# 5G Software Defined Vehicular Networks

Xiaohu Ge1, Zipeng Li1, Shikuan Li1
1School of Electronic Information and Communications,
Huazhong University of Science and Technology, Wuhan 430074, Hubei, P. R.
China.
Email: {xhge, zipengli91<EMAIL_ADDRESS>
Submitted to IEEE Communications Magazine on SI of Software Defined Vehicular
Networks: Architectures, Algorithms and Applications.The authors would like to
acknowledge the support from the NSFC Major International Joint Research
Project (Grant No. 61210002), the Fundamental Research Funds for the Central
Universities under the grant 2015XJGH011. This research is partially supported
by the EU FP7-PEOPLE-IRSES, project acronym WiNDOW (grant no. 318992) and
project acronym CROWN (grant no. 610524), China International Joint Research
Center of Green Communications and Networking (No. 2015B01008).

###### Abstract

With the emerging of the fifth generation (5G) mobile communication systems
and software defined networks, not only the performance of vehicular networks
could be improved but also new applications of vehicular networks are required
by future vehicles, e.g., pilotless vehicles. To meet requirements from
intelligent transportation systems, a new vehicular network architecture
integrated with 5G mobile communication technologies and software defined
network is proposed in this paper. Moreover, fog cells have been proposed to
flexibly cover vehicles and avoid frequently handover between vehicles and
road side units (RSUs). Based on the proposed 5G software defined vehicular
networks, the transmission delay and throughput are analyzed and compared.
Simulation results indicate that there exist a minimum transmission delay of
5G software defined vehicular networks considering different vehicle
densities. Moreover, the throughput of fog cells in 5G software defined
vehicular networks is better than the throughput of traditional transportation
management systems.

##  I Introduction

Nowadays the fifth generation (5G) mobile communication systems are developed
by industrial and academic researchers. With the development of millimeter
wave and massive multi-input multi-output (MIMO) technologies, the spectrum
efficiency and energy efficiency are obviously improved for 5G wireless
communications [1, 2]. With the emergence of pilotless vehicles, some rigorous
requirements, e.g., the transmission delay need to be less than 1 millisecond,
are required for intelligent transportation systems (ITSs) and vehicular
networks [3]. To meet these rigorous requirements, 5G mobile communication
technologies, cloud computing and software defined networks (SDNs) are
expected to be integrated into future vehicular networks. Therefore, it is
necessary to design a new network architecture for 5G vehicular networks.

Some basic issues have been investigated for vehicular networks [4, 5, 6, 7].
Considering drawbacks of IEEE 802.11p networks, e.g., the poor scalability,
the low capacity and the intermittent connectivity, the long term evolution
(LTE) mobile communication technologies were proposed to support vehicular
applications [4]. Moreover, the open issues of LTE vehicular networks were
discussed to promote potential solutions for future vehicular networks. In
reference [5] the basic characteristics of vehicular networks was introduced.
An overview of applications and associated requirements was presented and
challenges were discussed. Besides, the past major ITS programs and projects
in United States of America (USA), Japan and Europe were analyzed and
compared. An analytical model supporting multi-hop relay of infrastructure-
based vehicular networks was proposed to analyze uplink and downlink
connectivity probabilities [6]. Simulation and experiments results revealed
that there exists a trade-off between the proposed performance metrics and
system parameters, such as base station (BS) and vehicle densities, radio
coverage and the maximum number of hops in a path contains. When the LTE
communication technologies have been integrated into vehicular networks, the
interference cuts down the performance of LTE vehicular networks [7]. To
overcome this issue, the millimeter wave transmission technology was proposed
to connect users inside vehicles. On the other hand, the SDN was proposed as
an effective network technology to be capable of supporting the dynamic nature
of vehicular network functions and intelligent applications while lowering
operation costs through simplified hardwares, softwares and managements [8].
Consequently, some initial studies have been carried out to integrate the SDN
technology into vehicular networks [9, 10]. Utilizing the SDN technology, an
adaptive edge computing solution based on regressive admission control and
fuzzy weighted queueing was proposed to monitor and react to network QoS
changes within vehicular network scenarios [9]. Based on the SDN technology, a
cooperative data scheduling algorithm integrated at road side units (RSUs) was
developed to enhance the data dissemination performance by exploiting the
synergy between infrastructure-to-vehicle (I2V) and vehicle-to-vehicle (V2V)
communications [10]. However, the SDN technology in reference [10] is limited
in RSUs. When a lot of vehicles are connected with a RSU, the frequent
handover problem will reduce the performance of SDN at RSUs of vehicular
networks [11].

To meet the high performance requirements, such as the low transmission delay
and high throughput, a new architecture of 5G software defined vehicular
network is proposed in this paper. The main contributions of the proposed 5G
software defined vehicular network are list as follows:

  1. 1)

Based on the basic functions and requirements of vehicular networks, an
architecture of 5G software defined vehicular network integrated with the SDN,
cloud computing and fog computing technologies is proposed to form three
logistical planes in network architecture, i.e., the application plane, the
control plane and the data plane. Based on three logistical planes of network
architecture, the control and data functions of 5G software defined vehicular
networks are separated to improve the flexibility and scalability of vehicular
networks.

  2. 2)

The fog cell structure is proposed and performed at the edge of 5G software
defined vehicular networks. Based on the fog cell structure, the frequent
handover between the RSU and vehicles is avoided and the adaptive bandwidth
allocation scheme is adopted for vehicles in fog cells.

  3. 3)

The transmission delay and throughput of 5G software defined vehicular
networks are analyzed. Simulation results indicate that there exist a minimum
transmission delay of 5G software defined vehicular networks considering
different vehicle densities. Moreover, the throughput of fog cells in 5G
software defined vehicular networks is better than the throughput of
traditional transportation management systems.

In this article we propose a new architecture of 5G software defined vehicular
networks adapting the cloud computing and fog computing technologies.
Moreover, the control plane and data plane are separated by the SDN technology
in 5G software defined vehicular networks. To avoid frequent handover between
the RSU and vehicles, the fog cell is structured and multi-hop relay method is
adopted for vehicular communications in a fog cell. Furthermore, the
transmission delay and the throughput of fog cells are simulated for 5G
software defined vehicular networks. Finally, the challenges of vehicular
networks are discussed and the conclusion is drawn.

##  II 5G Software Defined Vehicular Networks

###  II-A Topology Structure of 5G Software Defined Vehicular Networks

The cloud computing and fog computing technologies are emerging for
applications of 5G vehicular networks. Moreover, the SDN is becoming a
flexible approach to connect wireless access networks and clouding computing
centers for 5G vehicular networks. Based on cloud computing and fog computing
technologies, a 5G software defined vehicular network is proposed in this
paper. The topology structure of 5G software defined vehicular networks is
illustrated by Fig. 1(a). 5G software defined vehicular networks are composed
of the cloud computing centers, SDN controllers (SDNCs), road side unit
centers (RSUCs), road side units (RSUs), BSs, fog computing clusters, vehicles
and users. Moreover, 5G software defined vehicular networks include
infrastructure to infrastructure (I2I) links, vehicle to infrastructure (V2I)
links and vehicle to vehicle (V2V) links. Based on 5G software defined
vehicular networks, the information is shared among vehicles and users under
the control of the fog computing clusters. To support the promptly responses
from vehicles and users, fog computing clusters are configured in the edge of
5G software defined vehicular networks. The network structure of fog computing
clusters is a distributed networks. Most of data in the edge of 5G software
defined vehicular networks is saved and processed by fog computing clusters
which include the RSUC, RSUs, BSs, vehicles and users. The SDNCs collect and
forward the state information of fog computing clusters into the cloud
computing centers. Moreover, the control information is replied to fog
computing clusters by SDNCs. The core of 5G software defined vehicular
networks composed by SDNCs and cloud computing centers is adopted by a
centered network structure which focuses on the data forwarding and resource
allocation. The detail logical structure of 5G software defined vehicular
networks is described in Fig. 1(b).

(a)

(b)

Figure 1: (a) Topology structure of 5G software defined vehicular networks;
(b) Logical structure of 5G software defined vehicular networks

###  II-B Logical Structure of 5G Software Defined Vehicular Networks

In Fig. 1(b), the Logical structure of 5G software defined vehicular networks
is composed by the data plane, the control plane and the application plane.

  1. a)

The data plane includes vehicles, BSs and RSUs. Functions of the data plane
are focused on the data collection, quantization and then forwarding data into
the control plane [12]. In detail, the vehicle can be configured with the
following function modules:

     * •

Information collection module of vehicles: the information collection module
is made up of different types of sensors in the vehicle. Utilizing sensors in
the vehicle, the information of the vehicle (e.g., the speed, direction and
type of the vehicle) and the environment (e.g., the number of adjacent
vehicles, the users in the vehicle and the road under the vehicle) is
collected for 5G software defined vehicular networks.

     * •

Position information module of vehicle: The position information of vehicles
include the independent position information and the dependent position
information. In general, the independent position information of vehicles is
obtained by the global position systems (GPS) which provide the detail
location of vehicles at the longitude and latitude of the earth. The dependent
position information of vehicles is obtained by sensors of vehicles which
provide the distance between adjacent vehicles. Compared with the independent
position information of vehicles, the dependent position information of
vehicles can provide a high location precision for 5G software defined
vehicular networks.

     * •

Communications module of vehicle: The communication module includes V2I and
V2V communication modules. The V2I communication module provides the wireless
communication between vehicles and the infrastructure along the road. The V2V
communication module provides the wireless communication among adjacent
vehicles.

BSs can provide the wireless communication for vehicles and RSUC. In 5G
software defined vehicular networks, BSs transmit wireless signals by
traditional long term evolution (LTE) frequency and provide a large coverage
for vehicles. In general, vehicles first access with RUSs but secondly access
with BSs when RUSs can not provide the enough resource for wireless accessing
in 5G software defined vehicular networks.

In 5G software defined vehicular networks, RSUs can be configured with the
following function modules:

  * •

Information collection module of RSU: Composed by different sensors, e.g.,
cameras and speed measurement sensors. The information collection module of
RSUs can provide the speed of vehicles, the traffic status and the road
status, etc.

  * •

Communication module of RSU: Including two types of links, one is the links
between RSUs and the RSUC and the other is the links between RSUs and
vehicles. The links between RSUs and the RSUC are performed by fronthaul links
in 5G software defined vehicular networks.

  1. b)

The control plane includes RSUCs and SDNC. The RSUC is the control center of a
fog cell. Considering the quick mobility of vehicles and the massive wireless
traffic between the RSU and vehicles, the frequent handover should be avoided
for wireless communications between the RSU and vehicles. To solve this issue,
the fog cell is proposed for 5G software defined vehicular networks. A fog
cell is composed by vehicles and a RSU. Millimeter wave links are adopted for
wireless relay communications among vehicles and the total bandwidth of
millimeter wave is shared by all vehicles in a fog cell. Since all vehicles
orderly move in an urban road, the total vehicle group can be assumed to be an
overall communication unit within millimeter wave links in a fog cell. When
one of vehicles in a vehicle group connects with the RSU, the total vehicle
group in the fog cell could be connected with the RSU. In this case, the
frequent handover can be avoided for vehicles and the RSU in a fog cell.
Hence, the RSUC is configured to allocate resources and improve the
transmission efficiency in a fog cell. The SDNC is the total control center
for 5G software defined vehicular networks and allocates resources among fog
cells. Therefore, the control plane takes charge of drawing the global
information map based on the data information forwarded from the data plane
and then generating the control information based on rules and strategies from
the application plane. To support above functions of the control plane, RSUCs
and SDNC are configured with the following function modules:

     * •

Information collection modules of RSUC and SDNC: drawing the global
information map based on the data information from the data plane.

     * •

Networking status module: monitoring the link status of 5G software defined
vehicular networks [13].

     * •

Computing module: deriving the control results based on the global information
map and the link status of 5G software defined vehicular networks. In general,
computing modules are deployed at the cloud computing center and fog computing
centers [14].

     * •

Hot caching module: saving the popular data context at RSUCs to decrease the
transmission delay for vehicle applications.

  1. c)

The application plane directly faces different application requirements from
users and vehicles. Based on application requirements from users and vehicles,
rules and strategies of 5G software defined vehicular networks are generated
by the application plane and forwarded into the control plane. In general, the
application plane includes the security service module, the service efficiency
module and the entertainment service module.

Based on the logical structure of 5G software defined vehicular networks in
Fig. 1(b), the data plane takes charge of collecting data, the control plane
takes charge of deriving control instructions and the application plane takes
charge of generating rules and strategies.

##  III Transmission delay and Throughput of 5G Software Defined Vehicular
Networks

Without loss of generality, the transmission delay and throughput analysis are
investigated in a fog cell of 5G software defined vehicular networks. A
typical fog cell is composed by a RSU and a number of vehicles in Fig. 2. To
avoid frequent handover between the RSU and vehicles in the fog cell, a
vehicle, i.e., the gateway vehicle is selected to connect with the RSU and
then other vehicles are connected with the gateway vehicle by a multi-hop
relay method. When a gateway vehicle is located in the coverage region of the
RSU, the gateway vehicle directly communicates with the RSU. When other
vehicles are located in the fog cell, even these vehicles do not directly
coveraged by the RSU in the fog cell, these vehicles will build a multi-hop
relay route to connect with the gateway vehicle and then the gateway vehicle
will forward those requests/data with the RSU in the fog cell. When the
gateway vehicle departs from the fog cell, a vehicle in the fog cell is handed
off to service as the gateway vehicle [15]. In this way, all vehicles in the
fog cell can maintain wireless communications with RSU while moving along the
road. Since the fog cell is the basic composition of proposed 5G software
defined vehicular networks, the transmission delay and throughput of the
vehicle in a fog cell is investigated in the following sections.

Figure 2: Vehicle communications in a typical fog cell

###  III-A Transmission Delay of 5G Software Defined Vehicular Networks

The transmission delay is one of core metrics for 5G software defined
vehicular networks. In this paper, the transmission delay of the vehicle in a
fog cell is analyzed for 5G software defined vehicular networks.

Figure 3: Transmission delay in a fog cell of 5G software defined vehicular
networks.

In Fig. 3, a RSU is located at a fog cell to service for all vehicles driving
at a road with the length of $L$. Without loss of generality, a vehicle marked
with red dashed circle, i.e., $V{E_{a}}$ is selected to analyze the
transmission delay in a fog cell of 5G software defined vehicular networks.
The distance between the RSU and the vehicle $V{E_{a}}$ is denoted as
${L_{a}}$. Based on the vehicle communication scheme in Fig. 2, the data
packet generated from $V{E_{a}}$ is transmitted to the RSU by a multi-hop
vehicle relay method.

Assumed that there exist $k$ hops between the RSU and the vehicle $V{E_{a}}$.
For a data packet, the transmission delay in a fog cell of 5G software defined
vehicular networks is expressed as
$T=k{T_{hop}}+\left({k-1}\right){T_{retran}}$ , where ${T_{hop}}$ is the
average transmission delay in one hop of vehicle communications,
${T_{retran}}$ is the retransmission delay which is the relay processing time
at the relay vehicles. In a hop of vehicle communications, the wireless
transmission is time slotted and one data packet is transmitted in each time
slot ${t_{slot}}$. Assumed that the success transmission probability of
vehicle relay communications is ${P_{hop}}$. As a consequence, the average
transmission delay in one hop of vehicle communications is calculated by
${T_{hop}}{\rm{=}}\frac{{{t_{slot}}}}{{{P_{hop}}}}$.

In this paper the millimeter wave transmission technique is adopted for
vehicle relay communications. Without loss of generality, the 60 GHz frequency
spectrum is assumed to be used for vehicle relay communications. Since the
wireless signal of vehicle relay communications are usually transmitted in
line of sight (LOS) scenarios, the interference is ignored for the vehicle
relay communications in this paper. When the signal-to-noise ratio (SNR)
threshold at the receiver is assumed as $\theta$, i.e., the data packet can be
successfully received only if the SNR of receive signal is larger than the
threshold $\theta$, the success transmission probability ${P_{hop}}$ is
calculated by ${P_{hop}}={\rm
P}\left({PL\leq{P_{tx}}(dB)-\theta(dB)-{N_{0}}{W_{mmWave}}(dB)}\right)$, where
$PL[dB](\delta)=69.6+20.9\log(\delta)+\xi$,
${\rm{}}\xi\sim\left({0,{\sigma^{2}}}\right)$ is the path loss fading over
millimeter wave wireless channels, $\delta$ is the wireless transmission
distance between the transmitter and receiver, ${P_{tx}}$ is the transmission
power of vehicles, ${N_{0}}$ is the noise power spectrum density,
${W_{mmWave}}$ is the bandwidth of millimeter wave links.

To analyze the transmission delay in a fog cell of 5G software defined
vehicular networks, the default parameters are configured as follows: the
noise power spectrum density is ${N_{0}}=-174$ dBm/Hz, the bandwidth of
millimeter wave links is ${W_{mmWave}}=2$ GHz, the retransmission delay is
${T_{retran}}=5$ microsecond, one time slot is ${t_{slot}}=5$ microsecond.
Moreover, the transmission distance of millimeter wave communications is
limited into 50 meters.

Figure 4: Transmission delay with respect to the vehicle density considering
different transmission distances

Fig. 4 illustrates the transmission delay in a fog cell of 5G software defined
vehicular networks with respect to the vehicle density considering different
transmission distances ${L_{a}}$. When the vehicle density is fixed, the
transmission delay increases with the increase of the transmission distances
${L_{a}}$. When the transmission distance ${L_{a}}$ is fixed, the transmission
delay first decreases with the increase of the vehicle density. However,
numerical results indicate there exist turning points for vehicle densities (
the turning points are 0.08, 0.09 and 0.105 for ${L_{a}}=300$ , 400 and 500,
respectively). When the vehicle density larger than or equal to the turning
point, the transmission delay increases with the increase of vehicle density.

The numerical results in Fig. 4 show that there exists a minimum value for the
transmission delay in the fog cell of 5G software defined vehicular networks.
The minimum transmission delay are 0.32, 0.46 and 0.63, corresponding to the
transmission distance of 300, 400 and 500 meters, respectively. When the
vehicle density is low, the distance among adjacent vehicles is far away and
then the success transmission probability of millimeter wave links is low. In
this case, the increasing of vehicle density will decrease the distance among
adjacent vehicles and then increase the success transmission probability of
millimeter wave links. Hence, the transmission delay first decreases with the
increase of the vehicle density. When the vehicle density is larger than a
threshold, the distance among adjacent vehicles is closed and the success
transmission probability of millimeter wave links approaches to a stationary
value. In this case, the transmission delay mainly dependent on the
retransmission delay in every hop vehicle communication. In this case, the
increasing of vehicle density will increase the number of relay hops and then
the total retransmission delay is increased. Therefore, the transmission delay
first increases with the increase of the vehicle density.

###  III-B Throughput of 5G Software Defined Vehicular Networks

In traditional bandwidth allocation scheme, all bandwidths are averagely
allocated to every vehicle in a fog cell. However, every vehicle needs
different bandwidth in practical applications. Based on the control function
of 5G software defined vehicular networks which is realized at the RSUC, an
adaptive bandwidth allocation scheme is proposed to optimize the throughput of
fog cells in this paper.

Without loss of generality, the available bandwidth in a fog cell is assumed
as $B$ and the maximum throughput of this fog cell is $C$. The average
bandwidth requirement of one vehicle is ${B_{ave}}$ and the throughput of this
vehicle is configured as ${C_{ave}}$. The total number of vehicles in a fog
cell is assumed as $N(N>0)$ and the signal-to-noise ratio (SNR) at every
vehicle is configured as the same. The interference is ignored in this paper.
Hence, in this paper the throughput of vehicle is proportion to the
communication bandwidth of vehicle. When there are $N$ vehicles in the fog
cell, the bandwidth requirement of vehicles is assumed to be governed by a
uniform distribution, i.e. ${B_{i}}\sim U(0,2{B_{ave}}),{\rm{}}1\leq i\leq N$.
Considering the real bandwidth requirement from $N$ vehicles, the bandwidth
requirement ${B_{i}}\sim U(0,2{B_{ave}}),{\rm{}}1\leq i\leq N$ from
$n,{\rm{}}n\leq B/{B_{ave}}$ vehicles is assumed to be less than the average
bandwidth requirement ${B_{ave}}$ in the fog cell. The throughput of a vehicle
is ${C_{j}}$ when the bandwidth of a vehicle is allocated by ${B_{j}}$. For
the traditional average bandwidth allocation scheme, the maximum available
bandwidth for a vehicle is ${B_{ave}}$ and then the total bandwidth allocated
for all vehicles in fog cell is
${B_{tra}}=\sum\limits_{j=1}^{n}{{B_{j}}}+(N-n)\times{B_{ave}}$. Consequently,
the throughput of the fog cell is
${C_{tra}}=\sum\limits_{j=1}^{n}{{C_{j}}}+(N-n)\times{C_{ave}}$. Based on the
proposed adaptive bandwidth allocation scheme, the un-occupied bandwidths of
$n$ vehicles can be reused for the other $N-n$ vehicles in the fog cell. The
total requirement bandwidth of the other $N-n$ vehicles is
$\sum\limits_{j=n+1}^{N}{{B_{j}}}$ and the total available bandwidth of the
other $N-n$ vehicles is $B-\sum\limits_{j=1}^{n}{{B_{j}}}$. Therefore, the
throughput of a fog cell adopting the adaptive bandwidth allocation scheme is
$Min\left\\{{\begin{array}[]{*{20}{c}}{\sum\limits_{j=1}^{N}{{B_{j}}}}&,&B\end{array}}\right\\}$.

When the parameter are configured as $C=1000$ Mbps and ${C_{ave}}=33$ Mbps,
the throughput of a fog cell is compared by two bandwidth allocation schemes
in Fig. 5. It is shown that the throughput of a fog cell with the adaptive
bandwidth allocation scheme is always larger than the throughput of a fog cell
with the average bandwidth allocation scheme. The reason is that the
unoccupied bandwidths in the average bandwidth allocation scheme could be
utilized in the adaptive bandwidth allocation scheme. When the bandwidth
allocation scheme is given, the throughput of a fog cell first increases with
the increase of the number of vehicles in a fog cell. When the number of
vehicles is larger than 30, the throughput of a fog cell keeps a stationary.
The reason is that all available bandwidths in a fog cell have already been
allocated for vehicles. In this case, there are not any bandwidths to be
allocated for additional vehicles even the number of vehicles is larger than a
specified threshold. Consequently, the throughput of a fog cell has to keep a
stationary when the number of vehicles is larger than a specified threshold.

Figure 5: Throughput with respect to the number of vehicles in a fog cell

##  IV Challenges of 5G Vehicular Networks

With the development of 5G mobile communication systems, the high speed
wireless communications are satisfied by millimeter wave and massive MIMO
technologies. Furthermore, multimedia wireless communications are expected to
be realized for 5G vehicular networks. Based on 5G high speed wireless
communications, pilotless vehicles are emerging to change our future life. It
is well known that future pilotless vehicles need to be supported by high
reliable and effective vehicular networks. However, some potential challenges
and issues still need to be further investigated for 5G vehicular networks.

  * •

The low delay issues. When pilotless vehicles are deployed for city transport
systems, not only traffic information but also road information should be
transmitted to pilotless vehicles by vehicular networks. In general, safety
message transmissions have a very low delay constrain, such as less than one
millisecond. When there exist many relay vehicles for a multi-hop relay
vehicular network, the transmission delay of the warning message will be
larger than a given threshold. For some extreme cases, the delay issues would
conduce to fatal accidents. How to optimize the route solution is still a key
technology for 5G vehicular networks.

  * •

The frequently handover issues. In this paper the fog cell is proposed to
solve the frequently handover between the RSU and vehicles. However, the
handover among vehicles is still an issue for the multi-hop relay link in a
fog cell. When a lot of vehicles are handed off between adjacent fog cells,
the handover will be simultaneously generated for fog cells and the multi-hop
relay links. In this case, the complexity of handover is obviously increased
for 5G vehicular networks. Moreover, the propagation delay of the warning
message needs to be minimized for vehicles handover in 5G vehicular networks.

  * •

The high service efficiency challenges. For the future pilotless vehicles,
vehicles are not only the transport tools but also entertainment centers for
users. Different multimedia services need to be provided by 5G vehicular
networks. Hence, the massive wireless traffic is expected to increase for 5G
vehicular networks. It is a great challenge to improve the service efficiency
for 5G vehicular networks.

  * •

The architecture of 5G vehicular networks. To reduce the transmission delay of
the warning messages, the distributed network architecture is adopted for the
fog cell of 5G vehicular networks. To support ITSs, the centralized network
architecture is adopted for the core network of 5G vehicular networks. In this
case, the SDN is proposed to flexibly connect different types of network
architectures. However, the scalability and compatibility of 5G vehicular
networks are great challenges, especially there exist two types of network
architectures in 5G vehicular networks.

##  V Conclusions

With the development of pilotless vehicles, vehicular networks have to face
rigorous performance requirements in future ITSs. 5G mobile communications,
cloud computing and SDN technologies provide potential solutions for future
vehicular networks. In this paper we propose a new architecture of 5G software
defined vehicular networks which integrate 5G mobile communications, cloud
computing and SDN technologies. Moreover, fog cells are established at the
edge of 5G software defined vehicular networks which utilize multi-hop relay
networks to reduce the frequent handover between the RSU and vehicles.
Simulation results indicate that there exist a minimum transmission delay of
5G software defined vehicular networks considering different vehicle
densities. Moreover, the throughput of fog cells in 5G software defined
vehicular networks is better than the throughput of traditional transportation
management systems. When the proposed challenges of 5G vehicular networks have
been solved, 5G software defined vehicular networks could provide enough
flexibility and compatibility to satisfy future pilotless vehicles and ITSs.

## References

  * [1] S. Chen, F. Qin, B. Hu, _et al._ , “User-Centric Ultra-Dense Networks (UUDN) for 5G: Challenges, Methodologies and Directions,” _IEEE Wireless Commun._ , vol. 23, no. 2, April 2016, pp. 78–85.
  * [2] M. X. Gong, R. Stacey, D. Akhmetov and S. Mao, “A Directional CSMA/CA Protocol for mmWave Wireless PANs,” in _Proc. IEEE WCNC._ , Apr. 2010, pp. 1–6.
  * [3] X. Ge, H. Chen, G. Mao, _et al._ , “Vehicular Communications for 5G Cooperative Small Cell Networks,” _IEEE Trans. on Vehicular Technology_ , vol. 65, no. 10, Oct. 2016, pp. 7882–7894.
  * [4] G. Araniti, C. Campolo, M. Condoluci, _et al._ , “LTE for Vehicular Networking: A Survey,” _IEEE Commun. Mag._ , vol. 51, no. 5, May 2013, pp. 148–157.
  * [5] G. Karagiannis, O. Altintas, E. Ekici, _et al._ , “Vehicular Networking: A Survey and Tutorial on Requirements, Architectures, Challenges, Standards and Solutions,” _IEEE Commun. Surveys Tuts._ , vol. 13, no. 4, July 2011, pp. 584–616.
  * [6] W. Zhang, Y. Chen, Y. Yang, _et al._ , “Multi-Hop Connectivity Probability in Infrastructure-Based Vehicular Networks,” _IEEE JSAC_ , vol. 30, no. 4, Apr. 2012, pp. 740–747.
  * [7] T. Taleb and A. Ksentini, “VECOS: A Vehicular Connection Steering Protocol,” _IEEE Trans. on Vehicular Technology_ , vol. 64, no. 3, Mar. 2015, pp. 1171–1187.
  * [8] S. Sezer, S. Scott-Hayward, P K. Chouhan, _et al._ , “Are We Ready for SDN? Implementation Challenges for Software-Defined Networks,” _IEEE Commun. Mag._ , vol. 51, no. 7, July 2013, pp. 36–43.
  * [9] M. Jutila, “An Adaptive Edge Router Enabling Internet of Things,” _IEEE Internet Things J._ , vol. 3, no. 6, Dec. 2016, pp. 1061–1069.
  * [10] K. Liu, J. Ng, V. Lee, _et al._ , “Cooperative Data Scheduling in Hybrid Vehicular Ad Hoc Networks: VANET as a Software Defined Network,” _IEEE/ACM Trans. Netw._ , vol. 24, no. 3, June 2016, pp. 1759–1773.
  * [11] T. Taleb, and K. Ben Letaief, “A Cooperative Diversity based Handoff Management Scheme,” _IEEE Trans. on Wireless Communications._ , vol. 9, no. 4, Apr 2010, pp. 1462–1471.
  * [12] M. Feng, S. Mao, and T. Jiang, “Enhancing the performance of future wireless networks with Software Defined Networking,” _Front. Inform. Technol. Electron. Eng._ , vol. 17, no. 7, July 2016, pp. 606–619.
  * [13] A. Bradai, K. Singh, T. Ahmed and T. Rasheed, “Cellular Software Defined Networking: A Framework,” _IEEE Commun. Mag._ , vol. 53, no. 6, June 2015, pp. 36–43.
  * [14] X. Ge, S. Tu, T. Han, Q. Li and G. Mao, “Energy Efficiency of Small Cell Backhaul Networks Based on Gauss-Markov Mobile Models,” _IET Networks._ , vol. 4, no. 2, Mar. 2015, pp. 158–167.
  * [15] I. Stojmenovic and S. Wen, “The Fog Computing Paradigm: Scenarios And Security Issues,” in _Proc. FedCSIS_ , 2014, pp. 1–8.

Xiaohu Ge [M’09-SM’11]<EMAIL_ADDRESS>is currently a full professor with
the School of Electronic Information and Communications at Huazhong University
of Science and Technology (HUST), China and an adjunct professor with at with
the Faculty of Engineering and Information Technology at University of
Technology Sydney (UTS), Australia. He received his Ph.D. degree in
information and communication engineering from HUST in 2003. He is the
director of China International Joint Research Center of Green Communications
and Networking. He has published more than 140 papers in international
journals and conferences. He served as the general Chair for the 2015 IEEE
International Conference on Green Computing and Communications (IEEE
GreenCom). He has served as an Editor for the _IEEE Transaction on Green
Communications and Networking_ , etc.
---
Zipeng Li received his Bachelor’s degree in telecommunication engineering and
Master’s degree in communication and information system from Huazhong
University of Science and Technology, Wuhan, China, in 2011 and 2014,
respectively, where he is currently working toward his Doctor ’s degree. His
research interests include vehicular networks and 5G mobile communication
systems.
---
Shikuan Li received his Bachelor’s degree in communication and information
system from Huazhong University of Science and Technology, Wuhan, China, in
2016, where he is currently working toward his Master’s degree. His research
interests include vehicular networks and 5G mobile communication systems.
---


University and INFN of Pisa - Pisa, Italy 13.25.Hw 11.30.Er 14.40.Nd 14.65.Fy
12.38.Qk

# Final measurement of mixing phase in the full CDF Run II data set

S. Leoins:x on behalf of the CDF collaboration ins:xins:x

###### Abstract

We report the final CDF measurement of the $B^{0}_{s}$ mixing phase, mean
lifetime, and decay-width difference through the fit of the time evolution of
flavor-tagged $B^{0}_{s}\kern-3.00003pt\to\kern-1.99997ptJ\\!/\\!\psi\phi$
decays. The measurement is based on the full data set of 1.96 TeV
$p\overline{p}$ collisions collected between February 2002 and September 2011
by the CDF experiment. The results are consistent with the standard model and
other experimental determinations and are amongst the most precise to date.

##  1 Introduction

Flavor physics of quarks is considered one of the most promising sectors for
indirect signs of new particles or interactions beyond the standard model
(SM). The $B^{0}_{s}$ dinamics in particular offers rich opportunities since
its experimental exploration has not reached in extension and precision
stringent constraints on the presence of NP in contrast to what happened in
leading (and some subleading) processes involving charged and neutral kaons
and bottom mesons. The $B^{0}_{s}$ oscillations are explained in terms of
second-order weak processes involving the the CKM matrix element $V_{ts}$: a
broad class of generic extensions of the SM is expected to affect the mixing
amplitude, modifying the mixing “intensity”–that is the oscillation
frequency–and the phase, $\beta_{s}$. A non-SM enhancement of $\beta_{s}$
would also decrease the size of the decay-width difference between the light
and heavy mass eigenstates of the $B^{0}_{s}$ meson, $\Delta\Gamma_{s}$ [1].
While the oscillation intensity has been measured precisely [2], only loose
constraints on the phase were available until recently. The most effective
determination of $\beta_{s}$ and $\Delta\Gamma_{s}$ is achieved through the
analysis of the time evolution of flavor–tagged
$B^{0}_{s}\kern-3.00003pt\to\kern-1.99997ptJ\\!/\\!\psi\phi$ decays.

The first such analysis was performed by the CDF experiment in 2008 [3].
Immediately after D0 joined. In 2010 the combination of CDF and D0 results
suggested a mild deviation from the SM expectation. However, updated
measurements [4, 5, 6] showed increased consistency with the SM, calling for
additional experimental information to clarify the picture.

Here we report the new CDF update using the final data set of 10 fb-1.

##  2 Analysis

The decays, collected by a low–momentum dimuon trigger, are fully
reconstructed using four tracks originating from a common displaced vertex,
two matched to muon pairs consistent with a $J\\!/\\!\psi$ decay
($3.04<m_{\mu\mu}<3.14$ $\mathrm{Ge\kern-1.00006ptV\\!/}c^{2}$), and two
consistent with a $\phi\kern-3.00003pt\to\kern-1.99997ptK^{+}K^{-}$ decay
($1.009<m_{KK}<1.028$ $\mathrm{Ge\kern-1.00006ptV\\!/}c^{2}$). The dimuon mass
constraint to the known $J\\!/\\!\psi$ mass combined with a transverse
momentum resolution of $\sigma_{p_{T}}/p_{T}\approx 0.07\%p_{T}$ ($p_{T}$ in
GeV/$c$) yield a mass resolution for our signals of about 9 MeV/$c^{2}$. The
$J\\!/\\!\psi K^{+}K^{-}$ mass distribution (fig. 1, left), shows a signal of
approximately 11 000 decays, overlapping a similar amount of constant
background dominated by the prompt combinatorial component, and smaller
contributions from mis-reconstructed $B$ decays.

Figure 1: Left: Distribution of $J\\!/\\!\psi K^{+}K^{-}$ mass with fit
projection overlaid. Right: Confidence regions at the 68% and 95% CL in the
($\beta_{s}$, $\Delta\Gamma_{s}$) plane.

The analysis relies on a joint fit to the time evolution of $B^{0}_{s}$ mesons
that resolve the fast oscillations by exploiting the 90 fs time resolution of
the CDF micro–vertex detector for these final states. Because the $B^{0}_{s}$
meson has spin zero and $J\\!/\\!\psi$ and $\phi$ have spin one, the
$B^{0}_{s}\kern-3.00003pt\to\kern-1.99997ptJ\\!/\\!\psi\phi$ decay involve
three independent amplitudes, each corresponding to one possible angular
momentum state of the $J\\!/\\!\psi\phi$ system which is also a $C\\!P$-odd or
$C\\!P$-even eigenstate. To enhance the sensitivity to $\beta_{s}$, the time-
evolution of the decay amplitudes is fitted independently by exploiting
differences in the distribution of the kaons’ and muons’ decay angles.
Sensitivity to $\beta_{s}$ can be further enhanced accounting for the
difference in the time evolution of initially produced $B^{0}_{s}$ and
$\bar{B}^{0}_{s}$. The flavor of the meson at the time of production is
inferred by two independent classes of algorithms: the opposite-side flavor
tag (OST) and the same-side kaon tag (SSKT) [2].

The OST performances have been determined with 82 000
$B^{\pm}\kern-3.00003pt\to\kern-1.99997ptJ\\!/\\!\psi(\kern-3.00003pt\to\kern-1.99997pt\mu^{+}\mu^{-})K^{\pm}$
decays fully reconstructed in the same sample as the signal. We found an
efficiency of $\varepsilon_{\rm{OST}}=(92.8\pm 0.1)\%$, an observed averaged
dilution, $D_{\rm{OST}}=1-2w_{\rm{OST}}$, equal to $(12.3\pm 0.4)\%$ and a
resulting effective tagging power of
$\varepsilon_{\rm{OST}}D^{2}_{\rm{OST}}=(1.39\pm 0.05)\%$. The SSKT algorithms
tag a smaller fraction of candidates with better precision. Its performances
have been previously determined [4] to be $\varepsilon_{\rm{SSKT}}=(52.2\pm
0.7)\%$, $D_{\rm{SSKT}}=(21.8\pm 0.3)\%$ and
$\varepsilon_{\rm{SSKT}}D^{2}_{\rm{SSKT}}=(3.2\pm 1.4)\%$.

Since SSKT algorithm has been calibrated for early data only, we
conservatively restrict its use to the events collected in that period.
Simulation shows that this results in a modest degradation in $\beta_{s}$
resolution.

The unbinned maximum likelihood joint fit uses 9 observables from each event
to determine 32 parameters including $\beta_{s}$ and $\Delta\Gamma$, other
physics parameters ($B^{0}_{s}$ lifetime, decay amplitudes at $t=0$ and
phases, etc), and several other (“nuisance”) parameters (experimental scale
factors, etc.).

##  3 Results

If $\beta_{s}$ is fixed to its SM value, the fit shows unbiased estimates and
gaussian uncertainties for $\Delta\Gamma_{s}$, $\tau_{s}$. We found
$\Delta\Gamma_{s}=0.068\pm 0.026(stat)\pm 0.007(syst)$ ps-1, and mean
$B^{0}_{s}$ lifetime, $\tau_{s}=1.528\pm 0.019(stat)\pm 0.009(syst)$ ps.
Systematic uncertainties include mismodeling of the signal mass model,
lifetime resolution, acceptance description, and angular distribution of the
background; a $\mathcal{O}(2\%)$ contamination by
$B^{0}\kern-3.00003pt\to\kern-1.99997ptJ\\!/\\!\psi K^{*}(892)^{0}$ decays
misreconstructed as
$B^{0}_{s}\kern-3.00003pt\to\kern-1.99997ptJ\\!/\\!\psi\phi$ decays; and the
silicon detector misalignment. These results are among the most precise
measurements from a single experiment.

If $\beta_{s}$ is free to float in the fit, tests in statistical trials show
that the maximum likelihood estimate is biased for the parameters of interest,
and the biases depend on the true values of the parameters. Hence, we
determine confidence regions in the $\beta_{s}$ and
$(\beta_{s},\Delta\Gamma_{s})$ spaces (fig. 1, right), by using a profile-
likelihood ratio statistic as a $\chi^{2}$ variable and considering all other
likelihood variables as nuisance parameters. Confidence regions are corrected
for non-Gaussian likelihood and systematic uncertainties such as to ensure
nominal coverage. By treating $\Delta\Gamma_{s}$ as a nuisance parameter, we
also obtain $\beta_{s}\in[-\pi/2,-1.51]\cup[-0.06,0.30]\cup[1.26,\pi/2]$ rad
at the 68% CL, and
$\beta_{s}\in[-\pi/2,-1.36]\cup[-0.21,0.53]\cup[1.04,\pi/2]$ rad at the 95%
CL. Included in the fit is also the CP-odd component originated by non
resonant $K^{+}K^{-}$ pair or by the $f_{0}(980)$ decays. The resulting S-wave
decay amplitude is found to be negligible. All results are consistent with the
SM expectation and with determinations of the same quantities from other
experiments [5, 6, 7].

## References

  * [1] Faller S., Fleischer R. Mannel T. Phys. Rev. D792009014005.
  * [2] Abulencia A. others CDF Collaboration, Phys. Rev. Lett.972006242003
  * [3] Aaltonen T. others CDF Collaboration, Phys. Rev. Lett.1002008161802; Abazov V.M. others D0 Collaboration, Phys. Rev. Lett.1012008241801
  * [4] Aaltonen T. others CDF Collaboration, Phys. Rev. D852012072002.
  * [5] Abazov V.M. others D0 Collaboration, Phys. Rev. D852012032006, 822010082001, 842011052007
  * [6] Aaij R. others LHCb Collaboration, Phys. Rev. Lett.1082012101803
  * [7] Aaij R. others LHCb Collaboration, arXiv:1202.4717 (2012).


# Explaining supernova remnant G352.7-0.1 as a peculiar type Ia supernova
inside a planetary nebula

Noam Soker  0000-0003-0375-8987 Department of Physics, Technion, Haifa,
3200003, Israel<EMAIL_ADDRESS>
###### Abstract

I identify a point-symmetric morphology of the supernova remnant (SNR)
G352.7-0.1 and propose that the outer axially-symmetric structure is the
remnant of a common envelope evolution (CEE) of the progenitor system, while
the inner structure is the ejecta of a thermonuclear explosion triggered by
the merger of a white dwarf (WD) and the core of an asymptotic giant branch
(AGB) star. The main radio structure of SNR G352.7-0.1 forms an outer (large)
ellipse. The bright X-ray emitting gas forms a smaller ellipse with a symmetry
axis inclined to the symmetry axis of the large radio ellipse. The high
abundance of iron and the energy of its X-ray lines suggest a type Ia
supernova (SN Ia). The massive swept-up gas suggests a relatively massive
progenitor system. I propose a scenario with progenitors of initial masses of
$M_{\rm ZAMS,1}\simeq 5-7M_{\odot}$ and $M_{\rm ZAMS,2}\simeq 4-5M_{\odot}$.
At a later phase, the WD remnant of the primary star and the AGB secondary
star experience a CEE that ejects the circumstellar material that swept up
more ISM to form the large elliptical radio structure. An explosion during the
merger of the WD with the core of the AGB star triggered a super-Chandrasekhar
thermonuclear explosion that formed the inner structure that is bright in
X-ray. A tertiary star in the system caused the misalignment of the two
symmetry axes. This study adds to the wide variety of evolutionary routes
within the scenarios of normal and peculiar SNe Ia.

Type Ia supernovae – Supernova remnants – Common envelope binary stars –
Planetary nebulae – Stellar jets

##  1 Introduction

The morphology of a supernova remnant (SNR) can reveal its progenitor and the
explosion mechanism of the parent supernova. This holds (for a recent review
see Soker 2024b) for both core-collapse supernovae (CCSNe) and type Ia
supernovae (SNe Ia). One prominent morphological feature is point symmetry,
where two or more pairs of twin structural components are on opposite sides of
the center of the nebula and the symmetry axes of different pairs are inclined
to each other. Axially symmetric structures in SNRs might result from the
circumstellar material (CSM) that the progenitor of the supernova blows before
the explosion and/or from the explosion itself.

In the case of SNe Ia, which are exploding white dwarfs (WDs), the CSM is
ionized by a WD (or even two) before the explosion and hence it is a planetary
nebula. An SN inside a planetary nebula is termed SNIP (e.g., Tsebrenko &
Soker 2015a). Many planetary nebulae are known to possess axially-symmetric or
point-symmetric morphologies (e.g., Balick 1987; Chu, Jacoby, & Arendt 1987;
Schwarz, Corradi, & Melnick 1992; Corradi & Schwarz 1995; Manchado et al.
1996; Sahai & Trauger 1998; Parker, Bojičić, & Frew 2016; Parker 2022, for
some catalogs). These point-symmetric morphologies of planetary nebulae and
post-asymptotic giant branch (AGB) nebulae are not always perfect (e.g., Sahai
et al. 2000; Sahai, Morris, & Villar 2011; Hrivnak, Kwok, & Su 2001). Namely,
the two opposite sides might be unequal in their distance from the center of
the nebula, their brightness, their exact shapes, and/or their sizes. The
point-symmetry of the type Ia SNR G1.9+0.3 suggests that it is due to the
point-symmetric morphology of the planetary nebula into which a spherical SN
Ia explosion took place (Soker, 2024a).

There are several SN Ia scenarios (for reviews from the last decade that cover
many aspects of SNe Ia and hundreds of references therein see Maoz et al.
2014; Maeda, & Terada 2016; Hoeflich 2017; Livio & Mazzali 2018; Soker 2018,
2019; Wang 2018; Jha et al. 2019; Ruiz-Lapuente 2019; Ruiter 2020; Aleo et al.
2023; Liu, Röpke, & Han 2023; Vinkó, Szalai, & Könyves-Tóth 2023; Soker
2024b). In Soker (2019) and Soker (2024b) I classified these scenarios
according to whether their explosion ejecta is spherical or not. I argued
there that for a spherical explosion ejecta, the explosion is of a lonely WD.

A lonely SN Ia scenario is one where at the explosion time itself there is
only a WD and without any close companion. The WD itself is a descendant of a
close binary interaction, i.e., binary merger. Two scenarios belong to the
lonely WD group, the core degenerate (CD) scenario where a WD merges with the
core of an AGB star during a common envelope evolution (CEE) and the explosion
occurs with a merger to explosion delay (MED) time, and the double degenerate
(DD) with MED scenario where two WDs merge but the explosion occurs after a
MED time (the DD-MED scenario; for the DD-MED scenario see also Neopane et al.
2022). The DD scenario, with a prompt explosion in a WD binary system, leads
to a non-spherical explosion (e.g., Pakmor et al. 2012, 2013, 2022; Perets et
al. 2019; Zenati et al. 2023). The WD-WD collision (WWC) scenario also leads
to non-spherical explosions (e.g., Kushnir et al. 2013; Glanz, Perets, &
Pakmor 2024). An axially-asymmetric explosion might result from the DD
scenario (without a MED time; e.g., Perets et al. 2019), or possibly from a
rapidly rotating lonely WD.

In this study, I examine the morphology of SNR G352.7-0.1, and identify a
point-symmetric morphology with two symmetry axes (section 3). Toledo-Roy et
al. (2014) conduct three-dimensional hydrodynamical simulations of a supernova
explosion inside a cloud that is bounded by an interstellar medium (ISM) to
reproduce the morphology of SNR G352.7-0.1. Zhang et al. (2023) consider their
model unlikely because it is not compatible with the molecular clouds’
properties with which SNR G352.7-0.1 interacts. Also, Toledo-Roy et al.
(2014), who did not consider jets, did not produce any symmetry axis. The
topics of the present study are the two symmetry axes of SNR G352.7-0.1 and
their implications on the progenitor.

There is a debate on whether G352.7-0.1 is a CCSN or an SN Ia (section 2). I
accept the view that it is an SN Ia and use the identified point symmetry to
suggest a peculiar SN Ia scenario for SNR G352.7-0.1 (section 4) where one
axis is due to the pre-explosion CSM and the other to the non-spherical
explosion. I summarize this study and place the results on a broader scope in
section 5.

##  2 The debate over the nature of SNR G352.7-0.1

In Figure 1 I present the X-ray (lower left panel), radio (lower right panel),
and a composite image (upper panels) of SNR G352.7-0.1. I return to this
figure and its analysis in section 3.

Figure 1:  Images from the Chandra X-Ray Observatory homepage
(https://chandra.harvard.edu/photo/2014/g352/). In all panels X-ray emission
is shown in blue, optical emission is shown in grayscale, infrared emission is
shown in orange, and radio emission is shown in pink. The lower-left panel is
a Chandra image in the $0.5–8.0{~{}\rm keV}$ band from Pannuti et al. (2014).
I added the two ellipses on three panels and the identification of two
symmetry axes, one by the radio image ($\rm{Axis}_{\rm R}$) and one by the
X-ray image (${\rm Axis}_{\rm X}$). Credit for the images: X-ray:
NASA/CXC/Morehead State Univ/T.Pannuti et al.; Optical: DSS; Infrared:
NASA/JPL-Caltech; Radio: NRAO/VLA/Argentinian Institute of
Radioastronomy/G.Dubner).

The age of SNR G352.7-0.1 is about several thousand years (e.g., Fujishige et
al. 2023). The SNR is well resolved in the X-ray (e.g., Kinugasa et al. 1998;
Giacani et al. 2009) and the radio (e.g., Caswell et al. 1983; Dubner et al.
1993; Giacani et al. 2009) bands. The X-ray and radio morphologies are not
identical, and hence this is classified as a mixed-morphology SNR (e.g., Vink
2012 for the mixed morphology classification). While some earlier studies
argue that SNR G352.7-0.1 is the remnant of a CCSN, some recent studies
attribute SNR G352.7-0.1 to an SN Ia.

Giacani et al. (2009) suggest that SNR G352.7-0.1 is a descendant of a CCSN.
They based this claim on the asymmetrical morphology and the massive swept-up
gas (see also Pannuti et al. 2014). Yamaguchi et al. (2014) classified SNRs
according to the ionization state of iron and found SNR G352.7-0.1 to be an
SNR Ia. Sezer & Gök (2014) and Fujishige et al. (2023) analyze Suzaku X-ray
observations of SNR G352.7-0.1. Based on the high iron abundance they derive,
Sezer & Gök (2014) argue that SNR G352.7-0.1 resulted from an SN Ia. Fujishige
et al. (2023) obtain plasma temperatures, ionization parameters, and
abundances, that are different from those that Sezer & Gök (2014) obtained.
Nonetheless, they also claim that SNR G352.7-0.1 is a descendant of an SN Ia.
Another support for the SN Ia classification is the non-detection of a central
compact object; Pannuti et al. (2014) could not find a central compact object
from Chandra observations.

Zhang et al. (2023) study the interaction of SNR G352.7-0.1 with molecular
clouds. Based on the general classification by Manchester (1987) of SNR radio
morphologies, they suggest that SNR G352.7-0.1 morphology is due mainly to the
progenitor wind. They estimate the duration of the wind as $\approx 3\times
10^{5}{~{}\rm yr}$ and the total energy of the progenitor wind to be $\approx
3\times 10^{48}{~{}\rm erg}$, and note that these are compatible with winds of
O stars, in the case of a CCSN origin of SNR G352.7-0.1. For an SN Ia
explosion, they conclude that the wind of an asymptotic giant branch (AGB)
star cannot account for this energy, and they suggest a wind from the WD
progenitor that accreted mass at a high rate from an AGB star and blew a
strong wind. In that case, one expects an AGB star inside the SNR. Zhang et
al. (2023) do not take a clear side on whether SNR G352.7-0.1 was a CCSN or an
SN Ia.

I will attribute the high energy of the CSM of SNR G352.7-0.1 to the ejection
of a common envelope from a relatively massive system, a WD of $M_{\rm
WD}\simeq 1M_{\odot}$ spiraling-in inside the envelope of an AGB star of
$M_{\rm AGB}\simeq 5-7M_{\odot}$. The zero-age main sequence (ZAMS) progenitor
of SNR G352.7-0.1 was a binary system of relatively massive stars (with a low
mass tertiary star; section 4). Namely, the primary star was on the upper mass
range that forms a CO WD, $M_{\rm ZAMS,1}\simeq 5-7M_{\odot}$, and the
secondary star was less massive, $M_{\rm ZAMS,2}\simeq 4-5M_{\odot}$, but
could have accreted mass from the primary before leaving the main sequence and
hence evolve faster than had it not accreted mass. Such a secondary star
evolves to the AGB in $\tau_{\rm ev}\simeq 10^{8}{~{}\rm yr}$. This relatively
short evolution time accounts for the presence of molecular clouds that this
SNR interacts with, despite possibly being a descendant of an SN Ia.

I am postponing more details of the proposed peculiar supernova scenarios to
section 4. In the next section, I reveal the two symmetry axes that I use to
construct the possible peculiar scenarios for SNR G352.7-0.1.

##  3 Revealing a point-symmetry in a composite X-ray/radio images

Because the morphologies in radio and X-ray observations differ, SNR
G352.7-0.1 is classified as a mixed-morphology SNR. Based on the recognition
that many SNRs have two or more morphological features with symmetry axes that
are inclined to each other, i.e., point-symmetric SNRs (section 1), I examine
the possibility that the mixed morphology of SNR G352.7-0.1 is a point
symmetric morphology.

In the upper panels of Figure 1 I present a composite image from the Chandra
X-Ray Observatory homepage of X-ray, radio, infrared (IR), and visible light.
On the upper-right panel and the lower panels, I added my identification of
two symmetry axes (dashed straight lines). The large ellipse marks the
approximate bright radio ellipse, best seen in the radio image on the lower-
right panel. I fit the ellipses and their axes by eyes, using the radio image
in Figure 1 and that from Giacani et al. (2009) that I present in Figure 2. In
Figure 2 the blue short arrows point at three minima along filaments in the
radio intensity map. The symmetry axis of the large ellipse very closely
coincides with the line that goes through the three minima. This strengthens
the identification of this symmetry axis. The same axis through the radio-
minima, the ${\rm Axis}_{\rm R}$ one, is seen in the right panel of Figure 3
as it crosses the two elongated minima in radio intensity (dark zones).

Figure 2:  Radio images from Giacani et al. (2009). I added the two symmetry
axes and the ellipses that are identical to those in Figure 1. The three blue
arrows point at minimum radio intensity in the corresponding filaments. The
two unrelated point-like sources are WBH2005 352.775-0.153 and WBH2005
352.772-0.149 (White, Becker, & Helfand, 2005).  Figure 3:  Figure 9 from
Pannuti et al. (2014) with my notations of the two symmetry axes, in dashed-
white lines, that I identify in Figures 1 and 2. From left to right: X-ray
(Chandra in $0.5–8.0{~{}\rm keV}$), infrared (Spitzer in 24 micron), and radio
(VLA 6 cm). The axis of the larger ellipse goes through the minimum in radio
intensity zones (two black regions in the right panel). I also added three
thick arrows pointing at opposite (relative to the center) infrared clumps. I
drew a double-headed arrow pointing at the opposite clumps, which practically
coincides with the axis of the smaller ellipse. The yellow arrow on the left
panel points at the outer X-ray arc.

The identification of the second symmetry axis is more delicate. To identify
the symmetry axis of the smaller ellipse and to draw the smaller ellipse, I
use both the X-ray and radio morphologies. I identify a bow-shaped radio
filament and a less clear bow-shaped X-ray zone (or bright X-ray clump), to be
two opposite structural features that were shaped together. I term them the
radio bow and X-ray bow as I mark on the upper right panel of Figure 1. I take
the center of these two bows to define the axis of a smaller ellipse and draw
a corresponding ellipse according to the X-ray map.

Giacani et al. (2009) suggest that SNR G352.7-0.1 has a barrel-shaped
morphology. The axis of the barrel includes the radio shell (large ellipse in
Figures 1 and 2), and the outer radio arc on the southwest (the incomplete
southwest radio arc on the lower right of radio images), and does not coincide
with either of the two symmetry axes that I identify. The projection on the
plane of the sky of a circular ring on a tilted barrel is an ellipse. The two
opposite tips of the longer axis of the projected ellipse (upper and lower
segments of the large ellipse in Figure 2) should be brighter than the rest of
the ellipse (because a longer line of sight through the ring relative to the
two perpendicular segments on the ring). However, the opposite holds for the
larger radio ellipse of Figure 2. I therefore prefer to consider the outer
radio arc as a structure further away from the center, rather than a symmetric
part to the southwest segment of the radio ellipse.

As evident from the literature, SNR G352.7-0.1 is puzzling in being non-
spherical and having a massive shell, properties typical to CCSNe, but with
high iron abundance and no central compact object, properties typical to SNRs
Ia. The identification of two symmetry axes in an SNR that is already puzzling
makes this a very rare case. I could not find a similar case. The closest SNR
in morphology is the SNR Ia DEM L71 in the Large Magellanic Cloud (for recent
images see Li et al. 2021; Alan & Bilir 2022). DEM L71 has an elliptical
structure with ears and a clear axis. However, it is less puzzling and I
cannot identify a clear second declined axis. Still, since it is classified as
a SNIP (Soker, 2022), it might well be that the interaction that shaped the PN
into which the progenitor of SNR DEM L71 exploded was shaped by triple star
interaction. But not necessarily so.

I turn to propose a scenario that accounts for the properties of SNR
G352.7-0.1.

##  4 Possible scenarios for SNR G352.7-0.1

As I discuss in section 2 the iron properties of SNR G352.7-0.1, mass and line
energy, suggest an SN Ia, while the highly non-spherical morphology, the
massive swept-up mass, and the molecular clouds in the ISM suggest a massive
stellar system progenitor. The location of SNR G352.7-0.1 towards the galactic
center, $(l,b)=(352^{\circ}.7579,-0^{\circ}.1236)$ and an estimated distance
of $6.8-8.4{~{}\rm kpc}$ (Fujishige et al., 2023) and up to $\approx
10.5{~{}\rm kpc}$ (Zhang et al., 2023), is compatible with possible recent
star formation and a massive stellar system progenitor, i.e., on the upper
mass zone for formation of CO WDs.

To these properties, I add my identification of two symmetry axes, as I mark
on the Figures and discuss in section 3. Pannuti et al. (2014) estimate the
mass of the X-ray emitting gas to be $2.6M_{\odot}$ and that of the swept-up
ISM mass to be $45M_{\odot}$. The high ISM mass suggests that the ISM
substantially influenced the SNR morphology. Nonetheless, I attribute the two
symmetry axes that I identify to shaping by the progenitor and the explosion
and not to the ISM.

To incorporate the above properties I suggest that SNR G352.7-0.1 is either a
peculiar SN Ia or a peculiar SN II (one that is not a CCSN), in both cases the
explosion is thermonuclear in a super-Chandrasekhar merger of two WDs.

The evolutionary phases and basic ingredients of the possible scenarios, as
well as their relations to the observed properties of SNR G352.7-0.1, are as
follows.

  1. 1.

The Progenitor triple system. The fundamental components of the progenitor are
two stars with initial masses of $M_{\rm ZAMS,1}\simeq 5-7M_{\odot}$ and
$M_{\rm ZAMS,2}\simeq 4-5M_{\odot}$. In addition, there was a tertiary star
around the primary star with an orbital plane that was inclined to that of the
main (outer) binary system (see point 5 below). The secondary stellar
evolution time to its AGB phase is $\approx 10^{8}{~{}\rm yr}$. During this
period the system did not move to a large distance from its formation location
and the ISM that supplied gas to star formation did not have time to fully
disperse. This accounts for the dense ISM and the molecular clouds in the
vicinity of SNR G352.7-0.1.

  2. 2.

Formation of the WD. The primary star formed a massive CO WD of $M_{\rm
WD,1}\simeq 1-1.1M_{\odot}$ (by initial-final mass relation, e.g., Marigo
2022; Cunningham, Tremblay, & W. O’Brien 2024). The secondary star avoided CEE
before it left the main sequence. However, the secondary star could have
accreted mass to become a star of $M_{2}\simeq 6-7M_{\odot}$. The tertiary
lower-mass main sequence star did enter a CEE and ended closer to the newly
born WD. The inner binary system, composed of the WD and the tertiary star,
could have been a cataclysmic variable. The mass that the primary star blew
during its evolution was already mixed with the ISM before the secondary star
left the main sequence.

  3. 3.

Common envelope evolution. As the secondary became an AGB star it engulfed the
WD and its main sequence low-mass star companion, and the system entered a
CEE. The triple system ejected most or all of the envelope of the secondary
star.

  4. 4.

The outcome of CEE and the explosion. After the formation of the CEE, there
are three possible scenarios.

    1. (a)

Peculiar SN Ia via the DD scenario. The system manages to eject the entire
envelope and the WD and the core end at a very close orbit that brings them to
merge within $t_{\rm CEED}\simeq{\rm few}\times 10^{5}{~{}\rm yr}$. This
relatively short CEE to explosion delay (CEED) time (see Soker 2022 for the
introduction of the CEED time) implies that the explosion ejecta collides with
the CSM that was formed in the CEE. The merger is driven by emitting
gravitational waves, by triple-star interaction, or both. Until the explosion,
the central core ionizes the CSM which is the ejected common envelope, and the
system is a planetary nebula. As the WD and the core merge, they explode. This
is the DD scenario (without a MED) that results in a peculiar SN Ia because
the combined mass of the core and the WD is $\simeq 1.6-2.2M_{\odot}$, i.e.,
super-Chandrasekhar. This is an SN Ia inside a planetary nebula (SNIP). In the
merging of the core with the WD, one of them is tidally destroyed and forms a
disk around the other. This disk launches jets that shape the explosion ejecta
that is observed in X-ray, i.e., the smaller ellipse in the figures. The axis
of the explosion ejecta is inclined to that of the CSM because of the triple-
star interaction (see point 5 below).

    2. (b)

Peculiar SN Ia via the CD scenario. The WD and the core merge during or at the
end of the CEE, and the merger remnant explodes after envelope ejection but
within a CEED time of $t_{\rm CEED}\simeq{\rm few}\times 10^{5}{~{}\rm yr}$.
This is again an SNIP, but a peculiar SN Ia via the CD scenario. In this case,
the explosion is expected to be close to spherical (unless there are two
opposite bullets along the rotation axis of the merger remnant). Therefore,
this scenario does not account for the elliptically-shaped X-ray ejecta and
its symmetry axis. This scenario is not likely for SNR G352.7-0.1.

    3. (c)

Peculiar SN II via the CD scenario. In this scenario the WD and the core merge
at the end of the CEE and explode before the entire envelope is ejected or
shortly after the ejection of the common envelope but before it becomes
transparent, a scenario that Livio & Riess (2003) studied. Because of the
massive hydrogen in the CSM, this might be classified as a peculiar type II
supernova. The explosion during the merger process ensures a non-spherical
explosion ejecta, as in route (a) above.

  5. 5.

Accounting for inclined symmetry axes. The two symmetry axes that I identify
are inclined to each other. Above I attributed the material that formed the
radio ellipse to the former common envelope that was ejected during the CEE. I
attribute the X-ray emitting gas to the explosion ejecta. I suggest that the
presence of a tertiary star with an inclined orbit to that of the two main
stars accounts for the inclination. Most likely, a lower mass star,
$M_{3}\simeq 0.3-1M_{\odot}$, orbited the primary star. As the primary formed
an AGB star, the tertiary might have spiraled-in inside a CEE to a close
orbit. The system of the WD and the tertiary might have been a catalytic
variable. The tertiary star induced the merger or influenced its plane, such
that the WD-core merger plane was inclined to the plane of the primary-
secondary system. This deserves further study. I note here that about half of
such massive progenitors are likely to be in triple-star systems (e.g., Moe &
Di Stefano 2017).

  6. 6.

The fate of the tertiary star. The tertiary star might end in one of a few
ways (e.g., Sabach & Soker 2015; Glanz & Perets 2021). It can be ejected from
the common envelope and become bound or unbound from the binary system. In any
case, after the explosion, it will be a lonely star. In principle, it should
still be inside the SNR now. More likely, because the tertiary star influenced
the merger process, it survived till the final stages of the CEE when it was
tidally destroyed by either the core or the WD. In this case, it does not
exist anymore.

I end this section by speculating on the nature of the incomplete southwestern
radio arc (outer radio arc). The lower-left panel of Figure 1 and the left
panel of Figure 3 show that there is an X-ray emitting gas just inner to the
outer radio arc which is disconnected from the inner main X-ray structure.
This I term the ‘outer X-ray arc’; the yellow arrow on the left panel of
Figure 3 points at this arc. I speculate that the shell that makes the main
radio ellipse is not complete, and that hot ejecta leaks out and interacts
with the outer CSM. The outer CSM is an outer shell, formed by the triple-star
interaction during the formation process of the planetary nebula. This
interaction forms the outer radio arc. This speculation can be tested with
hydrodynamical simulations.

##  5 Summary

I proposed that the explosion that formed SNR G352.7-0.1 was a super-
Chandrasekhar thermonuclear explosion during the merger of two degenerate
stars. The explosion occurred during the merger process of two WDs in a DD
scenario (route-a in point 4 of section 4) that resulted in a peculiar super-
Chandrasekhar SN Ia or during the merger of the core and the WD at the end of
a CEE in what could have been observed as a peculiar type II SN, although it
is a super-Chandrasekhar thermonuclear explosion as well (route-c there). The
super-Chandrasekhar thermonuclear explosion accounts for the relatively
massive ejecta as revealed by the X-ray emitting gas ($\simeq 2.6M_{\odot}$,
Pannuti et al. 2014), the high iron abundance, and the energy of iron X-ray
lines (section 2).

The relatively massive progenitors, $M_{\rm ZAMS,1}\simeq 5-7M_{\odot}$ and
$M_{\rm ZAMS,2}\simeq 4-5M_{\odot}$, account for the SNR being in a region of
dense ISM and the presence of molecular clouds (section 2). The pre-explosion
CEE of the WD remnant of the primary star inside the AGB envelope of the
secondary star formed a CSM that is the larger ellipse observed in radio
(Figures 1 and 2). The explosion ejecta is the material observed in the X-ray,
which defines the smaller ellipse and its symmetry axis.

To account for the misalignment of the two symmetry axes that I identify in
this study, I suggest the presence of a tertiary star (point 5 in section 4).

In Soker (2024a) I attributed the point-symmetric morphology of SNR G1.9+0.3
solely to the planetary nebula into which a spherical normal SN Ia explosion
took place. In the case of SNR G352.7-0.1 that I study here, on the other
hand, the point symmetry is attributed both to a planetary nebula progenitor
and a non-spherical peculiar SN Ia explosion.

Although not common, the proposed scenario is not extreme in its ingredients
and properties. Firstly, in the progenitor binary system mass range, $M_{\rm
ZAMS,1}\simeq 5-7M_{\odot}$, triple star systems are common, i.e., about half
of the binary systems are triple and higher order stellar systems (e.g., Moe &
Di Stefano 2017). Secondly, normal SN Ia explosions within several hundred
thousand years after the CEE, $t_{\rm CEED}\lesssim{\rm several}\times
10^{5}{~{}\rm yr}$ are common. The gas that was blown during the CEE forms a
planetary nebula as it is ionized by the WD remnant. The explosion inside a
planetary nebula is an SNIP. In Soker (2022) I estimated that the fraction of
SNIPs among normal SNe Ia is $f_{\rm SNIP}\simeq 0.5$. This study hints that
peculiar SNIPs are also common.

The present study adds to the rich variety of evolutionary routes within the
different scenarios of normal and peculiar SNe Ia.

## Acknowledgements

I thank an anonymous referee for useful comments. This research was supported
by a grant from the Israel Science Foundation (769/20).

## References

  * Alan & Bilir (2022) Alan N., Bilir S., 2022, MNRAS, 511, 5018.
  * Aleo et al. (2023) Aleo P. D., Malanchev K., Sharief S., Jones D. O., Narayan G., Foley R. J., Villar V. A., et al., 2023, ApJS, 266, 9.
  * Balick (1987) Balick B., 1987, AJ, 94, 671.
  * Caswell et al. (1983) Caswell J. L., Haynes R. F., Milne D. K., Wellington K. J., 1983, MNRAS, 203, 595.
  * Chu, Jacoby, & Arendt (1987) Chu Y.-H., Jacoby G. H., Arendt R., 1987, ApJS, 64, 529.
  * Corradi & Schwarz (1995) Corradi R. L. M., Schwarz H. E., 1995, A&A, 293, 871
  * Cunningham, Tremblay, & W. O’Brien (2024) Cunningham T., Tremblay P.-E., W. O’Brien M., 2024, MNRAS, 527, 3602.
  * Dubner et al. (1993) Dubner G. M., Moffett D. A., Goss W. M., Winkler P. F., 1993, AJ, 105, 2251.
  * Fujishige et al. (2023) Fujishige A., Yamauchi S., Nobukawa K. K., Nobukawa M., 2023, PASJ, 75, 907.
  * Giacani et al. (2009) Giacani E., Smith M. J. S., Dubner G., Loiseau N., Castelletti G., Paron S., 2009, A&A, 507, 841.
  * Glanz & Perets (2021) Glanz H., Perets H. B., 2021, MNRAS, 500, 1921.
  * Glanz, Perets, & Pakmor (2024) Glanz H., Perets H. B., Pakmor R., 2024, arXiv:2309.03300.
  * Hoeflich (2017) Hoeflich P., 2017, in Handbook of Supernovae, Springer International Publishing AG, 2017, p. 1151
  * Hrivnak, Kwok, & Su (2001) Hrivnak B. J., Kwok S., Su K. Y. L., 2001, AJ, 121, 2775.
  * Jha et al. (2019) Jha, S. W., Maguire, K., & Sullivan, M. 2019, Nature Astronomy, 3, 706
  * Kinugasa et al. (1998) Kinugasa K., Torii K., Tsunemi H., Yamauchi S., Koyama K., Dotani T., 1998, PASJ, 50, 249.
  * Kushnir et al. (2013) Kushnir D., Katz B., Dong S., Livne E., Fernández R., 2013, ApJL, 778, L37.
  * Li et al. (2021) Li C.-J., Chu Y.-H., Raymond J. C., Leibundgut B., Seitenzahl I. R., Morlino G., 2021, ApJ, 923, 141.
  * Liu, Röpke, & Han (2023) Liu Z.-W., Röpke F. K., Han Z., 2023d, RAA, 23, 082001.
  * Livio & Mazzali (2018) Livio, M., & Mazzali, P. 2018, Physics Reports, 736, 1
  * Livio & Riess (2003) Livio M., Riess A. G., 2003, ApJL, 594, L93.
  * Maeda, & Terada (2016) Maeda, K., & Terada, Y. 2016, International Journal of Modern Physics D, 25, 1630024
  * Manchado et al. (1996) Manchado A., Guerrero M. A., Stanghellini L., Serra-Ricart M., 1996, iacm.book (The IAC morphological catalog of northern Galactic planetary nebulae, Publisher: La Laguna, Spain: Instituto de Astrofisica de Canarias (IAC), 1996, Foreword by Stuart R. Pottasch, ISBN: 8492180609)
  * Manchester (1987) Manchester R. N., 1987, A&A, 171, 205
  * Maoz et al. (2014) Maoz, D., Mannucci, F., & Nelemans, G. 2014, ARA&A, 52, 107
  * Marigo (2022) Marigo P., 2022, Univ, 8, 243.
  * Moe & Di Stefano (2017) Moe M., Di Stefano R., 2017, ApJS, 230, 15.
  * Neopane et al. (2022) Neopane S., Bhargava K., Fisher R., Ferrari M., Yoshida S., Toonen S., Bravo E., 2022, ApJ, 925, 92.
  * Pakmor et al. (2012) Pakmor R., Kromer M., Taubenberger S., Sim S. A., Röpke F. K., Hillebrandt W., 2012, ApJL, 747, L10.
  * Pakmor et al. (2013) Pakmor R., Kromer M., Taubenberger S., Springel V., 2013, ApJL, 770, L8.
  * Pakmor et al. (2022) Pakmor R., Callan F. P., Collins C. E., de Mink S. E., Holas A., Kerzendorf W. E., Kromer M., et al., 2022, MNRAS, 517, 5260.
  * Pannuti et al. (2014) Pannuti T. G., Kargaltsev O., Napier J. P., Brehm D., 2014, ApJ, 782, 102.
  * Perets et al. (2019) Perets H. B., Zenati Y., Toonen S., Bobrick A., 2019, arXiv, arXiv:1910.07532.
  * Parker (2022) Parker Q. A., 2022, FrASS, 9, 895287.
  * Parker, Bojičić, & Frew (2016) Parker Q. A., Bojičić I. S., Frew D. J., 2016, JPhCS, 728, 032008.
  * Ruiter (2020) Ruiter A. J., 2020, IAUS, 357, 1.
  * Ruiz-Lapuente (2019) Ruiz-Lapuente, P. 2019, New A Rev., 85, 101523
  * Sabach & Soker (2015) Sabach E., Soker N., 2015, MNRAS, 450, 1716.
  * Sahai et al. (2000) Sahai R., Bujarrabal V., Castro-Carrizo A., Zijlstra A., 2000, A&A, 360, L9
  * Sahai, Morris, & Villar (2011) Sahai R., Morris M. R., Villar G. G., 2011, AJ, 141, 134.
  * Sahai & Trauger (1998) Sahai R., Trauger J. T., 1998, AJ, 116, 1357.
  * Schwarz, Corradi, & Melnick (1992) Schwarz H. E., Corradi R. L. M., Melnick J., 1992, A&AS, 96, 23
  * Sezer & Gök (2014) Sezer A., Gök F., 2014, ApJ, 790, 81.
  * Soker (2018) Soker N., 2018, SCPMA, 61, 49502.
  * Soker (2019) Soker N., 2019, NewAR, 87, 101535.
  * Soker (2022) Soker N., 2022, RAA, 22, 035025.
  * Soker (2024a) Soker N., 2024a, RAA, 24, 015012.
  * Soker (2024b) Soker N., 2024b, arXiv:2311.17732.
  * Toledo-Roy et al. (2014) Toledo-Roy J. C., Velázquez P. F., Esquivel A., Giacani E., 2014, MNRAS, 437, 898.
  * Tsebrenko & Soker (2015a) Tsebrenko D., Soker N., 2015a, MNRAS, 447, 2568.
  * Vink (2012) Vink J., 2012, A&ARv, 20, 49.
  * Vinkó, Szalai, & Könyves-Tóth (2023) Vinkó J., Szalai T., Könyves-Tóth R., 2023, Univ, 9, 244.
  * Wang (2018) Wang B., 2018, RAA, 18, 049.
  * White, Becker, & Helfand (2005) White R. L., Becker R. H., Helfand D. J., 2005, AJ, 130, 586.
  * Yamaguchi et al. (2014) Yamaguchi H., Badenes C., Petre R., Nakano T., Castro D., Enoto T., Hiraga J. S., et al., 2014, ApJL, 785, L27.
  * Zenati et al. (2023) Zenati Y., Perets H. B., Dessart L., Jacobson-Galán W. V., Toonen S., Rest A., 2023, ApJ, 944, 22.
  * Zhang et al. (2023) Zhang Q.-Q., Zhou P., Chen Y., Zhang X., Zhong W.-J., Zhou X., Zhang Z.-Y., et al., 2023, ApJ, 952, 107.