throughput and $\Phi_{\textrm{bkg},\lambda}$
represents the wavelength and line-of-sight-dependent background and
instrumental noise flux). We then compute Asimov likelihoods Cowan  _et al._
(2011) in each ring and filter and multiply the likelihoods in each ring to
obtain a joint likelihood. For each value of $m_{a}$, we solve for the 95%
upper limit on the axion-photon coupling strength $g_{a\gamma\gamma}^{95}$
such that SNR$|_{\lambda=2/m_{a}}=\sqrt{2.71}$, given that Wilks’ theorem
holds.

$\textrm{SNR}(\lambda)=\frac{N_{a}}{\sqrt{N_{\rm bkg}}}\propto
m_{a}^{3}\,g_{a\gamma\gamma}^{2}\,D_{\rm
eff}\,t_{\textrm{exp}}^{\frac{1}{2}}\epsilon_{\lambda}^{\frac{1}{2}}\Phi_{\textrm{bkg},\lambda}^{-\frac{1}{2}}.$
(5)

We present our projected 95% upper limits in Fig. 1, along with their 1- and
2-$\sigma$ enclosing regions. In particular, we show that JWST will have
leading sensitivity to axions over an order of magnitude in mass $0.18$ eV
$\leq m_{a}\leq 2.6$ eV. The NIRSpec IFU filters, covering axion masses
between $0.5$ eV $\leq m_{a}\leq 2.6$ eV, reach axion-photon couplings down to
$5.5\times 10^{-12}$ GeV-1. We show our MIRI MRS projections in the twelve
bands at smaller masses, which are somewhat weaker, although they promise to
probe astrophobic QCD axion scenarios down to $0.18$ eV. Our analysis shows
that JWST has the ability to rule out a QCD axion DM candidate above about 0.2
eV, whether or not it is coupled to baryonic matter, making this analysis
particularly complementary to other astrophysical probes.

Discussion & Conclusion—JWST is the first telescope with exquisite enough
sensitivity to near- and mid-IR emission lines to probe viable axion DM.
Although JWST was not designed with axion decay searches in mind, it is
nevertheless a powerful tool in the search for axions owing to its spectral
resolution, which is precise enough to resolve lines resulting from DM decay.
In this work we show that an analysis of the end-of-mission blank-sky
observations will cover novel axion parameter space in a region that is
currently unexplored by terrestrial experiments. This will effectively rule
out a QCD axion DM candidate heavier than about 0.2 eV, regardless of its
matter couplings. Importantly, the blank-sky observations discussed in this
work will be made in the course of the normal operations of JWST, and require
no changes in the observing strategy.

Another search strategy could be to observe a dwarf galaxy such as Draco dSph.
Typically the blank-sky strategy is stronger, but the JWST FOV is
significantly smaller than most telescopes used to search for DM decay, while
the dwarf D-factors increase when averaged over smaller FOVs around their
centers. Furthermore, dust extinction reduces the MW D-factor while it is
irrelevant for dwarfs not in the plane of the galaxy. Accounting for these
effects, Draco hosts a larger D-factor than any MW location, which we estimate
to be $\sim(9\pm 2.5)\times 10^{31}$ eV/cm2 in the JWST FOV (the variation
with observing mode is small) Evans  _et al._ (2016), which is conservatively
about three times as large as the MW average. The typical dwarf velocity
dispersion is also smaller than the MW, $\mathcal{O}(10^{-4})$ McConnachie
(2012), which means that DM decay lines originating in dwarfs would be
unresolved by JWST, but this has a relatively minor effect on our sensitivity.
Draco and other dwarfs have not to-date been observed by JWST except in
imaging modes, and are unlikely to be observed in normal operations. A typical
single-target observation could achieve total exposure times of around 100 ks,
about 200 times smaller than that of our combined exposure. Therefore, such an
analysis could not exceed the sensitivity of an end-of-mission blank-sky
analysis (except in the mass range from 2.55 to 2.66 eV, which is probed only
by the low-exposure F070LP filters). For example, assuming a 100 ks
observation of Draco across the four high-resolution NIRSpec modes, we
estimate a peak sensitivity of $g_{a\gamma\gamma}^{95}\approx 8\times
10^{-12}$ GeV-1. However, a 100 ks dwarf observation in one particular filter
would result in sensitivity over a smaller mass range which is competitive
with that forecasted here.

In this work we focus on forecasting the JWST end-of-mission sensitivity to
axion decay. JWST has now been in operation for $\sim$1.5 years, and therefore
has collected 15% of its total data. An analysis of only the currently-
available data would still provide leading sensitivity, but weaker than that
projected here by a factor $0.15^{-1/4}\sim 1.6$, which we leave to future
work.

Note added: During the preparation of this manuscript, Ref. Janish and Pinetti
(2023) appeared on the arXiv, also studying Milky Way axion decay signatures
using JWST. Our works have some overlap but are complementary; the main result
of that work is the analysis of two NIRSpec observations. While that work
projects the end-of-mission sensitivity for two NIRSpec filters through
extrapolation of their limits, we take into account spatial information in
both the decay signal and the astrophysical backgrounds to project sensitivity
for all JWST IFU detectors. We note that we find that our NIRSpec projections
are weaker by a factor $\sim$2.

##  I Acknowledgements

We thank Dylan Folsom, Joshua Foster, Mariia Khelashvili, Mariangela Lisanti,
Hongwan Liu, Benjamin Safdi, and the JWST Space Telescope Science Institute
help staff. A.P. acknowledges support from the Princeton Center for
Theoretical Science postdoctoral fellowship. The work of C.B. was supported in
part by NASA through the NASA Hubble Fellowship Program grant HST-
HF2-51451.001-A awarded by the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy, Inc.,
for NASA, under contract NAS5-26555. Part of this work was done at the Aspen
Center for Physics, which is supported by National Science Foundation grant
PHY-1607611. S.R. was supported by the Department of Energy (DOE) under Award
Number DE-SC0007968.

This research made extensive use of the publicly available codes astropy
Astropy Collaboration (2013, 2018, 2022), dust_extinction Gordon (2023),
dustmaps Green  _et al._ (2019), HEALPix Górski  _et al._ (2005), healpy Zonca
_et al._ (2019), IPython (Pérez and Granger, 2007), Jupyter (Kluyver  _et al._
, 2016), Mathematica Inc. , matplotlib (Hunter, 2007), NumPy (Harris  _et al._
, 2020), Python Van Rossum and Drake (2009) SciPy (Virtanen  _et al._ , 2020)
and unyt (Goldbaum  _et al._ , 2018).

## References

  * Peccei and Quinn (1977a) R. D. Peccei and H. R. Quinn, Phys. Rev. D16, 1791 (1977a).
  * Peccei and Quinn (1977b) R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977b).
  * Weinberg (1978) S. Weinberg, Phys. Rev. Lett. 40, 223 (1978).
  * Wilczek (1978) F. Wilczek, Phys. Rev. Lett. 40, 279 (1978).
  * Svrcek and Witten (2006) P. Svrcek and E. Witten, JHEP 06, 051 (2006), arXiv:hep-th/0605206 [hep-th] .
  * Arvanitaki  _et al._ (2010) A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, and J. March-Russell, Phys. Rev. D81, 123530 (2010), arXiv:0905.4720 [hep-th] .
  * Gendler  _et al._ (2023) N. Gendler, D. J. E. Marsh, L. McAllister, and J. Moritz, (2023), arXiv:2309.13145 [hep-th] .
  * Dolan  _et al._ (2022) M. J. Dolan, F. J. Hiskens, and R. R. Volkas, JCAP 10, 096 (2022), arXiv:2207.03102 [hep-ph] .
  * Arik  _et al._ (2009) E. Arik _et al._ (CAST), JCAP 02, 008 (2009), arXiv:0810.4482 [hep-ex] .
  * Arik  _et al._ (2014) M. Arik _et al._ (CAST), Phys. Rev. Lett. 112, 091302 (2014), arXiv:1307.1985 [hep-ex] .
  * Janish and Pinetti (2023) R. Janish and E. Pinetti, “Hunting dark matter lines in the infrared background with the james webb space telescope,” (2023), arXiv:2310.15395 [hep-ph] .
  * Todarello  _et al._ (2023) E. Todarello, M. Regis, J. Reynoso-Cordova, M. Taoso, D. Vaz, J. Brinchmann, M. Steinmetz, and S. L. Zoutendijk, (2023), arXiv:2307.07403 [astro-ph.CO] .
  * Irastorza and Redondo (2018) I. G. Irastorza and J. Redondo, Progress in Particle and Nuclear Physics 102, 89 (2018).
  * Arias  _et al._ (2012) P. Arias, D. Cadamuro, M. Goodsell, J. Jaeckel, J. Redondo, and A. Ringwald, JCAP 06, 013 (2012), arXiv:1201.5902 [hep-ph] .
  * Benabou  _et al._ (2023) J. N. Benabou, M. Buschmann, S. Kumar, Y. Park, and B. R. Safdi, “Signatures of primordial energy injection from axion strings,” (2023), arXiv:2308.01334 [hep-ph] .
  * Grilli di Cortona  _et al._ (2016) G. Grilli di Cortona, E. Hardy, J. Pardo Vega, and G. Villadoro, JHEP 01, 034 (2016), arXiv:1511.02867 [hep-ph] .
  * Gorghetto  _et al._ (2021) M. Gorghetto, E. Hardy, and G. Villadoro, SciPost Phys. 10, 050 (2021), arXiv:2007.04990 [hep-ph] .
  * Buschmann  _et al._ (2020) M. Buschmann, J. W. Foster, and B. R. Safdi, Phys. Rev. Lett. 124, 161103 (2020), arXiv:1906.00967 [astro-ph.CO] .
  * Buschmann  _et al._ (2022a) M. Buschmann, J. W. Foster, A. Hook, A. Peterson, D. E. Willcox, W. Zhang, and B. R. Safdi, Nature Commun. 13, 1049 (2022a), arXiv:2108.05368 [hep-ph] .
  * Buschmann  _et al._ (2022b) M. Buschmann, C. Dessert, J. W. Foster, A. J. Long, and B. R. Safdi, Phys. Rev. Lett. 128, 091102 (2022b), arXiv:2111.09892 [hep-ph] .
  * Lella  _et al._ (2023) A. Lella, P. Carenza, G. Co’, G. Lucente, M. Giannotti, A. Mirizzi, and T. Rauscher, (2023), arXiv:2306.01048 [hep-ph] .
  * Di Luzio  _et al._ (2018) L. Di Luzio, F. Mescia, E. Nardi, P. Panci, and R. Ziegler, Phys. Rev. Lett. 120, 261803 (2018), arXiv:1712.04940 [hep-ph] .
  * Björkeroth  _et al._ (2019) F. Björkeroth, L. Di Luzio, F. Mescia, and E. Nardi, JHEP 02, 133 (2019), arXiv:1811.09637 [hep-ph] .
  * Badziak and Harigaya (2023) M. Badziak and K. Harigaya, JHEP 06, 014 (2023), arXiv:2301.09647 [hep-ph] .
  * Co  _et al._ (2018) R. T. Co, L. J. Hall, and K. Harigaya, Phys. Rev. Lett. 120, 211602 (2018), arXiv:1711.10486 [hep-ph] .
  * Caputo and Reig (2019) A. Caputo and M. Reig, Phys. Rev. D 100, 063530 (2019), arXiv:1905.13116 [hep-ph] .
  * Visinelli and Gondolo (2010) L. Visinelli and P. Gondolo, Phys. Rev. D 81, 063508 (2010), arXiv:0912.0015 [astro-ph.CO] .
  * Co  _et al._ (2020) R. T. Co, L. J. Hall, and K. Harigaya, Phys. Rev. Lett. 124, 251802 (2020), arXiv:1910.14152 [hep-ph] .
  * Cyncynates and Thompson (2023) D. Cyncynates and J. O. Thompson, “Heavy qcd axion dark matter from avoided level crossing,” (2023), arXiv:2306.04678 [hep-ph] .
  * Armengaud  _et al._ (2019) E. Armengaud _et al._ (IAXO), JCAP 06, 047 (2019), arXiv:1904.09155 [hep-ph] .
  * Liu  _et al._ (2022) J. Liu, K. Dona, G. Hoshino, S. Knirck, N. Kurinsky, M. Malaker, D. W. Miller, A. Sonnenschein, M. H. Awida, P. S. Barry, K. K. Berggren, D. Bowring, G. Carosi, C. Chang, A. Chou, R. Khatiwada, S. Lewis, J. Li, S. W. Nam, O. Noroozian, and T. X. Z. and, Physical Review Letters 128 (2022), 10.1103/physrevlett.128.131801.
  * Baryakhtar  _et al._ (2018) M. Baryakhtar, J. Huang, and R. Lasenby, Phys. Rev. D 98, 035006 (2018), arXiv:1803.11455 [hep-ph] .
  * Barnett  _et al._ (1996) R. M. Barnett _et al._ (Particle Data Group), Phys. Rev. D 54, 1 (1996).
  * Note (1) At low frequency the decay rate is Bose-enhanced relative to the previously-quoted vacuum decay rate.
  * Caputo  _et al._ (2019) A. Caputo, M. Regis, M. Taoso, and S. J. Witte, JCAP 03, 027 (2019), arXiv:1811.08436 [hep-ph] .
  * Chan (2021) M. H. Chan, Sci. Rep. 11, 20087 (2021), arXiv:2109.11734 [astro-ph.CO] .
  * Sun  _et al._ (2022) Y. Sun, K. Schutz, A. Nambrath, C. Leung, and K. Masui, Phys. Rev. D 105, 063007 (2022), arXiv:2110.13920 [hep-ph] .
  * Grin  _et al._ (2007) D. Grin, G. Covone, J.-P. Kneib, M. Kamionkowski, A. Blain, and E. Jullo, Phys. Rev. D 75, 105018 (2007), arXiv:astro-ph/0611502 .
  * Dessert  _et al._ (2020) C. Dessert, N. L. Rodd, and B. R. Safdi, Science 367, 1465 (2020), arXiv:1812.06976 [astro-ph.CO] .
  * Foster  _et al._ (2021) J. W. Foster, M. Kongsore, C. Dessert, Y. Park, N. L. Rodd, K. Cranmer, and B. R. Safdi, Phys. Rev. Lett. 127, 051101 (2021), arXiv:2102.02207 [astro-ph.CO] .
  * Calore  _et al._ (2023) F. Calore, A. Dekker, P. D. Serpico, and T. Siegert, Mon. Not. Roy. Astron. Soc. 520, 4167 (2023), arXiv:2209.06299 [hep-ph] .
  * DeRocco  _et al._ (2022) W. DeRocco, S. Wegsman, B. Grefenstette, J. Huang, and K. Van Tilburg, Phys. Rev. Lett. 129, 101101 (2022), arXiv:2205.05700 [hep-ph] .
  * Blanco and Hooper (2019) C. Blanco and D. Hooper, JCAP 03, 019 (2019), arXiv:1811.05988 [astro-ph.HE] .
  * Greenhouse (2016) M. Greenhouse, in  _2016 IEEE Aerospace Conference_ (IEEE, 2016) pp. 1–11.
  * Jakobsen  _et al._ (2022) P. Jakobsen _et al._ , A&A 661, A80 (2022), arXiv:2202.03305 [astro-ph.IM] .
  * Wells  _et al._ (2015) M. Wells _et al._ , PASP 127, 646 (2015), arXiv:1508.03070 [astro-ph.IM] .
  * Dessert  _et al._ (2023a) C. Dessert, O. Ning, N. L. Rodd, and B. R. Safdi, (2023a), arXiv:2305.17160 [astro-ph.CO] .
  * (48) MAST 2021, MAST Portal Guide, eds. R.A. Shaw, B. Cherinka, P. Forshay (Version 2; Baltimore: STScI).
  * Lisanti  _et al._ (2018) M. Lisanti, S. Mishra-Sharma, N. L. Rodd, B. R. Safdi, and R. H. Wechsler, Phys. Rev. D 97, 063005 (2018), arXiv:1709.00416 [astro-ph.CO] .
  * Green  _et al._ (2019) G. M. Green, E. Schlafly, C. Zucker, J. S. Speagle, and D. Finkbeiner, The Astrophysical Journal 887, 93 (2019).
  * Schlegel  _et al._ (1998) D. J. Schlegel, D. P. Finkbeiner, and M. Davis, ApJ 500, 525 (1998), arXiv:astro-ph/9710327 [astro-ph] .
  * Schlafly and Finkbeiner (2011) E. F. Schlafly and D. P. Finkbeiner, The Astrophysical Journal 737, 103 (2011).
  * Gao  _et al._ (2013) J. Gao, A. Li, and B. W. Jiang, Earth, Planets and Space 65, 1127 (2013).
  * Navarro  _et al._ (1996) J. F. Navarro, C. S. Frenk, and S. D. M. White, Astrophys. J. 462, 563 (1996), arXiv:astro-ph/9508025 .
  * Navarro  _et al._ (1997) J. F. Navarro, C. S. Frenk, and S. D. M. White, Astrophys. J. 490, 493 (1997), arXiv:astro-ph/9611107 .
  * Cautun  _et al._ (2020) M. Cautun, A. Bení tez-Llambay, A. J. Deason, C. S. Frenk, A. Fattahi, F. A. Gómez, R. J. J. Grand, K. A. Oman, J. F. Navarro, and C. M. Simpson, Monthly Notices of the Royal Astronomical Society 494, 4291 (2020).
  * Leung  _et al._ (2022) H. W. Leung, J. Bovy, J. T. Mackereth, J. A. S. Hunt, R. R. Lane, and J. C. Wilson, Monthly Notices of the Royal Astronomical Society 519, 948 (2022).
  * (58) “Jwst user documentation,” .
  * Note (2) https://jwst-docs.stsci.edu/jwst-other-tools/jwst-backgrounds-tool.
  * Kelsall  _et al._ (1998) T. Kelsall, J. L. Weiland, B. A. Franz, W. T. Reach, R. G. Arendt, E. Dwek, H. T. Freudenreich, M. G. Hauser, S. H. Moseley, N. P. Odegard, R. F. Silverberg, and E. L. Wright, The Astrophysical Journal 508, 44 (1998).
  * Wright (1998) E. L. Wright, The Astrophysical Journal 496, 1 (1998).
  * Gorjian  _et al._ (2000) V. Gorjian, E. L. Wright, and R. R. Chary, The Astrophysical Journal 536, 550 (2000).
  * Lightsey and A. (2016) Lightsey and P. A., SPIE 9904, 99040A (2016).
  * Wainscoat  _et al._ (1992) R. J. Wainscoat, M. Cohen, K. Volk, H. J. Walker, D. E. Schwartz, R. J. Wainscoat, M. Cohen, K. Volk, H. J. Walker, and D. E. Schwartz, ApJS 83, 111 (1992).
  * Rigby  _et al._ (2023) J. R. Rigby _et al._ , Publications of the Astronomical Society of the Pacific 135, 048002 (2023).
  * Dessert  _et al._ (2023b) C. Dessert, J. W. Foster, Y. Park, and B. R. Safdi, (2023b), arXiv:2309.03254 [astro-ph.CO] .
  * (67) “Jwst exposure time calculator,” https://jwst.etc.stsci.edu/.
  * Frate  _et al._ (2017) M. Frate, K. Cranmer, S. Kalia, A. Vandenberg-Rodes, and D. Whiteson, (2017), arXiv:1709.05681 [physics.data-an] .
  * Cowan  _et al._ (2011) G. Cowan, K. Cranmer, E. Gross, and O. Vitells, Eur. Phys. J. C 71, 1554 (2011), [Erratum: Eur.Phys.J.C 73, 2501 (2013)], arXiv:1007.1727 [physics.data-an] .
  * Evans  _et al._ (2016) N. W. Evans, J. L. Sanders, and A. Geringer-Sameth, Phys. Rev. D 93, 103512 (2016), arXiv:1604.05599 [astro-ph.GA] .
  * McConnachie (2012) A. W. McConnachie, Astronomical Journal 144, 4 (2012), arXiv:1204.1562 [astro-ph.CO] .
  * Astropy Collaboration (2013) Astropy Collaboration, A&A 558, A33 (2013), arXiv:1307.6212 [astro-ph.IM] .
  * Astropy Collaboration (2018) Astropy Collaboration, AJ 156, 123 (2018), arXiv:1801.02634 [astro-ph.IM] .
  * Astropy Collaboration (2022) Astropy Collaboration, ApJ 935, 167 (2022), arXiv:2206.14220 [astro-ph.IM] .
  * Gordon (2023) K. Gordon, “dust_extinction: A python package for interstellar dust extinction laws and curves,” Available at https://github.com/karllark/dust_extinction (2023), accessed: October 2023.
  * Górski  _et al._ (2005) K. M. Górski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, and M. Bartelmann, ApJ 622, 759 (2005), arXiv:astro-ph/0409513 .
  * Zonca  _et al._ (2019) A. Zonca, L. Singer, D. Lenz, M. Reinecke, C. Rosset, E. Hivon, and K. Gorski, Journal of Open Source Software 4, 1298 (2019).
  * Pérez and Granger (2007) F. Pérez and B. E. Granger, Computing in Science and Engineering 9, 21 (2007).
  * Kluyver  _et al._ (2016) T. Kluyver _et al._ , Positioning and Power in Academic Publishing: Players, Agents and Agendas - Proceedings of the 20th International Conference on Electronic Publishing, ELPUB 2016 , 87 (2016).
  * (80) W. R. Inc., “Mathematica, Version 13.3,” Champaign, IL, 2023.
  * Hunter (2007) J. D. Hunter, Computing in Science & Engineering 9, 90 (2007).
  * Harris  _et al._ (2020) C. R. Harris _et al._ , Nature 585, 357 (2020).
  * Van Rossum and Drake (2009) G. Van Rossum and F. L. Drake,  _Python 3 Reference Manual_ (CreateSpace, Scotts Valley, CA, 2009).
  * Virtanen  _et al._ (2020) P. Virtanen _et al._ , Nature Methods 17, 261 (2020).
  * Goldbaum  _et al._ (2018) N. J. Goldbaum, J. A. ZuHone, M. J. Turk, K. Kowalik, and A. L. Rosen, Journal of Open Source Software 3, 809 (2018).
  * Mignard (2000) F. Mignard, A&A 354, 522 (2000).
  * Schönrich  _et al._ (2010) R. Schönrich, J. Binney, and W. Dehnen, Monthly Notices of the Royal Astronomical Society 403, 1829 (2010).
  * Draine (2003) B. T. Draine, Ann. Rev. Astron. Astrophys. 41, 241 (2003), arXiv:astro-ph/0304489 .

Supplemental Material for Sensitivity of JWST to eV-Scale Decaying Axion Dark
Matter
Sandip Roy, Carlos Blanco, Christopher Dessert, Anirudh Prabhu, Tea Temim

##  I Doppler Shifting and Broadening

In this section we describe our accounting for Doppler shifting and broadening
in the ETC. We closely follow the approach of Dessert  _et al._ (2023a), which
we do not repeat here. We assume a MW DM velocity dispersion of 220 km/s
throughout the entire MW. However, the decay line is also Doppler shifted due
to the solar motion relative to the DM rest frame. In galactic Cartesian
coordinates, we have $\textbf{v}_{\odot}=(11,232,7)$ km/s Mignard (2000);
Schönrich  _et al._ (2010). In our analysis we stack data within each
galactocentric annulus, so the quantity of interest is the root-mean-squared
line broadening due to solar Doppler shifting, given as
$\sigma_{\odot}=(\int_{\Omega}d\Omega|\hat{\textbf{n}}\cdot\textbf{v}_{\odot}|^{2}/\int_{\Omega}d\Omega)^{1/2}$,
where $\Omega$ is the area on the sky within the annulus. This is then added
in quadrature with the DM velocity dispersion, so that the line width we enter
into the ETC is given by $\Delta v=((220\
\textrm{km/s})^{2}+\sigma_{\odot}^{2})^{1/2}$. In Fig. S1, we show $\Delta v$
in each of our annuli.

Figure S1:  Expected width of the stacked axion decay signal in each analysis
annulus, including both Doppler shifting and broadening effects.

##  II Astrophysical Backgrounds

We use the jwst_backgrounds tool to compute the background flux at every point
along each annular ring, labeled by the azimuthal coordinate $\phi_{\rm GC}$.
In Fig. S2 we show the expected background at $5{\,{\rm\mu m}}$ at
$\theta_{\rm GC}=30^{\circ}$ and $60^{\circ}$ as a function of $\phi_{\rm
GC}$. Except for the masked GP regions, the background flux is maximized when
the ring intersects the ecliptic plane. The ETC takes in a coordinate at which
to evaluate the background flux. In our projections, we conservatively enter
the coordinate which maximizes the background over the ring.

We show the wavelength-dependence of the JWST backgrounds in Fig. S3 at the
point where the annuli intersect with the ecliptic plane. The JWST background
has four components: zodiacal (i.e. solar system) emission, interstellar
medium (ISM) emission, stray light which is scattered by the instrument from
outside the FOV into the detector, and thermal emission of the instrument
itself. At the lower galactic latitude, the in-field ISM emission is
comparable to the in-field zodiacal emission at wavelengths $\lesssim
5{\,{\rm\mu m}}$. At the greater galactic latitude, zodiacal emission
dominates ISM emission. Thermal self-emission dominates at wavelengths
$\gtrsim 15{\,{\rm\mu m}}$ in both cases. We sum these background components
to compute the background flux.

Figure S2: Expected JWST background flux at $5{\,{\rm\mu m}}$ at $\theta_{\rm
GC}=30^{\circ}$ and $60^{\circ}$ as a function of the galactic azimuthal
coordinate, $\phi_{\rm GC}$. Coordinates that intersect the ecliptic plane,
which hosts larger backgrounds due to zodiacal emission, are marked in a gray
vertical line. We shade the masked regions ($|\phi_{\rm GC}|\leq 10^{\circ}$
and $170^{\circ}\leq\phi_{\rm GC}\leq 190^{\circ}$). In our analysis, we
conservatively assume the background flux at the ecliptic plane holds over the
whole ring. Note that $0^{\circ}\leq\phi_{\rm GC}<360^{\circ}$, but we only
show $\phi_{\rm GC}\leq 180^{\circ}$ because the background is largely
symmetric.

Figure S3: Background components for $\theta_{\rm GC}=10^{\circ}$ and
$45^{\circ}$ and on the ecliptic plane, generated using the jwst_backgrounds
tool.

##  III Dust Extinction

In this section we describe our treatment of the extinction due to dust in the
MW. Electromagnetic radiation, particularly in the visual and UV bands, is
scattered and absorbed on dust particles in the MW, increasing the opacity of
the galaxy (for a review see Draine (2003)). In the near-IR the dust
absorption cross-section is much smaller because the wavelength of the
radiation is larger than the typical size of the dust particles. Although dust
extinction is important for us, it does not substantially affect our results.

Electromagnetic radiation of wavelength $\lambda$ produced at a distance $d$
from Earth and galactic coordinates $(l,b)$ is reduced by a factor
$\exp(-\int_{0}^{d}dsn_{d}(s,l,b)\sigma(\lambda))$. In the limit that the
emission is produced outside of the galaxy, this expression vastly simplifies
to $10^{-0.44A_{\lambda}}$, where $A_{\lambda}$ is known as the galactic
extinction (in units of magnitudes). We work in this limit throughout this
manuscript, although we note that this is a conservative assumption as the DM
decays throughout the galaxy. $A_{\lambda}$ varies both with sky coordinates
and wavelength. The spatial morphology of the extinction is mapped out and
computed in Schlegel  _et al._ (1998); Schlafly and Finkbeiner (2011), which
provide $A_{V}$, the V-band extinction. We then use known scaling relations to
compute the extinction at the relevant wavelengths, reproduced in Fig. S4. The
black lines correspond to models from Schlegel  _et al._ (1998) which are the
generic expectations in the MW. In this work we use Gao  _et al._ (2013),
which is the scaling relation derived using data at the Galactic Center. The
dust extinction maps at $1{\,{\rm\mu m}}$ and $10{\,{\rm\mu m}}$ are shown in
Fig. S5. In each analysis annulus, we compute the average effective D-factor
$D_{\rm eff}=\int_{\Omega}d\Omega\,D(l,b)\,10^{-0.44A_{\lambda}(l,b)}$, which
we show in Fig. S6 for a variety of GP cuts.

Figure S4:  Dust extinction curves for different benchmark models from
Schlegel  _et al._ (1998); Gao  _et al._ (2013) which we extrapolate
logarithmically to cover the wavelength range $0.5{\,{\rm\mu
m}}\,-\,100{\,{\rm\mu m}}$. We use the red curve from Gao  _et al._ (2013),
calibrated specifically on the GC, for our analysis.

Figure S5:  _Left panel_ : Dust extinction map at $1{\,{\rm\mu m}}$,
corresponding to $m_{a}=2.5{\,{\rm eV}}$, based on the dust models of Schlegel
_et al._ (1998); Schlafly and Finkbeiner (2011) and the extinction curve of
Gao  _et al._ (2013). The grey dotted lines delineate our ring edges and the
dotted black lines are $|b|=10^{\circ}$, between which is masked in our
analysis, similar to the scheme in Fig. 2. _Right panel_ : Same as left panel
but at $10{\,{\rm\mu m}}$, corresponding to $m_{a}=0.25{\,{\rm eV}}$. As the
mass of the axion decreases, the dust extinction becomes less significant
according to the extinction law in Fig. S4.  Figure S6:  Line-of-sight
averaged $D_{\rm eff}$ factors for different galactic latitude ($|b|$) masks.
As we increase the $|b|$ mask from $0^{\circ}$ to $10^{\circ}$, the mean
$D_{\rm eff}$ values near the GP experience less dust extinction. A too
aggressive mask results in a loss of sensitivity because we exclude regions of
large D-factor, as shown by the black line. Therefore we mask $|b|<10^{\circ}$
in our fiducial analysis.