# Properties and Asteroseismological analysis of a new ZZ ceti discovered by
TMTS

Jincheng Guo1,∗, Yanhui Chen2,∗, Xiaofeng Wang3,1,∗, Jie Lin3, Gaobo Xi3, Jun
Mo3,Alexei V. Filippenko4, Thomas Brink4, Xiao-Yu Ma5, Weikai Zong5, Yong
Yang6,7,Jingkun Zhao6,7, Xiangyun Zeng8, Zhihao Chen3, Ali Esamdin9, Fangzhou
Guo3,Abdusamatjan Iskandar9, Xiaojun Jiang6,7, Wenxiong Li10, Cheng Liu1,
Jianrong Shi6,7,Xuan Song1, Letian Wang9, Danfeng Xiang3, Shengyu Yan3,
Jicheng Zhang5,and Yonghui Yang2,11
1Department of Scientific Research, Beijing Planetarium, Xizhimenwai Street,
Beijing 100044, China
2Institute of Astrophysics, Chuxiong Normal University, Chuxiong 675000, China
3Physics Department and Tsinghua Center for Astrophysics, Tsinghua University,
Beijing 100084, China
4Department of Astronomy, University of California, Berkeley, CA 94720-3411,
USA
5Department of Astronomy, Beijing Normal University, Beijing 100875, China
6Key Laboratory of Optical Astronomy, National Astronomical Observatories,
Chinese Academy of Sciences, Beijing 100012, China
7University of Chinese Academy of Sciences, Beijing 100049, China
8Center for Astronomy and Space Sciences, China Three Gorges University,
Yichang, 443000, People’s Republic of China
9Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi
830011, China
10The School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978,
Israel
11Faculty of Science, Kunming University of Science and Technology, Kunming
650093, China
∗ E-mail<EMAIL_ADDRESS>(J,Guo<EMAIL_ADDRESS>(Y,Chen),
<EMAIL_ADDRESS>(X.Wang)

###### Abstract

Tsinghua university-Ma Huateng Telescope for Survey (TMTS) aims to discover
rapidly evolving transients by monitoring the northern sky. The TMTS catalog
is cross-matched with the white dwarf (WD) catalog of Gaia EDR3, and light
curves of more than a thousand WD candidates are obtained so far. Among them,
the WD TMTS J23450729+5813146 (hereafter J2345) is one interesting common
source. Based on the light curves from the TMTS and follow-up photometric
observations, periods of 967.113 s, 973.734 s, 881.525 s, 843.458 s, 806.916 s
and 678.273 s are identified. In addition, the TESS observations suggest a
3.39 h period but this can be attributed to the rotation of a comoving M dwarf
located within $3^{{}^{\prime\prime}}$. The spectroscopic observation
indicates that this WD is DA type with $T_{\rm eff}=11778\pm 617$ K, log
$g=8.38\pm 0.31$, mass=$0.84\pm 0.20$ M⊙ and age=$0.704\pm 0.377$ Gyrs.
Asteroseismological analysis reveals a global best-fit solution of $T_{\rm
eff}=12110\pm 10$ K and mass=$0.760\pm 0.005$ M⊙, consistent with the spectral
fitting results, and Oxygen and Carbon abundances in the core center are 0.73
and 0.27, respectively. The distance derived from the intrinsic luminosity
given by asteroseismology is 93 parsec, which is in agreement with the
distance of 98 parsec from Gaia DR3. Additionally, kinematic study shows that
this WD is likely a thick disk star. The mass of its zero-age main-sequence
mass is estimated to be 3.08 M⊙ and has a main-sequence plus cooling age of
roughly 900 Myrs.

###### keywords:

stars: white dwarfs - stars: variables: general - stars: oscillations - stars:
individual: TMTS J23450729+5813146

††pagerange: Properties and Asteroseismological analysis of a new ZZ ceti
discovered by TMTS–LABEL:lastpage††pubyear: 2022

##  1 Introduction

In our Milky Way, up to 97% of all stars will eventually evolve into white
dwarfs (WDs) (Heger et al., 2003). Main-sequence stars with masses no more
than 10-11 M⊙ (Woosley & Heger, 2015) will end up as WDs, depending on their
metallicity as well. WDs are objects of great importance that can provide
vital information in variety of research fields (Althaus et al., 2010). Owing
to a simple cooling mechanism, it is easier to derive relatively accurate ages
of WDs, making them suitable for studies on the ages of Galactic populations
(Kilic et al., 2019; Guo et al., 2019), which are important tools by studying
their luminosity functions (Munn et al., 2017; Lam et al., 2019) and mass
functions (Holberg et al., 2016; Hollands et al., 2018). Accurate WD
luminosity functions can be adopted to infer the structure and evolution of
the Galactic disk and open and globular clusters (Bedin et al., 2009; Campos
et al., 2016; García-Berro & Oswalt, 2016; Kilic et al., 2017; Guo et al.,
2018). Furthermore, massive carbon-oxygen (CO) WDs are progenitors of type Ia
supernovae (SNe Ia), which serve as standard candles for cosmological studies
(Maoz, Mannucci, & Nelemans, 2014). Ultra-short period double WDs are
potential gravitational wave sources likely to be detected by space
gravitational-wave facilities like LISA (Burdge et al., 2019).

With large spectroscopic surveys like Palomar-Green (Green, Schmidt, &
Liebert, 1986), SDSS (York et al., 2000) and LAMOST (Zhao et al., 2012), the
studies of WDs have entered a new era by increasing the numbers of WDs greatly
(Kleinman et al., 2013; Kepler et al., 2015, 2019; Zhao et al., 2013; Gentile
Fusillo et al., 2015; Guo et al., 2015b, 2022; Kong & Luo, 2021). Thanks to
the Gaia mission (Gaia Collaboration, et al., 2016), the studies of WD now
step into another new era. With the release of early Gaia DR3, the number of
WDs reached $\sim$ 359 000 (Gentile Fusillo et al., 2021). This catalog is
extremely helpful for studying light variability of WDs by cross-matching it
with some photometric surveys.

Asteroseismology makes the studies of internal structure of pulsating stars
become possible. This is also true for the studies of pulsating WDs (see a
recent review by Córsico et al. (2019)). Since the first discovery of
pulsating DA WDs (DAV, or ZZ ceti) HL Tau 76 (Landolt, 1968), there are as
many as 494 DAVs identified via photometric observations (Córsico, 2022),
including those discovered with TESS (Romero et al., 2022). Many of those DAVs
have been analysed with asteroseismology from different groups using different
models and asteroseismic approaches. Among them, two main methods are widely
adopted. One uses static stellar models with parametrized chemical profiles.
It allows a full exploration of the parameter space to find an optimal seismic
model, leading to good matches to the observed periods. (Bradley, 1998, 2001;
Castanheira & Kepler, 2009; Bischoff-Kim, Montgomery, & Winget, 2008;
Bischoff-Kim & Metcalfe, 2011; Bischoff-Kim et al., 2014; Giammichele et al.,
2017a, b). Another approach is using full evolutionary models, which is
generated by tracking the full evolution of the progenitor star, from the zero
age main sequence to the WD stage (Romero et al., 2012, 2013; Córsico et al.,
2013; De Gerónimo et al., 2017, 2018). It has been shown that detailed
analysis on individual DAV is needed to understand the precise parameters of
the white dwarf stars. In return, models can be improved based on
observations. In general, the instability strip of DAVs is in the range of 10
850 K and 12 270 K (Gianninas, Bergeron, & Ruiz, 2011), and the atmosphere of
these cool WDs are almost dominated by pure hydrogen as a result of
gravitational settling of other heavier elements. The hydrogen in the outer
envelope recombines at around $T_{\rm eff}\sim 12\,000\,K$, which causes a
huge increase in envelope opacity. Consequently, this restrains the flow of
radiation and eventually results in $g$-mode oscillations (Winget et al.,
1982). Owing to the fact that these oscillation-induced pulsation modes are
very sensitive to the stellar structure of DAVs, they can be used to study the
internal structures of these stars.

Over the past decade, the $Kepler$ (Borucki et al., 2010) and its $K2$ mission
(Howell et al., 2014) have made high-precision asteroseismology of WDs
possible (Hermes et al., 2011; Greiss et al., 2016). Later the $TESS$ mission
(Ricker et al., 2015) has enriched the sample, as it observes the whole sky
(Campante et al., 2016; Romero et al., 2022). However, $Kepler$ and $K2$
mainly focus on specific areas; while $TESS$ will cover the whole sky area,
but its size is too small for faint objects. Therefore, ground-based survey
telescope with short cadence is still vital for discovery and
asteroseismological study of faint pulsating WDs.

In this work, we report our discovery and results of asteroseismological
analysis of a new DAV star TMTS J23450729+5813146 (dubbed as J2345) discovered
by TMTS. This star, with coordinates of RA=23:45:07.29 and Dec=+58:13:14.6,
was first reported in Gaia DR2 WD catalogue as a WD candidate with a
probability being WD PWD=0.99 and G=16.88 mag (Gentile Fusillo et al., 2019).
Through SED fitting to hydrogen-rich and helium-rich atmosphere models, the
parameters of J2345 are estimated to be $T_{\rm eff}$=11 280 K, log $g$=8.04,
mass=0.63 and $T_{\rm eff}$=11 069 K, log $g$=7.93, mass=0.54, respectively.
Then it was studied in Gaia 100 pc infrared-excess WD sample (Rebassa-
Mansergas et al., 2019), as it seems to comove with a nearby faint (G=19.15
mag) M star. In their paper, the effective temperature of J2345 and the
companion are estimated to be 11 750 K and 2 800 K, respectively, via SED
fitting. No public spectrum data is available for J2345 so far.

This paper is arranged as follows: In Sect. 2, observational details of J2345
are listed. In Sect. 3, frequency solution and asteroseismological modelling
of J2345 are presented. Period from TESS is analyzed in Sect. 4, while
discussions and summary are given in Sect. 5 and 6, respectively.

##  2 Observations

###  2.1 TMTS

Figure 1: A part of the discovery TMTS light curve taken on December 2nd,
2020. The amplitude of variation is large for a DAV.

TMTS is a photometric survey with four 40-cm optical telescopes, located at
Xinglong station in China. It has a total field of view of $\sim$ 18 deg2 (4.5
deg2 each) and equipped with four 4k $\times$ 4k pixels CMOS cameras, which
allow less than a second read-out time and high speed photometry. The survey
operates in two observation modes. First, uninterrupted observing LAMOST areas
for the whole night with a cadence of 1 min, carrying out collaborative tasks
with the LAMOST. Second, supernova survey with a cadence of 1-2 d. For the
purpose of reaching out the full potential of observations, customized filter
covering 330-900 nm is used for the survey. The 3$\sigma$ detection limit of
TMTS can reach 19.4 mag for 1-min exposure. More description regarding the
performance of TMTS can be found in Zhang et al. (2020), Lin et al. (2022a)
and Lin et al. (2022b).

TMTS started the 1 min-cadence survey since 2020, producing uninterrupted
light curves for more than 10 million objects so far. The WD catalog generated
from Gaia EDR3 (Gentile Fusillo et al., 2021) is used to cross-match with the
TMTS catalog within 3′′, which yields more than a thousand WD common sources.
Based on visual inspections of each source, WD J2345 was selected as a
pulsating WD candidate for detailed study. WD J2345 was observed by TMTS on
two nights (see details in Table. 1). A part of the discovery light curve is
shown in Fig.1. The amplitude of variation is large for a ZZ ceti, roughly
0.2-0.3 mag.

Table 1: Observation logs of J2345. Telescope | instrument | obs_date | exposure (s)
---|---|---|---
TMTS | CMOS | 2020-11-01 | 60
(4$\times$40cm) | (330-900 nm) | 2020-11-02 | 60
SNOVA (40cm) | CCD | 2021-11-07 | 50
| (White light) | 2021-11-08 | 100
|  | 2021-11-10 | 100
|  | 2021-11-11 | 100
|  | 2021-11-14 | 100
Shane (3m) | Kast Double | 2021-11-07 | 3600
| Spectrograph | 2021-11-12 | 2400
TESS | CCD | 2019/Sector17 | 120/1800
| (600-1000 nm) | 2020/Sector24 | 120/1800

Figure 2: Spectrum taken by Lick 3 m Shane telescope and its spectral fitting.
From left to right, blue dashed lines in the upper panel mark the Hγ, Hβ, Hα,
and Ca II triplet lines, respectively. From bottom to top, black lines in the
lower panel are normalized Hα, Hβ, Hγ, and Hϵ lines, respectively. Red dashed
lines are the best model fitting after corrections for blueshift.

###  2.2 Spectral observations

Spectral follow-up observations have been carried out by 3 m Shane telescope
located at Lick observatory in 2021. Both spectra were taken by Kast double
spectrograph with slit width of 2${}^{{}^{\prime\prime}}$ and grism 2,
covering 3600-5700 Å in blue and 5400-10760 Å in red, providing a spectral
resolution of roughly 1.02 Å$\cdot pixel^{-1}$. The standard procedures of
dark current subtraction, bias subtraction, cosmic ray removal, 1D spectral
extraction are performed using IRAF. The signal to noise ratio (SNR) of the
spectrum taken on 12th November is much better than the other due to better
seeing, thus only the spectrum with higher SNR is used for spectral analysis.
Owing to its higher SNR, blueshifted lines are noticeably seen in the
spectrum. Spectral fitting with WDTOOLS (Chandra et al., 2020; Chandra, 2020)
yields a radial velocity of -67.7$\pm$17.2 km$\cdot s^{-1}$. After corrections
for the line shift, the parameters of J2345 are derived as $T_{\rm
eff}=11778\pm 617$ K, log $g=8.38\pm 0.31$, mass=$0.84\pm 0.20$ M⊙ and
age=$0.704\pm 0.377$ Gyrs, based on the spectral model fitting method
described in Guo et al. (2015b, 2022). The spectrum and best fitting are shown
in Figure. 2. The derived $T_{\rm eff}$ and mass are especially helpful for
providing independent check of the results from asteroseismological analysis.

###  2.3 Photometric follow-up

Additional follow-up photometric observations have been taken by a 40 cm
telescope called SNOVA located at Nanshan station in China. A total of 5
nights observations have been taken for J2345. All these observations are
observed in white light with exposure time of around 100 s. The standard image
processing, like bias correction, flat correction and source extraction are
performed with IRAF, then differential photometry is applied to obtain the
final light curves. In addition, TESS has also observed J2345 in 2 sectors in
2019 and 2020 (see Table. 1). Analysis of the light curves is presented in
section 4.

##  3 Analysis

Table 2: The frequency content detected from TMTS and SNOVA photometry and
their mode identifications.

ID | Freq. | $\sigma{\rm Freq.}$ | $\rm P$ |  $\sigma$ P | Amplitude | $\sigma\rm{Amp}$ | SNR |  Optimal P⋆ | $(l,k)_{\star}$ |  Optimal P† | $(l,k)_{\dagger}$
---|---|---|---|---|---|---|---|---|---|---|---
|  ($\mu$Hz) |  ($\mu$Hz) | (s) | (s) | (ppt) | (ppt) |  | (s) |  | (s) |
|  |  |  |  | TMTS 2020 |  |  |  |  |  |
$f_{1}$ | 1026.974 | 0.587 | 973.734 | 0.556 | 69.326 | 7.973 | 8.7 | 973.276 | (1,19) | 973.751 | (1,19)
|  |  |  |  | SNOVA 2021 |  |  |  |  |  |
$f_{05}^{*}$ | 1034.005 | 0.262 | 967.113 | 0.245 | 13.128 | 3.980 | 3.3 | 967.245 | (2,34) | 967.061 | (2,34)
$f_{03}$ | 1134.398 | 0.218 | 881.525 | 0.169 | 15.106 | 3.806 | 4.0 | 881.448 | (1,17) | 881.556 | (2,31)
$f_{02}$ | 1185.596 | 0.205 | 843.458 | 0.146 | 15.944 | 3.769 | 4.2 | 843.661 | (1,16) | 843.394 | (1,16)
$f_{04}^{*}$ | 1239.286 | 0.245 | 806.916 | 0.159 | 13.409 | 3.789 | 3.5 | 806.992 | (1,15) | 806.855 | (1,15)
$f_{01}$ | 1474.333 | 0.061 | 678.273 | 0.028 | 45.447 | 3.217 | 14.1 | 678.358 | (1,12) | 678.243 | (2,23)

  * •

∗ Frequencies below the 4.0 $\sigma$ detection limits.

  * •

⋆ Adopted solution.

  * •

† Additional solution found by freeing the value of $l$.

Figure 3: The Lomb-Scargle periodogram of TMTS and SNOVA observations taken in
2020 and 2021, respectively. The horizontal dashed lines (in blue) denote the
4.0 $\sigma$ significance threshold. The upside-down grey curves represent the
residuals of power spectra with significant frequencies being pre-whitened.

###  3.1 Frequency content

The flexible software package FELIX111Frequency Extraction for Lightcurve
exploitation, which was developed by Stéphane Charpinet. See details of the
code in (Charpinet et al., 2010). was used for Fourier decomposition of the
light curve, which incorporates the standard prewhitening and nonlinear least-
square fitting techniques for Fourier transformation (Deeming, 1975; Scargle,
1982). The threshold of acceptance for a significant frequency is set to be
4.0 $\sigma$ of the local noise level (see, e.g., Kuschnig et al., 1997).
Table 2 lists the frequencies with their attributes extracted with FELIX: the
ID ordered by their frequency (Column 2), amplitude (Column 6) and their
uncertainties (Columns 3, 7), the corresponding period and their uncertainties
(Columns 4, 5), the SNR (Column 8), the corresponding periods of optimal
model, which will be discussed in Section 3.3 (Column 9) and their $l,k$
(Column 10). We have barely detected one significant frequency, $f_{1}\sim
1027\mu$ Hz in the year of 2020 from TMTS, while three significant frequencies
and two suspected frequencies from SNOVA in the year of 2021.

Figure. 3 shows the Lomb-Scargle periodogram of TMTS and SNOVA observations
with one and five (including 2 frequencies below the detected limitation)
frequencies detected. We clearly see that the significant frequency in 2020
with period of about 973 s disappeared in 2021. However, the five frequencies
with period from 678 s to 967 s in 2021 were also not detected in 2020. This
indicates that significant frequency and amplitude variations happened in
J2345. Note that this phenomenon has been disclosed in pulsating white dwarf
stars from both ground-based and space-borne photometry (e.g., Vauclair et
al., 2011; Zong et al., 2016). A natural explanation could be that the
nonlinear mode interactions between resonant modes (Zong et al., 2016;
Buchler, Goupil, & Serre, 1995). We thus suggest that all of the above six
signals are real pulsations and will be used for construction of seismic
models.

###  3.2 Input physics and model calculations

The latest version of the White Dwarf Evolution Code (WDEC v16, Bischoff-Kim,
2018) is used in this work to evolve grids for DAV models. This code includes
the oxygen (O) profile in the core, parameterized by six parameters (i.e.
h1-3, w1-3). This feature provides more accurate fitting results than previous
version without it. The equation of state and opacity tables from the Modules
for Experiments in Stellar Astrophysics (MESA, Paxton et al., 2011) are
adopted in current version of WDEC. The standard mixing length theory (Bohm &
Cassinelli, 1971) and the mixing length parameter of 0.6 (Bergeron et al.,
1995) are adopted in the analysis. The explored parameter spaces of evolved WD
models are shown in Table. 3. For the initial ranges and crude steps in this
table, 7 558 272 WD models have been evolved. The model adopted here, differs
from those derived by considering the complete evolution. Firstly, this model
only considers the cooling phase of WD stars, while fully evolutionary models
take into account the complete evolution of the progenitor stars and the WD
cooling phases. Secondly, this model here is a large sample model grids
including parameterized central core, while fully evolutionary models are
typically not used for large sample model fitting. More details regarding the
core parameters can be found in the Fig. 1 of Bischoff-Kim (2018) and the user
manual (Bischoff-Kim & Montgomery, 2018). In the fitting process, fine steps
are used to optimize the fitting models.

Table 3: The explored parameter spaces of WDs evolved by WDEC.

Parameters | Initial ranges | Crude steps | Fine steps | Optimal values⋆ | Optimal values†
---|---|---|---|---|---
$M_{*}$/$M_{\odot}$ | [0.500,0.850] | 0.010 | 0.005 | 0.760$\pm$0.005 | 0.690$\pm$0.005
$T_{\rm eff}$(K) | [10600,12600] | 250 | 10 | 12110$\pm$10 | 12370$\pm$10
-log($M_{\rm env}/M_{\rm*}$) | [1.50,2.00,3.00] | 0.50/1.00 | 0.01 | 2.00$\pm$0.02 | 3.00$\pm$0.01
-log($M_{\rm He}/M_{\rm*}$) | [2.00,5.00] | 1.00 | 0.01 | 5.01$\pm$0.04 | 4.99$\pm$0.01
-log($M_{\rm H}/M_{\rm*}$) | [4.00,10.00] | 1.00 | 0.01 | 9.98$\pm$0.02 | 7.00$\pm$0.01
$X_{\rm He}$ in mixed C/He/H region | [0.10,0.90] | 0.16 | 0.01 | 0.25$\pm$0.01 | 0.56$\pm$0.01
$X_{\mathrm{O}}$ in the core |  |  |  |  |
h1 | [0.60,0.75] | 0.03 | 0.01 | 0.73$\pm$0.01 | 0.66$\pm$0.01
h2 | [0.65,0.71] | 0.03 | 0.01 | 0.66$\pm$0.01 | 0.71$\pm$0.01
h3 | 0.85 |  | 0.01 | 0.81$\pm$0.03 | 0.85$\pm$0.01
w1 | [0.32,0.38] | 0.03 | 0.01 | 0.35$\pm$0.01 | 0.37$\pm$0.01
w2 | [0.42,0.48] | 0.03 | 0.01 | 0.45$\pm$0.01 | 0.46$\pm$0.01
w3 | 0.09 |  | 0.01 | 0.09$\pm$0.01 | 0.12$\pm$0.01

  * •

$M_{*}$ denotes the stellar mass, while $M_{env}$ is the envelop mass. $M_{H}$
is the mass of hydrogen atmosphere, and $M_{He}$ is the mass of He layer.
$X_{He}$ is the He abundance in the mixed C/He/H region, and $X_{O}$ is the O
abundance in the core. The parameter h1 refers to the O abundance in the core
center, while w1 is the mass fraction of $X_{O}$=h1. Parameters h2 and h3 are
O abundance of two knee points on the reducing O profile. The w2 and w3 refer
to the masses of the gradient regions of O profile.

  * •

⋆ Adopted solution.

  * •

† Additional solution found by freeing the value of $l$.

Figure 4: Left panel: a color graph of fitting error $\sigma_{RMS}$ as
functions of stellar mass and $T_{\rm eff}$. A total of 14 271 DAV stellar
models are used in fit. Right panel: a color graph of fitting error
$\sigma_{RMS}$ as functions of He-layer mass and envelope mass. A total of 7
676 DAV stellar models are used in the fit.

###  3.3 The model fittings

For the model fittings, a root-mean-square residual $\sigma_{RMS}$ is adopted
in this work for the evaluation of fitting results.

$\sigma_{RMS}=\sqrt{\frac{1}{n}\sum_{n}(P_{obs}-P_{cal})^{2}}$ (1)

In Eq.1 above, $n$ is the number of fitted observed modes, i.e., 6 for J2345.
$P_{obs}$ and $P_{cal}$ are the observed periods and model calculated periods,
respectively. During model fittings, only 2 digits behind decimal points of
observed periods are used. Owing to the fact that periods 973.73 s and 967.11
s are close and the amplitude of period 973.73 s is large, we assume the
period of 967.11 s is $l$=2 mode, and the other 5 periods belong to the $l$=1
mode. Additional analysis has been checked as well, leaving free the value of
$l$ for all periods. For the initial fitting, the combinations of parameter
space ranges and crude steps are used to build the DAV models. This includes 7
558 272 models, which are adopted to fit the observed 6 modes. The crude steps
are chosen by considering the computational requirement for models. It takes
around 12 s to evolve one model. Then, the parameter steps of models are
narrowed down to fine steps around models with minimum $\sigma_{RMS}$. For the
fine steps, there are 3 to 5 grid points for each parameter. For fine steps of
mass, 0.005 is chosen because it’s the same step size adopted in WDEC. For the
other fine steps, they are all chosen to be much smaller than their crude
steps. In Table 3, there are 6 global parameters and 6 $X_{O}$ parameters. In
order to find the minimum fitting error, the $X_{O}$ parameters are first
fixed, and a grid of global parameters are generated. Then the global
parameters are fixed, and a grid of $X_{O}$ parameters are generated. The
chosen fitting model will be nearly convergent to an optimal fitting model
after repeating these two processes for a dozen times. Finally, the optimal
model is obtained when $\sigma_{RMS}$ = 0.21 s (The derived distance is
calculated later as 98 pc). For the additional analysis, the optimal model is
found when $\sigma_{RMS}$ = 0.046 s and its derived distance is 103 pc. The
optimal model parameters of adopted and additional solution are listed in the
fifth and last column of Table 3, respectively. Although the optimal solution
in additional analysis is achieved with a smaller fitting error of 0.046 s,
the solution with fitting error of 0.21 s is adopted, due to the latter
solution results in only one $l$=2 modes. With more high degree modes in the
adopted solution, more modes exist in the solution model as well, smaller
fitting errors can be achieved, but it is not a reasonable choice comparing to
the one with less high degree modes. In addition, in order to explore models
with thicker H and He-envelops, ($-log(M_{\rm He}/M_{\rm*})=2$ and
$-log(M_{\rm H}/M_{\rm*})=4$, which we did not include in the beginning due to
limited computational power), a model grid containing 314 928 models is
calculated. Independent model fittings are performed, yet the adopted solution
listed in the fifth column of Table 3 is still preferred after comparison. On
the other hand, in both solutions shown in Table 3, close periods 973.734 s
and 967.113 s are not both $l$=1, meaning they are not likely to be components
of a rotational triplet. The full width at half height of the reciprocal of
$n\sigma_{RMS}$ is estimated as the error of each optimal value. It is known
that modes with $k\gg$1 probe the most external part of the star. Thus the
lack of short period modes in our observation reflected in larger errors in
the core (h1-w3), compared to the errors estimated for L19-2 (Chen, 2022). For
L19-2, same models and approach have been applied, but its observations have
detected more short period modes, which yields much smaller errors in the
core. According to the derived optimal values, J2345 is a relatively massive
and hot DAV with a thin H atmosphere.

Figure 5: Sensitivity plots of 8 parameters of the optimal model. Subplots are
8 parameter values versus their root mean square residual $\sigma_{RMS}$.
Figure 6: The core composition profiles and corresponding Brunt-Väisälä
frequency for the optimal model. In the lower panel, the abundance of O, C, He
and H are plotted in red solid line, green dashed line, blue dashed line and
magenta dotted line, respectively. In the upper panel, the vertical axis is
the logarithm of the square of buoyancy frequency. Three little bumps are
present due to the existence of three element transition gradient zones.

A colour graph of fitting error $\sigma_{RMS}$ as functions of stellar mass
and $T_{\rm eff}$ is displayed in the left panel of Fig. 4. The colour
represents the fitting error $\sigma_{RMS}$ as defined in Eq.1. The grid
consisting of stellar mass in the range of 0.500 $M_{\odot}$ and 0.850
$M_{\odot}$ with a step of 0.005 $M_{\odot}$ and $T_{\rm eff}$ in the range of
10 600 K and 12 600 K with step of 10 K are included in the analysis, which
contains 14 271 DAV models. All of other parameters are fixed to their optimal
values in Table 3. The right panel of Fig. 4 shows $\sigma_{RMS}$ as functions
of He-layer mass and envelope mass, which involves 7 676 DAV models. The
logarithm of envelope mass ranges from -2.00 to -3.00 with a step of 0.02, and
the logarithm of He layer mass ranges from -4.01 to -6.01 with a step of 0.02.

The sensitivity plots of 8 parameters of the optimal model are shown in Fig.
5. Stellar mass, $T_{\rm eff}$, envelope mass, He-layer mass, H-atmosphere
mass, He abundance in mixed C/He/H region, h1 and w1 for the O profile versus
fitting error $\sigma_{RMS}$ are plotted in different subplots, respectively.
Each panel of these parameters is plotted when all other parameters are fixed
to the optimal values. The parameter values corresponding to the lowest
$\sigma_{RMS}$ indicate the optimal values. In Table 3, the mass of the shell
of H ranges from $10^{-10}\,M_{\ast}$ to $10^{-5}\,M_{\ast}$. But our fitting
is not limited to explore spaces in this range. Depending on the pre-optimal
solutions of each iteration in the search for final optimal values of J2345,
the initial ranges listed in Table 3 may be extended if pre-optimal value is
near the range limit. For instance, it is shown in Fig. 5 that H masses less
than $10^{-10}\,M_{\ast}$ have been explored as well, since the optimal value
is near the limit of initial lower range. Similar case can be found in the
mass of the shell of He, spaces as low as $10^{-6}\,M_{\ast}$ are explored as
well, exceeding the lower limit of $10^{-5}\,M_{\ast}$. The core composition
profiles and corresponding Brunt-Väisälä frequency for the optimal model are
shown in Fig. 6, where the bumps are caused by composition gradient in
different zones. There are some smaller bumps exist near horizontal axis 1 and
5 as well. After some simple investigations on this matter, we assume that
those have something to do with WDEC, rather than anything physical. One
should note that this kind of chemical profiles are in contrast with those
derived from fully evolutionary computations. The existence of a C-buffer and
several features in the chemical profile has been discussed extensively in De
Gerónimo et al. (2019) for a DBV star.

In order to check the self-consistency of the best fit model, the distance
derived from asteroseismology analyzed results can be used to do an
independent test. For the best-fit model, the luminosity of J2345 is
Log(L/L$\odot$) = -2.685. The bolometric magnitude of the optimal model is
$M_{bol}$=11.45, using the correction $M_{bol}=M_{bol,\odot}-2.5\times
Log(L/L_{\odot})$ and assuming the bolometric magnitude of the Sun
$M_{bol,\odot}=4.74$ (Cox, 2000). Since the bolometric correction (BC) in Gaia
G band is not provided for J2345 in DR3, the BC in V band is adopted. The
BC(V) for DA star model with $T_{\rm eff}$= 12 000 K and 13 000 K are -0.611
mag and -0.828 mag, respectively, as listed in Table 1 of Bergeron, Wesemael,
& Beauchamp (1995). Therefore, for J2345 with $T_{\rm eff}$= 12 110 K, the
linear interpolated BC(V) is -0.635 mag. The absolute V magnitude can be
derived as $M_{V}=M_{bol}-BC(V)=11.45-(-0.635)=12.085$. By using the equation
$d=10^{(m_{V}-M_{V})/5+1}$, the distance corresponding to the optimal model is
93 pc, given $m_{V}=16.93$ (Lasker et al., 2008). Comparing to the inverse
parallax distance of 98 pc from Gaia DR3, there is $\sim$5% error in the
optimal model derived distance. Furthermore, the results corresponding to the
optimal model are in agreement with the parameters obtained from spectral
model fitting in section 2.2. These two facts suggest that our
asteroseismological results are self consistent.

Figure 7: The Lomb-Scargle periodogram of TESS 120 s observations taken in
2019 and 2020, respectively. The 3.39 h period becomes much weaker in 2020
than in 2019.

##  4 Rotation period of nearby M dwarf from TESS

J2345 was observed by TESS in Sector 17 and 24. They are both recorded in 120
s and 1800 s exposures. Based on Lomb-Scargle (LS, Scargle, 1982) method, a
noticeable period $\sim$ 3.39 h is present in the power spectra of both TESS
observations (Figure 7), which is not detected in TMTS and SNOVA observations.
Rebassa-Mansergas et al. (2019) listed J2345 and another star named Gaia DR2
1999127510436274048 as comoving stars (see Table 1 in their paper), as they
are located within about 3′′ and have similar parallaxes and proper motions
from Gaia DR2. According to their SED fitting, the $T_{\rm eff}$ of these two
stars are 11 750 K and 2 800 K, respectively, indicating that the comoving
star is an M star. Since the image resolution of TESS is $\sim
21^{\prime\prime}$ per pixel and the brightness of M star is comparable to
J2345 in TESS red band, the detected 3.39 h period may originate from the M
star. Firstly, the 3.39 h period is not plausible to be the pulsation period
of J2345, as it is too long. Secondly, the power of 3.39 h period is much
weaker in 2020 than in 2019 (see Fig. 7). Combining the fact that this period
is not detected in 2021 observations from TMTS and SNOVA, it is most probable
that this period is due to the rotation of M star. The appearance and
disappearance of a large dark spot can cause the variation observed in 2019
and 2020. The non-detection in 2021 further rules out the possibility that
this period is due to eclipsing of a hidden companion, since the significance
of orbital period signal should be stable. To further validate our hypothesis,
the folded light curve of TESS observation in 2019 is fed to PHOEBE for
modelling.

It is known that modelling stellar spots is difficult, as the observed light
curve can be well fitted by one large spot or several smaller spots and etc.
Currently, PHOEBE does not have spot estimators for single stars. Therefore,
we manually tuned the spot parameters to reproduce a similar light curve to
mimic the phase-folded light curve of TESS in Sector 17 (Figure 8). The
parameters of the star are set as $T_{\rm eff}$=2 800 K, mass=0.21 M⊙, star
radius =0.15 R⊙, rotation period=3.39 h and inclination angle=90∘. The single
large spot setting results in: an angular radius of 80∘; the co-latitude of
the center of spot with respect to spin axis is 90∘,, longitude of the center
of the spot with respect to spin axis is 0∘ and the relative temperature of
the spot to the intrinsic temperature is 0.97. The direct image of this spot
setting is shown in Fig. 9, corresponding to the model light curve at phase
0.75. It should be noted that this does not necessarily mean this model
setting is the real case. It is simply a demonstration to show that the TESS
light curve in 2019 can be modelled by the rotation of a large dark spot on
the M dwarf.

Figure 8: Phase folded TESS light curve modelling with PHOEBE. Blue dots are
observed phase-folded TESS light curve in sector 17 with 30 min exposure,
while red line represents the PHOEBE reproduced light curve of a single star
with a single large dark spot. Figure 9: Mesh plot of PHOEBE model of a single
star with a single spot, corresponding to the red line light curve at
phase=0.75 with inclination angle of 90∘. The star rotates from left to right.

##  5 Discussion

According to the coordinates from Gaia DR3, the separation between J2345 and
the M star is roughly 2.67′′, corresponding to a projected separation of
$\sim$15 AU at 98 parsec away. Based on the parallaxes from Gaia DR3, the
distances of the two stars in the line of sight are 94.6288 and 97.7039
parsec, respectively. Therefore, the actual separation should be at least 3
parsec, indicating these two stars may be the result of a disrupted wide
binary (Oh et al., 2017). There is no third star with similar proper motion at
similar distance within 5${}^{{}^{\prime}}$ in Gaia DR3, thus they do not
belong to a large structure. The PanSTARRS
images222http://ps1images.stsci.edu/cgi-bin/ps1cutouts in $z$ and $y$ bands,
which have the earliest and latest available images taken 1 039 d and 743 d
apart, respectively, are checked as well. However, no obvious relative
movements can be observed.

Given the newly released Gaia DR3, it is worth to check whether J2345 is disk
or halo WD, since halo WD is rare object of interest. The accurate
measurements of J2345 include coordinates of ra=356.2808 deg, dec=58.2209 deg,
parallax of 10.2350 mas, proper motion of pmra=28.9359 mas$\cdot yr^{-1}$,
pmdec=5.8859 mas$\cdot yr^{-1}$. With the radial velocity of -67.7$\pm$17.2
km$\cdot s^{-1}$ derived from follow-up spectrum with WDTOOLS, the 3-D
heliocentric velocity $U$, $V$ and $W$ of J2345 can be calculated following
equations listed in Guo, Liu, & Liu (2016). The probability calculated from
$U$=-23.85 km$\cdot s^{-1}$, $V$=-53.87 km$\cdot s^{-1}$ and $W$=9.88 km$\cdot
s^{-1}$ suggests that J2345 is likely a thick disk star, not a halo WD (see
Fig.10). This result is consistent with the disrupted wide binary scenario, as
wide binaries in the disk may be disrupted by passing stars, Galactic tides
and molecular clouds (Weinberg, Shapiro, & Wasserman, 1987; Jiang & Tremaine,
2010). But halo wide binaries are less likely to be disrupted by passing stars
and molecular clouds since majority of their lifetime is spent outside the
disk. Although some halo wide binaries will travel through the disk, the short
duration due to their high spatial velocities makes it less probable to be
disrupted (Weinberg, Shapiro, & Wasserman, 1987).

Figure 10: Gaia DR3 selected 1 kpc sample and J2345 plotted in the V+220
km$\cdot s^{-1}$ vs. $(U^{2}+W^{2})^{1/2}$ km$\cdot s^{-1}$ plane. Halo, thick
disk, thin disk candidates are plotted in black, green and light blue,
respectively. Red and blue lines are lower and upper limits of the escape
velocity of the Milky Way. Magenta star marks the location of J2345.

Since the asterosesimological analysis has provided the accurate mass of
J2345, the rough evolution history of this WD can be learnt via stellar
evolution models. Firstly, the initial mass at zero age main-sequence (ZAMS)
can be calculated as 3.08 M⊙, based on Equation 2, which is derived from Eq. 5
in Cummings et al. (2018).

$M_{i}=(M_{f}-0.184M_{\odot})\div 0.187,\\\
(0.72M_{\odot}<M_{f}<0.86M_{\odot})$ (2)

Where $M_{i}$ is the initial mass, while $M_{f}$ is the final mass. This
equation is a MIST-based semi-empirical initial-final mass relation. In Table
1 of Renedo et al. (2010), for a WD star with Z=0.01 and MWD=0.767 M⊙, the
lifetime of its main-sequence phase lasts for 0.232 Gyr. Thus, the main-
sequence plus cooling age of J2345 with M${}_{WD}=0.760\pm 0.005\,M_{\odot}$
is TMS+T${}_{cooling}\approx$200+700=900 Myrs. This is less than one per cent
of the lifetime of the companion M star with $T_{\rm eff}$=2 800 K, assuming
they formed simultaneously.

On another note, if the initial mass of J2345 at ZAMS is 3.08 M⊙, it should be
a B9 or A0 type star (Cox, 2000). But the companion of its progenitor is a
late M type star. Therefore, it is also possible that there was an accretion
process, as binaries formed in the same region tend to have similar spectral
types, and the WD mass in accreting system (i.e. mean M${}_{WD}\sim$ 0.8 M⊙
for CV) is usually higher than the average mass ($\sim$ 0.6 M⊙) of single WD
(Zorotovic & Schreiber, 2020).

##  6 Summary

In this work, a newly discovered ZZ ceti J2345 is reported and analyzed. The
discovery is the result of searching for variable WDs from the minute-cadence
photometric survey TMTS. By cross-matching Gaia EDR3 WD catalog with the TMTS
catalog, there are more than a thousand common WD candidates. Each is planned
to be visually inspected for variation that can be attributed to WD pulsation,
binary eclipsing, and planetesimal transiting. Many interesting sources have
been identified, and this is the very first paper to report our findings in
TMTS.

Based on two and five night observations of TMTS and SNOVA, there are 6
pulsating modes identified after prewhitening. Those modes are used to perform
the asteroseismological analysis. By adopting the latest version of WDEC,
there are 7 558 272 WD models evolved for the parameter spaces listed in Table
3. To find the optimal model, parameter steps and spaces are slowly narrowed
down repeatedly, in accordance of the fitting result. At last, the optimal
model is found and its parameter values are listed in Table 3. To test our
mode identification, additional analysis of freeing the values of $l$ for all
periods has been checked and compared. Based on the comparison and analysis in
Section 3.3, we believe our identification is a more reasonable choice. From
the asteroseismological result, it can be learnt that J2345 is a massive and
relatively hot pulsating WD with moderately thin H atmosphere. The final
results are quite consistent with the parameters derived from spectral fitting
of follow-up spectrum. In addition, the distance deduced from
asteroseismological results is in agreement with the inverse parallax derived
distance from Gaia DR3, implying a good self-consistency.

An evident period of $\sim$3.39 h is found to exist in two observations of
TESS. Given the fact that the significance of this signal weakens considerably
between two TESS observations, we propose that this period is attributed to
the rotation of dark spot on a comoving M star. The TESS light curve taken in
2019 has been modelled by Phoebe with a single star plus one dark spot model.
The result suggests that an synthetic light curve representing a very large
dark spot, nearly covered half of the M dwarf’s surface can be reproduced to
mimic the observed TESS light curve. This implies that the identified period
and light curve evolution from TESS data can be explained by stellar spot. But
the resulted parameters of the spot should be treated with caution, as the
real case may be caused by several spots with different sizes and locations.
With the newly released Gaia DR3, the 3-D heliocentric velocity $UVW$ of J2345
is calculated, and the result indicates that J2345 is likely a thick disk star
instead of a halo WD. Furthermore, since the initial progenitor mass of WD can
be estimated from current mass, its whole evolution history can be learnt. By
comparing to a well-studied WD with similar mass, we estimate the lifetime of
the main-sequence phase of J2345 being as about 200 Myrs and current age as
900 Myrs plus cooling time.

## Acknowledgments

The authors acknowledge the National Natural Science Foundation of China
(NSFC) under grants 12203006, 12033003, 12288102, U1938113, 11773035,
12090044, 11833002 and 11633002. This work is also supported by the Ma Huateng
Foundation, the Scholar Program of Beijing Academy of Science and Technology
(DZ:BS202002), and the Tencent Xplorer Prize, and CSST projects: CMS-
CSST-2021-B03, the Innovation Project of Beijing Academy of Science and
Technology (11000023T000002062763-23CB059 and 11000022T000000443055).

This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This research has made use
of the SIMBAD database, operated at CDS, Strasbourg, France (Wenger et al.,
2000).

## DATA AVAILABILITY

The TESS data used in this article can be accessed via
https://archive.stsci.edu/missions-and-data/tess. The TMTS, SNOVA photometric
and 3 m spectral data can be obtained by contacting the corresponding authors.

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# Central exclusive production at LHCb

C. Van Hulse, on behalf of the LHCb Collaboration  University College Dublin
Belfield, Dublin 4, Ireland<EMAIL_ADDRESS>
###### Abstract

The LHCb collaboration has measured central exclusive production of $J/\psi$,
$\psi(2S)$, and $\Upsilon$ mesons as well as $J/\psi J/\psi$,
$J/\psi\psi(2S)$, $\psi(2S)\psi(2S)$, and $\chi_{c}\chi_{c}$ meson pairs in
proton-proton collisions. The analyses of $\Upsilon$ and charmonium pairs are
performed at the centre-of-mass energies of 7 TeV and 8 TeV, and those of
$J/\psi$ and $\psi(2S)$ are done at 7 TeV and 13 TeV. The analysis at 13 TeV
involves the use of new shower counters. These allow a reduction in the
background by vetoing events with activity in an extended region in rapidity.
The measurements of central exclusive production at LHCb are sensitive to
gluon distributions for Bjorken-$x$ values down to $2\times 10^{-6}$ (at 13
TeV). An overview of the LHCb results is presented and compared to existing
measurements of other experiments and theoretical calculations.

exclusive photoproduction, ultra-peripheral collisions, generalised parton
distributions, parton distribution functions

##  I Introduction

The nucleon structure can be described in three dimensions in terms of the
probability to find quarks and gluons as a function of their transverse
position inside the nucleon and their longitudinal momentum fraction with
respect to the nucleon momentum Bur1 ; Bur2 . The longitudinal direction
coincides here with the direction of the probe used to investigate the
nucleon. The corresponding probability distributions are called impact-
parameter-dependent parton distributions. They are Fourier transforms of
generalised parton distributions (GPDs) (see, e.g., Ref. Diehl ). These GPDs
do not have a probabilistic interpretation. Instead, they represent
probability amplitudes for a parton with longitudinal momentum fraction
$x+\xi$ to be emitted from a nucleon and a parton with longitudinal momentum
fraction $x-\xi$ to be absorbed by the nucleon. The nucleon stays intact, but
receives a four-momentum transfer squared equal to $-t$. This is represented
in Fig. 1, for quarks (left) and gluons (right).

Figure 1: Diagrams for exclusive production of vector mesons in deep-inelastic
scattering (left) and in photoproduction (right). The figure on the left
illustrates access to quark GPDs, while the figure on the right shows the
diagram for gluon GPDs.

Generalised parton distributions are accessible in exclusive reactions, such
as the exclusive production of photons or vector mesons, involving a hard
scale. The hard scale is necessary in order to factorise the process into
perturbatively calculable parts and non-perturbative parts, which are the GPDs
and meson distribution amplitudes in the case of exclusive meson production
Col97 ; Ra97 . Exclusive vector-meson production can be measured in deep-
inelastic scattering, as illustrated in Fig. 1, left. The hard scale is
provided here by the large virtuality, $Q^{2}=-q^{2}\gg 1$ GeV2, of the photon
exchanged between the lepton and the nucleon. There exists a multitude of such
measurements at fixed-target experiments clas17a ; clas17b ; compass14 ;
compass17 ; hallA11 ; her14 ; her15 ; her17  and at lepton-proton colliders,
by the H1 and ZEUS collaborations h105 ; h106 ; zeus04 ; zeus07 . The former
series of measurements are mainly sensitive to larger values of Bjorken-$x$,
$x_{B}$, with $\xi\approx x_{B}/(2-x_{B})$, and thus to quark GPDs, while the
latter probe lower values of $x_{B}$ down to $10^{-4}$, where gluons dominate.

Alternatively, it is possible to use a (quasi-)real photon ($Q^{2}\approx 0$
GeV2) to investigate the nucleon, provided that the particle created in the
final state has a large mass component. In the case of exclusive vector-meson
production, such as $J/\psi$ or $\Upsilon$ production, the large scale is then
provided by the large mass of the meson valence quarks (charm or bottom
quarks). The vector mesons originate, as illustrated in Fig. 1, right, from
the splitting of the real photon into a quark-antiquark pair ($c\bar{c}$ or
$b\bar{b}$). This pair interacts with a nucleon through the exchange of two
gluons, and as a result a vector meson is formed in the final state. Quasi-
real photoproduction of vector mesons has been measured in electron-proton
collisions by the H1 and ZEUS experiments h1ph02 ; h1ph06 ; h1ph13 ; zeus04 ;
zeusph09 . These measurements probe a photon-nucleon center-of-mass energy
ranging from 30 GeV to 300 GeV.

It is also possible to study photoproduction in ultra-peripheral collisions of
protons and ions. In such reactions, the beam particles interact at a large
enough distance from each other (in practice more than the sum of their
respective nuclear radii) so that they interact through the exchange of
colour-neutral objects. The flux of photons emitted by a beam particle is
proportional to the square of its atomic charge, and hence photon emission by
heavy ions is greater than for protons. There exist measurements of
exclusively produced vector mesons in gold-gold collisions by the PHENIX
experiment phen09 , in proton-antiproton collisions by the CDF experiment
cdf09 , in lead-lead and proton-lead collisions by the ALICE experiment
alice13 ; alice13b ; alice14  and in proton-proton and lead-lead collisions by
the LHCb experiment lhcb13 ; lhcb14 ; lhcb15 ; lhcb18 ; lhcblead . The covered
photon-nucleon center-of-mass energy ranges from 34 GeV, for the PHENIX
experiment, to 1.5 TeV, for the measurements performed by the LHCb
collaboration. The very high energy available at the LHC offers the unique
possibility to probe the GPDs down to Bjorken-$x$ values of the order of
$10^{-6}$, i.e., two orders of magnitude lower than for the existing
measurements in electron-proton collisions. At such low values of $x_{B}$, one
might also be sensitive to saturation effects arm14 . In addition, at such low
$x_{B}$, the exclusive cross section can be approximated in terms of standard
gluon parton distribution functions (PDFs) Rys ; jmrt ; Jones ; flett . This
cross section has a quadratic dependence on the gluon PDFs, and thus provides
a higher sensitivity than inclusive measurements, where the dependence is only
linear.

##  II LHCb measurements

In central exclusive production of vector mesons in ultra-peripheral
collisions, the proton (or ion) emitting the real photon is to a good
approximation not altered from its original trajectory, while the proton
interacting through the two gluons undergoes a small change in momentum, but
remains close to the beam line. The vector meson, in turn, is produced in the
central region. At LHCb, this vector meson is generally reconstructed through
its decay into a $\mu^{+}\mu^{-}$ pair. Hence, the experimental signature for
exclusive vector-meson production are two oppositely charged muons in the LHCb
detector, with large regions of rapidity, down to close to the beam line,
devoid of particle activity. There exists a different process with the same
final state, but where the oppositely charged muons originate from the
interaction of photons emitted by the respective beam particles. This process
is called the Bethe–Heitler process. This production mode of muons forms a
continuum background to the exclusive production of vector mesons, and needs
to be subtracted from the measured signal. Another source of background is the
production of higher-mass vector mesons that decay into the vector meson under
study without detection of the other decay products. Furthermore, the
production of vector mesons where one or both of the interacting protons
dissociate forms another background contribution.

The LHCb detector is a forward detector, covering a rapidity range between 2
and 5. The detector is fully instrumented for particle identification, and is
capable of detecting particles with transverse momenta as low as 200 MeV. The
LHCb experiment is not instrumented with detectors around the beam line for
the detection of protons emerging intact from the interaction or for products
from proton dissociation that remain close to the beam line. However, the LHCb
experiment is well suited for the measurement of exclusive processes. Firstly,
the average number of interactions per beam crossing at the LHCb interaction
point ranges only from 1.1 to 1.5, depending on running conditions. Secondly,
besides the coverage in rapidity from 2 to 5 by the fully instrumented LHCb
detector, the LHCb vertex locator is capable of detecting charged-particle
activity for rapidities between -3.5 and -1.5. Also, for Run 2 of the LHC
data-taking period (2015 – 2018), the LHCb experiment was additionally
equipped with a series of five stations of scintillators, HeRSCheL herschel ,
placed at -114 m to +114 m from the LHCb interaction point. This allowed for
the detection of particle showers in a rapidity range between -10 and -5, and
between +5 and +10, and hence for a supplementary reduction of the
contribution from background processes.

Figure 2: Dimuon invariant-mass distribution (left) and dimuon squared-
transverse-momentum distribution for muon pairs within the $J/\psi$ invariant
mass region (right) for data collected at $\sqrt{s}=13$ TeV, and satisfying
the selection requirement imposed by HeRSCheL. Different background
contributions are indicated in both figures, while the vertical lines in the
figure on the left indicate the selected range in invariant mass for the
measurement of $J/\psi$ and $\psi(2S)$.

Measurements of exclusive production of $J/\psi$ and $\psi(2S)$ mesons have
been performed by the LHCb experiment using data collected in proton-proton
collisions at a center-of-mass energy $\sqrt{s}=7$ TeV lhcb14 , and part of
the data collected at $\sqrt{s}=13$ TeV lhcb18 , amounting to an integrated
luminosity of respectively $929\pm 33$ pb-1 and $204\pm 8$ pb-1. This data set
allows to access $x_{B}$ down to $2\times 10^{-6}$. Both the $J/\psi$ meson
and the $\psi(2S)$ meson are reconstructed through their decay into muons,
which are required to lie in the LHCb detector acceptance, between 2 and 4.5
in rapidity. Furthermore, the transverse momentum squared of the dimuon pair,
$p_{T}^{2}\approx-t$, needs to be below 0.8 GeV2. Finally, the absence of any
other detector activity is required.

Figure 3: The distribution, normalised to unit area, of the HeRSCheL
discriminating variable $\chi^{2}_{HRC}$. The continuous, black line
corresponds to a sample highly enriched in exclusively produced muon pairs;
the blue, dashed line represents the distribution for events enriched in
inelastically produced $J/\psi$ mesons, while the purple, short-dashed line
contains events with more than four tracks.

In Fig. 2, left, the dimuon invariant-mass distribution is shown, while in
Fig. 2, right, the squared-transverse-momentum distribution of the muon pair
with invariant mass in the $J/\psi$ mass region is presented. The three
sources of background contamination to the $J/\psi$ signal are also shown. The
background contribution from the Bethe–Heitler process, labelled nonresonant
background, is obtained from a fit to the dimuon mass distribution (see Fig.
2, left). The background from feed-down from exclusive production of
$\psi(2S)$ and $\chi_{c}$ mesons is evaluated using $\psi(2S)$ and $\chi_{c}$
signals in experimental data and Monte-Carlo simulation. Finally, the
contamination from events where at least one of the protons dissociates is
evaluated for Run 1 through a fit of the dimuon transverse-momentum
distribution, while for the data collected in Run 2, HeRSCheL has been used.
The discriminating power of HeRSCheL is illustrated in Fig. 3. The figure
represents distributions of a discriminating variable related to detector
activity in HeRSCheL. The continuous, black line is the distribution for a
very pure sample of exclusively produced pairs of muons, while the other lines
indicate samples enriched in nonexclusive events. From the figure, it is clear
that for exclusive events, the discriminating variable is located at low
values, whereas for nonexclusive events, the variable extends to higher
values. For the selection of exclusive events in Run 2, only events below the
value indicated by the red, vertical line are selected. This results in a
signal purity of 76% (73%) for $J/\psi$ ($\psi(2S)$). For data collected in
Run 1, the signal purity amounts to 62% (52%), where the contribution from
proton-dissociative background is about twice as high.

Figure 4: Cross section differential in rapidity for exclusive $J/\psi$
production (left) and exclusive $J/\psi$ photoproduction cross section as a
function of the photon-proton invariant mass (right). The leading-order
(yellow band) and next-to-leading-order (green band and dotted line) JMRT
calculations jmrt  are also indicated.

The cross section differential in rapidity for exclusive production of
$J/\psi$ in proton-proton collisions at $\sqrt{s}=13$ TeV is shown in Fig. 4,
left. It is seen to decrease at larger values of rapidity. In addition to the
experimental data points, theoretical predictions (JMRT) jmrt , which
approximate the cross section in terms of standard gluon PDFs, are shown.
There are predictions at leading order in $\alpha_{S}$ (yellow band) and at
next-to-leading order in $\alpha_{S}$ (green band). The leading-order
predictions fail to describe the data at higher rapidities, while the next-to-
leading order calculations are in reasonable agreement with the data.

The exclusive vector-meson production cross section in proton-proton
collisions is related to the photoproduction cross section through

$\displaystyle\sigma_{pp\rightarrow p\psi p}$ $\displaystyle=$ $\displaystyle
r(W_{+})k_{+}\frac{dn}{dk_{+}}\sigma_{\gamma p\rightarrow\psi p}(W_{+})$ (1)
$\displaystyle+$ $\displaystyle r(W_{-})k_{-}\frac{dn}{dk_{-}}\sigma_{\gamma
p\rightarrow\psi p}(W_{-}),$

where $r$ represents the gap survival factor, $k_{\pm}$ the photon energy,
$dn/dk_{\pm}$ the photon flux, and $W^{2}_{\pm}=2k_{\pm}\sqrt{s}$ the photon-
proton invariant mass squared. The subscript $+$ ($-$) corresponds to the
situation where the downstream-going (upstream-going) proton is the photon
emitter. As can be seen from Eq. (1), the photoproduction cross section
appears twice in the expression. The reason resides in the ambiguity on the
identity of the proton emitting the real photon. Since the photoproduction
cross section corresponding to the low-energy solution $W_{-}$ only
contributes about one third of the time and it has been previously measured
and parametrised by the H1 collaboration, this parametrisation is used to fix
the low-energy photoproduction cross section, and extract the one at high
photon-proton invariant mass. The resulting photoproduction cross section is
presented in Fig. 4, right. The data points represented by the red circles are
the result at $\sqrt{s}=13$ TeV, while those indicated by the black squares
are those at $\sqrt{s}=7$ TeV. Also measurements from the H1 collaboration,
from which the parametrisation is taken, the ZEUS and ALICE collaborations as
well as from fixed-target experiments fix1 ; fix2 ; fix3  are presented. The
different data sets are in good agreement with each other. The parametrisation
from the H1 collaboration is indicated in the figure by the blue band. It is
seen to describe the data well at intermediate values of $W$, but fails at
lower and higher values. Also the next-to-leading order JMRT calculations are
shown, as indicated by the dotted line. They are in good agreement with the
data, describing it well also at low and high values of $W$. Also for the
proton-proton and photoproduction cross section of $\psi(2S)$ (not shown), the
next-to-leading order predictions in $\alpha_{S}$ describe the data well,
whereas the leading-order predictions fail to describe the data.

There exist also results from exclusive $\Upsilon$ production by the LHCb
collaboration, using data collected in proton-proton collisions in Run 1 at
$\sqrt{s}=7$ TeV and $\sqrt{s}=8$ TeV, corresponding to a respective
luminosity of 0.9 fb-1 and 2.0 fb-1 lhcb15 . The two data sets are combined in
order to increase statistical precision. The data-selection procedure follows
that of the measurement for exclusive $J/\psi$, with a $p_{T}^{2}$ restricted
to below $2.0$ GeV${}^{2}/c^{2}$. Given the larger mass of the $\Upsilon$
meson, the lowest values in $x_{B}$ reach down to $2\times 10^{-5}$. The total
proton-proton production cross section for $\Upsilon(1S)$ is determined to be
$9.0\pm 2.1\pm 1.7$ pb, where the first uncertainty is statistical and the
second systematic, while for $\Upsilon(2S)$ it is $1.3\pm 0.8\pm 0.3$ pb. For
$\Upsilon(3S)$ production, an upper limit on the cross section of $3.4$ pb at
the 95% confidence level is determined. For the $\Upsilon(1S)$ resonance, the
production cross section differential in rapidity and the photoproduction
cross section as a function of $W$ are also extracted. They are shown in Fig.
5. Also here, leading-order and next-to-leading order JMRT calculations are
presented, and only the next-to-leading order calculations describe the data
well. In the figure on the right, also results from the ZEUS and H1
collaborations are shown. These are not able to discriminate between the
leading-order and next-to-leading order calculations.

Figure 5: Cross section differential in rapidity for exclusive $\Upsilon(1S)$
production (left) and exclusive $\Upsilon(1S)$ photoproduction cross section
as a function of the photon-proton invariant mass (right). Next-to-leading-
order (leading-order) JMRT calculations jmrt  at $\sqrt{s}=7$ TeV are
indicated by the blue (yellow) band and include uncertainties. The mean value
of the next-to-leading-order (leading-order) calculations from JMRT jmrt  at
$\sqrt{s}=8$ TeV is indicated by the blue (red) line.

The LHCb collaboration also published results of exclusive production of the
charmonium pairs $J/\psi J/\psi$, $J/\psi\psi(2S)$, $\psi(2S)\psi(2S)$,
$\chi_{c0}\chi_{c0}$, $\chi_{c1}\chi_{c1}$, and $\chi_{c2}\chi_{c2}$ lhcb14p .
These are potentially sensitive to glueballs and tetraquarks. In the framework
of describing the exclusive cross section in terms of standard gluon PDFs,
they are sensitive to the forth power of these gluon PDFs. The measurements
combine the data collected in proton-proton collisions at $\sqrt{s}=7$ TeV and
$\sqrt{s}=8$ TeV. The production cross sections are measured to be
$\sigma(J/\psi J/\psi)=58\pm 10\pm 6$ pb;
$\sigma(J/\psi\psi(2S))=63^{+27}_{-18}\pm 10$ pb;
$\sigma(\psi(2S)\psi(2S))<237$ pb; $\sigma(\chi_{c0}\chi_{c0})<69$ nb;
$\sigma(\chi_{c1}\chi_{c1})<45$ pb; $\sigma(\chi_{c2}\chi_{c2})<141$ pb, where
for the four last pairs only an upper limit is determined. These results are
not corrected for proton dissociation, due to the limited statistical
precision. Only for the production of pairs of $J/\psi J/\psi$ it is possible
to estimate the contribution from central exclusive production, which amounts
to about 42%, and thus to determine the cross section corrected for proton
dissociation, which is $24\pm 9$ pb.

##  III Summary

Measurements of exclusive production of $J/\psi$, $\psi(2S)$, and
$\Upsilon(nS)$, with $n=1,2,3$, have been performed by the LHCb collaboration.
These measurements are sensitive to gluon GPDs and PDFs. The cross sections
are measured differentially in rapidity and the photoproduction cross section
is extracted as a function of the photon-proton invariant mass. Comparisons to
next-to-leading order JMRT calculations show good agreement with these data.
Also cross-section measurements of pairs of charmonia have been performed.
They are sensitive to the fourth power of the gluon PDFs and potentially to
glueballs and tetraquarks. Although not discussed here, there are also
preliminary measurements of Bethe-Heitler production in proton-proton
collisions conf_bh  and on exclusive $\chi_{c}$ production in proton-proton
collisions conf_bh , which is sensitive to the exchange of two gluon pairs.
Furthermore there are preliminary results on exclusive production of $J/\psi$
and $\psi(2S)$ in lead-lead collisions lhcblead , which give access to nuclear
GPDs and PDFs, and are sensitive to shadowing.

##  IV Acknowledgments

This project has received funding from the European Union’s Horizon 2020
research and innovation programme under the Marie Sklodowska-Curie grant
agreement No 792684.

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