figure table

# MR-Transformer: Vision Transformer for Total Knee Replacement Prediction
Using Magnetic Resonance Imaging

Chaojie Zhang  Department of Radiology, New York University Langone Health,
New York, NY, 10016, USA  Shengjia Chen  Department of Radiology, New York
University Langone Health, New York, NY, 10016, USA  Ozkan Cigdem  Department
of Radiology, New York University Langone Health, New York, NY, 10016, USA
Haresh Rengaraj Rajamohan  Center for Data Science, New York University, New
York, NY, 10011, USA  Kyunghyun Cho  Center for Data Science, New York
University, New York, NY, 10011, USA  Richard Kijowski  Department of
Radiology, New York University Langone Health, New York, NY, 10016, USA  Cem
M. Deniz  Department of Radiology, New York University Langone Health, New
York, NY, 10016, USA

### Summary

A transformer-based deep learning model, MR-Transformer, was developed to
predict total knee replacement using magnetic resonance imaging. The model
exhibited state-of-the-art performance on the Osteoarthritis Initiative and
Multicenter Osteoarthritis Study databases.

### Key Points

  * •

MR-Transformer incorporates the ImageNet pre-training and captures three-
dimensional spatial correlation to predict total knee replacement using MRI.

  * •

The model achieved areas under the receiver operating characteristic curve
(AUC) of 0.89 for coronal intermediate-weighted turbo spin-echo and 0.91 for
sagittal intermediate-weighted turbo spin-echo with fat suppression from the
Osteoarthritis Initiative database, as well as 0.82 for coronal short-tau
inversion recovery and 0.82 for sagittal proton density fat-saturated from the
Multicenter Osteoarthritis Study database.

  * •

Using the coronal short-tau inversion recovery MRI knee scans, MR-Transformer
outperformed other deep learning models in AUC (MR-Transformer: 0.82, TSE:
0.76 (P $<$ .001), 3DMeT: 0.74 (P = .005), and MRNet: 0.78 (P = .010)).

### List of Abbreviations

2D = two-dimensional, 3D = three-dimensional, OAI = Osteoarthritis Initiative,
MOST = Multicenter Osteoarthritis Study, TKR = total knee replacement, AUC =
area under receiver operating characteristic curve, COR IW TSE = coronal
intermediate-weighted turbo spin-echo, SAG IW TSE FS = sagittal intermediated-
weighted turbo spin-echo with fat suppression, COR STIR = coronal short-tau
inversion recovery, SAG PD FAT SAT = sagittal proton density fat-saturated

### Abstract

Purpose: To develop a transformer-based deep learning model that incorporates
the ImageNet pre-training and captures three-dimensional (3D) spatial
correlation to predict total knee replacement (TKR) using MRI.

Materials and Methods: A transformer-based deep learning model, MR-
Transformer, was developed for TKR prediction. The model adapted from the
ImageNet pre-trained vision transformer DeiT-Ti, directly utilizes 3D MR
images as input. A total of 353 case-control matched pairs of coronal
intermediate-weighted turbo spin-echo (COR IW TSE) and sagittal intermediated-
weighted turbo spin-echo with fat suppression (SAG IW TSE FS) knee MR scans
from the Osteoarthritis Initiative (OAI) and 270 case-control pairs of coronal
short-tau inversion recovery (COR STIR) and sagittal proton density fat-
saturated (SAG PD FAT SAT) knee MRI scans from the Multicenter Osteoarthritis
Study (MOST) databases were utilized in the study. The performance of the
proposed model was compared to existing state-of-the-art deep learning models
for knee injury diagnosis using MRI, with the area under the receiver
operating characteristic curve (AUC) as the evaluation metric.

Results: The proposed MR-Transformer model consistently achieved higher AUC
performance compared to TSE, 3DMeT, and MRNet models for both coronal and
sagittal knee MR scans from the OAI and MOST databases. Specifically, for COR
STIR, MR-Transformer achieved a significantly higher AUC (0.82) compared to
other DL models: TSE (0.76, P $<$ .001), 3DMeT (0.74, P = .005), and MRNet
(0.78, P = .010). Similarly, for COR IW TSE, SAG IW TSE FS, and SAG PD FAT
SAT, MR-Transformer achieved AUCs of 0.89, 0.91, and 0.82, respectively. These
were significantly higher than those of TSE (0.86, P = .009; 0.82, P $<$ .001;
0.75, P = .006) and 3DMeT (0.82, P = .004; 0.78, P $<$ .001; 0.63, P $<$
.001), respectively. While the proposed model achieved either similar or
slightly higher AUCs than MRNet (0.89, 0.90, and 0.81 for COR IW TSE, SAG IW
TSE FS, and SAG PD FAT SAT, respectively), the differences were not
statistically significant (P = .44, .070, and .20, respectively).

Conclusion: MR-Transformer exhibited state-of-the-art performance on TKR
prediction using MRI compared to currently available deep learning models.

##  1 Introduction

Knee osteoarthritis, the most prevalent type of arthritis, is a degenerative
joint disease that significantly diminishes the quality of life for millions
worldwide, resulting in pain, limited mobility, and disability [1, 2]. While
knee osteoarthritis has no cure, total knee replacement (TKR) offers a viable
treatment option for advanced stages of the disease [3]. Early identification
of patients at risk of TKR progression is crucial to facilitate the
development and implementation of potential disease-modifying therapies [3].
Knee osteoarthritis is also a structural disease that results in structural
changes within the joint, the diagnosis of it requires comprehensive
inspection of imaging studies like MRI, by an experienced radiologist.
Recently, deep learning methods have shown the potential to assist in TKR
prediction [4, 5, 6].

Several challenges arise when employing deep learning methods for predicting
TKR from MRI data: the three-dimensional (3D) nature of the data, the limited
size of medical datasets, and the inclusion of global structural information
pertinent to knee osteoarthritis. Current studies implemented 3D convolutional
neural networks to capture 3D spatial information on the MR images to predict
TKR[4, 5]. However, deep learning as a data-driven method, often requires a
large amount of data to achieve optimal performance. Deep learning models
without any pre-training usually achieve suboptimal performance on small
medical datasets[7]. To address this problem, MRNet used the ImageNet pre-
trained two-dimensional (2D) convolutional neural network to encode each MR
slice and aggregated all encoded features to diagnose knee injuries from knee
MRI scans[8]. This approach leverages large-scale pre-training but fails to
capture the 3D spatial correlation of MR images.

In this study, we proposed MR-Transformer, a novel deep learning model adapted
from the ImageNet pre-trained vision transformer DeiT-Ti[9], for TKR
prediction using MRI. The model inherits the ImageNet[10] pre-trained weights
and captures 3D spatial correlation of MR images. In addition, the transformer
architecture modeling long-range dependencies enables the model to better
capture global structural information from the MR images. We evaluated our
proposed model on TKR prediction using MR images from the Osteoarthritis
Initiative (OAI)[11] and Multicenter Osteoarthritis Study (MOST)[12]
databases. MR-Transformer exhibited state-of-the-art performance on TKR
prediction using MRI.

##  2 Materials and Methods

###  2.1 Data

In this study, we used MR images from two publicly available databases
established as prospective cohort studies: OAI[11] and MOST[12]. The OAI
database contains MRI examinations of different tissue contrasts from 4796
subjects with or at risk for knee osteoarthritis evaluated at baseline and 12,
24, 36, 48, 60, 72, 84, and 108-month follow-up. The MOST database contains
MRI examinations from 3026 subjects with or at risk for knee osteoarthritis
evaluated at baseline and 15, 30, 60, and 84-month follow-up. The OAI and MOST
databases were approved by the Internal Review Boards at University of
California at San Francisco, Boston University Medical Center, and each
individual clinical recruitment site and was performed in compliance with the
Declaration of Helsinki. All subjects signed written informed consent. In both
databases, balanced case–control cohorts were selected by matching case
subjects and control subjects using baseline demographic variables associated
with knee osteoarthritis progression including age, sex, ethnicity, and body
mass index. Case subjects were identified as individuals who underwent a TKR
after the baseline enrollment date, while control subjects were identified as
individuals who did not.

In the OAI database, a total of 353 case–control pairs were identified and
separated into the training group of 302 pairs and the test group of 51 pairs.
The deep learning models were trained on coronal intermediate-weighted turbo
spin-echo (COR IW TSE) and sagittal intermediated-weighted turbo spin-echo
with fat suppression (SAG IW TSE FS) MRI knee scans of the training group
using six-fold cross-validation.

In the MOST database, a total of 270 case–control pairs were identified and
separated into the training group of 231 pairs and the test group of 39 pairs.
The deep learning models were trained on coronal short-tau inversion recovery
(COR STIR) and sagittal proton density fat-saturated (SAG PD FAT SAT) MRI knee
scans of the training group using six-fold cross-validation.

###  2.2 Model Development

The proposed model, MR-Transformer, was adapted from the ImageNet pre-trained
tiny vision transformer DeiT-Ti[9]. The main idea of the adaptation is to
modify the 2D vision transformer to accommodate 3D input while retaining the
pre-trained model weights.

Different from traditional convolutional neural networks, vision transformers
separate the images into small 2D patches and encode the vectorized patches
using self-attention mechanisms. This patch-based processing enables vision
transformers to be flexible in handling images with different dimensions,
making the adaptation from 2D inputs to 3D inputs possible. In our adaptation,
we split the 3D MR images into 2D patches, retain the pre-trained model
weights, and modify the position embeddings of the model.

The model architecture of MR-Transformer is provided in Figure 1. In the
pipeline of MR-Transformer, the single grayscale channel of the MR image is
replicated to generate a three-color-channel input matrix. The 3D input matrix
is then separated into 16$\times$16 patches, with each patch being flattened
into a 768-dimensional vector. Then, the linear projection layer inherited
from DeiT-Ti project the flattened patch vectors into 192-dimensional patch
embeddings. The adapted learnable position embeddings are added to the
corresponding patch embeddings to retain the positional information of each 2D
patch. The patch embeddings, appended with an inherited learnable ”class”
embedding, are processed by the pre-trained transformer encoder from DeiT-Ti.
Then the final linear layer utilizes the encoded ”class” embedding to generate
the TKR prediction outcome.

MR-Transformer was designed to capture 3D spatial correlation of MR images,
meanwhile leveraging the advantages of 2D large-scale pre-training. Moreover,
the transformer architecture of MR-Transformer enabled the modeling of long-
range dependencies, facilitating the capture of global structural information
from the MR images.

Figure 1: Model architecture of MR-Transformer. The model inherited the model
weights of the ImageNet pre-trained vision transformer and processed knee MR
images by separating them into small 2D patches.

###  2.3 Position Embeddings

The key components of MR-Transformer can be easily inherited from the ImageNet
pre-trained DeiT-Ti except for the position embeddings. Position embeddings
are learnable vectors with the same dimension as the patch embeddings. They
are used to retain the positional information of different patches. To adapt
the 2D pre-trained position embeddings to the 3D MR images, we replicated the
2D pre-trained position embeddings for each MR slice. Then, 2D interpolation
was employed to the position embeddings when the MR slice had a larger size
than the pre-training images. Note that position embeddings are learnable
vectors that can be trained to learn the 3D spatial position information of MR
images.

###  2.4 Comparison with Other Models

The proposed MR-Transfomer model was compared to three different deep learning
models designed for knee injury diagnosis from MRI. MRNet is a convolutional
neural network-based model developed for detecting general abnormalities and
specific diagnoses on knee MRI exams, it employs the ImageNet pre-trained
AlexNet[13] to encode each MR slice and uses max pooling to aggregate the
encoded features[8]. TSE is a 3D convolutional neural network model developed
for TKR prediction, it captures 3D spatial correlation from knee MR images[4].
3DMeT is a 3D transformer-based model with a convolutional neural network
teacher mechanism, it was developed for knee cartilage defect assessment from
knee MRI[14].

###  2.5 Statistical Analysis

Receiver operator characteristic analysis for area under the curve (AUC) and
the calculation of 95% confidence interval were employed for individual model
evaluation. Sensitivity and specificity assessments were conducted at high
specificity (80%) and sensitivity (80%) thresholds, respectively. Statistical
analyses were implemented utilizing the R Project version 4.2.1 for
Statistical Computing Software[15]. The one-sided paired t-tests were used to
evaluate differences in performance between the different models. Statistical
significance was defined as a P value less than 0.05.

##  3 Results

###  3.1 Participant Characteristics

A total of 353 case–control pairs were derived from the 4796 subjects in the
OAI database, while 270 case–control pairs were derived from the 3026 subjects
in the MOST database. Subjects were excluded if they had TKR at baseline,
received partial knee replacement over the course of follow-up, were missing
baseline or 108-month follow-up information, or did not match with a case or
control subject. The flowcharts of selecting case-control pairs from the OAI
and MOST databases are provided in Figure 2. In the 353 case–control pairs,
there were 138 males aged from 45 to 78 with a mean$\pm$standard deviation of
64$\pm$8 and 215 females aged from 45 to 79 with a mean$\pm$standard deviation
of 63$\pm$8\. In 270 case–control pairs, there were 67 males aged from 50 to
78 with a mean$\pm$standard deviation of 65$\pm$7 and 203 females aged from 50
to 79 with a mean$\pm$standard deviation of 65$\pm$7\. The baseline
demographics of study cohorts are provided in Table 1.

Table 1: Summary Statistics of Demographic Variables for Matched Case-Control
Cohorts

Dataset | Parameter | Men | P Value | Women | P Value
---|---|---|---|---|---
Patients | Control Patients | Patients | Control Patients
OAI | No. of patients | 138 | 138 |  | 215 | 215 |
Age range (y) | 45-78 | 45-78 |  | 45-79 | 45-79 |
Mean age (y) |  64$\pm$8 |  64$\pm$8 | >0.99 |  63$\pm$8 |  63$\pm$8 | >0.99
Mean height (m) |  1.76$\pm$0.06 |  1.76$\pm$0.06 | 0.78 |  1.62$\pm$0.06 |  1.62$\pm$0.06 | 0.56
Mean weight (kg) |  93.4$\pm$14.1 |  92.0$\pm$12.7 | 0.38 |  78.5$\pm$14.8 |  77.0$\pm$13.6 | 0.28
Mean BMI (kg/m2) |  29.9$\pm$3.8 |  29.4$\pm$3.4 | 0.31 |  29.9$\pm$5.3 |  29.5$\pm$4.7 | 0.41
Ethnicity* | White | 126 | 126 |  | 177 | 177 |
African American | 10 | 10 |  | 33 | 33 |
Asian | 0 | 0 |  | 2 | 2 |
Other nonwhite | 2 | 2 |  | 3 | 3 |
MOST | No. of patients | 67 | 67 |  | 203 | 203 |
Age range (y) | 50-78 | 50-78 |  | 50-79 | 50-79 |
Mean age (y) |  65$\pm$7 |  65$\pm$7 | 0.99 |  65$\pm$7 |  65$\pm$7 | 0.99
Mean height (m) |  1.79$\pm$0.06 |  1.78$\pm$0.06 | 0.46 |  1.62$\pm$0.06 |  1.63$\pm$0.06 | 0.41
Mean weight (kg) |  94.8$\pm$13.0 |  96.7$\pm$18.2 | 0.61 |  81.6$\pm$13.6 |  81.6$\pm$12.6 | 0.99
Mean BMI (kg/m2) |  30.1$\pm$4.2 |  30.0$\pm$4.1 | 0.98 |  31.1$\pm$4.9 |  30.9$\pm$4.7 | 0.71
Ethnicity* | White | 67 | 67 |  | 188 | 188 |
African American | 0 | 0 |  | 15 | 15 |
Asian | 0 | 0 |  | 0 | 0 |
Other nonwhite | 0 | 0 |  | 0 | 0 |

  * •

Note: Mean data are presented as mean$\pm$standard deviation. The P-value
compares the differences in mean between case and control groups for each
variable. BMI = Body Mass Index, MOST= Multi-Center Osteoarthritis Study, OAI=
Osteoarthritis Initiative. *Number of patients are shown.

(a)

(b)

Figure 2: Selection of the study cohorts. a) 353 case–control pairs of
subjects in the OAI database, b) 270 case–control pairs of subjects in the
MOST database.

###  3.2 Comparison of Models

The comparison of models for TKR prediction is presented in Table 2. When
using MR images of different contrasts from the OAI and MOST databases, MR-
Transformer attained significantly higher AUCs (COR IW TSE: 0.89 and SAG IW
TSE: 0.91 and COR STIR: 0.82 and SAG PD FAT SAT: 0.82) than TSE (COR IW TSE:
0.86, P = .009 and SAG IW TSE: 0.82, P $<$ .001 and COR STIR: 0.76, P $<$ .001
and SAG PD FAT SAT: 0.75, P = .006) and 3DMeT (COR IW TSE: 0.82, P = .004 and
SAG IW TSE: 0.78, P $<$ .001 and COR STIR: 0.74, P = .005 and SAG PD FAT SAT:
0.63, P $<$ .001). Similarly, using COR STIR MR images from the MOST database,
MR-Transformer attained significantly higher AUC than MRNet (0.78, P = .010).
However, the utilization of MR images with other tissue contrasts did not
yield significant differences in AUCs between MR-Transformer and MRNet (COR IW
TSE: 0.89, P = .44 and SAG IW TSE: 0.90, P = .070 and SAG PD FAT SAT: 0.81, P
= .20).

Using COR IW TSE (OAI) MR scans, the MR-Transformer achieved a significantly
higher sensitivity (0.84) compared to TSE (0.75, P = .013) and 3DMeT (0.68, P
= .014). While the sensitivity of the MR-Transformer was also higher than
MRNet (0.80), this difference was not statistically significant (P = .10).
Similarly, the MR-Transformer’s specificity (0.80) was significantly higher
than TSE (0.74, P = .012) and 3DMeT (0.65, P = .010), yet not statistically
different from MRNet (0.78, P = .25). For SAG IW TSE (OAI), the MR-Transformer
achieved a sensitivity of 0.83, which was significantly higher than TSE (0.68,
P $<$ .001) and 3DMeT (0.64, P $<$ .001). Although the sensitivity of MR-
Transformer was lower than MRNet (0.84), the difference was not statistically
significant (P = .74). Similarly, the MR-Transformer’s specificity (0.84) was
significantly higher than TSE (0.69, P = .001) and 3DMeT (0.55, P $<$ .001),
yet not statistically different from MRNet (0.83, P = .33).

Using COR STIR (MOST) MR images, the MR-Transformer achieved a significantly
higher sensitivity (0.62) compared to 3DMeT (0.53, P = .037). Although the
sensitivity of the MR-Transformer was also higher than TSE (0.59) and MRNet
(0.57), these differences were not statistically significant (P = .17 and P =
.075, respectively). Conversely, the specificity of MR-transformer (0.66) was
significantly higher than TSE (0.47, P = .001), 3DMeT (0.49, P $<$ .001), and
MRNet (0.59, P = .032). For SAG PD FAT SAT (MOST), the MR-Transformer achieved
a sensitivity of 0.64, which was significantly higher than TSE (0.52, P =
.030) and 3DMeT (0.38, P = .002). Although the sensitivity of MR-Transformer
was also higher than MRNet (0.62), the difference was not statistically
significant (P = .16). Similarly, the MR-Transformer’s specificity (0.58) was
significantly higher than 3DMeT (0.30, P $<$ .001). Even though the
sensitivity of MR-Transformer was higher than 3DMeT (0.49) and lower than
MRNet (0.60), these differences were not statistically significant (P = .053
and P = .68, respectively).

Table 2: Comparison of Deep Learning Models for Total Knee Replacement
Prediction.

| Model | AUC | P Value |  | Sensitivity
---
(at 80% Specificity)
P Value |  | Specificity
---
(at 80% Sensitivity)
P Value
COR IW TSE | TSE | 0.86 ± 0.02 | .009 | 0.75 ± 0.07 | .013 | 0.74 ± 0.04 | .012
3DMeT | 0.82 ± 0.03 | .004 | 0.68 ± 0.07 | .014 | 0.65 ± 0.08 | .010
MRNet | 0.89 ± 0.01 | .44 | 0.80 ± 0.01 | .10 | 0.78 ± 0.03 | .25
MR-Transformer | 0.89 ± 0.01 | $*$ | 0.84 ± 0.04 | $*$ | 0.80 ± 0.03 | $*$
SAG IW TSE | TSE | 0.82 ± 0.01 | <.001 | 0.68 ± 0.03 | <.001 | 0.69 ± 0.02 | .001
3DMeT | 0.78 ± 0.02 | <.001 | 0.64 ± 0.03 | <.001 | 0.55 ± 0.08 | <.001
MRNet | 0.90 ± 0.00 | .070 | 0.84 ± 0.02 | .74 | 0.83 ± 0.02 | .33
MR-Transformer | 0.91 ± 0.01 | $*$ | 0.83 ± 0.02 | $*$ | 0.84 ± 0.03 | $*$
COR STIR | TSE | 0.76 ± 0.01 | <.001 | 0.59 ± 0.04 | .17 | 0.47 ± 0.06 | .001
3DMeT | 0.74 ± 0.03 | .005 | 0.53 ± 0.09 | .037 | 0.49 ± 0.06 | <.001
MRNet | 0.78 ± 0.01 | .010 | 0.57 ± 0.07 | .075 | 0.59 ± 0.03 | .032
MR-Transformer | 0.82 ± 0.01 | $*$ | 0.62 ± 0.04 | $*$ | 0.66 ± 0.03 | $*$
SAG PD FAT SAT | TSE | 0.75 ± 0.02 | .006 | 0.52 ± 0.08 | .030 | 0.49 ± 0.05 | .053
3DMeT | 0.63 ± 0.03 | <.001 | 0.38 ± 0.07 | .002 | 0.30 ± 0.05 | <.001
MRNet | 0.81 ± 0.01 | .20 | 0.62 ± 0.03 | .16 | 0.60 ± 0.02 | .68
MR-Transformer | 0.82 ± 0.02 | $*$ | 0.64 ± 0.04 | $*$ | 0.58 ± 0.07 | $*$

  * •

Note: The MR-Transformer model was compared against three baseline deep
learning models based on AUC, sensitivity at 80% specificity, and specificity
at 80% sensitivity. The metrics (AUC, sensitivity, specificity) are presented
as mean ± 95% confidence interval, calculated from six cross-validation folds.
AUC = area under receiver operating characteristic curve, COR IW TSE = coronal
intermediate-weighted turbo spin-echo, SAG IW TSE FS = sagittal intermediated-
weighted turbo spin-echo with fat suppression, COR STIR = coronal short-tau
inversion recovery, SAG PD FAT SAT = sagittal proton density fat-saturated,
$*$: the reference model for one-sided paired t-test.

###  3.3 Model Interpretation

Attention maps generated using Attention Rollout [16] can highlight crucial
regions within MR images. Figure 3 presents an MR image from a subject who
underwent a TKR within nine years. The highlighted area in the joint region
indicates informative regions from the MR image relevant to TKR prediction.

Figure 3: Example attention map for a knee MR image in the test set from a
subject who underwent a TKR within nine years. Highlighted regions indicate
areas where the MR-Transformer model focuses to make decisions regarding the
probability of TKR within nine years.

##  4 Discussion

In this study, we introduced MR-Transformer, a transformer-based deep learning
model designed for predicting TKR using sagittal and coronal MRI scans from
the OAI and MOST databases. The proposed model exhibits several advantages,
including leveraging large-scale ImageNet pre-training, capturing 3D spatial
correlation, and modeling long-range dependencies from MR images. For TKR
prediction using COR STIR knee MRI scans from the MOST database, MR-
Transformer achieved a significantly higher AUC (0.82) compared to other deep
learning models: TSE (0.76, P $<$ .001), 3DMeT (0.74, P = .005), and MRNet
(0.78, P = .010). Similarly, MR-Transformer also achieved significantly higher
AUCs compared to TSE and 3DMeT for other tissue contrasts in MRI scans: COR IW
TSE (0.89 vs 0.86, P = .009 and 0.82, P = .004), SAG IW TSE (0.91 vs 0.82, P
$<$ .001 and 0.78, P $<$ .001), and SAG PD FAT SAT (0.82 vs 0.75, P = .006 and
0.63, P $<$ .001), while differences compared to MRNet were not statistically
significant for these contrasts.

Compared with TSE and 3DMeT, MR-Transformer leveraged ImageNet pre-trained
weights and achieved better performance in TKR prediction, while TSE and 3DMeT
are models trained from scratch. The results demonstrate the importance of
large-scale pre-training in small medical datasets. As MRNet also leveraged
ImageNet pre-training, it achieved close performance to MR-Transformer in TKR
prediction. However, we still observed a better performance of MR-Transformer
when using COR STIR MR images. This could be attributed to MR-Transformer’s
capability to capture 3D spatial correlation and model long-range dependencies
from MR images.

Although MR-Transformer exhibited leading performance in TKR prediction using
MRI, some limitations of the model must be noted. The computation burden of
MR-Transformer is heavy especially when processing large MR images. Since the
self-attention mechanism of transformer models has quadratic computation
complexity to the number of input patches, the considerable number of
separated patches from a 3D MR image would bring an overwhelming computation
load (a $36\times 512\times 512$ MRI matrix would be separated into $36,864$
patches). It is recommended to use small MR images when the computational
resources are limited. As a future work, exploring the extension of MR-
Transformer to diverse MRI classification tasks can be considered, aiming to
investigate its generalizability and potential adaptations for various disease
diagnoses.

The application of deep learning models in disease diagnosis signals the
potential of artificial intelligence in medical fields. The proposed MR-
Transformer, incorporating ImageNet pre-training and capturing three-
dimensional spatial correlation, predicts TKR using MRI. It achieved superior
AUC performance compared to TSE, 3DMeT, and MRNet across coronal and sagittal
knee MR scans from the OAI and MOST databases, demonstrating its potential for
TKR prediction. The open-source implementation of our method is available at
https://github.com/denizlab/MR-Transformer.

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# Spectroscopic mapping of Io’s surface with HST/STIS: SO2 frost, sulfur
allotropes, and large-scale compositional patterns

Samantha K. Trumbo Cornell Center for Astrophysics and Planetary Science,
Cornell University, Ithaca, NY 14853, USA  M. Ryleigh Davis Division of
Geological and Planetary Sciences, California Institute of Technology,
Pasadena, CA 91125, USA  Benjamin Cassese Now at Department of Astronomy,
Columbia University, New York, NY 10027 USA  Division of Geological and
Planetary Sciences, California Institute of Technology, Pasadena, CA 91125,
USA  Michael E. Brown Division of Geological and Planetary Sciences,
California Institute of Technology, Pasadena, CA 91125, USA

(Accepted November 18, 2022)

###### Abstract

Io’s intense volcanic activity results in one of the most colorful surfaces in
the solar system. Ultraviolet and visible-wavelength observations of Io are
critical to uncovering the chemistry behind its volcanic hues. Here, we
present global, spatially resolved UV-visible spectra of Io from the Space
Telescope Imaging Spectrograph on the Hubble Space Telescope (HST), which
bridge the gap between previous highly resolved imagery and disk-integrated
spectroscopy, to provide an unprecedented combination of spatial and spectral
detail. We use this comprehensive dataset to investigate spectral endmembers,
map observed spectral features associated with SO2 frost and other sulfur
species, and explore possible compositions in the context of Io surface
processes. In agreement with past observations, our results are consistent
with extensive equatorial SO2 frost deposits that are stable over multi-decade
timescales, widespread sulfur-rich plains surrounding the SO2 deposits, and
the enrichment of Pele’s pyroclastic ring and the high-latitude regions in
metastable short-chain sulfur allotropes.

Galilean satellites (627), Io (2190), Planetary surfaces (2113), Surface
composition (2115)

††journal: PSJ††facilities: HST(STIS)††software: astropy (Astropy
Collaboration et al., 2013)

##  1 Introduction

Jupiter’s moon Io is the most volcanically active body in the solar system.
Explosive and effusive eruptions driven by the intense tidal heating
associated with its forced eccentric orbit (Peale et al., 1979) cause constant
volcanic resurfacing (e.g Williams & Howell, 2007; Geissler, 2003; Geissler &
Goldstein, 2007), making Io the body with the youngest surface in the solar
system as well. Its dynamic surface and coupled atmosphere are dominated by
volcanic products, which also feed neutral clouds and a plasma torus beyond Io
within Jupiter’s extensive magnetosphere (e.g Schneider & Bagenal, 2007),
resulting in the delivery of Iogenic material (primarily in the form of sulfur
and oxygen ions) all the way to the outer, icy Galilean satellites (Johnson et
al., 2004). On Io, these volcanic products give rise to an extremely colorful
surface, featuring dark lava lakes and flows, vividly red rings of volcanic
plume fallout, widespread plains of yellow, orange, and brown, and regions
coated in bright sulfur dioxide (SO2) frost (e.g. McEwen et al., 1998;
Geissler et al., 1999; Carlson et al., 2007). Ultraviolet- (UV) and visible-
wavelength observations of Io’s surface have been key to understanding the
composition behind these colors and what they reveal about the chemistry of
Io’s plumes and magma reservoirs.

Prior to the Voyager mission’s first flyby of the Jupiter system, Io’s unusual
color and low near-UV reflectance in Earth-based imagery (Harris, 1961;
Minton, 1973; Murray, 1975) and narrow-band spectrophotometry (Johnson &
McCord, 1970; Johnson, 1971; Wamsteker, 1973; Nelson & Hapke, 1978) were
variably suggested to reflect polysulfides (Johnson & McCord, 1971), elemental
sulfur (Wamsteker et al., 1974), sulfur-rich salt evaporite deposits featuring
irradiation-produced color centers (Fanale et al., 1974; Nash & Fanale, 1977;
Fanale et al., 1977), and mixtures of metastable sulfur allotropes and
possibly evaporite salts (Nelson & Hapke, 1978). Voyager’s discovery of active
volcanism (Morabito et al., 1979) and volcanic SO2 gas (Pearl et al., 1979) at
Io led to the focus on plausible volcanic species and the quick identification
of condensed surficial SO2 (Hapke, 1979; Fanale et al., 1979; Smythe et al.,
1979) via previously unidentified infrared bands (Cruikshank et al., 1978;
Pollack et al., 1978) and a UV absorption maximum near 280 nm measured by the
International Ultraviolet Explorer (IUE) (Bertaux & Belton, 1979; Nelson et
al., 1980). The variegated surface colors that Voyager revealed were suggested
to reflect various volcanic sulfur products, including elemental sulfur,
metastable allotropes, and possibly polysuflur oxides (PSO), disulfur monoxide
(S2O), and certain sulfides, though SO2 was still the only material identified
with any confidence (McEwen, 1988; McEwen et al., 1988).

Following the Voyager flybys, the existing disk-integrated spectrophotometry
measurements (e.g. Nelson & Hapke, 1978; McFadden et al., 1980), which
provided more spectral detail than the broadband images, but without spatial
resolution, were modeled using different subsets of these possible volcanic
species, with some authors favoring oxides (Hapke, 1989), some invoking a
mixture of oxides and sodium sulfide (Na2S) (Nash, 1993), and others favoring
quenched sulfur allotropes (Moses & Nash, 1991). Io’s UV-visible spectrum at
the full-disk scale is characterized by two strong, but not entirely
diagnostic, features—a strong absorption edge from $\sim$380 to 500 nm and a
second absorption edge between 550 and 700 nm, with a plateau between them
(e.g. Johnson & McCord, 1971). Later high-quality disk-integrated CCD
spectroscopy confirmed these absorptions, but still did not differentiate
between possible compositions (Spencer et al., 1995).

Ahead of the arrival of the Galileo spacecraft at Jupiter, Spencer et al.
(1997) used the Wide-Field/Planetary Camera 2 on the Hubble Space Telescope
(HST) to obtain images in filters targeting the absorption edges. Spencer et
al. (1997) created spectral ratio maps that suggested that the 550-700 nm band
edge was specifically associated with both the darkened high latitudes and the
ring of pyroclastic deposits surrounding the extremely active Pele volcano.
The authors suggested metastable tetrasulfur (S4), a likely red colorant in
laboratory studies of sulfur melts and S2O (e.g. Meyer et al., 1972a; Hapke,
1989), as a possible explanation. Images captured with the Galileo Solid State
Imaging (SSI) system’s expanded coverage into the red and near-infrared
wavelengths soon confirmed a distinct red color for Pele’s ring, as well as a
redness to the high latitudes (McEwen et al., 1998; Geissler et al., 1999),
which was originally noted from Earth by Minton (1973). Informed by the Earth-
based observations, interpretation of the corresponding broadband photometry
through comparison with laboratory data led to a general post-Galileo
compositional picture of yellow plains containing sulfur, bright deposits rich
in SO2, red materials possibly enriched in short-chain sulfur allotropes or
other colorants, and dark regions of exposed volcanic silicates accounting for
just 1% of the surface (Geissler et al., 1999; Carlson et al., 2007).

Though this understanding represents the culmination of decades of
observation, it still relies on inference to bridge the gap between spatially
resolved images, which lack spectral detail, and full-disk UV-visible
spectroscopy, which lack the necessary spatial information to link composition
with surface processes. To address this problem and complete our spectral
understanding of Io’s colorful surface, we used HST’s Space Telescope Imaging
Spectrograph (STIS) to obtain the first global, spatially resolved UV-visible
reflectance spectra of Io. We use this new dataset to investigate spectral
endmembers, identify and map observed spectral features, and discuss
compositional implications in the context of Io surface processes.

##  2 Observations and Data Reduction

We present spatially resolved spectra of Io from 200 to 1000 nm, which we
obtained with HST/STIS across 8 visits in 2020. Using the G230L, G430L, and
G750L first-order spectroscopy modes, we executed simple slit-scan patterns to
build up complete spatial coverage of Io’s disk during each visit. The G230L
UV observations used the STIS MAMA detector, while the longer-wavelength
gratings were used in combination with the STIS CCD. For G230L, we stepped the
0.2′′ slit across Io in 0.1′′ increments, which provided high-quality spectra
from 200 to 300 nm at an effective spatial resolution of 0.1′′ in the across-
slit direction (corresponding to $\sim$330 km at the sub-observer point). For
G430L and G750L, we used the 0.1′′ slit and stepped in 0.06′′ increments,
providing approximately twice the across-slit spatial resolution in the
300–1000 nm range. Details concerning the dates, geometries, and exposure
times associated with each visit and slit scan are given in Table 1.

Table 1: Table of HST/STIS Observations Date | Time | Central | Central | Angular | Gratings | Slit | Pixel | Resolving | Exposure
---|---|---|---|---|---|---|---|---|---
(UT) | (Start/End) | Lon. | Lat. | Diameter | Used | Width111The effective across-slit angular resolution is finer by roughly a factor of two for all settings because we overlapped subsequent slit positions in our stepping patterns, as described in Section 2. | Scale | Power | Time (s)
2020 Mar 25 | 02:59/03:31 | 225$\degree$W | -1.56$\degree$ | 0.93′′ | G230L | 0.2′′ | 0.025′′ | 500 | 167
2020 Aug 7 | 10:31/11:03 | 45$\degree$W | -1.33$\degree$ | 1.20′′ | G230L | 0.2′′ | 0.025′′ | 500 | 167
2020 Aug 11 | 09:50/10:22 | 134$\degree$W | -1.34$\degree$ | 1.19′′ | G230L | 0.2′′ | 0.025′′ | 500 | 167
2020 Aug 21 | 03:20/03:52 | 314$\degree$W | -1.34$\degree$ | 1.16′′ | G230L | 0.2′′ | 0.025′′ | 500 | 167
2020 Aug 18 | 11:48/12:22 | 136$\degree$W | -1.34$\degree$ | 1.17′′ | G430L/G750L | 0.1′′ | 0.05′′ | 500 | 7/6
2020 Aug 28 | 05:23/05:57 | 317$\degree$W | -1.35$\degree$ | 1.14′′ | G430L/G750L | 0.1′′ | 0.05′′ | 500 | 7/6
2020 Sep 10 | 22:21/22:55 | 226$\degree$W | -1.34$\degree$ | 1.10′′ | G430L/G750L | 0.1′′ | 0.05′′ | 500 | 7/6
2020 Sep 13 | 13:53/14:27 | 45$\degree$W | -1.34$\degree$ | 1.09′′ | G430L/G750L | 0.1′′ | 0.05′′ | 500 | 7/6

Flux- and wavelength-calibrated x2d files were provided by HST following
reduction with the standard STIS calibration pipeline (calstis). We
reprocessed the G750L data using the same pipeline, but executing additional
defringing procedures, in order to remove substantial fringes from the longest
wavelengths. We extracted individual spectra from each row of the two-
dimensional spectral images, corresponding to the 0.025′′ and 0.05′′ pixel
scales of the UV and visible gratings, respectively ($\sim$80 km and $\sim$160
km at the sub-observer point and comparable to the diffraction-limit at the
grating central wavelengths). We then divided each extracted spectrum by a
solar spectrum at the appropriate wavelengths to convert to reflectance. For
the mid-UV G230L spectra, we use solar spectra for the corresponding date, as
measured by the Total and Spectral Solar Irradiance Sensor (TSIS-1; Richard et
al., 2020) on the International Space Station and obtained via the LASP
Interactive Solar Irradiance Datacenter. Prior to division, we smoothed and
binned the TSIS spectra to match the STIS spectral resolution and sampling.
For the visible-wavelength G430L and G750L spectra, we used the ASTM E490
zero-airmass solar reference spectrum222https://www.nrel.gov/grid/solar-
resource/spectra-astm-e490.html. As the G430L and G750L data were taken using
identical slit scans during the same visits, we combined the extracted spectra
in these settings, scaling as necessary to correct small flux offsets, in
order to produce complete 300–1000 nm spectra for each surface location. We
calculated the geographic coordinates of each extracted pixel on Io using the
aperture geometry information in the HST FITS headers and the phase, angular
size, and pole orientation of Io obtained from JPL
Horizons333https://ssd.jpl.nasa.gov/horizons/.

Beyond 700 nm, the G750L spectra appeared to exhibit multiple artifacts
leftover from the defringing process, similar to those also seen in STIS
spectra of Mars and Europa (Bell & Antsy, 2007; Trumbo et al., 2020). In
addition, the broad point-spread function resulted in significant slit losses
throughout the G750L wavelengths ($\sim$550–1000 nm) that resulted in
artificial dropping reflectance toward the near infrared. To correct for these
effects, we compared a constructed disk-integrated spectrum of Io’s trailing
hemisphere from the HST data to corresponding ground-based spectra. We fit a
spline curve to the ground-based trailing-hemisphere spectrum of Spencer et
al. (1995), extrapolated the fit beyond 740 nm, which proved largely
consistent with the somewhat sparse spectral sampling of Clark & McCord (1980)
at these longer wavelengths, and then multiplied each HST spectrum by the
ratio of the fitted spline to the corresponding full-disk spectrum we
constructed from the HST observations. This approach simultaneously corrected
for the wavelength-dependent slit losses and defringing artifacts, while
maintaining all relative pixel-to-pixel variations and approximate spectral
shapes within the G750L data. An additional source of artifacts complicated
pixels very near to the limb of Io, where the signal was significantly
reduced. Beyond $\sim$900 nm, these pixels appeared to contain dominant
contributions from the so-called “red halo” of scattered light within the STIS
CCD, which created artificial spectral shapes. Though our reduction does not
correct for this effect, it hinders only the usefulness of the most extreme
limb data at the longest wavelengths.

##  3 Definition and Geography of Spectral Units

Coarse spectra produced from both the Voyager and Galileo imagery were
previously used to define distinct spectral units on Io’s surface. The Voyager
imagery could largely be described by smooth variation between three main
endmembers—one interpreted as primarily SO2 frost at low latitudes, a second
of an unknown composition possibly rich in elemental sulfur and apparently
associated with plume deposits, and a third of unknown composition constrained
to the visibly darkened high latitudes (McEwen, 1988). The Galileo images
identified four main color units: white materials, yellow materials, red
materials, and dark materials, each of which displayed distinct
characteristics in the SSI filters (Geissler et al., 1999). The white
materials, distinguished by their relatively shallow slopes between the short-
wavelength filters, closely matched the low-latitude Voyager SO2 unit and were
confirmed as SO2-rich based on infrared Galileo spectra. The yellow materials,
characterized by a steep short-wavelength slope and a sharp inflection at
green wavelengths, were shown to dominate the low-latitudes outside of the SO2
deposits. The red materials, featuring a steep slope from the violet to red
filters, were found to dominate the high latitudes, Pele’s ring, and smaller
red deposits associated with volcanic centers. In contrast, the dark
materials, accounting for just 1% of Io’s surface, exhibited a slight local
minimum in the 889 nm SSI filter, which was interpreted as a possible Fe2+
crystal field absorption of exposed orthopyroxenes (Geissler et al., 1999;
Carlson et al., 2007).

Figure 1: Example HST spectra of the white, yellow, and red color units
defined from Galileo imagery (Geissler et al., 1999). Colored dots on the
background USGS mosaic of Io indicate the pixel locations for the example
spectra. The white materials show generally shallower slopes than do the red
and yellow materials, with the exception of a steep drop short of $\sim$320 nm
that is indicative of SO2, as well as strong SO2 absorption (low relative
reflectivity) near 280 nm in the UV. The yellow materials are primarily
characterized by a steep positive slope from roughly 380 to 500 nm, while the
red materials exhibit a similarly strong slope in addition to a strong
absorption near 560 nm. We performed 7-pixel and 5-pixel moving average
smoothing to the shown UV and visible spectra, respectively.

In Figure 1, we show representative HST/STIS spectra of the white, yellow, and
red color units defined and mapped previously by Geissler et al. (1999) from
Galileo imagery. As expected, the spectrum of the so-called white material,
noted by Geissler et al. (1999) to realistically be more pale pink or yellow
in appearance, exhibits strong SO2 absorption in the UV, with characteristic
reflectance minima near 220 and 280 nm and a local maximum near 240 nm (Nash
et al., 1980; Hapke, 1981), and weaker spectral slopes than the rest of the
surface in the 400–700 nm range. However, its spectral slopes still indicate
some absorption in this visible wavelength range that is not expected for pure
SO2 frost. In addition, a very steep absorption edge shortward of 320 nm
appears in the visible-wavelength spectra of the white materials and is also
indicative of SO2 frost, as this edge marks the onset of the aforementioned
280 nm UV SO2 band (Nash et al., 1980; Hapke et al., 1981). The example
spectrum of yellow materials is less characteristic of SO2 frost and is
instead dominated by the strong 380–500 nm absorption edge observed previously
in ground-based spectra (e.g. Wamsteker et al., 1974; Spencer et al., 1995).
The other absorption visible in the ground-based data, described as either a
550–700 nm absorption edge (e.g. Spencer et al., 1995) or a 560 nm absorption
feature (e.g. Carlson et al., 2007), is only weakly visible in spectra of the
yellow materials, but appears to be a strong and defining feature of the red
materials seen by Galileo (Figure 1). These red regions also exhibit a strong
380–500 nm absorption edge, though it is interesting to note that the
inflection at the bottom of the band edge appears to shift to longer
wavelengths as one moves from white to yellow to red materials. Beyond 700 nm,
the spectra of all three units are largely flat, which is consistent with both
the ground-based and Galileo data.

Though the HST spectra span the wavelengths needed to confirm the tentative
890 nm absorption associated with the dark, likely silicate, materials, most
such regions are on the order of tens of kilometers in size (e.g Geissler et
al., 1999) and thus are below the spatial resolution of our data, which
approaches the $\sim$300 km diffraction limit for 890 nm wavelengths at the
sub-observer point. Thus, it is reasonable to expect the weak 890 nm minima
observed by Galileo to be diluted beyond detection in our spectra, and,
indeed, we see no clear spectral evidence for silicates. The only location
that may present a possible exception is Babbar Patera (38°S, 277°W), whose
400-kilometer-wide diffuse dark deposits are on par with the angular
resolution of our data (McEwen et al., 1998). Unfortunately, however, the
longitudes of Babbar appear near the limb of Io as observed from Earth for the
dates and times of our observations, such that the increasing contributions of
the long-wavelength scattered light described in Section 2 make the possible
appearance of an absorption there too uncertain to constitute a detection.
Future observations at more targeted geometries may be able to better address
the outstanding question of the possible 890 nm silicate absorption in dark
materials.

###  3.1 Endmember Extraction

In addition to examining the spectral characteristics of previously defined
Galileo color units, we take our own approach to identifying spectral
endmembers in the HST data. As the UV spectra provide lower spatial resolution
and appear to be dominated simply by variations in SO2 absorption, we focus
solely on the visible wavelengths for our endmember analysis. We follow a
similar method to that described in Fischer et al. (2015), in which we
decompose the spectra at each spatial pixel into a linear combination of the N
most extreme spatial pixels observed. To identify the N optimal endmember
spectra, we first exclude any pixels observed at greater than 60∘ from the
center of Io’s disk. We then take an iterative approach for identifying the
optimal set of endmember pixels. We input all of the spectra into a K-means
clustering algorithm and find N wavelength-dependent cluster centers. We then
identify the spatial pixels whose spectra are most similar to each cluster
center using the spectral angle mapping (SAM) criteria first described in
Kruse et al. (1993). The N spatial pixels with the smallest SAM angle $\theta$
from each k-means cluster center are then used as the initial set of spectral
endmembers and the remaining spatial pixels are modeled as a linear
combination of these endmembers using standard least-squares regression. The
residual root-mean-square (RMS) error is calculated for each pixel, and the
RMS of all pixels is summed to define a total RMS for the given set of
endmembers.

This initial endmember set is then iteratively improved by holding all but one
endmember constant, and randomly selecting a new endmember candidate from the
set of pixels composed of at least 70% that endmember in the linear models. A
candidate endmember is accepted if the total RMS error using the new candidate
set is smaller than that of the previous set of endmembers. This process
continues, alternating which endmember is substituted, until no new endmember
candidates are accepted for $100\cdot N$ iterations and the total deviation in
RMS between the last few accepted iterations has leveled off below $\sim$1%.
Figure 2 illustrates this minimization procedure for the $N=3$ case, where the
optimal endmember candidates converge to the 3 corners of the ternary diagram.

Figure 2: Ternary diagram demonstrating the progression of our endmember
extraction routine, in which the endmembers converge to the corners of the
diagram. The initial set of spectral endmembers is indicated by the encircled
stars, while colored dots show iteratively chosen subsequent endmembers that
lowered the overall RMS. Grey dots represent the remaining pixels as best-fit
linear combinations of the final three components.

To ensure convergence to the optimal endmember set, we run the minimization
procedure 100 times and find that 92 of the test cases converge to the lowest
total RMS. The remaining 6 test cases find an endmember set that is very
similar, both qualitatively and quantitatively, to the lowest RMS set, but
which has a slightly higher total RMS value. We also perform this spectral
decomposition routine for endmember sets with values of N ranging from 1 to 6.
The total RMS error of the final endmember set drops significantly from the
N=1 to N=2 case, and again from the N=2 to N=3 case. The residual maps also
reveal significant spatial structure for the N=1 and N=2 cases, revealing the
likely presence of additional endmembers. When moving from the N=3 to N=4 and
5 cases, the improvement in the total RMS is small. While there is still some
spatial structure in the residual map for the N=3 case, we cannot confidently
determine whether this is due to the presence of a fourth endmember or an
artifact of systematic noise, so we choose N=3 endmembers for our final
spectral decomposition model.

###  3.2 Endmember Spectra and Distributions

The endmember approach described above arrived at the three spectrally
distinct endmember components shown in Figure 3. In essentially every respect,
they are quite similar to the three spectra displayed in Figure 1—component 1
displays shallower slopes than the others, except for a steep drop near 320 nm
(akin to the white materials), component 2 exhibits a dramatic 380–500 nm
absorption edge (similar to the yellow materials), and component 3 possesses
the strongest 560 nm absorption (like the red materials). Maps of the
fractional abundance of each endmember in linear models of each pixel reveal
geographic distributions consistent with the primary units defined by Geissler
et al. (1999) (Figure 4). As with the white materials defined from Galileo
imagery, component 1 largely follows the Voyager SO2 unit (McEwen et al.,
1988), while component 2 correlates with the yellow regions seen to surround
such SO2-rich areas, largely avoiding the highest latitudes dominated by both
the red materials and component 3 from our endmember analysis (Figure 4). In
fact, component 2 appears to nearly always flank the fields dominated by
component 1, with a slight exception north of the equatorial patch at
$\sim$15$\degree$W.

Unsurprisingly given its red color and similarity to the upper latitudes in
coarse Galileo imaging spectra, Pele’s pyroclastic ring at roughly
19$\degree$S and 255$\degree$W also appears distinct in our map of component
3. It exhibits the strongest association with component 3 in its southernmost
portion and appears possibly broken in the northeast near Pillan Patera
(12$\degree$S, 243$\degree$W), which was seen to disrupt Pele’s ring following
its 1997 eruption during the Galileo mission (e.g. Davies et al., 2001;
Keszthelyi et al., 2001; Williams et al., 2001) and which has subsequently
been seen to erupt episodically from ground-based observations (de Pater et
al., 2016). In contrast, Pele’s center and the regions along the outer edge of
its ring deposit appear enriched in component 2. The most obvious exception to
the correspondence between our endmember maps and the color unit maps of
Geissler et al. (1999) occurs just southwest of Pele’s ring deposit and Babbar
Patera (38°S, 277°W) near Ülgen Patera (41°S, 287°W), which appears largely
red in the Geissler et al. (1999) maps, but is dominated by component 2 in
ours. This discrepancy may imply modification to Io’s surface composition at
this location in the decades between the Galileo and HST observations.
Elsewhere, and with the exception of Pele’s ring and the northwestern portion
of Colchis Regio, which appears rich in component 1, component 3 nearly always
flanks component 2 on the pole-ward side. Indeed, the combination of our three
component maps agrees well with the color unit geographies from Galileo,
suggesting that the surface compositional variation is well-captured by these
three primary units. In addition, they bear resemblance to some of the large-
scale geologic units mapped on Io (Williams et al., 2011, 2021), with
component 1 encompassing much of the mapped “white bright plains material” in
addition to some regions classified as “bright” or “undivided” flow material,
component 2 exhibiting fair correspondence to the “yellow bright plains
material”, and component 3 appearing largely in regions characterized as “red-
brown plains” (with the key exception of Pele’s ring).

Figure 3: The final three endmembers extracted from the visible-wavelength HST
dataset. The spectra have been smoothed by a 5-pixel moving average filter.
The first, second, and third components appear similar to spectra of the
Galileo white, yellow, and red materials, respectively.  Figure 4: The
geographic distributions of our extracted spectral endmembers. The given
fractional abundances are the coefficients of the best-fit linear combinations
of the three components at each pixel. White stars indicate the location of
the endmember pixels, and a black circle indicates the location of Pele
(19$\degree$S, 255$\degree$W). Component 1 closely follows the Voyager SO2
unit identified by McEwen et al. (1988) and also matches our SO2 map in Figure
5 well. Component 2 correlates with the yellow, likely sulfur-rich plains
immediately surrounding the SO2 deposits, while our map of component 3
highlights the upper latitudes and Pele’s pyroclastic ring (19$\degree$S,
255$\degree$W) in good correspondence to our map of Io’s 560 nm absorption in
Figure 7.

##  4 Spectral Feature Mapping

In addition to mapping spectral endmembers, which are determined based on the
entire 300–1000 nm continuum, we also map the strengths of individual spectral
features across the surface. Despite providing the first global, spatially
resolved spectra at these wavelengths, the HST data do not reveal any discrete
absorptions not already seen in past Earth-based observations (e.g. Nelson et
al., 1980; Spencer et al., 1995). The mid-UV absorption signatures and 320 nm
absorption edge of SO2, the 380–500 nm absorption edge, and the 560 nm feature
are the only features apparent in our data.

We map the distribution of Io’s SO2 frost using the contrast of its strong
absorption maximum near 280 nm to the surrounding continuum. Some of the fine
structure visible below 240 nm in our UV spectra may be sensitive to band
systems of Io’s atmospheric SO2 (e.g. Ballester et al., 1994), but the
measurement of this is outside the scope of this study of surface composition.
Though atmospheric SO2 also exhibits broad absorption across the mid-UV, in
addition to sharp structure, surface reflectance has been shown to dominate
the strength of the wide $\sim$280 nm band (e.g. Jessup et al., 2004; Jessup &
Spencer, 2015).

We fit a linear continuum from 236 to 315.5 nm, excluding the interval
corresponding to the absorption (239–313.5 nm), remove this continuum, and
integrate the residual absorption to obtain the equivalent width (width of a
100% absorption feature of the same area). We note that, as this band is the
culmination of the overall dropping reflectance across the near- to mid-UV
that begins at 320 nm, this continuum is likely non-physical, but simply
serves as a tool against which to measure the relative relief of the
absorption band.

We also map the strength of the two visible-wavelength absorptions, the
380–500 nm edge and the 560 nm feature, which are not characteristic of SO2
frost. Given the uncertainty in defining the unknown missing continua
associated with these features, we measure each in two different ways in order
to ensure a robust assessment of their geographies. For the 380–500 absorption
edge, we first define and remove a linear continuum, as above, from 324.5 to
440 nm, excluding the 332.5–425 nm region visibly associated with the
inflection of the absorption, and measure the residual area. Second, we
normalize the spectra to the mean reflectance between 488 and 490 nm near the
top of the absorption and measure the resulting slope from 400 to 490 nm,
interpreting steeper slopes as stronger absorption. Slopes across slightly
different wavelength bounds within the band edge produce comparable results.
Similarly, for the 560 nm feature, we assess the equivalent width by fitting
and removing a third-order polynomial from 460 to 745 nm, excluding the
visible absorption across 500–700 nm, and also normalize the spectra at the
top of the feature (663–665 nm) and measure the slope from 585 nm within the
absorption to 665 nm at the top. Second-order polynomial continua result in
equivalent, though slightly noisier, results. We then map all of these
measurements using the coordinates as obtained in Section 2 and compare their
distributions with those of each other, past observations, geology, and likely
surface processes.

###  4.1 SO2 Frost

Figure 5 shows the SO2 distribution we obtain based on the 280 nm mid-UV
feature. In agreement with distributions derived from Voyager and HST imaging
(McEwen et al., 1988; Sartoretti et al., 1996) and Galileo and ground-based
mapping of Io’s infrared SO2 bands (Carlson et al., 1997; Laver & de Pater,
2008, 2009; de Pater et al., 2020), we observe strong SO2 absorption at
equatorial latitudes within Bosphorus Regio and Colchis Regio between
$\sim$100 and 250$\degree$W. In fact, our SO2 map shows a distribution
qualitatively identical at our resolution to that produced from the Voyager
imagery (McEwen et al., 1988) and to the visibly bright regions of the USGS
Galileo/Voyager color mosaic of
Io444https://astrogeology.usgs.gov/search/map/Io/Voyager-
Galileo/Io_GalileoSSI-Voyager_Global_Mosaic_ClrMerge_1km, with all three
showing additional deposits near the sub-Jovian point, at localized high
northern latitudes, and within Tarsus Regio ($\sim$40$\degree$S,
55$\degree$W), which are less apparent in the infrared maps. In addition, the
SO2 map we produce corresponds extremely well to the geography of the first
spectral endmember (component 1) from Section 3. Based on comparisons between
the derived surface reflectance and atmospheric transmission signatures for
the SO2-rich Prometheus plume shown in Jessup et al. (2004) (their Figure 4),
we estimate that unaccounted for atmospheric contributions may introduce an
upper limit of $\sim$15% overestimation in our absolute band strengths.
However, the near identical correspondence to the aforementioned additional
proxies for SO2 frost mapped previously suggests that atmospheric
uncertainties are a small factor in determining the relative geography we
obtain.

It is interesting to note, however, that the distribution we observe lacks
resemblance to that produced via inversion of Galileo NIMS data with linear
spectral models, rather than by mapping of individual band strengths (Douté et
al., 2001). In their retrievals, Douté et al. (2001) find high fractional SO2
coverage at mid latitudes to high latitudes and relative depletions at the
more equatorial Colchis Regio and Bosphorus Regio, where we find the strongest
280 nm bands. From their models, the authors also estimate larger equivalent
widths at the equator and much larger equivalent widths southeast of Pele than
those measured by Carlson et al. (1997) from comparable NIMS spectra. To
explain such differences, the authors suggest a combination of an opposition
surge decreasing the band strengths observed by Carlson et al. (1997) and an
optically thin, yet often large-grained, frost at mid to high latitudes that
is insufficient to result in some of the weaker infrared SO2 bands measured by
Carlson et al. (1997), but that they suggest can be deduced from the modeling
of stronger bands. To justify the differences between their retrieved
distribution and those from the Voyager and Galileo imaging results, Douté et
al. (2001) invoke a different explanation, instead proposing that molecular
contamination of the mid- and high-latitude SO2 deposits with darker sulfur
suppresses their near-UV and visible albedos such that they do not appear in
maps produced from images at those wavelengths.

It is not clear, however, that either explanation adequately accounts for the
discrepancy with the map we produce from the strong mid-UV SO2 band. At such
short wavelengths, our observations should be sensitive to frost deposits,
even if they are optically thin at the infrared wavelengths observed with
Galileo NIMS. In addition, though sulfur is darker than SO2 in the visible,
SO2 frost is comparably dark in the mid-UV (e.g. Nash et al., 1980), which
calls into question the idea that molecular mixing with sulfur may be
responsible for masking the otherwise high near-UV and visible reflectivity of
SO2 frost at the mid to high latitudes in Voyager data. Thus, our results are
possibly contradictory to those of Douté et al. (2001) and may imply
additional effects not yet considered or perhaps limitations to the retrieval
technique they employed. However, our band-strength mapping cannot distinguish
between the often degenerate effects of abundance and grain size, and we do
not attempt to constrain these effects with our limited data, which
undoubtedly also contain spectral contributions from other surface species
that may be affecting the UV reflectance at the upper latitudes. Indeed, the
apparent SO2 concentrations within Bosphorus Regio and Colchis Regio in our
map do correspond well to the distributions of the largest equatorial to mid-
latitude SO2 grains inferred by Douté et al. (2001). In addition, the UV
spectral shape of SO2 frost varies slightly between different laboratory
experiments (e.g Nash et al., 1980; Hapke, 1981), depending on the frost
properties, and Io’s geographically varying surface conditions have not been
fully replicated in laboratory settings.

Future work involving simultaneous modeling of the UV, visible, and infrared
spectra and the consideration of grain size and frost structure, which is
outside the scope of this paper, may resolve the apparent discrepancies in
Io’s SO2 frost distribution. Nevertheless, all of the observations,
particularly the relative strength of the weaker infrared SO2 bands in the
ground-based and NIMS data, are broadly consistent with the thickest and/or
largest-grained and possibly purest SO2 deposits at equatorial latitudes.
Furthermore, the remarkable agreement between the Voyager, Galileo, and HST
maps indicates long-term stability of frost in these regions, despite the
constant activity and high resurfacing rates on Io.

Figure 5: Map of Io’s 280 nm SO2 absorption maximum from the UV HST/STIS G230L
spectra. This distribution corresponds extremely well to the Voyager SO2 frost
map of McEwen et al. (1988) and to the visibly bright regions of the above
USGS Galileo/Voyager mosaic. We observe strong SO2 bands within Colchis Regio
and Bosphorus Regio at low-latitudes between roughly 100$\degree$ and
250$\degree$W, which is also in agreement with ground-based mapping of weak
infrared SO2 bands (Laver & de Pater, 2008, 2009; de Pater et al., 2020). Such
agreement, in combination with the relative strengths of different SO2 bands
observed by Galileo NIMS (Carlson et al., 1997; Douté et al., 2001), is
consistent with these regions harboring the largest-grained, thickest, and/or
purest SO2 deposits, which appear stable over multi-decade timescales. For
context, the location of Pele is indicated by a black circle.

###  4.2 380–500 nm Absorption Edge

Maps of our two proxies for the strength of the 380–500 nm absorption edge are
shown in Figure 6. Both show qualitatively similar distributions with minima
associated with the aforementioned SO2 deposits and enhanced absorption at
some mid- to high-latitude locations, within the trailing/sub-Jovian quadrant,
and southeast of Pele (19$\degree$S, 255$\degree$W). Our maps are broadly
consistent with the 0.410/0.564 $\micron$ ratio map produced with HST images
of Io (Spencer et al., 1997) and with the understanding that overlying
deposits of bright SO2 mask underlying darker materials (e.g. Carlson et al.,
2007). The absorption edge appears strongly in both regions associated with
the yellow materials and in those containing the red materials defined from
Galileo imagery (Geissler et al., 1999). Indeed, simply mapping the strength
of this feature does a poorer job of spatially distinguishing between these
two units than does our endmember approach of Section 3, which maps yellow
materials as having a higher relative proportion of the endmember defined
almost exclusively by its strong 380–500 nm edge and finds the red materials
to have a higher relative proportion of the endmember defined by a combination
of a strong edge and 560 nm feature. This difference underscores how both
methods—endmember classification and spectral feature mapping—can complement
each other in the process of assessing geographic compositional variations.

Figure 6: Maps of Io’s 380–500 nm absorption edge, which we measure in two
ways. We create the top map by measuring the band area beneath a fitted linear
continuum across the inflection of the absorption, while we create the bottom
map by measuring the slope of the band edge normalized at its long-wavelength
end. The distributions of both proxies agree extremely well, demonstrating
that the absorption is entirely anti-correlated with the SO2 signature mapped
in Figure 5. Instead, it appears strong across much of the mid and high
latitudes on Io and in some low-latitude locations not covered by SO2
deposits. This geography is consistent with a wide distribution of sulfurous
material, potentially rich in S8 or S$\mu$. The location of Pele
(19$\degree$S, 255$\degree$W) is indicated by the black circle.

As noted in Section 3, the inflection at the bottom of the 380–500 nm
absorption appears to shift in wavelength between roughly 360 and 390 nm, with
shorter-wavelength minima corresponding to the SO2 deposits and the longest-
wavelength minima generally corresponding to regions of strongest absorption,
particularly within the trailing/sub-Jovian quadrant. It is possible that the
weak 360 nm feature of SO2 frost (Hapke et al., 1981), previously unobserved
on Io, is influencing the spectrum at that wavelength within the strongest SO2
deposits. Indeed, some such spectra appear to show a slight slope break just
short of 400 nm, possibly indicating the influence of a separate feature from
the overall band edge (see spectrum of white materials in Figure 1).
Otherwise, the distributions we obtain for the 380–500 nm absorption edge,
which are strongly anti-correlated with SO2 and span much of the yellow and
red-brown geologic plains units (individually well-matched by components 2 and
3 above, respectively; Williams et al., 2011, 2021), appear reasonable for the
prior interpretations of this feature as characteristic of some form of
elemental sulfur. It seems likely that the presence of such material is more
or less ubiquitous on Io at our spatial resolution, given that even the
apparently SO2-rich white materials display the 380–500 nm band edge to some
degree, but that it simply becomes partially obscured by overlying frost in
deposits like those seen in the Bosphorus, Colchis, and Tarsus Regiones.

###  4.3 560 nm Feature

Both of our methods for measuring the strength of Io’s 560 nm absorption
produced nearly identical distributions, which are shown in Figure 7. Most
strikingly, the high latitudes stand out as regions of strong absorption in
our maps, while the low latitudes are almost entirely devoid of strong 560 nm
features. The major exception, however, is the clear association of the 560 nm
band with Pele’s ring deposit (roughly 19$\degree$S, 255$\degree$W), which is
just visible in both maps. In both respects, our maps largely agree with the
0.564/0.781 $\micron$ ratio map produced from the past HST imaging
observations of Spencer et al. (1997), though Pele’s signature is somewhat
weaker relative to the high latitudes in our data. This may reflect the
decrease in Pele’s activity implied by measurements of its thermal emission
after 2002, which could have caused fading of its ring (de Pater et al.,
2016). In addition, we find stronger 560 nm absorption southeast of Pele’s
ring than southwest of it, which is opposite of the pattern in the HST imaging
ratio map (Spencer et al., 1997). Though the spatial correspondence is not
exact, it is also interesting to note that, despite Pele decreasing in
activity itself, a region southeast of Pele (near 35$\degree$S, 240$\degree$W)
appears to have initiated volcanic activity since the Galileo mission (de
Kleer et al., 2019). Convolution of our spectra with the WFPC2 filters used in
the imagery shows that such differences are not explained by the wide imaging
band passes and may instead imply such temporal changes in Io’s surface in the
more than 20 years between the imagery and our spectroscopic observations.
Indeed, as mentioned in Section 3, the region southwest of Pele near Ülgen
Patera also appears discrepant between our endmember maps and those of
previously defined Galileo color units (Geissler et al., 1999). Regardless,
however, the qualitative conclusions of the Galileo and both HST datasets are
consistent—Io’s 560 nm absorption relates to fresh plume deposits at Pele and
processes at high latitudes, and contributes to the reddish colors of such
regions.

Figure 7: Maps of Io’s 560 nm absorption, which we measure in two ways. We
retrieve the top distribution by measuring the band area beneath a fitted
polynomial continuum across the visible absorption, while we retrieve the
bottom distribution by measuring the slope of the 585–665 nm band edge
normalized at its long-wavelength end. Both maps agree extremely well and
indicate that the absorption is primarily constrained to the high latitudes
with the notable exception of a clear association with Pele’s ring of
pyroclastic material, the approximate center of which is indicated by the
black circle at 19$\degree$S and 255$\degree$W. This geography is potentially
indicative of a thermodynamically unstable species that is continuously
produced. In agreement with the interpretations of Spencer et al. (1997) and
Carlson et al. (2007), we suggest that the metastable short-chain allotrope S4
may form directly from plume gases at Pele and possibly be independently
produced by irradiation and/or preserved by low temperatures at the high
latitudes (see Section 5).

##  5 Implications for Composition and Surface Processes

The UV/VIS HST spectra of Io’s surface presented here provide an unprecedented
combination of spatial and spectral detail that can help constrain the
volcanic species behind Io’s colorful surface, as well as their relationships
with surface processes. However, with the exception of the diagnostic SO2
bands observed in the UV, the broad, non-unique, and potentially overlapping
nature of Io’s spectral features beyond 300 nm and those of candidate
laboratory materials make concrete identification on the sole basis of
spectral comparison essentially impossible. Instead, a combination of spectral
plausibility from laboratory comparison and spatial correspondence to a
conceptual model based in current understanding of Io surface processes
presents our best means of unraveling the surface composition. As our UV
spectra appear dominated by the simple modulation of the SO2 signatures, and
as many potentially relevant additional species lack laboratory spectra at UV
wavelengths, we focus on our visible-wavelength data for such comparisons.

Io’s 380–500 nm absorption edge has been widely accepted as characteristic of
sulfur, though the exact form has been variably suggested to be stable
elemental sulfur (orthorhombic cyclo-octal sulfur; $\alpha$-S8), the more
metastable allotropes monoclinic $\beta$-S8 and polymeric sulfur (Sμ), or some
combination of these species, all of which possess a strong band edge roughly
coincident in wavelength (e.g. Wamsteker, 1973; Moses & Nash, 1991; Spencer et
al., 1997; Carlson et al., 2007; Baklouti et al., 2008). Unfortunately, as the
wavelength of the sulfur band edge changes with temperature, impurity, and
irradiation, as well as with specific allotropes (Hapke & Graham, 1989; Kargel
et al., 1999; Carlson et al., 2007; Eckert & Steudel, 2003), its exact
location cannot readily distinguish between such possibilities. $\alpha$-S8 is
expected to be the most thermodynamically stable form at Io surface conditions
(Carlson et al., 2007; Eckert & Steudel, 2003), but $\beta$-S8 and Sμ rapidly
cooled from high-temperature sulfur may still be long-lived on Io (Moses &
Nash, 1991). In fact, as noted by Moses & Nash (1991) and Baklouti et al.
(2008), Sμ may provide a better explanation for the 330–400 nm region of Io’s
spectrum, which exhibits a significantly less abrupt slope transition than do
spectra of S8 (Figure 8). Alternatively, Hapke (1989) suggested polysulfur
oxide (PSO) formed via dissociation of SO2 in place of elemental sulfur, in
part to explain the 330–400 nm region. However, widespread PSO in such high
abundance as to explain the ubiquitous 380-500 nm band edge on Io may be
unlikely to accumulate at Io’s high resurfacing rates (McEwen & Lunine, 1990).
Given the spectral similarity of all of the aforementioned species to Io’s
spectra (Figure 8) and the laboratory understanding of their formation and
stability on the surface, it seems likely that all may be present in some
amount, with an undetermined combination of S8 and Sμ (perhaps akin to the
quenched sulfur melts of Moses & Nash (1991)) as the primary cause of the
380–500 nm absorption edge.

Figure 8: Example average HST spectra of Io compared to laboratory spectra of
candidate materials. Several species exhibit similar features to Io’s 380–500
nm absorption edge, which has long been attributed to some form of sulfur. The
inflection at the base of the band edge may be better matched by the presence
of metastable polymeric sulfur (Sμ; a significant component of the shown
sulfur melt freeze) than by S8 alone. Though the 560 nm band is perhaps best
matched by the spectrum of Na2S, considerations of Io’s plume chemistry and of
the geography of the feature point to the spectral influence of metastable S4
(also seen in the spectrum of red sulfur glass and likely that of S2O) as a
more likely cause. The S4 spectrum is from Carlson et al. (2009) after Meyer
et al. (1972b) and is scaled for clarity. The red sulfur glass spectrum is
from Meyer et al. (1972a). Both reflect samples at 77 K and are converted to
approximate reflectance from absorption profiles. The $\alpha$-S8 spectrum is
from Carlson et al. (2009) after Gradie et al. (1980) and was measured at room
temperature, the spectra of $\beta$-S8 and the sulfur melt freeze (from 453 K
melt) are of room-temperature samples from Moses & Nash (1991), and the Na2S
spectrum shows an irradiated sample at 170 K from Nash & Nelson (1979). The
S2O and PSO spectra are from Hapke & Graham (1989) and were taken at 77 K and
195 K, respectively. The shown SO2 frost spectrum from Hapke et al. (1981) (at
$\sim$77 K) lacks the above features. All spectra are normalized at their
longest wavelengths and, with the exception of the Pele spectrum, are offset
for clarity. The offsets used are 0.13, 0.4, 1.3, 1.4, 1.6, 2.3, 2.5, 3, 3.2,
and 3.4 units, respectively, from bottom (yellow plains) to top (SO2). Dashed
lines at 380 and 560 nm pass through Io’s primary visible absorptions.

The identity of Io’s 560 nm feature has also been a subject of debate.
Suggestions have ranged from ferric iron (Nash & Fanale, 1977) to sodium
sulfide (Na2S; Nash, 1993; Gradie & Moses, 1984; Nash & Nelson, 1979) to
tetrasulfur (S4; Nelson & Hapke, 1978; Spencer et al., 1997; Carlson et al.,
2007). As mentioned by Spencer et al. (1997), species containing ferric iron
usually have prominent bands at longer wavelengths, which are not seen on Io.
Between Na2S and S4, the former provides a better spectral match to Io’s 560
nm absorption (Figure 8), as it is broader and at slightly longer wavelengths
than the proposed band of S4, which is nominally closer to 520 or 530 nm (e.g.
Meyer et al., 1972a). However, though initially an attractive candidate as a
possible source for the Na in Io’s neutral clouds, Na2S is now expected to be
only a minor constituent of Io’s volcanic emissions (Fegley & Zolotov, 2000;
Moses et al., 2002; Schaefer & Fegley, 2005), which have since been shown to
contain sufficient NaCl to explain the Na cloud (Lellouch et al., 2003). Even
the more abundant NaCl likely only exists on the surface at an abundance of 1%
or less relative to SO2 (Carlson et al., 2007), which likely explains why our
HST spectra do not show the irradiation-induced NaCl color centers seen in
equivalent observations of Europa (Trumbo et al., 2019, 2022). Thus, S4 seems
the most likely of the discussed candidates for the 560 nm feature after
consideration of our current understanding of Io’s plume and atmospheric
chemistry.

In addition, it seems possible from a range of sulfur experiments that S4 may
variably affect the spectra of sulfur mixtures, potentially providing a better
spectral fit to Io under different conditions, despite the apparently poor
match to the 530 nm absorption of laboratory-prepared S4 (Figure 8). Indeed,
the spectrum of quenched red sulfur glass (Figure 8; Meyer et al., 1972a) and
various spectra of “purple”, “red”, or “brown” sulfur (e.g. Nelson & Hapke,
1978; Gradie et al., 1980) show broader and shifted absorption that has also
been attributed to the influence of S4 in the samples. Molten sulfur (e.g
Nelson et al., 1983) and some sulfur melt freezes (Moses & Nash, 1991) also
exhibit indistinct absorption at nearby wavelengths. In addition, S4 is
thought to be the likely source of the red color and strong absorption beyond
500 nm in laboratory samples of disulfur monoxide (S2O; Figure 8), which has
also been suggested as a possible Io surface species (Hapke & Graham, 1989;
Hapke, 1989). Therefore, while we have not seen a laboratory spectrum of S4 or
of an S4-containing substance that, on its own, presents a satisfactory
spectral match to Io’s 560 nm band, we still find it a spectrally plausible
species.

Importantly, S4 fits a conceptual model for the spatial distribution of the
560 nm absorption, which corresponds to the high latitudes and Pele’s plume
deposits (Figure 7; Spencer et al., 1997) and must therefore be tied to
corresponding processes. Pele’s plume contains gaseous S2, which may result in
the production of S4 via photolysis and polymerization or annealing after
deposition onto the surface (Spencer et al., 2000; Carlson et al., 2007). S2O
is also an expected minor plume species, which may thermally decompose to
produce S4, as discussed by Spencer et al. (1997). However, its expected low
abundance relative to S2 suggests that this mechanism would likely be a
secondary source (Zolotov & Fegley, 2000; Carlson et al., 2007). Regardless,
such direct production from continuously erupted plume gases may explain the
specific association of the 560 nm band with Pele’s ring, as well as the
smaller diffuse red deposits seen near other volcanic centers in Galileo
imagery (Geissler et al., 1999).

S4 is thermodynamically unstable at average Io surface temperatures (e.g.
Meyer et al., 1972a), and therefore must be continuously produced to explain
Io’s 560 nm feature. The plume mechanisms discussed above fulfill this
requirement for Pele’s ring, but do not as directly explain the feature’s
association with the high latitudes. However, x-ray irradiation of S8 can also
lead to the production of S4 (Nelson et al., 1990), and it is thus plausible
that particle radiolysis would do the same, as has been observed in
experiments with H2S-bearing ices (Mahjoub et al., 2017). Though particle
precipitation patterns on Io are complex and not entirely understood
(Paranicas et al., 2003), the low atmospheric density over its poles (e.g
Strobel & Wolven, 2001; Feaga et al., 2009; Lellouch et al., 2015) may
facilitate enhanced high-latitude particle bombardment relative to the rest of
the surface (Johnson, 1997; Bagenal & Dols, 2020), thereby providing a
radiolytic source of S4. In principle, precursors to its formation via this
mechanism could also include alteration products of SO2 that has condensed
onto the poles (perhaps S or S2O), which Wong & Johnson (1996) and Johnson
(1997) suggested could account for the darkened high latitudes.

In addition to the possibility of enhanced radiolytic production near the
poles, it seems plausible that their lower surface temperatures may also act
to increase the preservation of unstable S4, as posited by Spencer et al.
(1997). Based on this combination of potential factors, we agree with the
interpretations of Spencer et al. (1997) and Carlson et al. (2007) in
considering S4 the best current candidate for Io’s 560 nm absorption. However,
we find this identification tentative, given that laboratory experiments
involving S4 have yet to produce a satisfactory spectral match to the observed
band.

##  6 Conclusions

We present global, spatially resolved UV-visible spectra of the surface of Io
from 200 to 1000 nm, which we obtained with HST/STIS. Using these data, we
extract and map endmember components, obtain the geographies of observed
spectral features, and discuss potential compositional insights by considering
spectral comparison to laboratory samples as well as the context of Io’ plume
chemistry and surface processes. In agreement with past observations, our
results indicate low-latitude deposits of SO2, which have been stable across
the roughly 40 years since the Voyager flybys of Io. We suggest that future
modeling work simultaneously examining the UV, visible, and infrared
wavelengths may help resolve outstanding questions regarding the grain sizes
and physical structures of SO2 deposits across the surface. While we do not
definitively identify Io’s most prominent visible-wavelength absorptions—a
deep 380–500 nm absorption edge and a prominent 560 nm band—we confirm their
correspondence to the respective yellow and red materials investigated by
Galileo imagery and posit potential compositions. We agree with past
interpretations that the 380–500 nm absorption edge likely reflects elemental
sulfur, and suggest a composition featuring both S8 and Sμ as physically and
spectrally plausible. We also find our results to be consistent with past
suggestions of the potential enrichment of Pele’s pyroclastic ring and the
high latitudes in the metastable short-chain allotrope S4, which may form
continuously from plume gases at Pele and possibly be independently produced
via radiolytic processes and/or preserved by low temperatures toward the
poles.

Based on observations made with the NASA/ESA Hubble Space Telescope, obtained
at the Space Telescope Science Institute, which is operated by the Association
of Universities for Research in Astronomy, Inc., under NASA contract
NAS5-26555. These observations are associated with program $\\#$15925\.
Support for program $\\#$15925 was provided by NASA through a grant from the
Space Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.
S.K.T. is supported by the Heising-Simons Foundation through a 51 Pegasi b
postdoctoral fellowship. All of the data presented in this paper were obtained
from the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope
Science Institute. The specific observations analyzed can be accessed via
https://doi.org/10.17909/xd3d-wp93 (catalog 10.17909/t9-5tsd-s772). The
authors thank Katherine de Kleer and Jonathan Lunine for useful discussions.

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