# First Light Curve Analysis of NSVS 8294044, V1023 Her, and V1397 Her Contact
Binary Systems

Atila Poro<EMAIL_ADDRESS>Astronomy Department of the Raderon AI Lab.,
BC., Burnaby, Canada  Sabrina Baudart  Double Stars Committee, Société
Astronomique de France, Paris, France  Mahshid Nourmohammad  Independent
Astrophysics Researcher, Isfahan, Iran  Zahra Sabaghpour Arani  Akhtaran
Astronomical Society, Isfahan Province, Aran and Bidgol, Iran  Fatemeh Farhadi
Department of Physics, Faculty of Science, Zanjan University, Zanjan, Iran
Selda Ranjbar Salehian  Astronomy Students’ Scientific Association, University
of Tabriz, East Azerbaijan Province, Tabriz, Iran  Ahmad Sarostad  Yazd Desert
Night Sky Astronomy Institute, Yazd Province, Yazd, Iran  Saeideh Ranjbaryan
Iri Olya  Ayaz Astronomical Association, East Azerbaijan Province, Tabriz,
Iran  Maryam Hadizadeh  Khayyam Astronomy Association, Fars, Fasa, Iran
AmirHossein Khodaei  Department of Physics, Faculty of Science, Zanjan
University, Zanjan, Iran

###### Abstract

The first photometric light curve investigation of the NSVS 8294044, V1023
Her, and V1397 Her binary systems is presented. We used ground-based
observations for the NSVS 8294044 system and Transiting Exoplanet Survey
Satellite (TESS) data for V1023 Her and V1397 Her. The primary and secondary
times of minima were extracted from all the data, and by collecting the
literature, a new ephemeris was computed for each system. Linear fits for the
O-C diagrams were conducted using the Markov chain Monte Carlo (MCMC) method.
Light curve solutions were performed using the PHysics Of Eclipsing BinariEs
(PHOEBE) Python code and the MCMC approach. The systems were found to be
contact binary stars based on the fillout factor and mass ratio. V1023 Her
showed the O’Connell effect, and a cold starspot on the secondary component
was required for the light curve solution. The absolute parameters of the
system were estimated based on an empirical relationship between orbital
period and mass. We presented a new $T-M$ equation based on a sample of 428
contact binary systems and found that our three target systems were in good
agreement with the fit. The positions of the systems were also depicted on the
$M-L$, $M-R$, $q-L_{ratio}$, and $M_{tot}-J_{0}$ diagrams in the logarithmic
scales.

binaries: eclipsing – methods: photometry – stars: individual (NSVS 8294044)

##  1 Introduction

The degree of separation between the components describes different kinds of
eclipsing binaries, which may be identified by light curve shapes and include
detached, semi-detached, contact, and overcontact systems. Contact binary
stars are referred to as W UMa-type systems that have some interesting
physical properties (Drake et al. 2014).

Stars of the W UMa systems have filled their Roche lobes (Paczyński 1971) and
both of the components share a common convective envelope between the inner
and outer contact surfaces (Lucy 1968). The stars in these kinds of systems
share mass and energy, which causes their surface temperatures to be close to
one another and show light curves with almost similar eclipse depths.
Furthermore, W UMa stars consist of late spectral type main sequence stars
(Terrell et al. 2012).

The orbital period of contact binary systems is short and most of them fall
between 0.2 and 0.6 days (Qian 2003, Kouzuma 2018, Latković et al. 2021).
Studying contact systems provides an opportunity to use orbital period
variations impacted by system physical processes to gain a deeper
comprehension of star evolution (Li et al. 2021). Therefore, new observations
can always be useful to investigate these variations.

This study includes the first light curve analysis of three binary systems
NSVS 8294044 (R.A. $19^{h}$ $14^{m}$ $41.0475^{s}$, Dec. $+37^{\circ}$
$49^{\prime}$ $46.0465"$ (J2000)), V1023 Her (R.A. $15^{h}$ $58^{m}$
$25.2669^{s}$, Dec. $+49^{\circ}$ $26^{\prime}$ $51.0013"$ (J2000)), and V1397
Her (R.A. $17^{h}$ $07^{m}$ $16.8455^{s}$, Dec. $+17^{\circ}$ $25^{\prime}$
$36.6323"$ (J2000)). All three target systems have been introduced as contact
systems in the ASAS111The All Sky Automated Survey (ASAS),
http://www.astrouw.edu.pl/asas/ and VSX222The International Variable Star
Index (VSX), https://www.aavso.org/vsx/ catalogs. NSVS 8294044, V1023 Her, and
V1397 Her’s orbital periods are near to each other as reported at 0.3779846,
0.3222336, and 0.387745 days in the VSX database, respectively. Also, the
apparent magnitude of the NSVS 8294044 is $V_{max}=13.51^{mag}$, V1023 Her is
$V_{max}=11.93^{mag}$, and V1397 Her is $V_{max}=10.16^{mag}$, based on the
VSX database.

The structure of this paper is as follows: Section 2 is about ground- and
space-based observations and data reduction; Section 3 is related to
determining new ephemeris for each system; Section 4 explains the light curve
analysis; Section 5 describes the estimation of absolute parameters; Finally,
the discussion and conclusion are in Section 6.

##  2 Observation and Data Reduction

We observed NSVS 8294044 in August and September 2023. The observations were
carried out in a private observatory in Toulon, France, at a longitude of
$05^{\circ}$ $54^{\prime}$ $35"$ E and a latitude of $43^{\circ}$ $8^{\prime}$
$59"$ N, and an altitude of 68 meters above mean sea level. In the
observations, we used an Apochromatic Refractor TS Optics with a 102mm
aperture, a ZWO ASI 1600MM CCD, and a $V$ filter. The binning of the images
was $1\times 1$, with an 80-second exposure time, and the average temperature
of the CCD was $-15^{\circ}$C. Using the Siril 1.2.0-rc2 program and the bias,
dark, and flat fields image, the basic data reduction was done. We used GSC
02665-00244 (R.A. $19^{h}$ $17^{m}$ $21.4390^{s}$, Dec. $+37^{\circ}$
$11^{\prime}$ $51.0482"$ (J2000)) as a comparison star, and GSC 02665-01066
(R.A. $19^{h}$ $17^{m}$ $11.7567^{s}$, Dec. $+37^{\circ}$ $13^{\prime}$
$32.9641"$ (J2000)) and Gaia DR2 2051151521582207232 (R.A. $19^{h}$ $17^{m}$
$06.8187^{s}$, Dec. $+37^{\circ}$ $04^{\prime}$ $22.3909"$ (J2000)) as check
stars. According to our observations, the light curve’s maximum apparent
magnitude was obtained to be $V_{max}=13.24(11)^{mag}$.

TESS data were used in this investigation for V1023 Her (TIC 310170498) and
V1397 Her (TIC 143100813) binary systems. TESS observed V1023 Her in sectors
23, 24, 50, and 51. There were also observational data for the V1397 Her
system in sectors 12 and 13. TESS employed a 120-second exposure time for the
observation process of these sectors. The data is available at the Mikulski
Space Telescope Archive
(MAST)333https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.htmL.

##  3 New Ephemeris

We extracted the primary and secondary times of minima from ground-based and
TESS light curves. Gaussian distribution was used to determine these mid-
eclipse times. The amount of uncertainty was computed using the MCMC method.
The Barycentric Julian Date and Barycentric Dynamic Time ($BJD_{TDB}$) are
used to present all minima. The minima for three target systems that were
collected from the literature and extracted in this study are listed in Table
1. The extracted TESS mid-eclipse times for the V1023 Her and V1397 Her
systems are listed in the appendix tables.

Each epoch and O-C values were computed using reference ephemeris. We chose
$t_{0}=2458423.7230$ and $P_{ref}=0.3779833$ from the ASAS-SN catalog for the
NSVS 8294044 system as a reference ephemeris. V1023 Her’s $t_{0}=2459636.8875$
came from Nelson & Alton (2022) study and $P_{ref}=0.3222341(87)$ from the
WISE catalog of periodic variable stars. The reference ephemeris of V1397 Her
$t_{0}=2453833.6397$ and $P_{ref}=0.387745$ were from the Diethelm (2009)
study.

It is more appropriate to use a linear fit for O-C diagrams considering our
three binary systems have few observations and minimum times. O-C diagrams of
the systems are presented in Figure 1 with their corner plots of the posterior
distribution based on the MCMC sampling. To determine new ephemeris for each
system, we applied 20 walkers and 20000 iterations for each walker, with a
2000 burn-in period in the MCMC process. So, we used the PyMC3 package to
execute the MCMC sampling (Salvatier et al. 2016). New ephemeris for each
target system is presented in Equations 1 to 3:

$\left\\{\begin{array}[]{l}NSVS\ 8294044:\\\
Min.I(BJD_{T}DB)=2458423.72300(10)+0.377986034(9)\times E\\\
\end{array}\right.$ (1)

$\left\\{\begin{array}[]{l}V1023\ Her:\\\
Min.I(BJD_{T}DB)=2459636.89178(1)+0.322233134(3)\times E\\\
\end{array}\right.$ (2)

$\left\\{\begin{array}[]{l}V1397\ Her:\\\
Min.I(BJD_{T}DB)=2453833.63457(8)+0.387748745(6)\times E\\\
\end{array}\right.$ (3)

Table 1: The times of minima extracted in this study and collected from the literature were observed with CCD. System |  Min.($BJD_{TDB}$) | Error | Epoch | O-C | Reference
---|---|---|---|---|---
NSVS 8294044 | 2458423.7230 |  | 0 | 0 | ASAS-SN
| 2460176.4440 | 0.0012 | 4637 | 0.0124569 | This study
| 2460191.3750 | 0.0022 | 4676.5 | 0.01314655 | This study
V1023 Her | 2451274.6148 |  | -25951 | 0.0244 | ROTSE- Anton Paschke
| 2455976.6448 |  | -11359 | 0.0144 | VSX
| 2456687.9726 | 0.0002 | -9151.5 | 0.0105 | Nelson (2015)
| 2456745.4889 | 0.0024 | -8973 | 0.0080 | Hubscher & Lehmann (2015)
| 2457100.4327 | 0.0029 | -7871.5 | 0.0109 | Hubscher (2016)
| 2457100.5900 | 0.0019 | -7871 | 0.0071 | Hubscher (2016)
| 2457122.8228 | 0.0020 | -7802 | 0.0057 | Nelson (2016)
| 2459636.8875 |  | 0 | 0 | Nelson & Alton (2022)
V1397 Her | 2453833.6397 |  | 0 | 0 | Diethelm (2009)
| 2454623.6747 |  | 2037.5 | 0.0046 | VSX
| 2454998.8205 | 0.0007 | 3005 | 0.0070 | Diethelm (2009)
| 2455720.8049 | 0.0003 | 4867 | 0.0102 | Diethelm (2011)
| 2456054.8507 | 0.0005 | 5728.5 | 0.0137 | Diethelm (2012)
| 2458626.0127 |  | 12359.5 | 0.0386 | Kazuo (2020)
| 2458991.4659 | 0.0008 | 13302 | 0.0422 | Pagel (2021)
| 2459383.4822 | 0.0013 | 14313 | 0.0483 | Pagel (2022)
Figure 1: The O-C diagrams of three eclipsing binaries with linear fits and
corner plots. The shaded regions show the model parameters’ 68th percentile
values.

##  4 Light Curve Analysis

We utilized the PHOEBE Python code version 2.4.9 and the MCMC approach to
model the light curves of the NSVS 8294044, V1023 Her, and V1397 Her binary
systems (Prša & Zwitter 2005, Prša et al. 2016, Conroy et al. 2020). These
three target systems were analyzed for the first time. We selected contact
mode for the light curve solutions based on the appearance of the light curve
and short orbital period. The gravity-darkening coefficients and the
bolometric albedo were assumed to be $g_{1}=g_{2}=0.32$ (Lucy 1967) and
$A_{1}=A_{2}=0.5$ (Ruciński 1969), respectively. The limb darkening
coefficients were included in PHOEBE as a free parameter, and the Castelli &
Kurucz (2004) study was used to model the stellar atmosphere.

We applied the effective temperature reported from Gaia DR3 to the hotter
star. These temperature values are not fixed and will be free parameters
during the MCMC process. The effective temperature ratio was used to estimate
the initial temperature of another component. Additionally, we checked and
compared the effective temperatures of these systems from TESS through the
MAST portal444https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.htmL.
The TESS input v8.2 reported temperatures 5937(115), 5088(126), and 6440(113)
for NSVS 8294044, V1023 Her, and V1397 Her, respectively. These values were
close to those reported by Gaia DR3.

The $q$-search method was used to estimate the mass ratio of each binary
system, taking into account that only photometric data was available. We
performed a $q$-search on each of the target systems using a range of 0.1 to
9. We found the minimum sum of the squared residuals for each $q$-search. We
used the results as initial values and tried to fit a good synthetic light
curve to the observational data. Figure 2 displays the $q$-search results for
each of the three systems.

V1023 Her system’s light curve analysis required a cold starspot on the
secondary component due to the difference in the light curve maxima. Contact
systems are known for their magnetic activity, and O’Connell’s effect
describes it (O’Connell 1951).

We employed PHOEBE’s optimization tool to improve the output of light curve
solutions and obtain entitled results for beginning the MCMC process. The five
main parameters ($T_{1}$, $T_{2}$, $q$, $f$, $l_{1}$) were then processed
using the MCMC approach, and the values and uncertainty were obtained. We
employed 96 walkers and 1000 iterations for each walker. These walkers were
initially positioned from a Gaussian distribution based on our initial
parameter estimations, and their width was adjusted based on how sensitive the
light curves were to various parameter values.

The results of the light curve solutions of the NSVS 8294044, V1023 Her, and
V1397 Her binary systems are listed in Table 2. The observed and synthetic
light curves of the binary systems, along with the corner plots, are displayed
in Figure 3. Furthermore, the geometric structures of the systems are shown in
Figure 4.

Figure 2: Sum of the squared residuals as a function of the mass ratio. Table 2: Photometric light curve solutions of the systems. Parameter | NSVS 8294044 | V1023 Her | V1397 Her
---|---|---|---
$T_{1}$ (K) | $6070_{\rm-(120)}^{+(320)}$ | $4980_{\rm-(6)}^{+(6)}$ | $6326_{\rm-(6)}^{+(10)}$
$T_{2}$ (K) | $5630_{\rm-(100)}^{+(290)}$ | $4624_{\rm-(7)}^{+(6)}$ | $6413_{\rm-(8)}^{+(13)}$
$q=M_{2}/M_{1}$ | $2.819_{\rm-(69)}^{+(75)}$ | $2.199_{\rm-(25)}^{+(28)}$ | $0.873_{\rm-(11)}^{+(23)}$
$i^{\circ}$ | $83.68_{\rm-(79)}^{+(99)}$ | $48.54_{\rm-(21)}^{+(32)}$ | $65.98_{\rm-(15)}^{+(10)}$
$f$ | $0.152_{\rm-(25)}^{+(23)}$ | $0.121_{\rm-(13)}^{+(8)}$ | $0.112_{\rm-(6)}^{+(9)}$
$\Omega_{1}=\Omega_{2}$ | 6.282(41) | 5.458(37) | 3.486(24)
$l_{1}/l_{tot}$ | $0.359_{\rm-(3)}^{+(3)}$ | $0.406_{\rm-(1)}^{+(1)}$ | $0.520_{\rm-(4)}^{+(1)}$
$l_{2}/l_{tot}$ | 0.641(3) | 0.594(1) | 0.480(2)
$r_{1(mean)}$ | 0.303(2) | 0.322(2) | 0.402(3)
$r_{2(mean)}$ | 0.491(2) | 0.459(2) | 0.378(3)
Phase shift | 0.033(1) | -0.012(1) | 0.003(1)
Col.(deg) |  | 107 |
Long.(deg) |  | 320 |
Rad.(deg) |  | 16 |
$T_{spot}/T_{star}$ |  | 0.92 |
Component |  | Secondary |
Figure 3: Left: The observed light curves of the systems (green dots) and the
synthetic light curves were obtained from the light curve solutions (black
curves). Right: The corner plots of the three systems were determined by MCMC
modeling. Figure 4: Geometric structure of the NSVS 8294044, V1023 Her, and
V1397 Her systems based on their light curve solutions in 0, 0.25, 0.5, and
0.75 phases.

##  5 Absolute Parameters

We used empirical parameter relationships between mass and orbital period for
estimating absolute parameters (Poro et al. 2024). So, the following equation
was chosen from the Latković et al. (2021) study result of a large sample:

$M_{1}=(2.94\pm 0.21)P+(0.16\pm 0.08)$ (4)

Was considered on $q^{\prime}=1/q$ in the Latković et al. (2021) sample and
points mentioned in the Poro et al. (2024) study. Therefore, we set the
outcome’s mass from Equation 4 for the more massive star in the systems. Using
the mass ratio from the light curve solution, we obtained the mass of the
other companion star. Then, we computed $a(R_{\odot})$ by employing Kepler’s
third law. We estimated the radius of the stars of the system from the
equation $R=a\times r(mean)$. The known equation $L=4\pi R^{2}\sigma T^{4}$ is
also used to determine each star’s luminosity while having its effective
temperature and radius. Based on Pogson’s relation (Pogson 1856), $M_{bol1,2}$
can be calculated by $M_{bol}-M_{bol\odot}=-2.5log(L/L_{\odot})$, which
$M_{bol\odot}$ is taken as 4.73 magnitude (Torres 2010). We extracted the
Bolometric Correction (BC) from the Flower (1996) study tables and utilized
the well-known equation $M_{V}=M_{bol}-BC$ to compute $M_{V1,2}$. The surface
gravity ($g$) of the stars was calculated with the equation
$g=G_{\odot}(M/R^{2})$.

Estimated absolute parameters for the target systems are presented in Table 3.
The error values of Equation 4 and the parameters involved were used to
estimate the absolute parameter uncertainty.

Table 3: The absolute parameters estimation. | NSVS 8294044 | V1023 Her | V1397 Her
---|---|---|---
Parameter | Primary star | Secondary star | Primary star | Secondary star | Primary star | Secondary star
$M(M_{\odot})$ | 0.451(44) | 1.271(160) | 0.503(61) | 1.107(148) | 1.300(161) | 1.135(165)
$R(R_{\odot})$ | 0.799(189) | 1.295(303) | 0.746(170) | 1.064(240) | 1.210(216) | 1.138(204)
$L(L_{\odot})$ | 0.781(512) | 1.518(962) | 0.309(159) | 0.467(239) | 2.114(836) | 1.974(788)
$M_{bol}$(mag.) | 4.998(547) | 4.277(533) | 6.005(451) | 5.558(448) | 3.917(362) | 3.992(365)
$M_{V}$(mag.) | 5.034(547) | 4.386(533) | 6.320(451) | 6.074(448) | 3.925(362) | 3.993(365)
$log(g)(cgs)$ | 4.287(144) | 4.318(131) | 4.394(129) | 4.428(122) | 4.386(92) | 4.381(84)
$a(R_{\odot})$ | 2.637(604) | 2.318(511) | 3.010(511)
$logJ_{0}$ | 51.632(76) | 051.606(86) | 51.996(91)
$BC$ | -0.036 | -0.109 | -0.315 | -0.516 | -0.008 | -0.001

##  6 Discussion and Conclusion

We present the first light curve analysis of the NSVS 8294044, V1023 Her, and
V1397 Her binary systems. Ground-based observations were used for NSVS
8294044, and TESS observations were used for V1023 Her and V1397 Her systems.
The discussion and conclusion are presented as follows:

1\. We extracted times of minima from ground- and space-based photometric
data. Thus, by adding the literature, new ephemeris for each system were
obtained. A linear fit was the better option for the target systems on the O-C
diagram. The O-C diagram of V1023 Her has a decreasing trend based on the
linear fit, whereas systems NSVS 8294044 and V1397 Her display an increasing
trend (Figure 1).

2\. Light curve analysis of each target binary system was performed and V1023
Her required a cold starspot. The results of light curve solutions indicate
that the effective temperature range of the stars is between about 4600 K and
6400 K. Star1 is hotter than star2 except for system V1397 Her. The
temperature difference of the components for NSVS 8294044 is 440 K, for V1023
Her is 356 K, and for V1397 Her is 87 K. According to the temperature of the
stars and the Cox (2000) and Eker et al. (2018) studies, the spectral type of
the stars can be recognized: Star1=G0 and star2=G7 for NSVS 8294044; Star1=K1
and star2=K3 for V1023 Her; Star1=F6 and star2=F5 for V1397 Her.

3\. We used an empirical parameter relationship and orbital periods for
estimating the mass of each star. According to the absolute parameters, we
showed the stars’ positions on the Mass-Luminosity ($M-L$) and Mass-Radius
($M-R$) diagrams with the Zero-Age Main Sequence (ZAMS) and the Terminal-Age
Main Sequence (TAMS) (Figure 5a,b). The position of the systems on the
$q-L_{ratio}$ relationship provided by Poro et al. (2024) are also displayed
in Figure 5c, with which they are in good agreement with the model.

4\. We calculated the orbital angular momentum ($J_{0}$) of the systems based
on the equation presented by the Eker et al. (2006) study:

$J_{0}=\frac{q}{(1+q)^{2}}\sqrt[3]{\frac{G^{2}}{2\pi}M^{5}P}$ (5)

The results are listed in Table 3. Furthermore, as can be viewed in Figure 5d,
the $logM_{tot}-logJ_{0}$ diagram illustrates the systems’ positions and
indicates that all of them are located in the region of contact binary
systems. The parabolic fit in Figure 5d of the border between the two detached
and contact binaries comes from the Eker et al. (2006) study.

5\. The relationship between parameters in binary systems is one of the topics
of interest in studies. However, most of the investigations on the mass-
temperature ($M-T$)relationship have focused on detached and semi-detached
binary systems (e.g. Paczyński 1967, Harmanec 1988, Kovaleva 2002, Malkov
2007, Spada et al. 2013, Eker et al. 2018). In the Yakut & Eggleton (2005)
study, the $logM-logT$ diagram for contact binaries displays a sample of A-
and W-type systems with a ZAMS line. Additionally, the $M-T$ diagram for a
limited number of contact systems in the Kjurkchieva et al. (2019) study
indicates a weak relationship for this sample given the large dispersion that
appears.

The relationship between $P-T_{1}-M_{1}$ is presented using a machine learning
model in another work by Poro et al. (2024). They employed 134 contact systems
that were analyzed using spectroscopic data. This model is presented using the
Artificial Neural Network (ANN) and $M_{1}$ is the more massive component of
the system. Based on the ANN model, more massive stars 1.20(8), 0.99(9), and
1.27(6) have been estimated for systems NSVS 8294044, V1023 Her, and V1397
Her, respectively; these values are in the uncertainty range and good in
agreement with the results of this study.

We provided the $T_{1}-M_{m}$ diagram with a linear fit using 428 contact
systems from the sample of the Latković et al. (2021) study (Equation 6). We
named the more massive star $M_{m}$. Figure 6 shows the positions of our three
target systems are in good agreement with this fit and the other stars in the
sample.

$logM_{m}=(1.6185\pm 0.0150)\times logT_{1}+(-6.0186\pm 0.0562)$ (6)

6\. The first light curve study of binary stars is important to create larger
samples for deeper parameter investigations of these types of systems. This
investigation presented the new ephemeris and the first light curve analysis
of the target binary systems. We concluded that NSVS 8294044, V1023 Her, and
V1397 Her are contact binary systems based on the mass ratio, fillout factor,
inclination, absolute parameters, and the $logM_{tot}-logJ_{0}$ diagram.

Figure 5: The $logM-logL$, $logM-logR$, $logq-logL_{ratio}$, and
$logM_{tot}-logJ_{0}$ diagrams. Figure 6: Diagram of the effective temperature
($T_{1}$) and more massive component ($M_{m}$) of the contact binary systems.

## Data Availability

Ground-based data will be made available on request.

## Acknowledgements

This manuscript was prepared by the BSN project (https://bsnp.info/). We have
made use of data from the European Space Agency (ESA) mission Gaia
(http://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC). This work includes data from the TESS mission
observations. Funding for the TESS mission is provided by the NASA Explorer
Program.

## ORCID iDs

Atila Poro: 0000-0002-0196-9732
Sabrina Baudart: 0009-0004-8426-4114
Mahshid Nourmohammad: 0009-0006-0476-2055
Zahra Sabaghpour Arani: 0009-0009-7505-9190
Fatemeh Farhadi: 0009-0004-6762-9863
Selda Ranjbar Salehian: 0000-0002-5223-1332
Ahmad Sarostad: 0000-0001-6485-8696
Saeideh Ranjbaryan Iri Olya: 0009-0001-9087-2448
Maryam Hadizadeh: 0000-0003-1493-0295
AmirHossein Khodaei: 0009-0002-0058-415X

## Appendix

The appendix tables are related to the extracted TESS primary and secondary
times of minima for the V1023 Her and V1397 Her binary systems.

Table 4: Extracted times of minima for V1023 Her. All times of minima have
been reduced to 2400000. The error value for the minimum times extracted from
TESS is 0.0001.

8

Min. | Epoch | O-C | Min. | Epoch | O-C | Min. | Epoch | O-C | Min. | Epoch | O-C
---|---|---|---|---|---|---|---|---|---|---|---
58929.7499 | -2194.5 | 0.0051 | 58944.8956 | -2147.5 | 0.0058 | 58957.4632 | -2108.5 | 0.0063 | 58969.7077 | -2070.5 | 0.0059
58929.9136 | -2194.0 | 0.0077 | 58945.0574 | -2147.0 | 0.0065 | 58957.6242 | -2108.0 | 0.0062 | 58969.8693 | -2070.0 | 0.0064
58930.0726 | -2193.5 | 0.0056 | 58945.2181 | -2146.5 | 0.0061 | 58957.7855 | -2107.5 | 0.0063 | 58970.0301 | -2069.5 | 0.0060
58930.2357 | -2193.0 | 0.0076 | 58945.3803 | -2146.0 | 0.0072 | 58957.9463 | -2107.0 | 0.0061 | 58970.1919 | -2069.0 | 0.0068
58930.3944 | -2192.5 | 0.0051 | 58945.5398 | -2145.5 | 0.0055 | 58958.1071 | -2106.5 | 0.0057 | 58970.3522 | -2068.5 | 0.0060
58930.5577 | -2192.0 | 0.0073 | 58945.7020 | -2145.0 | 0.0066 | 58958.2691 | -2106.0 | 0.0066 | 58970.5138 | -2068.0 | 0.0064
58930.7173 | -2191.5 | 0.0059 | 58945.8625 | -2144.5 | 0.0060 | 58958.4296 | -2105.5 | 0.0059 | 58970.6746 | -2067.5 | 0.0061
58930.8803 | -2191.0 | 0.0077 | 58946.0243 | -2144.0 | 0.0067 | 58958.5910 | -2105.0 | 0.0063 | 58970.9964 | -2066.5 | 0.0056
58931.0397 | -2190.5 | 0.0060 | 58946.1842 | -2143.5 | 0.0055 | 58958.7520 | -2104.5 | 0.0061 | 58971.1584 | -2066.0 | 0.0065
58931.2020 | -2190.0 | 0.0071 | 58946.3465 | -2143.0 | 0.0067 | 58958.9131 | -2104.0 | 0.0061 | 58971.3188 | -2065.5 | 0.0059
58931.3629 | -2189.5 | 0.0069 | 58946.5070 | -2142.5 | 0.0060 | 58959.0744 | -2103.5 | 0.0063 | 58971.4799 | -2065.0 | 0.0058
58931.5246 | -2189.0 | 0.0075 | 58946.6690 | -2142.0 | 0.0070 | 58959.2352 | -2103.0 | 0.0060 | 58971.6417 | -2064.5 | 0.0065
58931.6840 | -2188.5 | 0.0058 | 58946.8284 | -2141.5 | 0.0052 | 58959.3966 | -2102.5 | 0.0063 | 58971.8027 | -2064.0 | 0.0064
58931.8467 | -2188.0 | 0.0074 | 58946.9914 | -2141.0 | 0.0071 | 58959.5575 | -2102.0 | 0.0061 | 58971.9639 | -2063.5 | 0.0064
58932.0064 | -2187.5 | 0.0060 | 58947.1505 | -2140.5 | 0.0051 | 58959.7187 | -2101.5 | 0.0062 | 58972.1251 | -2063.0 | 0.0065
58932.1692 | -2187.0 | 0.0077 | 58947.3135 | -2140.0 | 0.0069 | 58959.8796 | -2101.0 | 0.0059 | 58972.2863 | -2062.5 | 0.0066
58932.3284 | -2186.5 | 0.0057 | 58947.4728 | -2139.5 | 0.0052 | 58960.0405 | -2100.5 | 0.0057 | 58972.4472 | -2062.0 | 0.0064
58932.4914 | -2186.0 | 0.0076 | 58947.6359 | -2139.0 | 0.0072 | 58960.2026 | -2100.0 | 0.0067 | 58972.6080 | -2061.5 | 0.0060
58932.6508 | -2185.5 | 0.0059 | 58947.7953 | -2138.5 | 0.0054 | 58960.3632 | -2099.5 | 0.0061 | 58972.7694 | -2061.0 | 0.0064
58932.8136 | -2185.0 | 0.0076 | 58947.9579 | -2138.0 | 0.0069 | 58960.5246 | -2099.0 | 0.0065 | 58972.9305 | -2060.5 | 0.0063
58932.9731 | -2184.5 | 0.0059 | 58948.1174 | -2137.5 | 0.0053 | 58960.6851 | -2098.5 | 0.0059 | 58973.0918 | -2060.0 | 0.0066
58933.1355 | -2184.0 | 0.0073 | 58948.2802 | -2137.0 | 0.0070 | 58960.8468 | -2098.0 | 0.0064 | 58973.2527 | -2059.5 | 0.0064
58933.2953 | -2183.5 | 0.0059 | 58948.4397 | -2136.5 | 0.0053 | 58961.0071 | -2097.5 | 0.0056 | 58973.4140 | -2059.0 | 0.0065
58933.4581 | -2183.0 | 0.0076 | 58948.6028 | -2136.0 | 0.0073 | 58961.1688 | -2097.0 | 0.0062 | 58973.5749 | -2058.5 | 0.0063
58933.6171 | -2182.5 | 0.0056 | 58948.7622 | -2135.5 | 0.0056 | 58961.3296 | -2096.5 | 0.0059 | 58973.7366 | -2058.0 | 0.0069
58933.7806 | -2182.0 | 0.0079 | 58948.9246 | -2135.0 | 0.0068 | 58961.4913 | -2096.0 | 0.0064 | 58973.8969 | -2057.5 | 0.0061
58933.9397 | -2181.5 | 0.0058 | 58949.0847 | -2134.5 | 0.0059 | 58961.6521 | -2095.5 | 0.0061 | 58974.0583 | -2057.0 | 0.0064
58934.1028 | -2181.0 | 0.0079 | 58949.2469 | -2134.0 | 0.0070 | 58961.8135 | -2095.0 | 0.0064 | 58974.2188 | -2056.5 | 0.0057
58934.2621 | -2180.5 | 0.0060 | 58949.4067 | -2133.5 | 0.0056 | 58961.9739 | -2094.5 | 0.0057 | 58974.3809 | -2056.0 | 0.0067
58934.4243 | -2180.0 | 0.0072 | 58949.5686 | -2133.0 | 0.0064 | 58962.1355 | -2094.0 | 0.0062 | 58974.5411 | -2055.5 | 0.0058
58934.5845 | -2179.5 | 0.0063 | 58949.7295 | -2132.5 | 0.0062 | 58962.2963 | -2093.5 | 0.0059 | 58974.7030 | -2055.0 | 0.0066
58934.7467 | -2179.0 | 0.0073 | 58949.8912 | -2132.0 | 0.0068 | 58962.4576 | -2093.0 | 0.0060 | 58974.8634 | -2054.5 | 0.0059
58934.9068 | -2178.5 | 0.0062 | 58950.0514 | -2131.5 | 0.0058 | 58962.6184 | -2092.5 | 0.0057 | 58975.0253 | -2054.0 | 0.0066
58935.0688 | -2178.0 | 0.0072 | 58950.2133 | -2131.0 | 0.0067 | 58962.7799 | -2092.0 | 0.0061 | 58975.1854 | -2053.5 | 0.0056
58935.5514 | -2176.5 | 0.0064 | 58950.3735 | -2130.5 | 0.0057 | 58962.9409 | -2091.5 | 0.0060 | 58975.3476 | -2053.0 | 0.0067
58935.7133 | -2176.0 | 0.0072 | 58950.5350 | -2130.0 | 0.0061 | 58963.1025 | -2091.0 | 0.0064 | 58975.5086 | -2052.5 | 0.0066
58935.8730 | -2175.5 | 0.0057 | 58950.6962 | -2129.5 | 0.0062 | 58963.2625 | -2090.5 | 0.0054 | 58975.6705 | -2052.0 | 0.0073
58936.0356 | -2175.0 | 0.0073 | 58950.8576 | -2129.0 | 0.0065 | 58963.4244 | -2090.0 | 0.0062 | 58975.8304 | -2051.5 | 0.0061
58936.1955 | -2174.5 | 0.0060 | 58951.0177 | -2128.5 | 0.0055 | 58963.5852 | -2089.5 | 0.0058 | 58975.9921 | -2051.0 | 0.0068
58936.3580 | -2174.0 | 0.0074 | 58951.1797 | -2128.0 | 0.0064 | 58963.7469 | -2089.0 | 0.0064 | 58976.1527 | -2050.5 | 0.0062
58936.5177 | -2173.5 | 0.0060 | 58951.3405 | -2127.5 | 0.0060 | 58963.9077 | -2088.5 | 0.0061 | 58976.3141 | -2050.0 | 0.0065
58936.6801 | -2173.0 | 0.0073 | 58951.5024 | -2127.0 | 0.0068 | 58964.0680 | -2088.0 | 0.0053 | 58976.4748 | -2049.5 | 0.0061
58936.8399 | -2172.5 | 0.0059 | 58951.6625 | -2126.5 | 0.0058 | 58964.2296 | -2087.5 | 0.0057 | 58976.6366 | -2049.0 | 0.0068
58937.0022 | -2172.0 | 0.0072 | 58951.8243 | -2126.0 | 0.0065 | 58964.3912 | -2087.0 | 0.0062 | 58976.7968 | -2048.5 | 0.0058
58937.1623 | -2171.5 | 0.0061 | 58951.9850 | -2125.5 | 0.0060 | 58964.5518 | -2086.5 | 0.0057 | 58976.9591 | -2048.0 | 0.0070
58937.3245 | -2171.0 | 0.0072 | 58952.1469 | -2125.0 | 0.0068 | 58964.7131 | -2086.0 | 0.0059 | 58977.1190 | -2047.5 | 0.0058
58937.4839 | -2170.5 | 0.0055 | 58952.3068 | -2124.5 | 0.0056 | 58964.8747 | -2085.5 | 0.0064 | 58977.2812 | -2047.0 | 0.0069
58937.6464 | -2170.0 | 0.0068 | 58952.4686 | -2124.0 | 0.0064 | 58965.0355 | -2085.0 | 0.0061 | 58977.4409 | -2046.5 | 0.0055
58937.8071 | -2169.5 | 0.0064 | 58952.6293 | -2123.5 | 0.0059 | 58965.1964 | -2084.5 | 0.0058 | 58977.6032 | -2046.0 | 0.0067
58937.9691 | -2169.0 | 0.0073 | 58952.7910 | -2123.0 | 0.0065 | 58965.3576 | -2084.0 | 0.0059 | 58977.7636 | -2045.5 | 0.0060
58938.1287 | -2168.5 | 0.0058 | 58952.9514 | -2122.5 | 0.0058 | 58965.5183 | -2083.5 | 0.0055 | 58977.9258 | -2045.0 | 0.0070
58938.2913 | -2168.0 | 0.0073 | 58953.1130 | -2122.0 | 0.0062 | 58965.6803 | -2083.0 | 0.0064 | 58978.0856 | -2044.5 | 0.0057
58938.4510 | -2167.5 | 0.0059 | 58953.2739 | -2121.5 | 0.0060 | 58965.8406 | -2082.5 | 0.0056 | 58978.2479 | -2044.0 | 0.0069
58938.6136 | -2167.0 | 0.0074 | 58953.4355 | -2121.0 | 0.0065 | 58966.0030 | -2082.0 | 0.0069 | 58978.4074 | -2043.5 | 0.0053
58938.7734 | -2166.5 | 0.0061 | 58953.5960 | -2120.5 | 0.0059 | 58966.1624 | -2081.5 | 0.0052 | 58978.5707 | -2043.0 | 0.0074
58938.9355 | -2166.0 | 0.0071 | 58953.7574 | -2120.0 | 0.0062 | 58966.3249 | -2081.0 | 0.0065 | 58978.7300 | -2042.5 | 0.0057
58939.0951 | -2165.5 | 0.0055 | 58953.9185 | -2119.5 | 0.0062 | 58966.4848 | -2080.5 | 0.0053 | 58978.8920 | -2042.0 | 0.0065
58939.2576 | -2165.0 | 0.0069 | 58954.0797 | -2119.0 | 0.0062 | 58966.6475 | -2080.0 | 0.0069 | 58979.0523 | -2041.5 | 0.0057
58939.4173 | -2164.5 | 0.0055 | 58954.2405 | -2118.5 | 0.0059 | 58966.8076 | -2079.5 | 0.0059 | 58979.2144 | -2041.0 | 0.0067
58939.5804 | -2164.0 | 0.0074 | 58954.4023 | -2118.0 | 0.0067 | 58966.9693 | -2079.0 | 0.0065 | 58979.3746 | -2040.5 | 0.0058
58939.7398 | -2163.5 | 0.0058 | 58954.5629 | -2117.5 | 0.0060 | 58967.1291 | -2078.5 | 0.0051 | 58979.5367 | -2040.0 | 0.0068
58939.9025 | -2163.0 | 0.0074 | 58954.7245 | -2117.0 | 0.0066 | 58967.2916 | -2078.0 | 0.0066 | 58979.6969 | -2039.5 | 0.0059
58940.0617 | -2162.5 | 0.0055 | 58955.8522 | -2113.5 | 0.0065 | 58967.4527 | -2077.5 | 0.0065 | 58979.8588 | -2039.0 | 0.0066
58940.2246 | -2162.0 | 0.0072 | 58956.0127 | -2113.0 | 0.0059 | 58967.6133 | -2077.0 | 0.0060 | 58980.0184 | -2038.5 | 0.0051
58940.3841 | -2161.5 | 0.0056 | 58956.1748 | -2112.5 | 0.0068 | 58967.7740 | -2076.5 | 0.0056 | 58980.1816 | -2038.0 | 0.0072
58940.5466 | -2161.0 | 0.0070 | 58956.3355 | -2112.0 | 0.0064 | 58967.9357 | -2076.0 | 0.0062 | 58980.3409 | -2037.5 | 0.0053
58940.7069 | -2160.5 | 0.0062 | 58956.4970 | -2111.5 | 0.0068 | 58968.0972 | -2075.5 | 0.0065 | 58980.5035 | -2037.0 | 0.0068
58944.4140 | -2149.0 | 0.0075 | 58956.6578 | -2111.0 | 0.0065 | 58968.2581 | -2075.0 | 0.0064 | 58980.6635 | -2036.5 | 0.0057
58944.5733 | -2148.5 | 0.0058 | 58956.8197 | -2110.5 | 0.0072 | 58969.3854 | -2071.5 | 0.0058 | 58980.8256 | -2036.0 | 0.0068
58944.7352 | -2148.0 | 0.0066 | 58957.3020 | -2109.0 | 0.0062 | 58969.5470 | -2071.0 | 0.0063 | 58980.9855 | -2035.5 | 0.0055

Table 5: Continued for V1023 Her.

8  Min. Epoch O-C Min. Epoch O-C Min. Epoch O-C Min. Epoch O-C 58981.1479
-2035.0 0.0068 59677.3351 125.5 0.0072 59691.3486 169.0 0.0035 59706.1715
215.0 0.0037 58981.3076 -2034.5 0.0054 59677.4930 126.0 0.0040 59693.1246
174.5 0.0072 59706.3371 215.5 0.0081 58981.4704 -2034.0 0.0071 59677.6573
126.5 0.0072 59693.2824 175.0 0.0039 59706.4937 216.0 0.0036 58981.6294
-2033.5 0.0049 59677.8156 127.0 0.0044 59693.4468 175.5 0.0072 59706.6590
216.5 0.0078 58981.7926 -2033.0 0.0071 59677.9795 127.5 0.0071 59693.6049
176.0 0.0042 59706.8159 217.0 0.0036 58981.9516 -2032.5 0.0049 59678.1377
128.0 0.0042 59696.9916 186.5 0.0075 59706.9812 217.5 0.0078 58982.1145
-2032.0 0.0066 59678.3021 128.5 0.0075 59697.1495 187.0 0.0042 59710.0380
227.0 0.0033 59665.4117 88.5 0.0065 59683.4580 144.5 0.0076 59697.3137 187.5
0.0073 59710.2042 227.5 0.0084 59665.5696 89.0 0.0032 59683.6159 145.0 0.0045
59697.4712 188.0 0.0037 59710.3601 228.0 0.0032 59669.6010 101.5 0.0067
59683.7794 145.5 0.0068 59697.6361 188.5 0.0075 59710.5258 228.5 0.0078
59669.7583 102.0 0.0029 59683.9376 146.0 0.0039 59697.7938 189.0 0.0040
59710.6819 229.0 0.0028 59669.9238 102.5 0.0073 59684.1022 146.5 0.0074
59697.9583 189.5 0.0074 59710.8486 229.5 0.0084 59670.0807 103.0 0.0031
59684.2594 147.0 0.0035 59698.1158 190.0 0.0038 59711.0044 230.0 0.0031
59670.2454 103.5 0.0066 59684.4243 147.5 0.0073 59698.2804 190.5 0.0073
59711.1707 230.5 0.0082 59670.4036 104.0 0.0037 59684.5821 148.0 0.0039
59698.4379 191.0 0.0036 59711.3272 231.0 0.0036 59670.5681 104.5 0.0071
59684.7464 148.5 0.0072 59698.6028 191.5 0.0075 59711.4928 231.5 0.0081
59670.7251 105.0 0.0030 59684.9042 149.0 0.0038 59698.7596 192.0 0.0032
59711.6489 232.0 0.0030 59670.8896 105.5 0.0064 59685.0690 149.5 0.0075
59698.9248 192.5 0.0073 59711.8150 232.5 0.0080 59671.0478 106.0 0.0035
59685.2265 150.0 0.0038 59699.0824 193.0 0.0037 59711.9713 233.0 0.0032
59671.2124 106.5 0.0070 59685.3906 150.5 0.0068 59699.2473 193.5 0.0074
59712.1376 233.5 0.0084 59671.3700 107.0 0.0034 59685.5490 151.0 0.0041
59699.4044 194.0 0.0035 59712.2934 234.0 0.0031 59671.5338 107.5 0.0061
59685.7132 151.5 0.0072 59699.5693 194.5 0.0073 59712.4592 234.5 0.0078
59671.6922 108.0 0.0034 59685.8713 152.0 0.0042 59699.7266 195.0 0.0034
59712.6159 235.0 0.0034 59671.8567 108.5 0.0068 59686.0356 152.5 0.0074
59699.8913 195.5 0.0070 59712.7815 235.5 0.0078 59672.0144 109.0 0.0034
59686.1934 153.0 0.0041 59700.0490 196.0 0.0036 59712.9380 236.0 0.0032
59672.1789 109.5 0.0068 59686.3574 153.5 0.0070 59700.2139 196.5 0.0073
59713.1040 236.5 0.0081 59672.5010 110.5 0.0066 59686.5158 154.0 0.0042
59700.3709 197.0 0.0033 59713.2601 237.0 0.0031 59672.6591 111.0 0.0036
59686.6797 154.5 0.0070 59700.5357 197.5 0.0070 59713.4259 237.5 0.0077
59672.8232 111.5 0.0066 59686.8378 155.0 0.0040 59700.6932 198.0 0.0033
59713.5826 238.0 0.0033 59672.9812 112.0 0.0035 59687.0021 155.5 0.0072
59700.8586 198.5 0.0076 59713.7479 238.5 0.0075 59673.1458 112.5 0.0069
59687.1601 156.0 0.0041 59701.0159 199.0 0.0038 59713.9046 239.0 0.0031
59673.3034 113.0 0.0035 59687.3245 156.5 0.0074 59701.1807 199.5 0.0075
59714.0703 239.5 0.0078 59673.4683 113.5 0.0072 59687.4824 157.0 0.0041
59701.3376 200.0 0.0033 59714.2265 240.0 0.0028 59673.6257 114.0 0.0035
59687.6464 157.5 0.0070 59701.5027 200.5 0.0073 59714.3929 240.5 0.0081
59673.7901 114.5 0.0068 59687.8048 158.0 0.0043 59701.6601 201.0 0.0035
59714.5490 241.0 0.0031 59673.9480 115.0 0.0035 59687.9689 158.5 0.0072
59701.8249 201.5 0.0072 59714.7150 241.5 0.0079 59674.1125 115.5 0.0069
59688.1271 159.0 0.0043 59701.9823 202.0 0.0035 59714.8710 242.0 0.0028
59674.2701 116.0 0.0034 59688.2904 159.5 0.0065 59702.1471 202.5 0.0071
59715.0370 242.5 0.0077 59674.4348 116.5 0.0070 59688.4492 160.0 0.0043
59702.3049 203.0 0.0039 59715.1932 243.0 0.0028 59674.5924 117.0 0.0035
59688.6128 160.5 0.0067 59702.4697 203.5 0.0075 59715.3593 243.5 0.0078
59674.7568 117.5 0.0068 59688.7714 161.0 0.0042 59702.6272 204.0 0.0040
59715.5157 244.0 0.0031 59674.9148 118.0 0.0037 59688.9354 161.5 0.0070
59702.7913 204.5 0.0070 59715.6816 244.5 0.0078 59675.0791 118.5 0.0068
59689.0938 162.0 0.0043 59702.9494 205.0 0.0039 59715.8381 245.0 0.0032
59675.2373 119.0 0.0039 59689.2573 162.5 0.0067 59703.1141 205.5 0.0075
59716.0038 245.5 0.0078 59675.4017 119.5 0.0072 59689.4155 163.0 0.0038
59703.2713 206.0 0.0035 59716.1600 246.0 0.0029 59675.5594 120.0 0.0037
59689.5799 163.5 0.0071 59703.4364 206.5 0.0075 59716.3260 246.5 0.0078
59675.7233 120.5 0.0065 59689.7380 164.0 0.0041 59703.5936 207.0 0.0037
59716.4823 247.0 0.0030 59675.8823 121.0 0.0045 59689.9020 164.5 0.0069
59703.7583 207.5 0.0072 59716.6481 247.5 0.0077 59676.0458 121.5 0.0069
59690.0601 165.0 0.0040 59703.9156 208.0 0.0034 59716.8048 248.0 0.0032
59676.2043 122.0 0.0042 59690.2236 165.5 0.0063 59704.0808 208.5 0.0075
59716.9704 248.5 0.0077 59676.3681 122.5 0.0069 59690.3825 166.0 0.0041
59704.2380 209.0 0.0035 59717.1271 249.0 0.0032 59676.5262 123.0 0.0039
59690.5464 166.5 0.0069 59704.4030 209.5 0.0074 59717.2929 249.5 0.0080
59676.6901 123.5 0.0067 59690.7044 167.0 0.0038 59704.5603 210.0 0.0036
59717.4491 250.0 0.0031 59676.8488 124.0 0.0043 59690.8688 167.5 0.0071
59705.7282 213.5 0.0437 59677.0126 124.5 0.0069 59691.0268 168.0 0.0039
59705.8492 214.0 0.0036 59677.1714 125.0 0.0046 59691.1911 168.5 0.0071
59706.0149 214.5 0.0081

Table 6: Available times of minima for V1397 Her. All times of minima have
been reduced to 2400000. The error value for the minimum times extracted from
TESS is 0.0001.

8

Min. | Epoch | O-C | Min. | Epoch | O-C | Min. | Epoch | O-C | Min. | Epoch | O-C
---|---|---|---|---|---|---|---|---|---|---|---
58983.7128 | 13282 | 0.0439 | 58993.2124 | 13306.5 | 0.0438 | 59004.0692 | 13334.5 | 0.0437 | 59728.1921 | 15202 | 0.0528
58983.9061 | 13282.5 | 0.0434 | 58993.4064 | 13307 | 0.0440 | 59004.2635 | 13335 | 0.0441 | 59728.3864 | 15202.5 | 0.0533
58984.1005 | 13283 | 0.0439 | 58993.5999 | 13307.5 | 0.0435 | 59004.4570 | 13335.5 | 0.0438 | 59728.5798 | 15203 | 0.0528
58984.2939 | 13283.5 | 0.0435 | 58993.7942 | 13308 | 0.0440 | 59004.6511 | 13336 | 0.0440 | 59728.7736 | 15203.5 | 0.0528
58984.4882 | 13284 | 0.0439 | 58993.9877 | 13308.5 | 0.0437 | 59004.8446 | 13336.5 | 0.0437 | 59728.9683 | 15204 | 0.0536
58984.6814 | 13284.5 | 0.0432 | 58994.1820 | 13309 | 0.0440 | 59005.0455 | 13337 | 0.0507 | 59729.1614 | 15204.5 | 0.0529
58984.8760 | 13285 | 0.0439 | 58994.3758 | 13309.5 | 0.0440 | 59005.2323 | 13337.5 | 0.0436 | 59729.3554 | 15205 | 0.0529
58985.0696 | 13285.5 | 0.0437 | 58994.5697 | 13310 | 0.0440 | 59005.4268 | 13338 | 0.0443 | 59729.5488 | 15205.5 | 0.0524
58985.2636 | 13286 | 0.0438 | 58994.7634 | 13310.5 | 0.0438 | 59005.6201 | 13338.5 | 0.0437 | 59729.7431 | 15206 | 0.0529
58985.4572 | 13286.5 | 0.0436 | 58994.9574 | 13311 | 0.0440 | 59005.8144 | 13339 | 0.0441 | 59729.9369 | 15206.5 | 0.0528
58985.6512 | 13287 | 0.0437 | 58995.1510 | 13311.5 | 0.0437 | 59006.0087 | 13339.5 | 0.0446 | 59730.1309 | 15207 | 0.0530
58985.8449 | 13287.5 | 0.0435 | 58995.3452 | 13312 | 0.0440 | 59006.2022 | 13340 | 0.0442 | 59731.4879 | 15210.5 | 0.0529
58986.0393 | 13288 | 0.0440 | 58995.5389 | 13312.5 | 0.0439 | 59006.3957 | 13340.5 | 0.0437 | 59731.6820 | 15211 | 0.0531
58986.2329 | 13288.5 | 0.0437 | 58997.0899 | 13316.5 | 0.0439 | 59006.5900 | 13341 | 0.0442 | 59731.8756 | 15211.5 | 0.0528
58986.4269 | 13289 | 0.0439 | 58997.2841 | 13317 | 0.0442 | 59006.7834 | 13341.5 | 0.0437 | 59732.0652 | 15212 | 0.0485
58986.6204 | 13289.5 | 0.0435 | 58997.4777 | 13317.5 | 0.0439 | 59006.9777 | 13342 | 0.0441 | 59732.2633 | 15212.5 | 0.0528
58986.8143 | 13290 | 0.0436 | 58997.6717 | 13318 | 0.0441 | 59007.1712 | 13342.5 | 0.0438 | 59732.4575 | 15213 | 0.0531
58987.0082 | 13290.5 | 0.0435 | 58997.8654 | 13318.5 | 0.0439 | 59007.3655 | 13343 | 0.0442 | 59732.6513 | 15213.5 | 0.0530
58987.2023 | 13291 | 0.0438 | 58998.0596 | 13319 | 0.0442 | 59007.5588 | 13343.5 | 0.0436 | 59732.8452 | 15214 | 0.0530
58987.3960 | 13291.5 | 0.0436 | 58998.2524 | 13319.5 | 0.0431 | 59007.7532 | 13344 | 0.0442 | 59737.4979 | 15226 | 0.0528
58987.5902 | 13292 | 0.0439 | 58998.4472 | 13320 | 0.0440 | 59007.9467 | 13344.5 | 0.0438 | 59737.6917 | 15226.5 | 0.0528
58987.7838 | 13292.5 | 0.0437 | 58998.6408 | 13320.5 | 0.0438 | 59008.1410 | 13345 | 0.0442 | 59737.8858 | 15227 | 0.0530
58987.9779 | 13293 | 0.0438 | 58998.8351 | 13321 | 0.0442 | 59008.3345 | 13345.5 | 0.0439 | 59738.0794 | 15227.5 | 0.0527
58988.1718 | 13293.5 | 0.0440 | 58999.0280 | 13321.5 | 0.0433 | 59008.5286 | 13346 | 0.0441 | 59738.2735 | 15228 | 0.0529
58988.3655 | 13294 | 0.0437 | 58999.2227 | 13322 | 0.0441 | 59008.7220 | 13346.5 | 0.0436 | 59738.4671 | 15228.5 | 0.0527
58988.5588 | 13294.5 | 0.0432 | 58999.4163 | 13322.5 | 0.0438 | 59008.9165 | 13347 | 0.0443 | 59738.6613 | 15229 | 0.0530
58988.7533 | 13295 | 0.0438 | 58999.6106 | 13323 | 0.0442 | 59718.6922 | 15177.5 | 0.0527 | 59738.8547 | 15229.5 | 0.0525
58988.9471 | 13295.5 | 0.0437 | 58999.8040 | 13323.5 | 0.0438 | 59718.8861 | 15178 | 0.0528 | 59739.0490 | 15230 | 0.0529
58989.1411 | 13296 | 0.0438 | 58999.9982 | 13324 | 0.0441 | 59719.0800 | 15178.5 | 0.0527 | 59739.2434 | 15230.5 | 0.0535
58989.3348 | 13296.5 | 0.0437 | 59000.1917 | 13324.5 | 0.0437 | 59719.2739 | 15179 | 0.0528 | 59739.4366 | 15231 | 0.0528
58989.5287 | 13297 | 0.0437 | 59000.3860 | 13325 | 0.0442 | 59719.4676 | 15179.5 | 0.0526 | 59739.6304 | 15231.5 | 0.0527
58989.7227 | 13297.5 | 0.0438 | 59000.5795 | 13325.5 | 0.0438 | 59719.6617 | 15180 | 0.0528 | 59739.8245 | 15232 | 0.0529
58989.9166 | 13298 | 0.0438 | 59000.7738 | 13326 | 0.0442 | 59724.8961 | 15193.5 | 0.0527 | 59740.0085 | 15232.5 | 0.0430
58990.1105 | 13298.5 | 0.0439 | 59000.9674 | 13326.5 | 0.0439 | 59725.0901 | 15194 | 0.0528 | 59740.2123 | 15233 | 0.0530
58990.3042 | 13299 | 0.0437 | 59001.1616 | 13327 | 0.0442 | 59725.2838 | 15194.5 | 0.0527 | 59740.4060 | 15233.5 | 0.0528
58990.4982 | 13299.5 | 0.0438 | 59001.3550 | 13327.5 | 0.0438 | 59725.4778 | 15195 | 0.0528 | 59740.6000 | 15234 | 0.0530
58990.6920 | 13300 | 0.0438 | 59001.5491 | 13328 | 0.0440 | 59725.6716 | 15195.5 | 0.0527 | 59740.7938 | 15234.5 | 0.0528
58990.8859 | 13300.5 | 0.0438 | 59001.7427 | 13328.5 | 0.0437 | 59725.8655 | 15196 | 0.0528 | 59740.9878 | 15235 | 0.0530
58991.0798 | 13301 | 0.0438 | 59001.9370 | 13329 | 0.0442 | 59726.0598 | 15196.5 | 0.0531 | 59741.1815 | 15235.5 | 0.0528
58991.2736 | 13301.5 | 0.0438 | 59002.1306 | 13329.5 | 0.0439 | 59726.2532 | 15197 | 0.0527 | 59741.3755 | 15236 | 0.0530
58991.4676 | 13302 | 0.0438 | 59002.3246 | 13330 | 0.0440 | 59726.4471 | 15197.5 | 0.0528 | 59741.5693 | 15236.5 | 0.0529
58991.6614 | 13302.5 | 0.0438 | 59002.5184 | 13330.5 | 0.0439 | 59726.6410 | 15198 | 0.0528 | 59741.7632 | 15237 | 0.0529
58991.8552 | 13303 | 0.0437 | 59002.7123 | 13331 | 0.0440 | 59726.8348 | 15198.5 | 0.0526 | 59741.9570 | 15237.5 | 0.0528
58992.0493 | 13303.5 | 0.0440 | 59002.9059 | 13331.5 | 0.0437 | 59727.0289 | 15199 | 0.0529 | 59742.1510 | 15238 | 0.0529
58992.2432 | 13304 | 0.0440 | 59003.1003 | 13332 | 0.0443 | 59727.2219 | 15199.5 | 0.0520 | 59742.3441 | 15238.5 | 0.0522
58992.4369 | 13304.5 | 0.0438 | 59003.2936 | 13332.5 | 0.0436 | 59727.4164 | 15200 | 0.0526 | 59742.5387 | 15239 | 0.0529
58992.6307 | 13305 | 0.0437 | 59003.4879 | 13333 | 0.0441 | 59727.6102 | 15200.5 | 0.0526 | 59742.7326 | 15239.5 | 0.0529
58992.8245 | 13305.5 | 0.0437 | 59003.6814 | 13333.5 | 0.0437 | 59727.8047 | 15201 | 0.0533 | 59742.9265 | 15240 | 0.0530
58993.0185 | 13306 | 0.0438 | 59003.8756 | 13334 | 0.0440 | 59727.9981 | 15201.5 | 0.0528 |  |  |

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# Quantum key distribution over 658 km fiber with distributed vibration
sensing

###### Abstract

Twin-field quantum key distribution (TF-QKD) [1] promises ultra-long secure
key distribution which surpasses the rate distance limit [2] and can reduce
the number of the trusted nodes in long-haul quantum network [3]. Tremendous
efforts have been made towards implementation of TF-QKD, among which, the
secure key with finite size analysis can distribute more than 500 km in the
lab [4, 5, 6] and in the field [7]. Here, we demonstrate the sending-or-not-
sending TF-QKD [8] experimentally, achieving a secure key distribution with
finite size analysis over 658 km ultra-low-loss optical fiber, improve the
secure distance record by around 100 km. Meanwhile, in a TF-QKD system, any
phase fluctuation due to temperature variation and ambient variation during
the channel must be recorded and compensated, and all these phase information
can then be utilized to sense the channel vibration perturbations. With our
QKD system, we recovered the external vibrational perturbations on the fiber
generated by an artificial vibroseis and successfully located the perturbation
position with a resolution better than 1 km. Our results not only set a new
distance record of QKD, but also demonstrate that the redundant information of
TF-QKD can be used for remote sensing of the channel vibration, which can find
applications in earthquake detection and landslide monitoring besides secure
communication.

Jiu-Peng Chen,1,2,3,† Chi Zhang,1,2,3,† Yang Liu,3 Cong Jiang,3 Dong-Feng
Zhao,1 Wei-Jun Zhang,4 Fa-Xi Chen,3 Hao Li,4 Li-Xing You,4 Zhen Wang,4 Yang
Chen,1 Xiang-Bin Wang,2,3,5 Qiang Zhang,1,2,3 Jian-Wei Pan1,2

Hefei National Laboratory for Physical Sciences at Microscale and Department
of Modern Physics, University of Science and Technology of China, Hefei
230026, China

CAS Center for Excellence and Synergetic Innovation Center in Quantum
Information and Quantum Physics, University of Science and Technology of
China, Hefei 230026, China

Jinan Institute of Quantum Technology, Jinan, Shandong 250101, China

State Key Laboratory of Functional Materials for Informatics, Shanghai
Institute of Microsystem and Information Technology, Chinese Academy of
Sciences, Shanghai 200050, China

State Key Laboratory of Low Dimensional Quantum Physics, Department of
Physics, Tsinghua University, Beijing 100084, China
$\dagger$ These authors contributed equally: Jiu-Peng Chen, Chi Zhang.

## Introduction

Quantum key distribution (QKD) [9, 10, 11, 12, 13, 14] offers the theoretical
provable way to distribute secure keys. However, the channel loss is an
inevitable barrier for long distance QKD since a quantum signal cannot be
amplified. For a transmission $\eta$, the theoretical upper bound of the
secure key rate is limited to 1.44 $\eta$, known as the Pirandola-Laurenza-
Ottaviani-Bianchi (PLOB) bound [2]. This upper bound is valid for all the
repeaterless QKD protocols which include the commonly decoy-state based BB84
[15, 16, 17], and the measurement-device-independent QKD (MDIQKD) [18, 19]
which closes all security loopholes of measurement devices. Without the
practical quantum repeater, an intermediate solution to achieve long haul QKD
network is to set several trusted relay nodes. Although the trusted relay
networks are successfully demonstrated in the field [3], the increased number
of trusted relays might increase the security risk and raise the cost.

Different from the traditional QKD protocols, the twin-field QKD (TF-QKD) [1]
improves the secure key rate scaling to $\sqrt{\eta}$ without using quantum
memory. This may provides a solution to reach a longer distance and to reduce
the number of trusted relays. Recently, the feasibility of distributing secure
keys over long distance is proved experimentally [20, 21, 22, 23, 5, 4, 24, 6,
7]. Notably, with full security analysis considering the finite size effect,
experimental demonstration of sending or not sending TF-QKD (SNS-TF-QKD) [8]
is realized with record long-distance of more than 500 km in lab [5, 6] and in
field [7]. In order to achieve a secure final key, one needs to overcome the
challenging problem finite key effects with a relatively small data size. In
the case of not considering data finite size, one can even obtain a positive
key rate at a distance of 600 km [6].

Realizing TF-QKD is challenging, because the protocols requires phase
sensitive single-photon interference. Any phase differences, caused by laser
wavelength differences or channel fiber vibration may reduce the interference
visibility. Techniques such as time-frequency metrology [22, 5, 7], optical
phase locking loop (OPLL) [21, 20, 6] have been developed to eliminate the
wavelength difference; real-time [21, 6] or post-processing [22, 4, 5, 24, 7]
compensation have been developed to eliminate the fast fiber vibration.

Besides supporting TF-QKD, the obtained information in fast phase compensation
actually reflects the real-time phase variation of the transmitted light in
the optical fiber. This information can also be utilized to detect the
vibrational perturbation in the channel. As such, the redundant information
obtained in an installed TF-QKD system might be used as a fiber-optic sensor
to detect critical vibrations in the channel. Different from the well-known
distributed acoustic fiber sensing (DAS) [25, 26, 27] technique, the phase-
tracking method used in TF-QKD analyzes the transmitted light, not the back-
scattered light. This technique is similar to the phase-based frequency
metrology interferometric technique [28, 29, 30, 31, 32, 33], making it
possible to achieve an ultra-long vibrational sensing length. With this
interferometric method, the measured phase signal will be the result of
integration of perturbations along the whole fiber. Fortunately, by using the
simutaneous bidirectional phase-tracking [33], it is possible to identify the
perturbation location by cross-correlating the time difference between the
signals of Alice and Bob.

Here, we demonstrated SNS-TF-QKD [8] experimentally through a 658 km ultra-low
loss optical fiber with a total loss of 106 dB. The secure key rate is
$9.22\times 10^{-10}$ per pulse after collecting 27.8 hours data for
considering finite key size effect in security analysis. Meanwhile, we insert
an artificially vibroseis in the channel to generate specific vibration
signals. With the same TF-QKD experimental setup, we recovered the vibration
signals generated by the vibroseis. Further, by cross-correlating the
vibrational signals at the two users, we successfully located the vibroseis to
a 1 km precision over the 500 km frequency locking fibers, which is, as far as
we know the longest reported distance [33, 34].

## Protocol

We adopt the 4-intensity sending-or-not-sending (SNS) protocol [8] in the
experiment, and apply the actively odd parity pairing (AOPP) [35, 36, 37]
method for post data processing to achieve a higher key rate. In this
protocol, Alice and Bob send pulse pairs to the detection station, Charlie.
For the received pulse pair, if Charlie announces there is only one detector
clicks, it is a one-detector heralded events. In each side of Alice and Bob,
there are three weak coherent state (WCS) sources with intensities $\mu_{1}$,
$\mu_{2}$, 0 in the decoy windows, and two sources with intensity $\mu_{z}$
and 0 in the signal windows. The one-detector heralded events in the decoy
windows are used to perform decoy state analysis, and the corresponding bits
of the one-detector heralded events in the signal windows are used to extract
the final keys. See Supplemental Information for details of the theory
calculation method.

## Experiment

The experimental setup is shown in Fig 1. Alice and Bob use two independent
ultra-stable lasers of which the relative frequency difference is eliminated.
The light is modulated to a pattern that the single-photon-level quantum
signal pulses are time multiplexed with strong phase reference pulses. In each
period of 1 $\mu$s, 100 signal pulses with 240 ps pulse duration are sent
within the first 400 ns, and the phase reference pulses are sent in the
following 600 ns. The signals from Alice and Bob are sent to Charlie through
329.3 km and 329.4 km (658.7 km in total) ultra-low loss fiber spools with a
transmission of 52.9 dB and 53.1 dB (106 dB in total). After interference at
Charlie’s beam splitter (BS), the signals are detected by two superconducting
nanowire single photon detectors (SNSPDs), and recorded by a time tagger. (See
Supplemental Information for details of the experimental setup.)

The key to realize SNS-TF-QKD is the stable single photon interference, which
requires the Alice’s and Bob’s lasers are locked to the same frequency. We
solve this problem by adapting the frequency metrology technology. First, the
linewidth of Alice’s (Bob’s) seed laser is suppressed to sub-Hz by locking it
to an ultra-low-expansion (ULE) glass cavities using the Pound-Drever-Hall
(PDH) technique [38, 39]. After PDH locking, the relative frequency drift rate
is smaller than 0.1 Hz/s. Then, a 500 km fiber spools is set between Alice and
Bob to calibrate the relative frequency difference of their lasers. Heterodyne
detecting is performed to monitor the frequency difference on both sides, and
an acoustic-optic modulator (AOM) with adjustable carrier frequency is
inserted at Bob’s output to compensate the frequency difference. In this
frequency calibration setup, additional AOMs with fixed carrier frequency are
inserted at both ends of the link to eliminate the channel reflection in
frequency domain, and to shift transmitted laser wavelengths for heterodyne
detection.

To achieve single photon interference, the relative phase between Alice and
Bob should also be compensated. We adapted strong phase reference pulses time
multiplexed with the signal pulses to detect and compensate the fast phase
fluctuation. The phase drift is attributed to the change of the refractive
index and length of fiber. By neglecting the effect of the long-term
temperature drift, the phase difference at the interference is mainly
contributed by the accumulation of mechanical perturbations such as vibration
and sound through the long fiber channel. Now that the fast phase fluctuation
can be compensated in TF-QKD, the phase perturbations induced by vibration
through the channel can be derived straightforwardly. In other words, we can
regard the TF-QKD system as a sensing equipment to detect vibrations in the
channel.

Besides for the use of obtaining the relative frequency difference information
of the two laser sources, the frequency calibration link can also be used to
detect vibration. The vibration on the fiber will induce the frequency/phase
perturbations of the transmitted light by affecting the refractive index or
the length of the fiber. This frequency/phase perturbations of the transmitted
light is measured by detecting the phase of the radio frequency (RF) signal of
heterodyne. The relative delay of the detected frequency/phase perturbations
signals in Alice and Bob indicates the distance differences between Alice and
Bob to the vibroseis. Thus, the position of the vibroseis can be located by
cross-correlating the detected phase perturbations signals of Alice and Bob.
To investigate the vibration perturbations, we inserted program-controlled PZT
vibration generators in the quantum channel and frequency calibration channel,
as shown in Fig 1. (See Supplemental Materials for details of the vibration
test methods.)

## Results

In the experiment, we first explore the longest possible TF-QKD distribution
distance with our setup. A 658 km G.652 ultra-low loss fiber with a total loss
of 106 dB is used as the quantum channel, which is 0.161 dB/km on average,
including the connections. The component loss and insertion loss is optimized
to 1.3 dB in Charlie. Then, we adopted high performance SNSPDs with a
detection efficiency of 82% and an effective dark count rate of 4 Hz to detect
the interference, and set a time gate of 0.3 ns to suppress noise. The final
noise is optimized to be $6\times 10^{-9}$ per pulse, about 80% of which is
from re-Rayleigh scattering [5].

The main results of our experiment are shown in Tab. 1. In about 27.8 hours, a
total of $1.007\times 10^{13}$ signals are sent at the 100 MHz effective
system frequency, yielding $5.28\times 10^{6}$ valid detections. We observe a
quantum phase flip error rate (QBER) in X basis of around 5%, with a base-line
error rate of around 2.8%. The bit-flip error rate in Z basis is 26.29% before
actively odd parity pairing (AOPP) [36, 35], mainly contributed by the
optimized “sending” probability of 0.2717 in Z basis. The QBER in Z basis
decreases to 2.12% after AOPP, while the phase error rate increases to 13.36%
and the survived bits drops to 244731 from 558729.

The secure key rate is then calculated following Eq. (1), considering the
finite data size effect [35, 40]:

$\begin{split}R=&\frac{1}{N_{t}}\\{n_{1}^{\prime}[1-H(e_{1}^{ph})]-fn_{t}^{\prime}H(E_{Z})\\\
&-2\log_{2}\frac{2}{\varepsilon_{cor}}-2\log_{2}\frac{1}{\sqrt{2}\varepsilon_{PA}\hat{\varepsilon}}\\},\\\
\end{split}$ (1)

where $R$ is the final key rate, $n_{1}^{\prime}$, $e_{1}^{ph}$,
$n_{t}^{\prime}$ and $E_{Z}$ are the number of untagged-bits, the phase-flip
error rate, the number of survived bits, and the bit-flip error rate of
untagged-bits after AOPP. $f=1.16$ is the error correction efficiency. $N_{t}$
is the total number of signal pulses, $\varepsilon_{cor}=1\times 10^{-10}$ and
$\varepsilon_{PA}=1\times 10^{-10}$ are the failure probability of error
correction process and privacy amplification process,
$\hat{\varepsilon}=1\times 10^{-10}$ is the coefficient of the chain rules of
smooth min- and max- entropy.

The final secure key rate is $R=9.22\times 10^{-10}$, which is about 0.092 bit
per second (bps) considering 100 MHz effective system frequency. We summarize
our theoretical simulation and experimental result in Fig. 2. The obtained
secure key rate here is more than one order of magnitude higher than the
absolute PLOB bound. (See Supplemental Information for details of experimental
parameters and results.)

Table 1: Experimental results. The parameters $n_{1}^{\prime}$ is the number of untagged-bits, $e_{1}^{ph}$ is the phase-flip error rate, $n_{t}^{\prime}$ is the number of survived bits, $E_{Z}$ is the bit-flip error rate of untagged-bits after AOPP, and $N_{t}$ is the total number of signal pulses. $n_{t}^{\prime}$ | 558729
---|---
$n_{1}^{\prime}$ | 244731
$e_{1}^{ph}$ | 13.36%
$E_{Z}$ | 2.12%
$N_{t}$ | $1.007\times 10^{13}$
Valid detections | $5.28\times 10^{6}$
Key rate | $9.22\times 10^{-10}$

Next, we modulate the PZT vibration generators with fixed frequencies to
simulate the vibration perturbations in the channel. In the case the PZT
vibration takes place in the 658 km quantum channel, the phase drift is
recovered by consequently calculating the relative phase difference with the
phase reference pulses. We set the modulation to sinusoidal signal with
selected frequencies of 1 Hz, 10 Hz, 100 Hz, and 1 kHz, respectively, which is
the frequency range of interest in seismic and acoustic wave sensing. In the
time domain, the recovered phase variation perfectly matches the active
modulation signal, i.e., the externally applied vibration on the fiber. The
driving signals and the recovered phases are plotted in Fig. 3.

In the case the PZT vibration takes place in the frequency calibration
channel, we set the channel length to 0 km, 200 km, and 500 km, respectively,
and install the vibroseis at Alice with different vibration frequencies. Here,
the vibration signal is recovered by electronically decoding phase
perturbations of the RF signal of heterodyne. As shown in Fig. 4, the
recovered phase variation shows a frequency and waveform exactly the same as
that of the driving signal in all the fiber lengths. The vibroseis position is
measured by calculating the relative time delay of the vibration signals at
Alice and Bob. For the case of a fiber length of 500 km and the vibroseis
installed at Alice as an example, the relative time delay between the Alice
and Bob’s signals is measued as 2.531 ms by corss-correlation. By adopting the
speed of light in the fiber to be $2.0\times 10^{8}m/s$, this yields a
location of the vibtaion cource at 502.6 km away from Bob. Similarly, the
vibroseis is located to 200.0 km away from Bob, with the relative delay to be
1.000 ms, when the fiber length is set to 200 km and the vibroseis installed
at Alice. The precision of location is better than 1 km, which is mainly
limited by the sampling rate of our phase measurement.

## Conclusion

In conclusion, we demonstrated SNS-TF-QKD over 658 km ultra-low loss optical
fiber spools experimentally, achieving a secure key rate of $9.22\times
10^{-10}$ per pulse with the finite key size effect considered. We recover 1
Hz - 1kHz vibration perturbations on the fiber with the phase reference and
the frequency locking channel, and locate the vibroseis with a precision
better than 1 km over the 500 km fiber spools. Our work provides a proof of
principle that the TF-QKD architecture is able to be used for ultra-long
distance vibration sensing, while distributing secure keys. We expect that the
developed techniques may expand the application of QKD networks, specifically
in the field of earthquake detection, landslide monitoring and highway traffic
monitoring, etc, where a distributed seismic detection is necessary.

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This work was supported by the National Key R&D Program of China (Grants No.
2017YFA0303900, 2017YFA0304000, 2020YFA0309800), the National Natural Science
Foundation of China (T2125010 ), the Chinese Academy of Sciences (CAS), Key
R&D Plan of Shandong Province (Grant No. 2019JZZY010205, 2020CXGC010105), and
Anhui Initiative in Quantum Information Technologies.

The authors declare no competing interests.

Figure 1: Schematic of experimental setup. In Alice’s (Bob’s) lab, a seed
laser is locked to a ultra-low-expansion (ULE) glass cavity to achieve sub-Hz
linewidth by using the Pound-Drever-Hall (PDH) [38, 39] technique. The ultra-
stable laser is split to two parts, one is used to calibrate the wavelength
difference between the local and remote users, and the other is used as the
QKD source. In the wavelength calibration part, the light passes an acoustic-
optic modulator (AOM) with 40 MHz (70 MHz) fixed carrier frequency in Alice
(Bob), to filter the noise in the channel. Then the light is sent to Bob
(Alice) for heterodyne detection with a photodiode (PD). An AOM with 500 MHz
$\pm$ 5 MHz adjustable carrier frequency is inserted at Bob to eliminate the
frequency difference of Alice’s and Bob’s light source. The wavelength
calibration light travels through about 500 km SMF-28 spools between Alice and
Bob. Bidirectional erbium-doped fiber amplifiers (bi-EDFAs) are inserted every
50 km to maintain the power of the transmitted light. In the QKD part, the
light is modulated with phase modulators (PMs) and intensity modulators (IMs)
and attenuate to single photon level with an attenuator (ATT), to generate the
quantum signals with the phase reference signals. The light is finally sent to
Charlie via 329.3 km and 329.4 km ultra-low loss fiber spools (658.7 km) for
detection. Charlie uses a Dense Wavelength Division Multiplexer (DWDM), a
circulator (CIR) to filter the noises before the polarization beam splitter
(PBS) and the beam splitter (BS). The interference results are detected by
superconducting nanowire single-photon detectors (SNSPDs). Additionally, the
fiber stretchers are insert in the QKD channel and the wavelength calibration
channel, as the artificial vibroseis. EPC: electric polarization controller,
PC: polarization controller.

Figure 2: Secure key rates of the SNS-TF-QKD experiment. The green star
indicates the experimental result over 658 km ULL fibers, with the secure key
rate of $R=9.22\times 10^{-10}$. The yellow diamond, purple circle and blue
triangle indicate the experimental results of ref. [4], ref. [5] and ref. [6]
in the lab. The black square indicates the experimental result of ref. [7] in
field. The red curve is the simulation result with the experimental
parameters. The brown dotted line and cyan dotted line show the absolute and
relative PLOB bound [2].

Figure 3: Vibration test results via QKD link. The program-controlled PZT is
inserted in the QKD channel which is set to a length of 658 km. The modulation
signal of program-controlled PZT is set to sinusoidal wave with selected
frequencies of 1 Hz, 10 Hz, 100 Hz, and 1 kHz, respectively. The blue curve
indicates the recovered relative phase variation signal. The gray dotted line
indicates the modulation signal of program-controlled PZT.

Figure 4: Vibration test results via frequency calibration link. The program-
controlled PZT is inserted in the frequency calibration channel which is set
to a length of 0 km, 200 km and 500 km. The corresponding modulation signal of
PZT is set to 200 Hz sinusoidal wave, direct current (DC) combined with 2 kHz
sinusoidal wave, and DC combined with 1 kHz sinusoidal wave, respectively. The
blue curve and red curve indicate the recovered phase variation signals of
Alice and Bob. The gray dotted line indicates the modulation signal of
program-controlled PZT.