11institutetext: Department of Physics & Physical Oceanography, Memorial
University of Newfoundland & Labrador, St. John’s, NL, Canada A1C 5S7
11email<EMAIL_ADDRESS>22institutetext: Sternwarte Freimann, 80939 Munich,
Germany 33institutetext: Parton, Scotland, UK 44institutetext: Department of
Physics & Astronomy, East Tennessee State University, Johnson City, TN 37614,
USA 55institutetext: Astrophysics Research Institute, Liverpool John Moores
University, Liverpool Science Park, 146 Brownlow Hill, Liverpool, L3 5RF, UK
66institutetext: Steward Observatory, University of Arizona, 933 North Cherry
Avenue, Tucson, AZ 85721-0065, USA

# A Multi-Year Photopolarimetric Study of the Semi-Regular Variable V CVn and
Identification of Analogue Sources

H. Neilson A Multi-Year Photopolarimetric Study of the Semi-Regular Variable V
CVn and Identification of Analogue SourcesA Multi-Year Photopolarimetric Study
of the Semi-Regular Variable V CVn and Identification of Analogue Sources N.
Steenken A Multi-Year Photopolarimetric Study of the Semi-Regular Variable V
CVn and Identification of Analogue SourcesA Multi-Year Photopolarimetric Study
of the Semi-Regular Variable V CVn and Identification of Analogue Sources J.
Simpson A Multi-Year Photopolarimetric Study of the Semi-Regular Variable V
CVn and Identification of Analogue SourcesA Multi-Year Photopolarimetric Study
of the Semi-Regular Variable V CVn and Identification of Analogue Sources R.
Ignace A Multi-Year Photopolarimetric Study of the Semi-Regular Variable V CVn
and Identification of Analogue SourcesA Multi-Year Photopolarimetric Study of
the Semi-Regular Variable V CVn and Identification of Analogue Sources M.
Shrestha A Multi-Year Photopolarimetric Study of the Semi-Regular Variable V
CVn and Identification of Analogue SourcesA Multi-Year Photopolarimetric Study
of the Semi-Regular Variable V CVn and Identification of Analogue SourcesA
Multi-Year Photopolarimetric Study of the Semi-Regular Variable V CVn and
Identification of Analogue SourcesA Multi-Year Photopolarimetric Study of the
Semi-Regular Variable V CVn and Identification of Analogue Sources C. Erba A
Multi-Year Photopolarimetric Study of the Semi-Regular Variable V CVn and
Identification of Analogue SourcesA Multi-Year Photopolarimetric Study of the
Semi-Regular Variable V CVn and Identification of Analogue Sources G. Henson A
Multi-Year Photopolarimetric Study of the Semi-Regular Variable V CVn and
Identification of Analogue SourcesA Multi-Year Photopolarimetric Study of the
Semi-Regular Variable V CVn and Identification of Analogue Sources

The semi-regular variable star V Canum Venaticorum (V CVn) is well-known for
its unusual linear polarization position angle (PA). Decades of observing V
CVn reveal a nearly constant PA spanning hundreds of pulsation cycles. This
phenomenon has persisted through variability that has ranged by 2 magnitudes
in optical brightness and through variability in the polarization amplitude
over 0.3% and 6.9%. Additionally, the polarization fraction of V CVn varies
inversely with brightness.

This paper presents polarization measurements obtained over three pulsation
cycles. We find that the polarization maximum does not always occur precisely
at the same time as the brightness minimum. Instead, we observe a small lead
or lag in relation to the brightness minimum, spanning a period of a few days
up to three weeks. Furthermore, the PA sometimes exhibits a non-negligible
rotation, especially at lower polarization levels.

To elucidate the unusual optical behavior of V CVn, we present a list of
literature sources that also exhibit polarization variability with a roughly
fixed PA. We find this correlation occurs in stars with high tangential space
velocities, i.e., “runaway” stars, suggesting that the long-term constant PA
is related to how the circumstellar gas is shaped by the star’s high-speed
motion through the interstellar medium.

###### Key Words.:

Polarization – Stars: V CVn (HD 115898), L2 Pup, UZ Ari, AK Peg, RX Boo, Z UMa
– Mass-loss, Circumstellar matter, AGB, post-AGB

##  1 Introduction

Semi-regular variable stars (SRVs) are intriguing objects. They are evolved,
pulsating red giant stars that reflect the future of our own Sun. SRVs are
distinguished from Mira-type stars by their smaller brightness amplitude that
is less than 2.5 mag(V). In particular, SRV stars of type ’a’ (SRa) show an
identifiable and sustainable primary pulsation period and in many cases
secondary pulsation periods.

SRV stars, which are bright and so have been observed for centuries, are
recognized as important standard candles that also follow a number of period-
luminosity relations (Trabucchi et al., 2017; Lebzelter et al., 2019). This
correspondence contributes to our understanding of their evolution, and makes
SRVs valuable to extragalactic and cosmological studies. Even after so many
observations and studies SRVs continue to present a number of questions,
including the role of convection, stellar and circumstellar magnetic fields,
atmospheric dynamics, winds, along with how these stars interact with their
circumstellar medium (Kerschbaum & Hron, 1992; Kudashkina, 2019).

One of the more surprising questions arises from linear polarization
measurements of some SRV stars. Kruszewski et al. (1968) and Shawl (1975a, b)
presented early polarization measurements for V CVn (HD 115898). This
M4e-M6eIIIa late AGB star has a highly variable polarization and is located at
a distance of 501 pc (Gaia Collaboration, 2020). Linear polarization
measurements of unresolved sources can measure deviations from circular
symmetry as projected onto the sky. Thus, the detection of linear polarization
from a star may indicate an asymmetry that due to the presence of convection,
wind bow shocks, or disks (Shrestha et al., 2021).

Kruszewski et al. (1968) presented time-domain polarization measurements of V
CVn showing that the polarization fraction changes over the approximate 194
day primary pulsation period, while the position angle remains constant. What
is more curious is that the polarization fraction appears to be anti-
correlated to the brightness of the star: when the star is brightest, the
polarization is at a minimum; and when the star is dimmest, the polarization
is at a maximum. This surprising behaviour was confirmed to be a function of
wavelength by Magalhaes et al. (1986a, b). While still unexplained, this
phenomenon is not unique to V CVn.

Kruszewski et al. (1968) identified similar polarization variability in the
star L2 Puppis. This result added to the challenge of understanding these two
stars, but resolved polarimetric observations provided information about the
circumstellar structure of the L2 Pup system. Kervella et al. (2015) used VLT
SPHERE/ZIMPol polarimetric observations to discover the presence of a
circumstellar disk. This disk is remarkable as its asymmetry projected on the
sky explains the constant position angle of the unresolved linear
polarization, but _not_ the variation of the polarization itself.

Neilson et al. (2014) reviewed time-domain polarization measurements for V
CVn, and confirmed the periodic variability of the polarization while the
position angle stays approximately constant. They also confirmed that the
maximum value of the polarization appeared to correspond to minimum
brightness, and the minimum polarization to maximum brightness. They suggested
that the polarization and position angle time-domain observations could be
explained by a pulsation-driven, spherically symmetric dusty wind that
interacts with an asymmetric stellar wind bow shock. The presence of a
constant bow shock could explain the constant position angle. When the star
approaches maximum brightness, it also approaches maximum radius and minimum
effective temperature. Thus, dust will form in the spherically symmetric
outflow, and that dust will be more likely to interact with scattering photons
from the star. This will cause the polarization to decrease to a minimum.
Conversely, as the shell expands, the density decreases and the shell will
interact with the bow shock, creating a highly asymmetric system, and
resulting in a maximum polarization value, as shown by Shrestha et al. (2021).

An alternative model was proposed by Safonov et al. (2019) based on
differential speckle polarimetric observations of V CVn. They introduced the
idea of scattering arcs or reflection nebulae in the circumstellar envelope of
the star; hereafter we refer to these as simply ”blobs”. In their model, some
blobs are in the background, and some are in the foreground of the system. In
this geometry, the authors argued that the polarization variability could be
explained if the star undergoes a form of non-radial variability of its
brightness which could be either dipolar pulsation or rotational variation,
such that when the star appears brightest, an observer behind the star would
see V CVn at maximum brightness, and vice versa. Because one blob appears to
be behind the star, when we see V CVn at minimum light, the distant blob will
see intercept photons from the star at maximum brightness on the far side, and
thus there will be more backscattered photons, hence the polarization will be
greatest.

The polarization variability of V CVn can thus be explained by both of these
scenarios, but they each depend on the circumstellar medium (CSM) structures
of V CVn and L2 Pup. Understanding the CSM of these stars offers important
insights into how evolved semi-regular variable stars lose mass, and
potentially connects to their future evolution into planetary nebulae. In a
collaboration between professional and amateur astronomers, we consider here
new time-domain polarization observations of V CVn (led by co-authors Steenken
and Simpson) that offer new tests of the two models mentioned. This is an
especially valuable collaboration because V CVn is too bright for most large
telescopes. Therefore it was advantageous to perform this investigation in
cooperation with amateur astronomers. In Section 2, we discuss the tools and
methods used to obtain new observations of V CVn. In Section 3, we compare the
polarimetric observations with the visual brightness of the star. Section 4
then presents a review of potential analogues to V CVn and L2 Pup, and we
suggest that these stars are actually the prototypes of a class of
polarimetric semi-regular variable stars (“V CVn type” stars). We discuss the
various CSM and polarizations models for V CVn to discern if and how these new
observations might provide new insights into this system. Finally, Section 5
presents our conclusions and suggestions for future observations.

##  2 Observations and Data Reduction

Optical polarization observations and photometry of V CVn were carried out
independently by two of the co-authors (Steenken and Simpson; hereafter
“observers”) operating Schmidt-Cassegrain-Telescopes (SCT). The observers are
located in Munich/Germany (Steenken, Ob1) and in Parton/Scotland (Simpson,
Ob2). Both telescopes have Dual-Beam-Polarimeters with V-band filters and
cooled CCD cameras mounted at the Cassegrain focus. Customary SCTs were used,
with OB1 having a focal length of 2800 mm and aperture of 280 mm, and OB2
using a two different SCTs with focal lengths of 1500 and 2000 mm and
apertures of 150 and 200 mm (Ob2) on a German equatorial mount. Object
centering and autoguiding was achieved with separate guide scopes and guiding
cameras.

Both polarimeters were built and calibrated in 2018-2019 to measure the linear
optical polarization ($P$) of stars brighter than 9 mag, with an error of $\pm
0.1$ % polarization and $\pm 5$ degrees of polarization position angle (PA) in
the relevant polarization range of V CVn in the past i.e. 0.3% - 6.9%. An
achromatic Half-Wave-Plate (HWP) was manually rotated into the positions 0,
22.5, 45 and 67.5 degrees to rotate the polarization plane 0, 45, 90 and 135
degrees. The 0 degree position is aligned with the celestial North direction.
The instrumental 0 deg position has been nominally aligned with the celestial
NS reference and offsets from this are checked during each observing session,
using measurements obtained either by plate solving a stacked measurement
image and/or by disabling tracking so as to generate an EW trace on measured
images and therefore a NS reference. These offsets are removed during data
processing. Calibration, later performed, uses high polarisation standards to
correct instrumental position angle offsets arising from any half-wave
plate/Wollaston prism misalignments. A Wollaston prism splits of the star into
a parallel and a perpendicular beam. The beams are passed through a V-band
filter and focused onto a CCD detector of $1392\times 1040$ pixels for a
cooled 16-bit Astro camera. The optical design is shown in Fig. 1.

Figure 1:  Optical design of the dual-beam-polarimeter, with components along
the optical path identified and labeled.

The images were captured and analyzed with standard image capturing and
photometry software (for Ob1: AstroArt 6111www.msb-astroart.com and for Ob2:
AstroImageJ222www.astro.louisville.edu). The exposure times vary from 2 to 15
seconds depending on the star brightness, weather conditions and telescope.
For one observation, 40 to 100 images in each rotation position of the HWP
were exposed. Batch processing was used for the dark field correction, stellar
alignment, and photometry of the parallel and perpendicular stellar images.
Aperture radii selection, based on the image’s full width at half maximum
[FWHM] – typically 1.5-2 times FWHM for the signal and 3 resp. 5 times FWHM
respectively for inner/outer annuli for sky background evaluation – provided a
flux measurement that is robust against seeing variations, giving confidence
in the method even when the object images were slightly distorted. Signal-to-
noise ratios (SNR) of over 400 of each image taken as calculated by the
photometry software were achieved, subject to atmospheric conditions. Fig. 2
shows an example of an image made by Ob 1.

Figure 2:  An example of one image of V CVn split into parallel (bright star
at top) and perpendicular beams (bright star at bottom) from 2022-07-03 at 0
degree rotation position. The star left below V CVn is BD+46 1863.

Fluxes of parallel $f_{par_{i}}$ and perpendicular beams $f_{perp_{i}}$ were
measured for every image $i$ with the photometry software. Polarization ($P$),
including correction for bias, and Position Angle (PA) were calculated as
described in Clarke (2010). For the error analysis, the study by Patat &
Romaniello (2006) was used.

To calculate the measured Stokes $Q_{m}$ and $U_{m}$ parameters, parallel and
perpendicular flux measurements are combined in the following way, for angle
positions $\theta$:

$\displaystyle N_{\theta}$ $\displaystyle=$
$\displaystyle\frac{\sum{f_{par_{i}}}-\sum{f_{perp_{i}}}}{\sum{f_{par_{i}}}+\sum{f_{perp_{i}}}},$
(1) $\displaystyle Q_{m}$ $\displaystyle=$
$\displaystyle\frac{1}{2}\\{N_{0}-N_{45})\leavevmode\nobreak\ {\rm and}$ (2)
$\displaystyle U_{m}$ $\displaystyle=$
$\displaystyle\frac{1}{2}\\{N_{22.5}-N_{67.5})$ (3)

where $N_{\theta}$ is the fractional photon count between parallel and
perpendicular beams at the specified angel of the Half-Wave-Plate.

Any optical design of a polarimeter has to deal with instrumental polarization
caused by the telescope or the optical components in the polarimeter,
including the filter. To remove the instrumental polarization effects, the
Stokes parameters of unpolarized stars in Table 1 were measured as zero-point
offsets and calibrated Stokes parameters calculated using:

Table 1: Unpolarized stars used as standards, and their polarization according to Schmidt et al. (1992) Star | $mag(V)$ |  $P$ (%) |  $\sigma_{P}$ (%) | Observer
---|---|---|---|---
$\beta$ Cas | 2.3 | 0.037 | 0.024 | 1,2
$\theta$ UMa | 3.2 | 0.037 | 0.014 | 1,2
$\beta$ UMa | 2.4 | 0.009 | 0.019 | 2
HD 21447 | 5.1 | 0.051 | 0.020 | 1

$\displaystyle Q_{cal}$ $\displaystyle=$ $\displaystyle
Q_{m}-Q_{0},\leavevmode\nobreak\ {\rm and}$ (4) $\displaystyle U_{cal}$
$\displaystyle=$ $\displaystyle U_{m}-U_{0}$ (5)

Calibration standard high polarization stars like $\phi$ Cas and 2H Cam were
measured in agreement to the published values of Hsu & Breger (1982) as shown
in Table 2.

Table 2: Highly polarized stars measurements and comparison to reference Star | JD | $P_{cal}$ | $PA_{cal}$ | Ob
---|---|---|---|---
$\phi$ Cas | 2459077 | 3.30% | 98.8 | 1
$\phi$ Cas | 2459280 | 3.42% | 95.7 | 1
$\phi$ Cas | 2459448 | 3.32% | 95.6 | 1
$\phi$ Cas | 2459452 | 3.12% | 96.6 | 1
$\phi$ Cas | 2459599 | 3.35% | 93.8 | 1
$\phi$ Cas | 2459599 | 3.34% | 92.7 | 1
$\phi$ Cas | 2459622 | 3.29% | 92.8 | 1
$\phi$ Cas | 2459808 | 3.44% | 96.0 | 1
$\phi$ Cas | Average | 3.32% | 95.3 | 1
|  |  |  |
$\phi$ Cas | 2459287 | 3.41% | 93.3 | 2
$\phi$ Cas | 2459287 | 3.24% | 92.0 | 2
$\phi$ Cas | 2459314 | 3.44% | 92.7 | 2
$\phi$ Cas | Average | 3.36% | 92.7 | 2
$\phi$ Cas | Hsu & Breger (1982) | 3.34% | 92.3 |
|  |  |  |
2H Cam | 2459319 | 3.37% | 115.2 | 2
2H Cam | 2459543 | 3.53% | 115.0 | 2
2H Cam | Average | 3.45% | 115.1 | 2
2H Cam | Hsu & Breger (1982) | 3.49% | 116.6 |

Both the instrumental set-ups and zero-point offsets were kept unchanged
during the observing seasons from January until September to ensure comparable
results. Calibration stars were observed each season to determine the
stability and the reliability of the polarization position angle.

V-band photometry of V CVn was obtained directly before or after the
polarimetric measurements with nearby comparison stars. Ob1 selected nearby
star HD 116957, with $mag(V)=5.87$, as comparison. Ob2 used an ensemble of the
four AASVO comparison stars 333Chart X28069ADU, AAVSO Variable Star Database.

The measured polarization is composed of the intrinsic polarization of V CVn
and the interstellar polarization.

The star BD+46 1863 is located only about 2 arcmin south-west of V CVn at a
distance of about 1670 pc and was used estimate the interstellar polarization.
The measurements performed on the nearby stars TYC 3460-1345-1 and TYC
3460-2045-1 gave values of polarization between 0 and 0.5%. However, due to
the high measurement uncertainties, these measurements were not used. The
estimate is as shown in table 3 and is the basis for the calculation of the
intrinsic polarization of V CVn.

Table 3: Estimate of interstellar polarization based on nearby star BD+46 1863  $P_{is}$ | $PA_{is}$ | $Q_{is}$ | $U_{is}$ | $\sigma_{Q}$ | $\sigma_{U}$
---|---|---|---|---|---
0.34% | 123 | -0.14% | -0.31% | 0.010% | 0.009%

Intrinsic Stokes $Q_{intr}$ and $U_{intr}$ parameters were calculated
according to:

$\displaystyle Q_{intr}$ $\displaystyle=$ $\displaystyle
Q_{cal}-Q_{is},\leavevmode\nobreak\ {\rm and}$ (6) $\displaystyle U_{intr}$
$\displaystyle=$ $\displaystyle U_{cal}-U_{is}$ (7)

Intrinsic Polarization $P_{intr}$ and intrinsic polarization angle $PA_{intr}$
according to:

$\displaystyle P_{intr}$ $\displaystyle=$
$\displaystyle\sqrt{Q_{intr}^{2}+U_{intr}^{2}},\leavevmode\nobreak\ {\rm and}$
(8) $\displaystyle PA_{intr}$ $\displaystyle=$
$\displaystyle\frac{1}{2}\,\tan^{-1}\left(\frac{U_{intr}}{Q_{intr}}\right).$
(9)

The standard error of the mean values of Stokes Q, U were calculated according
to Clarke (2010) using the student-t distribution for 95% confidence limits.
Errors of P and PA and were calculated as follows:

$\sigma_{P}=\frac{\sqrt{Q^{2}\sigma_{Q}^{2}+U^{2}\sigma_{U}^{2}}\leavevmode\nobreak\
{\rm}}{P}$ (10)

$\sigma_{PA}=\frac{\sqrt{Q^{2}\sigma_{U}^{2}+U^{2}\sigma_{Q}^{2}}}{2P^{2}}$
(11)

In the data reduction process polarization has been de-biased using the Wardle
& Kronberg (1974) formulation:

$P_{debias}=\sqrt{P_{cal}^{2}-\sigma_{P}^{2}}$ (12)

A total of 227 measurements were taken on 51 nights in 2020, 89 nights in
2021, and 87 nights in 2022, with a table of measurements in Appendix B444All
raw data can be obtained from https://zenodo.org/record/7997101. During this
span of time, V CVn went through 5 pulsation cycles, as shown in Fig. 3. The
polarization measurements covered the first pulsation cycle in 2020, 2021 and
2022 (hereafter 1/2020, 1/2021 and 1/2022).

Figure 3:  The V-band light curve of V CVn from 2020-2022. The red triangles
are the photometry measurements provided by Ob1 and Ob2. The grey dots are for
AASVO data (CCD measurements only). The three pulsation cycles covered by
polarization measurements in this study in red, namely at the left pulsation
cycle 1/2020 in the middle 1/2021 and at the right cycle 1/2022. It can be
seen that the data from AASVO agrees well with the data measured by Ob1 and
Ob2. Pulsation cycle 1/2021 showed the lowest brightness of all minima
considered.

##  3 Results

The relationship between intrinsic polarization and brightness over the course
of all three pulsation cycles is shown in Fig. 4. The polarization in the
V-Band is highly variable, and is generally anti-correlated with brightness.
The larger polarizations were measured around brightness minima, and are
consistent with earlier studies by Serkowski & Shawl (2001) and Davidson et
al. (2014).

Figure 4:  Photopolarimetry of the observed pulsation cycles. Intrinsic
polarization curves in red are shown in the upper row. The light curves in
blue are shown in the middle row. The intrinsic position angle (PA) is shown
in the lower row as black. In all three pulsation cycles polarization and
photometry are generally anti-correlated, especially true around times of
brightness maxima and minima. However, the curves are not exactly anti-
correlated as indicated by the grey arrows. A phase shift between polarization
and total light is most clearly visible around the brightness minimum of
pulsation cycle 1/2021, but also seen in pulsation cycles 1/2020 and 1/2022.
Comparison between the 3 cycles reveals that the polarization curve can either
lead or lag the light curve. The intrinsic PA ranges generally within 80 – 120
degrees, except when the star is brighter than 7 mag(V) and/or the
polarization drops significantly below 0.7%. At such times, the PA can drop
below 50 degrees.

Thanks to the high cadence of measurements covering three pulsation cycles,
the temporal relationship between the star’s light curve and polarization can
be analyzed in more detail. Pulsation cycle 1/2021 showed the strongest
obscuration associated with the highest measured intrinsic polarization of all
three observed pulsation cycles. Of particular interest is the observation
that the maximum polarization does not occur exactly at the time of the
minimum brightness of V CVn. We observe that in the three cycles that the
polarization maximum can lead the brightness minimum by several weeks as well
as lag it. Especially in cycle 1/2021 polarization led by about 16 days and in
cycle 1/2022 polarization lagged again by about 20 days. This lead/lag
phenomenon was observed around brightness minima and is indicated by a grey
arrows in Fig. 4. The pulsation cycle 1/2020 is shown in the left column of
the figures. Polarisation maximum of 1.47% was reached at JD 2459024. The
brightness at 7.68 mag(V) minimum occurred 11 days (JD 2459013) before.
Polarization was lagging the light curve. In the pulsation cycle 1/2021
(middle column) polarization was leading the light curve. The maximum of
intrinsic polarization of 2.70% was measured at JD 2459338 16 days before the
first minimum of the light curve which occured at JD 2459354 and reached 7.99
mag(V). In this pulsation cycle, the star darkened significantly more and
reached much higher polarization values than in the other two cycles. In the
pulsation cycle 1/2022 (right column) polarization was lagging again the light
curve. Second light minimum occurred on JD 2459743 at 7.79 mag(V) which was
followed by the polarization maximum of 2.11% on JD 2459763 20 days later. Due
to the irregular course of the light curve and the daily variations in
brightness and polarization, an exact determination of the shift is not
possible. Polarization showed strong variations while going through the
maximum. There are indications that phase shifts between the curves may occur
when the polarization changes significantly within a few weeks. During periods
of little change in brightness, there appears to be little correlation between
the curves. The position angle PA stays generally within a range of 80 - 120
degrees, except when the intrinsic polarization drops below 0.7%.

##  4 Discussion

###  4.1 A New Class of V CVn-type Stars

The Combined General Catalog of Variable Stars (Samus et al., 2004) lists 348
SRa and 1201 SRb stars, yet polarimetric measurements have only been published
for a few of them. As a consequence, it is unknown whether significant
variation of the polarization during a pulsation cycle of more than 1% is
typical or exceptional for semi-regular variables.

While V CVn is not the only semi-regular evolved star with significant
variable polarization, it by far has the greatest number of polarization
measurements obtained since the 1960s. Table 4 (A) lists the basic stellar
parameters of five other semi-regular stars that show polarimetric behavior
similar to V CVn itself. The following list summarizes their observed
properties:

  * •

UZ Ari (IRC +20052) appears similar to V CVn in many respects. It is situated
at high galactic latitude ($-$31 deg) at a similar distance (539 pc), and has
a tangential velocity of 59 km/sec. The period of UZ Ari is 163 days, about 30
days shorter than of V CVn. UZ Ari has a spectral class of M8, with an
apparent brightness that is significantly lower than V CVn, and varies between
11.8 and 12.6 mag(V). Baug et al. (2014) were able to measure the diameter of
the star in K-band during three lunar occultations. They found values of 4.5 -
6.0 $\pm$ 0.5 mas without a correlation to phase. The few published
polarization measurements in the V-band vary between 2 and 3.5%, with a decade
long stable PA around 130 deg (Kruszewski & Coyne, 1976; Baug et al., 2014).
If future polarization measurements of UZ Ari confirm the stable range of PA,
then the physical origin of the asymmetry could be the same as in V CVn.

  * •

AK Peg has a very similar period of variability and spectral type to V CVn. At
its distance of 1329 pc, the star ranges in brightness between 8.6 - 10.2
mag(V). The few polarization measurements published by Serkowski & Shawl
(2001) indicated polarization values between 1.5 and 3.4%, a fairly large
intrinsic level of polarimetric variability similar to UZ Ari.

  * •

RX Boo has variabilty that is classified as an SRb, with a distance of 156 pc.
Using the Infrared Optical Array Imaging Interferometer (IOTA), Ragland et al.
(2006) measured a stellar diameter of 17.5 mas in H-Band that showed no
asymmetry. Unfortunately, only a few older polarization measurements are
available for this star (Vartanyan, 1968), with values ranging from 0.4 to
1.9%. The change in polarization is comparable to UZ Ari and AK Peg.

  * •

Z UMa is an SRb star at a distance of 296 pc. Dyck & Jennings (1971) published
polarization measurements ranging between 0.2 and 1.8%. Measurements at 5
epochs by Ob1 in 2021 (Fig. 5) confirmed variable polarization from 0.13 to
1.0%, showing an anti-correlation with brightness. Again, the amplitude of
variable polarization is comparable to the previous three objects.

  * •

L2 Pup is an SRb star on the southern hemisphere. The polarization
measurements of Magalhaes et al. (1986b) reveal a high level of polarization
variabilty between 0 and 8%, accompanied by a steady PA of 165-180 degrees. If
the few historical polarization V-band measurements are compared with
photometric data from the AASVO, the polarization appears anti-correlated with
brightness level. This level of variable polarization is considerably larger
than the four preceding stars, but is comparable to V CVn.

Figure 5:  Polarization measurements (red triangles) and photometry (blue
dots) of Z UMa in 2021 (Ob1). Five epochs of photopolarimetric measurements
were obtained. The data give indications of an anti-correlation between the
measured polarization and brightness.

Due to a distance of only 56 pc, and the superior imaging performance of VLT
SPHERE/ZIMPol, it has been possible to detect a dust disk responsible for the
asymmetry of L2 Pup (Kervella et al., 2015). For the other stars listed above,
the reasons for the asymmetries remain unclear. None of these stars are
located in the galactic plane, with its higher interstellar density, but some
of them show high tangential or radial velocities.

Figure 6:  Maximum polarization vs. tangential velocity of the stars in Table
4, indicating an higher maximum polarization with increased tangential
velocity.

In Fig. 6, we see hints of a relationship between the tangential velocity and
the observed maximum polarization. Stars with significant tangential
velocities and slow winds, such as those from cool, evolved stars, would be
expected to host a bow shock along the plane of the sky. That bow shock, if
unresolved, would create a significant asymmetry on the plane of the sky with
an associated polarization signature (Shrestha et al., 2021). The amount of
polarization would depend on both the shape and density of the bow shock,
along with the properties of the stellar wind. Shrestha et al. (2021) showed
that polarization is a function of the type of dust in the bow shock, the
density of the local interstellar medium, and the wind properties of the stars
in question, so the apparent correlation of Figure 6 could be consistent with
the model proposed by Neilson et al. (2014). The polarization would be
variable if, during the phase where V CVn is brightest, the star ejects a
dusty shell whose density is sufficient to wash out the bow shock signal and
make the system appear more symmetric (Shrestha et al., 2021).

Safonov et al. (2019) argued that V CVn cannot have a bow shock, due to a low
ISM density expected from its high galactic latitude. However, the star is
located only a few arcmin away from a molecular cloud discovered by Reach et
al. (1994). The molecular cloud G107.4 +70.9 is one of the densest clouds in
that region, and lies roughly at the same distance as V CVn, according to a
study from Gladders et al. (1998). It is plausible that the interstellar
density near the fast moving V CVn could be large enough to allow the
formation of a bow shock.

###  4.2 Possible models of the polarimetric variability

The polarimetric variability of V CVn is surprising and counterintuitive. When
the star reaches maximum light, the polarization approaches a minimum, and
vice-versa. One might expect that if the source of the polarization were
constant – which would yield a constant position angle – then at maximum
light, the number of polarized photons would also be at a maximum. However,
since the polarization is a normalized quantity, one would find that the
polarization is also constant. Satisfying the observations requires either of
the following scenarios:

  1. 1.

The source of the polarization interacts with a different number of photons
relative to what the observer sees (Safonov et al., 2019); or

  2. 2.

The source of the polarization changes, yet maintains the same deviation of
symmetry on the sky (Neilson et al., 2014).

The results of this work impose an additional requirement that a viable model
should explain observed time differences between the polarization maximum and
the light minimum.

If we consider the first option, Safonov et al. (2019) suggest that one of the
dusty “blobs” is behind the star relative to the observer (c.f., Sec. 1). They
suggest that if the light variation is not due to radial pulsation, and
instead is some type of dipolar variability or rotational variability, then
when the observer measures minimum light, the other side of the star appears
at maximum light – hence the blob “sees” the greatest number of polarizing
photons that get backscattered to the observer. This model is intriguing, but
requires the stellar variability to be asymmetric and non-radial. The
pulsation amplitude of V CVn is about 2 mag(V), and there are no known stars
that pulsate with this amplitude non-radially. If this were a rotational
phenomena, combining a period of about $\approx 194$ d with an assumed stellar
radius of order 100 $R_{\odot}$ implies the rotation rate is about 25 km s-1,
and is the same order as the critical rotation rate for the star.

An additional challenge for this model is the apparent lead and lag time
between polarization and flux. If the issue was only that the polarization
maximum lagged behind the luminosity, one might explain it as a light-time
delay of $t_{d}=22d_{b}/c$, where $d_{b}$ is the distance between the star and
blob. Safonov et al. (2019) reported a radius of the blobs around V CVn of 35
$\pm$ 1 mas. Using the latest distance data from Gaia Collaboration (2020) of
501 pc, this results in a distance of the bipolar cloud of 17.5 AU. The time
delay caused by the light travelling between the assumed bipolar cloud and the
star is then 2.5 hr, and thus by far not enough to explain the observed time
difference in our observational data between the light and polarization curves
of up to two weeks.

Neilson et al. (2014) suggest that the variable polarization is caused by a
pulsation-driven dusty wind shell (see also Willson, 2000; Höfner & Freytag,
2022) that collides with a stellar wind bow shock, which is expected since V
CVn is a runaway star. They argue that the shell is driven outwards from the
star near maximum light, and because the shell is symmetric, the polarization
is then at a minimum. However, the position angle will remain constant because
of the constant presence of the asymmetric bow shock around the shell. As the
shell expands and its density decreases, the polarization is set more by the
near-constant density bow shock. This result is consistent with the apparent
connection between the polarization amplitude and the tangential velocity
observed for V CVn and its potential analogues, as described in Section 4.1.
However, this model does not explain the apparent lead/lag time.

Additionally, instead of an asymmetry due to the presence of bow shocks, the
wind may simply be asymmetric and variable. Simulations performed by Aronson
et al. (2017) using non-spherical circumstellar shells that contain clumped
material predicted significant net polarization signals. If the maximum
polarization occurs near the minimum light then the wind, at that phase, could
be most asymmetric, and at maximum light and minimum polarization, the wind
would be most symmetric. It is worth noting that this argument is independent
of wind density – since the polarization observed for V CVn is normalized –
and is thus only concerned with changes in the symmetry of the wind as
projected against the sky.

Asymmetric stellar winds are rare, but can be caused by rapid rotation as
suggested for Be supergiants (e.g., Granada et al., 2010; Georgy et al.,
2011), magnetic fields as seen in hot, massive stars with strong magnetic
fields (e.g. Erba et al., 2021; Subramanian et al., 2022), or perhaps
convection as suggested for massive evolved red supergiant stars (e.g.,
Kamiński, 2019; López Ariste et al., 2022). There is no evidence that V CVn is
a rapidly rotating star. However, given its evolved stage of evolution, its
critical rotational velocity is small. Rotation might be important, and could
be consistent with a small population of variable-polarization evolved stars.
Furthermore, one would expect the rotation to be slow; however, it is possible
there were dynamic events between the progenitors of these stars, and a
companion spun up the progenitor (e.g., Staritsin, 2022), while a supernova
explosion or another dynamic event ejected the companion (Dorigo Jones et al.,
2020). In that case, the progenitor would evolve into a runaway red giant star
with rapid rotation. While this scenario may be possible, it is not obvious
how to test this idea, and the proposed scenario should be a rare occurrence
at best.

Strong magnetic fields ($>1kG$) are not common among evolved stars (Grunhut et
al., 2010); however, strong magnetic fields in hot stars are known to shape
their stellar winds and make them asymmetric (e.g. ud-Doula & Owocki, 2002).
In hot (O- and B-type) stars, the magnetic field tends to be nearly dipolar,
while in evolved stars the magnetic field is more tangled, and similar to that
of the Sun. It is not clear that magnetic fields in this case can impact the
wind structure in a meaningful manner, but the existence of a maser (Wolak et
al., 2012) around V CVn implies that follow-up measurements would be a
valuable test, and could be related to the observed polarization lead/lag.

Convection is unlikely to be the main source of polarizing photons in these
red giant stars. Convection is not constant, and will create spots of some
lifetime over different parts of a star that is not periodic. As such, the
variable polarization should not be correlated with the brightness variation.

Figure 7:  A schematic representation of the interaction between the pulsating
star and the bow shock. Top: at maximum brightness and minimum polarization,
the dust is accelerated from the photosphere in a dense shell (circle) and the
mass-loss rate is greatest. The star moves relative to the interstellar medium
in the direction of the arrow. The wind shell is denser than the bow shock
(light blue), and dominates the fraction of scattered light. Bottom: Around
minimum light there is less radiative acceleration, and dust forms in the
photosphere, while the mass-loss rate is much smaller. The shell formed at the
previous flux maximum has expanded asymmetrically. The cloud-like structure of
the dust envelope is supposed to show turbulence. A bow shock (blue) dominates
the observed polarization, and is incorporated into the smaller density CSM. A
lead/lag of the polarization and the light-curve can occur if convection
causes the dust density in the line of sight and in the bow shock to develop
differently.

Although convection cannot be the main source of polarization, it is possible
that the polarization lead/lag is caused by convection. It is known that, for
pulsating Cepheids, convection can perturb their regular light curves to vary
cycle-to-cycle (Derekas et al., 2012; Neilson & Ignace, 2014; Derekas et al.,
2017), and this is a potential cause of pulsation instability in variable red
giant and supergiant stars. For V CVn, it is likely that convection and
granulation make the times of maximum and minimum light unstable and variable
in the same way. However, if the stellar wind is due to a dust shell being
formed in the photosphere, then the wind is correlated more with the
variability of the stellar radius and NOT the variability of the stellar
luminosity. In Fig. 7, we have sketched the relationship between the pulsating
star and the bow shock. We assume that with each pulsation cycle a different
pattern of convection cells is created. In a pulsation cycle – where the dust
is most dense first along the line of sight and only delayed in the direction
of the bow shock – the brightness minimum occurs before the polarization
maximum, and the polarization curve lags behind the brightness curve, as
observed in pulsation cycle 1/2020, and vice-versa as in cycle 1/2021.

##  5 Conclusions

The new high-cadence photopolarimetry of V CVn presented here raises new
questions about the nature of the polarization variability both of this star
and other semi-regular variable stars. In particular, we find that the
polarization maximum does not occur at the same time as light minimum, and
that time will be a lead or a lag. This phenomenon is not naturally explained
by the models proposed by either Neilson et al. (2014) or Safonov et al.
(2019). Our investigation supports the hypothesis that the variable
polarization is caused by a bow shock, and that the observed phase-shifts
between polarization and light curves are caused by convective processes in
the stellar photosphere. As such, we find that more high-cadence polarization
measurements and simulations of V CVn-type stars would be important if we wish
to understand the relationship between their stellar properties, their
motions, and their circumstellar media.

###### Acknowledgements.

The authors gratefully thank the Referee for the constructive comments and
recommendations which helped to improve the paper. We acknowledge with thanks
the variable star observations from the AAVSO International Database
contributed by observers worldwide and used in this research. We thank
Zenodo.org for hosting our data (https://zenodo.org/record/7997101). 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. MS is supported by an STFC
consolidated grant number (ST/R000484/1) to LJMU. HN acknowledges funding from
NSERC.

## References

  * Aronson et al. (2017) Aronson, E., Bladh, S., & Höfner, S. 2017, A&A, 603, A116
  * Baug et al. (2014) Baug, T., Chandrasekhar, T., & Ganesh, S. 2014, MNRAS, 443, 3624
  * Clarke (2010) Clarke, D. 2010, Stellar Polarimetry
  * Davidson et al. (2014) Davidson, J. W., Bjorkman, K. S., Hoffman, J. L., et al. 2014, Journal of Astronomical Instrumentation, 3, 1450009
  * Derekas et al. (2017) Derekas, A., Plachy, E., Molnár, L., et al. 2017, MNRAS, 464, 1553
  * Derekas et al. (2012) Derekas, A., Szabó, G. M., Berdnikov, L., et al. 2012, MNRAS, 425, 1312
  * Dorigo Jones et al. (2020) Dorigo Jones, J., Oey, M. S., Paggeot, K., Castro, N., & Moe, M. 2020, ApJ, 903, 43
  * Dyck & Jennings (1971) Dyck, H. M. & Jennings, M. C. 1971, AJ, 76, 431
  * Erba et al. (2021) Erba, C., David-Uraz, A., Petit, V., et al. 2021, MNRAS, 506, 5373
  * Gaia Collaboration (2020) Gaia Collaboration. 2020, VizieR Online Data Catalog, I/350
  * Georgy et al. (2011) Georgy, C., Ekström, S., Granada, A., & Meynet, G. 2011, in Active OB Stars: Structure, Evolution, Mass Loss, and Critical Limits, ed. C. Neiner, G. Wade, G. Meynet, & G. Peters, Vol. 272, 640–641
  * Gladders et al. (1998) Gladders, M., Clarke, T., Burns, C., et al. 1998
  * Granada et al. (2010) Granada, A., Jiménez, A., Curé, M., & Cidale, L. 2010, in Revista Mexicana de Astronomia y Astrofisica Conference Series, Vol. 38, Revista Mexicana de Astronomia y Astrofisica Conference Series, 60–60
  * Grunhut et al. (2010) Grunhut, J. H., Wade, G. A., Hanes, D. A., & Alecian, E. 2010, MNRAS, 408, 2290
  * Höfner & Freytag (2022) Höfner, S. & Freytag, B. 2022, arXiv e-prints, arXiv:2204.09728
  * Hsu & Breger (1982) Hsu, J. C. & Breger, M. 1982, ApJ, 262, 732
  * Kamiński (2019) Kamiński, T. 2019, A&A, 627, A114
  * Kerschbaum & Hron (1992) Kerschbaum, F. & Hron, J. 1992, A&A, 263, 97
  * Kervella et al. (2015) Kervella, P., Montargès, M., Lagadec, E., et al. 2015, A&A, 578, A77
  * Kruszewski & Coyne (1976) Kruszewski, A. & Coyne, G. V. 1976, AJ, 81, 641
  * Kruszewski et al. (1968) Kruszewski, A., Gehrels, T., & Serkowski, K. 1968, AJ, 73, 677
  * Kudashkina (2019) Kudashkina, L. S. 2019, Astrophysics, 62, 556
  * Lebzelter et al. (2019) Lebzelter, T., Trabucchi, M., Mowlavi, N., et al. 2019, A&A, 631, A24
  * López Ariste et al. (2022) López Ariste, A., Georgiev, S., Mathias, P., et al. 2022, A&A, 661, A91
  * Magalhaes et al. (1986a) Magalhaes, A. M., Codina-Landaberry, S. J., Gneiding, C., & Coyne, G. V. 1986a, A&A, 154, 1
  * Magalhaes et al. (1986b) Magalhaes, A. M., Coyne, G. V., & Benedetti, E. K. 1986b, AJ, 91, 919
  * Magalhaes et al. (1986c) Magalhaes, A. M., Coyne, G. V., Codina-Landaberry, S. J., & Gneiding, C. 1986c, A&A, 154, 1
  * Neilson & Ignace (2014) Neilson, H. R. & Ignace, R. 2014, A&A, 563, L4
  * Neilson et al. (2014) Neilson, H. R., Ignace, R., Smith, B. J., Henson, G., & Adams, A. M. 2014, A&A, 568, A88
  * Patat & Romaniello (2006) Patat, F. & Romaniello, M. 2006, Publications of the Astronomical Society of the Pacific, 118, 146
  * Ragland et al. (2006) Ragland, S., Traub, W. A., Berger, J. P., et al. 2006, ApJ, 652, 650
  * Reach et al. (1994) Reach, W. T., Koo, B.-C., & Heiles, C. 1994, ApJ, 429, 672
  * Safonov et al. (2019) Safonov, B. S., Dodin, A. V., Lamzin, S. A., & Rastorguev, A. S. 2019, Astronomy Letters, 45, 453
  * Samus et al. (2004) Samus, N. N., Durlevich, O. V., & et al. 2004, VizieR Online Data Catalog, II/250
  * Samus’ et al. (2017) Samus’, N. N., Kazarovets, E. V., Durlevich, O. V., Kireeva, N. N., & Pastukhova, E. N. 2017, Astronomy Reports, 61, 80
  * Schmidt et al. (1992) Schmidt, G. D., Elston, R., & Lupie, O. L. 1992, AJ, 104, 1563
  * Serkowski (1966) Serkowski, K. 1966, Information Bulletin on Variable Stars, 141, 1
  * Serkowski & Shawl (2001) Serkowski, K. & Shawl, S. J. 2001, AJ, 122, 2017
  * Shawl (1975a) Shawl, S. J. 1975a, AJ, 80, 602
  * Shawl (1975b) Shawl, S. J. 1975b, AJ, 80, 595
  * Shrestha et al. (2021) Shrestha, M., Neilson, H. R., Hoffman, J. L., Ignace, R., & Fullard, A. G. 2021, MNRAS, 500, 4319
  * Staritsin (2022) Staritsin, E. 2022, arXiv e-prints, arXiv:2209.00270
  * Subramanian et al. (2022) Subramanian, S., Balsara, D. S., ud-Doula, A., & Gagné, M. 2022, MNRAS, 515, 237
  * Trabucchi et al. (2017) Trabucchi, M., Wood, P. R., Montalbán, J., et al. 2017, ApJ, 847, 139
  * ud-Doula & Owocki (2002) ud-Doula, A. & Owocki, S. P. 2002, ApJ, 576, 413
  * Vartanyan (1968) Vartanyan, R. A. 1968, Astrophysics, 4, 51
  * Wardle & Kronberg (1974) Wardle, J. F. C. & Kronberg, P. P. 1974, ApJ, 194, 249
  * Willson (2000) Willson, L. A. 2000, ARA&A, 38, 573
  * Wolak et al. (2012) Wolak, P., Szymczak, M., & Gérard, E. 2012, A&A, 537, A5

##  Appendix A The sample variable polarization semi-regular variable stars.

[b]  V CVn UZ Ari AK Peg RX Boo Z UMa L2 Pup Spectral Type1 M4e-M6eIIIa M8
M4-M8e M6.5e-M8IIIe M5IIIe M5IIIe-M6IIIe Galactic latitude (∘) 70 -31 -43 69
57 -15 Period (d)1 194 163 194 162 195 - $\Delta mag(V)$1 2.0 0.8 1.6 2.7 3.2
3.6 Polarimetric data (yr) 19662 \- 20222 19723 /20134 19675 19675 , 19706
19667 , 19706 19678 -19829 Polarization (%)10 0.3 - 6.9 2 - 3.5 1.3 - 3.3 0.4
- 1.9 0.2 - 1.8 0 - 8 Postion angle (∘)11 80 - 120 126 - 132 21 - 50 40 - 153
8 - 132 165 - 180 Stability in $\Delta PA$12 yes yes unknown unknown unknown
yes Distance (pc)13 501 539 1329 156 296 56 $\mu$ (mas yr-1)13 40 23 45 53 12
340 $V_{\rm t}$ (km s-1)13 95 59 28 39 17 90 $V_{\rm r}$ (km s-1)13 -47 n.a.
-4 -9 -53 53

Table 4:  V CVn type stars: semi-regular variables with significant variable
polarization.

  * 1

General catalog of variable stars Samus’ et al. (2017)

  * 2

Kruszewski et al. (1968), Dyck & Jennings (1971), Serkowski & Shawl (2001),
Davidson et al. (2014), This study

  * 3

Kruszewski & Coyne (1976)

  * 4

Baug et al. (2014)

  * 5

R.A. Vartanyan, Intrinsic Polarization of Stellar Light From RX Boo, AB Cyg,
Astrofyzika, 1968

  * 6

Dyck & Jennings (1971)

  * 7

Serkowski (1966)

  * 8

Kruszewski et al. (1968)

  * 9

Magalhaes et al. (1986c)

  * 10

Range of measured polarization in V-Band as published in the above mentioned
studies (RX Boo: intrinsic P)

  * 11

Range of measured polarization angles in V-Band as published in the above
mentioned studies

  * 12

Yes, if position angle remains constant over the period of available
polarization data

  * 13

Gaia Collaboration (2020)

##  Appendix B The recorded photometric measurements of V CVn

Table 5:  Photopolarimetry journal of pulsation cycle 1/2020. JD | $P_{cal}$ | $PA_{cal}$ | $Q_{cal}$ | $\sigma_{Q}$ | $U_{cal}$ | $\sigma_{U}$ | $mag(V)$ | $\sigma_{mag(V)}$ | $Exp.$ | $Ob.$
---|---|---|---|---|---|---|---|---|---|---
(d) | (debiased) | (∘) |  |  |  |  |  |  | (sec) |
2458947.3 | 0.0133 | 98.6 | -0.0128 | 0.0018 | -0.0039 | 0.0013 | 7.46 | 0.02 | 8 | 1
2458948.3 | 0.0149 | 106.1 | -0.0126 | 0.0014 | -0.0080 | 0.0013 | 7.43 | 0.02 | 8 | 1
2458950.3 | 0.0127 | 103.3 | -0.0114 | 0.0010 | -0.0057 | 0.0010 | 7.31 | 0.02 | 10 | 1
2458954.3 | 0.0127 | 102.8 | -0.0117 | 0.0024 | -0.0056 | 0.0027 | 7.13 | 0.02 | 10 | 1
2458956.3 | 0.0130 | 108.3 | -0.0105 | 0.0011 | -0.0078 | 0.0011 | 7.13 | 0.02 | 10 | 1
2458960.3 | 0.0097 | 100.7 | -0.0091 | 0.0007 | -0.0036 | 0.0008 | 7.35 | 0.02 | 10 | 1
2458961.3 | 0.0112 | 110.8 | -0.0085 | 0.0014 | -0.0075 | 0.0013 | 7.16 | 0.02 | 10 | 1
2458962.3 | 0.0124 | 106.0 | -0.0105 | 0.0007 | -0.0066 | 0.0010 | 7.2 | 0.02 | 10 | 1
2458963.3 | 0.0133 | 103.8 | -0.0119 | 0.0008 | -0.0062 | 0.0008 | 7.18 | 0.02 | 10 | 1
2458966.3 | 0.0140 | 107.5 | -0.0115 | 0.0015 | -0.0081 | 0.0010 | 7.19 | 0.02 | 10 | 1
2458967.3 | 0.0136 | 109.9 | -0.0105 | 0.0012 | -0.0088 | 0.0010 | 7.26 | 0.02 | 10 | 1
2458969.3 | 0.0120 | 108.8 | -0.0095 | 0.0007 | -0.0073 | 0.0015 | 7.2 | 0.02 | 10 | 1
2458976.3 | 0.0123 | 107.3 | -0.0102 | 0.0008 | -0.0070 | 0.0009 | 7.08 | 0.02 | 10 | 1
2458977.3 | 0.0137 | 106.3 | -0.0116 | 0.0008 | -0.0074 | 0.0012 | 7.3 | 0.02 | 10 | 1
2458980.3 | 0.0135 | 111.2 | -0.0101 | 0.0009 | -0.0092 | 0.0020 | 7.32 | 0.05 | 10 | 1
2458987.3 | 0.0110 | 102.5 | -0.0100 | 0.0010 | -0.0047 | 0.0012 | 7.33 | 0.02 | 10 | 1
2458988.3 | 0.0105 | 106.5 | -0.0089 | 0.002 | -0.0058 | 0.0009 | 7.28 | 0.02 | 10 | 1
2458990.3 | 0.0119 | 105.2 | -0.0103 | 0.0009 | -0.006 | 0.0012 | 7.34 | 0.02 | 10 | 1
2458991.3 | 0.0121 | 105.9 | -0.0104 | 0.0009 | -0.0064 | 0.0012 | 7.35 | 0.02 | 10 | 1
2458996.3 | 0.0097 | 96.0 | -0.0095 | 0.0012 | -0.002 | 0.0012 | 7.34 | 0.02 | 10 | 1
2458997.3 | 0.0100 | 103.0 | -0.009 | 0.0011 | -0.0044 | 0.0014 | 7.51 | 0.02 | 10 | 1
2458999.4 | 0.0085 | 102.1 | -0.008 | 0.0019 | -0.0036 | 0.0012 | 7.59 | 0.02 | 10 | 1
2459002.4 | 0.0133 | 100.5 | -0.0125 | 0.0012 | -0.0048 | 0.0009 | 7.52 | 0.02 | 10 | 1
2459003.4 | 0.0119 | 97.8 | -0.0115 | 0.0009 | -0.0032 | 0.0013 | 7.55 | 0.02 | 10 | 1
2459013.4 | 0.0155 | 101.2 | -0.0144 | 0.0011 | -0.0059 | 0.0014 | 7.68 | 0.02 | 10 | 1
2459019.4 | 0.0144 | 105.1 | -0.0126 | 0.0028 | -0.0073 | 0.0014 | 7.63 | 0.02 | 10 | 1
2459024.4 | 0.0175 | 107.0 | -0.0146 | 0.0013 | -0.0098 | 0.0012 | 7.57 | 0.02 | 10 | 1
2459031.4 | 0.0161 | 110.3 | -0.0122 | 0.0008 | -0.0105 | 0.001 | 7.27 | 0.02 | 10 | 1
2459034.4 | 0.0170 | 109.8 | -0.0131 | 0.001 | -0.0108 | 0.001 | 7.22 | 0.02 | 10 | 1
2459035.4 | 0.0151 | 110.6 | -0.0114 | 0.0011 | -0.01 | 0.0013 | 7.23 | 0.02 | 10 | 1
2459036.4 | 0.0148 | 109.1 | -0.0116 | 0.0011 | -0.0092 | 0.0011 | 7.18 | 0.02 | 10 | 1
2459038.4 | 0.0122 | 109.8 | -0.0094 | 0.0007 | -0.0078 | 0.001 | 7.06 | 0.02 | 10 | 1
2459040.4 | 0.0147 | 110.1 | -0.0112 | 0.001 | -0.0095 | 0.0009 | 6.98 | 0.02 | 10 | 1
2459043.4 | 0.0130 | 111.6 | -0.0095 | 0.0011 | -0.0089 | 0.001 | 7.04 | 0.02 | 10 | 1
2459050.4 | 0.0114 | 112.0 | -0.0083 | 0.0012 | -0.008 | 0.0025 | 6.8 | 0.05 | 10 | 1
2459051.4 | 0.0089 | 117.7 | -0.0051 | 0.001 | -0.0074 | 0.0011 | 6.79 | 0.02 | 10 | 1
2459054.4 | 0.0094 | 110.8 | -0.0071 | 0.0012 | -0.0063 | 0.0014 | 6.75 | 0.02 | 10 | 1
2459056.4 | 0.0083 | 108.5 | -0.0068 | 0.0016 | -0.0051 | 0.0016 | 6.74 | 0.02 | 10 | 1
2459058.4 | 0.0073 | 102.5 | -0.0067 | 0.0011 | -0.0031 | 0.0009 | 6.63 | 0.02 | 10 | 1
2459060.4 | 0.0046 | 102.7 | -0.0042 | 0.0009 | -0.002 | 0.001 | 6.58 | 0.02 | 10 | 1
2459061.4 | 0.0053 | 101.0 | -0.005 | 0.0006 | -0.002 | 0.0013 | 6.63 | 0.02 | 10 | 1
2459062.3 | 0.0034 | 101.1 | -0.0034 | 0.0011 | -0.0014 | 0.0009 | 6.61 | 0.02 | 10 | 1
2459067.3 | 0.0064 | 93.7 | -0.0064 | 0.001 | -0.0008 | 0.001 | 6.74 | 0.02 | 10 | 1
2459069.3 | 0.0026 | 98.8 | -0.0029 | 0.0015 | -0.0009 | 0.0012 | 6.67 | 0.02 | 10 | 1
2459072.3 | 0.0034 | 83.3 | -0.0036 | 0.0015 | 0.0009 | 0.0016 | 6.65 | 0.02 | 10 | 1
2459077.3 | 0.0047 | 78.9 | -0.0045 | 0.0011 | 0.0018 | 0.0016 | 6.77 | 0.02 | 10 | 1
2459081.3 | 0.0071 | 74.4 | -0.0062 | 0.0013 | 0.0037 | 0.0017 | 6.96 | 0.02 | 10 | 1
2459110.4 | 0.0079 | 76.8 | -0.0071 | 0.0008 | -0.0035 | 0.0011 | 7.2 | 0.02 | 20 | 2
2459113.4 | 0.0103 | 82.4 | -0.0101 | 0.0011 | -0.0027 | 0.0009 | 7.2 | 0.02 | 20 | 2
2459118.4 | 0.0093 | 82.5 | -0.009 | 0.0002 | -0.0024 | 0.0007 | 7.17 | 0.02 | 30 | 2
2459119.4 | 0.0082 | 81.9 | -0.0079 | 0.0003 | -0.0023 | 0.0012 | 7.17 | 0.02 | 30 | 2
Table 6:  Journal of measurements from 2021, part 1. JD | $P_{cal}$ | $PA_{cal}$ | $Q_{cal}$ | $\sigma_{Q}$ | $U_{cal}$ | $\sigma_{U}$ | $mag(V)$ | $\sigma_{mag(V)}$ | $Exp.$ | $Ob.$
---|---|---|---|---|---|---|---|---|---|---
(d) | (debiased) | (∘) |  |  |  |  |  |  | (sec) |
2459266.4 | 0.0112 | 96.5 | -0.011 | 0.0014 | -0.0025 | 0.0015 | 6.68 | 0.02 | 7 | 1
2459267.4 | 0.0121 | 95.0 | -0.0121 | 0.0017 | -0.0021 | 0.0022 | 6.7 | 0.02 | 10 | 1
2459268.4 | 0.0122 | 87.8 | -0.0123 | 0.0019 | 0.001 | 0.0024 | 6.77 | 0.02 | 7 | 1
2459269.4 | 0.0126 | 91.5 | -0.0127 | 0.0017 | -0.0007 | 0.0021 | 6.83 | 0.02 | 10 | 1
2459270.4 | 0.0106 | 87.8 | -0.0106 | 0.0014 | 0.0008 | 0.0016 | 6.83 | 0.02 | 10 | 1
2459271.4 | 0.0097 | 87.1 | -0.0096 | 0.0014 | 0.0010 | 0.0015 | 6.87 | 0.02 | 7 | 1
2459273.3 | 0.0133 | 94.0 | -0.0133 | 0.0013 | -0.0018 | 0.0015 | 6.91 | 0.02 | 7 | 1
2459274.3 | 0.0147 | 86.4 | -0.0149 | 0.0026 | 0.0019 | 0.0027 | 6.87 | 0.02 | 7 | 1
2459275.3 | 0.0108 | 86.3 | -0.0109 | 0.0015 | 0.0014 | 0.001 | 6.92 | 0.02 | 10 | 1
2459276.3 | 0.0103 | 77.1 | -0.0094 | 0.0015 | 0.0046 | 0.0015 | 6.9 | 0.02 | 10 | 1
2459276.4 | 0.0100 | 73.4 | -0.0084 | 0.0008 | 0.0055 | 0.0007 | 6.93 | 0.02 | 10 | 2
2459279.3 | 0.0114 | 64.8 | -0.0073 | 0.0009 | 0.0088 | 0.0011 | 6.97 | 0.02 | 10 | 2
2459280.3 | 0.0101 | 64.3 | -0.0068 | 0.0041 | 0.0086 | 0.0045 | 6.74 | 0.02 | 10 | 1
2459282.3 | 0.0112 | 80.5 | -0.0106 | 0.0012 | 0.0037 | 0.0015 | 7.02 | 0.02 | 10 | 2
2459287.4 | 0.0110 | 79.8 | -0.0104 | 0.0012 | 0.0039 | 0.0015 | 7.03 | 0.02 | 10 | 2
2459290.4 | 0.0114 | 80.6 | -0.0108 | 0.0009 | 0.0037 | 0.0009 | 7.04 | 0.02 | 12 | 2
2459292.4 | 0.0109 | 81.2 | -0.0104 | 0.0005 | 0.0033 | 0.0007 | 7.08 | 0.02 | 10 | 2
2459295.4 | 0.0116 | 85.7 | -0.0115 | 0.0005 | 0.0017 | 0.0008 | 7.08 | 0.02 | 10 | 2
2459297.3 | 0.0125 | 92.3 | -0.0124 | 0.0004 | -0.001 | 0.0016 | 7.1 | 0.02 | 10 | 1
2459298.3 | 0.0107 | 89.7 | -0.0107 | 0.0005 | 0.0001 | 0.0006 | 7.11 | 0.02 | 10 | 1
2459303.3 | 0.0125 | 95.1 | -0.0123 | 0.0006 | -0.0022 | 0.0007 | 7.35 | 0.02 | 10 | 1
2459304.3 | 0.0134 | 96.6 | -0.013 | 0.0006 | -0.003 | 0.0006 | 7.26 | 0.02 | 10 | 1
2459305.4 | 0.0133 | 92.3 | -0.0133 | 0.001 | -0.001 | 0.0007 | 7.17 | 0.02 | 5 | 1
2459307.3 | 0.0149 | 98.3 | -0.0143 | 0.0003 | -0.0043 | 0.0007 | 7.23 | 0.02 | 5 | 1
2459308.4 | 0.0161 | 94.4 | -0.0159 | 0.0006 | -0.0025 | 0.0007 | 7.2 | 0.02 | 10 | 2
2459309.3 | 0.0168 | 101.1 | -0.0156 | 0.0008 | -0.0064 | 0.0007 | 7.2 | 0.02 | 5 | 1
2459313.3 | 0.0203 | 104.0 | -0.018 | 0.0006 | -0.0096 | 0.0007 | 7.35 | 0.02 | 5 | 1
2459314.4 | 0.0232 | 103.8 | -0.0206 | 0.0006 | -0.0108 | 0.0009 | - | - | 5 | 1
2459316.3 | 0.0249 | 105.8 | -0.0212 | 0.0003 | -0.0131 | 0.0007 | 7.25 | 0.02 | 5 | 1
2459317.4 | 0.0234 | 99.6 | -0.0221 | 0.0005 | -0.0077 | 0.0007 | 7.25 | 0.02 | 10 | 2
2459319.4 | 0.0248 | 99.9 | -0.0233 | 0.0005 | -0.0084 | 0.0007 | 7.28 | 0.02 | 11 | 2
2459320.4 | 0.0241 | 100.7 | -0.0225 | 0.0006 | -0.0087 | 0.0007 | 7.29 | 0.02 | 11 | 2
2459321.3 | 0.0242 | 106.5 | -0.0203 | 0.0007 | -0.0132 | 0.0007 | 7.36 | 0.02 | 5 | 1
2459325.3 | 0.0258 | 108.7 | -0.0205 | 0.0011 | -0.0157 | 0.0013 | 7.44 | 0.02 | 5 | 1
2459326.4 | 0.0272 | 103.8 | -0.0241 | 0.0007 | -0.0126 | 0.0009 | 7.4 | 0.02 | 10 | 2
2459327.3 | 0.0241 | 108.3 | -0.0194 | 0.0006 | -0.0144 | 0.0007 | 7.43 | 0.02 | 5 | 1
2459328.3 | 0.0249 | 109.5 | -0.0193 | 0.0007 | -0.0157 | 0.0007 | 7.48 | 0.02 | 5 | 1
2459329.3 | 0.0255 | 110.1 | -0.0195 | 0.0015 | -0.0165 | 0.0009 | 7.6 | 0.02 | 5 | 1
2459330.3 | 0.0255 | 110.2 | -0.0194 | 0.0008 | -0.0165 | 0.0008 | 7.55 | 0.02 | 5 | 1
2459331.3 | 0.0263 | 108.9 | -0.0208 | 0.0007 | -0.0161 | 0.0007 | 7.54 | 0.02 | 5 | 1
2459332.3 | 0.0253 | 109.6 | -0.0196 | 0.0008 | -0.016 | 0.0007 | 7.55 | 0.02 | 5 | 1
2459338.3 | 0.0300 | 110.4 | -0.0227 | 0.001 | -0.0197 | 0.0007 | 7.78 | 0.02 | 5 | 1
2459340.4 | 0.0235 | 110.6 | -0.0177 | 0.0006 | -0.0155 | 0.0009 | - | - | 5 | 1
2459340.4 | 0.0252 | 105.4 | -0.0217 | 0.0009 | -0.0129 | 0.0009 | 7.74 | 0.02 | 15 | 2
2459340.5 | 0.0258 | 106.3 | -0.0221 | 0.0011 | -0.0134 | 0.0009 | 7.74 | 0.02 | 15 | 2
2459342.5 | 0.0257 | 106.3 | -0.0217 | 0.0009 | -0.0138 | 0.001 | 7.78 | 0.02 | 15 | 2
2459342.3 | 0.0257 | 109.5 | -0.0199 | 0.0005 | -0.0162 | 0.0007 | 7.75 | 0.02 | 5 | 1
2459343.4 | 0.0212 | 112.9 | -0.0148 | 0.0006 | -0.0152 | 0.0008 | 7.79 | 0.02 | 5 | 1
2459353.4 | 0.0190 | 104.6 | -0.0167 | 0.0028 | -0.0094 | 0.0008 | 7.92 | 0.02 | 15 | 2
2459354.3 | 0.0212 | 114.0 | -0.0143 | 0.0028 | -0.0159 | 0.0011 | 7.99 | 0.02 | 5 | 1
2459364.4 | 0.0117 | 109.7 | -0.0091 | 0.0005 | -0.0074 | 0.0011 | 7.72 | 0.02 | 5 | 1
2459365.4 | 0.0140 | 117.6 | -0.008 | 0.0006 | -0.0115 | 0.0007 | 7.57 | 0.02 | 5 | 1
Table 7:  Journal of measurements from 2021, part 2. JD | $P_{cal}$ | $PA_{cal}$ | $Q_{cal}$ | $\sigma_{Q}$ | $U_{cal}$ | $\sigma_{U}$ | $mag(V)$ | $\sigma_{mag(V)}$ | $Exp.$ | $Ob.$
---|---|---|---|---|---|---|---|---|---|---
(d) | (debiased) | (∘) |  |  |  |  |  |  | (sec) |
2459367.4 | 0.0120 | 111.6 | -0.0088 | 0.0006 | -0.0082 | 0.0008 | 7.57 | 0.02 | 5 | 1
2459370.4 | 0.0118 | 106.5 | -0.0099 | 0.0008 | -0.0064 | 0.0010 | 7.66 | 0.02 | 5 | 1
2459374.4 | 0.0104 | 106.3 | -0.0088 | 0.0011 | -0.0056 | 0.0012 | 7.38 | 0.02 | 5 | 1
2459377.4 | 0.0116 | 104.4 | -0.0102 | 0.0006 | -0.0056 | 0.0009 | 7.51 | 0.02 | 5 | 1
2459379.4 | 0.0111 | 102.1 | -0.0101 | 0.0006 | -0.0046 | 0.0008 | 7.16 | 0.02 | 5 | 1
2459380.4 | 0.0101 | 111.6 | -0.0088 | 0.002 | -0.0053 | 0.0007 | 7.1 | 0.02 | 5 | 1
2459381.4 | 0.0120 | 102.0 | -0.011 | 0.0007 | -0.0049 | 0.0009 | 7.15 | 0.02 | 5 | 1
2459383.4 | 0.0112 | 99.8 | -0.0105 | 0.0006 | -0.0038 | 0.0007 | 7.18 | 0.02 | 5 | 1
2459389.4 | 0.0123 | 100.8 | -0.0115 | 0.0006 | -0.0045 | 0.0008 | 7.09 | 0.02 | 5 | 1
2459392.4 | 0.0135 | 98.4 | -0.013 | 0.0006 | -0.0039 | 0.0008 | 6.88 | 0.02 | 5 | 1
2459401.4 | 0.0120 | 98.3 | -0.0115 | 0.001 | -0.0035 | 0.0009 | 7.07 | 0.02 | 5 | 1
2459405.4 | 0.0128 | 99.2 | -0.0122 | 0.0007 | -0.004 | 0.0011 | 7.35 | 0.02 | 5 | 1
2459407.3 | 0.0140 | 98.7 | -0.0134 | 0.001 | -0.0042 | 0.0007 | 7.31 | 0.02 | 5 | 1
2459412.3 | 0.0133 | 97.7 | -0.0129 | 0.0013 | -0.0035 | 0.0012 | 7.31 | 0.02 | 5 | 1
2459412.5 | 0.0133 | 93.6 | -0.0132 | 0.0007 | -0.0017 | 0.0008 | 7.35 | 0.02 | 10 | 2
2459413.5 | 0.0132 | 93.3 | -0.0131 | 0.0008 | -0.0015 | 0.0009 | 7.36 | 0.02 | 10 | 2
2459414.4 | 0.0145 | 99.3 | -0.0138 | 0.0007 | -0.0046 | 0.0014 | 7.34 | 0.02 | 5 | 1
2459415.3 | 0.0112 | 99.1 | -0.0107 | 0.0008 | -0.0035 | 0.0009 | 7.44 | 0.02 | 5 | 1
2459416.3 | 0.0112 | 96.6 | -0.0109 | 0.0009 | -0.0026 | 0.0009 | 7.3 | 0.02 | 5 | 1
2459416.5 | 0.0128 | 92.2 | -0.0128 | 0.0006 | -0.001 | 0.0008 | 7.31 | 0.02 | 10 | 2
2459417.3 | 0.0108 | 95.6 | -0.0107 | 0.001 | -0.0021 | 0.0008 | 7.25 | 0.02 | 5 | 1
2459417.6 | 0.0107 | 91.3 | -0.0108 | 0.0013 | -0.0003 | 0.0013 | 7.33 | 0.02 | 10 | 2
2459418.3 | 0.0111 | 95.6 | -0.011 | 0.0012 | -0.0022 | 0.0013 | 7.3 | 0.02 | 5 | 1
2459419.3 | 0.0086 | 93.2 | -0.0086 | 0.0013 | -0.001 | 0.0012 | 7.26 | 0.02 | 5 | 1
2459425.3 | 0.0078 | 89.2 | -0.0078 | 0.0006 | 0.0002 | 0.0009 | 7.16 | 0.02 | 5 | 1
2459429.5 | 0.0063 | 85.9 | -0.0063 | 0.0005 | 0.0009 | 0.0007 | 6.98 | 0.02 | 12 | 2
2459436.3 | 0.0043 | 66.9 | -0.003 | 0.001 | 0.0032 | 0.001 | 6.76 | 0.02 | 5 | 1
2459437.3 | 0.0037 | 63.0 | -0.0023 | 0.0013 | 0.0032 | 0.0012 | 6.69 | 0.02 | 5 | 1
2459439.3 | 0.0033 | 69.4 | -0.0026 | 0.001 | 0.0023 | 0.0011 | 6.71 | 0.02 | 2 | 1
2459440.3 | 0.0039 | 67.3 | -0.0029 | 0.0014 | 0.003 | 0.001 | 6.77 | 0.02 | 3 | 1
2459441.3 | 0.0046 | 67.5 | -0.0033 | 0.0007 | 0.0033 | 0.0011 | 6.87 | 0.02 | 3 | 1
2459453.4 | 0.0052 | 81.6 | -0.005 | 0.0005 | 0.0015 | 0.0007 | 6.77 | 0.02 | 12 | 2
2459454.4 | 0.0048 | 79.9 | -0.0045 | 0.0005 | 0.0017 | 0.0007 | 6.8 | 0.02 | 12 | 2
2459459.4 | 0.0046 | 86.0 | -0.0046 | 0.0005 | 0.0006 | 0.0006 | 6.86 | 0.02 | 15 | 2
2459465.4 | 0.0075 | 84.1 | -0.0074 | 0.0005 | 0.0015 | 0.0006 | 6.93 | 0.02 | 15 | 2
2459477.4 | 0.0080 | 100.6 | -0.0075 | 0.0004 | -0.0029 | 0.0006 | 7.1 | 0.02 | 15 | 2
2459487.4 | 0.0097 | 99.8 | -0.0092 | 0.001 | -0.0032 | 0.0013 | 7.23 | 0.02 | 15 | 2
Table 8:  Journal of measurements from 2022, part 1. JD | $P_{cal}$ | $PA_{cal}$ | $Q_{cal}$ | $\sigma_{Q}$ | $U_{cal}$ | $\sigma_{U}$ | $mag(V)$ | $\sigma_{mag(V)}$ | $Exp.$ | $Ob.$
---|---|---|---|---|---|---|---|---|---|---
(d) | (debiased) | (∘) |  |  |  |  |  |  | (sec) |
2459609.4 | 0.0140 | 91.7 | -0.014 | 0.0005 | -0.0008 | 0.0006 | 7.36 | 0.02 | 15 | 2
2459617.4 | 0.0120 | 91.4 | -0.012 | 0.0004 | -0.0006 | 0.0006 | 7.01 | 0.02 | 15 | 2
2459619.4 | 0.0103 | 93.0 | -0.0103 | 0.0003 | -0.0011 | 0.0006 | 6.89 | 0.02 | 5 | 1
2459620.4 | 0.0092 | 89.6 | -0.0092 | 0.0004 | 0.0001 | 0.0007 | 6.82 | 0.02 | 5 | 1
2459622.4 | 0.0099 | 90.7 | -0.01 | 0.0008 | -0.0002 | 0.001 | 6.79 | 0.02 | 5 | 1
2459623.4 | 0.0089 | 78.7 | -0.0083 | 0.0004 | 0.0034 | 0.0007 | 6.78 | 0.02 | 5 | 1
2459624.3 | 0.0088 | 90.0 | -0.0088 | 0.0003 | 0.0000 | 0.0006 | 6.67 | 0.02 | 5 | 1
2459625.4 | 0.0090 | 91.2 | -0.009 | 0.0004 | -0.0004 | 0.0006 | 6.68 | 0.02 | 15 | 2
2459626.4 | 0.0102 | 90.6 | -0.0102 | 0.0005 | -0.0002 | 0.0007 | 6.61 | 0.02 | 5 | 1
2459630.4 | 0.0090 | 94.1 | -0.0089 | 0.0003 | -0.0013 | 0.0006 | 6.58 | 0.02 | 5 | 1
2459634.4 | 0.0080 | 90.2 | -0.008 | 0.0004 | 0.0000 | 0.0007 | 6.57 | 0.02 | 5 | 1
2459637.4 | 0.0078 | 93.3 | -0.0077 | 0.0004 | -0.0009 | 0.0007 | 6.52 | 0.02 | 5 | 1
2459637.4 | 0.0092 | 95.3 | -0.009 | 0.0004 | -0.0017 | 0.0006 | 6.54 | 0.02 | 15 | 2
2459639.4 | 0.0076 | 90.9 | -0.0077 | 0.0005 | -0.0002 | 0.0007 | 6.63 | 0.02 | 5 | 1
2459640.3 | 0.0080 | 93.1 | -0.008 | 0.0003 | -0.0009 | 0.0006 | 6.62 | 0.02 | 5 | 1
2459640.4 | 0.0074 | 90.7 | -0.0074 | 0.0004 | -0.0002 | 0.0006 | 6.56 | 0.02 | 14 | 2
2459642.4 | 0.0064 | 88.8 | -0.0065 | 0.0003 | 0.0003 | 0.0006 | 6.57 | 0.02 | 5 | 1
2459644.4 | 0.0071 | 93.0 | -0.0071 | 0.0004 | -0.0007 | 0.0006 | 6.61 | 0.02 | 15 | 2
2459646.3 | 0.0076 | 99.9 | -0.0072 | 0.0004 | -0.0026 | 0.0006 | 6.61 | 0.02 | 13 | 2
2459653.5 | 0.0093 | 94.0 | -0.0092 | 0.0004 | -0.0013 | 0.0006 | 6.68 | 0.02 | 10 | 2
2459657.4 | 0.0067 | 80.4 | -0.0063 | 0.0004 | 0.0022 | 0.0006 | 6.76 | 0.02 | 10 | 2
2459658.4 | 0.0083 | 92.5 | -0.0083 | 0.0004 | -0.0007 | 0.0006 | 6.77 | 0.02 | 10 | 2
2459659.4 | 0.0085 | 93.6 | -0.0084 | 0.0005 | -0.0011 | 0.0006 | 6.79 | 0.02 | 15 | 2
2459661.4 | 0.0100 | 96.0 | -0.0098 | 0.0005 | -0.0021 | 0.0007 | 6.83 | 0.02 | 15 | 2
2459664.4 | 0.0101 | 96.9 | -0.0098 | 0.0004 | -0.0024 | 0.0006 | 6.92 | 0.02 | 13 | 2
2459666.4 | 0.0090 | 89.1 | -0.009 | 0.0005 | 0.0003 | 0.0006 | 6.95 | 0.02 | 11 | 2
2459669.4 | 0.0128 | 91.2 | -0.0128 | 0.0005 | -0.0005 | 0.0007 | 7.01 | 0.02 | 11 | 2
2459679.3 | 0.0171 | 98.2 | -0.0164 | 0.0021 | -0.0048 | 0.0021 | 7.24 | 0.02 | 5 | 1
2459681.3 | 0.0172 | 101.3 | -0.0159 | 0.0003 | -0.0066 | 0.0007 | 7.29 | 0.02 | 5 | 1
2459683.3 | 0.0171 | 98.4 | -0.0164 | 0.0004 | -0.0049 | 0.0007 | 7.23 | 0.02 | 5 | 1
2459684.3 | 0.0158 | 94.5 | -0.0157 | 0.0005 | -0.0025 | 0.0008 | 7.28 | 0.02 | 5 | 1
2459686.3 | 0.0180 | 103.5 | -0.0161 | 0.0006 | -0.0082 | 0.0008 | 7.24 | 0.02 | 5 | 1
2459687.3 | 0.0186 | 105.1 | -0.0161 | 0.0005 | -0.0094 | 0.0007 | 7.21 | 0.02 | 5 | 1
2459688.4 | 0.0182 | 105.7 | -0.0156 | 0.0005 | -0.0095 | 0.0007 | 7.24 | 0.02 | 5 | 1
2459691.3 | 0.0184 | 110.7 | -0.0138 | 0.0016 | -0.0122 | 0.0017 | 7.27 | 0.02 | 5 | 1
2459692.4 | 0.0190 | 105.6 | -0.0163 | 0.0004 | -0.0098 | 0.0006 | 7.22 | 0.02 | 12 | 2
2459697.4 | 0.0166 | 107.9 | -0.0135 | 0.0004 | -0.0097 | 0.0007 | 7.2 | 0.02 | 12 | 2
2459698.4 | 0.0157 | 115.2 | -0.0101 | 0.0021 | -0.0122 | 0.0022 | 7.2 | 0.02 | 5 | 1
2459709.4 | 0.0107 | 114.1 | -0.0071 | 0.0005 | -0.008 | 0.0008 | 7.16 | 0.02 | 5 | 1
2459715.3 | 0.0104 | 109.5 | -0.0081 | 0.0006 | -0.0065 | 0.0008 | 7.06 | 0.02 | 5 | 1
2459717.3 | 0.0095 | 108.3 | -0.0076 | 0.0004 | -0.0057 | 0.0007 | 7.22 | 0.02 | 5 | 1
2459718.3 | 0.0092 | 107.4 | -0.0076 | 0.0005 | -0.0053 | 0.0007 | 7.29 | 0.02 | 5 | 1
2459721.3 | 0.0082 | 103.2 | -0.0073 | 0.0006 | -0.0036 | 0.0008 | 7.37 | 0.02 | 5 | 1
2459725.3 | 0.0117 | 106.8 | -0.0098 | 0.0007 | -0.0065 | 0.0009 | 7.41 | 0.02 | 5 | 1
Table 9:  Journal of measurements from 2022, part 2. JD | $P_{cal}$ | $PA_{cal}$ | $Q_{cal}$ | $\sigma_{Q}$ | $U_{cal}$ | $\sigma_{U}$ | $mag(V)$ | $\sigma_{mag(V)}$ | $Exp.$ | $Ob.$
---|---|---|---|---|---|---|---|---|---|---
(d) | (debiased) | (∘) |  |  |  |  |  |  | (sec) |
2459726.4 | 0.0128 | 109.5 | -0.01 | 0.0007 | -0.0081 | 0.0009 | 7.45 | 0.02 | 5 | 1
2459730.4 | 0.0124 | 104.2 | -0.011 | 0.0005 | -0.0059 | 0.0008 | 7.54 | 0.02 | 5 | 1
2459733.4 | 0.0137 | 102.8 | -0.0124 | 0.0007 | -0.006 | 0.0009 | 7.59 | 0.02 | 5 | 1
2459741.4 | 0.0175 | 90.0 | -0.0175 | 0.0005 | 0.0000 | 0.0007 | 7.71 | 0.02 | 5 | 1
2459742.4 | 0.0176 | 101.2 | -0.0163 | 0.0007 | -0.0067 | 0.0009 | 7.71 | 0.02 | 5 | 1
2459743.4 | 0.0183 | 99.9 | -0.0172 | 0.0007 | -0.0062 | 0.0009 | 7.79 | 0.02 | 5 | 1
2459745.4 | 0.0188 | 99.1 | -0.0179 | 0.001 | -0.0059 | 0.0011 | 7.74 | 0.02 | 5 | 1
2459750.4 | 0.0199 | 93.3 | -0.0198 | 0.0009 | -0.0023 | 0.001 | 7.76 | 0.02 | 5 | 1
2459760.3 | 0.0198 | 97.8 | -0.0191 | 0.0012 | -0.0053 | 0.0013 | 7.63 | 0.02 | 5 | 1
2459762.4 | 0.0153 | 90.5 | -0.0153 | 0.0006 | -0.0003 | 0.0008 | 7.58 | 0.02 | 5 | 1
2459763.4 | 0.0228 | 94.4 | -0.0226 | 0.0007 | -0.0035 | 0.0009 | 7.58 | 0.02 | 5 | 1
2459764.4 | 0.0150 | 84.2 | -0.0147 | 0.0009 | 0.003 | 0.001 | 7.47 | 0.02 | 5 | 1
2459766.4 | 0.0193 | 92.5 | -0.0193 | 0.0006 | -0.0017 | 0.0008 | 7.53 | 0.02 | 5 | 1
2459769.4 | 0.0188 | 94.8 | -0.0186 | 0.0005 | -0.0031 | 0.0007 | 7.52 | 0.02 | 5 | 1
2459771.4 | 0.0172 | 90.0 | -0.0172 | 0.0002 | 0.0000 | 0.0006 | 7.54 | 0.02 | 5 | 1
2459773.3 | 0.0189 | 93.7 | -0.0188 | 0.0017 | -0.0025 | 0.0018 | 7.52 | 0.02 | 5 | 1
2459777.3 | 0.0177 | 91.8 | -0.0177 | 0.0009 | -0.0011 | 0.0011 | 7.46 | 0.02 | 5 | 1
2459778.3 | 0.0182 | 93.4 | -0.0181 | 0.0006 | -0.0022 | 0.0008 | 7.45 | 0.02 | 5 | 1
2459780.3 | 0.0170 | 94.8 | -0.0168 | 0.0005 | -0.0028 | 0.0007 | 7.43 | 0.02 | 5 | 1
2459782.3 | 0.0181 | 93.3 | -0.018 | 0.001 | -0.0021 | 0.0012 | 7.38 | 0.02 | 5 | 1
2459785.3 | 0.0182 | 95.7 | -0.0179 | 0.0007 | -0.0036 | 0.0009 | 7.32 | 0.02 | 5 | 1
2459787.3 | 0.0155 | 93.5 | -0.0154 | 0.0013 | -0.0019 | 0.0014 | 7.28 | 0.02 | 5 | 1
2459794.3 | 0.0157 | 96.7 | -0.0153 | 0.0005 | -0.0036 | 0.0007 | 7.19 | 0.02 | 5 | 1
2459795.3 | 0.0182 | 100.6 | -0.017 | 0.0005 | -0.0066 | 0.0008 | 7.2 | 0.02 | 5 | 1
2459796.3 | 0.0178 | 98.5 | -0.0171 | 0.0006 | -0.0052 | 0.0008 | 7.16 | 0.02 | 5 | 1
2459800.3 | 0.0175 | 99.2 | -0.0166 | 0.0008 | -0.0055 | 0.001 | 7.2 | 0.02 | 5 | 1
2459801.3 | 0.0148 | 97.0 | -0.0144 | 0.0007 | -0.0036 | 0.0009 | 7.21 | 0.02 | 5 | 1
2459802.3 | 0.0159 | 99.0 | -0.0151 | 0.0007 | -0.0049 | 0.0009 | 7.28 | 0.02 | 5 | 1
2459802.5 | 0.0186 | 94.2 | -0.0184 | 0.0004 | -0.0027 | 0.0006 | 7.22 | 0.02 | 12 | 2
2459803.4 | 0.0161 | 94.5 | -0.0159 | 0.0006 | -0.0024 | 0.0007 | 7.22 | 0.02 | 11 | 2
2459808.3 | 0.0164 | 97.6 | -0.0158 | 0.0008 | -0.0043 | 0.0009 | 7.25 | 0.02 | 5 | 1
2459810.5 | 0.0175 | 95.6 | -0.0172 | 0.0007 | -0.0034 | 0.0007 | 7.25 | 0.02 | 14 | 2
2459815.4 | 0.0160 | 95.9 | -0.0157 | 0.0009 | -0.0033 | 0.001 | 7.2 | 0.02 | 14 | 2
2459824.4 | 0.0164 | 100.6 | -0.0153 | 0.0005 | -0.0059 | 0.0006 | 7.17 | 0.02 | 13 | 2
2459833.4 | 0.0145 | 97.1 | -0.0141 | 0.0006 | -0.0036 | 0.0008 | 7.21 | 0.02 | 15 | 2
2459837.4 | 0.0112 | 95.4 | -0.011 | 0.0005 | -0.0021 | 0.0007 | 7.17 | 0.02 | 15 | 2
2459845.3 | 0.0107 | 100 | -0.0101 | 0.0005 | -0.0037 | 0.0007 | 7.12 | 0.02 | 15 | 2
2459847.3 | 0.0116 | 97.8 | -0.0112 | 0.0004 | -0.0031 | 0.0007 | 7.12 | 0.02 | 15 | 2
2459849.3 | 0.0132 | 95.2 | -0.013 | 0.0005 | -0.0024 | 0.0006 | 7.1 | 0.02 | 15 | 2
2459850.3 | 0.0128 | 103.7 | -0.0114 | 0.0005 | -0.0059 | 0.0006 | 7.08 | 0.02 | 15 | 2
2459865.4 | 0.0173 | 111.5 | -0.0126 | 0.0004 | -0.0118 | 0.0007 | 6.98 | 0.02 | 15 | 2
2459867.3 | 0.0169 | 111.9 | -0.0122 | 0.0005 | -0.0117 | 0.0007 | 7.00 | 0.02 | 15 | 2
2459887.7 | 0.0184 | 124.0 | -0.0069 | 0.0006 | -0.0171 | 0.0008 | 7.33 | 0.02 | 15 | 2