Metastable and Superconducting Cosmic Strings in $E_{6}$
Adeela Afzala,111E-mail<EMAIL_ADDRESS>Qaisar Shafib,222E-mail:
<EMAIL_ADDRESS>and Amit Tiwarib,333E-mail<EMAIL_ADDRESS>
aDepartment of Physics, Quaid-i-Azam University, Islamabad, 45320, Pakistan
bBartol Research Institute, Department of Physics and Astronomy, University of
Delaware, Newark, DE 19716, USA

We discuss an $E_{6}$ based extension of the Standard Model (SM) that contains
both superheavy metastable strings and intermediate scale effectively stable
superconducting strings. We employ an extended version of the velocity-
dependent one-scale (VOS) model, recently discussed by several authors, to
estimate the gravitational wave (GW) spectrum emitted by the metastable
strings with a dimensionless string tension $G\mu$ of order $10^{-7}$ and
carrying right handed neutrino zero modes. Compatibility with the most recent
NANOGrav data and LIGO O3 bounds requires a relatively small current on the
metastable string. The lighter superconducting strings with $G\mu\lesssim
10^{-11}$ may be detected in future experiments via their emission of
gravitational and electromagnetic radiation.

##  1 Introduction

A number of Pulsar Timing Array (PTA) experiments NANOGrav:2023gor;
NANOGrav:2023hvm; EPTA:2023fyk; Reardon:2023gzh; Xu:2023wog have recently
reported evidence for the presence of a stochastic gravitational wave
background (SGWB) in the nanohertz frequency range. This is potentially
exciting news for the scenario based on cosmic strings (CSs) that emit
gravitational waves (GWs) in a wide frequency range, including the nanohertz
region relevant for the above experiments. It appears to be generally accepted
that a CS explanation of the latest PTA data requires the dimensionless string
tension parameter $G\mu$ to be of order $10^{-7}$. Moreover, these CSs must be
metastable (or quasi-stable Lazarides:2023ksx), and decay within a certain
time frame in order to avoid conflict with observations in the wider frequency
range. A number of realistic models, mostly based on $SO(10)$ and its various
subgroups, have been put forward Buchmuller:2020lbh; Buchmuller:2021mbb;
Afzal:2022vjx; Ahmed:2022rwy; Buchmuller:2023aus; Antusch:2023zjk;
Lazarides:2023rqf; Ahmed:2023rky; Maji:2023fhv; Ahmed:2023pjl; Afzal:2023cyp;
Fu:2023mdu; Lazarides:2023ksx; Lazarides:2023bjd to implement this explanation
for the SGWB. For a more general discussion of composite topological
structures including metastable strings, see Ref. Lazarides:2023iim. As an
example of an explanation of PTA observation in terms of domain walls see Ref.
King:2023ayw. Metastable CSs with $G\mu\simeq 10^{-6}$ provide a somewhat
better fit to the data provided that the string network undergoes some period
of inflation during its evolution. This is necessary in order to avoid
conflict with the LIGO O3 measurements around $100$ hertz frequency range.

This paper is largely motivated by the PTA data as well as by Witten’s
observation that superconducting strings appear in realistic extensions of the
Standard Model (SM) Witten:1984eb. In particular, superconducting strings
readily appear in $E_{6}$ grand unification Witten:1984eb; Widrow:1988rc;
Hebbar:2017fit and other models Lazarides:1984zq; Lazarides:1986di;
Lazarides:1987rq, and they radiate both electromagnetic and gravitational
radiation. We propose an $E_{6}$ inspired extension of the SM that yields a
superheavy metastable string with $G\mu$ of order $10^{-7}$ that is known to
be compatible with the recent PTA measurements. In addition, the model
contains an intermediate scale superconducting string with $G\mu\lesssim
10^{-11}$, which is essentially stable and potentially detectable in the
multitude of ongoing gravitational and astrophysical experiments.

In the models we consider the $E_{6}$ symmetry can be broken to the SM in
different ways in order to yield a superheavy metastable string and an
intermediate scale superconducting string. In our first example, $E_{6}$ is
assumed to be directly broken to $G_{\text{SM}}\times U(1)_{\chi}\times
U(1)_{\psi}$, $G_{\text{SM}}$ being the gauge group of SM, which produces
three varieties of monopoles including the unconfined GUT monopole that
carries one unit of Dirac magnetic charge $(2\,\pi/e)$ as well as some color
magnetic charge. Next, the symmetry $U(1)_{\chi}\times U(1)_{\psi}$ breaks to
$U(1)_{\psi^{\prime}}$ at a scale close to $M_{\text{GUT}}$ which produces the
metastable string with $G\mu$ close to $10^{-7}$. The string is metastable
because it can be broken by the quantum mechanical tunneling of monopole-
antimonopole pairs produced during the first breaking. The breaking of
$U(1)_{\psi^{\prime}}$ at a scale well below $M_{\text{GUT}}$ yields the
intermediate scale superconducting CS which is effectively stable because the
quantum mechanical tunneling is exponentially suppressed. Here the group
$U(1)_{\psi^{\prime}}$ is generated by a suitable linear combination of the
generators of $U(1)_{\chi}$ and $U(1)_{\psi}$. We mention two additional
symmetry breaking schemes in which the metastable string appears if the
$SO(10)$ subgroup of $E_{6}$ is broken to the SM via $SU(4)_{c}\times
SU(2)_{L}\times U(1)_{R}$ or via $SU(3)_{c}\times SU(2)_{L}\times
SU(2)_{R}\times U(1)_{B-L}$. The breaking of $U(1)_{\psi}$ at an intermediate
scale yields the superconducting string.

In estimating the GWs emitted by the superheavy metastable string we ignore
the potential complications that could arise due to the presence of two
distinct varieties of CSs. The metastable string in the three symmetry
breaking schemes we consider carries right handed neutrino zero modes. We
employ the velocity-dependent one-scale (VOS) model, recently discussed in
Rybak:2022sbo; Auclair:2022ylu, to incorporate this feature of the metastable
string in the estimation of the emitted gravitational spectrum. [Note that
previous studies only worked with a stable string]. The VOS model for
superconducting CSs is also investigated in Martins:2020jbq; Martins:2021cid.
We find that the chiral current allowed on the metastable string is tiny, in
order to be compatible with NANOGrav and the LIGO O3 bound. The
superconducting string emits gravitational and electromagnetic radiation and
we present an example of a dimensionless string tension of order $10^{-11}$.

The paper is organized as follows. In Section 2, we discuss three distinct
symmetry breaking chains in an $E_{6}$ model that yield a superheavy
metastable string as well as an essentially stable superconducting string. In
Section 3 we display the gravitational wave spectrum emitted by the metastable
string over a wide frequency range, taking into account the presence of the
right handed neutrino zero modes. We also show a figure to highlight the fact
that the current on the metastable string has to be sufficiently low if
agreement with the NANOGrav results is to be maintained. Our conclusions are
summarized in Section 4.

##  2 Metastable and superconducting strings in $E_{6}$

Matter fields | Representations under $G_{\rm SM}$ | $2\sqrt{6}\,Q_{\chi^{\prime}}$ | $2\sqrt{10}\,Q_{\psi^{\prime}}$
---|---|---|---
$q$ | $({\bf 3,2},1/6)$ | $-1$ | $1$
$u^{c}$ | $({\bf\bar{3},1},-2/3)$ | $-1$ | $1$
$d^{c}$ | $({\bf\bar{3},1},1/3)$ | $2$ | $2$
$l$ | $({\bf 1,2},-1/2)$ | $2$ | $2$
$\nu^{c}$ | $({\bf 1,1},0)$ | $-4$ | $0$
$e^{c}$ | $({\bf 1,1},1)$ | $-1$ | $1$
$H_{u}^{\alpha}$ | $({\bf 1,2},1/2)$ | $2$ | $-2$
$H_{d}^{\alpha}$ | $({\bf 1,2},-1/2)$ | $-1$ | $-3$
$D_{i}$ | $({\bf 3,1},-1/3)$ | $2$ | $-2$
$D_{i}^{c}$ | $({\bf\bar{3},1},1/3)$ | $-1$ | $-3$
$N_{i}$ | $({\bf 1,1},0)$ | $-1$ | $5$
Table 1: Transformation properties of the matter fields under the Standard
Model (SM) gauge group $G_{\text{SM}}$, and their charges under local
$U(1)_{\chi^{\prime}}$ and $U(1)_{\psi^{\prime}}$ symmetries. Here
$Q_{\chi^{\prime}}=1/4(\sqrt{15}\,Q_{\chi}-Q_{\psi})$ and
$Q_{\psi^{\prime}}=1/4(Q_{\chi}+\sqrt{15}\,Q_{\psi})$, where $Q_{\chi}$ and
$Q_{\psi}$ are the normalized GUT generators of $U(1)_{\chi}$ and
$U(1)_{\psi}$ respectively.

The $15$ chiral matter fields per family of the SM reside in the $27$
dimensional fundamental representation of $E_{6}$. The quantum numbers of the
$27$ fields under $G_{\text{SM}}$ are listed in Table 1. In addition to the
well-known right handed neutrino $\nu^{c}$, we also have a $SO(10)$ $10$-plet
and a $SO(10)$ singlet $N_{i}$, where $i$ denotes the family index. Consider
the breaking chain

$\displaystyle E_{6}$ $\displaystyle\longrightarrow SO(10)\times U(1)_{\psi}$
(1) $\displaystyle\longrightarrow SU(5)\times U(1)_{\chi}\times U(1)_{\psi}$
$\displaystyle\longrightarrow G_{\text{SM}}\times U(1)_{\chi}\times
U(1)_{\psi}$

With the electric charge embedded in $SU(5)$ the last step in the above
breaking chain yields the topologically stable GUT monopole that carries a
single unit of Dirac magnetic charge as well as color magnetic charge which is
screened. The monopoles associated with the factors $U(1)_{\chi}$ and
$U(1)_{\psi}$ are not topologically stable because they are both spontaneously
broken symmetries, and the corresponding monopoles are therefore confined
through the formation of flux tubes that we refer to as strings. Note that if
the monopoles are inflated away the stability of the corresponding string is
determined by the rate of production on the string of a monopole-antimonopole
pair via quantum mechanical tunneling. Depending on this rate the strings can
be metastable or essentially stable.

For an explanation of the pulsar timing data we are interested in a superheavy
metastable string with a dimensionless string tension $G\mu$ of order
$10^{-7}$ NANOGrav:2023hvm. This effectively means that the symmetry breaking
scales associated with the monopole and the corresponding string should be
suitably close together. It is therefore convenient to consider the symmetry
breaking

$\displaystyle E_{6}\longrightarrow G_{\text{SM}}\times U(1)_{\chi}\times
U(1)_{\psi}.$ (2)

This yields a variety of monopoles which include the topologically stable GUT
monopole associated with the breaking of $SU(5)$ to $G_{\text{SM}}$. A Higgs
scalar field with the quantum numbers of $\nu^{c}$ in Table 1 breaks the
symmetry $U(1)_{\chi}\times U(1)_{\psi}$ to $U(1)_{\psi^{\prime}}$, which
produces the desired metastable string that carries the flux associated with
the broken generator orthogonal to $U(1)_{\psi^{\prime}}$.

Next, the spontaneous breaking at an intermediate scale of
$U(1)_{\psi^{\prime}}$ by a Higgs scalar $N$ with the quantum numbers of the
field $N_{i}$ in Table 1 yields a superconducting CS which is essentially
stable. The string is superconducting because the new electrically charged
fermions in Table 1 acquire masses from their Yukawa coupling to $N$, and they
reside as zero modes on string Witten:1984eb. Also, being of intermediate mass
scale the string is practically stable because the corresponding monopole-
antimonopole associated with it have GUT scale masses. For our discussion
below we will assume that the dimensionless string tension parameter
associated with the superconducting strings $G\mu\lesssim 10^{-11}$.

We have shown within a specific symmetry breaking pattern in $E_{6}$ that a
superheavy metastable string is accompanied by an intermediate scale
superconducting string that is effectively stable. It is possible to construct
other breaking chains for $E_{6}$ that yield similar results. As another
realistic example consider the breaking chain:

$\displaystyle E_{6}$ $\displaystyle\longrightarrow SO(10)\times U(1)_{\psi}$
(3) $\displaystyle\longrightarrow SU(4)_{c}\times SU(2)_{L}\times
U(1)_{R}\times U(1)_{\psi}$ $\displaystyle\longrightarrow SU(3)_{c}\times
U(1)_{B-L}\times SU(2)_{L}\times U(1)_{R}\times U(1)_{\psi}$
$\displaystyle\longrightarrow G_{\text{SM}}\times U(1)_{\psi}$
$\displaystyle\longrightarrow G_{\text{SM}}.$

The first breaking produces an $E_{6}$ monopole and is associated with an
ultraheavy symmetry breaking scale that is larger than $M_{\text{GUT}}$. The
second breaking yields the unconfined GUT monopole, and the third breaking
produces a $SU(4)_{c}$ monopole, whose flux is confined in the fourth step in
Equation 3. This latter system forms the superheavy metastable string
structure, following a discussion similar to Ref. Afzal:2023cyp. In the final
step, $U(1)_{\psi}$ is spontaneously broken which yields the intermediate
scale superconducting string. This string is effectively stable because the
quantum tunneling of the ultraheavy $E_{6}$ monopole-antimonopole pair is
exponentially suppressed.

To confirm these assertions, we note that a rotation by $2\,\pi$ along
$T_{R}^{3}=\text{diag}(1,-1)$, the generator of $U(1)_{R}$, brings us back to
the identity element. Since we are looking for the GUT monopole with the
minimal Dirac charge of $2\pi/e$, we perform a rotation by $\pi$ along
$T_{R}^{3}$, which corresponds to a curve between 1 and -1. Following Ref.
Lazarides:2019xai, we next include a curve in $SU(4)_{c}$ along the generator
$X=(B-L)+2\,T_{c}^{8}/3$, where $B$ and $L$ denote baryon and lepton number
operators respectively, and $T_{c}^{8}=\text{diag}(1,1,-2)$ is the color
hypercharge. A rotation by $\pi$ along X yields a curve between 1 and -1 in
$SU(4)_{c}$. With $SU(2)_{L}$ still unbroken, we also include a rotation by
$\pi$ along it’s generator $T_{L}^{3}=\text{diag}(1,-1)$. The overall loop
then corresponds to a rotation by $2\,\pi$ along
$(X+T_{L}^{3}+T_{R}^{3})/2=Q+T_{c}^{8}/3$, where $Q$ is the electric charge
operator. This shows that the monopole is indeed the topologically stable GUT
monopole that carries one unit $(2\,\pi/e)$ of Dirac magnetic charge, as well
as color magnetic charge.

It is instructive to see how an unconfined monopole carrying two units of
Dirac magnetic charge arises in the breaking of $SO(10)$ to $SU(4)_{c}\times
SU(2)_{L}\times U(1)_{R}$. As a first step, we perform a $2\,\pi$ rotation in
$U(1)_{R}$. We next include $2\,\pi$ rotations along $X$ and $T_{L}^{3}$,
which are contractible loops in the unbroken $SU(4)_{c}$ and $SU(2)_{L}$
respectively. Therefore, overall we have a $4\,\pi$ rotation along
$Q+T_{c}^{8}/3$, which yields a magnetic monopole carrying two units of Dirac
charge as well as color magnetic charge.

As our final example consider the spontaneous breaking of $SO(10)$ to the
left-right symmetric group $H=SU(3)_{c}\times SU(2)_{L}\times SU(2)_{R}\times
U(1)_{B-L}$. This breaking produces the unconfined GUT monopole, which can be
explicitly checked by considering the first homotopy group of $H$, and taking
into account that $SO(10)$ (Spin ($10$)) is simply connected. The magnetic
monopole, as expected, carries one unit of Dirac magnetic charge (
$2\,\pi/e$), as well as color magnetic charge. In order to produce a
metastable string network we next break $SU(2)_{R}$ to $U(1)_{R}$, which
yields a monopole, followed by the breaking of $U(1)_{R}\times U(1)_{B-L}$ to
$U(1)_{Y}$ that produces the string which confines this monopole. Again, the
right handed neutrinos $\nu^{c}$ acquire masses from the last breaking and
appear as zero modes on the string. Superconducting strings carrying electric
current arise from the breaking of $U(1)_{\psi}$ at an intermediate scale, as
in the previous two cases.

Recall that in the three examples we have considered so far, the intermediate
scale superconducting string is effectively stable, and the superheavy
metastable string carrying the right handed neutrino current is responsible
for the observable gravitational waves in the nHz range. To obtain a
superheavy metastable string that is electrically superconducting, consider
the $E_{6}$ breaking

$\displaystyle E_{6}\rightarrow G_{\text{SM}}\times U(1)_{\psi^{\prime}}$ (4)

This breaking produces the superheavy GUT monopole as well as monopoles
carrying magnetic $U(1)_{\psi^{\prime}}$ charges, and all of these monopoles
are inflated away. Also, since the Higgs scalar that breaks the $B-L$ gauge
symmetry carries the quantum numbers of $\nu_{c}^{*}$, there are no
topologically stable strings in the model. The breaking of
$U(1)_{\psi^{\prime}}$ at a scale close to $M_{\text{GUT}}$ provides the
superheavy metastable string that is electrically superconducting. Such
strings radiate both electromagnetic and gravitational radiation which we will
not explore in this paper.

##  3 Gravitational waves from metastable and superconducting strings

Figure 1: GWs from metastable and stable superconducting CSs. [Adeela: The
metastable strings for $G\mu\simeq 10^{-7}$ and $\sqrt{\kappa}\simeq 8.2$ with
negligibly small zero mode current can explain the NANOGrav excess at
2$\sigma$ as manifested in Figure 2]. The colored shaded regions indicate the
sensitivity curves of present (solid boundaries) LIGO O3 KAGRA:2021kbb, CMB
Lasky:2015lej and future (dashed boundaries) LiteBIRD LiteBIRD:2022cnt, PIXIE
A_Kogut_2011, SKA Smits:2008cf, THEIA Garcia-Bellido:2021zgu, LISA
amaroseoane2017laser, ET Punturo:2010zz, BBO Corbin:2005ny experiments. CSs
with current strength $Y\lesssim 0.8$ can evade the LIGO O3 bounds.

The stable and metastable CSs produced in the above mentioned symmetry
breaking patterns are superconducting. For the stable case we assume, for
simplicity, a negligibly small electric current such that the dominant decay
channel for the loops will be GWs. For the metastable case, we have the right
handed neutrino zero mode chiral current, with the GW as the only decay
channel. Our analysis is based on the VOS model for the evolution of CSs, and
for a detailed discussion we refer the reader to Refs. Auclair:2019wcv;
Sousa:2020sxs; Buchmuller:2021mbb. [Adeela: We consider the major contribution
for GWs is coming from loops characterized by $\alpha=0.1$ with cusps]. We
assume that the zero mode chiral current associated with the metastable CSs is
present from their formation until decay. We follow the treatment of Ref.
Rybak:2022sbo and implement it here for the metastable CSs. A slightly more
conservative treatment of current carrying CS is available in Auclair:2022ylu
where the evolution of the power emission factor $\Gamma$ of GWs is not
discussed but is later expounded in Rybak:2022sbo. We present the stable and
metastable superconducting strings GW spectra in Figure 1 with the color
coding as labeled. [Adeela: We summed upto $10^{5}$ harmonic modes]. As
previously mentioned in Ref. Rybak:2022sbo, a significant enhancement in the
amplitude of the power spectrum can be seen for $Y\gtrsim 0.8$ that is also
shown in Figure 1. Here $Y$ is the averaged current strength and in order to
evade the LIGO O3 bounds, we estimate that $Y\lesssim 0.8$ for $G\mu\simeq
10^{-7}$ and $\sqrt{\kappa}\simeq 8.2$. Taking into account the LIGO O3
bounds, the predicted gravitational spectrum is in agreement with the NANOGrav
signal at the $2\sigma$ level for $Y\simeq 0$ as shown in Figure 2, [Adeela:
where we perform a power law fit and move into the ($\gamma,\mathcal{A}$)
plane. Here $\gamma$ is the slope or the spectral index and $\mathcal{A}$ is
the strain amplitude.]

Figure 2: GWs signal from metastable CSs compared to the NANOGrav observation
for $\sqrt{\kappa}=8.2$ with different values of $Y$ and the variation in
$G\mu$ is shown by a vertical green pink tone colored bar. The floral-violet
shaded region shows the 3$\sigma$, 2$\sigma$ and 1$\sigma$ NANOGrav posterior
contours NANOGrav:2023gor. The gray vertical line at $\gamma=13/3$ represents
the slope expected for the supermassive black hole binary (SMBHB) merger.

##  4 Conclusion

We have considered a realistic $E_{6}$ based extension of the SM which yields
a superheavy metastable CS and also an intermediate scale superconducting
string through a number of distinct symmetry breaking chains. The
superconducting string is essentially stable, and with a dimensionless string
tension $G\mu$ of order $10^{-11}$, it can be detected in a variety of
gravitational wave experiments and through astrophysical observations. The
existence of a metastable string with $G\mu$ of order $10^{-7}$ is compatible
with the latest pulsar timing experiments, and its predicted gravitational
spectrum over a wide frequency range can be tested in the ongoing and future
experiments. We employ some recently developed extensions of the VOS model to
evaluate this gravitational spectrum, and provide an estimate for the upper
bound on the chiral current associated with the right handed neutrino zero
modes present on the metastable string.

## Acknowledgment

AT is partially supported by the Bartol Research Institute, University of
Delaware. QS thanks George Lazarides and Rinku Maji for helpful discussions.


Further author information: (Send correspondence to Li Ji)
Li Ji: E-mail<EMAIL_ADDRESS>Telephone: 86 25 83332162

# Mapping Diffuse Emission in Lyman UV band

Li Ji  Purple Mountain Observatory, CAS, Nanjing, China  Key Laboratory of
Dark Matter and Space Astronomy, CAS, Nanjing, China  Zheng Lou  Purple
Mountain Observatory, CAS, Nanjing, China  Jinlong Zhang  Institute of
Precision Optical Engineering, School of Physics Science and Engineering,
Tongji University, Shanghai, China  Keqiang Qiu  National Synchrotron
Radiation Laboratory, University of Science and Technology of China, Hefei,
China  Shuangying Li  Institute of Precision Optical Engineering, School of
Physics Science and Engineering, Tongji University, Shanghai, China  Wei Sun
Purple Mountain Observatory, CAS, Nanjing, China  Key Laboratory of Dark
Matter and Space Astronomy, CAS, Nanjing, China  Shuping Yan  Purple Mountain
Observatory, CAS, Nanjing, China  Key Laboratory of Dark Matter and Space
Astronomy, CAS, Nanjing, China  Shuinai  Purple Mountain Observatory, CAS,
Nanjing, China  Key Laboratory of Dark Matter and Space Astronomy, CAS,
Nanjing, China  Zhang  Purple Mountain Observatory, CAS, Nanjing, China  Key
Laboratory of Dark Matter and Space Astronomy, CAS, Nanjing, China  Yuan Qian
Purple Mountain Observatory, CAS, Nanjing, China  Sen Wang  National
Astronomical Observatories, CAS, Beijing, China  Klaus Werner  Institute for
Astronomy and Astrophysics, Universität Tübingen, Tübingen, Germany  Taotao
Fang  Department of Astronomy, Xiamen University, Xiamen, China  Tinggui Wang
Department of Astronomy, University of Science and Technology of China, Hefei,
China  Jürgen Barnstedt  Institute for Astronomy and Astrophysics, Universität
Tübingen, Tübingen, Germany  Sebastian Buntrock  Institute for Astronomy and
Astrophysics, Universität Tübingen, Tübingen, Germany  Mingsheng Cai  Purple
Mountain Observatory, CAS, Nanjing, China  Key Laboratory of Dark Matter and
Space Astronomy, CAS, Nanjing, China  Wen Chen  Innovation of Academy for
Microsatellites of CAS, Shanghai, China  Lauro Conti  Institute for Astronomy
and Astrophysics, Universität Tübingen, Tübingen, Germany  Lei Deng
Innovation of Academy for Microsatellites of CAS, Shanghai, China  Sebastian
Diebold  Institute for Astronomy and Astrophysics, Universität Tübingen,
Tübingen, Germany  Shaojun Fu  National Synchrotron Radiation Laboratory,
University of Science and Technology of China, Hefei, China  Jianhua Guo
Purple Mountain Observatory, CAS, Nanjing, China  Key Laboratory of Dark
Matter and Space Astronomy, CAS, Nanjing, China  Lars Hanke  Institute for
Astronomy and Astrophysics, Universität Tübingen, Tübingen, Germany  Yilin
Hong  National Synchrotron Radiation Laboratory, University of Science and
Technology of China, Hefei, China  Christoph Kalkuhl  Institute for Astronomy
and Astrophysics, Universität Tübingen, Tübingen, Germany  Norbert Kappelmann
Institute for Astronomy and Astrophysics, Universität Tübingen, Tübingen,
Germany  Thomas Kaufmann  Institute for Astronomy and Astrophysics,
Universität Tübingen, Tübingen, Germany  Shijun Lei  Purple Mountain
Observatory, CAS, Nanjing, China  Key Laboratory of Dark Matter and Space
Astronomy, CAS, Nanjing, China  Fu Li  Xi’an Institute of Optics and Precision
Mechanics of CAS, Xi’an, China  Xinfeng Li  Technology and Engineering Center
for Space Utilization, CAS, Beijing, China  Wei Liu  Purple Mountain
Observatory, CAS, Nanjing, China  Kevin Meyer  Institute of Energy Research
and Physical Technologies, Clausthal University of Technology, Clausthal,
Germany  Thomas Rauch  Institute for Astronomy and Astrophysics, Universität
Tübingen, Tübingen, Germany  Ping Ruan  Xi’an Institute of Optics and
Precision Mechanics of CAS, Xi’an, China  Daniel M. Schaadt  Institute of
Energy Research and Physical Technologies, Clausthal University of Technology,
Clausthal, Germany  Thomas Schanz  Institute for Astronomy and Astrophysics,
Universität Tübingen, Tübingen, Germany  Qian Song  National Astronomical
Observatories, CAS, Beijing, China  Beate Stelzer  Institute for Astronomy and
Astrophysics, Universität Tübingen, Tübingen, Germany  Zhanshan Wang
Institute of Precision Optical Engineering, School of Physics Science and
Engineering, Tongji University, Shanghai, China  Jianfeng Yang  Xi’an
Institute of Optics and Precision Mechanics of CAS, Xi’an, China  Wei Zhang
Purple Mountain Observatory, CAS, Nanjing, China

###### Abstract

The CAFE (Census of warm-hot intergalactic medium, Accretion, and Feedback
Explorer) and LyRIC (Lyman UV Radiation from Interstellar medium and Circum-
galactic medium) have been proposed to the space agencies in China
respectively. CAFE was first proposed in 2015 as a joint scientific CAS-ESA
small space mission. LyRIC was proposed in 2019 as an independent external
payload operating on the Chinese Space Station. Both missions are dedicated to
mapping the Lyman UV emission (ionized oxygen (O vi) resonance lines at 103.2
and 103.8 nm, and Lyman series) for the diffuse sources in our Galaxy and the
circum-galactic mediums of the nearby galaxies. We present the primary science
objectives, mission concepts, the enabling technologies, as well as the
current status.

###### keywords:

Small Explorer, ultraviolet, line emission

##  1 INTRODUCTION

The “Lyman ultraviolet” (LUV; 91.2–121.6 nm), the least explored window of
astrophysical investigations, is rich in the unique physical line diagnostics
including neutral hydrogen (H i) Lyman series lines and ionized oxygen (O vi)
resonance lines at 103.2 and 103.8 nm. Tumlinson et al. (2012)[1] and Green et
al. (2014)[2] pointed out that with modern photon-counting detectors, the LUV
region has been fully covered by the Far Ultraviolet Spectroscopic Explorer
(FUSE)[3], the Spectroscopy of Plasma Evolution from Astrophysical Radiation
(SPEAR)[4], and the Hubble Space Telescope (HST)/COS after cycle 20[5].
However, both FUSE and HST/COS are mainly targeting the point sources, not
optimized to the larger structures of the diffuse emission from the
astronomical sources. SPEAR ever provided the images of LUV diffuse emission
line sources in our Galaxy but with relatively low effective area and
insufficient effective angular resolution.

With the characteristic temperature of 104–106 K, diffuse gas is the key to
understand the circum-galactic medium (CGM) surrounding nearby galaxies, high-
velocity clouds (HVCs) in our Galaxy, and superbubbles etc. Aiming at the
missions with the exploration size, we have proposed two LUV emission
explorers to the space science community in China. One is CAFE (Census of
warm-hot intergalactic medium, Accretion, and Feedback Explorer), first
proposed in 2015 as a joint scientific CAS-ESA small space mission. The other
is LyRIC (Lyman UV Radiation from Interstellar medium and Circum-galactic
medium), proposed in 2019 as an independent external payload operating on the
Chinese Space Station. We present here the primary science objectives, mission
concepts, the enabling technologies, as well as the current status.

##  2 Primary Science Objectives

###  2.1 Where are the Missing Baryons?

In the low redshift universe, only about half of the total baryons in the
$\Lambda$CDM cosmological model can be accounted for in stars, cold or warm
interstellar matter, hot intracluster gas, and residual photo-ionized
intergalactic medium[6, 7]. The remainder is still “missing” and under hot
debate[8, 9, 10]. Numerical simulations predicted that most of this missing
baryonic component should be in the form of warm-hot intergalactic medium
(WHIM, $T\sim$105–107 K)[11, 12], which provide vast filamentary reservoirs of
material that continually feed star formation in galaxies. Finding this
component and thereby producing a census of the mass budget of the local
Universe is crucial to confine the standard cosmological model. These baryons
are difficult to observe. The presence of the WHIM has been inferred from the
detection of discrete UV absorption features in the spectra of bright
background targets[13]. However, such observations yield a relatively small
number (few hundred) of random sight-lines, from which physical conditions
mostly have to be analyzed statistically; they give no real information on the
shapes and flow patterns of the intergalactic gas. With sensitivity down to
500 PU (Photons s-1 cm-2 sr-1), CAFE will detect and map the O vi doublet
emission from the denser and warmer parts of WHIM (i.e. in the vicinity of
galaxies), as well as carry out a census of baryons in about 200 galaxy halos,
which would critically test the physics in the hydrodynamic simulations.

###  2.2 How do accretion and feedback affect galaxy evolution?

Accretion and feedback are two of the most important and most poorly
understood topics of present-day studies of galaxy evolution. Direct
observation of gas accretion onto galaxies remains sparse due to the faintness
of the measurable signals and the limited sensitivities of current
observatories [14]. H i Ly$\alpha$ is the best sensitive probe for the
inflowing gas with the temperature of $\sim 10^{4}$–105 K between galaxies and
the IGM, and a few cases of inflows have been revealed at high redshifts[15].
By mapping the Ly$\alpha$ emission in the crucial outskirt region of nearby
galaxies, CAFE will directly observe the spatial distribution and kinematics
of the inflowing gas, and thereby will test prevailing accretion ideas.

The feedback is normally in the form of multi-phase outflows, including cold
neutral clouds ($10^{3}$ K), warm ionized gas ($10^{4}$ K), and coronal plasma
($10^{5}$ to perhaps $10^{7}$ K). However, only the coronal plasma may
transport mass, momentum, energy, and heavy elements into the CGM and IGM. The
hot ($>10^{6}$ K) phase can be studied in X-ray emission, and several large
X-ray missions have been proposed with enough sensitivities for mapping large
scale structures. The best tracers of the gas in the $10^{5}-10^{6}$ K
temperature range are the O vi doublet, as oxygen is the most abundant metal
and the dominant coolant for gas at temperatures of a few times 105 K[16].
Current observations are dominated by absorption studies, but again, this type
of observation has very little information about the transverse extent of the
absorbing gas clouds. With the O vi emission mapping, the CAFE census would
form the foundation for building a physical understanding of galaxy feedback.
In addition, the kinematic mapping of the followed deeper CAFE observations
and the spectroscopy power of LyRIC will provide insight into the interactions
between multi-phase gas in galactic winds and galactic fountains. CAFE will
also study cooling, accretion, and feedback in galaxy clusters.

###  2.3 Baryon cycle and Energetic Feedback in the Milky Way and Magellanic
Clouds

Due to its closeness, the characterization of the plasma in the Milky Way and
the Magellanic Clouds will be the first step to understand the astrophysics of
gaseous halos of galaxies. The HVCs revealed by the H i 21cm-line observations
and the UV absorption studies are gas flows in Galactic halo[14], and thought
to be a reservoir to sustain star formation in the Milky Way[17]. However,
either their origin or fate is still under debate. Their infalling process
toward the galactic disk is accompanied by the interaction with the hot
gaseous halo[18, 19], and forms a warm-hot transition layer of 105-7 K that
revealed by the absorption features of highly ionized species such as O vi, N
v, and C iv in the FUV band[20]. Therefore, a census of the line absorption
and emission properties will provide valuable information, especially in the
Lyman-UV regime that cannot be probed with current facilities. The O vi
$\lambda$1032 emission feature in the Milky Way has been detected by FUSE and
exhibits intensities of 1900–8600 PU[21], which places a sensitivity
requirement to the proposed LUV missions.

Besides that, hot bubbles including supernova remnants and superbubbles
surrounding massive star formation regions are the sites of the stellar
feedback process. The ionizing photons, mechanical energy, and synthesized
metals shed or ejected from newly formed stars shape ambient medium, closing
the baryon cycle in normal galaxies, or even triggering galactic outflow that
influences CGM/IGM in starburst cases[22]. However, a common query on its
efficiency is that radiation carries away most of the feedback energy
presumably[23]. The characterization of transition layer between the hot
interior and cold gas shell is of unique importance to probe the efficiency
issue, because most of the processes that govern the bubble evolution and
radiation property, including thermal conduction, radiation momentum transfer,
shell fragmentation, hot gas leakage, etc., all happen at the transition
layer. Therefore, the radiation property of high ions in the hot bubbles
probed with LUV missions will provide the most important piece to the multi-
wavelength study of stellar feedback process.

##  3 Proposed Missions in China

###  3.1 LyRIC

LyRIC is designed to take advantage of the mature technology, long-slit
spectrograph (LSS) operating on Chinese Space Station to fulfill the high
quality spectroscopic radiation measurements from CGM of nearby galaxies with
big angular sizes, HVCs in our Galaxy and M31, and the diffuse sources in our
Galaxy and SMC/LMC for the first time. Besides the scientific significance,
such a scientific payload will also help us to verify our LUV technologies in
space.

Figure 1: Optical design for LyRIC

Limited by the size and weight of the independent external payload operating
on CSS, the major specifications for LyRIC is summarized in Table 1. LyRIC
will have a mirror with aperture less than 30 cm, spectral resolution R$\sim$
3000, and spatial resolution about 30 arcsec, working in the wavelength range
of 91-115 nm for a lifetime longer than 5 years.

National Astronomical Observatory in China (NAOC) has succeeded in building
the prototype LSS and vacuum test facilities. The prototype FUV LSS is
sensitive down to 102 nm, which gives us a precious experience.

LyRIC adopts a traditional optical design for long-slit spectrograph as shown
in Fig. 1. The primary mirror is an off-axial paraboloidal mirror with a focal
ratio of F/3.3. Light collected by the primary mirror is first folded by a
small planar mirror and then passes an entrance slit of $18\times 0.2$ mm. A
spherical holographic grating with a diameter of 250 mm and focal ratio of
F/1.5 is placed behind the entrance slit and refocus the diffracted lights
onto a microchannel plate (MCP) detector. The holographic grating has an
effective groove density of 3600 g/mm and its first-order diffraction is used.
LyRIC has a dimensional FOV of $1^{\circ}\times 0.5^{\prime}$ with
$30^{\prime\prime}$ spatial resolution in the cross-diffraction direction. The
one-dimensional imaging spectrum covers a wavelength of 91–115 nm and occupies
a physical area of $64\times 16$ mm on the MCP detector. The preliminary
design for the LyRIC instrument is shown in Fig. 2.

Figure 2: The outlook (left) and inside view (right) of LyRIC instrument. Table 1: Major specifications for LyRIC Aperture | 300 mm
---|---
Wavelength | 91 – 115 nm
Spectral Resolution | $R\approx 3000$
Instantaneous FOV | 1${}^{\circ}\times 0.5^{\prime}$
Angular Resolution | 30′′
Payload Envelope |  $1.0\times 0.6\times 0.4$ m

###  3.2 CAFE

Figure 3: CAFE optical layout

CAFE will use a novel optical design[24] and an advanced photon-counting MCP
detector (see section 4.3) for two identical multi-channel narrow band
imagers, mainly observing the O vi and H i emission lines at the redshifts of
the pre-selected target galaxies in the local Universe (z=0-0.05) with FOV
about $20^{\prime}\times 20^{\prime}$ and spatial resolution at least
$30^{\prime\prime}$. Our 3-yr baseline mission has low inclination and low
earth orbit, mounted on an agile spacecraft, with a survey mode
($R=\lambda/\Delta\lambda=500$) and a mapping mode (R=2000). CAFE must achieve
a $3\sigma$ detection limit of 500 PU and the instrument must allow co-adding
to achieve higher sensitivity. The major specifications are summarized in
Table 2. The outlook and inside view of CAFE instrument are shown in Fig 4.

The optical layout is shown in Fig 1. An offset Gregorian telescope collects
the incident light and feeds its converging beams into a monochromator system.
The monochromator consists of an entrance slit, a highly dispersive grating,
and six exit slits defining six narrow-band imaging channels. The entrance
slit is located on the image of the primary formed by the Gregorian system
immediately after the secondary. Therefore, the entrance slit defines the
usable aperture of the primary. Note that such a design is significantly
different from a traditional long-slit spectrograph design where the entrance
slit is located on the focal plane. The grating is placed at some distance
after the Gregorian focus. It disperses the incident light according to the
wavelength and at the same time forms another pupil plane along its exit
directions. Six exit slits are placed on this pupil plane to define six
distinct wavelength channels. The three O vi channels are centered at 103,
104.8 and 106.6 nm, while the three H i $\rm Ly\alpha$ channels are centered
at 125.0, 126.2 and 127.4 nm, respectively. The central wavelengths of the
imaging channels are tunable by rotating the exit slits from z=0 to 0.05 (O
vi) while from z=0.03 to 0.05 (H i $\rm Ly\alpha$ for the low orbit design),
imaging mirrors and MCP detector together along a circular path centered at
the grating. Pupils of different channels are well separated in the dispersive
direction so that the light from any field of one channels does not overlap
with any field of another channel. The bandwidth (or spectral resolution) of
each channel is adjustable by varying the width of the entrance and exit
slits. Finally, each exit slit is followed by an imaging mirror which forms
the full-field ($20^{\prime}\times 20^{\prime}$) image of a particular channel
on a planar MCP detector. The three O vi channels share the same detector
while the three H i Ly$\alpha$ channels share another detector.

Table 2: Major design specifications and constraints for the CAFE imager Parameter | Specification
---|---
Wavelength Coverage | 102 – 130 nm
Number of Imaging Channels | 3 O vi \+ 3 H i Ly$\alpha$
Spectral Resolution | 500/1000/2000
Field of View | 20${}^{\prime}\times 20^{\prime}$
Spatial Resolution | $<30^{\prime\prime}$
Sensitivity | 500 PU (3$\sigma$, 104 s, $R=500$)
Payload Dimension Constraint |  $<1000\times 500\times 500$ mm
MCP Size and Resolution |  $39\times 39$ mm, 20 $\mu$m

Figure 4: The outlook (left) and inside view (right) of CAFE instrument.

The grating in the CAFE optics has to provide sufficient chromatic dispersion
to separate images of different wavelength channels. It also creates a pupil
plane after the grating to place the exit slits as well as helps to control
the optical aberrations. Holographic gratings are favored because they allow
the use of a spherical substrate. In our design, the grating is a third-order
holographic concave grating with a spherical substrate and an effective
density of 3350 g/mm. The holographic recording geometry is optimized to
achieve the desired imaging and spectral performances, while the groove
profile is optimized to maximize grating efficiency for the third-order
diffraction. The typical spot diagram of the imaging channels is shown in Fig.
5. The 80% energy encircle diameter is less than 21 arcsec for all channels
and across the full fields of $20^{\prime}\times 20^{\prime}$, which meet the
specification of 30 arcsec by 30% margin.

Figure 5: CAFE spot diagram for the 104.8 nm imaging channel

##  4 Enabling Technologies

###  4.1 Mirror Coatings

It has been found that Al coating has a high reflectance in the far
ultraviolet range and good adhesion to the substrate, which is the best choice
for the preparation of high-quality mirrors. However, the surface of the Al
film is easily oxidized to form a thin layer of $\rm Al_{2}O_{3}$, which has a
large absorption below 160 nm. Much work have been done to improve the
reflectivity by plating a protective layer[25, 26]. A fluoride is well suited
as protective coating for the Al film because of its low intrinsic absorption,
like lithium fluoride (LiF), magnesium fluoride ($\rm MgF_{2}$) and $\rm
AlF_{3}$[27, 28, 29]. Al coating protected with MgF2 has been used in HST, and
LiF protected Al coatings have been used in FUSE, with the reflectivity about
50% at 98-118.7 nm[30, 3]. The capabilities of sensitive instruments were
limited by the poor performance of conventional mirrors. The NASA TFCL has
produced Al+eLiF and Al+eMgF2 mirror coatings by heating the substrate to
$\sim$220 ∘C during the deposition process, which increase the reflectivity up
to 70% at 110 nm (Al+eLiF), 80% at 115 nm ($\rm Al\times eMgF_{2}$), closer to
the theoretical maximum[31, 32].

Our laboratory has done a lot of experiments to study Al mirror coatings,
prepared Al+eMgF2 at different temperatures, and characterized the variety of
surface and reflectivity after 30 months. Al+eMgF2 coating showed higher
reflectivity above 110 nm prepared at 200 ∘C and 300 ∘C, with lower roughness
and better stability. Because LiF is the first choice of overcoat at the short
wavelength end of the spectrum, whose absorption edge is at 102 nm. We
prepared Al+eLiF at 300 ∘C, it was found that the reflectivity dropped about
40% in 2 months that stored in 40% relative humidity (RH), which is more
quicker than that stored in the 20% RH. Therefore, it is necessary to add a
protective overcoat layer to reduce the hygroscopic sensitivity of the Al+eLiF
coating, The $\rm Al+LiF+eMgF_{2}$ mirror coating was prepared by heating the
substrate to $\sim{}200$ ∘C during the deposition process, and the measured
reflectivity is shown in Fig. 6.

It is reported that the reflectivity can be effectively improved when the
Al+eLiF mirror coating overcoated by a thin AlF3 film deposited by atomic
layer deposition (ALD)[33]. And the SiC seems to be a protective layer
material worth considering, which shows a reflectivity about 40% at LUV. We
will focus on the study of the protective overcoat layer on Al+eLiF coatings
in the future, like AlF3, SiC and so on, as well as the performance in
different environments.

Figure 6: The reflectivity of Al+LiF+eMgF2

###  4.2 Grating

As a critical component, varied line-space concave gratings (VLSCG) have been
widely used in soft X-ray to visible spectrum instruments, including FUSE
mission. FUSE operates in a band of 90-120 nm, which contains two channels,
each with two VLSCGs, with working in bands 91 – 103 nm and 104 – 120 nm,
respectively.

CAFE is composed of an incident slit, a concave grating and six exit slits
(see Session 3.2). With the VLSCG, beams with the same wavelength from
diﬀerent ﬁeld of view converge on the same exit slit, and the exit slits for
different channels are distributed along a ring centered on the grating.
Similar to the incident slit, the exit slit is placed at the exit pupil
surface formed by the concave grating, and the width of the slit is used to
limit the spectral bandwidth. Different wavelengths are separated by the
concave grating with suﬃciently high dispersion capability. On the other hand,
the grating is also used as an imaging element to image the incident slit and
form an exit pupil surface for diﬀerent central wavelengths, while reducing
the aberration of the system. In addition, limited space puts a constraint on
the size of the system envelope, thus imaging optical elements including
gratings have relatively short focal length and small F number.

Experiences in the design and fabrication of VLSCGs in soft X-ray band (0.5–6
nm)[34] and large scale multilayer dielectric grating via interference
lithography and ion-beam etching techniques[35] enable a VLSG with central
density of 3350 gr/mm, size of 112 mm (L)$\times$118 mm (H) . The design of
the concave grating for CAFE has been completed so far. The influence of
alignment errors in holographic optics path on groove density distribution
will be systemically analyzed. The grating patterns are recorded into
photoresist using aspheric wave-front recording optics. The groove depth and
duty cycle of photoresist grating are adjusted through RIE with O2 for high
diffraction efficiency. At last, the grating will be coated with a layer of
Al+LiF+eMgF2 for high reflectivity. In addition, we plan to transfer the
photoresist patterns into fused silica substrate by reactive ion beam etching
for a higher diffraction efficiency, which is predicted up to 40%.

The design of the holographic recording configuration and fabrication process
of the VLSCG for CAFE are in process, with a targeted delivery date in the
winter of 2021.

###  4.3 Advanced MCP Detectors

At the “Institut für Astronomie und Astrophysik Tübingen” (IAAT), advanced
imaging and photon counting MCP detectors[36] are developed for CAFE. The
detectors make use of gallium nitride (GaN) as photocathode material and
comprise a stack of two MCPs and a coplanar cross-strip (CS) anode with
advanced readout electronics.

The GaN photocathode is adopted to fulfill the requirement of high quantum
efficiency for the CAFE detector. For the 124 – 130 nm band the detector will
be sealed with a MgF2 window on which a Cs-activated photoactive layer of GaN
is grown. For the 102-108 nm line emission the transmission rate through a
window would be too low and a door will be used instead of the window. In this
“open design” we grow GaN directly on the MCP. The sealing of the detector
with a window or a door is to prevent a degradation of the photocathode. The
effect of temperature on the growth of GaN on MgF2 by plasma-assisted
molecular beam epitaxy (PA-MBE) has been investigated[37, 38]. We have also
optimized the thickness of the GaN layer and studied the effect of Mg-doping
concentration.

Long-life MCPs (by PHOTONIS Technologies) or ALD MCPs will be used to achieve
the goal of the desired low dark rate. The coplanar CS anode with 64 strips in
each direction was designed by IAAT in cooperation with the manufacturer (VIA
electronic GmbH, Hermsdorf, Germany). Each of the 128 anode strips is linked
to an input channel of a special chip, an ASIC developed by the Max Planck
Institute for Nuclear Physics in Heidelberg for the LHCb experiment[39]. The
chip is a charge preamplifier and shaper. It provides sampling frequencies of
up to 40 MHz, a very small equivalent noise charge of only a few hundred
electrons and can store up to 160 samples for each channel[40]. We have
already defined promising centroiding algorithms for the CS-anode signals.

##  5 Status

LyRIC has been proposed to the China Manned Space Engineering Office in 2019.
We are highly recommended among the astronomical instruments. Since then, we
have made a couple of modifications according to the requirements of CSS
accommodations and interfaces. Further optimization is anticipated to
compromise among science, technology, as well as the requirement of the
external payload operating on CSS.

CAFE is at the stage of Key Technologies Investigation in China (2016-2021).
The optical elements are ready to be fabricated by Nanjing Institute of
Astronomical Optics and Technology of CAS. Mirror coatings will be completed
in Tongji University in Shanghai. Grating will be made in the Great grating
group in University of Science and Technology of China. The mechanical
structures will be made by Xi’an Institute of Optics and Precision Mechanics
of CAS. MCP detectors will be developed by Institute for Astronomy and
Astrophysics, Universität Tübingen in Germany. Purple Mountain Observatory
will build the Lyman UV lab at Xianlin Campus to do the assembling and
verification. After the key technology development period, a positive outcome
will allow us to be ready to the competition of Phase A studies for Space
Missions in China. The final design of CAFE will be subject to mission
opportunities in China in the future.

In addition to undertake instrument performance analysis and to produce
simulated surveys for mission- and science studies, we are carrying out the
end-to-end simulation with the Monte Carlo based simulator SIXTE[41, 42], in
collaboration with the software developer at the Remeis Observatory of der FAU
Erlangen-Nürnberg in Germany.

###### Acknowledgements.

The scientific program described here was originally developed by members of
CAFE and LyRIC teams including: Q.S. Gu, P. Zhou, Y. Chen, Z. Li, J. Zhou, X.
Hou, X. Luo (NJU), Y. Gao, X.Z. Zheng, X. Kang, L. Feng, X.J. Jiang, C. Ge, J.
Ji, S. Wang, G. Chen, S. Jin, X. Zhou, Y. Zhang, X. Long, W. Shan (PMO), F.
Cheng, X. Kong, G. Liu (USTC), J. Wang, F. Zhang (Xiamen U.), L. Ho (KIAA), X.
Fang, L. Gao, J. Liu (NAOC), Z. Cai (Tsinghua U.), H.G. Xu, J. Shen (Shanghai
Jiaotong U.), L. Hao (SHAO), J.R. Mao (YNOC) from China, and our international
collaborators: M. Baes (U. Gent, Belgium), M. A. Barstow (U. Leicester, UK),
R. de Grijs (Macquarie U., Australia), M. Hayes, R. Lallement (GEPI, France),
F. Nicastro (Istituto Nazionale di Astrofisica, Italy), P. Richter (University
of Potsdam, Germany), D. Valls-Gabaud (GEPI, France), J. Bregman, J. Li, Z. Qu
(U. Michigan, USA), Q. D. Wang (UMASS, USA), Kinwah Wu (MSSL, UK), and J.
Wilms (FAU Erlangen-Nürnberg, Germany). L. Ji acknowledges support from NSFC
grant U1531248 and CAS International Cooperation Key Project grant
114332KYSB20180013.

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