#  A study of Be stars in the time domain
I. Spectral data and polarimetry

A. Castañón Esteban,1 I.A. Steele,1 H. Jermak1
1Astrophysics Research Institute, Liverpool John Moores University, 146
Brownlow Hill, Liverpool L3 5RF, UK
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present the first part of a spectroscopic and polarimetric study on a
sample of 58 Be stars that have been measured since 1998. The aim of the study
is to understand the timescales of disk variability, formation and dissipation
as a function of the properties (mass, luminosity and rotational velocity) of
the underlying B star. In this paper we classified the sample based on the
presence of emission or absorption of the H$\alpha$ line, and the shape of the
peak as single or double peak, as well as noting changes between emission and
non-emission states. We find a probability of $\sim 0.75$ percent per year
that an object in the sample will undergo such a change. We also present re-
derived values of the projected rotational velocities for the sample. When we
compare our polarization values with those from the literature, we find that
most of the stars do not show a change in the value of the polarization angle,
however a small number show significant changes which could be attributed to
either disk strength (optical depth) or geometry changes. Finally we show how,
by combining the (interstellar corrected) degree of polarization and the
projected rotational velocity, we can construct an inclination angle-free
parameter that includes the true equatorial velocity. Using this inclination
angle-independent parameter we show that the populations of single and double
peak stars are indistinguishable, giving further evidence that Be star line
profiles are essentially inclination angle driven.

###### keywords:

techniques: spectroscopic – techniques: polarimetric – stars: emission-line,
Be

††pubyear: 2023††pagerange: A study of Be stars in the time domain  I.
Spectral data and polarimetry–A

##  1 Introduction

Be stars are, on a fundamental level, B stars that show, or have shown in the
past, one or more Balmer lines in emission (Collins, 1987). The origin of this
emission is currently understood as a circumstellar disk around the star that
has been created by material lost by the star (Poeckert & Marlborough, 1978;
Quirrenbach, 1994).

The mechanism that creates this disk is still debated: It is understood that a
rapid rotational velocity ($v$) plays an important role (Slettebak, 1979),
although in general they do not rotate at the full break-up velocities
(Porter, 1996). Mechanisms proposed include single-star radial pulsation
(Baade, 1988; Rivinius et al., 1998), but it is unclear if this is enough to
create the disk (Owocki, 2006; Cranmer, 2009). Magnetic fields may also play a
role (Cassinelli et al., 2002; Brown et al., 2008), but no magnetic fields
have been found on Be stars, in contrast with B stars (Wade et al., 2014).
Another possibility is that the creation of the disk is due to interaction
with a companion star (Kriz & Harmanec, 1975; Pols et al., 1991), where the
accreting star in the transfer not only increases its mass but also its
angular momentum (Hastings et al., 2021). A study from Oudmaijer & Parr (2010)
found that only $\sim$30% of stars are found in binaries, while a study from
Bodensteiner et al. (2020) found that while none of the Be stars studied were
in visible binaries with main sequence stars, a large fraction of the fast-
rotating B stars were, supporting the idea that binarity may be the cause of
the fast rotation and the companion is barely visible anymore after the mass
transfer. At the same time, while no main sequence stars have been found as
companions of Be systems, subdwarf O and B stars have been found, with
characteristics similar to remnant core of a star that did lose most of its
envelope (Mourard et al., 2015). A more detailed discussion on the importance
of the binarity channel in the creation of the disk around the B star is given
by Jones et al. (2022).

In order to help constrain models, observational studies of the properties and
variability of the Be phenomenon are likely to be key. For example,
understanding the timescales of disk loss and reformation as a property of
stellar mass, temperature and equatorial velocity is likely to be important
(Barnsley & Steele, 2013). Understanding these dependencies is, however,
complicated by the effect of inclination. The disk will have a certain
inclination, $i$, with respect to the observation plane and the Earth. As a
result, the observed rotational velocity is $v\sin i$. This value is useful as
a lower bound for the rotational velocity, but at the same time the actual
rotational velocity $v$ can be much higher. An upper bound on the $v$ will be
the critical velocity ($v_{\rm crit}$), at which point the rotational and
gravitational forces at the equator of the star are balanced. A value often
used to see how close to this point a star is the critical fraction
$W=v/v_{\rm crit}$.

The variability and shape of the emission line has also been a matter of
study: It can be a single or double peak (Hanuschik et al., 1988) with
variable values of asymmetry between the peaks (Hanuschik et al., 1995) or
have the shape of shell lines (Hanuschik, 1995). These profiles have been
successfully modelled and theoretically reproduced (Silaj et al., 2010).

As well as showing emission line variability, the polarization of Be stars is
also variable with time (Coyne & Gehrels, 1967). The polarization is caused by
radiation scattering due to free electrons (Coyne & Kruszewski, 1969) and is a
function of the inclination angle. As such the combination of spectroscopic
and polarimetric observations can help constrain the true rotational velocity
$v$.

In this paper we present the first in a series of new analyses of the
properties of a sample of Be stars (Steele et al., 1999) that have been
observed spectroscopically for more than two decades. The overall aim of the
project is to understand the variability timescales of the objects and how
that relates to the properties (mass, luminosity, rotational velocity) of the
underlying B star. For this first paper we concentrate on combining new
polarimetric observations with the historical spectral data in order to
understand the rotational velocity distribution of the sample. This will then
be used in future papers to explore the impact on line emission variability at
various wavelengths.

In section 2 we describe the properties of the sample and previous work that
has been carried out on it. In section 3 we describe the acquisition and data
reduction of our spectroscopic and polarimetric dataset and in section 4 make
a basic classification of the appearance and variability of the H$\alpha$ line
profile for each object. Section 5 describes the calculation of projected
rotational velocities and critical velocities for the sample. Similarly,
section 6 describes the correction for each object of polarization degrees and
angles for the effects of interstellar polarization. In Section 7 we combine
the results of the previous two sections to derive rotational velocities
corrected for the effect of inclination angle. Finally in section 8 we make
some concluding remarks.

##  2 Sample selection

Our sample is the same as the one introduced in Steele et al. (1999). The 58
stars in the sample were were initially classified as Be stars in the database
presented in Jaschek & Egret (1982), and were selected to cover several
objects for each spectral and luminosity class for Be stars, to make it as
representative as possible. However, because Be stars are variable, some of
the stars classified as Be stars in 1982 might not show H$\alpha$ emission
anymore. As the raw data used in their initial classification is generally
unavailable and was compiled from a wide variety of sources, they may also
have been misclassified. Several of the stars might also have changed to no
emission at some point before or between the observations.

Previous work on the sample is described in a series of five papers published
between 1999 and 2013. In paper I (Steele et al., 1999), the criteria for the
selection of the sample was presented. A basic study of the rotational
velocities of the stars was done based on a single spectrum of each object, as
well as a reclassification of their spectral type. Paper II (Clark & Steele,
2000) studied the same sample plus another 8 sources in the K band (2.05-2.22
$\mu$m). It determined that some objects do not show Br$\gamma$ emission
($\lambda=21660$ Å), which might indicate no hydrogen emission in general,
putting in doubt their classification as a Be star. Different sets of the
spectra showed H I, He I, Mg II, Fe II and Na I lines, with He I and Mg II
features as a good diagnostic of early spectral type. At the same time, stars
that did not show Br$\gamma$ emission seemed to have a lower projected
rotational velocity. Paper III (Steele & Clark, 2001) studied 57 of the stars
from paper 1 in the H band (1.53-1.69 $\mu$m). H I Brackett lines were again
examined, as well as Fe II. It showed that the analysis of the H band spectra
alone only allows for the classification into "early" (B0e-B4e) and "late"
(B5e-B9e) types. Paper IV (Howells et al., 2001) studied 52 of the stars from
paper 1 with $JHK$ infrared photometry, separating values for the interstellar
reddening and the circumstellar excess, and finding a strong correlation
between the derived interstellar reddening values and the equivalent width of
the interstellar sodium lines, giving confidence in the measured reddening.
Paper V (Barnsley & Steele, 2013) studied the equivalent width variability of
the H$\alpha$ line for the measurements taken for 55 stars between 1998 and
2010, finding that stars of earlier types, with higher values of the projected
rotational velocity, show a higher degree of variability in the H$\alpha$
emission.

##  3 Data

###  3.1 Observations and Data Reduction

The objects in our sample have been observed several times between 1998 and
2022 with multiple instruments. This work includes observations taken in 1998
and 2002 using the IDS spectrograph on the Isaac Newton Telescope (INT), 2009
observations with the medium resolution settings ($R\sim 2500$) of the
FRODOspec spectrograph on the Liverpool Telescope (LT) (Morales-Rueda et al.,
2004), 2010 to 2021 observations with the high resolution ($R\sim 5000$)
FRODOspec settings, and 2022 observations with the low resolution ($R\sim
350$) SPRAT spectrograph also on the LT (Piascik et al., 2014). The years of
observation, as well as the total number of observations, are shown in Table
5. All INT and LT data were re-reduced using the aspired pipeline (Lam et al.,
2020) for consistency.

In addition to these spectra, we have polarimetric observations taken with the
MOPTOP polarimeter on the Liverpool Telescope (Jermak et al., 2016, 2018) in
October 2022. Our sample is very bright, with apparent magnitudes in the range
of $V=4.04$ and $V=10.60$ (Steele et al., 1999). For this reason, if we try to
observe the brightest objects directly, the observation will be instantly
saturated. To avoid this, we defocussed the telescope, with different values
depending on how bright the stars are, allowing us to spread the light without
saturating the detector. We also used the MOPTOP fast-rotation mode, which
completes a cycle of 16 positions in 8 seconds, to avoid saturation as much as
possible. The values used for the defocussing are shown in Table 1 to aid
future observers of bright objects with the instrument.

Reduction of the MOPTOP data was carried out using aperture photometry
routines from astropy (Astropy Collaboration et al., 2022). The extracted
photometric counts were converted to Stokes $q$ and $u$ values following the
procedure outlined in Shrestha et al. (2020), with corrections for
instrumental polarization made using the calibration values presented in
Steele et al. (2023).

Table 1: The values given for the defocus of the telescope when using MOPTOP for the different sources, depending on their apparent magnitude V. V | Defocus (mm)
---|---
$m>9.75$ | $0.0$
$9.75>m>6.75$ | $1.0$
$6.75>m>4.9$ | $2.0$
$4.9>m>4.04$ | $2.5$

###  3.2 Additional data

As additional data, we have included the distances and the reddening. The
distances have been calculated from parallax values obtained from the Gaia
database (Gaia Collaboration et al., 2022), except in 3 cases where they have
been taken from the Hipparcos catalog (van Leeuwen, 2007) because they were
not available or the error of the Gaia values was larger than the actual
values. The reddening $E(B-V)$ was obtained in Howells et al. (2001), where we
could find values for 52 of the stars in our data. These values have been
added to Table 6.

##  4 H$\alpha$ classification

The most basic classification that we can make for Be stars from their spectra
is taking into account the shape of the H$\alpha$ line: some Be stars will
show a single peak emission, while others will show a mostly symmetric double
peak emission. We show an example of this in Figure 1. At the same time,
others will not show any H$\alpha$ emission anymore, and will show absorption
of the line instead. Even more interesting, with a long time study like this
one, we can also see some changing with time. We will discuss this in a
quantitative fashion in future papers. However for now we simply classify them
based on their overall appearance. In the most complicated cases of the ones
with changing emission type, we will choose the most recent observation, as it
is the most closely related to their polarization status.

From our sample of 58 stars, 10 never showed any H$\alpha$ emission between
1998 and our last observation. 16 show a single peak in all of our
observations, while 21 show a double peak in all of them. The remaining 11 in
our sample have changed with time, with 3 of them showing emission and 8 not
showing emission in our last observation. In total, from our last observation,
18 do not show hydrogen emission and 40 show hydrogen emission lines (Figure
2).

Examining the 11 objects that changed with time in more detail, we see that 9
of them at least spent some time as no emission, with another 2 always
emitting and changing only between double peak and single peak. We can
therefore assume a change rate between emission and absorption of 9/48 in 24
years, or 0.78% of the total sample changing between emission and absorption
every year (counting only the objects that we have observed actively changing
from our first observation). Similarly if we instead assume all the objects
that did not show any absorption in 1998 are changed from their original
observations, compiled in Jaschek & Egret (1982) but originally from the 1960s
and 1970s, we would have a fraction 19/58 over an estimated time of 45 years
(0.73%/year).

Previous determinations of this change rate (McSwain et al., 2008, 2009;
Barnsley & Steele, 2013; Dimitrov et al., 2018) over shorter time periods
(4–12 years) have ranged between 0.3 and 25 %/year. This wide range can be
attributed to how the different samples used for the studies were constructed.
Using the same sample as here but only between 1998 and 2010 Barnsley & Steele
(2013) found 2 changing objects over 55 analyzed Be stars over a period of 12
years, or 0.30%/year. However (McSwain et al., 2008) observed 16 Be stars in a
sample of 191 B stars, with 11 of them changing between emission and no
emission during a period of observation of 4 years. If these 11 are counted
only from the 16 Be stars, then the change rate would be of 11/16 over 4
years, or 17%/year. Alternatively if we count them over the whole sample of B
stars, then the change rate would be 11/191 over 4 years, or 1.4%/year. A
similar study McSwain et al. (2009) observed 45 Be stars in a sample of 296 B
stars over 2 years, with 23 of them showing variability in emission. Counting
only 23/45 for 2 years would give us a change rate of 25.5%/year, while 23/296
for 2 years would give us instead a change rate of 3.89%/year. Finally
Dimitrov et al. (2018) observed 60 Be stars over a period on 3 years, and 4 of
them changed in emission giving a change rate of 2.2%/year. Overall comparing
the values with at least similar methodologies (including our latest
determination) it appears that a change rate of no more than a few percent per
year is something like the true value.

Figure 1: Representative plots of the three types of H$\alpha$ peaks in our
sample, extracted from the 1998 observations. HD4180 is an example of a single
peak, HD22192 is an example of a double peak, and HD164741 is instead an
example of absorption in H$\alpha$. The rest wavelength of H$\alpha$ is
indicated by the vertical line. Figure 2: The distribution of our sample for
the three different types of observed H$\alpha$, in this case, "NP" for "No
peak", "SP" for "Single peak", and "DP" for "Double peak", classified from
their last observation.

##  5 Results: rotation

Figure 3: A plot, showing the fit to the helium I lines. In this case, it is
the observation of star HD4180 taken in August 1998. We fit each line to a
Gaussian profile and obtained the FWHM from them, and hence the velocity as
described in Section 5. The results for each line in this example are
vsini$(\lambda=4026$Å$)=193.7\pm 3.2$ km/s, vsini $(\lambda=4143$Å$)=190.8\pm
4.9$ km/s, vsini $(\lambda=4387$Å$)=187.7\pm 4.9$ km/s, vsini
$(\lambda=4471$Å$)=181.9\pm 3.9$ km/s.

###  5.1 Calculation of the rotational velocities

One of the most common values for Be stars is the rotational velocity of the
central star, $vsini$. The way that we have chosen to obtain these values is
using the He-I absorption lines in our spectra, more precisely the lines at
wavelengths 4026 Å, 4143 Å, 4387 Å and 4471 Å. We first fit a Gaussian profile
to each of these lines, obtaining this way $\sigma$, the standard deviation of
the Gaussian distribution, that then can be converted into the full width half
maximum (FWHM) using:

$FWHM=2\sqrt{2\ln 2}\sigma$ (1)

These values of FWHM are not yet a measurement of the rotational velocity
itself, since rotation is not the only line broadening mechanism. We therefore
convert them using the FWHM-$v\sin i$ relation derived from observational fits
to rotationally broadened line profiles of model atmospheres of a wide sample
of early type stars (Slettebak et al., 1975). We will first do a linear fit
for the values of FWHM and $vsini$ of the He-I line ($\lambda=4471$Å) shown in
the tables 1 and 2 of Slettebak et al. (1975), as shown in Figure 4, and then
use this relation to convert our values to rotational velocities, applying a
Doppler shift to the FWHM dependent slope to change the values to the other
three near He-I lines ($\lambda=4387$ Å,$\lambda=4143$ Å,$\lambda=4026$ Å).
The final equations obtained were:

$\begin{split}v\sin i=42.68F(\lambda=4471)-36.84{\rm kms^{-1}}\\\ v\sin
i=43.50F(\lambda=4387)-36.84{\rm kms^{-1}}\\\ v\sin
i=46.06F(\lambda=4143)-36.84{\rm kms^{-1}}\\\ v\sin
i=47.40F(\lambda=4026)-36.84{\rm kms^{-1}}\end{split}$ (2)

with $F(\lambda)$ being the FWHM for the line at the corresponding wavelength.

Figure 4: A plot of the rotational velocities of B stars vs the FWHM of the He
I 4471 Åline, extracted from tables 1 and 2 in Slettebak et al. (1975). The
results of the linear fit $y=Ax+B$ are $A=42.68\pm 0.93$, $B=-36.84\pm 4.17$,
$R=0.9746$

For any particular object the results of the fits to these lines will show
certain variation: a number of factors can cause this effect such as the noise
in the spectrum or blending with another line. For that reason, we have chosen
to calculated the weighted mean and standard deviation of the four lines and
reject any values that are more than 4 $\sigma$ away from the average value.
With this, we have obtained a series of values in time for the rotational
velocity of the star. We do not expect any changes in the rotational velocity
of a star over the span of just a few decades, so we take the weighted mean of
these values for each object. These results are shown in Table 2 and
represented in Figure 5.

Table 2:  List of observed objects, comparing their rotational velocities vs the rotational velocities obtained in Steele et al. (1999) Object | Other |  $v\sin i$ (km/s) |  $v\sin i$ (km/s)
---|---|---|---
| Identifier | (2023) | (1999)
CD-28 14778 | HD 171757 |  141 $\pm$ 23 |  153 $\pm$ 21
CD-27 11872 | HD 161103 |  210 $\pm$ 17 |  224 $\pm$ 33
CD-27 16010 | HD 214748 |  188.6 $\pm$ 7.2 |  187 $\pm$ 32
CD-25 12642 | HD 164741 |  100 $\pm$ 24 |  77 $\pm$ 18
CD-22 13183 | HD 172158 |  169 $\pm$ 79 |  174 $\pm$ 10
BD-20 5381 | HD 177015 |  197 $\pm$ 72 |  202 $\pm$ 10
BD-19 5036 | HD 170682 |  126 $\pm$ 17 |  121 $\pm$ 10
BD-12 5132 | HD 172252 |  98 $\pm$ 11 |  120 $\pm$ 43
BD-02 5328 | HD 196712 |  170.2 $\pm$ 8.4 |  151 $\pm$ 15
BD-01 3834 | HD 187350 |  166 $\pm$ 12 |  168 $\pm$ 34
BD-00 3543 | HD 173371 |  224 $\pm$ 15 |  271 $\pm$ 54
BD+02 3815 | HD 179343 |  197 $\pm$ 10 |  224 $\pm$ 14
BD+05 3704 | HD 168797 |  211 $\pm$ 59 |  221 $\pm$ 10
BD+17 4087 | HD 350559 |  204 $\pm$ 79 |  156 $\pm$ 39
BD+19 578 | HD 23016 |  215 $\pm$ 17 |  240 $\pm$ 70
BD+20 4449 | HD 191531 |  90 $\pm$ 43 |  81 $\pm$ 11
BD+21 4695 | HD 210129 |  157 $\pm$ 17 |  146 $\pm$ 10
BD+23 1148 | HD 250289 |  87 $\pm$ 77 |  101 $\pm$ 10
BD+25 4083 | HD 339483 |  161 $\pm$ 83 |  79 $\pm$ 11
BD+27 797 | HD 244894 |  197 $\pm$ 18 |  148 $\pm$ 74
BD+27 850 | HD 246878 |  121 $\pm$ 18 |  112 $\pm$ 25
BD+27 3411 | HD 183914 |  170 $\pm$ 13 |  194 $\pm$ 10
BD+28 3598 | HD 333452 |  113 $\pm$ 50 |  90 $\pm$ 12
BD+29 3842 | HD 333226 |  81 $\pm$ 20 |  91 $\pm$ 16
BD+29 4453 | HD 205618 |  247 $\pm$ 26 |  317 $\pm$ 20
BD+30 3227 | HD 171406 |  207.5 $\pm$ 8.3 |  218 $\pm$ 21
BD+31 4018 | HD 193009 |  225 $\pm$ 30 |  211 $\pm$ 11
BD+36 3946 | HD 228438 |  178 $\pm$ 23 |  186 $\pm$ 21
BD+37 675 | HD 18552 |  223 $\pm$ 21 |  207 $\pm$ 29
BD+37 3856 | HD 228650 |  119 $\pm$ 18 |  104 $\pm$ 17
BD+40 1213 | HD 33604 |  122.3 $\pm$ 7.4 |  128 $\pm$ 20
BD+42 1376 | HD 37657 |  195.6 $\pm$ 9.6 |  196 $\pm$ 10
BD+42 4538 | HD 216581 |  236 $\pm$ 30 |  282 $\pm$ 10
BD+43 1048 | HD 276738 |  205 $\pm$ 46 |  220 $\pm$ 20
BD+45 933 | HD 27846 |  135 $\pm$ 14 |  148 $\pm$ 16
BD+45 3879 | HD 211835 |  186 $\pm$ 10 |  193 $\pm$ 10
BD+46 275 | HD 6811 |  111 $\pm$ 20 |  113 $\pm$ 21
BD+47 183 | HD 4180 |  167 $\pm$ 12 |  173 $\pm$ 12
BD+47 857 | HD 22192 |  227 $\pm$ 12 |  212 $\pm$ 16
BD+47 939 | HD 25940 |  153.0 $\pm$ 8.0 |  163 $\pm$ 12
BD+47 3985 | HD 217050 |  232 $\pm$ 14 |  284 $\pm$ 20
BD+49 614 | HD 13867 |  140 $\pm$ 110 |  90 $\pm$ 27
BD+50 825 | HD 23552 |  184 $\pm$ 11 |  187 $\pm$ 10
BD+50 3430 | HD 207232 |  198 $\pm$ 19 |  230 $\pm$ 15
BD+51 3091 | HD 20551 |  139.8 $\pm$ 8.5 |  106 $\pm$ 10
BD+53 2599 | HD 203356 |  223 $\pm$ 22 |  191 $\pm$ 23
BD+55 552 | HD 13669 |  243 $\pm$ 29 |  292 $\pm$ 17
BD+55 605 | HD 14605 |  142 $\pm$ 25 |  126 $\pm$ 35
BD+55 2411 | HD 195554 |  192.8 $\pm$ 9.2 |  159 $\pm$ 90
BD+56 473 | V356 Per |  218 $\pm$ 23 |  238 $\pm$ 19
BD+56 478 | HD 13890 |  152 $\pm$ 30 |  157 $\pm$ 12
BD+56 484 | V502 Per |  182 $\pm$ 39 |  173 $\pm$ 16
BD+56 493 | - |  175 $\pm$ 41 |  270 $\pm$ 10
BD+56 511 | - |  108 $\pm$ 54 |  99 $\pm$ 14
BD+56 573 | - |  210 $\pm$ 51 |  250 $\pm$ 58
BD+57 681 | HD 237056 |  155 $\pm$ 20 |  147 $\pm$ 49
BD+58 554 | HD 237060 |  209 $\pm$ 17 |  229 $\pm$ 10
BD+58 2320 | HD 239758 |  244 $\pm$ 39 |  243 $\pm$ 20
Figure 5: A plot comparing the values obtained for the rotational velocity in
2023 vs the values obtained for the rotational velocity in 1999. The red line
is a 1:1 line for comparison that allows us to see that our rotational
velocities seem to be similar when compared with the lower values of 1999, but
lower when compared with the higher values of 1999. The cause of this
difference might be that our results are the average of many years of
observations, versus only one observation as in 1999.

###  5.2 Calculation of the critical velocity

The critical velocity of a Be star is the theoretical equilibrium velocity at
which the central B star would need to rotate over to eject the material on
its equator purely by compensating gravity with rotation. We can find the
formula for example in Townsend et al. (2004):

$v_{crit}=\sqrt{\frac{2}{3}\frac{GM}{R_{P}}}$ (3)

with M the mass of the central star and $R_{P}$ its polar radius.

To obtain these values for our sample, we use classification of the spectral
types from Steele et al. (1999) (reproduced in our Table 6) to take stellar
luminosities from de Jager & Nieuwenhuijzen (1987); Cox (2000). Masses and
radii were then derived from those luminosity values using the equations shown
in Tables 4 and 5 of Eker et al. (2018).

First, we have calculated the masses from the luminosities, following the set
of equations:

$\begin{split}&\log M=(\log L-0.010)/4.329;1.05<M/M_{\odot}\leq 2.40\\\ &\log
M=(\log L-0.093)/3.967;2.4<M/M_{\odot}\leq 7\\\ &\log M=(\log
L-1.105)/2.865;7<M/M_{\odot}\\\ \end{split}$ (4)

calculating the three values and choosing the appropriate ones for their
range.

From those values, and following the indications in Eker et al. (2018), we
have calculated as well the effective temperature:

$\log T_{\mathrm{eff}}=-0.170(\log M)^{2}+0.888\log M+3.671$ (5)

and then we finally calculate the radius of the star using Stefan-Boltzmann
law:

$R=\sqrt{\frac{L}{4\pi\sigma T_{\mathrm{eff}}^{4}}}$ (6)

After obtaining the values of the mass and radius of the star, we can
calculate the $v_{crit}$ and the value of the critical fraction $W$, to show
how close the obtained equatorial rotational velocity is to the critical
value:

$W=\frac{v}{v_{crit}}$ (7)

We have also calculated the value of $Wsini$, where in equation 7 we used
$vsini$ instead of $v$. All of these values are listed in Table 6.

##  6 Results: polarization

###  6.1 Calculation of the polarization degree and angle

After calculating the values for the rotational velocity ($v\sin i$), we move
to the calculation of the polarization degree and angle of each band. We first
calculate the Stokes parameters following the instructions for the double
camera settings as shown in Shrestha et al. (2020). After obtaining the Stokes
parameters, we calculated the polarization degree and angle for each band
according to the standard formulation. We have derived the polarization degree
($P$) and angle ($\theta$) values for the bands $V$, $B$ and $R$. These
results can be found in Tables 7 and 8. As most of the values that we will
compare our polarization values (section 7) with are full-range/white-light
instead of individual bands, we have calculated the average of the values q
and u for the three bands and calculated the average values for the
polarization degree ($\bar{P}$) and the angle ($\bar{\theta}$) from them.

We note here that MOPTOP polarimetry suffers from a systematic errors of $\sim
0.002$ in $P$ and $1^{\circ}$ in $\theta$ (Shrestha et al., 2020). These
systematic errors are not included in the values presented in Tables 7 and 8
but are incorporated into the final interstellar corrected values calculated
in the next section.

###  6.2 Separation of the interstellar and intrinsic polarization

We have attempted to separate interstellar polarization from the total
polarization. To obtain the values for the interstellar polarization we have
first selected stars from the 9286 object catalogue (Heiles, 2000) within an
angular distance of 5 degrees on the sky from each of our sample stars. We
then found the distances to these group of stars using the Gaia catalog. We
have separated the values of the Stokes parameters $q$ and $u$ from the
catalogue polarization degree and angle for these stars, then performed a
linear fit to them to find the values of interstellar $q$ and $u$ with respect
the distance. Then we calculated $q_{is}$ and $u_{is}$ for our sample stars
depending on their distance, using the previous linear fit, as shown in Figure
6. The errors for the interstellar polarization are derived from the values of
the linear fit. We then subtracted the values of the interstellar $q$ and $u$
for our sample stars from the total values of their Stokes parameters,
obtaining the intrinsic values ($q_{in}$ and $u_{in}$), and then calculated
the values for both the interstellar and intrinsic polarization degree and
angle as shown in Table 11.

Figure 6: Here we see the polarization coefficient $q$ of nearby stars (in
blue) compared to our object, BD+31 4018 (in green). The red line is a fit to
the nearby star data.

##  7 Analysis

###  7.1 Comparison of $\bar{P}$ and $\bar{\theta}$ with other authors

41 of the stars in our sample have had polarization measurements previously,
so we can compare our values for $\bar{P}$ and $\bar{\theta}$ to the ones from
previous authors. The sources for these reference values are Hall (1958), Behr
(1959), Coyne & Gehrels (1967), Coyne & Kruszewski (1969), Serkowski (1968),
Serkowski (1970), McLean & Clarke (1976), Coyne (1976), Poeckert & Marlborough
(1976), McLean & Brown (1978) and Yudin (2001). We have reduced these to
1950s, 1960s, 1970s and 2000s for simplicity, taking the average of all values
where there is more than one.

Table 3: The values $\bar{P}$ and $\bar{\theta}$ shown here are the weighted average of their years. For the 1950s, we have used the ones shown in Hall (1958) and Behr (1959), for the 1960s we have used the ones shown in Coyne & Gehrels (1967), Coyne & Kruszewski (1969) and Serkowski (1968), for the 1970 we have used Serkowski (1970), McLean & Clarke (1976), Coyne (1976), Poeckert & Marlborough (1976) and McLean & Brown (1978), for 2001 we have used the ones shown in Yudin (2001), and for 2022 our own calculated values. In bold, the values for the polarization angles that have shown a difference bigger than 10° over the past 70 years. Object | Other identifier | 1950s | 1960s | 1970s | 2001 | 2022 | Peak
---|---|---|---|---|---|---|---
$\bar{P}$ (%) | $\bar{\theta}$ |  $\bar{P}$ (%) | $\bar{\theta}$ |  $\bar{P}$ (%) | $\bar{\theta}$ | $\bar{P}(\%)$ | $\bar{\theta}$ | $\bar{P}(\%)$ | $\bar{\theta}$
CD-27 11872 | HD 161103 | 11.1 | 171 | - | - | - | - | 4.83 | 172 | 7.1 | 170 | SP
CD-27 16010 | HD 214748 | - | - | - | - | 1.75 | 163 | 0.09 | 155 | 0.4 | 169 | DP
CD-25 12642 | HD 164741 | 1.7 | 14 | - | - | - | - | - | - | 3.2 | 14 | NP
CD-22 13183 | HD 172158 | 1.7 | 178 | - | - | - | - | 4.65 | 143 | 1.2 | 175 | SP
BD-20 5381 | HD 177015 | 1.1 | 0 | - | - | - | - | 0.51 | 0 | 1.3 | 179 | DP
BD-01 3834 | HD 187350 | 1.7 | 82 | - | - | - | - | 0.78 | 82 | 0.4 | 80 | SP
BD+05 3704 | HD 168797 | 1.7 | 64 | - | - | - | - | 0.78 | 64 | 1.4 | 30 | Change
BD+19 578 | HD 23016 | - | - | - | - | 1.48 | 87 | 0.60 | 87 | 0.5 | 87 | Change
BD+29 4453 | HD 205618 | 2.7 | 26 | - | - | - | - | 1.24 | 26 | 1.0 | 39 | SP
BD+30 3227 | HD 171406 | 0.6 | 13 | - | - | - | - | 0.28 | 13 | 1.6 | 65 | Change
BD+31 4018 | HD 193009 | 1.4 | 75 | - | - | - | - | 0.65 | 75 | 1.4 | 80 | SP
BD+40 1213 | HD 33604 | 2.8 | 168 | - | - | - | - | 1.29 | 168 | 1.5 | 165 | SP
BD+42 1376 | HD 37657 | 3.6 | 174 | - | - | - | - | 1.66 | 174 | 1.5 | 175 | Change
BD+46 275 | HD 6811 | 2.08 | 90 | - | - | 8.75 | 94 | 7.4 | 90 | 0.9 | 89 | Change
BD+47 183 | HD 4180 | 1.975 | 84 | 1.05 | 84 | 0.815 | 82 | 0.70 | 85 | 1.1 | 82 | SP
BD+47 857 | HD 22192 | 1.55 | 42 | - | - | 1.07 | 42 | 0.80 | 45 | 0.2 | 64 | DP
BD+47 939 | HD 25940 | 2.28 | 173 | 1.09 | 158 | 1.025 | 172 | 0.25 | 145 | 1.1 | 174 | SP
BD+47 3985 | HD 217050 | 3.9 | 75 | 1.65 | 69 | 1.123 | 71 | 1.55 | 75 | 0.4 | 53 | Change
BD+55 605 | HD 14605 | 8.2 | 118 | - | - | - | - | 3.78 | 118 | 4.2 | 121 | Change
BD+56 478 | HD 13890 | 7.5 | 107 | - | - | - | - | 3.46 | 107 | 3.7 | 112 | DP

In Table 3 we compare our values with the most studied Be stars from our
sample, for a historical perspective, while in Table 9 we compare our entire
sample with the ones from Yudin (2001). We can see that the polarization
degree changes with time, and while the polarization angle is mostly constant
(Figure 7), there are a number of objects with significant ($>10^{\circ}$)
changes over the 70 year time baseline. We highlight these objects in bold in
Table 3. We note that large changes in polarization angle are typically
associated with large changes in the degree of polarization (either positive
or negative). However, we note that the objects that show such angle changes
seem to be spread fairly evenly between those which do and do not show changes
in the H$\alpha$ peak morphology (see last line of table). Overall the
changing polarization angle can be interpreted as either a varying ratio of
interstellar and circumstellar polarization (which naturally have random
polarization angles with respect to each other) as the disk strength varies,
or as a change in the disk geometry as a function of time. Such behaviour has,
for example, been seen in the interferometric and polarimetric measurements
presented by Quirrenbach et al. (1997). We will explore this question on an
object-by-object basis in a future paper.

Figure 7: A plot of our (2022) polarization angles vs the polarization angles
measured by Yudin (2001).

###  7.2 Removal of the inclination dependence

As radiation escapes the Be star and is scattered through the disk, it will
get polarized. This polarization has been modeled by Brown & McLean (1977):

$P\simeq\bar{\tau}(1-3\gamma)\sin^{2}i$ (8)

with P the polarization degree, $\bar{\tau}$ the average electron optical
depth, $\gamma$ a shape factor that describes the asymmetry of the disk, and
$i$ the inclination.

It is impossible for us to separate these values without knowing the value of
the inclination. However, as we have measured previously the rotational
velocity $v\sin i$, this allows us to obtain instead:

$\frac{P}{(v\sin i)^{2}}=\frac{K}{v^{2}}$ (9)

with $K=\bar{\tau}(1-3\gamma)$.

This allows us to derive a value for $v$ that is not dependent on the
inclination of the star (although there is now an uncertainty related to the
mean optical depth instead). Similarly we can multiply the values shown in
equation 9 by the critical velocity:

$\frac{P}{(v\sin i)^{2}}v_{\rm crit}^{2}=\frac{K}{v^{2}}v_{\rm
crit}^{2}=\frac{K}{W^{2}}$ (10)

obtaining a measurement of the critical fraction $W$.

Figure 8: Two histograms showing the distribution of stars for different
values and types of emission of the H$\alpha$ line with respect to $Wsini$.
Figure 9: A histogram showing the distribution of stars for single and double
peak H$\alpha$ line with respect to $\frac{W^{2}}{K}$.

###  7.3 Testing the population differences

In order to test the validity of the above procedure, we can compare the
distribution of the various quantities $v\sin i$, $W\sin i$, $W^{2}/K$ and
$v^{2}/K$ against the H$\alpha$ emission classification we made in Section 4.
To do this we used Kolmogorov-Smirnov tests to compare the histograms of these
quantities for the permutations of no- (NP), single peaked- (SP), and double
peaked-emission DP). The results of the tests are shown in Table 4.

Table 4: Results from the KS tests. Distributions which are apparently drawn from the same parent population (i.e. $p>0.05$) are highlighted in bold.  Values | NP vs P | NP vs SP | NP vs DP | SP vs DP
---|---|---|---|---
$v\sin i$ | 0.00 | 0.04 | 0.00 | 0.00
$W\sin i$ | 0.00 | 0.01 | 0.00 | 0.00
$W^{2}/K$ | - | - | - | 0.64
$v^{2}/K$ | - | - | - | 0.98

In all cases, when considering the distributions that include the $\sin i$
inclination term, the distributions for different H$\alpha$ emission
properties all indicate a different parent population.

For example Figure 8 (left) shows the distributions of P and NP objects are
different in terms of $W\sin i$, with the first showing showing faster $W\sin
i$ associated with $H\alpha$ emission, and the showing slower $W\sin i$
associated with $H\alpha$ absorption as expected from previous studies.

Similarly the right panel shows the difference between single and double
peaks, with double peaks seemingly rotating faster in terms of $W\sin i$.
However, when we remove the angular dependence on the inclination ($W^{2}/K$)
the null hypothesis can not be rejected 9. This can be interpreted as evidence
for the idea that the cause of the difference between single and double peak
H$\alpha$ emission is the inclination of the disk, as predicted by emission
line modelling (e.g. Poeckert & Marlborough (1976, 1978), Sigut et al.
(2020)). If that theory is taken as accepted, then our method of using
polarization to eliminate the dependence on the inclination angle appears to
work for the sample distribution.

##  8 Conclusions

Using a sample of 58 stars previously classified as Be, we have used spectra
taken over multiple epochs over a 24 year period to classify them based on
their their qualitative $H\alpha$ line appearance. We classified these stars
in three groups depending on whether they have emission in the shape of a
single peak, in the shape of a double peak, or no emission. We found a
probability of $\sim 0.75$ percent per year that an object would change state
between emission and non-emission.

We also calculated the projected rotational velocity ($v\sin i$) from multiple
measurements of the He-I line profiles. We then compared polarization
measurements taken in 2022 with those from previous authors, revealing that
the majority of objects show no significant changes in the polarization angle.
This is to be expected if this were a mainly geometric parameter based on the
system having a stable 3d space orientation. However we do find a small sample
of objects which seem to show genuine polarization angle variability which may
be interpreted as either varying disk strength (optical depth) or geometry.
This will be investigated further in a future paper.

For each object we have used the degree of polarization to estimate a quantity
that, when combined with the $v\sin i$, is related to the true equatorial
rotational velocities. We find a clear separation between Be stars with
$H\alpha$ emission and stars that do not emit. Once the angular inclination
factor is removed, the populations of single and double peak H$\alpha$
emitters are indistinguishable at least on a population basis. In a future
paper we will consider how to use quantitative measures of the variability of
emission line properties of the objects in conjunction with this approach to
constrain variability timescales in an inclination-independent fashion.

## Acknowledgements

We want to thank the Isaac Newton Group of Telescopes and the Liverpool
Telescope for providing the measurements used for this publication. This paper
makes use of data obtained from the Isaac Newton Group of Telescopes Archive
which is maintained as part of the CASU Astronomical Data Centre at the
Institute of Astronomy, Cambridge. The Liverpool Telescope is operated on the
island of La Palma by Liverpool John Moores University in the Spanish
Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de
Canarias with financial support from the UK Science and Technology Facilities
Council under UKRI grant ST/T00147X/1. The authors want to thank Maurizio
Salaris for his help with some of the calculations. ACE thanks LJMU for
financial support for his PhD studentship.

## Data Availability

All the data used for this publication is publicly available on the Isaac
Newton Telescope and Liverpool Telescope data archives.

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##  Appendix A Tables of data

We have added here some tables that were too big to be inserted in the paper.

Table 5: The list of observations taken for the respective objects. Object | Alias | Observation dates | Total number of observations
---|---|---|---
CD-28 14778 | HD 171757 | 1998, 2010, 2018, 2019 | 6
CD-27 11872 | V3892 Sgr, HD 161103 | 1998, 2009, 2010, 2018, 2019, 2020 | 9
CD-27 16010 |  $\epsilon$ PsA, HR 8628, HD 214748 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 15
CD-25 12642 | HD 164741 | 1998, 2009, 2010, 2018, 2019, 2020 | 8
CD-22 13183 | HD 172158 | 1998, 2009, 2010 | 3
BD-20 5381 | HD 177015 | 1998, 2009, 2010, 2019 | 5
BD-19 5036 | V3508 Sgr, HD 170682 | 1998, 2009, 2018, 2019 | 7
BD-12 5132 | HD 172252 | 1998, 2018, 2019, 2020 | 5
BD-02 5328 | HD 196712 | 1998, 2009, 2010, 2013, 2018, 2019, 2022 | 12
BD-01 3834 | HD 187350 | 1998, 2009, 2010, 2018, 2019, 2020, 2022 | 11
BD-00 3543 | HD 173371 | 1998, 2009, 2010, 2018, 2019, 2020 | 9
BD+02 3815 | HD 179343 | 1998, 2009, 2010, 2018, 2019, 2020 | 10
BD+05 3704 | HD 168797 | 1998, 2002, 2009, 2010, 2018, 2019, 2020 | 10
BD+17 4087 | HD 350559 | 1998, 2018, 2019, 2020, 2022 | 9
BD+19 578 | 13 Tau, HR 1126, HD 23016 | 1998, 2009, 2010, 2013, 2017, 2018, 2019, 2020, 2022 | 13
BD+20 4449 | HD 191531 | 1998, 2009, 2010, 2022 | 5
BD+21 4695 | 25 Peg, HD 210129 | 1998, 2009, 2010, 2013, 2018, 2020, 2022 | 9
BD+23 1148 | HD 250289 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2021, 2022 | 12
BD+25 4083 | HD 339483 | 1998, 2009, 2010, 2018, 2019, 2020, 2022 | 12
BD+27 797 | HD 244894 | 1998, 2009, 2010, 2013, 2018, 2019, 2022 | 19
BD+27 850 | HD 246878 | 1998, 2009, 2010, 2013, 2018, 2020, 2021, 2022 | 12
BD+27 3411 |  $\beta$2 Cyg, HR 7418, HD 183914 | 1998, 2002, 2009, 2010, 2018, 2019, 2020, 2022 | 12
BD+28 3598 | HD 333452 | 1998, 2009, 2010, 2018, 2019, 2020, 2022 | 7
BD+29 3842 | HD 333226 | 1998, 2009, 2010, 2018, 2019, 2020, 2022 | 9
BD+29 4453 | HD 205618 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 12
BD+30 3227 | HR 6971, HD 171406 | 1998, 2002, 2009, 2010, 2018, 2019, 2020, 2021, 2022 | 13
BD+31 4018 | V2113 Cyg, HD 193009 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 13
BD+36 3946 | HD 228438 | 1998, 2002, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 15
BD+37 675 | HR 894, HD 18552 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 10
BD+37 3856 | HD 228650 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 14
BD+40 1213 | HD 33604 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2021, 2022 | 14
BD+42 1376 | V434 Aur, HD 37657 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2021, 2022 | 13
BD+42 4538 | HD 216581 | 1998, 2002, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 12
BD+43 1048 | HD 276738 | 1998, 2009, 2010, 2013, 2018, 2019, 2022 | 11
BD+45 933 | HD 27846 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 13
BD+45 3879 | HD 211835 | 1998, 2002, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 12
BD+46 275 |  $\varphi$ And, HR 335, HD 6811 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 15
BD+47 183 | 22 Cas, HR 193, HD 4180 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 14
BD+47 857 |  $\psi$ Per, HR 1087, HD 22192 | 1998, 2009, 2010, 2013, 2017, 2018, 2019, 2020, 2022 | 13
BD+47 939 | 48 Per, HR 1273, HD 25940 | 1998, 2001, 2009, 2010, 2013, 2017, 2018, 2019, 2020, 2022 | 15
BD+47 3985 | EW Lac, HR 8731, HD 217050 | 1998, 2002, 2005, 2017, 2018, 2019, 2020, 2022 | 12
BD+49 614 | HD 13867 | 1998, 2009, 2010, 2013, 2018, 2022 | 9
BD+50 825 | HR 1160, HD 23552 | 1998, 2007, 2009, 2010, 2013, 2018, 2019, 2020, 2021, 2022 | 15
BD+50 3430 | HD 207232 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 15
BD+51 3091 | HR 8259, HD 20551 | 1998, 2009, 2010, 2013, 2018, 2019, 2022 | 12
BD+53 2599 | HD 203356 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 14
BD+55 552 | HD 13669 | 1998, 2009, 2010, 2013, 2018, 2019, 2022 | 12
BD+55 605 | V361 Per, HD 14605 | 1998, 2009, 2010, 2013, 2018, 2022 | 8
BD+55 2411 | HD 195554 | 1998, 2002, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 17
BD+56 473 | V356 Per | 1998, 2009, 2010, 2013, 2018, 2022 | 7
BD+56 478 | V358 Per, HD 13890 | 1998, 2002, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 10
BD+56 484 | V502 Per | 1998, 2009, 2010, 2013, 2018, 2020, 2022 | 12
BD+56 493 | - | 1998, 2009, 2010, 2013, 2018, 2019, 2022 | 9
BD+56 511 | - | 1998, 2009, 2010, 2013, 2018, 2019, 2021, 2022 | 11
BD+56 573 | - | 1998, 2009, 2010, 2013, 2018, 2019, 2022 | 12
BD+57 681 | HD 237056 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 13
BD+58 554 | HD 237060 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 12
BD+58 2320 | HD 239758 | 1998, 2009, 2010, 2013, 2018, 2019, 2020, 2022 | 12
Table 6: The list of objects, including the spectral and luminosity classes, distances, theoretical luminosities, masses and radius of the star, theoretical critical velocity and reddening. $\dagger$ indicates that the distances are from the Hipparcos catalog instead of Gaia. All the theoretical $log(L/L_{\odot})$ values come from de Jager & Nieuwenhuijzen (1987) and they only depend on the spectral type, while the $M/M_{\odot}$, $R/R_{\odot}$ and $v_{crit}$ are derived from equations 3, 4, 5 and 6. The values of the reddening $E(B-V)$ come from Howells et al. (2001). Object | Spectral Type | d (pc) | $log(L/L_{\odot})$ | $M/M_{\odot}$ | $R/R_{\odot}$ |  $v_{crit}$ (km/s) | $E(B-V)$
---|---|---|---|---|---|---|---
CD-28 14778 | B2III | $1624\pm 73$ | 4.047 | 10.638 | 5.490 | 496.1 | 0.54
CD-27 11872 | B0.5V-III | $1270\pm 38$ | 4.258 | 12.604 | 5.855 | 522.9 | 0.86
CD-27 16010 | B8IV | $168.9\pm 8.4$ | 2.337 | 3.678 | 2.844 | 405.3 | 0.16
CD-25 12642 | B0.7III | $1414\pm 39$ | 5.034 | 23.517 | 7.983 | 611.7 | -
CD-22 13183 | B7V | $882\pm 38$ | 2.203 | 3.403 | 2.719 | 398.7 | 0.27
BD-20 5381 | B5V | $643\pm 16$ | 2.681 | 4.491 | 3.220 | 420.9 | -
BD-19 5036 | B4III | $667\pm 16$ | 3.562 | 7.204 | 4.889 | 432.6 | 0.51
BD-12 5132 | BN0.2III | $1630\pm 190$ | 4.846 | 20.219 | 7.328 | 592.0 | 0.78
BD-02 5328 | B7V | $350.4\pm 6.6$ | 2.203 | 3.403 | 2.719 | 398.7 | -0.06
BD-01 3834 | B2IV | $2010\pm 110$ | 3.84 | 9.008 | 5.197 | 469.2 | 0.08
BD-00 3543 | B7V | $287.1\pm 3.0$ | 2.203 | 3.403 | 2.719 | 398.7 | 0.06
BD+02 3815 | B7-8sh | $790\pm 510^{\dagger}$ | 2.094 | 3.195 | 2.624 | 393.2 | -0.03
BD+05 3704 | B2.5V | $418.8\pm 7.7$ | 3.332 | 6.554 | 4.206 | 444.9 | -0.13
BD+17 4087 | B6III-V | $2096\pm 64$ | 2.758 | 4.697 | 3.316 | 424.1 | 0.08
BD+19 578 | B8V | $159.3\pm 2.1$ | 1.985 | 2.999 | 2.536 | 387.6 | -
BD+20 4449 | B0III | $2130\pm 180$ | 4.928 | 21.596 | 7.600 | 600.8 | 0.16
BD+21 4695 | B6III-V | $204.5\pm 3.7$ | 3.08 | 5.662 | 3.774 | 436.5 | 0.03
BD+23 1148 | B2III | $2180\pm 130$ | 4.047 | 10.638 | 5.490 | 496.1 | 0.89
BD+25 4083 | B0.7-1III | $1269\pm 22$ | 4.573 | 16.236 | 6.549 | 561.1 | -
BD+27 797 | B0.5V | $1977\pm 58$ | 4.258 | 12.604 | 5.855 | 522.9 | 1.59
BD+27 850 | B1.5IV | $1231\pm 29$ | 4.081 | 10.933 | 5.544 | 500.4 | 0.65
BD+27 3411 | B8V | $122.1\pm 1.2$ | 1.985 | 2.999 | 2.536 | 387.6 | -0.18
BD+28 3598 | BO9II | $2295\pm 71$ | 5.516 | 34.643 | 10.253 | 655.1 | 1.18
BD+29 3842 | B1II | $4560\pm 250$ | 4.93 | 21.631 | 7.607 | 601.0 | 0.73
BD+29 4453 | B1.5V | $1224\pm 48$ | 3.733 | 8.266 | 5.067 | 455.2 | 0.11
BD+30 3227 | B4V | $364.5\pm 9.1$ | 2.936 | 5.208 | 3.557 | 431.2 | 0.12
BD+31 4018 | B1.5V | $885\pm 18$ | 3.733 | 8.266 | 5.067 | 455.2 | -0.36
BD+36 3946 | B1V | $2350\pm 140$ | 3.998 | 10.228 | 5.415 | 489.8 | 0.58
BD+37 675 | B7V | $224.1\pm 2.8$ | 2.203 | 3.403 | 2.719 | 398.7 | 0.13
BD+37 3856 | B0.5V | $2195\pm 56$ | 4.258 | 12.604 | 5.855 | 522.9 | 1.11
BD+40 1213 | B2.5IV | $1102\pm 33$ | 3.716 | 8.153 | 5.048 | 452.9 | 0.17
BD+42 1376 | B2V | $698\pm 16$ | 3.465 | 6.670 | 4.798 | 420.2 | 0.31
BD+42 4538 | B2.5V | $594.6\pm 9.9$ | 3.332 | 6.553 | 4.206 | 444.9 | 0.27
BD+43 1048 | B6IIIsh | $971\pm 27$ | 3.08 | 5.662 | 3.774 | 436.5 | 0.39
BD+45 933 | B1.5V | $957\pm 26$ | 3.733 | 8.266 | 5.067 | 455.2 | 0.51
BD+45 3879 | B1.5V | $1876\pm 73$ | 3.733 | 8.266 | 5.067 | 455.2 | -
BD+46 275 | B5III | $220\pm 29^{\dagger}$ | 3.319 | 6.504 | 4.182 | 444.5 | 0.2
BD+47 183 | B2.5V | $216\pm 18^{\dagger}$ | 3.332 | 6.554 | 4.206 | 444.9 | 0.19
BD+47 857 | B4V-III | $167.7\pm 3.7$ | 2.936 | 5.208 | 3.557 | 431.2 | 0.37
BD+47 939 | B2.5V | $156.8\pm 7.2$ | 3.332 | 6.554 | 4.206 | 444.9 | 0.41
BD+47 3985 | B1.5V | $287.4\pm 5.8$ | 3.733 | 8.266 | 5.067 | 455.2 | 0.32
BD+49 614 | B5III | $499\pm 86$ | 3.319 | 6.504 | 4.182 | 444.5 | 0.23
BD+50 825 | B7V | $249.8\pm 2.1$ | 2.203 | 3.403 | 2.719 | 398.7 | 0.46
BD+50 3430 | B8V | $384.8\pm 4.4$ | 1.985 | 2.999 | 2.536 | 387.6 | 0.07
BD+51 3091 | B7III | $457.7\pm 6.3$ | 2.576 | 4.226 | 3.096 | 416.3 | 0.13
BD+53 2599 | B8V | $637\pm 23$ | 1.985 | 2.999 | 2.536 | 387.6 | -
BD+55 552 | B4V | $699\pm 11$ | 2.936 | 5.208 | 3.557 | 431.2 | 0.07
BD+55 605 | B1V | $2311\pm 84$ | 3.998 | 10.227 | 5.415 | 489.8 | 0.78
BD+55 2411 | B8.5V | $305.7\pm 9.2$ | 1.884 | 2.828 | 2.459 | 382.2 | 0.27
BD+56 473 | B1V-III | $2460\pm 98$ | 3.998 | 10.228 | 5.415 | 489.8 | 0.57
BD+56 478 | B1.5V | $2100\pm 230$ | 3.733 | 8.266 | 5.067 | 455.2 | 0.6
BD+56 484 | B1V | $2381\pm 90$ | 3.998 | 10.228 | 5.415 | 489.8 | 0.78
BD+56 493 | B1V | $2850\pm 160$ | 3.998 | 10.228 | 5.415 | 489.8 | 0.57
BD+56 511 | B1III | $2590\pm 120$ | 4.508 | 15.409 | 6.389 | 553.5 | 0.72
BD+56 573 | B1.5V | $2200\pm 120$ | 3.733 | 8.266 | 5.067 | 455.2 | 0.89
BD+57 681 | B0.5V | $1132\pm 33$ | 4.258 | 12.604 | 5.855 | 522.9 | 1.17
BD+58 554 | B7V | $662.2\pm 6.9$ | 2.203 | 3.403 | 2.719 | 398.7 | 0.27
BD+58 2320 | B2V | $1254\pm 24$ | 3.465 | 6.670 | 4.798 | 420.2 | 0.62
Table 7: The list of objects, with the calculated polarization degrees for each BVR band, and the weighted polarization average of them, for the Oct 2022 observations. The errors quoted in this table have been calculated only from photon counting statistics and do not include the MOPTOP systematic errors of $\sim 0.002$. Because the error from the calculations is smaller than the systematic error, the final value of the error for the average polarization degree is $S(\bar{P})=0.002$. Final polarization measurements incorporating the systematic error and the effect of interstellar polarization are given in Table 11. Object | $P_{V}$ | S($P_{V}$) | $P_{B}$ | S($P_{B}$) | $P_{R}$ | S($P_{R}$) | $\bar{P}$
---|---|---|---|---|---|---|---
CD-28 14778 | 0.03467 | $6\cdot 10^{-5}$ | 0.0367 | 0.0001 | 0.02589 | $3\cdot 10^{-5}$ | 0.032
CD-27 11872 | 0.07152 | $3\cdot 10^{-5}$ | 0.07755 | $6\cdot 10^{-5}$ | 0.06398 | $2\cdot 10^{-5}$ | 0.071
CD-27 16010 | 0.0035203 | $8\cdot 10^{-7}$ | 0.005 | 0.003 | 0.0025063 | $3\cdot 10^{-7}$ | 0.004
CD-25 12642 | 0.03264 | $5\cdot 10^{-5}$ | 0.0420 | 0.0001 | 0.02167 | $3\cdot 10^{-5}$ | 0.032
CD-22 13183 | 0.010014 | $9\cdot 10^{-6}$ | 0.0142 | 0.0002 | 0.01086 | $2\cdot 10^{-5}$ | 0.012
BD-20 5381 | 0.0162 | 0.0001 | 0.0122 | 0.0004 | 0.00977 | $3\cdot 10^{-5}$ | 0.013
BD-19 5036 | 0.006470 | $2\cdot 10^{-6}$ | 0.0442 | $4\cdot 10^{-5}$ | 0.03798 | $1\cdot 10^{-5}$ | 0.029
BD-12 5132 | 0.106 | 0.001 | 0.106 | 0.001 | 0.064 | 0.001 | 0.091
BD-02 5328 | 0.003889 | $3\cdot 10^{-6}$ | 0.0046 | 0.0003 | 0.0036205 | $9\cdot 10^{-07}$ | 0.004
BD-01 3834 | 0.003 | 0.001 | 0.0040 | 0.0003 | 0.00516 | $6\cdot 10^{-5}$ | 0.004
BD-00 3543 | 0.008073 | $6\cdot 10^{-6}$ | 0.008 | 0.005 | 0.006470 | $2\cdot 10^{-6}$ | 0.007
BD+02 3815 | 0.010120 | $8\cdot 10^{-6}$ | 0.01210 | $2\cdot 10^{-5}$ | 0.007586 | $3\cdot 10^{-6}$ | 0.010
BD+05 3704 | 0.005612 | $1\cdot 10^{-6}$ | 0.009922 | $8\cdot 10^{-6}$ | 0.030378 | $6\cdot 10^{-6}$ | 0.014
BD+17 4087 | 0.0221 | 0.0003 | 0.02 | 0.02 | 0.0206 | 0.0002 | 0.022
BD+19 578 | 0.004838 | $1\cdot 10^{-6}$ | 0.0055 | 0.0001 | 0.0046032 | $7\cdot 10^{-7}$ | 0.005
BD+20 4449 | 0.01052 | $2\cdot 10^{-5}$ | 0.01025 | $8\cdot 10^{-5}$ | 0.007306 | $9\cdot 10^{-6}$ | 0.009
BD+21 4695 | 0.002800 | $3\cdot 10^{-6}$ | 0.004 | 0.004 | 0.001353 | $1\cdot 10^{-6}$ | 0.002
BD+23 1148 | 0.03 | 0.08 | 0.0316 | 0.0003 | 0.0311 | 0.0009 | 0.032
BD+25 4083 | 0.016 | 0.001 | 0.02 | 0.01 | 0.02 | 0.06 | 0.016
BD+27 797 | 0.02 | 0.03 | - | - | 0.02 | 0.01 | 0.017
BD+27 850 | 0.0099 | 0.0001 | 0.010 | 0.001 | 0.00595 | $5\cdot 10^{-5}$ | 0.009
BD+27 3411 | 0.0040326 | $7\cdot 10^{-7}$ | 0.005223 | $2\cdot 10^{-6}$ | 0.020104 | $1\cdot 10^{-6}$ | 0.010
BD+28 3598 | 0.0538 | 0.0002 | 0.0633 | 0.0003 | 0.037 | 0.009 | 0.051
BD+29 3842 | 0.0167 | 0.0001 | 0.0202 | 0.0004 | 0.01389 | $5\cdot 10^{-5}$ | 0.017
BD+29 4453 | 0.01030 | $3\cdot 10^{-5}$ | 0.0104 | 0.0002 | 0.00929 | $1\cdot 10^{-5}$ | 0.010
BD+30 3227 | 0.01325 | $1\cdot 10^{-5}$ | 0.0247 | 0.0004 | 0.009893 | $7\cdot 10^{-6}$ | 0.016
BD+31 4018 | 0.0140 | 0.0009 | 0.01481 | $4\cdot 10^{-5}$ | 0.01329 | $2\cdot 10^{-5}$ | 0.014
BD+36 3946 | 0.00725 | $5\cdot 10^{-5}$ | 0.0062 | 0.0002 | 0.00746 | $1\cdot 10^{-5}$ | 0.007
BD+37 675 | 0.00427 | $2\cdot 10^{-5}$ | 0.00553 | $4\cdot 10^{-5}$ | 0.004496 | $6\cdot 10^{-6}$ | 0.005
BD+37 3856 | 0.0154 | 0.0001 | 0.0124 | 0.0005 | 0.01304 | $7\cdot 10^{-5}$ | 0.014
BD+40 1213 | 0.016 | 0.006 | 0.015 | 0.002 | 0.0146 | 0.0002 | 0.015
BD+42 1376 | 0.0156 | 0.0002 | 0.02 | 0.01 | 0.02 | 0.02 | 0.015
BD+42 4538 | 0.00922 | $3\cdot 10^{-5}$ | 0.0093 | 0.0003 | 0.00704 | $2\cdot 10^{-5}$ | 0.008
BD+43 1048 | 0.027 | 0.004 | 0.024 | 0.003 | 0.024 | 0.002 | 0.025
BD+45 933 | 0.0229 | 0.0001 | 0.02446 | $8\cdot 10^{-5}$ | 0.0230 | 0.0002 | 0.023
BD+45 3879 | 0.00539 | $3\cdot 10^{-5}$ | 0.0064 | 0.0002 | 0.00665 | $1\cdot 10^{-5}$ | 0.006
BD+46 275 | 0.009412 | $1\cdot 10^{-6}$ | 0.00966 | $3\cdot 10^{-5}$ | 0.0089211 | $6\cdot 10^{-7}$ | 0.009
BD+47 183 | 0.011340 | $1\cdot 10^{-6}$ | 0.010746 | $3\cdot 10^{-6}$ | 0.0098539 | $7\cdot 10^{-7}$ | 0.011
BD+47 857 | 0.0045151 | $4\cdot 10^{-7}$ | 0.00568 | $3\cdot 10^{-5}$ | 0.0032336 | $1\cdot 10^{-7}$ | 0.002
BD+47 939 | 0.0115475 | $3\cdot 10^{-7}$ | 0.0120 | 0.0002 | 0.0109207 | $1\cdot 10^{-7}$ | 0.011
BD+47 3985 | 0.004066 | $2\cdot 10^{-6}$ | 0.004237 | $5\cdot 10^{-6}$ | 0.0024482 | $8\cdot 10^{-7}$ | 0.004
BD+49 614 | 0.01308 | $5\cdot 10^{-5}$ | 0.01 | 0.14 | 0.01148 | $2\cdot 10^{-5}$ | 0.012
BD+50 825 | 0.006995 | $2\cdot 10^{-6}$ | 0.00843 | $4\cdot 10^{-5}$ | 0.006553 | $1\cdot 10^{-6}$ | 0.007
BD+50 3430 | 0.00559 | $1\cdot 10^{-5}$ | 0.01 | 0.01 | 0.004803 | $4\cdot 10^{-6}$ | 0.005
BD+51 3091 | 0.007973 | $6\cdot 10^{-6}$ | 0.00772 | $2\cdot 10^{-5}$ | 0.006755 | $3\cdot 10^{-6}$ | 0.007
BD+53 2599 | 0.00668 | $4\cdot 10^{-5}$ | 0.007 | 0.002 | 0.00465 | $2\cdot 10^{-5}$ | 0.006
BD+55 552 | 0.03 | 0.01 | 0.0297 | 0.0004 | 0.02 | 0.01 | 0.027
BD+55 605 | 0.04 | 0.01 | 0.0460 | 0.0006 | 0.04 | 0.02 | 0.042
BD+55 2411 | 0.001685 | $6\cdot 10^{-6}$ | 0.00424 | $4\cdot 10^{-5}$ | 0.001212 | $2\cdot 10^{-6}$ | 0.002
BD+56 473 | 0.0485 | 0.0006 | 0.0501 | 0.0002 | 0.043 | 0.008 | 0.047
BD+56 478 | 0.0386 | 0.0007 | 0.0392 | 0.0002 | 0.03 | 0.03 | 0.037
BD+56 484 | - | - | 0.0417 | 0.0006 | 0.0327 | 0.0006 | 0.037
BD+56 493 | 0.046 | 0.008 | 0.0475 | 0.0005 | 0.040 | 0.002 | 0.044
BD+56 511 | 0.041 | 0.001 | 0.0437 | 0.0003 | 0.04 | 0.14 | 0.041
BD+56 573 | 0.04 | 0.03 | 0.0475 | 0.0006 | 0.036 | 0.003 | 0.042
BD+57 681 | 0.05971 | $2\cdot 10^{-5}$ | 0.06348 | $6\cdot 10^{-5}$ | 0.05678 | $1\cdot 10^{-5}$ | 0.060
BD+58 554 | 0.0325 | 0.0002 | 0.0346 | 0.0002 | 0.032 | 0.001 | 0.033
BD+58 2320 | 0.0201 | 0.0007 | 0.02 | 0.04 | 0.0162 | 0.0002 | 0.017
Table 8: The list of objects, with the calculated polarization angles for each BVR band, and the weighted polarization angle average of them, for the Oct 2022 observations. The angle values are between 0 and 180°. The errors quoted in this table have been calculated only from photon counting statistics and do not include the MOPTOP systematic errors of $\sim 1^{\circ}$. Because the error from the calculations is smaller than the systematic error, the final value of the error for the average polarization degree is $S(\bar{\theta})=1^{\circ}$. Final polarization measurements incorporating the systematic error and the effect of interstellar polarization are given in Table 11. Object | $\theta_{V}$ | S($\theta_{V}$) | $\theta_{B}$ | S($\theta_{B}$) | $\theta_{R}$ | S($\theta_{R}$) | $\bar{\theta}$
---|---|---|---|---|---|---|---
CD-28 14778 | 184.97 | 0.04 | 184.93 | 0.07 | 181.62 | 0.02 | 4
CD-27 11872 | 169.86 | 0.01 | 170.67 | 0.03 | 170.052 | 0.009 | 170
CD-27 16010 | 172.87 | 0.05 | 164 | 7 | 172.89 | 0.02 | 169
CD-25 12642 | 191.84 | 0.03 | 193.46 | 0.05 | 196.29 | 0.03 | 14
CD-22 13183 | 174.011 | 0.005 | 179.9 | 0.1 | 169.74 | 0.04 | 175
BD-20 5381 | 182.2 | 0.2 | 177.2 | 0.6 | 177.41 | 0.06 | 179
BD-19 5036 | 176.200 | 0.003 | 190.06 | 0.02 | 191.528 | 0.007 | 10
BD-12 5132 | 169.07 | 0.03 | 169.07 | 0.02 | 162.5 | 0.1 | 168
BD-02 5328 | 257.16 | 0.02 | 284 | 53 | 268.998 | 0.002 | 91
BD-01 3834 | 268 | 191 | 163 | 18 | 260.9 | 0.4 | 80
BD-00 3543 | 185.47 | 0.02 | 186 | 3 | 176.200 | 0.003 | 3
BD+02 3815 | 179.84 | 0.03 | 180.23 | 0.08 | 178.28 | 0.01 | 0
BD+05 3704 | 281.803 | 0.003 | 286.00 | 0.01 | 218.018 | 0.005 | 30
BD+17 4087 | 186 | 3 | 189 | 1231 | 188 | 5 | 8
BD+19 578 | 259.407 | 0.004 | 275 | 2 | 265.906 | 0.002 | 87
BD+20 4449 | 190.21 | 0.08 | 191.0 | 0.4 | 188.05 | 0.02 | 10
BD+21 4695 | 157.5 | 0.3 | 134 | 47 | 149.57 | 0.09 | 155
BD+23 1148 | 162 | 62 | 164.8 | 0.2 | 164.0 | 0.5 | 164
BD+25 4083 | 345 | 3 | 259 | 27 | 343 | 63 | 166
BD+27 797 | 187 | 25 | - | - | 189 | 17 | 8
BD+27 850 | 147.1 | 0.9 | 155 | 4 | 142.1 | 0.4 | 149
BD+27 3411 | 331.280 | 0.006 | 246.54 | 0.02 | 332.0686 | 0.0007 | 153
BD+28 3598 | 218.73 | 0.05 | 219.54 | 0.08 | 221 | 3 | 40
BD+29 3842 | 260.6 | 0.2 | 260.5 | 0.5 | 259.00 | 0.07 | 80
BD+29 4453 | 39.14 | 0.02 | 39.4 | 0.2 | 38.94 | 0.01 | 39
BD+30 3227 | 244.82 | 0.02 | 334.8 | 0.4 | 246.98 | 0.02 | 65
BD+31 4018 | 259.1 | 0.8 | 261.90 | 0.03 | 257.30 | 0.02 | 80
BD+36 3946 | 266 | 2 | 257 | 6 | 342.77 | 0.06 | 168
BD+37 675 | 144.2 | 0.3 | 149 | 2 | 148.33 | 0.05 | 147
BD+37 3856 | 307.5 | 0.2 | 306.0 | 0.8 | 307.6 | 0.1 | 127
BD+40 1213 | 162 | 5 | 166 | 2 | 166.9 | 0.4 | 165
BD+42 1376 | 172.6 | 0.4 | 176 | 19 | 176 | 51 | 175
BD+42 4538 | 81.7 | 0.2 | 92 | 1 | 83.0 | 0.1 | 86
BD+43 1048 | 356 | 1 | 90.7 | 0.4 | 178 | 2 | 88
BD+45 933 | 318.1 | 0.4 | 318.8 | 0.4 | 318 | 1 | 138
BD+45 3879 | 27.0 | 0.2 | 21.7 | 0.8 | 25.12 | 0.03 | 24
BD+46 275 | 85.205 | 0.002 | 91.30 | 0.02 | 90.0299 | 0.0009 | 89
BD+47 183 | 81.48 | 0.02 | 81.8 | 0.6 | 82.590 | 0.009 | 82
BD+47 857 | 38.778 | 0.001 | 54.9 | 0.3 | 47.7664 | 0.0004 | 64
BD+47 939 | 354.3414 | 0.0003 | 175.51 | 0.04 | 352.6755 | 0.0001 | 174
BD+47 3985 | 58.11 | 0.06 | 44.23 | 0.06 | 55.27 | 0.04 | 53
BD+49 614 | 102.87 | 0.03 | 106 | 25 | 103.123 | 0.007 | 104
BD+50 825 | 326.338 | 0.002 | 328.02 | 0.05 | 322.430 | 0.001 | 146
BD+50 3430 | 189.9 | 0.1 | 191 | 19 | 9.62 | 0.02 | 10
BD+51 3091 | 24.57 | 0.07 | 22.3 | 0.6 | 19.93 | 0.02 | 22
BD+53 2599 | 37.3 | 0.6 | 113 | 52 | 40.5 | 0.3 | 33
BD+55 552 | 110 | 9 | 114.3 | 0.4 | 110 | 3 | 112
BD+55 605 | 119 | 15 | 123.6 | 0.8 | 119 | 13 | 121
BD+55 2411 | 141.5 | 0.2 | 146.8 | 0.4 | 310.8 | 0.3 | 149
BD+56 473 | 108.0 | 0.1 | 110.50 | 0.05 | 109 | 1 | 109
BD+56 478 | 110.7 | 0.4 | 114.0 | 0.1 | 111 | 13 | 112
BD+56 484 | - | - | 126.8 | 0.9 | 123.6 | 0.7 | 124
BD+56 493 | 120 | 8 | 123.5 | 0.6 | 121 | 2 | 122
BD+56 511 | 111.8 | 0.4 | 115.8 | 0.1 | 113 | 36 | 114
BD+56 573 | 118 | 36 | 120.0 | 0.6 | 119 | 3 | 119
BD+57 681 | 307.438 | 0.002 | 309.860 | 0.005 | 307.1085 | 0.0005 | 128
BD+58 554 | 296.2 | 0.2 | 298.0 | 0.1 | 296.8 | 0.7 | 117
BD+58 2320 | 58 | 1 | 67 | 34 | 55.6 | 0.5 | 60
Table 9: Comparison of our values with the ones from Yudin (2001). Object | Object (2001) |  $vsini$ (2001) (km/s) |  $P$ (%) (2001) |  $\theta$ (2001) |  $vsini$ (2022) (km/s) |  $\bar{P}$ (2022) |  $\bar{\theta}$ (2022)
---|---|---|---|---|---|---|---
CD-28 14778 | HD 171757 | $182\pm 18$ | $0.43\pm 0.10$ | 36 | 141 $\pm$ 23 | 3.2 | 4
CD-27 11872 | HD 161103 | $260\pm 26$ | $4.83\pm 0.12$ | 172 | 210 $\pm$ 17 | 7.1 | 170
CD-27 16010 | HD 214748 | $222\pm 26$ | $0.09\pm 0.10$ | 155 | 189 $\pm$ 7 | 0.4 | 169
CD-22 13183 | HD 172158 | $232\pm 26$ | $0.54\pm 0.10$ | 143 | 169 $\pm$ 79 | 1.2 | 175
BD-20 5381 | HD 177015 | $236\pm 24$ | $0.51\pm 0.20$ | 0 | 197 $\pm$ 72 | 1.3 | 179
BD-19 5036 | HD 170682 | $121\pm 12$ | - | - | 126 $\pm$ 17 | 2.9 | 10
BD-12 5132 | HD 172252 | $146\pm 15$ | $4.65\pm 0.20$ | 148 | 98 $\pm$ 11 | 9.1 | 168
BD-02 5328 | HD 196712 | $199\pm 19$ | $0.35\pm 0.04$ | 95 | 170 $\pm$ 8 | 0.4 | 91
BD-01 3834 | HD 187350 | $199\pm 20$ | $0.78\pm 0.20$ | 82 | 166 $\pm$ 12 | 0.4 | 80
BD-00 3543 | HD 173371 | $291\pm~{}4$ | - | - | 224 $\pm$ 15 | 0.7 | 3
BD+02 3815 | HD 179343 | $261\pm 36$ | - | - | 197 $\pm$ 10 | 1.0 | 0
BD+05 3704 | HD 168797 | $251\pm~{}6$ | $0.78\pm 0.20$ | 64 | 211 $\pm$ 59 | 1.4 | 30
BD+17 4087 | HD 350559 | $186\pm 19$ | - | - | 204 $\pm$ 79 | 2.2 | 8
BD+19 578 | HD 23016 | $278\pm 14$ | $0.60\pm 0.04$ | 87 | 215 $\pm$ 17 | 0.5 | 87
BD+20 4449 | HD 191531 | $~{}80\pm~{}3$ | - | - | 90 $\pm$ 43 | 0.9 | 10
BD+21 4695 | HD 210129 | $201\pm 32$ | $0.28\pm 0.04$ | 7 | 157 $\pm$ 17 | 0.2 | 155
BD+23 1148 | HD 250289 | $125\pm 13$ | $2.95\pm 0.18$ | 162 | 87 $\pm$ 77 | 3.2 | 164
BD+27 797 | HD 244894 | $177\pm 18$ | $1.61\pm 0.18$ | 19 | 197 $\pm$ 18 | 1.7 | 8
BD+27 850 | HD 246878 | $137\pm 14$ | $0.55\pm 0.18$ | 133 | 121 $\pm$ 18 | 0.9 | 149
BD+27 3411 | HD 183914 | $220\pm 25$ | - | - | 170 $\pm$ 13 | 1.0 | 153
BD+29 4453 | HD 205618 | $299\pm 65$ | $1.24\pm 0.20$ | 26 | 247 $\pm$ 26 | 1.0 | 39
BD+30 3227 | HD 171406 | $264\pm 10$ | $0.28\pm 0.20$ | 13 | 208 $\pm$ 8 | 1.6 | 65
BD+31 4018 | HD 193009 | $220\pm 26$ | $0.65\pm 0.20$ | 75 | 225 $\pm$ 30 | 1.4 | 80
BD+36 3946 | HD 228438 | $219\pm 22$ | $1.15\pm 0.20$ | 170 | 178 $\pm$ 23 | 0.7 | 168
BD+37 675 | HD 18552 | $260\pm 12$ | - | - | 223 $\pm$ 21 | 0.5 | 147
BD+40 1213 | HD 33604 | $134\pm 20$ | $1.29\pm 0.20$ | 168 | 122 $\pm$ 7 | 1.5 | 165
BD+42 1376 | HD 37657 | $216\pm 20$ | $1.66\pm 0.20$ | 174 | 196 $\pm$ 10 | 1.5 | 175
BD+42 4538 | HD 216581 | $282\pm 28$ | - | - | 236 $\pm$ 30 | 0.8 | 86
BD+43 1048 | HD 276738 | $220\pm 22$ | - | - | 205 $\pm$ 46 | 2.5 | 88
BD+45 933 | HD 27846 | $134\pm 15$ | - | - | 135 $\pm$ 14 | 2.3 | 138
BD+45 3879 | HD 211835 | $207\pm 15$ | - | - | 186 $\pm$ 10 | 0.6 | 24
BD+46 275 | HD 6811 | $~{}88\pm 13$ | $0.74\pm 0.12$ | 90 | 111 $\pm$ 20 | 0.9 | 89
BD+47 183 | HD 4180 | $221\pm~{}9$ | $0.70\pm 0.13$ | 85 | 167 $\pm$ 12 | 1.1 | 82
BD+47 857 | HD 22192 | $297\pm 41$ | $0.80\pm 0.15$ | 45 | 227 $\pm$ 12 | 0.2 | 64
BD+47 939 | HD 25940 | $198\pm 31$ | $0.25\pm 0.10$ | 145 | 153 $\pm$ 8 | 1.1 | 174
BD+47 3985 | HD 217050 | $301\pm 16$ | $1.55\pm 0.20$ | 75 | 232 $\pm$ 14 | 0.4 | 53
BD+49 614 | HD 13867 | $~{}93\pm 16$ | - | - | 135 $\pm$ 114 | 1.2 | 104
BD+50 825 | HD 23552 | $218\pm~{}3$ | $0.55\pm 0.05$ | 140 | 184 $\pm$ 11 | 0.7 | 146
BD+50 3430 | HD 207232 | $281\pm 28$ | - | - | 198 $\pm$ 19 | 0.5 | 10
BD+55 552 | HD 13669 | $304\pm 22$ | - | - | 243 $\pm$ 29 | 2.7 | 112
BD+55 605 | HD 14605 | $150\pm~{}3$ | $3.78\pm 0.20$ | 118 | 142 $\pm$ 25 | 4.2 | 121
BD+55 2411 | HD 195554 | $215\pm 21$ | - | - | 193 $\pm$ 9 | 0.2 | 149
BD+56 473 | V356 Per | $258\pm 26$ | $4.38\pm 0.18$ | 111 | 218 $\pm$ 23 | 4.7 | 109
BD+56 478 | HD 13890 | $179\pm~{}8$ | $3.46\pm 0.18$ | 107 | 152 $\pm$ 30 | 3.7 | 112
BD+56 484 | V502 Per | $228\pm 24$ | $3.46\pm 0.18$ | 124 | 182 $\pm$ 39 | 3.7 | 124
BD+56 493 | BD+56 493 | $311\pm 31$ | $3.64\pm 0.18$ | 126 | 175 $\pm$ 41 | 4.4 | 122
BD+56 511 | BD+56 511 | $111\pm 11$ | - | - | 108 $\pm$ 54 | 4.1 | 114
BD+56 573 | BD+56 573 | $335\pm 34$ | - | - | 210 $\pm$ 51 | 4.2 | 119
BD+57 681 | HD 237056 | $160\pm 17$ | $5.90\pm 0.18$ | 125 | 155 $\pm$ 20 | 6.0 | 128
BD+58 2320 | HD 239758 | $281\pm 28$ | $2.12\pm 0.18$ | 59 | 244 $\pm$ 39 | 1.7 | 60
Table 10: The distance D to the object, and the minimum and maximum distance (d) that we take. The stars included in this range are used for our linear fits to obtain an estimation of the interstellar polarization. The large variation in these ranges is due to two main reasons: loss of linearity at big distances away from the star, or lack of data covering any other suitable range. Object | D (pc) | S(D) (pc) | Min d (pc) | Max d (pc)
---|---|---|---|---
CD-28 14778 | 1625 | 73 | 78 | 4926
CD-27 11872 | 1270 | 38 | 93 | 3657
CD-27 16010 | 168.9 | 8.4 | 50.4 | 1268.6
CD-25 12642 | 1414 | 39 | 698 | 2395
CD-22 13183 | 882 | 38 | 43 | 997
BD-20 5381 | 643 | 16 | 74 | 4714
BD-19 5036 | 667 | 16 | 108 | 3898
BD-12 5132 | 1630 | 190 | 43 | 597
BD-02 5328 | 350.4 | 6.6 | 40.7 | 1425.2
BD-01 3834 | 2010 | 110 | 49 | 1822
BD-00 3543 | 287.1 | 3 | 42.5 | 4714.2
BD+02 3815 | 790 | 510 | 132 | 2700
BD+05 3704 | 418.8 | 7.7 | 46.3 | 779.9
BD+17 4087 | 2096 | 64 | 131 | 3986
BD+19 578 | 159.3 | 2.1 | 145.7 | 4405.5
BD+20 4449 | 2130 | 180 | 131 | 381
BD+21 4695 | 204.5 | 3.7 | 46.8 | 434.4
BD+23 1148 | 2180 | 130 | 50 | 1263
BD+25 4083 | 1269 | 22 | 93 | 4693
BD+27 797 | 1977 | 58 | 854 | 3344
BD+27 850 | 1231 | 29 | 54 | 374
BD+27 3411 | 122.1 | 1.2 | 163.4 | 350.4
BD+28 3598 | 2295 | 71 | 72 | 3527
BD+29 3842 | 4560 | 250 | 126 | 1753
BD+29 4453 | 1224 | 48 | 13 | 201
BD+30 3227 | 364.5 | 9.1 | 43.4 | 597.3
BD+31 4018 | 885 | 18 | 2005 | 3455
BD+36 3946 | 2350 | 140 | 2005 | 3779
BD+37 675 | 224.1 | 2.8 | 46.4 | 2005.2
BD+37 3856 | 2195 | 56 | 126 | 4464
BD+40 1213 | 1102 | 33 | 107 | 2449
BD+42 1376 | 698 | 16 | 2007 | 4924
BD+42 4538 | 594.6 | 9.9 | 37 | 963.7
BD+43 1048 | 971 | 27 | 115 | 1879
BD+45 933 | 957 | 26 | 2005 | 3346
BD+45 3879 | 1876 | 73 | 51 | 1910
BD+46 275 | 220 | 29 | 79 | 4446
BD+47 183 | 216 | 18 | 102 | 162
BD+47 857 | 167.7 | 3.7 | 147.6 | 4926.9
BD+47 939 | 156.8 | 7.2 | 27.6 | 1224
BD+47 3985 | 287.4 | 5.8 | 53.7 | 406.2
BD+49 614 | 499 | 86 | 56 | 4578
BD+50 825 | 249.8 | 2.1 | 2005.3 | 3455.3
BD+50 3430 | 384.8 | 4.4 | 31.8 | 583.7
BD+51 3091 | 457.7 | 6.3 | 24.5 | 582.2
BD+53 2599 | 637 | 23 | 127 | 4254
BD+55 552 | 699 | 11 | 43 | 3812
BD+55 605 | 2311 | 84 | 101 | 4446
BD+55 2411 | 305.7 | 9.2 | 111.2 | 515.9
BD+56 473 | 2460 | 98 | 44 | 515
BD+56 478 | 2100 | 230 | 38 | 964
BD+56 484 | 2381 | 90 | 62 | 698
BD+56 493 | 2850 | 160 | 28 | 96
BD+56 511 | 2590 | 120 | 41 | 800
BD+56 573 | 2200 | 120 | 2005 | 3963
BD+57 681 | 1132 | 33 | 1527 | 4945
BD+58 554 | 662.2 | 6.9 | 38.1 | 963.7
BD+58 2320 | 1254 | 24 | 74 | 4714
Table 11: The calculated values for the interstellar and intrinsic polarization degrees and angles. The estimated systematic error from MOPTOP is $S(\bar{P})=0.002$ and $S(\bar{\theta})=1$ degree. The error of the interstellar polarization values has been obtained from the linear fit to nearby stars, while the error of the intrinsic polarization values has been obtained from the calculations of $q_{in}$ and $u_{in}$ and the following derivation of $P_{in}$ and $\theta_{in}$. Object | $\bar{P}$ | $\bar{\theta}$ | $P_{is}$ | $S(P_{is})$ | $\theta_{is}$ | $S(\theta_{is})$ | $P_{in}$ | $S(P_{in})$ | $\theta_{in}$ | $S(\theta_{in})$
---|---|---|---|---|---|---|---|---|---|---
CD-28 14778 | 0.032 | 4 | 0.0063 | 0.0005 | 23.72 | 0.05 | 0.01 | 0.01 | 171 | 3
CD-27 11872 | 0.071 | 170 | 0.019 | 0.001 | 24.54 | 0.03 | 0.010 | 0.02 | 145.7 | 0.5
CD-27 16010 | 0.004 | 169 | 0.0195 | 0.0005 | 34.92 | 0.01 | 0.015 | 0.005 | 16.7 | 0.3
CD-25 12642 | 0.032 | 14 | 0.013 | 0.001 | 29.66 | 0.04 | 0.020 | 0.04 | 166 | 2
CD-22 13183 | 0.012 | 175 | 0.0277 | 0.0009 | 23.17 | 0.02 | 0.001 | 0.007 | 141.6 | 0.9
BD-20 5381 | 0.013 | 179 | 0.0079 | 0.0005 | 31.15 | 0.02 | 0.010 | 0.004 | 1 | 4
BD-19 5036 | 0.029 | 10 | 0.00072 | 0.00005 | 42.312 | 0.004 | 0.009 | 0.005 | 25.9 | 0.3
BD-12 5132 | 0.091 | 168 | 0.0044 | 0.0001 | 24.95 | 0.02 | 0.006 | 0.005 | 28.6 | 0.4
BD-02 5328 | 0.004 | 91 | 0.0069 | 0.0004 | 34.24 | 0.01 | 0.011 | 0.005 | 176 | 2
BD-01 3834 | 0.004 | 80 | 0.020 | 0.001 | 23.58 | 0.03 | 0.01 | 0.01 | 132.8 | 0.1
BD-00 3543 | 0.007 | 3 | 0.029 | 0.003 | 28.85 | 0.04 | 0.02 | 0.02 | 135.45 | 0.01
BD+02 3815 | 0.010 | 0 | 0.011 | 0.002 | 35.72 | 0.05 | 0.01 | 0.01 | 150.9 | 0.7
BD+05 3704 | 0.014 | 30 | 0.0065 | 0.0003 | 27.88 | 0.02 | 0.007 | 0.005 | 31.9 | 0.2
BD+17 4087 | 0.022 | 8 | 0.00094 | 0.00009 | 44.8314 | 0.0004 | 0.071 | 0.007 | 9.6 | 0.2
BD+19 578 | 0.005 | 87 | 0.00083 | 0.00007 | 44.7854 | 0.0004 | 0.032 | 0.006 | 13.3 | 0.3
BD+20 4449 | 0.009 | 10 | 0.002 | 0.002 | 20.6 | 0.7 | 0.014 | 0.006 | 25.6 | 0.2
BD+21 4695 | 0.002 | 155 | 0.001 | 0.002 | 27 | 1 | 0.001 | 0.005 | 34 | 1
BD+23 1148 | 0.032 | 164 | 0.032 | 0.002 | 35.26 | 0.01 | 0.029 | 0.005 | 41.04 | 0.02
BD+25 4083 | 0.016 | 166 | 0.0101 | 0.0005 | 19.86 | 0.04 | 0.004 | 0.004 | 78 | 1
BD+27 797 | 0.017 | 8 | 0.006 | 0.005 | 26.7 | 0.5 | 0.01 | 0.07 | 163 | 9
BD+27 850 | 0.009 | 149 | 0.004 | 0.001 | 5.1 | 0.8 | 0.01 | 0.01 | 178 | 23
BD+27 3411 | 0.010 | 153 | 0.007 | 0.001 | 7.9 | 0.4 | 0.00 | 0.09 | 107 | 32
BD+28 3598 | 0.051 | 40 | 0.030 | 0.002 | 12.86 | 0.06 | 0.01 | 0.02 | 114 | 1
BD+29 3842 | 0.017 | 80 | 0.0038 | 0.0002 | 3.9 | 0.2 | 0.00 | 0.01 | 26 | 5
BD+29 4453 | 0.010 | 39 | 0.001 | 0.002 | 30.4 | 0.8 | 0.004 | 0.006 | 8 | 4
BD+30 3227 | 0.016 | 65 | 0.0068 | 0.0005 | 21.78 | 0.05 | 0.00 | 0.01 | 125 | 1
BD+31 4018 | 0.014 | 80 | 0.039 | 0.006 | 20.5 | 0.1 | 0.003 | 0.008 | 86 | 10
BD+36 3946 | 0.007 | 168 | 0.052 | 0.004 | 20.11 | 0.06 | 0.021 | 0.006 | 81.8 | 0.5
BD+37 675 | 0.005 | 147 | 0.12 | 0.01 | 4.6 | 0.3 | 0.12 | 0.01 | 94.4 | 0.4
BD+37 3856 | 0.014 | 127 | 0.011 | 0.001 | 9.8 | 0.2 | 0.007 | 0.007 | 100 | 2
BD+40 1213 | 0.015 | 165 | 0.008 | 0.003 | 17.2 | 0.3 | 0.00 | 0.01 | 114 | 2
BD+42 1376 | 0.015 | 175 | 0.014 | 0.001 | 27.40 | 0.04 | 0.01 | 0.01 | 129.9 | 0.2
BD+42 4538 | 0.008 | 86 | 0.0043 | 0.0002 | 5.2 | 0.1 | 0.003 | 0.004 | 83 | 3
BD+43 1048 | 0.025 | 88 | 0.023 | 0.002 | 22.48 | 0.05 | 0.015 | 0.004 | 77.2 | 0.3
BD+45 933 | 0.023 | 138 | 0.042 | 0.002 | 20.75 | 0.03 | 0.015 | 0.005 | 71.4 | 0.3
BD+45 3879 | 0.006 | 24 | 0.0074 | 0.0006 | 3.6 | 0.3 | 0.007 | 0.004 | 68.7 | 0.4
BD+46 275 | 0.009 | 89 | 0.0021 | 0.0001 | 4.8 | 0.2 | 0.027 | 0.007 | 10.4 | 0.4
BD+47 183 | 0.011 | 82 | 0.0043 | 0.0003 | 36.82 | 0.01 | 0.01 | 0.04 | 158 | 5
BD+47 857 | 0.002 | 64 | 0.0050 | 0.0006 | 29.39 | 0.05 | 0.01 | 0.06 | 170 | 10
BD+47 939 | 0.011 | 174 | 0.007 | 0.001 | 29.36 | 0.07 | 0.004 | 0.004 | 54.0 | 0.2
BD+47 3985 | 0.004 | 53 | 0.0039 | 0.0008 | 5.1 | 0.6 | 0.007 | 0.008 | 10 | 2
BD+49 614 | 0.012 | 104 | 0.014 | 0.002 | 23.4 | 0.1 | 0.078 | 0.007 | 9.9 | 0.1
BD+50 825 | 0.007 | 146 | 0.041 | 0.003 | 20.41 | 0.05 | 0.012 | 0.006 | 68.3 | 0.3
BD+50 3430 | 0.005 | 10 | 0.005 | 0.001 | 13.5 | 0.2 | 0.004 | 0.004 | 79 | 1
BD+51 3091 | 0.007 | 22 | 0.0020 | 0.0003 | 20.91 | 0.09 | 0.003 | 0.004 | 49.9 | 0.2
BD+53 2599 | 0.006 | 33 | 0.023 | 0.002 | 17.83 | 0.07 | 0.010 | 0.006 | 11.7 | 0.9
BD+55 552 | 0.027 | 112 | 0.009 | 0.001 | 36.84 | 0.03 | 0.004 | 0.006 | 144.5 | 0.3
BD+55 605 | 0.042 | 121 | 0.0013 | 0.0002 | 28.49 | 0.06 | 0.031 | 0.006 | 3 | 1
BD+55 2411 | 0.002 | 149 | 0.0009 | 0.0001 | 20.29 | 0.07 | 0.001 | 0.006 | 29 | 2
BD+56 473 | 0.047 | 109 | 0.009 | 0.003 | 26.5 | 0.1 | 0.005 | 0.006 | 171 | 2
BD+56 478 | 0.037 | 112 | 0.0032 | 0.0002 | 10.90 | 0.06 | 0.005 | 0.005 | 46.85 | 0.04
BD+56 484 | 0.037 | 124 | 0.012 | 0.002 | 12.4 | 0.2 | 0.00 | 0.02 | 164 | 4
BD+56 493 | 0.044 | 122 | 0.0024 | 0.0004 | 15.0 | 0.1 | 0.003 | 0.005 | 45.66 | 0.02
BD+56 511 | 0.041 | 114 | 0.0026 | 0.0001 | 19.27 | 0.04 | 0.01 | 0.01 | 175 | 8
BD+56 573 | 0.042 | 119 | 0.047 | 0.003 | 20.12 | 0.05 | 0.009 | 0.005 | 90.0 | 0.9
BD+57 681 | 0.060 | 128 | 0.0106 | 0.0005 | 37.25 | 0.01 | 0.007 | 0.005 | 19.3 | 0.5
BD+58 554 | 0.033 | 117 | 0.0040 | 0.0004 | 28.60 | 0.04 | 0.009 | 0.005 | 176 | 3
BD+58 2320 | 0.017 | 60 | 0.016 | 0.001 | 25.66 | 0.03 | 0.038 | 0.004 | 45.843 | 0.002