# A Change Detection Reality Check

Isaac Corley
University of Texas at San Antonio
San Antonio, TX, USA
<EMAIL_ADDRESS>
&Caleb Robinson & Anthony Ortiz
Microsoft AI for Good Research Lab
Redmond, WA, USA
<EMAIL_ADDRESS>
###### Abstract

In recent years, there has been an explosion of proposed change detection deep
learning architectures in the remote sensing literature. These approaches
claim to offer state-of-the-art performance on different standard benchmark
datasets. However, has the field truly made significant progress? In this
paper we perform experiments which conclude a simple U-Net segmentation
baseline without training tricks or complicated architectural changes is still
a top performer for the task of change detection. All experiments are openly
available at github.com/isaaccorley/a-change-detection-reality-check.

##  1 Introduction

The task of change detection from remotely sensed imagery is a canonical and
important problem that allows us to analyze how our planet changes over time.
It is crucial that change detection methods are highly accurate given their
primary applications for building damage assessment disaster response (Gupta
et al., 2019a; Sublime & Kalinicheva, 2019) and monitoring of the environment
(Cambrin et al., 2024; Watch, 2002). The machine learning and remote sensing
fields are currently experiencing their ImageNet (Deng et al., 2009)
benchmarking era with new proposed model architectures claiming incremental
performance gains on standard benchmark datasets at a rapid rate. For example,
the Changer paper (Fang et al., 2023) – first preprint released on Sep. 2022 –
is cited by 56 papers, the majority of them proposing a new architecture for
change detection while also not releasing any open-source code or model
checkpoints (Ren et al., 2024; Zhang et al., 2024b; Zhou et al., 2024; Li &
Wu, ; Liu et al., 2024; Huang et al., 2024; Lin et al., 2024; Wang et al.,
2024; Lu et al., 2024; Tan et al., 2024; Xu et al., 2024; Yan et al., 2024;
Peng et al., 2023; Wan et al., 2023; Zhao et al., 2023c; Liu et al., 2023c;
Quan et al., 2023; Wang et al., 2023; Liu et al., 2023b; Fazry et al., 2023).
Many of these proposed methods contain complicated architectural layers and
modules specifically designed to better handle the bi-temporal image change
detection task (Bai et al., 2023; Zhang et al., 2024a; Yuan et al., 2024; Li
et al., 2024; Pang et al., 2024; Zheng et al., 2024; Zhao et al., 2023a; Li et
al., 2023; Yan et al., 2023; Chen et al., 2023; Liu et al., 2023a; Zhao et
al., 2023b). Notably many of these papers are peer-reviewed and published at
reputable conferences and journals. However, this begs the question if these
new methods are actually improvements over generic segmentation architectures
or have the benchmarks just been poorly executed? In this paper, we seek to
answer this question.

##### Background

When proposing a new model architecture it is common to perform a comparison
to prior works through benchmark experiments to show statistically significant
improvement. However over time, comparisons become less fair due to
differences in training methodologies that are misconstrued as achieving
state-of-the-art performance. Put simply, baseline experiments are often
underpowered. This has been shown to be prevalent in many areas of research
such as deep metric learning (Musgrave et al., 2020), unsupervised domain
adaption (Musgrave et al., 2021), image classification (Bello et al., 2021),
deep reinforcement learning (Henderson et al., 2018), point cloud
classification (Uy et al., 2019), and video recognition (Du et al., 2021).
Furthermore, these analyses commonly conclude that simple baselines outperform
complicated and task-specific architectures. Most recently, Gerard et al.
(2024) discovered that a generic architecture like U-Net, without training or
evaluation tricks, is still competitive on the xBD dataset from the xView2
challenge (Gupta et al., 2019b).

When analyzing relevant change detection papers and source code for
benchmarking we find that it is common for authors to just compare to metrics
reported in prior literature rather than re-running experiments with the prior
methods in a consistent training setup. Further, we find that recent work
often changes multiple aspects of the experimental setup, including the
training routine (optimization methods, learning rate schedule, etc.) and loss
functions, beyond just the proposed model architecture. This is problematic as
any observed improvements on the benchmark dataset could be due to any
combination of the new architecture, training routine, or loss function. This
has the potential to result in unfair comparisons, especially if the
improvement in quantitative performance is very small.

In this paper we revisit bi-temporal change detection benchmarks with simple
baselines to get an overview on progress. Specifically, we experiment with a
simple semantic segmentation U-Net architecture, and siamese network variants
(Koch et al., 2015), to explore how these baselines perform against the latest
state-of-the-art change detection methods. We find that this baseline
architecture, from 2015, is a top performer on change detection benchmark
datasets.

##  2 Methods

##### State-of-the-Art Models

In our experiments, in addition to compiling results from many prior change
detection works, we retrain and evaluate the following state-of-the-art
methods for change detection: BIT (Chen et al., 2021b) is a transformer-based
siamese network architecture which uses a shared convolutional backbone to
extract image features and transformer encoder decoder networks to perform
change detection. ChangeFormer (Bandara & Patel, 2022b) is an end-to-end
transformer-based siamese network architecture for change detection. TinyCD
(Codegoni et al., 2023) is a change detection architecture which uses an
EfficientNet (Tan & Le, 2019) backbone to extract convolutional features to
feed to a custom attention-based decoder network.

##### Our Baseline Models

(Daudt et al., 2018) proposed three fully-convolutional (FC) architectures for
change detection. The first is Early Fusion (FC-EF) which is an encoder-
decoder style architecture with the change detection image pair concatenated
as input. The other methods contain shared siamese encoders which either
concatenate intermediate feature maps (FC-Siam-Conc) or take the difference
(FC-Siam-Diff). While these networks are similar to the U-Net architecture
(Ronneberger et al., 2015), the original implementation is customized and
hardcoded to be lightweight in parameter count and thus are unable to take
advantage of pretrained encoder backbones like ResNet (He et al., 2016). These
methods are commonly seen in change detection benchmarks being compared to
methods which utilize pretrained ImageNet backbones.

In our experiments, we generalize these implementations to use the standard
U-Net framework which is able to take advantage of numerous ImageNet
pretrained backbones. To avoid confusion with the original implementations of
(Daudt et al., 2018), we refer to these architectures in our experiments as
simply U-Net, U-Net SiamConc, and U-Net SiamDiff. Specifically, we utilize the
implementations of these models in the TorchGeo (Stewart et al., 2022) library
for reproducibility. We perform benchmarks using the ResNet-50 and
EfficientNet-B4 (Tan & Le, 2019) backbones.

Table 1: Comparison of state-of-the-art and change detection architectures to
a U-Net baseline on the LEVIR-CD dataset. We report the test set precision,
recall, and F1 metrics of the positive change class. For the baseline
experiments we perform 10 runs while varying random the seed and report
metrics from the highest performing run. All other metrics are taken from
their respective papers. The top performing methods are highlighted in bold.
Gray rows indicate our baseline U-Net and siamese encoder variants.

Model | Backbone | Precision | Recall | F1
---|---|---|---|---
FC-EF (Daudt et al., 2018) | - | 86.91 | 80.17 | 83.40
FC-Siam-Conc (Daudt et al., 2018) | - | 91.99 | 76.77 | 83.69
FC-Siam-Diff (Daudt et al., 2018) | - | 89.53 | 83.31 | 86.31
DTCDSCN (Liu et al., 2020) | SE-Resnet34 | 88.53 | 86.83 | 87.67
STANet (Chen & Shi, 2020) | ResNet-18 | 83.81 | 91.00 | 87.26
CDNet (Chen et al., 2021a) | ResNet-18 | 91.60 | 86.50 | 89.00
BIT (Chen et al., 2021b) | ResNet-18 | 89.24 | 89.37 | 89.31
ChangeFormer (Bandara & Patel, 2022b) | MiT-b1 | 92.59 | 89.68 | 91.11
Tiny-CD (Codegoni et al., 2023) | EfficientNet-b4 | 92.68 | 89.47 | 91.05
ChangerVanilla (Fang et al., 2023) | ResNet-18 | 92.66 | 89.60 | 91.10
ChangerEx (Fang et al., 2023) | ResNet-18 | 92.97 | 90.61 | 91.77
U-Net (Ronneberger et al., 2015) | EfficientNet-b4 | 92.69 | 87.16 | 89.25
U-Net (Ronneberger et al., 2015) | ResNet-50 | 91.97 | 89.78 | 90.38
U-Net SiamConc | ResNet-50 | 92.87 | 89.48 | 90.41
U-Net SiamDiff | ResNet-50 | 93.21 | 89.50 | 90.46

###  2.1 Datasets

For comparisons of change detection architectures we utilize the following
benchmark datasets:

LEVIR-CD

(Chen & Shi, 2020) A binary change detection dataset containing 637 high
resolution (0.5m) 1024 × 1024 image pairs extracted from Google Earth. We
utilize the splits provided with the dataset and, following other change
detection papers, we convert the images to non-overlapping 256 × 256 patches.

WHU-CD

(Ji et al., 2018) A binary change detection dataset containing one pair of
high-resolution (0.075m) aerial images of size 32507 × 15354. We utilize the
train and test splits provided with the dataset and convert the images to non-
overlapping 256 × 256 patches. During training runs we randomly split a 10%
holdout set from the train set to use as a validation set.

##  3 Experiments

###  3.1 Baseline Training Details

Throughout our baseline training experiments we use the same hyperparameter
setup from the BIT (Chen et al., 2021b) source which consists of batch size of
8, 200 epochs, stochastic gradient descent (SGD) optimizer with an initial
learning rate $\gamma=0.01$, momentum $\mu=0.9$, weight decay $\alpha=5E-4$,
and a linear decaying scheduler. We train each model by optimizing a cross
entropy loss on a multiclass segmentation output where the number of classes
is 2 for binary change detection. We select the checkpoint with the top
performance based on the validation loss and do not perform any early
stopping. We note that this setup results in a number of iterations which
allows each model to converge.

During training we use augmentations consisting of random horizontal and
vertical flips with probability $p=0.5$ and random resize crop with scale in
the range $[0.8,1.0]$, aspect ratio of $1$, and $p=1$. For image normalization
we simply rescale the images to the range $[-1,1]$ following the BIT (Chen et
al., 2021b) source.

###  3.2 Updated WHU-CD Benchmarks

Many papers utilize a preprocessed and randomly split version of the WHU-CD
dataset created in (Bandara & Patel, 2022a) for change detection benchmarks.
However these sets have been known to introduce data leakage (Bandara, 2023) –
$\approx 85\%$ of the test set is included in the train set due to a bug in
the preprocessing scripts – which makes them impossible to use to benchmark
methods. We perform a new benchmark using the original train and test set
splits from the WHU-CD dataset and retrain the BIT, ChangeFormer, and TinyCD
models for comparison. We use the same experimental settings described in
Section 3.1.

We find that performance of some models, particularly the transformer based
methods BIT and ChangeFormer, can vary significantly over different random
seeds, therefore we train each model on each dataset for runs with 10
different seeds. For comparisons we select the results from the highest
performing run as well as report the average and standard deviation over runs
for transparency. Any additional parameters can be found in our open source
implementation.

Table 2: Experimental results on the WHU-CD dataset. We retrain several state-
of-the-art methods using the original dataset’s train/test splits instead of
the commonly used randomly split preprocessed version created in Bandara &
Patel (2022a). We find that these state-of-the-art methods are outperformed by
a U-Net baseline. We report the test set precision, recall, F1, and IoU
metrics of the positive change class. For each run we select the model
checkpoint with the lowest validation set loss. We provide metrics averaged
over 10 runs with varying random seed as well as the best seed. Gray rows
indicate our baseline U-Net and siamese encoder variants.

Model | Backbone | F1 | Pre. | Rec. | IoU
---|---|---|---|---|---
Averaged Over 10 Seeds
ChangeFormer | MiT-b1 | 75.65 ± 1.58 | 77.06 ± 3.22 | 74.67 ± 1.97 | 61.60 ± 2.05
TinyCD | EfficientNet-b4 | 78.53 ± 1.28 | 80.15 ± 2.49 | 77.56 ± 2.13 | 65.52 ± 1.72
BIT | ResNet-18 | 72.67 ± 2.69 | 70.30 ± 6.36 | 76.84 ± 4.53 | 58.06 ± 3.24
U-Net | ResNet-50 | 81.85 ± 1.32 | 83.72 ± 2.65 | 80.39 ± 2.32 | 69.96 ± 1.83
U-Net SiamConc | ResNet-50 | 81.33 ± 1.08 | 79.30 ± 2.78 | 84.19 ± 1.55 | 69.40 ± 1.52
U-Net SiamDiff | ResNet-50 | 82.02 ± 1.48 | 83.82 ± 3.80 | 80.92 ± 2.51 | 70.29 ± 2.00
Best Seed
ChangeFormer | MiT-b1 | 77.75 | 82.60 | 78.57 | 64.22
TinyCD | EfficientNet-b4 | 78.53 | 80.15 | 77.56 | 65.52
BIT | ResNet-18 | 77.68 | 78.58 | 82.13 | 64.34
U-Net | ResNet-50 | 84.17 | 88.65 | 83.08 | 73.23
U-Net SiamConc | ResNet-50 | 82.75 | 83.69 | 86.56 | 71.15
U-Net SiamDiff | ResNet-50 | 84.01 | 88.56 | 85.63 | 73.02

##  4 Discussion

##### Results

In Table 1 we provide experimental results for our baseline on the LEVIR-CD
dataset. We compare to prior work by compiling results from their respective
papers. While the compiled results represent the best reported metrics for
each previous method, it still is evident that a simple U-Net baseline is a
top performer. Table 2 provides additional updated experimental results for
the WHU-CD dataset and compares several state-of-the-art change detection
architectures. Again, we can see that the baselines outperform all other
methods.

Regarding the siamese variants of our U-Net baseline (U-Net SiamDiff and U-Net
SiamConc), our experimental results indicate that processing each image in the
bi-temporal pair with a shared encoder results in reasonable gains and is a
promising approach. Methods such as Changer (Fang et al., 2023) also conclude
that additional feature interaction is key for achieving performance
improvements for change detection.

##### Limitations

Due to the fast pace of the field of change detection, with new architectures
being proposed almost weekly, it is difficult to benchmark each new method.
Furthermore, we do not compare to methods which propose a technique, e.g. a
loss function, which is dependent on the architecture or methods, or to
methods which do not publish open source code to reproduce the experimental
results.

We note that there exists several other common change detection datasets such
as DSIFN-CD (Zhang et al., 2020), S2Looking (Shen et al., 2021), SECOND (Yang
et al., 2020), LEVIR-CD+ (Shen et al., 2021), and xBD (Gupta et al., 2019b).
While we do not benchmark against these, we leave this for future work.

##  5 Conclusion and Next Steps

In this paper we analyzed whether the field of change detection has actually
made significant improvements on benchmark datasets in recent years. We
conclude that many claimed improvements are questionable by demonstrating that
a simple baseline of U-Net is still a top-performing method. To be clear, this
is not an issue unique to change detection; other machine learning fields such
as language modeling are finding it crucial to standardize fair benchmarking
(Srivastava et al., 2022) when new methods are rapidly proposed. To mitigate
this, we recommend utilizing and contributing proposed models to libraries and
projects such as OpenCD (Li, 2022), GEO-Bench (Lacoste et al., 2023), and
TorchGeo (Stewart et al., 2022) which standardize datasets and trainers for
reliable benchmarking of remote sensing tasks. As this field has important
downstream applications, we hope our results motivate the community to perform
more reliable benchmarks of performance so that realistic advancements in
change detection can be achieved.

#### Acknowledgments

We thank Jonathan Lwowski, Conor Wallace, Robin Cole, Sebastian Gerard, and
Juan M. Lavista Ferres for their valuable feedback.

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# The EMU view of the Large Magellanic Cloud: Troubles for sub-TeV WIMPs

Marco Regis  Javier Reynoso-Cordova  Miroslav D. Filipović  Marcus Brüggen
Ettore Carretti  Jordan Collier  Andrew M. Hopkins  Emil Lenc  Umberto Maio
Joshua R. Marvil  Ray P. Norris  and Tessa Vernstrom

###### Abstract

We present a radio search for WIMP dark matter in the Large Magellanic Cloud
(LMC). We make use of a recent deep image of the LMC obtained from
observations of the Australian Square Kilometre Array Pathfinder (ASKAP), and
processed as part of the Evolutionary Map of the Universe (EMU) survey. LMC is
an extremely promising target for WIMP searches at radio frequencies because
of the large J-factor and the presence of a substantial magnetic field. We
detect no evidence for emission arising from WIMP annihilations and derive
stringent bounds on the annihilation rate as a function of the WIMP mass, for
different annihilation channels. This work excludes the thermal cross section
for masses below 480 GeV and annihilation into quarks.

##  1 Introduction

The nature of dark matter (DM) is one of the defining mysteries of modern
physics. One of the most attractive candidates proposed to solve the DM puzzle
is given by hypothetical particles that are more massive than baryons and
weakly interacting, the so-called WIMPs [1].

WIMPs have masses in the GeV-TeV range and can annihilate in pairs into
lighter particles. In particular, electrons and positrons can be directly or
indirectly injected by WIMP annihilations, and a sizable final branching ratio
of annihilation into $e^{+}-e^{-}$ is a rather generic feature of WIMP models
(see, e.g., Fig. 4 in Ref. [2]). Emitted in an environment with a background
magnetic field, high-energy electrons and positrons give rise to synchrotron
radiation typically peaking at radio frequencies.

The Large Magellanic Cloud (LMC) is the most massive satellite galaxy of the
Milky Way. The large dark matter mass (with the LMC virial mass being around
$10^{11}\,M_{\odot}$ [3]) and the proximity to Earth (distance around 50 kpc
[4]) make the LMC one of the best targets for indirect searches of WIMPs. The
so-called J-factor, namely, the integral of the density squared over the line-
of-sight and solid angle, amounts to $\sim 10^{20}{\rm GeV^{2}/cm^{5}}$ [5],
second only to the Galactic center. The presence in LMC of a $\mu$G magnetic
field [6] suggests an investigation of a possible WIMP signature at radio
frequencies.

The idea of deriving bounds on WIMPs from radio observations of the LMC is not
new [7, 8]. The improvement presented in the current analysis with respect to
Refs. [7] and [8] arises from new, more sensitive, data, an updated model
(with the inclusion of spatial diffusion in the computation of the DM signal),
and the choice of statistical approach (comprising a morphological analysis
with pixel by pixel comparison of the observed and predicted signals).

We use observations of the LMC obtained by the Australian Square Kilometre
Array Pathfinder (ASKAP [9]), as part of the ASKAP commissioning and early
science (ACES, project code AS033) verification and made available to the
Evolutionary Map of the Universe (EMU) project [10]. These data were used to
obtain a deep image of the LMC at 888 MHz [11], which will be the starting
point of the analysis of this work.

The structure of the paper is as follows. Section 2 describes the ASKAP
observations and how the LMC radio image has been created. The model of DM and
interstellar medium in the LMC is presented in Section 3. We introduce the
statistical analysis and present the results in Section 4, while Section 5
provides a comparison with previous works. Conclusions are drawn in Section 6.
The Appendix is devoted to consistency checks.

##  2 Observational Maps

In this work we make use of the observations of the LMC taken as part of the
ASKAP commissioning and early science at 888 MHz with a bandwidth of 288 MHz,
and analysed as part of the EMU project [11]. The observations cover a total
field of view of 120 deg2, with a total exposure time of about 12h40m. Data
processing was performed using ASKAPsoft by the ASKAP operations team and the
resulting images are available on the CSIRO ASKAP Science Data Archive. The
beam size of the map shown in Fig. 1 (left) is $13.9^{\prime\prime}\times
12.1^{\prime\prime}$ and the median Root Mean Squared (RMS) noise is $\sim
58\,\mu$Jy/beam. For more details see Ref. [11].

Structures on scales $\lesssim 2^{\circ}$ can be recovered thanks to the short
baselines of the ASKAP array (with shortest one being 22 m). We expect the DM-
induced emission to be diffuse but showing variations on scales below
$2^{\circ}$ (see next Section). We confirm the sensitivity of the image to DM
diffuse emissions by performing a test detailed in the Appendix.

Our search looks for a possible diffuse emission associated to the LMC halo,
and all the small-scale discrete sources (in the LMC or in the
background/foreground) are a contaminant that we attempt to mask.  We identify
discrete sources by running the publicly available tool SExtractor [12], which
is also used to derive the RMS map, in the same way as described in Ref. [13].
The threshold for a source to be masked is set to $3\times RMS$, and the
result is shown in Fig. 1 (right). We also mask negative pixels using the same
criterion, i.e., absolute value larger than $3\times RMS$. They are likely due
to missing short-spacing data.

Since the expected emission from DM has a size of several arcmin, we further
smooth the masked image (using the task SMOOTH in Miriad [14]) to
FWHM$=2^{\prime}$, in order to be more stable against small-scale residuals
and fluctuations.

Figure 1: Left panel: Observational map of the LMC at 888 MHz obtained from
ASKAP data in Ref. [11]. Right panel: Same as left panel but blanking masked
pixels. The red cross indicates the position of the dynamical center and the
blue circle encloses the region of interest for this work.

##  3 LMC description

We compute the radio emission induced by WIMP DM by combining the synchrotron
power associated with the LMC magnetic field with the equilibrium distribution
($n_{e}$) of electrons and positrons injected by DM. In order to compute
$n_{e}$, we solve a transport equation describing the cooling and spatial
diffusion experienced by the electrons and positrons after injection. We
describe it in the limit of spherical symmetry and stationarity:

$-\frac{1}{r^{2}}\frac{\partial}{\partial r}\left[r^{2}D\frac{\partial
f}{\partial r}\right]+\frac{1}{p^{2}}\frac{\partial}{\partial
p}(\dot{p}p^{2}f)=s(r,p)\;,$ (3.1)

where $f(r,p)$ is the $e^{+}/e^{-}$ distribution function at the
equilibrium,111We assume equilibrium since the timescales associated to
diffusion and cooling are around 10-30 Myr (see below), much smaller than the
age of the LMC (around 1 Gyr). at a given radius $r$ (from the LMC dynamical
center) and at a given momentum $p$. The distribution $f$ is related to the
number density in the energy interval $(E,E+dE)$ by:
$n_{e}(r,E)dE=4\pi\,p^{2}f(r,p)dp$; analogously, for the $e^{+}/e^{-}$ source
function, we have $q_{e}(r,E)dE=4\pi\,p^{2}\,s(r,p)dp$. The first term on the
left-hand side describes the spatial diffusion, with $D(r,p)$ being the
diffusion coefficient. The second term accounts for the energy loss due to
radiative processes; $\dot{p}(r,p)=\sum_{i}dp_{i}(r,p)/dt$ is the sum of the
rates of momentum loss associated to the radiative process $i$. The DM source
$q_{e}$ scales with the number density of WIMP pairs locally in space, i.e.,
with $\rho^{2}/(2\,M_{\chi}^{2})$, where $\rho(r)$ is the halo mass density
profile, and $M_{\chi}$ is the mass of the DM particle.222In the case of WIMP
as a Dirac fermion, the number density of WIMP pairs goes as
$\rho^{2}/(4\,M_{\chi}^{2})$, while $\rho^{2}/(2\,M_{\chi}^{2})$ is
appropriate for the more common cases of WIMP as a boson or Majorana fermion.
We neglect substructure contributions and assume the DM spatial distribution
to be spherically symmetric and static. The source term associated to the
production of $e^{+}/e^{-}$ is given by:

$q^{a}_{e}(E,r)=\langle\sigma_{a}v\rangle\,\frac{\rho(r)^{2}}{2\,M_{\chi}^{2}}\times\frac{dN_{e}^{a}}{dE}(E)\;,$
(3.2)

where $\langle\sigma_{a}v\rangle$ is the velocity-averaged annihilation rate,
and $dN_{e}^{a}/dE$ is the number of electrons/positrons emitted per
annihilation in the energy interval $(E,E+dE)$ for a given annihilation
channel.

We solve Eq. (3.1) numerically using finite-differencing Crank-Nicolson
scheme, for details see Ref. [13]. Boundary conditions are set to be Neumann’s
one at the centre and Dirichlet’s one at the farthest boundary, the latter
chosen to be ten times the radius of our region of interest (RoI). A recent
semi-analytical treatment of Eq. (3.1) can be found in Ref. [15].

The properties we want to constrain are the DM mass and annihilation rate,
while the ingredients we need to model are the DM spatial profile, the
magnetic field, the spatial diffusion coefficient, the CMB and LMC
interstellar radiation fields (ISRF, for inverse Compton losses) and the gas
density (for bremsstrahlung losses), that we describe in detail in the
following sections. Since our goal is to derive conservative bounds on the
WIMP signal, we will model the above quantities taking lower limits for the DM
profile and magnetic field, while upper limits for diffusion coefficient and
ISRF and gas densities.

To limit uncertainties in the model description, our RoI for the analysis will
be defined by a relatively small region around the LMC center, corresponding
to 1.3 kpc in radius ($1.5^{\circ}$ in angular units). The loss in terms of
J-factor, if compared to considering the full LMC halo, is limited, around a
factor of two, depending on the profile. As we will describe in the following,
in such RoI we have a more robust determination of the various ingredients
entering the computation, such as the magnetic field, the gas and ISRF
distributions, and the DM profile. Moreover, we exclude the bulk of the
contamination from the 30 Doradus region (south-west in Fig. 1).

###  3.1 Dark matter profile

To model the radio emission of the LMC due to annihilating DM, the spatial
particle distribution $\rho(r)$ is a key ingredient, see Eq. (3.2). Previous
work has explored different functional forms for the DM density profile in the
LMC [16, 5, 8, 17, 18, 19, 20] and analysed H i rotational [21] and carbon
star data [22] to constrain the parameters of $\rho(r)$. In this work we are
interested in the inner region, so we make use of the H i data [21] that
provide the most accurate rotation velocities at small distances from the LMC
dynamical center. We explore four different profiles and fit $\rho(r)$ up to a
radius of $\sim 2.7$ kpc from the center333We discard the last points in Fig.
2, since they might be affected by systematic errors, mainly due to non-
circular motions [21] ., which corresponds to about twice our RoI. In
particular, we consider two different “cuspy” DM profiles from the NFW model
(Navarro-Frenk-White) [23] and Hernquist [24]:

$\rho_{\rm{NFW}}(r)=\frac{\rho_{s}}{\left(\frac{r}{r_{S}}\right)\left(1+\frac{r}{r_{s}}\right)^{2}}\;\;\;,\;\;\;\rho_{\rm{Her}}(r)=\frac{\rho_{s}}{\left(\frac{r}{r_{s}}\right)\left(1+\frac{r}{r_{s}}\right)^{3}}\;,$
(3.3)

and two “cored” profiles, the isothermal sphere [25] and the Burkert profile
[26]:

$\rho_{\rm{Iso}}(r)=\frac{\rho_{s}}{1+\left(\frac{r}{r_{s}}\right)^{2}}\;\;\;,\;\;\;\rho_{\rm{Bur}}(r)=\frac{\rho_{s}}{\left(1+\frac{r}{r_{s}}\right)\left(1+\left(\frac{r}{r_{s}}\right)^{2}\right)}\;.$
(3.4)

The main reason for considering different shapes is related to our poor
knowledge about DM physics at small scales, including the possible role of
baryons in affecting the DM spatial profile. The range of possibilities
encompassed by the above functional forms should bracket the uncertainty.

The free parameters of the different profiles are the scale radius $r_{s}$ and
the normalization $\rho_{s}$. We fit these values for each profile using the H
i rotation velocity data and the fact that the velocity $v(r)$ measured up to
a radius $r$ is given by the expression

$v(r)=\sqrt{\frac{GM_{\rm{tot}}(r)}{r}},$ (3.5)

where $M_{\rm{tot}}(r)$ is the total mass contained within a radius $r$, given
by DM plus contributions from the stellar and gas components. We model the
stellar potential $\phi_{\star}(R,z)$ using a Plummer-Kuzmin disk [27] as a
function of the disk radial distance $R$ and vertical height $z$ in
cylindrical coordinates:

$\phi_{\star}(R,z)=GM_{\star}\left[R^{2}+\left(a_{\star}+\sqrt{z^{2}+b_{\star}^{2}}\right)^{2}\right]^{-1/2},$
(3.6)

where $a_{\star}$ and $b_{\star}$ are the radial scale length and vertical
scale height, respectively, for which we take $a_{\star}=1.7$ kpc and
$b_{\star}=0.34$ kpc [28, 29]. The stellar mass $M_{\star}$ is left as a free
parameter in the fit. The contribution to the mass density $\rho_{g}(R,z)$
from the gas follows the expression given in Ref. [29] (with radial scale
length $a_{g}=a_{\star}$ and vertical scale height $b_{g}=b_{\star}$):

$\rho_{g}(r,z)=\frac{M_{g}}{2\pi a_{g}^{2}b_{g}}\,0.5^{2}\,{\rm
sech}\left(\frac{R}{a_{g}}\right){\rm sech}\left(\frac{|z|}{b_{g}}\right).$
(3.7)

Once we have the total mass contribution from the different components to the
rotation velocity at some radius $r$, we proceed to fit the parameters
$r_{s}$, $\rho_{s}$ and $M_{\star}$ using a least squares method through the
python package scipy.optimize. The best-fit parameters for the different DM
density profiles are shown on Table 1. For simplicity, and since the gas
component provides a subdominant contribution to the matter density, we set
$M_{g}=5\times 10^{8}\,M_{\odot}$. Nevertheless, we checked that the results
for $r_{s}$ and $\rho_{s}$ reported on Table 1 are unchanged if $M_{g}$ is
left as a free parameter in the fit.

Previous work has suggested that the LMC virial mass is around $2\times
10^{11}M_{\odot}$, but estimates can have significant uncertainties [3, 20,
18]. On the other hand, the virial mass is mostly related to the DM profile at
larger radii than the one relevant for our analysis (the enclosed mass in our
RoI is $\lesssim 2\times 10^{10}M_{\odot}$), making these uncertainties of
little relevance for our results. We adopt different values for the LMC virial
mass, corresponding to Table 2 from Ref. [20], in order to normalize the
profiles. We find that the rotation velocity within $\sim 5$ kpc from the
center of the LMC, as well as the profile parameters determined by our fit, do
not change considerably with different choices for the mass normalization.
Therefore we adopt a (low) virial mass of $10^{11}M_{\odot}$.

Profile |  $r_{s}$ [kpc] |  $\rho_{s}$ $[M_{\odot}/\rm{kcp}^{3}]$ |  $M_{\star}$ $[M_{\odot}]$
---|---|---|---
NFW | 9.8 | $5.1\times 10^{6}$ | $1.0\times 10^{9}$
Isothermal | 1.1 | $5.7\times 10^{7}$ | $1.9\times 10^{9}$
Burket | 4.7 | $3.1\times 10^{7}$ | $1.9\times 10^{9}$
Hernquist | 21.8 | $2.1\times 10^{6}$ | $1.0\times 10^{9}$
Table 1: Parameters for the LMC DM density profiles and stellar mass derived
from the rotation curve fit, see Section 3.1.

The results are shown in Figure 2, where we report the contributions to the
rotation velocity from DM (dashed lines), stellar and gas components (red dots
and green crosses respectively). The orange points represent the H i rotation
data from Ref. [21] and the solid lines show the contribution from the sum of
all components.

Figure 2: LMC rotation curve. The H i rotation data points are shown as orange
dots [21]. Dashed lines show the contribution from the enclosed DM mass for
the different profiles assumed (see Section 3.1). Red dots and green crosses
denote the stellar and gas contributions respectively. Solid lines correspond
to the contribution of all the enclosed mass within a radius $r$
(DM+stellar+gas).

###  3.2 Magnetic field and diffusion coefficient

The strength of the large-scale coherent component of the LMC magnetic field
is found to be $1\,\mu$G, as determined via Faraday rotation measure of
polarized background sources [6], and with diffuse polarized data [30] (see
also [31]). The turbulent component is expected to be larger than the regular
one, by a factor $>3$, as generically found in galaxies (see, e.g., Ref.
[32]), and confirmed by the scatter observed in the LMC rotation measures
[30]. In Ref. [6], the total LMC magnetic field strength on large scales has
been estimated to be $B=4.3\,\mu$G, and we take this as our reference value.
We focus on a relatively small and central region of LMC, where rotation
measures do not show significant dependence on the radial distance, so we can
assume a uniform strength, in agreement with the model in Ref. [30].
Amplifications on small scales [6] are disregarded. A recent analysis based on
the equipartition assumption and on observations of the LMC synchrotron
emission at 166 MHz [33] suggests a higher value, $B=7.7\pm 1.1\,\mu$G. Since
the magnetic field is (together with the DM properties) the most crucial
ingredient of our analysis, we show how our results change for a range of
total strength $B=2-8\,\mu$G. This range is in agreement with estimates
stemming from the cosmic-ray density derived from $\gamma$-ray data and again
applying the equipartition assumption [30].

Data on supernovae remnants [34] and on large-scale diffuse emission [35]
indicate that the transport of cosmic-rays in the LMC proceeds in a similar
way as in other nearby galaxies, and can be explained as diffusive propagation
in a turbulent regime. In this scenario, the diffusion coefficient can be
estimated as [35]:

$D\simeq 3\,\times 10^{27}\,\left(\frac{d_{L}}{{\rm
kpc}}\right)^{2}\,\left(\frac{10^{15}\,{\rm
s}}{\tau}\right){\rm\frac{cm^{2}}{s}}\;,$ (3.8)

where $d_{L}$ is the diffusion length and $\tau$ is the cooling time. Radio
observations suggest $d_{L}\simeq 1-2$ kpc in the vertical direction (larger
along the disk), consistent with findings in other galaxies where the
confinement region is a few times the disk height. The discussion on radiative
losses below leads to $\tau\simeq 10^{15}$ s, in agreement with the limit of
$\tau>10^{14}$ s estimated in Ref. [34].

Thus observations point towards a value somewhat lower than in the Galaxy. For
clarity, and in the spirit of making conservative assumptions, we assume the
same strength and energy dependence of the diffusion coefficient as at large
scales in the Galaxy, taking the latest determination from Ref. [36] (BIG
model, which provides $2\,\times 10^{28}\,{\rm cm^{2}/s}$ at 4 GeV). Recall
that the larger the diffusion coefficient the smaller the DM signal, since
diffusion can remove electrons and positrons from the RoI before they emit
synchrotron radiation at the frequency of interest.

###  3.3 Gas and interstellar radiation fields

We determine the central value of the gas density from Eq. (3.7) and taking
$M_{g}=5\times 10^{8}\,M_{\odot}$, which is the neutral hydrogen mass observed
by Ref. [21]. Then we assume a flat spatial profile, normalized to the maximal
value, i.e., the central value, which leads to the gas number density
$n_{g}=\rho(0,0)/m_{H}=0.8\,{\rm cm^{-3}}$ (where $m_{H}=0.938$ GeV is the
hydrogen atom mass). This is clearly a conservative approach. Moreover it
simplifies the computation by avoiding uncertainties related to the radial and
vertical scale lengths of the gas distribution and allowing us to keep
assuming spherical symmetry. We checked this description by deriving the gas
density from the hydrogen column density in Fig.4 of Ref. [37] divided by a
disk thickness of 350 pc [37]. The spatial profile does not show significant
variations in our RoI (justifying a flat model) and the average value for the
column density is $6\times 10^{20}\,{\rm cm}^{-2}$, which translates into
$n_{g}\simeq 0.5\,{\rm cm^{-3}}$, confirming the above assumption for $n_{g}$
as an upper limit.

We assume the gas to be composed solely of neutral atomic hydrogen, since
molecular hydrogen and ionised gas are subdominant components [38, 39, 6],
negligible in this analysis.

The ISRF spectrum is taken to have the same shape as that of the Milky-Way
[40]. Observationally, this is found to be a good approximation [41].
Moreover, even though we implement a full computation, the Klein-Nishina
corrections are subdominant (the energy of the emitting electrons is $\lesssim
10$ GeV), so the exact ISRF spectral shape is not critical, and the size of
the inverse Compton losses is essentially set by the integral over energy.

The normalization is chosen such that the integral of the spectrum provides
$U_{\rm{ISRF}}=1\,{\rm eV/cm^{3}}$, consistent with the parameter
$X_{\rm{ISRF}}$ found in Ref. [41]. We note that a somewhat lower density can
be derived from the LMC SED of Ref. [42], see Ref. [43] who found
$U_{\rm{ISRF}}=0.57\,{\rm eV/cm^{3}}$, and using the estimate of Ref. [35]
where $U_{\rm{ISRF}}\simeq 0.3\,{\rm eV/cm^{3}}$. Again, our choice is in the
spirit of adopting a realistic upper limit.

As for the gas density, we conservatively take a spatially flat profile.

Figure 3: Left panel: Model of LMC diffuse emission: disk+DM. Right panel:
WIMP emission profile as a function of the angular distance from the LMC
center, for different WIMP masses, annihilation channels, and spatial profiles
(with the magnetic field strength taken to be $B=4.3\,\mu$G).

##  4 Results

We assume the likelihood associated with the LMC diffuse emission to be
described by a Gaussian:

$\mathcal{L}=e^{-\chi^{2}/2}\;\;\;{\rm
with}\;\;\;\chi^{2}=\frac{1}{N_{pix}^{FWHM}}\sum_{i=1}^{N_{pix}}\left(\frac{S_{th}^{i}-S_{obs}^{i}}{\sigma_{rms}^{i}}\right)^{2}\;,$
(4.1)

where $S_{th}^{i}$ is the theoretical estimate for the flux density in the
pixel $i$, $S_{obs}^{i}$ is the observed flux density and $\sigma_{rms}^{i}$
is the r.m.s. error, both described in Sec. 2. $N_{pix}$ is the total number
of pixels in the RoI (excluding masked pixels) and $N_{pix}^{FWHM}$ is the
number of pixels within the FWHM of the synthesized beam. We only include the
DM signal coming from inside a sphere of radius of 1.3 kpc around the LMC
center (thus disregarding other line-of-sight DM contributions inside the
angular region of $90^{\prime}$). The theoretical estimate is provided by the
WIMP emission, computed from the solution of Eq. (3.1) and following Sec. 4.1
in Ref. [13], plus a disk component and a spatially flat term.

The disk is described through a Gaussian
$S_{disc}^{i}=S_{0}\,\exp{[-\theta_{d,i}^{2}/(2\,\theta_{0}^{2})]}$, where
$\theta_{d,i}$ is the angular distance of the pixel $i$ from the axis of the
disk, and $S_{0}$ and $\theta_{0}$ are free parameters. The position angle of
the LMC disk has been found to be between $122.5^{\circ}$ and $170.5^{\circ}$,
depending on the tracer (see Ref. [44] and references therein). In our
analysis we assume a value determined by fitting the map without including the
DM component. We find $138^{\circ}$, similar to that found recently using Gaia
DR2 data [45].

In Fig. 3 (left), we show the shape of the model given by disk plus DM. We use
arbitrary normalization and fix the FWHM of the Gaussian describing the disk
to $0.45^{\circ}$ (which is the best-fit value found in the fit).

On top of the disk component we add a spatially flat term $S_{flat}$. This is
included in the fit to account for possible offsets or a large-scale
foreground component. The parameters $S_{flat}$, $S_{0}$ and $\theta_{0}$ are
treated as nuisance parameters.

In Fig. 3 (right), we show the WIMP emission as a function of the angular
distance from the center, for different masses, annihilation channels and DM
density profiles. Note that the size of the DM source is below 2 degrees. The
NFW profile is the most concentrated case (together with the Hernquist
profile, which is not shown since it is nearly identical to the NFW at small
distances). The Burkert and isothermal profiles provide more extended
distributions. Note that high masses and leptonic channels imply a less
concentrated profile than low masses and hadronic channels. This can be
understood by noting that at the frequency of the observations (888 MHz) and
for a magnetic field of $4.3\,\mu$G, the synchrotron emission is mostly
provided by $e^{+}/e^{-}$ with energy around a few GeV. High energy electrons
take time to cool down to few GeV and thus can travel long distances,
flattening the central overdensity. Recall that leptonic channels provide
harder $e^{+}e^{-}$ spectra than in the $b\bar{b}$ case.

Bounds on the parameter $\langle\sigma_{a}v\rangle$ are computed at any given
mass $M_{\chi}$ through a profile likelihood technique [46], namely “profiling
out” the nuisance parameters $\vec{\Pi}=(S_{flat},S_{0},\theta_{0})$. We
assume that
$\lambda_{c}(\langle\sigma_{a}v\rangle)=-2\ln[\mathcal{L}(\langle\sigma_{a}v\rangle,\vec{\Pi}^{b.f.})/\mathcal{L}(\langle\sigma_{a}v\rangle^{b.f.},\vec{\Pi}^{b.f.})]$
follows a $\chi^{2}$-distribution with one d.o.f. and with one-sided
probability given by
$P=\int^{\infty}_{\sqrt{\lambda_{c}}}d\chi\,e^{-\chi^{2}/2}/\sqrt{2\,\pi}$,
where $\langle\sigma_{a}v\rangle^{b.f.}$ denotes the best-fit value for the
annihilation rate at that specific WIMP mass. Therefore, the 95% C.L. upper
limit on $\langle\sigma_{a}v\rangle$ at mass $M_{\chi}$ is obtained by
increasing the signal from its best-fit value until $\lambda_{c}=2.71$,
keeping $\vec{\Pi}$ fixed to its best-fit value.

The possible presence of a DM signal is investigated by evaluating the
difference
$\Delta\chi^{2}=\chi^{2}(\vec{\Pi}^{b.f.},\langle\sigma_{a}v\rangle=0)-\chi^{2}(\vec{\Pi}^{b.f.},\langle\sigma_{a}v\rangle_{b.f.})$,
We always find $\Delta\chi^{2}<1$, and thus no evidence for a diffuse
component associated with WIMP-induced emission.

Figure 4: 95% C.L. upper limits on $\langle\sigma_{a}v\rangle$ as a function
of $M_{\chi}$ for the annihilation channels $b\bar{b}$ (blue),
$\mu^{+}\mu^{-}$ (orange), $\tau^{+}\tau^{-}$ (red), and $W^{+}W^{-}$ (green),
with the magnetic field strength taken to be $B=4.3\,\mu$G.

Results are shown in Fig. 4, reporting the upper limits on
$\langle\sigma_{a}v\rangle$. The boundaries of the uncertainty band are
determined by taking the weakest/strongest bound among those obtained using
the four different DM profiles described in Section 3.1. More concentrated
profiles provide more stringent constraints. The NFW and Hernquist cases set
the lower boundary of the band, while Burkert at low masses and Isothermal at
high masses set the upper boundary. The dashed black line is the so-called
thermal cross section, namely the self-annihilation cross section needed in
the early Universe in order to provide the DM mass density observed today
[47]. A common way to see Fig. 4 is to consider “canonical” WIMPs excluded for
masses where the bound is below the thermal value.

The trend of the bound is similar for the $b\bar{b}$ (blue) and $W^{+}W^{-}$
(green) channels, on one hand, and for $\tau^{+}\tau^{-}$ (red) and
$\mu^{+}\mu^{-}$ (orange) channels, on the other. The reason is related to the
injection spectrum of $e^{+}e^{-}$. Let us first remind that the key quantity
is the density of $e^{+}/e^{-}$ induced by the specific DM model at energies
of a few GeV. The injection spectrum of $e^{+}e^{-}$ is harder in the leptonic
cases, where WIMPs with mass of tens of GeV have therefore a significant
injection of $e^{+}e^{-}$ with energy around the peak of the synchrotron
power. This makes the bounds in the $\tau^{+}\tau^{-}$ and $\mu^{+}\mu^{-}$
cases very tight at low masses. Clearly, the picture is the opposite at high
masses where the injection energy is “too high” and the $e^{+}e^{-}$ undergo
energy losses and diffusion before emitting synchrotron radiation. In the
cases of $b\bar{b}$ and $W^{+}W^{-}$, the peak in the injection of
$e^{+}e^{-}$ occurs at around $M_{\chi}/20$. Therefore, they are more
efficiently constrained in the range of masses around hundreds of GeV (so
that, again, the production of $e^{+}/e^{-}$ is peaked around a few GeV).

Since we consider non-relativistic DM, the WIMP mass has to be larger than the
mass of the annihilation products, and this is the reason of the cut in the
$W^{+}W^{-}$ bound.

The overall increase of the constraints with the WIMP mass, occurring for all
the channels, can be understood from Eq. (3.2).

The bottom line of Fig. 4 is that the thermal cross-section is excluded for
masses below (480, 358, 192, 164) GeV for the ($b\bar{b}$, $W^{+}W^{-}$,
$\tau^{+}\tau^{-}$, $\mu^{+}\mu^{-}$) annihilation channel.

Figure 5: Left panel: Impact of the magnetic field strength on the bound on
$\langle\sigma_{a}v\rangle$, in an example taking $M_{\chi}=100$ GeV,
annihilation into $b\bar{b}$, and NFW DM profile. The red dot shows the
reference value adopted in this work. Right panel: 95% C.L. upper limits on
the decay rate $\Gamma$ as a function of $M_{\chi}$ for the decay channels
$b\bar{b}$ (blue), $\mu^{+}\mu^{-}$ (orange), $\tau^{+}\tau^{-}$ (red), and
$W^{+}W^{-}$ (green), with the magnetic field strength taken to be
$B=4.3\,\mu$G.

In Fig. 5 (left), we show how the magnetic field strength affects the bound on
$\langle\sigma_{a}v\rangle$. We consider an example with $M_{\chi}=100$ GeV,
annihilation into $b\bar{b}$, and NFW DM profile. The bound approximately
scales with the inverse of the square of the magnetic field for small
strengths, and flattens as the strength increases. As already stated, in Fig.
4 we adopted $B=4.3\,\mu$G.

Throughout the paper, we have been assuming annihilating DM. In the right
panel of Fig. 5 we show the bounds that can be obtained for decaying DM. The
only difference from the above analysis consists in the replacement of Eq.
(3.2) with

$q^{d}_{e}(E,r)=\Gamma_{d}\,\frac{\rho(r)}{M_{\chi}}\times\frac{dN_{e}^{d}}{dE}(E)\;,$
(4.2)

where $\Gamma_{d}$ is the decay rate, and $dN_{e}^{d}/dE$ is the number of
electrons/positrons emitted per decay in the energy interval $(E,E+dE)$.

The different behaviour of the four decaying channels can be understood in a
very similar way to that already discussed above for the annihilating case.
Note that the uncertainty band of the curves in Fig. 5 is smaller than in the
annihilating cases of Fig. 4. This is because the source function of
annihilating DM depends on $\rho^{2}$, while the decaying scenario scales
linearly with $\rho$, and thus uncertainties in the DM spatial profile affect
the former more than the latter.

##  5 Comparison with previous work

We focus the comparison with previous analyses on work investigating the LMC
and dwarf galaxies, i.e., satellites of the Milky Way, since they share a
similar analysis as that conducted here. We do not attempt to make comparisons
with completely different targets (e.g., the Galactic Center) or channels
(e.g., antiprotons). For other analyses using radio data to constrain WIMP
annihilations in extragalactic objects, see, e.g., Refs. [48, 49, 50] (M31),
[51, 52] (M33), [53, 54] (clusters), [55, 56] (cosmological emission).

###  5.1 Comparison with radio analyses

An analysis similar to the one presented here was conducted in Ref. [8]. They
employed ATCA+Parkes data and obtained the black curve in Fig. 6 (left). The
great improvement in the constraining power of our analysis is not due to the
model, for which we adopted a more conservative description than Ref. [8], but
to the different statistical approach and to the more limited residuals and
higher rms sensitivity in the ASKAP image compared to the ATCA+Parkes image.
Concerning the statistical analysis, Ref. [8] derived the bound from
individual lines of sight, while we developed a morphological analysis. The
latter allows us to ascribe part of the LMC emission to a disk component and
combines $\sim 10^{4}$ lines of sight. This is important since the
constraining power scales roughly as the square root of this number.

There have been a few attempts to detect WIMP-induced radio signals in dwarf
spheroidal galaxies of the Local Group. We expect the signal from LMC to be
stronger than from dSphs since the magnetic field strength is higher (it is
actually unknown in dSph, but typically assumed to be around 1 $\mu$G [13]),
the J-factor is higher than (or at the level of) that in the most promising
dSphs, and the LMC is bigger (which means diffusion effects are less relevant
in depleting the signal than in dSphs). In Fig. 6, we include bounds derived
from the observations of different samples of dSphs with the ATCA from Ref.
[57] (taking their model with $B=1\,\mu{\rm G}\;,\;D_{0}=3\,\times
10^{28}\,{\rm cm^{2}/s}$, red solid line) and Ref. [58] (AVE model, red dashed
line), GMRT [59] ($B=2\,\mu{\rm G}\;,\;D_{0}=3\,\times 10^{28}\,{\rm
cm^{2}/s}$, violet line), LOFAR [60] ($B=1\,\mu{\rm G}\;,\;D_{0}=10^{27}\,{\rm
cm^{2}/s}$, orange line), MWA+GMRT [61] ($B=2\,\mu{\rm G}\;,\;D_{0}=3\,\times
10^{28}\,{\rm cm^{2}/s}$, magenta line). Other relevant campaigns have been
conducted with the GBT [62, 63, 64] and MWA [65]. Their bounds are not in a
suitable form to be shown in Fig. 6, but correspond to about
$\langle\sigma_{a}v\rangle\lesssim 10^{-24}{\rm cm^{3}/s}$ for $M_{\chi}=100$
GeV and the $b\bar{b}$ channel.

###  5.2 Comparison with $\gamma$-ray analyses

In Fig. 6 (right), we compare the results of this work with the bounds
obtained by the Fermi-LAT Collaboration from the analysis of the LMC [16] and
dSphs [66]. For completeness we also show the expected LMC bounds from the
Cherenkov Telescope Array [67], since they can be more constraining than those
from Fermi-LAT at high WIMP masses.

One can immediately see that the LMC radio constraints are much stronger than
$\gamma$-ray ones. This should not come as a surprise. Indeed, generically, in
WIMP models, the luminosity associated with the induced $\gamma$-rays is
comparable to or smaller than that of the injected electrons and positrons.
For hadronic channels, the $\gamma$-ray emission mainly proceeds through the
production and decay of neutral pions, while electron/positron injection is
related to charged pions, and so the two mechanisms are tightly related. For
leptonic channels, GeV electrons and positrons have a larger yield than the
final state radiation of $\gamma$-ray photons. Therefore, if the cooling
time/diffusion length is small enough, so that the energy of the
electron/positron is radiated within the source, and the synchrotron loss is
the dominant (or, at least, among the most relevant) radiation mechanism in
the astrophysical object under investigation, the luminosity produced as
synchrotron radiation is comparable to or higher than that from $\gamma$-rays
[2]. Since radio telescopes are much more sensitive than $\gamma$-ray
telescopes for all sources having related mechanisms of emission in the two
bands (see, e.g., the level of detail in the ASKAP LMC image compared to the
$\gamma$-ray image of the LMC [68]), radio bounds on WIMPs are significantly
stronger, when above conditions are satisfied, and in particular for objects
with low astrophysical diffuse radio background, such as the LMC.

The picture is different for dSphs, since there the diffusion length is
typically larger than the galaxy itself and the magnetic field is thought to
be rather small (and so too the synchrotron radiation), which implies a less
favourable ratio between radio and $\gamma$ bounds, even though still
comparable (see red solid line in the left panel versus orange line in the
right panel).

Fig. 6 shows that the bound derived in this work is the most stringent bound
on WIMPs coming from indirect searches in extragalactic objects.

Figure 6: Left panel: Comparison with other radio searches, see text for
details. “DW” labels analyses of dwarf spheroidal galaxies. Right panel:
Comparison with $\gamma$-ray Fermi-LAT searches on dwarf spheroidals [66]
(orange) and on the LMC [16], and with the expected sensitivity of CTA for LMC
[67].

##  6 Conclusions

We analysed the ASKAP radio image at 888 MHz of the LMC, in order to search
for synchrotron emission induced by WIMP DM annihilations.

The large J-factor of the LMC implies it is one of the best targets for DM
indirect searches. The presence of a magnetic field with strength $>1\,\mu$G
makes radio searches in the LMC particularly suited for this purpose.

We detect no evidence for emission arising from WIMP annihilations and derive
stringent bounds. Annihilations into leptonic channels provide the most
constraining bounds at low masses with the thermal cross-section excluded for
masses below 192 GeV ($\tau^{+}\tau^{-}$) and 164 GeV ($\mu^{+}\mu^{-}$).
Annihilations into quarks and gauge bosons are the most constraining cases at
intermediate and high masses with the thermal cross-section excluded below 480
GeV ($b\bar{b}$) and 358 GeV ($W^{+}W^{-}$).

The comparison with the state-of-the-art in Fig. 6 shows that the bounds on
WIMPs derived in this work are extremely competitive.

We adopted a simple and conservative approach, limiting the analysis to a
relatively small region, where simplified assumptions and well-motivated data-
driven descriptions can be taken for the astrophysical ingredients entering
the model prediction. For the two most relevant quantities, the DM spatial
profile and the magnetic field, we defined reference models according to
observations [21, 6]. For the other components (which are important for the
computation, but to a somewhat lesser extent), such as the spatial diffusion
coefficient, the interstellar radiation fields, and the gas density, we
consider their upper or lower limits (all in the direction of minimising the
DM signal).

Our results imply there is little hope to detect a signal from low mass
thermal WIMPs in laboratories (i.e., in direct and collider searches), whilst
very massive thermal WIMPs remain a viable DM candidate. They can be probed by
different techniques, including observations from future radio telescopes,
such as the SKA, in particular going to higher frequencies. On a shorter
timescale, the addition of short spacing data coming from forthcoming
observations with the Parkes telescope will provide a complete picture of the
LMC at different scales. With such image at hand, a more refined 3D modeling
of the synchrotron emission from the entire LMC can be attempted, with the
possibility of further tightening the bounds derived in this analysis.

## Acknowledgement

The Australian SKA Pathfinder is part of the Australia Telescope National
Facility which is managed by CSIRO. Operation of ASKAP is funded by the
Australian Government with support from the National Collaborative Research
Infrastructure Strategy. ASKAP uses the resources of the Pawsey Supercomputing
Centre. Establishment of ASKAP, the Murchison Radio-astronomy Observatory and
the Pawsey Supercomputing Centre are initiatives of the Australian Government,
with support from the Government of Western Australia and the Science and
Industry Endowment Fund. We acknowledge the Wajarri Yamatji people as the
traditional owners of the Observatory site.

M.R. would like to thank G. Bernardi and M. Taoso for long-standing
discussions on the topic of this work. M.R. acknowledges support by
“Deciphering the high-energy sky via cross correlation” funded by the
agreement ASI-INAF n. 2017-14-H.0 and by the “Department of Excellence” grant
awarded by the Italian Ministry of Education, University and Research (MIUR).
M.R. and J.R. acknowledge funding from the PRIN research grant “From Darklight
to Dark Matter: understanding the galaxy/matter connection to measure the
Universe” No. 20179P3PKJ funded by MIUR and from the research grant TAsP
(Theoretical Astroparticle Physics) funded by Istituto Nazionale di Fisica
Nucleare (INFN). M. B. acknowledges funding by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s
Excellence Strategy – EXC 2121 ‘Quantum Universe’ – 390833306.

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##  Appendix A Consistency checks

In this Appendix, we describe a few consistency checks we performed.

First, a key and not obvious (for an interferometric image) point is the
actual sensitivity of the image to large scale diffuse emissions. In order to
understand how the sensitivity scales as a function of the size of the source,
we taper the visibilities by different angular scales, generate an image with
robust weighting, and then measure the standard deviation in the image. For
technical reasons and since here we are mainly interested in understanding the
trend but not the absolute value, we performed the analysis on Stokes V and
considering one of the LMC pointings (all pointings were taken at similar
directions and times). The rms sensitivity normalized to one at 2 arcmin is
plotted in Fig. 7 (red line) as a function of the tapering size.

In the same figure, the blue line reports the total flux of a source which is
excluded at 95% C.L. by the analysis described in the main text, as a function
of the angular scale of the source. Again values are normalized to one for a
source with FWHM$=2$ arcmin. One can quickly check that, in the case of
uniform rms, no masking and no confusion, Eq. (4.1) would imply a linear
scaling. The blue curve is derived by considering Gaussian sources of
different widths (essentially replacing the DM component with a Gaussian
emission and then repeating all the steps described in Sects. 3 and 4). The
actual behaviour is close to linear scaling.

The bottom-line of Fig. 7 is that the “theoretical” degradation of the
sensitivity as the angular scale of the sources increases, as assumed by the
analysis described in the paper, is higher if compared to the results obtained
through the tapering test. This ensures our bounds are conservative.

Figure 7: The red line shows the rms sensitivity of the LMC image as a
function of the tapering size. The blue curve shows the total flux excluded by
the analysis described in the main text as a function of the size of the
source. Both curves are normalized to one at two arcmin.

To test against possible systematics associated to the selected region of the
image, we re-do the same analysis outlined in the main text, but now centering
the DM distribution on different positions across the map. Since we are
dealing with a non-detection, they should all provide similar bounds, because
the RMS sensitivity is approximately uniform across the map. We compare five
different positions, as listed in Fig. 8 (left). Concerning the DM model we
take the same description as in Section 3, but centered in the new positions.
This is clearly not realistic, but functional to our test. We find that
positions that are far from the LMC disk (i.e., $C$ and $D$ in Fig. 8) provide
slightly more constraining bounds, with the component $S_{disc}$ compatible
with zero. Positions located on the LMC disk (i.e., $B$ and $E$ in Fig. 8)
lead to bounds similar to the ones described in the main text (case $A$), with
the fit requiring a disk component different from zero. Fig. 8 (left) reports
the bound in the case of the NFW profile and annihilation into $b\bar{b}$.

Figure 8: Left panel: Comparison of the bounds obtained by centering the DM
distribution on different positions across the map (labeled as A, B, C, D and
E to easy their reference in the text). Right panel: Comparison of the bounds
obtained in the reference analysis of this work (solid) with the bounds one
would obtain considering the maximal ideal sensitivity of the EMU image
(dashed) and analysing the ATCA+Parkes image of Ref. [69] (dotted).

In Fig. 8 (right) we compare our results with the maximal sensitivity that can
be achieved with the image we have at hand. The latter is derived by keeping
the original resolution (FWHM=13”) and evaluating
$\chi^{2}=\sum_{i=1}^{N_{pix}}\left(\frac{S_{DM}^{i}}{\sigma_{rms}^{i}}\right)^{2}/N_{pix}^{FWHM}$,
which can be seen as setting to zero all pixels in the map (after RMS
determination). We show the result for the Burkert profile since it is the
most extended case, so where the number of pixels relevant for the $\chi^{2}$
determination is largest, which implies the sensitivity difference is largest.
As expected the bound derived with such ideal sensitivity is more constraining
than for our reference analysis, but by a rather limited factor (between 2 and
3).

In the same Figure, we derive WIMP bounds from the LMC map at 1.4 GHz
presented in Ref. [69]. Such map contains all scales above $40^{\prime\prime}$
being a combination of ATCA and (single-dish) Parkes data, contrary to the
ASKAP image having only interferometric data. This means that the very large-
scale emission would need a more careful treatment than the simple model
introduced in Section 3. For this reason, we perform the comparison in the
“ideal-sensitivity” case. The analysis of ATCA+Parkes data is performed in the
same way as for the ASKAP map. From the ratio of the RMS sensitivity of the
two maps (300 versus 58 $\mu$Jy/beam), and considering the different frequency
(1.4 versus 0.888 GHz) and beam (40” versus 13”), we expect the ATCA+Parkes
bound to be a factor around 5 weaker than the ASKAP one. Results are along the
line of expectations, see dotted versus dashed lines, providing a consistency
check.