Short-Period Light Variation of an Eclipsing Binary System: RZ ...

THE ASTRONOMICAL JOURNAL, 122 : 418È424, 2001 July ( 2001. The American Astronomical Society. All rights reserved. Printed in U.S.A.

SHORT-PERIOD LIGHT VARIATION OF AN ECLIPSING BINARY SYSTEM : RZ CASSIOPEIAE OSAMU OHSHIMA,1 SHIN-YA NARUSAWA,2 HIDEHIKO AKAZAWA,3 KIKUICHI ARAI,4 MITSUGU FUJII,5 TETSUYA KAWABATA,6 KOICHI MORIKAWA,7 NOBUO OHKURA,8 AND MINE TAKEUTI9 Received 2000 December 26 ; accepted 2001 March 23

ABSTRACT The eclipsing binary system RZ Cas is known to exhibit variation in its light curves at the primary minimum, usually showing a partial-eclipseÈtype curve but sometimes indicating a Ñat minimum, which is evidence for a total eclipse. We observed RZ Cas not only during the primary eclipse, but also during the out-of-eclipse phase, and we have found a short-period light variation with a frequency of 62.20 cycles day~1 (period of 23.15 minutes), whose maximum amplitude is 0.02 mag. This short-period variation can modulate the shape of the light curve at the primary minimum e†ectively. The brightness-color relationship of the short-period variation suggests a d Scuti type oscillation. Key words : binaries : eclipsing È d Scuti È stars : individual (RZ Cassiopeiae)

1.

INTRODUCTION

1995). Such variability appearing at the primary minima is known for several systems. Olson (1982) has pointed out that U Cep, RW Tau, U Sge, U CrB, and RZ Cas are active Algol binaries that show transient variability in primary minima. Heintze (1990) reported that U CrB sometimes shows the same clear ““ Ñat segment ÏÏ at mid-eclipse as is observed in RZ Cas. The e†ect of a starspot has been suggested as the cause of such a Ñat bottom (HegeduŽs 1993 ; Maxted et al. 1994 ; Sarna, Muslimov, & Yerli 1997). The existence of such a starspot is suggested based on photometric observations in the J and K bands (Varricatt, Ashok, & Chandrasekhar 1998). The existence of the spot is also suggested by the activity in radio (Umana, Trigilio, & Catalano 1998 ; Umana et al. 1999) and X-ray observations (Singh, Drake, & White 1995). The circumstellar matter surrounding the primary, possibly modifying the light curve at the primary minimum, is also suggested (Olson 1982 ; Varricatt et al. 1998). The nonsymmetric distribution of the circumstellar matter is suggested based on the detection of single-peak emission of Ha (Richards & Albright 1999). The existence of a transient annulus is a possible cause of the light variations at the primary minima of the active Algol systems. NNY discussed the problems and concluded that the cause of the occurrence of the Ñat bottom is still uncertain. The short-period light variability was reported by Olson (1982). The observational results of Edwin & Gears (1992) suggest a short-period oscillation, and recently Davis & Balonek (1996) and Davis (1996) have found ““ quasiperiodic oscillations ÏÏ with a period of 25 minutes and an amplitude of ^0.04 mag. Several of the authors of the present paper discussed during a workshop10 that the d Scuti type oscillation of a component can modulate the light curve. A cooperative observation campaign in Japan was performed to elucidate the quasi-periodic oscillations. A part of our results, which shows the existence of the d Scuti type oscillation, has been published already (Ohshima et al. 1998, hereafter O98). In the present paper,

RZ Cas (BD ]69¡179 \ HD 17138 ; V \ 6.18 mag, P \ 1.195 days) is a bright, short-period, eclipsing variable star. Its spectral type is A3 V (Duerbeck & HaŽnel 1979 ; Maxted, Hill, & Hilditch 1994). The most fundamental problem with this system has been uncertainty in the type of primary minimumÈwhether it is a partial eclipse or a total one. The results of the UBV light-curve analysis, using the Yamasaki code and assuming the Roche model, show that the system is semidetached, and the primary minimum is a partial eclipse (Narusawa, Nakamura, & Yamasaki 1994, hereafter NNY). The light curves were analyzed by the LIGHT2 method (Maxted et al. 1994) and by the WD code (Riazi, Bagheri, & Faghihi 1994). Both analyses also show that the primary minimum is a partial eclipse. The light curve at the primary minimum, originating from the partial eclipse, should not be Ñat, but several observers have reported Ñat minima yielded by a total eclipse. Szafraniec (1960) reported that the minimum shows a Ñat bottom with a duration of 14 minutes. NNY have found Ñat-bottom minima four times among 12 observed primary minima and have summarized the shape of the light curve at the primary minima in published results. It should be noted that a Ñatbottom event continued for 20 minutes. Recently, a 10 minute and a 21 minute Ñat bottom were reported (Dumont ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ 1 Kamogata Senior High School, Kamogata, Okayama, 719-0243, Japan ; ohshima=bao.go.jp. 2 Nishi-Harima Astronomical Observatory, Sayo, Hyogo, 679-5313, Japan ; narusawa=nhao.go.jp. 3 Konkoh Junior High School, Konkoh, Okayama, 719-0105, Japan ; akazawa=sqr.or.jp. 4 Hanyu-Jitsugyo Senior High School, Hanyu, Saitama, 348-0055, Japan ; karai=dreams.ne.jp. 5 Fujii-Bisei Observatory, 4500 Kurashiki, Tamashima, Okayama, 7138126, Japan ; aikow=po.harenet.ne.jp. 6 Bisei Astronomical Observatory, Bisei, Okayama 714-1411, Japan ; kawabata=bao.go.jp. 7 Ibara Board of Education, Ibara, Okayama, 715-0014, Japan ; koichi=morikawa.org. 8 Postal address : 25 Senoh, Okayama, 701-0205, Japan ; HAE00500=nifty.ne.jp. 9 Astronomical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan ; takeuti=astr.tohoku.ac.jp.

ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ 10 Related reports can be found in the proceedings of the Workshop on Binary and Variable Star Study 1997 held at Akita, Japan.

418

RZ CASSIOPEIAE we report the results of our campaign and discuss the d Scuti type oscillation of the primary of RZ Cas.

ANALYSIS AND RESULTS

3.1. Short-Period L ight V ariation The data obtained at the six sites were compared with each other, and the atmospheric conditions on every night were also discussed. We have found that the B-band photometry shows a smaller scatter than other passbands. Finally, to study the light curve of the short-period variability, we chose the observations from six nights for which the atmospheric conditions were better than the other nights tabulated in Table 1. Three of the nights cover the primary minima, and the other three nights cover the out-of-eclipse phases. To study the properties of the short-period light variability, we analyze the data of the out-of-eclipse and eclipse phases separately, and then we obtain the synthesized curve including both data. We have studied the periodicity of the light variation using the folding method and have also decomposed the light variation into the sinusoidal curves. The data of the out-of-eclipse phase, the last three nights in Table 1, are analyzed by using the programming code Period98 (Sperl 1998).11 The data from two of the nights are plotted in the ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ 11 See http ://www.deltascuti.net/Dperiod98/. TABLE 1 SELECTED OBSERVATIONS TO DETERMINE FREQUENCY HJD (2,450,000])

Orbital Phase

Data Points

747.1011È747.1477 . . . . . . 753.0549È753.1157 . . . . . . 771.0018È771.0603 . . . . . . 806.0263È806.1258 . . . . . . 807.0254È807.1424 . . . . . . 829.9719È830.1009 . . . . . . Total . . . . . . . . . . . . . . . . . .

0.98È0.02 0.96È0.01 0.98È0.03 0.28È0.36 0.12È0.22 0.32È0.42 ...

55 59 115 129 164 187 709

0.30

0.32

Orbital Phase 0.34

0.36

0.38

-0.02 -0.01 0 0.01 0.02

OBSERVATIONS

The cooperative observations were performed from 1997 September to 1998 January at six sites in Japan. The observational instruments used by H. A., N. O., M. F., and T. K. were reported in O98. K. A. and K. M. used a 28 cm Schmidt Cassegrain telescope with a photoelectric photometer (Optec SSP-5) and a 25 cm Schmidt Cassegrain telescope with a CCD camera (SBIG ST-7), respectively. All the observations analyzed in the present paper are in the standard Johnson-Kron-Cousins system. Observations were carried out over 21 nights, and a total of 10,064 data points were obtained. Among them, 147 are in the U band, 2598 data in B, 2324 in V , 2872 data in R, and 2123 in I. In the observational data obtained outside the eclipse, we have found the short-period light variability with a period of approximately 20 minutes. Such variability has also been detected in the data during the primary minimum. The highest recorded amplitude is 0.02 mag (O98). 3.

0.28

806.02

806.04 0.12

delta B

2.

419

806.06 0.14

806.08 0.16

806.10

806.12

0.18

806.14

0.20

0.22

-0.02 -0.01 0 0.01 0.02 807.02

807.04

0.32

807.06 0.34

807.08 0.36

807.10

807.12

0.38

807.14

0.40

0.42

-0.02 -0.01 0 0.01 0.02 829.98

830.00

830.02 830.04 Hel.J.D. +2450000.0

830.06

830.08

830.10

FIG. 1.ÈLight variation of RZ Cas during the out-of-eclipse phase. The Ðlled circles indicate the observational data, and the curves are the synthesized light variation based on the period analysis.

middle and bottom panels of Figure 1. The number of data points is 480. Three prominent modes are shown in Table 2. The light curves are well described by the expression *B \ ; A sin [(T /f ) ] / ] . (1) i i i The values for A , f , and / are tabulated in Table 2. The i i i frequency of the dominant mode is 64.240 cycles day~1. 3.2. L ight Curves during Eclipse To study the property of the short-period light variation during the eclipse, we assume that the light curve consists of the eclipse curve, which is symmetric with its minimum, and the short-term curve. Following such an assumption, we determine the time of the minimum of the eclipse curve, t , 0 by calculating it to minimize the scattering of the data for an assumed time of the light minimum. We then use a fourth-order polynomial, in which the coefficients of the odd terms are zero, to express the eclipse curve. Least-squares Ðtting is used to obtain the time of the minimum and the coefficients of the polynomials. We obtain the eclipse curve in the form I(*t) \ a (*t)4 ] a (*t)2 ] const , (2) 4 2 where the brightness, I, is in the intensity scale and *t \ t [ t in days. The coefficients a for the Ðrst three nights of Tablei 1 are given in Table 3. iBecause the night-to-night di†erence in the coefficients is not negligible, we used the eclipse curve adopted for each night to derive the shortterm light variations. The data used here are indicated by Ðlled circles in Figure 2. We obtain the short-term curve by subtracting the calculated eclipse curve from the observed brightness expressed TABLE 2 SINUSOIDAL COMPONENT OF THE SHORT-PERIOD VARIABILITY IN THE OUT-OF-ECLIPSE PHASE

i

f i (cycles day~1)

A i (mag)

1............ 2............ 3............

64.240 8.892 25.320

0.0078 0.0026 0.0024

/

i 0.089 0.116 0.041

NOTE.ÈPhases are referred to HJD \ 2,450,000.0.

420

OHSHIMA ET AL. TABLE 3

TABLE 5

POLYNOMIAL COEFFICIENTS FOR THE ECLIPSE CURVE

SINUSOIDAL COMPONENT OF THE SHORT-PERIOD VARIABILITY

Observation HJD (2,450,000])

a

a 2 158.100 177.413 156.755

4 [24,312.311 [22,520.333 [18,975.972

747.1011È747.1477 . . . . . . 753.0549È753.1157 . . . . . . 771.0018È771.0603 . . . . . .

in the intensity scale and then converting it to the magnitude. The results are shown in Figure 2. We can see shortterm oscillations with periods of approximately 20 minutes. The amplitude seems larger than the out-of-eclipse phase. Because these data are a†ected by the procedure for deriving the eclipse curve, it is not certain that the amplitude is really large during the primary minimum. We analyze the periodicity of the short-term curve during the eclipse by using the programming code Period98 and obtain the periodic modes as indicated in Table 4. The frequency of the dominant mode is 63.027 cycles day~1, which is close to the frequency of the dominant mode out of eclipse. The amplitude and the phase are also similar to those out of eclipse. Because the second and third components are di†erent from those in Table 2, we may conclude that only the Ðrst component is real. 3.3. Composite Periodicity We study the composite data consisting of the out-ofeclipse and eclipse-phase data. The folding was performed

-0.04

Orbital Phase 0.00

-0.02

0.02

0.04

-0.02 -0.01 0 0.01 0.02 747.06

747.08 -0.04

747.10 -0.02

747.12 0.00

747.14

747.16 0.02

753.06 -0.04

753.08 -0.02

753.10 0.00

753.12 0.02

753.14

753.16 0.04

-0.02 -0.01 0 0.01 0.02 770.98

771.00

771.02 771.04 Hel.J.D. +2450000.0

771.06

771.08

FIG. 2.ÈSame as Fig. 1, but during the primary minimum

TABLE 4 SINUSOIDAL COMPONENT OF THE SHORT-PERIOD VARIABILITY OBTAINED FROM THE DATA DURING THE ECLIPSE

i

f i (cycles day~1)

A i (mag)

1...... 2...... 3......

63.027 29.290 31.218

0.0113 0.0068 0.0059

/

i 0.115 0.372 0.026

NOTE.ÈPhases are referred to HJD \ 2,450, 000.0.

i

f i (cycles day~1)

A i (mag)

1............ 2............ 3............ 4............ 5............

64.199 62.076 26.274 59.084 32.113

0.0108 0.0037 0.0037 0.0034 0.0028

/

i 0.110 0.654 0.395 0.652 0.817

NOTE.ÈPhases are referred to HJD \ 2,450,000.0.

by using the phase dispersion minimization method (Stellingwerf 1978) and the programming code of A. Wijaya.12 We applied a running mean over Ðve successive observed points and analyzed them. The periodicity is found at D63, D32, and D22 cycles day~1 in the range between 80 and 10 cycles day~1. The Ðrst mode is dominant, and the others look like its subharmonic modes. The detailed study around 63 cycles day~1 yields the clearest periodicity at 64.198 cycles day~1 (period of 0.015577 days). This is the same as the period reported previously (O98). The decomposition into the sinusoidal curves was carried out by using the programming code Period98. The results are tabulated in Table 5, and a frequency of 64.20 cycles day~1 is conÐrmed. The synthesized light curve based on the sinusoidal components is drawn in Figures 1 and 2. Observations from three of the nights not used to calculate the short-term curve are also compared with the synthesized curves in Figures 3 and 4. The Ðgures clearly show the coincidence between the observations and the synthesized curves. In Figure 5, we demonstrate the continuous observations, covering a start of the primary eclipse to a postminimum instant. The synthesized light curve coincides well with the observational data.

747.18 0.04

-0.02 -0.01 0 0.01 0.02 753.04

Vol. 122

3.4. Appearance of the Flat-Bottom Minima In our campaign, we observed the primary minima indicated in Table 6 on 10 nights. We classiÐed the light curves at the primary minimum into three types : the F type, the Ñat bottom ; the V type, the V-shaped curve ; and the S type, the slant, increasing or decreasing smoothly. The subtype Sa indicates the ascending slant and Sb the descending one. The light curves for cycle numbers, E, of 1495, 1501, 1505, 1515, and 1561 are demonstrated in Figures 2, 3, and 5. These types are easily understood by assuming that the observed light curve is synthesized by the light variation of the partial eclipse and that of the short-period quasi-regular variation. We mimic the observed light curves by adding the observed short-period light curve to the light curve of the eclipse derived from the theoretical model. The timescale of the eclipse and the pulsation Ðt to each other, so that the light curve becomes Ñat when the light maximum of pulsation comes to the center of the eclipse. Then we can see the F-type one. When the light minimum of pulsation coincides with the light minimum of eclipse, the V-type light curve is seen. The intermediate case yields the S type. ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ 12 Obtained from http ://www.kusastro.kyoto-u.ac.jp/vsnet/etc/ prog.html.

No. 1, 2001

RZ CASSIOPEIAE Orbital Phase -0.04 -0.02 0.00 0.02 0.04 0.8

Orbital Phase -0.04 -0.02 0.00 0.02 0.04 0.8

421 Orbital Phase -0.04 -0.02 0.00 0.02 0.04 0.8

1

1

1

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2

2

2

2.2

2.2 747.10 747.13 747.16 Hel.J.D. +2450000.0

2.2 753.07 753.10 753.13 Hel.J.D. +2450000.0

771.00 771.03 771.06 Hel.J.D. +2450000.0

FIG. 3.ÈComparison of the observations and the synthesized short-term light variations for RZ Cas. The Ðlled circles and the curves are the same as Fig. 1.

NNY derived the ephemeris for the primary minima as Min. I \ HJD 2,448,960.2122 ] 1.1952572E .

(3)

1.2

0.2

1.4

0.4

1.6

0.6

delta B

delta B

We may then predict the occurrence of the Ñat bottom based on the frequency for the orbital motion, 0.8366400 cycles day~1, and for the pulsation. When we adopt 64.199 ^ 0.0005 cycles day~1 for the pulsation, one cycle of the eclipse corresponds to 76.7343 ^ 0.0006 pulsation cycles. The di†erence of six cycles of the orbital motion, 7.172 days, and 460 cycles of the pulsation yields the di†erence of [0.05 in the phase of pulsation. This seems adequate to explain the occurrence of the F and/or Sa light minima at E \ 1495 and 1501. In addition, the di†erence of 15 cycles of the orbital motion 17.929 days and 1151 cycles of the pulsation yields the di†erence of [0.0003 ^ 0.0001 in the phase of pulsation. This is adequate for the V light minima at E \ 1505 and 1520. Lastly, for the Sb light minima at E \ 1515 and 1546, the time interval of 31 cycles of the orbital motion 37.053 days and that of 2379 cycles of the pulsation di†ers by 0.003 ^ 0.0003 in the phase of pulsation. The occurrence of similar light curves at the primary

minimum does not contradict the short-period light variability derived from our observations. The bump of the light curve in the descending and ascending branches is also useful for studying the shortperiod light variation. The examples are shown in Figure 3 (obtained by H. A. and N. O. at the light minima, E \ 1515). Such a bump was reported by Archer (1958). In his observations, in which the e†ective wavelength is 0.400 km, a ““ temporary halt ÏÏ of dimming for 42 minutes, from the phase 0.938 to 0.973, was observed on 1958 January 24. The star halted at a magnitude 0.30 brighter than the usual light minimum. On 1958 February 12, the halt of the dimming was again observed at the phase 0.958È0.988. The halt continued for 36 minutes at a magnitude 0.25 brighter than the minimum. It is interesting to point out that the interval of the two occasions is 19 days, which corresponds to 16 cycles for the period 1.1952341 days, adopted for the years 1958.0È1960.9 by Herczeg & Frieboes-Conde (1974). The time interval for two events is 19.14 days, which corresponds to 1229 cycles of the short-period light variation for a frequency of 64.210 cycles day~1. When we use 64.16 or

1.8

0.8

2

1

754.26

754.28 754.30 754.32 Hel.J.D. +2450000.0

825.98

FIG. 4.ÈSame as Fig. 3

826.00 826.02 Hel.J.D. +2450000.0

826.04

422

OHSHIMA ET AL.

Vol. 122

64.26 cycles day~1, 1228 or 1230 cycles also covers the same time interval. We have no decisive reason for conÐrming which frequency is adequate, but 64.210 cycles day~1 is very close to ours, 64.199 cycles day~1.

0.20 0.40 0.60 0.80

delta B

1.00 1.20 1.40 1.60 1.80 2.00 2.20 758.98

759.00

759.02

759.04

759.06

759.08

759.10

Hel.J.D. +2450000.0

FIG. 5.ÈLight variation of RZ Cas. The Ðlled circles and the curve are the same as Fig. 1.

3.5. T iming of the Primary Minimum and the Orbital Period The times of the whole primary minima found in our observations are tabulated in Table 6. The time indicates the center of the minimum and is determined by using the bisection method. In the table, E and O[C are derived from equation (3). This relation is calculated from the data after HJD 2,448,581. The change in the interval of the successive primary minima occurs at a time between HJD 2,448,220 and 2,448,581 (NNY). Narusawa et al. (1997) reported no such change in the period for 5 yr after HJD 2,448,581. The primary minima indicated in Table 6 show no change in period because there is no systematic changes of O[C. We have found that

TABLE 6 TIMING AND SHAPE OF THE PRIMARY MINIMA HJD (2,450,000]) E \ 1474 :a 722.0242 . . . . . . E \ 1479 : 728.001 . . . . . . . E \ 1495 : 747.1252 . . . . . . 747.1247 . . . . . . 747.1258 . . . . . . E \ 1501 : 754.2947 . . . . . . 754.2957 . . . . . . E \ 1505 : 759.0770 . . . . . . 759.0765 . . . . . . 759.0764 . . . . . . 759.0761 . . . . . . E \ 1515 : 771.0289 . . . . . . 771.0300 . . . . . . 771.0284 . . . . . . E \ 1520 : 777.0077 . . . . . . 777.0065 . . . . . . 777.0070 . . . . . . 777.0071 . . . . . . E \ 1546 : 808.0829 . . . . . . 808.0828 . . . . . . 808.0831 . . . . . . 808.0832 . . . . . . 808.0825 . . . . . . 808.0833 . . . . . . E \ 1551 : 814.0593 . . . . . . E \ 1561 : 826.0125 . . . . . . 826.0123 . . . . . .

O[Ca

Filter

Shapeb

Observer

]0.0029

R

...

M. F.

HD 12413

]0.003

R

...

M. F.

HD 12413

]0.0035 ]0.0030 ]0.0041

V B R

Fd Sa ...

H. A. H. A. M. F.

HR 791 HR 791 HD 12413

]0.0014 ]0.0024

V B

FÈSa ? FÈSa ?

H. A. H. A.

HR 791 HR 791

]0.0027 ]0.0022 ]0.0021 ]0.0018

B R V B

V V ... ...

K. A. M. F. N. O. N. O.

HR 791 HD 12413 HR 791 HR 791

]0.0020 ]0.0031 ]0.0015

R V B

Sb Sb Sb

M. F. N. O. N. O.

HD 12413 HR 791 HR 791

]0.0046 ]0.0034 ]0.0039 ]0.0040

V B V B

V V ... ...

H. A. H. A. N. O. N. O.

HR HR HR HR

791 791 791 791

]0.0031 ]0.0030 ]0.0033 ]0.0030 ]0.0027 ]0.0035

V B V B U I

Sb Sb Sb Sb P P

H. A. H. A. N. O. N. O. N. O. M. F.

HD HD HD HD HD HD

15784 15784 15784 15784 15784 12413

]0.0032

I

...

K. M.

GSC 4317-1437

]0.0038 ]0.0036

V B

P SaÈP

N. O. N. O.

HD 15784 HD 15784

Comparison Starc

a The E and O[C values are calculated from ephemeris 1. b (V) V-shape ; (P) partial eclipse ; (F) Ñat bottom ; (Sa) smoothly dimming ; (Sb) smoothly brightening. Null entries were not resolved. c See Ohshima et al. (O98). d Duration 20 minutes.

No. 1, 2001

RZ CASSIOPEIAE

there is no evidence for the period changes between HJD 2,448,581 and 2,450,826.

-0.06

DISCUSSION

4.1. Origin of the Short-Period V ariability The quasi-periodic light variations of RZ Cas were reported several years ago (Davis & Balonek 1996 ; Davis 1996). Such variability can be caused by the hot spot on the primary produced by the direct impact of the accreting matter. Because the falling matter makes a spot at the same position on the primary, the light from such a hot spot will be Ðxed in orbital phase. If the variability is caused by the nonstationary property of the accreting Ñow, a periodic variation should not be expected. Taking the fact that the time span of 83 days of our observations covers approximately 70 orbital rotations of the system and 5 ] 103 cycles of the short-period oscillation, we prefer the stellar pulsation to the origin of the variability. The most plausible stellar pulsation of an A3 V star is a d Scuti type one. The d Scuti stars are found in the lower end of the Cepheid instability strip and are characterized by the relatively small amplitude and multiple periodicity, indicating quasi-periodicity. Compared with the distribution of the d Scuti stars, RZ Cas, an A3 V star, will be at the blue edge (see, e.g., Moskalik 1995). Because the bluer variables have the shorter period, it is reasonable that RZ Cas pulsates with a very short period. A period of 0.016 days will be acceptable for the d Scuti stars. Examples of the short period of this type are 0.0205 days for V624 Tau and 0.03 days for V377 Cas. V816 Cen (\HD 101065), whose period is 0.0084 days, is listed in the General Catalogue of Variable Stars (Kholopov 1985) as a suspected d Scuti star. This star has a shorter period than RZ Cas but is PrzybylskiÏs star, which is well known by its chemically peculiar feature. It seems difficult to compare it with RZ Cas. The d Scuti type pulsation has been found in many binary systems (Lampens & Boffin 2000). The rapidly oscillating Ap stars also have short periods and small amplitudes, but no Ap feature has been reported in spectroscopic observations for RZ Cas. Further spectroscopic observations will be required to check the Ap feature of RZ Cas. 4.2. Brightness-Color Relation The relationship between brightness and color is used for judging the stellar pulsation because the brightening of the pulsating star is usually produced by the increase of the e†ective temperature of the stellar atmosphere. We used the data of Ðve of the out-of-eclipse nights tabulated in Table 7. To study the correlation between brightness and color, we use the di†erence from the mean B magnitude of each night, *B, and the di†erence from the TABLE 7 DATA USED IN THE BRIGHTNESS-COLOR DIAGRAM Observation HJD (2,450,000])

Data Points

Observer

788.0418È788.1246 . . . . . . 788.0775È788.1437 . . . . . . 801.0482È801.1828 . . . . . . 806.0008È806.0711 . . . . . . 829.9707È830.1021 . . . . . .

72 89 146 85 193

H. A. N. O. H. A. H. A. N. O.

-0.04

-0.02 delta B-V

4.

423

0.00

0.02

0.04

0.06 -0.06

-0.04

-0.02

0.00 delta B

0.02

0.04

0.06

FIG. 6.ÈColor-magnitude diagram of the short-period variability. The horizontal axis indicates *B, and the vertical axis indicates *(B[V ).

mean color of each night, *(B[V ). We plot *(B[V ) versus *B in Figure 6. The data are expressed by the relation *(B[V ) \ 0.414 *B ,

(4)

with a correlation factor of 0.702. The star is bluer in brighter phase. This coincides with the property of the stellar pulsation. We can see a similar feature in Figure 11 of Olson (1982). Based on such a feature, we may assume that RZ Cas is the d Scuti star with the shortest period. 4.3. Physical Properties of the Primary Once we adopt the short-period variability of the primary component as being the result of stellar pulsation, we can estimate the physical parameters by using the period of the stellar pulsation. The parameters of the RZ Cas system were given by Maxted et al. (1994). For the primary component, they have found a mass of 2.205 ^ 0.075 M and a radius of 1.67 ^ 0.03 R with an e†ective _temperature of _ on the spectroscopic study in which 8600 ^ 100 K, based they detected the lines of the secondary component. In the Hipparcos database, we have found an annual parallax of 15.99 ^ 0.62 mas, corresponding to a distance of 62.5 ^ 2.5 pc for RZ Cas. The value derived from radial velocity data and UBV light curves is 73 ^ 2 pc on the assumption of zero interstellar extinction (Maxted et al. 1994). It is not clear how this discrepancy may be resolved. The pulsation parameter Q is deÐned as Q \ PJM/R3 ,

(5)

where M, the mass, and R, the radius, are in solar units, and P, the period, is in days. The radius derived from preHipparcos studies is approximately 1.67 R and gives _ Q B 0.011. This value suggests nonradial oscillations with a higher order mode. The pulsation properties do not conÑict with d Scuti type pulsation. We are indebted to M. Morimoto and A. Yamasaki for useful comments, and to Tomoko Ono and Noritaka Tokimasa for their kind help. We wish to thank K. Szatmary for sending a useful catalog to S. N.

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