11institutetext: Computational Intelligence Applications Research Group,
Nottingham Trent University, Clifton Campus, NG11 8NS, UK,
%First␣names␣are␣abbreviated␣in␣the␣running␣head.%If␣there␣are␣more␣than␣two␣authors,␣’et␣al.’␣is␣used.https://www.ntu.ac.uk/research/groups-
and-centres/groups/computational-intelligence-applications-research-group
11email:
n0932346<EMAIL_ADDRESS>22institutetext: School of Animal, Rural and Environmental Sciences,
Nottingham Trent University, Brackenhurst, Southwell, NG25 0QF, UK
https://www.ntu.ac.uk/study-and-courses/academic-schools/animal,-rural-and-
environmental-sciences
22email<EMAIL_ADDRESS>33institutetext: Mediprospects AI, 5-7 High
Street, London, E13 0AD, UK
https://www.mediprospects.ai/
33email<EMAIL_ADDRESS>
# WeedScout: Real-Time Autonomous blackgrass Classification and Mapping using
dedicated hardware

Matthew Gazzard 11 Helen Hicks 22 0000-0003-1325-2293 Isibor Kennedy Ihianle
11 0000-0001-7445-8573 Jordan J. Bird 11 0000-0002-9858-1231 Md Mahmudul Hasan
33 0000-0003-2543-3112 Pedro Machado 11 0000-0003-1760-3871

###### Abstract

Blackgrass (Alopecurus myosuroides) is a competitive weed that has wide-
ranging impacts on food security by reducing crop yields and increasing
cultivation costs. In addition to the financial burden on agriculture, the
application of herbicides as a preventive to blackgrass can negatively affect
access to clean water and sanitation. The WeedScout project introduces a Real-
Rime Autonomous Black-Grass Classification and Mapping (RT-ABGCM), a cutting-
edge solution tailored for real-time detection of blackgrass, for precision
weed management practices. Leveraging Artificial Intelligence (AI) algorithms,
the system processes live image feeds, infers blackgrass density, and covers
two stages of maturation. The research investigates the deployment of You Only
Look Once (YOLO) models, specifically the streamlined YOLO v8 and YOLO-NAS,
accelerated at the edge with the NVIDIA Jetson Nano (NJN). By optimising
inference speed and model performance, the project advances the integration of
AI into agricultural practices, offering potential solutions to challenges
such as herbicide resistance and environmental impact. Additionally, two
datasets and model weights are made available to the research community,
facilitating further advancements in weed detection and precision farming
technologies.

###### Keywords:

SDG12, SDG13, SDG15, YOLOv8, YOLO-NAS, Blackgrass, Robotics, NVIDIA Jetson
nano

##  1 Introduction

Blackgrass (Alopecurus myosuroides) is a problematic weed that has potential
impact on food security due to its interruption of oilseed rape and several
winter cereals. As weed species became increasingly resistant to herbicides,
managing weed populations became more difficult. Varah et al. [1] concluded
that herbicide resistant blackgrass resulted in £400 million lost gross profit
and 0.8 million tonnes lost yield in England alone. Furthermore, Varah et al.
[1] predicted that in the absence of herbicide control, losses could reach £1
billion and 3.4 million tonnes annually. In this paper, the WeedScout project
presents an Artificial Intelligence (AI)solution tailored to detect blackgrass
in wheat crops, streamline farmers’ identification processes, and resource
allocation. The innovative approach not only facilitates precision weed
management, but also holds promise in reducing herbicide costs and hindering
the advancement of herbicide resistance. The contributions of the paper
include the compilation and sharing of a diverse blackgrass dataset, employing
state-of-the-art Deep Learning (DL) algorithms, and the deployment of the
models on dedicated hardware. Initially, our focus was on exploring the use of
AI in object detection, with particular emphasis on real-time implementations,
given the challenge of accurately mapping blackgrass. Furthermore, our work
contributes annotated two blackgrass datasets [2, 3] to support future work.
The WeedScout delivers Real-Rime Autonomous Black-Grass Classification and
Mapping (RT-ABGCM)powered by the NVIDIA Jetson Nano (NJN). By leveraging the
computational prowess of the NJN, AI inference is accelerated at the edge,
enabling swift detection and analysis of blackgrass. Moreover, the proposed
approach not only maps the blackgrass density but also provides real-time
geolocation, obviating the necessity for a continuous internet connection.
Thus, WeedScout offers a comprehensive and efficient means of managing
blackgrass infestations in wheat fields.

The paper is organised into the following sections: section 2 reviews relevant
works; section 3 elaborates on the proposed methodology; section 4 conducts an
analysis of the results; and, section 5 presents the concluding remarks and
outlines future research directions.

##  2 Literature Review

Weeds are commonly recognised as the most significant biotic factor affecting
crop production [4]. However, it is noteworthy that low densities of weeds can
also provide agronomic and ecological benefits [4]. Therefore, weeds should be
viewed as agricultural entities that require management rather than outright
elimination. Historically, herbicides have been the most widely employed
method for weed management, aimed at maximising crop yield while minimising
human effort and cost [1, 4]. However, extensive use of herbicides has led to
the evolution of resistance on a large scale, jeopardising yield benefits as
herbicide efficacy decreases [1, 4, 5, 6]. Resistance to herbicides presents a
significant problem, as resistance to one class of herbicides can indicate
resistance to multiple types, and the use of herbicide mixtures in hopes of
reducing specialist resistance can paradoxically lead to more general
resistance [5, 6]. Such reliance on herbicides as the primary weed management
strategy is unsustainable, given the expense and time required to formulate
new weed-killing chemicals, coupled with the inevitable development of
resistance rendering them obsolete [5]. Additionally, it is crucial to
acknowledge the adverse environmental impacts of herbicides, which harm
biodiversity, water, and soil quality [1].

The abundance of A. myosuroides weeds is currently mediated by herbicide
resistance [5], a phenomenon supported by Varah et al. [1]. The consequential
impact of A. myosuroides on yield stands out as the most economically
significant weed in Western Europe due to its high yield impact [5]. Comont et
al. [6] discuss how glyphosate has emerged as one of the final lines of
defence in controlling A. myosuroides, yet A. myosuroides is already
developing resistance to the herbicide. Resistance to herbicides mirrors the
broader trend of resistance in agricultural sectors, posing a substantial
challenge. Given the increasing difficulties in herbicide-based weed
management, it becomes imperative to explore more diverse methods of weed
management that integrate targeted site management, an area where AI proves
invaluable.

Ahmed et al. [7] delineate the concept of challenging environments which
includes occlusion, poor lighting, and objects merging into backgrounds as
typical scenarios where object detection using AI has historically struggled.
Leveraging the definition alongside Hasan et al. [8], crop fields emerge as
exemplary instances of such environments. Although two-stage detectors
generally offer higher accuracy, their slower processing speed renders them
unsuitable for real-time applications [9]. Given the planned integration of
embedded or edge devices in the proposed blackgrass detection solution, it
becomes imperative to employ object detection methodologies optimised for
limited computational resources [7]. Consequently, the utilisation of two-
stage detectors is discounted, a notion corroborated by Zaidi et al. [9], who
emphasise the importance of lightweight models. When considering object
detection algorithms, You Only Look Once (YOLO)is lauded for its adeptness in
striking a balance between speed and accuracy, rendering it ideal for real-
time object detection [10, 11, 12]. While other models may offer superior
accuracy, the equilibrium holds significant value. Moreover, YOLO provides a
range of model scales to tailor its performance to specific application
requirements and hardware capabilities [10, 11, 12]. Therefore, YOLO models
have already found deployment on edge devices such as robots and drones and
boast a history of successful implementation in agricultural contexts [10, 11,
12].

In agriculture, AI deployment for weed detection and mapping is increasingly
prevalent, as evidenced by studies such as those conducted by Krähmer et al.
[13], Xu et al. [14], Jabir and Falih [15], Hasan et al. [8], Wu et al. [16],
Xu et al. [17], and Dainelli et al. [18]. Krähmer et al. [13] further specify
that herbicide resistance distribution can also be effectively mapped. In the
context of wheat crops, Xu et al. [14] elaborate on the tillering stage as the
opportune time for weed detection due to reduced occlusion between wheat and
weeds, a factor alleviating some challenges encountered in challenging
environments [7, 8]. However, despite the availability of numerous datasets,
challenges persist in training models specifically for weed detection within
crop fields. Dainelli et al. [18] highlight limitations in data collection
methods and availability, stressing the costliness and time-consuming nature
of creating custom datasets. Krähmer et al. [13] underscore the difficulty in
identifying growth stages and the challenge detection algorithms face in
distinguishing between similar weeds and a plethora of unknown species [19].
Nonetheless, finding an automated solution for weed detection remains
imperative, as manual methods prove economically unviable [19]. While the
hardware for weed monitoring may incur initial expenses, the resulting
reductions in herbicide usage offset costs and offer environmental benefits.
Moreover, the inefficiency of manual weed detection underscores the potential
of technologies such as Unmanned Aerial Vehicles (UAVs) or robots to
supplement or replace manual labor. UAVs equipped with high-resolution cameras
are particularly effective in detecting low-density weed patches [16].
However, limitations exist, as most UAV applications involve capturing images
solely above the crop canopy, potentially missing crucial information [13].
Thus, a solution closely monitoring wheat fields is desirable. Examples of
such solutions already exist, contributing to Integrated weed Management (IWM)
and Site-Specific Weed Management (SSWM). For instance, BonnBot-I [20] serves
as a precision weed management and field monitoring platform, utilising
ground-based rovers for weed detection and herbicide application. Moreover,
Mattivi et al. [21] exemplify the successful deployment of cost-effective UAVs
equipped with open-source software for implementing smart farming techniques,
even on small-scale farms. These systems play pivotal roles in advancing
Agriculture 4.0 initiatives [16, 17]. Localised herbicide application can be
realised through the utilisation of weed maps or real-time sensors [19]. The
WeedScout project extends upon the literature reviewed in the present section
by perform RT-ABGCM, independent of internet connectivity, and leveraging edge
acceleration with the NJN.

##  3 Methodology

The WeedScout system receives live image feeds, executes AI inference on the
NJN, and produces an output depicting the density of detected blackgrass,
potentially discerning various stages of maturation. The chapter provides a
detailed description of the RT-ABGCM module which is the core of the
WeedScout.

As discussed in the previous section, YOLO models are well-known for their
efficacy in weed detection. However, due to limited computational resources on
edge devices, larger AI models, despite their higher accuracy compared to
smaller ones, are not feasible for deployment. Moreover, larger YOLO models
exhibit increased latency, rendering them unsuitable for real-time detection
systems. To determine the veracity of the effectiveness of YOLO-NAS, YOLO v8
models were also trained on the same two custom datasets [2, 3] and
benchmarked for determining which model type works best in the problem domain.

The developed models were deployed on the cost-effective NJN. The compact
computer is purpose-built for AI applications and leverages Compute Unified
Device Architecture (CUDA) 111Available online,
https://developer.nvidia.com/cuda-zone, last accessed: 08/05/2024 for
accelerating AI operations. However, given the edge deployment’s limited
resources, training the model directly on the device is impractical.
Therefore, the models will undergo training on a separate, more powerful
machine. The models performed inference on video inputs of blackgrass,
generating video output with overlays of the model’s detections.

Figure 1: NVIDIA Jetson Nano.

The NJN (see Fig. 1) was flashed with JetPack SDK 2222Available online,
/urlhttps://developer.nvidia.com/embedded/jetpack, last accessed: 08/05/2024
(see Fig. 3), running Robotic Operating System 2 (ROS2) Dashing333Available
online, https://docs.ros.org/en/dashing/index.html, last accessed 08/05/2024
powered by Ubuntu 18.04.06 LTS 444Available online,
https://releases.ubuntu.com/18.04/, last accessed: 08/05/2024 (see Figure 6).
The JetPack SDK provides all the NVIDIA libraries necessary for AI edge
applications and ROS2 is necessary for compatibility with mobile robotic
platforms.

Figure 2: NVIDIA JetPack SDK 2.0. |  Figure 3: NJN AI inference.
---|---

###  3.1 WeedScout Platform Workflow

A meticulously designed and implemented prototype for RT-ABGCM is depicted in
Figure 4. The system integrates an NJN equipped with an Intel RealSense D435i
depth sensor. The NJN serves as the computational backbone for accelerating
the YOLO v8 and YOLO-NAS inference at the edge. Specifically tailored for a
myriad of tasks, the NJN handles image identification, object detection, data
segmentation, and speech processing. It boasts a robust configuration,
featuring a 128-core Maxwell Graphics Processing Unit (GPU), a quad-core ARM
A57 Application Processor Unit (APU) operating at 1.43 GHz, and 4 GB of 64-bit
LPDDR4 memory running at 25.6 GB/s. Moreover, the system is bolstered by the
inclusion of a pre-trained DL models, enhancing its detection capabilities.

Figure 4: The proposed WeedScout architecture workflow.

While semantic segmentation would be beneficial for clearly delineating
boundaries between blackgrass and wheat, annotating a sufficiently large
dataset would be exceedingly time-consuming due to the likelihood of images
containing numerous individual plants. Annotating images for object detection
is comparatively simpler as it does not require drawing complex polygons
around the desired objects. Moreover, it was determined that employing object
detection would not adversely affect the performance of the generated models.
Therefore, object detection was chosen as the computer vision methodology.

Object detection necessitates annotating a given dataset by drawing bounding
boxes around objects within images and assigning each box to the corresponding
object class. Roboflow555Available online, https://roboflow.com/, last
accessed: 10/05/2024 was used to increase productivity. Leveraging Roboflow
proved advantageous as it facilitated the easy management and storage of
datasets; annotated images could be categorised into training, validation, and
test sets before undergoing augmentation and export.

The dataset for mature blackgrass was collected using an Intel RealSense
D435i666Available online, https://www.intelrealsense.com/depth-camera-d435i/,
last accessed: 10/05/2024 at a wheat field in England, UK. The Intel RealSense
D435i was used to capture Red, Green, Blue and depth (RGBd) data and stored in
a bag file. Consequently, it was necessary to extract standard video footage
from the file using Intel RealSense SDK777Available online,
https://www.intelrealsense.com/sdk-2/, last accessed: 10/05/2024. The process
yielded thousands of PNGs of standard images alongside thousands of images
containing depth data. Since the depth data was unnecessary for the proposed
work, it was discarded, and a random selection of 780 PNGs was extracted using
a PowerShell script to form an initial dataset.

Following the loading of the 780 images into Roboflow, 156 (20%) were
allocated for validation, and 78 (10%) for testing, leaving the remaining 546
(70%) for training. Subsequently, all images were annotated using Roboflow’s
annotation tool, categorising blackgrass into three different density
categories: low, medium, and high. To augment the size and diversity of the
initial dataset, data augmentation techniques were applied to decrease the
likelihood of overfitting and enhance model performance. Augmentations were
applied to both the images and the bounding box annotations (refer to Table
1). Additionally, a version of the dataset without augmentations was preserved
for training, enabling performance comparison.

Table 1: Dataset augmentations Type | Applied to | Option
---|---|---
Flip | Image, Bounding Box | Horizontal, Vertical
90° Rotate | Image, Bounding Box | Clockwise, Counter-Clockwise, Upside, Down
Crop | Image, Bounding Box | 0% Minimum Zoom, 20% Maximum Zoom
Rotation | Image, Bounding Box | Between -15° and +15°
Shear | Image, Bounding Box | ±15° Horizontal, ±15° Vertical
Hue | Image | Between -25° and +25°
Saturation | Image | Between -30% and +30%
Brightness | Image, Bounding Box | Between -25% and +25%
Exposure | Image, Bounding Box | Between -14% and +14%
Blur | Image | Up to 2.5px
Noise | Image, Bounding Box | Up to 1.99% of pixels
Cutouth | Image | 3 boxes with 10% size
Mosaic | Image | Applied

A separate approach was also explored on Roboflow utilising blackgrass
seedling dataset obtained from the Plant seedling datasets available on Kaggle
888Available online, https://www.kaggle.com/datasets/vbookshelf/v2-plant-
seedlings-dataset, last accessed: 10/05/2024. The images of the plant seedling
dataset were annotated, and data augmentation was applied due to the limited
size of the dataset (see Table 1). The seedling dataset comprised only one
class, blackgrass as it was not intended for detecting weed density. Instead,
it was envisaged that any resulting model could be used for precision weed
management in newly planted wheat fields.

Developing YOLO-NAS models required the utilisation of the open-source model
library SuperGradients999Available online, https://github.com/Deci-AI/super-
gradients, last accessed: 10/05/2024. In addition to facilitating the training
of regular models, the library enables the SuperGradients libraries to
quantitise models through its post-training quantisation and quantization
aware training functionalities. SuperGradients also provides the ability to
connect third-party monitoring software to display the metrics tracked during
model training and validation. Given the iterative nature of training AI
models, where adjustments to the dataset or hyperparameters may be necessary
based on training outcomes, it is crucial to monitor performance at both
training and validation stages to assess the impact of any modifications.
Weights and Biases (WnB) serves as a platform for storing AI model data,
facilitating the comparison and evaluation of model performance. Any
monitoring data collected during model training was hosted on WnB, enabling
the automatic generation of graphs for essential metrics such as mean Average
Precision (mAP), precision, and recall for use in model comparison. The use of
WnB also served as the project’s test suite, as the performance metrics of the
models are intrinsically linked to the successful video inference. Although
training AI models is resource intensive, maximising the use of the hardware
used for training is crucial to ensuring models are trained within an
acceptable timeframe. Although it is possible to train AI models using a
computer’s Central Processor Unit (CPU), the method is not the most efficient.
Leveraging CUDA with an NVIDIA GPU can significantly reduce training time by
accelerating processing through GPU-acceleration. Thus, training with GPU-
acceleration is the preferred methodology, either by using available resources
or using cloud solutions such as Google Collab.

Using a GPU offers benefits beyond accelerated training; it also enables
faster model inference. This is essential as any recorded footage of
blackgrass should be inferred at the fastest possible speed to maintain
usability. The chosen training machine utilised an NVIDIA GeForce RTX 3080
10GB GPU with CUDA version 12.4 (see Figure 13). Before starting training, it
was necessary to prepare the training machine by downloading the CUDA Toolkit,
as it does not come pre-installed. SuperGradients utilises PyTorch, a Python-
based machine learning framework. To enable PyTorch to utilise CUDA, it is
necessary to download versions of it that come packaged explicitly with CUDA
capabilities. Without these specific packages, training and inference using
NVIDIA GPUs would be impossible.

Before deploying models to the NJN, it was essential to devise a design for
presenting the blackgrass detections to users. By default, the prediction
function of SuperGradients draws labelled bounding boxes around the
detections, indicating the confidence threshold of the prediction (see Figure
5). However, the objective of blackgrass inference is to identify areas with
varying densities of blackgrass weeds, and SuperGradients does not offer a
density overlay option. Additionally, SuperGradients cannot be used to infer
YOLOv8 models, necessitating the creation of a custom overlay.

Figure 5: Blackgrass detection overlay initial design. Yellow is being used to
demonstrate low density and orange is being used to demonstrate medium
density. High density patches would have a red overlay.

Inspiration was drawn from heatmaps, where higher densities are represented by
increasingly warmer colours. For instance, lower densities may be highlighted
in yellow, while higher densities can be depicted in orange. Areas with the
highest densities could have a red overlay to denote their severity. Figure 5
was devised to provide guidance for designing the output of model inference
returned to users.

##  4 Results Analysis

In this section, we will discuss the diverse results obtained for the two
datasets tested against both YOLO v8 and YOLO-NAS.

###  4.1 blackgrass Seedling dataset

To evaluate the suitability of the seedlings dataset (see Table 2) tested
against the YOLO v8.

Table 2: Number of images within augmented blackgrass seedling datasets Train | Validation | Test | Total
---|---|---|---
2820 | 168 | 112 | 3100

For the seedling dataset, there was only the blackgrass class to be detected.
From the results obtained, the True Positive (TP) value of 0.81 indicated the
model’s success, as the vast majority of blackgrass in the positive samples
was detected. While metrics for mAP quickly converged within approximately 20
epochs, the values failed to reach 1.0 The validation loss
(LABEL:fig:cls_seed_yolo) gradually decayed as expected, but training loss
exhibited greater stability than its validation counterparts. Nevertheless,
the results from creating a YOLO-NAS model using the blackgrass seedling
dataset provided clearer insights into overfitting compared to the YOLO v8
model. Convergence was remarkably swift for both mAP and recall during
training and validation. The final values for mAP and recall metrics during
training were also strikingly close to 1. While validation precision remained
high, it was noticeably lower compared to its training counterpart, which
tended towards 1.0 like training mAP and recall. Therefore, an interesting
trend was observed when comparing the training loss and validation loss, where
training loss decreased while validation loss increased. The results indicate
that the model was overfitting. Combined with other trends observed during
both YOLO-NAS and YOLO v8 training and validation, it was concluded that
overfitting negatively impacted the performance of models trained on the
blackgrass seedling dataset. Unfortunately, beyond the existing data
augmentations, there was no effective way to further increase the size and
diversity of the blackgrass seedling dataset. Therefore, the focus shifted to
prioritising the detection of mature blackgrass.

###  4.2 Mature blackgrass dataset

The mature blackgrass dataset (see Table 3 was generated using the same
augmentations described in Table 1.

Table 3: Dataset Details Dataset | Train | Validation | Test | Total
---|---|---|---|---
Blackgrass mature | 6552 | 624 | 312 | 7488

Given the state-of-the-art performance typically associated with YOLO-NAS
models, it was expected that similar models would surpass YOLO v8 in later
epochs. However, the mAP for the YOLO v8 model demonstrated a slight
improvement compared to its YOLO-NAS counterpart. Furthermore, the recall for
the YOLO v8 model outperformed YOLO-NAS when running on NVIDIA Jetson nano,
although both precision and recall to be similar. The observation is
intriguing considering that the YOLO v8 nano model. The discrepancy in size
makes it obvious that the YOLO v8 model has a better performance than the
YOLO-NA model. Additionally, the absence of loss escalation during validation
with the YOLO v8 model contrasts with the trend observed in the YOLO-NAS
models, where validation loss increases.

The models contained in Table 4 ran inference on a video containing high
densities of blackgrass.

Table 4: Models used in inference testing and the confidence used to perform inference. Model | Confidence |  | Frames with
---
detections
YOLO-NAS | 0.7 | 444
YOLO v8 | 0.7 | 799

To assess the run-time performance of the mature blackgrass models, a brief
5-second video was employed for inference. Upon examining the inference times
of various models listed in Table 5, it became evident that the YOLO v8 model,
trained on the mature blackgrass dataset, exhibited notably faster inference
speeds compared to the YOLO-NAS models. The discrepancy can be attributed to
the variance in model size and possibly to differences in the efficiency of
prediction functions between Ultralytics101010Available onine,
https://docs.ultralytics.com/, last accessed: 12/05/2024 and SuperGradients.

In order to utilise GPU, the NJN was configured to run the inference using the
pre-trained YOLO v8 weights. The runtime for inference on the same video used
for training on the testing machine is presented in Table 5). Although the
inference time is notably longer, the results were anticipated as YOLO-NAS
runs on the CPU while YOLO v8 utilises GPU. Given the significantly longer
inference time compared to the supplied source video, optimisations to the
model and code are imperative to reduce inference time and potentially enable
real-time detection.

Table 5: Mean average time for mature blackgrass models to inference a 5s long video on the CPU only, and CPU and GPU accelerated. Model |  | Inference 1
---
[s]
| Inference 2
---
[s]
| Inference 3
---
[s]
| Mean inference
---
[s]
|  YOLO v8 (CPU and GPU)
---
82.98 | 86.25 | 82.69 | 83.97
|  YOLO-NAS (CPU only)
---
229.71 | 223.75 | 217.93 | 223.80

##  5 Conclusions and Future Work

This paper introduces a novel RT-ABGCM designed to operate effectively at the
edge. Following multiple iterations of dataset augmentation and annotation,
two types of models were developed capable of successfully detecting
blackgrass. Given constraints with the blackgrass seedling dataset, the
emphasis shifted towards detecting mature blackgrass. Surprisingly, YOLOv8
proved more effective for the task compared to YOLO-NAS. However, both models
encountered challenges in detecting low and medium density blackgrass.The
challenge arose from the mature blackgrass dataset’s significant bias towards
high-density patches, making it challenging to generate annotated datasets
containing an adequate number of images depicting lower densities for robust
training. Rectifying the challenge requires obtaining a more diverse dataset
and conducting additional experimentation to identify the best mix of training
hyperparameters and dataset augmentations for refining density detection
models. Despite these challenges, models were successfully deployed on the
NJN, demonstrating the efficacy of the model production pipeline. While the
NJN enables inference, it operates at sub-optimal GPU acceleration, resulting
in slower inference times that preclude real-time performance.

Inference speed of the current solution could be improved by investigating
other methods of model inferencing. Other lightwight AI frameworks such as
TensorRT and DeepStream SDK could be utilised to improve the frame rate.
Improving the Frames Per Second (FPS) is necessary for real-time inference. If
real-time inference at a stable FPS was achieved, it would be possible to
create an automated sprayer or electric discharge combined with more research
into detecting blackgrass seedlings so that blackgrass could be tackled at the
earliest possible stage.

####  5.0.1

The authors have no competing interests to declare that they are relevant to
the content of this article.

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In this work we have presented seven new compact triply eclipsing triples with
a full solution to their stellar and orbital parameters. All of these systems
were found by searching through millions of TESS photometric light curves
looking for third body eclipses in binary systems (see e.g., Kristiansen et
al. 2022; Rappaport et al. 2022).

We utilized the TESS photometric light curves, the ETV points derived from the
light curves, archival SED data, archival photometry from ASAS-SN and ATLAS,
and in some cases, ground-based follow up RV observations as well as eclipse
photometry. These were combined in a complex photodynamical analysis where we
solve for all the system parameters, as well as the distance to the source.
Typical uncertainties on the masses and radii are in the range of a couple of
per cent to not much more than $\sim$5 per cent. Uncertainties on the angles
associated with the orbital planes (e.g., $i_{\rm out}$ and $i_{\rm mut}$)
range from a fraction of a degree to about a degree. See Tables 6 through 9.

In Fig. 22 we present a set of four correlation plots among some of the
physically interesting parameters associated with our collection of 33
recently analyzed triply eclipsing triples. To the seven sources presented in
this work, we have added the 15 triples from our previous closely related
papers (Rappaport et al., 2022) and (Rappaport et al., 2023), as well as
eleven triples studied in Borkovits et al. (2019a, 2020b, 2022a, 2022b),
Czavalinga et al. (2023b), and Mitnyan et al. (2020) using largely the same
selection criteria and methods of analysis.

The top left panel in Fig. 22 shows how $e_{\rm out}$ varies with $P_{\rm
out}$. In general, there is little correlation, except for the fact that the
most circular outer orbits tend to have the relatively shorter outer periods,
where the circularization may be brought about by tidal damping with an
evolved tertiary. See also Fig. 19 and the associated discussion.

Figure 23: Comparison of Gaia distances (Bailer-Jones et al., 2021) to 40
triple systems with distances found from our photodynamical fits to the system
parameters. The systems marked in red are 6 from the current work with fitted
distances. The blue curve is the line where the Gaia and our photometric
distances would match. The formal correlation coefficient between the two sets
of data is 0.994, and the fitted slope is $1.010\pm 0.003$. There is one
system, TIC 52041148, at a Gaia distance of $5931\pm 400$ pc and photometric
distance of $1357\pm 30$, that is off the plot.

The top right panel of Fig. 22 shows the inclination angle of the outer orbit
vs. the mutual inclination angle of the inner binary with respect to the outer
orbit. The fact that most of the values of $i_{\rm out}$ lie near $90^{\circ}$
is a selection effect since these triples were, in fact, discovered from the
presence of third-body eclipses. To a lesser extent, the same selection also
holds for the small values of $i_{\rm mut}$, otherwise third body eclipses
would be somewhat more difficult to detect. Two of the systems have large
enough $i_{\rm mut}$ (20∘ and 40∘) to undergo substantial precession of their
orbital planes. Finally, there is one triple (TIC 276162169) in a nearly flat
system, but where the outer orbit is retrograde with respect to the inner EB.
These are rare systems.

The $q_{\rm in}$ vs. $q_{\rm out}$ plot (lower left panel in Fig. 22) shows an
interesting feature, namely that the ratio of $q_{\rm out}\equiv M_{\rm
B}/M_{\rm EB}$ never exceeds unity (and not just by definition) and has a
median value of 0.62. This result is not obviously caused by any selection
effects. For purposes of this plot only we define $q_{\rm in}$ as the ratio of
the lower mass to the higher mass star in the EB.

This result for $\bar{q}_{\rm out}$ having a mean of $\sim$0.62 and never
exceeding unity, favors a formation scenario for tight triples involving
sequential disk fragmentation and subsequent accretion proposed by Tokovinin &
Moe (2020) (see also Tokovinin, 2021; Offner et al., 2023, for recent
reviews), In this scenario, the accretion rate onto the protostellar cores has
an inverse relation with their mass-ratio. Hence, the less massive core of the
progenitor EB secondary accretes faster while it has lower mass. Similarly,
the tertiary, with the youngest core, will accrete faster while it has lower
mass than the sum of the elder, inner cores. Consequently, under the
assumption that there is enough matter, the triple tends toward a ‘double
twin’ scenario, which means that both $q_{\rm in}$ and $q_{\rm out}$ would be
about unity. Naturally, the accretion may stop earlier, resulting in $q_{\rm
out}<1$, but it does not allow for $q_{\rm out}>1$.

The bottom right panel of Fig. 22 shows the relation between the tertiary
radius and its mass. About a dozen of the stars lie fairly near the main
sequence, roughly represented by the $R=M$ line in the figure. However, the
other $\sim$20 of the tertiary stars have evolved distinctly away from the
main sequence. That is due both to an observational selection effect involving
the detectability of third-body eclipses, and the fact that the EB stars
cannot grow as large as the tertiaries without overflowing their Roche lobes.

A couple of the statistical plots rely on the following assumption made in our
photodynamical analyses. Here we have generally adopted the assumption that
the inner EB stars are coeval with the tertiary stars and, specifically, that
no mass has been transferred among the stars or lost from the system. In turn,
this includes the assumption that the tertiary star itself was always a single
star, and not the merger product of another binary star.

Another item worthy of a brief discussion is the photometric distance we
derive vs. the parallactic distance found by Gaia. Our distances are plotted
in Fig. 23 where they are compared to Gaia’s distances. These are the same 33
triply eclipsing systems discussed above (of which we have photometric
distances for 31), and augmented by 9 other triple systems analyzed in the
same manner, but which are not triply eclipsing. These latter sources are
taken from Borkovits et al. (2020a, 2022b), Gaulme et al. (2022), and
Borkovits & Mitnyan (2023).

The overall general agreement between the Gaia distances and our photometric
distances is quite striking, and with generally comparable error bars. The
formal correlation coefficient between the two sets of distances is 0.993 and
the fitted slope between them is $1.028\pm 0.004$. Aside from this general
agreement, there are a fair number of points where the two distances differ by
more than a few statistical error bars. In these cases, it is not obvious from
an inspection of this figure which distance is the more accurate one. This may
be a case where one or both sets have underestimated uncertainties. In the
case of Gaia, the outer orbit, which can be of the order of a 1/2-1 year, may
be slightly distorting the parallax measurement161616In this context we note
that it was pointed out in Sect. 5.3 of Borkovits et al. (2022a) that, in the
case of TIC 52041148, the extreme outlier Gaia EDR3 parallax-derived distance
of Bailer-Jones et al. (2021) cannot be physically realistic.. For our
photometric distances, there may be issues with inhomogeneous SED data, some
of which may be taken during eclipses, the PARSEC isochrones are based on
isolated and non-rotating stars, and there are uncertainties in the
wavelength-dependent interstellar extinction that we use.

Now that the 33 triply eclipsing triples discussed above (see Fig. 22) have
their basic parameters determined, and all but three have outer periods
shorter than a year, this would make for an interesting follow-up ground-based
eclipse timing project. Most of these systems are accessible with modest-size
amateur telescopes since the majority of the 33 objects have G magnitudes of
$\lesssim 13$. The ETV data from TESS itself was typically quite fundamental
in the determination of the systems parameters via the photodynamical
analyses. Therefore, future timing observations of the regular EB eclipses in
these systems could significantly improve the parameter determinations. The
ETV delays are typically in the minute range, so readily within the reach of
amateur observations. Since there are a large number of these triply eclipsing
triples, there should be a system to observe nearly every night.

###### Acknowledgements.

This project has received funding from the HUN-REN Hungarian Research Network.
T. B., T. M., I. B. B. and A. P. acknowledge the financial support of the
Hungarian National Research, Development and Innovation Office – NKFIH Grants
K-147131 and K-138962. This paper makes extensive use of data collected by the
TESS mission. Funding for the TESS mission is provided by the NASA Science
Mission directorate. Some of the data presented in this paper were obtained
from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by
the Association of Universities for Research in Astronomy, Inc., under NASA
contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA
Office of Space Science via grant NNX09AF08G and by other grants and
contracts. Distances and other astrometric properties for all targets, and
outer orbits for two of our sources, were taken from the archives of European
Space Agency (ESA) mission Gaia171717https://www.cosmos.esa.int/gaia,
processed by the Gaia Data Processing and Analysis Consortium
(DPAC)181818https://www.cosmos.esa.int/web/gaia/dpac/consortium. Funding for
the DPAC has been provided by national institutions, in particular the
institutions participating in the Gaia Multilateral Agreement. Some of the SED
fluxes and magnitudes were obtained with the Wide-field Infrared Survey
Explorer, which is a joint project of the University of California, Los
Angeles, and the Jet Propulsion Laboratory/California Institute of Technology,
funded by the National Aeronautics and Space Administration. Additionally,
some of the SED fluxes and magnitudes were obtained with the Two Micron All
Sky Survey, which is a joint project of the University of Massachusetts and
the Infrared Processing and Analysis Center/California Institute of
Technology, funded by the National Aeronautics and Space Administration and
the National Science Foundation. We used the Simbad service operated by the
Centre des Données Stellaires (Strasbourg, France) and the ESO Science Archive
Facility services (data obtained under request number 396301). This research
has also made use of the VizieR catalogue access tool, CDS, Strasbourg, France
(DOI : 10.26093/cds/vizier). The original description of the VizieR service
was published in Ochsenbein et al. (2000). Our searches for outer orbital
periods from photometry utilized archival data from the Asteroid Terrestrial-
impact Last Alert System (ATLAS) project. The Asteroid Terrestrial-impact Last
Alert System (ATLAS) project is primarily funded to search for near earth
asteroids through NASA grants NN12AR55G, 80NSSC18K0284, and 80NSSC18K1575;
byproducts of the NEO search include images and catalogs from the survey area.
This work was partially funded by Kepler/K2 grant J1944/80NSSC19K0112 and HST
GO-15889, and STFC grants ST/T000198/1 and ST/S006109/1. The ATLAS science
products have been made possible through the contributions of the University
of Hawaii Institute for Astronomy, the Queen’s University Belfast, the Space
Telescope Science Institute, the South African Astronomical Observatory, and
The Millennium Institute of Astrophysics (MAS), Chile. Our searches for outer
orbital periods also made use of archival data from ASAS-SN data for this
work. The ASAS-SN Sky Patrol (All-Sky Automated Survey for Supernovae) is an
automated program to search for supernovae and other astronomical transients,
headed by astronomers from Ohio State University (US). It has 20 robotic
telescopes in both the northern and southern hemispheres and surveys the
entire sky approximately once every day.

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##  Appendix A Eclipse times of the inner EBs of the seven triples

In this appendix we tabulate the times of the individual primary and secondary
eclipses of the inner EBs of the triples considered in this study. These
naturally include mostly eclipses from TESS, plus a few that were observed
from the ground (Tables 11–17).

Table 11: Eclipse times for TIC 133771812

BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev.
---|---|---|---|---|---|---|---|---|---|---|---
$-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$
58495.15572 | -0.5 | 0.00129 | 58538.30974 | 3.0 | 0.00107 | 59261.99860 | 61.5 | 0.00484 | 59985.53480 | 120.0 | 0.00044
58501.18645 | 0.0 | 0.00051 | 59230.98511 | 59.0 | 0.00059 | 59274.37006 | 62.5 | 0.00490 | 59991.73798 | 120.5 | 0.00114
58507.52038 | 0.5 | 0.00597 | 59243.35923 | 60.0 | 0.00052 | 59966.99857 | 118.5 | 0.00099 | 59997.91101 | 121.0 | 0.00029
58513.56058 | 1.0 | 0.00052 | 59249.63045 | 60.5 | 0.00090 | 59973.15918 | 119.0 | 0.00038 | 60004.10785 | 121.5 | 0.00073
58519.89039 | 1.5 | 0.00158 | 59255.73720 | 61.0 | 0.00181 | 59979.36605 | 119.5 | 0.00101 | 60010.28418 | 122.0 | 0.00041
58525.93650 | 2.0 | 0.00051 |  |  |  |  |  |  |  |  |

Notes. Integer and half-integer cycle numbers (here and the following tables)
denote primary and secondary eclipses, respectively.

Table 12: Eclipse times for TIC 176713425

BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev.
---|---|---|---|---|---|---|---|---|---|---|---
$-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$
58738.87091 | -0.5 | 0.00016 | 58760.71389 | 11.0 | 0.00015 | 58784.43845 | 23.5 | 0.00015 | 59869.56727 | 595.0 | 0.00007
58739.82153 | 0.0 | 0.00026 | 58761.66181 | 11.5 | 0.00020 | 58785.38567 | 24.0 | 0.00015 | 59870.51853 | 595.5 | 0.00010
58740.77369 | 0.5 | 0.00023 | 58762.60987 | 12.0 | 0.00014 | 58786.33606 | 24.5 | 0.00015 | 59871.46504 | 596.0 | 0.00007
58741.72591 | 1.0 | 0.00018 | 58765.45725 | 13.5 | 0.00024 | 58787.28548 | 25.0 | 0.00016 | 59872.41525 | 596.5 | 0.00009
58742.67534 | 1.5 | 0.00014 | 58766.40505 | 14.0 | 0.00019 | 58788.23455 | 25.5 | 0.00038 | 59873.36401 | 597.0 | 0.00008
58743.62592 | 2.0 | 0.00024 | 58767.35647 | 14.5 | 0.00011 | 58789.18950 | 26.0 | 0.00086 | 59874.31226 | 597.5 | 0.00009
58744.57356 | 2.5 | 0.00019 | 58768.30415 | 15.0 | 0.00013 | 59758.49509a | 536.5 | 0.00004 | 59875.26216 | 598.0 | 0.00010
58745.52534 | 3.0 | 0.00010 | 58769.25387 | 15.5 | 0.00022 | 59853.43423 | 586.5 | 0.00009 | 59876.21071 | 598.5 | 0.00009
58746.47509 | 3.5 | 0.00019 | 58770.20236 | 16.0 | 0.00013 | 59854.38270 | 587.0 | 0.00009 | 59877.15953 | 599.0 | 0.00009
58747.42357 | 4.0 | 0.00014 | 58771.15121 | 16.5 | 0.00020 | 59855.33184 | 587.5 | 0.00009 | 59878.10921 | 599.5 | 0.00010
58748.37530 | 4.5 | 0.00022 | 58772.10136 | 17.0 | 0.00011 | 59856.28088 | 588.0 | 0.00011 | 59879.05671 | 600.0 | 0.00009
58749.32190 | 5.0 | 0.00015 | 58773.04374 | 17.5 | 0.00196 | 59857.23138 | 588.5 | 0.00008 | 59880.00742 | 600.5 | 0.00011
58750.27213 | 5.5 | 0.00024 | 58773.99852 | 18.0 | 0.00022 | 59858.17868 | 589.0 | 0.00010 | 59880.95465 | 601.0 | 0.00008
58752.17061 | 6.5 | 0.00019 | 58774.94872 | 18.5 | 0.00023 | 59859.13005 | 589.5 | 0.00011 | 59881.90507 | 601.5 | 0.00010
58753.12064 | 7.0 | 0.00015 | 58775.89613 | 19.0 | 0.00031 | 59860.07715 | 590.0 | 0.00009 | 60135.38686b | 735.0 | 0.00010
58754.06873 | 7.5 | 0.00016 | 58777.79345 | 20.0 | 0.00017 | 59861.02787 | 590.5 | 0.00013 | 60208.48369b | 773.5 | 0.00003
58755.01904 | 8.0 | 0.00012 | 58778.74329 | 20.5 | 0.00025 | 59861.97509 | 591.0 | 0.00008 | 60209.43240b | 774.0 | 0.00004
58755.96778 | 8.5 | 0.00016 | 58779.69151 | 21.0 | 0.00018 | 59862.92622 | 591.5 | 0.00009 | 60267.35271b | 804.5 | 0.00003
58756.91576 | 9.0 | 0.00027 | 58780.64248 | 21.5 | 0.00015 | 59866.72126 | 593.5 | 0.00009 | 60268.30225b | 805.0 | 0.00007
58757.86637 | 9.5 | 0.00019 | 58781.59047 | 22.0 | 0.00013 | 59867.66957 | 594.0 | 0.00008 | 60286.34061b | 814.5 | 0.00003
58758.81356 | 10.0 | 0.00014 | 58782.53835 | 22.5 | 0.00020 | 59868.61941 | 594.5 | 0.00010 | 60344.24895b | 845.0 | 0.00004
58759.76472 | 10.5 | 0.00019 | 58783.48854 | 23.0 | 0.00010 |  |  |  |  |  |

Notes. a: Observed at BAO; b: Observed at GAO; the other eclipses observed
with TESS.

Table 13: Eclipse times for TZ Pyx (TIC 185615681)

BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev.
---|---|---|---|---|---|---|---|---|---|---|---
$-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$
58518.16959 | 0.0 | 0.00009 | 59238.09281 | 310.5 | 0.00003 | 59274.02312 | 326.0 | 0.00003 | 59986.98206 | 633.5 | 0.00002
58519.34246 | 0.5 | 0.00009 | 59239.24465 | 311.0 | 0.00004 | 59275.18922 | 326.5 | 0.00004 | 59988.14316 | 634.0 | 0.00002
58520.48810 | 1.0 | 0.00013 | 59240.41124 | 311.5 | 0.00003 | 59276.34210 | 327.0 | 0.00003 | 59989.30061 | 634.5 | 0.00002
58521.66086 | 1.5 | 0.00007 | 59242.72960 | 312.5 | 0.00003 | 59277.50798 | 327.5 | 0.00003 | 59990.46173 | 635.0 | 0.00002
58522.80632 | 2.0 | 0.00009 | 59243.88184 | 313.0 | 0.00003 | 59278.66089 | 328.0 | 0.00003 | 59991.61920 | 635.5 | 0.00002
58523.97938 | 2.5 | 0.00008 | 59245.04810 | 313.5 | 0.00003 | 59279.82680 | 328.5 | 0.00004 | 59992.78021 | 636.0 | 0.00002
58525.12478 | 3.0 | 0.00006 | 59246.20042 | 314.0 | 0.00005 | 59963.79769 | 623.5 | 0.00002 | 59993.93777 | 636.5 | 0.00002
58526.29777 | 3.5 | 0.00010 | 59247.36660 | 314.5 | 0.00004 | 59964.95824 | 624.0 | 0.00003 | 59996.25634 | 637.5 | 0.00002
58527.44319 | 4.0 | 0.00011 | 59248.51888 | 315.0 | 0.00004 | 59967.27669 | 625.0 | 0.00002 | 59997.41758 | 638.0 | 0.00002
58528.61638 | 4.5 | 0.00008 | 59249.68494 | 315.5 | 0.00004 | 59968.43440 | 625.5 | 0.00002 | 59998.57505 | 638.5 | 0.00002
58530.93462 | 5.5 | 0.00009 | 59250.83729 | 316.0 | 0.00004 | 59969.59564 | 626.0 | 0.00004 | 59999.73656 | 639.0 | 0.00005
58535.57206 | 7.5 | 0.00009 | 59252.00343 | 316.5 | 0.00004 | 59970.75292 | 626.5 | 0.00002 | 60000.89359 | 639.5 | 0.00005
58536.71703 | 8.0 | 0.00010 | 59253.15574 | 317.0 | 0.00004 | 59971.91399 | 627.0 | 0.00002 | 60002.05537 | 640.0 | 0.00002
58537.89034 | 8.5 | 0.00010 | 59256.64039 | 318.5 | 0.00003 | 59973.07121 | 627.5 | 0.00002 | 60003.21247 | 640.5 | 0.00002
58539.03562 | 9.0 | 0.00011 | 59257.79257 | 319.0 | 0.00005 | 59974.23254 | 628.0 | 0.00002 | 60004.37418 | 641.0 | 0.00002
58540.20874 | 9.5 | 0.00008 | 59258.95891 | 319.5 | 0.00004 | 59976.55100 | 629.0 | 0.00002 | 60005.53109 | 641.5 | 0.00002
58541.35423 | 10.0 | 0.00008 | 59260.11101 | 320.0 | 0.00004 | 59977.70821 | 629.5 | 0.00002 | 60006.69298 | 642.0 | 0.00002
59229.97068 | 307.0 | 0.00004 | 59261.27743 | 320.5 | 0.00004 | 59978.86955 | 630.0 | 0.00002 | 60007.84981 | 642.5 | 0.00002
59231.13745 | 307.5 | 0.00004 | 59262.42937 | 321.0 | 0.00004 | 59980.02659 | 630.5 | 0.00002 | 60009.01147 | 643.0 | 0.00002
59232.28914 | 308.0 | 0.00004 | 59263.59588 | 321.5 | 0.00004 | 59981.18779 | 631.0 | 0.00002 | 60010.16837 | 643.5 | 0.00002
59233.45587 | 308.5 | 0.00004 | 59264.74799 | 322.0 | 0.00004 | 59983.50631 | 632.0 | 0.00002 | 60011.32996 | 644.0 | 0.00002
59234.60749 | 309.0 | 0.00004 | 59265.91448 | 322.5 | 0.00004 | 59984.66356 | 632.5 | 0.00002 | 60012.48686 | 644.5 | 0.00002
59235.77432 | 309.5 | 0.00003 | 59267.06667 | 323.0 | 0.00004 | 59985.82477 | 633.0 | 0.00002 | 60013.64839 | 645.0 | 0.00002
59236.92609 | 310.0 | 0.00004 | 59272.87044 | 325.5 | 0.00003 |  |  |  |  |  |

Table 14: Eclipse times for TIC 287756035

BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev.
---|---|---|---|---|---|---|---|---|---|---|---
$-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$
58597.24221 | -1.0 | 0.09984 | 58623.26018 | 11.5 | 0.00368 | 59336.13166 | 354.0 | 0.00281 | 60041.73549 | 693.0 | 0.00109
58598.27373 | -0.5 | 0.00665 | 59308.03345 | 340.5 | 0.00214 | 59337.16701 | 354.5 | 0.00323 | 60042.78350 | 693.5 | 0.00173
58599.31567 | 0.0 | 0.00452 | 59309.07420 | 341.0 | 0.00187 | 59338.20811 | 355.0 | 0.00230 | 60043.81491 | 694.0 | 0.00149
58600.35967 | 0.5 | 0.00178 | 59313.29341 | 343.0 | 0.00326 | 59339.24448 | 355.5 | 0.00283 | 60044.85216 | 694.5 | 0.00216
58601.40239 | 1.0 | 0.00181 | 59314.28649 | 343.5 | 0.00230 | 59340.30039 | 356.0 | 0.00243 | 60049.01666 | 696.5 | 0.00268
58602.43427 | 1.5 | 0.00197 | 59315.31438 | 344.0 | 0.00171 | 59341.33582 | 356.5 | 0.00191 | 60050.05709 | 697.0 | 0.00119
58603.47656 | 2.0 | 0.00287 | 59316.35173 | 344.5 | 0.00173 | 59342.37244 | 357.0 | 0.00175 | 60051.09339 | 697.5 | 0.00169
58604.52050 | 2.5 | 0.00177 | 59317.39805 | 345.0 | 0.00126 | 59343.41287 | 357.5 | 0.00139 | 60052.13384 | 698.0 | 0.00146
58605.55465 | 3.0 | 0.00206 | 59318.45364 | 345.5 | 0.00198 | 59344.46241 | 358.0 | 0.00121 | 60053.17517 | 698.5 | 0.00140
58606.59093 | 3.5 | 0.00339 | 59320.52522 | 346.5 | 0.00240 | 59345.50382 | 358.5 | 0.00176 | 60054.22572 | 699.0 | 0.00123
58607.63434 | 4.0 | 0.00276 | 59321.56601 | 347.0 | 0.00180 | 59347.57886 | 359.5 | 0.00250 | 60056.29312 | 700.0 | 0.00144
58608.67791 | 4.5 | 0.00162 | 59322.59519 | 347.5 | 0.00209 | 59348.61854 | 360.0 | 0.00194 | 60057.33468 | 700.5 | 0.00128
58611.79733 | 6.0 | 0.14594 | 59323.64770 | 348.0 | 0.00162 | 59349.65894 | 360.5 | 0.00157 | 60058.38237 | 701.0 | 0.00136
58612.82854 | 6.5 | 0.01613 | 59324.69195 | 348.5 | 0.00193 | 59350.70147 | 361.0 | 0.00163 | 60059.42664 | 701.5 | 0.00177
58613.88105 | 7.0 | 0.02453 | 59325.71101 | 349.0 | 0.00163 | 59351.74403 | 361.5 | 0.00250 | 60060.45615 | 702.0 | 0.00129
58614.92035 | 7.5 | 0.00293 | 59326.74897 | 349.5 | 0.00241 | 59352.78385 | 362.0 | 0.00221 | 60061.50146 | 702.5 | 0.00194
58615.96147 | 8.0 | 0.00275 | 59327.80051 | 350.0 | 0.00170 | 59353.81992 | 362.5 | 0.00290 | 60062.55115 | 703.0 | 0.00127
58617.00661 | 8.5 | 0.00457 | 59328.83824 | 350.5 | 0.00197 | 59354.86158 | 363.0 | 0.00164 | 60063.59200 | 703.5 | 0.00167
58618.04633 | 9.0 | 0.00338 | 59329.88489 | 351.0 | 0.00171 | 59355.90671 | 363.5 | 0.00237 | 60064.63478 | 704.0 | 0.00149
58619.08382 | 9.5 | 0.00349 | 59330.92391 | 351.5 | 0.00194 | 59356.94344 | 364.0 | 0.00228 | 60065.67316 | 704.5 | 0.00227
58620.12676 | 10.0 | 0.18136 | 59331.95671 | 352.0 | 0.00185 | 59357.98665 | 364.5 | 0.00497 | 60066.70700 | 705.0 | 0.00271
58621.16943 | 10.5 | 0.00432 | 59334.05750 | 353.0 | 0.00395 | 59359.02178 | 365.0 | 0.00192 | 60067.74751 | 705.5 | 0.00188
58622.21359 | 11.0 | 0.00359 | 59335.09428 | 353.5 | 0.00328 | 59360.06104 | 365.5 | 0.00397 |  |  |

Table 15: Eclipse times for TIC 321978218

BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev.
---|---|---|---|---|---|---|---|---|---|---|---
$-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$
55432.54833 | -6369.5 | 0.00031 | 59064.81212 | 5.0 | 0.00006 | 59097.29401 | 62.0 | 0.00005 | 60170.53185 | 1945.5 | 0.00009
55432.83201 | -6369.0 | 0.00015 | 59065.09753 | 5.5 | 0.00013 | 59097.57864 | 62.5 | 0.00009 | 60170.81671 | 1946.0 | 0.00004
55803.49700 | -5718.5 | 0.00034 | 59065.38192 | 6.0 | 0.00005 | 59097.86390 | 63.0 | 0.00007 | 60171.10179 | 1946.5 | 0.00010
56180.70955 | -5056.5 | 0.00033 | 59065.66669 | 6.5 | 0.00012 | 59098.14911 | 63.5 | 0.00011 | 60171.38676 | 1947.0 | 0.00007
56180.99554 | -5056.0 | 0.00029 | 59065.95165 | 7.0 | 0.00006 | 59098.43374 | 64.0 | 0.00006 | 60171.67182 | 1947.5 | 0.00007
56533.99015 | -4436.5 | 0.00044 | 59066.23684 | 7.5 | 0.00012 | 59098.71815 | 64.5 | 0.00015 | 60171.95628 | 1948.0 | 0.00005
56534.27516 | -4436.0 | 0.00017 | 59066.52152 | 8.0 | 0.00006 | 59099.00333 | 65.0 | 0.00012 | 60172.24210 | 1948.5 | 0.00007
56896.10467 | -3801.0 | 0.00031 | 59066.80643 | 8.5 | 0.00010 | 59099.28814 | 65.5 | 0.00010 | 60172.52667 | 1949.0 | 0.00005
58354.25863 | -1242.0 | 0.00005 | 59067.09170 | 9.0 | 0.00012 | 59099.57334 | 66.0 | 0.00007 | 60172.81093 | 1949.5 | 0.00008
58354.54400 | -1241.5 | 0.00053 | 59067.37738 | 9.5 | 0.00006 | 59099.85891 | 66.5 | 0.00014 | 60173.09665 | 1950.0 | 0.00005
58354.82840 | -1241.0 | 0.00077 | 59067.66102 | 10.0 | 0.00005 | 59100.14269 | 67.0 | 0.00017 | 60173.38171 | 1950.5 | 0.00009
58355.11293 | -1240.5 | 0.00041 | 59067.94616 | 10.5 | 0.00010 | 59100.99845 | 68.5 | 0.00045 | 60173.66615 | 1951.0 | 0.00005
58355.39782 | -1240.0 | 0.00005 | 59068.23123 | 11.0 | 0.00006 | 59101.28153 | 69.0 | 0.00013 | 60173.95097 | 1951.5 | 0.00008
58355.68338 | -1239.5 | 0.00037 | 59068.51567 | 11.5 | 0.00006 | 59102.42163 | 71.0 | 0.00010 | 60174.23623 | 1952.0 | 0.00005
58355.96786 | -1239.0 | 0.00006 | 59068.80059 | 12.0 | 0.00007 | 59102.70658 | 71.5 | 0.00010 | 60174.52103 | 1952.5 | 0.00011
58356.25342 | -1238.5 | 0.00029 | 59069.08609 | 12.5 | 0.00014 | 59102.99178 | 72.0 | 0.00007 | 60174.80594 | 1953.0 | 0.00006
58356.53756 | -1238.0 | 0.00023 | 59069.37046 | 13.0 | 0.00005 | 59103.27701 | 72.5 | 0.00008 | 60175.37574 | 1954.0 | 0.00005
58356.82293 | -1237.5 | 0.00009 | 59069.65543 | 13.5 | 0.00009 | 59103.56120 | 73.0 | 0.00007 | 60175.66128 | 1954.5 | 0.00006
58357.10703 | -1237.0 | 0.00026 | 59069.94014 | 14.0 | 0.00007 | 59103.84650 | 73.5 | 0.00010 | 60175.94620 | 1955.0 | 0.00006
58357.39208 | -1236.5 | 0.00008 | 59070.22620 | 14.5 | 0.00014 | 59104.13146 | 74.0 | 0.00003 | 60176.23119 | 1955.5 | 0.00009
58357.67696 | -1236.0 | 0.00004 | 59070.51025 | 15.0 | 0.00010 | 59104.41625 | 74.5 | 0.00012 | 60176.51561 | 1956.0 | 0.00004
58357.96167 | -1235.5 | 0.00007 | 59070.79605 | 15.5 | 0.00007 | 59104.70096 | 75.0 | 0.00004 | 60176.80099 | 1956.5 | 0.00009
58358.24659 | -1235.0 | 0.00039 | 59071.08036 | 16.0 | 0.00009 | 59104.98676 | 75.5 | 0.00013 | 60177.08567 | 1957.0 | 0.00005
58358.53170 | -1234.5 | 0.00053 | 59071.36490 | 16.5 | 0.00014 | 59105.27098 | 76.0 | 0.00004 | 60177.37105 | 1957.5 | 0.00010
58358.81611 | -1234.0 | 0.00005 | 59071.64989 | 17.0 | 0.00008 | 59105.55572 | 76.5 | 0.00012 | 60177.65572 | 1958.0 | 0.00006
58359.10180 | -1233.5 | 0.00008 | 59071.93526 | 17.5 | 0.00024 | 59105.84032 | 77.0 | 0.00006 | 60177.94107 | 1958.5 | 0.00012
58359.38589 | -1233.0 | 0.00012 | 59072.78988 | 19.0 | 0.00012 | 59106.12549 | 77.5 | 0.00013 | 60178.22531 | 1959.0 | 0.00005
58359.67124 | -1232.5 | 0.00033 | 59073.07423 | 19.5 | 0.00016 | 59106.41026 | 78.0 | 0.00009 | 60178.51088 | 1959.5 | 0.00010
58359.95639 | -1232.0 | 0.00016 | 59073.35993 | 20.0 | 0.00008 | 59106.69512 | 78.5 | 0.00011 | 60178.79519 | 1960.0 | 0.00006
58360.24095 | -1231.5 | 0.00013 | 59073.64513 | 20.5 | 0.00013 | 59106.98023 | 79.0 | 0.00006 | 60179.08063 | 1960.5 | 0.00012
58360.52551 | -1231.0 | 0.00017 | 59073.92936 | 21.0 | 0.00013 | 59107.26571 | 79.5 | 0.00011 | 60179.36579 | 1961.0 | 0.00006
58360.81125 | -1230.5 | 0.00048 | 59075.35427 | 23.5 | 0.00014 | 59107.54988 | 80.0 | 0.00005 | 60179.64921 | 1961.5 | 0.00017
58361.09545 | -1230.0 | 0.00011 | 59075.63916 | 24.0 | 0.00007 | 59107.83547 | 80.5 | 0.00010 | 60179.93525 | 1962.0 | 0.00011
58361.95049 | -1228.5 | 0.00009 | 59075.92461 | 24.5 | 0.00006 | 59108.11935 | 81.0 | 0.00008 | 60181.92901 | 1965.5 | 0.00018
58362.23444 | -1228.0 | 0.00007 | 59076.20896 | 25.0 | 0.00007 | 59108.40407 | 81.5 | 0.00012 | 60184.49411 | 1970.0 | 0.00006
58362.52030 | -1227.5 | 0.00006 | 59076.49390 | 25.5 | 0.00010 | 59108.68935 | 82.0 | 0.00006 | 60184.77872 | 1970.5 | 0.00009
58362.80462 | -1227.0 | 0.00043 | 59076.77904 | 26.0 | 0.00006 | 59108.97479 | 82.5 | 0.00011 | 60185.06332 | 1971.0 | 0.00004

Note. The first eight eclipse times are SWASP seasonal normal minima.

Table 15: Eclipse times for TIC 321978218 (continued)

BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev.
---|---|---|---|---|---|---|---|---|---|---|---
$-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$
58363.09051 | -1226.5 | 0.00044 | 59077.06362 | 26.5 | 0.00012 | 59109.25888 | 83.0 | 0.00004 | 60185.34860 | 1971.5 | 0.00009
58363.37465 | -1226.0 | 0.00018 | 59077.34871 | 27.0 | 0.00004 | 59109.54467 | 83.5 | 0.00012 | 60185.63322 | 1972.0 | 0.00003
58363.65930 | -1225.5 | 0.00036 | 59077.63344 | 27.5 | 0.00010 | 59109.82896 | 84.0 | 0.00006 | 60185.91880 | 1972.5 | 0.00008
58363.94412 | -1225.0 | 0.00011 | 59077.91895 | 28.0 | 0.00007 | 59110.11457 | 84.5 | 0.00012 | 60186.20319 | 1973.0 | 0.00006
58364.22942 | -1224.5 | 0.00073 | 59078.20347 | 28.5 | 0.00008 | 59110.39867 | 85.0 | 0.00005 | 60186.48824 | 1973.5 | 0.00008
58364.51351 | -1224.0 | 0.00022 | 59078.48835 | 29.0 | 0.00004 | 59110.68353 | 85.5 | 0.00010 | 60186.77318 | 1974.0 | 0.00005
58364.79930 | -1223.5 | 0.00028 | 59078.77336 | 29.5 | 0.00010 | 59110.96839 | 86.0 | 0.00007 | 60187.05835 | 1974.5 | 0.00009
58365.08375 | -1223.0 | 0.00072 | 59079.05850 | 30.0 | 0.00006 | 59111.25309 | 86.5 | 0.00016 | 60187.34295 | 1975.0 | 0.00004
58365.65311 | -1222.0 | 0.00008 | 59079.34428 | 30.5 | 0.00011 | 59111.53759 | 87.0 | 0.00005 | 60187.62724 | 1975.5 | 0.00010
58365.93808 | -1221.5 | 0.00027 | 59079.62838 | 31.0 | 0.00007 | 59111.82388 | 87.5 | 0.00011 | 60189.33714 | 1978.5 | 0.00010
58366.22315 | -1221.0 | 0.00005 | 59079.91356 | 31.5 | 0.00010 | 59112.10796 | 88.0 | 0.00005 | 60189.62196 | 1979.0 | 0.00004
58366.50759 | -1220.5 | 0.00026 | 59080.19822 | 32.0 | 0.00007 | 59112.39400 | 88.5 | 0.00011 | 60189.90762 | 1979.5 | 0.00009
58366.79308 | -1220.0 | 0.00006 | 59080.48254 | 32.5 | 0.00010 | 59112.67687 | 89.0 | 0.00006 | 60190.19141 | 1980.0 | 0.00004
58367.07824 | -1219.5 | 0.00025 | 59080.76794 | 33.0 | 0.00007 | 59112.96266 | 89.5 | 0.00013 | 60190.47693 | 1980.5 | 0.00007
58368.78739 | -1216.5 | 0.00014 | 59081.05359 | 33.5 | 0.00011 | 59113.24702 | 90.0 | 0.00008 | 60190.76149 | 1981.0 | 0.00005
58369.07163 | -1216.0 | 0.00020 | 59081.33822 | 34.0 | 0.00006 | 59113.53268 | 90.5 | 0.00017 | 60191.04627 | 1981.5 | 0.00008
58369.35674 | -1215.5 | 0.00014 | 59081.62342 | 34.5 | 0.00013 | 59113.81609 | 91.0 | 0.00017 | 60191.33106 | 1982.0 | 0.00006
58369.64203 | -1215.0 | 0.00012 | 59081.90811 | 35.0 | 0.00008 | 59114.38750 | 92.0 | 0.00016 | 60191.61713 | 1982.5 | 0.00011
58369.92672 | -1214.5 | 0.00012 | 59082.19335 | 35.5 | 0.00009 | 60154.86236 | 1918.0 | 0.00005 | 60191.90127 | 1983.0 | 0.00006
58370.21158 | -1214.0 | 0.00004 | 59082.47818 | 36.0 | 0.00006 | 60155.14715 | 1918.5 | 0.00010 | 60192.47097 | 1984.0 | 0.00005
58370.49678 | -1213.5 | 0.00073 | 59082.76255 | 36.5 | 0.00010 | 60155.43215 | 1919.0 | 0.00004 | 60192.75595 | 1984.5 | 0.00011
58370.78086 | -1213.0 | 0.00010 | 59083.04770 | 37.0 | 0.00006 | 60155.71622 | 1919.5 | 0.00011 | 60193.04077 | 1985.0 | 0.00008
58371.06578 | -1212.5 | 0.00485 | 59083.33232 | 37.5 | 0.00010 | 60156.00186 | 1920.0 | 0.00006 | 60193.32650 | 1985.5 | 0.00008
58371.35077 | -1212.0 | 0.00021 | 59083.61766 | 38.0 | 0.00008 | 60156.28589 | 1920.5 | 0.00012 | 60193.61105 | 1986.0 | 0.00009
58371.63632 | -1211.5 | 0.00038 | 59083.90258 | 38.5 | 0.00015 | 60156.57152 | 1921.0 | 0.00006 | 60195.31965 | 1989.0 | 0.00007
58371.92021 | -1211.0 | 0.00017 | 59084.18769 | 39.0 | 0.00005 | 60156.85597 | 1921.5 | 0.00007 | 60195.60460 | 1989.5 | 0.00009
58372.20573 | -1210.5 | 0.00022 | 59084.47272 | 39.5 | 0.00010 | 60157.14150 | 1922.0 | 0.00005 | 60195.88963 | 1990.0 | 0.00004
58372.49022 | -1210.0 | 0.00012 | 59084.75741 | 40.0 | 0.00006 | 60157.42597 | 1922.5 | 0.00009 | 60196.17532 | 1990.5 | 0.00008
58372.77538 | -1209.5 | 0.00015 | 59085.04258 | 40.5 | 0.00013 | 60157.71122 | 1923.0 | 0.00005 | 60196.45910 | 1991.0 | 0.00005
58373.06046 | -1209.0 | 0.00006 | 59085.32708 | 41.0 | 0.00005 | 60157.99562 | 1923.5 | 0.00012 | 60196.74417 | 1991.5 | 0.00009
58373.34500 | -1208.5 | 0.00020 | 59085.61266 | 41.5 | 0.00016 | 60158.28095 | 1924.0 | 0.00008 | 60197.02894 | 1992.0 | 0.00005
58373.91459 | -1207.5 | 0.00045 | 59085.89765 | 42.0 | 0.00009 | 60158.56504 | 1924.5 | 0.00009 | 60197.31481 | 1992.5 | 0.00006
58374.19894 | -1207.0 | 0.00056 | 59086.18239 | 42.5 | 0.00021 | 60158.85060 | 1925.0 | 0.00006 | 60197.59918 | 1993.0 | 0.00005
58374.48490 | -1206.5 | 0.00020 | 59086.46679 | 43.0 | 0.00005 | 60159.13523 | 1925.5 | 0.00009 | 60197.88383 | 1993.5 | 0.00009
58374.76950 | -1206.0 | 0.00017 | 59086.75295 | 43.5 | 0.00014 | 60159.42018 | 1926.0 | 0.00005 | 60198.16890 | 1994.0 | 0.00005
58375.05473 | -1205.5 | 0.00054 | 59087.03672 | 44.0 | 0.00025 | 60159.70487 | 1926.5 | 0.00009 | 60198.45395 | 1994.5 | 0.00012
58375.33894 | -1205.0 | 0.00015 | 59088.46235 | 46.5 | 0.00013 | 60159.99034 | 1927.0 | 0.00006 | 60198.73804 | 1995.0 | 0.00005
58375.62430 | -1204.5 | 0.00019 | 59088.74683 | 47.0 | 0.00008 | 60160.27437 | 1927.5 | 0.00009 | 60199.02389 | 1995.5 | 0.00010
58375.90879 | -1204.0 | 0.00004 | 59089.03181 | 47.5 | 0.00005 | 60160.55997 | 1928.0 | 0.00005 | 60199.30817 | 1996.0 | 0.00004
58376.19406 | -1203.5 | 0.00264 | 59089.31654 | 48.0 | 0.00005 | 60160.84398 | 1928.5 | 0.00009 | 60199.59430 | 1996.5 | 0.00008
58376.47909 | -1203.0 | 0.00014 | 59089.60100 | 48.5 | 0.00010 | 60161.12967 | 1929.0 | 0.00004 | 60199.87805 | 1997.0 | 0.00006
58376.76409 | -1202.5 | 0.00013 | 59089.88607 | 49.0 | 0.00008 | 60161.41383 | 1929.5 | 0.00009 | 60200.16360 | 1997.5 | 0.00009
58377.04837 | -1202.0 | 0.00010 | 59090.17046 | 49.5 | 0.00008 | 60161.69909 | 1930.0 | 0.00007 | 60200.44787 | 1998.0 | 0.00007
58377.61802 | -1201.0 | 0.00004 | 59090.45626 | 50.0 | 0.00007 | 60162.26977 | 1931.0 | 0.00006 | 60200.73325 | 1998.5 | 0.00008
58377.90299 | -1200.5 | 0.00026 | 59090.74131 | 50.5 | 0.00009 | 60162.55352 | 1931.5 | 0.00007 | 60201.01743 | 1999.0 | 0.00005
58378.18822 | -1200.0 | 0.00021 | 59091.02573 | 51.0 | 0.00006 | 60162.83907 | 1932.0 | 0.00005 | 60201.30270 | 1999.5 | 0.00008
58378.47388 | -1199.5 | 0.00006 | 59091.31199 | 51.5 | 0.00009 | 60163.12455 | 1932.5 | 0.00009 | 60201.87283 | 2000.5 | 0.00008
58378.75741 | -1199.0 | 0.00018 | 59091.59603 | 52.0 | 0.00010 | 60163.40869 | 1933.0 | 0.00007 | 60202.15700 | 2001.0 | 0.00007
58379.04321 | -1198.5 | 0.00044 | 59091.88104 | 52.5 | 0.00013 | 60163.69397 | 1933.5 | 0.00008 | 60202.44170 | 2001.5 | 0.00012
58379.32794 | -1198.0 | 0.00013 | 59092.16592 | 53.0 | 0.00006 | 60163.97868 | 1934.0 | 0.00003 | 60202.72691 | 2002.0 | 0.00004
58379.61339 | -1197.5 | 0.00020 | 59092.44995 | 53.5 | 0.00015 | 60164.54811 | 1935.0 | 0.00006 | 60203.01175 | 2002.5 | 0.00007
58379.89794 | -1197.0 | 0.00005 | 59092.73559 | 54.0 | 0.00008 | 60164.83315 | 1935.5 | 0.00012 | 60203.29637 | 2003.0 | 0.00006
58380.18249 | -1196.5 | 0.00030 | 59093.02059 | 54.5 | 0.00010 | 60165.68847 | 1937.0 | 0.00016 | 60203.58142 | 2003.5 | 0.00011
58380.46717 | -1196.0 | 0.00014 | 59093.30530 | 55.0 | 0.00008 | 60165.97246 | 1937.5 | 0.00011 | 60203.86651 | 2004.0 | 0.00005
58380.75321 | -1195.5 | 0.00061 | 59093.59059 | 55.5 | 0.00008 | 60166.25749 | 1938.0 | 0.00013 | 60204.15125 | 2004.5 | 0.00008
59061.96391 | 0.0 | 0.00004 | 59093.87482 | 56.0 | 0.00004 | 60167.96658 | 1941.0 | 0.00011 | 60204.43604 | 2005.0 | 0.00005
59062.24885 | 0.5 | 0.00012 | 59094.16049 | 56.5 | 0.00010 | 60168.25338 | 1941.5 | 0.00011 | 60204.72083 | 2005.5 | 0.00012
59062.53368 | 1.0 | 0.00005 | 59094.44458 | 57.0 | 0.00006 | 60168.53695 | 1942.0 | 0.00005 | 60205.00588 | 2006.0 | 0.00005
59062.81852 | 1.5 | 0.00009 | 59094.72981 | 57.5 | 0.00008 | 60168.82209 | 1942.5 | 0.00009 | 60205.29123 | 2006.5 | 0.00009
59063.10327 | 2.0 | 0.00005 | 59095.01455 | 58.0 | 0.00008 | 60169.10719 | 1943.0 | 0.00004 | 60205.57546 | 2007.0 | 0.00006
59063.38898 | 2.5 | 0.00009 | 59095.29898 | 58.5 | 0.00006 | 60169.39239 | 1943.5 | 0.00009 | 60205.85994 | 2007.5 | 0.00008
59063.67320 | 3.0 | 0.00005 | 59096.43927 | 60.5 | 0.00013 | 60169.67701 | 1944.0 | 0.00004 | 60206.14508 | 2008.0 | 0.00008
59063.95823 | 3.5 | 0.00008 | 59096.72412 | 61.0 | 0.00005 | 60169.96218 | 1944.5 | 0.00009 | 60206.43015 | 2008.5 | 0.00013
59064.24238 | 4.0 | 0.00004 | 59097.00893 | 61.5 | 0.00018 | 60170.24681 | 1945.0 | 0.00005 | 60206.71478 | 2009.0 | 0.00007
59064.52777 | 4.5 | 0.00010 |  |  |  |  |  |  |  |  |

Table 16: Eclipse times for TIC 323486857

BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev.
---|---|---|---|---|---|---|---|---|---|---|---
$-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$
58569.76629 | 0.0 | 0.00043 | 58611.31389 | 47.0 | 0.00030 | 59335.30793 | 866.0 | 0.00042 | 60056.64267 | 1682.0 | 0.00029
58570.20988 | 0.5 | 0.00031 | 58611.75668 | 47.5 | 0.00037 | 59335.74280 | 866.5 | 0.00071 | 60057.08554 | 1682.5 | 0.00023
58570.65159 | 1.0 | 0.00051 | 58612.19847 | 48.0 | 0.00033 | 59336.18785 | 867.0 | 0.00061 | 60057.52397 | 1683.0 | 0.00031
58571.09320 | 1.5 | 0.00072 | 58612.63979 | 48.5 | 0.00029 | 59336.63213 | 867.5 | 0.00056 | 60057.96929 | 1683.5 | 0.00035
58571.53535 | 2.0 | 0.00022 | 58613.08175 | 49.0 | 0.00029 | 59337.07349 | 868.0 | 0.00046 | 60058.40908 | 1684.0 | 0.00029
58571.97855 | 2.5 | 0.00027 | 58613.52515 | 49.5 | 0.00041 | 59337.51399 | 868.5 | 0.00074 | 60058.85300 | 1684.5 | 0.00030
58572.41999 | 3.0 | 0.00032 | 58613.96601 | 50.0 | 0.00043 | 59337.95543 | 869.0 | 0.00056 | 60059.29364 | 1685.0 | 0.00022
58572.86354 | 3.5 | 0.00069 | 58614.41042 | 50.5 | 0.00046 | 59338.40096 | 869.5 | 0.00050 | 60059.73704 | 1685.5 | 0.00033
58573.30288 | 4.0 | 0.00026 | 58614.84916 | 51.0 | 0.00023 | 59338.84369 | 870.0 | 0.00068 | 60060.17791 | 1686.0 | 0.00023
58573.74551 | 4.5 | 0.00052 | 58616.18135 | 52.5 | 0.00022 | 59340.16948 | 871.5 | 0.00046 | 60060.61934 | 1686.5 | 0.00035
58575.07036 | 6.0 | 0.00033 | 58616.62435 | 53.0 | 0.00031 | 59340.60799 | 872.0 | 0.00044 | 60061.06166 | 1687.0 | 0.00034
58575.51230 | 6.5 | 0.00024 | 58617.06071 | 53.5 | 0.00038 | 59341.05470 | 872.5 | 0.00045 | 60061.50254 | 1687.5 | 0.00033
58575.95563 | 7.0 | 0.00039 | 58617.50064 | 54.0 | 0.00022 | 59341.49356 | 873.0 | 0.00046 | 60061.94381 | 1688.0 | 0.00033
58576.39925 | 7.5 | 0.00036 | 58617.94355 | 54.5 | 0.00017 | 59341.93654 | 873.5 | 0.00055 | 60063.71521 | 1690.0 | 0.00034
58576.83874 | 8.0 | 0.00042 | 58618.38582 | 55.0 | 0.00040 | 59342.37567 | 874.0 | 0.00067 | 60064.15847 | 1690.5 | 0.00037
58577.28074 | 8.5 | 0.00012 | 58618.83083 | 55.5 | 0.00044 | 59342.82239 | 874.5 | 0.00041 | 60064.59739 | 1691.0 | 0.00030
58577.72402 | 9.0 | 0.00037 | 58619.27046 | 56.0 | 0.00021 | 59343.26177 | 875.0 | 0.00053 | 60065.04066 | 1691.5 | 0.00030
58578.16485 | 9.5 | 0.00026 | 58619.71444 | 56.5 | 0.00034 | 59343.70379 | 875.5 | 0.00071 | 60065.48196 | 1692.0 | 0.00029
58578.60739 | 10.0 | 0.00046 | 58620.15474 | 57.0 | 0.00056 | 59344.14506 | 876.0 | 0.00042 | 60065.92317 | 1692.5 | 0.00027
58579.04978 | 10.5 | 0.00045 | 58620.59589 | 57.5 | 0.00040 | 59344.59012 | 876.5 | 0.00054 | 60066.36728 | 1693.0 | 0.00030
58579.49038 | 11.0 | 0.00030 | 58621.03823 | 58.0 | 0.00018 | 59345.03023 | 877.0 | 0.00045 | 60066.80792 | 1693.5 | 0.00038
58579.93289 | 11.5 | 0.00048 | 58621.48190 | 58.5 | 0.00024 | 59345.47615 | 877.5 | 0.00066 | 60067.24872 | 1694.0 | 0.00028
58580.37447 | 12.0 | 0.00036 | 58621.92189 | 59.0 | 0.00022 | 59345.91006 | 878.0 | 0.00076 | 60067.69553 | 1694.5 | 0.00024
58580.82057 | 12.5 | 0.00034 | 58622.36610 | 59.5 | 0.00048 | 59347.68278 | 880.0 | 0.00051 | 60069.01844 | 1696.0 | 0.00058
58581.25860 | 13.0 | 0.00033 | 58622.80536 | 60.0 | 0.00021 | 59348.12482 | 880.5 | 0.00066 | 60069.46017 | 1696.5 | 0.00046
58581.70065 | 13.5 | 0.00011 | 58623.25098 | 60.5 | 0.00022 | 59348.56668 | 881.0 | 0.00067 | 60069.89970 | 1697.0 | 0.00037
58583.02629 | 15.0 | 0.00032 | 58623.68970 | 61.0 | 0.00019 | 59349.00738 | 881.5 | 0.00062 | 60070.34433 | 1697.5 | 0.00050
58583.46947 | 15.5 | 0.00064 | 59307.45870 | 834.5 | 0.00048 | 59349.44945 | 882.0 | 0.00046 | 60070.78644 | 1698.0 | 0.00052
58583.90988 | 16.0 | 0.00024 | 59307.90346 | 835.0 | 0.00030 | 59349.89660 | 882.5 | 0.00049 | 60071.23112 | 1698.5 | 0.00037
58584.35359 | 16.5 | 0.00033 | 59308.34274 | 835.5 | 0.00033 | 59350.33224 | 883.0 | 0.00062 | 60071.67084 | 1699.0 | 0.00061
58584.79381 | 17.0 | 0.00033 | 59308.78486 | 836.0 | 0.00031 | 59350.77254 | 883.5 | 0.00048 | 60072.10753 | 1699.5 | 0.00066
58585.23743 | 17.5 | 0.00030 | 59309.22788 | 836.5 | 0.00047 | 59351.21601 | 884.0 | 0.00048 | 60072.55328 | 1700.0 | 0.00048
58585.68021 | 18.0 | 0.00032 | 59309.66930 | 837.0 | 0.00037 | 59351.66064 | 884.5 | 0.00057 | 60072.99538 | 1700.5 | 0.00052
58586.12364 | 18.5 | 0.00031 | 59310.11184 | 837.5 | 0.00023 | 59352.09770 | 885.0 | 0.00052 | 60073.44014 | 1701.0 | 0.00043
58586.56482 | 19.0 | 0.00039 | 59310.55204 | 838.0 | 0.00030 | 59352.54232 | 885.5 | 0.00055 | 60073.88186 | 1701.5 | 0.00064
58587.00787 | 19.5 | 0.00027 | 59310.99457 | 838.5 | 0.00035 | 59352.98380 | 886.0 | 0.00055 | 60074.32231 | 1702.0 | 0.00066
58587.44784 | 20.0 | 0.00022 | 59311.43751 | 839.0 | 0.00025 | 59353.42594 | 886.5 | 0.00042 | 60074.76122 | 1702.5 | 0.00050
58587.89134 | 20.5 | 0.00022 | 59311.87970 | 839.5 | 0.00039 | 59353.87131 | 887.0 | 0.00059 | 60075.20774 | 1703.0 | 0.00046
58588.33155 | 21.0 | 0.00015 | 59312.32043 | 840.0 | 0.00022 | 59354.31209 | 887.5 | 0.00053 | 60075.65137 | 1703.5 | 0.00068
58588.77622 | 21.5 | 0.00014 | 59312.76598 | 840.5 | 0.00031 | 59354.75179 | 888.0 | 0.00047 | 60076.53155 | 1704.5 | 0.00061
58589.21430 | 22.0 | 0.00139 | 59313.20262 | 841.0 | 0.00037 | 59355.19564 | 888.5 | 0.00047 | 60076.97495 | 1705.0 | 0.00061
58589.65949 | 22.5 | 0.00025 | 59313.65069 | 841.5 | 0.00024 | 59355.63353 | 889.0 | 0.00043 | 60077.41750 | 1705.5 | 0.00052
58590.09857 | 23.0 | 0.00030 | 59314.08602 | 842.0 | 0.00032 | 59356.07916 | 889.5 | 0.00050 | 60077.86026 | 1706.0 | 0.00052
58590.54181 | 23.5 | 0.00017 | 59314.53014 | 842.5 | 0.00041 | 59356.51878 | 890.0 | 0.00062 | 60078.29890 | 1706.5 | 0.00051
58590.98400 | 24.0 | 0.00035 | 59314.97102 | 843.0 | 0.00031 | 59356.96604 | 890.5 | 0.00082 | 60078.74227 | 1707.0 | 0.00048
58591.42658 | 24.5 | 0.00036 | 59315.41203 | 843.5 | 0.00034 | 59357.40351 | 891.0 | 0.00055 | 60079.18897 | 1707.5 | 0.00049
58591.86852 | 25.0 | 0.00022 | 59315.85605 | 844.0 | 0.00026 | 59357.84515 | 891.5 | 0.00039 | 60079.62981 | 1708.0 | 0.00044
58592.31010 | 25.5 | 0.00038 | 59316.30190 | 844.5 | 0.00031 | 59358.28964 | 892.0 | 0.00051 | 60080.06855 | 1708.5 | 0.00063
58592.75126 | 26.0 | 0.00039 | 59316.74043 | 845.0 | 0.00026 | 59358.73201 | 892.5 | 0.00048 | 60080.50730 | 1709.0 | 0.00053
58593.19595 | 26.5 | 0.00026 | 59317.18404 | 845.5 | 0.00038 | 59359.16913 | 893.0 | 0.00052 | 60080.95305 | 1709.5 | 0.00051
58593.63629 | 27.0 | 0.00045 | 59317.62363 | 846.0 | 0.00031 | 59359.61948 | 893.5 | 0.00051 | 60081.39369 | 1710.0 | 0.00047
58594.07894 | 27.5 | 0.00024 | 59318.06535 | 846.5 | 0.00044 | 60041.16669 | 1664.5 | 0.00030 | 60081.83729 | 1710.5 | 0.00058
58594.52186 | 28.0 | 0.00039 | 59320.27523 | 849.0 | 0.00029 | 60041.61872 | 1665.0 | 0.00025 | 60082.27957 | 1711.0 | 0.00046
58597.17258 | 31.0 | 0.00026 | 59320.71976 | 849.5 | 0.00023 | 60042.94206 | 1666.5 | 0.00029 | 60082.72362 | 1711.5 | 0.00060
58597.61472 | 31.5 | 0.00038 | 59321.16077 | 850.0 | 0.00034 | 60043.38255 | 1667.0 | 0.00034 | 60083.16379 | 1712.0 | 0.00058
58598.05540 | 32.0 | 0.00032 | 59321.60364 | 850.5 | 0.00031 | 60043.82585 | 1667.5 | 0.00023 | 60084.49029 | 1713.5 | 0.00049
58598.49952 | 32.5 | 0.00033 | 59322.04407 | 851.0 | 0.00035 | 60044.26715 | 1668.0 | 0.00025 | 60084.93224 | 1714.0 | 0.00038
58598.94008 | 33.0 | 0.00027 | 59322.48491 | 851.5 | 0.00023 | 60044.70862 | 1668.5 | 0.00028 | 60085.37741 | 1714.5 | 0.00048
58599.38361 | 33.5 | 0.00029 | 59322.92837 | 852.0 | 0.00030 | 60045.14974 | 1669.0 | 0.00029 | 60085.81676 | 1715.0 | 0.00037
58599.82437 | 34.0 | 0.00023 | 59323.37305 | 852.5 | 0.00034 | 60045.59309 | 1669.5 | 0.00039 | 60086.25885 | 1715.5 | 0.00039
58600.26685 | 34.5 | 0.00036 | 59323.81164 | 853.0 | 0.00028 | 60046.03571 | 1670.0 | 0.00035 | 60086.69829 | 1716.0 | 0.00044
58600.70610 | 35.0 | 0.00037 | 59324.25592 | 853.5 | 0.00025 | 60046.47768 | 1670.5 | 0.00026 | 60087.14042 | 1716.5 | 0.00049
58601.15038 | 35.5 | 0.00036 | 59324.69728 | 854.0 | 0.00028 | 60046.91919 | 1671.0 | 0.00020 | 60087.58317 | 1717.0 | 0.00044
58601.59086 | 36.0 | 0.00032 | 59325.13993 | 854.5 | 0.00043 | 60047.36298 | 1671.5 | 0.00025 | 60088.02407 | 1717.5 | 0.00049
58602.03462 | 36.5 | 0.00023 | 59325.58062 | 855.0 | 0.00024 | 60047.80250 | 1672.0 | 0.00026 | 60088.46892 | 1718.0 | 0.00046
58602.47502 | 37.0 | 0.00022 | 59326.02314 | 855.5 | 0.00047 | 60048.68766 | 1673.0 | 0.00028 | 60088.90923 | 1718.5 | 0.00048
58602.91879 | 37.5 | 0.00026 | 59326.46614 | 856.0 | 0.00023 | 60049.12895 | 1673.5 | 0.00026 | 60089.35204 | 1719.0 | 0.00038

Table 16: Eclipse times for TIC 323486857 (continued)

BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev.
---|---|---|---|---|---|---|---|---|---|---|---
$-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$
58603.35927 | 38.0 | 0.00027 | 59326.90804 | 856.5 | 0.00025 | 60049.57184 | 1674.0 | 0.00029 | 60089.79635 | 1719.5 | 0.00086
58603.80102 | 38.5 | 0.00023 | 59327.34780 | 857.0 | 0.00034 | 60050.01534 | 1674.5 | 0.00022 | 60090.23819 | 1720.0 | 0.00098
58604.24427 | 39.0 | 0.00032 | 59327.78911 | 857.5 | 0.00036 | 60050.45400 | 1675.0 | 0.00024 | 60090.67897 | 1720.5 | 0.00063
58604.68696 | 39.5 | 0.00034 | 59328.23375 | 858.0 | 0.00034 | 60050.90010 | 1675.5 | 0.00029 | 60091.11812 | 1721.0 | 0.00049
58605.12795 | 40.0 | 0.00024 | 59328.67518 | 858.5 | 0.00027 | 60051.33576 | 1676.0 | 0.00024 | 60091.55560 | 1721.5 | 0.00064
58605.56796 | 40.5 | 0.00028 | 59329.11724 | 859.0 | 0.00033 | 60051.78066 | 1676.5 | 0.00030 | 60091.99793 | 1722.0 | 0.00051
58606.01130 | 41.0 | 0.00028 | 59329.56032 | 859.5 | 0.00033 | 60052.22169 | 1677.0 | 0.00027 | 60092.44365 | 1722.5 | 0.00061
58606.45355 | 41.5 | 0.00027 | 59330.00054 | 860.0 | 0.00031 | 60052.66168 | 1677.5 | 0.00026 | 60092.88863 | 1723.0 | 0.00042
58606.89314 | 42.0 | 0.00024 | 59330.44647 | 860.5 | 0.00034 | 60053.10468 | 1678.0 | 0.00031 | 60093.32787 | 1723.5 | 0.00063
58607.33810 | 42.5 | 0.00029 | 59330.88656 | 861.0 | 0.00025 | 60053.54895 | 1678.5 | 0.00027 | 60093.76998 | 1724.0 | 0.00052
58607.77827 | 43.0 | 0.00036 | 59331.32648 | 861.5 | 0.00029 | 60053.99122 | 1679.0 | 0.00027 | 60094.21013 | 1724.5 | 0.00050
58608.22090 | 43.5 | 0.00030 | 59331.76958 | 862.0 | 0.00041 | 60054.43533 | 1679.5 | 0.00034 | 60094.65193 | 1725.0 | 0.00058
58608.66302 | 44.0 | 0.00039 | 59332.21264 | 862.5 | 0.00028 | 60054.87346 | 1680.0 | 0.00025 | 60095.09516 | 1725.5 | 0.00055
58609.10723 | 44.5 | 0.00030 | 59333.98326 | 864.5 | 0.00090 | 60055.30942 | 1680.5 | 0.00058 | 60095.53596 | 1726.0 | 0.00048
58609.54582 | 45.0 | 0.00071 | 59334.42102 | 865.0 | 0.00033 | 60055.75857 | 1681.0 | 0.00031 | 60095.98375 | 1726.5 | 0.00049
58610.88147 | 46.5 | 0.00087 | 59334.86242 | 865.5 | 0.00040 | 60056.20025 | 1681.5 | 0.00027 | 60096.42393 | 1727.0 | 0.00070

Table 17: Eclipse times for TIC 650024463

BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev. | BJD | Cycle | std. dev.
---|---|---|---|---|---|---|---|---|---|---|---
$-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$ | $-2\,400\,000$ | no. | $(d)$
58327.08816 | -0.5 | 0.00110 | 58654.64552 | 45.0 | 0.00049 | 59079.24315 | 104.0 | 0.00037 | 60122.70738 | 249.0 | 0.00042
58330.79614 | 0.0 | 0.00050 | 58658.16613 | 45.5 | 0.00115 | 59082.83269 | 104.5 | 0.00108 | 60129.91097 | 250.0 | 0.00033
58334.27812 | 0.5 | 0.00069 | 58661.83767 | 46.0 | 0.00048 | 59086.43768 | 105.0 | 0.00050 | 60133.57915 | 250.5 | 0.00093
58337.98821 | 1.0 | 0.00030 | 58669.02564 | 47.0 | 0.00051 | 59367.04776 | 144.0 | 0.00040 | 60137.11216 | 251.0 | 0.00043
58341.46618 | 1.5 | 0.00114 | 58672.54609 | 47.5 | 0.00100 | 59370.68081 | 144.5 | 0.00100 | 60140.77733 | 251.5 | 0.00086
58345.17921 | 2.0 | 0.00042 | 58676.22071 | 48.0 | 0.00053 | 59374.25614 | 145.0 | 0.00042 | 60144.31914 | 252.0 | 0.00029
58348.65041 | 2.5 | 0.01546 | 58679.73200 | 48.5 | 0.00111 | 59377.89761 | 145.5 | 0.00084 | 60147.98837 | 252.5 | 0.00108
58352.36818 | 3.0 | 0.00053 | 59043.21409 | 99.0 | 0.00048 | 59381.45739 | 146.0 | 0.00036 | 60155.19765 | 253.5 | 0.00099
58625.84233 | 41.0 | 0.00112 | 59046.80730 | 99.5 | 0.00102 | 59385.08446 | 146.5 | 0.00079 | 60158.74801 | 254.0 | 0.00030
58629.36316 | 41.5 | 0.00144 | 59050.42746 | 100.0 | 0.00036 | 59388.67342 | 147.0 | 0.00037 | 60162.39658 | 254.5 | 0.00094
58633.05334 | 42.0 | 0.00067 | 59054.01795 | 100.5 | 0.00108 | 60101.12259 | 246.0 | 0.00029 | 60165.94101 | 255.0 | 0.00044
58636.57755 | 42.5 | 0.00082 | 59057.63048 | 101.0 | 0.00045 | 60104.77423 | 246.5 | 0.00074 | 60169.58876 | 255.5 | 0.00076
58643.78601 | 43.5 | 0.00103 | 59064.84274 | 102.0 | 0.00041 | 60108.31387 | 247.0 | 0.00037 | 60173.13221 | 256.0 | 0.00033
58647.45317 | 44.0 | 0.00055 | 59068.42848 | 102.5 | 0.00101 | 60111.95859 | 247.5 | 0.00251 | 60176.77814 | 256.5 | 0.00111
58650.97684 | 44.5 | 0.00119 | 59075.63588 | 103.5 | 0.00079 | 60115.50744 | 248.0 | 0.00028 | 60180.32145 | 257.0 | 0.00053

##  Appendix B Radial velocities of TICs 287756035 and 321978218

In this appendix we list the RV data obtained for two tertiary components out
of our seven triples (Tables 18-19). All of these data were obtained with the
CHIRON spectrometer on the SMARTS telescope.

Table 18: Measured radial velocities of the tertiary component of TIC 287756035. The date is given as BJD – 2 400 000, while the RVs are in km s-1. Date | RVB | Date | RVB | Date | RVB
---|---|---|---|---|---
$59700.608356$ | $7.628$ | $59738.546993$ | $21.727$ | $60053.676004$ | $3.070$
$59722.571059$ | $16.556$ | $59793.483242$ | $24.726$ |  |
Table 19: Measured radial velocities of the tertiary component of TIC 321978218. The date is given as BJD – 2 400 000, while the RVs are in km s-1. Date | RVB | Date | RVB |  |
---|---|---|---|---|---
$59197.534786$ | $-49.069$ | $59378.910596$ | $-20.313$ | $59828.655080$ | $-51.324$
$59201.567894$ | $-38.221$ | $59383.923361$ | $-3.060$ | $59866.610970$ | $38.891$
$59189.515319$ | $-21.500$ | $59384.912542$ | $0.014$ | $59872.611652$ | $26.137$
$59195.592569$ | $-49.890$ | $59397.889185$ | $33.266$ | $59877.609567$ | $-5.269$
$59371.888074$ | $-45.392$ | $59399.767719$ | $37.061$ | $59881.591328$ | $-36.279$
$59373.907426$ | $-38.801$ | $59400.828602$ | $38.036$ |  |