# Dynamic-OFA: Runtime DNN Architecture Switching for Performance Scaling on
Heterogeneous Embedded Platforms

Wei Lou Authors contributed equally. Lei Xun11footnotemark: 1 Amin Sabet  Jia
Bi  Jonathon Hare  Geoff V. Merrett
University of Southampton  UK
{wl4u19, lx2u16, ms4r18, J.Bi, jsh2<EMAIL_ADDRESS>
###### Abstract

Mobile and embedded platforms are increasingly required to efficiently execute
computationally demanding DNNs across heterogeneous processing elements. At
runtime, the available hardware resources to DNNs can vary considerably due to
other concurrently running applications. The performance requirements of the
applications could also change under different scenarios. To achieve the
desired performance, dynamic DNNs have been proposed in which the number of
channels/layers can be scaled in real time to meet different requirements
under varying resource constraints. However, the training process of such
dynamic DNNs can be costly, since platform-aware models of different
deployment scenarios must be retrained to become dynamic. This paper proposes
Dynamic-OFA, a novel dynamic DNN approach for state-of-the-art platform-aware
NAS models (Once-for-all network (OFA)). Dynamic-OFA pre-samples a family of
sub-networks from a static OFA backbone model, and contains a runtime manager
to choose different sub-networks under different runtime environments. As
such, Dynamic-OFA does not need the traditional dynamic DNN training pipeline.
Compared to the state-of-the-art, our experimental results using ImageNet on a
Jetson Xavier NX show that the approach is up to 3.5x (CPU), 2.4x (GPU) faster
for similar ImageNet Top-1 accuracy, or 3.8% (CPU), 5.1% (GPU) higher accuracy
at similar latency.

##  1 Introduction

(a)

(b)

Figure 1: Experimental results illustrating how inference latency constraints
characterised at design-time can be violated at runtime by changes in
available hardware resources and executing tasks. (a) denotes the latency on
GPU and (b) on CPU. The tables above indicate the combinations of workload and
frequency. Figure 2: The workflow of Dynamic-OFA. Using pre-trained OFA
networks that contain $2\times{10}^{19}$ sub-network architectures as the
backbone, sub-network architectures are sampled from OFA for both CPU and GPU
at the offline stage. These architectures have different performance (latency,
accuracy) and are stored in a look-up table to build a dynamic version of OFA
without any additional training required. Then, at runtime, Dynamic-OFA
selects and switches to optimal sub-network architectures to fit time-varying
available hardware resources.

Modern heterogeneous embedded systems typically execute multiple applications
concurrently. DNNs are increasingly being executed on embedded platforms due
to the superior performance in many applications such as computer vision and
natural language processing. Compared to cloud-based solutions, DNN inference
on embedded platforms brings many advantages in latency, privacy and
connectivity. However, DNN inference is both computationally and memory
intensive, making it a challenge to deploy on embedded platforms.

Many approaches have been proposed to reduce the computational demands of DNN
inference, such as platform-aware filter pruning [22, 6] and Neural
Architecture Search (NAS) [2, 3]. These approaches produce a static DNN
architecture with fixed parameters for the target application performance
requirements based on the measurement on a fixed hardware resources. However,
since available hardware resources dynamically change at runtime, performance
requirements can be violated [20, 19]. Fig 1 illustrates these problems by
using experimental results from a Jetson Xavier NX, where bar $A$ represents
an optimized DNN model executing on all GPU cores at 1.1GHz to deliver a 50ms
target latency. However, under the same target latency, the optimization at
design-time is invalid if the operating frequency changes or the DNN shares
GPU cores with other applications at runtime, as shown by bars $B$, $C$ and
$D$. The same applies in the CPU case, shown by bars $E$, $F$, $G$ and $H$.

Since both software performance requirements and hardware resource
availability can change dynamically at runtime [20, 19], various dynamic DNNs
[25, 24, 23, 21] have been proposed to address this issue. These dynamic DNNs
contain various sub-networks that each have a different accuracy and latency.
Given different available hardware resources and application requirements,
different sub-networks can be selected. However, two problems still remain in
the previous approaches. First, previous dynamic DNNs involve an additional
training pipeline which retrains the backbone network (MobileNet[8, 15],
ResNet[5]) from scratch. The total training would be costly in real deployment
scenarios, since platform-aware pruning/NAS need to be applied before dynamic
DNN process, and all model variants of different deployment scenarios have to
be retrained to become dynamic. Second, prior works re-scale the network
architecture to obtain sub-networks by either channel scaling [25, 24, 23, 21]
or layer scaling [9]. However, the most efficient DNN architectures on CPUs
typically have more layers but fewer channels, while the opposite is true for
GPUs [3]. Therefore, previous scaling methods limit the application of dynamic
DNN on heterogeneous System on Chip (SoC) platforms, since modern SoCs
integrate multiple computing elements including CPU, GPU and NPU. As a result,
different dynamic DNNs are needed for different heterogeneous computing
elements.

This paper proposes Dynamic-OFA, a novel approach to provide dynamic DNN
architectures for different software and hardware resource requirements.
Dynamic-OFA works with state-of-the-art platform-aware NAS methods (Once-for-
all network (OFA)) without requiring any additional model retraining.
Moreover, to improve previous dynamic approaches, Dynamic-OFA scales the
entire DNN architecture, including width, depth, filter sizes, and input
resolutions to provide more efficient DNNs architectures for both CPU and GPU
with one shared backbone.

Fig 2 shows the workflow of Dynamic-OFA with two main steps. In the first
offline step, different sub-networks are extracted from the OFA [2] super-
network. Accuracy and latency of extracted sub-networks are evaluated to find
a family of efficient sub-networks on the Pareto-front for both CPU and GPU.
In the second step, and during runtime, Dynamic-OFA uses a runtime manager to
switch between the optimal sub-network based on the runtime accuracy and
latency requirements of the application, and available resources on the
platform.

The contributions of this paper are:

  1. 1.

A novel dynamic DNN approach that combines OFA with dynamic DNN. Compared to
the state-of-the-art, our experimental results on Nvidia Jetson Xavier NX show
that our approach is up to 3.5x (CPU), 2.4x (GPU) faster for similar ImageNet
Top-1 accuracy, or 3.8% (CPU), 5.1% (GPU) higher accuracy at similar latency.

  2. 2.

An improved search algorithm to efficiently search a family of sub-networks
from the OFA super-network, by jointly considering inference accuracy and
latency.

  3. 3.

A runtime approach to dynamically switch between sub-networks to meet time-
varying performance constraints and/or available hardware resources.

##  2 Related work

#### Neural Architecture Search (NAS)

Many handcrafted efficient DNN models like MobileNet [8, 15] and ShuffleNet
[13] achieve state-of-the-art performance. However, these models need to be
further compressed to fit constraints of the target device using platform-
aware compression techniques[22, 6]. Since compression needs to be conducted
for each new constraint, the time required for large-scale deployment is
expensive. Furthermore, designing handcrafted DNN models needs expert
knowledge and can be a challenging and time-consuming task. NAS automates
architecture design, directly searching for the most efficient DNN
architectures for target constraints. However, given new platform constraints,
DNN models need to be researched and retrained; therefore, the required time
is still prohibitive for large-scale deployments. For example, Tan et al.[16]
introduced MnasNet, a multi-objective NAS approach that uses reinforcement
learning to find the architecture for maximizing accuracy and latency on
target hardware platforms. MnasNet cost 40,000 GPU hours (Nvidia V100 GPU) to
find a single DNN architecture, and this raises a significant issue since the
number of combinations of hardware platforms and software performance targets
are significant. Cai et al.[3] proposed ProxylessNAS, which uses weight-
sharing and differentiable architecture search; however, the search cost for
each model is still 200 GPU hours which is also significant for large scale
deployments.

Cai et al.[2] proposed the Once-for-all network (OFA), a NAS approach that
supports large-scale deployments. Only one DNN model (a super-network) needs
to be trained, and enables $2\times{10}^{19}$ sub-networks to be used for
different software performance requirements on different hardware platforms.
While OFA offers a number of significant advantages, the available hardware
resources in modern SoCs, containing heterogeneous computing elements that use
energy-efficient features such as DVFS and task mapping, vary dynamically. OFA
is not a dynamic DNN by default, since its search process is still too time-
consuming (hours on Nvidia Jetson Xavier NX). This prevents real-time
architecture switching at runtime, and motivates us to propose a general
approach for building dynamic DNNs for OFA super-networks.

#### Dynamic DNNs

Dynamic DNNs can switch the DNN architecture to fit time-varying available
hardware resources and software performance requirements. A variety of
approaches have been proposed to change the width of the backbone networks,
like ‘Slimmable’ [25], ‘Universally Slimmable’ [24] and ‘AutoSlim’ [23]. These
models can run different active channels and achieve instant and adaptive
accuracy-latency trade-offs. MutualNet [21] shows improved performance by
adding input resolutions with width as switchable dimensions. For different
constraints, different sub-networks with varying widths and resolutions can be
chosen and built as a query table. Approaches such as MSDNet [9] can change
the depths of the backbone networks. However, the most efficient models for
different hardware resources are usually different in architecture. For
example GPUs prefer shallow and wide DNN architectures with early pooling,
while CPUs prefer deep and narrow DNN architectures with late pooling [3]. The
switchable dimensions for previous approaches are either width or depth;
therefore, they cannot provide the most efficient architecture for both CPU
and GPU on the modern SoCs. The Dynamic-OFA approach presented in this paper
switches in four dimensions (width, depth, filter sizes, and input
resolutions) to provide efficient architectures for both GPUs and CPUs by
using a share backbone model.

##  3 Dynamic-OFA

As illustrated in Fig 2, Dynamic-OFA use the following process: a pre-trained
OFA model [2] is used as the backbone (super-network), as introduced in
Section 3.1. As an offline process, sub-networks with different latency and
accuracy are sampled from the pre-trained super-network at design-time
(Section 3.2). The sampling process is conducted separately for CPU and GPU
because the most efficient sub-network architectures are different for
heterogeneous computing resources. The batch-normalization (batch-norm)
parameters of each sub-network are recalculated and stored (Section 3.3). At
runtime, the sampled sub-network architecture can be switched to meet latency
and accuracy requirements on time-varying available hardware resources
(Section 3.4). No additional training is needed, and since all sub-networks
share the same OFA model as the backbone, only a single model needs to be
stored on the device.

###  3.1 Backbone Network: Once-For-All (OFA)

The OFA network [2] supports $2\times{10}^{19}$ sub-networks with different
sizes by a single super-network, covering four dimensions of the DNN
architecture: depth, width, kernel, and input resolutions. OFA uses
progressive shrinking to train the super-network model. Progressive shrinking
optimizes super-network parameters such that each supported sub-network
maintains almost the same level of accuracy as independently training a
network with the same architecture configuration. After training the super-
network model, OFA uses an evolutionary search algorithm [14] to find sub-
network architectures in a super-network model with different accuracy and
latency trade-offs. OFA only requires a single set of parameters to store all
sub-networks, since all sub-networks share the same parameters. OFA is able to
select sub-network architectures for different hardware platforms, and then
calibrates the batch-norm parameters for those selected sub-networks. The
process of searching for sub-networks and calibrating batch-norm parameters
take minutes on a GPU or hours on a CPU111The platform is Nvidia Jetson Xavier
NX. The time includes measure the accuracy of selected sub-network on ImageNet
50k validation set, since the accuracy prediction is not accurate enough, more
details in section 3.2. Batch-norm is calculated on 2000 images.. The actual
search time at runtime depends on how tight the constraints are, and how the
search problem shares hardware resources with other applications, and hence
OFA cannot be used to adapt to resource changes at runtime.

Our approach identifies a family of efficient sub-networks on the Pareto-front
for each computation element in a heterogeneous platform, and pre-calculates
batch-norm parameters for those sub-networks offline. This allows switching
the network architecture at runtime. Furthermore, since Dynamic-OFA conducts
all the sub-network search at design-time on a server, the search cost is
dramatically reduced to that of the single search cost, multiplied by the
number of sub-networks.

Algorithm 1 Random Search Algorithm of Dynamic-OFA.

1:maximum accuracy constraint ($Acc_{max}$), accuracy suitable range
($Acc_{r}$), latency ($Lat$), maximum latency constraint ($Lat_{max}$),
initial latency ($Lat_{init}$), extracted sub-networks ($Parents$), latency
constraint increment ($Lat_{add}$), $n$ iterations of searching ($itr_{n}$),
maximum iterations number ($itr_{max}$)

2:qualified network architecture ($Arch$), predicted accuracy ($Acc_{p}$),
predicted latency ($Lat_{p}$)

3:function Random_Search

4: $Lat\leftarrow Lat_{init}$

5: $i=0$

6: while $i<itr_{max}$ do

7: if $i\%itr_{n}=0$ and $Lat<Lat_{max}$ then

8: $Lat\leftarrow Lat+Lat_{add}$

9: end if

10: $Arch=Random\\_Arch()$

11: $Acc_{p}=Predict\\_Accuracy(Arch)$

12: $Lat_{p}=Predict\\_Latency(Arch)$

13: if $Acc_{p}>Acc_{max}-Acc_{r}$ and $Lat_{p}<Lat$ then

14: if $Arch$ not in $Parents$ then

15: return $Arch,Acc_{p},Lat_{p}$

16: end if

17: end if

18: $i\leftarrow i+1$

19: end while

20: end function

###  3.2 Optimal Sub-network Architecture Search

OFA’s search is solely based on the latency constraint, as it selects sub-
networks with the highest accuracy that meets a latency constraint. It uses a
combination of a random search and evolutionary search: (1) a random search
algorithm finds sub-networks that meet the latency constraints; (2) the
evolutionary search performs refinement to mutate those random selected sub-
network configurations, and then keeps the one which has the highest accuracy.
Although this approach works for a single sub-network architecture search, it
is not efficient for searching a family of sub-networks. To build dynamic-
DNNs, multiple sub-network architectures with different accuracy-latency
trade-offs are required to be dynamically switched at runtime. If we only use
latency as the constraint (which is the original OFA search method), the
random search algorithm often outputs the sub-networks with the same accuracy
for different latency constraints. For example, a 75% accuracy, 30 ms model is
searched under 30 ms, 40 ms and 50 ms constraints, but ideally we want models
with higher accuracy when the latency is relaxed. The OFA algorithm only
requires the latency of searched sub-networks to be lower than constraint but
not for accuracy, and this prevents us from getting the Pareto trade-off
curve. In our random search algorithm 1, by adding accuracy as a hard
constraint, it forces the search algorithm to find sub-networks under certain
latency constraints and have better accuracy (75% accuracy under 30 ms, 76 %
accuracy under 40 ms, 77% accuracy under 50 ms etc).

In Algorithm 1, accuracy and latency predictors are used to reduce the time
cost of the search process. We use the original accuracy predictor that comes
with the pre-trained OFA model; it is a three-layer neural network trained
using 5000 network architectures and their accuracy data. However, since we
want the dynamic DNN to have 1% accuracy steps between sub-networks, the
accuracy of all searched models are re-measured on the ImageNet 50K validation
set since the original OFA accuracy predictor is not accurate enough (normally
2-4% higher than our measurement). We adapted the latency predictor in OFA for
Nvidia Jetson Xavier GPU and CPU as a heterogeneous platform. A lookup table
is used to record the latency for different DNN computing operations such as
convolution, pooling, input and output. The latency of all operations is
profiled at design-time by timing the execution time of all operations at all
size variants. Moreover, the separate lookup table is built for different
hardware platforms and different computing cores on these platforms (CPU,
GPU). The latency of a sub-network can be predicted by summing up the latency
of sub-network operations. The latency are also re-measured on devices for
more accurate data.

To search for sub-networks, the latency constraint is initialized with a user-
defined value $Lat_{init}$, shown in algorithm 1 line 2. An accuracy
constraint is also fixed at a user-defined range
$[Acc_{max}-Acc_{r},Acc_{max}]$. Then, RANDOM_SEARCH starts searching for sub-
networks by randomly generating sub-network architectures $Random\\_Arch()$
(line 8), different depths, width, kernel sizes and input resolutions.
$Predict\\_Latency()$ and $Predict\\_Accuracy()$ predict the latency and
accuracy of each sub-network in lines 9 and 10. If none of the found
architectures provide a latency of less than $Lat$ and an accuracy in the
range of $[Acc_{max}-Acc_{r},Acc_{max}]$ for n iterations of searching
($itr_{n}$), the latency constraint is relaxed by increasing $Lat_{add}$ (line
6). However, this relaxation cannot exceed a maximum threshold $Lat_{max}$.
The discovered network architecture is stored in $Parents$ (line 13), which is
subsequently used for mutation operations of the evolutionary search algorithm
to search for the best sub-network.

We use the state-of-the-art pre-trained OFA [2] super-network model as the
backbone network for image classification. This model uses MobileNet v3 [7] as
the fundamental network architecture and is trained with the progressive
shrinking approach [2] to enable $2\times{10}^{19}$ sub-networks. A random
search, Algorithm 1, is used within the evolutionary search algorithm222The
same evolutionary search algorithm that the OFA used. [14] to search for
potential efficient sub-networks. It is notable that for given accuracy and
latency constraints, numerous sub-network architectures can be found in the
search process for each computation element, CPU, GPU in a heterogeneous
platform. However, most architectures are sub-optimal because they provide
lower accuracy or higher latency. The optimal sub-network architectures are on
the Pareto curve of accuracy-latency scatter plot, and they are selected for
building the Dynamic-OFA. Fig 3 shows the accuracy-latency scatter plot of
extracted sub-networks for the GPU of Nvidia Jetson Xavier NX platform. Among
obtained sub-networks, only those located on the Pareto-front (red line) are
considered as a family of optimal sub-networks for use by Dynamic-OFA.

Figure 3: The accuracy and latency of potential sub-network architectures. The
optimal architectures are on the Pareto curve.

(a) GPU

(b) Single-core CPU

Figure 4: Experimental results of Dynamic-OFA’s accuracy-latency trade-offs on
the a) GPU and b) CPU of the Nvidia Jetson Xavier NX. State of the art
approaches (shown in different colours) are also plotted, including static [2]
and dynamic DNNs [25, 24, 23, 21]. Dynamic-OFA is 2.4x (GPU) and 3.5x (CPU)
faster (at similar accuracy) or has 5.1% (GPU) and 3.8% (CPU) higher Top-1
ImageNet accuracy (at similar latency) than AutoSlim-MnasNet [23]. Figure 5:
Experimental results of Dynamic-OFA’s accuracy-FLOPs trade-offs. Compare with
state-of-the-art approaches, Dynamic-OFA achieves up to 50% FLOPs reduction
(at similar accuracy) and 2.95% higher Top-1 ImageNet accuracy (at similar
FLOPs) than AutoSlim-MnasNet [23].

###  3.3 Batch-norm Calibration

Searching sub-networks at runtime is computationally expensive. Therefore, to
make OFA dynamic at runtime, the search algorithm is run offline, and the
optimal sub-network configurations are stored as a lookup table to achieve
fast architecture switching at runtime. Moreover, the batch-norm parameters
[10] differ for each sub-network architecture and need to be recalculated for
different sub-networks. However, the calibration can take minutes on GPU and
hours on CPU, which is unacceptable for real-time DNN architecture switching
at runtime. Since we have selected a small number of optimal sub-network
architectures, the batch-norm parameters can be pre-calculated at design-time.
At runtime, sub-network architectures can be switched to meet different
performance requirements on time-varying available hardware resources. The
pre-stored batch-norm parameters (about 2KB for each sub-network) can be
loaded, significantly reducing the architecture switching time.

###  3.4 Runtime Architecture Switching

At runtime, sub-network architectures of Dynamic-OFA can be switched to meet
different performance requirements on time-varying available hardware
resources. Because of the stored sub-network architectures and their batch-
norm parameters, Dynamic-OFA supports real-time architecture switching for the
dynamic computing environments. We consider two operating scenarios:

  1. 1.

When a single dynamic-OFA runs on the device, a look-up table is used to
directly find the sub-network ‘level’ to meet different user-defined accuracy
and latency constraints. This is a similar approach to previous dynamic DNNs
like Slimmable [25, 24, 23] and MutualNet [21].

  2. 2.

When two workloads share the same GPU resources (one dynamic-OFA with another
workload, or two dynamic-OFAs), a reactive control approach is used instead of
a look-up table, due to the increased state space. The latency of the current
Dynamic-OFA model is measured over a certain time interval using a sliding
window. The RTM continually monitors the latency of all Dynamic-OFA workloads
at runtime. When a latency constraint violation occurs, the RTM gradually
changes sub-network levels while observing whether latency constraints are
subsequently met. Although the design-time profiled look-up table is not used,
the trade-off between sub-networks still holds.

The overhead of the RTM includes the monitoring of latency and the calculation
of average latency, neither of which are computationally expensive in
comparison to the task being monitored. Detailed overhead measurement will be
shown in the next section.

##  4 Experimental evaluation

Dynamic-OFA is developed for both the CPU and GPU of the Nvidia Jetson Xavier
NX platform, and the accuracy and latency are empirically measured. The
results are compared with both state-of-the-art static OFA backbone [2] and
dynamic DNNs [25, 24, 23, 21]. We have also executed other applications
(online model training[1] or a 2nd Dynamic-OFA) alongside our Dynamic-OFA, to
demonstrate runtime management of the sub-network architectures for
accommodating both applications on the same GPU.

###  4.1 Experimental Setup

We deploy and evaluate Dynamic-OFA on the Nvidia Jetson Xavier NX. The
platform has a 384-core GPU, a 6-core CPU, and 8 GB of unified memory. The
frequency is locked at the maximum333Due to the intensive nature of DNN
workloads, current DVFS governors will typically operate the SoC at the
maximum frequency.. A single-core CPU is used for all CPU experiments since
the program is single-threaded. We use the open-source pre-trained OFA model
(MobileNet v3, $w=1.2$ [2]) as the backbone for Dynamic-OFA. We evaluate the
accuracy of Dynamic-OFA on the ImageNet[4] 50K validation images for a more
accurate measurement than OFA’s accuracy predictor.

Figure 6: Runtime management of dynamic-OFA to meet the dynamic latency
constraints. Latency constraints are denoted by dashed lines. Different sub-
networks with different accuracies are denoted using different colours.

###  4.2 Top-1 Accuracy and Latency

Dynamic-OFA contains six optimal sub-networks for the GPU, which span a 20-100
ms latency range (Fig 4a). The same model also contains seven optimal sub-
networks for the CPU, spanning a range from 500-3000 ms (Fig 4b). The search
range for Top-1 accuracy is 70% to 85% for both CPU and GPU. In this paper, we
denote sub-networks using “levels.” Different levels have different latency
and accuracy. For example, level 1 is the sub-network architecture that has
the lowest latency and accuracy. On GPU, level 6 is the architecture that has
the highest latency and accuracy, whereas, on CPU, level 7 has the highest
latency and accuracy.

Dynamic-OFA achieves up to 79% Top-1 accuracy on ImageNet; close to the 80%
accuracy of the static OFA backbone [2] which is considered the state-of-the-
art under mobile settings ($<$600M MACs). The reason our Dynamic-OFA has 1%
lower accuracy is because OFA applies extra fine-tuning steps for its
individual model, whereas our model cannot be easily fine-tuned since it
contains 13 different sub-networks. Compared to state-of-the-art dynamic DNNs
[23], Dynamic-OFA is up to 2.4x (GPU) and 3.5x (CPU) faster (at a similar
accuracy) or has 5.1% (GPU) and 3.8% (CPU) higher Top-1 ImageNet accuracy (at
a similar latency). Furthermore, since previous dynamic DNNs are designed
using FLOPs rather than latency, they can access less hardware information
during design-time. Hence we also compared our Dynamic-OFA with them on a
accuracy-FLOPs trade-off curve (Fig 5). Dynamic-OFA achieves up to 50% FLOPs
reduction (at similar accuracy) and 2.95% higher Top-1 ImageNet accuracy (at
similar FLOPs) than prior art.

Model |  Time
---|---
Static OFA[2] |  minutes to hours
MutualNet-MBv2 [21] |  17 ms
AutoSlim-MnasNet [23] |  33 ms
Dynamic OFA |  73 ms

Table 1: Comparison of average runtime DNN architecture switching time on GPU

At runtime, different sub-network architectures can be used to meet dynamic
software performance requirements and available hardware resources. The
runtime architecture switching time is shown in Table 1; Dynamic-OFA supports
real-time DNN architecture switching, its switching time is much faster than
the static OFA model [2] since we only do search in a small subset of sub-
networks. Furthermore, loading the pre-calculated batch-norm takes only 2ms.
Dynamic-OFA is only slightly slower than AutoSlim[23] and MutualNet[21] due to
larger memory footprint, but it has a much better accuracy-latency/FLOPs
trade-offs (Figs 4 and 5). Such a small difference is not a considerable issue
in real applications, since new operating environments (software performance
requirements, available hardware resources) normally last much longer (minutes
to hours).

###  4.3 Dynamic Performance Requirements

The sub-network architectures of Dynamic-OFA can be switched to meet the
dynamic latency constraints at runtime. When only Dynamic-OFA is running on
the device, all hardware resources are available to it. A look-up table that
contains all accuracy-latency trade-offs can be obtained at design-time. RTMs
can choose different operating points at runtime. As shown in Fig 6, the
Dynamic-OFA model is deployed on the GPU and runs at the level 6 architecture
while the latency constraint is 65ms at the beginning. At around 2500 ms, the
latency constraint gets increased to 40 ms. Therefore the sub-network
architecture is switched to level 2 for speedup at the cost of trading 4.13%
accuracy. Then, accuracy is recovered when the latency constraint is later
reduced to 55ms.

The RTM, uses the sliding window to calculate the average latency every 10
images. Based on the latency of our model on the GPU, the reaction time of the
RTM is approximately 1-2s (about 50 image classifications). The time overhead
of the RTM is around 15 ms for each architecture switching, including the
latency of monitoring 50 images and calculating the average time across the
sliding windows.

Figure 7: At $t=0$, a single DNN is executing. After 2.5 s, a second
application begins executing, reducing available GPU resource and impacting on
the DNN inference latency. The runtime adapts, reducing the DNN accuracy until
the performance constraint is met.

###  4.4 Managing Concurrent Workloads

The sub-network architectures of Dynamic-OFA can be switched to meet software
performance constraints while fewer computing resources are available. Fig 7
shows results where GPU computing resources are shared between Dynamic-OFA and
a training task of a static DNN. The static DNN is an Nvidia open-source plant
classification based on ResNet-18 [1]. The training tasks starts to run at
2500 ms (donated by ‘X’), and Dynamic-OFA becomes slower since fewer GPU cores
are available to it. The sub-network architecture is gradually switched from
level 4 to level 2 to meet the latency constraint by trading 2.6% accuracy.

Two Dynamic-OFA models can also coexist of when they share the same GPU. Fig 8
shows two Dynamic-OFA models deployed on the same GPU, and their latency
constraint become violated. The sub-network architecture of two Dynamic-OFA
models are switched collectively so that the latency constraint of both models
can be met, while keeping accuracy as high as possible. The constraints for
model A and model B are 65 ms and 55 ms, respectively. Model A runs at the
highest level at the beginning, and model B runs at level 5. To match the
latency constraints, model A switches to level 5, but model B is still slower
than the constraint, so model B switches to level 4: leaving both models
meeting their constraints.

##  5 Conclusions

This paper has proposed Dynamic-OFA, a novel dynamic DNN approach. Dynamic-OFA
brings together two concepts: the OFA model and dynamic DNNs, which provide
solid improvements over the previous state-of-the-art. Dynamic-OFA does not
require any additional dynamic DNN model retraining and has the architecture
flexibility for all heterogeneous computing elements with a share backbone. We
empirically evaluated our approach against the start-of-the-art, our results
show that our approach can provide better accuracy-latency trade-offs, up to
3.5x (CPU), 2.4x (GPU) faster for similar ImageNet Top-1 accuracy, or 3.8%
(CPU), 5.1% (GPU) higher accuracy at similar latency.

Figure 8: Runtime management of two concurrently executing Dynamic-OFA models,
each with its own latency constraint (dashed lines).

Dynamic-OFA is a general approach for building dynamic DNNs, and the backbone
network could be any super-networks trained by the OFA training pipeline. Our
future work will investigate other applications such as network for IoT
devices [12], transformers for natural language processing (NLP) tasks [18],
generative adversarial networks (GANs) [11], 3D DNNs [17], etc.

##  6 Acknowledgements

This work was supported in part by the Engineering and Physical Sciences
Research Council (EPSRC) under Grant EP/S030069/1. Experimental data can be
found at: https://doi.org/10.5258/SOTON/D1804. Code is available open-source
on https://github.com/UoS-EEC.

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# The First Detection of CH2CN in a Protoplanetary Disk

Alessandra Canta Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Richard Teague Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Romane Le Gal Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France  IRAM, 300 rue de la piscine, F-38406 Saint-Martin d’Hères, France  Karin I. Öberg Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA

###### Abstract

We report the first detection of the molecule cyanomethyl, CH2CN, in a
protoplanetary disk. Until now, CH2CN had only been observed at earlier
evolutionary stages, in the giant molecular clouds TMC-1 and Sgr 2, and the
prestellar core L1544. We detect six transitions of ortho-CH2CN towards the
disk around nearby T Tauri star TW Hya. An excitation analysis reveals that
the disk-averaged column density, $N$, for ortho-CH2CN is $(6.3\pm 0.5)\times
10^{12}$ cm-2, which is rescaled to reflect a 3:1 ortho-para ratio, resulting
in a total column density, $N_{\rm tot}$, of $(8.4\pm 0.7)\times 10^{12}$
cm-2. We calculate a disk-average rotational temperature, $T_{\rm{rot}}$ =
$40\pm 5$ K, while a radially resolved analysis shows that $T_{\rm{rot}}$
remains relatively constant across the radius of the disk. This high rotation
temperature suggests that in a static disk and if vertical mixing can be
neglected, CH2CN is largely formed through gas-phase reactions in the upper
layers of the disk, rather than solid-state reactions on the surface of grains
in the disk midplane. The integrated intensity radial profiles show a ring
structure consistent with molecules such as CN and DCN. We note that this is
also consistent with previous lower-resolution observations of centrally
peaked CH3CN emission towards the TW Hya disks, since the observed emission
gap disappears when convolving our observations with a larger beam size. We
obtain a CH2CN/CH3CN ratio ranging between 4 and 10. This high CH2CN/CH3CN is
reproduced in a representative chemical model of the TW Hya disk that employs
standard static disk chemistry model assumptions, i.e. without any additional
tuning.

astrochemistry — protoplanetary disk — pre-biotic astrochemistry — surface
ices — T Tauri stars

modules = all, formula = mhchem

##  1 Introduction

Figure 1: Spectrum of the observed CH2CN transitions. The 6 brightest peaks
are shown with their quantum numbers. The noise is calculated to be 2.9 mJy,
with the horizontal dashed lines showing 1, 2 and $3~{}\sigma$ levels.

The composition of planets, and therefore their suitability to host biological
life, is largely dictated by the physical structure and chemical composition
of ice and dust grains in the protoplanetary disks surrounding young stars
(e.g., Nomura et al., 2016; Andrews et al., 2012). Nitriles are of specific
interests since they have, in fact, often been identified as key precursors in
the synthesis of RNA and amino acids (Powner et al., 2009; Patel et al.,
2015). Observations of comets and meteors reveal that molecules such as HCN
and CH3CN were present in the chemical environment of our early Solar Nebula,
and were likely available for prebiotic reactions (Mumma & Charnley, 2011;
Altwegg et al., 2020). Nitrile existence in both our early Solar system and in
the disks of young stars has implications for our understanding of the
trajectory of the organic chemistry as it evolves during planet formation.
This is important to estimate the organic inventory on newly-formed planets
and to determine what factors contribute to the chemical habitability of
nascent planets (Bergner et al., 2018).

HCN and CN were among the first compounds to be observed in a protoplanetary
disk, and since their detection in 1997 over 25 new species have been
identified in disks (Kastner et al., 1997; McGuire, 2018). However, it was not
until the advent of ALMA that more complex molecules such as acetonitrile,
CH3CN, and methanol, CH3OH, were observed (Öberg et al., 2015; Walsh et al.,
2016). Other nitriles that have been detected include HNC and cyanopolyyne,
HC3N, as well as various isotopologues of HCN and CN, including H13CN, HC15N,
DCN and C15N (Dutrey et al., 1997; Chapillon et al., 2012; Guzmán et al.,
2015; Qi et al., 2003; Hily-Blant et al., 2017). Together these nitriles
constitute a substantial fraction of the detected organics in disks, which
points to an interesting variations in chemical composition at different
stages of a star’s life: the early stellar stages seem to have significantly
less oxygen-rich species than protoplantary disks (Oberg & Bergin, 2020). This
could be as a result of the oxygen being locked up in molecules such as CO and
H2O and thus unavailable for chemistry, or of a generally oxygen-poor grain-
surface chemistry (Oberg & Bergin, 2020).

The formation of complex organic molecules (COMs) in protoplanetary disks can
happen via two distinct pathways: through grain-surface or gas-phase
reactions. Freeze-out reactions on the surface of grains seem to be the
greatest contributors to the abundance of COMs in disks, and they involve the
absorption of UV radiation from both the central star and the interstellar
radiation field (ISRF), formation of radicals and subsequent rearrangement
into more complex organics (Oberg, 2016). Gas-phase reactions are dominated by
a variety of reactions including radiative association (molecules collide and
emit a photon), neutral-neutral and neutral-ion reactions and dissociative
recombination, where a positive ion recombines with an electron. This was
found to be the main reaction pathway for the formation of CH3CN in TW Hya and
of CH2CN in the protostellar core L1544 (Loomis et al., 2018a; Vastel et al.,
2015). Whether this is also the case for CH2CN in disks has not previously
been possible to evaluate since there have been no reported observations of
this molecule.

In this paper, we report the first observation of the molecule CH2CN (in its
ortho state) in a protoplanetary disk, specifically in the disk around the
nearby T Tauri star TW Hya. This molecule has previously been observed in
diffuse molecular clouds SgrB2 and TMC-1, in the pre-stellar core L1544, and
in the circumstellar envelope surrounding the star IRC +10216 but never in a
protoplanetary disk (Vastel et al., 2015; Irvine et al., 1988; Agúndez et al.,
2008). Liszt et al. (2018) also attempted to place upper limits on the
abundance of CH2CN in diffuse molecular gas. TW Hya is a $\sim 0.8M_{\odot}$
solar-like T Tauri star that is often used in astrochemical observations
because of its proximity (60.1 pc Bailer-Jones et al., 2018) and its face-on
orientation, $i\approx 5\arcdeg$, which allows for easier interpretation of
the data. The details of the detection, the data reduction and the
observational results are outlined in §2. In §3, we proceed by using a disk-
averaged rotational diagram analysis to obtain the total column density for
ortho-CH2CN and an excitation temperature. We also perform a radially resolved
analysis to obtain radial profiles for both these parameters. In §4 we compare
our findings to a chemical model of TW Hya, which we use to complement our
discussion of the chemistry of both CH3CN and CH2CN. Finally, we present a
summary of our findings in §5.

Figure 2: Integrated intensity images of individual observed transitions. All
the panels share the same intensity scale. The synthesised beam is shown in
the bottom left corner. We find $\sigma$ to be $0.06~{}{\rm
mJy~{}beam}^{-1}~{}{\rm km~{}s}^{-1}$.

##  2 Observations

These observations were taken as part of an ALMA project 2018.A.00021 (PI:
Teague), designed to observe 12CO (2-1), CS (5-4) and CN (2-1) emission at
high spatial and spectral resolution from the disk around TW Hya (J2000 R.A.
11h01m51.905s, Decl. -34d42m17.03s). The correlator set-up included a single
frequency divided mode (FDM) window centered on 241.5 GHz to provide continuum
on which to self-calibrate. In this window six strong emission lines were
detected and identified as CH2CN lines, and a single C^34S line.

###  2.1 Data Reduction

Table 1: Observed CH2CN Transitions

$N^{\prime}-N^{\prime\prime}$ | $K_{a}$ | $K_{c}$ | $J^{\prime}-J^{\prime\prime}$ | $\nu_{0}$ | $g_{u}$ | $A_{ul}$ | $S_{\rm ij}\mu^{2}$ | $E_{\rm upper}$ | Int. Flux Density
---|---|---|---|---|---|---|---|---|---
|  |  |  | (GHz) |  | $({\rm s}^{-1})$ | $({\rm D}^{2})$ | (K) | $({\rm mJy~{}km~{}s}^{-1})$
12-11 | 0 - 0 | 12 - 11 | 25/2 - 23/2 | 241.3335423 | 234 | $9.62\times 10^{-4}$ | 1376.0 | 75 | $126.1\pm 6.0$
12-11 | 0 - 0 | 12 - 11 | 23/2 - 21/2 | 241.3458390 | 216 | $9.59\times 10^{-4}$ | 1265.6 | 75 | $109.3\pm 6.0$
12-11 | 2 - 2 | 11 - 10 | 23/2 - 21/2 | 241.3860255 | 216 | $9.33\times 10^{-4}$ | 1230.5 | 128 | $43.4\pm 6.0$
12-11 | 2 - 2 | 11 - 10 | 25/2 - 23/2 | 241.3913950 | 234 | $9.36\times 10^{-4}$ | 1337.7 | 128 | $37.8\pm 6.0$
12-11 | 2 - 2 | 10 - 9 | 23/2 - 21/2 | 241.4925510 | 216 | $9.34\times 10^{-4}$ | 1230.6 | 128 |  $25.2\pm 6.0$ aaThis peak includes two distinct transitions: the one that we observe and the another one associated with para-CH2CN. The latter has a significantly lower $A_{ul}$ ($\sim 3.5\times 10^{-6}$s-1), thus we assume that all the integrated flux observed comes from the ortho line Endres et al. (2016).
12-11 | 2 - 2 | 10 - 9 | 25/2 - 23/2 | 241.4970603 | 234 | $9.37\times 10^{-4}$ | 1337.7 | 128 | $25.2\pm 6.0$

Note. — All data for column $N$’ - $N$’ through to $E_{upper}$ was obtained
from The Cologne Database for Molecular Spectroscopy (CDMS; Müller et al.,
2001).

The data consists of six executions, two in a compact configuration with
baselines spanning 15 m – 500 m on April 4th 2019, and four in a more extended
configuration with baselines ranging between 15 m and 2.62 km on September
29th 2019. The shorter baseline executions included 41.7 minutes on-source
integration while the longer baseline executions used 51.1 minutes on-source
for a total on-source time of 4.9 hours. The quasar J1037-2934 was used for
both bandpass and flux calibration for all executions while the phase
calibration was performed with J1147-3812 for the short baseline data and
J1126-3828 for the long baseline data.

Initial calibration was performed using the standard pipeline procedure in
CASA v5.6.2 (McMullin et al., 2007). The data were then self-calibrated
following the self-calibration procedure used in the DSHARP program (Andrews
et al., 2018). In brief, all spectral windows were used, masking out any lines
in each spectral window. These line-free observations were used to solve for
the phase solutions which were then applied to the entire dataset. Prior to
combining the different executions, the executions were aligned to the same
phase center and the continuum fluxes were compared. All executions yielded
fluxes that were within 2% of one another, except for the final long baseline
execution which varied by about 10%. The final long baseline execution was
rescaled using the gaincal task such that the total flux matched that of the
other three long baseline executions. The continuum was subtracted using the
uvcontsub.

The continuum FDM window was imaged using the multi-scale CLEAN algorithm and
adopting a Briggs weighting with a robust parameter of 2 (similar to natural
weighting) yielding a synthesized beam of $0\farcs 34\times 0\farcs 32$ at a
position angle of 104.8°. The data was imaged at the native spectral
resolution of the FDM window of $1.4~{}{\rm km\,s^{-1}}$.

Figure 1 shows the six detected transitions in the form of three sets of
doublets with their associated quantum labelling. Since our emission is not
spectrally resolved (due to the spectral-set up and face on orientation of the
disk), we were unable to extract our spectra using either a matched filtering
approach (e.g., Loomis et al., 2018b) or a line-stacking approach, such as in
GoFish (Teague, 2019a). The detected transitions are also depicted as
integrated intensity (moment-0) maps in Figure 2. While four of the six lines
are fairly weak, the two at 241.3335423 and 241.3458390 GHz are robustly
detected, exhibiting a clear ring morphology. To better visualize the CH2CN
morphology, we create a high signal-to-noise map by stacking the 6 transitions
together. The resulting image is shown in the left panel of Figure 3.

For a more direct comparison with the results presented in Loomis et al.
(2018a), we create a version of the images which were smoothed to the same
spatial resolution, $1\farcs 05\times 0\farcs 83$, using the imsmooth task in
CASA. As the weaker transitions are more clearly detected in the smoothed
images, we use the smoothed images for both the radially-resolved analysis in
§3.3 and the disk-averaged analysis in §3.2. The higher spatial resolution
data is only used in the plotting of the channel maps (Figure 2) and of the
radial profile (Figure 3) to better constrain the ring morphology.

###  2.2 Observational Results

The disk-averaged integrated flux measurements reported in Table 1 were
obtained by integrating the peaks highlighted in Figure 1 over the two
independent 1.5 km/s channels showing emission out to $\sim 2.5$″ (where the
intensity reaches 0 in the right panel of Figure 3). Under the assumption of
spectrally independent pixels, the uncertainty in the integrated flux is
calculated using the equation:

$\delta M_{0}=\sqrt{\sum\limits_{i(I_{i}>0)}^{N}\sigma_{i}^{2}\cdot\Delta
v^{2}_{{\rm chan},i}},$ (1)

where $\delta M_{0}$ indicates the uncertainty in moment-zero (integrated
intensity) values; $\sigma_{i}$ is the signal-to-noise ratio in the spectrum;
and $\Delta v_{{\rm chan},i}$ is the channel width (Teague, 2019b).

We plot radial profiles to see how the integrated flux changes over the radius
of the disk. We radially bin the integrated flux from each transition into
0.05″ ($\sim$3 au)-wide bins. The beam size was 0.3″ ($\sim$18 au), therefore
our chosen bin size is a sixth of the beam major FWHM. We use a position angle
of 152$\arcdeg$ and an inclination, $i=5\arcdeg$ (Huang et al., 2018). We use
the native resolution data to plot the radial profile in Figure 3b, which
shows the ring morphology quite clearly. For the purpose of our excitation
analysis, however, we use the lower spatial resolution smoothed data, with the
radial profiles from the individual transitions using this data set shown in
Fig. 4B.

The stacked image radial profile shows a ring morphology (Figure 3a), which is
also observed in the individual transitions in Fig 2. We fitted the radial
profile in Figure 3 with a Gaussian function (Figure 3b) to infer the location
of the center of our ring and the ring width. We find the center to be at 0.4″
($\sim$24 au) and, full width at half maximum of 1.1″ ($\sim$69 au). We also
see some excess emission between 1.5″ and 2.5″ when compared to a single
Gaussian ring, however, further characterisation of this feature requires more
sensitive observations.

In contrast to the native resolution data, the smoothed data appears to be
consistent with a centrally-peaked morphology which is also seen with CH3CN
(Loomis et al., 2018a). The similar distibution suggests a chemical link
between the two molecules, which is explored further in Section 4.

Figure 3: Left panel: Integrated intensity map made from the stacked 6
transitions. The noise is calculated to be 0.14 mJy beam-1km s-1. Right panel:
the azimuthally averaged integrated intensity radial profile obtained from the
stacked native resolution data. Shaded areas represent $1\sigma$
uncertainties, where $\sigma$ represents the standard deviation in each radial
bin.

##  3 CH2CN Excitation Analysis

The rotational temperature, $T_{\rm rot}$, and the total column density of
CH2CN, N, can be constrained through the use of a rotational diagram analysis.
This implicitly assumes that the molecular excitation can be described by a
single temperature and that the molecules are in local thermodynamic
equilibrium (LTE). As we assume that the critical densities for CH2CN and
CH3CN are similar ($2.0\times 10^{6}$ cm-3 and $2.6\times 10^{6}$ cm-3 for the
transitions $J=13-12$ and $J=12-11$ at 40 K, respectively), and that chemical
models of TW Hya suggest that even atmospheric densities exceed $10^{9}$ cm-3
(e.g., Cleeves et al., 2015), it is reasonable to assume that both CH2CN would
be thermalized. As such, we can assume that the excitation temperature is
equal to the gas kinetic temperature (Shirley, 2015; Guzmán et al., 2018;
Loomis et al., 2018a). These parameters allow us to draw conclusions about the
physical conditions where CH2CN is found and its potential interactions with
molecules that exist in a similar environment.

###  3.1 Method

We start our analysis by constraining the disk-averaged rotational
temperature, $T_{\rm rot}$, and the total column density, $N$. Following
Goldsmith & Langer (1999), we obtain the rotational diagram shown in Figure 4A
by using the equation

$\ln\frac{{N_{\rm{u}}^{\rm thin}}}{g_{\rm u}}+\ln C_{\tau}=\ln N-\ln Q(T_{\rm
rot})-\frac{E_{\rm u}}{kT_{\rm rot}},$ (2)

where $N_{\rm{u}}^{\rm thin}$ is the column density of molecules in the upper
state of each transition without the correction for the optical depth effect,
$C_{\tau}$ is the optical correction factor, and $Q(T_{\rm rot})$ is the
molecular partition function and $E_{\rm u}$ is the upper state energy. We use
the molecular partition function from The Cologne Database for Molecular
Spectroscopy (CDMS; Müller et al., 2001) 111Available at
https://cdms.astro.uni-koeln.de. using a linear interpolation to obtain our
$Q$ values (Endres et al., 2016). Degeneracies due to the hyperfine structure
are included in the calculation of $Q$.

We calculate the $N_{\rm{u}}^{\rm thin}$ for each transition through the
equation:

$N_{\rm{u}}^{\rm thin}=\frac{4\pi S_{v}\Delta v}{A_{\rm ul}\Omega hc},$ (3)

where $A_{\rm ul}$ is the Einstein coefficient, $S_{\nu}$ is the disk-averaged
integrated flux density calculated as described in §2.2 and using a bin-size
of 2.5″, $\Delta$ is the width of the two channels that we used for
integration and $\Omega$ is the solid angle subtended by the source.

The optical correction factor is obtained through the equation:

$\displaystyle C_{\tau}=\frac{\tau}{1-e^{-\tau}}.$ (4)

where the optical depth, $\tau$, can be related to the upper level population
through the equation:

$\tau_{\rm ul}=\frac{A_{\rm ul}c^{3}}{8\pi\nu^{3}\Delta
v}N_{u}(e^{h\nu/kT_{\rm rot}}-1).$ (5)

Given that our emission is dominated by Doppler broadening, the line width,
$\Delta v$, is given by

$\Delta v=\sqrt{\frac{2kT_{\rm rot}}{m_{u}\,m_{H}}},$ (6)

with $m_{u}$ being the molecular weight of CH2CN (40 g/mol) and $m_{H}$ being
the mass of a hydrogen atom.

We create a model that relates $N_{u}$, $C_{\tau}$ and $\Delta v$ to Equation
2 and we derive the values of $T_{\rm rot}$ and $N$ by matching the observed
$N_{u}/g_{u}$ values. We use Scipy’s curve_fit function to minimize $\chi^{2}$
and find the best estimate of our desired parameters (Jones et al., 2001).
$\ln(N_{u}/g_{u})$ can then be plotted against the upper state energies,
$E_{u}$ to obtain Figure 4A, where the slope and the $y$-intercept of the line
respectively represent $-T_{\rm rot}^{-1}$ and $N$.

Figure 4: Panel A: ortho-CH2CN disk-averaged rotational diagram. Panel B: the
radial profiles for the six detected transitions. Shaded areas represent
1$\sigma$ uncertainties. Panels C & D: radial profiles of respectively the
CH2CN total column density and the rotational temperature. The colour dark
blue indicates radially resolved values, whereas green is used for values we
obtained from disk-averaged analysis. Shaded areas represent 1$\sigma$
uncertainties.

###  3.2 Disk-averaged Analysis

Table 2: Formation and destruction pathways for CH2CN

Reaction | Reactants |  | Products | Mechanism | Rates of Reaction
---|---|---|---|---|---
Type |  |  |  |  |  |  |  $\alpha$ $[{\rm cm^{3}~{}s^{-1}}]$ | $\beta$ | $\gamma$ | rate typeccRate formulae (1) Modified Arrhenius Equation $k(t)=\alpha(T/300)^{\beta}e^{-\gamma/T}$ (2) Ion-polar rate coefficient computed using Su-Chesnavich capture approach $k(t)=\alpha\beta(0.62+0.4767\gamma(T/300)^{0.5})$ (Woon & Herbst, 2009) (3) Photo-dissociation reaction rate $k(t)=\alpha e^{-\gamma A_{v}}$ where $A_{v}$ is the visual extinction (Draine, 1978a; van Dishoeck, 1994).
Formation |  CN |  CH3 |  -> |  H |  CH2CN | Neutral-Neutral | $1.00(-10)$ | $0.00$ | 0.00 | (1)
N |  C2H3 |  -> |  H |  CH2CN | Neutral-Neutral | $6.40(-11)$ | $0.17$ | $0.00$ | (1)
C |  CH2NH |  -> |  H |  CH2CN | Neutral-Neutral | $1.00(-10)$ | $0.00$ | $0.00$ | (1)
CH3CN+ | $e^{-}$ |  -> |  H |  CH2CN | DRaaDR = Dissociative Recombination | $2.00(-7)$ | $-0.50$ | $0.00$ | (1)
CH3CNH+ | $e^{-}$ |  -> |  2H |  CH2CN | DRaaDR = Dissociative Recombination | $8.00(-8)$ | $-0.50$ | $0.00$ | (1)
s-CNbbs- indicates solid-state reactions, i.e. reactions occurring on the surface of grains. |  s-CH2bbs- indicates solid-state reactions, i.e. reactions occurring on the surface of grains. |  -> | CH2CN | Grain Surface |  |  |  |
Destruction |  CH2CN |  C+ |  -> |  C |  CH2CN+ | Ion-Polar | $1.00$ | $1.61(-9)$ | $5.81$ | (2)
CH2CN | H${}_{3}^{+}$ |  -> |  H2 |  CH3CN+ | Ion-Polar | $1.00$ | $2.94(-9)$ | $5.81$ | (2)
CH2CN | h$\nu{}$ |  -> |  CN |  CH2 | Photodissociation | $1.56(-9)$ | $0.00$ | $1.95$ | (3)
CH2CN | h$\nu{}$ |  -> |  CH2CN+ |  e- | Photodissociation | $5.29(-10)$ | $0.00$ | $3.11$ | (3)
CH2CN |  |  -> | s-CH2CNbbs- indicates solid-state reactions, i.e. reactions occurring on the surface of grains. | Freeze-out |  |  |  |

Note. — Table showing all the possible formation and destruction pathways of
CH2CN based on the astrochemical disk model by Le Gal et al. (2019). The rates
of reactions are reproduced from the Kinetic Database for Astrochemistry
available at http://kida.astrophy.u-bordeaux.fr (Wakelam et al., 2012).

In this paper, we will denote the column density of ortho-CH2CN using N,
whereas the total column density of CH2CN (including both the ortho and the
para isomers) will be indicated using $N_{\rm tot}$. We obtain a disk-averaged
rotational temperature of $40\pm 5$ K and a disk-averaged total column
density, $N$, of $(6.3\pm 0.5)\times 10^{12}$ cm-2 for ortho-CH2CN. As
described in Le Gal et al. (2017), for a molecule containing two identical
Hydrogen nuclei, such as CH2CN, we expect a statistical ortho/para ratio of
3:1, and therefore we infer a total column density, $N_{\rm tot}$, of $(8.4\pm
0.7)\times 10^{12}$ cm-2. Indeed, due to the $X^{2}$B1 symmetry of the ground
electronic state of CH2CN, the ortho-to-para ratio of CH2CN decreases toward
the statistical 3:1 value with increasing temperature as NH2 (Le Gal et al.,
2016). CH2CN is a heavier molecule than NH2, therefore, its ortho-to-para
ratio will reach the statistical ratio for lower temperatures than NH2. Thus,
according to Fig. 1 of Le Gal et al. (2016), the relatively high rotational
temperature we derived confirms that it is reasonable to consider a 3:1
statistical ortho-para ratio for CH2CN. Given this ratio, we can calculate the
expected para column density and using this value and the the expected
integrated intensity of the para lines that we do not detect (located at
241.353 and 241.381).

Finally, having obtained $T_{\rm rot}$, we calculate the optical depth,
$\tau$, of our transitions. In all cases, we obtained a value of $\tau\ll 1$,
with values of range $4\times 10^{-4}$ to $3.4\times 10^{-3}$. Therefore, our
detected transitions were of negligible optical thickness. In addition to
this, using these parameters we can calculate the predicted strength of the
lines that we do not detect. For the transitions at 241.353 and at 241.382
(which belong to para-CH2CN) we obtain integrated intensities of 1.26 and 1.37
mJy km s-1, which are significantly below our calculated intensities, thus
confirming that we would not have been able to detect these lines with our
spectral set-up. The disk-averaged values obtained in Section 3.1 are
calculated out to a radius of 1.75″ as we can see from Figure 4b that at this
radius, all six transitions are detected. As a comparison, we calculate an
average $T_{\rm rot}$ and $N$ for the outer region of the disk where the
weaker emission lines are almost completely lost. For this, we integrated out
to a radius of 2.5″. For this outer region, we find a total column density of
$(3.5\pm 0.3)\times 10^{12}$ ($(4.7\pm 0.4)\times 10^{12}$ for ortho-CH2CN)
cm-2, and a rotational temperature of $38\pm 5$ K. Comparing the total column
density that we obtained out to a radius 1.75″ to that out to 2.5″ confirms
that the outer radii are contributing very little to the total column density,
as we would expect from the radial profiles in Figure 4B and in the right
panel of Figure 3.

###  3.3 Radially Resolved Analysis

To further observe the behaviour of $T_{\rm rot}$ and Ntot across the disk, we
use the radial integrated intensities from each of the transitions in Figure
4B and we repeat the steps outlined in Section 3.2 to obtain rotational
diagrams at different radii. The results are summarised in panel 4C and D.

Figure 4C shows that the column density decreases from $5\times 10^{13}$ to
$0.6\times 10^{13}$ cm-2across the radius of the disk. This is consistent with
the disk-averaged column density. The $T_{\rm rot}$ ranges between 45 and 37
K, which is consistent with the disk-averaged $T_{\rm rot}$ (40 $\pm$5 K). We
note that this is very similar to the CH3CN excitation temperature of
$32.7^{+3.9}_{-3.4}$ K in the same disk (Loomis et al., 2018a). On the other
hand, the column density of CH3CN, $1.82^{+0.25}_{-0.19}\times 10^{12}$ cm-2,
is $\sim$10 times lower than our observed CH2CN’s $N_{\rm tot}$. This is
consistent with our chemical model, as discussed in Section 4.1.

##  4 Discussion

###  4.1 CH2CN/CH3CN Ratio & Disk Models Results

We use the chemical models by Le Gal et al. (2019) to explore the predicted
column densities of CH2CN and CH3CN as a function of radius, as shown in
Figure 5a & b. The original model has been modified to fit TW Hya using the
physical parameters described in Table 3, and a standard cosmic-ray ionization
rate of $1\times 10^{-17}$ s-1. We used a C/O ratio of 1 which was the best
C/O ratio found in Le Gal et al. (2019) to reproduce the column densities of
the nitriles detected in abundance in disks. Overall, the model is in good
accordance with our observations as it predicts that CH2CN is more abundant
than CH3CN at all radii. However, the CH2CN/CH3CN ratio in the model is larger
than the ratio of $\sim$5 we found observationally. Inspecting Fig. 5a&b, we
see that the model correctly predicts the column density of CH2CN and under-
predicts that of CH3CN. This suggests that while the column density of CH2CN
is well reproduced by standard astrochemical model assumptions, there are
missing chemical pathways that lead to the formation of CH3CN. Detailed
astrochemical disk modeling effort needs to be made to further constrain the
main reaction pathways driving both the observed CH3CN abundance and
CH2CN/CH3CN ratio in the TW Hya protoplanetary disk, but they are beyond the
scope of this paper and will be the subject of a future dedicated study. For
now, the use of chemical models allows us to confirm that a ratio of
CH2CN/CH3CN$>$1 is indeed plausible in our disk and allows us to give a more
comprehensive overview of CH2CN in TW Hya. Figure 5c&d show the abundance
distribution of CH3CN and CH2CN with respect to height and the radius of TW
Hya. Once again, we can see that CH2CN is more abundant than CH3CN at all
radii and heights in the disk and that the region of brightest emission for
both of these molecules is co-localised and between a radius of $\sim$50-100
au and a height of $\sim$10 au. This is consistent with our observations as
the model in Figure 5a shows that our observed $N_{\rm tot}$ for CH2CN arises
from a radius of $\sim$100 au.

Table 3: Physical parameters used for the disk chemistry modeling

Parameters | TW Hyaa
---|---
Stellar mass: $M_{\star}$ ($M_{\odot}$) | 0.8
Characteristic radius: $R_{\rm{c}}$ (AU) | 10
Density power-law index | 1.5
Midplane temperature at $R_{\rm{c}}$ (K) | 20
Atmosphere temperature at $R_{\rm{c}}$ (K) | 104
Surface density at $R_{\rm{c}}$ (g cm-2) | 0.79
Temperature power-law index | 0.55
Vertical temperature gradient index | 2
UV Fluxb at $R_{\rm{c}}$ (in Draine (1978b)’s units) | 3400

  * a Andrews et al. (2012)

  * b Herczeg et al. (2004)

###  4.2 CH2CN Chemistry

Figure 5: Panel a) & b): Total column densities of CH2CN (a) and CH3CN (b) as
a function of radius, predicted by the chemical models of Le Gal et al. (2019)
that we adapted to TW Hya as described in §4.1. The column density radial
profile derived from the observations presented in Sect. 3.3 for CH2CN (a)
from the observation of CH3CN obtained by Loomis et al. (2018a) (b) are also
shown. Panel c) & d): The abundance of CH2CN and CH3CN as a function of radius
and height. The region of highest emission for both molecules is located
between $\sim 50-100$ au and at a height of $\sim 10$ au.

Formation of molecular species in protoplanetary disks can occur via two
distinct routes: gas-phase and grain-surface reactions, and in the case of
CH2CN both pathways are a priori possible. Based on the astrochemical disk
model of Le Gal et al. (2019), several formation and destruction pathways are
involved in the chemistry of CH2CN. These are summarized in Table 2.

As previously mentioned, CH3CN and CH2CN are found to have similar excitation
temperatures and morphologies, therefore it is unsurprising that they also
share a comparable chemistry. Both CH3CN and CH2CN share a very similar grain-
surface formation chemistry where both can be formed via solid state reactions
with CN as follows,

(7)

(Herbst, 1985). From these reactions we can infer that the relative formation
rates of CH3CN and CH2CN will depend on the relative abundance of CH2 and CH3
radicals on the grain surface. The similarities extend beyond these grain-
surface reactions, as these molecules share a common gas-phase reaction
pathway. The electronic dissociative recombination of CH3CNH+ has been
identified as the dominant contributor to the gas-phase formation of both
CH3CN and CH2CN (Vastel et al., 2015; Loomis et al., 2018a). The full reaction
route, including the formation of the ion intermediate, is as follows:

(8) (9)

(Herbst & Leung, 1990). This does not seem to be the main formation pathway
for CH2CN in either the model or in ‘reality’ since the electronic
dissociative recombination (DR) of CH3CNH+ leads to a branching ratio of
$\sim$1.5 in favour of CH3CN according to the Kinetic Database for
Astrochemistry222http://kida.astrophy.u-bordeaux.fr (see Table 2) while we
find that CH2CN $\gg$ CH3CN. The branching ratio for this reaction is
arbitrary and it is loosely based on the fact that the energy in the CH3CN + H
channel is greater than the secondary dissociation energy in the CH2CN + 2H
channel (Wakelam et al., 2012). In light of this, we suggest that the grain
surface formation pathway is the most important source of CH2CN in disks. A
similar conclusion was made with respect to CH3CN by (Le Gal et al., 2019) and
(Loomis et al., 2018a). However, grain-surface reactions are poorly
constrained both theoretically and experimentally and therefore more
experimental studies need to be carried out to verify the significance of this
solid-state reaction. Finally we note that CH2CN can also form through several
neutral-neutral reactions (Table 2), whose possible contributions also warrant
further investigation.

###  4.3 Morphology

As mentioned in Section 2.2, CH2CN is found in a ring morphology when imaged
at the native resolution of $\approx 0.3\arcsec{}$. The ring morphology is not
unique to CH2CN as CN and C2H are also analogously distributed in TW Hya,
however, their rings peak at considerably larger radii at $\sim$ 45 au (0.75″)
and 60 au (1″), respectively (Bergin et al., 2016; Teague & Loomis, 2020).
These nested rings of potentially chemically related species provide clues as
to what processes are regulating the abundance of these molecules. One
possible source of rings is the increased penetration of UV radiation beyond
the edge of the dust continuum, leading to more photo-desorption of frozen out
molecules from grain surfaces (Cleeves, 2016). However, the edge of the dust
continuum is at $\sim 60$ au, which is inconsistent with the peak of the CH2CN
ring ($\sim 24$ au) therefore this is not a plausible explanation for the
morphology of CH2CN.

The chemical model results for CH2CN shown in Figure 5 seem to replicate the
morphology that we observed in Figure 4C. This suggests the presence of a
‘Goldilocks zone’ for the dominant formation pathway where the observed
morphology can be attributed to the balance between formation and destruction
reactions under fiducial disk conditions. Within this zone of the disk, the
conditions may be particularly favourable for the production of CH2CN (i.e.
optimal UV radiation flux or temperature of the disk molecular layer).

Another possible factor that could shape the distribution of CH2CN is enhanced
destruction in the inner disk due to reactions with gas-phase carbon and
oxygen atoms. Chemical modeling by Du et al. (2015) has shown that C and O
depletion is needed to reproduce the observed molecular abundances of CO and
H2O in TW Hya. Further, nitrile column density is enhanced by $\sim$2 orders
of magnitude where C and O depletion takes place (Du et al., 2015). One disk
location that may present a rapid change in the C and O abundance is the CO
snowline, where CO ice sublimates back into the gas-phase. The CO snowline
zone in TW Hya is found at 17-30 au (Schwarz et al., 2016; Qi et al., 2013).
We find that CH2CN peaks at $\sim$ 24 au, so the CO snowline and the CH2CN
peak may reflect the presence of C- and O-depleted gas just exterior to the CO
snowline. Exterior to this region, carbon and oxygen would primarily exist as
CO ice, therefore not interfere with nitrile chemistry.

##  5 Summary

We have presented the first detection of CH2CN (cyanomethyl) in a
protoplanetary disk. The 6 emission lines detected correspond to 6 transitions
of CH2CN in its ortho state. We find a disk-averaged rotational temperature of
$40\pm 5$ K and a disk-averaged total column density of $(6.3\pm 0.5\times
10^{12}$ cm-2. Assuming a thermal ortho/para ratio of 3:1, we infer a total
CH2CN column density of $(8.4\pm 0.7)\times 10^{12}$ cm-2. The molecule is
observed to be in a ring whereas at lower spatial resolutions it presents a
centrally-peaked profile consistent with previously reported CH3CN morphology.
Comparison with CH3CN total column density shows that CH2CN is 10 times more
abundant. This result is consistent with chemical models for TW Hya, where
CH2CN$\gg$CH3CN at all disk radii. We identify possible pathways that
contribute to the formation and destruction of this molecule and we suggest
that grain-surface reactions are the likely formation pathway for both CH2CN
and CH3CN.

We thank the anonymous referees for their valuable input in clarifying the
results presented in this paper. We also wish to thank Ryan Loomis for sharing
radial profiles of CH3CN. This paper makes use of the following ALMA data:
ADS/JAO.ALMA#2018.A.00021. ALMA is a partnership of ESO (representing its
member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST
and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the
Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and
NAOJ. The National Radio Astronomy Observatory is a facility of the National
Science Foundation operated under cooperative agreement by Associated
Universities, Inc. AC acknowledges funding from the Origins of Life
Initiative. This work was supported by an award from the Simons Foundation
(SCOL # 321183, KÖ).

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