Results of 5-year photometric monitoring of the intermediate
polar V2306 Cygni: correction of the
orbital period and evidence of 2-day periodicity
V.Breus
1∗
, K. Petrík
2
, S. Zoªa
3,4
, A. Baransky
5
, T.Hegedus
6
Advances in Astronomy and Space Physics, 5, 17-20 (2015)
© V.Breus, K. Petrík, S. Zoªa, A.Baransky, T.Hegedus, 2015
1
Department of High and Applied Mathematics, Odesa National Maritime University, Odesa, Ukraine
2
Hlohovec Astronomical Observatory, Hlohovec, Slovak Republic
3
Astronomical Observatory of the Jagiellonian University, Krakow, Poland
4
Mt. Suhora Observatory, Pedagogical University, Krakow, Poland
5
Astronomical Observatory, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
6
Baja Astronomical Observatory, Baja, Hungary
We present the results of 6 years of photometric monitoring of the magnetic cataclysmic variable V2306 Cygni
(formerly known as 1WGAJ1958.2+3232) obtained at collaborating observatories. Using (O-C) analysis we tried
to study variability of the spin period of the white dwarf, however we cannot make a rm conclusion based on
the scatter. Simultaneously, using (O-C) diagram of orbital minima, we found that the value of 0.181545(3) days
better corresponds with the light curve, than do previously published orbital period values. We also found that the
variability has a 2.01 day period; this variability may be interpreted as possible precession of the accretion disk in
this system.
Key words: stars: binaries: close  stars: novae, cataclysmic variables  stars: individual (V2306 Cygni)  stars:
binaries: close  accretion disks  novae, cataclysmic variables
introduction
The pulsating X-ray source 1WGAJ1958.2+3232
was discovered by Israel et al. [4]. Authors discussed
the possible nature of the 12-min pulsations and con-
cluded that the source may be a long-period, low-
luminosity X-ray pulsar, or an intermediate polar.
Later on, Negueruela et al. [7] classied this object as
an intermediate polar by its X-ray and optical char-
acteristics. They noticed the double-peaked struc-
ture of the emission lines that indicates the presence
of the accretion disc.
Uslenghi et al. [9] suggested that the true spin pe-
riod of the white dwarf could be 24min rather than
12min, and mentioned that this object has one of
the slowest rotators exhibiting a double-peaked spin
prole.
Zharikov et al. [10] reported the detection of the
orbital period of 4h36m (0d.1802±0d.0065) from pho-
tometry and the nal value of 0d.18152 ± 0d.00011
from radial velocity variations. They conrmed the
(733.82± 1.25) s. spin period of the white dwarf us-
ing the spectroscopy and photometry and interpreted
strong modulations with orbital period in the emis-
sion lines as a presence of a bright hot spot on the
edge of the accretion disk.
Later on, Norton et al. [8] reported that the or-
bital period is (5.387 ± 0.006) hours, corresponding
to the ∼ 1 day alias of the period found by Zharikov
et al. [10] and conrmed that the rotational period
of the white dwarf is twice the pulse period.
Soon afterwards, Zharikov et al. [11] repeated the
analysis using own data along with the data pro-
vided by A.Norton. They conrmed their previous
results and published the nal value of 0d.181195 ±
0d.000339. However, they mentioned that a longer
time base of observations is needed to improve this
value.
The star was named as V2306Cyg in 2003. In this
paper we present the results of the long-term multi-
colour photometric CCD monitoring of this system.
observations
The CCD photometric observations of the
V2306Cyg were obtained using 60-cm Zeiss-
Cassegrain telescope at the Observatory and Plane-
tarium in Hlohovec, Slovakia (ZC600) equipped with
SBIG ST-9 camera, 50-cm Zeiss reector at the
Fort Skala Observatory in Krakow, Poland (Zeiss50)
equipped with Andor DZ936 camera, 70-cm AZT-
8 telescope at the Astronomical Observatory of
the Taras Shevchenko National University of Kyiv,
∗
Vitaly.Breus@gmail.com
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Advances in Astronomy and Space Physics V.Breus, K. Petrík, S. Zoªa, A. Baransky, T.Hegedus
Ukraine (AZT-8) equipped with PL47-10 FLI and
50-cm reector of Baja Astronomical Observatory,
Hungary (50 cm) using Apogee camera. Along with
our time series we analyzed all long CCD time series
published in the AAVSO database (14 runs). The
observations log is presented in Table 1. The length
of the observational run is given in hours. HJD is
given with subtracted 2450000.0. The telescope col-
umn shows the telescope name from listed above, or
3-4 letter AAVSO observer code.
The CCD frames were processed using
C-MuniPack software package. The nal time series
were obtained using the program MCV [2] taking into
account multiple comparison stars method [5], the
same software was used for periodogram analysis.
To determine spin maxima and orbital minima
timings we used trigonometric polynomial approxi-
mation. We chose a 2-periodic variability model for
smoothing:
m(t) = m0−r1 cos [ω1(t− T01)]−r2 cos [ω2(t− T02)] ,
where m(t) is the smoothed value of brightness at
time t, m0 is average brightness on theoretical curve
(generally dierent from the sample mean [1], ωj =
2pi/Pj , rj is semi-amplitude, T0j is the epoch for
maxima of brightness of photometric wave with num-
ber j and period Pj . We calculated only one moment
per set of observations (i. e., per night) because the
accuracy estimate is much better then for individual
extrema. This method is regularly used for approx-
imation of observations of intermediate polars, e. g.,
MUCam [6], EXHya [3].
We took into account only best 41 spin and 41
orbital timings from 46 determined using all pho-
tometric data. To study period variations we used
(O-C) analysis. Two O-C diagrams were built: for
spin maxima and for orbital minima timings.
Contrary to a classical representation of the O-
C diagram as a dependence of the timings from an
ephemeris, i. e.,
O − C = T − (T0 + P · E)
on the cycle number E we have used phases instead,
i. e. φ = (O − C)/P . For a correct ephemeris, the
phases should be concentrated near the zero value.
variability of the
white dwarf spin period
Period variations are frequently observed in inter-
mediate polars and are typically detectable at a time
scale of decades. Using polynomial ts to the (O-C)
diagrams it is possible to study variations of the spin
period of the white dwarf. Using coecients of these
approximations after many years of monitoring, it is
possible to determine the value of the period more
precisely, nd period variability and (in some cases)
detect second derivatives of the period, e. g. accel-
eration of the spin period of the white dwarf. Dur-
ing our research in some objects we found a spin-up,
sometimes the period increase was turned to a period
decrease, sometimes the period is constant.
We tried to study variations of the spin period of
V2306Cygni the same way. Unfortunately, the rela-
tively short timescale and large scatter at the (O-C)
makes all attempts to correct cycle miscount am-
biguous. Longer time base is needed, but we found
no published spin maxima timings or time series ob-
tained earlier.
on the orbital period
We used the preliminary value of the orbital pe-
riod of 0d.22446[8] among two published aliases of
each other for (O-C) analysis due to larger ampli-
tude of variations at the phase curves for some se-
lected nights of observations. We found regular cy-
cle miscount, and minima timings obtained during
dierent years looked like separate trends not con-
nected to each other. Using consecutive photometric
runs obtained in May-June 2014 (see Figure 1) we
got the true cycle miscount and corrected it for all
(O-C) data. After this, we smoothed the (O-C) di-
agram with a polynomial of statistically-optimal de-
gree, which ended up being a linear approximation
(see Figure 2). Using coecients of the polynomial,
we determined a more accurate value for the orbital
period of V2306Cyg, which was 0.2232685(24) days.
Fig. 1: (O-C) diagram of V2306Cyg for orbital minima
using data obtained in MayJune 2014
Then we checked the (O-C) diagram for the pe-
riod of 0d.1825179, which is a daily alias of our cor-
rected value and close to that published by Zharikov
et al. [10]. There were same separate linear trends
from year to year. Using similar calculations we
determined the new value of the orbital period of
0d.181545±0d.000003 which is slightly dierent from
the value of 0d.181195± 0d.000339 determined from
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Advances in Astronomy and Space Physics V.Breus, K. Petrík, S. Zoªa, A. Baransky, T.Hegedus
radial velocities by Zharikov et al. [11].
Of course, longer time series and a larger time
base enables to determine the orbital period of the
system with better accuracy.
Fig. 2: (O-C) diagram of V2306Cyg for orbital minima
using data obtained in 2010-2014
two-day period
Periodogram analysis for the entire available time
series revealed a prominent peak, which corresponds
to the double value of the beat period of the orbital
one and previously unknown one (P = 2d.0183).
This new period is visible at the larger range pe-
riodogram. Despite the fact that this value is a mul-
tiple of the length of the day and observations cover
only part of the phase curve, we noticed signicant
ascending and descending branches of it due to dier-
ent mean brightness from night to night (see Fig. 3).
It is worth noting that the phase curve in V has
a much larger amplitude than in R lter, so if this
variability is real, it may be interpreted as a possible
precession of the accretion disk in this system.
results and conclusions
We tried to nd variability of the white dwarf
spin period in the intermediate polar V2306Cyg on
the timescale of 5 years (20092014). Unfortunately,
we found no unambiguous correction of present cycle
miscount. However, using (O-C) analysis we cor-
rected the value of the orbital period of this bi-
nary system and obtained the result 0d.181545 ±
0d.000003 which is consistent with the value pub-
lished by Zharikov et al. [11]. Orbital phase curves
of V2306Cyg calculated with this period show larger
amplitudes than all previously published or obtained
by us for most seasons. Currently the accuracy esti-
mate of our result is 113 times better. We report the
detection of the P = 2d.0183 periodicity, which may
be interpreted as the precession of the accretion disk
in this system.
acknowledgement
We would like to thank William Gof, Etienne
Morelle, James Jones, Richard Sabo, J. Ulowetz
and the administration of the AAVSO International
Database contributed by observers worldwide for the
observations used in this research.
references
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[3] Andronov I. L. & BreusV.V. 2013, Astrophysics, 56, 518
[4] IsraelG. L., Angelini L., Campana S. et al. 1998, MN-
RAS, 298, 502
[5] KimY., Andronov I. L. & JeonY.-B. 2004, J. Astron.
Space Sci., 21, 191
[6] KimY.-G., Andronov I. L., Park S.-S. et al. 2005, J. As-
tron. Space Sci., 22, 197
[7] Negueruela I., ReigP. & Clark J. S. 2000, A&A, 354, L29
[8] NortonA. J., Quaintrell H., Katajainen S. et al. 2002,
A&A, 384, 195
[9] UslenghiM., Bergamini P., Catalano S., Tommasi L. &
TrevesA. 2000, A&A, 359, 639
[10] Zharikov S.V., TovmassianG.H., Echevarría J. & Cár-
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A&A, 390, L23
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Advances in Astronomy and Space Physics V.Breus, K. Petrík, S. Zoªa, A. Baransky, T.Hegedus
Table 1: The observations log
Date HJD start Length Filter Telescope Date HJD start Length Filter Telescope
08.08.2009 5052.3750 5.50 V, R 50cm 04.09.2011 5808.6818 7.06 CV SRIC
16.08.2009 5060.2994 7.79 V 50cm 05.09.2011 5809.6591 6.81 CV SRIC
21.08.2009 5065.3480 6.46 V, R 50cm 08.06.2012 6086.6755 4.83 CV UJHA
26.08.2009 5070.3032 7.80 V, R 50cm 08.07.2012 6116.5184 1.62 V, R ZC600
14.10.2010 5483.6355 2.11 CV GFB 08.07.2012 6117.3566 5.44 V, R ZC600
14.10.2010 5484.2885 3.48 CV MEV 16.07.2012 6125.3642 4.48 V, R ZC600
15.10.2010 5484.6344 2.07 CV GFB 27.07.2013 6501.3376 4.27 V, R ZC600
15.10.2010 5485.2551 1.91 CV MEV 28.07.2013 6502.3183 4.78 V, R ZC600
16.10.2010 5485.6194 2.06 CV GFB 19.08.2013 6524.3219 3.36 B, V, R AZT-8
18.10.2010 5487.6122 3.42 CV JJI 19.05.2014 6797.3526 5.72 V, R Zeiss50
20.10.2010 5489.6194 2.09 CV GFB 20.05.2014 6798.3538 2.07 V, R Zeiss50
21.10.2010 5490.6186 1.67 CV GFB 09.06.2014 6818.3482 5.39 V, R ZC600
27.10.2010 5496.6146 2.06 CV GFB 13.06.2014 6822.3542 4.78 V, R ZC600
01.11.2010 5501.5970 2.09 CV GFB 17.06.2014 6826.3506 5.52 V, R ZC600
02.11.2010 5502.6016 2.06 CV GFB 30.06.2014 6839.4021 1.27 V, R ZC600
Fig. 3: Phase curve of V2306Cyg for the period P = 2d.0183 using data obtained in Hlohovec in 2013 and
2014.
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