# SU Lyn - a transient symbiotic star

Krystian Iłkiewicz,1 Joanna Mikołajewska,2 Simone Scaringi,1 François
Teyssier,3 Kiril A. Stoyanov,4 and Matteo Fratta1
1Centre for Extragalactic Astronomy, Department of Physics, University of
Durham, South Road, Durham, DH1 3LE, UK
2 Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences,
Bartycka 18, 00716 Warsaw, Poland
3Observatoire Rouen Sud, 67 rue Jacques Daviel, 76100 Rouen, France
4Institute of Astronomy and National Astronomical Observatory, Bulgarian
Academy of Sciences, Tsarigradsko Shose 72, BG-1784 Sofia, Bulgaria E-mail:
<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

SU Lyn is a binary system composed of a white dwarf and a red giant star.
Although it is known to be bright and variable at X-ray wavelengths, the
optical counterpart of the source appeared as a single red giant without
prominent emission lines. Because of the lack of optical features typical for
interacting systems, the system was classified as a hidden symbiotic star. We
present the results of optical monitoring of the system. While SU Lyn did not
show substantial photometric variability, the spectroscopic observations
revealed a complex behavior. The system showed strong emission line
variability, including P Cygni profiles, changing line emission environments,
and variable reddening. Both X-ray and optical observations indicate that the
components of SU Lyn were interacting only for a short time during the last
twelve years of monitoring. For the first time we showed that SU Lyn resembled
a classical symbiotic star when it was X-ray bright, and remained hidden
afterwards. We also discuss the current evolutionary status of the red giant,
as well as possible future evolution of the system. We suggest that SU Lyn
could be a progenitor of a classical, persistent symbiotic system.

###### keywords:

accretion, accretion discs – binaries: symbiotic – (stars:) novae, cataclysmic
variables – stars: individual: SU Lyn

††pubyear: 2020††pagerange: SU Lyn - a transient symbiotic star–A

##  1 Introduction

Symbiotic stars are interacting binaries with red giant donors. The mass
accretor is typically a white dwarf, while in some systems a neutron star is
present instead of the white dwarf. Their orbital periods range from hundreds
of days to decades (Gromadzki et al., 2009, 2013). The circumstellar material
in symbiotic stars is ionized by the mass accretor, which leads to the
production of emission lines. The main source of energy in symbiotic stars is
often the accretion itself. However, in some systems the white dwarf
experiences steady shell-burning, which is providing more radiation energy
ionizing the circumbinary material, resulting in more prominent emission
lines..

SU Lyn was discovered as a semi-regular variable star with a period of
$\sim$126 days by Kippenhahn (1955). The spectral type of the giant in SU Lyn
was first estimated to be M2 (University of Virginia, 1956). Later, the
spectral type was derived to be M6 (Grasdalen et al., 1983) and finally it was
refined to be between M5.6 and M5.9 (Mukai et al., 2016). Based on optical and
infrared magnitudes the red giant in SU Lyn was estimated to have a diameter
of $\sim$3.5 mas (Bourgés et al., 2014). No water maser emission was detected
from SU Lyn (Szymczak & Engels, 1995).

Mukai et al. (2016) identified SU Lyn with a hard X-ray source 4PBC
J0642.9+5528 detected by the Swift satellite. In addition to X-ray radiation,
Mukai et al. (2016) detected UV variability, weak Balmer, [Ne iii] and Ca ii
emission lines, and red giant optical spectrum. Based on X-ray and UV
variability, Mukai et al. (2016) classifies SU Lyn as a symbiotic star that is
not showing strong emission lines typical for this class of objects. They also
argued that SU Lyn does not show strong emission lines because it is not a
shell-burning system. The symbiotic star nature of SU Lyn was later supported
by the discovery of high-excitation emission lines in SU Lyn UV spectrum
(Kumar et al., 2021). A detailed review of SU Lyn optical properties is given
by Munari et al. (2021). Because SU Lyn would not be detected as a symbiotic
star in optical surveys Mukai et al. (2016) suggested that this system
represents a large hidden population of symbiotic stars. These stars would not
show typical symbiotic features in the optical spectrum similar to SU Lyn, and
there is no estimate of the size of their population. However, the infrared
colors of SU Lyn seem to match the symbiotic star population (Akras et al.,
2019b).

SU Lyn showed strong variability in X-ray and UV bands (Mukai et al., 2016;
Lopes de Oliveira et al., 2018; Kumar et al., 2021). Lopes de Oliveira et al.
(2018) showed that SU Lyn harbors a relatively massive (>0.7 M⊙) white dwarf.
The mass transfer rate in the system decreased by nearly 90% between 2015 and
2016 (Lopes de Oliveira et al., 2018). Moreover, Lopes de Oliveira et al.
(2018) showed that there is a strong, variable source of absorption in the
system and that the boundary layer of the white dwarf became more optically
thin with time.

Here we show results of long optical monitoring of SU Lyn, study the
evolutionary status of the red giant as well as discuss the nature of the
system. In particular, we show that SU Lyn optical spectrum resembled that of
a classical symbiotic system when the system was X-ray bright. We argue that
the SU Lyn can evolve into a classical, stable symbiotic star.

##  2 Observations

###  2.1 Photometry

We collected all of the photometry available in the literature for SU Lyn.
Archival data from the Harvard College Observatory in the photographic mpg
filter were collected from DASH (Digital Access to a Sky Century at Harvard;
Laycock et al., 2010). Optical observations in a proprietary filter were
collected from the Wide Angle Search for Planets ($WASP$) project (Butters et
al., 2010). Data in the standard optical filters were collected from the
International Gamma Ray Astrophysics Laboratory ($INTEGRAL$) Optical
Monitoring Camera (OMC; Mas-Hesse et al., 2003), All-Sky Automated Survey for
Supernovae (ASAS-SN; Shappee et al., 2014; Kochanek et al., 2017) and American
Association of Variable Star Observers (AAVSO) database. The available
photometric data ranged from years 1887 to 2021, with major gaps in 1960’s and
from years 1989 to 2006. The collected light curve of SU Lyn is presented in
Fig. 1.

Figure 1: Long-term light curve of SU Lyn. The cyan line marks the date of
SOPHIE spectrum. The red line marks the observation of Lopes de Oliveira et
al. (2018). The gray area marks the X-ray high state observed by Mukai et al.
(2016).

###  2.2 Spectroscopy

We collected spectroscopic observations from the Astronomical Ring for Access
to Spectroscopy database111https://aras-
database.github.io/database/symbiotics.html (ARAS; Teyssier 2019). The low-
resolution spectra (R$<$10000) of SU Lyn do not show any significant changes
compared to the spectra presented in the literature. Hence, we analyzed only
high-resolution spectra available in ARAS. The list of observations is
presented in Table LABEL:logspec. All the spectra were reduced by the
individual observers following standard procedures. Since the spectra from
ARAS were carried out using different instruments, we normalized all of the
spectra to the local continuum in order to avoid inconsistent
spectrophotometric calibration. As the emission lines in SU Lyn are relatively
weak they can be hidden within the red giant absorption spectrum. To improve
their visibility we subtracted from ARAS spectra a spectrum of a M5 III star
spectroscopic standard. For the spectroscopic standard spectrum we chose a
spectrum of 13 Lyr carried out by François Teyssier that was shifted to the SU
Lyn radial velocity. For the radial velocity, we used the mean radial velocity
of the red giant (Section 3.4). We did not subtract the 13 Lyr spectrum from
the region near the Na D1 line spectra region to avoid contamination coming
from Na D1 lines originating from the interstellar reddening of 13 Lyr. The
emission lines and Na D1 absorption lines are presented collectively in Fig.
2.

Figure 2: Emission lines in ARAS spectra after normalization, subtracting a
normalized spectrum of 13 Lyr as well as Na D1 absorption line for witch no
subtracting was performed (see text). All the spectra were shifted by the
system mean radial velocity. The emission line region spectra were shifted by
+1 in the flux scale for clarity. SOPHIE spectrum was not plotted. The non-
variable combination of stellar and interstellar profiles of Na D1 line is
denoted by ”S+I” and a variable circumstellar component of Na D1 line is
denoted as ”CS”.

We supplemented our observations with the archival spectrum obtained with
SOPHIE spectograph mounted on a 1.93m telescope in the Haute Provence
Observatory (Moultaka et al., 2004; Bouchy & Sophie Team, 2006). The SOPHIE
spectrum was carried out on 2012-03-12 with an exposure time of 600 s. A
spectrum of 13 Lyr was not subtracted from the SU Lyn SOPHIE spectrum because
in the SOPHIE spectrum the emission lines are significantly stronger than the
red giant absorption features (Fig. 3).

Figure 3: The SOPHIE spectrum of SU Lyn from the year 2012, when the system
was X-ray bright. The spectrum was not flux-calibrated and it is affected by
the instrumental flux modulation.

We measured spectral lines using two methods. In order to measure equivalent
widths (EWs), full-width at half maxima (FWHM) and radial velocities we fitted
Gaussian profiles. In order to measure individual pieces of lines consisting
of two components (H$\alpha$ and [O iii]) we fitted two Gaussian profiles.
This resulted in an error of the measured EWs of up to 10%, accuracy of the
FWHM of 0.1 Å, and the accuracy of the radial velocities of 3 km/s. In the
case of the total EWs of lines with two components (H$\alpha$ and [O iii]) we
measured the EWs by integrating spectral region in the $\pm$400 km/s range
after the red giant continuum was subtracted. This resulted in an accuracy of
0.1 Å. Measurements of emission lines, as well as Na D1 absorption line, are
presented in Tab LABEL:logspec.

##  3 Results

###  3.1 X-ray variability

SU Lyn was first observed in the X-ray range by the ROSAT satellite in the
1990s (1RXS J064255.9+552835; Voges et al. 1999). The optical counterpart of
this X-ray source was identified to be SU Lyn by Mukai et al. (2016). In the
Swift observations of Mukai et al. (2016) with the energy range of 15–35 keV
the system showed a high state between 14th of October 2010 and 1st of August
2012. During the high state, SU Lyn appeared to maintain a constant, high
X-ray luminosity. The remaining Swift observations out the X-ray high state
showed a constant low X-ray brightness, between the years 2005–2010 and
between the years 2012-2015.

As opposed to the Swift observations, where the system seemed to plateaued at
maximum, the data from the MAXI/GSC X-Ray Source Catalog (3MAXI; Kawamuro et
al. 2018) indicates that the system showed a more flare-like behavior (Fig.
4). The 3MAXI observations in the 4–10 keV range are consistent with the
results of Mukai et al. (2016), where the authors argued that the mass
transfer rate decreased after the X-ray high state observed by Mukai et al.
(2016). Because of the difference in the energy ranges covered by 3MAXI and
Swift the apparent differences in the light curves can be due to different
behavior of SU Lyn in these two energy ranges. This behavior could be
associated with the variable source of absorption in the system (Lopes de
Oliveira et al., 2018). However, the X-ray spectrum seems to consist of only
one component (Mukai et al., 2016; Lopes de Oliveira et al., 2018). Therefore,
it is possible that the 3MAXI observations have a higher signal to noise ratio
and the flare-like behavior reflects the real variability. This implies the
X-ray maximum occurred in the year 2011 rather than between the years 2010 and
2012. Hence, we will refer to the X-ray maximum as an X-ray flare rather than
the bright state that was used in the literature. There are no X-ray
observations carried out after 2016 that are published, therefore it is not
certain whether the X-ray luminosity continued to decrease. However, given the
spectroscopic variability (Section 3.3) it seems likely that no X-ray flare
occurred after the 2010–2012 brightening.

Figure 4: An X-ray light curve of SU Lyn in the 4–10 keV range. The red line
marks the observation of Lopes de Oliveira et al. (2018). The gray area marks
the X-ray high state observed by Mukai et al. (2016). The cyan line marks the
date of the SOPHIE spectrum.

###  3.2 Photometric variability

The historical light curve in the of SU Lyn in the mpg and $B$ filters did not
show any significant changes in the visual brightness during the last century
(Fig. 1). While there are significant gaps in the data, this suggests that
there were no nova-like or Z-And type outbursts in the recent history of the
system.

Observations just before the X-ray flare show SU Lyn at $V\simeq$ 8.5 mag
(Fig. 1). WASP observations, which were carried out with a photometric filter
relatively close to the $V$ band (Pollacco et al., 2006), suggest that there
were no major changes in the SU Lyn brightness up to a few years before the
X-ray flare. During the high state, the system faded by $\sim 0.5$ mag in the
$V$ band. Conversely, after the X-ray flare, the system experienced a
brightening by $\sim 0.5$ mag in the $V$ band. In 2014 the brightness of SU
Lyn returned to $V\simeq$ 8.5 mag. After that, SU Lyn gradually increased its
visual brightness and reached $V\simeq$ 8.0 mag between the years 2014 and
2020. Munari et al. (2021) showed that the $B-V$ color did not change
significantly during this increase in the visual brightness.

The visual variability does not follow the UV observations, where the maximum
flux was observed in 2015 (Mukai et al., 2016; Lopes de Oliveira et al., 2018;
Kumar et al., 2021). However, no UV observations exist from the time of X-ray
flare and 2015 observations are the first observations after the flare. Only
two UV observations from the years 2006 and 2007 exist from before the X-ray
flare (Kumar et al., 2021). A similar decrease in the UV component flux was
observed between 2015 and 2017 in the optical spectra of Munari et al. (2021).

The amplitude of variability in the $R$ band was significantly higher compared
to the $V$ band. SU Lyn brightness changed from $R\simeq$8.3 mag to
$R\simeq$6.9 mag (Fig. 1). The $R$ brightness from before the X-ray flare is
less precisely estimated due to the scarcity of observations. A brightness of
$R$=7.60 mag reported by (Monet et al., 2003) may suggest that variability in
the $R$ band follows the variability in the $V$ band, but with a higher
amplitude.

SU Lyn semi-regular pulsations were observed with a period of 126 days between
the years 1932 and 1938 (Kippenhahn, 1955). In the ASAS-SN $g$ data we find
semi-regular pulsations with a period of $\sim$134 days. A similar variability
was observed by Munari et al. (2021), where the authors noted that they did
not find any strict periodicity based on data covering a similar time period.
We note that our results are consistent with that of Munari et al. (2021),
since we do not claim a strict periodicity, but rather a quasi-period that is
expected to vary in semi-regular pulsators. In order to study the variability
of the pulsation period, we analyzed the historical mpg observations. We find
that the pulsations were strongest between the years 1910 and 1920 with a
period of $\sim$118 days. The pulsations seem weaker before and after that
dates, including the period observed by (Kippenhahn, 1955). However, we note
that the historical data are not of sufficient quality for conclusive results.
Interestingly, the pulsations were not present in data from the DIRBE infrared
survey (Price et al., 2010) taken between the years 1990 and 1993. This does
not imply that the pulsations were not present at this time, as similar semi-
regular pulsations are not always seen in the DIBRE data. For example, while
semiregular-pulsators UU Dra and U Del were classified as variable objects by
DIBRE, no variability was detected from semiregular-pulsators TT Peg and SV
Peg (Price et al., 2010). In summary, all the available data can suggest that
there is a possible evolution of pulsations in SU Lyn, but the results are
inconclusive.

###  3.3 Spectral variability

The first spectra of SU Lyn were carried out by Feast et al. (1972), where no
emission lines were noted. However, they did not present the spectrum itself.
Mukai et al. (2016) showed that weak emission lines were present in SU Lyn
spectrum. This was later confirmed by Kumar et al. (2021), which also showed
that there are emission lines present in the UV spectral range. Because only
weak emission lines were present in the optical spectrum of SU Lyn, Mukai et
al. (2016) suggested that SU Lyn is a hidden symbiotic star. The limitation of
the Mukai et al. (2016) hypothesis is that the only available spectra analyzed
by them were from a limited period of time. In particular, the earliest
spectrum of Mukai et al. (2016) was from the year 2016, four years after the
X-ray flare.

####  3.3.1 Balmer lines

The SOPHIE spectrum is the only spectrum available from the time near the
X-ray flare (Fig. 1). In the SOPHIE spectrum, strong Balmer lines are present,
in contrast to the spectrum presented by Mukai et al. (2016). While systematic
comparison of these lines with the entire population of known symbiotic stars
is beyond the scope of this work, a comparison with EG And shows that these
lines were as strong as at lest in some of the other symbiotic stars (Fig. 5),
while they were significantly fainter afterwards (Mukai et al., 2016).

Figure 5: Balmer lines in SU Lyn from the time of X-ray high state (2012) and
out of the X-ray high state (2020). A classical symbiotic star spectrum of EG
And is shown for comparison. The EG And spectrum was carried out by François
Teyssier on 26.01.2017 and was taken from the ARAS database. The date of EG
And spectrum was chosen to be close to the median H$\alpha$ emission strength
observed in this object by Shagatova et al. (2021). The EG And spectrum has
been shifted to fit the SU Lyn radial velocity.

Interestingly, no forbidden lines such as [O iii] are present in the SOPHIE
spectrum. The Balmer and [O iii] lines are present on all of the ARAS spectra.
Our spectral range does not cover the [Ne iii] 3868 line reported by Mukai et
al. (2016) and Kumar et al. (2021). On the first ARAS spectrum from
JD=2457513, the H$\alpha$ line has a profile typical for a symbiotic star,
with a broad emission (FWHM=2.5 Å) and a narrow absorption from the red giant.
After removing the red giant features, which remained constant throughout our
observations, the second ARAS spectrum from JD=2457775 revealed a P Cygni
profile. The absorption part of the P Cygni profile evolved with time,
changing its width, the mean radial velocity, as well as depth (Fig. 2). We
measured its evolution by fitting two Gauss functions, one for the evolving
absorption and one for the emission part of the P Cygni profile. The radial
velocity of the absorption first increased sharply towards bluer wavelengths
and then decreased the velocity gradually (Fig. 6). Similarly, the width of
the absorption first rose sharply and then decreased gradually. Both the
radial velocity and width of the P Cygni absorption reached their maxima at
JD$\simeq$2457840\. While the equivalent width of the absorption experienced
behavior similar to the other two studied parameters, its maximum was delayed
by at least $\sim$50 days (Fig. 6). The reason for the delay is unclear, but
the delay may be due to the pulsations of the red giant, which would change
the flux at the base of the line and introduce a shift in the measured
equivalent width. The last spectrum in which the P Cygni profile is visible is
from JD=2458252 and on all further spectra only the emission is present. It
seems that the P Cygni profile observed by us is associated with a ,,second
absorption component” discovered by Munari et al. (2021). However, Munari et
al. (2021) reported on the emergence of this absorption profile only at the
time of our observed absorption radial velocity maximum, while we observed a
gradual increase in the radial velocity. Moreover, Munari et al. (2021)
reported that the new absorption component merged with the red giant
absorption line, while we observed a gradual decrease in its equivalent width.

Figure 6: Evolution of an absorption component of the P Cygni profile in the
H$\alpha$ line. The magenta error bars indicate the typical error of the
measurements.

The equivalent width of all of the lines showed significant variability (Fig.
7). For the Balmer lines analysis, we restricted ourselves to analyzing the
H$\beta$ line since it did not seem to show the P Cygni profile. However, we
note that the emission component of H$\alpha$ line seemed to follow the same
variability. The Balmer lines were strongest in the SOPHIE spectrum, right
after the X-ray flare. On the next available spectra, equivalent widths of
H$\beta$ were decreasing, until they reached a minimum at JD$\simeq$2457800\.
Afterward, the equivalent width of H$\beta$ was increasing, until it reached a
local maximum at JD$\simeq$2458550\. After the local maximum, the H$\beta$
strength continued to decrease until our last observation. This result is
consistent with the observations of Munari et al. (2021), where the H$\alpha$
emission seemed to reach a local maximum in the year 2018. It seems that no
photometric variability accompanied the changes in H$\beta$ emission line. We
note, that the H$\beta$ equivalent widths showed variability on shorter
timescales than the one discussed here. However, this variability can be
attributed to pulsations of the red giant and resulting changes in the
continuum level. These changes would not be removed by subtracting the
spectrum of 13 Lyr, as both spectra of SU Lyn and 13 Lyr were normalized to
the local continuum before the subtraction.

Figure 7: Evolution of the equivalent widths of emission lines and blue-
shifted component on Na D absorption lines in SU Lyn compared to the
photometric variability in the $V$ band. All emission lines were measured
after subtraction of a reference spectrum of 13 Lyr. The measurements of [O
iii] emission line equivalent width included simultaneous measurement of the
two line components. The magenta error bars indicate the typical error of the
measurements.

####  3.3.2 [O iii] 5007 line

The integrated [O iii] emission line flux showed variability similar to the
H$\beta$ line (Fig. 7). However, upon closer inspection it is clear that
sometimes the [O iii] emission consist of two components (Fig. 2). The blue
component was stronger and was located at -12 km/s relative to the red giant
radial velocity. The red component of the [O iii] emission was located at +39
km/s relative to the red giant radial velocity. This stands in contrast to the
H$\beta$ emission, which seemed to be red-shifted on average, but remained
consistent with the red giant radial velocity within our error of 3 km/s. Both
the components seemed to follow the variability of the H$\beta$ line strength
(Fig. 8). The red component was not detected in our last observations. Both
components line widths seemed correlated with the line strengths (Fig. 9).
However, the blue component of [O iii] line seemed to be narrower than during
the rise of the line strength than during the decrease in the line strength.
The opposite might be true for the red component, but the data accuracy for
this component of the [O iii] line is too low for a conclusive result.

Figure 8: Variability of the blue and red components of the [O iii] emission
line. Figure 9: Relation between the line width and line strength of two [O
iii] emission line components – the blue component (left panel) and red
component (right panel).

####  3.3.3 Na D lines

In the SU Lyn spectra Na D absorption lines are present at the red giant
radial velocity. These lines are expected for the spectral type of the red
giant in SU Lyn and are also present in the spectrum of 13 Lyr. Moreover, the
stellar Na D lines are blended with an interstellar component detected at -4.1
km/s by Mukai et al. (2016). However, an additional blue-shifted component of
the Na D lines is present at the radial velocity of -88 km/s (Fig. 2). While
the Na D lines connected to the red giant remained constant, the blue-shifted
absorption showed strong variability. Namely, the blue-shifted Na D absorption
showed a maximum at JD$\simeq$2457800, when the emission lines showed a
minimum (Fig. 7). After that date, the blue-shifted Na D absorption was
decreasing independently from the variability of emission lines. The exception
was a local maximum of the blue-shifted absorption at JD$\simeq$2459112, where
it seemed that the [O iii] emission experienced a local minimum (Fig. 2)

The changing equivalent width of the blue-shifted Na D absorption can be
connected to a changing circumstellar component of extinction. This is
consistent with the observed changing column density towards the white dwarf
observed by Lopes de Oliveira et al. (2018). The equivalent width of Na D1
line can be used to calculate the change in reddening (Munari & Zwitter,
1997). The minimum Na D1 equivalent width measured at JD=2456000 corresponds
to circumstellar extinction of E($B-V$)=0.01 mag. Afterward, the change in
reddening is following the changes in equivalent widths of Na D lines, with
the maximum circumstellar extinction at E($B-V$)=0.18 mag at JD=2457841. The
circumstellar extinction reached a significantly larger value than the
constant interstellar extinction E($B-V$)=0.07 mag estimated by Mukai et al.
(2016) on JD=2457409 We note that the [K i] 7699 line that should behave
similarly to Na D lines was outside the spectral range of our spectra.

###  3.4 Red giant radial velocity

We searched for possible changes in the red giant radial velocity using cross-
correlation of SU Lyn spectra with 13 Lyr spectrum. We did not find any
significant variability within our accuracy of 3 km/s. This is consistent with
the reported limit on radial velocity variability of $<2$ km/s reported by
Munari et al. (2021). The mean red giant radial velocity in our spectra was
-22 km/s.

###  3.5 The red giant evolution status

Mukai et al. (2016) estimated a distance to SU Lyn of 640$\pm$100 pc. A
similar distance of 659${}^{+46}_{-40}$ pc was obtained using Gaia DR2 data
(Bailer-Jones et al., 2018) and a distance of 710${}^{+31}_{-35}$ pc using
Gaia DR3 data (Bailer-Jones et al., 2021). The effective temperature of the RG
estimated in Gaia DR2 was $T_{\mathrm{eff,RG}}$=3544${}^{+249}_{-256}$ K,
while the luminosity $L_{\mathrm{RG}}$=2261$\pm$176 L⊙ (Gaia Collaboration et
al., 2018). No red giant parameters were estimated in Gaia DR3 (Gaia
Collaboration et al., 2021). We note that the distance and luminosity
estimated by Gaia may be unreliable since currently the Gaia archive does not
account for the astrometric motion due to the binary nature of the system
(e.g. Blind et al., 2011). The red giant temperature of
$T_{\mathrm{eff,RG}}\simeq$3565 K was estimated by Akras et al. (2019a). We
estimated the effective temperature and luminosity of the RG by fitting models
to the spectral energy distribution (SED) using the VO Sed Analyzer (VOSA;
Bayo et al., 2008).

For the SED fit we used data from TYCHO-2 (Høg et al., 2000), Pan-STARRS
(Flewelling et al., 2016), 2MASS (Skrutskie et al., 2006), AKARI/IRC (Ishihara
et al., 2010), IRAS PSC/FSC (Abrahamyan et al., 2015) and unWISE (Schlafly et
al., 2019) surveys. In order to avoid contamination from the white dwarf and
any dust emission we limited the fit only to data ranging from 420 to 52000
nm. Since all of the employed observations were obtained before the X-ray
flare and the changes in the circumstellar reddening, we limited the reddening
correction to only the interstellar component equal to E($B-V$)=0.07 mag
(Mukai et al., 2016). We also assumed the distance of 710${}^{+31}_{-35}$ pc
(Bailer-Jones et al., 2021).

As a result of the SED fit, we obtained Teff,RG=3200$\pm$100 K and
LRG=7700$\pm$1000 L⊙. The estimated luminosity was higher than the one
observed by Gaia, while the effective temperature was lower. We note that our
estimate of the red giant effective temperature is consistent with the M5
spectral type derived by Mukai et al. (2016), while the Gaia effective
temperature is too high for this spectral type. Hence, the parameters
estimated using VOSA are more consistent. In order to estimate the
evolutionary status of the RG, we compared the red giant parameters to the
MESA Isochrones and Stellar Tracks (MIST; Dotter 2016, Choi et al. 2016).
Using Teff,RG and LRG from Gaia and VOSA we identify the donor in SU Lyn as a
relatively young thermally pulsating RG (Fig. 10). Using the parameters
derived with VOSA we estimate log(Age/yr)=8.70${}^{+0.36}_{-0.23}$ and
MRG=2.78${}^{+0.62}_{-0.64}$ M⊙. The RG stellar parameters are summarized in
Table 1. If the red giant in SU Lyn experienced a thermal pulse in recent
history, this can be associated with changes in the pulsation period, which
would be consistent with discussion in Section 3.2. Changes in the observed
pulsation period due to a thermal pulse were e.g. observed in another
semiregularly pulsating star RU Vul (Uttenthaler et al., 2016).

Figure 10: The stellar parameters of RG in SU Lyn (Table 1; red cross) compared to single star evolution models from MIST. The tracks have been computed using zero-age main sequence masses in the range of 0.5-8 M⊙ with a step of 0.05 M⊙. The evolutionary track best fitting VOSA estimates is highlighted with a gray line. Table 1:  Summary of the derived stellar parameters of the RG in SU Lyn.  Teff,RG [K] | LRG [L⊙] | MRG [M⊙] | RRG [R⊙] | log(Age/yr)
---|---|---|---|---
3200$\pm$100 | 7700$\pm$1000 | 2.78${}^{+0.62}_{-0.64}$ | 280$\pm$40 | 8.70${}^{+0.36}_{-0.23}$

The red giant 2MASS magnitudes $J$=2.979 and $K$=1.618 mag translate to a
Weisenheit index equal to $W_{JK}$=0.684 mag. Scaling this index to the Large
Magellanic Cloud distance of 49.59 kpc (Pietrzyński et al., 2019) we obtain
$W_{JK}^{\mathrm{LMC}}$=10.15 mag. Together with the pulsation period of
$\mathrm{P}_{\mathrm{pul}}$=126 days, this indicates that the red giant in SU
Lyn belongs to a C’ sequence (Wood, 2015). Using our VOSA analysis we
estimated the red giant radius to be RRG=280$\pm$40 R⊙. This gives a pulsation
constant
$Q=\mathrm{P}_{\mathrm{pul}}(\mathrm{M}_{\mathrm{RG}}/\mathrm{M}_{\odot})^{1/2}(\mathrm{R}_{\mathrm{RG}}/\mathrm{R}_{\odot})^{-3/2}\simeq$0.044
days. This pulsation constant is consistent with pulsations in the first
overtone (e.g. Fox & Wood, 1982).

##  4 Discussion

SU Lyn shows a very complex behaviour. In particular, optical emission line
changes correlated with photometric and X-ray variability. Whereas it might
not be easy to identify mechanism(s) behind the variability, it is clear that
not only the X-ray emission showed a transient brightening, but also the
optical appearance of the system was transient in nature.

###  4.1 Nature of variability

SU Lyn is the first object of its kind ever observed (Mukai et al., 2016).
Because of this, a comparison to variability of other binary systems is not
trivial. However, we would like to propose a few directions which future
studies could explore. While not much is known about the system orbital
parameters, the only certain thing is that the system consists of a white
dwarf and a red giant (Mukai et al., 2016; Lopes de Oliveira et al., 2018;
Kumar et al., 2021). Therefore, all proposed scenarios will include both
binary components. Moreover, SU Lyn was observed as an X-ray emitting object
before the X-ray flare (Mukai et al., 2016), therefore a possibility of
recurring or periodic X-ray flashes will be explored.

The simplest scenario involves a highly eccentric orbit. During a periastron
passage, the tidal forces would lead to an enhanced mass loss from the red
giant, allowing for an increased mass transfer rate. This scenario could be
confirmed if the discussed SU Lyn behaviour would be repeatable. However, the
orbital period of SU Lyn is unknown and the object should be monitored
continuously for at least two additional cycles to confirm this hypothesis. A
similar, quasi-periodic enhanced mass transfer rate near a periastron passage
was observed in a symbiotic stars BX Mon (Anupama et al., 2012; Gromadzki et
al., 2013), CD-43 14304 (Gromadzki et al., 2013), and GX 1+4 (Iłkiewicz et
al., 2017).

The mechanism triggering the variability could be related to a potential He-
shell flash of the red giant. Such a flash could be related to a mass ejection
event (e.g. Mattsson et al., 2007), which would lead to a temporary increase
in the mass accretion rate by the white dwarf. Furthermore, it is possible
that the white dwarf would then heat up and be able to ionize the material
close to the red giant, potentially ionizing the wind acceleration zones and
decreasing the radiation pressure. The material would build up in these wind
acceleration zones until it would cool and the radiation pressure could build
up again, ejecting a shell of matter. When this shell would encounter the
white dwarf, it would be partially accreted. This cycle of heating material in
the wind acceleration would then repeat, leading to the observed variability
of SU Lyn.

Independently from the mechanism triggering the variability, the variability
is associated with a strong mass loss from the system. This is demonstrated by
the detection of a transient P Cygni profile and appearance of Na D lines at a
high blue-shift. Mass loss in symbiotic stars can lead to a binary-induced
spiral structure around the binary (e.g. Mohamed & Podsiadlowski, 2012; Booth
et al., 2016). Presence of such a spiral could explain the variability of the
[O iii] 5007 line (Section 3.3.2). Namely, the presence of a blue and red
components of [O iii] line could originate in two opposite spiral arms. The
apparent increase of width of the blue component of the [O iii] line could be
explained if a new, closer loop of the spiral formed later in time. This more
distant loop would have a lower radial velocity due to interaction with the
interstellar material. However, the difference would not be larger and both
blue components would blend in our observations, resulting in a single, wider
line. A similar structure is present in a nearby symbiotic star, R Aqr, where
the spiral structure was formed due to a highly eccentric orbit (Bujarrabal et
al., 2021). The circumstellar material present in R Aqr shows radial velocity
amplitude of $\sim$10 km/s (Bujarrabal et al., 2021), which is of the same
order of magnitude as the observed radial velocities of the blue and red
components of the [O iii] line in SU Lyn. The caveat is that the spiral
structure in R Aqr consists of dusty molecular dust, while the material around
SU Lyn is ionized. This difference could be due to the fact that the structure
around SU Lyn is newly formed and transient in nature, implying shocks in the
outer region of the forming spiral ionizing the inner parts of the loop.
Alternatively, the white dwarf in SU Lyn could be more efficient in ionizing
the material in the spiral structure.

###  4.2 SU Lyn as a transient symbiotic star

Symbiotic stars are defined as interacting binaries with a red giant donor and
a compact companion. An observational manifestation of this interaction is the
presence of emission lines in the optical part of the spectrum. Because no
strong emission lines were present in the optical part of the SU Lyn spectrum
and there was evidence of high mass transfer rate during the X-ray flare,
Mukai et al. (2016) argued that SU Lyn is a hidden symbiotic star. This is
because a high mass accretion rate indicates interaction between the red giant
and the white dwarf, making the system an interacting binary system – a
symbiotic star. However, we showed that when the mass transfer rate was high,
the optical emission lines were as strong as at least in some other classical
symbiotic stars (Fig. 5). Therefore, when the system was interacting, the
spectrum of SU Lyn was that of a typical symbiotic star, and the nature of the
system was not ”hidden” in the optical spectra.

The problem with the classification of SU Lyn as a symbiotic star is due to
the intensity of the binary interaction. The mass accretion rate changed from
$\sim$1.0$\times$10-8 M⊙ yr-1 during the X-ray flare (Mukai et al., 2016) to
1.5–2.2$\times$10-10 M⊙ yr-1 when system was X-ray faint (Lopes de Oliveira et
al., 2018). The mass accretion rate outside of the X-ray flare is smaller than
the mass accretion rate of $\sim$10-9 M⊙ yr-1 that is the minimum mass
accretion rate typical for a symbiotic star (Kenyon & Webbink, 1984).

The population of symbiotic stars is studied assuming that as a result of
interaction between the system components the mass accretion rate is high
enough to power the production of emission lines. In theoretical studies, this
is quantified by assuming that the accretion powered luminosity is higher than
at least 10 $L_{\odot}$ (e.g. Mikolajewska & Kenyon, 1992; Lü et al., 2006;
Belloni et al., 2020). The white dwarf mass in SU Lyn was estimated to be in
the range of 0.69–0.92 M⊙ (Lopes de Oliveira et al., 2018). Using a white
dwarf radius calculated with eq. 15 of Verbunt & Rappaport (1988) the
accretion power luminosity of the white dwarf changed from 18–33 L⊙ during the
X-ray flare to <0.5 L⊙ during Lopes de Oliveira et al. (2018) observations.
Therefore, the accretion powered luminosity was high enough to be classified
as a symbiotic star during the X-ray flare and not high enough after the
flare. Again, this is confirmed by the presence of emission lines with
strengths typical for a symbiotic star during the X-ray flare and their
absence afterward (Fig. 5).

In conclusion, all metrics used to classify a system as a symbiotic star – the
presence of emission lines, mass accretion rate, and accretion powered
luminosity – point at that SU Lyn could be classified as a symbiotic star only
during a short period. Therefore, SU Lyn can transition between being a hidden
and a classical symbiotic star. Mukai et al. (2016) argued that the known
population of symbiotic stars is biased in favor of shell-burning systems and
SU Lyn is a hidden accretion powered system. This could be interpreted as that
SU Lyn would be a classical symbiotic star if there was shell-burning present
in the system. However, the presence of shell burning requires mass accretion
rate between $\sim$10-7 and $\sim$$10^{-8}$ M⊙ yr-1 depending on the white
dwarf mass (e.g. Nomoto et al., 2007). Therefore, SU Lyn could never be a
shell-burning system due to the low mass transfer rate – the system is not
interacting strongly enough. However, if the white dwarf is not a newly formed
remnant after the asymptotic giant branch phase of evelution, the nuclear-
burning shell must be ignited. Therefore, all symbiotic stars were first
accreting only symbiotic stars, and experience at least one thermonuclear nova
eruption. A similar transition was recently observed in a symbiotic star AG
Peg (e.g. Ramsay et al., 2016; Tomov et al., 2016; Skopal et al., 2017).
Hence, whether or not the SySt can sustain the shell-burning after ignition
depends mainly on how strong the system components are interacting.

Another object that showed variability similar to SU Lyn is DASCH
J075731.1+201735. This object showed a Z And type outburst in the 1940s,
classifying it as a shell-burning symbiotic star at that time. However, it now
appears as a non-interacting binary with a red giant and possibly a white
dwarf (Tang et al., 2012). More similar, transient objects could be present in
the known population of variable stars, but no systematic search for them has
been performed thus far.

Inspired by the suggestion that SU Lyn represent a potentially large sample of
hidden symbiotic stars, Munari et al. (2021) searched for new candidates for
symbiotic stars with weak emission lines and found 33 candidates. We note that
some of the stars found by Munari et al. (2021) have accretion luminosity
lower than 10 $L_{\odot}$. Such systems should be clearly distinguished from
the classical symbiotic stars to avoid confusion in theoretical population
studies, for the reasons given above. However, they represent a potentially
interesting new population of systems, as was noted by Mukai et al. (2016). We
note that the systems discovered by Munari et al. (2021) are not necessarily
similar to SU Lyn, as we showed that interaction in SU Lyn was transient, and
there is no proof of transient interaction in Munari et al. (2021) systems,
with the exception of GaSS 1-31. Moreover, Munari et al. (2021) stated that
”the results of this paper are independent on the actual nature of the
accreting star”, which means that at least some of their systems could host a
main-seaquence accretor.

###  4.3 SU Lyn as a progenitor of a classical symbiotic star

We note that SU Lyn may evolve towards a stable, typical symbiotic star. The
mass loss of the red giant can increase significantly during the last stages
of its evolution, which could result in an increased mass accretion of the red
giant wind by the white dwarf on a long timescale. This could result in a mass
transfer rate high enough to reach the lower limit of the accretion powered
luminosity, making the system a persistent symbiotic star. However, in order
to predict the future evolution of SU Lyn orbital parameters need to be known,
to predict the mass transfer mode (e.g. Iłkiewicz et al., 2019). We studied
the future mass loss of the RG using the single star evolution models fitted
to the VOSA RG parameters (Fig. 10). We found that in all of the models the
red giant mass loss will increase by at least an order of magnitude. Assuming
that the mass transfer rate would scale linearly with the mass loss from the
red giant, this would imply that the mass transfer rate will increase from the
current mass transfer rate of 10-10 M⊙ yr-1 (Lopes de Oliveira et al., 2018)
to mass transfer rate sufficient to make this system a classical symbiotic
star. If the increase in mass loss would be due to a He-flash, the evolution
of SU Lyn could be relatively fast (e.g. Mattsson et al., 2007; Dotter, 2016).
The fast timescale of increase in the mass accretion rate would be similar to
the evolution of CH Cyg, which did not resemble a symbiotic star until
$\sim$1960s since at least 1885 (e.g. Mikolajewski et al., 1990, and
references therein). Moreover, changes in the pulsation period of CH Cyg red
giant were attributed to a recent He-flash (Mikolajewski et al., 1992).
However, no direct link between the He-flash in CH Cyg and the change in its
spectroscopic appearance was made thus far, hindering a direct comparison to
SU Lyn. We predict that sufficient increase in the mass transfer rate in SU
Lyn could happen anytime between the next 102–105 years, therefore it is
unlikely that it will be observed in the near future. Nonetheless, SU Lyn
could serve as an useful case study of symbiotic star progenitors.

##  5 Conclusions

SU Lyn showed a period of high X-ray luminosity and strong UV variability,
which lead Mukai et al. (2016) to classify this system as a symbiotic star.
However, due to lack of strong emission lines Mukai et al. (2016) classified
SU Lyn as a member of a new class of hidden symbiotic stars. We showed that at
the time of high X-ray luminosity the Balmer lines were as strong as in the
case of classical symbiotic stars. Combined with the variable mass transfer
rate it is clear that SU Lyn can transition between being hidden and a
classical symbiotic star.

We presented optical monitoring of SU Lyn, which revealed a strong variability
in the emission lines and a weak photometric variability. The Balmer and [O
iii] lines showed strong variability that appeared to not be accompanied by
any photometric variability. Among the strongest spectroscopic features was
the appearance of a transient P Cygni profile in the H$\alpha$ line. The [O
iii] 5007 line showed two variable components that followed the variability of
Balmer lines. In the most recent spectra, a variable, blue-shifted absorption
component of the Na D lines is present, suggesting a strong variability in the
circumstellar reddening. This is consistent with a variable source of
absorption observed in the X-ray range by Lopes de Oliveira et al. (2018).

We estimated the RG effective temperature to be 3200$\pm$100 K and its
luminosity to be 7700$\pm$1000 L⊙. A comparison of the RG stellar parameters
to the single star evolution models revealed that the RG is a low mass star
(2.78${}^{+0.62}_{-0.64}$ M⊙) relatively early in the thermally-pulsating
stage of evolution. The single star evolution models show that the RG mass
loss will increase by at least an order of magnitude in the future, which
suggests that SU Lyn will evolve towards a persistent symbiotic star.

We note that one of the main challenges with any interpretation of SU Lyn
variability is understanding whether all of the observed optical variability
is associate with the X-ray flare. While it is likely that the Balmer lines
were related to the X-ray flare (Fig. 5), the variability observed in the most
recent years could occur independently from the 2010–2012 X-ray event.
Therefore, future monitoring and detection of possible subsequent X-ray
variability will reveal the nature of the system.

## Acknowledgements

We are grateful to all the observers that made their observations available
for this research. In particular, we are grateful to Paolo Berardi (BER),
Christophe Boussin (CBO), Sean Curry (CUR), David Boyd (DBO), Forrest Sims
(FAS), Franck Boubault (FBO), Francisco Campos (FCA), Martineau Buchet
(GMAYBU), Ibrahima Diarrasouba (IBR), John P. Coffins (JCO), Joan Guarro Flo
(JGF), Jacques Michelet (JMI), Jacques Montier (JMO), Jim Edlin (JPE), Jean-
Paul Godard (JPG), Jean-Pierre Masviel (JPM), Jean-Philippe Nougayrede (JPN),
James R. Foster (JRF), Kevin Gurney (KGU), Keith Shank (KSH), Tim Lester
(LES), Michel Verlinden (MER), Olivier Garde (OGA), Pavol A. Dubovský (PAD),
Paolo Cazzato (PCA), Stéphane Charbonnel (SCH), Umberto Sollecchia (SOL) and
Tony Rodda (TRO) for their excellent spectroscopic observations. We
acknowledge with thanks the variable star observations from the AAVSO
International Database contributed by observers worldwide and used in this
research.

This work was supported by STFC [ST/T000244/1]. This research has been funded
by the National Science Centre, Poland, through grant OPUS No.
2017/27/B/ST9/01940 and through grant K$\Pi$-06-H28/2 08.12.2018 "Binary stars
with compact object" (Bulgarian National Science Fund).

Based on data retrieved from the SOPHIE archive at Observatoire de Haute-
Provence (OHP), available at atlas.obs-hp.fr/SOPHIE. This publication makes
use of VOSA, developed under the Spanish Virtual Observatory project supported
by the Spanish MINECO through grant AyA2017-84089. VOSA has been partially
updated by using funding from the European Union’s Horizon 2020 Research and
Innovation Programme, under Grant Agreement nº 776403 (EXOPLANETS-A). This
paper makes use of data from the first public release of the WASP data
(Butters et al. 2010) as provided by the WASP consortium and services at the
NASA Exoplanet Archive, which is operated by the California Institute of
Technology, under contract with the National Aeronautics and Space
Administration under the Exoplanet Exploration Program. This work has made use
of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. The DASCH project at Harvard
is grateful for partial support from NSF grants AST-0407380, AST-0909073, and
AST-1313370.

## DATA AVAILABILITY

The data underlying this article is publicly available. The derived data
generated in this work will be shared on a reasonable request to the
corresponding author.

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##  Appendix A Log of spectroscopic observations

Table 2:  List of spectroscopic observations, equivalent widths of emission lines and equivalent widths of the circumbinary absorption component of the Na D lines. The list of ARAS observers and the site names can be found at the ARAS website (https://aras-database.github.io/database/symbiotics.html).  JD-2450000 | Observer | Site | EW(H$\alpha$) [Å] | EW(H$\beta$) [Å] | EW([O iii] 5007) [Å] | EW(Na D1) [Å] | EW(Na D2) [Å]
---|---|---|---|---|---|---|---
5999.30 |  | Sophie | 6.4 | 4.0 |  | 0.03 | 0.09
7513.39 | FTE | ROU-FR | 2.3 | 2.7 | 1.4 | 0.22 | 0.30
7775.28 | FTE | ROU-FR | 1.0 | 1.1 | 0.4 | 0.29 | 0.44
7801.30 | FTE | ROU-FR | 0.7 | 1.1 | 0.2 | 0.32 | 0.48
7840.35 | FTE | ROU-FR | 1.3 | 1.1 | 0.4 | 0.35 | 0.51
7841.43 | OGA | OTO-FR | 1.2 | 0.9 | 0.5 | 0.40 | 0.52
7842.33 | JGF | PIE-SP | 1.1 | 1.1 | 0.7 | 0.39 | 0.53
7846.34 | FTE | ROU-FR | 1.4 | 1.3 | 0.6 | 0.36 | 0.54
7847.46 | JGF | PIE-SP | 1.9 | 1.6 | 0.8 | 0.37 | 0.53
7850.44 | JGF | PIE-SP | 1.8 | 1.6 | 0.8 | 0.35 | 0.48
7856.43 | JGF | PIE-SP | 1.7 | 1.6 | 0.7 | 0.33 | 0.49
7864.35 | OGA | OTO-FR | 1.9 | 1.5 | 1.0 | 0.36 | 0.49
7864.38 | FTE | ROU-FR | 2.0 | 1.6 | 0.9 | 0.36 | 0.49
7883.36 | OGA | OTO-FR | 1.7 | 1.3 | 0.9 | 0.35 | 0.51
7884.37 | FTE | ROU-FR | 1.3 | 1.3 | 0.6 | 0.37 | 0.51
8029.67 | FTE | ROU-FR | 1.2 | 1.2 | 1.0 | 0.35 | 0.50
8058.70 | FTE | ROU-FR | 1.3 | 1.5 | 1.1 | 0.33 | 0.51
8061.71 | LES | MRO-CA | 1.3 | 1.3 | 1.0 | 0.30 | 0.46
8130.45 | JGF | PIE-SP | 1.3 | 1.7 | 1.4 | 0.33 | 0.46
8140.36 | JGF | SMM-SP | 1.2 | 1.6 | 1.4 | 0.28 | 0.48
8141.47 | JGF | SMM-SP | 1.1 | 1.7 | 1.5 | 0.31 | 0.44
8142.38 | OGA | OTO-FR | 1.1 | 1.6 | 1.4 | 0.30 | 0.49
8142.47 | JGF | PIE-SP | 1.2 | 1.7 | 1.2 | 0.34 | 0.49
8152.48 | JGF | PIE-SP | 1.3 | 1.8 | 1.6 | 0.33 | 0.48
8154.32 | FTE | ROU-FR | 1.6 | 1.9 | 1.9 | 0.32 | 0.49
8157.43 | JGF | PIE-SP | 1.7 | 2.0 | 1.9 | 0.32 | 0.44
8162.34 | OGA | OTO-FR | 1.3 | 1.9 | 1.7 | 0.29 | 0.43
8164.58 | LES | MRO-CA | 1.2 | 1.5 | 1.4 | 0.33 | 0.42
8173.29 | FTE | ROU-FR | 1.8 | 2.0 | 1.6 | 0.33 | 0.43
8174.47 | JGF | SMM-SP | 1.3 | 1.6 | 1.1 | 0.34 | 0.44
8186.34 | FTE | ROU-FR | 1.5 | 1.7 | 1.7 | 0.30 | 0.43
8198.33 | FTE | ROU-FR | 0.9 | 1.2 | 1.2 | 0.31 | 0.44
8198.43 | JGF | SMM-SP | 1.0 | 0.8 | 1.0 | 0.32 | 0.45
8229.59 | LES | MRO-CA | 1.2 | 1.2 | 1.9 | 0.31 | 0.44
8251.60 | LES | MRO-CA | 1.1 | 1.4 | 1.8 | 0.30 | 0.43
8510.41 | JGF | SMM-SP | 1.1 | 1.6 | 1.4 | 0.28 | 0.40
8518.31 | FTE | ROU-FR | 0.8 | 1.6 | 1.0 | 0.26 | 0.41
8524.49 | JGF | SMM-SP | 1.4 | 1.8 | 1.9 | 0.25 | 0.41
8528.30 | FTE | ROU-FR | 1.5 | 1.8 | 2.2 | 0.27 | 0.40
8531.44 | JGF | SMM-SP | 1.2 | 1.9 | 1.9 | 0.26 | 0.38
8540.35 | FTE | ROU-FR | 1.3 | 2.0 | 2.3 | 0.27 | 0.42
8545.42 | JGF | SMM-SP | 1.3 | 2.1 | 2.1 | 0.26 | 0.38
8550.31 | FTE | ROU-FR | 1.5 | 2.1 | 2.1 | 0.25 | 0.39
8551.67 | LES | MRO-CA | 1.3 | 2.0 | 1.9 | 0.27 | 0.38
8553.34 | JGF | SMM-SP | 1.4 | 2.1 | 1.9 | 0.24 | 0.38
8563.32 | OGA | OTO-FR | 1.1 | 1.7 | 1.4 | 0.25 | 0.39
8566.56 | LES | MRO-CA | 0.9 | 1.4 | 1.4 | 0.27 | 0.39
8568.36 | JGF | PIE-SP | 0.9 | 1.5 | 1.4 | 0.25 | 0.38
8574.36 | SCH | DUR-FR | 1.0 | 1.5 | 1.4 | 0.24 | 0.39
8585.37 | SCH | DUR-FR | 0.8 | 1.2 | 0.9 | 0.26 | 0.38
8587.45 | JGF | SMM-SP | 1.0 | 1.4 | 1.2 | 0.25 | 0.38
8594.38 | SCH | DUR-FR | 1.1 | 1.4 | 1.3 | 0.20 | 0.39
8595.58 | LES | MRO-CA | 1.1 | 1.4 | 1.3 | 0.22 | 0.40
8603.38 | FTE | ROU-FR | 1.1 | 1.3 | 1.3 | 0.22 | 0.38
8819.39 | FTE | SMM-SP | 0.8 | 1.3 | 1.5 | 0.22 | 0.34
8848.41 | OGA | OTO-FR | 0.9 | 1.5 | 1.2 | 0.19 | 0.36
8861.31 | FTE | ROU-FR | 1.0 | 1.5 | 1.3 | 0.20 | 0.37
8885.46 | SCH | DUR-FR | 0.7 | 1.2 | 1.0 | 0.21 | 0.35
8895.32 | FTE | SMM-SP | 0.8 | 1.4 | 1.1 | 0.18 | 0.30
8923.34 | FTE | ROU-FR | 1.1 | 1.2 | 1.0 | 0.18 | 0.36
8933.59 | LES | MRO-CA | 1.3 | 1.5 | 1.0 | 0.23 | 0.40
8935.31 | FTE | ROU-FR | 1.1 | 1.4 | 0.9 | 0.25 | 0.39
8955.36 | FTE | ROU-FR | 0.9 | 1.4 | 0.7 | 0.20 | 0.39
8962.60 | LES | MRO-CA | 1.0 | 1.4 | 1.0 | 0.23 | 0.40
8964.62 | LES | MRO-CA | 1.1 | 1.5 | 0.9 | 0.19 | 0.38
9111.82 | LES | MRO-CA | 0.8 | 0.9 | 0.1 | 0.29 | 0.45
9162.72 | LES | MRO-CA | 0.7 | 1.1 | 0.5 | 0.29 | 0.47
9242.43 | JGF | PIE-SP | 0.7 | 0.8 | 0.7 | 0.20 | 0.37
9273.32 | FTE | ROU-FR | 0.7 | 0.6 | 0.5 | 0.18 | 0.36
9289.35 | JGF | SMM-SP | 0.8 | 0.7 | 0.7 | 0.16 | 0.31
9294.45 | JGF | SMM-SP | 0.8 | 1.1 | 0.7 | 0.19 | 0.36