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Nature of the oscillating semi-detached eclipsing binary system IO Ursae Majoris

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Abstract

This paper presents results from analysing spectroscopic and multicolour photometric observations of the neglected semi-detached eclipsing binary system IO Ursae Majoris (IO UMa). For the first time, the orbital parameters of the system and fundamental physical properties of its components were determined from simultaneous analysis of BVR light curves and radial velocities of the components. The masses and radii of the primary and secondary components were found to be M1 = 2.11 ± 0.07 M⊙, M2 = 0.29 ± 0.02 M⊙ and R1 = 3.00 ± 0.04 R⊙ and R2 = 3.92 ± 0.05 R⊙, respectively. Derived absolute parameters yield the photometric distance of IO UMa as 263 ± 13 pc. The projected rotational velocity of the mass-accreting hotter component was measured as 34.5 ± 2 km s−1, just 1.28 times faster than the synchronous value. The hotter component of the system, located in the region of the instability strip, indicates pulsational variation with short period and small amplitude. Frequency analysis after subtracting the theoretical light curve from photometric data revealed that the more massive component shows δ Scuti type pulsation with four detected frequencies. The total amplitude of the variation in the V filter was found to be 0.03 mag. Mode identification using amplitude ratios and phase differences in different filters suggests that the main pulsation frequency of 22.0148 d−1 is probably a radial mode.
MNRAS (2013) doi:10.1093/mnras/stt678
Nature of the oscillating semi-detached eclipsing binary system IO Ursae
Majoris
F. Soydugan,1,2E. Soydugan,1,2 C¸.Kanvermez
1,2 and A. Liakos3
1Department of Physics, Faculty of Arts and Sciences, C¸ anakkale Onsekiz Mart University, TR-17100 C¸ anakkale, Turkey
2Astrophysics Research Center and Ulupınar Observatory, C¸ anakkale Onsekiz Mart University, TR-17100 C¸ anakkale, Turkey
3Department of Astrophysics, Astronomy and Mechanics, National and Kapodistrian University of Athens, GR-157 84 Zografos, Athens, Greece
Accepted 2013 April 18. Received 2013 April 17; in original form 2013 January 18
ABSTRACT
This paper presents results from analysing spectroscopic and multicolour photometric obser-
vations of the neglected semi-detached eclipsing binary system IO Ursae Majoris (IO UMa).
For the first time, the orbital parameters of the system and fundamental physical properties of
its components were determined from simultaneous analysis of BVR light curves and radial
velocities of the components. The masses and radii of the primary and secondary components
were found to be M1=2.11 ±0.07 M,M2=0.29 ±0.02 Mand R1=3.00 ±0.04 R
and R2=3.92 ±0.05 R, respectively. Derived absolute parameters yield the photometric
distance of IO UMa as 263 ±13 pc. The projected rotational velocity of the mass-accreting
hotter component was measured as 34.5 ±2kms
1, just 1.28 times faster than the synchronous
value. The hotter component of the system, located in the region of the instability strip, in-
dicates pulsational variation with short period and small amplitude. Frequency analysis after
subtracting the theoretical light curve from photometric data revealed that the more massive
component shows δScuti type pulsation with four detected frequencies. The total amplitude
of the variation in the Vfilter was found to be 0.03 mag . Mode identification using amplitude
ratios and phase differences in different filters suggests that the main pulsation frequency of
22.0148 d1is probably a radial mode.
Key words: binaries: eclipsing – stars: fundamental parameters – stars: individual: IO UMa.
1 INTRODUCTION
Double-lined eclipsing binary stars provide directly measurements
of the radii and masses of their components. One of the most popular
groups in this research area is eclipsing binary systems with pul-
sating components. In addition to variations due to eclipses, these
binaries may indicate light and radial velocity (RV) changes be-
cause of proximity effects, pulsations and physical processes such
as magnetic activity, mass loss and/or transfer and accretion struc-
tures. Oscillating eclipsing binaries are important sources for de-
termining the absolute parameters of pulsating components. This
provides us with the means to test stellar models more precisely.
Only nine systems were known to be eclipsing binary systems with a
δScuti component in the year 2000 (Rodr´
ıguez & Breger 2001), but
the number has increased rapidly following discoveries in the last
few years (e.g. Dimitrov, Kraicheva & Popov 2008a,b, 2009a,b;
Dvorak 2009; Liakos & Niarchos 2009; Soydugan et al. 2009;
Dimitrov et al. 2010), and reached 74 in the list given by Liakos
et al. (2012).
E-mail: fsoydugan@comu.edu.tr
IO Ursae Majoris (IO UMa) (HD 115268, HIP 64636) was dis-
covered by the Hipparcos satellite mission and classified as an
Algol-type binary with an orbital period of 5.52 d and a spectral
type of A3 (ESA 1997). In the literature, the system has not been
studied in detail so far. IO UMa was listed as a candidate system for
pulsations in the catalogue of eclipsing binaries with a δScuti com-
ponent (Soydugan et al. 2006a). It was confirmed as an oscillating
Algol-type binary by Liakos et al. (2012), in whose study the main
oscillating frequency was given as 0.0528 d1. IO UMa is one of
the brightest systems (V8.18 mag) among the eclipsing binaries
with a δScuti component in the list given by Soydugan et al. (2011).
This research presents a spectroscopic and photometric study of
the neglected eclipsing binary system IO UMa. In Sections 2 and 3,
information about observations and the updated ephemeris is given.
Section 4 includes RV measurements of the components and the first
orbital solution of the system, followed by spectral disentangling.
In this section, measurement of the projected rotational velocity
and estimation of the effective temperature and surface gravity of
the hotter component are also presented. Section 5 contains a mod-
elling of the multicolour light curves of the system and a frequency
analysis of the hotter component. Finally, we report the absolute
parameters of the components of the system and discuss the results.
C
2013 The Authors
Published by Oxford University Press on behalf of the Royal Astronomical Society
MNRAS Advance Access published May 13, 2013
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2 OBSERVATIONS
Photometric observations of IO UMa were made at the
C¸ anakkale Onsekiz Mart University Observatory (COMUO) and
Gerostathopoulion Observatory of the University of Athens (UOA)
during the 2010 and 2011 observing seasons. The photometric ob-
servations at COMUO were carried out using a 30-cm Schmidt–
Cassegrain telescope equipped with the CCD camera STL-1001E.
A total of 3670, 3818 and 3807 observational points were collected
over 40 nights in the Bessell B, V and Rfilters, respectively. GSC
3849590 and GSC 3849279 were selected as the comparison and
check stars, respectively. The observations at UOA were made with
a 20-cm Newtonian and a 40-cm Cassegrain telescope equipped
with the ST8XMEI and ST10XME CCD cameras, respectively.
The data were obtained using the Bessell B, V and Rphotometric
filters over 44 nights. During the observations, GSC 38490258
and GSC 38490125 were used as the comparison and check stars,
respectively.
Spectroscopic observations of the system were performed using
the ´
echelle spectrograph (FRESCO) fed by the 91-cm Cassegrain
telescope at the Catania Astrophysical Observatory (CAO) –
M. G. Fracastoro station (Serra La Nave, Mt. Etna). FRESCO is
a fibre-fed spectrograph with 300 lines mm1and a spectral re-
solving power of about 21 000. A thinned back-illuminated SITe
CCD of 1024 ×1024 pixels (size 24 ×24 µm) was used to record
data with 19 orders spanning from about 4300 to 6650 Å. During
two observation runs between 2004 April 9–July 27 and 2008 May
15–June 18, 26 spectra for IO UMa were taken with a signal-to-
noise ratio (S/N) between 30 and 100 at the continuum around the
Hαregion. Exposure times were selected between 2200 and 3600 s
depending on atmospheric conditions. θLeo (A3V) and Vega (A0V)
were also observed as RV standard stars for the primary component,
while spectra of αBoo (K1.5III) were taken as the standard for the
secondary component. Data reduction was made using the ECHELLE
task of the IRAF1package with the following steps: background sub-
traction, division by a flat-field spectrum given by a halogen lamp,
wavelength calibration using the emission lines of a Th–Ar lamp
and normalization to the continuum using a polynomial fit.
We also used ELODIE data to measure the RVs of the compo-
nents of IO UMa. ELODIE is the fibre-fed high-resolution ´
echelle
spectrograph at the 1.93-m telescope of the Observatoire de Haute-
Provence (OHP), France. The spectral resolution was about 42 000
and data consisted of 67 orders in the wavelength range 3892–6800
Å. 12 reduced and wavelength-calibrated spectra for IO UMa and
some spectra for the standard stars (Vega and αBoo) were extracted
from the public archive2(Moultaka et al. 2004). Spectra for IO UMa
were collected between 2001 May 9 and 2002 June 6 at OHP. The
S/N achieved was between 37 and 92.
3 EPHEMERIS
In order to determine a more accurate ephemeris of IO UMa, we
used all available published minima times. During photometric ob-
servations of the system at COMUO, two primary minima were
obtained. The minima times were calculated using the method of
Kwee & van Woerden (1956) as HJD 245 5367.3880 (±0.0006) and
245 5378.4307 (±0.0007), which are the mean values obtained in
the B, V and Rfilters. In addition, seven minima times obtained from
1http://iraf.noao.edu/
2http://atlas.obs-hp.fr/elodie/
the observations at UOA, available in the data base ‘O-C Gateway3’,
were used. Finally, the updated linear ephemeris was found using
all collected minima times, as follows:
HJD (Min I)=244 8500.2800(1) +5.520 1878(1) d ×E. (1)
For the orbital phase calculation in the diagrams of the light and
RV curves, the updated ephemeris was used.
4 SPECTRAL ANALYSIS
4.1 Radial velocity measurements and orbital solution
In the current study, the cross-correlation technique (CCT) was
preferred for measuring the RV values of the components of IO
UMa. This method is commonly used in spectroscopy, especially
for RV determination. After the development of the detector and
spectrograph technologies, the precision of RV measurements using
the CCT is now about a few m s1. This enables detailed research to
be carried out on different astrophysical sources such as exoplanets,
additional components around stars and pulsating variables (e.g.
Wilson 1993; Gunn et al. 1996; Zima et al. 2006; Desort et al. 2007;
Naef et al. 2007).
The spectroscopic data obtained at CAO and those taken from
the ELODIE data base were used to measure the RVs of the com-
ponents in the system. In total, 38 spectra for the system were
collected in order to determine the RV. RVs of the components
were obtained by the CCT using the IRAF task FXCOR. During the
application, the bright, slowly rotating standard stars, Vega (A0V,
RV =−13.9 km s1)andθLeo (A2V, RV =7.6 km s1) for the
primary component and αBoo (K1.5III, RV =−5.19 km s1)for
the secondary component, were used as template stars for the cross-
correlation. The studied wavelength range was chosen to exclude
Balmer and Na ID2lines and regions affected by telluric absorption
lines.
Measured RVs of the components of IO UMa are given in Table 1
together with their standard mean errors, which are the weighted av-
erages of the RVs deduced from the cross-correlation. The weights
of RVs and their standard errors were calculated as used in several
studies (e.g. Topping 1972; Tonry & Davis 1979; Frasca et al. 2000).
As given in Table 1, the standard errors of RV measurements are
less than 1 km s1for the primary and approximately 2–5 km s1for
the secondary component. The orbital solution of the system was
obtained assuming a circular orbit, as expected for classical Algols
due to their evolutionary status. The orbital parameters of IO UMa
and their errors are given in Table 2. In Fig. 1, the measured RVs of
the primary (Vh) and secondary (Vc) components are indicated as
a function of orbital phase. Theoretical RV curves, calculated us-
ing the orbital parameters in Table 2, are also shown in this figure.
According to the orbital solution, the semi-amplitudes of the RV
curves of the primary and secondary components were found to be
18.6 ±0.2 and 135.7 ±0.5 km s1, respectively.
4.2 Spectral disentangling
In order to model the composite spectra of IO UMa, the FORTRAN-
based code KOREL developed by Hadrava (1995, 2004) was used.
The program runs in the Fourier wavelength domain and decom-
poses the composite spectra into the mean separate spectra of the
3http://var.astro.cz/ocgate/
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Oscillating eclipsing binary system IO UMa 3
Tab l e 1. RV measurements of IO UMa.
Observatory HJD Orbital phase VhVc
(2450 000+)(kms
1)(kms
1)
CAO 3137.4057 0.0304 6.6 ±1.0 –
CAO 3126.4262 0.0414 7.6 ±0.6 –
OHP 2039.3840 0.1202 3.4 ±0.6 100.1 ±0.9
CAO 3143.4557 0.1264 1.6 ±0.7 111.8 ±3.0
OHP 2431.4216 0.1391 0.9 ±0.6 114.4 ±1.8
CAO 4617.4228 0.1403 0.2 ±0.6 114.8 ±2.4
CAO 3110.5228 0.1605 2.4 ±0.6 129.0 ±3.2
CAO 3138.4354 0.2170 5.6 ±0.8 148.3 ±3.0
CAO 3127.4311 0.2235 6.6 ±0.6 150.4 ±2.7
CAO 3105.4859 0.2480 4.2 ±1.0 155.0 ±5.8
OHP 2299.5779 0.2552 4.6 ±0.7 153.7 ±2.9
OHP 2040.5082 0.3239 3.8 ±0.6 140.1 ±3.0
OHP 2090.3503 0.3529 0.1 ±0.7 129.6 ±3.2
CAO 3183.3721 0.3574 1.1 ±0.6 120.5 ±3.2
CAO 4635.3904 0.3952 1.1 ±0.7 105.1 ±3.3
CAO 3139.5030 0.4104 2.6 ±0.8 92.2 ±4.2
CAO 4602.3871 0.4166 4.2 ±0.7 85.1 ±3.7
CAO 3106.5138 0.4343 5.9 ±0.8 78.8 ±4.5
OHP 2300.5982 0.4400 5.2 ±0.5 69.4 ±2.8
CAO 3156.4848 0.4848 11.1 ±0.6 28.7 ±2.1
CAO 3173.4067 0.5521 18.2 ±0.7 38.2 ±3.3
CAO 3140.4296 0.5782 20.5 ±0.6 47.5 ±3.7
CAO 4636.4483 0.5869 22.3 ±0.9 60.1 ±3.4
OHP 1931.6047 0.5956 24.0 ±0.5 67.8 ±0.9
CAO 3157.4316 0.6582 29.1 ±0.6 99.7 ±2.4
OHP 2042.4582 0.6771 30.5 ±0.8 111.4 ±2.5
CAO 3124.4541 0.6842 31.7 ±0.6 113.4 ±3.0
CAO 3185.3732 0.7199 32.5 ±0.7 127.0 ±3.1
OHP 2092.3785 0.7203 32.8 ±0.7 122.1 ±2.2
CAO 3152.5222 0.7688 31.3 ±0.8 126.2 ±3.1
CAO 3108.4705 0.7887 32.6 ±0.7 120.0 ±3.4
OHP 2302.5968 0.8021 31.1 ±0.7 113.1 ±2.4
OHP 2098.4049 0.8120 31.2 ±0.6 111.4 ±2.9
OHP 2043.8506 0.8506 27.9 ±0.7 88.6 ±2.2
CAO 3125.4484 0.8643 25.8 ±0.8 90.0 ±3.0
CAO 3142.3963 0.9345 22.3 ±0.6 45.2 ±3.4
CAO 3214.3763 0.9739 22.5 ±0.9 –
CAO 3203.3715 0.9803 20.5 ±0.9 –
components. During analysis, RVs of the components are also cal-
culated simultaneously. We used the version of KOREL11b available
in the VO-KOREL website4as an application of the Czech Virtual
Observatory.
18 spectra obtained at CAO were used for the disentangling.
Three wavelength regions were selected, including Hβand several
metallic lines, which are suitable for measuring the effective tem-
perature and surface gravity of the hotter component: 4830–4890,
5180–5215 and 5280–5345 Å. After trials, we decided to use the or-
bital parameters given in Table 2, which do not indicate significant
changes. The light factors of the components are taken from the
light-curve solutions in Table 3. The three selected spectral regions
were disentangled independently. In Fig. 2, the observed composite
spectra (at orbital phases 0.217, 0.484, 0.768 and 0.934) and model
spectra, being the sum of the separate disentangled spectra of the
components and residuals from the fits, are illustrated in the wave-
length region 5280–5345 Å . The calculated spectra are wavelength
Doppler-shifted according to the RV solution.
4http://vokorel.asu.cas.cz
Tab l e 2 . Spectroscopic orbital ele-
ments of IO UMa.
Parameter Value
T0(HJD) 2448 500.280a
Porb (d) 5.520 1878a
Vγ(km s1) 13.4 ±0.1
K1(km s1) 18.6 ±0.2
K2(km s1) 135.7 ±0.5
a1sin i(106km) 1.41 ±0.01
a2sin i(106km) 10.30 ±0.04
M1sin 3i(M)1.85±0.02
M2sin 3i(M)0.25±0.01
q(=M2/M1) 0.137 ±0.001
aThe ephemeris was adopted from
equation (1).
Figure 1. RV curves of the components of IO UMa plotted as a function of
orbital phase. The filled and open circles represent the RVs of the primary
and secondary components, respectively. The solid line represents the orbital
solution for the more massive component and the dashed line for the less
massive component.
4.3 Projected rotational velocity of the hotter component
Classical Algol-type binaries are semi-detached interacting sys-
tems. When the orbital solutions of many classical Algols are re-
viewed, it may be noticed that the eccentricity value of their orbits
is zero, as expected. Furthermore, the synchronization time is less
than that of the semi-detached phase and the circularization time of
their orbits. Therefore, rotational periods can be expected to be syn-
chronous with the orbital periods of this type of binaries. However,
it has been reported in many studies that the gainer (more massive)
components of classical Algols with an orbital period longer than
5–6 d indicate higher projected rotational velocities (vsin i)than
their synchronous values due to the mass-transfer effect (e.g. Olson
& Etzel 1994; Glazunova 1999; Soydugan et al. 2007; Dervis¸o˘
glu,
Tout & ˙
Ibano˘
glu 2010). Consequently, higher vsin ivalues of the
gainer components may be evidence of mass transfer in semi-
detached binaries (SDBs).
In this study, we measured the vsin iof the more massive, hotter
component of the system. Mean disentangled spectra of the primary
component obtained from KOREL analysis were used in this proce-
dure. To determine a calibration for the full width at half-maximum
(FWHM) versus vsin i,θLeo was chosen as the template star.
The spectrum of θLeo was synthetically broadened by increasing
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Tab l e 3. Parameters of IO UMa obtained
from the simultaneous analysis of BVR light
curves and RVs of the components.
Parameter W–D solution
a(R) 17.58 ±0.11
i() 78.32 ±0.09
Vγ(km s1) 13.5 ±0.4
T1(K) 7800a
T2(K) 4260 ±30
16.012 ±0.062
22.062
Phase shift 0.0008 ±0.0001
q(=M2/M1) 0.135 ±0.003
g1,g21.0, 0.32
A1,A21.0, 0.5
L1/(L1+L2)B0.938 ±0.003
L1/(L1+L2)V0.906 ±0.004
L1/(L1+L2)R0.872 ±0.004
L2/(L1+L2)B0.062
L2/(L1+L2)V0.094
L2/(L1+L2)R0.128
r1(mean) 0.171 ±0.001
r2(mean) 0.223 ±0.001
aAdopted from the spectroscopic analysis.
Figure 2. KOREL fits (thick line) to the observed composite spectra (thin
line) of IO UMa (a), and residuals from the fits (b) at four different orbital
phases in the wavelength range 5280–5345 Å.
vsin iin steps of 5 km s1. Then, the CCT was applied to the broad-
ened spectra of θLeo using the original spectrum of the star as
a template. The measured FWHM values of the cross correlation
function (CCF) were used to establish the calibration of FWHM
versus vsin i.Finally,thevsin ivalue was determined using the
FWHM of its CCF peaks through the aforementioned relationship.
We found vsin i=34.5 ±2.0 km s1, which is the weighted av-
erage value of all measurements for the primary component of
IO UMa.
Figure 3. Comparison between the observed (dotted) Hβline and the best-
fitting model with Teff =7800 K (solid line), and models with Teff =7500K
(dotted line) and Teff =8000 K (dashed line).
4.4 Atmospheric parameters of the hotter component
In the current study, atmospheric parameters of the hotter compo-
nent, namely effective temperature and surface gravity (log g), are
needed to be estimated to carry out photometric analysis and deter-
mine absolute parameters. These estimations are also important to
establish mode identification for the pulsating component. In classi-
cal Algols, the spectrum of the cooler component contributes about
10 per cent or less of the total light in the optical region. Therefore,
the hotter component may contribute almost all light in the system.
In this case, if the spectral resolution and S/N are not high enough,
it is not possible to carry out atmosphere modelling for the cooler
components in Algols. In the case of IO UMa, the magnitude dif-
ference between the components is about 2.7 mag in the Vband and
the average S/N of all spectra is about 50. Therefore, we could not
find reliable atmospheric parameters for the cooler component us-
ing spectroscopic analysis. For the hotter component, the effective
temperature and surface gravity values were determined as follows.
In order to estimate the effective temperature of the massive
component, we used disentangled Hβlines, which are useful indi-
cators for Teff.However,usingHβlines suffers from degeneracy
between Teff and log g(Smalley 2005). Therefore, the log gvalue
of the primary component was first fixed at 3.81 calculated from
the analysis of the light and RV curves of the system, as given in
Table 6 (given later). The procedure for determining the Teff of the
hotter component based on minimization of the difference between
the observed and synthetic spectra for the Hβline was applied.
Model atmospheres were calculated using the ATLAS9 code (Kurucz
1993) and the synthetic spectra were formed using the SPECTRUM
code5(Gray & Corbally 1994). The models were produced assum-
ing the solar metallicity, a microturbulent velocity of 2 kms1and
vsin i=34.5 km s1. The grid includes models with intervals of
7000 Teff 8500 K (in steps of 100 K). The resulting effective
temperature value of the primary component determined from the
χ2
min method was 7800 ±150 K. The χ2
min +1 method (Lampton,
Margon & Bowyer 1976) was used to estimate the uncer-
tainty of Teff, taking into account the normalization problems for
Balmer lines. Fig. 3 shows the observed spectrum of the primary
5http://www1.appstate.edu/dept/physics/spectrum/
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Oscillating eclipsing binary system IO UMa 5
Figure 4. Comparison between the observed and disentangled spectra of
the primary component (dots) and the best-fitting model with Teff =7800 K
and log g=3.84 (solid line) in the 5180–5215 Å wavelength region,
including the Mg Iline (5183 Å).
component (dots) compared to various models for the Hβline. As
seen, the best-fitting Teff is 7800 K.
We estimated the surface gravity of the primary component using
line-profile fitting. For this, one component of the Mg Itriplet at
5183 Å, an Fe II line at 5284 Å and an Fe II line at 5317 Å were
selected. The effective temperature of the component was fixed to
7800 K and other atmospheric parameters (metallicity, microtur-
bulent and rotation velocities) were adopted as applied for the Hβ
line. We used the version 2012 of the SME (Spectroscopy Made Easy)
code for line-profile fitting (Valenti & Piskunov 1996). This code
has been preferred in many studies to determine the atmospheric
parameters of stars by matching observed and synthetic spectra by
selecting model atmospheres; among them are the Kurucz (1993),
NextGen (Hauschildt et al. 1999) and MARCS (Gustafsson et al.
2008) models. SME requires atomic line data in the format of the
Vienna Atomic Line Database (Piskunov et al. 1995). For this ap-
plication, Kurucz model atmospheres (Kurucz 1993) were selected
to fit the lines. This procedure yielded surface gravity values of
3.86 ±0.07, 3.84 ±0.09 and 3.82 ±0.10 for Mg Iand two Fe II
lines (at 5284 and 5317 Å ), respectively. Uncertainties were esti-
mated by using the χ2
min +1 method as applied for Hβ. We adopt
a weighted average value of log g=3.84 ±0.05 for the primary
component of IO UMa. In Fig. 4, a comparison between the ob-
served and synthetic spectra of the primary component in the spec-
tral range 5180–5215 Å is shown.
5 PHOTOMETRIC ANALYSIS
5.1 Light-curve modelling
In order to determine the photometric and absolute parameters of
the components of IO UMa, we analysed BVR light and RV curves
simultaneously using the Wilson–Devinney (W–D) code (Wilson
& Devinney 1971). The photometric data obtained at COMUO
wereusedtoformtheBVR light curves. All magnitude values ob-
tained in the BVR filters were converted into relative intensities
and normalized to a unit using the mean magnitude around an or-
bital phase of 0.25. The temperature of the primary component
(T1) of the system and the mass ratio (q) are important parameters
for light-curve analysis of eclipsing binaries. Both T1and qwere
estimated, as mentioned in the previous sections. Therefore, dur-
ing light-curve analysis, the temperature of the hotter component
was adopted to be 7800 K determined from spectroscopic analysis.
The input value for the mass ratio was taken as 0.137, determined
from the orbital solution of the system. Values of the following
parameters, which can be estimated from corresponding theoretical
Figure 5. Observed and theoretical light curves of IO UMa in the BVR
filters.
models for the components, were adopted during the analysis: log-
arithmic limb darkening coefficients were taken from van Hamme
(1993); bolometric gravity-darkening coefficients (g1,2) were fixed
to 1.0 for radiative envelopes (von Zeipel 1924) and 0.32 for con-
vective envelopes (Lucy 1967), and bolometric albedos (A1,2) were
set to 1.0 and 0.5 for radiative and convective envelopes, respec-
tively (Rucinski 1969). The rotational parameter of the secondary
component (F2) was assumed to be 1.0, which means that the com-
ponent rotates synchronously, while the rotational parameter for
the primary component (F1) was fixed at 1.28, determined from
the spectroscopic analysis. According to the orbital solution given
in Section 4.1, a circular orbit (e=0) was used in the analysis.
Adjustable parameters were the length of the semi-major axis of the
relative orbit (a), RV of the centre-of-mass of the system (Vγ), phase
shift, orbital inclination (i), surface temperature of the secondary
component (T2), non-dimensional normalized surface potential of
the primary component (1), mass ratio of the components (q=
m2/m1) and fractional luminosity of the primary component (L1).
Although the shape of the light curves of IO UMa appears similar
to that of semi-detached classical Algols, the W–D code in Mode 2
(detached eclipsing binaries) was used for the first trials. At the end
of the tests, the value of the surface potential of the secondary com-
ponent reached its Roche limit. We continued the analysis in Mode
5 (semi-detached configuration) since the secondary component of
the system fills its Roche lobe. During analysis, the existence of a
third light contribution in the light curves of the system was also in-
vestigated; however, no meaningful value was found. The iterations
were ended when corrections of the free parameters became smaller
than their probable errors. Results of the light-curve modelling are
given in Table 3. A comparison between observed data and the best
theoretical fits achieved for the BVR filters is shown in Fig. 5.
5.2 Frequency analysis and mode identification
Short time variations in the light curves of IO UMa, especially in
phases outside the primary eclipse, can be seen in Fig. 5. Frequency
analysis was carried out to determine this light variation. First,
theoretical light curves obtained from the binary solution were sub-
tracted from each of the observational data. In this way, proximity
effects were excluded from the observed light curves of the system.
Then, data between phases 0.94 and 1.0 were eliminated for more re-
liable frequency analysis. Frequency analysis was performed using
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6F. Soydugan et al.
Figure 6. Spectral window (panel a), power spectra and significance limits
(horizontal line) for detected frequencies (panels b–e).
the PERIOD04 program (Lenz & Breger 2005) based on the Fourier
transform method. In the frequency analysis, 6665, 6689 and 6718
data points collected at COMUO and the Gerostathopoulion Ob-
servatory were used in the B, V and Rfilters, respectively. The
periodograms showed four significant peaks at f1=22.0153 d1
(65.4 min), f2=17.3055 d1(83 min), f3=16.5979 d1(86.8 min)
and f4=16.8815 d1(85.3 min) above the significance limit ac-
cording to the criterion by Breger et al. (1993). The spectral window
and power spectra for all frequencies found are indicated in Fig. 6.
Tab l e 4. Pulsational properties of the hotter component of IO UMa.
Frequency Filter A(semi-amplitude) φ(phase) S/N
(d1) (mag) (rad)
f1=22.0148 ±0.0001 B0.0065 ±0.0002 0.1910 ±0.0052 13.4
V0.0050 ±0.0002 0.1984 ±0.0065 12.8
R0.0038 ±0.0002 0.2047 ±0.0087 10.1
f2=17.3052 ±0.0002 B0.0053 ±0.0002 0.8803 ±0.0064 11.4
V0.0042 ±0.0002 0.8724 ±0.0079 11.3
R0.0031 ±0.0002 0.8816 ±0.0108 8.5
f3=16.5982 ±0.0002 B0.0046 ±0.0002 0.4667 ±0.0074 10.2
V0.0031 ±0.0002 0.4790 ±0.0109 8.4
R0.0025 ±0.0002 0.4786 ±0.0133 7.2
f4=16.8806 ±0.0002 B0.0038 ±0.0002 0.9592 ±0.0091 8.4
V0.0027 ±0.0002 0.9791 ±0.0125 7.3
R0.0022 ±0.0002 0.9806 ±0.0157 6.1
Only peaks having S/N 4 were considered reliable. The frequency
analysis was stopped when the fifth frequency value was found to
be under the significance limit. Although the value obtained from
the frequency analysis matches the range of frequency values for δ
Scuti stars, it was not found to be meaningful because of S/N <3.
Results of the frequency analysis are listed in Table 4. Peak-to-
peak total pulsation amplitudes of 0.04, 0.03 and 0.023 mag were
calculated for the B, V and Rfilters, respectively.
The majority of astrophysical information about pulsating stars
can be derived from determined modes. The spherical harmonic de-
gree (l) and azimuthal order (m) related to the pulsational frequency
can be determined using mode identification. Modes can be iden-
tified by both photometric and spectroscopic methods. While the
photometric mode determination method depends on the time series
of multicolour photometry, the spectroscopic method is based on
the time series of line-profile variations. Photometric data with high
sensibility and spectroscopic data of high resolution are necessary
to ascertain the sensibility mode. The spherical harmonic degree (l),
which can be detected by several photometric methods, was com-
puted using the FAM IAS (Frequency Analysis and Mode Identification
for Asteroseismology) code (Zima 2008) in this study. Due to the
fact that the hot component of IO UMa shows δScuti-type light vari-
ation, we used the pulsational model computed by ATO N (Ventura,
D’Antona & Mazzitelli 2008) and MAD (Montalb´
an & Dupret 2007)
for δScuti stars. For photometric mode identification by the FAMIAS
code, the amplitude ratios and phase differences used were based on
theoretical models (Balona & Stobie 1979; Watson 1988; Cugier,
Dziembowski & Pamyatnykh 1994, Daszy´
nska-Daszkiewicz et al.
2002). The observed parameters were compared with pre-computed
grids of atmospheric parameters and non-adiabatic models in the
photometric mode identification module. The pulsation frequen-
cies, amplitudes, phases and their errors are given in Table 4. The
effective temperature, surface gravity and their errors of the pulsat-
ing component and stellar model parameters were selected as input
parameters in the origin of mode analysis. The amplitude ratios and
observed phase shifts greatly depend on these stellar parameters.
The values of the mass, effective temperature and surface gravity
were taken to be 2.1 M, 7800 K and 3.84, respectively. Observed
amplitude ratios and phase differences were computed for each pul-
sational frequency value according to all derived pulsation models.
The results with respect to the selected reference Vfilter in the
Johnson–Cousins system were listed in Table 5. On the left-hand
side of Fig. 7, amplitude ratios are plotted against wavelength, while
phase differences are plotted against wavelength in the right-hand
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Oscillating eclipsing binary system IO UMa 7
Tab l e 5. Observed phase shifts and amplitude ratios for the pulsating component of IO UMa.
Frequency φBφVφRφVAB/AVAR/AV
(d1) (rad) (rad)
f10.0074 ±0.0117 0.0063 ±0.0152 1.3000 ±0.0656 0.7600 ±0.0502
f20.0079 ±0.0143 0.0092 ±0.0187 1.2619 ±0.0767 0.7381 ±0.0592
f30.0123 ±0.0183 0.0004 ±0.0242 1.4839 ±0.1154 0.8065 ±0.0829
f40.0199 ±0.0216 0.0015 ±0.0282 1.4074 ±0.1279 0.8148 ±0.0956
Figure 7. Comparison of observed amplitude ratios (left-hand panels) and phase differences (in rad, right-hand panels) with theoretical models for determined
frequencies. The lines indicate different spherical harmonic degrees (l=0, 1, 2 and 3).
panels. Amplitude ratios and phase differences in Fig. 7 were calcu-
lated for models with the effective temperature in the range 7700–
7900 K and log gvalues in the range 3.80–3.90. According to the
amplitude ratio and phase differences, the lvalue for f1frequency
may be 0, while the spherical harmonic degree for f2frequency may
be l=0,1or3exceptforl=2. If f1is a fundamental radial mode,
f2can be a first radial-mode overtone. In this case, the f2/f1ratio is
expected to be between 0.77 and 0.78 according to the Petersen dia-
gram (Petersen & Jørgensen 1972; Su´
arez, Garrido & Moya 2007).
However, the value of the f2/f1ratio is 0.786, which is outside this
range. From this argument, we can conclude that f1and f2cannot
both be radial modes. Therefore, it is more probable that the spher-
ical harmonic degree for f2is l=1 or that both f1and f2are l=1
modes. Because of large error bars for the amplitude and phase
difference values of f3and f4,theirlvalues could not be estimated
reliably.
The range of the possible mode visibility in eclipsing binaries is
only l=0andm=0; l=1andm1; l=2andm2; l=2
and m=0; l=3andm3, or l=3andm1 (Mkrtichian
et al. 2004). Consequently, the azimuthal order value is m=0for
l=0 concerning f1in this study. If the spherical harmonic degree is
l=1 for both f1and f2, the azimuthal order value can be m1.
6 DISCUSSION
The simultaneous analysis of BVR light curves together with
the RVs of the components of IO UMa enabled us to calculate
the fundamental astrophysical parameters of its components for the
first time. IO UMa was found to be a semi-detached system from
the photometric solutions in which the less massive component fills
its Roche volume, while the massive component is within its Roche
lobe. Using the parameters given in Table 3, the absolute param-
eters for both components of the system were derived, as listed
in Table 6. For the calculations, the bolometric corrections of the
components were taken from Drilling & Landolt (2000) together
with solar values (Teff=5777 K, Mbol=4.74 mag). From spec-
troscopic analysis, the effective temperature and surface gravity of
the primary component were determined to be 7800 ±150 K and
3.84 ±0.05 (cgs), respectively. log gis consistent with the value
determined using the mass and radius of the primary component
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8F. Soydugan et al.
Tab l e 6. Fundamental astrophysical parameters of IO UMa.
Parameter Primary Secondary
Mass (M)2.11±0.07 0.29 ±0.02
Radius (R)3.00±0.04 3.92 ±0.05
Temperature (K) 7800 ±150 4260 ±150
log L(L)1.48±0.04 0.66 ±0.07
log g(cgs) 3.81 ±0.02 2.71 ±0.04
log gsp (cgs) 3.84 ±0.05a
Orbital period (d) 5.520 1878 ±1×107
Orbital separation (R) 17.58 ±0.11
Mass ratio 0.135 ±0.003
Systemic velocity (km s1) 13.4 ±0.4
Distance (pc) 263 ±13
V(mag) 8.21b
BV(mag) 0.24c
E(BV) (mag) 0.01
(BV)0(mag) 0.23
Mbol (mag) 1.05 ±0.11 3.09 ±0.18
BC (mag) 0.12 0.77
MV(mag) 1.19 ±0.11 3.85 ±0.18
Measured vsin i(km s1) 34.5 ±2.0 –
Synchronous vsin i(km s1) 26.9 ±0.1 35.2 ±0.1
aValue measured spectroscopically.
bSIMBAD data base.
cHipparcos catalogue (ESA 1997).
within an error range. Due to spectra with low S/N and also because
of binary effects, the error of the surface gravity value of the hotter
component, determined using spectroscopic analysis, is larger than
that of log gfrom the simultaneous analysis of light and RV data.
The masses and radii of the components are derived with a precision
of about 3 and 1.5 per cent, respectively. Therefore, IO UMa has
been added to the list of SDBs with more accurately determined
absolute parameters (˙
Ibano˘
glu et al. 2006).
The photometric distance of IO UMa was calculated to be
263 ±13 pc based on data given in Table 6. Its trigonometric par-
allax was also measured by the Hipparcos mission, at 3.55 ±0.72
mas, which corresponds to a distance of 282+71
48 pc (ESA 1997).
Van Leeuwen (2007) re-analysed the Hipparcos data and ascer-
tained the distance of the system to be 305+78
52 pc from the parallax
of 3.28 ±0.67 mas. Our distance estimation is consistent with the
value based on Hipparcos data due to the wide range of error in the
Hipparcos parallax.
The (BV) colour of IO UMa is reported in the Hipparcos
catalogue to be 0.24 ±0.01 mag (ESA 1997). Weused the reddening
maps of Schlegel, Finkbeiner & Davis (1998) and NASA/IPAC
Extragalactic Database6to calculate the E(BV) value of the
system, taking the distance of the system to be 263 pc. Interstellar
reddening for the system was determined as E(BV)0.01 mag,
which is to be expected due to its high Galactic latitude (l=117.
3,
b=+57.
6). The intrinsic (BV) colour can be estimated as
0.23 mag.
In the recent catalogue of SDBs by ˙
Ibano˘
glu et al. (2006), there
are 61 classical Algols. This list includes only 38 double-lined
eclipsing binaries. So far, the parameters of a very limited num-
ber of classical Algols have been known accurately. In Fig. 8,
the components of IO UMa together with well-known classical
Algols compiled from ˙
Ibano˘
glu et al. (2006) are indicated in the
plane of log L–log Teff. In this diagram, similar to the components
6http://nedwww.ipac.caltech.edu/forms/calculator.html
Figure 8. Locations of the primary (filled circles) and secondary (open
circles) components of SDBs given by ˙
Ibano˘
glu et al. (2006) together with
the components of IO UMa indicated with the filled (primary) and open
triangles (secondary) in the log L–log Teff plane. The continuous and dotted
lines represent the zero-age main sequence (ZAMS) and terminal-age main
sequence (TAMS) for the solar chemical composition, respectively. Evolu-
tionary tracks are also shown for 1, 2 and 5 Mand are taken, together
with ZAMS and TAMS lines, from Girardi et al. (2000).The instability-strip
zone is indicated by the dashed lines, as per Rolland et al. (2002).
of the SDBs, the more massive component of IO UMa is located
in the main-sequence band, while the less massive component has
evolved away from the main sequence. The absolute parameters, es-
pecially the surface gravity of the primary component, indicate that
this star evolved inside the main-sequence band. As can be seen
from the location of the primary component in the Hertzsprung–
Russell diagram (HRD) in Fig. 8, the more massive component
is close to the turn-off point from the main sequence. The mass
of the hotter component was found as 2.11 ±0.07 Mand its
location in the HRD shown in Fig. 8 is very close to the evolu-
tionary track for 2 M. Among well-known classical Algols, the
properties of IO UMa are similar to those of S Vel and XX Cep
regarding the mass ratio of the systems and masses of the primary
components.
The mass–luminosity relationship (MLR) determined using pri-
mary components of well-known detached eclipsing binaries was
given by ˙
Ibano˘
glu et al. (2006) to be L1M3.92
1. They derived the
MLR as L1M3.20
1for the more massive components of SDBs. A
significant difference in the empirical MLRs indicates that the pri-
mary components of SDBs are less luminous than those of detached
systems with the same mass. This may be interpreted as the result of
mass transfer from the less massive component to the more massive
one and its effect on the evolution of the gainer component. The
mass and luminosity values of the hotter component of IO UMa are
compatible with the MLR of the primaries of SDBs within error
limits.
The orbital angular momentum (J(P)) distribution of detached
eclipsing binaries and SDBs was also discussed by ˙
Ibano˘
glu et al.
(2006). Using the formalism in the aforementioned study, the J(P)
value of IO UMa can be calculated as 1×1052 in cgs units,
which is smaller than the mean value of J(P) (5.7 ×1052)for
SDBs given by ˙
Ibano˘
glu et al. (2006). This slight disagreement can
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Oscillating eclipsing binary system IO UMa 9
Figure 9. Locations of gainer components of some classical Algols together
with IO UMa showing rotational parameter (F) against fractional radius (r1)
based on data from Dervis¸o˘
glu et al. (2010). The open circles and solid
dots indicate classical Algols with Porb <5dandPorb >5 d, respectively.
The triangle represents IO UMa. The dotted horizontal line corresponds to
synchronous rotational velocities (F=1).
be interpreted as being due to angular momentum loss during the
evolution of the system because of possible magnetic activity in the
cooler component of IO UMa and/or mass transfer.
In semi-detached Algol-type binaries, the projected rotational
velocities of the gainer components can be used as evidence of
the mass-transfer process (e.g. Olson & Etzel 1994; Mukherjee,
Peters & Wilson 1996; Soydugan et al. 2007; Dervis¸o˘
glu et al.
2010). If the mass-gainer component rotates faster than the ex-
pected synchronous value, mass transfer can be expected in the sys-
tem. Dervis¸o˘
glu et al. (2010) reported in their theoretical study that
a small amount of mass transfer is enough to spin the mass-gainer
component up to its critical rotational velocity. However, the pro-
jected rotational velocities of these components in classical Algols
are much slower than the critical velocity. The difference between
observed and theoretical velocities may be interpreted as being due
to the balance between mass transfer and the stellar wind caused by
the magnetic field (Dervis¸o˘
glu et al. 2010). The projected rotational
velocity of the massive component of IO UMa was derived from
the calibration of the FWHM of the CCF and vsin i. The measured
vsin ivalue of the hotter component is 34.5 ±2.0 km s1,which
is very close to the synchronous value (26.9km s1). The synchro-
nized rotational velocities of the system’s components were also
calculated (Table 6). The rotational parameter (F), derived from the
ratio of the observed rotational velocity to the synchronous velocity
[(vsin i)obs/(vsin i)sync ], was found to be 1.28 for the gainer com-
ponent of the system. Fig. 9 plots the primaries of the SDBs in the
plane of rotational parameter (F) against fractional radius (r1), using
the data from Dervis¸o˘
glu et al. (2010). In this diagram, the gainer
components of all classical Algols with Porb >5 d rotate faster than
the synchronous velocities and all have F>2exceptIOUMa.On
the other hand, the primaries of the short-period Algols (Porb <5d)
rotate synchronously (F1) except SW Cyg and U Cep, which
appear to exhibit much greater active mass transfer than the others.
IO UMa is a new member among oscillating SDBs listed recently
by Liakos et al. (2012). The results derived from the frequency
analysis indicate that the hotter component is a δScuti-type variable.
The pulsating component has four frequencies and a total amplitude
of about 0.03 mag in the Vfilter. Among oscillating SDBs, IO UMa
has the highest Porb/Ppuls ratio (122) after AS Eri (approximately
158, according to Liakos et al. 2012). For eclipsing binaries with δ
Scuti-type components, the PorbPpuls relationship was determined
by Soydugan et al. (2006b) and updated by Liakos et al. (2012).
The orbital and pulsation periods of IO UMa may be accepted as
consistent with the above-mentioned relationship.
7 CONCLUSIONS
Results of this study indicate that IO UMa is an interesting semi-
detached oscillating Algol-type binary system. The orbital parame-
ters and absolute dimensions of the components of the system were
determined for the first time. This is important since the number
of classical Algols with accurately determined absolute parame-
ters is very limited. Another interesting result is that the projected
rotational velocity of the mass-gainer component of the system is
very close to the synchronous value despite the fact that classical
Algols with Porb >5 d rotate faster than their expected velocities.
This shows that IO UMa is in a different evolutionary process com-
pared to classical Algols with similar orbital periods. The system
has a δScuti-type primary component exhibiting pulsation of a very
short period compared to systems having similar orbital periods. In
order to research the existence of other frequencies and also am-
plitude variation due to the possible mass-transfer process and/or
tidal effects, multisite photometric and spectroscopic campaigns are
needed.
ACKNOWLEDGEMENTS
The authors would like to thank the staff of the Catania Astrophysi-
cal Observatory for their kind hospitality, the allocation of telescope
time and assistance during observations. We wish to thank the ref-
eree for the substantial suggestions and comments that enabled us to
improve the manuscript considerably. We also thank the Scientific
and Technological Research Council of Turkey (T ¨
UB˙
ITAK, Grant
Nos 111T224 and 107T634) and C¸ anakkale Onsekiz Mart Univer-
sity Science Foundation (Project No. 2011/014) for supporting this
study. The current research is part of the MSc thesis of C¸K. This
research made use of the VIZIER and SIMBAD data bases at CDS,
Strasbourg, France.
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... Therefore, the LC residuals in the B, V, and I bands were subjected to frequency analysis using period0.4 software (Lenz & Breger 2005), which is based on the Fourier analysis (e.g., Soydugan et al. 2013). To perform this analysis, we subtracted Table 1 for RY Aqr. ...
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We present simultaneous new BVI light curves along with radial velocity curve analysis of the RY Aqr system, using the PHysics Of Eclipsing BinariEs code. The analysis indicates that while the primary is completely inside its Roche critical surface, the secondary has filled out its Roche surface. In addition, the positions of the system components on M–R, H–R diagrams are specified, which show that the primary is a main-sequence or nearly main-sequence star while the secondary is an evolved subgiant. In addition, analysis of the period and luminosity variations of the system were carried out. Fourier frequency analysis of light variation indicates that the primary is a pulsating, δ-scuti variable star. Moreover, O–C curve analysis shows that the period of the system is secularly decreasing with a rate of dp/dt = 0.074 s yr−1. This decrease in the orbital period variations was attributed to a mass and angular momentum loss from the system with a rate of [$2.57\times {10}^{-10}{M}_{\odot }\;{\mathrm{yr}}^{-1}.$] Apart from the secular period decreases, the orbital period of the system is modulated by a cyclic period of 72.69 year, which was attributed to a third body orbiting around the barycenter of the system.
... 3 All those systems for which we could not find L 2 /L 1 but for which we have got their data are solved in this study using the Wilson-Devinney code (Wilson & van Hamme 2014) in the usual way (e.g. Soydugan et al. 2013;Bakış, Yücel & Bakış 2018). Since the light and radial-velocity curves of all these 33 systems have already been analysed in the literature, the effective temperature of the primary (T 1 ) and the mass ratios of the system (q) were adopted from Table 2 and kept fixed during the analysis. ...
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... We could study the short-term dynamical processes such as the acceleration and braking of stellar rotation and the evolution of systems through this feature. However, only 11 oEA stars were studied using double-lined RV curves with/without light curves (Hoffman 2009;Tkachenko et al. 2009Tkachenko et al. , 2010Lampens et al. 2011;Soydugan et al. 2013;Hong et al. 2015). We studied the oEA star Y Cam as the first target (Hong et al. 2015). ...
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Oscillating Algol-type eclipsing binaries (oEA) are very interesting objects that have three observational features of eclipse, pulsation, and mass transfer. Direct measurement of their masses and radii from the double-lined radial velocity data and photometric light curves would be the most essential for understanding their evolutionary process and for performing the asteroseismological study. We present the physical properties of the oEA star XX Cep from high-resolution time-series spectroscopic data. The effective temperature of the primary star was determined to be 7,946 $\pm$ 240 K by comparing the observed spectra and the Kurucz models. We detected the absorption lines of the secondary star, which had never been detected in previous studies, and obtained the radial velocities for both components. With the published $BVRI$ light curves, we determined the absolute parameters for the binary via Wilson-Devinney modeling. The masses and radii are $M_{1} = 2.49 \pm 0.06$ $M_\odot$, $M_{2} = 0.38 \pm 0.01$ $M_\odot$, $R_{1} = 2.27 \pm 0.02$ $R_\odot$, and $R_{2} = 2.43 \pm 0.02$ $R_\odot$, respectively. The primary star is about $45 \%$ more massive and $60 \%$ larger than the zero-age main sequence (ZAMS) stars with the same effective temperature. It is probably because XX Cep has experienced a very different evolutionary process due to mass transfer, contrasting with the normal main sequence stars. The primary star is located inside the theoretical instability strip of $\delta$ Sct-type stars on HR diagram. We demonstrated that XX Cep is an oEA star, consisting of a $\delta$ Sct-type pulsating primary component and an evolved secondary companion.
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We analysed photometric time series of the active, semidetached Algol-type system RZ Cas obtained in 1999–2009, in order to search for seasonal and short-term variations in the oscillation spectrum of RZ Cas A. The orbital period shows ±1 s cyclic variations on time-scales of 6–9 years. We detected six low-degree p-mode oscillations with periods between 22.3 and 26.22 min and obtained safe mode identifications using the periodic spatial filter method. The amplitudes and frequencies of all modes vary. We tested and confirm the hypothesis that rapid variations in the pulsation spectrum of the mass-accreting component and rapid increases in the orbital period are driven by high mass transfer and accretion outbursts caused by the cyclic magnetic activity of the Roche lobe-filling donor star. Two rapid pulsation-amplitude decays observed in 2001 and 2009 can be explained by high-mass transfer events separated by the duration of the last 9-yr long magnetic cycle. We also tested and confirm the hypothesis of an acceleration of the outer envelope of the pulsating component. We discovered synchronous, modal m-dependent variations in the frequencies of three identified modes, in good agreement with results of our mode identification using the periodic spatial filter method. We suggest that m-dependent pulsation frequency variations are caused via the Doppler-effect by variations of the rotation speed of the outer envelope of the pulsating gainer. With this method, we obtained the first asteroseismic detection and accurate measurement of the accretion driven acceleration of the outer envelope of the mass-accreting component of an Algol-type star.
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Eclipsing binaries with a $\delta$ Sct component are powerful tools to derive the fundamental parameters and probe the internal structure of stars. In this study, spectral analysis of 6 primary $\delta$ Sct components in eclipsing binaries has been performed. Values of $T_{\rm eff}$, $v \sin i$, and metallicity for the stars have been derived from medium-resolution spectroscopy. Additionally, a revised list of $\delta$ Sct stars in eclipsing binaries is presented. In this list, we have only given the $\delta$ Sct stars in eclipsing binaries to show the effects of the secondary components and tidal-locking on the pulsations of primary $\delta$ Sct components. The stellar pulsation, atmospheric and fundamental parameters (e.g., mass, radius) of 92 $\delta$ Sct stars in eclipsing binaries have been gathered. Comparison of the properties of single and eclipsing binary member $\delta$ Sct stars has been made. We find that single $\delta$ Sct stars pulsate in longer periods and with higher amplitudes than the primary $\delta$ Sct components in eclipsing binaries. The $v \sin i$ of $\delta$ Sct components is found to be significantly lower than that of single $\delta$ Sct stars. Relationships between the pulsation periods, amplitudes, and stellar parameters in our list have been examined. Significant correlations between the pulsation periods and the orbital periods, $T_{\rm eff}$, $\log g$, radius, mass ratio, $v \sin i$, and the filling factor have been found.
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On the basis of the NSVS data search the star GSC 4588-0883 was discovered as a new Algol-type system. According to Rozhen CCD observations orbital period of the star is P_orb=3.25855 days and amplitude of primary minimum is A_R=0.62 mag. Short-period oscillations with amplitude up to 0.015 mag in R and main periodicity in the interval 71 div 78 minutes were found. Preliminary physical parameters of the system are computed.
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On the basis of the NSVS data the star GSC 4293-0432 was discovered as a new Algol-type system. During the photometric campaign the multi-periodic oscillations with a peak-to-peak amplitude of up to 0.04 mag in V were observed. From the Rozhen spectral and photometric CCD observations some physical parameters of the system were estimated.
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Four Algol-type systems: SX Dra, RT UMi, V548 Cyg, and V728 Cyg were explored for short-period oscillations. Only in one of them - SX Dra, oscillations were detected with peak-to-peak amplitude up to 0.040 mag. in V.
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This little book is written in the first place for students in technical colleges taking the National Certificate Courses in Applied Physics; it is hoped it will appeal also to students of physics, and pernaps chemistry, in the sixth forms of grammar schools and in the universltIes. For wherever experimental work in physics, or in science generally, is undertakcn the degree of accuracy of the measurements, and of the res,!lts of the experiments, must be of the first importance. Every teacher of experimental physics knows how "results" given to three or four decimal plaees are often in error in the first place; students suffer from "delusions of accuracy. " At a higher level too, more experieneed workers sometimes claim a degree of accuracy which cannot be justified. Perhaps a considera­ tion of the topics discussed in this monograph will stimulate in students an attitude to experimental results at onee more modest and more profound. The mathematical treatment throughout has been kept as simple as possible. It has seemed advisable, however, to explain the statistical concepts at the basis of the main considerations, and it is hoped that Chapter 2 contains as elementary an account of the leading statistical ideas involved as is possible in such small compass. It is a necessary link between the simple introduction to the nature and estimation of errors given in Chapter 1, and the theory of errors discussed in Chapter 3.