# Time-Space Transformers for Video Panoptic Segmentation

Andra Petrovai
Technical University of Cluj-Napoca
Cluj-Napoca, Romania
<EMAIL_ADDRESS>Sergiu Nedevschi
Technical University of Cluj-Napoca
Cluj-Napoca, Romania
<EMAIL_ADDRESS>
###### Abstract

We propose a novel solution for the task of video panoptic segmentation, that
simultaneously predicts pixel-level semantic and instance segmentation and
generates clip-level instance tracks. Our network, named VPS-Transformer, with
a hybrid architecture based on the state-of-the-art panoptic segmentation
network Panoptic-DeepLab, combines a convolutional architecture for single-
frame panoptic segmentation and a novel video module based on an instantiation
of the pure Transformer block. The Transformer, equipped with attention
mechanisms, models spatio-temporal relations between backbone output features
of current and past frames for more accurate and consistent panoptic
estimates. As the pure Transformer block introduces large computation overhead
when processing high resolution images, we propose a few design changes for a
more efficient compute. We study how to aggregate information more effectively
over the space-time volume and we compare several variants of the Transformer
block with different attention schemes. Extensive experiments on the
Cityscapes-VPS dataset demonstrate that our best model improves the temporal
consistency and video panoptic quality by a margin of 2.2%, with little extra
computation.

##  1 Introduction

Video panoptic segmentation [22] extends panoptic segmentation [24] to video
and provides a holistic scene understanding across space and time by
performing pixel level segmentation and instance level classification and
tracking. The task has a broad applicability in many real-world systems such
as robotics and automated driving, which naturally process video streams,
rather than single frames. Video panoptic segmentation is more challenging
than its image-level counterpart, because it requires temporally consistent
inter-frame predictions.

Figure 1: High level overview of our VPS-Transformer network, which processes
video frames and outputs panoptic segmentation and consistent instance
identifiers. We propose a Transformer based video module to model temporal and
spatial correlations among pixels from the current frame features and past
frames features. Instance tracking is performed by warping the previous
panoptic prediction with optical flow and associating the instance IDs with
the current instance segmentation.

Video sequences provide rich information, such as temporal cues and motion
patterns, which could be exploited for more accurate and consistent panoptic
segmentation. Although we can clearly benefit from modeling the temporal
correlations between frames, new challenges arise when processing video data.
We can generally assume a high level of temporal consistency across
consecutive frames, however, this could be broken by occlusions and new
objects caused by fast scene evolution. In this context, temporal information
should be carefully used such that we avoid introducing outdated information
in our predictions [29, 21]. On the other hand, extending a single frame
solution to process multiple video frames often incurs a high computational
cost [22], causing overhead in training and inference. However, striking a
balance between efficiency and accuracy is important from a practical point of
view.

Unlike panoptic image segmentation [24], which has received increased
attention from the research community [23, 9, 19], video panoptic segmentation
[22] is a newly introduced task that has been less studied. Existing methods,
such as VPSNet [22] and ViP-DeepLab [34] focus on improving the panoptic
segmentation quality, however with a high computational cost. To increase
consistency among frames, VPSNet [22] designs a temporal fusion module based
on optical flow, that aggregates five neighboring past and future warped
features. In contrast, our network is more accurate and efficient, although it
operates in an online fashion: only the current frame is processed, while the
Transformer block reads past features from the memory and attends to relevant
positions in order to provide an enhanced representation. ViP-DeepLab [34]
models video panoptic segmentation as concatenated image panoptic segmentation
and achieves the state-of-the-art for this task. Compared to this work, we
explicitly encode spatio-temporal correlations for a boost in performance and
obtain competitive results with a more lightweight network.

As shown in Figure 1, we propose a novel video panoptic segmentation approach
by extending the single frame panoptic segmentation network Panoptic-DeepLab
[9] with a Transformer video module and a motion estimation decoder. Our
module, inspired by the pure Transformer block [38], refines the current
backbone output features by processing the sequence of spatio-temporal
features from current and past frames. As we strive to develop an efficient
network, we design a lightweight variant of the pure Transformer block that is
faster than the original implementation [38]. We also present several ways to
factorize the attention operation of the Transformer over space and time and
compare their accuracy and efficiency in extensive ablation studies. Given the
enhanced feature representations from the Transformer module, three
convolutional decoders recover the spatial resolution of the input image and
multiple heads perform semantic segmentation, instance center prediction,
instance offset regression and optical flow estimation. To ensure consistent
instance identifiers for the same instance across frames, we implement a
simple tracking module [27, 43] based on mask propagation with optical flow
and instance ID association between warped and predicted instance masks based
on the class label and the intersection over union. Our video panoptic
segmentation network is designed to achieve a good trade-off between speed and
accuracy. Each newly introduced module is carefully designed to preserve the
efficiency of the system. The proposed network can be trained in a weakly
supervised regime with a sparsely annotated dataset, since it does not require
labels for previous frames. We perform extensive experiments on the
Cityscapes-VPS [22] dataset and demonstrate that the proposed methods improve
both image and video-based panoptic segmentation.

To summarize, our main contributions are the following:

  1. 1.

We propose a novel video panoptic segmentation network with a pure
Transformer-based video module that applies spatial self-attention and
temporal self-attention on sequences of current and past image features for
more accurate panoptic prediction.

  2. 2.

We extend our panoptic segmentation network with an optical flow decoder that
is used for instance mask warping in the tracking process. Instance ID
association between warped and predicted panoptic segmentation ensures
temporally consistent instance identifiers across frames in a video sequence.

  3. 3.

We propose a lightweight Transformer module inspired by the pure Transfomer
architecture with three different designs of the attention mechanism: space
self-attention, global time-space attention and local time-space attention. We
compare the variants in extensive experiments.

  4. 4.

We perform extensive experiments on the Cityscapes-VPS dataset and demonstrate
that the proposed modules increase accuracy and temporal consistency, without
introducing significant extra computational cost.

##  2 Related Work

Panoptic Segmentation Proposal-based approaches employ an object detector for
generating bounding box proposals, which are further segmented into instances.
Semantic segments are usually merged with instance masks with a post-
processing step that solves overlaps and semantic class conflicts. There are
many works [23, 32, 25] that build their networks on top of the two-stage
instance segmentation framework Mask-RCNN [16], which is extended with a
semantic segmentation head. UPSNet [44] proposes a parameter-free panoptic
segmentation head supervised with an explicit panoptic segmentation loss.
Seamless Segmentation [33] introduces a lightweight DeepLab-inspired
segmentation head [8] and achieves high panoptic quality. Motivated by the
recent success of one-shot detectors, FPSNet [11] adopts RetinaNet [26] for
proposal generation, and achieves fast inference speed. [42] extends RetinaNet
with a semantic segmentation head and a pixel offset center prediction head,
which is used for clustering pixels into instances. DenseBox [19] proposes a
parameter-free mask construction method that reuses bounding box proposals
discarded in the Non-Maxima Suppression step. Panoptic DeepLab [9] achieves
state-of-the-art results on multiple benchmarks with a bottom-up network that
performs semantic segmentation and instance center regression. Axial-DeepLab
[39] builds a stand-alone attention model with factorized self-attention along
the height and width dimension.

Figure 2: We introduce a Transformer video module between the backbone and the
decoders for more accurate prediction. We propose three variants of the module
with various attention mechanisms: space attention, global time-space
attention and local time-space attention.

Video Panoptic Segmentation This task has been recently introduced in [22],
which also proposes the baseline VPSNet network. VPSNet is built on top of the
two-stage detector Mask R-CNN [16] and the panoptic segmentation network
UPSNet [44]. The authors propose a module for pixel level fusion by gathering
feature maps from the previous and next five frames, aligning them using
optical flow and fusing them with spatio-temporal attention. Tracking is
performed at object level with a MaskTrack head [45]. ViP-DeepLab [34] is a
newly proposed network for video panoptic segmentation, which also performs
monocular depth estimation. The authors extend the Panoptic-DeepLab [9]
network with a next-frame instance decoder which regresses the next-frame
instance center offsets. A stitching algorithm based on mask IoU between
region pairs is used for propagating instance identifiers from one frame to
another. Concurrent work [43] explores various tracking methods for panoptic
video segmentation such as IoU association, SORT association [5] and mask
propagation with an external optical flow network [37].

Transformer The Transformer network has been proposed in [38] for the task of
machine translation. Recently, the Transformer architecture has been adopted
for computer vision tasks. DETR [6] employs the encoder-decoder architecture
of the Transformer for object detection and demonstrates on par accuracy and
run-time performance with the state-of-the-art CNN object detectors [16]. ViT
[13] applies Transformers on image patches and shows that when trained on
large-scale datasets, it achieves state-of-the-art results for the task of
image classification. Recently, the Transformer network has been adopted for
the task of semantic segmentation [46]. Self-attention with convolutional
layers [41, 20] has been explored in several works as a mechanism to increase
accuracy for image-level recognition and temporal self-attention has been
proposed for video object segmentation [30] and semantic segmentation [31]. In
[2, 4], the authors explore several designs of a spatio-temporal Transformer
network for video classification. Motivated by the recent success of the pure
Transformer architecture in several tasks, especially video classification, we
propose a novel Transformer-based video module in the context of a hybrid
video panoptic segmentation network, where it can successfully model temporal
dependencies between frames.

##  3 Video Panoptic Segmentation Network

We propose a video panoptic segmentation network, named VPS-Transformer, by
extending Panoptic-DeepLab [9] to perform panoptic segmentation and tracking
of instances. In this section, we present the network architecture and
implementation details.

###  3.1 Model Architecture

Figure 3: The three attention schemes studied in this work. We present an
example with three consecutive frames. The query token, shown in orange in
frame $k$, attends to other tokens in the space and time dimension. When the
space-time attention is factorized, we use blue for space and violet for time.
We increase the granularity for visualization, but in practice each location
from the sequence of features acts as a query.

Baseline We build our solution on top of the bottom-up image panoptic
segmentation network Panoptic-DeepLab [9]. The network regresses instance
offsets and predicts semantic segmentation and instance centers. Class-
agnostic instance segmentation is obtained by grouping foreground pixels to
their closest center based on the predicted offsets. The final panoptic
segmentation is generated by merging the semantic segmentation with the class-
agnostic instance segmentation results by using a majority voting principle.
The network consists of a shared backbone, dual decoders for semantic and
instance segmentation and three heads for semantic, instance center and
instance offset regression. We change the original implementation by reducing
the output stride of the backbone from 16 to 32, and achieve similar panoptic
quality and faster inference speed.

Lightweight Transformer Video Module Our network sequentially processes frames
from a video sequence. A video module, plugged in between the backbone and the
decoder, aggregates features of past frames in order to improve the current
feature representation. We denote the past frames as memory frames, while the
current frame is denoted as the query frame. Our video module is inspired from
the original Transformer architecture [38] with attention and self-attention
mechanisms, as well as a multi-layer perceptron (MLP).

The compute of the self-attention block scales quadratically with the size of
the input as observed in [36, 35], especially when processing high dimensional
data. To reduce the complexity of the Transformer block, we wrap the
Transformer between two pointwise convolutions in order to first reduce the
number of channels and then to recover the original dimensionality, as seen in
Figure 2. In practice, we apply a $1\times 1$ convolution to the backbone
output features and map the number of channels from $C=2048$ to $d=1024$ and
vice-versa. As the Transformer operates on sequences of input tokens of size
$B\times N\times d$, we reshape the input query features F
$\in\mathbb{R}^{B\times H\times W\times d}$ to a sequence of flattened tokens
f $\in\mathbb{R}^{B\times HW\times d}$, where the first dimension is the batch
dimension, the second one is the sequence length and the last one represents
the embedding dimension. $B$ is the batch size, while $H$ and $W$ are the
height and width of the feature maps. In the global time-space attention
block, we map the memory features from the previous $T$ frames, M
$\in\mathbb{R}^{B\times T\times H\times W\times d}$ into a sequence of tokens
m $\in\mathbb{R}^{B\times THW\times d}$. In the local time-space attention
design, we reshape the memory tokens to $\mathbb{R}^{BT\times HW\times d}$.
The spatial Transformer, which processes only the query frame, is further
composed of a Multi-Head Self-Attention layer, Layer Normalization [3] and a
1-hidden-layer MLP. When processing sequences of frames with the Time-Space
Attention design, we add another temporal Multi-Head Attention layer that
operates on the temporal dimension. After each attention module we employ
residual connections and layer normalization [3]. We employ the same number of
heads for all the Attention blocks. We obtain the best scores with one head
configuration. The attention layer receives as input a query and a tuple of
$(key,values)$ and returns a weighted sum of the values based on a similarity
function of the query and key. In the self-attention module, the query, key
and values come from the same source and are computed from the input f by
linear projections with learnable weights $W^{Q}\in\mathbb{R}^{d\times d}$,
$W^{K}\in\mathbb{R}^{d\times d}$, $W^{V}\in\mathbb{R}^{d\times d}$. Since the
Transformer architecture lacks positional information, which is important for
dense prediction, we inject learned position embeddings by adding them to the
key and queries. In the time-space attention, we also inject learned temporal
embeddings.

Given query, keys and values packed into Q $\in\mathbb{R}^{HW\times d}$, K
$\in\mathbb{R}^{HW\times d}$, V $\in\mathbb{R}^{HW\times d}$, the attention
operation can be formally defined as:

$\text{Attention({Q}, {K},
{V})}=\text{Softmax}\Big{(}\frac{\textbf{QK}^{T}}{\sqrt{d}}\Big{)}\textbf{V}$
(1)

A MLP with two fully connected layers and a GeLU [18] activation in between
gives the Transformer output sequence o $\in\mathbb{R}^{B\times HW\times d}$.
The inner layer dimension of the MLP is equal to $d$. Finally, the output is
reshaped to $\mathbb{R}^{B\times H\times W\times d}$ and the expansion
pointwise convolution is applied. To obtain the refined feature
representation, we apply a residual connection by adding the input, which is
then followed by a ReLU non-linearity.

Attention Variants We propose several attention schemes for the Transformer
video module, as seen in Figure 2. An example of how each scheme attends to
different temporal and spatial tokens is given in Figure 3. Spatio-temporal
attention in Transformer networks have also been recently explored for the
video classification task [2, 4].

Space Attention In this configuration the panoptic network only processes the
query frame. We employ the Transformer module with spatial self-attention to
model interactions between every position in the query frame features. This
attention module performs $(H\cdot W)$ comparisons per query location.

Global Time-Space Attention This module employs past frames features from the
memory. The attention operation is factorized along the query space and memory
time-space dimension. First, a spatial Multi-Head Self-Attention over the
query is performed. Next, a Time-Space Multi-Head Attention module extracts
global temporal correspondences between every position in the query and the
memory. The query is given by the query frame while the key and values are
given by the memory. For a query spatial position, $(H\cdot W\cdot T$)
comparisons are needed in the Time-Space Multi-Head Attention.

Local Time-Space Attention This module models spatio-temporal attention, but
more efficiently than the previous module. After the spatial Multi-Head Self-
Attention, we apply the Time Multi-Head Attention that computes attention
locally on the temporal dimension only among the tokens located at the same
spatial position. Time Multi-Head Attention performs $(H\cdot W+T)$
comparisons for each query token.

Table 1: Video panoptic segmentation results on the Cityscapes-VPS dataset
with various Transformer Video Module variants. Each cell shows
$\text{VPQ}_{k}/\text{VPQ}_{k}^{Th}/\text{VPQ}_{k}^{St}$. VPQ is averaged over
window size $k=\\{1,5,10,15\\}$. $\text{VPQ}_{1}$ is equal to PQ. We vary the
number of input frames to the Transformer Video Module from $S=0$ to $S=4$.
With $S=0$ the network processes only the current frame.

Models $\text{VPQ}_{k}/\text{VPQ}_{k}^{Th}/\text{VPQ}_{k}^{St}$ for temporal
window size $k$ VPQ Time (ms) k = 1 k = 5 k = 10 k = 15 Baseline (B) S = 0
63.0 / 52.1 / 70.9 51.1 / 27.3 / 68.5 48.0 / 21.2 / 67.5 45.9 / 17.4 / 66.7
52.0 / 29.5 / 68.4 86 B + Tracking 63.0 / 52.1 / 70.9 55.4 / 37.4 / 68.5 51.1
/ 30.9 / 67.5 49.9 / 27.0 / 66.7 55.1 / 36.8 / 68.4 100 Local Time-Space
Attention B + Transformer Video Module S = 1 64.8 / 54.9 / 72.0 52.9 / 30.4 /
69.2 49.6 / 24.0 / 68.1 47.5 / 20.4 / 67.1 53.7 / 32.5 / 69.1 97 B +
Transformer Video Module S = 1 + Tracking 64.8 / 54.9 / 72.0 55.4 / 36.5 /
69.2 51.8 / 29.4 / 68.1 49.8 / 26.0 / 67.1 55.5 / 36.7 / 69.1 111 B +
Transformer Video Module S = 2 64.7 / 54.7 / 72.0 53.1 / 30.8 / 69.3 49.8 /
24.5 / 68.2 47.7 / 20.8 / 67.2 53.8 / 32.7 / 69.1 98 B + Transformer Video
Module S = 2 + Tracking 64.7 / 54.7 / 72.0 56.2 / 38.2 / 69.3 52.8 / 31.5 /
68.2 50.6 / 27.8 / 67.2 56.0 / 38.0 / 69.1 112 B + Transformer Video Module S
= 3 64.7 / 54.7 / 71.8 53.0 / 30.9 / 69.1 49.7 / 24.4 / 68.0 47.6 / 20.5 /
67.3 53.8 / 32.6 / 69.1 99 B + Transformer Video Module S = 3 + Tracking 64.7
/ 54.7 / 71.8 57.4 / 41.1 / 69.1 54.2 / 35.0 / 68.0 52.2 / 31.3 / 67.3 57.1 /
40.5 / 69.1 113 B + Transformer Video Module S = 4 64.6 / 54.6 / 71.9 53.0 /
30.8 / 69.2 49.9 / 24.7 / 68.2 47.7 / 21.0 / 67.0 53.8 / 32.7 / 69.0 100 B +
Transformer Video Module S = 4 + Tracking 64.6 / 54.6 / 71.9 57.4 / 41.1 /
69.2 54.2 / 35.0 / 68.2 52.0 / 31.2 / 67.0 57.0 / 40.5 / 69.0 114 Global Time-
Space Attention B + Transformer Video Module S = 1 64.8 / 54.7 / 72.1 53.3 /
31.0 / 69.4 49.9 / 24.6 / 68.3 47.8 / 20.9 / 67.3 54.0 / 32.8 / 69.3 98 B +
Transformer Video Module S = 1 + Tracking 64.8 / 54.7 / 72.1 57.6 / 41.4 /
69.4 54.4 / 35.2 / 68.3 52.2 / 31.5 / 67.3 57.3 / 40.7 / 69.3 112 B +
Transformer Video Module S = 2 64.7 / 54.8 / 72.0 53.2 / 31.0 / 69.3 49.9 /
24.7 / 68.2 48.0 / 21.2 / 67.3 53.9 / 33.0 / 69.3 101 B + Transformer Video
Module S = 2 + Tracking 64.7 / 54.8 / 72.0 57.6 / 41.3 / 69.3 54.3 / 35.2 /
68.2 52.2 / 31.3 / 67.3 57.2 / 40.6 / 69.3 115 B + Transformer Video Module S
= 3 64.7 / 54.8 / 71.9 53.1 / 30.9 / 69.3 50.0 / 24.7 / 68.4 47.9 / 21.2 /
67.4 54.0 / 32.9 / 69.2 105 B + Transformer Video Module S = 3 + Tracking 64.7
/ 54.8 / 71.9 56.0 / 37.7 / 69.3 52.6 / 31.0 / 68.4 50.5 / 27.2 / 67.4 56.0 /
37.7 / 69.2 119 Space Attention B + Transformer Module S = 0 64.5 / 54.3 /
71.9 52.8 / 30.0 / 69.3 49.5 / 23.9 / 68.2 47.4 / 20.2 / 67.2 53.6 / 32.1 /
69.2 94 B + Transformer Module S = 0 + Tracking 64.5 / 54.3 / 71.9 57.2 / 40.5
/ 69.3 54.0 / 34.2 / 68.2 51.7 / 30.3 / 67.3 56.8 / 39.8 / 69.2 108

Instance Tracking. We perform instance tracking by matching predicted instance
masks with warped instance masks from the previous frame. Warping is performed
using optical flow. We implement an optical flow decoder on top of the shared
backbone. The first layer in the optical flow decoder is the correlation layer
[14] computed between the previous frame features and the current frame
features. The rest of the decoder follows a similar design to the instance
decoder. For training the optical flow in an unsupervised setting, we employ
the photometric loss that measures the photometric difference between the
warped and the actual image. For ID association we follow the following
algorithm. Given the panoptic segmentation at frame $t$ and the warped
panoptic segmentation from frame $t-1$ to frame $t$, we compute the
intersection over union (IoU) between every instance mask from the panoptic
segmentation and the warped panoptic segmentation and vice-versa. For each
instance, we store the corresponding instance with which it shares the
semantic class and has the maximum IoU. Also, the IoU should be greater than a
threshold, which we set to 0.3. Two pairs of instances are considered matched
if they point to each other, that is, they have the maximum IoU. The instance
identifier from the warped panoptic segmentation will be propagated to the
matched instance in the current frame. Instances, that have not been matched,
will receive a new instance identifier.

###  3.2 Implementation Details

We train and test our network on the Cityscapes-VPS dataset [22]. Network
training is done in three stages. In the first stage, the panoptic
segmentation network is trained for image panoptic segmentation. We employ
ImageNet pre-training [12]. For Panoptic-DeepLab, we train the network with a
batch size of 8 and we generally follow the training settings from [9]. Next,
we freeze the backbone and the semantic and instance decoders, and train the
optical flow decoder and the Transformer from scratch. The linear layers of
the Transformer video are initialized by Xavier initialization [15]. In this
stage, the network is trained using a minibatch of 8 images for a few epochs
in order to get a rough initialization. We use the Adam optimizer, polynomial
learning rate decay with a base learning rate of $1e-3$. We apply image
augmentation, such as random horizontal flipping and random scaling with a
factor in $[0.5,2.0]$ from the original resolution $1024\times 2048$. In the
third stage, we fine-tune the CNN and the Transformer with fixed batch
normalization layers. We set the learning rate to $1e-4$, and we train until
convergence. Usually, our network converges within 30 epochs.

##  4 Experiments

In this section, we provide experimental results on two datasets which provide
pixel-level annotations, Cityscapes [10] and Cityscapes-VPS [22]. We then
discuss ablation studies and compare our results with the state-of-the-art for
video panoptic segmentation.

###  4.1 Experimental Setup

Datasets Cityscapes [10] is an urban driving dataset with 5000 high-resolution
images of size 1024 $\times$ 2048 pixels. The dataset is split into 2975
training, 500 validation and 1525 test images. Cityscapes provides instance-
level annotations for 8 things classes and semantic-level annotations for 19
classes.

Cityscapes-VPS [22] extends Cityscapes [10] to panoptic video by providing
annotations to every 5 frames from the 30-frame sequence in the validation
set. The annotations in a video snippet are temporally aligned with consistent
instance IDs across frames. The dataset provides 3000, 300 and 300, training,
validation and test images.

Evaluation metrics For panoptic segmentation, we adopt Panoptic Quality (PQ),
Semantic Quality (SQ) and Recognition Quality (RQ) as defined in [24]. Video
panoptic segmentation is evaluated using the video panoptic quality (VPQ)
metric, which measures image level quality, but also the temporal consistency
across frames in a temporal window of size k={1, 5, 10, 15}. While VPQ
measures the segmentation quality of both things and stuff classes, we also
provide VPQTh and VPQSt scores, which are the VPQ averaged over the things
classes and over the stuff classes, respectively.

Inference time We report the inference time of the network by measuring the
forward pass of the network and the post-processing steps on a NVIDIA Tesla
V100 GPU with a batch size of one.

###  4.2 Ablation Study

Baseline The baseline network for our panoptic video segmentation network is
the panoptic image segmentation network Panoptic-DeepLab [9]. Since our video
panoptic segmentation network includes extra modules such as the optical flow
decoder and the Transformer video module, the inference time of the network
increases. In order to preserve the efficiency of the video network, we first
reduce the inference time of the image-level baseline network. We perform
several experiments on the Cityscapes dataset using the baseline as seen in
Table 2. The ResNet50 [17] backbone is used throughout this study. The
original architecture of Panoptic-DeepLab [9] features two ASPP modules with
depthwise convolutions for context aggregation, dual decoders, for instance
and semantic segmentation and a backbone output stride of 16. The network
achieves a PQ score of 59.7% with a reported time of the forward pass of 117
ms. By setting the output stride of the backbone to 32 and introducing another
upsampling stage in the decoder we reduce the time to 86 ms and increase PQ
with 1%. In another experiment, we remove the instance segmentation decoder
and place the instance center head and the offset regression head on top of
the semantic segmentation decoder and get 59.8% PQ. By replacing the depthwise
convolutions in the ASPP decoder with simple convolutions, we increase PQ with
0.2% and the inference time with 3 ms. The configuration that we use as the
baseline is the one with dual decoders, depthwise convolutions in the ASPP and
output stride of 32, which achieves the best trade-off between accuracy and
efficiency.

Table 2: Ablation study of the baseline panoptic image segmentation Panoptic-
DeepLab [9] network on the Cityscapes val set. We vary the number of decoders
for instance and semantic segmentation, the type of convolutions in the ASPP
context module and the output stride of the backbone.

Decoder OS PQ mIoU Time (ms) Dual + depthwise ASPP [9] 16 59.7 - 117 Dual +
depthwise ASPP (our impl.) 16 60.5 79.6 111 Single + depthwise ASPP 32 59.8
79.0 82 Single + ASPP 32 60.0 79.0 89 Dual + depthwise ASPP 32 60.7 79.3 86

Figure 4: Qualitative results on a sequence of three consecutive frames. On
the second row we present the results of the baseline panoptic image
segmentation nework, while on the third row we employ the Transformer video
module with Global Time-Space Attention with $S=1$. The encircled area with a
rider and a motorcycle is zoomed in for better visualization. While the image-
level panoptic segmentation network (second row) correctly segments the rider
and motorcycle in the first two frames, it fails to segment the motorcycle in
the third frame. We observe that the Transformer video module provides better
temporal consistency and the rider and motorcycle are correctly segmented in
all three frames (third row).

Attention Variants We compare the proposed models with variants of the
Transformer Video Module on the Cityscapes-VPS dataset in terms of accuracy
and efficiency, in Table 1. All models employ a ResNet50 backbone. The
reported time is measured before and after tracking. For tracking, we measure
the runtime of the network with an optical flow decoder, and also of the
warping and the ID association algorithms. The baseline network, without the
Transformer Video Module, performs single frame panoptic segmentation and
achieves 63.0% PQ and 52.0% VPQ. Since video panoptic quality requires
consistency between instance IDs across a video sequence, we observe a large
accuracy drop when evaluating on a larger temporal window. Our tracking module
solves instance IDs consistencies by propagating the IDs across frames and
improves VPQTh for all k greater than 1 with more than 3%. The Space Attention
model which introduces the Transformer Module with self-attention increases PQ
by 1.5%, VPQ by 1.6% and VPQ after tracking by 1.7%. In this variant, the
Transformer Module proves to be a powerful mechanism to improve the current
frame features only by spatial self-attention without using past information.
The Space Attention model incurs a moderate computational cost of 12 ms over
the baseline when processing high resolution images of 1024 $\times$ 2048
pixels. The Global Time-Space Attention models spatio-temporal correlations
between every pair of pixels from the current frame and past frames features.
This model yields the best scores among all the variants, and increases VPQ by
2% and after tracking by 2.6%, compared to the baseline. The results confirm
that meaningful information from the past can be used to improve the current
prediction. Also, the consistency between frames increases, thus enabling
better ID association between instances in consecutive frames. A global view
of the memory proves beneficial in this dense prediction task since it is not
affected by the movement of instances between two frames. In terms of
computational cost, this model requires slightly more compute than the Space
Attention model since the Transformer module features an extra Multi-Head
Attention block. The extra compute is also determined by the increased number
of input tokens, as the memory size increases. However, our best performing
model variant uses only one past frame ($S=1$) and adds 14 ms to the baseline.
The Local Time-Attention model is a slightly more efficient configuration of
the Transformer Video Module. Since the Time Attention block computes
attention temporally, among the tokens from the same spatial position, we
observe a minimal change in inference speed when processing a higher number of
frames. In order to achieve its best potential, this module requires a bigger
memory of features. For $S=3$, the Local Time-Attention model increases the
VPQ score with 1.8% and 2% after tracking compared to the baseline. For both
Time-Attention modules, during inference when every frame is processed
sequentially, we keep a memory of past backbone features in order to avoid
feature re-computation.

Memory Size In this study, we analyze how the memory size affects the Global
Time-Space Attention Transformer and the Local Time-Space Attention
Transformer. We vary the memory size from 1 to 4 past frames, corresponding to
$S=\\{1,2,3,4\\}$ as seen in Table 1. For both configurations, all memory
sizes improve the VPQ compared to the baseline from 1.8% to 2.0% before
tracking. The Local Time-Space Attention module benefits from long-term
memory, achieving the best score for a memory of 3 frames. For this
configuration, the tracking module further increases VPQ with 3.3%, suggesting
improved temporal consistency among frames. With a smaller memory of 1 or 2
frames, the tracking module has a slightly lower impact on the final score,
with an improvement of 2.2%. On the other hand, the Global Time-Space
Attention memory can model complex correlations between pixels in the query
frame and every pixel in the memory. This variant achieves the best scores
when using a short-term memory of 1 frame. For $S=2$, the accuracy remains the
same, however for bigger memories, the accuracy degrades, as the Transformer
module is not capable of making very long-range global connections.

Transformer Configuration We compare the model equipped with a pure
Transformer [38] to our lightweight variant in Table 3. The pure Transformer
follows the original implementation, but uses no dropout. Our module is faster
and provides increased video panoptic quality.

In Table 4 we present the results of the Space Attention model with different
number of channels in the Transformer module. In practice, we apply a $1\times
1$ convolution on the backbone features in order to reduce the number of
feature maps from 2048 to a lower dimension. All the other operations in the
Transformer module, including the Attention and MLP blocks keep the
dimensionality constant. We observe that projecting to a higher number of
channels increases the accuracy. Using $d=2048$ channels, we measure a time
overhead of 21 ms. However, we select $d=1024$, since it achieves a good
trade-off between accuracy and efficiency.

Table 3: The proposed lightweight Transformer module versus the pure
Transformer [38] with spatial self-attention only. We obtain higher video
panoptic quality and inference speed.

Transformer module k =1 k = 5 k = 10 k = 15 VPQ Time (ms) Pure Transformer
[38] 64.0 52.8 49.4 47.0 53.3 101 Ours 64.5 52.8 49.5 47.4 53.6 94

Table 4: The effect of varying the number of channels in the Transformer Video
Module with Space Attention. We report the total inference time of the model
and the time overhead over the baseline on the Cityscapes-VPS val set without
tracking.

Channels mIoU PQ VPQ $\Delta$T (ms) Time (ms) 512 78.9 63.8 52.7 +4 90 768
79.1 64.0 52.9 +6 92 1024 79.8 64.5 53.6 +8 94

Qualitative Results In Figure 4 we provide a comparison between the baseline
panoptic image segmentation network and the proposed video counterpart. In
this example, the baseline panoptic segmentation network is not able to
correctly segment the motorcycle in the last frame. However, by using the
Transformer video module the temporal consistency is increased and the
motorcycle is correctly segmented over time.

###  4.3 Comparison to the State-of-the-Art

In Table 5, we compare our results with the state-of-the-art on the
Cityscapes-VPS dataset [22]. VPSNet [22] and our VPS-Transformer network are
pretrained on the Cityscapes fine train dataset [10]. Although VPSNet fuses
features from 10 neighboring frames, from both past and future, we achieve
better performance with 1.2% higher VPQ using our model with ResNet50 backbone
[17]. At the same time, our network is 7$\times$ faster. With a more powerful
backbone, HRNet-W48 [40], we surpass VPSNet with 3.7% VPQ, while still being 4
$\times$ faster. ViP-DeepLab [34] is a network that extends Panoptic-DeepLab
[9] and solves the task of depth-aware video panoptic segmentation. We do not
have access to the results of the ViP-DeepLab network pretrained on the
Cityscapes fine train dataset for a fair comparison. Therefore, we present the
ViP-DeepLab results of the network pretrained on a much larger set of images,
on Mapillary Vistas dataset [28] and Cityscapes [10] train dataset with
pseudo-labels, as this is the most similar to our setting. ViP-DeepLab does
not disclose the inference time, but we approximate it to be more than 400 ms,
which is the time of its baseline panoptic image segmentation network
Panoptic-DeepLab with WR-41 [7]. ViP-DeepLab extends its baseline by adding an
ASPP module [8], a next-frame instance decoder and a next-frame instance
center regression head. Although our VPS-Transformer network with a HRNet-W48
backbone does not enjoy the same powerful pretraining, we achieve similar VPQ
scores, 59.8% vs 59.9% VPQ. However, our VPS-Transformer network runs at least
twice faster than ViP-Deeplab with an inference time of 185 ms. Our network
shows a good trade-off between speed and accuracy and the potential to be used
in real-world applications, such as automated driving.

Table 5: Comparison to state-of-the-art video panoptic segmentation networks
on the Cityscapes-VPS val set. VPSNet and our VPS-Transformer are pretrained
on the Cityscapes fine train set. ViP-DeepLab is pretrained on Mapillary
Vistas (MV) and on Cityscapes fine train set extended with pseudo-labels. ViP-
DeepLab* results are obtained by running the model provided by the authors in
[1].

Method Backbone PQ VPQ Time (ms) VPSNet [22] ResNet50 62.7 56.1 770 ViP-
DeepLab* [1] ResNet-50 60.6 52.8 - ViP-DeepLab + MV [34] WR-41 67.9 59.9 $>$
400 Baseline - Panoptic DeepLab [9] ResNet50 63.0 52.0 86 VPS-Transformer
(ours) ResNet50 64.8 57.3 112 Baseline - Panoptic DeepLab [9] HRNet-W48 66.1
55.1 168 VPS-Transformer (ours) HRNet-W48 67.6 59.8 185

##  5 Conclusions

In this paper, we introduce a novel video module inspired by a pure
Transformer block to model spatio-temporal correlation between consecutive
frames in the context of video panoptic segmentation. The proposed module can
aggregate past features from the memory in order to refine the current
panoptic prediction and increase temporal consistency. We introduce a
lightweight video module design with several attention mechanism variations
and perform extensive experiments and comparisons in terms of accuracy and
efficiency. Finally, we implement an instance tracking module with optical
flow and instance ID association. Experiments demonstrate that the our network
achieves considerably better video panoptic quality and temporal consistency
without introducing a significant extra computational cost.

## Acknowledgment

This work was supported by the SEPCA project PN III PCCF no. 9/2018.

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Vol.0 (200x) No.0, 000–000

11institutetext: 1Purple Mountain Observatory, Chinese Academy of Sciences,
Nanjing 210008, China
2Shanghai Observatory, Chinese Academy of Sciences, Shanghai 200030, China
11email<EMAIL_ADDRESS>
# A multiwavelength study of massive star-forming region IRAS 22506+5944

Yuan-Wei Wu 11 Ye Xu 11 Ji Yang 11 Jing-Jing Li 22

(Received 2001 month day; accepted 2001 month day)

###### Abstract

We present a multi-line study of the massive star-forming region IRAS
22506+5944. A new 6.7 GHz methanol maser was detected. 12CO, 13CO, C18O and
HCO+ J = 1-0 transition observations reveal a star formation complex
consisting mainly of two cores. The dominant core has a mass of more than 200
M⊙, while another one only about 35 M⊙. Both cores are obviously at different
evolutionary stages. A 12CO energetic bipolar outflow was detected with an
outflow mass of about 15 M⊙.

###### keywords:

infrared: ISM — ISM: individual (IRAS 22506+5944) — ISM: jets and outflows —
masers — stars: formation

##  1 Introduction

Massive stars play an important role in the evolution of the interstellar
medium (ISM) and galaxies; nevertheless their formation process is still
poorly understood because of large distances, high extinction, and short
timescales of critical evolutionary phases. In addition, massive stars do not
form in isolation but often in clusters and associations, which make the
environment of massive star formation regions more complex.

The 6.7 GHz transition of methanol has been found to be a particularly useful
signpost to trace massive star formation (Minier et al. [2003], Xu et al.
[2003]). On the other hand, the maser phase encompasses the outflow phase (Xu
et al. [2006]), which give us another powerful tool to study the dynamics of
massive star formations.

IRAS 22506+5944, with an infrared luminosity of 1.5$\times$104L⊙, belongs to
the Cepheus molecular cloud complex. Harju et al. ( [1993]) made a NH3 map of
this region, and found a NH3 core is coincident with the peak of the IRAS
source. Both H2O maser (Wouterloot & Walmsley [1986]) and SiO (Harju et al.
[1998]) have been detected. Although searches for 6.7 GHz methanol maser
(Szymczak et al. [2000]) show negative results, recently, we found a weak 6.7
GHz methanol maser in this region. Despite its high luminosity and FIR color
characteristics of the ultra-compact HII region, no radio emission was
detected (Molinari et al. [1998]). The distances used in literatures for this
source range from 5.0 kpc to 5.7 kpc. Here we use the value of 5.0 kpc.

In this paper, we present a multi-line study of this star-forming region. In
Sect. 2, we describe our observations. The results are given in Sect.3. We
give analysis and discussion in Sect.4, and summarize in Sect.5.

##  2 Observations

###  2.1 The Effelsberg 100 m Telescope

Observations of the methanol (CH3OH) maser were made using the Effelsberg 100
m telescope in February 2006. The rest frequency adopted for the 51-60 A+
transition was 6668.519 MHz (Breckenridge & Kukolich [1995]). The spectrometer
was configured to have a 10 MHz bandwidth with 4096 channels yielding a
spectral resolution of 0.11 km s-1 and a velocity coverage of 450 km s-1. The
half-power beam width was $\sim$ 2′ and the telescope has an rms pointing
error of 10′′. The observations were made in position switched mode. The
system temperature was typically around 35 K during our observations. The flux
density scale was determined by observations of NGC7027 (Ott et al. [1994]).
The absolute calibration for flux density is estimated to be accurate to
$\sim$ 10%. The integration time on source was 10 minutes, with a rms noise
level of $\sim$ 0.05 Jy in the spectra. The pointing position was R.A.(J2000)
22h52m36.9s, DEC.(J2000) = +60∘00′48′′.

###  2.2 The PMO 13.7 m Telescope at Delingha

The 12CO, 13CO, C18O and HCO+ J = 1-0 maps were observed with the PMO 13.7 m
millimeter-wave telescope at Delingha, China, during 2008 November. A cooled
SIS receiver was employed, and system temperatures was $\sim 250$ K during the
observations. Three AOS (acousto-optical spectrometer) were used to measure
the J = 1-0 transitions of 12CO, 13CO, C18O and the FFTS (Fast Fourier
Transform Spectrometer) were used to measure the HCO+ J = 1-0 lines. All the
observations were performed in position switch mode. The pointing and tracking
accuracy was better than 10′′. The obtained spectra were calibrated in the
scale of antenna temperature T${}^{*}_{A}$ during the observation, corrected
for atmospheric and ohmic loss by the standard chopper wheel method. The grid
spacings of the mapping observations were 30′′. Table1 summarizes the basic
information about our observations, including: the transitions, the center
rest frequencies $\nu_{rest}$, the half-power beam widths (HPBWs), the
bandwidths, the equivalent velocity resolutions ($\Delta\nu_{res}$), and the
typical rms levels of measured spectra. All of the spectral data were
transformed from the T${}^{*}_{A}$ to the main beam brightness temperature
T${}^{*}_{MB}$ scale. The absolute calibration for intensity was about 10%.

The GILDAS software package (CLASS & GREG) was used for the data reduction.

Table 1: Observation Parameters

Translation | $\nu_{rest}$ | HPBW | Bandwidth | $\Delta\nu_{res}$ | 1$\sigma$ rsma
---|---|---|---|---|---
| (GHz) | (′′) | (MHz) | (km s-1) | (K)
12CO J = 1-0 | 115.271204 | 58 | 145 | 0.37 | 0.10
13CO J = 1-0 | 110.201353 | 61 | 43 | 0.11 | 0.10
C18O J = 1-0 | 109.782182 | 62 | 43 | 0.12 | 0.09
HCO+ J = 1-0 | 89.188521 | 75 | 43 | 0.16 | 0.10

  * 1

_a_ typical value in the scale of $T_{R}^{*}$.

##  3 Results and Discussion

###  3.1 spectra

####  3.1.1 6.7 GHz CH3OH maser spectrum

The spectrum of the CH3OH maser detected in this region is shown in Fig. 1.
There are two features that are separated by about 2.2 km s-1. The stronger
feature is at the LSR (local standard of rest) velocity of -53.7 km s-1, with
a flux density of 0.52 Jy, while the other is only about 0.2 Jy. In order to
get high signal to noise spectra, we did not attempt to refine the position
and just integrated the time at the same position. Hence, the actual position
could be off by 1 arcminute.

Figure 1: Spectrum of the 6.7-GHz CH3OH maser. The spectral resolution is 0.11
km s-1.

####  3.1.2 12CO, 13CO, C18O and HCO+ spectra

Spectra of 12CO, 13CO, C18O and HCO+ are presented in Fig. 2. The spectra in
left panel come from the peak of core A (dominant core in Fig. 3). Both 12CO
and HCO+ show remarkable broad line wings, with a FW (full width) of 24 km s-1
and 6 km s-1 at 1$\sigma$ level, respectively. Spectra in the right panel are
correspondent to the peak of core B, and spectra at the conjunctive point of
the two cores are given in middle panel. Details of the line in positions of
the peak, including the line central velocities, the fitted line widths, the
bright temperatures and integrated intensity were listed in Table 2.

Table 2: Result of molecular line measurements.

Translation | VLSR | $\Delta\nu_{res}$ | T${}^{*}_{MB}$ |  $\int$ T${}^{*}_{MB}$ _d_ $\upsilon$
---|---|---|---|---
(GHz) | (km s-1) | (km s-1) | (K) | (K km s-1)
12CO J = 1-0 _a_ | -51.4 | 4.3 | 22.3 | 98.3
12CO J = 1-0 _b_ | -51.5 | 3.3 | 14.1 | 48.9
13CO J = 1-0 _a_ | -51.4 | 2.3 | 9.5 | 22.1
13CO J = 1-0 _b_ | -51.5 | 1.8 | 6.1 | 11.4
C18O J = 1-0 _a_ | -51.6 | 1.8 | 1.2 | 2.3
C18O J = 1-0 _b_ | -51.5 | 1.1 | 0.9 | 1.0
HCO+ J = 1-0 _a_ | -51.1 | 3.8 | 2.1 | 6.9
HCO+ J = 1-0 _b_ | -51.6 | 2.0 | 0.4 | 0.9

  * 1

_a_ and _b_ indicate Core A and Core B.

Figure 2: _Left panel:_ spectra at the C18O east peak. _Middle panel:_ spectra
at the conjunctive point of the two C18O cores. _Right panel:_ spectra at the
C18O west peak. The horizontal dot line is 1$\sigma$ level of each line (Table
1).

###  3.2 Mapping

####  3.2.1 13CO, C18O and HCO+ maps

Contour maps of the total integrated 13CO J = 1-0, C18O J = 1-0 and HCO+ J =
1-0 line emissions were presented in Figure 3. We used MSX E band (21$\mu$m)
image as background images of the integrated contours to compare the
distributions between gas and dust. The filled triangle denotes 3 millimeter
continuum peak (Su et al. [2004]). H2O (Wooterloot & Walmsley [1986]), SiO
(Harju et al. [1998]) and CH3OH masers were indicated with the open triangle,
star and square, respectively. The IRAS error ellipse is also marked. Contour
levels are 20% to 90% by steps of 10% of the peak emission with the exception
of HCO+ J = 1-0 line, whose contour levels are 10%, 15% and 20% to 90% by
steps of 10%.

From Figure 3, we see that both molecular line and dust emission peak are
roughly coincident with the IRAS source. 13CO and HCO+ are dominated with a
single core. 13CO shows a little elongation. C18O map clearly shows two cores
(Core A and Core B), indicating that such optical thin line traces the inner
part of a molecular cloud than other two lines. The center of the Core A with
an angular extent of (70′′, 60′′), coincides with IRAS 22506+5944 and MSX
peak, indicates that they may be the same source. The Core B has an offset of
(100′′, 60′′) at the north-west of the Core A. The size of Core A is slightly
larger than the Core B (70′′, 60′′). In order to show the kinematic relation
of the two cores we also give the channel maps of the 13CO J = 1-0 lines in
Figure 4.

Figure 3: _upper left_ : contour map of the total integrated 13CO J = 1-0 line
emission in the velocity range from -53.4 to -49.5 km s-1 overlaid on MSX E
band 21 $\mu$m image. _upper right_ : contour map of the total integrated C18O
J = 1-0 line emission in the velocity range from -52.1 to -50.8 km s-1. _lower
left_ : contour map of the total integrated HCO+ J = 1-0 line emission in the
velocity range from -52.6 to -49.5 km s-1. _lower right_ : Contour map for the
12CO J = 1-0 outflow. The blue wing (solid line) emission was integrated over
-60 to -54 km s-1 and -49 to -42 km s-1 for red wing (dashed
line),respectively. Contour levels of the plots are all from 20% to 90% by
steps of 10% of each peak emission with the exception of HCO+ J = 1-0 lines,
whose contour levels are 10%, 15% and 20% to 90% by steps of 10%. 50% contour
levels used to determine core size are plotted with thicker lines. The small
crosses in the contour plots show the measured positions and the ellipses mark
IRAS error ellipse. The filled triangles denote 3 mm continuum peak (Su et al
2004). H2O (Wooterloot & Walmsley 1986), SiO (Harju et al 1998) and CH3OH
masers are indicated with open symbols of triangle, star and square,
respectively. Figure 4: Channel maps of 13CO J = 1-0 lines with contour levels
starting at 0.4 K km s-1 and separated by 0.3 K km s-1.

We derive the physical parameters of the cores, assuming LTE (local
thermodynamic equilibrium) and with an abundance ratio $[H_{2}]/[{}^{12}CO]$ =
104. Given a distance of the source to galactic center, DGC $\sim$ 11.4 kpc
,we adopt an abundance ratio $[{}^{12}CO]/[C^{18}O]\simeq 707$ and
$[{}^{12}CO]/[{}^{13}CO]\simeq 93$ estimated from the relationship
$[{}^{16}O]/[^{18}O]=(58.8\pm 11.8)D_{GC}+(37.1\pm 82.6)$ and
$[{}^{12}C]/[{}^{13}C]=(7.5\pm 1.9)D_{GC}+(7.6\pm 12.9)$ (Wilson & Rood
[1994]). Excitation temperature is calculated Using equation 1, assuming 12CO
J = 1-0 lines are optical thick:

$T_{ex}^{*}=5.532\left\\{\ln\left[1+\frac{5.532}{\left(T_{R}^{*}\left({}^{12}CO\right)+0.819\right)}\right]\right\\}^{-1},$
(1)

13CO and C18O J = 1-0 line optical depths, $\tau$, are estimated with formulas
below:

$\tau(^{13}CO)\thickapprox-\ln[1-\frac{T_{R}^{*}(^{13}CO)}{T_{R}^{*}({}^{12}CO)}]$
(2)

$\tau(C^{18}O)\thickapprox-\ln[1-\frac{T_{R}^{*}(C^{18}O)}{T_{R}^{*}({}^{12}CO)}]$
(3)

13CO and C18O column densities are derived using equation 4 (Kawamura et al.
[1998]) and equation 5 (Sato et al. [1994]). $\tau$ and $\Delta\nu$ are
optical depth and intrinsic line width:

$N\left({}^{13}CO\right)=2.42\times
10^{14}\frac{T_{ex}\tau(^{13}CO)\Delta\nu(^{13}CO)}{1-\exp\left(-5.29/T_{ex}\right)}cm^{-2},$
(4)

$N\left(C^{18}O\right)=2.24\times
10^{14}\frac{T_{ex}\tau(C^{18}O)\Delta\nu(C^{18}O)}{1-\exp\left(-5.27/T_{ex}\right)}cm^{-2}.$
(5)

The nominal core size, _l_ , is determined by de-convolving the telescope
beam, using equation 6:

$l=D\left(A_{1/2}-\theta_{MB}^{2}\right)^{1/2},$ (6)

where _D_ is the distance (5.0 kpc), _A_ 1/2 is the area within the contour at
the half- integrated intensity of the peak and $\theta_{MB}$ is the main beam
size (see Table 1).

Core masses are computed with equation 7, where _m_ is the mass of the
hydrogen molecule, $\mu$ the ratio of total gas mass to hydrogen mass,
$\mu\approx$ 1.36 (Hildebrand [1983]), $N_{H_{2}}$ the column density of H2
and _l_ the de-convolved half power size defined above.

$M_{LTE}=\mu mN_{H_{2}}l^{2}/4$ (7)

The physical parameters derived are tabulated in Table 3.

Table 3: Physical parameters of Core A and Core B

Name | $\Delta\alphaup$ | $\Delta\delta$ | _l_ | Tex |  $\Delta\nuup$ _a_ | N(13CO) | N(C18O) | N(H2) _b_ | M(LTE)
---|---|---|---|---|---|---|---|---|---
| (arcsec) | (arcsec) | (pc) | (K) | km s-1 | (cm${}^{-2})$ | (cm-2) | (cm-2) | (M⊙)
core A | 90 | 70 | 0.9 | 26 | 1.5 | 2.7E+16 | 1.7E+15 | 2.7E+22 | 228
core B | 85 | 60 | 0.5 | 18 | 1.0 | 10.7E+15 | 7.5E+14 | 1.1E+22 | 35

  * 1

_a_ : $\Delta\nuup$ has been corrected using $\frac{\Delta V_{line}}{\Delta
V_{true}}=\sqrt{\frac{\ln\left[\tau/\ln\left(2/\left(1+e^{-\tau}\right)\right)\right]}{\ln
2}}$ ,considering line broadening due to optical depth.

  * 2

_b_ : H2 column densities were derived using 13CO column densities, assuming
$[H_{2}]/[{}^{13}CO]$ = 9.3$\times$105.

####  3.2.2 Outflows

Molecular outflows are an important signature of the earlier stage in star
formation. An outflow has been detected (Wu et al. [2005]) using the 12CO J =
2-1 line. A comparison of two different transitions will be helpful to our
better understanding of the physical properties of outflows. In Fig. 3, we
present a similar work with the 12CO (1-0) line. The red and blue lobes are
largely overlapped, while the IRAS source is located at the center of the
outflow, probably the driving source of the outflow. Morphology of the 12CO J
= 1-0 outflow is similar to that of the 12CO J = 2-1 outflow (Wu et al.
[2005]), but the former extends a larger area than the latter, spreading from
Core A to Core B.

The outflow parameters, except for 12CO column density which is derived from
Snell et al. ( [1988]), are estimated with the method of Beuther et al. (
[2002]). We assume that the gas is in LTE and the line wings are optically-
thin. Excitation temperature and $[H_{2}]/[{}^{12}CO]$ abundance ratio adopted
are the same as Sect. 3.2.1. In order to better define the kinematics of the
high gas, we divided the wings into low velocity and high velocity segments.
The physical properties, including velocity range, size, column density, mass,
momentum and kinetic energy are summarized in Table 4.

Following the method of Beuther et al. ([2002]), we obtain the characteristic
time scale, _t_ $\approx 8.1\times$ 104 yr, the mass loss rate,
$\dot{M}_{out}\approx 1.8\times 10^{-4}$M⊙ yr-1 , the mechanical force,
F${}_{m}\approx 2.2\times 10^{-3}$ M⊙ km s-1 yr-1, and the mechanical
luminosity, L${}_{m}\approx 2.2$ L⊙. The mass and kinetic energy of the
outflow are significantly larger than typical values from low-mass star
forming regions (Bontemps et al. 1996).

Table 4: Outflow properties

Compoent | Vrange | Size _a_ | N(H2) | Mass | P | Ek
---|---|---|---|---|---|---
| (km s-1) | (pc) | (cm-2) | M⊙ | (M⊙ km s-1) | (erg)
red lobe(L) | (-48.2 -44.0) | 0.8 | 1.3E+20 | 5.3 | 72 | 9.6E+45
red lobe(H) | (-44.0 -38.0) | 0.8 | 4.2E+19 | 2.1 | 29 | 3.8E+45
blue lobe(L) | (-54.7 -59.0) | 1.0 | 1.0E+20 | 6.6 | 68 | 7.1E+45
blue lobe(H) | (-59.0 -62.0) | 1.0 | 1.7E+19 | 1.0 | 11 | 1.1E+45
total | — | —- | — | 15.0 | 180 | 2.2E+46

  * 1

_a_ : size of lobes are computed using formula 6.

###  3.3 evolutionary scenario

HCO+ usually traces the geometrically thick envelope of a core, while C18O is
expected to trace the inner part of the core. The C18O map clearly shows two
cores, Core A and Core B, which likely consist of two star forming regions.
Core A has obvious star forming evidences, such as strong middle and far
infrared emission, masers and outflows, while Core B is only associated with
some cold molecular lines, indicating that core A and core B are in different
evolutionary stages, Core A at the phase of protostar core, while Core B
probably at the phase of pre-stellar core. The mass of Core A is more than 200
$M_{\odot}$, while the IRAS source has a luminosity of 1.5 $\times 10^{4}$
$L_{\odot}$. According to the relation between mass and luminosity, $L\sim
M^{3.5}$, the core mass is around one order of magnitude larger than that of
the IRAS source. This indicates there are other sources within the core, which
are not detected due to the resolution limit of the employed telescope. With a
rising steep spectrum, the IRAS colors imply that the source is deeply
embedded in a dense molecular cloud. This IRAS source could be the exciting
source of the H2O, SiO and CH3OH masers. Core B has a mass of about 35
$M_{\odot}$, which might form several low or/and medium mass stars in the
future. The energetic outflow driven by IRAS 22506+5944 covers the whole
region, including both Core A and Core B, and could greatly affect its
surrounding and accelerate Core B to form stars. In summary, the whole region
is a star formation complex, in which stars at different evolutionary stages
live in the same cluster and interact with each other.

##  4 Summary

Our multi-line study reveals a star formation complex around IRAS 22506+5944,
in which a weak 6.7 GHz CH3OH maser was detected. Multi-line Maps reveal a
two-core structure: core A with mass of $\sim$230 M⊙ contains the IRAS source
which is driving an energetic bipolar outflow, while Core B, significantly
smaller than core A, has a large offset from the IRAS source. The two cores
are at different evolutionary stages. The energy released by the more evolved
core (Core A) is influencing the relatively less evolved core (Core B) to
accelerate its step to form stars.

###### Acknowledgements.

We wish to thank all the staff at Qinghai Station of Purple Mountain
Observatory for their assistance with our observations. This work was
supported by the National Natural Science Foundation of China (Grant Nos.
10673024, 10733030, 10703010 and 10621303) and National Basic Research Program
of China-973 Program 2007CB815403.

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11institutetext: Dipartimento di Fisica, Sapienza Universitá di Roma, Piazzale
Aldo Moro 5, I-00185 Roma, Italy 22institutetext: Departamento de Física
Téorica, Módulo 15, Facultad de Ciencias, Universidad Autónoma de Madrid,
E-28049 Madrid, Spain 33institutetext: Centro de Investigación Avanzada en
Física Fundamental (CIAFF), Facultad de Ciencias, Universidad Autónoma de
Madrid, E-28049 Madrid, Spain 44institutetext: Univ. Grenoble Alpes, CNRS,
LPSC-IN2P3, 53, avenue des Martyrs, 38000 Grenoble, France 55institutetext:
Institute for Astronomy, University of Edinburgh, Edinburgh EH9 3HJ, United
Kingdom

# Velocity dispersion vs cluster mass: a new scaling law with The Three
Hundred clusters

Antonio Ferragamo 11<EMAIL_ADDRESS>Marco De Petris 11 Gustavo
Yepes 2233 Juan Macías-Pérez 44 Weiguang Cui 5533 Alejandro Jiménez-Muñoz 44

###### Abstract

The Planck Collaboration has shown that the number of clusters as a function
of their mass and redshift is an extremely powerful tool for cosmological
analyses. However, the true cluster mass is not directly measurable. Among the
possible approaches, clusters mass could be related to different observables
via self similar scaling law. These observables are related to the baryonic
components of which a cluster is composed. However, the theoretical relations
that allow the use of these proxies often are affected by observational and
physical biases, which impacts on the determination of the cluster mass.
Fortunately, cosmological simulations are an extremely powerful tool to assess
these problems. We present our calibration of the scaling relation between
mass and velocity dispersion of galaxy members from the study of the simulated
clusters of The Three Hundred project with mass above $10^{13}M_{\odot}$. In
order to investigate the presence of a redshift dependence, we analyzed 16
different redshifts between $z=0$ and $z=2$. Finally, we investigated the
impact of different AGN feedback models.

##  1 Introduction

According to the hierarchical bottom-up scenario, galaxy clusters (GC) are the
last structure to form, and are, therefore, the perfect tracers of the
evolution of structures along the history of the Universe. They reside in the
deepest potential wells of the Large Scale Structure (LSS), generate by
accretion of Dark matter (DM) springel05 , therefore their number as a
function of their mass is very sensitive to the underlying Cosmology allen11 .
Although GC are dominated by DM, they include several forms and phases of the
baryonic matter. Indeed, the galactic component is surrounded by the so called
Intra-Cluster Medium (ICM) composed by warm and hot gas and non-thermal
plasma. Each component is characterised by its own physical process. Therefore
we can measure different quantities, such as the X-ray temperature, The
integrated Compton parameter or the velocity dispersion of the galaxies, by
observing different regions of the electromagnetic spectrum. Under the
assumption of relaxed systems, these observables can be directly related to
the cluster mass trough scaling relation. Since GC formation is gravitationaly
driven starting from initial density fluctuations, they evolve self-similarly
Kaiser86  and this allow us to approximate these scaling relation to power
laws. This property has been shown to be fundamental for the use of clusters
in cosmology, as their mass is not directly measurable. In fact, it is crucial
to constrain the scaling relations as accurately and precisely as possible.
For this purpose, cosmological simulations play a fundamental role being the
perfect laboratories in which it is possible to calibrate and to test new
scaling relations understanding possibly biases and physical limitations.

This paper is organised as follows. In section 2 we describe the simulation
and the data-set we used for our analysis. In sec. 3 we present the results of
the scaling relation $\sigma-M$. Finally in section 4 we presents our
conclusions.

##  2 The Three Hundred

The dataset of simulated GCs that we used in this study is selected within The
Three Hundred (The300) Cui2018 . This is a zoomed re-simulation of the 324
most massive Lagrangian region of a MultiDark Planck 2 simulation (MDPL2)
Klypin2016 . The MDPL2 consists in a $1h^{-1}\mathrm{Gpc}$ volume populated
with $3840^{3}$ DM particles of mass $1.5\times
10^{9}h^{-1}\mathrm{M_{\odot}}$, consistent with the cosmology of Planck 2015
data release planck15_par  ($h=0.678$, $n=0.96$, $\sigma_{8}=0.823$,
$\Omega_{\Lambda}=0.693$, $\Omega_{m}=0.307$ and $\Omega_{b}=0.048$).

The region of a radius of $15h^{-1}\mathrm{Mpc}$ around the center each of the
324 selected Lagrangian regions are then populated with gas particles with
initial mass of $2.36\times 10^{8}h^{-1}\mathrm{M_{\odot}}$ and they are re-
simulated with several codes. In this work we focus our analysis in the
results of the Gadget-X Murante2010 ; rasia15  and GIZMO-SIMBA Dave2019
hydrodynamical simulations codes that implement different feedback mechanisms.

###  2.1 Dataset

Within each region the bounded structures (halos and sub-halos) are identified
by using the Amiga Halo Finder (AHF) AHF2009 . For our purpose, we consider
only halos with total mass $M_{200}\geq 10^{13}h^{-1}\mathrm{M_{\odot}}$ and
with at least 5 DM sub-halos or galaxies that are not contaminated by black
holes (BH) particles. The sub-halos are structure of at least 20 DM particles
with mass above $10^{11}h^{-1}\mathrm{M_{\odot}}$. Whereas, in analogy with
munari13  (hereafter M13), we call the galaxy with more than $\sim 20$ stars
($M_{*}\gtrsim 10^{9}h^{-1}\mathrm{M_{\odot}}$) within the sub-halo. This
definition of galaxy assures the selection of all the sub-halos and many more
with mass lower than $10^{11}\mathrm{M_{\odot}}$.

Finally, in order to study the possible redshift evolution of the $\sigma-M$
scaling relation we selected 16 redshifts between $z=0$ and $z=2$ within the
128 snapshots stored by The300.

The final selection of GC contains more than 1000 clusters at each redshift
both in the Gadget-X and GIZMO catalogs.

Figure 1: Sub-halos velocity dispersion $\sigma_{200}$ as a function of total
mass $h(z)M_{200}$, at $z=0$, for the Gadget-X simulation run. The right and
left top panels show the cases $n_{gal}\geq 5$ and $n_{gal}\geq 10$,
respectively. The solid black line represents the best-fitting relation. In
the bottom panels there are depicted the corresponding residuals.

Figure 2: Galaxies velocity dispersion $\sigma_{200}$ as a function of total
mass $h(z)M_{200}$, at $z=0$, for the Gadget-X simulation run. The right and
left top panels show the cases $n_{gal}\geq 5$ and $n_{gal}\geq 10$,
respectively. The solid black line represents the best-fitting relation. In
the bottom panels there are depicted the corresponding residuals.

##  3 Scaling relation results

In analogy with the previous works in literature on the dynamical scaling
relation (e.g. evrard08, ; saro13, ; munari13, ), we characterised the
parameters of a power law relation

$\frac{\sigma_{200}}{\rm
km\,s^{-1}}=A\;\left(\frac{h(z)\,M_{200}}{10^{15}\,\rm
M_{\odot}}\right)^{\alpha},$ (1)

where $\sigma_{200}$ and $M_{200}$ are the velocity dispersion and the mass of
the cluster within the radius $R_{200}$, respectively. For all the clusters
described in sec. 2.1 we used the Biweight estimator beers90  to estimate the
one-dimensional velocity dispersion $\sigma_{200}=\sigma_{200}^{3D}/\sqrt{3}$.
Subsequently, we performed the fit with a linear function in the relation in
the logarithmic space by using the python routine scipy.optimize.curve_fit.

In order to investigate the impact of the number of galaxy members on the
scaling relation, we performed the entire analysis taking into account two
different thresholds for the minimum number of galaxy members: $n_{gal}\geq 5$
and $n_{gal}\geq 10$. Figures 1 and 2 show the fitted relations for the
Gadget-X run in the two cases at redshift $z=0$ for sub-halos and galaxies,
respectively. We see that the slope of the best fit is less steep when the
minimum number of galaxy members is 10. Furthermore, the scatter is higher in
the case with $n_{gal}\geq 5$. We can explain these evidence with the
combinations of two effects. From one side the scatter increases because lower
the number of galaxies higher the uncertainties on the velocity dispersion.
From the other side the cluster sample in the case with $n_{gal}\geq 5$ is
affected by selection effects such as the Eddigton bias eddington1913 . For
these reasons we present the results obtained with the sample $n_{gal}\geq
10$.

Figure 3: Best fit parameters $\alpha$ (top panels) and $A$ (bottom panels) as
a function of redshift, for sub-halos (left panels) and galaxies (right
panels). Light blue and coral dots represent the results from the Gadget-X and
Gizmo analyses, respectively. The M13 result are represented by the black
squares, while the grey band represents their weighted mean.

###  3.1 Redshift dependence

In figure 3 we show the parameter of the $\sigma-M$ relation along the
redshift between $z=0$ and $z=2$ that we took into account for sub-halos and
galaxies in the left and right panel, respectively. The black squares are the
M13 results (slope in the top panel and the normalization in the central
panel) for the AGN sample only at the 10 investigated redshifts, while the
shaded regions represent the weighted mean of the 10 redshifts. In light blue
and orange we plotted the best fit values obtained with the Gadget-X and the
GIZMO runs of the The300. Since the Dianoga simulation and the Gadget-X
implement the same baryonic physics recipe, in this section we only focus on
the comparison between the M13 and Gadget-X results. The comparison with GIZMO
is reported in sec. 3.2. In the cases of sub-halos and galaxies, the two
results are in an excellent agreement at $z<0.8$. Whereas, going towards
higher redshift we observe an increasing value of the slope that is not
present in M13 results. differently from the normalization where any redshift
dependence is noticeable.

The GIZMO best fits show the same behaviour for both slope and normalization.
For this reason we decided to take into account the redshift dependence of the
slope in our parametrization of the scaling relation by fitting a linear
relation between the redshift and the slope. In Tables 1 and 2 we list the
parameters of the $\sigma-M$ relation

$\frac{\sigma_{200}}{\rm
km\,s^{-1}}=A\;\left(\frac{h(z)\,M_{200}}{10^{15}\,\rm
M_{\odot}}\right)^{(\alpha+\beta\,z)}.$ (2)

Table 1: Best fit parameter of equation 2 for sub-halos | A | $\alpha$ | $\beta$
---|---|---|---
Gadget-X | $1216.2\pm 0.6$ | $0.358\pm 0.002$ | $0.027\pm 0.003$
GIZMO-SIMBA | $1198.8\pm 0.7$ | $0.341\pm 0.002$ | $0.026\pm 0.002$
Table 2: Best fit parameter of equation 2 for galaxies | A | $\alpha$ | $\beta$
---|---|---|---
Gadget-X | $1172.7\pm 0.8$ | $0.357\pm 0.002$ | $0.029\pm 0.002$
GIZMO-SIMBA | $1171.5\pm 0.6$ | $0.340\pm 0.001$ | $0.016\pm 0.001$

###  3.2 Gadget-X vs GIZMO-SIMBA

It is interesting to report that in Fig. 3 the GIZMO parameters are always
lower than the Gadget-X. The ratio between parameters obtained from the
Gadget-X and GIZMO runs are shown in Fig. 4. On one hand, the slope $\alpha$
from GIZMO is $\sim 5\%$ lower than the slope obtained in the Gadget-X fits in
the whole redshift range for the sub-halos, whereas for the galaxies the
offset increases with the redshift passing from $5\%$ at $z=0$ to a $\sim
10\%$ at $z=2$. On the other hand, the bias in the normalization, $A$, is much
smaller for the sub-halos and completely absent for the galaxies. This
evidence can be explained with the differences in the baryonic physics recipes
between the Gadget-X and the GIZMO-SIMBA runs of The300, in particular in the
differences in the AGN feedback, dramatically affecting the less massive
halos, which can explain the shallower slope of GIZMO relations.

Figure 4: Ratio of the best fit parameters from GIZMO and Gadget-X runs (red
line), for sub-halos (left panel) and galaxies right panel). The slope,
$\alpha$, and the normalization, $A$, are represented in top and bottom
panels, respectively.

##  4 Conclusions

In this work we presented the calibration of a scaling relation between the
velocity dispersion and the mass of GCs. For this purpose we used the
synthetic clusters from the The300 simulation with mass $M_{200}\geq
10^{13}\mathrm{M_{\odot}}$, at 16 different redshifts between $z=0$ and $z=2$,
from two different runs, Gadget-X and GIZMO-SIMBA. In analogy with M13, we
constrained the relation by using different tracers such as sub-halos and
galaxies. As a consequence of the similarities between the Gadget-X run of
The300 and the Dianoga simulation used in M13 (in particular with the AGN
feedback model), we performed a direct comparison of the results of these two
studies. We were able to reproduce the M13 results at redshift $z=0$. We
obtained results in very good agreement with respect M13 up to $z=0.8$. After
this point the two relations begin to diverge. In fact, we observed a
dependence of the slope of the relation with the redshift. Furthermore, we
investigated the effect of different model of AGN feedback on the parameters
of $\sigma-M$. We compared the results from Gadget-X and GIZMO-SIMBA. The
slope obtained wit GIZMO is a $\sim 5\%$ smaller than the Gadget-X one for
both tracers and in the whole range of redshifts.

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