COMMISSION 27 OF THE I. A. U.
INFORMATION BULLETIN ON VARIABLE STARS
Number 3010
Konkoly Observatory
Budapest
16 April 1987
HU ISSN 0374-0676
AN IMPROVEMENT OF THE ROTATIONAL PERIOD OF CQ UMa
CQ UMa = HR 5153 = HD 119 213 is an SrCrEu Ap star which exhibits light,
spectral and magnetic variations with the period of about 2.450 days. All
the variations can be explained by the oblique rotator model with extensive
"photometric" and "spectroscopic" spots or belts (Mikulasek 1980) and nearly
dipole magnetic field (Mikulasek et al. 1984). To build a realistic model of
the distribution of these spots on the surface and their relation with magnetic
field geometry, we need to know the rotational period with sufficient
accuracy.
All the previous determinations of the period of variations of CQ UMa
were based on the analysis of photometric data. Light variations of the star
in the B and U colours were found by Burke and Howard (1972) on the basis
of their UBV observations carried out in the years 1970 and 1971. They
obtained a period of 1.706 days. Winzer (1974) derived a period of 1.6980
days from his own UBV measurements. Both periods are incorrect (s. the discussion
in Mikulasek et al. 1978). Wolff and Morrison (1975) derived the period
of 2.451 days, Mikulasek (1975) 2.45002 days, Mikulasek et al. (1978)
2.449967 days not excluding the double value: 4.899934 days. The double
period was then rejected as it is incompatible with the observed projection
of the rotational velocity (33 km.sE-1) and the expected radius of star
2.0 R )(Pavlovski 1979, Mikulasek 1980). Gathering all UBV observations Pavlovski
(1979) arrived at the period of 2.449981 days. Musielok et al. (1980) presented
the period 2.44988 days based on their 10-colour photometry and ubvy
photometry of Wolff and Morrison (1975).
A new set of 25 ubvy measurements of CQ UMa obtained by Pyper and Adelman
(1985) substantially enlarges the time interval covered by photoelectric
observations of the star to 14 years, that induced us to improve the period
of CQ UMa. In our paper we submit the period based on the whole available
photometric data which span more than 2000 revolutions of the star. There is
impossible to use all the photometric data directly, as they were obtained
in various photometric systems (see Table I ).
Table I
Type of photo- Mean
Authors metry B epoch (O-C)
Burke, Howard (1972) rel.UBV 28(2excl.) 86 0.001+/-0.036
Winzer (1974) rel.UBV 18 197 0.000+/-0.015
Wolff, Morrison (1975) rel.uvby 25 427 0.000+/-0.009
Mikulasek et al.(1978) abs.UBV 9 585 -0.012+/-0.036
Musielok et al. (1980) rel.10col.+ 29 755 -0.005+/-0.011
Pavlovski (1979) abs.UBV 19 1089 0.020+/-0.019
Pyper,Adelman (1985) abs.uvby 25 1843 -0.002+/-0.015
+ see in Schoneich, Staude (1976), N - number of nights
Nevertheless, it follows from the analysis of light curves in the blue region
where light variations are most pronounced that light curves here are similar.
Light variations may be then expressed in the from:
mi(phi) = mi - Ai f(phi) (1)
where F is the phase, mi(phi) magnitude in the particular colour, mi - the mean
value of the magnitude in i - colour, Ai - the amplitude of variations. f(phi)
is the normalized mean light curve in the blue region with an unit amplitude
and zero mean value.
For the determination of light elements and mean light curve f(phi)
measurements in B (UBV photometry), b and v (ubvy photometry), X and Y colours
(in 10-colour photometry) have been used. Using the least squares method we
have obtained the following approximation for f(phi):
f(phi) = 0.486 cos 2 pi (phi + 0.067) + 0.102 cos 4 pi(phi -0.142) ( 2 )
The mean light curve is rather asymmetric with a flat maximum occurring
at phi = 0.000 +/- 0.009 and a deeper minimum at phi = 0.416 +/- 0.004.
The zero points of the function are situated at the phases 0.207 +/- 0.003 and
0.649 +/- 0.004. fmax / (-fmin) = 0.72 +/- 0.04.
The phase will be given by the relation:
phi = FRAC (JDhel - 2 440 747.746) / 2.449909 ( 3 )
The ephemeris for the moments of maxima in the blue region has been calculated
by the least squares method, too.
JDBmax = 2442487.181 + 2.449909 (E - 710), ( 4 )
+/-7 +/-11
where 2 442 487.181 is the moment of the basic maximum, 2.449909 days is present
improved rotational period. The beginning of counting of cycles (E = 0)
has been put just before the first observation of CQ UMa.
ZDENEK MIKULASEK
N. Copernicus Observatory and Planetarium
616 00 Brno,
Czechoslovakia
References:
Burke E.W., Howard J. T.: 1972, Astrophys. J. 178, 491 [BIBCODE 1972ApJ...178..491B ]
Mikulasek Z.: 1975, IAU Inform. Bull. Var. Stars No 1003
Mikulasek Z.: 1980, unpublished Thesis, Brno
Mikulasek Z., Harmanec P., rygar J., Zdarsky F.: 1978, Bull. Astron. Inst.
Czechosl. 29, 44 [BIBCODE 1978BAICz..29...44M ]
Mikulasek Z., Glagolevskij Ju. V., Romaniuk I. I., Shtol' V. G.,
Bytchkov V. D.: 1984, Magnetic Stars 13, Riga [BIBCODE 1984mast.conf...13M ]
Musielok B., Lange D., Schoneich W., Hildebrandt G., Zelwanova E.,
Hempelmann A.: 1980, Astron. Nachr. 301, 71 [BIBCODE 1980AN....301...71M ]
Pavlovski K.: 1979, Astron. Astrophys. 76, 362 [BIBCODE 1979A&A....76..362P ]
Pyper D. M., Adelman S. J.: 1985, Astron. Astrophys. Suppl. Ser. 59, 369 [BIBCODE 1985A&AS...59..369P ]
Schoneich W., Staude J.: 1976, Physics of Ap Stars, ed.: Weiss,
Jenkner, Wood, Vienna, 387 [BIBCODE 1976paps.coll..387S ]
Winzer, J.E.: 1974, unpubl. Thesis, Univ. of Toronto [BIBCODE 1974PhDT........61W ]
Wolff S. C., Morrison N. D.: 1975, Publ. Astron Soc. Pacific 87, 231 [BIBCODE 1975PASP...87..231W ]