# Neural Representations of Dynamic Visual Stimuli

Jacob Yeung
Carnegie Mellon University
<EMAIL_ADDRESS>
Andrew F. Luo
Carnegie Mellon University
<EMAIL_ADDRESS>
Gabriel Sarch
Carnegie Mellon University
<EMAIL_ADDRESS>
Margaret M. Henderson
Carnegie Mellon University
<EMAIL_ADDRESS>
Deva Ramanan
Carnegie Mellon University
<EMAIL_ADDRESS>
Michael J. Tarr
Carnegie Mellon University
<EMAIL_ADDRESS>
###### Abstract

Humans experience the world through constantly changing visual stimuli, where
scenes can shift and move, change in appearance, and vary in distance. The
dynamic nature of visual perception is a fundamental aspect of our daily
lives, yet the large majority of research on object and scene processing,
particularly using fMRI, has focused on static stimuli. While studies of
static image perception are attractive due to their computational simplicity,
they impose a strong non-naturalistic constraint on our investigation of human
vision. In contrast, dynamic visual stimuli offer a more ecologically-valid
approach but present new challenges due to the interplay between spatial and
temporal information, making it difficult to disentangle the representations
of stable image features and motion. To overcome this limitation – given
dynamic inputs, we explicitly decouple the modeling of static image
representations and motion representations in the human brain. Three results
demonstrate the feasibility of this approach. First, we show that visual
motion information as optical flow can be predicted (or decoded) from brain
activity as measured by fMRI. Second, we show that this predicted motion can
be used to realistically animate static images using a motion-conditioned
video diffusion model (where the motion is driven by fMRI brain activity).
Third, we show prediction in the reverse direction: existing video encoders
can be fine-tuned to predict fMRI brain activity from video imagery, and can
do so more effectively than image encoders. This foundational work offers a
novel, extensible framework for interpreting how the human brain processes
dynamic visual information.

##  1 Introduction

From a car driving down the street to waves crashing against the shore, our
daily lives are filled with visual stimuli that are constantly in motion. The
dynamic and spatiotemporally rich nature of visual perception is a cornerstone
of our daily experience, and the human visual system has evolved to extract
meaningful patterns from the dynamics of the visual environment. Yet, dynamics
have often been omitted in the study of the neural basis of high-level visual
perception, with static images being the primary focus of many studies. Such
inputs only capture a snapshot of the visual world, omitting the rich temporal
information that is inherent in our everyday experiences. This omission is
largely due to the relative computational simplicity of static images, which,
while leading to significant advances in our understanding of the neural
representations of visual features, has come at the cost of neglecting the
dynamic aspects of visual perception. For example, a video of a person walking
affords not only information about the visual features of the walker, but also
about motion patterns, context, and relationships between the different
elements in the scene (e.g., sudden increase in gait implies urgency). This
interplay between spatial and temporal information may be impossible to
capture from static images. Consequently, the neural responses evoked by
dynamic visual stimuli are likely to differ from those evoked by static
images, and understanding these differences is a significant challenge in
developing a complete theory of visual perception.

In this paper, we propose a novel framework for analyzing dynamic visual
stimuli, which explicitly decouples the modeling of static image
representations and motion representations in the human brain. By doing so, we
can provide a framework for studies that will enable a deeper understanding of
how the brain processes dynamic visual stimuli. In particular, while some
scene semantics are available from static images, dynamic visual perception is
important to understanding ecologically critical domains such as social
interaction and action representation. In the former domain, social roles are
are often inferred through the relative physical motions of different actors
[1] and in the latter domain, different actions often appear the same in
static images, for example, opening versus closing a door, or standing up
versus sitting down. For both, adding motion removes ambiguity.

Contributions. Our contributions are as follows. First, we demonstrate that
visual motion information in the form of optical flow can be predicted (or
decoded) from brain activity as measured by fMRI. Second, we show that this
predicted motion can be used to realistically animate static images using a
motion-conditioned video diffusion model (where the motion is driven by fMRI
brain activity). We demonstrate that brain activity can produce more reliable
animations than image-conditioned video diffusion models trained on massively-
large datasets. Finally, we show prediction in the reverse direction: recent
video encoders (such as VideoMAE and VC-1 [2, 3]) can more effectively predict
fMRI brain activity from video imagery as compared to image encoders. Overall
these results demonstrate the effectiveness of our approach as a novel,
extensible framework for interpreting how the human brain processes dynamic
visual information.

Figure 1: Motion Prediction & Initial Frame Animation. We predict future
optical flow fields using fMRI brain activity and the initial frame. We
combine our predicted optical flow with a motion-conditioned video prior,
DragNUWA, to animate the initial frame.

##  2 Related Work

#### Image decoding from fMRI

Reconstructing visual images from human brain activity, such as that measured
by functional magnetic resonance imaging (fMRI), has significantly advanced
through the use of deep learning models trained on extensive datasets of
natural images [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. Recently, the
number of approaches that integrate various aspects of visual experiences to
reconstruct visual perceptions has increased rapidly [17, 18, 19, 20, 21, 22,
23, 24, 25, 26, 27, 28]. This progress is largey due to the availability of
large, publicly accessible fMRI datasets with well-annotated stimuli, such as
BOLD5000 [29] and the Natural Scenes Dataset (NSD) [30], along with multimodal
deep generative models that have been pre-trained on very large datasets, such
as Stable Diffusion [31].

#### Video Decoding from fMRI

While there has been extensive decoding work on image reconstruction from
fMRI, there has been much less work on video reconstruction. The most notable
example of the latter is perhaps MindVideo [19], which performs pretraining to
align temporal semantics from fMRI and simultaneously generate frames across
time. Notably, our approach explicitly disentangles the representations of
motion information (represented as optical flow) from static images in fMRI
signals. This allows us to differentiate our present work from previous work
by enabling interpretability. Specifically, we isolate and focus on decoding
motion (as optical flow) from fMRI signals, as opposed to more difficult to
interpret mixture of static image features and motion. This disentanglement
allows us to learn an explicit representation of motion which can be directly
compared to groundtruth and be more directly related to spatially localized
neural mechanisms, as opposed to an entangled mixture of static image and
dynamic features.

##  3 Methods

Figure 2: Motion decoding & video generation. (a) Our model takes in neural
data and image features, from DINOv2, extracted from the initial frame to
predict consecutive future dense optical flow fields. We then mask out salient
objects, using FlowSAM, to obtain the masked object flow. Snowflakes are
frozen models. Flames are actively trained. (b) We can realistically animate
the initial frame using our predicted motion and a motion-conditioned video
diffusion model, DragNUWA.

In order to understand how the brain processes dynamic visual stimuli, we
focus on three directions. In the first, we examine the motion representation
contained in the brain by decoding dense optical flow conditioned on the
initial frame. In the second, we visualize the predicted motion by
reconstructing the observed dynamic visual stimuli by leveraging a motion
conditioned image diffusion model (DragNUWA). Finally, we examine which visual
features, (static vs dynamic; semantic vs visual similarity) best explain
brain activity on a voxel-wise level.

###  3.1 Motion Prediction

Our primary objective is to extract the information relevant to visual motion
in order to predict the optical flow in videos observed by subjects. To
enhance interpretability, we’ve architecturally separated static image
features from dynamic features. By conditioning the model on the initial frame
alongside neural data, we enable our model to focus on extracting dynamic
visual information. This approach improves interpretability compared to models
like MindVideo, which simultaneously predict both dynamic and static features.
In contrast, our approach disentangles the specific contributions of dynamic
components.

At a given fMRI scan at index $i$ we have fMRI voxels $B_{i}\in\mathbb{R}^{n}$
and corresponding video frames $\mathcal{I}_{i}\in\mathbb{R}^{T\times H\times
W\times 3}$. We obtain optical flow fields $O_{i}\in\mathbb{R}^{(T-1)\times
H\times W\times 2}$ from RAFT [32], which consist of $(T-1)\times H\times W$
optical flow vectors in $\mathbb{R}^{2}$. Prior work [33] has found that
reformulating optical flow prediction as classification improves performance.
We take a similar approach and quantize the optical flow vectors into a
codebook of $k$ clusters using k-means. We obtain image features with
pretrained vision model $G$. More concretely, we learn a function $M_{\theta}$
that classifies the fMRI voxels $B_{i}$ and image features of the
corresponding initial frame $G(\mathcal{I}_{i,1})$ to the quantized future
predicted optical flows fields:
$M_{\theta}([B_{i},\mathcal{I}_{i,1}])\rightarrow O_{i}$

In order to focus our evaluation on salient objects in a scene, we apply
masking using FlowSAM [34] to track and identify salient objects. Consistent
with claims in their paper, we found this method was effective in identifying
salient objects.

Visualizing the Predicted Motion. We can visualize the predicted motion by
passing in the predicted optical flow field and the initial frame to a
pretrained motion-conditioned video diffusion model, DragNUWA [35]. This
allows us to generate the dynamic vision stimuli (observed by the subject) or
(driving the neural response).

###  3.2 Visual Stimuli-To-Brain Encoding.

Here we describe a complementary approach to understanding dynamic visual
stimuli processing in the brain. We consider models trained on different
tasks:

  1. 1.

Static Image: These models are trained on static visual stimuli without
guidance from dynamics. The features extracted can identify brain voxels that
are semantically and spatially tuned.

    1. (a)

Supervised: ResNet-50 is trained on ImageNet to categorize images into
semantic classes [36].

    2. (b)

Self-supervised: DINOv1 and DINOv2 are vision transformer-based models trained
to learn similar representations for visually similar patches of images
without supervision on semantic similarity [37, 38].

    3. (c)

Semantically-supervised: CLIP (ViT-B-32) and CLIP ConvNeXt are trained to
learn align semantics and images. CLIP uses a visual transformer architecture
and CLIP ConvNeXt uses a convolutional backbone, sharing inductive biases with
ResNet-50 but trained with a different objective. CLIP AF and CLIP ConvNeXt AF
consist of CLIP and CLIP ConvNeXt features averaged over frames spanning the
video [39, 40].

  2. 2.

Video: These models are trained on dynamic visual stimuli. The features
extracted can identify brain voxels that are spatially and dynamically tuned.

    1. (a)

Self-supervised: VideoMAE, VideoMAE Large, Hiera Base Plus, and Hiera Huge are
vision transformer-based architectures trained on Kinetics 400 with a masked
autoencoder loss. The encoder learns embeddings used for downstream video
tasks like action recognition [2, 41].

    2. (b)

Semantically-supervised: X-CLIP is a CLIP model fine-tuned with cross-frame
attention to learn temporal relations [42].

  3. 3.

Embodied AI: These models are trained to align representations of single
frames across time for embodied AI visuomotor manipulation. The features
extracted can identify brain voxels tuned to action representation.

    1. (a)

Self-supervised: VIP is a ResNet-50 based architecture trained on the large-
scale human egocentric video dataset Ego4D. VC-1 is a vision transformer-based
architecture trained on seven human egocentric video datasets, including
Ego4D. For both models, we also test an encoder trained on features averaged
over frames spanning the video (VIP AF and VC-1 AF [43, 3]).

    2. (b)

Semantically-supervised: R3M is a ResNet-50 based architecture trained on
Ego4D to align frames that are close in time and semantically similar [44].

We train ridge regression models on visual stimuli features from different
vision encoding models to predict fMRI voxel-wise responses.

##  4 Experiments

In this section, we describe the specific experiments we use to explore
dynamic visual representations in the human brain. In 4.1, we describe the
dataset and preprocessing used. In 4.2 we explore motion decoding
(reconstruction) conditioned on initial image and brain information, and
augment quantitative analysis with visualizations derived from a motion-
conditioned diffusion model. Finally in 4.3 , we explore the performance of
different visual backbones in predicting brain activations.

###  4.1 Dataset

We utilize the Dynamic Natural Vision dataset [45], a public fMRI dataset
composed of brain responses from 3 participants viewing diverse naturalistic
video clips. The dataset contains 11.5 hours of fMRI data, with the 3 subjects
viewing the same videos. The fMRI data was recorded using a 3T MRI system with
a 2 second TR and the videos were presented at 30 FPS. 18 8-minute videos were
seen twice and 5 8-minute videos were seen 10 times, including the train and
test sets which have no overlapping videos. We use the same train/test split
described in [45]. The fMRI data is preprocessed and aligned with presented
stimuli using the pipeline from the Human Connectome Project. We further
normalized the fMRI activations so that each voxel’s response was zero-mean
and unit variance on a session basis. Then we average the response across
repeated viewings of the same visual stimuli.

In practice, we temporally downsample the flows to $c=3$ frames, selected in
equal intervals over the corresponding 2 second fMRI brain scan, and aim to
predict the $c$ quantized consecutive optical flow fields. We also spatially
downsample the flow to a resolution of $32\times 32$ and quantize the flows
into 40 clusters. We extract image features from the first frame using DINOv2.
During test time, we take a weighted-sum over all the classes per pixel,
following [33]. We train the model using cross entropy loss. We train all
models on a single Nvidia Titan RTX with 24GB GPU RAM and 48GB CPU RAM for up
to 12 hours. We illustrate our model’s pipeline in Figure 2.

fMRI captures the blood oxygen level dependent (BOLD) signal, which peaks
approximately 4 seconds after stimulus presentation and slowly decays after,
due to nature of the hemodynamic response. During preprocessing, the fMRI data
is shfited to temporally align the peak of the response to the onset of its
corresponding visual stimuli presentation. However, due to the long time scale
of the fMRI response, fMRI scans 4 seconds or 2 TRs prior and after the
current TR may have information shared with the current TR. In order to
leverage all relevant neural responses, when predicting the motion in the
video presented at TR=$i$, we concatenate fMRI data from TRs
$[i-2,i-1,i,i+1,i+2]$. We generate the video frames conditioned on the
predicted motion using DragNUWA [35].

###  4.2 Motion Decoding

(a) Direction cosine similarity.

(b) End Point Error.

Figure 3: Quantitative motion decoding evaluation. We find that models trained
with neural data statistically significantly better at predicting optical flow
than the model trained without neural data. (a) We average the cosine
similarity between the predicted and ground truth masked optical flow vectors.
Higher values are better. Paired t-test results between models trained on
neural data and the model trained without neural data: Subject 1 p-value:
7.340e-15; Subject 2 p-value: 5.951e-09; Subject 3 p-value: 1.530e-09. (b) We
average the end point error over the predicted and ground truth masked optical
flow vectors. Lower values are better. Paired t-test results: Subject 1
p-value: 2.429e-13; Subject 2 p-value: 1.491e-14; Subject 3 p-value:
1.280e-10.

#### Quantitative Flow Evaluation.

First we report evaluations of the decoded optical flow vectors on both
direction and end point error on the test set. We quantitatively compare the
models trained on the 3 subjects against a baseline of the motion decoder that
does not use neural data and only image features from DINOv2 in Figure 3.
Since this baseline model is not conditioned on neural data, the model learns
to regress plausible flows which do not necessarily align with the true flow.
Indeed, we observe that the models trained on neural data perform
significantly better on both end point error ([$1.72,1.72,1.76$] vs $2.00$,
$p\ll 0.001$ for the three models trained on neural data) and cosine
similarity ([$0.174,0.0854,0.1103$] vs $-0.133$, $p\ll 0.001)$. In addition,
across the testing dataset, we find that models trained on neural data predict
directions that are positively aligned with the true flow directions. In
contrast, the model trained without neural data predicts flow directions that
are actually anti-aligned with the true flow directions.

Figure 4: Side-by-side comparison of motion predicted & video reconstructions
with and without neural data. We find that motion predicted using brain data
and a static reference image is qualitatively both plausible and aligned with
the original video, compared to motion predicted from only the reference
image. Motion predicted from purely image features is plausible but not
aligned with the original video. In this case, the model is hallucinating
flows. (a) We show an example where there are multiple plausible actions. (b)
We show an example where camera motion overrides the plausible motion. (c) We
show an example where there is ambiguity of stationary objects.

#### Reasoning With and Without fMRI.

Here we present examples and explain why the models trained on neural data
outperform the model trained without neural data (Figure 4).

First, there exists ambiguity of action given static images - a frame may
contain multiple possible actions. For instance, in Figure 4a we show an eagle
flying. Given the first frame, the eagle could be plausibly either flapping
its wings or gliding. The model trained on neural data is able to identify
that the eagle is gliding. However, the model trained without neural data
incorrectly predicts that the eagle is flapping its wings. Second, even if the
action is not ambiguous, there exists camera motion in the videos which can
change the direction of the flow fields. For example, in Figure 4b we show a
space shuttle flying into the sky. In this case, with no camera motion the
direction of motion is clearly upwards and to the right, which the model
trained without neural data correctly predicts. However, because the video is
centered on the space shuttle with camera motion, the exhaust from the space
shuttle appears to be going downwards and to the left. This causes the optical
flow vectors to point downwards and to the left. Again, the model trained with
neural data is able to correctly predict the motion of the object. Third,
there exists ambiguity of direction of motion in static images of stationary
objects. For instance, if the first frame contains just a stationary portion
of the Eiffel Tower, what movement should be predicted? One could choose to
predict no motion, or arbitrarily predict a direction of camera motion.
Indeed, we see in Figure 4c that the trained model without neural data chooses
an arbitrary camera motion pointing leftwards. However, the model trained with
neural data correctly predicts the true direction which is camera panning
downwards.

The results derived from these scenarios indicate that the neural data
contains information about the correct movement which cannot be derived from
just image features.

Figure 5: Static Image Animation Results. We show optical flow predicted from
fMRI brain activity compared against the ground truth flow. In addition, we
show results on animating the initial frame by combining the brain conditioned
motion prediction with DragNUWA.

We show additional motion decoding results along with the video reconstruction
from DragNUWA (Figure 5). We find that the motion we predict from the fMRI
brain activity is not only aligned with the ground truth motion, but also
generates realistic videos. We further demonstrate that we are able to decode
motion that is consistent and that suddenly changes direction, i.e. the
airplane example in Figure 5.

###  4.3 Identifying Brain Regions Tuned to Dynamic Features

Having demonstrated the ability to predict motion from fMRI brain activity, we
now aim to identify brain regions selective for dynamic visual features. To do
so, we test various vision encoding models to determine which best predict the
fMRI brain activity of subjects watching dynamic visual stimuli. Specifically,
we extract visual features using these models and construct voxel-wise
encoding models using ridge regression [46, 47, 48, 49]. These voxel-wise
encoding models predict the fMRI brain activity of subjects watching dynamic
visual stimuli based on the extracted features.

Importantly, we test models spanning multiple visual properties, such as image
versus video and semantic versus visual similarity, to help identify the
brain’s functional properties. By analyzing the differences in encoding
capabilities, we can identify brain regions more selective to dynamic visual
features.

Figure 6: Brain Encoding Prediction Performance. Here we analyze the ability
of visual encoders (VideoMAE and CLIP ConvNeXt) to predict (encode) fMRI brain
activity from visual stimuli. Overall we find that self-supervise video
models, namely VideoMAE and VideoMAE Large, are best at predicting fMRI brain
activity. We look in depth at brain regions best predicted by VideoMAE Large
in Figure 7. For static image models, we find that semantically-supervised
models, namely CLIP ConvNeXt, perform best. Finally, we find that VC-1
performs best for embodied AI models. We compare the relative encoding
performance of the best video (VideoMAE) and static image (CLIP ConvNeXt)
models in Figure 8.

We find that the best performing video encoding model, VideoMAE Large,
outperforms the best static image encoding models at predicting fMRI brain
activity (Subject 1: $0.285$, Subject 2: $0.314$, Subject 3: $0.324$, $p\ll
0.001$). This suggests that fMRI data during video viewing contain dynamic
information which is not captured in features from static images.

Within the image encoding models, we find that CLIP ConvNeXt predicts fMRI
brain activity best across all three subjects (Subject 1: $0.219$, Subject 2:
$0.263$, Subject 3: $0.272$, $p\ll 0.001$), corroborating prior results [50]
that guidance from semantics is useful for predicting brain responses to
visual stimuli. We also find that incorporating temporal information by
averaging embeddings over multiple frames from encoding models that are not
trained to be aligned over time does not improve performance.

We also find that the best performing embodied AI vision encoding models,
VC-1, outperforms the best static image encoding models at predicts fMRI brain
activity (Subject 1: $0.260$, Subject 2: $0.290$, Subject 3: $0.294$, $p\ll
0.001$). Interestingly, VC-1 has been found to be better performing than the
other embodied AI vision encoding models on average across a series of tasks
[3]. This suggests a possible avenue of ranking embodied AI vision encoding
models on predicting fMRI brain activity.

These results suggest that models which explicitly model temporal
relationships are better at capturing neural responses to dynamic visual
stimuli.

Figure 7: VideoMAE Voxel-wise Prediction Performance. Here we plot the voxel-
wise fMRI voxel encoding accuracy of the best encoding model, VideoMAE Large,
quantified as the Pearson correlation between measured and predicted
responses. Please refer to Figure 9 for a labeled fMRI data parcellation of
brain regions. We note that majority of the voxels in the visual cortex are
predicted well by VideoMAE. Interestingly, we find that VideoMAE predicts
areas TPOJ1, STV, PGi, and 7PC (all subjects, Left Hemisphere, Lateral View)
particularly well. These brain areas process visual and motor information and
are important for high-level brain functions, including motor planning and
theory of mind [51]. This suggests that VideoMAE is capturing dynamic
representations relevant for motor planning. Figure 8: Voxel-wise Prediction
Difference Between VideoMAE and CLIP ConvNeXt. Here we plot the voxel-wise
difference of fMRI voxel encoding accuracy between the best encoding model,
VideoMAE Large, and the best performing static image encoding model, CLIP
ConvNeXt, quantified as the Pearson correlation between measured and predicted
responses. Blue indicates fMRI voxels where the VideoMAE encoder predicts
better and red indicates fMRI voxels where CLIP ConvNeXt predicts better.
Please refer to Figure 9 for a labeled fMRI data parcellation of brain
regions. We note that majority of the visual cortex is better predicted by
VideoMAE. Interestingly, we also find that VideoMAE predicts areas 5m, 5mv,
23c, 4, 24dd, and 24dv much better than CLIP ConvNeXt (Subject 1 and Subject
2, Left and Right Hemispheres, Medial View). These areas are part of the
somatosensory cortex and integrate visuomotor and somatosensory (tactile,
proprioceptive information) information for precise motor control and spatial
awareness [52, 53]. This suggests that VideoMAE is capturing representations
of action which are less prevalent in static image models.

#### Interpreting Feature Performance.

We plot voxel-wise encoding performance of the best performing model,
VideoMAE, on an inflated cortical map to interpret the voxel-wise selectivity
for dynamic visual stimuli features in Figure 7. Please refer to the caption
for more detailed analysis. We identify fMRI brain voxels that are motion
selective by taking the voxel-wise encoding performance difference between the
best encoding video model, VideoMAE Large, and the best encoding static image
model, CLIP ConvNeXt, illustrated in Figure 8. We find results that suggest
encoding visual stimuli with VideoMAE better predicts fMRI brain activity
across visual cortex and in somatosensory cortex. Additionally, we show the
voxel-wise encoding performance of all models on inflated cortical maps in the
supplementary information.

##  5 Conclusion

#### Limitations and Future Work.

Our methods successfully decode motion of salient objects from fMRI brain
activity on the Dynamic Vision Dataset [45]. However, the generalizability of
our conclusions to different dataset distributions remains unclear. Future
datasets with fine-grained motion can help determine the limits of motion
decodability from fMRI brain activity. Furthermore, our subject-specific
training approach could be improved by exploring cross-subject alignment
methods, as has been shown to improve decoding performance for static stimuli
[54, 55].

#### Conclusion and Impact.

To summarize, in this paper we propose to study neural representations of
motion by disentangling the modeling of static image features and motion. We
show that brain activity can be used to predict visual motion, demonstrate
that our predicted motion can animate static images to reconstruct the
observed dynamic visual stimuli, and identify regions in the brain that are
tuned for dynamic stimuli. Our results lay the groundwork for better
understanding how the brain represents visual motion, and may help researchers
construct better brain-machine interfaces.

## References

  * Heider and Simmel [1944] F. Heider and M. Simmel.  An experimental study of apparent behaviour.  _American Journal of Psychology_ , 13, 1944.
  * Tong et al. [2022] Zhan Tong, Yibing Song, Jue Wang, and Limin Wang.  VideoMAE: Masked autoencoders are data-efficient learners for self-supervised video pre-training.  In _Advances in Neural Information Processing Systems_ , 2022.
  * Majumdar et al. [2023] Arjun Majumdar, Karmesh Yadav, Sergio Arnaud, Yecheng Jason Ma, Claire Chen, Sneha Silwal, Aryan Jain, Vincent-Pierre Berges, Pieter Abbeel, Jitendra Malik, Dhruv Batra, Yixin Lin, Oleksandr Maksymets, Aravind Rajeswaran, and Franziska Meier.  Where are we in the search for an artificial visual cortex for embodied intelligence?  2023\.
  * Yamins et al. [2014] Daniel LK Yamins, Ha Hong, Charles F Cadieu, Ethan A Solomon, Darren Seibert, and James J DiCarlo.  Performance-optimized hierarchical models predict neural responses in higher visual cortex.  _Proceedings of the national academy of sciences_ , 111(23):8619–8624, 2014.
  * Horikawa and Kamitani [2017] Tomoyasu Horikawa and Yukiyasu Kamitani.  Generic decoding of seen and imagined objects using hierarchical visual features.  _Nature communications_ , 8(1):15037, 2017.
  * Kietzmann et al. [2019] Tim C Kietzmann, Courtney J Spoerer, Lynn KA Sörensen, Radoslaw M Cichy, Olaf Hauk, and Nikolaus Kriegeskorte.  Recurrence is required to capture the representational dynamics of the human visual system.  _Proceedings of the National Academy of Sciences_ , 116(43):21854–21863, 2019.
  * Güçlü and van Gerven [2015] Umut Güçlü and Marcel AJ van Gerven.  Deep neural networks reveal a gradient in the complexity of neural representations across the ventral stream.  _Journal of Neuroscience_ , 35(27):10005–10014, 2015.
  * Groen et al. [2018] Iris IA Groen, Michelle R Greene, Christopher Baldassano, Li Fei-Fei, Diane M Beck, and Chris I Baker.  Distinct contributions of functional and deep neural network features to representational similarity of scenes in human brain and behavior.  _Elife_ , 7, 2018.
  * Wen et al. [2018] Haiguang Wen, Junxing Shi, Yizhen Zhang, Kun-Han Lu, Jiayue Cao, and Zhongming Liu.  Neural encoding and decoding with deep learning for dynamic natural vision.  _Cerebral cortex_ , 28(12):4136–4160, 2018.
  * Kell et al. [2018] Alexander JE Kell, Daniel LK Yamins, Erica N Shook, Sam V Norman-Haignere, and Josh H McDermott.  A task-optimized neural network replicates human auditory behavior, predicts brain responses, and reveals a cortical processing hierarchy.  _Neuron_ , 98(3):630–644, 2018.
  * Koumura et al. [2019] Takuya Koumura, Hiroki Terashima, and Shigeto Furukawa.  Cascaded tuning to amplitude modulation for natural sound recognition.  _Journal of Neuroscience_ , 39(28):5517–5533, 2019.
  * Schrimpf et al. [2021] Martin Schrimpf, Idan Asher Blank, Greta Tuckute, Carina Kauf, Eghbal A Hosseini, Nancy Kanwisher, Joshua B Tenenbaum, and Evelina Fedorenko.  The neural architecture of language: Integrative modeling converges on predictive processing.  _Proceedings of the National Academy of Sciences_ , 118(45):e2105646118, 2021.
  * Goldstein et al. [2022] Ariel Goldstein, Zaid Zada, Eliav Buchnik, Mariano Schain, Amy Price, Bobbi Aubrey, Samuel A Nastase, Amir Feder, Dotan Emanuel, Alon Cohen, et al.  Shared computational principles for language processing in humans and deep language models.  _Nature neuroscience_ , 25(3):369–380, 2022.
  * Caucheteux and King [2022] Charlotte Caucheteux and Jean-Rémi King.  Brains and algorithms partially converge in natural language processing.  _Communications biology_ , 5(1):1–10, 2022.
  * Schmitt et al. [2021] Lea-Maria Schmitt, Julia Erb, Sarah Tune, Anna U Rysop, Gesa Hartwigsen, and Jonas Obleser.  Predicting speech from a cortical hierarchy of event-based time scales.  _Science Advances_ , 7(49):eabi6070, 2021.
  * Sun et al. [2023] Jingyuan Sun, Mingxiao Li, Zijiao Chen, Yunhao Zhang, Shaonan Wang, and Marie-Francine Moens.  Contrast, attend and diffuse to decode high-resolution images from brain activities.  _arXiv preprint arXiv:2305.17214_ , 2023.
  * Takagi and Nishimoto [2023] Yu Takagi and Shinji Nishimoto.  High-resolution image reconstruction with latent diffusion models from human brain activity.  In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ , pages 14453–14463, 2023.
  * Zeng et al. [2023] Bohan Zeng, Shanglin Li, Xuhui Liu, Sicheng Gao, Xiaolong Jiang, Xu Tang, Yao Hu, Jianzhuang Liu, and Baochang Zhang.  Controllable mind visual diffusion model.  _arXiv preprint arXiv:2305.10135_ , 2023.
  * Chen et al. [2023a] Zijiao Chen, Jiaxin Qing, and Juan Helen Zhou.  Cinematic mindscapes: High-quality video reconstruction from brain activity.  _arXiv preprint arXiv:2305.11675_ , 2023a.
  * Ozcelik and VanRullen [2023] Furkan Ozcelik and Rufin VanRullen.  Brain-diffuser: Natural scene reconstruction from fmri signals using generative latent diffusion.  _arXiv preprint arXiv:2303.05334_ , 2023.
  * Lin et al. [2022] Sikun Lin, Thomas Sprague, and Ambuj K Singh.  Mind reader: Reconstructing complex images from brain activities.  _arXiv preprint arXiv:2210.01769_ , 2022.
  * Lu et al. [2023] Yizhuo Lu, Changde Du, Dianpeng Wang, and Huiguang He.  Minddiffuser: Controlled image reconstruction from human brain activity with semantic and structural diffusion.  _arXiv preprint arXiv:2303.14139_ , 2023.
  * Scotti et al. [2023] Paul S Scotti, Atmadeep Banerjee, Jimmie Goode, Stepan Shabalin, Alex Nguyen, Ethan Cohen, Aidan J Dempster, Nathalie Verlinde, Elad Yundler, David Weisberg, et al.  Reconstructing the mind’s eye: fmri-to-image with contrastive learning and diffusion priors.  _arXiv preprint arXiv:2305.18274_ , 2023.
  * Koide-Majima et al. [2023] Naoko Koide-Majima, Shinji Nishimoto, and Kei Majima.  Mental image reconstruction from human brain activity.  _bioRxiv_ , pages 2023–01, 2023.
  * Gu et al. [2022] Zijin Gu, Keith Jamison, Amy Kuceyeski, and Mert Sabuncu.  Decoding natural image stimuli from fmri data with a surface-based convolutional network.  _arXiv preprint arXiv:2212.02409_ , 2022.
  * Chen et al. [2023b] Zijiao Chen, Jiaxin Qing, Tiange Xiang, Wan Lin Yue, and Juan Helen Zhou.  Seeing beyond the brain: Conditional diffusion model with sparse masked modeling for vision decoding.  In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ , pages 22710–22720, 2023b.
  * Ferrante et al. [2023] Matteo Ferrante, Furkan Ozcelik, Tommaso Boccato, Rufin VanRullen, and Nicola Toschi.  Brain captioning: Decoding human brain activity into images and text.  _arXiv preprint arXiv:2305.11560_ , 2023.
  * Liu et al. [2023] Yulong Liu, Yongqiang Ma, Wei Zhou, Guibo Zhu, and Nanning Zheng.  Brainclip: Bridging brain and visual-linguistic representation via clip for generic natural visual stimulus decoding from fmri.  _arXiv preprint arXiv:2302.12971_ , 2023.
  * Chang et al. [2019] Nadine Chang, John A Pyles, Austin Marcus, Abhinav Gupta, Michael J Tarr, and Elissa M Aminoff.  Bold5000, a public fMRI dataset while viewing 5000 visual images.  _Scientific Data_ , 6(1):1–18, 2019.
  * Allen et al. [2022a] Emily J. Allen, Ghislain St-Yves, Yihan Wu, Jesse L. Breedlove, Jacob S. Prince, Logan T. Dowdle, Matthias Nau, Brad Caron, Franco Pestilli, Ian Charest, J. Benjamin Hutchinson, Thomas Naselaris, and Kendrick Kay.  A massive 7t fmri dataset to bridge cognitive neuroscience and artificial intelligence.  _Nature Neuroscience_ , 25:116–126, 1 2022a.  ISSN 15461726.
  * Rombach et al. [2022] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer.  High-resolution image synthesis with latent diffusion models.  In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ , pages 10684–10695, 2022.
  * Teed and Deng [2020] Zachary Teed and Jia Deng.  Raft: Recurrent all-pairs field transforms for optical flow, 2020.
  * Walker et al. [2015] Jacob Walker, Abhinav Gupta, and Martial Hebert.  Dense optical flow prediction from a static image, 2015.
  * Xie et al. [2024] Junyu Xie, Charig Yang, Weidi Xie, and Andrew Zisserman.  Moving object segmentation: All you need is sam (and flow).  _arXiv preprint arXiv:2404.12389_ , 2024.
  * Yin et al. [2023] Shengming Yin, Chenfei Wu, Jian Liang, Jie Shi, Houqiang Li, Gong Ming, and Nan Duan.  Dragnuwa: Fine-grained control in video generation by integrating text, image, and trajectory, 2023.
  * He et al. [2015] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.  Deep residual learning for image recognition, 2015.
  * Caron et al. [2021] Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin.  Emerging properties in self-supervised vision transformers.  In _Proceedings of the International Conference on Computer Vision (ICCV)_ , 2021.
  * Oquab et al. [2023] Maxime Oquab, Timothée Darcet, Theo Moutakanni, Huy V. Vo, Marc Szafraniec, Vasil Khalidov, Pierre Fernandez, Daniel Haziza, Francisco Massa, Alaaeldin El-Nouby, Russell Howes, Po-Yao Huang, Hu Xu, Vasu Sharma, Shang-Wen Li, Wojciech Galuba, Mike Rabbat, Mido Assran, Nicolas Ballas, Gabriel Synnaeve, Ishan Misra, Herve Jegou, Julien Mairal, Patrick Labatut, Armand Joulin, and Piotr Bojanowski.  Dinov2: Learning robust visual features without supervision, 2023.
  * Radford et al. [2021] Alec Radford, Jong Wook Kim, Chris Hallacy, A. Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, and Ilya Sutskever.  Learning transferable visual models from natural language supervision.  In _ICML_ , 2021.
  * Cherti et al. [2023] Mehdi Cherti, Romain Beaumont, Ross Wightman, Mitchell Wortsman, Gabriel Ilharco, Cade Gordon, Christoph Schuhmann, Ludwig Schmidt, and Jenia Jitsev.  Reproducible scaling laws for contrastive language-image learning.  In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ , pages 2818–2829, 2023.
  * Ryali et al. [2023] Chaitanya Ryali, Yuan-Ting Hu, Daniel Bolya, Chen Wei, Haoqi Fan, Po-Yao Huang, Vaibhav Aggarwal, Arkabandhu Chowdhury, Omid Poursaeed, Judy Hoffman, Jitendra Malik, Yanghao Li, and Christoph Feichtenhofer.  Hiera: A hierarchical vision transformer without the bells-and-whistles.  _ICML_ , 2023.
  * Ma et al. [2022] Yiwei Ma, Guohai Xu, Xiaoshuai Sun, Ming Yan, Ji Zhang, and Rongrong Ji.  X-CLIP:: End-to-end multi-grained contrastive learning for video-text retrieval.  _arXiv preprint arXiv:2207.07285_ , 2022.
  * Ma et al. [2023] Yecheng Jason Ma, Shagun Sodhani, Dinesh Jayaraman, Osbert Bastani, Vikash Kumar, and Amy Zhang.  Vip: Towards universal visual reward and representation via value-implicit pre-training, 2023.
  * Nair et al. [2022] Suraj Nair, Aravind Rajeswaran, Vikash Kumar, Chelsea Finn, and Abhinav Gupta.  R3m: A universal visual representation for robot manipulation, 2022.
  * Wen et al. [2017] Haiguang Wen, Junxing Shi, Yizhen Zhang, Kun-Han Lu, Jiayue Cao, and Zhongming Liu.  Neural Encoding and Decoding with Deep Learning for Dynamic Natural Vision.  _Cerebral Cortex_ , 28(12):4136–4160, 10 2017.  doi: 10.1093/cercor/bhx268.  URL https://doi.org/10.1093/cercor/bhx268.
  * Kay et al. [2008] Kendrick N Kay, Thomas Naselaris, Ryan J Prenger, and Jack L Gallant.  Identifying natural images from human brain activity.  _Nature_ , 452(7185):352–355, March 2008.  ISSN 1476-4687, 0028-0836.  doi: 10.1038/nature06713.  Epub 2008 Mar 5.
  * Sarch et al. [2023] Gabriel H Sarch, Michael J Tarr, Katerina Fragkiadaki, and Leila Wehbe.  Brain dissection: fmri-trained networks reveal spatial selectivity in the processing of natural images.  _bioRxiv_ , pages 2023–05, 2023.
  * Naselaris et al. [2011] Thomas Naselaris, Kendrick N Kay, Shinji Nishimoto, and Jack L Gallant.  Encoding and decoding in fmri.  _Neuroimage_ , 56(2):400–410, 2011.
  * Allen et al. [2022b] Emily J Allen, Ghislain St-Yves, Yihan Wu, Jesse L Breedlove, Jacob S Prince, Logan T Dowdle, Matthias Nau, Brad Caron, Franco Pestilli, Ian Charest, et al.  A massive 7t fmri dataset to bridge cognitive neuroscience and artificial intelligence.  _Nature neuroscience_ , 25(1):116–126, 2022b.
  * Wang et al. [2023] A. Y. Wang, K. Kay, T. Naselaris, M. J. Tarr, and L. Wehbe.  Better models of human high-level visual cortex emerge from natural language supervision with a large and diverse dataset.  _Nature Machine Intelligence_ , 5(12):1415–1426, 2023.  doi: 10.1038/s42256-023-00753-y.
  * Baker et al. [2018a] C. M. Baker, J. D. Burks, R. G. Briggs, A. K. Conner, C. A. Glenn, K. N. Taylor, G. Sali, T. M. McCoy, J. D. Battiste, D. L. O’Donoghue, and M. E. Sughrue.  A connectomic atlas of the human cerebrum-chapter 7: The lateral parietal lobe.  _Operative Neurosurgery (Hagerstown)_ , 15(suppl_1):S295–S349, December 2018a.  doi: 10.1093/ons/opy261.
  * Baker et al. [2018b] C. M. Baker, J. D. Burks, R. G. Briggs, J. R. Sheets, A. K. Conner, C. A. Glenn, G. Sali, T. M. McCoy, J. D. Battiste, D. L. O’Donoghue, and M. E. Sughrue.  A connectomic atlas of the human cerebrum-chapter 3: The motor, premotor, and sensory cortices.  _Operative Neurosurgery (Hagerstown)_ , 15(suppl_1):S75–S121, December 2018b.  doi: 10.1093/ons/opy256.
  * Baker et al. [2018c] C. M. Baker, J. D. Burks, R. G. Briggs, J. Stafford, A. K. Conner, C. A. Glenn, G. Sali, T. M. McCoy, J. D. Battiste, D. L. O’Donoghue, and M. E. Sughrue.  A connectomic atlas of the human cerebrum-chapter 4: The medial frontal lobe, anterior cingulate gyrus, and orbitofrontal cortex.  _Operative Neurosurgery (Hagerstown)_ , 15(suppl_1):S122–S174, December 2018c.  doi: 10.1093/ons/opy257.
  * Huang et al. [2023] S. Huang, L. Sun, M. Yousefnezhad, M. Wang, and D. Zhang.  Functional alignment-auxiliary generative adversarial network-based visual stimuli reconstruction via multi-subject fmri.  _IEEE Transactions on Neural Systems and Rehabilitation Engineering_ , 31:2715–2725, 2023.  doi: 10.1109/TNSRE.2023.3283405.  Epub 2023 Jun 20.
  * Andreella et al. [2023] Angela Andreella, Livio Finos, and Martin A Lindquist.  Enhanced hyperalignment via spatial prior information.  _Human Brain Mapping_ , 44(4):1725–1740, 2023.
  * Rolls et al. [2022] Edmund T. Rolls, Gustavo Deco, Chu-Chung Huang, and Jianfeng Feng.  The human language effective connectome.  _NeuroImage_ , 258:119352, 2022.  ISSN 1053-8119.  doi: https://doi.org/10.1016/j.neuroimage.2022.119352.  URL https://www.sciencedirect.com/science/article/pii/S1053811922004712.

Supplementary Material:
Neural Representations of Dynamic Visual Stimuli

##  Appendix A HCP Parcellation Map

Figure 9: HCP Parcellation Map. Here are the parcellated (labeled) brain
regions on an inflated cortex. The parcellation is from HCP-MMP, taken from
[56].

Here we show the parcellation (labeling) of the brain Figure 9.

##  Appendix B Additional Dataset Information

We use the Dynamic Vision Dataset collected by [45]. They release the dataset
under a CC0 1.0 universal license. The url for the dataset can be found at
https://purr.purdue.edu/publications/2805/1.

##  Appendix C Encoding Models Voxel-wise Prediction Performance on Inflated
Cortex

Here we show the voxel-wise fMRI prediction performance, quantified as the
Pearson correlation (r) between measured and predicted responses, for the
remaining visual encoding models in alphabetical order.

Note that all following plots of encoding accuracy on inflated cortical maps
are on the same scale for ease of comparison.

Figure 10: CLIP Voxel-wise Prediction Performance. Here we plot the voxel-wise
fMRI voxel encoding accuracy of CLIP quantified as the Pearson correlation
between measured and predicted responses. Please refer to Figure 9 for a
labeled fMRI data parcellation of brain regions. Figure 11: CLIP AF Voxel-wise
Prediction Performance. Here we plot the voxel-wise fMRI voxel encoding
accuracy of CLIP AF (averaged frames) quantified as the Pearson correlation
between measured and predicted responses. Please refer to Figure 9 for a
labeled fMRI data parcellation of brain regions. Figure 12: CLIP ConvNeXt
Voxel-wise Prediction Performance. Here we plot the voxel-wise fMRI voxel
encoding accuracy of CLIP ConvNeXt quantified as the Pearson correlation
between measured and predicted responses. Please refer to Figure 9 for a
labeled fMRI data parcellation of brain regions. Figure 13: CLIP ConvNeXt
Voxel-wise Prediction Performance. Here we plot the voxel-wise fMRI voxel
encoding accuracy of CLIP ConvNeXt AF (averaged frames) quantified as the
Pearson correlation between measured and predicted responses. Please refer to
Figure 9 for a labeled fMRI data parcellation of brain regions. Figure 14:
DINOv1 Voxel-wise Prediction Performance. Here we plot the voxel-wise fMRI
voxel encoding accuracy of DINOv1 quantified as the Pearson correlation
between measured and predicted responses. Please refer to Figure 9 for a
labeled fMRI data parcellation of brain regions. Figure 15: DINOv2 Voxel-wise
Prediction Performance. Here we plot the voxel-wise fMRI voxel encoding
accuracy of DINOv2 quantified as the Pearson correlation between measured and
predicted responses. Please refer to Figure 9 for a labeled fMRI data
parcellation of brain regions. Figure 16: Hiera Base Plus Voxel-wise
Prediction Performance. Here we plot the voxel-wise fMRI voxel encoding
accuracy of Hiera Base Plus quantified as the Pearson correlation between
measured and predicted responses. Please refer to Figure 9 for a labeled fMRI
data parcellation of brain regions. Figure 17: Hiera Huge Voxel-wise
Prediction Performance. Here we plot the voxel-wise fMRI voxel encoding
accuracy of Hiera Huge quantified as the Pearson correlation between measured
and predicted responses. Please refer to Figure 9 for a labeled fMRI data
parcellation of brain regions. Figure 18: R3M Voxel-wise Prediction
Performance. Here we plot the voxel-wise fMRI voxel encoding accuracy of R3M
quantified as the Pearson correlation between measured and predicted
responses. Please refer to Figure 9 for a labeled fMRI data parcellation of
brain regions. Figure 19: R3M AF Voxel-wise Prediction Performance. Here we
plot the voxel-wise fMRI voxel encoding accuracy of R3M AF (averaged frames)
quantified as the Pearson correlation between measured and predicted
responses. Please refer to Figure 9 for a labeled fMRI data parcellation of
brain regions. Figure 20: ResNet50 Voxel-wise Prediction Performance. Here we
plot the voxel-wise fMRI voxel encoding accuracy of ResNet50 quantified as the
Pearson correlation between measured and predicted responses. Please refer to
Figure 9 for a labeled fMRI data parcellation of brain regions. Figure 21: VC1
Voxel-wise Prediction Performance. Here we plot the voxel-wise fMRI voxel
encoding accuracy of VC1 quantified as the Pearson correlation between
measured and predicted responses. Please refer to Figure 9 for a labeled fMRI
data parcellation of brain regions. Figure 22: VC1 AF Voxel-wise Prediction
Performance. Here we plot the voxel-wise fMRI voxel encoding accuracy of VC1
AF (averaged frames) quantified as the Pearson correlation between measured
and predicted responses. Please refer to Figure 9 for a labeled fMRI data
parcellation of brain regions. Figure 23: VideoMAE Voxel-wise Prediction
Performance. Here we plot the voxel-wise fMRI voxel encoding accuracy of
VideoMAE quantified as the Pearson correlation between measured and predicted
responses. Please refer to Figure 9 for a labeled fMRI data parcellation of
brain regions. Figure 24: VIP Voxel-wise Prediction Performance. Here we plot
the voxel-wise fMRI voxel encoding accuracy of VIP quantified as the Pearson
correlation between measured and predicted responses. Please refer to Figure 9
for a labeled fMRI data parcellation of brain regions. Figure 25: VIP AF
Voxel-wise Prediction Performance. Here we plot the voxel-wise fMRI voxel
encoding accuracy of VIP AF (averaged frames) quantified as the Pearson
correlation between measured and predicted responses. Please refer to Figure 9
for a labeled fMRI data parcellation of brain regions. Figure 26: XCLIP Voxel-
wise Prediction Performance. Here we plot the voxel-wise fMRI voxel encoding
accuracy of XCLIP quantified as the Pearson correlation between measured and
predicted responses. Please refer to Figure 9 for a labeled fMRI data
parcellation of brain regions.


# The Rise and Fall of the Eclipsing Binary HS Hydrae

James. R. A. Davenport Astronomy Department, University of Washington, Box
951580, Seattle, WA 98195, USA  Diana Windemuth  Astronomy Department,
University of Washington, Box 951580, Seattle, WA 98195, USA  Karen Warmbein
Astronomy Department, University of Washington, Box 951580, Seattle, WA 98195,
USA  Erin L. Howard Department of Physics & Astronomy, Western Washington
University, Bellingham, WA 98225  Courtney Klein Department of Physics and
Astronomy, University of California Irvine, CA 92697, USA  Jessica Birky
Astronomy Department, University of Washington, Box 951580, Seattle, WA 98195,
USA

###### Abstract

HS Hydrae is a short period eclipsing binary ($P_{orb}=1.57$ day) that belongs
to a rare group of systems observed to have rapidly changing inclinations.
This evolution is due to a third star on an intermediate orbit, and results in
significant differences in eclipse depths and timings year-to-year. Zasche &
Paschke (2012) revealed that HS Hydrae’s eclipses were rapidly fading from
view, predicting they would cease around 2022. Using 25 days of photometric
data from Sector 009 of the Transiting Exoplanet Survey Satellite (TESS), we
find that the primary eclipses for HS Hydrae were only $0.00173\pm 0.00007$
mag in depth in March 2019. This data from TESS likely represents the last
eclipses detected from HS Hydrae. We also searched the Digitization of the
Harvard Astronomical Plate Collection (DASCH) archive for historic data from
the system. With a total baseline of over 125 years, this unique combination
of data sets – from photographic plates to precision space-based photometry –
allows us to trace the emergence and decay of eclipses from HS Hydrae, and
further constrain its evolution. Recent TESS observations from Sector 035
confirm that eclipses have ceased for HS Hya, and we estimate they will begin
again in 2195.

††software: Python, IPython (Pérez & Granger, 2007), NumPy (Oliphant, 2007),
Matplotlib (Hunter, 2007), SciPy (Jones et al., 2001–), Pandas (Wes McKinney,
2010), Astropy (Astropy Collaboration et al., 2013), Lightkurve (Lightkurve
Collaboration et al., 2018), emcee (Foreman-Mackey et al., 2013), eleanor
(Feinstein et al., 2019)

##  1 Introduction

Eclipsing binary stars (EBs) are the most important benchmark systems for
calibrating models of the fundamental properties of stars (Stassun et al.,
2009). By observing both the eclipses with photometry and radial velocity
variations throughout the orbit with spectroscopy, we can directly estimate
the masses, radii, and surface brightness for both stars. In the modern era of
ultra-precise, space-based photometry, EBs enable incredibly precise and
accurate measurements of the fundamental properties of stars (Miller et al.,
2020). Such precision also allows us to search for low-amplitude signals from
the EB, which can be due to companion stars or second-order physical effects
(Bloemen et al., 2013).

A rare class of EB systems are those with observable changes in their
inclinations or alignments over time. Such systems are often discovered as EBs
with observable eclipse depths and/or eclipse times that vary over many years.
In the case of changing inclination systems, this results in a window of time
(typically decades) where eclipses are visible to our line of sight, and
longer time spans (often centuries) where they are not. Some binaries with
historical eclipse data are now classified as former EBs due to this
precession (e.g. QX Cas; Bonaro et al., 2009).

This evolution is typically ascribed to the influence of a gravitationally
bound third star. These rapidly evolving systems are therefore unique and
important windows into the structure and dynamics of triple star systems
(Soderhjelm, 1975). Wide-area sky surveys are now regularly producing large
catalogs EBs (Jayasinghe et al., 2018), and have started to produce catalogs
of these dynamic systems, such as from the Magellenic Clouds via changing
eclipse depths (Juryšek et al., 2018) or precise eclipse timing variations
(Borkovits et al., 2016). However, only a few inclination-changing EBs have
been well studied within the Milky Way (Guinan et al., 2012; Juryšek et al.,
2018).

HS Hydrae has long been known to be an EB (Strohmeier et al., 1965), and has
been studied in detail as a normal binary system (Gyldenkerne et al., 1975).
Torres et al. (1997) first identified the presence of a third stellar body in
the system, estimating the outer orbital period to be 190 days. Zasche &
Paschke (2012) found that HS Hya belongs to the rare class of precessing,
inclination-changing EBs. Zasche & Paschke (2012) further predicted eclipses
would cease for HS Hya around 2022, and presented the need for additional
precision follow-up for the system.

Here we present a comprehensive archival study of the inclination-changing EB,
HS Hya. We combine historical archival photometry from photographic plate
archives, ground-based surveys, and new precision space-based light curves in
§2. In total we have assembled a unique data set that spans over 125 years.
This data set maps the entire observable history of eclipses from HS Hya,
which we model in §3. We believe that the TESS mission (Ricker et al., 2015)
serendipitously captured the final observable eclipses in 2019, and in §4 we
predict that HS Hya will resume eclipsing around 2195. In §6 we review similar
systems that TESS is uniquely suited for studying, and finally provide a brief
summary and discussion in §7.

##  2 A Century of Data

HS Hya is a bright system at $V\sim$8.1 mag, and relatively nearby with a
distance of $103\pm 7$ pc (Gaia Collaboration et al., 2020). As such,
considerable data exists for HS Hya in photometric archives and historical
literature. Bright stars are also ideal targets the current generation of
exoplanet-hunting missions with high precision and high cadence photometry. In
this section we detail the wide range of data gathered for for our study of HS
Hya, reaching back over a 125 year baseline.

###  2.1 Archival Data

Figure 1:  Phase-folded light curves for HS Hydrae from various photometric
studies and archives. As in Zasche & Paschke (2012), a clear decay in eclipse
depth and precession of eclipse phase can be seen from 1975 to the faintly
detectable eclipses in 2008.

As Zasche & Paschke (2012) note, several sources of archival data for HS Hya
exist. In this section we briefly review the history of observations for the
system, starting by reviewing the archival data used by Zasche & Paschke
(2012), shown in Figure 1.

HS Hya was first identified as an eclipsing binary in 1964 as part of a survey
of bright variable stars (Strohmeier et al., 1965). Though the orbital period
was not correctly identified, the approximate depth of the primary eclipse can
be estimated from their Figure 5. We use the approximate eclipse depth in
later analysis, but are unable to phase-fold their data into our ensemble in
Figure 1.

Popper (1971) published the first radial velocity curves, as well as the
correct orbital period (1.568024 days), and raised the need for more
photometric data for HS Hya. Gyldenkerne et al. (1975) then obtained 533
observations over 12 nights of extremely precise Strömgren $ubvy$ photometry
for HS Hya, shown in Figure 1 (blue points). We use the primary eclipse
ephemeris from Gyldenkerne et al. (1975) and orbital period from Popper (1971)
throughout our work:

$\phi_{pri}=2441374.5934+1.^{\kern-1.75pt{\rm d}}568024\times E$ (1)

where $\phi_{pri}$ is the orbital phase of the primary eclipse, the period is
in days, and the ephemeris is in Julian date. The Hipparcos mission (Perryman
et al., 1997) was able to capture 79 additional epochs of high quality
photometry for HS Hya (Figure 1, orange points).

As Zasche & Paschke (2012) show, the All Sky Automated Survey (ASAS;
Pojmanski, 1997, 2002) provided many years of photometric monitoring for HS
Hya. We obtained the latest version of the ASAS $V$-band light curve for HS
Hya, which had a total of 662 epochs of usable photometry with the GRADE=‘A’
quality flag set. We grouped the ASAS data into four portions of roughly equal
time resolution. The mean year within each time range is noted in Figure 1.

We also searched for other modern catalogs for useful data to compliment the
ensemble listed above. We queried both the individual epoch (L1b) data from
the infrared WISE mission (Wright et al., 2010), as well as the optical
ground-based ASAS-SN survey Kochanek et al. (2017), which has been used to
generate large samples of eclipsing and variable sources (e.g. Jayasinghe et
al., 2020). Light curves for HS Hya were available from both catalogs, but the
photometric precision was not high enough in either to detect the eclipses,
where were already below 0.1 mag in amplitude in 2008.

###  2.2 DASCH

We were then able to substantially extend the baseline of the archival data
used in our analysis. The Digital Access to a Sky Century at Harvard (DASCH)
is an effort to create a uniform digital catalog of photometric measurements
from astro-photographic plates taken between 1885 to 1992 (Laycock et al.,
2010; Tang et al., 2013). Each plate is digitized by back-illuminating it and
scanning using a CCD camera. That image is then calibrated based on the
plate’s sensitivity, and PSF photometry is computed for each source in the
image.

Figure 2:  Phase-folded historical light curves from DASCH for the
inclination-changing, eclipsing binary system, HS Hydrae in six bins of time.
Time ranges for each bin are noted in brackets. While we believe eclipses
started in $\sim$1897, measurable eclipses from photometric plates were not
apparent for the system until the 1920’s.

Setting an upper limit for the photometric uncertainty of $\sigma<0.3$ mag, we
found 1390 usable observations for HS Hya from the DASCH archive. This light
curve spanned from 1893 to 1989, and the phase-folded data is shown in Figure
2. These data had a mean photometric uncertainty of 0.2 mag, which was
remarkably stable throughout the time series. As with the ASAS data, we binned
the light curve into ranges of time with roughly equal numbers of observations
to illustrate in Figure 2 the changing system inclination (or eclipse depth)
over time. We discard data after 1955, as the available archive of plates
became very sparse in time. In total we only omitted 121 “good” epochs between
1955 and 1989.

No sign of the eclipsing nature for HS Hya is apparent for the first several
decades of DASCH data in Figure 2. The EB begins to reveal itself clearly in
the early 1920’s, as the eclipse depth begins to reach above 0.1 mag. By the
final time window in our DASCH data, between 1945 and 1955, the primary
eclipse has a very large depth of at least 0.5 mag.

###  2.3 TESS

Figure 3:  TESS Sector 9 phase-folded light curve for HS Hydrae. As in Figures
1 and 2, the TESS data have been phased using the orbital period and ephemeris
from Gyldenkerne et al. (1975). Very small amplitude primary (Phase$\sim$0.1)
and secondary (Phase$\sim$0.6) eclipses are visible, as well as out-of-eclipse
ellipsoidal variation, and possible variability due to starspots. As this
system is rapidly precessing, we believe these may be the final observable
eclipses for HS Hya for almost two centuries.

The Transiting Exoplanet Survey Satellite (TESS; Ricker et al., 2015) is a
NASA mission currently studying bright stars from over 80% of the sky. In its
primary mission, TESS provides nearly continuous light curves with between
$\sim$27 day and 1-year baselines. TESS captures 30-minute cadence imaging for
its entire field of view, and generating 2-minute cadence light curves for
$\sim$20,000 pre-selected targets simultaneously.

HS Hya (also known as TIC 434479378) was observed in Sector 009 of the TESS
primary mission, and was selected to receive 2-minute (short) cadence data
shown in Figure 3. The observations for Sector 009 spanned 2019-02-28 through
2019-03-26, with the characteristic TESS mid-Sector gap for data down-link.
The apparent magnitude of HS Hya is ideal for generating an ultra high
precision light curve, as shown in Figure 3 with a mean photometric error in
relative flux of 3$\times 10^{-4}$.

The phase-folded TESS light curve for HS Hya is dominated by a $\sim$1% flux
modulation that is remarkably stable throughout the Sector. This periodic
modulation is due to the ellipsoidal variation of the system, as the binary is
on very short period orbit. Small variations in the ellipsoidal variation are
likely due to small amplitude systematic errors in detrending the TESS data
across the entire quarter.

Very small amplitude eclipses are visible in the phase-folded TESS light curve
in Figure 3. To compare the eclipse depths with the previous measurements, we
convert the relative fluxes to magnitudes using the typical approach of
$\Delta mag=-2.5\log_{10}f_{rel}$. Using a simple Gaussian fit to the eclipse,
we estimate the grazing eclipse of HS Hya had an amplitude of $0.00173\pm
0.00007$ mag in 2019.

As with many EBs observed by missions like Kepler and TESS, ultra high
precision constraints are possible on both the fluxes due to the photometric
precision (e.g. small amplitude features as shown here), and for the temporal
information due to the dense light curve sampling (e.g. the phase of the
eclipse). For HS Hya, the TESS data show the ellipsoidal variation does not
align with the eclipses exactly in orbital phase. The primary eclipse in
Figure 3 leads the bulge by a very small but significant amount of the orbital
phase. We find the eclipse leads the light curve minimum by $0.0114\pm 0.0004$
in phase. The precision of this phase lag may be useful for constraining the
tidal synchronization for such systems (Zahn, 1977; Barnes, 2011).

##  3 Modeling 125 Years of HS Hya

Our photometric data for HS Hya spans a +125 year baseline, from 1893 to 2019.
As Figures 1–3 show, there is significant evolution in both the amplitude and
phase of the eclipses. The phase of the primary eclipse visibly moves from
-0.2 in the early DASCH data (Figure 2), to 0.11 in the TESS data (Figure 3).
These effects are due to orbital precession and inclination evolution of the
system owing to a third body in orbit around the eclipsing components, as
described by Zasche & Paschke (2012).

Figure 4:  Eclipse depths as a function of time for HS Hydrae, combining data
spanning over 125 years. Primary eclipses within each time span were fit using
a simple Gaussian profile. A Gaussian profile (red line) was fit to illustrate
the system’s entire history as an eclipsing binary. We find the maximum
eclipse depth occurred in $\sim$1959\.

To illustrate the “rise and fall” of eclipses from HS Hya, in Figure 4 we show
a phenomenological model of the observed eclipse depths over time. We fit the
primary eclipse from the phase curves shown in Figures 1–3 using a Gaussian
curve to estimate the eclipse depth within each window of time. Additionally
we include the EB discovery epoch from Strohmeier et al. (1965), where the
eclipse depth and uncertainty are estimated by eye, following Zasche & Paschke
(2012). Figure 4 shows the eclipses were barely visible near the beginning of
the 20th century. By the 1940’s, the EB is well detected. As the inclination
evolves approximately linearly with time for these systems (Torres, 2001), the
resulting change in eclipse depth over time is, to first order, a Gaussian
profile (e.g. Fig 4 of Drechsel et al., 1994). This simple summary model of
the eclipse depths over 125 years in Figure 4 shows HS Hya was at maximum
eclipse depth around $\sim$1959.

To determine the inclination of HS Hya over time, we then generated eclipsing
binary models for each of the phase curves in Figures 1–3. We utilized the
detached EB modeling framework KEBLAT, developed by Windemuth et al. (2019).
KEBLAT leverages stellar evolution models (Bressan et al., 2012) to infer
robust physical parameters for EBs using only photometry and without radial
velocity data – e.g. with data from missions like Kepler and TESS. We refer
the reader to Windemuth et al. (2019) for details about the photodynamical
modeling, and describe below how we adapt KEBLAT to fit light curves from
disparate photometric surveys and model the time varying physical parameters.

We use an iterative approach to fit the entire data set, which spans 12 epochs
of V-band data and 1 epoch of TESS data (i.e. Figures 1–3). We individually
fit each epoch in a self-consistent way, and then cumulatively combine the
epochs into one model to measure inclination and time of primary eclipse as a
function of the $i^{th}$ mid-epoch, $E_{i}$. We hold masses and temperatures
fixed to radial velocity-derived masses and temperatures from Torres et al.
(1997), as they are more accurate, and we lack multi-band photometry required
for KEBLAT to infer masses via stellar isochrones alone. Note that we also do
not fit for a “third light” component for the system.

We first initialized our KEBLAT model using only the data from Gyldenkerne et
al. (1975). We started with this epoch as it had the highest signal-to-noise
eclipse data, and was close to the epoch of maximum eclipse depth for the
system according to Figure 4. We set initial parameter values for the orbital
period and time of primary eclipse ($P$ and $t_{\mathrm{pe}}$) to literature
values; radii and flux ratio values to PARSEC stellar isochrone predictions
based on the RV-derived masses (Bressan et al., 2012); eccentricity vectors
$e\sin\omega$, $e\cos\omega$) using primary and secondary eclipse widths and
separations; and finally random small initial values to impact parameter $b$
and limb darkening coefficients. We then used lmfit, a non-linear least
squares optimizer, to solve for the free parameters corresponding to the
Gyldenkerne et al. (1975) epoch.

We then successively added the remaining 11 epochs of V-magnitude data to our
KEBLAT model. We assume that binary period and eccentricity, as well as
physical parameters associated with the binary components themselves (i.e.
stellar radii, V-band flux ratio, limb darkening coefficients) do not evolve
on the century timescale of our data set, and thus hold them fixed at the
optimum values from the Gyldenkerne et al. (1975) epoch. We allow each epoch’s
impact parameter (inclination) and time of primary eclipse to float in our
combined V-band data set, and solve for the best-fit values via lmfit.

Finally, we include the TESS epoch in our cumulative model, and fit for impact
parameter and time of primary eclipse for all epochs of data. We use the
PARSEC isochrone model grid to solve for a self-consistent TESS-band flux
ratio, based on the published masses and effective temperatures for the binary
components. We note that uncertainties in this transformation may result in
over-estimating the inclination precision for the TESS epoch. However we
believe this impact is minimal, as the EB has a nearly equal-mass ratio, i.e.
ratio of eclipse depths will not be strongly wavelength dependent.

We emphasize that KEBLAT did not parameterize any time dependent evolution for
HS Hya. Instead, we created a final single solution for our data, solving for
the point-in-time inclination and time of primary eclipse for each epochal
data set as free parameters. Since our goal was to examine the evolution of
system inclination, we do not consider the system properties (i.e. radii, flux
ratios, eccentricity vectors) that KEBLAT estimated from the Gyldenkerne et
al. (1975) epoch are robust determinations of the true values. As such, we did
not produce uncertainties on these parameters. We do note that these values
are all close to more detailed modeling of the system from Torres et al.
(1997), and for completeness we include them in Table 1.

##  4 The Final Eclipses

From our KEBLAT model we have derived estimates of the inclination HS Hya in
13 individual epochs spanning over a century. These inclinations, and their
standard 1-$\sigma$ uncertainties, are shown in Figure 5.

We find that the inclination for HS Hya changes nearly linear over the
125-year baseline, as expected from the evolution of other similarly evolving
triple star systems (Torres, 2001). The inclination angle for an eclipsing
binary is typically defined between $0^{\circ}$ (pole-on, no eclipse) and
$90^{\circ}$ (equator-on, deepest eclipse), and our KEBLAT fits from §3 are
defined within this range. However, in Figure 5 we choose to flip the
inclinations for the DASCH epochs above $90^{\circ}$, making this linear
evolution more clear. Conceptually this corresponds to the system starting to
eclipse as the secondary star begins to graze the “top” of the primary in the
early 1900’s (i.e. $i\sim 108.7^{\circ}$), and eclipses end as the secondary
star grazes the “bottom” of the primary (i.e. the critical inclination of
$i\sim 71.3^{\circ}$).

Figure 5:  Derived inclination over time for HS Hya. For data before
$\sim$1960, actual fits are shown (thin crosses), as well as inclinations
flipped above $90^{\circ}$ to enable a linear fit throughout the observations.
Draws from the posterior distribution of this linear model are shown (red
lines). The median model predicts that eclipses from HS Hya will be
undetectable by TESS in September 2020, and that eclipses will cease in
January 2021 when HS Hya reaches the critical inclination of $i=71.3^{\circ}$.

We fit the inclination evolution in Figure 5 using a linear model (Torres,
2001). We initialize this fit using a least-squares regression to the
inclinations and their uncertainties. This was then used to initialize an
affine invariant Markov Chain Monte Carlo (MCMC) parameter exploration using
emcee. In Figure 5 we show 50 draws from the posterior distribution of this
MCMC fit, and we adopt the median values from the posteriors as our preferred
inclination evolution model going forward.

According to our KEBLAT modeling, HS Hya will cease to have eclipses from our
line of sight at the critical inclination of $i\sim 71.3^{\circ}$. Our MCMC
fit to the evolution predicts that HS Hya will reach this inclination at year
$2021.1\pm 0.5$ (Feb 2021). Despite sampling a +125 year baseline, a half year
uncertainty remains in the precise time. HS Hya is scheduled to be observed
again during Cycle 3 of the TESS mission, in Sector 035 (Feb–Mar 2021). While
it is possible the system will still be eclipsing at this time, the eclipse
amplitudes will be so small that it is unlikely even TESS will be able to
detect them as distinct from the ellipsoidal modulations. We therefore believe
the TESS Sector 009 data in Figure 3 are the final observable eclipses for HS
Hya during this era.

Our linear inclination evolution modal predicts that HS Hya will reach the
critical inclination again in the year $2195\pm 3$. The ellipsoidal variations
will continue to be observable by facilities like TESS for many decades to
come. Their amplitudes will decrease as the system continues to precess, which
can be used to continue tracing the orbital evolution of the system using
tools designed for modeling tidally distorted EBs such as PHOEBE (Prša et al.,
2016).

Rather than a linear model, Zasche & Paschke (2012) estimated the “nodal
period” of the system using a sinusoidal function fit to $\cos(i)$, following
the approach Drechsel et al. (1994) used for IU Aur. They found $P_{nodal}\sim
631$ yr for HS Hya. Since only a small portion of the nodal period for HS Hya
is observed in the past 125 years, sinusoidal functions are under-constrained
by the data, as Zasche & Paschke (2012) note. For completeness we have
replicated this approach using our longer observation baseline for HS Hya. A
sinusoidal least-squares fit to the $\cos(i)$ estimates from KEBLAT yields
$P_{nodal}=973$ years. Our linear inclination evolution model can also be
restated as a “tumble” period for the system (i.e. how long it takes for the
inclination to change by $360^{\circ}$). We find this tumble period to be
$P_{nodal}=1194\pm 20$ years for HS Hya.

##  5 The Third Star

Throughout this work we have focused on the observed properties of the
eclipsing component of HS Hya, while largely neglecting the third stellar body
in the system. Torres et al. (1997) have produced the only substantial
characterization of star $C$, estimating it to have an orbital period of
$P=190.529\pm 0.061$ around the eclipsing $AB$ stars, and a spectral type of
M0 (0.5$M_{\odot}$). The orbit for star $C$ was also estimated to be nearly
co-planar to the inner stars’ orbits, though no eclipses from star $C$ were
reported.

Using our 125-year archive of photometry, we searched for any signs of
eclipses from the third star in HS Hya. We searched each of the ground-based
archival light curves shown in Figures 1 and 2 for any periodic signals around
$P=190$ days, using both Lomb-Scargle (e.g. VanderPlas & Ivezic, 2015) and Box
Least Squares (Kovács et al., 2002) periodogram techniques. No eclipses
besides the expected $P=1.5$d were found in any of the ground-based datasets
from §2.1, though we note the DASCH data did show some low-amplitude signal in
the Lomb Scargle periodogram broadly centered around 190 days. The origin of
this signal was unclear, however, as it could occur due to e.g. half of the
natural 1-year alias in the data.

The TESS light curve for HS Hya (Figure 3) only covers a small portion of the
190d orbital period for star $C$, and no extra eclipse features were detected
for the system. In total the TESS data covered 13.5% of the outer orbital
period. Using the ephemeris for the predicted time of periastron for the third
body by Torres et al. (1997) (HJD=$2448063.8\pm 3.6$ d), TESS narrowly misses
the predicted periastron time for the third body, with the light curve
starting 0.32 days after. There remains substantial uncertainty in the time of
periastron without an eclipse. As HS Hya continues to dynamically evolve, and
the third star is predicted to be nearly co-planar with the primary (formerly
eclipsing) components, an eclipse of the inner stars by the third body is a
possibility. Unfortunately we cannot predict from our data when such an event
may occur, nor if it has occurred over the past century given the sparse
sampling of our historic light curves.

Besides photometric (e.g. transits) and spectroscopic detection, the third
star in HS Hya could potentially be characterized from precision astrometric
monitoring. As Stassun & Torres (2021) note, for unresolved binaries the Gaia
“RUWE” statistic may be a useful metric for inferring motion of the system’s
photocenter, which could occur due to the presence of a third star. RUWE
characterizes the error of the astrometric solution for a system over the
available data. HS Hya has a value from Gaia EDR3 of RUWE=2.38, far greater
than the nominal range of 1–1.4 expected for single stars. This is an
excellent indication that the eclipsing $AB$ components are moving due to the
tertiary star. Stassun & Torres (2021) further produced an empirical relation
between RUWE and the expected photocenter motion from known eclipsing systems.
Using this relation, we find HS Hya has an estimated photocenter motion from
the Gaia EDR3 RUWE of 0.58 mas. This is larger than the expected photocenter
shift of the system from the small third star alone of $\sim$0.2 mas, but we
note that the RUWE value for HS Hya is larger than any in the empirical
relation provided by Stassun & Torres (2021).

In Table 1 we summarize the relevant system properties for HS Hya from the
literature and this work, including values for the third star.

Table 1:  System Properties

Property |  Value |  Ref
---|---|---
$P_{orb,AB}$ | 1.568024 d | a
$t_{0,AB}$ | 2441374.5954 JD | b
$P_{orb,C}$ |  $190.529\pm 0.061$ d | c
$t_{0,C}$ |  $2448063.8\pm 3.6$ JD | c
$M_{A}$ | $1.255\pm 0.008M_{\odot}$ | c
$M_{B}$ | $1.219\pm 0.007M_{\odot}$ | c
$M_{C}$ |  $\sim$0.5 $M_{\odot}$ | c
$T_{eff,A}$ |  $6500\pm 50$ K | c
$T_{eff,B}$ |  $6400\pm 50$ K | c
$R_{A}$ | $1.2747\pm 0.0072R_{\odot}$ | c
$R_{B}$ | $1.2161\pm 0.0071R_{\odot}$ | c
$dist$ |  $103\pm 7$ pc | d
$P_{nodal}$ |  $1194\pm 20$ years | e
$i_{crit}$ | $71.3^{\circ}$ | e
$R_{2}/R_{1}$ | 0.934 | e
$R_{2}+R_{1}$ | 2.455 | e
$F_{2}/F_{1}$ | 0.800 | e
$e\sin\omega$ | 0.00 | e
$e\cos\omega$ | 0.00 | e

aafootnotetext:  (Popper, 1971)

bbfootnotetext:  (Gyldenkerne et al., 1975)

ccfootnotetext:  (Torres et al., 1997)

ddfootnotetext:  (Gaia Collaboration et al., 2020)

eefootnotetext:  This Work

##  6 Similar Systems with TESS

Aside from HS Hya, several other inclination-changing EB systems are known
that can be studied with TESS. Along with surveying the Magellenic Clouds for
EBs whose eclipse depths change over time, Juryšek et al. (2018) provided the
most comprehensive list of well characterized inclination-changing EBs within
the Milky Way. A total of 11 systems, including HS Hya, have been discovered
from ground-based data around bright stars. Thanks to its unmatched
photometric precision and long time baseline, Kepler also discovered 42
additional inclination changing EBs in the Milky Way (Borkovits et al., 2016).

To illustrate the utility in studying such systems with TESS, we searched for
available TESS data for the 10 additional systems listed in Table 1 of Juryšek
et al. (2018). For each system we used Eleanor (Feinstein et al., 2019) to
produce a 30-minute cadence light curve from the available Full Frame Image
data from TESS Cyles 1 and 2 (Sectors 001–0026). Only one of the 11 systems
did not have coverage from the current available TESS imaging, SV Gem. This is
approximately the yield expected for TESS, now that the mission has imaged
$\sim$80% of the sky.

Many of the systems have clear eclipses still visible in the Eleanor light
curves, including: RW Per, IU Aur, AH Cep, and V685 Cen. Three of the systems
had either no clear sign of eclipses in their light curves, or the data were
too noisy to identify eclipses in this by-eye analysis: V669 Cyg, V907 Sco,
and SS Lac. Of these, only SS Lac has been previously found to no longer
eclipse. The TESS light curve for AY Mus shows $<$1% sinusoidal variability at
the previously published orbital period listed by Juryšek et al. (2018), but
no clear sign of eclipse, indicating this system is also now a former EB.

A periodogram analysis for QX Cas, which was previously reported to no longer
have eclipses (Bonaro et al., 2009), shows very weak modulation at the
published orbital period (P=6.00 days). This weak signal is likely due to the
ellipsoidal modulations of QX Cas. Interestingly, the TESS light curve for QX
Cas has two additional periodic signals: starspot-like sinusoidal modulation
at a shorter period (1.7 day), as well as an eclipse signature with a period
of 1.04 day. As the TESS pixel scale is quite large, it is entirely possible
these new periodic signals may be due to contamination from a background star.
However, the nearest star (TIC 2047793341) is 3.66” away, and $\sim$24 times
(3.4 mag) fainter. This makes it unclear how the relatively high amplitude
spot modulations observed (1.5% flux modulations) could be due to such a faint
background star, unless the fainter star had very larger amplitude spots. It
is also unclear if the P=1.04 day eclipse period is associated with this
background star. If instead the new rotation and eclipse signatures are from
the QX Cas system, then we speculate they may be due to the tertiary stellar
component. This interesting system clearly warrants further analysis with
higher spatial resolution facilities.

This brief exploration of known and bright systems highlights the potential
for TESS to revolutionize the study of inclination-changing systems within the
Milky Way. The excellent photometric precision of TESS means that systems with
grazing eclipses such as HS Hya can be easily detected. As TESS continues into
its first extended mission, the years-long baseline means that tiny changes in
eclipse depth can be discovered, even for systems with potentially a 1000-year
nodal period, as demonstrated by Kepler (Borkovits et al., 2016). The nearly
full-sky coverage of TESS means that analysis of millions of bright stars
within the Full Frame Image data will almost certainly yield the largest
homogeneous catalog of EBs and inclination-changing EBs ever assembled. As the
stars studied by TESS are relatively bright, such EBs are also ideal for
ground-based follow-up spectroscopic characterization from moderate aperture
facilities.

##  7 Discussion

We have examined data for the eclipsing binary HS Hydrae spanning a remarkable
baseline of +125 years. This system is remarkable both in that it belongs to
the rare class of precessing or inclination-changing binaries, and also in
that its entire history as an eclipsing binary has been recorded in the modern
era. The range of data analyzed here – from photographic plates to space-based
cameras – shows the power in deep archival astronomy on the century timescale.
We believe TESS will be a revolution for such long-duration projects, and may
indeed lay the foundation for archival research of bright stars for the next
century to come.

As we have noted in §6, TESS will be an excellent platform for discovering and
tracking inclination-changing EBs, with nearly all the known systems within
the Milky Way already having precision data from TESS Cycles 1 and 2
available. As HS Hya continues to change orientation, subsequent visits by
TESS should be able to track the decline of the ellipsoidal variation,
however. Excitingly, TESS should be able to detect slow, monotonic increases
in ellipsoidal variations, which may become future EBs.

Finally we note that after submission of this manuscript, TESS again observed
the HS Hya system in Sector 35 (2021-Feb-09 to 2021-Mar-07). This is quite
close to our predicted date for the system reaching the critical inclination
(i.e. eclipses ceasing to be observable). As expected from our modeling of the
inclination precession in §4, no eclipses are now visible in the Sector 35
light curve. HS Hya therefore has now indeed become a former eclipsing binary.

The authors wish to thank the anonymous referee and journal editing team,
whose timely and helpful suggestions substantially improved this manuscript.
The authors wish to thank Edward Guinan and Petr Zasche for their helpful
discussions about HS Hya and QX Cas. We thank Trevor Dorn-Wallenstein, Tyler
Gordon, Guadalupe Tovar Mendoza, Spencer Wallace, and Kevin R. Covey for their
ongoing discussions and collaboration in analyzing TESS data. JRAD wishes to
acknowledge the late Roger Griffin, whose work on long-duration binary
monitoring helped inspire this work (Griffin, 2012). JRAD gratefully
acknowledges support from the Heising-Simons Foundation, and from the Research
Corporation for Science Advancement for hosting the 2019 Scialog meeting on
Time Domain Astrophysics. JRAD also acknowledges support from the DIRAC
Institute in the Department of Astronomy at the University of Washington. The
DIRAC Institute is supported through generous gifts from the Charles and Lisa
Simonyi Fund for Arts and Sciences, and the Washington Research Foundation.
The work of Erin L. Howard was supported in part by the Distributed Research
Experiences for Undergraduates (DREU) program, a joint project of the CRA
Committee on the Status of Women in Computing Research (CRA-W) and the
Coalition to Diversify Computing (CDC), which is funded in part by the NSF
Broadening Participation in Computing program (NSF BPC-A #1246649). Courtney
Klein was supported by a National Science Foundation Graduate Research
Fellowship Program under grant DGE-1839285. Jessica Birky was supported by a
National Science Foundation Graduate Research Fellowship Program under grant
DGE-1762114. The DASCH project at Harvard is grateful for partial support from
NSF grants AST-0407380, AST-0909073, and AST-1313370. This paper includes data
collected by the TESS mission, which are publicly available from the Mikulski
Archive for Space Telescopes (MAST). Funding for the TESS mission is provided
by NASA’s Science Mission directorate.

## References

  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068
  * Barnes (2011) Barnes, R. 2011, Q (Tidal Quality Factor), ed. M. Gargaud, R. Amils, J. C. Quintanilla, H. J. J. Cleaves, W. M. Irvine, D. L. Pinti, & M. Viso (Berlin, Heidelberg: Springer Berlin Heidelberg), 1395–1395, doi: 10.1007/978-3-642-11274-4_1319
  * Bloemen et al. (2013) Bloemen, S., Degroote, P., Conroy, K., et al. 2013, in EAS Publications Series, Vol. 64, EAS Publications Series, ed. K. Pavlovski, A. Tkachenko, & G. Torres, 269–276, doi: 10.1051/eas/1364037
  * Bonaro et al. (2009) Bonaro, M., Guinan, E. F., Prsa, A., & Zola, S. 2009, in American Astronomical Society Meeting Abstracts, Vol. 213, American Astronomical Society Meeting Abstracts #213, 432.16
  * Borkovits et al. (2016) Borkovits, T., Hajdu, T., Sztakovics, J., et al. 2016, MNRAS, 455, 4136, doi: 10.1093/mnras/stv2530
  * Bressan et al. (2012) Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127, doi: 10.1111/j.1365-2966.2012.21948.x
  * Drechsel et al. (1994) Drechsel, H., Haas, S., Lorenz, R., & Mayer, P. 1994, A&A, 284, 853
  * Feinstein et al. (2019) Feinstein, A. D., Montet, B. T., Foreman-Mackey, D., et al. 2019, arXiv e-prints, arXiv:1903.09152.  https://arxiv.org/abs/1903.09152
  * Foreman-Mackey et al. (2013) Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306, doi: 10.1086/670067
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, ArXiv e-prints.  https://arxiv.org/abs/1804.09365
  * Gaia Collaboration et al. (2020) —. 2020, arXiv e-prints, arXiv:2012.01533, doi: https://doi.org/10.1051/0004-6361/202039657
  * Griffin (2012) Griffin, R. F. 2012, in New Horizons in Time Domain Astronomy, ed. E. Griffin, R. Hanisch, & R. Seaman, Vol. 285, 75–80, doi: 10.1017/S1743921312000282
  * Guinan et al. (2012) Guinan, E. F., Engle, S. G., & Devinney, E. J. 2012, Journal of the American Association of Variable Star Observers (JAAVSO), 40, 467
  * Gyldenkerne et al. (1975) Gyldenkerne, K., Jørgensen, H. E., & Carstensen, E. 1975, A&A, 42, 303
  * Hunter (2007) Hunter, J. D. 2007, Computing In Science & Engineering, 9, 90, doi: 10.1109/MCSE.2007.55
  * Jayasinghe et al. (2018) Jayasinghe, T., Stanek, K. Z., Kochanek, C. S., et al. 2018, arXiv e-prints.  https://arxiv.org/abs/1809.07329
  * Jayasinghe et al. (2020) —. 2020, MNRAS, 491, 13, doi: 10.1093/mnras/stz2711
  * Jones et al. (2001–) Jones, E., Oliphant, T., Peterson, P., et al. 2001–, SciPy: Open source scientific tools for Python.  http://www.scipy.org/
  * Juryšek et al. (2018) Juryšek, J., Zasche, P., Wolf, M., et al. 2018, A&A, 609, A46, doi: 10.1051/0004-6361/201730655
  * Kochanek et al. (2017) Kochanek, C. S., Shappee, B. J., Stanek, K. Z., et al. 2017, PASP, 129, 104502, doi: 10.1088/1538-3873/aa80d9
  * Kovács et al. (2002) Kovács, G., Zucker, S., & Mazeh, T. 2002, A&A, 391, 369, doi: 10.1051/0004-6361:20020802
  * Laycock et al. (2010) Laycock, S., Tang, S., Grindlay, J., et al. 2010, AJ, 140, 1062, doi: 10.1088/0004-6256/140/4/1062
  * Lightkurve Collaboration et al. (2018) Lightkurve Collaboration, Cardoso, J. V. d. M., Hedges, C., et al. 2018, Lightkurve: Kepler and TESS time series analysis in Python, Astrophysics Source Code Library.  http://ascl.net/1812.013
  * Miller et al. (2020) Miller, N. J., Maxted, P. F. L., & Smalley, B. 2020, MNRAS, 497, 2899, doi: 10.1093/mnras/staa2167
  * Oliphant (2007) Oliphant, T. E. 2007, Computing in Science Engineering, 9, 10, doi: 10.1109/MCSE.2007.58
  * Pérez & Granger (2007) Pérez, F., & Granger, B. E. 2007, Computing in Science and Engineering, 9, 21, doi: 10.1109/MCSE.2007.53
  * Perryman et al. (1997) Perryman, M. A. C., Lindegren, L., Kovalevsky, J., et al. 1997, A&A, 500, 501
  * Pojmanski (1997) Pojmanski, G. 1997, AcA, 47, 467
  * Pojmanski (2002) —. 2002, AcA, 52, 397
  * Popper (1971) Popper, D. M. 1971, ApJ, 166, 361, doi: 10.1086/150965
  * Prša et al. (2016) Prša, A., Conroy, K. E., Horvat, M., et al. 2016, ApJS, 227, 29, doi: 10.3847/1538-4365/227/2/29
  * Ricker et al. (2015) Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, Journal of Astronomical Telescopes, Instruments, and Systems, 1, 014003, doi: 10.1117/1.JATIS.1.1.014003
  * Soderhjelm (1975) Soderhjelm, S. 1975, A&A, 42, 229
  * Stassun et al. (2009) Stassun, K. G., Hebb, L., López-Morales, M., & Prša, A. 2009, in The Ages of Stars, ed. E. E. Mamajek, D. R. Soderblom, & R. F. G. Wyse, Vol. 258, 161–170, doi: 10.1017/S1743921309031810
  * Stassun & Torres (2021) Stassun, K. G., & Torres, G. 2021, ApJ, 907, L33, doi: 10.3847/2041-8213/abdaad
  * Strohmeier et al. (1965) Strohmeier, W., Knigge, R., & Ott, H. 1965, Information Bulletin on Variable Stars, 107, 1
  * Tang et al. (2013) Tang, S., Grindlay, J., Los, E., & Servillat, M. 2013, PASP, 125, 857, doi: 10.1086/671760
  * Torres (2001) Torres, G. 2001, AJ, 121, 2227, doi: 10.1086/319942
  * Torres et al. (1997) Torres, G., Stefanik, R. P., Andersen, J., et al. 1997, AJ, 114, 2764, doi: 10.1086/118685
  * VanderPlas & Ivezic (2015) VanderPlas, J. T., & Ivezic, Z. 2015, ApJ, 812, 18, doi: 10.1088/0004-637X/812/1/18
  * Wes McKinney (2010) Wes McKinney. 2010, in Proceedings of the 9th Python in Science Conference, ed. Stéfan van der Walt & Jarrod Millman, 56 – 61, doi: 10.25080/Majora-92bf1922-00a
  * Windemuth et al. (2019) Windemuth, D., Agol, E., Ali, A., & Kiefer, F. 2019, MNRAS, 489, 1644, doi: 10.1093/mnras/stz2137
  * Wright et al. (2010) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868, doi: 10.1088/0004-6256/140/6/1868
  * Zahn (1977) Zahn, J. P. 1977, A&A, 500, 121
  * Zasche & Paschke (2012) Zasche, P., & Paschke, A. 2012, A&A, 542, L23, doi: 10.1051/0004-6361/201219392