# On-board Change Detection for Resource-efficient Earth Observation with LEO
Satellites

Van-Phuc Bui1, Thinh Q. Dinh24, Israel Leyva-Mayorga1, Shashi Raj Pandey1, Eva
Lagunas3, Petar Popovski1 This work was supported by the Villum Investigator
Grant “WATER” from the Velux Foundation, Denmark. The work of Eva Lagunas has
received funding from the Luxembourg National Research Fund (FNR) under the
project SmartSpace (C21/IS/16193290). 1Department of Electronic Systems,
Aalborg University, Denmark ({vpb, ilm, srp<EMAIL_ADDRESS>
2University of Information Technology, Ho Chi Minh City, Vietnam
<EMAIL_ADDRESS>
4Vietnam National University, Ho Chi Minh City, Vietnam
3University of Luxembourg, Luxembourg<EMAIL_ADDRESS>
###### Abstract

The amount of data generated by Earth observation satellites can be enormous,
which poses a great challenge to the satellite-to-ground connections with
limited rate. This paper considers problem of efficient downlink communication
of multi-spectral satellite images for Earth observation using change
detection. The proposed method for image processing consists of the joint
design of cloud removal and change encoding, which can be seen as an instance
of semantic communication, as it encodes important information, such as
changed multi-spectral pixels (MPs), while aiming to minimize energy
consumption. It comprises a three-stage end-to-end scoring mechanism that
determines the importance of each MP before deciding its transmission.
Specifically, the sensing image is (1) standardized, (2) passed through a
high-performance cloud filtering via the Cloud-Net model, and (3) passed to
the proposed scoring algorithm that uses Change-Net to identify MPs that have
a high likelihood of being changed, compress them and forward the result to
the ground station. The experimental results indicate that the proposed
framework is effective in optimizing energy usage while preserving high-
quality data transmission in satellite-based Earth observation applications.

###### Index Terms:

Satellite communication, Semantic communication, Change detection, Image
processing.

##  I Introduction

Remote sensing satellites are vital for environmental monitoring as they
swiftly provide comprehensive coverage of targeted regions, allowing for land
use surveys, urban studies, and hazard management through image acquisition
[1]. The application of high-resolution sensors results in large volumes of
sensor data, necessitating significant communication resources and on-board
data storage capacity for transmitting data to ground-based end-users.
However, the conventional approach of transmitting captured images to the
ground for analysis and distribution is no longer practical due to the vast
amounts of data generated by Earth observation satellites, prompting the need
for novel processing techniques. For instance, the Sentinel-2 system acquires
an extensive amount of data (2.4 Terabits per day) for transmitting to the
terrestrial gateway, with each surface location being captured at periodic
intervals of five days [2]. While forwarding the complete dataset can be
advantageous for the accurate detection of any alterations or anomalies, it is
not regarded as efficient in terms of data storage and transmission
capabilities. Consequently, numerous forthcoming satellite missions aim to
address memory and bandwidth limitations by implementing on-board processing
operations that allow for data processing transfer from the ground segment to
the space segment. The adoption of the new processing workflow is projected to
significantly improve the efficiency of downlink data transmission leading to
a decrease in the necessary transmission resources. Furthermore, by selecting
solely the pertinent information to transmit, both the memory and
communication costs of the on-board platform can be reduced [3]. There has
been substantial interest in managing data in small Low Earth orbit (LEO)
satellites due to their diminutive size, low power consumption, brief
development cycle, and economic nature. It is important to note, however, that
the communications capabilities of these LEO satellites are limited, in
contrast to their large captured data on a daily basis.

Figure 1: Proposed end-to-end scoring architecture.

With the latest developments in remote sensing applications based on
artificial intelligence, the attention for machine learning grows steadily
also for space information networks.

Deep learning-based approaches have exhibited remarkable efficacy across
numerous image-processing applications, and scientists working in remote
sensing have investigated the potential utility of these techniques in the
context of Earth observation. Numerous Fully Convolutional Neural Networks
(FCNNs) have been implemented for the purpose of semantic image segmentation,
with many of them utilizing an encoder-decoder structure akin to that of the
U-Net architecture [4]. The effectiveness of U-Net in delineating clouds in
Landsat 8 imagery, aided by automatically generated Ground Truths (GTs), has
been firmly established [5]. The domain of change detection has its origins in
the early stages of aerial imaging [6]. Convolutional Neural Networks (CNNs),
a category of machine learning algorithms specialized in image analysis, have
been employed for image comparison in diverse settings [7]. It is immediate to
see that such predictor cannot achieve perfect accuracy and, in fact, it has
been observed that change detection accuracy is in the range of $20-92\%$ even
using all spectral bands for computing [8]. In addition, resource allocation
in Space Information System is studied in [9, 10]. Scheduling problems that
maximized the sum priorities of the successfully scheduled tasks in [9] or the
sum network utility [10] have been considered. In those works, it is assumed
that all collected information from the satellites needs to be transmitted.

The aforementioned works have primarily either focused on improving the
performance of noise removal, such as clouds, or enhancing the accuracy of
change detection methods (at the ground after receiving whole satellite’s
data), without fully considering the importance of transmitting critical
information contained within noisy sensing images to the gateway. Multi-
spectral images are particularly susceptible to noise, such as cloud cover,
which can result in the loss of useful information, including changing MPs.
Therefore, the selection of pertinent MPs for downlink is crucial in
conserving transmission resources at the satellite, as well as processing and
storage space at both gateway and satellites. Consequently, this paper
presents an end-to-end system that utilizes deep learning-based architecture
to process and transmit valuable information from noisy sensing images
captured by satellites. Our contributions are listed as follows:

  * •

To the best of our knowledge, this is the first study to examine an end-to-end
change extraction system for satellite-based Earth observation. This system
can help reduce energy required for processing and transmitting encoded
information, thereby enabling more efficient information storage.

  * •

We propose an architecture that is designed to remove cloud and assess the
significant role of each MP in sensing images through scoring algorithm,
enabling the selection of only essential MPs for encapsulation and
transmission.

  * •

The proposed algorithm is evaluated through numerical simulations that utilize
standard datasets and real-world data obtained from Sentinel-2 about North
Jutland Region, Denmark. The results demonstrate that our system can
effectively reduce the amount of encoding and transmission data required while
preserving critical information.

##  II System Model and Problem Formulation

###  II-A System Model

We consider a satellite system as illustrated in Fig. 1, where there is a LEO
satellite communicating with a gateway deployed at ground level, which is
directly connected to a server. The satellite is in charge of capturing multi-
spectral images and is equipped with an AI-module intended for image feature
extraction. These features,such as potential pixel changes and their
associated coordinates, must be transmitted within the limited time period
when the satellite and gateway are connected. Consider two coregistered multi-
spectral satellite images taken at different time instances
$\mathbf{X}^{t_{0}}=\\{x^{t_{0}}(i,j,k)|1\leq i\leq H,1\leq j\leq W,1\leq
k\leq D\\}$ and $\mathbf{X}^{t_{1}}=\\{x^{t_{1}}(i,j,k)|1\leq i\leq H,1\leq
j\leq W,1\leq k\leq D\\}$ of size $H\times W\times D$, where $H$, $W$, and $D$
are the size of height, width, and spectral bands, respectively.
$\mathbf{X}^{t_{0}}$ is the reference image taken at the reference time
$t_{0}$ and $\mathbf{X}^{t_{1}}$ is the newly observed image taken at time
$t_{1}$.

Our objective is to communicate the changed multi-spectral pixels (MPs) from
the sensing image $\mathbf{X}^{t_{1}}$ captured by the satellite to Earth
while minimizing the data transmitted to ground and the energy consumption of
the entire process. Specifically, given
$\mathcal{X}^{t_{1}}=\\{\mathbf{x}_{ij}^{t_{1}}\\}$ as a set of available MPs
in image $\mathbf{X}^{t_{1}}$, e.g., $\mathbf{x}_{ij}^{t_{1}}$ could be
represented by the MP $(i,j)$ including all spectral bands, we need to select
a subset $\mathcal{P}$ MPs among $\mathcal{X}^{t_{1}}$
$(|\mathcal{P}|\leq|\mathcal{X}^{t_{1}}|)$. The reference pixel set
$\mathcal{X}^{t_{0}}=\\{\mathbf{x}_{ij}^{t_{0}}\\}$ of the reference image
$\mathbf{X}^{t_{0}}$ is processed as analogous. We define
$\mathcal{S}=\\{s_{ij}\\}$ as the accurate change map where
$s_{ij}\in\\{0,1\\}$ represents the changed/unchanged MP. In particular,
$s_{ij}=1$ if there is a pixel change at location $(i,j)$, and vice versa.

######  Definition 1.

Pixel change is defined as the temporal variation occurring of coregistered
images at a specific location, including changes in land use, urban coverage,
deforestation, and other similar types of deviation [11, 12].

###  II-B Energy consumption

In our analysis, we evaluate the energy utilization of the satellite by
calculating the combined energy consumption associated with image compression
and communication. These factors are greatly influenced by the data capacity
transmitted between the satellite and the gateway.

We denote $\alpha_{ij}\in\\{0,1\\}$ is a binary decision variable with
$\boldsymbol{\alpha}\triangleq\\{\alpha_{ij}\\}$, where $\alpha_{ij}=1$ if we
select the MP $\mathbf{x}_{ij}^{t_{1}}$ as a candidate of $\mathcal{P}$. As a
consequence, the transmission set $\mathcal{P}$ could be construct as

$\displaystyle\mathcal{P}\triangleq\\{\alpha_{ij}\mathbf{x}_{ij}^{t_{1}}\\},\quad\forall\alpha_{ij},\mathbf{x}_{ij}^{t_{1}}.$
(1)

Then, the total amount of data $C(\boldsymbol{\alpha})$ to transmit the set
$\mathcal{P}$ is

$\displaystyle
C(\boldsymbol{\alpha})=\sum_{\alpha_{ij}\in\boldsymbol{\alpha}}D\alpha_{ij}.$
(2)

The model to calculate the satellite’s energy spending for processing tasks
captures the most relevant CPU parameters [13, 14]. The model establishes a
direct relationship between the energy consumed per clock cycle and the square
of the CPU clock frequency $f_{\text{CPU}}$ multiplied by the effective
capacitance coefficient, which is specific to the processor under
consideration [14]. Thereby, we have
$E_{\text{cycle}}^{\text{proc}}={P^{\text{proc}}(f_{\text{CPU}})}/{f_{\text{CPU}}},$
where $P^{\text{proc}}(f_{\text{CPU}})$ is the power consumption during
processing at the maximum CPU frequency. Noting that the supplied power is
linear with the number of processor cores $N_{\text{CPU}}$, the energy
consumption to process data $E^{\text{proc}}(\boldsymbol{\alpha})$ is modeled
as

$\displaystyle
E^{\text{proc}}(\boldsymbol{\alpha})=C(\boldsymbol{\alpha})\hat{R}^{\text{comp}}E_{\text{cycle}}^{\text{proc}},$
(3)

where $\hat{R}^{\text{comp}}=e^{\kappa\rho}-e^{\kappa}$ is the compressing
complexity, which is defined as the number of CPU cycles to compress one bit
of data by a compression ratio $\rho$ and the positive constant $\kappa$
depending on used compression algorithm [15].

For communication energy, we consider an interference-free communication
channel affected by additive-white Gaussian noise (AWGN) with free space path
loss, and the noise power is denoted by $\varpi^{2}$ [16]. Consequently, the
signal-to-noise ratio (SNR) for the downlink satellite-to-ground link at a
particular time $t$, represented by $\gamma_{t}$, is calculated as

$\displaystyle\gamma_{t}=G_{\text{tx}}G_{\text{rx}}P_{\text{tx}}\left(\frac{c}{4\pi
d_{t}f_{c}\varpi}\right)^{2},$ (4)

where $G_{\text{tx}}$ and $G_{\text{rx}}$ stand for the transmitter and
receiver antenna gains. $P_{\text{tx}}$ is the transmission power at the
satellite, $f_{c}$ is the carrier frequency, and $c=2.998\times 10^{8}$ is the
speed of light. $d_{t}$ can be calculated due to satellite’s predefined
connection time to the gateway, orbit time, and satellite’ altitude. Once we
know the SNR, a proper modulation and coding scheme is selected to achieve the
reliable communication following the DVB-S2 system [17]. We denote a given
throughput $\bar{R}$ [bps] and $\gamma_{\text{min}}(\bar{R})$ as the minimum
SNR to achieve a reliable rate $\bar{R}$, the set of ordered pairs is defined
as $\mathcal{Q}_{\text{DVB-S2}}=\\{(\bar{R},\gamma_{\text{min}}(\bar{R})\\}$.
The selection of the transmission rate for selected set $\mathcal{P}$ is
determined by adapting the modulation and coding scheme in order to attain the
maximum data rate for reliable communication. Let $\gamma_{t}$ be minimum SNR
experienced at the gateway at time $t$, when the transmission of the data is
initiated. At this time instant, the rate is selected as

$\displaystyle
R_{\mathcal{P}}=\max\big{\\{}\bar{R}\in\mathcal{Q}_{\text{DVB-S2}}:$
$\displaystyle\ \gamma_{t}\geq\gamma_{\min}(\bar{R})\big{\\}}$ (5)

The downlink energy consumption for download all data $\mathcal{P}$ is
therefore calculated as

$\displaystyle
E^{\text{trans}}(\boldsymbol{\alpha})=\frac{P_{\text{tx}}C(\boldsymbol{\alpha})}{R_{\mathcal{P}}}.$
(6)

Summing up, the total energy for processing and transmitting the selected data
$\mathcal{P}$ is derived as

$\displaystyle
E^{\text{tot}}(\boldsymbol{\alpha})=E^{\text{proc}}(\boldsymbol{\alpha})+E^{\text{trans}}(\boldsymbol{\alpha}).$
(7)

###  II-C Energy Efficient Data Downloading With Change-Detection Constraint

In contrast to conventional approaches aimed at improving efficiency of the
change detection algorithm that is applied to the sensed images at the
satellite [8], our focus is centered on the reduction of the energy required
to transmit all changed to the nearby gateway, which shifts the focus towards
the communication aspects of the system. That is, all $x_{ij}$ that have
change map $s_{ij}=1$ will be scheduled to the transmission set $\mathcal{P}$.
This is achieved by setting the values of the decision variable
$\boldsymbol{\alpha}$ as $\alpha_{ij}\geq
s_{ij},~{}\forall\alpha_{ij},s_{ij}$, which ensures that all the changed MPs
are transmitted. Accordingly, the optimization problem is to minimize the
communication energy subject to change detection constraints, which is
formulated as

$\displaystyle\text{P1}:\min_{\boldsymbol{\alpha}}$
$\displaystyle~{}~{}E^{\text{tot}}(\boldsymbol{\alpha})$ (8a)
$\displaystyle\mathrm{s.t.}~{}~{}$ $\displaystyle\alpha_{ij}\geq s_{ij}.$ (9a)

######  Proposition 1.

The problem P1 achieves optimality when the constraints (9a) satisfy
$\alpha_{ij}=s_{ij},\forall i=\\{1,2,\dots,H\\},j=\\{1,2,\dots,W\\}$. This is
straightforward to prove due to the fact that the energy decreases
monotonously as the number of transmitted pixels, identified by the number of
non-zero entries in $\boldsymbol{\alpha}$, decreases.

Note that (8a) can only be solved if the satellite knows the indexes of all
the changed MPs beforehand but this is not the case in reality. Instead, it is
necessary to implement an AI model at the satellite to estimate $s_{ij}$ and,
hence, perform inference on the changed MPs, which in turn requires a
reformulation of P1.

###  II-D Approximate Formulation of Data Downloading with Change Detectors

Motivated by the above discussion, a practical solution for MP scheduling is
developed in this paper where we would like to build a predictor which can
recognize most of the change MPs. We define $s_{ij}^{p}\in\\{0,1\\}$ as the
predictor for $s_{ij}$ given by the selected change detection algorithm, which
achieves an error level $\epsilon$. Then, P1 is reformulated as follows:

$\displaystyle\text{P2}:\min_{\\{\alpha_{ij}\\}}$
$\displaystyle\sum_{i=1}^{H}\sum_{j=1}^{W}\alpha_{ij}$ (10)
$\displaystyle\mathrm{s.t.}\ $ $\displaystyle\alpha_{ij}\geq s_{ij}^{p},$
(11a) $\displaystyle\mathrm{Pr}(s_{ij}^{p}=0|s_{ij}=1)\leq\epsilon,$ (12a)

where $\epsilon$ is the threshold that ensures a sufficient number of change
MPs are selected. It is evident that when the value of epsilon is decreased,
the criteria for identifying change MPs become more rigorous, necessitating
the selection of additional pixels for transmission. As an illustration, when
setting $\epsilon=0.05$, the problem (10) is devised to guarantee the
selection and labeling of no less than $95\%$ of change MPs. Accordingly, we
propose an algorithm to obtain an efficient suboptimal solution to the problem
(10).

##  III Preprocessing and Semantic Encoding

In the following, we describe the steps to detect change MPs in Earth
observation applications, which include preprocessing to remove cloud cover
and the use of a deep learning model to determine the likelihood that each
specific pixel is changed from previous versions of the image. Algorithm 1
summarizes these steps. The aim is to ensure that the reconstructed images at
the gateway are as precise as possible, thereby facilitating their accurate
interpretation by human/domain experts in Earth Observation.

1:Geometrical multi-spectral image pair $\mathbf{X}^{t_{0}}$ and
$\mathbf{X}^{t_{1}}$

2:The transmission set $\mathcal{P}$, Reconstructed MP image
$\hat{\mathbf{X}}^{t_{1}}$, and Energy requirement for processing and
transmission

3:Preprocessing and Cloud Removing

4:Select process bands (R, G, B, Nir) for cloud removing and (R, G, B) for
change detection

5:Standardize $\mathbf{X}^{t_{0}}$ and $\mathbf{X}^{t_{1}}$

6:Cloud detection and removing using Cloud-Net

7:Change Scoring and Semantic Encoding

8:Scoring MPs using Change-Net and update $\\{s_{ij}^{p}\\}$ as in (15)

9:Perform threshold segmentation to get the transmission set
$\mathcal{P}=\\{\mathbf{x}^{t_{1}}_{ij}|s^{p}_{ij}=1,i=1,2,\dots,H,j=1,2,\dots,W\\}$

10:Update $\alpha_{ij}=s^{p}_{ij}\ \forall i,j$ and calculate required energy
$E^{\text{tot}}(\boldsymbol{\alpha})$ as in (7)

Algorithm 1 Proposed algorithm for problem (10)

###  III-A Preprocessing and Cloud Removing

As part of the preprocessing stage, the following steps are undertaken: $(1)$
the selection of bands representative of the complete set of MP images; $(2)$
the adjustment of illumination levels to facilitate the detection (cloud and
change) in the subsequent stage; and $(3)$ the elimination of cloud cover from
the observed image. First, $N\ (N<D)$ useful bands are selected for processing
based on the principle that a group of appropriate bands (e.g., visible and
near-infrared bands) could reduce the processing requirements for both
training and execution phases. This is consistent with realizing cloud
detection on the satellite with limited hardware and processing capabilities.
Before removing clouds, a radiometric correction procedure is implemented to
rectify radiometric disparities among multi-spectral images stemming from
diverse imaging conditions such as sun angle, light intensity, and atmospheric
circumstances. The chosen approach is relative radiometric normalization,
which is founded on the z-score method, which normalizes images to zero mean
and a unit standard deviation. Given a MP pair, denoted by
$\mathbf{x}_{ij}^{t_{0}}=[x_{1}^{t_{0}},x_{2}^{t_{0}},\dots,x_{N}^{t_{0}}]$
and
$\mathbf{x}_{ij}^{t_{1}}=[x_{1}^{t_{1}},x_{2}^{t_{1}},\dots,x_{N}^{t_{1}}]$.
The radiometric relative normalization can be expressed as [18]
$\hat{x}_{n}^{t_{0}}=({x_{n}^{t_{0}}-\mu_{\mathbf{x}_{n}^{t_{0}}}})/{\sigma_{\mathbf{x}_{n}^{t_{0}}}^{2}};\hat{x}_{n}^{t_{1}}=({x_{n}^{t_{1}}-\mu_{\mathbf{x}_{n}^{t_{1}}}})/{\sigma_{\mathbf{x}_{n}^{t_{1}}}^{2}},$
where $\mu_{\mathbf{x}_{n}^{t_{k}}}$ is the mean and
$\sigma_{\mathbf{x}_{n}^{t_{k}}}^{2}$ is the variance for band $n$ of image
$\mathbf{X}^{t_{k}},(k\in\\{0,1\\})$ . The radiometric correction would
suppress the radiometric difference between multi-spectral images caused by
different conditions.

Cloud removing: In this work, the Cloud-Net model for identifying cloud
regions in multi-spectral Sentinel-2 images based on U-Net using a combination
of thresholding and deep learning techniques is deployed. This approach
utilizes four spectral bands - Red, Green, Blue, and Near Infrared (RGBNir) -
for both training and prediction, making it practical for use in satellite
hardware for cloud detection. As each spectral band in Sentinel-2 encompasses
a substantial number of pixels (approximately $10980\times 10980$), it is
necessary to segment them into smaller image patches using a cropping
technique. This is achieved by dividing the selected spectral band image into
$384\times 384\times 4$ non-overlapping patches, with each of the four patches
corresponding to the Red, Green, Blue, and Nir bands being combined to create
a 4D input. To enhance the resilience of the methodology towards cloud
patterns or similar patterns, the input patches underwent geometric
transformations, such as horizontal flipping, rotation, and zooming. The
output probability map is obtained via the use of a sigmoid activation
function in the final convolution layer of the network. The cloud learning set
consists of tuples
$\mathcal{D}_{\text{cloud}}=\\{(\mathbf{a}_{i},z_{i})\in(\mathcal{A}\times\mathcal{Z})|i=1,\dots,M_{\text{cloud}})\\}$
obtained from an unknown joint distribution $P_{\mathcal{D}_{\text{cloud}}}$
over $\mathcal{A}\times\mathcal{Z}$, where $M_{\text{cloud}}$ is the total
number of instances, and $z_{i}$ represents the corresponding label of the
input $\mathbf{a}_{i}$. Our aim is to estimate a function
$g(\mathbf{a}_{i}|\boldsymbol{\psi})$ that maps inputs $\mathbf{a}_{i}$ to
outputs $z_{i}$, where $\boldsymbol{\psi}$ is a set of parameters that are
optimized using the training set. To estimate $\boldsymbol{\psi}$, the Adam
gradient descent [19] method is utilized to implement the Cross Entropy loss
function as

$\displaystyle\mathcal{L}(\hat{z}_{\boldsymbol{\psi},i},z_{i})=-\big{(}z_{i}\log(\hat{z}_{\boldsymbol{\psi},i})$
$\displaystyle+(1-z_{i})\log(1-\hat{z}_{\boldsymbol{\psi},i})\big{)},$ (13)

with $\hat{z}_{\boldsymbol{\psi},i}=g(\mathbf{a}_{i}|\boldsymbol{\psi})$ is
the output of the model. The well-trained weights of the Cloud-Net model are
then applied to the target image to generate a predicted cloud probability
map. This map is binarized using a global threshold of $\gamma$ and multiplied
with the image ${\mathbf{X}}^{t_{1}}$ to produce the cloud-removed image
$\tilde{\mathbf{X}}^{t_{1}}$ with
$\tilde{\mathcal{X}}^{t_{1}}=\\{\tilde{\mathbf{x}}^{t_{1}}_{ij}\\}$ as a set
of MPs in $\tilde{\mathbf{X}}^{t_{1}}$.

(a)

(b)

(c)

Figure 2: (a) ROC curve over change dataset (the AUC scores are shown in the
legends). (b) Cumulative Percentage Downloaded vs score of multi-spectral
image with median AUC. (c) Probability of changed and unchanged MPs vs score
of multi-spectral image with median AUC.

###  III-B Change Scoring and Semantic Encoding

In this stage, we have been provided with two multi-spectral images that have
been geometrically aligned, have consistent lighting conditions, and have had
cloud cover removed. Our goal is to propose a computationally efficient
automatic change detection method for these two images that are practical for
satellite applications. Motivated by [20, 4], the Change-Net based on U-Net
model is developed to perform semantic segmentation of images. We use a
negative log-likelihood loss function to classify every MP in the observed
images as either changed or not. Specially, we are considering a change
learning set consisting of tuples
$\mathcal{D}_{\text{change}}=\\{(\mathbf{b}_{i},y_{i})\in(\mathcal{B}\times\mathcal{Y})|i=1,\dots,M_{\text{change}}\\}$,
with inputs $\mathbf{b}_{i}$, and labels $y_{i}$. With $\boldsymbol{\theta}$
as a set of learnable parameters to be optimized, the likelihood
$p(\mathbf{b}_{i},\boldsymbol{\theta})$ is defined as the joint density of the
observed data, which can be viewed as a function of $\boldsymbol{\theta}$ that
maps any given input $\mathbf{b}_{i}$ to outputs $y_{i}$. By denoting $m$ as
the mini-batch size, the parameter set $\boldsymbol{\theta}_{\text{model}}$ is
then achieved through training process as

$\displaystyle\boldsymbol{\theta}_{\text{model}}=\underset{\boldsymbol{\theta}}{\arg\max}\prod_{i=1}^{m}p(y_{i}|\mathbf{b}_{i},\boldsymbol{\theta}).$
(14)

In our case, the system output $\bar{s}_{ij}\in[0,1]$ is defined as the change
score of the corresponding cloud-removed MP $\tilde{\mathbf{x}}^{t_{1}}_{ij}$,
which is the probability of
$p(s_{ij}=1|\tilde{\mathbf{x}}^{t_{1}}_{ij},\boldsymbol{\theta}_{\text{model}})=\xi(\boldsymbol{\theta}_{\text{model}}^{T}\tilde{\mathbf{x}}^{t_{1}}_{ij})$
with $\xi(\cdot)$ is the Log Softmax function. As $\bar{s}_{ij}$ is close to
$1$, it is likely that there is a change in location $(i,j)$. Thus, to make a
good prediction, we would like to learn a scoring system such that

$\displaystyle s_{ij}^{p}=\mathbf{1}(\bar{s}_{ij}\geq\tau),$ (15)

where $\tau$ is the predefined threshold, derived experimentally to satisfy
the constraint (12a). Our proposed architecture is summarized in Algorithm 1.

##  IV Numerical Results

TABLE I: Simulation Parameters

Parameter | Value | Parameter | Value
---|---|---|---
Carrier frequency ($f_{c}$) | 20 GHz | Altitude of satellites ($h$) [2] | 786 km
Processor frequency ($f_{\text{CPU}}$) | 1.8 GHz | Compression factor $(\rho)$ | 5
Power consumption |  | Complexity of the image |
for processing ($P^{\text{proc}}(f_{\text{CPU}})$) | 10 W | processing algorithm $(\kappa)$ | 0.1
Bandwidth ($B$) | 500 MHz | Noise power $(\varpi^{2})$ | -115 dB
Satellite antenna gain $(G_{\text{tx}})$ | 32.13 dBi | Gateway antenna gain $(G_{\text{rx}})$ | 34.2 dBi
Performance in change detection $(\epsilon)$ | 0.05 | Transmission power $(P_{\text{tx}})$ | 10 W
Communications duration ( $T^{\mathrm{pass}}$ ) | 15 min | Orbital period | 100 min

####  IV-1 Implementation Details

We evaluate our proposed algorithm in the Sentinel-2 system when the
transmission process initiates upon the satellite’s entry into the gateway’s
coverage area. This is a worst-case scenario for the energy consumption for
communication. Other important parameters for performance analysis are
included in Table I. We use the 38-Cloud dataset [21] for training and testing
Cloud-Net, which covers 38 Landsat-8 scene images and their manually extracted
pixel-level ground truths for cloud detection. For Change-Net model, we
conduct the Onera Satellite Change Detection dataset, publicly available on
the IEEE-DataPort repository [22], widely used in the literature to detect
changes in multispectral images of Sentinel- 2 satellite [23]. The weights
were assigned inversely proportional to the number of examples in each class
in order to address class imbalances between the two categories (change versus
no change). The features are preprocessed classically to facilitate training.
The dataset was split into a shuffled and stratified training set and a test
set, comprising $60\%$ and $40\%$ of the data, respectively. Both Cloud-Net
and Change-Net are trained on the ground and applied to satellites for further
processing of sensing data. Following training and evaluation on the dataset
with annotated ground truth, we apply the trained algorithm to real-world data
collected from a Sentinel-2 image to identify changes at the pixel level
relative to reference images. These identified changed map $\mathcal{S}$ are
subsequently labeled and encoded prior to being transmitted to the gateway.

(a) Reference image

(b) Captured image (on 19/09/2022)

(c) Reconstructed image at Earth gateway (PSNR = 60.1 dB)

(d) Percentage of cloud and change prediction

(e) Energy requirement for processing and transmission

Figure 3: The performance of proposed algorithm on the real Sentinel-2 data
(the multi-spectral images were acquired in the North Jutland Region of
Denmark during the period from 23/08/2022 to 24/09/2022, with the reference
image captured on 23/08/2022 (figures (a), (b), and (c) are display using RGB
channels).

####  IV-2 Results

We evaluate the ROC of the change detection model with different thresholds.
Herein, the True Positive Rate (TPR) and False Positive Rate (FPR) are
respectively defined as $\text{TPR}={\text{TP}}/({\text{TP}+\text{FN}}),$ and
$\text{FPR}={\text{FP}}/({\text{FP}+\text{TN}}).$ Based on ROC, the Area Under
the ROC Curve (AUC) could be calculated, which measures how well predictions
are ranked.

Fig. 2(a) plots the ROC of 3 representative images in the OSCD dataset with
the highest, median, and lowest AUC levels, respectively. The efficacy of our
trained Change-Net model can be readily observed, as it achieves a high level
of performance with the maximum AUC of 0.98 and a minimum AUC of 0.80.
Therefore, selecting the appropriate score threshold to guarantee the
fulfillment of constraint (9) while simultaneously ensuring the selection of
an adequate number of modified points can be considered a dependable approach.
Fig. 2(b) and Fig. 2(c) depict the percentage of downloads accumulated and the
probability of the image that has the median AUC score, respectively, while
also presenting a threshold score of 0.6 to guarantee the selection of $95\%$
of modified MPs. Remarkably, MPs labeled 0 and 1 distribute overlap as in Fig.
2(c). Hence, to guarantee the selection of a sufficient number of altered MPs
(at a rate of 95%), we have labeled approximately 50% of unchanged MPs with a
value of 1, leading to the requirement of encoding and transmitting
approximately 50% of the entire sensing data. We also emphasize that our
approach prioritizes the establishment of a threshold for labeling a specific
portion of change MPs after training rather than evaluating the model’s
performance metrics over the test set.

To assess our architecture’s efficacy, we incorporated real-world data from
the Sentinel-2 system, taking into consideration both the quantity of reduced
data and the computational required energy for processing and transmission.
Remarkably, Fig. 3(a)-(c) illustrate a specific use case of images. The
results indicate that Change-Net yields advantages when the Peak signal-to-
noise ratio (PSNR) between the reconstructed image (Fig. 3(c)) and the
captured image (Fig. 3(b)) is 60.1 dB subsequent to cloud removal and without
compression. In order to attain this outcome, Change-Net opted to select up to
60% of MPs (as in Fig. 3(d) on 04/09/2023) in order to ensure a sufficient
selection of change MPs. Fig. 3(e) shows the required energy to compress and
transmit data from the satellite. Compare to the conventional scheme (transmit
the whole sensing image), our architecture saves at least 40% in required
energy, thereby directly saving both energy for data processing and
transmission from satellites, as well as storage space and processing time at
Earth gateways.

##  V Conclusion

This research examined the Earth observation scenario in order to enhance
processing efficiency and minimize energy usage at edge devices during the
transmission and storage of sensing data. To achieve this objective, we
proposed an effective deep learning-based scoring framework that automatically
identifies and encodes semantic MPs from multi-spectral sensing images. The
numerical outcomes demonstrated that our end-to-end solution had superior data
detection capability and energy consumption performance.

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galaxies: active — X-rays: galaxies — gamma rays: galaxies

#  Relationship between Gamma-ray loudness and
X-ray spectra of Radio Galaxies

Taishu Kayanoki11affiliation: Department of Physics, Graduate School of
Advanced Science and Engineering, Hiroshima University 1-3-1 Kagamiyama,
Higashi-Hiroshima, Hiroshima 739-8526, Japan **affiliationmark:
<EMAIL_ADDRESS>Yasushi Fukazawa11affiliationmark:

###### Abstract

The Fermi satellite has detected $\sim$60 radio galaxies (RGs). In this study,
we investigate the difference in the properties of X-ray spectra between GeV-
loud RGs and GeV-quiet RGs. Our sample comprises 68 objects: 36 RGs detected
with Fermi and 32 RGs not detected with gamma rays. We analyzed the X-ray
spectra of these 68 objects using data from the XMM-Newton, Chandra, NuSTAR,
and Swift satellites. Our results show that most GeV-loud RGs do not exhibit
significant absorption, while $\sim$50% of the GeV-quiet RGs exhibit
significant absorption. This suggests that the jet of GeV-loud RGs is viewed
from a small angle, and thus the emission is not easily blocked by the torus.
Moreover, we reported that RGs with a heavy absorption are mostly in the X-ray
luminosity range of $10^{43}-10^{45}$erg s-1; however, few RGs with lower and
higher luminosity suffer from heavy absorption. This is the same trend as that
of Seyfert galaxies.

##  1 Introduction

Radio galaxies (RGs) are radio-loud Active galactic nuclei (AGN) with jets
misaligned to the line of sight. Therefore, unlike blazars in which beamed jet
emissions are dominant, RGs are objects in which emission from both
disk/corona and jet is observed. RGs are classified in FR-I and FR-II based on
their radio luminosity and morphology (Fanaroff & Riley (1974)). Radio
luminosity of FR-Is is less than $10^{26}~{}\rm{W\,Hz^{-1}}$ at 178 MHz, and
radio flux is higher near the core and fades toward the outer region. Radio
luminosity of FR-IIs is higher than $10^{26}~{}\rm{W\,Hz^{-1}}$ at 178 MHz,
and radio flux is low close to the core and becomes bright toward the lobe
edge region with bright hot spots. FR-I is considered to have a low mass
accretion rate, while FR-II is considered to have a high mass accretion rate.
Others that do not fall into this classification are Compact Steep Spectrum
(CSS). CSS is a radio source associated with an AGN, which is characterized by
its small radio emission size and steep slope of the radio spectrum.

Because jets of RGs are viewed at a larger angle from the line of sight, the
gamma-ray luminosity of RGs is lower than that of blazars by several orders of
magnitude, and the number of detections in the GeV band is small. Therefore,
it was difficult to statistically study the difference in properties between
GeV-loud RGs and GeV-quiet RGs. However, with the 4th Fermi-LAT catalog (4FGL-
DR2) (Ballet et al., 2020), the number of RGs detected in the GeV gamma-ray
band detections has increased and statistical analysis can be performed.
Hereafter, we call Fermi-detected RGs as GeV-loud RGs and other RGs as GeV-
quiet RGs. However, the number of RGs detected with Fermi is around 10%
compared with those detected in the radio band, based on the comparison of
logN-logS relation and flux ratio between radio and GeV gamma-ray bands
(Inoue, 2011). As shown later in our sample RGs, radio-bright RGs are not
necessarily detected in the gamma-ray band; only $\sim$10% of the RGs seem to
be GeV-loud. This could be caused by the difference in viewing angle of jets;
for GeV-loud RGs, their jet is viewed with a smaller viewing angle. Inoue
(2011) pointed out this possibility. Fukazawa et al. (2015) systematically
compiled the angle of the jets to be 10–30 degrees by the multi-wavelength
Spectral Energy Distribution (SED) modeling with the Synchrotron Self-Compton
(SSC) model for 10 RGs listed in the first Fermi-LAT catalog Abdo et al.
(2010a). However, their uncertainties are large. In addition, SED of RGs
consists of not only jet emission component but also other components from the
host galaxy, disk/corona, and interstellar medium and thus SED modeling is
often difficult. In some cases, a viewing angle of jets was estimated from the
radio flux ratio between two sides of the jet (Fujita & Nagai, 2017), but such
cases of estimation are still limited.

AGN emission from the central region close to the supermassive black hole
(SMBH) can be observed as a power-law shape continuum emission in the X-ray
band. AGN central region is often surrounded by the torus. When the central
region viewed through this matter, X-ray continuum emission is observed as an
absorbed power-law shape. About 80% of Seyfert galaxies with X-ray luminosity
of $\sim 10^{43}\rm{erg\,s^{-1}}$ show a large absorption column density of
$N\rm{{}_{H}}>10^{22}\rm{cm^{-2}}$; however, less than 50% of Seyfert galaxies
with X-ray luminosity of $<10^{42}\rm{erg\,s^{-1}}$ or
$>10^{44}\rm{erg\,s^{-1}}$ do (Beckmann et al., 2009; Burlon et al., 2011).

Since the jet direction is considered to be almost the same as the torus axis,
we can know about the viewing angle of jets by using torus X-ray absorption.
In previous reports (e.g. Kang et al. (2020); Panessa et al. (2016)), the
nature of the X-ray spectra of RGs has been statistically investigated, and a
similar trend was found for RGs compared with radio-quiet AGNs. However, no
comparison has been made between GeV-loud and GeV-quiet RGs, since the number
of GeV-loud RGs has been limited. Therefore, a large number of RGs in the
4FGL-DR2 catalog for the first time enables us to compare the X-ray absorption
between GeV-loud and GeV-quiet RGs. In this paper, we systematically analyzed
available X-ray observational data of RGs and studied the dependence of X-ray
absorption on gamma-ray detection. Cosmological parameters ($H_{0}$,
$\Omega_{m}$, $\Omega_{\Lambda}$) used in this study are
$H_{0}=70\,\rm{km\,s^{-1}Mpc^{-1}}$, $\Omega_{M}=0.3$, $\Omega_{\Lambda}=0.7$.

##  2 Sample and X-ray data

###  2.1 Sample Radio Galaxies

We use the 4FGL-DR2 catalog to select GeV-loud RGs, and radio flux-limited
sample RG (Mingo et al., 2014; Massaro et al., 2015) to select GeV-quiet RGs.
The 4FGL-DR2 catalog was published (Ballet et al., 2020) as the 4th Fermi/LAT
Gamma-ray source catalog. The 4FGL-DR2 catalog contains 61 misaligned AGNs, of
which 43 are classified as RG, 5 as CSS, and 11 as AGN111One of object classes
name in 4FGL-DR2. This class corresponds to non-blazar AGNs whose existing
data do not allow an unambiguous determination of their AGN types.. Also,
Mingo et al. (2014) listed 45 RGs with fluxes of $>$2 Jy at 2.7 GHz. These are
southern RGs and have a flat radio spectrum. Massaro et al. (2015) compiled 93
RGs in the 3CR catalogue that have been observed in Chandra. We selected RGs
for which X-ray data of the XMM-Newton, Chandra, Swift, or NuSTAR are
available. If the X-ray emission can not be clearly seen at the RG position or
most of X-ray emission is extended, such RGs were excluded from our sample. We
defined GeV-loud RGs in our sample as those listed in the 4FGL-DR2 catalog and
selected 38 GeV-loud RGs. For GeV-quiet RGs, we first selected RGs from Mingo
et al. (2014), but their sample is poor in FR-Is while GeV-loud RGs are rich
in FR-Is. Therefore, we selected FR-Is from Massaro et al. (2015). If RGs
listed in Mingo et al. (2014) or Massaro et al. (2015) is also listed in 4FGL-
DR2, we define them as GeV-loud RGs. Consequently, our sample contains 36 GeV-
loud RGs (19 FR-I, 12 FR-II and 5 CSS) and 32 GeV-quiet RGs (11 FR-I, 20 FR-
II, and 1 CSS); a total of 68 RGs. Our sample is given in Table 1. Figure 1
shows distributions of redshift and radio flux at 178 MHz for our sample RGs.
Both of GeV-loud and GeV-quiet RGs have a similar distribution.

Black hole masses in Table 1 are quoted from literatures if available or
estimated from $K_{s}$-Band and $B$-Band magnitudes if not previously
reported. The formula used to estimate a BH mass $M_{\rm BH}$ from the
$K_{s}$-Band magnitude $K_{s}$ is
$\log\left({M\rm{{}_{BH}}/M_{\odot}}\right)=-0.45K_{s}-2.5$ (Dong & De
Robertis (2006)), and that used to estimate from $B$-Band magnitude $M_{\rm
B}$ is $\log\left({M\rm{{}_{BH}}/M_{\odot}}\right)=-1.58-0.488M_{\rm B}$
(Marchesini et al., 2004).

###  2.2 X-ray Data

X-ray data used in this study are obtained from the XMM-Newton, Chandra, Swift
and NuSTAR satellites. The priority of the satellite data selection was XMM-
Newton, Chandra, and Swift satellites in that order. The NuSTAR satellite data
were used if the X-ray spectra suffer from significant absorption. For
multiple observations of the same object by the same satellite, the data with
the highest photon count were used for XMM-Newton; moreover, the data with the
longest observation time were used for the other three satellites.

The XMM-Newton data were reprocessed and analyzed using Science Analysis
System (SAS) version 19.0.0 and the latest calibration data CCF (Current
Calibration Files) as of April 18, 2021. Chandra data were calibrated using
version 4.12 of CIAO (Chandra Interactive Analysis of Observations) and
version 4.9.3 of CALDB (calibration database), and spectra were created using
specextract. Swift data were calibrated using XRTPIPELINE version 0.13.5 and
CALDB version 20200724 of High Energy Astrophysics Science Archive Research
Center (HEASARC). Spectral files and ancillary response files were created
using xselect. For Nustar data, data were calibrated using NUPIPELINE version
0.4.8 and version 20200912 of CALDB, and spectra were created using
nuproducts.

##  3 Spectral Fitting and Result

###  3.1 Spectral Fitting

Spectral fitting was performed using Xspec ver.12.11.1. If pile-up occurred in
the Chandra data, we used Sherpa ver.2 to correct the pile-up and performed
the analysis. If the pile-up rate was larger than $10\%$, the data were not
used, and we used data from Nustar and Swift.

We set the minimum count for one bin to be one and performed fitting using the
C-statistic. When correcting the Chandra satellite data for pile-up with
Sherpa, we used a minimum count of 20 in one bin and performed the fitting
using the $\chi^{2}$ test. We confirmed for all objects that the spectral
fitting was good with a reduced $\chi^{2}$ value of $<1.3$ and no residual
features are seen.

The components of the model used in this study are phabs, zphabs, pegpwrlw,
zgauss, and apec. phabs represents the photoelectric absorption by our Galaxy.
Hydrogen column density ($N\rm{{}_{H}}$) of this component was referred to the
HESOFT command nh which uses the HI4PI collaboration 2016 database. In the
following analyses, when a model is redshift-dependent, the redshift is fixed
to the value in Table 1. zphabs represents the absorption in the parent
galaxy. pegpwrlw represents the power-law model typically found in AGN. The
normalization of this component is the flux in the specified energy range.
zgauss is the Gaussian function to represent the iron emission line. apec is a
hot plasma emission model. This model is used when there is high-temperature
plasma around the AGN. The metal abundances of this component were fixed to
0.5 solar. const component was introduced to fit spectra of the XMM-Newton and
Nustar satellites, which have multiple detectors, to adjust relative
normalizations. zedge was introduced for Fornax A to show the absorption edge.

By combining of these model components, spectra were fitted by the following
model A$\sim$H. Model A is a single power-law model as phabs*pegpwrlw. Model B
is a power-law model with absorption by the parent galaxy as
phabs*zphabs*pegpwrlw. Model C as phabs*(zphabs*pegpwrlw+zgauss) has a
gaussian in addition to the model B. Model D as
phabs*(pegpwrlw+zphabs*pegpwrlw) is a double power-law model; one of two
power-law component is absorbed by the torus. Model E as
phabs*(pegpwrlw+zphabs* pegpwrlw+zgauss) has a gaussian in addition to the
model D. Model F as phabs*(apec+pegpwrlw), model G as
phabs*(apec+zphabs*pegpwrlw), and model H as
phabs*(apec+pegpwrlw+zphabs*pegpwrlw) have a high-temperature plasma component
in addition to the model A, B, and D. Here, the models with two pegpwrlw
components has a common photon index. Figure 2 shows an example of spectral
fitting by each model. For objects which do not require an intrinsic
absorption, an upper limit of intrinsic $N\rm{{}_{H}}$ was estimated by
multiplying the unabsorbed power-law (best-fit model) by an additional zpha.

###  3.2 Result

Table 2 summarizes the best fit parameters obtained based on the spectral
analysis. Error for each parameter is the 90% confidence interval for one
parameter. Table 2 shows that there are four sources with the iron emission
line and 10 sources with the apec component. Table 3 shows the X-ray
luminosity $L_{\rm X}$ and Eddington luminosity ratio for the power-law
component. The luminosity of the power-law component is corrected for
absorption. The 2-10 keV X-ray luminosity is in the range of $1.35\times
10^{40}$–$9.19\times 10^{45}\,\rm{erg\,s^{-1}}$. For the 64 objects whose BH
mass was available, the estimated Eddington luminosity ratio for the X-ray
power-law emission is mostly in the range of $6.54\times 10^{-7}$–1.76.

Figures 3 and 4 show an example of spectra of GeV-quiet and GeV-loud RGs,
respectively. We can see that most of GeV-loud RGs do not show a significant
absorption in the soft X-ray band; however, many GeV-quiet RGs suffer from
heavy absorption. Table 4 shows a fraction of sources with absorption
$N\rm{{}_{H}}$ greater than $10^{22}\rm{cm}^{-2}$ for GeV-loud and GeV-quiet
RGs. From this table, we can see that few GeV-loud RGs undergo absorption,
while $\sim 50\%$ of GeV-quiet RGs undergo absorption. Table 4 shows a
fraction for each of RG classifications. The fraction of sources with heavy
absorption for FR-II RGs is as high as 40%, while that of others are
$\leq$20%.

##  4 Discussion

###  4.1 Absorption $N\rm{{}_{H}}$ and Gamma-ray loudness

We reported that $\sim 50\%$ of the GeV-quiet RGs have a large absorption
column density $N\rm{{}_{H}}$, while few GeV-loud RGs have a large
$N\rm{{}_{H}}$. The radiation from the center of AGNs is absorbed by the torus
depending on the viewing angle. Therefore, the absorption is large when the
torus is viewed from the side, while the absorption is small when it is viewed
from a small inclination angle to the torus axis. Because the jet and torus
axis are the same, we can assume that the viewing angle of the jet is smaller
as the absorption becomes smaller. The jets of RGs could be brighter in gamma
rays when the jet viewing angle is small and thus the beaming effect is large.
This suggests that the GeV-loud RGs are observed from a relatively small
viewing angle to the jet axis. When the jet is seen from a small angle, it is
suggested that the X-ray radiation from the center of AGNs is not blocked by
the torus and thus the absorption is small.

On the other hand, GeV-quiet RGs can be considered to have a weak jet beaming
effect and thus gamma-ray radiation is faint, making them difficult to detect
with Fermi. Therefore, we can assume that the GeV-quiet RGs are observed from
a large viewing angle to the jet axis. In that case, we observe the center of
AGNs through the torus. Therefore, it can be understood that the X-ray
emission from the center of AGNs is easily blocked by the torus and most of
the GeV-quiet RGs show absorbed spectra.

###  4.2 Absorption $N\rm{{}_{H}}$ and X-ray luminosity $L\rm{{}_{x}}$

From Tables 2 and 3, we created a scatter plot of the absorption column
density $N\rm{{}_{H}}$ and X-ray luminosity (Figure 5). This figure shows that
$\sim 50\%$ of the medium-luminosity ($10^{43}-10^{45}$ erg s-1 RGs show a
large $N\rm{{}_{H}}$, while few of the low and high luminosity RGs show a
large $N\rm{{}_{H}}$. The previous studies of the relationship between
absorption and luminosity of RGs (Panessa et al. 2016, Kuraszkiewicz et al.
2021) show the relation of mid- and high-luminosity RGs, and our results are
consistent with these studies. Moreover, our result on low-luminosity RGs is
novel.

In Seyfert galaxies, as shown by Beckmann et al. (2009) and Burlon et al.
(2011), $\sim 50\%$ of the medium-luminosity sources show a large
$N\rm{{}_{H}}$, and few low and high luminosity sources show a large
$N\rm{{}_{H}}$. This suggests that the absorption-luminosity relation for RGs,
including low-luminosity RGs, follows the same trend as that for Seyfert
galaxies. Because the fraction of AGNs with a large $N\rm{{}_{H}}$ at high
luminosities is small, the dust torus is not formed with a large solid angle
or a large thickness for brighter AGNs. This can be attributed to a physical
process in which the high radiation flux from the center of AGNs affects the
physical structure of the torus (Ueda et al., 2003). Similarly, the fraction
of AGNs with a large $N\rm{{}_{H}}$ at low luminosities is small. It is
suggseted that the torus is not formed in low-luminosity ANGs (e.g., Burlon et
al. (2011)). The same scenario can be applied to RGs, and thus they may not
have a torus at low luminosities. Furthermore, as reported by Fukazawa et al.
(2015), the X-ray emission of low-luminosity RGs could be synchrotron
radiation from the jet. In that case, the emission is not absorbed by the
torus.

###  4.3 Photon index $\Gamma\rm{{}_{x}}$ and Eddington ratio
$L\rm{{}_{x}}/{\it L}\rm{{}_{Edd}}$

Figures 6 and 7 are a scatter plot of X-ray luminosity as well as power-law
index and that of the power-law index and absorption column density
$N\rm{{}_{H}}$. These figures demonstrated no dependence of photon index on
$N\rm{{}_{H}}$ and X-ray luminosity. The average of photon index is
$1.83\,(0.46)$, $1.94\,(0.42)$ and $1.70\,(0.46)$ for all RGs, GeV-loud RGs
and GeV-quiet RGs, respectively, where values in the parentheses are standard
deviation. It is $1.88\,(0.47)$ and $1.70\,(0.42)$ for RGs with
NH$<10^{22}\rm{cm}^{-2}$ and those with NH$>10^{22}\rm{cm}^{-2}$,
respectively.

Sambruna et al. (1999), reported weak evidence that Broad Line Radio Galaxies
(BLRGs) have a flatter X-ray spectrum than that of the radio-quiet Seyfert 1
galaxies. Kang et al. (2020) reported that the power-law photon index of RGs
is flatter than that of radio-quiet AGNs. They analyzed the NuSTAR data of
non-Compton-thick RGs and compared them with the results of Panagiotou &
Walter (2019) on radio-quiet AGNs. The average of photon index in Kang et al.
(2020) is $1.73\,(0.15)$ and $1.90\,(0.21)$ for RGs and radio-quiet AGNs,
respectively.

Photon index $1.83\,(0.46)$ for all RGs in our result is steeper than the
photon index for RGs in Kang et al. (2020). Because the photon index of the
GeV-loud RGs appears to be larger, we performed a KS test on the distribution
of the photon index of GeV-loud RGs and that of GeV-quiet RGs and obtained a
p-value of 0.3, indicating that the GeV-loud and GeV-quiet RGs have a
significantly different photon index distribution. If the high-energy tail of
synchrotron radiation from the jet is observed in the X-ray band, the photon
index is expected to be larger (Fukazawa et al., 2015); therefore, the photon
index of GeV-loud RGs could be affected by the jet. The photon index of the
GeV-quiet RGs may be flatter than that of the radio-quiet AGN (Kang et al.,
2020); however, because $\sim$half of the GeV-quiet RGs suffer from the
absorption, this flatness might be caused by the systematic effect from
absorption.

Photon index could depend on the Eddington luminosity ratio. Therefore, we
investigated the relation between photon index and Eddington luminosity ratio;
however, we do not identify any dependence within errors.

The authors thanks to the editor and the anonymous referee for their helpful
comments to improve the paper. This research made use of the XMM-Newton,
Chandra, Swift and NuSTAR Data, and also the NASA/IPAC Extragalactic Database
(NED).

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Table 1: Sample of Radio Galaxies No. | Sourcea | Datab | ObsID | Redshift | $N\rm{{}_{H}}\rm{{}^{c}}$ | F${}_{178}\rm{{}^{d}}$ | classe | $M\rm{{}_{BH}}\rm{{}^{f}}$ | Referenceg
---|---|---|---|---|---|---|---|---|---
|  |  |  |  | $10^{20}\,\rm{cm^{-2}}$ | Jy |  | $10^{8}M_{\odot}$ |
GeV-quiet RGs
1 | 3C 433 | Chandra | 7881 | 0.10160 | 8.21 | 57.5 | FR-I | 16.5 | 2, 1
2 | PKS 0409-75 | XMM-Newton | 0651281901 | 0.69300 | 7.92 | 55.9 | FR-II | 10.5i | 1, 7
3 | PKS 2356-61 | XMM-Newton | 0677180601 | 0.09631 | 1.33 | 51.5 | FR-II | 9.10 | 1, 1
4 | PKS 1814-63 | XMM-Newton | 0146340601 | 0.06466 | 6.01 | 43.7 | CSS | 6.80 | 1, 1
5 | PKS 0442-28 | Swift | 80964002 | 0.14700 | 2.46 | 41.8 | FR-II | 13.3 | 1, 1
6 | PKS 1559+02 | Chandra | 6841 | 0.10480 | 5.70 | 36.3 | FR-II | 13.8 | 1, 1
7 | 3C 459 | XMM-Newton | 0651280101 | 0.22012 | 5.30 | 29.2 | FR-II | 19.5h | 1, 4
8 | 3C 227 | Nustar | 60061329002 | 0.08627 | 1.99 | 28.6 | FR-II | 8.40 | 1, 1
9 | PKS 1938-15 | XMM-Newton | 0671871001 | 0.45200 | 7.40 | 25.8 | FR-II | - | 1, 1
10 | 3C 403 | Nustar | 60061293002 | 0.05900 | 13.2 | 25.2 | FR-II | 9.20 | 1, 1
11 | 3C 032 | XMM-Newton | 0651281001 | 0.40000 | 1.60 | 25.1 | FR-II | 19.6 | 1, 1
12 | 3C 445 | Nustar | 60160788002 | 0.05588 | 4.80 | 24.6 | FR-II | 11.8 | 1, 1
13 | 3C 327.1 | XMM-Newton | 0651281201 | 0.46200 | 6.89 | 23.4 | FR-II | - | 1, -
14 | PKS 0039-44 | XMM-Newton | 0651280901 | 0.34600 | 2.63 | 23.2 | FR-II | 14.6 | 1, 1
15 | 3C 062 | Chandra | 10320 | 0.14700 | 1.62 | 21.9 | FR-II | 10.3 | 1, 1
16 | PKS 0349-27 | Chandra | 11497 | 0.06569 | 0.737 | 21.5 | FR-II | 3.60 | 1, 1
17 | PKS 0043-42 | Chandra | 10319 | 0.05280 | 1.12 | 21.0 | FR-II | 9.40 | 1, 1
18 | PKS 1954-55 | Chandra | 11505 | 0.05810 | 4.46 | 16.5 | FR-I | 33.5 | 1, 4
19 | 3C 015 | Chandra | 17128 | 0.07338 | 2.19 | 16.4 | FR-I | 5.96i | 2, 5
20 | 3C 031 | XMM-Newton | 0551720101 | 0.01700 | 5.22 | 16.3 | FR-I | 8.20 | 2, 1
21 | 3C 105 | Nustar | 60261003002 | 0.08900 | 10.4 | 16.2 | FR-II | 4.10 | 1, 1
22 | 3C 029 | Chandra | 12721 | 0.04503 | 3.19 | 15.7 | FR-I | 7.63i | 2, 5
23 | PKS 1547-79 | XMM-Newton | 0651281401 | 0.48300 | 10.3 | 12.4 | FR-II | 34.4 | 1, 1
24 | 3C 346 | Chandra | 3129 | 0.16201 | 4.99 | 12.0 | FR-I | 17.0 | 2, 1
25 | PKS 0347+05 | XMM-Newton | 0651280801 | 0.33900 | 12.8 | 11.8 | FR-II | 32.8 | 1, 1
26 | 3C 130 | Chandra | 14957 | 0.10900 | 36.0 | 10.8 | FR-I | 20.8h | 2, 4
27 | 3C 296 | XMM-Newton | 0201860101 | 0.02470 | 1.84 | 10.4 | FR-I | 12.3 | 2, 1
28 | PKS 1306-09 | XMM-Newton | 0671871201 | 0.46685 | 3.01 | 9.79 | FR-II | 33.3 | 1, 1
29 | 3C 402 | XMM-Newton | 0823050101 | 0.02595 | 11.9 | 9.55 | FR-I | 1.81i | 2, 5
Table 1. (Continued)
---
No. | Sourcea | Datab | ObsID | Redshift | $N\rm{{}_{H}}\rm{{}^{c}}$ | F${}_{178}\rm{{}^{d}}$ | classe | $M\rm{{}_{BH}}\rm{{}^{f}}$ | Referenceg
|  |  |  |  | $10^{20}\,\rm{cm^{-2}}$ | Jy |  | $10^{8}M_{\odot}$ |
30 | PKS 0620-52 | XMM-Newton | 0852980601 | 0.05110 | 3.71 | 8.96 | FR-I | 22.7 | 1, 1
31 | PKS 1934-63 | XMM-Newton | 0784610201 | 0.18129 | 5.83 | 7.37 | FR-II | 10.9 | 1, 1
32 | 3C 213.1 | Chandra | 9307 | 0.19392 | 2.57 | 6.60 | FR-I | 4.04h | 2, 4
GeV-loud RGs
33 | Pictor A | XMM-Newton | 0206390101 | 0.03501 | 3.62 | 441 | FR-II | 1.21h | 3, 4
34 | Fornax A | XMM-Newton | 0502070201 | 0.00591 | 1.99 | 273 | FR-I | 0.544h | 3, 4
35 | PKS 2153-69 | XMM-Newton | 0152670101 | 0.02827 | 2.49 | 81.7 | FR-II | 1.39h | 3, 4
36 | PKS 0521-36 | XMM-Newton | 065760201 | 0.05655 | 3.27 | 71.7 | FR-II | 11.4h | 3, 4
37 | 3C 380 | Swift | 81221001 | 0.69000 | 6.29 | 65.5 | CSS | 27.8i | 3, 5
38 | Cen B | XMM-Newton | 092140101 | 0.01292 | 68.0 | 50.0 | FR-I | 0.988h | 3, 4
39 | NGC 4261 | XMM-Newton | 0502120101 | 0.00726 | 1.61 | 44.1 | FR-I | 0.460h | 3, 4
40 | 3C 264 | XMM-Newton | 0602390101 | 0.02160 | 1.87 | 25.3 | FR-I | 5.60 | 3, 1
41 | 3C 286 | Chandra | 15006 | 0.84989 | 1.11 | 25.2 | CSS | 3.16 | 3, 6
42 | 3C 309.1 | Chandra | 3105 | 0.90500 | 2.89 | 24.2 | CSS | 42.6i | 3, 5
43 | PKS 1839-48 | Chandra | 10321 | 0.11080 | 5.25 | 23.4 | FR-I | 21.1 | 1, 1
44 | PKS 1821-327 | XMM-Newton | 0650591401 | 0.35500 | 12.4 | 23.3 | FR-II | - | 3, -
45 | PKS 0625-35 | XMM-Newton | 0302440601 | 0.05459 | 6.36 | 21.6 | FR-I | 12.9 | 1, 1
46 | 3C 216 | Chandra | 15002 | 0.67002 | 1.34 | 21.2 | CSS | 0.100 | 3, 6
47 | 3C 138 | Chandra | 14996 | 0.76000 | 20.1 | 21.0 | CSS | 6.30 | 3, 1
48 | PKS 2324-02 | XMM-Newton | 0405860101 | 0.18873 | 4.49 | 11.5 | FR-II | 13.5h | 3, 4
49 | 3C 303 | Nustar | 60463048002 | 0.14121 | 1.68 | 11.3 | FR-II | 3.18i | 3, 5
50 | NGC 2484 | XMM-Newton | 0602390101 | 0.04083 | 4.74 | 9.35 | FR-II | 2.39h | 3, 4
51 | B2 1113+29 | XMM-Newton | 0550270101 | 0.04868 | 1.19 | 7.44 | FR-I | 1.92i | 3, 5
52 | PKS 2300-18 | Swift | 31729002 | 0.12893 | 1.90 | 5.48 | FR-II | 10.4h | 3, 4
53 | NGC 315 | XMM-Newton | 0305290201 | 0.01648 | 5.88 | 5.20 | FR-I | 0.951h | 3, 4
54 | 4C +40.01 | Chandra | 5669 | 0.25500 | 5.93 | 5.10 | FR-II | 12.5h | 3, 4
55 | PKS 1514+00 | XMM-Newton | 0103860601 | 0.05259 | 4.14 | 3.90 | FR-I | - | 3, -
56 | NGC 6328 | XMM-Newton | 0804520301 | 0.01443 | 5.90 | 2.97 | FR-I | 0.968h | 3, 4
57 | 4C +39.12 | Chandra | 857 | 0.02020 | 12.5 | 2.70 | FR-I | 1.61h | 3, 4
58 | TXS 1516+064 | XMM-Newton | 018741001 | 0.10208 | 2.91 | 1.14 | FR-II | 6.17h | 3, 4
Table 1. (Continued)
---
No. | Sourcea | Datab | ObsID | Redshift | $N\rm{{}_{H}}\rm{{}^{c}}$ | F${}_{178}\rm{{}^{d}}$ | classe | $M\rm{{}_{BH}}\rm{{}^{f}}$ | Referenceg
|  |  |  |  | $10^{20}\,\rm{cm^{-2}}$ | Jy |  | $10^{8}M_{\odot}$ |
59 | TXS 0149+710 | Swift | 10149002 | 0.02281 | 30.7 | 1.06 | FR-I | 1.06h | 3, 4
60 | IC 1531 | XMM-Newton | 0202190301 | 0.02564 | 2.41 | 1.05 | FR-I | 1.44h | 3, 4
61 | NGC 2329 | Chandra | 5900 | 0.01933 | 7.49 | 0.943 | FR-I | 1.46h | 3, 4
62 | IC 310 | XMM-Newton | 0151560101 | 0.01885 | 11.4 | 0.732 | FR-I | 1.29h | 3, 4
63 | B2 1447+27 | Swift | 40619002 | 0.03059 | 2.89 | 0.600 | FR-I | 2.66i | 3, 5
64 | PKS 2331-240 | XMM-Newton | 0760990101 | 0.04770 | 1.65 | 0.577 | FR-I | 1.18h | 3, 4
65 | NGC 2892 | Chandra | 18038 | 0.02246 | 4.19 | 0.566 | FR-I | 1.41h | 3, 4
66 | B3 0309+411B | XMM-Newton | 0306680301 | 0.13400 | 10.1 | 0.547 | FR-II | 7.49h | 3, 4
67 | NGC 3894 | Chandra | 10389 | 0.01077 | 1.83 | 0.371 | FR-I | 0.589h | 3, 4
68 | B3 1009+427 | Swift | 85352004 | 0.36491 | 1.58 | 0.177 | FR-II | 27.8h | 3, 4
a: Name of objects. b: Satellite of X-ray data. c: Galactic hydrogen column
density (HI4PI collaboration 2016).
d: Radio flux at 178MHz. e: Classification of RGs. f: BH masses. (h) BH mass
estimated using $K_{s}$-band data.
(i) BH mass estimated using $B$-band data. g: Left and right are references
for object selection and BH mass,
respectively. 1: Mingo et al. (2014) 2: Massaro et al. (2015) 3: 4FGL-DR2
catalog
4: $K_{s}$-Band magnitude (2MASS catalog) 5: Marchesini et al. (2004) 6: Yuan
et al. (2018) 7: Massardi et al. (2008)

Figure 1: Distributions of redshift (left) and radio flux at 178 MHz (right)
of GeV-loud RGs and GeV-quiet RGs in our sample. The solid line shows GeV-
quiet RGs and the dashed line GeV-loud RGs.

(a) PKS 0625-35 (model A)

(b) 3C 227 (model B)

(c) 3C 105 (model C)

(d) 3C 032 (model D)

Figure 2: Example of spectra fitted with the Model A-H. Panel (a), (d), (e),
(f), (g) and (h) are XMM-Newton data, where black, red, and blue symbols are
MOS1, MOS2 and PN spectra, respectively. Panel (b) and (c) are NuSTAR data,
where black and red symbols are FPMA and FPMB spectra, respectively. The solid
line represents the best-fit total model, while dotted lines are the model
components. The bottom panels show the residuals in units of $\sigma$. (a) PKS
0625-35 with model A (phabs*pegpwrlw). (b) 3C 227 with model B
(phabs*zphabs*pegpwrlw). (c) 3C 105 with model C
(phabs*(zphabs*pegpwrlw+zgauss)). (d) 3C 032 with model D
(phabs*(pegpwrlw+zphabs*pegpwrlw)).

(e) PKS 2356-61 (model E)

(f) NGC 2484 (model F)

(g) 3C 031 (model G)

(h) NGC 4261 (model H)

Figure 2: (Continued) (e) PKS 2356-61 with model E (phabs*(pegpwrlw +zphabs* pegpwrlw+zgauss)). (f) NGC 2484 with model F (phabs*(apec+pegpwrlw)). (G) 3C 031 with model G (phabs*(apec+zphabs*pegpwrlw)). (h) NGC 4261 with model H (phabs*(apec+pegpwrlw+zphabs*pegpwrlw)). Table 2: Summary of best-fit parameters of x-ray data spectral fitting |  | apec | None absorbed pegpwrlw | zphabs | absorbed pegpwrlw | zgauss |
---|---|---|---|---|---|---|---
No. | Model | kT | Norm | $\Gamma_{u}$ | Norm1 | Intrinsic $N\rm{{}_{H}}$ | $\Gamma_{a}$ | Norm2 | EW | ${\it C}\rm{-stat}/\rm{d.o.f.}$
|  | keV | $10^{-5}$ |  | $10^{-12}\,\rm{erg\,cm^{-2}\,s^{-1}}$ | $10^{22}\rm{cm^{-2}}$ |  | $10^{-12}\,\rm{erg\,cm^{-2}\,s^{-1}}$ | eV |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
1 | D | - | - | $1.55^{+0.24}_{-0.23}$ | $3.08^{+1.52}_{-1.02}\times 10^{-2}$ | $9.13^{+1.04}_{-0.96}$ | $1.55^{+0.24}_{-0.23}$ | $4.42^{+0.38}_{-0.29}$ | - | 136.5/116*
2 | A | - | - | $1.99\pm 0.07$ | $2.46^{+0.31}_{-0.28}\times 10^{-1}$ | $<1.40\times 10^{-1}$ | - | - | - | 1010.3/1156
3 | E | - | - | $2.11^{+0.36}_{-0.35}$ | $5.46^{+3.83}_{-2.30}\times 10^{-2}$ | $20.7^{+2.9}_{-2.8}$ | $2.11^{+0.36}_{-0.35}$ | $9.27^{+1.88}_{-1.46}$ | $432^{+301}_{-237}$ | 672.0/755
4 | C | - | - | - | - | $1.89^{+0.16}_{-0.15}$ | $1.37^{+0.09}_{-0.08}$ | $4.57^{+0.29}_{-0.25}$ | $108^{+68}_{-54}$ | 2353.2/2830
5 | D | - | - | $2.02^{+0.39}_{-0.37}$ | $1.23^{+1.90}_{-0.86}\times 10^{-1}$ | $1.50^{+0.57}_{-0.50}$ | $2.02^{+0.39}_{-0.37}$ | $4.15^{+0.66}_{-0.58}$ | - | 192.1/260
6 | E | - | - | $2.93\pm 0.19$ | $2.16^{+0.66}_{-0.51}\times 10^{-2}$ | $25.8^{+11.3}_{-7.3}$ | $2.93\pm 0.19$ | $4.63^{+2.50}_{-1.50}\times 10^{-1}$ | $1625^{+925}_{-625}$ | 294.1/242
7 | F | $0.89\pm 0.09$ | $2.35^{+0.68}_{-0.58}$ | $0.90^{+0.19}_{-0.20}$ | $1.50^{+0.34}_{-0.29}\times 10^{-1}$ | $<4.80\times 10^{-1}$ | - | - | - | 730.2/746
8 | B | - | - | - | - | $1.96^{+1.47}_{-1.45}$ | $1.77\pm 0.07$ | $13.1^{+0.93}_{-0.85}$ | - | 844.0/828
9 | B | - | - | - | - | $1.84^{+0.46}_{-0.45}$ | $1.70\pm 0.06$ | $1.43^{+0.09}_{-0.08}$ | - | 1834.5/2211
10 | C | - | - | - | - | $21.5^{+4.8}_{-4.5}$ | $1.45^{+0.16}_{-0.15}$ | $5.36^{+0.86}_{-0.79}$ | $169^{+149}_{-80}$ | 743.6/807
11 | D | - | - | $1.58\pm 0.19$ | $1.41^{+0.53}_{-0.38}\times 10^{-1}$ | $15.6^{+2.7}_{-2.4}$ | $1.58\pm 0.19$ | $1.30^{+0.19}_{-0.17}$ | - | 1153.7/1371
12 | C | - | - | - | - | $12.2^{+2.4}_{-2.7}$ | $1.42^{+0.09}_{-0.14}$ | $9.39^{+0.94}_{-1.22}$ | $<235$ | 777.5/832
13 | A | - | - | $1.75\pm 0.03$ | $1.20\pm 0.06$ | $<4.99\times 10^{-2}$ | - | - | - | 2239.2/2492
14 | D | - | - | $1.86\pm 0.23$ | $2.17^{+1.06}_{-0.72}\times 10^{-2}$ | $16.6^{+2.3}_{-2.2}$ | $1.86\pm 0.23$ | $1.16^{+0.18}_{-0.16}$ | - | 1049.0/1168
15 | D | - | - | $1.75^{+0.40}_{-0.38}$ | $2.52^{+2.52}_{-1.23}\times 10^{-2}$ | $16.2^{+2.6}_{-2.3}$ | $1.75^{+0.40}_{-0.38}$ | $5.33^{+1.20}_{-0.61}$ | - | 60.7/54*
16 | B | - | - | - | - | $4.08^{+1.51}_{-1.25}$ | $1.22^{+0.60}_{-0.50}$ | $1.09^{+0.17}_{-0.13}$ | - | 20.1/21*
17 | E | - | - | $1.09\pm 0.71$ | $2.44^{+5.62}_{-1.70}\times 10^{-2}$ | $7.79^{+3.47}_{-2.93}$ | $1.09\pm 0.71$ | $5.14^{+1.50}_{-1.13}\times 10^{-1}$ | $1457^{+1180}_{-680}$ | 118.5/170
18 | B | - | - | - | - | $1.66^{+1.64}_{-1.51}\times 10^{-1}$ | $2.43^{+0.50}_{-0.46}$ | $3.42^{+1.41}_{-1.03}\times 10^{-2}$ | - | 136.7/112
19 | D | - | - | $1.38\pm 0.09$ | $1.72^{+0.37}_{-0.30}\times 10^{-1}$ | $1.48\pm 0.16$ | $1.38\pm 0.09$ | $8.79^{+0.60}_{-0.48}\times 10^{-1}$ | - | 207.8/209*
20 | G | $0.84\pm 0.02$ | $7.67^{+0.63}_{-0.61}$ | - | - | $7.97^{+4.66}_{-4.43}\times 10^{-2}$ | $2.17\pm 0.16$ | $1.07^{+0.13}_{-0.12}\times 10^{-1}$ | - | 1665.0/1868

Table 2 (Continued)
---
|  | apec | None absorbed pegpwrlw | zphabs | absorbed pegpwrlw | zgauss |
No. | Model | kT | Norm | $\Gamma_{u}$ | Norm1 | Intrinsic $N\rm{{}_{H}}$ | $\Gamma_{a}$ | Norm2 | EW | ${\it C}\rm{-stat}/\rm{d.o.f.}$
|  | keV | $10^{-5}$ |  | $10^{-12}\,\rm{erg\,cm^{-2}\,s^{-1}}$ | $10^{22}\rm{cm^{-2}}$ |  | $10^{-12}\,\rm{erg\,cm^{-2}\,s^{-1}}$ | eV |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
21 | C | - | - | - | - | $38.6^{+13.8}_{-13.5}$ | $1.31^{+0.32}_{-0.37}$ | $2.72^{+1.25}_{-0.89}$ | $469^{+245}_{-174}$ | 647.3/747
22 | A | - | - | $1.09\pm 0.41$ | $8.90^{+5.77}_{-3.63}\times 10^{-2}$ | $<8.42\times 10^{-1}$ | - | - | - | 33.4/43
23 | A | - | - | $0.68^{+0.27}_{-0.28}$ | $2.11^{+0.97}_{-0.71}\times 10^{-1}$ | $<6.01\times 10^{-1}$ | - | - | - | 142.20/136
24 | A | - | - | $1.67\pm 0.05$ | $4.31^{+0.29}_{-0.28}\times 10^{-1}$ | $<4.18\times 10^{-2}$ | - | - | - | 432.1/375
25 | D | - | - | $1.93^{+0.27}_{-0.26}$ | $3.99^{+1.89}_{-1.31}\times 10^{-2}$ | $90.1^{+25.2}_{-22.0}$ | $1.93^{+0.27}_{-0.26}$ | $1.12^{+0.72}_{-0.45}$ | - | 391.1/428
26 | A | - | - | $2.04^{+0.28}_{-0.26}$ | $2.56^{+0.83}_{-0.67}\times 10^{-2}$ | $<1.27\times 10^{-1}$ | - | - | - | 97.0/138
27 | F | $0.83\pm 0.02$ | $7.90^{+0.75}_{-0.71}$ | $1.47\pm 0.11$ | $2.00^{+0.22}_{-0.20}\times 10^{-1}$ | $<6.98\times 10^{-3}$ | - | - | - | 1352.6/1513
28 | B | - | - | - | - | $1.80^{+0.59}_{-0.0.57}\times 10^{-1}$ | $1.85\pm 0.09$ | $2.71^{+0.27}_{-0.25}\times 10^{-1}$ | - | 1371.4/1576
29 | F | $0.74\pm 0.06$ | $2.45^{+0.45}_{-0.43}$ | $2.14^{+0.14}_{-0.15}$ | $5.33^{+0.85}_{-0.76}\times 10^{-2}$ | $<1.20\times 10^{-1}$ | - | - | - | 1131.1/1256
30 | F | $0.91^{+0.07}_{-0.06}$ | $2.01^{+0.41}_{-0.38}$ | $2.33^{+0.03}_{-0.04}$ | $1.48\pm 0.06\times 10^{-1}$ | $<1.75\times 10^{-2}$ | - | - | - | 2039.9/2263
31 | A | - | - | $1.67\pm 0.07$ | $1.30^{+0.18}_{-0.16}\times 10^{-1}$ | $<8.76\times 10^{-2}$ | - | - | - | 785.0/959
32 | A | - | - | $1.68^{+0.37}_{-0.35}$ | $5.39^{+3.02}_{-2.07}\times 10^{-2}$ | $<3.29\times 10^{-1}$ | - | - | - | 52.2/50
33 | A | - | - | $1.750\pm 0.005$ | $10.1\pm 0.1$ | $<3.92\times 10^{-4}$ | - | - | - | 5300.99/5294
34 | G* | $0.88^{+0.02}_{-0.01}$ | $48.4\pm 0.2$ | - | - | $4.87^{+2.45}_{-1.97}$ | $2.27^{+0.56}_{-0.50}$ | $2.55^{+0.65}_{-0.39}\times 10^{-1}$ | - | 2132.5/2203
35 | A | - | - | $1.82\pm 0.01$ | $7.12\pm 0.10$ | $<1.64\times 10^{-3}$ | - | - | - | 4663.7/4666
36 | A | - | - | $1.78\pm 0.01$ | $8.38\pm 0.10$ | $<1.24\times 10^{-1}$ | - | - | - | 5047.38/4919
37 | A | - | - | $1.53\pm 0.10$ | $4.39^{+0.55}_{-0.50}$ | $<1.35\times 10^{-1}$ | - | - | - | 280.3/333
38 | B | - | - | - | - | $9.37^{+0.48}_{-0.32}\times 10^{-1}$ | $1.56\pm 0.04$ | $6.60\pm 0.14$ | - | 4468.1/4663
39 | H | $0.75\pm 0.01$ | $30.1^{+1.2}_{-1.1}$ | $1.70^{+0.18}_{-0.19}$ | $1.59^{+0.05}_{-0.04}\times 10^{-1}$ | $8.73^{+1.36}_{-1.31}$ | $1.70^{+0.18}_{-0.19}$ | $9.65^{+1.27}_{-1.23}\times 10^{-1}$ | - | 2412.1/2710
40 | A | - | - | $2.26\pm 0.04$ | $1.53\pm 0.09$ | $<2.45\times 10^{-2}$ | - | - | - | 2072.8/2190

Table 2 (Continued)
---
|  | apec | None absorbed pegpwrlw | zphabs | absorbed pegpwrlw | zgauss |
No. | Model | kT | Norm | $\Gamma_{u}$ | Norm1 | Intrinsic $N\rm{{}_{H}}$ | $\Gamma_{a}$ | Norm2 | EW | ${\it C}\rm{-stat}/\rm{d.o.f.}$
|  | keV | $10^{-5}$ |  | $10^{-12}\,\rm{erg\,cm^{-2}\,s^{-1}}$ | $10^{22}\rm{cm^{-2}}$ |  | $10^{-12}\,\rm{erg\,cm^{-2}\,s^{-1}}$ | eV |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
41 | A | - | - | $2.12^{+0.29}_{-0.28}$ | $2.54^{+1.08}_{-0.78}\times 10^{-1}$ | $<3.22\times 10^{-1}$ | - | - | - | 51.2/81
42 | A | - | - | $1.49\pm 0.04$ | $2.19\pm 0.11$ | $<1.34\times 10^{-2}$ | - | - | - | 393.7/438
43 | A | - | - | $1.54\pm 0.19$ | $9.05^{+2.38}_{-1.95}\times 10^{-2}$ | $<1.53\times 10^{-1}$ | - | - | - | 125.3/141
44 | A | - | - | $1.67\pm 0.01$ | $5.43^{+0.11}_{-0.10}$ | $<4.07\times 10^{-3}$ | - | - | - | 4230.7/4445
45 | A | - | - | $2.49\pm 0.02$ | $2.85^{+0.08}_{-0.07}$ | $<1.35\times 10^{-2}$ | - | - | - | 2547.4/2809
46 | A | - | - | $1.47\pm 0.18$ | $1.14^{+0.27}_{-0.23}$ | $<4.52\times 10^{-1}$ | - | - | - | 120.8/151
47 | A | - | - | $1.37\pm 0.15$ | $2.48^{+0.43}_{-0.37}$ | $<1.24\times 10^{-1}$ | - | - | - | 208.6/206
48 | A | - | - | $1.74\pm 0.10$ | $7.66^{+1.17}_{-1.06}\times 10^{-1}$ | $<4.06\times 10^{-2}$ | - | - | - | 1759.5/1964
49 | A | - | - | $1.70^{+0.11}_{-0.10}$ | $2.22^{+0.18}_{-0.17}$ | $<6.33$ | - | - | - | 501.4/539
50 | F | $0.79\pm 0.03$ | $4.08^{+0.46}_{-0.44}$ | $2.08\pm 0.06$ | $1.36^{+0.11}_{-0.10}\times 10^{-1}$ | $<1.17\times 10^{-2}$ | - | - | - | 1698.3/2002
51 | A | - | - | $2.26^{+0.17}_{-0.16}$ | $3.82^{+1.07}_{-0.90}\times 10^{-2}$ | $<8.36\times 10^{-2}$ | - | - | - | 383.7/496
52 | A | - | - | $1.57\pm 0.11$ | $6.18^{+0.91}_{-0.81}$ | $<4.65\times 10^{-2}$ | - | - | - | 287.3/280
53 | G | $0.70\pm 0.01$ | $23.8\pm 1.1$ | - | - | $6.57^{+1.62}_{-1.65}\times 10^{-1}$ | $1.82\pm 0.12$ | $7.50^{+0.40}_{-0.39}\times 10^{-1}$ | - | 2598.5/2747
54 | A | - | - | $1.88\pm 0.11$ | $1.35^{+0.20}_{-0.18}$ | $<1.12\times 10^{-1}$ | - | - | - | 209.0/218
55 | A | - | - | $1.74\pm 0.02$ | $1.97\pm 0.08$ | $<4.46\times 10^{-3}$ | - | - | - | 2664.7/2928
56 | A | - | - | $1.70\pm 0.04$ | $3.82^{+0.25}_{-0.24}\times 10^{-1}$ | $<1.94\times 10^{-2}$ | - | - | - | 2875.2/3121
57 | A | - | - | $2.19\pm 0.12$ | $4.41^{+0.75}_{-0.65}\times 10^{-1}$ | $<1.14\times 10^{-1}$ | - | - | - | 162.6/179
58 | A | - | - | $2.11\pm 0.02$ | $4.79\pm 0.13$ | $<4.69\times 10^{-3}$ | - | - | - | 2833.1/3144
59 | A | - | - | $1.99^{+0.40}_{-0.39}$ | $9.14^{+4.55}_{-3.17}\times 10^{-1}$ | $<4.66\times 10^{-1}$ | - | - | - | 39.7/63
60 | F | $0.62^{+0.04}_{-0.05}$ | $7.03^{+0.87}_{-0.84}$ | $2.18\pm 0.07$ | $2.21^{+0.20}_{-0.18}\times 10^{-1}$ | $<1.29\times 10^{-2}$ | - | - | - | 1447.6/1643

Table 2 (Continued)
---
|  | apec | None absorbed pegpwrlw | zphabs | absorbed pegpwrlw | zgauss |
No. | Model | kT | Norm | $\Gamma_{u}$ | Norm1 | Intrinsic $N\rm{{}_{H}}$ | $\Gamma_{a}$ | Norm2 | EW | ${\it C}\rm{-stat}/\rm{d.o.f.}$
|  | keV | $10^{-5}$ |  | $10^{-12}\,\rm{erg\,cm^{-2}\,s^{-1}}$ | $10^{22}\rm{cm^{-2}}$ |  | $10^{-12}\,\rm{erg\,cm^{-2}\,s^{-1}}$ | eV |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
61 | A | - | - | $2.06^{+0.19}_{-0.18}$ | $5.97^{+1.45}_{-1.20}\times 10^{-1}$ | $<1.47\times 10^{-1}$ | - | - | - | 125.6/141
62 | B | - | - | - | - | $3.34^{+0.85}_{-0.84}\times 10^{-2}$ | $2.53\pm 0.03$ | $1.44^{+0.04}_{-0.03}$ | - | 30146.8/3278
63 | A | - | - | $2.61^{+0.83}_{-0.76}$ | $1.18^{+1.66}_{-0.72}\times 10^{-1}$ | $<2.70\times 10^{-1}$ | - | - | - | 23.0/27
64 | A | - | - | $1.72\pm 0.01$ | $10.7\pm 0.1$ | $<1.69\times 10^{-3}$ | - | - | - | 4732.4/4842
65 | A | - | - | $3.49^{+0.63}_{-0.59}$ | $1.17^{+1.08}_{-0.58}\times 10^{-2}$ | $<1.51\times 10^{-1}$ | - | - | - | 40.6/39
66 | A | - | - | $1.75\pm 0.03$ | $3.03^{+0.14}_{-0.13}$ | $<3.78\times 10^{-2}$ | - | - | - | 2493.7/2722
67 | D | - | - | $1.58^{+0.44}_{-0.45}$ | $2.57^{+2.87}_{-1.30}\times 10^{-2}$ | $4.90^{+1.42}_{-1.26}$ | $1.58^{+0.44}_{-0.45}$ | $2.56^{+0.51}_{-0.46}\times 10^{-1}$ | - | 176.2/237
68 | A | - | - | $2.44^{+0.38}_{-0.36}$ | $1.08^{+0.67}_{-0.43}$ | $<6.45\times 10^{-1}$ | - | - | - | 53.0/65
(1) Object number in Table 1. (2) Spectral model; A: phabs*pegpwrlw B:
phabs*zphabs*pegpwrlw C: phabs*(zphabs*pegpwrlw+zgauss)
D: phabs*(pegpwrlw+zphabs*pegpwrlw) E: phabs*(pegpwrlw+zphabs*pegpwrlw+zgauss)
F: phabs*(apec+pegpwrlw)
G: phabs*(apec+zphabs*pegpwrlw) H: phabs*(apec+pegpwrlw+zphabs*pegpwrlw), XMM-
Newton and NuSTAR have multiple datasets
(e.g., XMM-Newton has three data sets: mos1, mos2, and pn), and thus the
models are multiplied by const. We also multiplied the absorbing
edge model (zedge) for the No. 34 source, whose model is marked with *. (3)
Temperature of the plasma. (4) Normalization of the apec model.
(5) Photon index of unabsorbed power-law component. (6) Flux of unabsorbed
power-law component in 2–10 keV. (7) Intrinsic hydrogen column
density. (8) Photon index of absorbed power-law component. (9) Flux of
absorbed power-law component in 2–10 keV.
(10) Equivalent width of the Iron emission line. (11) C-statistics and degree
of freedom. In the case of the analysis using Sherpa (noted by *),
the binning min was set to 1 and used $\chi^{2}$.
Table 3: X-ray luminosity and Eddington luminosity ratio No. | $L_{2-10}$ | $L_{2-10}/L{\rm{}_{Edd}}$ |  | No. | $L_{2-10}$ | $L_{2-10}/L{\rm{}_{Edd}}$
---|---|---|---|---|---|---
| $\rm{erg\,s^{-1}}$ |  |  |  | $\rm{erg\,s^{-1}}$ |
(1) | (2) | (3) |  | (1) | (2) | (3)
1 | $1.17^{+0.10}_{-0.07}\times 10^{44}$ | $5.61^{+0.48}_{-0.36}\times 10^{-4}$ |  | 35 | $1.30\pm 0.02\times 10^{43}$ | $7.45^{+0.11}_{-0.10}\times 10^{-4}$
2 | $5.21^{+0.65}_{-0.59}\times 10^{44}$ | $3.94^{+0.49}_{-0.45}\times 10^{-3}$ |  | 36 | $6.40\pm 0.07\times 10^{43}$ | $4.46\pm 0.05\times 10^{-4}$
3 | $2.18^{+0.44}_{-0.34}\times 10^{44}$ | $1.90^{+0.38}_{-0.29}\times 10^{-3}$ |  | 37 | $9.19^{+1.16}_{-1.05}\times 10^{45}$ | $2.62^{+0.33}_{-0.30}\times 10^{-2}$
4 | $4.61^{+0.29}_{-0.25}\times 10^{43}$ | $5.38^{+0.34}_{-0.29}\times 10^{-4}$ |  | 38 | $2.47\pm 0.05\times 10^{42}$ | $1.98\pm 0.04\times 10^{-4}$
5 | $2.49^{+0.40}_{-0.35}\times 10^{44}$ | $1.48^{+0.24}_{-0.21}\times 10^{-3}$ |  | 39 | $1.32^{+0.15}_{-0.14}\times 10^{41}$ | $2.27^{+0.26}_{-0.25}\times 10^{-5}$
6 | $1.36^{+0.70}_{-0.42}\times 10^{43}$ | $7.81^{+4.05}_{-2.42}\times 10^{-5}$ |  | 40 | $1.62^{+0.10}_{-0.09}\times 10^{42}$ | $2.30^{+0.14}_{-0.13}\times 10^{-5}$
7 | $2.14^{+0.48}_{-0.41}\times 10^{43}$ | $8.69^{+1.95}_{-1.66}\times 10^{-5}$ |  | 41 | $8.89^{+3.78}_{-2.74}\times 10^{44}$ | $2.23^{+0.95}_{-0.69}\times 10^{-2}$
8 | $2.42^{+0.17}_{-0.16}\times 10^{44}$ | $2.29^{+0.16}_{-0.15}\times 10^{-3}$ |  | 42 | $8.93^{+0.46}_{-0.44}\times 10^{45}$ | $1.66\pm 0.08\times 10^{-2}$
9 | $1.08^{+0.07}_{-0.06}\times 10^{45}$ | - |  | 43 | $2.86^{+0.75}_{-0.62}\times 10^{42}$ | $1.08^{+0.28}_{-0.23}\times 10^{-5}$
10 | $4.47^{+0.72}_{-0.66}\times 10^{43}$ | $3.86^{+0.62}_{-0.57}\times 10^{-4}$ |  | 44 | $2.32\pm 0.04\times 10^{45}$ | -
11 | $8.16^{+1.01}_{-0.86}\times 10^{44}$ | $3.31^{+0.41}_{-0.35}\times 10^{-3}$ |  | 45 | $2.02\pm 0.05\times 10^{43}$ | $1.25\pm 0.03\times 10^{-4}$
12 | $7.00^{+0.70}_{-0.91}\times 10^{43}$ | $4.71^{+0.47}_{-0.61}\times 10^{-4}$ |  | 46 | $2.22^{+0.53}_{-0.44}\times 10^{45}$ | $1.76^{+0.42}_{-0.35}$
13 | $9.54^{+0.48}_{-0.46}\times 10^{44}$ | - |  | 47 | $6.58^{+1.14}_{-0.99}\times 10^{45}$ | $8.29^{+1.43}_{-1.25}\times 10^{-2}$
14 | $4.73^{+0.74}_{-0.65}\times 10^{44}$ | $2.57^{+0.40}_{-0.35}\times 10^{-3}$ |  | 48 | $7.74^{+1.18}_{-1.07}\times 10^{43}$ | $4.55^{+0.69}_{-0.63}\times 10^{-4}$
15 | $3.12^{+0.70}_{-0.35}\times 10^{44}$ | $2.40^{+0.54}_{-0.27}\times 10^{-3}$ |  | 49 | $1.18\pm 0.09\times 10^{44}$ | $2.95^{+0.23}_{-0.22}\times 10^{-3}$
16 | $1.13^{+0.17}_{-0.13}\times 10^{43}$ | $2.50^{+0.38}_{-0.30}\times 10^{-4}$ |  | 50 | $5.30^{+0.42}_{-0.40}\times 10^{41}$ | $1.76^{+0.14}_{-0.13}\times 10^{-5}$
17 | $3.57^{+0.99}_{-0.75}\times 10^{42}$ | $3.01^{+0.84}_{-0.63}\times 10^{-5}$ |  | 51 | $2.13^{+0.60}_{-0.50}\times 10^{41}$ | $8.83^{+2.47}_{-2.08}\times 10^{-6}$
18 | $2.76^{+1.14}_{-0.83}\times 10^{41}$ | $6.54^{+2.70}_{-1.97}\times 10^{-7}$ |  | 52 | $2.71^{+0.40}_{-0.35}\times 10^{44}$ | $2.07^{+0.30}_{-0.27}\times 10^{-3}$
19 | $1.38^{+0.09}_{-0.07}\times 10^{43}$ | $1.84^{+0.12}_{-0.10}\times 10^{-4}$ |  | 53 | $4.58^{+0.25}_{-0.24}\times 10^{41}$ | $3.83^{+0.21}_{-0.20}\times 10^{-5}$
20 | $7.00^{+0.82}_{-0.75}\times 10^{40}$ | $6.77^{+0.79}_{-0.73}\times 10^{-7}$ |  | 54 | $2.69^{+0.40}_{-0.36}\times 10^{44}$ | $1.71^{+0.26}_{-0.23}\times 10^{-3}$
21 | $5.37^{+2.48}_{-1.77}\times 10^{43}$ | $1.04^{+0.48}_{-0.34}\times 10^{-3}$ |  | 55 | $1.29\pm 0.05\times 10^{43}$ | -
22 | $4.24^{+2.75}_{-1.73}\times 10^{41}$ | $4.41^{+2.86}_{-1.80}\times 10^{-6}$ |  | 56 | $1.78^{+0.12}_{-0.11}\times 10^{41}$ | $1.46^{+0.10}_{-0.09}\times 10^{-5}$
23 | $1.87^{+0.85}_{-0.62}\times 10^{44}$ | $4.30^{+1.97}_{-1.43}\times 10^{-4}$ |  | 57 | $4.07^{+0.69}_{-0.60}\times 10^{41}$ | $2.01^{+0.34}_{-0.30}\times 10^{-5}$
24 | $3.11^{+0.21}_{-0.20}\times 10^{43}$ | $1.45^{+0.10}_{-0.09}\times 10^{-4}$ |  | 58 | $1.27^{+0.04}_{-0.03}\times 10^{44}$ | $1.63^{+0.05}_{-0.04}\times 10^{-3}$
25 | $4.46^{+2.79}_{-1.70}\times 10^{44}$ | $1.08^{+0.67}_{-0.31}\times 10^{-3}$ |  | 59 | $1.08^{+0.54}_{-0.37}\times 10^{42}$ | $8.09^{+4.03}_{-2.80}\times 10^{-5}$
26 | $7.82^{+2.52}_{-2.04}\times 10^{41}$ | $2.98^{+0.96}_{-0.78}\times 10^{-6}$ |  | 60 | $3.32^{+0.30}_{-0.28}\times 10^{41}$ | $1.83^{+0.16}_{-0.15}\times 10^{-5}$
27 | $2.79^{+0.30}_{-0.27}\times 10^{41}$ | $1.80^{+0.19}_{-0.18}\times 10^{-6}$ |  | 61 | $5.04^{+1.23}_{-1.01}\times 10^{41}$ | $2.74^{+0.67}_{-0.55}\times 10^{-5}$
28 | $2.21^{+0.22}_{-0.20}\times 10^{44}$ | $5.26^{+0.52}_{-0.48}\times 10^{-4}$ |  | 62 | $1.16\pm 0.03\times 10^{42}$ | $7.11^{+0.18}_{-0.17}\times 10^{-5}$

Table 3 (Continued)
---
No. | $L_{2-10}$ | $L_{2-10}/L{\rm{}_{Edd}}$ |  | No. | $L_{2-10}$ | $L_{2-10}/L{\rm{}_{Edd}}$
| $\rm{erg\,s^{-1}}$ |  |  |  | $\rm{erg\,s^{-1}}$ |
(1) | (2) | (3) |  | (1) | (2) | (3)
29 | $8.20^{+1.30}_{-1.16}\times 10^{40}$ | $3.59^{+0.57}_{-0.51}\times 10^{-6}$ |  | 63 | $2.55^{+3.57}_{-1.54}\times 10^{41}$ | $7.60^{+10.65}_{-4.61}\times 10^{-6}$
30 | $9.15^{+0.39}_{-0.38}\times 10^{41}$ | $3.20^{+0.14}_{-0.13}\times 10^{-6}$ |  | 64 | $5.75\pm 0.07\times 10^{43}$ | $3.87\pm 0.05\times 10^{-3}$
31 | $1.20^{+0.16}_{-0.15}\times 10^{43}$ | $8.77^{+1.19}_{-1.07}\times 10^{-5}$ |  | 65 | $1.35^{+1.24}_{-0.66}\times 10^{40}$ | $7.58^{+6.99}_{-3.74}\times 10^{-7}$
32 | $5.79^{+3.24}_{-2.22}\times 10^{42}$ | $1.14^{+0.64}_{-0.44}\times 10^{-4}$ |  | 66 | $1.44\pm 0.06\times 10^{44}$ | $1.53\pm 0.07\times 10^{-3}$
33 | $2.86\pm 0.02\times 10^{43}$ | $1.88\pm 0.02\times 10^{-3}$ |  | 67 | $7.30^{+1.31}_{-1.19}\times 10^{40}$ | $9.83^{+1.77}_{-1.60}\times 10^{-6}$
34 | $1.97^{+0.50}_{-0.31}\times 10^{40}$ | $2.88^{+0.73}_{-0.45}\times 10^{-6}$ |  | 68 | $4.91^{+3.06}_{-1.95}\times 10^{44}$ | $1.40^{+0.87}_{-0.56}\times 10^{-6}$
(1) Object number in Table 1. (2) Absorption-corrected luminosity at 2–10 keV.
(3) Eddington luminosity ratio.
Table 4: Fraction of absorbed RGs ($N\rm{{}_{H}}>10^{22}cm^{-2}$) | FR-I | FR-II | CSS | total
---|---|---|---|---
GeV-quiet | 0.18 | 0.70 | 1 | 0.53
GeV-loud | 0.16 | 0 | 0 | 0.08
total | 0.17 | 0.44 | 0.17 | 0.29

3C 032

3C 403

3C 327.1

PKS 0039-44

Figure 3: Example of X-ray spectra of GeV-quiet RGs. Details are the same as
Figure 2.

IC 1531

PKS 0625-35

Pictor A

PKS 1514+00

Figure 4: Example of X-ray spectra of GeV-loud RGs. Details are the same as
Figure 2.

Figure 5: X-ray luminosity $L\rm{{}_{x}}$ vs Absorption column density
$N\rm{{}_{H}}$. Blue circles, black squares, green triangles, red circles,
orange squares and yellow triangles represent GeV-quiet FR-I, GeV-quiet FR-II,
GeV-quiet CSS, GeV-loud FR-I, GeV-loud FR-II and GeV-loud CSS, respectively.
Figure 6: X-ray luminosity $L\rm{{}_{x}}$ vs photon index $\Gamma\rm{{}_{x}}$.
Markers are the same as figure 5 Figure 7: Photon index $\Gamma\rm{{}_{x}}$ vs
Absorption column density $N\rm{{}_{H}}$. Markers are the same as figure 5