# BD +36 3317: An Algol Type Eclipsing Binary in Delta Lyrae Cluster

O. Özdarcan<EMAIL_ADDRESS>E. Sipahi  H. A. Dal  Ege University,
Science Faculty, Department of Astronomy and Space Sciences, 35100 Bornova,
İzmir, Turkey

###### Abstract

In this paper, we present standard Johnson $UBV$ photometry of the eclipsing
binary BD +36 3317 which is known as a member of Delta Lyrae (Stephenson 1)
cluster. We determined colors and brightness of the system, calculated
$E(B-V)$ color excess. We discovered that the system shows total eclipse in
secondary minimum. Using this advantage, we found that the primary component
of the system has $B9-A0$ spectral type. Although there is no published
orbital solution, we tried to estimate the physical properties of the system
from simultaneous analysis of $UBV$ light curves with 2003 version of Wilson -
Devinney code. Then we considered photometric solution results together with
evolutionary models and estimated the masses of the components as $M_{1}$ =
2.5 $M_{\odot}$ and $M_{2}$ = 1.6 $M_{\odot}$. Those estimations gave the
distance of the system as 353 pc. Considering the uncertainties in distance
estimation, resulting distance is in agreement with the distance of Delta
Lyrae cluster.

###### keywords:

techniques: photometric - (stars:) binaries: eclipsing - stars: individual:
(BD +36 3317)

††journal: New Astronomy

##  1 Introduction

BD +36 3317 (SAO 67556, $\alpha_{2000}$ = 18h 54m 22s, $\delta_{2000}$ = 36∘
51′ 07′′, $V$ = 8m.77) is an Algol type eclipsing binary which is in the same
area with Delta Lyrae cluster ($\alpha_{2000}$ = 18h 54m, $\delta_{2000}$ =
36∘ 49′, Kharchenko et al. (2005)) in the sky. The system is considered as a
member of the cluster (Eggen, 1972, 1983; Anthony-Twarog, 1984). The existence
of the cluster was suggested by Stephenson (1959) for the first time. Further
photometric evidence for the existence of the cluster was provided by Eggen
(1968). However, possible members of the cluster, included BD +36 3317, have
considerably different distance modulus values (Anthony-Twarog, 1984) and this
makes harder to confirm real members, even the existence of cluster. After
all, mean distance modulus for the cluster is given as 7m.29 with $E(B-V)$ =
0m.04 by Anthony-Twarog (1984). More recent distance modulus value was given
by Kharchenko et al. (2005) as 7m.98 (their $E(B-V)$ value is 0m.04, too) with
the distance of 373 pc. Kharchenko et al. (2004) calculated the Delta Lyrae
membership probability of BD +36 3317 as 0.67, 0.91 and 1.0, in terms of
proper motion, photometry and spatial position, respectively. This calculation
seems to support the membership of BD +36 3317 to the cluster.

Spectroscopic binary nature of the star has been first noticed by Eggen (1968)
via its large radial velocity variation from $-$90 km s-1 to 17 km s-1.
However, eclipses of the system has been discovered by Violat-Bordonau and
Arranz Heras (2008), many years after the discovery of its spectroscopic
binary nature. No orbital solution via radial velocity measurements has been
published up to know. At that point, BD +36 3317 has the advantage of to be an
eclipsing binary in terms of estimating its absolute physical properties and
distance. Furthermore, one can calculate its distance and compare it with the
distance of the cluster and check the membership of the system to the cluster.
For those purposes, we obtained standard Johnson $UBV$ observations of the
system in 2008 and 2009. By using standard photometric data, we calculated
$E(B-V)$ value of the system and estimated their spectral type. Although the
lack of spectroscopic mass ratio and orbital solution is a disadvantage in
terms of determination of the absolute dimension of the system, we made a fair
estimation for physical properties of BD +36 3317, including the distance of
the system, by using the photometric solution. In the next section, we give
summary of our observations. In section 3 we refine the light elements of the
system via $O-C$ analysis. In section 4, we give basic photometric properties
of the system and investigate the effect of interstellar extinction. In
section 5 we present the simultaneous analysis of $UBV$ light curves and our
estimation for the absolute dimension of the system. In the last section we
discuss the results.

##  2 Observations

We carried out Johnson $UBV$ observations of the star at Ege University
Observatory ($EUO$). We observed the star on 41 separate nights in 2008 and
2009. Our instrumental setup was 0.3 m Schmidth-Cassegrain telescope equipped
with uncooled SSP5 photometer. BD +36 3314 was comparison star in our
observations, while BD +36 3313 was check star. In many observing run, when no
primary or secondary minimum occurred, we only performed a short observing
sequence as $S-C2-C1-VVVV-S-C2-C1-VVVV-C1-C2-S$, where $S$ is sky, $C2$ is
check star, $C1$ is comparison star and $V$ is variable star. For those kind
of nights, we used average atmospheric extinction coefficients of $EUO$ in
order to correct all differential magnitudes in terms of $V-C1$, $V-C2$ and
$C2-C1$. For other nights, when a primary or a secondary minimum occurred, we
performed an all night observing run. For those nights, we calculate
atmospheric extinction coefficients via measurements of $C1$ and made all
corrections for atmospheric extinction on differential magnitudes according to
those coefficients. We estimate average standard deviations of observations
from $C2-C1$ measurements and resulting average standard deviations are
0m.053, 0m.019 and 0m.017 for $U$, $B$ and $V$ filters, respectively. We
observed 11 stars from IC 4665 cluster (Menzies and Marang, 1996) on 29th July
2008 and 9 stars from the list of Andruk et al. (1995) on 17th August 2009, in
order to calculate coefficients of the transformation of the instrumental
system to the standard one. By those coefficients, we applied color
corrections for all differential measurements. Then, we directly calculated
average standard magnitudes and colors of the comparison star from those two
nights. Finally, by using standard magnitude and colors of the comparison
star, we calculate standard magnitude and colors of the variable.

##  3 $O-C$ Analysis

It is not possible to make a comprehensive $O-C$ analysis for BD +36 3317
since there is not enough minimum time observations. Only the first ephemeris
of the system is available in literature (Violat-Bordonau and Arranz Heras,
2008) as

$(HJD)_{MinI}=2,454,437.25921+4^{d}.30216\ \times\ E\ .$ (1)

where $(HJD)_{MinI}$ is epoch, which corresponds to a time of a primary
minimum of BD +36 3317, and $E$ is integer eclipse cycle number. We have
already had three primary minima (Type I) and one secondary minimum (Type II)
in our observations (Sipahi et al., 2009). In Table 1, we list those minima
with corresponding $O-C$ values.

Table 1: The times of light minima of BD +36 3317. In the first column, the errors are given for the last digit of the measurements. HJD | E | $O-C$ | Filter | Type
---|---|---|---|---
(24 00000 +) |  | (day) |  |
54652.3522(4) | 50.0 |  $-$0.0025 | $UBV$ | I
54667.4148(5) | 53.5 | 0.0026 | $UBV$ | II
55052.4561(2) | 143.0 | 0.0004 | $UBV$ | I
55078.2683(4) | 149.0 |  $-$0.0004 | $UBV$ | I

Application of linear least squares method to primary and secondary minima
data gives very small amount of corrections in the ephemeris. The new light
elements and their errors are as follows:

$(HJD)_{MinI}=2,454,437.2466(30)+4^{d}.302162(27)\ \times\ E\ .$ (2)

For further analysis of light curves, we use those final light elements.

##  4 Basic Photometric Parameters and Interstellar Extinction

We show phased light and color curves of the system in Figure 1.

Figure 1: Phase folded and standardized light and color curves of BD +36 3317.

One can easily notice clear variations in $B-V$ in primary and secondary
minima, which indicate quite large temperature difference among the components
of the system. We determined brightnesses and colors of the system in maximum
light, primary and secondary minima, which would give us some hints about
components. We list those values in Table 2.

Table 2: Magnitude and colors of BD +36 3317. | Max | Min I | Min II
---|---|---|---
| (mag) | (mag) | (mag)
V | 8.798 | 9.715 | 9.053
U-B | -0.108 | -0.090 | -0.119
B-V | 0.066 | 0.167 | 0.009

We can inspect effect of interstellar extinction via $UBV$ color - color
diagram, by considering the colors at maximum light. We used $UBV$ standard
star data from Drilling and Landolt (2000) for this purpose. First, we used
magnitude and colors of maximum light (see $Max$ column in Table 2) by
assuming $E(U-B)/E(B-V)=0.72$ as the slope of the reddening vector in $UBV$
color - color diagram. Resulting $E(B-V)$ and $A_{v}$ values are 0m.139 and
0m.43, respectively, under the assumption of $R$ = 3.1. Then, de-reddened
total color for the system is $(B-V)_{0}$ = -0m.07. Now we can make an
estimation for the temperature of the primary component, by assuming that the
maximum contribution to the total light comes from the primary component.
However, during the light curve analysis, we noticed that orbital inclination
value of the system shows very small variations around 89.4 degrees which
makes the secondary minimum total eclipse. Then, the secondary component is
completely hidden behind the primary component at the middle of the secondary
minimum, hence, the magnitude and colors of that phase corresponds to the
direct measurements of the primary component. Here, we refer the reader to the
next section for justification of
${}^{\prime\prime}total~{}eclipse~{}at~{}secondary~{}minimum^{\prime\prime}$
case. In this case, we have direct measurements of the primary component
(third column in Table 2) and total colors and magnitude of the system (first
column in Table 2), therefore we can easily calculate magnitude and colors of
the secondary component as $V$ = 10m.497, $U-B$ = $-$0m.053 and $B-V$ =
0m.316. This case is also an advantage in terms of more accurate determination
of the interstellar reddening and intrinsic colors of the components
separately. Therefore, we repeated the calculation of the interstellar
reddening as described above, but this time by using the direct measurements
of the primary component at the middle of the secondary minimum. We list
intrinsic colors of the components together with the more accurate
interstellar reddening and extinction estimation in Table 3.

Table 3: Intrinsic colors and magnitude of the components of BD +36 3317 together with the amount of interstellar reddening and extinction. | Primary | Secondary
---|---|---
| (mag) | (mag)
$V_{0}$ | 8.833 | 10.277
$(U-B)_{0}$ | -0.170 | -0.104
$(B-V)_{0}$ | -0.062 | 0.245
$E(B-V)$ | 0.07
$A_{v}$ | 0.22

According to Table 3, colors of the primary component indicates $B9$ spectral
type while secondary components corresponds about $A8$ spectral type.

##  5 Analysis of Light Curves

Under the assumption of total eclipse in secondary minimum, we can estimate
the effective temperature of the primary component directly, which is very
critical for light curve analysis. We adopted calibration of Gray (2005) for
effective temperature estimation of the primary component and resulting
temperature for $(B-V)_{0}$ = $-$0m.062 is $T_{1}$ = 10750 $K$ with the error
of $\sigma_{T_{1}}$ = 470 $K$. The error of the temperature is calculated from
the standard deviation of $B-V$ color in our observations.

Before starting analysis, we chose 0.25 phase as normalisation phase and
converted all magnitude measurements into normalised flux according to the
light level at that phase. For light curve analysis, we used 2003 version of
the Wilson - Devinney code (Wilson and Devinney, 1971; Wilson, 1979, 1990).
Photometric properties of the components gives us hints for some parameters to
reduce the number of free parameters in photometric solution. We adopt the
gravity brightening coefficients $g_{1}$ = $g_{2}$ = 1 and albedos $A_{1}$ =
$A_{2}$ = 1 for stars which have radiative envelopes. We assume synchronised
rotation for both components, so $F_{1}$ = $F_{2}$ = 1. We took the band-pass
dependent ($x_{1,2}$, $y_{1,2}$) and bolometric ($x_{1,2}(bol)$,
$y_{1,2}(bol)$) limb darkening coefficients from van Hamme (1993) by assuming
square root law (Díaz-Cordovés and Giménez, 1992) which is more appropriate
for stars hotter than 8500 $K$. Since there is no radial velocity study in
literature, we do not have any information about mass ratio, which is another
critical parameter for light curve analysis. Although it is not an efficient
way to determine $q$ from photometry in detached systems, we searched for the
best solution for different $q$ values, starting from $q$ = 0.30 until $q$ =
0.90, by using $UBV$ data simultaneously. Orbital inclination ($i$), effective
temperature of the secondary component ($T_{2}$), $\Omega$ potentials of
primary and secondary ($\Omega_{1}$, $\Omega_{2}$) and luminosity of the
primary component ($L_{1}$) are free parameters in the solution. The errors of
the best solutions for individual $q$ values are very close to each other
between $q$ = 0.45 and $q$ = 0.70. At that point, we considered mass -
luminosity relation as $L\propto M^{4}$ by using the resulting absolute
luminosities at the end of the solution (see later results in this section).
We repeated solutions for many $q$ values between $q$ = 0.45 and $q$ = 0.70.
In most cases, $L\propto M^{4}$ relation indicates the $q$ value close to
0.65, hence, we finally accepted $q$ = 0.65 and applied a final light curve
solution. In Table 4, we give final light curve analysis results. We note that
the error of $T_{2}$ is internal to the Wilson - Devinney code and its error
should be similar to the error of $T_{2}$. In the table, $\langle
r_{1,2}\rangle$ denotes average of three fractional radius values ($pole$,
$side$ and $back$ values in solution output) relative to the semi-major axis
of the orbit, for corresponding component. We give the normalised fluxes for
$U$, $B$, and $V$ filters and corresponding theoretical light curves for our
final solution in Figure 2.

Table 4: Light curve analysis results of BD +36 3317. Errors are given in parenthesis. $q(=M{{}_{2}}/M{{}_{1}})$ | 0.65 (fixed)
---|---
$T_{1}(K)$ | 10750 (fixed)
$g_{1}$ = $g_{2}$ | 1.0
$A_{1}$ = $A_{2}$ | 1.0
$F_{1}$ = $F_{2}$ | 1.0
$i~{}(^{\circ})$ | 89.61(11)
$T_{2}(K)$ | 7711 (10)
$\Omega_{1}$ | 10.571 (25)
$\Omega_{2}$ | 8.997 (23)
$L_{1}$/($L_{1}$+$L_{2})_{U}$ | 0.851(17)
$L_{1}$/($L_{1}$+$L_{2})_{B}$ | 0.831(15)
$L_{1}$/($L_{1}$+$L_{2})_{V}$ | 0.789(15)
$x_{1}(bol),x_{2}(bol)$ | 0.558, 0.215
$y_{1}(bol),y_{2}(bol)$ | 0.172, 0.525
$x{{}_{1}},y{{}_{1}}(U)$ | 0.082 , 0.590
$x{{}_{1}},y{{}_{1}}(B)$ |  $-$0.058 , 0.846
$x{{}_{1}},y{{}_{1}}(V)$ |  $-$0.047 , 0.723
$x{{}_{2}},y{{}_{2}}(U)$ | 0.184 , 0.646
$x{{}_{2}},y{{}_{2}}(B)$ | 0.105 , 0.822
$x{{}_{2}},y{{}_{2}}(V)$ | 0.096 , 0.711
$\langle r_{1}\rangle,\langle r_{2}\rangle$ | 0.1009(3), 0.0832(2)
rms | 0.011
Figure 2: Representation of observational data (points) in terms of normalised
flux and theoretical solution (continuous line).

In Figure 3, we zoom to the primary (left panels) and secondary (right panels)
minima to show the shapes of the eclipses. One can notice that the secondary
minimum is certainly total eclipse which lasts for a short phase range. At the
primary minimum, we observe non-flat bottomed light variation which shows the
effects of annular eclipse and limb darkening together.

Figure 3: Close look to the primary and secondary minima in each filter. In
secondary minimum, one can notice the short total eclipse.

Comparison among photometric solution results, mass - luminosity relation and
evolutionary models of Girardi et al. (2000) indicates that the mass of the
primary $M_{1}$ is close to the 2.5 $M_{\odot}$, therefore we assume $M_{1}$ =
2.5 $M_{\odot}$. This assumption makes the mass of the secondary component
$M_{2}$ = 1.6 $M_{\odot}$ according to the $q$ value.

Since we estimated the masses of the components, we can go one step further
and calculate the absolute parameters and the distance of the system. By the
aid of Kepler’s third law, we can calculate semi-major axis of the orbit $a$.
After that point, one can easily calculate absolute radii of the components by
using average fractional radii in Table 4. Now we have effective temperatures
and absolute radii of the components and we can calculate their luminosities
in solar unit via $Stefan-Boltzmann$ law, by using $T_{\odot}$ = 5770 K. We
list absolute parameters of the system in Table 5. Finally, we can calculate
the distance of the system by using primary and secondary component
separately, via their photometric and absolute properties. In distance
calculation, we adopted bolometric corrections from Gray (2005). Photometric
properties of the primary component leads to a distance of 353 pc. We only use
primary component in order to estimate the distance since its signal is very
strong relative to the secondary component.

Table 5: Absolute Physical Properties of BD +36 3317. Solar $M_{bol}$ value of 4.m74 is used to calculate $M_{bol}$ values of the components. Parameter | Primary | Secondary
---|---|---
Mass $(M_{\odot})$ | 2.5 | 1.6
Radius $(R_{\odot})$ | 1.8 | 1.5
Luminosity $(L_{\odot})$ | 39 | 7
$M_{bol}$ (mag) | 0.76 | 2.62
$log(g)$ (cgs) | 4.32 | 4.31

##  6 Summary and conclusions

We presented standard Johnson $UBV$ photometry of the Algol type eclipsing
binary BD +36 3317 with a fairly good phase coverage and reasonably accurate
observational data. During observations, we obtained three primary and one
secondary minima. We refined the epoch and the period of the system by
applying linear least squares method to the timings of those light minima. We
determined standard colors and magnitude of the system in maximum light,
primary minimum and secondary minimum. During the analysis, we noticed that
the secondary minimum is total eclipse, which is an advantage in analysis and
means that the measurement at that phase corresponds to direct measurements of
the primary component. Using this advantage, we first determined interstellar
reddening and extinction via direct measurements of the primary component.
Then, we were able to calculate de-reddened colors and magnitudes of the
components, separately. This case was an another advantage in order to make a
more accurate estimation of $T_{1}$, hence enabled us to reduce the number of
free parameters more reliably in simultaneous $UBV$ light curve solution.
Photometric solution justified that the secondary minimum was total eclipse.

Lack of an orbital solution based on radial velocity measurements prevented us
from determining the accurate absolute parameters of the system and their
uncertainties. Hence, we can only make a rough estimation for the
uncertainties and check how those uncertainties affect our results.

If we assume that the $q$ is between 0.6 and 0.7 and $M_{1}$ is between 2.4
$M_{\odot}$ and 2.6 $M_{\odot}$, then we can calculate a lower and upper limit
for $a$ via Kepler’s third law. Those lower and upper limits of $a$ put
$R_{1}$ between 1.76 $R_{\odot}$ \- 1.84 $R_{\odot}$ when we consider the
average fractional radius of the primary component from photometric solution.
Same calculation puts $R_{2}$ between 1.45 $R_{\odot}$ \- 1.52 $R_{\odot}$. A
similar method can be used for the luminosities of the components by using
$Stefan-Boltzmann$ law and $T_{\odot}$ = 5770 K. Assuming a lower and upper
limits for $T_{1}$ and $T_{2}$ via $\sigma_{T_{1}}$ = 470 $K$, we can
calculate the ranges of $L_{1}$ and $L_{2}$ as 31 $L_{\odot}$ \- 49
$L_{\odot}$ and 5 $L_{\odot}$ \- 9 $L_{\odot}$, respectively.

We show preliminary plots of the components in log $T_{eff}$ \- log $L$ plane
in Figure 4. Evolutionary tracks for solar abundance ($Z$ = 0.019) comes from
Girardi et al. (2000). The components of the system seem close to the ZAMS and
in good agreement with solar metal abundance. However, spectroscopic analysis
is necessary to revise or refine it.

Figure 4: Positions of the components (filled stars) in log $T_{eff}$ \- log
$L$ plane. All tracks for $Z$ = 0.019 are from Girardi et al. (2000).

We can make an estimation for the uncertainty of the distance in a similar
way, as described above. If we assume the same ranges for $q$, $M_{1}$ and
$T_{1}$ as in previous uncertainty estimations, we can calculate the range of
absolute bolometric magnitude of the primary component as 1m.01 - 0m.52. Here,
we adopt bolometric corrections from Gray (2005) for corresponding temperature
limits in order to calculate limit visual absolute magnitudes ($M_{V}$) of the
primary component. Using de-reddened $V$ magnitude and $M_{V}$ limits of the
primary component in distance modulus, we can calculate the range of the
distance as 329 - 377 pc and this leads a mean value of 353 pc which is our
estimation in previous section. The uncertainty in the distance might be
slightly exaggerated since we make a rough uncertainty estimation for related
parameters. However, our distance estimation differs only by 20 pc from
distance value of the cluster (Kharchenko et al., 2005). This confirms the
membership of BD +36 3317 to Delta Lyrae cluster. Nevertheless, comprehensive
spectroscopic study of the system, in terms of radial velocity measurements,
would help to refine or revise the physical properties and distance of the
system. Further spectroscopy would also give a chance to check the metal
abundance of the system which also contains some hints about the nature of the
cluster.

## Acknowledgments

The authors acknowledge generous allotments of observing time at the Ege
University Observatory.

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