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Peremennye Zvezdy (Variable Stars) 26, No. 2, 2006 Received 19 February; accepted 25 March.
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Article in PDF |
Photometric elements and stellar parameters for the contact binary RZ UMi
Van Cauteren, P.1,3; Lampens, P.2; Wils, P.3
- Beersel Hills Observatory, Laarheidestraat 166, B-1650 Beersel, Belgium,
email: PaulVanCauteren@skynet.be
- Koninklijke Sterrenwacht van België, B-1180 Brussel, Belgium,
email: Patricia.Lampens@oma.be
- Vereniging Voor Sterrenkunde, Belgium, email: Patrick.Wils@cronos.be
The contact binary RZ UMi (= SVS 2310 = GSC 4642-0832 =
1RXS J145418.3+864338;
;
) was discovered by
Goranskij (1982), who also attributed it to the W UMa class with
a period of 0.33735283 days. No other observations of this star
have been published since.
We therefore re-observed RZ UMi at Beersel Hills Observatory on
nine nights between May 2001 and March 2003. The instrument used
was a 0.4 m Newtonian telescope, equipped first with a SBIG ST7E
CCD camera (2001-2002) and later with a ST10 XME camera (2003).
The 2001 observations are unfiltered. From 2002 onwards, a 
filter according to the specifications of Bessell (1995) was used.
The exposure times varied between 120 and 180 seconds. All images
were reduced with the aperture photometry procedure of the Mira
AP software package1 and darkframed and flatfielded according to
standard procedures.
The brightness of the variable was measured with respect to
GSC 4642-0777 (GSC average photographic magnitude 14.3), while
GSC 4642-0752 (mag. 14.4) and GSC 4642-0833 (mag. 15.1) served
as check stars. RZ UMi has magnitude 12.9 according to the
GSC 1.2, while its instrumental magnitude with respect to the
comparison star averaged
. For the check stars
we found
and
respectively,
with nightly standard deviations on the order of 0
04 and
007.
The new times of minima determined by fitting a second degree
polynomial through the data around the observed minimum are given
in Table 1. The table also includes a normal minimum derived from
data from the Northern Sky Variability Survey (NSVS; Wozniak et
al., 2004). The O-C1 values are with respect to ephemeris
provided by Goranskij (1982), and the E and O-C2 values are
listed with respect to the ephemeris derived below.
| HJD | Type | O-C1 | E | O-C2 | Filter | ||
| 2451442.659 | I | -0.091 | -2750 | -0.007 | NSVS | ||
| 2452052.4248 | II | -0.0906 | -942 | .5 | 0.0000 | None | |
| 2452370.3769 | I | -0.0936 | 0 | 0.0003 | V | ||
| 2452371.3888 | I | -0.0938 | 3 | 0.0001 | V | ||
| 2452372.4019 | I | -0.0927 | 6 | 0.0012 | V | ||
| 2452386.4015 | II | -0.0933 | 47 | .5 | 0.0008 | V | |
| 2452720.3774 | II | -0.0967 | 1037 | .5 | 0.0007 | V |
From these minima and the computed time of minimum given by Goranskij (1982), the following improved ephemeris
was deduced:
| Min = HJD 2452370.3766 | + 0.33734941d x E. |
| ± 0.0008 | ± 0.00000011 |
Within the accuracy of Goranskij's data, the orbital period is found to be constant.
The parameters of the system were derived using the
Wilson-Devinney (WD) code (Wilson, 1998). The average temperature
of the primary star was assumed to be 
K, from the
rough period-colour relation for W UMa stars (Eggen, 1967).
Values for gravity darkenings (0.32) and bolometric albedos (0.5)
typical for contact binaries were assumed. Limb darkening
coefficients have been taken from the tables by Van Hamme (1993).
Best fits were then derived with the temperature of the secondary
(
), the inclination (
), and the surface potential and the
relative monochromatic luminosity of the primary star as free
parameters, assuming different values of the mass ratio 
. These calculations showed that any mass ratio between
0.8 and 2.2 fitted the data almost equally well (see Fig. 1). The
value for the temperature of the secondary star stays almost
constant at
K throughout this interval, while
the value for the inclination increases from
(for 
) to
(for 
).
.
Fig. 2 shows the phased light curve (2002-2003) superposed on
the model fit with 
, as well as the residuals after
subtraction of the model. The remaining scatter after subtraction
is of the order of 004. Differential data are given in
Table 2.
Acknowledgements: The authors are pleased to acknowledge Prof. R. Wilson (University of Florida) for providing the Wilson-Devinney code. P. Lampens acknowledges support from the Fund for Scientific Research (FWO) - Flanders (Belgium) through project G.0178.02. P. Van Cauteren is grateful to the Royal Observatory of Belgium for putting at his disposal material acquired by the same FWO project. A part of these data were acquired with equipment purchased thanks to a research fund financed by the Belgian National Lottery (1999).
References:
Bessell, M.S., 1995, CCD Astronomy, 2, 20
Eggen, O.J., 1967, Mem. R. Astron. Soc., 70, 111
Goranskij, V.P., 1982, Peremennye Zvezdy Prilozhenie, 4:20, 169
Van Hamme, W., 1993, Astron. J., 106, 2096
Wilson, R.E., 1998, Computing Binary Star Observables, (Reference manual to the Wilson-Devinney program), Department of Astronomy, University of Florida, Gainesville, FL, 1998 edition
Wozniak, P.R., Vestrand, W.T., Akerlof, C.W., Balsano, R., Bloch, J., Casperson, D., Fletcher, S., Gisler, G., Kehoe, R., Kinemuchi, K., Lee, B.C., Marshall, S., McGowan, K.E., McKay, T.A., Rykoff, E.S., Smith, D.A., Szymanski, J., Wren, J., 2004, Astron. J., 127, 2436
| HJD-2452000 |  |
HJD-2452000 | |
HJD-2452000 | |
| 370.3697 | -1.595 | 371.4647 | -2.214 | 386.3425 | -2.239 |
| 370.3718 | -1.600 | 371.4668 | -2.213 | 386.3442 | -2.262 |
| 370.3739 | -1.575 | 371.4702 | -2.233 | 386.3459 | -2.190 |
| 370.3761 | -1.543 | 371.4723 | -2.195 | 386.3475 | -2.161 |
| 370.3782 | -1.518 | 371.4744 | -2.225 | 386.3492 | -2.225 |
| 370.3803 | -1.581 | 371.4766 | -2.179 | 386.3508 | -2.187 |
| 370.3824 | -1.565 | 371.4787 | -2.209 | 386.3525 | -2.204 |
| 370.3845 | -1.630 | 371.4808 | -2.207 | 386.3542 | -2.186 |
| 370.3867 | -1.673 | 371.4829 | -2.193 | 386.3558 | -2.110 |
| 370.3888 | -1.727 | 371.4851 | -2.188 | 386.3575 | -2.115 |
| 370.3909 | -1.734 | 371.4872 | -2.199 | 386.3592 | -2.166 |
| 370.3930 | -1.771 | 371.4893 | -2.168 | 386.3608 | -2.067 |
| 370.3952 | -1.903 | 371.4914 | -2.193 | 386.3625 | -2.040 |
| 370.3973 | -1.923 | 371.4936 | -2.197 | 386.3641 | -2.096 |
| 370.3994 | -1.895 | 371.4957 | -2.174 | 386.3658 | -2.088 |
| 370.4015 | -1.963 | 371.4978 | -2.226 | 386.3675 | -2.054 |
| 370.4037 | -1.967 | 371.4999 | -2.172 | 386.3691 | -2.088 |
| 370.4058 | -1.911 | 371.5020 | -2.152 | 386.3708 | -2.039 |
| 370.4079 | -2.046 | 371.5042 | -2.203 | 386.3725 | -2.019 |
| 370.4100 | -1.996 | 371.5063 | -2.164 | 386.3741 | -1.963 |
| 370.4122 | -2.020 | 371.5084 | -2.142 | 386.3758 | -2.037 |
| 370.4143 | -2.081 | 371.5105 | -2.179 | 386.3774 | -1.973 |
| 370.4164 | -2.131 | 371.5127 | -2.118 | 386.3791 | -1.963 |
| 370.4185 | -2.148 | 371.5148 | -2.114 | 386.3808 | -1.875 |
| 370.4207 | -2.130 | 371.5169 | -2.091 | 386.3824 | -1.912 |
| 370.4228 | -2.087 | 371.5191 | -2.096 | 386.3841 | -1.796 |
| 370.4249 | -2.135 | 371.5212 | -2.062 | 386.3857 | -1.833 |
| 370.4270 | -2.168 | 371.5233 | -2.070 | 386.3874 | -1.774 |
| 370.4292 | -2.171 | 371.5254 | -2.039 | 386.3891 | -1.749 |
| 370.4313 | -2.202 | 371.5275 | -2.027 | 386.3907 | -1.703 |
| 370.4334 | -2.143 | 371.5297 | -1.991 | 386.3924 | -1.702 |
| 370.4355 | -2.202 | 371.5318 | -1.967 | 386.3941 | -1.617 |
| 370.4377 | -2.160 | 371.5339 | -1.947 | 386.3957 | -1.647 |
| 370.4398 | -2.225 | 371.5361 | -1.916 | 386.3974 | -1.652 |
| 370.4419 | -2.190 | 371.5382 | -1.873 | 386.3990 | -1.619 |
| 370.4440 | -2.251 | 371.5403 | -1.797 | 386.4007 | -1.603 |
| 370.4462 | -2.239 | 371.5424 | -1.796 | 386.4024 | -1.646 |
| 370.4483 | -2.225 | 371.5445 | -1.732 | 386.4040 | -1.568 |
| 370.4504 | -2.235 | 371.5467 | -1.681 | 386.4057 | -1.606 |
| 370.4525 | -2.192 | 371.5488 | -1.666 | 386.4073 | -1.641 |
| 370.4554 | -2.191 | 372.3188 | -2.150 | 386.4090 | -1.656 |
| 370.4575 | -2.202 | 372.3209 | -2.218 | 386.4107 | -1.691 |
| 370.4597 | -2.204 | 372.3230 | -2.152 | 386.4123 | -1.703 |
| 370.4618 | -2.191 | 372.3251 | -2.148 | 386.4140 | -1.738 |
| 370.4639 | -2.249 | 372.3273 | -2.150 | 386.4157 | -1.801 |
| 370.4660 | -2.200 | 372.3294 | -2.139 | 386.4173 | -1.854 |
| 370.4681 | -2.227 | 372.3315 | -2.249 | 386.4190 | -1.867 |
| 370.4703 | -2.203 | 372.3337 | -2.181 | 386.4206 | -1.908 |
| 370.4724 | -2.216 | 372.3358 | -2.156 | 386.4233 | -1.912 |
| HJD-2452000 | |
HJD-2452000 | |
HJD-2452000 | |
| 370.4745 | -2.170 | 372.3379 | -2.217 | 386.4254 | -1.947 |
| 370.4767 | -2.211 | 372.3400 | -2.143 | 386.4275 | -1.970 |
| 370.4788 | -2.212 | 372.3421 | -2.083 | 386.4296 | -1.970 |
| 370.4809 | -2.196 | 372.3443 | -2.141 | 386.4318 | -1.977 |
| 370.4830 | -2.173 | 372.3464 | -2.098 | 386.4339 | -2.004 |
| 370.4852 | -2.173 | 372.3485 | -2.082 | 386.4360 | -2.011 |
| 370.4873 | -2.135 | 372.3506 | -2.149 | 386.4381 | -2.063 |
| 370.4894 | -2.135 | 372.3528 | -2.119 | 386.4403 | -2.095 |
| 370.4915 | -2.188 | 372.3549 | -2.079 | 386.4424 | -2.118 |
| 370.4936 | -2.126 | 372.3570 | -2.132 | 386.4445 | -2.098 |
| 370.4958 | -2.129 | 372.3591 | -2.072 | 386.4466 | -2.079 |
| 370.4979 | -2.146 | 372.3613 | -2.036 | 386.4488 | -2.199 |
| 370.5000 | -2.108 | 372.3634 | -2.085 | 386.4509 | -2.159 |
| 371.3394 | -2.170 | 372.3655 | -2.005 | 386.4530 | -2.118 |
| 371.3412 | -2.099 | 372.3676 | -2.001 | 386.4551 | -2.173 |
| 371.3430 | -2.091 | 372.3719 | -2.002 | 386.4573 | -2.174 |
| 371.3448 | -2.124 | 372.3740 | -1.895 | 720.3325 | -2.238 |
| 371.3465 | -2.152 | 372.3761 | -1.936 | 720.3340 | -2.215 |
| 371.3483 | -2.083 | 372.3783 | -1.883 | 720.3354 | -2.180 |
| 371.3501 | -2.066 | 372.3804 | -1.857 | 720.3369 | -2.174 |
| 371.3519 | -2.061 | 372.3825 | -1.839 | 720.3383 | -2.213 |
| 371.3536 | -2.085 | 372.3846 | -1.796 | 720.3398 | -2.163 |
| 371.3554 | -2.039 | 372.3868 | -1.747 | 720.3412 | -2.129 |
| 371.3572 | -2.013 | 372.3889 | -1.705 | 720.3427 | -2.167 |
| 371.3590 | -2.024 | 372.3910 | -1.670 | 720.3441 | -2.179 |
| 371.3607 | -2.003 | 372.3931 | -1.618 | 720.3455 | -2.144 |
| 371.3625 | -1.955 | 372.3953 | -1.606 | 720.3470 | -2.107 |
| 371.3643 | -1.929 | 372.3974 | -1.547 | 720.3484 | -2.043 |
| 371.3661 | -1.933 | 372.3995 | -1.531 | 720.3499 | -2.036 |
| 371.3679 | -1.884 | 372.4016 | -1.522 | 720.3513 | -1.965 |
| 371.3696 | -1.873 | 372.4038 | -1.547 | 720.3528 | -2.041 |
| 371.3714 | -1.826 | 372.4059 | -1.582 | 720.3542 | -1.974 |
| 371.3732 | -1.839 | 372.4080 | -1.609 | 720.3557 | -1.910 |
| 371.3750 | -1.768 | 372.4101 | -1.570 | 720.3571 | -1.914 |
| 371.3767 | -1.722 | 372.4123 | -1.688 | 720.3586 | -1.915 |
| 371.3785 | -1.641 | 372.4172 | -1.749 | 720.3600 | -1.845 |
| 371.3803 | -1.642 | 372.4193 | -1.796 | 720.3615 | -1.872 |
| 371.3821 | -1.628 | 372.4214 | -1.840 | 720.3629 | -1.780 |
| 371.3838 | -1.627 | 372.4235 | -1.887 | 720.3643 | -1.800 |
| 371.3856 | -1.600 | 372.4257 | -1.904 | 720.3658 | -1.693 |
| 371.3874 | -1.521 | 372.4278 | -1.948 | 720.3672 | -1.694 |
| 371.3892 | -1.557 | 372.4299 | -1.961 | 720.3687 | -1.654 |
| 371.3910 | -1.537 | 372.4320 | -1.990 | 720.3701 | -1.675 |
| 371.3927 | -1.598 | 372.4342 | -2.004 | 720.3716 | -1.604 |
| 371.3945 | -1.626 | 372.4363 | -2.097 | 720.3730 | -1.547 |
| 371.3963 | -1.634 | 372.4384 | -2.066 | 720.3745 | -1.590 |
| 371.3981 | -1.687 | 372.4405 | -2.100 | 720.3759 | -1.567 |
| 371.3998 | -1.709 | 372.4427 | -2.149 | 720.3773 | -1.550 |
| 371.4016 | -1.730 | 372.4448 | -2.083 | 720.3788 | -1.595 |
| HJD-2452000 | |
HJD-2452000 | |
HJD-2452000 | |
||
| 371.4034 | -1.788 | 372.4469 | -2.119 | 720.3802 | -1.547 | ||
| 371.4052 | -1.798 | 372.4490 | -2.111 | 720.3817 | -1.584 | ||
| 371.4069 | -1.835 | 372.4511 | -2.087 | 720.3831 | -1.615 | ||
| 371.4087 | -1.887 | 372.4533 | -2.137 | 720.3846 | -1.702 | ||
| 371.4105 | -1.927 | 372.4554 | -2.113 | 720.3860 | -1.681 | ||
| 371.4137 | -1.952 | 372.4575 | -2.183 | 720.3875 | -1.670 | ||
| 371.4158 | -1.976 | 372.4597 | -2.125 | 720.3889 | -1.672 | ||
| 371.4179 | -1.986 | 372.4618 | -2.140 | 720.3903 | -1.841 | ||
| 371.4201 | -2.020 | 372.4639 | -2.200 | 720.3918 | -1.717 | ||
| 371.4222 | -2.005 | 372.4660 | -2.150 | 720.3932 | -1.829 | ||
| 371.4243 | -2.060 | 372.4681 | -2.199 | 720.3947 | -1.859 | ||
| 371.4264 | -2.097 | 372.4703 | -2.193 | 720.3961 | -1.849 | ||
| 371.4286 | -2.080 | 372.4724 | -2.201 | 720.3976 | -1.896 | ||
| 371.4307 | -2.078 | 372.4745 | -2.184 | 720.3990 | -1.923 | ||
| 371.4328 | -2.101 | 372.4766 | -2.165 | 720.4005 | -1.994 | ||
| 371.4349 | -2.149 | 372.4788 | -2.189 | 720.4019 | -2.010 | ||
| 371.4371 | -2.117 | 372.4809 | -2.216 | 720.4034 | -2.072 | ||
| 371.4392 | -2.110 | 372.4830 | -2.187 | 720.4048 | -2.026 | ||
| 371.4413 | -2.142 | 372.4852 | -2.218 | 720.4063 | -2.004 | ||
| 371.4434 | -2.179 | 372.4873 | -2.189 | 720.4077 | -2.041 | ||
| 371.4456 | -2.162 | 372.4894 | -2.179 | 720.4091 | -2.069 | ||
| 371.4477 | -2.167 | 372.4915 | -2.211 | 720.4106 | -2.116 | ||
| 371.4498 | -2.186 | 372.4936 | -2.212 | 720.4120 | -2.129 | ||
| 371.4519 | -2.181 | 372.4958 | -2.169 | 720.4135 | -2.124 | ||
| 371.4541 | -2.213 | 372.4979 | -2.213 | 720.4149 | -2.094 | ||
| 371.4562 | -2.161 | 372.5000 | -2.173 | 720.4164 | -2.167 | ||
| 371.4583 | -2.187 | 386.3375 | -2.272 | 720.4178 | -2.157 | ||
| 371.4604 | -2.229 | 386.3392 | -2.237 | 720.4193 | -2.184 | ||
| 371.4626 | -2.216 | 386.3409 | -2.246 | 720.4207 | -2.183 |
Footnotes
- ... package1 The Mira AP software is produced by Mirametrics Inc.