Collision Detection: An Improved Deep Learning Approach Using SENet and ResNext

Aloukik Aditya, Liudu Zhou, Hrishika Vachhani, Dhivya Chandrasekaran, Vijay Mago

Department of Computer Science
Lakehead University

Thunder Bay, Ontario, Canada

Email: {aaditya, lzhou9, hdhirend, dchandra<EMAIL_ADDRESS>
In recent days, with increased population and traffic on roadways, vehicle collision is one of the leading causes of death worldwide. The automotive industry is motivated on developing techniques to use sensors and advancements in the field of computer vision to build collision detection and collision prevention systems to assist drivers. In this article, a deep-learning-based model comprising of ResNext architecture with SENet blocks is proposed. The performance of the model is compared to popular deep learning models like VGG16, VGG19, Resnet50, and stand-alone ResNext. The proposed model outperforms the existing baseline models achieving a ROC-AUC of $0.91$ using a significantly less proportion of the GTACrash synthetic data for training, thus reducing the computational overhead.

§ INTRODUCTION

Vehicle collision is one of the significant causes of death in the transportation industry. Human errors and distractions are the leading causes of fatal accidents, and these deaths can be prevented using collision prediction techniques. The main aim of collision prediction systems (collision avoidance systems) is to predict the occurrence of collision as early as possible. In order to achieve this, a wide variety of input data is required, based on which the probability of collision is estimated <cit.>. These include velocity, thrust, torque, video feeds, data from accelerometer sensors, gyroscopic sensors, and resting episodes <cit.>.

Each type of input data has its own significance and contributes uniquely to optimally predict peripheral detection, lane marking detection, and vehicle detection thus aiding in collision prediction. Hence identifying the correct data or combination of data is critical for effective prediction of collision. Recent research use sensor inputs from Light Detection and Ranging (LiDAR) systems and images from monochrome cameras to achieve better performance in collision avoidance systems. Advanced Driving Assistance System (ADAS) <cit.> and Automatic Emergency Braking (AEB) <cit.> systems use various combinations of input data to assist driving and automatic application of brakes when in risk-prone areas.

However, the addition of these sensors not only increases the cost of these vehicles but also poses challenges in their ergonomic design. To address this issue researchers have attempted to exploit the advancements in the field of computer vision. But deep learning models require significantly large data to effectively predict collision and collecting labeled data of real-world accidents is quite challenging. <cit.> built a hybrid dataset comprising videos of both real-world accidents captured and uploaded on YouTube[https://www.youtube.com/] and synthetic data generated using the video game Grand Theft Auto-5 (GTA). The dataset comprises of approximately $750,000$ samples of accident and non accident incidents. They further demonstrate the performance of various convolutional neural network models and the best performance (AUC $0.9097$) is achieved by the ResNet50 model.

In this article we use ResNext - an enhanced version of Resnet, appended with Sequence and Excitation (SE) blocks to achieve increased performance by exploiting approximately only 4% of the training data, thus reducing the compuational overhead significantly. We further compare the performance of various models like VGG16, VGG19, ResNet50, Efficientnet_B5, ResNext with our proposed model. Our model outperforms these models achieving a ROC-AUC of $0.9115$. There have been various attempts to develop an elegant solution for a collision-avoidance system, and researchers have exploited recent advancements in deep learning models to achieve better performance. But these models require large datasets and are computationally expensive. The motivation behind this research is to offer a solution that outperforms the existing models while reducing the computational overhead by utilizing lesser number of data points.

The remainder of the article is organized as follows. Section <ref> discusses the related work carried out in the field of Automated Collision Detection. Section <ref> describes in detail the methodology of the proposed model. Section <ref> presents results obtained and Section <ref> concludes the work by summarizing the work done providing the scope of future research.

§ RELATED WORK

§.§ Collision prediction algorithms

For an efficient collision detection system, predicting the trajectory and motion of the vehicle is crucial. The survey by [6] discusses the different approaches that can predict a vehicle's trajectory. It compares the trade-off between the model completeness and real-time implementations of such systems. The survey also highlights the fact that the choice of risk assessment methods is dependent on motion prediction models. They have categorized the motion prediction models into three main categories. First, the physics-based motion model - where the model depends on the law of physics; second, the maneuver-based models - where the model considers the maneuvers that the driver intends to perform. And finally, the interaction-aware motion models - where models consider the inter-dependencies between different vehicles' maneuvers.

Awareness of the surroundings of the vehicle can prevent accidents that occur between the vehicle and peripheral objects such as pedestrians. For peripheral detection systems, [7] have proposed a method using five different architectures of CNN networks to recognize the painted symbolic road markings (lane markings). Their non-conventional approach, which consists of MSER (Maximally Stable Extremal Regions) feature extraction of the IPM (Inverse Perspective Mapping) image, has proven advantageous.

The idea of using deep reinforcement learning in which algorithms learn from the experience of trial and error has been proven to be useful in the navigation system. For instance, the collision avoidance mechanism by self-supervised learning using a standard stereo camera with the navigation model outperforms the Double Q-learning method resulting in a fully autonomous navigation experience <cit.>. Double Q-learning is a part of deep reinforcement leaning and their approach has seventeen times farther crash distance than random policy and seven times more distant than the double Q-Learning method. Deep reinforcement learning can also be advantageous in decentralized vehicular networks. [9] have implemented a application of deep reinforcement learning, which uses a decentralized collision avoidance algorithm for finding the optimal path. They have developed a value network that encodes the destination's expected time considering neighbors' position and velocity. Based on the particular vehicle's value network and surrounding vehicle's value network, the optimal path with the lowest collision likelihood is predicted. The simulation for multiple vehicles having source and destination combination resulted in $26$ % improvement in the optimal path's quality than the general path without considering other vehicles. In another approach, [10] have taken a step further by using deep reinforcement learning in decentralized vehicular collision avoidance mechanism. Their approach has used sensors to communicate with their Policy Gradient Algorithm, which consists of parameters such as success rate, collision avoidance performance, and generalization capability. This method consists of numerous rich and complex environments resulting in time-efficient and collision-free paths in a massive scale decentralized system.

Intersections on the roads are the weakest point because the driver needs to focus on various aspects like the traffic signal, the incoming traffic, the pedestrians, etc. Due to this, collisions at the intersections are prominent. [11] designed intelligent self-driving policies that reduce the severity of the incidents at the crossroads, majorly due to traffic signal violations. They used a deep reinforcement learning approach that provides collision avoidance irrespective of the intersection's destination end. This approach outperforms both human drivers and Autonomous Emergency Braking (AEB) system. However, as the authors mentioned, there are some limitations, for instance, the inability to detect lanes on the road because of only lidar sensors.

Collisions at the back of the vehicle are frequent, as the driver can not continuously monitor the vehicle's back end. [12] proposed a method based on a GA-optimized Neural Network that calculates the variables and controls a collision's likelihood at the rear end of the vehicle. They also used deep learning using BP (Back Propagation) model to optimize collision risk parameters. As a result, they achieved a Mean Square Error (MSE) of nearly zero.

Detecting traffic accidents in major cities is even more challenging than in rural areas due to more vehicles, roads, and intersections. [13] used the Chicago dataset[Dataset collected and archived by the Illinois Department of Transportation (IDOT). The accident cases occurred on the Chicago metropolitan expressways between December $2016$ and December $2017$] which contains $244$ accident cases and $6,073$ non-accident cases which occurred on Chicago metropolitan expressways. They used the Extreme Gradient Boosting (XGBoost) technique to predict accidents in real-time. They have considered various factors such as traffic, demographics, weather, and many more for prediction. In addition to that, the authors have done feature dependency analysis on the data and achieved a significant increase in the real-time accident detection rate.

Numerous machine learning methods have been applied to self-driving systems resulting in better detection systems. [14] have incorporated a complete overview of self-driving car's system architecture, organized into perception system and decision-making system of vehicles. They have tokenized their thorough research of perception systems based on self-driving-car localization, moving obstacles tracking, static obstacles mapping, and road mapping. Decision-making systems help the vehicle navigate from starting location to the final spot; it is divided into several subsystems, such as route planning, motion planning, control, and behavior selection.

§.§ Domain adaptation
Collecting and labeling quality datasets is both costly and time-consuming. One of the solutions to address this problem is generating synthetic data. However, it is essential to understand that there is a significant gap between real and synthetic data. In order to bridge this gap, domain adaptation techniques are employed to annotate unlabelled datasets using a labeled dataset from the same domain.

One approach to solving the domain gap between real and synthetic data is to use both synthetic data and real data when training a task. [15] presented an approach to produce pixel-accurate semantic label maps for images synthesized by modern computer games and have shown that this approach can increase the performance of semantic segmentation models on real-world images. This idea can be extended to produce a continuous video stream. [16] is the first to present a crowd counting method via domain adaptation; by realizing this method, the domain gap between the synthetic and real data can be significantly reduced.

Another approach is unsupervised domain adaptation, which can solve a significant performance drop when a model is trained on a source domain and tested on a target domain. Particularly, in image level adaptation, images collected from different cameras such as DSLR cameras and web cameras are much different. A classifier trained on the DSLR cameras may fail to train on the web cameras without adaptation. To build an efficient classifier, it is necessary to consider the shift between these two distributions. [17] at first used a Generative adversarial Network(GAN) to transfer the image styles from the source domain to a target domain, so the transferred image has a similar style with the target. Second, the style-transferred images and the associate labels were used in supervised learning in the target domain. Generally, the aim is to train powerful classifiers for the target samples; it is known that a GAN objective function can be used to learn target features identical from the source ones. [18], extend this GAN framework by enforcing domain invariance and performing feature augmentation which leads to superior performance.

With the successful development of GANs, image-to-image translation tasks are dominated by GANs because of the high fidelity in generated images. [19] have used conditional GANs to propose a model known as Pix2Pix where they condition on an input image to generate a corresponding output image. They use their model to test various tasks and datasets, including graphics tasks (photo generation) and vision tasks (semantic segmentation.) The conditional GANs map from an input image to an output image and learns loss function to train this mapping. [20] propose a two-step learning method that utilizes conditional GAN to learn the global feature of different domains using unlabeled images without specifying any correspondence between them; it also helps in avoiding the need for labeled data.

Obtaining paired (two similar image datasets) training data can be difficult and expensive; [21] have shown success dealing with unpaired data. They presented a system called CycleGAN, which learns to capture unique characteristics of one image collection and apply these features to a new image. Their method often succeeds in translation tasks involving color and texture changes but with little success when exploring tasks requiring geometric changes.

Unsupervised image-to-image translation attempts to learn a mapping that can translate an input image into a similar image in two different domains. Even though the existing unsupervised image-to-image translation models can generate realistic translations, they still have some drawbacks, like the need for extensive training datasets and the inability to create images from unseen domains. [22], argue the limits they use and seek a few-shot about the unsupervised image to image translation framework. Their model achieves this few shot generation capability by coupling an adversarial training scheme with a novel network design. They verify their effectiveness of the proposed framework by the comparisons of several baseline methods on benchmark datasets.

Some works extend the unsupervised image translation to multiple domains. They learn a mapping between various seen domains simultaneously. [23] show improved results over the following properties in an excellent image to image translation model; diversity of generated images and scalability over multiple domains. To address scalability, they propose a single framework called StarGAN v$2$ which is an extensible approach that can generate diverse images across multiple domains. However, An earlier model (StarGAN) learns the mappings between all available domains using a single generator. StarGAN v$2$ can generate images with rich styles across numerous domains, outperforming the former methods.

§ METHODOLOGY

§.§ Dataset

The proposed model is trained using synthetic data and tested on real-world data. The process adopted by [5] to build the GTACrash and YouTubeCrash datasets is described in this section. Both datasets have two classes, $accident$ and $non-accident$, positive cases are labeled as accident, negative cases are labeled as non-accident. Each class has JPEG and JSON files. The raw JPEG image resolution is $400 \times 710$ pixels, but it was reduced to $130 \times 355$ pixels during the preprocessing. The JSON files have sensitive information about the vehicle scenario, including coordinates, wheel angle, acceleration, angular velocity, etc. as shown in Figure <ref>.

GTACrash JSON file structure

The game GTA-5 was played for $72$ hours straight using the automated script of the GTACrash synthetic data in the original paper, which produced $3,661$ non-accident scenes and $7,720$ accident cases. Each case has $20$ frames and $20$ JSON files, making the total accident frame $20,000$ and non-accident to $10,000$. The images were collected under various day and weather conditions like sunny, rainy, nights, snow, etc. These attributes positively affect the algorithm of this project. The software called ScriptHook V was used to attain the data; one of the attributes was bounding_box, it extracted the coordinates of the X and Y axis for the nearby vehicles. These coordinates were later used by the algorithm to classify dangerous (red box) or safe vehicles (green box). However, we have reduced the original dataset and only use $1,000$ accidental cases and $500$ non-accident cases.

As shown in Table <ref>, YouTubeCrash data is split randomly into training and testing. This dataset was collected from dashcam videos (uploaded on a YouTube channel called Car Crashes Time). The videos in the YouTubeCrash dataset have $122$ clips which were further divided into accident and non-accident classes with 20 frames per case. Accident and non-accident images were collected using each dashcam video: if an accident happened at the $5$th second of the video, then from $3$ to $5$ seconds (just $2$ seconds before an accident), $20$ frames were collected and labeled as “accident". While $0$ to $3$ seconds of the video was marked as “non-accident".
The dataset contains diverse accident scenarios such as abrupt lane changes, sudden stops, and signal violations; it can help the model to solve real-world problems in future mixed conditions. There are JSON files for the YouTubeCrash dataset as well, but the parameters such as position, acceleration, and angular velocity are set to $NA$. As shown in Table <ref>, we have reduced the number of instances for the GTACrash dataset, but instances in the YouTubeCrash dataset were used the same as the original paper. Table <ref> illustrates the cases for the original dataset, while Table <ref> shows the instances of ours.

We also explore other car crash image datasets, including the KITTI dataset. <cit.>, which were created in the city of Karlsruhe (urban as well as rural areas). In each image, there are up to 15 cars and 30 people (depends on the location), and the engine hood and the sky region have been cropped to achieve better performance. Also, both color and grayscale images were stored with lossless compression using $8$-bit PNG files. The second dataset is $Cityscapes$ <cit.>; it contains a diverse set of video sequences recorded in street scenes from 50 different cities, with high-quality pixel-level annotations of $5,000$ frames in addition to a more extensive collection of $20,000$ weakly annotated frames. These datasets helped us understand the diverse conditions of the accidents and non-accident scenes that occur in urban and rural areas but this research focuses on the use of synthetic data for training.

Statistics of Original YouTubeCrash and GTACrash

Number of      YouTubeCrash      GTACrash
Orignal accident scenes        122      7720
Orignal nonaccident scenes     100      3661
Total accident frames          2440     154400
Total non accident frames      2000     73220

Statistics of Ours YouTubeCrash and GTACrash

Number of      YouTubeCrash      GTACrash
Ours accident scenes          122      1000
Ours nonaccident scenes       100      500
Total accident frames         2440     20000
Total non accident frames     2000     10000

§.§ Experimental Setup

We have implemented and tested various models such as VGG16, VGG19, ResNext, Efficientnet B($0$-$7$), and ResNext_SENet on the dataset and obtained different outcomes.
Our proposed method, ResNext + SENet with ROC-AUC of $0.9115$, surpassed the existing methods Resnet50 and VGG16 with ROC-AUC of $0.9069$. We have also implemented other deep learning models but the best performing in terms of ROC-AUC and complexity is ResNext+SENet model.

Images and JSON file as $D_{whole}$ ($D_{train}$, $D_{test}$, $D_{val}$)

$reduce\_size$ $\gets$ reduce_size($D_{whole}$)
*resize to 130 x 355

$JSON\_files \gets$ build_sample_list($D_{whole}$)
*reading JSON parameter: bounding_box, wheel_angle etc.
$merge \gets$ frame_per_vehicle($reduce\_size ,JSON\_files$ )
*JSON and img merged as one

$preprocessing \gets$ preprocess_batch($merge$)
*data augmentation, resize boundingbox

$enqueue \gets$ enqueue_batch($preprocessing$)
*batch of 512 is collected

$dequeue \gets$ dequeue_batch($enqueue$)
*batch of 512 is ready to release into neural network
Pseudocode for Preprocessing of Data

As shown in Algorithm <ref>, there are training, testing, and validation sets, and each set has an equal number of images and JSON files selected from the respective folders in the dataset. Initially, the image size is reduced from $400 \times 710$ pixels to $130 \times 355$ pixels and then read the JSON file parameters such as acceleration, wheel angle, angular velocity, etc. Using the merge function, the images and JSON files are merged as one instance. After that, preprocessing has been done using data augmentation and bounding_box resize, which also helped to get the bounding box coordinates. Finally, using $enqueue$ and $dequeue$ functions, the input data has been passed into the neural network with a batch size of $512$, which helped avoid memory errors.

§.§.§ ResNext

ResNext is an enhanced version of Resnet, which has one extra dimension called cardinality. This new dimension is the basically the size of the set of transformations <cit.>. Cardinality splits the network into $n$ branches, and these branches perform convolution transformations that aggregate together using summation, as shown in Figure <ref>. The left side is a block of Resnet, and the right side indicates ResNext with a cardinality of $32$. Also, Resnet is a particular case of ResNext in which cardinality is set to $1$ as there is only one path. ResNext is capable of performing better than Resnet but has 50% more complexity. According to [27], ResNext can not perform well with small networks since it uses costly dense $1 \times 1$ convolution.

Resnet vs ResNext from [26]

§.§.§ Squeeze and excitation networks

Squeeze and Excitation Networks (SENet) are the special types of networks that can be applied to any CNN network; they can improve channel inter-dependencies without computational cost <cit.>. In simple words, it can excite relevant features in the CNN layer and suppress irrelevant features without any additional processing. The main objective of convolution layers is to detect elements like edges, color, corners, etc. As we go deeper into the network, it can also detect shapes, digits, faces, etc., and all these features are fused with channel information of the image ($W \times H \times C$). SENet is generally applied to each convolution layer; it works best when the network is deep because of more spatial features. The weights of CNN channel are equal when a feature map is created, and these weights are modified after passing through SENet.

SENet architecture from [28]

The work of SENet is straightforward; it is a four-step network used in each convolution layer in the CNN network. Initially, we have an output from the convolution block ($W \times H \times C$), which is squeezed to $1 \times 1 \times C$ using global average pooling. Next, a fully connected layer followed by the Relu activation function is applied; it helps in getting the non-linearity to the features by removing all negative values. A fully connected layer followed by a Sigmoid activation function is implemented after that, resulting in shape $1 \times 1 \times C$. This final shape $1 \times 1 \times C$ is multiplied with the original input feature map of size ($H \times W \times C$), which basically scales the original input based on the important spatial features. The main task of the Squeeze and Excitation Network is to get the most critical features (excited by multiplying the vector in the final step) and to reduce irrelevant features (squeezed by global average pooing in the beginning).

Architecture of ResNext + Squeeze and excitation network

§.§ Proposed Method

The complete architecture of the proposed method can be seen in Figure <ref>. In this research, a deep-learning-based model comprising of ResNext architecture with SENet blocks is proposed. Initially, normalization of the data using mean and standard deviation has been done, which helped remove the outliers or extreme values. Three residual layers have been used because of the bottleneck problem and over-fitting, and each of them contains three sub-layers: split, transition, and Squeeze-Excitation layer. Firstly, the split layer divides the layers into two branches as the cardinality is $2$. Secondly, the transition layer is the pooling layer plus the convolution layer, which results in the reduced dimension of the images. Finally, as discussed before, Figure <ref> shows the Squeeze-excitation network, which helped achieve better ROC-AUC without any additional computational cost and processing time. After that, we passed the features to the generator layer, which downsampled the features, and by using global average pooling, it fixed the problem of over-fitting. Two dense layers were used as classification layers with a size of $1,500$ and $2$, respectively. Our model has a depth of $64$, which speeds up the processing time and makes it less complex. Also, in residual layers, we set the output dimension to $64$ in the first layer, and then it was increased to $128$ in the second layer and $256$ in the third layer.

VGG16 and Resnet50 have been deployed and found that VGG16 not only has a reduced ROC-AUC but has a significant number of parameters. In addition to that, the training time of VGG16 was comparatively more than the Resnet50. The ResNext model gives the equivalent ROC-AUC compared to Resnet50, but the compilation time is relatively minor. A small additional method SENet added to the existing ResNext model, generates the best ROC-AUC, see section <ref>.Adam optimizer is used in the proposed model because it can handle sparse gradient and noisy problems. Adam optimizer is not only adaptive, but it is highly correlated to Adagrad and Rmsprop optimizer. Our study implemented Adam, momentum, SGD, and Rmspropo optimizer; Adam optimizer performed best because our images deal with the vehicle motion.

§.§ Computational resources

Our project was supported by Compute Canada(http://www.computecanada.ca). We used the Cedar cluster, running on 24 CPU cores with 100GB memory and allocated time for 24.5 hours for eash task (the time for each task was about 4 hours with the output stored in a slurm file). The jobs were requested to run on 32GV100s.

§ RESULTS

While implementing ResNext, the variety of depth and width of the network have been experimented and observed that cardinality of $2$ with a depth of $64$ were the most optimized parameters for the network.

Global average pooling, max pooling, and $tf.reduced\_mean$ were deployed and found that Global average pooling worked best in ResNext_SENet because of synthetic data. However, in Resnet50 and VGG16, $tf.reduced\_mean$ works better than global average pooling because it computes the mean of elements across dimensions of a tensor. At the end of the structure of ResNext_SENet, two fully connected layers ($1,500$ and $2$ neurons respectively) were used, which helped the model to understand the spatial features more accurately and resulted in the best ROC-AUC of $0.9115$. The hyperparameters of ResNext_SENet were optimzed as shown in Figure <ref> which helped us acheiving better ROC-AUC from 0.81 to 0.9115.

Hyperparameter tuning

Hyperparameters                                Before      Optimized
Optimizer                                     SGD                               Adam
Cardinality                                   8                                 2
Depth                                         32                                64
Pooling                                       tf.reduce_mean                   Global_Average_pooling
1|l|Dense layer neurons     64                                1500
ROC_AUC                       0.81               0.9115

EfficientNets are the most recent successful deep learning approach, but in this research, it was observed that results were not good as ResNext_SENet. It is based on three parameters: width, depth, and resolution of the image. Here, width is the number of channels used in each layer, depth is the number of layers used in a network, and resolution is the the size of an input image. EfficientNet has its functionality called compound scaling; it can scale these parameters to get the most optimal and best accuracies with lesser flops and lesser parameters. Depth, width, and resolution are tuned using EfficientNet itself. All models of EfficientNet (B$0$-B$7$) were deployed, and each model has a different architecture based on image size. It was observed that EfficientNet B$5$ performed best with ROC-AUC of $0.85$ because it has the most similar image size architecture compared to synthetic images, which were used in this research. The performance of the EfficientNets could be improved by optimizing the hyperparameters but it requires significant amount of memory.

ResNext_SENet was used with sliced GTACrash dataset and achieved the ROC-AUC of $0.915$ as we can see in Figure <ref>. Previously, [5] implemented Resnet50 with original GTACrash dataset which resulted the ROC-AUC of $0.9097$. In the future, we will deploy Rand augmentation and auto augmentation, which we believe can significantly improve the performance of the proposed model.

ROC-AUC performance comparison

§ CONCLUSION

With the increasing number of deaths due to road accidents, research focus on building collision avoidance and collision prediction systems have gained significance. Researchers use data from various sources to efficiently predict accidents and provide assisstance to In this article a deep learning-based approach trained using synthetic data provided by [5] is proposed. The proposed model uses ResNext architecture with SENet blocks to outperform the existing base-line models while using significantly less training data.

§ ACKNOWLEDGMENTS

This research was enabled in part by support provided by Lakehead University (https://www.lakeheadu.ca/) and Compute Canada (www.computecanada.ca).
The authors would like to thank Andrew Fisher for his support in implementation and development of the article. Publication costs are funded by NSERC Discovery Grant (RGPIN-2017-05377), held by  Vijay Mago.

[1]
S. Taghvaeeyan and R. Rajamani, “Two-dimensional sensor system for automotive
crash prediction,” IEEE Transactions on Intelligent Transportation
Systems, vol. 15, no. 1, pp. 178–190, 2013.

[2]
Y. Ba, W. Zhang, Q. Wang, R. Zhou, and C. Ren, “Crash prediction with
behavioral and physiological features for advanced vehicle collision
avoidance system,” Transportation Research Part C: Emerging
Technologies, vol. 74, pp. 22–33, 2017.

[3]
K. Bayoudh, F. Hamdaoui, and A. Mtibaa, “Transfer learning based hybrid 2d-3d
cnn for traffic sign recognition and semantic road detection applied in
advanced driver assistance systems,” Applied Intelligence, vol. 51,
no. 1, pp. 124–142, 2021.

[4]
B. Fildes, M. Keall, N. Bos, A. Lie, Y. Page, C. Pastor, L. Pennisi, M. Rizzi,
P. Thomas, and C. Tingvall, “Effectiveness of low speed autonomous emergency
braking in real-world rear-end crashes,” Accident Analysis &
Prevention, vol. 81, pp. 24–29, 2015.

[5]
H. Kim, K. Lee, G. Hwang, and C. Suh, “Crash to not crash: Learn to identify
dangerous vehicles using a simulator,” in Proceedings of the AAAI
Conference on Artificial Intelligence, vol. 33, 2019, pp. 978–985.

[6]
S. Lefèvre, D. Vasquez, and C. Laugier, “A survey on motion prediction and
risk assessment for intelligent vehicles,” ROBOMECH journal, vol. 1,
no. 1, pp. 1–14, 2014.

[7]
T. Ahmad, D. Ilstrup, E. Emami, and G. Bebis, “Symbolic road marking
recognition using convolutional neural networks,” in 2017 IEEE
Intelligent Vehicles Symposium (IV).1em plus 0.5em minus 0.4emIEEE, 2017, pp. 1428–1433.

[8]
G. Kahn, A. Villaflor, B. Ding, P. Abbeel, and S. Levine, “Self-supervised
deep reinforcement learning with generalized computation graphs for robot
navigation,” in 2018 IEEE International Conference on Robotics and
Automation (ICRA).1em plus 0.5em minus 0.4emIEEE, 2018, pp.

[9]
Y. F. Chen, M. Liu, M. Everett, and J. P. How, “Decentralized
non-communicating multiagent collision avoidance with deep reinforcement
learning,” in 2017 IEEE international conference on robotics and
automation (ICRA).1em plus 0.5em minus 0.4emIEEE, 2017, pp.

[10]
P. Long, T. Fan, X. Liao, W. Liu, H. Zhang, and J. Pan, “Towards optimally
decentralized multi-robot collision avoidance via deep reinforcement
learning,” arXiv preprint arXiv:1709.10082, 2017.

[11]
M. Kim, S. Lee, J. Lim, J. Choi, and S. G. Kang, “Unexpected collision
avoidance driving strategy using deep reinforcement learning,” IEEE
Access, vol. 8, pp. 17 243–17 252, 2020.

[12]
C. Chen, H. Xiang, T. Qiu, C. Wang, Y. Zhou, and V. Chang, “A rear-end
collision prediction scheme based on deep learning in the internet of
vehicles,” Journal of Parallel and Distributed Computing, vol. 117,
pp. 192–204, 2018.

[13]
A. B. Parsa, A. Movahedi, H. Taghipour, S. Derrible, and A. K. Mohammadian,
“Toward safer highways, application of xgboost and shap for real-time
accident detection and feature analysis,” Accident Analysis &
Prevention, vol. 136, p. 105405, 2020.

[14]
C. Badue, R. Guidolini, R. V. Carneiro, P. Azevedo, V. B. Cardoso, A. Forechi,
L. Jesus, R. Berriel, T. M. Paixão, F. Mutz et al., “Self-driving
cars: A survey,” Expert Systems with Applications, p. 113816, 2020.

[15]
S. R. Richter, V. Vineet, S. Roth, and V. Koltun, “Playing for data: Ground
truth from computer games,” in European conference on computer
vision.1em plus 0.5em minus 0.4emSpringer, 2016, pp. 102–118.

[16]
Q. Wang, J. Gao, W. Lin, and Y. Yuan, “Learning from synthetic data for crowd
counting in the wild,” in Proceedings of the IEEE/CVF Conference on
Computer Vision and Pattern Recognition, 2019, pp. 8198–8207.

[17]
J. Hoffman, E. Tzeng, T. Park, J.-Y. Zhu, P. Isola, K. Saenko, A. Efros, and
T. Darrell, “Cycada: Cycle-consistent adversarial domain adaptation,” in
International conference on machine learning.1em plus 0.5em
minus 0.4emPMLR, 2018, pp. 1989–1998.

[18]
R. Volpi, P. Morerio, S. Savarese, and V. Murino, “Adversarial feature
augmentation for unsupervised domain adaptation,” in Proceedings of
the IEEE Conference on Computer Vision and Pattern Recognition, 2018, pp.

[19]
P. Isola, J.-Y. Zhu, T. Zhou, and A. A. Efros, “Image-to-image translation
with conditional adversarial networks,” in Proceedings of the IEEE
conference on computer vision and pattern recognition, 2017, pp. 1125–1134.

[20]
H. Dong, P. Neekhara, C. Wu, and Y. Guo, “Unsupervised image-to-image
translation with generative adversarial networks,” arXiv preprint
arXiv:1701.02676, 2017.

[21]
J.-Y. Zhu, T. Park, P. Isola, and A. A. Efros, “Unpaired image-to-image
translation using cycle-consistent adversarial networks,” in
Proceedings of the IEEE international conference on computer vision,
2017, pp. 2223–2232.

[22]
M.-Y. Liu, X. Huang, A. Mallya, T. Karras, T. Aila, J. Lehtinen, and J. Kautz,
“Few-shot unsupervised image-to-image translation,” in Proceedings of
the IEEE/CVF International Conference on Computer Vision, 2019, pp.
10 551–10 560.

[23]
Y. Choi, Y. Uh, J. Yoo, and J.-W. Ha, “Stargan v2: Diverse image synthesis for
multiple domains,” in Proceedings of the IEEE/CVF Conference on
Computer Vision and Pattern Recognition, 2020, pp. 8188–8197.

[24]
P. Zhu, L. Wen, X. Bian, H. Ling, and Q. Hu, “Vision meets drones: A
challenge,” arXiv preprint arXiv:1804.07437, 2018.

[25]
M. Cordts, M. Omran, S. Ramos, T. Rehfeld, M. Enzweiler, R. Benenson,
U. Franke, S. Roth, and B. Schiele, “The cityscapes dataset for semantic
urban scene understanding,” in Proc. of the IEEE Conference on
Computer Vision and Pattern Recognition (CVPR), 2016.

[26]
S. Xie, R. Girshick, P. Dollár, Z. Tu, and K. He, “Aggregated
residual transformations for deep neural networks,” in 2017 IEEE
Conference on Computer Vision and Pattern Recognition (CVPR), 2017, pp.

[27]
X. Zhang, X. Zhou, M. Lin, and J. Sun, “Shufflenet: An extremely
efficient convolutional neural network for mobile devices,” in 2018
IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018, pp.

[28]
J. Hu, L. Shen, and G. Sun, “Squeeze-and-excitation networks,” in
Proceedings of the IEEE conference on computer vision and pattern
recognition, 2018, pp. 7132–7141.

[A]ADASAdvanced Driving Assistance System
[A]AEBAutomatic Emergency Braking
[A]SENetSqueezing and Excitation Network
[A]ROCReceiver Operator Characteristic
[A]AUCArea Under the Curve
[A]MSERMaximally Stable Extremal Regions
[A]IPMInverse Perspective Mapping
[A]BPBack Propagation
[A]MSEMean Square Error
[A]XGBoostExtreme Gradient Boosting
[A]DSLRDigital Single-Lens Reflex
[A]GANGenerative Adversarial Network
[A]JSONJavaScript Object Notation
[A]JPEGJoint Photographic Experts Group
[A]CNNConvolutional Neural Network
[A]PNGPortable Network Graphics
[A]SGDSaccharomyces Genome Database
[A]CPUCentral Processing Unit

[N]YouTubeCrashDataset collected from dashcam videos uploaded on YouTube
[N]GTACrashDataset collected from a video game named
Grand Theft Auto 5


11institutetext: Grupo de Astrofísica Molecular, Instituto de Física
Fundamental (IFF-CSIC), C/ Serrano 121, 28006 Madrid, Spain. 11email:
<EMAIL_ADDRESS><EMAIL_ADDRESS>22institutetext: Department of
Applied Chemistry, Science Building II, National Yang Ming Chiao Tung
University, 1001 Ta-Hsueh Rd., Hsinchu 300098, Taiwan 33institutetext:
Observatorio Astronómico Nacional (IGN), C/ Alfonso XII, 3, 28014, Madrid,
Spain. 44institutetext: Centro de Desarrollos Tecnológicos, Observatorio de
Yebes (IGN), 19141 Yebes, Guadalajara, Spain.

# Discovery of the cyclic C5H radical in TMC-1 ††thanks: Based on observations
carried out with the Yebes 40m telescope (projects 19A003, 20A014, 20D023, and
21A011). The 40m radio telescope at Yebes Observatory is operated by the
Spanish Geographic Institute (IGN; Ministerio de Transportes, Movilidad y
Agenda Urbana).

C. Cabezas 11 M. Agúndez 11 R. Fuentetaja 11 Y. Endo 22 N. Marcelino 3344 B.
Tercero 3344 J. R. Pardo 11 P. de Vicente and J. Cernicharo 4411

(Received; accepted)

Cyclic C5H ($c$-C5H), the radical formed by substituting an ethynyl group CCH
for the hydrogen atom in the $c$-C3H radical, has been detected for the first
time in the space. The $c$-C5H species is an isomer of the well-known linear
radical $l$-C5H and is $\sim$ 6 kcal/mol less stable. A total of 17 rotational
transitions were detected for the $c$-C5H species in TMC-1 within the
31.0–50.3 GHz range using the Yebes 40m radio telescope. We derive a column
density of (9.0 $\pm$ 0.9) $\times$ 1010 cm-2 for $c$-C5H. Additionally, we
observed 12 lines for $l$-C5H and derive a column density for it of (1.3 $\pm$
0.3) $\times$ 1012 cm-2, which results in an abundance ratio $c$-C5H/$l$-C5H
of 0.069. This is in sharp contrast with the value found for the analogue
system $c$-C3H/$l$-C3H, whose ratio is 5.5 in TMC-1. We discuss the formation
of $c$-C5H and conclude that this radical is probably formed in the reaction
of atomic carbon with diacetylene.

###### Key Words.:

Astrochemistry — ISM: molecules — ISM: individual (TMC-1) — line:
identification — molecular data

##  1 Introduction

Carbon can be considered the most versatile element for building molecules in
the interstellar medium (ISM). In fact, about 80% of the nearly 260 molecules
detected to date in space (CDMS111https://cdms.astro.uni-koeln.de/, Müller et
al. 2005) contain at least one carbon atom, and one-fourth are hydrocarbons.
The chemistry of hydrocarbons is dominated to a large extent by highly
unsaturated (low H/C ratios) carbon chain molecules such as the CnH family.
The hydrocarbon radicals CnH detected in space range from the methylidene
radical, CH (Dunham 1937), to C8H (Cernicharo & Guélin 1996; Bell et al.
1999). The smaller ones, such as C2H, C3H, and C4H, are observed in star-
forming regions (Tucker et al. 1974), photon-dominated regions (Teyssier et
al. 2004), cold dark clouds (Wootten et al. 1980; Irvine et al. 1981; Thaddeus
et al. 1985), translucent molecular clouds (Turner et al. 2000), circumstellar
envelopes (Guélin et al. 1978; Pardo & Cernicharo 2007), and the diffuse
medium (Bell et al. 1983; Nyman 1984). The larger ones, C5H, C6H, C7H, and
C8H, are mainly observed in cold dense molecular clouds (Cernicharo et al.
1987; Saito et al. 1987; Bell et al. 1999; Araki et al. 2017) and in the
expanding envelope of the carbon-rich star IRC+10216 (Cernicharo et al.
1986a, b; Suzuki et al. 1986; Cernicharo & Guélin 1996; Guélin et al. 1996).

The C3H radical shows a particular behaviour because it exists in two isomeric
forms, a cyclic one ($c$-C3H) and a linear one ($l$-C3H), with $c$-C3H lower
in energy. Both have been widely observed in the ISM, and in general the
$c$-C3H isomer (Yamamoto et al. 1987; Mangum & Wootten 1990; Turner et al.
2000; Cernicharo et al. 2000; Zhang et al. 2009; Liszt et al. 2014) is found
to have a larger abundance than $l$-C3H (Thaddeus et al. 1985; Turner et al.
2000; Pardo & Cernicharo 2007). The C5H radical is predicted to adopt up to
seven different structures, including linear, cyclic, and bent ones (Crawford
et al. 1999). Conversely to C3H, the linear structure, $l$-C5H, is the most
stable one. It has been detected in the ISM by Cernicharo et al.  (1986a, b,
1987). The cyclic isomer, $c$-C5H, which is analogous to the $c$-C3H isomer
but with the H atom replaced by a ethynyl (-CCH) group, is the second most
stable isomer (6.1 kcal/mol; Crawford et al. 1999). As $l$-C5H (McCarthy et
al. 1999), $c$-C5H was characterized in the laboratory (Apponi et al. 2001),
but it had not yet been detected in the ISM.

In this Letter we report the detection of the $c$-C5H radical towards the cold
dark cloud TMC-1. The derived abundance is compared with that of the linear
isomer $l$-C5H, and the plausible reactions that could lead to the formation
of this species are discussed with the aid of a chemical model.

##  2 Observations

The observational data used in this article consist of spectra of TMC-1 taken
with the Yebes 40m telescope towards the cyanopolyyne peak of TMC-1,
$\alpha_{J2000}=4^{\rm h}41^{\rm m}41.9^{\rm s}$ and
$\delta_{J2000}=+25^{\circ}41^{\prime}27.0^{\prime\prime}$. The observations
are part of the ongoing QUIJOTE222Q-band Ultrasensitive Inspection Journey to
the Obscure TMC-1 Environment. line survey (Cernicharo et al. 2021a) carried
out during different observing runs between November 2019 and January 2022.
The observations were performed using the frequency-switching mode with a
frequency throw of 10 MHz in the very first observing runs, in November 2019
and February 2020, 8 MHz in the observations of January-November 2021, and 10
MHz again in the last observing run that took place between October 2021 and
January 2022. The total on-source telescope time is 430 h in each polarization
(twice this value after averaging the two polarizations), which can be split
into 238 and 192 hours for the 8 MHz and 10 MHz frequency throws. The QUIJOTE
line survey uses a 7 mm receiver covering the Q band (31.0-50.3 GHz) with
horizontal and vertical polarizations. Receiver temperatures in 2019 and 2020
varied from 22 K at 32 GHz to 42 K at 50 GHz. In 2021, some power adaptation
carried out in the down-conversion chains changed the receiver temperatures to
16 K at 32 GHz and 25 K at 50 GHz. The backends are 16 Fourier transform
spectrometers, which provide a bandwidth of 8 $\times$ 2.5 GHz in each
polarization, thus covering practically the whole Q band, with a spectral
resolution of 38.15 kHz. The system is described in detail by Tercero et al.
(2021).

The intensity scale used is antenna temperature, $T_{A}^{*}$, which is
calibrated using two absorbers at different temperatures and the ATM package
(Cernicharo 1985; Pardo et al. 2001). Calibration uncertainties were assumed
to be 10% based on the observed repeatability of the line intensities between
different observing runs. All data were analysed using the software
GILDAS333http://www.iram.fr/IRAMFR/GILDAS/.

Figure 1: FTMW spectra for $c$-C5H. Coloured lines show spectra using argon
(magenta) and neon (black) as the carrier gas in the supersonic expansion.
Each line is split into two Doppler components because the direction of the
supersonic jet expansion is parallel to the standing wave in the Fabry-Pérot
cavity of the spectrometer. The difference in the magnitude of Doppler
splitting when different carrier gases – neon and argon – are used is related
to the velocity of the molecule in the jet; it is reciprocal to the square
root of the atomic mass of the carrier gas.

##  3 Results

###  3.1 New laboratory data for $c$-C5H

Figure 2: Observed lines of $c$-C5H in TMC-1 in the 31.0-50.3 GHz range.
Frequencies and line parameters are given in Table 1. Quantum numbers for the
observed transitions are indicated in each panel. The red line shows the
synthetic spectrum computed for a rotational temperature of 6 K and a column
density of 9.0$\times$1010 cm-2 (see text). Blanked channels correspond to
negative features created in the folding of the frequency-switching data. The
label U corresponds to unidentified features above 4$\sigma$.

Apponi et al. (2001) observed the rotational spectrum of the $c$-C5H radical
in the laboratory. It has a ${}^{2}B_{2}$ electronic ground state with
$C_{2v}$ symmetry. Owing to the Bose statistics of the two equivalent off-axis
carbon nuclei, only rotational levels with odd $K_{a}$ occur, and rotational
transitions with $K_{a}$=0 are thus forbidden. Apponi et al. (2001) found two
series of lines, with $K_{a}$=0 and $K_{a}$=1 values, which were fitted
separately. The $K_{a}$=1 series was ascribed to the ground state of $c$-C5H,
while the origin of the $K_{a}$=0 lines was not totally clear. Our hypothesis
is that the $K_{a}$=0 lines arise from a low frequency vibrationally excited
state with different vibrational symmetry (either $B_{1}$ or $B_{2}$) from
that for the ground state ($A_{1}$). To gain some insight into this, we
carried out Fourier transform microwave (FTMW) spectroscopy experiments using
as carrier gases either neon or argon.

The rotational spectrum of the $c$-C5H radical was observed using a Balle-
Flygare narrow-band-type FTMW spectrometer operating in the frequency region
4-40 GHz (Endo et al. 1994; Cabezas et al. 2016). We observed some of the
rotational transitions reported before by Apponi et al. (2001). The short-
lived species $c$-C5H was produced in a supersonic expansion by a pulsed
electric discharge of a gas mixture of C2H2 (0.3%) diluted in neon or argon.
The gas mixture was flowed through a pulsed-solenoid valve that is
accommodated in the backside of one of the cavity mirrors and aligned parallel
to the optical axis of the resonator. A pulse voltage of 1000 V with a
duration of 450 $\mu$s was applied between stainless-steel electrodes attached
to the exit of the pulsed discharge nozzle, resulting in an electric discharge
synchronized with the gas expansion. The resulting products generated in the
discharge were then probed by FTMW spectroscopy, which allowed small hyperfine
splittings to be resolved.

Previous studies have shown that heavier inert gases have an enhanced cooling
efficiency in supersonic expansions due to the larger collision energies they
provide (Cabezas et al. 2018). Consequently, an argon-seeded expansion is
expected to favour the population of the lower frequency vibrational states,
while higher vibrational states will be populated in a neon-seeded expansion.
Figure 1 shows the spectra recorded using argon and neon gases. When argon is
used, only the $K_{a}$=1 lines are observed, but in the neon experiments both
$K_{a}$=0 and $K_{a}$=1 are observed. We note that the intensity of the
$K_{a}$=1 lines decreases when neon is used due to a fraction of its
population being distributed between higher vibrationally excited states. In
light of our experimental observations, we infer that the $K_{a}$=0 series of
lines come from a low frequency vibrationally excited state, probably an in-
plane or out-of-plane bending mode (Crawford et al. 1999).

###  3.2 Identification of $c$-C5H in TMC-1

Table 1: Observed line parameters for $c$-C5H in TMC-1.

Transition |  $\nu_{obs}$ a |  $\int T_{A}^{*}dv$ b |  $\Delta v$ c | $T_{A}^{*}$
---|---|---|---|---
$N^{\prime}_{K^{\prime}_{a,}K^{\prime}_{c}}$$\leftarrow$$N_{K_{a,}K_{c}}$ |  $J^{\prime}$$\leftarrow$$J$ |  $F^{\prime}$$\leftarrow$$F$ | (MHz) |  (mK km s-1) |  (km s-1) | (mK)
$5_{1,5}$$\leftarrow$$4_{1,4}$ |  11/2$\leftarrow$9/2 |  6$\leftarrow$5 | 33093.924 |  0.58$\pm$0.09 |  0.79$\pm$ 0.14 |  0.69$\pm$0.11
$5_{1,5}$$\leftarrow$$4_{1,4}$ |  11/2$\leftarrow$9/2 |  5$\leftarrow$4 | 33094.088 |  0.50$\pm$0.08 |  0.62$\pm$ 0.14 |  0.75$\pm$0.11
$5_{1,5}$$\leftarrow$$4_{1,4}$ |  9/2$\leftarrow$7/2 |  5$\leftarrow$4 | 33121.256 |  0.50$\pm$0.06 |  0.86$\pm$ 0.09 |  0.55$\pm$0.11
$5_{1,5}$$\leftarrow$$4_{1,4}$ |  9/2$\leftarrow$7/2 |  4$\leftarrow$3 | 33121.338 |  0.28$\pm$0.05 |  0.64$\pm$ 0.08 |  0.41$\pm$0.11
$5_{1,4}$$\leftarrow$$4_{1,3}$ |  11/2$\leftarrow$9/2 |  6$\leftarrow$5 | 34387.798 |  0.33$\pm$0.07 |  0.66$\pm$ 0.17 |  0.46$\pm$0.10
$5_{1,4}$$\leftarrow$$4_{1,3}$ |  11/2$\leftarrow$9/2 |  5$\leftarrow$4 | 34388.431 |  0.54$\pm$0.08 |  0.72$\pm$ 0.12 |  0.70$\pm$0.10
$5_{1,4}$$\leftarrow$$4_{1,3}$ |  9/2$\leftarrow$7/2 |  5$\leftarrow$4 | 34397.987 |  0.72$\pm$0.12 |  0.68$\pm$ 0.14 |  1.00$\pm$0.20
$5_{1,4}$$\leftarrow$$4_{1,3}$ |  9/2$\leftarrow$7/2 |  4$\leftarrow$3 | 34398.472 |  0.55$\pm$0.11 |  0.60$\pm$ 0.14 |  0.86$\pm$0.20
$6_{1,6}$$\leftarrow$$5_{1,5}$ |  13/2$\leftarrow$11/2 |  7$\leftarrow$6 | 39712.806 |  0.67$\pm$0.12 |  0.60$\pm$ 0.14 |  1.05$\pm$0.19
$6_{1,6}$$\leftarrow$$5_{1,5}$ |  13/2$\leftarrow$11/2 |  6$\leftarrow$5 | 39712.830 |  0.67$\pm$0.18 |  0.76$\pm$ 0.18 |  0.83$\pm$0.19
$6_{1,6}$$\leftarrow$$5_{1,5}$ |  11/2$\leftarrow$9/2 |  6$\leftarrow$5 | } 39738.002 | 0.91$\pm$0.09 | 0.64$\pm$ 0.08 | 1.34$\pm$0.14
$6_{1,6}$$\leftarrow$$5_{1,5}$ |  11/2$\leftarrow$9/2 |  5$\leftarrow$4
$6_{1,5}$$\leftarrow$$5_{1,4}$ |  13/2$\leftarrow$11/2 |  7$\leftarrow$6 | 41263.639 |  0.65$\pm$0.22 |  0.60$\pm$ 0.22 |  1.02$\pm$0.23
$6_{1,5}$$\leftarrow$$5_{1,4}$ |  13/2$\leftarrow$11/2 |  6$\leftarrow$5 | 41265.018 |  0.83$\pm$0.27 |  0.90$\pm$ 0.38 |  0.87$\pm$0.23
$6_{1,5}$$\leftarrow$$5_{1,4}$ |  11/2$\leftarrow$9/2 |  6$\leftarrow$5 | 41270.899 |  0.44$\pm$0.12 |  0.77$\pm$ 0.27 |  0.54$\pm$0.23
$6_{1,5}$$\leftarrow$$5_{1,4}$ |  11/2$\leftarrow$9/2 |  5$\leftarrow$4 | 41272.163 |  0.45$\pm$0.08 d |  0.55$\pm$ 0.28 |  0.76$\pm$0.23
$7_{1,7}$$\leftarrow$$6_{1,6}$ |  15/2$\leftarrow$13/2 |  8$\leftarrow$7 | } 46329.587 | 0.85$\pm$0.17 | 0.66$\pm$ 0.13 | 1.22$\pm$0.25
$7_{1,7}$$\leftarrow$$6_{1,6}$ |  15/2$\leftarrow$13/2 |  7$\leftarrow$6
$7_{1,7}$$\leftarrow$$6_{1,6}$ |  13/2$\leftarrow$11/2 |  7$\leftarrow$6 | } 46353.556 | 1.01$\pm$0.22 | 0.69$\pm$ 0.17 | 1.37$\pm$0.25
$7_{1,7}$$\leftarrow$$6_{1,6}$ |  13/2$\leftarrow$11/2 |  6$\leftarrow$5
444 $a$$a$footnotetext: Observed frequencies towards TMC-1 for which we
adopted a vLSR of 5.83 km s-1. The frequency uncertainty is 10
kHz.$b$$b$footnotetext: Integrated line intensity in mK km s-1.
$c$$c$footnotetext: Full width at half maximum derived by fitting a Gaussian
function to the observed line profile (in km s-1).$d$$d$footnotetext: Line
overlaps with an unidentified line.

Table 2: Spectroscopic parameters of $c$-C5H (all in MHz).

Parameter |  Lab + TMC-1 a |  Laboratory b
---|---|---
$A$ |  45018.0 c |  45018(20)
$B$ |  3504.062107(299) d |  3504.0621(3)
$C$ |  3246.94141(37) |  3246.9414(4)
$\Delta_{N}$ $\times$ 103 |  0.2888(52) |  0.288 e
$\varepsilon_{aa}$ |  165.1446(216) |  165.15(2)
$\varepsilon_{bb}$ |  5.1476(56) |  5.152(6)
$\varepsilon_{cc}$ |  $-$28.1469(38) |  $-$28.148(4)
$a_{F}$(H) |  $-$11.8018(140) |  $-$11.79(2)
$T_{aa}$(H) |  6.1686(234) |  12.13(7)
$T_{bb}$(H) |  $-$0.170(49) |  5.8(1)
$\sigma$(kHz) |  9.4 |  -
$N_{lines}$ |  42 |  34
555 $a$$a$footnotetext: Merged molecular parameters from a fit to the
laboratory and TMC-1 frequencies.$b$$b$footnotetext: Molecular parameters
derived by Apponi et al. (2001). c Fixed to the previous determined
value.$c$$c$footnotetext: Fixed to the previous determined value.
$d$$d$footnotetext: Numbers in parentheses are 1$\sigma$ uncertainties in
units of the last digits.$e$$e$footnotetext: Fixed to the C5H2 ring chain
value; see Apponi et al. (2001).

Figure 3: Observed lines of C5H in TMC-1 in the 31.0-50.3 GHz range.
Frequencies and line parameters are given in Table 3. Quantum numbers for the
observed transitions are indicated in each panel. The red line shows the
synthetic spectrum computed for a rotational temperature of 6 K and a column
density of 1.3$\times$1012 cm-2 (see text). Blanked channels correspond to
negative features created in the folding of the frequency-switching data.
Table 3: Observed line parameters for $l$-C5H in TMC-1.

Transition |  $\nu_{obs}$ a |  $\int T_{A}^{*}dv$ b |  $\Delta v$ c | $T_{A}^{*}$
---|---|---|---|---
$J^{\prime}$$\leftarrow$$J$ |  $F^{\prime}$$\leftarrow$$F$ | Parity | (MHz) |  (mK km s-1) |  (km s-1) | (mK)
15/2$\leftarrow$13/2 |  8$\leftarrow$7 | $e$ | 35802.786 |  26.79$\pm$0.13 |  0.70$\pm$ 0.01 |  36.19$\pm$0.17
15/2$\leftarrow$13/2 |  7$\leftarrow$6 | $e$ | 35803.024 |  23.10$\pm$0.13 |  0.68$\pm$ 0.01 |  31.81$\pm$0.17
15/2$\leftarrow$13/2 |  8$\leftarrow$7 | $f$ | 35806.828 |  26.36$\pm$0.09 |  0.69$\pm$ 0.01 |  35.73$\pm$0.14
15/2$\leftarrow$13/2 |  7$\leftarrow$6 | $f$ | 35807.078 |  24.00$\pm$0.09 |  0.69$\pm$ 0.01 |  32.69$\pm$0.14
17/2$\leftarrow$15/2 |  9$\leftarrow$8 | $e$ | 40576.724 |  22.85$\pm$0.19 |  0.54$\pm$ 0.01 |  39.42$\pm$0.20
17/2$\leftarrow$15/2 |  8$\leftarrow$7 | $e$ | 40576.931 |  20.37$\pm$0.20 |  0.57$\pm$ 0.01 |  33.53$\pm$0.20
17/2$\leftarrow$15/2 |  9$\leftarrow$8 | $f$ | 40580.854 |  23.55$\pm$0.17 |  0.58$\pm$ 0.01 |  38.45$\pm$0.15
17/2$\leftarrow$15/2 |  8$\leftarrow$7 | $f$ | 40581.071 |  20.82$\pm$0.17 |  0.55$\pm$ 0.01 |  35.62$\pm$0.15
19/2$\leftarrow$17/2 |  10$\leftarrow$9 | $e$ | 45350.645 |  18.04$\pm$0.15 |  0.58$\pm$ 0.01 |  29.00$\pm$0.20
19/2$\leftarrow$17/2 |  9$\leftarrow$8 | $e$ | 45350.829 |  12.68$\pm$0.15 |  0.55$\pm$ 0.01 |  21.63$\pm$0.20
19/2$\leftarrow$17/2 |  10$\leftarrow$9 | $f$ | 45354.877 |  17.68$\pm$0.20 |  0.60$\pm$ 0.01 |  27.80$\pm$0.35
19/2$\leftarrow$17/2 |  9$\leftarrow$8 | $f$ | 45355.070 |  16.07$\pm$0.20 |  0.59$\pm$ 0.01 |  25.66$\pm$0.35
666 $a$$a$footnotetext: Observed frequencies towards TMC-1 for which we
adopted a vLSR of 5.83 km s-1. The frequency uncertainty is 10
kHz.$b$$b$footnotetext: Integrated line intensity in mK km s-1.
$c$$c$footnotetext: Full width at half maximum derived by fitting a Gaussian
function to the observed line profile (in km s-1).

Line identification in this work was done using the catalogues MADEX
(Cernicharo 2012), CDMS (Müller et al. 2005), and JPL (Pickett et al.  1998).
As of May 2022, the MADEX code contained 6434 spectral entries corresponding
to the ground and vibrationally excited states, together with the
corresponding isotopologues, of 1734 molecules. Once the assignment of all
known molecules and their isotopologues is done, QUIJOTE will permit us to
search for molecules for which frequencies are known. Moreover, QUIJOTE also
allows us to perform rotational spectroscopy in space of new species for which
no previous rotational spectroscopic laboratory information is available, such
as HC5NH+ (Marcelino et al.  2020), HC3O+(Cernicharo et al. 2020a), HC3S+
(Cernicharo et al. 2021b), CH3CO+ (Cernicharo et al. 2021c), HCCS+ (Cabezas et
al.  2022a), C5H+ (Cernicharo et al. 2022), HC7NH+ (Cabezas et al.  2022b),
and HCCNCH+ (Agúndez et al. 2022).

Only the $K_{a}$=1 series of lines of $c$-C5H are expected to be observed in
TMC-1. We used the rotational parameters reported by Apponi et al. (2001) to
predict, using the SPFIT program (Pickett 1991), the frequency transition
lines in the Q band. We used a dipole moment of 3.39 D, following Crawford et
al. (1999). The molecule was implemented in the MADEX code (Cernicharo 2012),
which was used to search for the $K_{a}$=1 lines. A total of 17 lines of
$c$-C5H were detected in TMC-1 above the 3$\sigma$ level; they are shown in
Fig. 2. These 17 lines correspond to 20 hyperfine components, three of which
are not resolved, from five $K_{a}$=1 rotational transitions with $N$=5, 6,
and 7. The derived line parameters are given in Table 1. A fit to the observed
line profiles assuming a source diameter of 40 ′′ (Fossé et al. 2001) provides
a rotational temperature of 6.0 $\pm$ 0.5 K and a column density of
N($c$-C5H)= (9.0 $\pm$ 0.9) $\times$ 1010 cm-2. The synthetic spectra are
compared with observations in Fig. 2 (red line). No lines with $K_{a}$=0 were
detected, which is in line with our conclusion that those lines belong to a
vibrationally excited state that would be under-populated in TMC-1 due to the
low kinetic temperature of the cloud.

Using the new observed frequencies in TMC-1 and those measured in the
laboratory (Apponi et al. 2001), we have derived, using the SPFIT program
(Pickett 1991), a new set of molecular constants for $c$-C5H, which are shown
in Table 2. The new molecular constants are practically identical to those
provided by Apponi et al. (2001), with the exception of the dipole-dipole
constants, $T_{aa}$(H) and $T_{bb}$(H). We believe that the definition of
these parameters in the fitting code used by Apponi et al. (2001) may be
different to that employed by the Pickett program, used in this work, which
results in the values being different.

We also observed several lines for the $l$-C5H isomer. A total of 12 hyperfine
components for the $J$=15/2-13/2, 17/2-15/2, and 19/2-17/2 transitions, which
belong to the 2$\Pi_{1/2}$ spin sub-level, were detected (see Fig. 3 and Table
3) with antenna temperatures around 30 mK. An analysis of the line intensities
through a line model fitting procedure (Cernicharo et al. 2021d) provides a
rotational temperature of 6.0 $\pm$ 0.5 K and a column density of
N($l$-C5H)=(1.3 $\pm$ 0.3) $\times$ 1012 cm-2. We assumed a dipole moment of
4.88 D for $l$-C5H (Woon 1995). Therefore, the abundance ratio $c$-C5H/$l$-C5H
is 0.069 in TMC-1. This value is far from that found in TMC-1 for the analogue
system $c$-C3H/$l$-C3H, whose ratio is 5.5 (Loison et al. 2017).

##  4 Chemistry

In order to shed some light on the formation of $c$-C5H in TMC-1, we carried
out gas-phase chemical modelling calculations similar to those presented in
Cabezas et al. (2021). Briefly, we adopted physical conditions typical of cold
dark clouds: a volume density of H nuclei of 2 $\times$104 cm-3, a gas kinetic
temperature of 10 K, a visual extinction of 30 mag, a cosmic-ray ionization
rate of H2 of 1.3 $\times$ 10-17 s-1, and the so-called set of low-metal
elemental abundances (e.g., Agúndez & Wakelam 2013). We employed the chemical
network RATE12 from the UMIST database (McElroy et al. 2013), which has been
updated with results from Lin et al. (2013) and expanded with the subset of
gas-phase chemical reactions involving C3H and C3H2 isomers revised by Loison
et al. (2017).

Figure 4: Calculated fractional abundances of the cyclic and linear isomers of
C3H and C5H as a function of time. The abundances observed in TMC-1 for the
isomers of C3H (Loison et al. 2017) and C5H (this study) are indicated by
dotted horizontal lines.

The cyclic isomer of C5H is not included in either the UMIST (McElroy et al.
2013) or KIDA (Wakelam et al. 2015) databases, and information on reactions
involving it are lacking in the literature. Our main aim here is thus to
explore whether plausible reactions of formation of $c$-C5H can account for
the abundance observed in TMC-1. Since $c$-C5H can be viewed as the result of
substituting an H atom in $c$-C3H with a C2H group, an obvious reaction of
formation of $c$-C5H is

$\rm c-C_{3}H+C_{2}H\rightarrow c-C_{5}H+H.$ (1)

We thus included this reaction with a rate coefficient of 3 $\times$ 10-10 cm3
s-1, which is similar to rate coefficients measured at low temperature for
other reactions of C2H with closed-shell unsaturated hydrocarbons (Chastaing
et al. 1998). Another interesting potential source of $c$-C5H is the reaction
between atomic carbon and diacetylene,

$\displaystyle\rm C+C_{4}H_{2}$ $\displaystyle\rightarrow\rm l-C_{5}H+H,$ (2a)
$\displaystyle\rightarrow\rm c-C_{5}H+H,$ (2b)

where both the linear and cyclic isomers of C5H are in principle possible,
although chemical networks only consider the linear isomer as product (Smith
et al. 2004; Loison et al. 2014). Reaction (2) is thought to occur rapidly at
low temperatures based on experimental studies of reactions of C with closed-
shell unsaturated hydrocarbons such as C2H2 (Chastaing et al. 2001). Takahashi
(2000) studied this reaction theoretically and concluded that both the linear
and cyclic isomers of C5H can be formed without an entrance barrier. On the
other hand, calculations by Sun et al. (2008) show that only the linear isomer
of C5H should be formed. The different conclusions are likely due to the fact
that reaction (2b) was found to be exothermic by 1 kcal mol-1 by Takahashi
(2000) but endothermic by 0.7 kcal mol-1 by Sun et al. (2008). That is,
formation of $c$-C5H is nearly thermo-neutral. Here we assume that reaction
(2b) occurs with a branching ratio of just 10 %. Finally, we assumed that
$c$-C5H reacts fast with neutral atoms (H, C, N, and O) and cations that are
known or expected to be abundant in TMC-1, such as C+ and HCO+.

In Fig. 4 we show the calculated abundances of the cyclic and linear isomers
of C3H and C5H. It is seen that the peak calculated abundances, reached in the
105-106 yr time range, agree well with the observed values. If we focus on
cyclic C5H, according to the chemical model the main reaction of formation is
C + C4H2. That is, if this reaction produces cyclic C5H with only a branching
ratio of 10 %, then it can by itself explain the abundance of $c$-C5H observed
in TMC-1. Further studies to evaluate the branching ratios of the reaction C +
C4H2 would allow the chemistry of the linear and cyclic isomers of C5H in cold
dark clouds to be better constrained.

##  5 Conclusions

We have reported the first identification of the $c$-C5H radical towards
TMC-1. We observed 17 rotational transitions within the 31.0–50.3 GHz range
using the Yebes 40m radio telescope. The derived $c$-C5H/$l$-C5H abundance
ratio of 0.069 is very different from that found for $c$-C3H/$l$-C3H, whose
ratio is 5.5 in TMC-1. A state-of-the-art chemical model reproduces the
observed abundance of $c$-C5H and indicates that this radical can probably be
formed in the reaction of atomic carbon with diacetylene.

###### Acknowledgements.

We acknowledge funding support from Spanish Ministerio de Ciencia e Innovación
through grants PID2019-106110GB-I00, PID2019-107115GB-C21, and
PID2019-106235GB-I00 and from the European Research Council (ERC Grant 610256:
NANOCOSMOS). We would like to thank María Eugenia Sanz for her useful comments
on the laboratory experiments of $c$-C5H radical.

## References

  * Agúndez & Wakelam (2013) Agúndez, M., & Wakelam, V. 2013, Chem. Rev., 113, 8710
  * Agúndez et al. (2022) Agúndez, M., Cabezas, C., Marcelino, N. et al. 2022, A&A, 659, L9
  * Apponi et al. (2001) Apponi, A. J., Sanz, M. E., Gottlieb, C. A., et al. 2001, ApJL, 547, L65
  * Araki et al. (2017) Araki, M., Takano, S., Sakai, N., et al. 2017, ApJ, 847, 51
  * Bell et al. (1983) Bell, M. B., Feldman, P. A., & Matthews, H. E. 1983, ApJ, 273, L35
  * Bell et al. (1999) Bell, M. B., Feldman, P. A., Watson, J. K. G., et al. 1999, ApJ, 518, 740
  * Cabezas et al. (2016) Cabezas, C., Guillemin, J.-C., & Endo, Y. 2016, J. Chem. Phys., 145, 184304
  * Cabezas et al. (2018) Cabezas, C., Guillemin, J.-C., & Endo, Y. 2018, J. Chem. Phys., 149, 084309
  * Cabezas et al. (2021) Cabezas, C., Tercero, B., Agúndez, M., et al. 2021, A&A, 650, L9
  * Cabezas et al. (2022a) Cabezas, C., Agúndez, M., Marcelino, N. et al. 2022a, A&A, 657, L4
  * Cabezas et al. (2022b) Cabezas, C., Agúndez, M., Marcelino, N. et al. 2022b, A&A, 659, L8
  * Cernicharo (1985) Cernicharo, J. 1985, Internal IRAM report (Granada: IRAM)
  * Cernicharo et al. (1986a) Cernicharo, J., Kahane, K., Gómez-Gónzalez, J., & Guélin, M. 1986a, A&A, 164, L1
  * Cernicharo et al. (1986b) Cernicharo, J., Kahane, K., Gómez-Gónzalez, J., & Guélin, M. 1986b, A&A, 167, L5
  * Cernicharo et al. (1987) Cernicharo, J., Guélin, M., & Walmsley, C. M. 1987, A&A, 172, L5
  * Cernicharo & Guélin (1996) Cernicharo, J., & Guélin, M. 1996, A&A, 309, L27
  * Cernicharo et al. (2000) Cernicharo, J., Guélin, M., & Kahane, C. 2000, A&ASuppl. Ser., 142, 181
  * Cernicharo (2012) Cernicharo, J. 2012, in European Conference on Laboratory Astrophysics, eds. C. Stehlé, C. Joblin, & L. d’Hendecourt, EAS Publication Series, 58, 251
  * Cernicharo et al. (2020a) Cernicharo, J., Marcelino, N, Agúndez, M., et al. 2020a, A&A, 642, L17
  * Cernicharo et al. (2021a) Cernicharo, J., Agúndez, M., Kaiser, R., et al. 2021a, A&A, 652, L9
  * Cernicharo et al. (2021b) Cernicharo, J., Cabezas, C., Endo, Y., et al. 2021b, A&A, 646, L3
  * Cernicharo et al. (2021c) Cernicharo, J., Cabezas, C., Bailleux, S., et al. 2021c, A&A, 646, L7
  * Cernicharo et al. (2021d) Cernicharo, J., Agúndez, M., Cabezas, C., et al. 2021d, A&A, 649, L15
  * Cernicharo et al. (2022) Cernicharo, J., Agúndez, M., Cabezas, C. et al. 2022, A&A, 657, L16
  * Chastaing et al. (1998) Chastaing, D., James, P. L., Sims, I. R., & Smith, I. W. M. 1998, Faraday Discuss. 109, 165
  * Chastaing et al. (2001) Chastaing, D., Le Picard, S., Sims, I. R., & Smith, I. W. M. 2001, A&A, 365, 241
  * Crawford et al. (1999) Crawford, T. D., Stanton, J. F., Saeh, J. C., & Schaefer, H. F. 1999, JACS, 121, 1902
  * Dunham (1937) Dunham, Jr., T. 1937, PASP, 49, 26
  * Endo et al. (1994) Endo, Y., Kohguchi, H., & Ohshima, Y. 1994, Faraday Discuss., 97, 341.
  * Fossé et al. (2001) Fossé, D., Cernicharo, J., Gerin, M., & Cox, P. 2001, ApJ, 552, 168
  * Guélin et al. (1978) Guélin, M., Green, S., & Thaddeus, P. 1987, ApJ, 224, L27
  * Guélin et al. (1996) Guélin, M., Cernicharo, J., Travers, M. J., et al. 1996, A&A, 317, L1
  * Irvine et al. (1981) Irvine, W. M., Hoglund, B., Friberg, P., et al. 1981, ApJL 248, L113
  * Lin et al. (2013) Lin, Z., Talbi, D., Roueff, E., et al. 2013, ApJ, 765, 80
  * Liszt et al. (2014) Liszt, H. S., Pety, J., Gerin, M., & Lucas, R. 2014, A&A, 564, A64
  * Loison et al. (2014) Loison, J. -C., Wakelam, V., Hickson, K. M., et al. 2014, MNRAS, 437, 930
  * Loison et al. (2017) Loison, J. -C., Agúndez, M., Wakelam, V., et al. 2017, MNRAS 470, 4075
  * Nyman (1984) Nyman, L.-$\AA$. 1984, ApJ, 141, 323
  * Marcelino et al. (2020) Marcelino, N., Agúndez, M., Tercero, B. et al. 2020, A&A, 643, L6
  * Mangum & Wootten (1990) Mangum, J. G., & Wootten, A. 1990, A&A, 239, 319
  * McCarthy et al. (1999) McCarthy, M. C., Chen, W., Apponi, A. J., et al. 1999, ApJ, 520, 158
  * McElroy et al. (2013) McElroy, D., Walsh, C., Markwick, A. J., et al. 2013, A&A, 550, A36
  * Müller et al. (2005) Müller, H.S.P., Schlöder, F., Stutzki, J., & Winnewisser, G. 2005, J. Mol. Struct., 742, 215
  * Pardo & Cernicharo (2007) Pardo, J. R., & Cernicharo, J. 2007, ApJ, 654, 978
  * Pardo et al. (2001) Pardo, J. R., Cernicharo, J., & Serabyn, E. 2001, IEEE Trans. Antennas and Propagation, 49, 12
  * Pickett (1991) Pickett, H. M. 1991, J. Mol. Spectr., 148, 371
  * Pickett et al. (1998) Pickett, H.M., Poynter, R. L., Cohen, E. A., et al. 1998, J. Quant. Spectrosc. Radiat. Transfer, 60, 883
  * Saito et al. (1987) Saito, S., Kawaguchi, K., Suzuki, H. et al. 1987, PASJ, 39, 193
  * Smith et al. (2004) Smith, I. W. M., Herbst, E., & Chang, Q. 2004, MNRAS, 350, 323
  * Sun et al. (2008) Sun, B. J., Huang, C. Y., Kuo, H. H., et al. 2008, J. Chem. Phys., 128, 244303
  * Suzuki et al. (1986) Suzuki, H., Ohishi, M., Kaifu, N. et al. 1986, PASJ, 38, 911
  * Takahashi (2000) Takahashi, J. 2000, PASJ, 52, 401
  * Tercero et al. (2021) Tercero, F., López-Pérez, J. A., Gallego, J. D., et al. 2021, A&A, 645, A37
  * Teyssier et al. (2004) Teyssier, D., Fossé, D., Gerin, M., et al. 2004, A&A, 417 135
  * Thaddeus et al. (1985) Thaddeus, P., Gottlieb, C. A., Hjalmarson, $\AA$., et al. 1985, ApJ, 294, L49
  * Tucker et al. (1974) Tucker, K. D., Kutner, M. L., & Thaddeus, P. 1974, ApJ, 193, L115
  * Turner et al. (2000) Turner, B. E., Herbst, E., & Terzieva, R. 2000, ApJS, 126, 427
  * Wakelam et al. (2015) Wakelam, V., Loison, J.-C., Herbst, E., et al. 2015, ApJS, 217, 20
  * Woon (1995) Woon, D. E. 1995, Chem. Phys. Lett., 244, 45
  * Wootten et al. (1980) Wootten, A., Bozyan, E. P., Garrett, D. B., et al. 1980, ApJ, 239, 944
  * Yamamoto et al. (1987) Yamamoto, S., Saito, S., Ohishi, M., et al. 1987, ApJ, 322, L55
  * Zhang et al. (2009) Zhang, Y., Kwok, S., & Nakashima, J.-I. 2009, ApJ, 700, 1262