higher-spin states packaged in a single higher-spin field, and finally one
with a single quantum spin. When available, we also considered several
possible classical asymptotic states. In the classical limit we found that
simple maps connect the amplitudes of the various cases and reached the
conclusion that the presence of states beyond those of a spin-$s$ particle
leads to additional Wilson coefficients. These Wilson coefficients govern
transitions between states of different spin which in turn lead to changes in
the magnitude of the classical spin vector even for conservative dynamics.
While the magnitude of the spin vector can change in theories with additional
propagating states, the magnitude of the spin tensor is conserved.

We found that these results have an interpretation in a more conventional
worldline framework and exposed it by analyzing two distinct worldline
theories. The first one corresponds to the standard construction [41, 168]
where a spin supplementary condition is imposed. The second theory relaxes
this constraint, introducing additional degrees of freedom. As for field
theories with transitions between states with different spin, the dynamics of
this theory allows for changes in the magnitude of the spin vector along
classical trajectories.

While the results of all of our field theories can be obtained as limits of
results of these two worldline theories, we did not find a worldline theory
that reproduces observables obtained from ${\cal A}^{\text{FT1s}}$ whose
asymptotic states are limited to a single quantum spin. It would be
interesting to pursue the construction of such a theory; to this end it may be
profitable to interpret ${\cal A}^{\text{FT1s}}$ as a sequence of absorption
amplitudes and match them with a worldline theory with additional non-
asymptotic states, along the lines of Ref. [176]. Another interesting
direction would be to generalize FT3, which was constructed using spin $s$ and
$(s-1)$ states, to include spin $(s-k)$ state with $k\geq 2$, in order to
describe interactions beyond the spin-orbit case.

We evaluated tree-level Compton amplitudes to provide a direct comparison
between the various field and worldline theories. We carried out this
comparison to second order in the spin tensor. Field theories restricted to
propagate only the states of a spin-$s$ particle preserve the magnitude of the
classical spin vector, and the results match those of the worldline with a
spin supplementary condition imposed, compatible with Refs. [173, 95]. In
contrast, if states of different spin propagate and transitions are allowed
between them, the field-theory Compton amplitudes contain additional Wilson
coefficients and match those of the worldline with no spin supplementary
condition. The results of the theory with propagating states of a single
spin-$s$ particle are reproduced for special values of the Wilson
coefficients; thus, for these values, the SSC condition is effectively imposed
(albeit not actively), and the spin gauge symmetry is restored. This holds
true both for the field theory where some of the additional spin states were
negative norm [76] and for the alternative construction with all positive-norm
states.

To establish a closer connection between the extra degrees of freedom present
in the various field-theory descriptions of spinning bodies and classical
observables, we constructed a pair of two-body Hamiltonians where the obtained
amplitudes match the field-theory amplitudes [76]. The first of these
Hamiltonians is the standard two-body one including the standard spin-orbit
terms. The second incorporates the mass moment as a new (boost) degree of
freedom, and is the one that can match both the field theories with
transitions between states of different spins and the worldline with no spin
supplementary condition imposed. We carried out detailed comparisons of the
impulse, and spin and mass-moment kicks through ${\mathcal{O}}(\alpha^{2}S)$
between the predictions of these two-body Hamiltonians and the corresponding
worldline approaches and found agreement to this order. It would be
interesting to generalize our field theory with two propagating fields to
contain multiple propagating fields and in this way verify the connection to
the worldline through ${\mathcal{O}}(\alpha^{2}S^{k\geq 2})$.

We also succeeded in finding a compact way to express scattering observables
via an eikonal formula. The spin eikonal formula of Ref. [76] provides a
direct connection between amplitudes and scattering observables and bypasses
explicit use of the Hamiltonian. We found a generalization of this formula,
which is valid through $\mathcal{O}(\alpha^{2}S)$, compactly contains the
intricate results of Hamilton’s equations for scattering observables and
includes extra degrees of freedom (in the form of the rest-frame boost vector)
and all Wilson coefficients. It would be interesting to extent this comparison
to higher powers of the spin and boost vectors. While this eikonal formula was
not derived from first principles, its existence strongly suggests that a
first-principles derivation should exist.

Our primary conclusion is that, whether using a four-dimensional field-theory
or a worldline description of spinning bodies, the extra Wilson coefficients
are directly associated with additional propagating degrees of freedom. These
extra coefficients induce a dynamical change in the magnitude of the rest-
frame spin vector even for conservative dynamics. This change in spin
magnitude is necessarily associated with a change in the mass moment, which in
turn induces a change in the electric dipole moment. It would be very
interesting to identify physical systems where these additional degrees of
freedom lead to observable effects whether in electrodynamics or general
relativity.

We expect that carrying out similar field theory, worldline and effective two-
body Hamiltonian constructions and comparisons for general relativity should
be straightforward. We look forward to studying the phenomena described here
in detail for the case of general relativity where they were originally
observed.

### Acknowledgments

We thank Thibault Damour, Henrik Johansson, Callum Jones, Jung-Wook Kim, Maxim
Pospelov, Francesco Serra, Mikhail Solon and Jan Steinhoff. Z. B., and T. S.
are supported by the U.S. Department of Energy (DOE) under award number DE-
SC0009937. D. K. is supported by the Swiss National Science Foundation under
grant no. 200021-205016. A. L. is supported by funds from the European Union’s
Horizon 2020 research and innovation program under the Marie Sklodowska-Curie
grant agreement No. 847523 ‘INTERACTIONS’. R. R. and F. T. are supported by
the U.S. Department of Energy (DOE) under award number DE-SC00019066. We are
also grateful to the Mani L. Bhaumik Institute for Theoretical Physics for
support.

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Vol.0 (20xx) No.0, 000–000

11institutetext: School of Science, Western Sydney University, Locked Bag
1797, Penrith, NSW 2751, Australia<EMAIL_ADDRESS>
22institutetext: Department of Electronics, Electrical Engineering and
Microelectronics, Silesian University of Technology, Akademicka 16, 44120
Gliwice, Poland 33institutetext: Instituto de Astronomía, UNAM. A.P. 877,
22800 Ensenada, BC, México 44institutetext: Astronomical Observatory, Volgina
7, 11060 Belgrade, Serbia
Received 20xx month day; accepted 20xx month day

# Photometric and Spectroscopic study of Ten Low Mass Ratio Contact Binary
Systems: Orbital Stability, O’Connell Effect and Infra-red Calcium Line
Filling.

Surjit S. Wadhwa 11 Adam Popowicz 22 Raúl Michel 33 Petar Kostić 44 Oliver
Vince 44 Nick F. H. Tothill 11 Ain Y. De Horta 11 Miroslav D. Filipović 11

###### Abstract

Low mass ratio contact binary systems are more likely to have unstable orbits
and potentially merge. In addition, such systems exhibit characteristics such
as starspots and high energy emissions (UV) suggestive of chromospheric and
magnetic activity. Light curve modelling of ten contact binary systems is
reported. All were found to be of extreme low mass ratio ranging from 0.122 to
0.24 and three were found to be potentially unstable and possible merger
candidates. Filling of the infrared Calcium absorption lines is a marker of
increased chromospheric activity. We use the available LAMOST spectra along
with matched standard spectra (broadened for rotation) to measure the excess
filling of the central core depression flux of the two main infrared Calcium
absorption lines $\lambda 8542$ and $\lambda 8662$. We find that all reported
contact binaries have excess filling of the core flux in the infrared Calcium
lines. Three of the systems reported were also observed by the GALEX mission
and we find that all three have features of excess ultraviolet emissions
further adding evidence for increased chromospheric activity in low mass ratio
contact binaries. Analysis of both orbital stability and absorption line
filling is dependent on the determination of geometric and absolute parameters
from light curve modelling. Not an insignificant number of contact binary
light curves exhibit the O’Connell effect, usually attributed to starspots. We
discuss the inclusion of starspots in light curve solutions and how they
influence the geometric and absolute parameters.

###### keywords:

binaries: eclipsing – stars: mass-loss – techniques: photometric

##  1 Introduction

Contact binaries usually comprise of a low mass (spectral class F to K)
primary with an even lower mass secondary. Both stars are distorted such that
they fill their respective Roche lobes and are surrounded by a common
envelope. The primary acts much like a main sequence star of similar mass and
there is significant transfer of energy between the components such that the
common envelope usually has temperature similar to that of the primary
component (Yildiz & Doğan 2013). The orbital period ranges from about 0.2 to 1
day with most systems having periods between 0.3 and 0.4 days (Latković et al.
2021). The orbit is thought to be circular and synchronous. High orbital and
rotation speeds combined with the common envelope geometry usually results in
significantly increased magnetic and chromospheric activity manifesting as
high energy (UV) excess and potentially starspots, flares, accretion gas
impacts or Coriolis heating (Marsh et al. 2017). In addition, such increased
magnetic activity is postulated to result in magnetic breaking and orbital
instability leading to potential merger of the components. Theoretical
considerations suggests that for low mass contact binaries, merger is most
likely at very low mass ratios (Arbutina 2007, 2009).

Most contact binary systems show some type of choromospheric and coronal
activity signals. The most common photometric phenomenon is the asymmetry in
the light curve maxima (O’Connell effect) thought to be the result of
starspots. Significant emission excesses have also been noted particularly at
shorter wavelengths (X-Ray, UV, MgII, H$\alpha$, CaII) (Mitnyan et al. 2020).
Unfortunately, optical spectral evaluation of the Magnesium, Hydrogen and
Calcium emissions requires high resolution imaging due to the presence of
other nearby emission lines. The infrared part of the spectrum is relatively
quiet and offers potential to review chromospheric spectral changes in contact
binaries with low to medium resolution spectra. Li et al. (2022); Liu et al.
(2023) have published results of potential filling of the infrared H$\alpha$
absorption line as a marker of increased chromospheric activity. In this study
we explore the utility of filling of the infrared CaII $\lambda$8542 and
$\lambda$8662 lines from the The Large Sky Area Multi-Object Fibre
Spectroscopic Telescope (LAMOST) survey spectra as a potential marker of
increased chromospheric activity in low mass ratio contact binary systems. In
addition, we briefly look at increased ultraviolet emissions as a marker for
increased chromospheric activity in three systems.

Ever since the confirmation that luminous red novae are likely the product of
contact binary merger (Tylenda et al. 2011) the topic of orbital stability of
such systems has been an active area of investigation. Theoretical
considerations have demonstrated that merger is likely to occur at very low
mass ratios however there is no global minimum mass ratio at which merger will
occur with each system having a unique instability value depending on its
Roche geometry (Wadhwa et al. 2021). Application of these theoretical
considerations has resulted in the identification of over 20 potential merger
candidates (Wadhwa et al. 2021, 2022a, 2023a). We use recently published
(Wadhwa et al. 2022b) techniques to identify ten likely extreme low mass ratio
potential merger candidates. In addition, we use the LAMOST survey medium
resolution spectra to characterise the filling of infrared CaII absorption
lines for nine of these systems. Since the initial start of the current study,
partial analysis of two systems reported in this study have been published and
we discuss our review considering the published findings.

##  2 Observations

###  2.1 Image acquisition and light curves

The basic identification details, abbreviations (used going forward) along
with comparison and check stars are summarised in Table 1. A0304, A0727,
A0748, A0806 and IT Cnc were observed with the Las Cumbres Observatory (LCO)
network of 40cm telescopes equipped with either the SBIG STL6303 camera with
resolution of 0.571 arcsec/pixel or QHY600 CMOS camera with resolution of 0.73
arcsec/pixel. Both cameras are equipped with standard photometric filters.
A0346 was observed at the Vidojevica observatory with the 60cm Telescope
Nedeljković equipped with FLI ProLine PL230 CCD camera with a resolution of
0.52 arcsec/pixel and standard filters. Some imaging of A0346 was also
performed with the LCO network. V1359 Cas, N6978 and N3650 were observed with
Silesian University of Technology Observatories (SUTO111www.suto.aei.polsl.pl)
0.3m remotely operated telescope equipped with ASI ZWO1600MM cooled CMOS
camera with resolution of 0.7 arcsec/pixel. PS Com was observed at the San
Pedro Mártir Observatory using the 84cm Ritchey-Chretien telescope equipped
with Marconi 5 CCD camera with resolution of 0.25 arcsec/pixel. All systems
were observed using standard V band filters (Bessel or Johnston).

Table 1: Name, Abbreviation (used in text), comparison star and check star identifiers for the ten contact binary systems. Name | Abbrv | Comparison Star | Check Star
---|---|---|---
NSVS 3650324 | N3650 | TYC 2790-1689-1 | 2MASS J00141483+4151308
V1359 Cas | V1359 Cas | 2MASS J02525135+6628000 | 2MASS J02530271+6631067
ASAS J030424+0611.8 | A0304 | 2MASS J03034648+0620469 | 2MASS J03040675+0608231
ASASSN-V J034633.63+410815.8 | A0346 | 2MASS J03461525+4107406 | 2MASS J03461737+4109029
NSVS 6798913 | N6798 | HD279807 | 2MASS J04255488+3658220
ASAS J072718+0837.8 | A0727 | UCAC4 494-043214 | 2MASS J07271257+0835408
ASAS J074829+1904.1 | A0748 | TYC 1370-475-1 | 2MASS J07482414+1859391
ASAS J080638+1150.4 | A0806 | 2MASS J08063654+1154126 | 2MASS J08064318+1147557
IT Cnc | IT Cnc | TYC 1359-656-1 | 2MASS J08424202+2126055
PS Com | PS Com | 2MASS J11585295+1414392 | 2MASS J11591312+1410221

Aperture photometry was performed using the AstroImage J software package
(Collins et al. 2017) with comparison and check stars as indicated in Table 1.
Comparison and check star magnitudes were adopted from the AAVSO Photometric
All-Sky Survey (Henden et al. 2015). The software package provides an estimate
of the photometric error and all observations with estimated error greater
than 0.01 magnitude were excluded. Photometric data was folded using published
ephemera from the All Sky Automated Survey - Super Novae (ASAS-SN) (Shappee et
al. 2014; Jayasinghe et al. 2018). Basic light curve characteristics are
summarised in Table 2. Only two systems, A0727 and PS Com, demonstrated the
O’Connell effect of greater than 0.01 magnitude. Given the lack of high
cadence historical observations a formal period study could not be accurately
performed on the systems.

Table 2: Light curve V band magnitudes of the ten systems observed. V1(Max) = first maximum after the primary eclipse (= phase 0.25), V2(max) = second maximum after the secondary eclipse (= phase 0.75), V(Sec) = secondary eclipse and V(Primary) = Primary Eclipse. Epoch (+2450000) and Period adopted from ASAS-SN SYSTEM | V1 (Max) | V2 (Max) | V (Sec) | V (Primary) | Epoch (HJD) | Period (d)
---|---|---|---|---|---|---
N3650 | 11.82 | 11.81 | 12.15 | 12.21 | 6454.06703 | 0.3792974
V1359 Cas | 12.12 | 12.13 | 12.37 | 12.39 | 8430.93255 | 0.3602919
A0304 | 11.59 | 11.59 | 11.94 | 11.97 | 7385.78282 | 0.2753578
A0346 | 13.37 | 13.37 | 13.70 | 13.72 | 7422.79980 | 0.3071700
N6798 | 11.37 | 11.37 | 11.67 | 11.73 | 7766.75601 | 0.3625408
A0727 | 12.12 | 12.06 | 12.47 | 12.48 | 7397.84334 | 0.315709
A0748 | 12.67 | 12.66 | 13.03 | 13.03 | 7802.88997 | 0.3055999
A0806 | 12.04 | 12.04 | 12.36 | 12.41 | 8046.85314 | 0.2974811
IT Cnc | 12.43 | 12.44 | 12.73 | 12.74 | 7036.07919 | 0.3636616
PS Com | 12.88 | 12.92 | 13.34 | 13.40 | 8117.08614 | 0.2527505

###  2.2 Mass of the primary component

Apart from high resolution spectral radial velocity observations there is no
direct way to measure the mass of the component stars in a binary system. As
the primary component acts like a main sequence star (Yildiz & Doğan 2013),
investigators have used colour or other empirical relationships such as
period-luminosity (Li et al. 2021) or period-separation (Li et al. 2022) to
estimate the mass of the primary ($M_{1}$). Release of highly accurate
distance estimates from the GAIA mission (Anders et al. 2022) affords an
opportunity to estimate absolute magnitude and mass more directly from
observations. We estimate the mass of the primary as the mean of an infrared
colour calibration, and one based on the observed absolute magnitude of the
primary ($M_{V1}$). As all systems have very low mass ratios (see below) the
apparent magnitude at phase 0.5 (mid eclipse) represents the apparent
magnitude of the primary component. As described in Wadhwa et al. (2023a) we
adjust the apparent magnitude with a distance corrected extinction and then
use the standard distance modulus and the GAIA distance to estimate the
absolute magnitude of the primary component. We use the April 2022 update
calibrations from Pecaut & Mamajek (2013) for low mass main sequence stars to
estimate the mass of the primary from the absolute magnitude estimate. The
infrared colour calibration was chosen as measurements are little influenced
by extinction and the observations by The Two Micron All SKY Survey (2MASS)
Skrutskie et al. (2006) were acquired simultaneously. We use the J-H colour
from the 2MASS survey along with the same calibration tables to estimate the
colour-based mass of the primary. We adopt the mean of the two estimates as
the mass of the primary component. The photometric error has little influence
on the estimation of absolute magnitude and does not introduce significant
error to the estimation of the mass of the primary. As all systems are
relatively close, the most distant A0806 has a distance estimate of less than
600pc, the GAIA error for the distances is quite low. Based on the GAIA
distances the estimated mass of the primary varies by no more than 0.02$\rm
M_{\sun}$ between the 16th and 85th percentiles of the distance estimate. We
report this error in this study. There are likely to be errors associated with
the calibration tables however these could not be reliably determined from the
cited reference and we have not taken these into consideration. Where
appropriate all other error estimates were propagated from this value. Primary
component mass estimates for each system are summarised along with other
absolute parameters (see below) in Table 4.

Two systems, N6798 and N3650, have been observed previously (Li et al. 2022).
The authors estimate the mass of the primary component using a period-
separation relationship. Our estimates of the mass of the primary components
are somewhat lower in both cases. We estimate the mass of the primary
component of N6798 as $0.91M_{\sun}$ against their estimate of $1.48M_{\sun}$.
We note the recently published StarHorse data for 8 spectroscopic surveys
Queiroz et al. (2023) estimates the mass of the system as between
$0.96M_{\sun}-1.02M_{\sun}$ while the GAIA DR 3 estimate is $1.01M_{\sun}$. We
have chosen to adopt our estimate for the remainder of this study. In the case
of N3650 the published estimate for the mass of the primary is $1.49M_{\sun}$
against our estimate of $1.18M_{\sun}$. As with N6798, StarHorse data for 8
spectroscopic surveys estimates the mass of N3650 as $1.18M_{\sun}$and the
GAIA DR 3 estimated mass is $1.28M_{\sun}$ and we adopt our estimate for the
remainder of this study.

##  3 Light Curve Analysis

We use the 2013 version of the Wilson-Devenney light curve modelling code (WD-
Code) and the well described and accepted mass ratio grid search method to
find the best fitting modelled light curve against the observed light curve
(Wilson 1990; Kallrath et al. 1998; Nelson 2021). The temperature of the
primary component ($T_{1}$) is usually fixed during the grid search process.
As all systems were observed with the LAMOST spectral survey we adopt the
temperature reported from the seventh data release (DR7) (Qian et al. 2020)
except in the case of V1359 Cas where no DR7 data is available, we use
published data from the eighth release (DR8) (Wang et al. 2023). As has been
clearly shown, the absolute value of $\rm T_{1}$ has little influence on the
geometric light curve solution and absolute parameter determinations are not
greatly influenced if temperature-based calibrations are not adopted when
determining them (Wadhwa et al. 2023c). As all systems are of relatively low
mass and have temperatures of less than $7000\rm K$, the bolometric albedoes
were set equal $\rm A_{1,2}=0.5$, gravity darkening coefficients were also
equal $\rm g_{1,2}=0.32$ and simple reflection treatment was applied. Limb
darkening coefficients were interpolated from van Hamme (1993).

During the grid search procedure, the temperature of the secondary component
($\rm T_{2}$), the fillout factor ($\rm f$), inclination ($\rm i$) and the
scaling luminosity factor ($\rm L_{1}$) were the adjustable parameters. The
initial mass ratio ($\rm q$) search was carried out for fixed values of $\rm
q$ from 0.05 to 1.0 in steps of 0.05. The search grid was then refined in
steps of 0.01 and 0.001 following the best fit from the previous search. In
all cases iterations were carried out until the predicted correction was less
than the reported standard deviation for all adjustable parameters. In the
final iteration the mass ratio was also made an adjustable parameter and the
reported standard deviations (one sigma) along with an adjustment for
potential random error (see below) were adopted as the error for all
parameters. In the cases of A0727 and PS Com, the two systems with significant
O’Connell effect, we chose not to adopt a solution with starspots even though
the fit was much better for reasons we explain below. The light curve
solutions for all systems are summarised in Table 3. Fitted and observed light
curves are illustrated in Figure 1.

####  3.0.1 WD-Code and Error Estimation

Although it is well known that light curve solutions of contact binary systems
with complete eclipses are highly accurate there has been some discussion with
respect to the reported errors of the geometric solution. The Monte Carlo
algorithm has been used in individual cases (Poro et al. 2024) however there
exists only one comprehensive error analysis study of contact binaries based
on the WD-Code (Liu 2021). The study by Liu (2021) simulated the process of
repeated measurements (Monte Carlo algorithm) for 48 different models of
contact binaries taking into account variable photometric accuracy, variable
timing accuracy, multiple values for the mass ratio, inclination, third light
and temperatures of the secondary. The core aim of the study was to reduce the
influence of random errors on the light curve solution. The main conclusions
of the study were that in the absence of a third light and in a setting of
complete eclipses the random errors in the solution are quite small. Higher
cadence observations do not increase accuracy of the solution. The precision
of the photometric measurement does have an influence mainly in cases where
the eclipse is not total. In this study we err on the side of caution and
report the one sigma value from the WD-Code plus the random error from the
closest model (photometric precision of 0.01 magnitude, complete eclipses and
no third light) from Liu (2021).

Figure 1: Observed and modelled light curves for the ten systems. The green light curves represent the V band and the black line represents the WD modelled curve. The orange curve represents the check star flux (vertically shifted for clarity) and the purple curve represents the residual between the observed (green) and modelled (black) curves. Both the phase 0.25 and 0.75 normalised curves are shown for the two systems exhibiting the O’Connell effect (A0727 and PS Com). The vertical axis labelled NrFlux represents the normalised flux. Table 3: Light curve solution summary for the observed systems. ($q_{inst}$) Range = instability mass ratio range. For A0727 and PS Com solutions for maximum light at phases 0.25 and 0.75 are presented along with a mean solution. Name | $T_{1}(K)$ Fixed | $T_{2}(K)$ | Incl $(^{\circ})$ | Mass Ratio ($q$) | Fillout (%) | $q_{inst}$ Range
---|---|---|---|---|---|---
N3560 | 6568 | $6411\pm 21$ | $79.3\pm 0.5$ | $0.147\pm 0.001$ | $92\pm 3$ | 0.077 - 0.087
V1359 Cas | 5944 | $5877\pm 24$ | $79.7\pm 0.6$ | $0.123\pm 0.001$ | $54\pm 5$ | 0.121 - 0.147
A0304 | 5463 | $5505\pm 34$ | $75.9\pm 0.5$ | $0.190\pm 0.002$ | $2\pm 2$ | 0.113 - 0.134
A0346 | 5877 | $5837\pm 28$ | $88.3\pm 1.3$ | $0.137\pm 0.001$ | $69\pm 5$ | 0.122 - 0.147
N6978 | 6115 | $5940\pm 18$ | $89.1\pm 0.8$ | $0.122\pm 0.001$ | $80\pm 3$ | 0.113 - 0.135
A0727 (0.25) | 5880 | $5876\pm 40$ | $79.9\pm 1.4$ | $0.181\pm 0.004$ | $33\pm 10$ | 0.099 - 0.116
A0727 (0.75) | 5880 | $5890\pm 40$ | $80.3\pm 1.8$ | $0.183\pm 0.004$ | $25\pm 10$ | 0.099 - 0.116
A0727 (Mean) | 5880 | $5883\pm 40$ | $80.1\pm 1.6$ | $0.182\pm 0.004$ | $29\pm 10$ | 0.099 - 0.116
A0748 | 6107 | $6085\pm 27$ | $76.6\pm 2.0$ | $0.178\pm 0.002$ | $25\pm 5$ | 0.091 - 0.105
A0806 | 6767 | $6737\pm 22$ | $90.00^{+0.00}_{-0.5}$ | $0.143\pm 0.001$ | $55\pm 8$ | 0.063 - 0.069
IT Cnc | 6127 | $5995\pm 30$ | $77.2\pm 0.7$ | $0.123\pm 0.002$ | $39\pm 9$ | 0.083 - 0.094
PS Com (0.25) | 5061 | $4939\pm 31$ | $86.4\pm 2.9$ | $0.242\pm 0.007$ | $38\pm 10$ | 0.136 - 0.166
PS Com (0.75) | 5061 | $4951\pm 37$ | $88.6\pm 2.1$ | $0.239\pm 0.007$ | $32\pm 9$ | 0.136 - 0.166
PS Com (Mean) | 5061 | $4945\pm 34$ | $87.5\pm 2.5$ | $0.240\pm 0.007$ | $35\pm 10$ | 0.136 - 0.166

###  3.1 O’Connell effect and the light curve solution

The light curves of contact binaries not infrequently show the two out of
eclipse maxima as unequally high. The observations were initially thought to
be related tidal distortion (Roberts 1906) or Hydrogen absorption (Mergentaler
1950). The first major study of the phenomenon was carried out by O’Connell
(1951). There is no single broadly applicable theory to explain the asymmetry
principally because the O’Connell effect is known to be highly variable. The
asymmetry may shift between the two maxima (Xu et al. 2022), the asymmetry
shifts between bands, that is the first maxima maybe brighter in one colour
band but fainter in another colour during simultaneous observations (Samec et
al. 2011), the O’Connell effect maybe transient or even reverse over very
short time frames (Wang et al. 2022; Zhou et al. 2016). Given the observed
variations in the O’Connell effect many theories have been proposed to explain
it including starspots (Wilsey & Beaky 2009), asymmetric distribution of
circumference binary matter (Liu & Yang 2003), Coriolis heating of the
photosphere (Zhou & Leung 1990) and gas stream impacts leading to an accretion
hot spot (Gu et al. 2004; Gray et al. 1995).

Incorporation of starspots in the derivation of light curve solutions is
almost ubiquitous in systems exhibiting the O’Connell effect. The popularity
of spotted solutions is most likely the result of their support with the
widely used Wilson-Devenney modelling code. A well-placed spot will lead to a
better fitting modelled light curve however if no justification is provided
for the existence of such a spot(s) than confidence in the solution is
actually reduced even if the curve fit look better. Prša (2018) in his book
strongly advocates the use of starspots only if there is definitive proof,
such as high-resolution Doppler spectroscopy, for the existence of spots.
Similarly, Drake et al. (2014) argue against starspots as the cause for the
O’Connell effect. One can understand such concerns when one examines the major
issues that exist with the uniqueness of spotted solution and the strong
correlations between geometric parameters and atmospheric spot parameters. As
shown by Maceroni & van’t Veer (1993) photometric analysis cannot distinguish
between bright and dark spots being incorporated onto each component or the
connecting neck. They find photometric solutions can vary by as much as 50% in
the mass ratio, fillout factor can change by almost 100%, temperature
difference can vary by over 200$\rm K$ and inclination can also change
substantially. Such variations are continually being reported, Hu et al.
(2022) reported essentially indistinguishable fits for four different spot
parameters. The main issue of concern is the different geometric solution each
case produced. Similarly, Sriram et al. (2016) report similar fits with
different spot parameters with different geometric parameters. Unfortunately,
the popularity of spotted solutions remains because a well fitted curve looks
aesthetically more pleasing even though as pointed out by authors including
Hall (1994); Olah et al. (1997); Anders et al. (1992) that an infinite number
of solutions may exist with equally good fits as there are infinite
combinations of number, sizes, locations, and shapes of starspots. In reality,
there cannot exist any single spotted solution and each equally well fitted
solution will have a different geometric solution (Eker 1999). The current
interest in orbital stability of contact binary systems and the theoretical
framework underpinning it requires a stable estimation of geometric parameters
and given the problem with the uniqueness of spotted solutions and the
potentially large variations in fitted geometric parameters it is difficult to
accept such solutions for further analysis. For this reason, we chose to model
the light curves of A0727 and PS Com twice firstly with maximum light at the
first maximum (phase 0.25) and secondly with the maximum light set at the
second maximum (phase 0.75). We adopted the mean of the two solutions to
derive our geometric and absolute parameters.

##  4 Absolute Parameters and Orbital Stability

Parts of the geometric light curve solution such as the mass ratio can be used
to derive the mass of the secondary component ($M_{2}$) and from the period
and Kepler’s 3rd law the separation ($A$) between the components can be
determined. The light curve solution also provides fractional radii of the
components in different orientations and the geometric mean of these
($r_{1},r_{2}$) is used to estimate the absolute radii of the components as
$(R_{1},R_{2})$ = $A\times(r_{1},r_{2})$. As noted by Wadhwa et al. (2023b),
small variations as low as 200$K$ can lead to a greater than 10% change in the
estimation of the mass of the primary and subsequent greater discrepancy in
the estimation of instability parameters. Absolute parameter estimations based
on the light curve solution geometric elements are not temperature dependent
as clearly shown by Wadhwa et al. (2023c). Additionally, black body
estimations assume a spherical configuration, components of contact binary
systems are highly distorted by the Roche geometry such that the mean radius
of both components are larger than their main sequence equivalents (Wadhwa et
al. 2022b). For these reasons we prefer the use of observational and geometric
elements from light curve solutions as a method of approximating absolute
parameters. The absolute parameters are summarised in Table 4.

Although it is well known that orbital instability is likely to occur when the
mass ratio is low, it has only recently been shown that there is no global
minimum mass ratio at which instability will ensue, instead the instability
mass ratio ($q_{inst}$) is unique for each system (Wadhwa et al. 2021). The
same study also provides two simple quadratic relations as follows:

$q_{inst}=0.1269M_{1}^{2}-0.4496M_{1}+0.4403(f=1)$ (1)

and

$q_{inst}=0.0772M_{1}^{2}-0.3003M_{1}+0.3237(f=0).$ (2)

from which we can determine the instability mass ratio range from marginal
contact (f=0) to full overcontact (f=1) depending on the mass of the primary
component. We calculate the instability mass ratio range for each system as
recorded in Table 3. We note that for three systems, A0346, V1359 Cas and
N6798, the modelled mass ratio is within the instability mass ratio range and
as such the systems would be classified as potential merger candidates. The
remainder of the systems have mass ratios greater than the maximum instability
mass ratio and therefore would be considered stable.

Table 4: Absolute parameters of the systems studied Name | $M_{1}/M_{\sun}$ | $M_{2}/M_{\sun}$ | $R_{1}/R_{\sun}$ | $R_{2}/R_{\sun}$ | $A/R_{\sun}$ | $M_{V1}$
---|---|---|---|---|---|---
N3560 | $1.18\pm 0.02$ | $0.14\pm 0.02$ | $1.42\pm 0.05$ | $0.68\pm 0.03$ | $2.43\pm 0.08$ | $3.68\pm 0.01$
V1359 Cas | $0.89\pm 0.01$ | $0.11\pm 0.01$ | $1.23\pm 0.3$ | $0.50\pm 0.02$ | $2.11\pm 0.02$ | $5.54\pm 0.02$
A0304 | $0.96\pm 0.01$ | $0.17\pm 0.02$ | $0.97\pm 0.01$ | $0.45\pm 0.01$ | $1.83\pm 0.02$ | $5.16\pm 0.01$
A0346 | $0.86\pm 0.01$ | $0.12\pm 0.01$ | $1.10\pm 0.01$ | $0.49\pm 0.02$ | $1.90\pm 0.02$ | $5.77\pm 0.02$
N6978 | $0.91\pm 0.01$ | $0.11\pm 0.01$ | $1.27\pm 0.03$ | $0.54\pm 0.02$ | $2.16\pm 0.02$ | $5.72\pm 0.02$
A0727 | $1.01\pm 0.02$ | $0.18\pm 0.02$ | $1.12\pm 0.02$ | $0.53\pm 0.02$ | $2.07\pm 0.03$ | $4.70\pm 0.02$
A0748 | $1.06\pm 0.01$ | $0.15\pm 0.01$ | $1.10\pm 0.01$ | $0.52\pm 0.01$ | $2.04\pm 0.02$ | $4.51\pm 0.01$
A0806 | $1.31\pm 0.02$ | $0.16\pm 0.02$ | $1.22\pm 0.02$ | $0.54\pm 0.02$ | $2.13\pm 0.02$ | $3.58\pm 0.02$
IT Cnc | $1.13\pm 0.01$ | $0.14\pm 0.01$ | $1.34\pm 0.02$ | $0.54\pm 0.02$ | $2.32\pm 0.02$ | $3.97\pm 0.01$
PS Com | $0.77\pm 0.01$ | $0.19\pm 0.01$ | $0.87\pm 0.01$ | $0.47\pm 0.01$ | $1.67\pm 0.02$ | $6.48\pm 0.01$

##  5 Chromospheric Activity

Loss of angular momentum is thought to be a major factor leading to orbital
instability of contact binaries and magnetic breaking is likely a significant
contributor (Li et al. 2021). Binary systems with outer convective envelopes
almost always show signatures of magnetic activity with observable features
such as starspots, spectra showing chromospheric emissions, and excess overall
emissions at shorter wavelengths. In this section we report, for the first
time, filling of the infrared Calcium absorption lines centered on
$\lambda$8542 and $\lambda$8662 in low mass ratio contact binaries. In
addition, we look at excess ultraviolet emissions in three systems observed by
the Galaxy Evolution Explorer (GALEX) mission.

###  5.1 CaII infrared filling and chromospheric activity

The infrared CaII triplet (CaII IRT) lines at $\lambda$8498, $\lambda$8542 and
$\lambda$8663 are a distinct spectral feature of cool low mass stars (Martin
et al. 2017). Analysis of CaII infrared lines (usually limited to the
$\lambda$8542 and $\lambda$8662 lines) is somewhat easier than the CaII lines
in the bluer part of the spectrum as the continuum is much better-defined
making normalization simpler (Busà et al. 2007). The CaII IRT has been used as
a diagnostic indicator of chromospheric activity for some time. Unlike the
wings of the CaII IRT which are quite extended and affected by multiple
photospheric layers and the atmospheric temperature distribution (Andretta et
al. 2005); the cores of the CaII IRT lines are due to the uppermost
atmospheric layers (chromosphere), their central depression has been shown to
be sensitive to the degree of activity and correlate well with the Mount-
Wilson $R^{{}^{\prime}}_{HK}$ activity indicator (Chmielewski 2000).

Few authors have pointed to some problems with the use of CaII IRT lines for
chromospheric diagnostics. The main concerns relate to significant dependence
of the central depth due to rotation and to a lesser extent potential
photospheric contributions (Busà et al. 2007). Both concerns can be addressed
by using the subtraction technique whereby the spectrum of a carefully
selected (matched for temperature and metallicity) comparison star is
artificially broadened to the target star rotational velocity and then
subtracted from the spectrum of the target star (Martin et al. 2017). The
result is a purely activity related excess flux without photospheric or basal
flux contributions. As noted above the wings of the CAII IRT lines are more
dependent on non chromospheric atmospheric layers and as such only the central
depth of the line cores is considered a chromospheric activity indicator. The
central depth is usually reported as the normalised amplitude relative to the
continuum (Andretta et al. 2005).

The Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) has
been conducting spectroscopic sky survey for over 10 years with regular data
releases since 2013. All systems reported in this study, except V1359 Cas,
were observed by the LAMOST survey and medium resolution spectra are available
through data release 7 (DR7). Ji et al. (2023) recently published a spectral
library based on LAMOST spectra. As part of this library, they include a
second library of over 1100 spectral templates which essentially represent
smoothed averaged spectra of similar parameters. They suggest the secondary
atlas can be used as a standard atlas for comparing LAMOST spectra. We
artificially broaden the spectrum of a standard star from the atlas with
similar parameters to the primary component of each system. We calculate the
excess flux of the central depression as a "filling" of the normalised central
flux defined as normalised flux amplitude (standard star) - normalised flux
amplitude (primary component). A value greater than zero would indicate excess
flux in the contact binary. Detailed procedure is described below.

###  5.2 CaII IRT Excess Flux

####  5.2.1 Primary Component Spectrum and Broadening of the Standard Spectrum

As noted above for all systems, except V1359 Cas, LAMOST spectra are
available. Where more than one spectrum was available, we chose the one with
the highest signal to noise ratio. The resolution of LAMOST spectra is
relatively low and our study is limited to the $\lambda$8542 and $\lambda$8662
lines. The observed spectra is usually normalised to the average of the
continuum a few angstrom on either side of the wings of the main absorption
line (Li et al. 2022). In our case we normalise to a 5Å region from 8525 -
8529Å and 8561 - 8565Å for the $\lambda$8542 line and because the
$\lambda$8662 line demonstrates slightly asymmetric wings we used 8650 - 8654Å
and 8676 - 8680Å regions. As noted, the resolution of the LAMOST spectra is
low, rather than using the mean of the flux to calculate the continuum which
could be influenced significantly by a single outlier reading over the short
continuum length, we first "smoothed" the wings and continuum of the LAMOST
spectrum while maintaining the observed absorption depth by applying a locally
estimated non-parametric regression method (LOESS) (Cleveland & Devlin 1988).
The spectra were then normalised using the WinMK24a package (Mortara 2003).

As noted above central depression filling of the infrared line core can be
achieved through subtraction of a matched standard spectrum that has been
corrected for broadening. The LAMOST survey not only provides an estimate of
the effective temperature but also the metallicity for each system. We use the
LAMOST temperature and metallicity to select the nearest match from the
standard sample atlas (grouped by temperature and metallicity) as our standard
star. In the case of A0346 the LAMOST survey does have a spectrum of the
system but does not provide an effective temperature or metallicity. In this
case we use the GAIA EDR3 estimate of for the temperature and metallicity. The
GAIA metallicity was corrected as described by Andrae et al. (2023). Contact
binary orbits are thought to be synchronous and as such it is possible to
calculate the rotation speed of the primary from the period and estimated
radius. Our estimates of the absolute radii are summarised in Table 4. The
spectrum of the standard star was then broadened by applying the estimated
rotational velocity and inclination with the recently published script
(Carvalho & Johns-Krull 2023).

####  5.2.2 Central Depression Filling

The excess flux of the CaII IRT absorption lines was calculated as the
difference between the normalised amplitude of the central depression of the
broadened standard star and the normalised amplitude of the central depression
of the contact binary as advocated by Busà et al. (2007). Given slight
variations due to radial velocity and red shift we shifted the template
spectra to keep the corresponding spectral line wavelengths consistent, as per
(Liu et al. 2023). A positive result for excess filling was confirmed when the
central depression of the broadened lines of the standard star was deeper than
that of the lines of the primary component. Calculations were carried out for
the $\lambda$8542 and $\lambda$8662 lines in all cases except V1359 Cas where
no LAMOST spectrum was available. Effects of the broadening on the filling of
the central depression of the standard star and excess filling due to
chromospheric activity are illustrated in Figure 2. Table 5 summarises the
temperature and metallicity characteristics of the contact binary systems and
the selected standard stars along with central depression filling for
$\lambda$8542 and $\lambda$8662 lines. We note that the reported metallicity
for A0806 at -1.62 is very low with estimated temperature 6767$K$. We could
not find a standard star with such low metallicity and similar temperature. We
chose the closest match with metallicity -0.55 and temperature 6751$K$.

Figure 2: Broadening and filling of infrared calcium lines. The blue line is
the un-broadened spectrum of the standard star. The orange the broadened line
(standard star) and the black line is the spectral line of the contact binary.
The top panel illustrates the $\lambda 8542$ line and the bottom panel the
$\lambda 8662$ line. The vertical axis labelled NFlux represents the
normalised flux.

As noted above observational signals of excess chromospheric activity are
common in contact binary systems. The CaII IRT lines have been shown to be
very useful in detection of increased chromospheric activity, so it is not
surprising that all our systems demonstrate some degree of filling of the
central depression in $\lambda$8542 and $\lambda$8662 lines. The extent of
filling for each line was similar with the mean ($\pm SD$) normalised flux
filling of $0.091\pm 0.036$ for the $\lambda$8542 line and $0.082\pm 0.029$
for the $\lambda$8662 line. The usual method of equivalent width assessment
for determining excess flux is not suited for the CaII IRT lines as the
broadened wings of the lines are highly dependent on denser photospheric
elements and difficult to separate from less dense upper atmospheric
(chromospheric) emissions. The line cores and in particular the central
depressions are less dependent on photospheric emissions (Andretta et al.
2005). We are not suggesting that only low mass ratio contact binaries have
excess CaII IR filling. It is possible, in fact likely, that many contact
binaries will demonstrate this feature. The finding is another marker of
increased chromospheric activity that can be looked for in the absence other
markers or as supporting evidence for enhanced chromospheric activity.

Table 5: Temperature and metallicity of the systems observed from LAMOST DR 7
with temprature and metallicity of the selected standard star. (CN) =
catalogue number from the atlas of standard star. Last two columns summarise
the normalised flux filling for each system at $\lambda 8542$ and $\lambda
8662$.
A0346∗ \- No LAMOST parameters available - GAIA parameters used Name | System | Standard Star | $\lambda 8542$ | $\lambda 8662$
---|---|---|---|---
| Temp(K) / [Fe/H] | Temp(K) / [Fe/H] (CN) | Filling | Filling
N3560 | 6568 / -0.213 | 6547 / -0.171 (526) | 0.063 | 0.053
A0304 | 5463 / -0.665 | 5454 / -0.547 (629) | 0.054 | 0.057
A0346∗ | 5877 / -0.113 | 5865 / -0.151 (583) | 0.161 | 0.095
N6978 | 6115 / -0.228 | 6109 / -0.256 (556) | 0.090 | 0.121
A0727 | 5880 / -0.06 | 5911 / -0.028 (292) | 0.068 | 0.078
A0748 | 6107 / -0.646 | 6157 / -0.631 (188) | 0.061 | 0.059
A0806 | 6767 / -1.62 | 6751 / -0.550 (505) | 0.096 | 0.072
IT Cnc | 6127 / -0.016 | 6115 / -0.079 (469) | 0.076 | 0.067
PS Com | 5061 / 0.054 | 5066 / 0.012 (713) | 0.146 | 0.140

###  5.3 Ultraviolet Emissions

Another hallmark of increased chromospheric activity is increased ultraviolet
(UV) emissions. As with assessment of the CaII IRT filling, the UV emissions
can be contaminated by photospheric emissions and only emissions from the far
UV part of the spectrum (below 1800Å) can be regarded as being mainly from
chromospheric activity (Smith & Redenbaugh 2010). Like correlation between
$R^{{}^{\prime}}_{HK}$ and central depression of CaII IRT lines, Smith &
Redenbaugh (2010) explored the relationship between $R^{{}^{\prime}}_{HK}$ and
the far ultraviolet (FUV) magnitudes from the Galaxy Evolution Explorer
(GALEX) mission. They defined a UV colour excess $\Delta(m_{FUV}-B)$ as
follows:

$(m_{FUV}-B)_{base}=6.73(B-V)+7.43,$ (3)

which defines $m_{FUV}-B$ for stars with the weakest emissions and low
activity; and

$\Delta(m_{FUV}-B)=(m_{FUV}-B)-(m_{FUV}-B)_{base}$ (4)

where $m_{FUV}$ represents the GALEX far ultraviolet magnitude.

They correlated the UV colour excess with $R^{{}^{\prime}}_{HK}$ and found
that active stars have a colour excess below -0.5 (usually below -1.0) while
inactive stars have colour excess well above -0.5.

Three of the systems presented in the current study, A0748, A0806 and N3650
were observed by the GALEX mission with measured $m_{FUV}$. We use the
published values for $B-V$ for the systems to calculate the UV colour excess
for the three system as follows -2.31, -3.61 and -2.16 respectively. All three
have a UV colour excess well below -0.5 again pointing to significant
chromospheric activity.

##  6 Summary and Concluding Remarks

Orbital stability of contact binaries has received significant attention
particularly since the confirmation that Nova Sco 2008 (=V1309 Sco), a red
nova, was in fact a merger event of a low mass ratio contact binary (Tylenda
et al. 2011). It was recognised some time ago that merger events are only
likely if the mass ratio of a contact binary system was low. For quite some
time investigators attempted to define a global minimum mass ratio at which
merger was likely. Unfortunately, systems with mass ratios smaller than the
proposed global minimum were being continually identified placing the concept
of a global mass ratio into the doubtful column. Recently Wadhwa et al. (2021)
published revised orbital stability criteria and found that there is not one
global minimum mass ratio at which merger would occur, instead each system has
its unique potential merger mass ratio dependent on the mass of the primary
component. They showed that for systems where the primary is of $0.6M_{\sun}$
the instability mass ratio is more than 0.2 while for a system where the
primary is of $1.6M_{\sun}$ the instability mass ratio is closer to 0.05.

We selected ten contact binary systems from various sky surveys whose
photometry suggested that they were likely to have low mass ratios and as such
potentially merger candidates. We undertook ground-based observations and
analysis of the light curves and confirm that all ten are indeed of low mass
ratio ranging from 0.122 - 0.24. Using the instability criteria from Wadhwa et
al. (2021) we find that three of our systems A0346, V1359 Cas and N6798 are
potentially unstable with mass ratios in the instability range.

Loss of angular momentum due to magnetic breaking is considered as a potential
mechanism leading to eventual orbital instability. Increased magnetic activity
can be suspected in the presence of increased chromospheric activity. Although
many indicators of increased chromospheric have been used, spectroscopic
excess of certain emission and absorption lines and excess emission at higher
energy (ultraviolet) have been among the most widely used. Nine of the ten
systems reported in this study had available medium resolution spectra from
the LAMOST survey. We used these along with matched standard stars to measure
the excess flux for two of the three CaII IRT lines. We chose to look at the
core of the absorption lines rather than the full width as the line wings are
more influenced by photospheric contamination. The amplitude of the core of
CaII IRT lines has been shown to be a good marker of increased chromospheric
activity and all nine of the systems reported in this study with available
spectra have significant filling of the central depression compared to matched
standard stars. The extent of central depression filling was similar for the
two lines examined. In addition to infrared spectroscopic evidence for
increased chromospheric activity we were able to look at increased ultraviolet
emissions for three systems observed with GALEX mission. All three systems
show a UV colour excess well below the level indicative of a chromospherically
active star and when combined with increased CaII IRT flux strengthen the case
for increased chromospheric activity in contact binary stars.

The main light curve feature attributed to possible increased chromospheric
activity has been the O’Connell effect and that only if one attributes the
observed asymmetry in the maxima to starspots. There exists ample evidence to
indicate that light curve solutions incorporating starspots may lead to
erroneous estimations of geometric and absolute parameters. Lack of confidence
in the light curve solution would then flow onto reduced confidence in orbital
stability and spectroscopic broadening considerations. Due to issues with the
uniqueness of the light curve solution incorporating starspots, we adopted
solutions without spots for two systems, A0727 and PS Com, which show
significant O’Connell effect. A0727 demonstrates central depression filling
somewhat less than the mean of the nine systems presented while PS Com
demonstrates greater filling than the mean filling. From the small sample
presented here all low mass ratio contact binary appear to have increased
chromospheric activity without necessarily having significant light curve
features. We agree with authors such as Prša (2018) that starspots should only
be considered as part of the light curve solution if there is significant
other evidence such as Doppler spectroscopy confirming their existence on a
particular star. Otherwise, the light curve fit may well look better however
with high risk of an erroneous overall solution.

Two of the systems presented in this study, N6798 and N3650 have previously
published light curve solutions. Li et al. (2022) analysed multi-band and TESS
photometry for both systems. For N3650 they report a mass ratio of 0.142 with
fillout 96.3% and inclination of 77.8∘ from ground-based photometry and 0.146
with fillout 99.7% and inclination 77.2∘ from TESS photometry. They report no
O’Connell effect. For N6798 they analysed ground-based and TESS photometry
from two sectors. They observed the O’Connell effect in the ground-based
observations and in one of the TESS sectors. They report a mass ratio of 0.128
with a fillout of 57.3% and inclination of 87.5∘ for a spotted solution from
ground based observations and mass ratios of 0.136, fillout 97.3% and
inclination of 85.9∘ for the TESS sector with no O’Connell effect and mass
ratio of 0.135, fillout 84.6% and inclination 87.6∘ for a spotted solution of
the TESS photometry with detectable O’Connell effect. These results again
demonstrate potential pitfalls of introducing spots with respect to the
geometric light curve solutions. For N3650 there is no significant difference
with respect to the three main geometric parameters between the ground based
and TESS photometry. In the case of N6798 there is over a 6% difference in the
mass ratio, 70% difference in the fillout and about a 2% difference in
inclination between the spotted and unspotted solutions. The difference in the
estimated mass ratio is particularly concerning as it has a very direct effect
on the determination of the absolute parameters. Our solution for N3650 with a
mass ratio of 0.147, fillout 92% and inclination 79.3∘ is in general
agreement. Our solution for N6798 with no observed O’Connell effect finds the
mass ratio lower at 0.122 with a fillout of 80% and high inclination at 89.1∘.
Clearly the system has some unusual features and ongoing observations are
warranted.

## Acknowledgements

This research has made use of the SIMBAD database, operated at CDS,
Strasbourg, France.

This work makes use of observations from the Las Cumbres Observatory global
telescope network

Authors acknowledge the assistance of Joel Balzan and Evan Crawford from
Western Sydney University in implementation of the broadening script.

OV and PK acknowledge support by the Astronomical station Vidojevica, funding
from the Ministry of Science, Technological Development and Innovation of the
Republic of Serbia (contract No. 451-03-66/2024-03/200002), by the EC through
project BELISSIMA (call FP7-REGPOT-2010-5, No. 265772).

AP was financed by Silesian University of Technology Statutory Activities
Grant No. BK-250/RAu-11/2024

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