11institutetext: Technical University of Denmark, DTU Compute, Kgs. Lyngby,
Denmark 22institutetext: University of Copenhagen, Department for Computer
Science, Copenhagen, Denmark 33institutetext: Rigshospitalet, Neurobiology
Research Unit, Copenhagen, Denmark
33email<EMAIL_ADDRESS>33email<EMAIL_ADDRESS>33email<EMAIL_ADDRESS>
# Feature robustness and sex differences in medical imaging: a case study in
MRI-based Alzheimer’s disease detection

Eike Petersen 11 0000-0003-0097-3868 Aasa Feragen 11 0000-0002-9945-981X Maria
Luise da Costa Zemsch 11 Anders Henriksen 11 Oskar Eiler Wiese Christensen 11
Melanie Ganz for the Alzheimers Disease Neuroimaging Initiative Data used in
preparation of this article was obtained from the Alzheimers Disease
Neuroimaging Initiative (ADNI) database (http://www.adni-info.org/). The
investigators within the ADNI contributed to the design and implementation of
ADNI and/or provided data, but did not participate in analysis or writing of
this report.2233 0000-0002-9120-8098

###### Abstract

Convolutional neural networks have enabled significant improvements in medical
image-based diagnosis. It is, however, increasingly clear that these models
are susceptible to performance degradation when facing spurious correlations
and dataset shift, leading, e.g., to underperformance on underrepresented
patient groups. In this paper, we compare two classification schemes on the
ADNI MRI dataset: a simple logistic regression model using manually selected
volumetric features, and a convolutional neural network trained on 3D MRI
data. We assess the robustness of the trained models in the face of varying
dataset splits, training set sex composition, and stage of disease. In
contrast to earlier work in other imaging modalities, we do not observe a
clear pattern of improved model performance for the majority group in the
training dataset. Instead, while logistic regression is fully robust to
dataset composition, we find that CNN performance is generally improved for
both male and female subjects when including more female subjects in the
training dataset. We hypothesize that this might be due to inherent
differences in the pathology of the two sexes. Moreover, in our analysis, the
logistic regression model outperforms the 3D CNN, emphasizing the utility of
manual feature specification based on prior knowledge, and the need for more
robust automatic feature selection.

###### Keywords:

Deep Learning MRI Alzheimer’s Disease Robustness

##  1 Introduction

In recent years, various groups have reported highly accurate detection of
Alzheimer’s disease (AD) and progressive mild cognitive impairment (pMCI) –
which represents an earlier disease stage that continues to progress into AD
or other types of dementia [17] – based on magnetic resonance imaging (MRI)
volumes using convolutional neural networks (CNNs) [27]. Simultaneously, the
potential brittleness of deep learning has become apparent due to issues like
model underspecification [8], spurious correlations [12], and susceptibility
to dataset shift [5]. Multiple reviews in the medical domain have shown that
deep learning-based publications often suffer from inadequate model reporting
and overly optimistic performance estimates [14, 28]. Wen et al. [27] found in
their systematic review that half of the studies reporting on MRI-based AD
detection using deep learning potentially suffered from data leakage, likely
leading to inflated performance estimates. Additionally, in clinical
applications with low-dimensional input spaces, several systematic reviews
have found no performance benefit of machine learning-based techniques over
simple logistic regression [7, 18], raising the question of whether simple
models based on manually extracted, low-dimensional features may also perform
competitively in medical imaging.

In a parallel development, the question of sex and gender-related performance
disparities of machine learning models has lately received a lot of attention
[19, 24]. Studies have shown that CNNs can accurately identify a patient’s
age, sex, and ethnicity from chest x-ray images [6, 29], and that chest x-ray
classifiers tend to underdiagnose underserved patient populations [24].
Larrazabal et al. [15] have analyzed the effect of training dataset sex
imbalance on a chest x-ray classifier’s performance for male and female
subgroups, finding a consistent decrease in performance for the
underrepresented sex. To the authors’ knowledge, similar analyses have yet to
be performed in the brain MRI classification setting, even though it is known
that AD presents differently in males and females [17, 22].

Figure 1: Slices of an exemplary recording used in this study, skull-stripped
and registered to a common space. Hippocampus and entorhinal cortex (yellow
and red, segmented using FreeSurfer) are highlighted. Left to right: sagittal,
coronal, and axial view.

Training on a sex-imbalanced dataset and then evaluating model performance on
the underrepresented group represents a particular type of _dataset shift_
[23], and the close connection between model robustness (to dataset shift and
other challenges) and algorithmic fairness has been emphasized recently [2].
To achieve robustness to dataset shifts, the _feature space_ in which
classification is performed plays a crucial role: to be robust against dataset
shifts, estimation must be performed in a feature space that gives rise to a
classifier that is optimal across different environments [3]. This feature
space can either be manually crafted or automatically inferred, as is usually
the case in deep learning [1].

In this paper, we analyze the robustness of two different MRI-based
classifiers to distribution shifts. Both classifiers are trained to detect
Alzheimer’s disease, based on different feature representations. The first is
a simple logistic regression model using manually selected volumetric
features, which are obtained using standard MRI processing tools [4, 11]. The
second is a CNN using full 3D MRI volumes. Both models are considered state-
of-the-art for Alzheimer’s disease classification. For analyzing the
classifiers’ robustness, we consider two separate types of distribution
shifts: Firstly, we analyze the effect of differing training dataset sex and
age compositions on the performance for male/female or young/old test
subjects, similar to the analysis of Larrazabal et al. [15]. And secondly,
like various other groups have done [27] (although not combined with the sex
and age imbalance analyses we perform), we evaluate the performance of
classifiers trained on subjects diagnosed with AD and healthy controls on a
test set consisting of subjects with stable and progressive MCI.

##  2 Methods

###  2.1 Dataset

Table 1: Composition of the dataset used in this study (based on the ADNI dataset [13]), stratified by sex and field strength. Diagnosis | Male | Female | $1.5\text{\,}\mathrm{T}$ | $3\text{\,}\mathrm{T}$ | Total
---|---|---|---|---|---
AD | 181 (54.03%) | 154 (45.97%) | 175 (52.24%) | 160 (47.76%) | 335
HC | 282 (43.52%) | 366 (56.48%) | 219 (33.80%) | 547 (66.20%) | 648
pMCI | 149 (58.66%) | 105 (41.34%) | 184 (72.44%) | 70 (27.56%) | 254
sMCI | 155 (59.62%) | 105 (40.38%) | 122 (46.92%) | 138 (53.08%) | 260

We use MRI volumes from the ADNI dataset [13] (700, 463, and 334 recordings
from ADNI1, ADNI2, and ADNI3, respectively), including a single T1-weighted
structural MRI volume (acquired on different MR scanners using a field
strength of either $1.5\text{\,}\mathrm{T}$ or $3\text{\,}\mathrm{T}$) per
subject in our experiments. Like various other studies [27], we consider two
groups of subjects, giving rise to two classification tasks: firstly, healthy
control (HC) and Alzheimer’s disease (AD) subjects and, secondly, stable and
progressive mild cognitive impairment (sMCI, pMCI) subjects. Subjects were
labeled as pMCI in our analysis if they were diagnosed with MCI at the time of
the recording and then were diagnosed with AD at any point during the
following five years. (This definition only encompasses (progressive)
_amnestic_ MCI, since non-amnestic MCI may develop into non-AD dementias
[17].) Subjects were labeled as sMCI if they were diagnosed with MCI at the
time of the recording, not diagnosed with AD at any point during the five-year
follow-up period, and if there was at least one valid diagnosis from years
three to five after the initial recording was made. The dataset is summarized
in table 1. The median age across the whole dataset was $73.0$ years; the
average age of the different subject cohorts was $74.99\pm 7.08$ (males),
$72.70\pm 6.94$ (females), $75.13\pm 7.83$ (AD/pMCI cases), $73.08\pm 6.58$
(HC/sMCI cases), $75.70\pm 7.91$ (male AD/pMCI cases), and $71.96\pm 6.46$
(female AD/pMCI cases).

###  2.2 AD Classification using logistic regression

Intracranial volume (ICV) was quantified as the combined volumes of gray- and
white matter and cerebrospinal fluid [16], segmented with SPM12 [4].
Hippocampal volume (HCV) and entorhinal cortex volume (ECV) was extracted from
structural MRI volumes using FreeSurfer v7.1.1 [11], see fig. 1 for an
example.

A simple logistic regression (LR) model of the form

$P(\mathrm{AD})\approx
q_{\mathrm{AD}}=\sigma(\theta_{1}\cdot\mathrm{Age}+\theta_{2}\cdot\mathrm{ICV}+\theta_{3}\cdot\mathrm{HCV}+\theta_{4}\cdot\mathrm{ECV}),$
(1)

with $\sigma(\cdot)$ denoting the sigmoid function, was fitted using
stochastic gradient descent for 4000 epochs (initial learning rate $10^{-3}$,
automatic learning rate scheduling – if there is no improvement in the
validation loss for 10 epochs, the learning rate is halved –, momentum $0.9$,
early stopping based on the validation loss, batch size 256). The loss
function was binary cross-entropy with $L_{2}$ regularization (regularization
constant $10^{-4}$).

###  2.3 AD Classification using CNNs

The subject-specific MRI images were skull-stripped and registered to a common
space (MNI305) using FreeSurfer v7.1.1 [11], resulting in spatially normalized
grayscale volumes of the dimensionality $256\times 256\times
256\,$\mathrm{m}\mathrm{m}^{3}$$. These were then cropped to include the whole
brain ($186\times 186\times 191\,$\mathrm{m}\mathrm{m}^{3}$$). Dataset
augmentation was performed using torchio [21]: During training, 80% of the
training samples were transformed using one (randomly selected) of the
following transformations: rotation, elastic deformation, flipping, blurring,
addition of Gaussian noise, and addition of an MRI bias field, spike,
ghosting, or motion artifact.

A convolutional neural network (CNN) was trained, using the preprocessed 3D
MRI volumes as inputs and the subject’s AD/HC label as the target. The model
architecture was inspired by Tinauer et al. [25] and Wen et al. [27], and was
(manually) selected based on validation set performance. The convolutional
part of the model consists of eight consecutive convolution layers (all with
sixteen channels), each followed by a rectified linear unit (ReLu). The first
two layers use kernels of size $5\times 5\times 5$; the subsequent six layers
use $3\times 3\times 3$ kernels. Every second layer uses a stride of two, thus
progressively reducing image resolution. This is followed by a dropout layer
($p=0.5$), a fully connected linear layer with 32 output channels, a ReLu,
another dropout layer ($p=0.5$), and the final, fully connected classification
layer with sigmoid activation. The model has 337,000 trainable parameters,
which are estimated using the Adam optimization algorithm (initial learning
rate $10^{-4}$, automatic learning rate scheduling based on the validation
loss as described above, 200 epochs, batch size 6, early stopping based on the
validation loss) to minimize binary cross-entropy (no regularization).

###  2.4 Performance and robustness evaluation

Figure 2: Visualization of the AD/HC dataset and two exemplary splits. Each
marker represents 25 subjects (rounded). For clarity, only one of the five
test sets and only two of the five training and validation datasets for this
test set (all with different male–female ratios
$\mathrm{FR}=\frac{n_{\\!f}}{n_{\\!f}+n_{m}}$, with $n_{\\!f}$ and $n_{m}$ the
number of females and males in the combined training and validation dataset)
are shown.

To evaluate the two models’ overall performance and robustness, we trained
them on 125 (LR) and 50 (CNN) different training datasets and evaluated them
on six different test sets. First, five AD/HC test sets of size 100 were drawn
from the full dataset with 25 samples each of male/female AD/HC subjects, with
no subject overlap between the test sets. For each of the five test sets, five
training and validation sets of combined size 379 were drawn from the
remaining AD/HC subjects (without replacement), with five different male-to-
female ratios ($0\text{\,}\mathrm{\char 37\relax}$ to
$100\text{\,}\mathrm{\char 37\relax}$ females in $25\text{\,}\mathrm{\char
37\relax}$ increments) and a constant fraction of $34.1\text{\,}\mathrm{\char
37\relax}$ AD cases, corresponding to the fraction of AD cases in the whole
dataset. The gender-specific datasets were nested: female subjects used at a
female ratio (FR) of $50\text{\,}\mathrm{\char 37\relax}$ represent a subset
of female subjects used at an FR of $75\text{\,}\mathrm{\char 37\relax}$, etc.

Each of the 25 combined training and validation sets was then split randomly
into five folds following standard recommendations [26]. For the logistic
regression, each fold was used once as the validation set, resulting in a
total of five training–validation set combinations per test set (of which
there are five) and sex ratio (of which there are five), yielding a total of
125 different training and validation datasets. For the CNNs, due to the
computational effort, only the first two of the five fold combinations were
used per sex ratio, thus yielding a total of 50 different training and
validation datasets. Each model was then evaluated on both the respective
AD/HC test set and the full sMCI/pMCI dataset (which had not been used for
training), calculating performance metrics on both males and females. Figure 2
illustrates the full AD/HC dataset and two exemplary data splits.

The decision thresholds for all models were selected to maximize the geometric
mean of sensitivity and specificity on the validation dataset [10]. All models
were implemented and trained using PyTorch Lightning v.1.5.9 [9] and training
one CNN took about twelve hours on a single NVIDIA Titan X GPU. When the
performance of models trained on the same datasets was compared, statistical
significance was assessed using Wilcoxon signed-rank tests.

An analogous analysis was also performed with respect to age groups instead of
sex; its details and results can be found in the supplementary material.

##  3 Results

(A)

(B)

Figure 3: Distribution of (A) the area under the curve (AUC) of the receiver-
operating characteristic and (B) the accuracy achieved by the trained models
(first row in both panels: LR, second row: CNN) on the different test sets.
FR: ratio of female subjects in the training and validation set, $m$: slope of
the regression line ($\pm$ standard deviation), Bonferroni corrected p-value
null hypothesis: $m=0$, $\mu$: average AUC / ACC ($\pm$ standard deviation)
across all sex ratios. Random jitter is added to all x coordinates to prevent
excessive overlap – all points are sampled at
$\mathrm{FR}\in\\{0,0.25,0.5,0.75,1.0\\}$, as indicated by the five different
colors. Note the truncation of all y-axes.

Figure 3 shows the distribution of the area under the curve (AUC) of the
receiver-operating characteristic and the accuracy (ACC) achieved by the
trained models on the different test sets. To assess the dependence of model
performance for males and females on the training dataset sex composition,
regression lines were fit and a t-test was performed to assess whether the
slope was significantly different from zero. To account for multiple
comparisons, a Bonferroni correction with a factor of eight was performed. The
figure reports the corrected p-values.

As also found in previous studies [27], both models drop in performance on
sMCI vs. pMCI classification compared to HC vs. AD classification, for which
they were trained. The LR model achieves consistently high AUC and ACC across
all training and validation sets, and performance is similar for male and
female test subjects, although significantly better for females
($p_{\textrm{corr}}=$5.5\text{\times}{10}^{-4}$$ and
$p_{\textrm{corr}}=$5.9\text{\times}{10}^{-22}$$ for AUC on AD/HC and
pMCI/sMCI, respectively, with Bonferroni correction factor $2$). For the LR
model, all regression slopes were non-significant ($p_{\textrm{corr}}\gg
0.05$), indicating no significant effect of dataset composition on model
performance. The CNN performed significantly worse compared to the LR
($p_{\textrm{corr}}=$2.8\text{\times}{10}^{-25}$$ for AUC,
$p_{\textrm{corr}}=$6.2\text{\times}{10}^{-12}$$ for ACC, with Bonferroni
correction factor $2$), and it exhibited a stronger dependence of performance
for male and female test subjects on the training dataset composition. Three
statistically significant positive correlations were observed: between FR and
AUC in male pMCI/sMCI subjects
($p_{\textrm{corr}}=$5.4\text{\times}{10}^{-3}$$), and between FR and ACC in
female ($p_{\textrm{corr}}=$2.1\text{\times}{10}^{-2}$$) and male
($p_{\textrm{corr}}=$1.9\text{\times}{10}^{-2}$$) pMCI/sMCI subjects.

##  4 Discussion & conclusion

In the present study, motivated by recent work demonstrating performance
disparities in medical image classifiers between patient populations [15, 24],
we have analyzed the robustness of two state-of-the-art brain MRI classifiers
and their associated feature representations to multiple types of distribution
shift. Logistic regression using manually extracted volumetric features was
compared to a standard 3D CNN classifier using the full 3D MRI volumes as
inputs. Both models performed within the range reported for state-of-the-art
CNN-based AD classification in the review of Wen et al. [27] for studies
without suspected data leakage. The (valid) studies that report higher
performance either use significantly more recordings or multiple modalities,
and they only report the performance of a single training run. (Some of our
runs performed significantly better than the mean accuracy reported above, see
fig. 3.) The LR model, using manually selected volumetric features, performed
significantly better on average than the 3D CNN using the full MRI images.
While this might change for larger dataset sizes, our sample size is
comparable to typical sample sizes used in this domain.

We analyzed the effect of different ratios of male and female examples in the
training dataset on the performance of the trained classifier for male and
female test subjects. In our study, only the CNN’s performance showed a
dependence on training dataset composition, while the LR model was robust to
this variation. This is not surprising, given that the LR model is based on a
given representation (the extracted brain volumes and subject age), whereas
the CNN performs representation learning and is, thus, prone to tailor the
learned representation specifically to the training dataset. An important
avenue for future research concerns the question of whether environment-
invariant feature representations can be inferred automatically; an end
towards which various methods have been proposed [3, 20, 30]. This would
potentially allow for mitigating the effect of training dataset composition on
male and female test subject performance. Generalization to different
populations remains an unsolved problem in brain MRI AD analysis [27], with
important consequences for the general robustness and fairness of the
resulting systems. Finally, as a general trend, we observe that the influence
of training dataset composition on accuracy seems to be larger than the
influence on AUC, as indicated by larger slopes in fig. 3. This appears
plausible, given that the accuracy is influenced by one additional, dataset-
dependent processing step compared to AUC: threshold selection.

Interestingly, we find that CNN performance (as measured by AUC and ACC) is
improved in both men and women by including more women in the training
dataset. This differs from the results of our age splitting experiment, where,
while most relationships are not statistically significant, we observe
performance on younger subjects to improve the more younger subjects are in
the training dataset, whereas performance on older subjects tends to decline.
These contrasting results underline the complexity of the relationship between
dataset composition and subgroup performance. We hypothesize that the
beneficial influence of female subjects in the training dataset on model
performance on male test subjects may be explained by sex differences in
pathological severity between AD study subjects. Several epidemiological
studies have shown that neurodegeneration and clinical symptoms occur more
rapidly for females once a diagnosis is suspected [22]. Moreover, women might
present stronger cognitive decline than men with the same level of brain
pathology [17], thus being diagnosed with AD at an earlier stage of disease
progression than men. This might render female subjects more helpful as
training examples to a CNN classifier compared to male subjects, and it would
also explain why we generally observe better performance for females subjects.
More research is certainly required to further investigate and explain these
observations, however.

One potential limitation of our study concerns the preprocessing employed for
both models. The employed segmentation steps are partially based on MRI
atlases, which have been extracted from study databases. Thus, even in the
cases in which the training dataset nominally contained no males or no
females, this preprocessing step still incorporated some information about
male and female subjects. The degree to which this influenced our analyses is
challenging to quantify, but it represents a potentially confounding factor
that might cause us to underestimate the effect of the training dataset
composition. However, practical applications also typically employ atlas-based
preprocessing, making our analysis closer to practical scenarios than if we
had omitted these preprocessing steps.

#### Code & data availability

The full code for all implemented models, dataset splitting, and statistical
analyses is available online in our GitHub repository:
https://github.com/e-pet/adni-bias.

#### Acknowledgements

We thank Morten Rieger Hannemose for helpful comments on the manuscript and
the statistical analysis. This research was supported by Danmarks Frie
Forskningsfond (9131-00097B), the Novo Nordisk Foundation through the Center
for Basic Machine Learning Research in Life Science (NNF20OC0062606) and the
Pioneer Centre for AI, DNRF grant number P1. Data collection and sharing for
this project was funded by the ADNI (National Institutes of Health Grant U01
AG024904). ADNI is funded by the National Institute on Aging, the National
Institute of Biomedical Imaging and Bioengineering, and through generous
contributions from private sector institutions. The Canadian Institutes of
Health Research is providing funds to support ADNI clinical sites in Canada.
Private sector contributions are facilitated by the Foundation for the
National Institutes of Health (www.fnih.org). The grantee organization is the
Northern California Institute for Research and Education, and the study is
coordinated by the Alzheimer’s Disease Cooperative Study at the University of
California, San Diego. ADNI data are disseminated by the Laboratory for Neuro
Imaging at the University of California, Los Angeles.

## References

  * [1] Abrol, A., Fu, Z., Salman, M., Silva, R., Du, Y., Plis, S., Calhoun, V.: Deep learning encodes robust discriminative neuroimaging representations to outperform standard machine learning. Nature Communications 12(1) (2021). https://doi.org/10.1038/s41467-020-20655-6
  * [2] Adragna, R., Creager, E., Madras, D., Zemel, R.: Fairness and robustness in invariant learning: A case study in toxicity classification. In: NeurIPS Workshop on Algorithmic Fairness through the Lens of Causality and Interpretability (2020), https://arxiv.org/abs/2011.06485
  * [3] Arjovsky, M., Bottou, L., Gulrajani, I., Lopez-Paz, D.: Invariant risk minimization. arXiv (2019), https://arxiv.org/abs/1907.02893
  * [4] Ashburner, J.: SPM: a history. Neuroimage 62(2), 791–800 (2012). https://doi.org/10.1016/j.neuroimage.2011.10.025
  * [5] Azulay, A., Weiss, Y.: Why do deep convolutional networks generalize so poorly to small image transformations? Journal of Machine Learning Research 20(184), 1–25 (2019), http://jmlr.org/papers/v20/19-519.html
  * [6] Banerjee, I., Bhimireddy, A.R., Burns, J.L., Celi, L.A., Chen, L.C., Correa, R., et al.: Reading race: AI recognises patient’s racial identity in medical images. arXiv (2021), https://arxiv.org/abs/2107.10356
  * [7] Cowling, T.E., Cromwell, D.A., Bellot, A., Sharples, L.D., van der Meulen, J.: Logistic regression and machine learning predicted patient mortality from large sets of diagnosis codes comparably. Journal of Clinical Epidemiology 133, 43–52 (2021). https://doi.org/10.1016/j.jclinepi.2020.12.018
  * [8] D’Amour, A., Heller, K., Moldovan, D., Adlam, B., Alipanahi, B., Beutel, A., et al.: Underspecification presents challenges for credibility in modern machine learning. CoRR (2020), https://arxiv.org/abs/2011.03395
  * [9] Falcon, W., the PyTorch Lightning team: PyTorch Lightning (version 1.5.9) (2019), https://www.pytorchlightning.ai
  * [10] Fernández, A., García, S., Galar, M., Prati, R.C., Krawczyk, B., Herrera, F.: Performance measures. In: Learning from Imbalanced Data Sets, pp. 47–61. Springer International Publishing (2018). https://doi.org/10.1007/978-3-319-98074-4_3
  * [11] Fischl, B.: Freesurfer. Neuroimage 62(2), 774–781 (2012). https://doi.org/10.1016/j.neuroimage.2012.01.021
  * [12] Geirhos, R., Jacobsen, J.H., Michaelis, C., Zemel, R., Brendel, W., Bethge, M., Wichmann, F.A.: Shortcut learning in deep neural networks. Nature Machine Intelligence 2(11), 665–673 (2020). https://doi.org/10.1038/s42256-020-00257-z
  * [13] Jack, C.R., Bernstein, M.A., Fox, N.C., Thompson, P., Alexander, G., Harvey, D., et al.: The Alzheimer’s disease neuroimaging initiative (ADNI): MRI methods. Journal of Magnetic Resonance Imaging 27(4), 685–691 (2008). https://doi.org/10.1002/jmri.21049
  * [14] Jacobucci, R., Littlefield, A.K., Millner, A.J., Kleiman, E.M., Steinley, D.: Evidence of inflated prediction performance: A commentary on machine learning and suicide research. Clinical Psychological Science 9(1), 129–134 (2021). https://doi.org/10.1177/2167702620954216
  * [15] Larrazabal, A.J., Nieto, N., Peterson, V., Milone, D.H., Ferrante, E.: Gender imbalance in medical imaging datasets produces biased classifiers for computer-aided diagnosis. Proceedings of the National Academy of Sciences 117(23), 12592–12594 (2020). https://doi.org/10.1073/pnas.1919012117
  * [16] Malone, I.B., Leung, K.K., Clegg, S., Barnes, J., Whitwell, J.L., Ashburner, J., Fox, N.C., Ridgway, G.R.: Accurate automatic estimation of total intracranial volume: A nuisance variable with less nuisance. NeuroImage 104, 366–372 (2015). https://doi.org/10.1016/j.neuroimage.2014.09.034
  * [17] Mielke, M., Vemuri, P., Rocca, W.: Clinical epidemiology of Alzheimer’s disease: assessing sex and gender differences. Clinical Epidemiology p. 37 (2014). https://doi.org/10.2147/clep.s37929
  * [18] Nusinovici, S., Tham, Y.C., Yan, M.Y.C., Ting, D.S.W., Li, J., Sabanayagam, C., et al.: Logistic regression was as good as machine learning for predicting major chronic diseases. Journal of Clinical Epidemiology 122, 56–69 (2020). https://doi.org/10.1016/j.jclinepi.2020.03.002
  * [19] Obermeyer, Z., Powers, B., Vogeli, C., Mullainathan, S.: Dissecting racial bias in an algorithm used to manage the health of populations. Science 366(6464), 447–453 (2019). https://doi.org/10.1126/science.aax2342
  * [20] Pawlowski, N., Castro, D.C., Glocker, B.: Deep structural causal models for tractable counterfactual inference. In: Advances in Neural Information Processing Systems. vol. 33, pp. 857–869. Curran Associates, Inc. (2020), https://proceedings.neurips.cc/paper/2020/file/0987b8b338d6c90bbedd8631bc499221-Paper.pdf
  * [21] Pérez-García, F., Sparks, R., Ourselin, S.: TorchIO: A python library for efficient loading, preprocessing, augmentation and patch-based sampling of medical images in deep learning. Computer Methods and Programs in Biomedicine 208, 106236 (2021). https://doi.org/10.1016/j.cmpb.2021.106236
  * [22] Podcasy, J.L., Epperson, C.N.: Considering sex and gender in Alzheimer disease and other dementias. Dialogues in Clinical Neuroscience 18(4), 437–446 (2016). https://doi.org/10.31887/dcns.2016.18.4/cepperson
  * [23] Quiñonero-Candela, J., Sugiyama, M., Lawrence, N.D., Schwaighofer, A.: Dataset shift in machine learning. MIT Press (2009)
  * [24] Seyyed-Kalantari, L., Zhang, H., McDermott, M.B.A., Chen, I.Y., Ghassemi, M.: Underdiagnosis bias of artificial intelligence algorithms applied to chest radiographs in under-served patient populations. Nature Medicine 27(12), 2176–2182 (2021). https://doi.org/10.1038/s41591-021-01595-0
  * [25] Tinauer, C., Heber, S., Pirpamer, L., Damulina, A., Schmidt, R., Stollberger, R., et al.: Interpretable brain disease classification and relevance-guided deep learning. medRxiv (2021). https://doi.org/10.1101/2021.09.09.21263013
  * [26] Varoquaux, G., Raamana, P.R., Engemann, D.A., Hoyos-Idrobo, A., Schwartz, Y., Thirion, B.: Assessing and tuning brain decoders: cross-validation, caveats, and guidelines. NeuroImage 145, 166–179 (2017). https://doi.org/10.1016/j.neuroimage.2016.10.038
  * [27] Wen, J., Thibeau-Sutre, E., Diaz-Melo, M., Samper-González, J., Routier, A., Bottani, S., et al.: Convolutional neural networks for classification of Alzheimer's disease: Overview and reproducible evaluation. Medical Image Analysis 63, 101694 (2020). https://doi.org/10.1016/j.media.2020.101694
  * [28] Wynants, L., Van Calster, B., Collins, G.S., Riley, R.D., Heinze, G., Schuit, E., et al.: Prediction models for diagnosis and prognosis of covid-19: systematic review and critical appraisal. BMJ 369, m1328 (2020). https://doi.org/10.1136/bmj.m1328
  * [29] Yi, P.H., Wei, J., Kim, T.K., Shin, J., Sair, H.I., Hui, F.K., et al.: Radiology “forensics”: determination of age and sex from chest radiographs using deep learning. Emergency Radiology 28(5), 949–954 (2021). https://doi.org/10.1007/s10140-021-01953-y
  * [30] Zhao, Q., Adeli, E., Pohl, K.M.: Training confounder-free deep learning models for medical applications. Nature Communications 11(1) (2020). https://doi.org/10.1038/s41467-020-19784-9

## Supplementary material

To analyze the influence of age, the same analysis as described in the main
text was repeated, but splitting subjects into two age groups on the median
age (group y: $\text{age}\leq 73.0$, and group o: $\text{age}>73.0$) instead
of splitting based on sex. In this case, the logistic regression model
included sex as a variable, i.e., the model reads

$P(\mathrm{AD})\approx
q_{\mathrm{AD}}=\sigma(\theta_{1}\cdot\mathrm{Age}+\theta_{2}\cdot\mathrm{ICV}+\theta_{3}\cdot\mathrm{HCV}+\theta_{4}\cdot\mathrm{ECV}+\theta_{5}\cdot\mathrm{Sex}).$
(2)

The results of this analysis can be found in fig. 4, where YR denotes the
ratio of younger patients in the training dataset. Only two relationships are
both statistically significant and show a relevant effect size: the effect of
YR on ACC in younger AD/HC subjects using LR
($p_{\textrm{corr}}=$3.2\text{\times}{10}^{-5}$$, $m=0.069\pm 0.014$) and the
effect of YR on ACC in younger pMCI/sMCI subjects using the CNN
($p_{\textrm{corr}}=$0.047$$, $m=0.080\pm 0.028$). These relationships are as
expected: the performance on young subjects improves as more young subjects
are part of the training dataset.

(A)

(B)

Figure 4: Distribution of (A) the area under the curve (AUC) of the receiver-
operating characteristic and (B) the accuracy achieved by the trained models
(first row in both panels: LR, second row: CNN) on the different test sets.
YR: ratio of younger ($\text{age}\leq 73.0$) subjects in the training and
validation set, $m$: slope of the regression line ($\pm$ standard deviation),
p-value null hypothesis: $m=0$, $\mu$: average AUC / ACC ($\pm$ standard
deviation) across all younger/older ratios. Random jitter is added to all x
coordinates to prevent excessive overlap – all points are sampled at
$\mathrm{YR}\in\\{0,0.25,0.5,0.75,1.0\\}$, as indicated by the five different
colors. Note the truncation of all y-axes.


# Recurrent Activity from Active Asteroid (248370) 2005 QN173: A Main-belt
Comet

Colin Orion Chandler Department of Astronomy and Planetary Science, Northern
Arizona University, PO Box 6010, Flagstaff, AZ 86011, USA  Chadwick A.
Trujillo Department of Astronomy and Planetary Science, Northern Arizona
University, PO Box 6010, Flagstaff, AZ 86011, USA  Henry H. Hsieh Planetary
Science Institute, 1700 East Fort Lowell Rd., Suite 106, Tucson, AZ 85719, USA
Institute of Astronomy and Astrophysics, Academia Sinica, P.O. Box 23-141,
Taipei 10617, Taiwan

###### Abstract

We present archival observations of main-belt asteroid (248370) 2005 QN173
(also designated 433P) that demonstrate this recently discovered active
asteroid (a body with a dynamically asteroidal orbit displaying a tail or
coma) has had at least one additional apparition of activity near perihelion
during a prior orbit. We discovered evidence of this second activity epoch in
an image captured 2016 July 22 with the DECam on the 4 m Blanco telescope at
the Cerro Tololo Inter-American Observatory in Chile. As of this writing,
(248370) 2005 QN173 is just the 8th active asteroid demonstrated to undergo
recurrent activity near perihelion. Our analyses demonstrate (248370) 2005
QN173 is likely a member of the active asteroid subset known as main-belt
comets, a group of objects that orbit in the main asteroid belt that exhibit
activity that is specifically driven by sublimation. We implement an activity
detection technique, wedge photometry, that has the potential to detect tails
in images of solar system objects and quantify their agreement with computed
antisolar and antimotion vectors normally associated with observed tail
directions. We present a catalog and an image gallery of archival
observations. The object will soon become unobservable as it passes behind the
Sun as seen from Earth, and when it again becomes visible (late 2022) it will
be farther than 3 au from the Sun. Our findings suggest (248370) 2005 QN173 is
most active interior to 2.7 au (0.3 au from perihelion), so we encourage the
community to observe and study this special object before 2021 December.

minor planets, asteroids: individual ((248370) 2005 QN173), comets: individual
(433P)

††facilities: Astro Data Archive, Blanco (DECam), CFHT (MegaCam), Gaia, IRSA,
PO:1.2m (PTF, ZTF), PS1, Sloan, VST (OmegaCAM)††software: astropy (Robitaille
et al., 2013), astrometry.net (Lang et al., 2010), FTOOLS, JPL Horizons
(Giorgini et al., 1996), SAOImageDS (Joye, 2006), SkyBot (Berthier et al.,
2006), Vizier (Ochsenbein et al., 2000)

##  1 Introduction

Figure 1: The 126″$\times$126″thumbnail image (left) shows (248370) 2005 QN173
(green dashed arrow) at center with a tail (white arrows) oriented towards 5
o’clock. This 89 s $z$-band exposure captured with the DECam is the only image
in which we could unambiguously identify activity. We conducted wedge
photometry (right) that shows the tail orientation is $251\fdg 3\pm 1\fdg 4$
(blue star), in close agreement with the $251\fdg 6$ antisolar angle (yellow
$\odot$) and the $251\fdg 7$ antimotion vector (red $v$) as computed by JPL
Horizons. The plot shows counts radially outward from the the object center at
(0,0).

Active asteroids are objects that are dynamically asteroidal but that display
comet-like activity such as a tail or coma (Hsieh & Jewitt, 2006a). Activity
may be caused by mechanisms unrelated to volatiles (e.g., impact, rotational
disruption) or by sublimation as is typically the case with comets.
Sublimation driven active objects provide key insights into the present-day
volatile distribution in our solar system, as well as clues about the origins
of those volatiles and how they arrived on Earth (Hsieh & Jewitt, 2006b).
These objects have been persistently difficult to study because of the small
numbers detected to date: fewer than 30 active asteroids, of which roughly
half are thought to exhibit sublimation driven activity; see Chandler et al.
2018 for a summary.

When the aforementioned sublimation driven activity is connected with a main-
belt asteroid, the object is classified as a main-belt comet (MBC). MBCs are
often characterized by activity near perihelion and the absence of activity
elsewhere in the orbit (Hsieh et al., 2015; Agarwal et al., 2017; Hsieh et
al., 2018), suggesting that the primary activity mechanism is sublimation of
volatiles such as water ice (Snodgrass et al., 2017).

By contrast, stochastic events like impacts may result in comet-like activity
but, in such cases, the appearance of activity is expected to cease once the
material dissipates. Roughly 60% of known active asteroids have been observed
to display activity during only a single apparition (Chandler et al., 2018).

Asteroid (7968), now comet 133P/Elst-Pizarro, was the first active main-belt
asteroid to be discovered. While it was unclear at the time whether the
activity was sublimation driven (Boehnhardt et al., 1996, 1998) or due to a
one-time event (Toth, 2000), subsequent apparitions showing activity indicated
sublimation was the cause (Hsieh et al., 2004, 2010). This example illustrates
the importance of detecting additional activity epochs.

Asteroid (248370) 2005 QN173 is a 3.2$\pm$0.4 km diameter (Hsieh et al., 2021)
outer main-belt asteroid ($a$=3.075 au, $e$=0.226, $i$=$0\fdg 067$) that has a
5.37 yr orbit that ranges from a perihelion distance of $q$=2.374 au to an
aphelion distance of $Q$=3.761 au. The object first drew particular attention
when it was reported as active on 2021 July 9 (Fitzsimmons et al., 2021).
Subsequently, Zwicky Transient Facility (ZTF) data were used to help constrain
the activity onset to between 2020 July 10 and 2021 June 11 (Kelley et al.,
2021).

We set out to locate archival astronomical images of (248370) 2005 QN173 in
order to characterize prior activity. We made use of solar system object
thumbnails (small image cutouts like Figure 1) derived from publicly available
archival data. We previously demonstrated how our data sources, such as the
Dark Energy Camera (DECam), are well suited to discovering and characterizing
active objects (Chandler et al., 2018, 2019, 2020).

Here we report activity of (248370) 2005 QN173 on 2016 July 22 (Chandler et
al., 2021), an apparition prior to the 2021 outburst. We describe the process
by which the activity was identified and examine the implications of this
discovery.

##  2 Second Activity Epoch

In order to find an additional activity epoch for (248370) 2005 QN173, we
searched, assessed, and analyzed publicly available archival image data,
building upon the methods of Chandler et al. (2018, 2019, 2020).

###  2.1 Data Acquisition

To locate archival images of (248370) 2005 QN173, we queried our own database
of publicly available observation metadata (see Chandler et al., 2018). This
database, which updates daily, includes observing details such as sky
coordinates, exposure time, and filter selection. Additionally, we searched
Palomar Transient Factory (PTF) and ZTF data through 2021 August 31 through
online search tools (listed in Appendix A) as well as a ZTF Alert Stream
search and retrieval tool we created for this purpose. All instruments and
data sources we made use of are listed in Appendix A, and we note that some
data were found or retrieved via more than one pathway.

Table 1: (248370) 2005 QN173 Observations

Image111Label in image gallery figures. |  Obs. Date222UT observing date in year-month-day format. | Source |  N333Number of images. |  Exp. [s]444Exposure time for each image. | Filter |  $V$555Apparent $V$-band magnitude (Horizons). |  r [au]666Heliocentric distance. |  STO [$\arcdeg$]777Sun–target–observer angle. |  $\nu$ [$\arcdeg$]888True anomaly. |  %Q→q999Percentage to perihelion $q$ from aphelion $Q$. |  Act?101010Activity observed. | Archive
---|---|---|---|---|---|---|---|---|---|---|---|---
a | 2004-07-08 | MegaPrime | 3 | 180 | i | 20.7 | 2.74 | 17.6 | 287.5 | 73% | N | CADC,*
b | 2005-06-08 | SuprimeCam | 3 | 60 | W-J-VR | 21.0 | 2.42 | 23.8 | 18.6 | 96% | N | CADC,SMOKA
c | 2010-06-14 | Pan-STARRS1 | 2 | 30 | z | 20.2 | 2.42 | 21.1 | 339.2 | 96% | N | CADC
d | 2010-08-02 | Pan-STARRS1 | 1 | 45 | i | 19.0 | 2.39 | 3.9 | 353.5 | 99% | N | CADC
e | 2010-08-05 | Pan-STARRS1 | 1 | 40 | r | 18.9 | 2.39 | 2.5 | 355.4 | 99% | N | CADC
f | 2010-08-06 | Pan-STARRS1 | 1 | 43 | g | 18.8 | 2.39 | 2.0 | 354.7 | 99% | N | CADC
g | 2010-08-28 | PTF | 2 | 60 | r | 19.2 | 2.39 | 8.4 | 1.2 | 99% | N | IRSA/PTF
h | 2010-08-31 | Pan-STARRS1 | 2 | 45 | i | 19.3 | 2.39 | 9.7 | 2.1 | 99% | N | CADC
i | 2010-09-01 | PTF | 2 | 60 | r | 19.3 | 2.39 | 10.1 | 2.3 | 99% | N | IRSA/PTF
j | 2010-09-06 | Pan-STARRS1 | 2 | 43 | g | 19.5 | 2.39 | 12.2 | 3.8 | 99% | N | CADC
k | 2010-09-12 | Pan-STARRS1 | 2,2 | 43,40 | g,r | 19.6 | 2.40 | 14.5 | 5.6 | 98% | N | CADC
l | 2010-09-15 | PTF | 2 | 60 | r | 19.7 | 2.39 | 15.5 | 6.5 | 99% | N | IRSA/PTF
m | 2010-10-30 | Pan-STARRS1 | 2 | 30 | z | 20.6 | 2.41 | 23.8 | 19.6 | 97% | N | CADC
n | 2011-07-14 | Pan-STARRS1 | 1 | 40 | r | 21.8 | 2.86 | 15.8 | 84.2 | 65% | N | CADC
o | 2011-11-24 | Pan-STARRS1 | 2,2 | 43,40 | g,r | 20.6 | 3.15 | 4.0 | 109.3 | 44% | N | CADC
p | 2011-11-30 | Pan-STARRS1 | 2 | 45 | i | 20.4 | 3.16 | 1.8 | 110.3 | 43% | N | CADC
q | 2011-12-01 | Pan-STARRS1 | 2 | 43 | g | 20.4 | 3.16 | 1.4 | 110.5 | 43% | N | CADC
r | 2014-03-01 | OmegaCam | 5 | 360 | r | 21.4 | 3.53 | 7.0 | 218.2 | 17% | N | CADC,ESO
s | 2016-07-22 | DECam | 1 | 89 | z | 21.2 | 2.59 | 22.7 | 56.5 | 84% | Y | CADC,*
t | 2019-07-03 | DECam | 9 | 40 | VR | 22.6 | 3.55 | 14.6 | 216.9 | 15% | N | CADC,*
u | 2020-02-04 | DECam | 1 | 38 | r | 21.6 | 3.16 | 18.1 | 248.9 | 43% | N | CADC,*
v | 2020-02-10 | DECam | 1 | 199 | z | 21.8 | 3.15 | 18.2 | 249.9 | 44% | N | CADC,*
w | 2020-04-25 | ZTF | 1,1 | 30,30 | g,r | 20.0 | 2.99 | 4.4 | 263.3 | 55% | N | IRSA/ZTF
x | 2020-05-18 | ZTF | 1,1 | 30,30 | g,r | 19.9 | 2.93 | 4.7 | 267.7 | 60% | N | IRSA/ZTF
x | 2020-05-27 | ZTF | 1,1 | 30,30 | g,r | 20.1 | 2.91 | 8.4 | 269.5 | 61% | N | IRSA/ZTF
x | 2020-06-11 | ZTF | 1,3 | 30,30 | g,r | 20.3 | 2.88 | 13.3 | 272.5 | 63% | N | IRSA/ZTF
x | 2020-06-14 | ZTF | 1,1 | 30,30 | g,r | 20.4 | 2.87 | 14.1 | 273.1 | 64% | N | IRSA/ZTF
x | 2020-06-17 | ZTF | 2,2 | 30,30 | g,r | 20.4 | 2.87 | 14.9 | 273.8 | 64% | N | IRSA/ZTF
x | 2020-06-20 | ZTF | 2,2 | 30,30 | g,r | 20.5 | 2.86 | 15.7 | 274.4 | 65% | N | IRSA/ZTF
x | 2020-06-23 | ZTF | 2,1 | 30,30 | g,r | 20.5 | 2.85 | 16.5 | 275.0 | 65% | N | IRSA/ZTF
x | 2020-06-26 | ZTF | 4,1 | 30,30 | g,r | 20.6 | 2.85 | 17.2 | 275.6 | 65% | N | IRSA/ZTF

Note W-J-VR is a single wide-band filter. See Appendix A for image source and
archive details. * indicates the data were obtained from our local repository.
Table entries with multiple comma-separated values contain groups of exposures
taken with different filters.

We identified candidate images where (248370) 2005 QN173 was expected to be
within the field of view (FOV) based on observation times, pointing centers,
and FOV sizes and orientations, downloaded associated data, and extracted
image cutouts. We organized data by instrument and observation date and
summarize observation details in Table 1.

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---|---|---|---|---
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Figure 2: Archival images of (248370) 2005 QN173 with the best activity
detection potential (i.e., sufficient depth and observing conditions) for
(248370) 2005 QN173. For all images, north is up, east is left, the FOV is
30″$\times$30″, the antisolar (yellow -$\odot$) and antimotion (red -$v$)
directions are shown with the origin at image center. See Appendix A for
instrument and archive details. Panel (s) is from the only thumbnail in which
we could identify activity unambiguously (Figure 1). (a) 2004 July 8 MegaPrime
3$\times$180 s $i$ band. (b) 2005 June 8 SuprimeCam 3$\times$60 s W-J-VR band.
(c) 2010 June 14 PS1 2$\times$60 s $z$ band. (d) 2010 August 2 PS1 1$\times$45
s $i$ band. (e) 2010 August 5 PS1 1$\times$40 s $r$ band. (f) 2010 August 6
PS1 1$\times$43 s $g$ band. (g) 2010 August 28 PTF 2$\times$60 s $r$ band. (h)
2010 August 31 PS1 $\times$45 s $i$ band. (i) 2010 September 1 PTF 2$\times$60
s $r$ band. (j) 2010 September 6 PS1 2$\times$43 s $g$ band. (k) 2010
September 12 PS1 2$\times$40 s $r$ band + 2$\times$43 s $g$ band. (l) 2010
September 15 PTF 2$\times$60 s $r$ band. (m) 2010 October 30 PS1 2$\times$30 s
$z$ band. (n) 2011 July 14 PS1 1$\times$40 s $r$ band. (o) 2011 November 24
PS1 2$\times$40 s $r$ band + 2$\times$43 s $g$ band. (p) 2011 November 30 PS1
2$\times$45 s $i$ band. (q) 2011 December 1 PS1 2$\times$43 s $g$ band. (r)
2014 January 31 OmegaCAM 5$\times$360 s $r$ band. (s) 2016 July 22 1$\times$89
s z band. (t) 2019 July 3 DECam 9$\times$40 s VR band. (u) 2020 February 4
DECam 1$\times$38 s r band. (v) 2020 February 10 DECam 1$\times$199 s $z$
band. (w) 2020 April 25 ZTF 1$\times$30 s g band + 1$\times$30 s r band. (x)
2020 May 18, 27 + 2020 June 11, 14, 17, 20, 23, & 26 ZTF 9$\times$30 s r band
+ 12$\times$30 s g band.

We extracted eighty-one $480\times 480$ pixel thumbnail images (such as the
image shown in Figure 1) in which we could confidently identify (248370) 2005
QN173 (Table 1). We coadded images from the same instrument when observations
were close enough in time for computed tail orientation to be in close
agreement such that coaddition could enhance activity, if present. The
thumbnails with the “best activity detection potential” – meaning the images
were judged to have observing conditions (e.g., seeing) and depth (i.e.,
magnitude limit) amenable to activity detection – are shown in Figure 2. To
allow for uniform spatial comparisons and to magnify the region of interest
around (248370) 2005 QN173, all thumbnail images in Figure 2 are displayed
with 30″$\times$30″fields of view.

###  2.2 Image Assessment

We vetted each thumbnail by visually confirming (248370) 2005 QN173 was
visible. In cases where the object could not be readily identified, we
employed our pipeline to produce comparison thumbnails derived from DECam data
that showed the same region of sky, instrument, broadband filter, and exposure
time, but from epochs when the object was not in the FOV. We made use of Gaia
DR2 (Gaia Collaboration et al., 2018) and Sloan Digital Sky Survey Release 9
(SDSS DR-9) catalogs (Ahn et al., 2012) to visually validate World Coordinate
System of images within the SAOImageDS9 Vizier (Ochsenbein et al., 2000)
catalog query system.

We next identified vetted thumbnails that were suitable for coaddition by
clustering images based on instrument and date. For compatible image sets that
included multiple broadband filters, we carried out coaddition among matching
filters as well as combining all images. Finally, we visually examined the
results and flagged images with potential activity.

We found a single image with clear evidence of activity (Figure 1) in an 89 s
$z$-band exposure captured 2016 July 22 by Dustin Lang and Alistair Walker as
part of the DECam Legacy Survey (DECaLS; Dey et al., 2019). This discovery
makes (248370) 2005 QN173 the ninth recurrently active main-belt asteroid to
be identified to date. The other objects, 238P/Read, 259P/Garradd, 288P,
311P/PANSTARRS, 313P/Gibbs, 324P/La Sagra, (6478) Gault, and (7968) Elst-
Pizarro, have all demonstrated recurrent activity near perihelion, with the
exception of (6478) Gault (Chandler et al., 2019).

We measured the tail length to be about $2\farcm 14$ ($2.4\times 10^{5}$ km)
in this image but a longer tail may well have been revealed with a longer
exposure (see Hsieh et al. (2021) for 2021 apparition tail measurement).
Applying our wedge photometry technique (Section 2.3), we produced a
diagnostic plot (Figure 1) and measured a position angle on the sky of
$251\fdg 3\pm 1\fdg 4$ for the tail, in close agreement with the Horizons
computed $251\fdg 6$ antisolar and $251\fdg 7$ antimotion vectors.

###  2.3 Wedge Photometry Tail Tool

We crafted a new algorithm to (a) identify potentially active objects by
detecting likely tails, and (b) quantify alignment between an observed tail
and predicted antisolar and antimotion vectors, which are commonly associated
with tail direction. Currently, the tool is designed to analyze single tails
$<15\arcdeg$ in angular extent, though we plan to address multiple tails and
comae in the future. The technique, which we refer to as wedge photometry,
sums all pixel values in a variable-width wedge bound between an inner and
outer radius and identifies wedges containing excess flux relative to other
wedges, if present. A similar approach was used in Sonnett et al. (2011) but
we have made improvements in angular resolution and algorithmic efficiency.
Excess flux within a particular wedge may indicate the presence of a tail, and
testing tail alignment with antisolar and antimotion vectors provides
additional weight that a detected tail is real. Here we focused on quantifying
tail orientation and position angle agreement.

To optimize the process, we convert Cartesian pixel coordinates ($x$,$y$) to
polar coordinates ($r$,$\theta$) where the central thumbnail pixel is defined
as (0,0). The resulting three-dimensional array has columns $r$, $\theta$, and
$c$ (counts).

For a series of wedge sizes $\theta$ ($1\arcdeg$–$10\arcdeg$ in $1\arcdeg$
increments) we summed pixel values in annular segments spanning an angle
$\pm\theta/2$ along a radial component $r$ from an inner bound, $r_{0}=5$
pixels, to a maximum of $r_{\mathrm{max}}=50$ pixels (13″for our DECam data),
as given by

$c(\theta,\Delta\theta)=\sum_{\theta=-\Delta\theta/2}^{\theta=+\Delta\theta/2}\sum_{r=r_{0}}^{r=r_{\mathrm{max}}}c(r,\theta).$
(1)

We further optimize the procedure by selecting for the target a starting
radius $r_{0}$ outside the FWHM, and choosing a maximum radius max that allows
for a wedge length long enough to ensure that all bins have sufficient counts
to avoid necessitating resampling of any individual pixels. Thus, pixels are
assigned to wedges based solely on their precise pixel center coordinate, and
any fractional flux from a pixel that spans a wedge boundary is automatically
assigned to the wedge containing the pixel center coordinate. We then compute
the mean and standard deviation of the resulting counts for each $\theta$ to
compare with the predicted antisolar and antimotion vectors.

We produce a polar plot (Figure 1) to aid assessing relative radial flux
distribution. Most position angles have a $1\sigma$ of $\sim$200 counts. The
tail is clearly identified by our algorithm at $>7\sigma$ for several
$\Delta\theta$ wedge sizes.

##  3 Main-belt Comet Classification

Once we had identified a previous activity epoch we set out to determine if
(248370) 2005 QN173 could be an MBC.

###  3.1 Prerequisites

For (248370) 2005 QN173 to qualify as an MBC it must (1) be an active
asteroid, (2) orbit within the Main Asteroid Belt, and (3) exhibit sublimation
driven activity.

(1) To qualify as an active asteroid, a body must typically meet three
criteria (see Jewitt 2012 for discussion): (i) A coma or tail must have been
observed visually (as is the case in this work) or, potentially, through
alternate means such as spectroscopy (e.g., Küppers et al., 2014; Busarev et
al., 2018) or detecting magnetic field enhancements (e.g., Russell et al.,
1984). (ii) The semi-major axis $a$ must not be exterior to that of Jupiter
($a_{\mathrm{J}}\approx$ 5.2 au) as is the case for comets and active Centaurs
(Jewitt, 2009); (248370) 2005 QN173 has $a=$3.1 au. And (iii) the Tisserand
parameter with respect to Jupiter, $T_{\mathrm{J}}$, must be greater than 3;
this is because objects with $T_{\mathrm{J}}<3$ are canonically considered
cometary and $T_{\mathrm{J}}>3$ asteroids (Vaghi, 1973a, b).

$T_{\mathrm{J}}$ describes how an orbit is related to Jupiter by

$T_{\mathrm{J}}=\frac{a_{\mathrm{J}}}{a}+2\sqrt{\frac{a\left(1-e^{2}\right)}{a_{\mathrm{J}}}}\cos\left(i\right).$
(2)

where $e$ is the eccentricity and $i$ is the orbital inclination.
$T_{\mathrm{J}}$ for (248370) 2005 QN173 is 3.192 and thus it qualifies as
asteroidal. (248370) 2005 QN173 properties are provided in Appendix B, and are
established with this criterion.

(2) (248370) 2005 QN173 orbits between 2.4 au and 3.76 au and thus does not
cross the orbits of either Mars or Jupiter. With a semi-major axis of 3.1 au,
(248370) 2005 QN173 is an outer main-belt asteroid orbiting between the
Kirkwood gaps corresponding to the 7:8 and 2:1 mean motion resonances with
Jupiter.

(3) Recurrent activity near perihelion is diagnostic of volatile sublimation
as the most likely mechanism responsible for the observed activity (e.g.,
Hsieh et al., 2012). However, other underlying causes of recurrent activity
are known, so this point warrants further investigation.

###  3.2 Activity Mechanism

We demonstrated in Section 2 that (248370) 2005 QN173 has been active during
at least two epochs. This helps rule out activity mechanisms such as impact
events (e.g., (596) Scheila; Bodewits et al. 2011; Ishiguro et al. 2011;
Moreno et al. 2011) that are only expected to produce one-time outbursts but
which can expel dust and produce comet-like activity. Aside from temperature-
correlated volatile sublimation (which we examine further in Section 3.3)
other mechanisms for producing recurrent activity have been proposed.

Rotational destabilization causes dust to be flung from a body in a
potentially multiepisodic manner, as may be the case for (6478) Gault
(Chandler et al., 2019; Kleyna et al., 2019). Taxonomic classification can
help diagnose rotational destabilization, as with $S$-type (6478) Gault,
because activity from desiccated asteroid classes is unlikely to be
sublimation driven. As discussed in Section 3.3, the taxonomic class of
(248370) 2005 QN173 is not yet known but it is likely a C-type asteroid. An
accurate rotation period for (248370) 2005 QN173 is currently unavailable, and
as such, we can neither confirm nor rule out destabilization as a contributing
factor to the observed activity at this time.

Rubbing binaries is a hypothetical scenario whereby two merging asteroids
repeatedly collide and eject material. Proposed as a possible mechanism for
the activity of 311P/PANSTARRS (Hainaut et al., 2014), the rubbing binary
scenario has yet to be confirmed for that object (Jewitt et al., 2018) or any
other. As of this writing, there is no evidence that (248370) 2005 QN173 is a
binary asteroid, and activity spans two epochs separated by 5 yr, so we would
expect merging processes to have either finished or that the binary orbit
would have stabilized (see Jewitt et al. 2018 for additional discussion
concerning dissipation timescales). Therefore we find it unlikely that rubbing
causes the activity associated with (248370) 2005 QN173.

Geminid meteor stream parent (3200) Phaethon undergoes extreme temperature
changes ($\sim$600 K) and peaks at 800 K to 1100 K, well above the 573 K
serpentine-phyllosilicate decomposition threshold (Ohtsuka et al., 2009).
These temperatures likely induce thermal fracture (Licandro et al., 2007;
Kasuga & Jewitt, 2008) leading to mass shedding (Li & Jewitt, 2013; Hui & Li,
2017).

Two mechanisms, thermal fracture and temperature-correlated volatile
sublimation warrant further inquiry into the thermophysical properties of
(248370) 2005 QN173.

###  3.3 Temperature Estimation

Estimating temperatures experienced by (248370) 2005 QN173 aids us in
understanding direct thermal effects (e.g., thermal fracture) as well as
assessing long-term volatile survival, especially water. For these reasons, we
computed temperatures for an airless body over the course of an orbit similar
to that of (248370) 2005 QN173.

Following Hsieh et al. (2015), the energy balance equation for a gray body on
which water ice sublimation is occurring is

${F_{\odot}\over r_{h}^{2}}(1-A)=\chi\left[{\varepsilon\sigma
T_{eq}^{4}+Lf_{D}\dot{m}_{w}(T_{eq})}\right]$ (3)

where $r_{h}$ is the object’s heliocentric distance, $T_{\mathrm{eq}}$ is the
equilibrium surface temperature, $F_{\odot}=1360$ W m-2 is the solar constant,
$r_{h}$ is in au, $A=0.05$ is the assumed Bond albedo of the body, $\chi$
accounts for the distribution of solar heating over the object’s surface,
$\sigma$ is the Stefan–Boltzmann constant, and $\varepsilon=0.9$ is the
assumed effective infrared emissivity, and $L=2.83$ MJ kg-1 is the latent heat
of sublimation of water ice (which we approximate here as being independent of
temperature), $f_{D}$ represents the reduction in sublimation efficiency
caused by mantling, where $f_{D}=1$ in the absence of a mantle, and
$\dot{m}_{w}$ is the water mass-loss rate due to sublimation of surface ice.

In this equation, $\chi=1$ corresponds to a flat slab facing the Sun, known as
the subsolar approximation, and produces the maximum expected temperature for
an object, while $\chi=4$ applies to objects with fast rotation or low thermal
inertia, known as the isothermal approximation, and produces the minimum
expected temperature for an object.

Next, the sublimation rate of ice into a vacuum can be computed using

$\dot{m}_{w}=P_{v}(T)\sqrt{\mu\over 2\pi kT}$ (4)

where $\mu=2.991\cdot 10^{-26}$ kg is the mass of one water molecule, and $k$
is the Boltzmann constant, and the equivalent ice recession rate,
$\dot{\ell}_{i}$, corresponding to $\dot{m}_{w}$ is given by
$\dot{\ell}_{i}=\dot{m}_{w}/\rho$, where $\rho$ is the bulk density of the
object.

Finally, the Clausius–Clapeyron relation,

$P_{v}(T)=611\times\exp\left[{{\Delta H_{\mathrm{subl}}\over
R_{g}}\left({{1\over 273.16}-{1\over T}}\right)}\right]$ (5)

gives the vapor pressure of water, $P_{v}(T)$, in Pa, where $\Delta
H_{\mathrm{subl}}=51.06$ MJ kmol-1 is the heat of sublimation for ice to vapor
and $R_{g}=8314$ J kmol-1 K-1 is the ideal gas constant. Solving these three
equations iteratively, one can calculate the equilibrium temperature of a gray
body at a given heliocentric distance on which water ice sublimation is
occurring.

In Figure 3, we plot the object’s expected equilibrium temperature over
several orbit cycles, as computed by solving the system of equations above. We
plot temperatures computed using both $\chi=1$ and $\chi=4$ to show the full
range of possible temperatures.

---
Figure 3: (248370) 2005 QN173 heliocentric distance (top plot), observability
timeline (middle plot) and temperature (bottom plot), beginning the year of
our first archival data (2004) through 2022. Top: triangles represent positive
(filled red) and negative (unfilled blue) activity detections. Markers
indicate when the object was inbound (downward pointing triangles) or outbound
(upward pointing triangles). Table 1 lists observation details. Middle:
apparent $V$-band magnitude (solid green line) and our “observability” metric
(yellow dashed line) that represents hours during a given UT observing date
the object is above $>15\arcdeg$ elevation while the Sun is below the horizon.
Peaks in apparent magnitude coinciding with observability occur during
opposition events, and observability troughs indicate solar conjunctions when
(248370) 2005 QN173 was only above the horizon during daylight. Perihelion
(orange $q$) and aphelion (blue $Q$) events are indicated. Bottom: temperature
$T$ (K) by date for different $\chi$ values, where $\chi=1$ (top line)
represents a “flat slab” and $\chi=4$ (bottom line) an isothermal body.

Figure 3 (top) shows two parameters key to observing (248370) 2005 QN173
between 2015 and 2023: apparent $V$-band magnitude and “observability,” which
we define as the number of hours an object remains above $15\arcdeg$ elevation
during nighttime for a given UT observing date. This plot informs us of
potential observational biases or geometric effects that may bias activity
detection, such as preferential activity discovery during opposition events,
as was the case with (6478) Gault (Chandler et al., 2019).

Figure 3 (bottom) illustrates (248370) 2005 QN173’s heliocentric distance and
temperature (as computed using Equations 3-5) over time, plus dates of
observed activity and images where no visible activity was conclusively
identified. Throughout its entire orbit the surface of (248370) 2005 QN173 is
consistently warmer than 145 K, the temperature above which water ice is not
expected to survive over timescales on the order of the age of the solar
system (Schorghofer, 2008; Snodgrass et al., 2017).

However, it is possible for water ice to remain preserved over long (Gyr)
timescales on small asteroids at depths as shallow as a few centimeters to 30
cm below the surface (Schorghofer, 2008; Prialnik & Rosenberg, 2009), where
present-day activity may be triggered by meter-scale impactors that excavate
subsurface ice. We note that water ice has been detected on the surface of
main-belt asteroid (24) Themis (Campins et al., 2010; Rivkin & Emery, 2010),
but the mechanism by which that water ice is able to persist on its surface –
likely requiring continual replenishment from subsurface volatile reservoirs –
is not well understood, and furthermore may not have the same effectiveness on
kilometer-scale objects like (248370) 2005 QN173 as it does on the 200 km
diameter (24) Themis.

The surface temperature of (248370) 2005 QN173 varies at most between 145 K
and 190 K over its orbit (Figure 3), far less than the 600 K temperature
swings peaking at 800–1000 K described in Section 3.2. We consider it is
unlikely that thermal fracture is the primary cause of (248370) 2005 QN173’s
activity.

###  3.4 Nondetection of Activity

The two known epochs of activity for (248370) 2005 QN173 both occurred when
the object was interior to a heliocentric distance of 2.7 au. However,
(248370) 2005 QN173 was observed in 2005 and 2010 when the object was interior
to 2.7 au but no activity was detected. We believe the circumstances of these
epochs preclude a definitive assessment of activity.

The 2010 Pan-STARRS1 data suffer from image artifacts that are significant
enough to obscure activity that may have been present. The 2005 SuprimeCam
observations should have been well suited to detecting activity as the 8 m
Subaru telescope has a large aperture, exposure times (60 s) were sufficiently
long, the W-J-VR filter covered a broad wavelength range, and the object was
well placed in the sky in terms of airmass/elevation during the observations.
However, extinction varied significantly over the observing sequence as the
summit log for that
night111111https://smoka.nao.ac.jp/calendar/slog/2005/slog_20050608.txt
indicated that conditions were windy with cirrus clouds and the differential
image motion monitor measured significant seeing variation (roughly $0\farcs
8$ to
$>3\arcsec{}$)121212https://smoka.nao.ac.jp/calendar/subaruseeing/20050608.gif,
potentially contributing to a considerable reduction in our ability to detect
activity. All sources in the field could be matched to SDSS DR-9 stars but the
faintest stars we were able match to the SDSS DR-9 catalog were $r\approx
21.3$, very similar to the JPL Horizons computed $V$=21.0 for (248370) 2005
QN173. The Subaru Exposure Time Calculator estimates an equivalent $r$-band
exposure would deliver a signal-to-noise ratio of 66 for a source of
equivalent magnitude, but we estimate the images are at best $\sim$0.5 mag
deeper than necessary to detect the object and thus we find it unlikely that
activity would be detectable unless the object was undergoing a significant
outburst at the time.

Although we cannot definitively rule out the presence of activity in 2005 or
2010 from these observations, another possibility is that a triggering event
(e.g., impact, rotational destabilization) that started (248370) 2005 QN173’s
current activity occurred between 2005 June and 2016 July. This would explain
the object’s apparent inactivity and activity on each of those dates,
respectively.

###  3.5 Main-belt Comet Membership

Given the above reasoning, we find it most likely that the activity associated
with (248370) 2005 QN173 is sublimation driven, in which case the object is an
MBC. However, we emphasize that in order to rule out rotational
destabilization as the root cause of the observed activity, additional work is
needed. Moreover, confirmation of a third activity epoch would lend further
evidence favoring sublimation as the primary agency of activity.

##  4 Summary and Future Work

We harvested eighty-one images of (248370) 2005 QN173 (also designated 433P)
spanning thirty-one observing dates. We found clear evidence of a previous
activity epoch on 2016 July 22. We provide a catalog of archival observations
along with an image gallery. Making use of wedge photometry – a novel tail
detection and characterization tool we introduce in this Letter – we measure
tail orientation to be in close agreement with the antisolar and antimotion
vectors computed by Horizons. We showed that (248370) 2005 QN173 is a likely
member of the MBCs, a group of active asteroids orbiting within the Main
Asteroid Belt that are active due to volatile sublimation.

The current observing window for this object ends around 2021 December, and
when it returns in late 2022 it will be over 3 au from the Sun and less likely
to show activity. We did not find any images showing (248370) 2005 QN173
active at beyond 3 au, so we call on observers to make use of the present
activity apparition while it is still possible to do so. Continued monitoring
to study the evolution of the tail’s brightness, including surface brightness
measurements, can lead to better characterization of ejected dust grain sizes
and total mass loss during this apparition. Once activity subsides, time-
series observations to measure a rotation period will be especially useful for
diagnosing rotational breakup. Preliminary color measurements suggest (248370)
2005 QN173 is a C-type asteroid (Hsieh et al., 2021), but a robust taxonomic
classification would help further solidify our assessment of the underlying
activity mechanism.

##  5 Acknowledgements

The authors thank the anonymous referee whose comments greatly improved the
quality of this Letter.

We thank Dr. Mark Jesus Mendoza Magbanua (University of California San
Francisco) for his frequent and timely feedback on the project. The authors
express their gratitude to Prof. Mike Gowanlock (NAU), Dr. Annika Gustafsson
(NAU, Lowell Observatory, Southwest Research Institute), Jay Kueny (Steward
Observatory), and the Trilling Research Group (NAU), all of whom provided
invaluable insights which substantially enhanced this work. The unparalleled
support provided by Monsoon cluster administrator Christopher Coffey (NAU) and
the High Performance Computing Support team facilitated the scientific
process.

This material is based upon work supported by the National Science Foundation
Graduate Research Fellowship Program under grant No. (2018258765). Any
opinions, findings, and conclusions or recommendations expressed in this
material are those of the author(s) and do not necessarily reflect the views
of the National Science Foundation. C.O.C., H.H.H. and C.A.T. also acknowledge
support from the NASA Solar System Observations program (grant 80NSSC19K0869).

Computational analyses were run on Northern Arizona University’s Monsoon
computing cluster, funded by Arizona’s Technology and Research Initiative
Fund. This work was made possible in part through the State of Arizona
Technology and Research Initiative Program. World Coordinate System (WCS)
corrections facilitated by the Astrometry.net software suite (Lang et al.,
2010).

This research has made use of data and/or services provided by the
International Astronomical Union’s Minor Planet Center. This research has made
use of NASA’s Astrophysics Data System. This research has made use of The
Institut de Mécanique Céleste et de Calcul des Éphémérides (IMCCE) SkyBoT
Virtual Observatory tool (Berthier et al., 2006). This work made use of the
FTOOLS software package hosted by the NASA Goddard Flight Center High Energy
Astrophysics Science Archive Research Center. This research has made use of
SAOImageDS9, developed by Smithsonian Astrophysical Observatory (Joye, 2006).
This work made use of the Lowell Observatory Asteroid Orbit Database astorbDB
(Bowell et al., 1994; Moskovitz et al., 2021). This work made use of the
astropy software package (Robitaille et al., 2013).

This project used data obtained with the Dark Energy Camera (DECam), which was
constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES
Projects has been provided by the U.S. Department of Energy, the U.S. National
Science Foundation, the Ministry of Science and Education of Spain, the
Science and Technology Facilities Council of the United Kingdom, the Higher
Education Funding Council for England, the National Center for Supercomputing
Applications at the University of Illinois at Urbana-Champaign, the Kavli
Institute of Cosmological Physics at the University of Chicago, Center for
Cosmology and Astro-Particle Physics at the Ohio State University, the
Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M
University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho
de Amparo, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de
Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de
Desenvolvimento Científico e Tecnológico and the Ministério da Ciência,
Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft and the
Collaborating Institutions in the Dark Energy Survey. The Collaborating
Institutions are Argonne National Laboratory, the University of California at
Santa Cruz, the University of Cambridge, Centro de Investigaciones
Enérgeticas, Medioambientales y Tecnológicas–Madrid, the University of
Chicago, University College London, the DES-Brazil Consortium, the University
of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi
National Accelerator Laboratory, the University of Illinois at Urbana-
Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the Institut de
Física d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-
Maximilians Universität München and the associated Excellence Cluster
Universe, the University of Michigan, the National Optical Astronomy
Observatory, the University of Nottingham, the Ohio State University, the
University of Pennsylvania, the University of Portsmouth, SLAC National
Accelerator Laboratory, Stanford University, the University of Sussex, and
Texas A&M University.

Based on observations at Cerro Tololo Inter-American Observatory, National
Optical Astronomy Observatory (NOAO Prop. ID 2016A-0190, PI: Dey), which is
operated by the Association of Universities for Research in Astronomy (AURA)
under a cooperative agreement with the National Science Foundation. This
research has made use of the NASA/IPAC Infrared Science Archive, which is
funded by the National Aeronautics and Space Administration and operated by
the California Institute of Technology.

The Legacy Surveys consist of three individual and complementary projects: the
Dark Energy Camera Legacy Survey (DECaLS; Proposal ID #2014B-0404; PIs: David
Schlegel and Arjun Dey), the Beijing-Arizona Sky Survey (BASS; NOAO Prop. ID
#2015A-0801; PIs: Zhou Xu and Xiaohui Fan), and the Mayall z-band Legacy
Survey (MzLS; Prop. ID #2016A-0453; PI: Arjun Dey). DECaLS, BASS and MzLS
together include data obtained, respectively, at the Blanco telescope, Cerro
Tololo Inter-American Observatory, NSF’s NOIRLab; the Bok telescope, Steward
Observatory, University of Arizona; and the Mayall telescope, Kitt Peak
National Observatory, NOIRLab. The Legacy Surveys project is honored to be
permitted to conduct astronomical research on Iolkam Du’ag (Kitt Peak), a
mountain with particular significance to the Tohono O’odham Nation. BASS is a
key project of the Telescope Access Program (TAP), which has been funded by
the National Astronomical Observatories of China, the Chinese Academy of
Sciences (the Strategic Priority Research Program “The Emergence of
Cosmological Structures” Grant # XDB09000000), and the Special Fund for
Astronomy from the Ministry of Finance. The BASS is also supported by the
External Cooperation Program of Chinese Academy of Sciences (Grant #
114A11KYSB20160057), and Chinese National Natural Science Foundation (Grant #
11433005). The Legacy Survey team makes use of data products from the Near-
Earth Object Wide-field Infrared Survey Explorer (NEOWISE), which is a project
of the Jet Propulsion Laboratory/California Institute of Technology. NEOWISE
is funded by the National Aeronautics and Space Administration. The Legacy
Surveys imaging of the DESI footprint is supported by the Director, Office of
Science, Office of High Energy Physics of the U.S. Department of Energy under
Contract No. DE-AC02-05CH1123, by the National Energy Research Scientific
Computing Center, a DOE Office of Science User Facility under the same
contract; and by the U.S. National Science Foundation, Division of
Astronomical Sciences under Contract No. AST-0950945 to NOAO.

Based in part on data collected at Subaru Telescope and obtained from the
SMOKA, which is operated by the Astronomy Data Center, National Astronomical
Observatory of Japan (Baba et al., 2002).

##  Appendix A Equipment and Archives

Table 2: Equipment and Archives

Instrument | Telescope | Pixel Scale | Location | NOIR | ESO | IRSA | SMOKA | SSOIS | STScI
---|---|---|---|---|---|---|---|---|---
|  | [″/pix] |  |  |  |  |  |  |
DECam | 4 m Blanco | 0.263 | Cerro Tololo, Chile | S,R |  |  |  | S |
OmegaCAM | 2.6 m VLT Survey | 0.214 | Cerro Paranal, Chile |  | R |  |  | S |
GigaPixel1 | 1.8 m Pan-STARRS1 | 0.258 | Haleakalā, Hawaii |  |  |  |  | S | R
MegaPrime | 3.6 m CFHT | 0.185 | Mauna Kea, Hawaii |  |  |  |  | S,R |
PTF/CFHT 12K | 48” Samuel Oschin | 1.010 | Mt. Palomar, California |  |  | S,R |  |  |
SuprimeCam | 8.2 m Subaru | 0.200 | Mauna Kea, Hawaii |  |  |  | R | S |
ZTF Camera | 48” Samuel Oschin | 1.012 | Mt. Palomar, California |  |  | S,R |  |  |

R indicates repository for data retrieval. S indicates search capability.
NOIR: NSF National Optical Infrared Labs AstroArchive
(https://astroarchive.noirlab.edu).
ESO: European Space Organization Archive (https://archive.eso.org).
IRSA: NASA/CalTech Infrared Science Archive (https://irsa.ipac.caltech.edu).
SMOKA: NAOJ Subaru-Mitaka-Okayama-Kiso Archive Science Archive
(https://smoka.nao.ac.jp).
SSOIS: CADC Solar System Object Image Search (https://www.cadc-ccda.hia-
iha.nrc-cnrc.gc.ca/en/ssois/).
STScI: Space Telescope Science Institute (https://www.stsci.edu/).

Table 2 lists the instruments and telescopes used in this work, along with
their respective pixel scales, locations, and data archives.

##  Appendix B (248370) 2005 QN173 Data

We provide current information regarding (248370) 2005 QN173 below.

Table 3: (248370) 2005 QN173 Properties Parameter | Value | Source
---|---|---
Discovery Date | 2005 August 29 | Minor Planet Center
Discovery Observers | Near-Earth Asteroid Tracking (NEAT) | Minor Planet Center
Discovery Observatory | Palomar | Minor Planet Center
Activity Discovery Date | 2021 July 7 | CBET 4995
Activity Discoverer(s) | A. Fitzsimmons / ATLAS | CBET 4995 (Fitzsimmons et al., 2021)
Orbit Type | Outer Main-belt | IMCCE, AstOrb
Taxonomic Class | C-type (unconfirmed) | Hsieh et al. (2021)
Diameter |  $D=3.6$ km; 3.4$\pm$0.4 km | Horizons, Harris & Lagerros (2002) ; Hsieh et al. (2021)
Absolute $V$-band Magnitude | $H=16.02$ | Horizons
Geometric Albedo | 0.054 | Horizons, Mainzer et al. (2019)
Rotation Period | unknown |
Orbital Period |  $P=5.37$ yr | Horizons
Semimajor Axis |  $a=3.075$ au | Horizons
Eccentricity | $e=0.226$ | Horizons
Inclination | $i=0.067\arcdeg$ | Horizons
Longitude of Ascending Node | $\Omega=174.28$ | Minor Planet Center
Mean Anomaly | $M=8.79\arcdeg$ | Minor Planet Center
Argument of Perihelion | $\omega=146.09\arcdeg$ | Horizons
Perihelion Distance |  $q=2.374$ au | Horizons
Aphelion Distance |  $Q=3.761$ au | Horizons
Tisserand Parameter w.r.t. Jupiter | $T_{J}=3.192$ | AstOrb

## References

  * Ahn et al. (2012) Ahn, C. P., Alexandroff, R., Allende Prieto, C., et al. 2012, ApJS, 203, 21, doi: 10.1088/0067-0049/203/2/21
  * Agarwal et al. (2017) Agarwal, J., Jewitt, D., Mutchler, M., Weaver, H., & Larson, S. 2017, Natur, 549, 357, doi: 10.1038/nature23892
  * Baba et al. (2002) Baba, H., Yasuda, N., Ichikawa, S.-I., et al. 2002, Astronomical Data Analysis Software and Systems XI, ASP Conference Proceedings, 281, 298 https://ui.adsabs.harvard.edu/abs/2002ASPC..281..298B
  * Berthier et al. (2006) Berthier, J., Vachier, F., Thuillot, W., et al. 2006, SkyBoT, a New VO Service to Identify Solar System Objects https://ui.adsabs.harvard.edu/abs/2006ASPC..351..367B/abstract
  * Bodewits et al. (2011) Bodewits, D., Kelley, M. S., Li, J. Y., et al. 2011, ApJL, 733, L3, doi: Artn L3 10.1088/2041-8205/733/1/L3
  * Boehnhardt et al. (1996) Boehnhardt, H., Schulz, R., Tozzi, G. P., et al. 1996, IAU Circ., 6495 https://ui.adsabs.harvard.edu/abs/1996IAUC.6495....2B
  * Boehnhardt et al. (1998) Boehnhardt, H., Sekanina, Z., Fiedler, A., et al. 1998, HiA, 11A, 233 https://ui.adsabs.harvard.edu/abs/1998HiA....11..233B/abstract
  * Bowell et al. (1994) Bowell, E., Muinonen, K., & Wasserman, L. H. 1994, Asteroids, Comets, Meteors 1993, 160, 477 https://ui.adsabs.harvard.edu/abs/1994IAUS..160..477B/abstract
  * Busarev et al. (2018) Busarev, V. V., Makalkin, A. B., Vilas, F., Barabanov, S. I., & Scherbina, M. P. 2018, Icar, 304, 83, doi: 10.1016/j.icarus.2017.06.032
  * Campins et al. (2010) Campins, H., Hargrove, K., Pinilla-Alonso, N., et al. 2010, Natur, 464, 1320, doi: 10.1038/nature09029
  * Chandler et al. (2018) Chandler, C. O., Curtis, A. M., Mommert, M., Sheppard, S. S., & Trujillo, C. A. 2018, PASP, 130, 114502, doi: 10.1088/1538-3873/aad03d
  * Chandler et al. (2019) Chandler, C. O., Kueny, J., Gustafsson, A., et al. 2019, ApJL, 877, L12, doi: 10/gg3qw6
  * Chandler et al. (2020) Chandler, C. O., Kueny, J. K., Trujillo, C. A., Trilling, D. E., & Oldroyd, W. J. 2020, ApJL, 892, L38, doi: 10/gg36xz
  * Chandler et al. (2021) Chandler, C. O., Trujillo, C. A., & Hsieh, H. H. 2021, Central Bureau Electronic Telegrams, #5005, http://www.cbat.eps.harvard.edu/iau/cbet/005000/CBET005005.txt
  * Dey et al. (2019) Dey, A., Schlegel, D. J., Lang, D., et al. 2019, AJ, 157, 168, doi: 10/gmg6sw
  * Fitzsimmons et al. (2021) Fitzsimmons, A., Erasmus, N., Thirouin, A., Hsieh, H. H., & Green, D. 2021, Central Bureau Electronic Telegrams, #4995 http://www.cbat.eps.harvard.edu/iau/cbet/004900/CBET004995.txt
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1, doi: 10.1051/0004-6361/201833051
  * Giorgini et al. (1996) Giorgini, J. D., Yeomans, D. K., Chamberlin, A. B., et al. 1996, in AAS/Division for Planetary Sciences Meeting Abstracts #28, AAS/DPS Meeting Abstracts, Bulletin of the American Astronomical Society, Vol. 28, p.1158 https://ui.adsabs.harvard.edu/abs/1996DPS....28.2504G/abstract
  * Hainaut et al. (2014) Hainaut, O. R., Boehnhardt, H., Snodgrass, C., et al. 2014, A&A, 563, A75, doi: 10.1051/0004-6361/201322864
  * Harris & Lagerros (2002) Harris, A. W., & Lagerros, J. S. V. 2002, Asteroids III, W. F. Bottke Jr., A. Cellino, P. Paolicchi, and R. P. Binzel (eds), University of Arizona Press, Tucson, p.205-218 https://ui.adsabs.harvard.edu/abs/2002aste.book..205H/abstract
  * Hsieh & Jewitt (2006a) Hsieh, H. H., & Jewitt, D. 2006a, Asteroids, Comets, Meteors, Proceedings of the 229th Symposium of the International Astronomical Union, D. Lazzaro, S. Ferraz-Mello & J.A. Fernández (Cambridge, Massachusetts: Cambridge University Press) pp.425-437, doi: 10.1017/S1743921305006897
  * Hsieh & Jewitt (2006b) —. 2006b, Science, 312, 561, doi: 10.1126/science.1125150
  * Hsieh et al. (2010) Hsieh, H. H., Jewitt, D., Lacerda, P., Lowry, S. C., & Snodgrass, C. 2010, MNRAS, 403, 363, doi: 10.1111/j.1365-2966.2009.16120.x
  * Hsieh et al. (2004) Hsieh, H. H., Jewitt, D. C., & Fernández, Y. R. 2004, AJ, 127, 2997, doi: 10.1086/383208
  * Hsieh et al. (2012) Hsieh, H. H., Yang, B., & Haghighipour, N. 2012, ApJ, 744, 9, doi: 10.1088/0004-637X/744/1/9
  * Hsieh et al. (2015) Hsieh, H. H., Denneau, L., Wainscoat, R. J., et al. 2015, Icar, 248, 289, doi: 10.1016/j.icarus.2014.10.031
  * Hsieh et al. (2018) Hsieh, H. H., Ishiguro, M., Kim, Y., et al. 2018, AJ, 156, 223, doi: 10.3847/1538-3881/aae528
  * Hsieh et al. (2021) Hsieh, H. H., Chandler, C. O., Denneau, L., et al. 2021, arXiv:2109.14822
  * Hui & Li (2017) Hui, M. T., & Li, J. 2017, AJ, 153, 23, doi: 10.3847/1538-3881/153/1/23
  * Ishiguro et al. (2011) Ishiguro, M., Hanayama, H., Hasegawa, S., et al. 2011, ApJL, 740, L11, doi: 10.1088/2041-8205/740/1/L11
  * Jewitt (2009) Jewitt, D. 2009, AJ, 137, 4296, doi: 10.1088/0004-6256/137/5/4296
  * Jewitt (2012) —. 2012, AJ, 143, 66, doi: 10.1088/0004-6256/143/3/66
  * Jewitt et al. (2018) Jewitt, D., Weaver, H., Mutchler, M., et al. 2018, AJ, 155, 231, doi: 10.3847/1538-3881/aabdee
  * Joye (2006) Joye, W. A. 2006, Astronomical Data Analysis Software and Systems XV, ASP Conference Series, Carlos Gabriel, Christophe Arviset, Daniel Ponz, and Enrique Solano (San Francisco, California: Astronomical Society of the Pacific), p.574 https://ui.adsabs.harvard.edu/abs/2006ASPC..351..574J/abstract
  * Kasuga & Jewitt (2008) Kasuga, T., & Jewitt, D. 2008, AJ, 136, 881, doi: 10.1088/0004-6256/136/2/881
  * Kelley et al. (2021) Kelley, M. S. P., Bolin, B. T., Buzzi, L., et al. 2021, Central Bureau Electronic Telegrams, #4998 http://www.cbat.eps.harvard.edu/iau/cbet/004900/CBET004998.txt
  * Kleyna et al. (2019) Kleyna, J. T., Hainaut, O. R., Meech, K. J., et al. 2019, ApJL, 874, L20, doi: 10.3847/2041-8213/ab0f40
  * Küppers et al. (2014) Küppers, M., O’Rourke, L., Bockelée-Morvan, D., et al. 2014, Nature, 505, 525. doi:10.1038/nature12918
  * Lang et al. (2010) Lang, D., Hogg, D. W., Mierle, K., Blanton, M., & Roweis, S. 2010, AJ, 139, 1782, doi: 10.1088/0004-6256/139/5/1782
  * Li & Jewitt (2013) Li, J., & Jewitt, D. 2013, AJ, 145, 154, doi: 10/gg28ch
  * Licandro et al. (2007) Licandro, J., Campins, H., Mothe-Diniz, T., Pinilla-Alonso, N., & de Leon, J. 2007, A&A, 461, 751, doi: 10/d5txvm
  * Mainzer et al. (2019) Mainzer, A. K., Bauer, J. M., Cutri, R. M., et al. 2019, NASA Planetary Data System. doi:10.26033/18S3-2Z54
  * Moreno et al. (2011) Moreno, F., Licandro, J., Ortiz, J. L., et al. 2011, ApJ, 738, 130, doi: 10/dnk4jg
  * Moskovitz et al. (2021) Moskovitz, N., Burt, B., Schottland, R., et al. 2021, , meeting #53, id. 101.04, Bulletin of the American Astronomical Society, Vol. 53, No. 7 e-id 2021n7i101p04 https://ui.adsabs.harvard.edu/abs/2021DPS....5310104M/abstract
  * Ohtsuka et al. (2009) Ohtsuka, K., Nakato, A., Nakamura, T., et al. 2009, PASJ, 61, 1375, doi: 10/ggw3dx
  * Ochsenbein et al. (2000) Ochsenbein, F., Bauer, P., & Marcout, J. 2000, A&AS, 143, 23, doi: 10.1051/aas:2000169
  * Prialnik & Rosenberg (2009) Prialnik, D., & Rosenberg, E. D. 2009, MNRASL, 399, L79, doi: 10/cnz3rm
  * Rivkin & Emery (2010) Rivkin, A. S., & Emery, J. P. 2010, Natur, 464, 1322, doi: 10/d8j7cb
  * Robitaille et al. (2013) Robitaille, T. P., Tollerud, E. J., Greenfield, P., et al. 2013, A&A, 558, A33, doi: 10/gfvntd
  * Russell et al. (1984) Russell, C. T., Aroian, R., Arghavani, M., et al. 1984, Science, 226, 43. doi: :10.1126/science.226.4670.43
  * Schorghofer (2008) Schorghofer, N. 2008, ApJ, 682, 697, doi: 10/br2vgb
  * Snodgrass et al. (2017) Snodgrass, C., Agarwal, J., Combi, M., et al. 2017, A&ARv, 25, 5, doi: 10/ggw3ff
  * Sonnett et al. (2011) Sonnett, S., Kleyna, J., Jedicke, R., & Masiero, J. 2011, Icar, 215, 534, doi: 10/d3vp56
  * Toth (2000) Toth, I. 2000, A&A, 360, 375 https://ui.adsabs.harvard.edu/abs/2000A%26A...360..375T/abstract
  * Vaghi (1973a) Vaghi, S. 1973, A&A, 24, 41 https://ui.adsabs.harvard.edu/abs/1973A%26A....24..107V/abstract
  * Vaghi (1973b) Vaghi, S. 1973, A&A, 29, 85 https://ui.adsabs.harvard.edu/abs/1973A%26A....29...85V/abstract