A Photometric Study of ZZ Microscopium

PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE PACIFIC, 121:478 484, 2009 May 2009. The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A. A Photometric Study of ZZ Microscopium CHULHEE KIM AND B.-K. MOON 1 Division of Science Education and Institute of Fusion Science, Chonbuk National University, Jeonju, 561-756, South Korea; ckim@chonbuk.ac.kr Received 2008 November 28; accepted 2009 April 15; published 2009 May 8 ABSTRACT. New photometric (uvbyβ) observations of ZZ Mic are described. Reddening values Eðb yþ ¼ 0:00 mag and ½Fe=HŠ ¼ 0:078 were derived from the photometry. Intrinsic ðb yþ and c 1 values indicate a mean effective temperature of T eff ¼ 7780 K and a mean surface gravity of log g ¼ 3:84. Theoretical evolutionary tracks yielded a mass of 1:75 M and an age of 0.56 Gyr. However, the pulsation mass was determined as 1:0 M. ZZ Mic in most respects resembles a typical Population I dwarf Cepheid. We collected 34 times of maximum light from the literature and our observation in order to investigate the variations of the O C values, and we confirmed a sign that the period is increasing. 1. INTRODUCTION ZZ Mic (HD 199757, α ¼ 21 h 00 m 35 s, δ ¼ 42 39:3 0 [2000], 9.27 9.69 V) is classified in the General Catalogue of Variable Stars (GCVS) as a δ Scuti type variable star. We prefer the older designation of the dwarf Cepheid to the large-amplitude δ Scuti variable. McNamara (1985) has presented evidence indicating that the so-called large-amplitude δ Scuti variables, ΔV >0:3 mag (here designated as dwarf Cepheids), differ from the small amplitude δ Scuti variables in a number of fundamental physical parameters other than light amplitude. Thus, when properties such as rotational velocity are considered, the term dwarf Cepheid seems much less arbitrary. ZZ Mic was first discovered photometrically to be a variable star by Churms & Evans (1961). They found that the period was 0.0671 days, and the amplitude of the light variation was appreciable, on the order of 0.37 mag in blue light. The same period was also applied to the radial velocity variation on the order of 30 km s 1 (Churms & Evans 1962). Leung (1968) refined the period to 0.0671575 days and discovered that the light amplitude was slightly variable. Percy (1976) analyzed Leung s data and deduced the presence of two periods: 0.0513 and 0.0654 days. Balona & Martin (1978) presented BV photometry and estimated its radius at 1.7 solar radii using the velocity amplitude determined by Churms & Evans (1962). Recently, Derekas et al. (2006) confirmed the double-mode nature of ZZ Mic. A period of 0.067 days and an amplitude of about 0.42 mag of ZZ Mic are in the range of SX Phe type variables. The characteristics of SX Phe variables are short periods (0.03 0.08 days) and metal poor with typical amplitudes of 0.3 0.7 mag. They are found in the general field as well as in globular clusters and nearby dwarf galaxies (Rodríguez & 1 Corresponding author; moonbk@chonbuk.ac.kr López-González 2000). In addition, the double periodicity found in ZZ Mic has also been discovered in a few SX Phe type variables such as SX Phe (Kim et al. 1993), BL Cam (Kim et al. 2003), V2314 Oph (Martin & Rodríguez 1995), and BQ Psc (Kim et al. 2002). The period ratio of 0.763 or 0.777 for ZZ Mic from Percy (1976) and Derekas et al. (2006) can be compared with 0.777 for SX Phe. ZZ Mic is similar to the SX Phe type variables in many respects. Actually, Churms & Evans (1961, 1962) suggested that ZZ Mic was related to ultrashort-period variables such as SX Phe and AI Vel. On the other hand, the atmospheric parameters of ZZ Mic have not been investigated. Thus, we have undertaken this photometric study to investigate the temperature and surface-gravity variations as well as the metal abundance of ZZ Mic with evolutionary status and to compare these with those of other SX Phe variables. Furthermore, we have undertaken differential CCD photometric observations of ZZ Mic to investigate its multiperiodicity, binarity, and pulsational characteristics. 2. OBSERVATIONS Photometric observations of ZZ Mic in the uvbyβ system were secured on three nights during the summer of 1995. The data were obtained using a single-channel photometer employing an EMI 978Ia photomultiplier attached to the 1 m telescope at the Cerro Tololo Inter-American Observatory (CTIO). Observations were made through the BYU uvbyβ filters detailed in Joner & Taylor (1995). The data were transformed to the Hyades Coma system using methods detailed in Joner et al. (1995). A comparison star (COMP in Table 1), HD 199709, was used to obtain differential y magnitudes of ZZ Mic. By adding the mean magnitude of the comparison star back into the differential magnitudes for ZZ Mic, standard magnitudes for the variables were formed. The following magnitude, color indices, and 478

A PHOTOMETRIC STUDY OF ZZ MICROSCOPIUM 479 TABLE 1 UVBYΒ PHOTOMETRY OF ZZ MIC Star HJD y b y m 1 c 1 β COMP.... 6.6070 10.154 0.315 0.493 0.382 2.654 ZZ Mic.... 6.6160 9.504 0.124 0.180 0.914 2.813 ZZ Mic.... 6.6178 9.524 0.128 0.171 0.910 2.799 ZZ Mic.... 6.6196 9.544 0.125 0.184 0.890 2.821 ZZ Mic.... 6.6217 9.556 0.129 0.185 0.875 2.789 ZZ Mic.... 6.6235 9.572 0.125 0.196 0.862 2.796 ZZ Mic.... 6.6252 9.580 0.136 0.184 0.864 2.773 COMP.... 6.6290 10.114 0.326 0.490 0.345 2.652 ZZ Mic.... 6.6335 9.604 0.152 0.184 0.819 2.764 ZZ Mic.... 6.6351 9.609 0.157 0.178 0.804 2.770 ZZ Mic.... 6.6368 9.617 0.164 0.155 0.817 2.758 ZZ Mic.... 6.6389 9.589 0.155 0.172 0.820 2.797 ZZ Mic.... 6.6407 9.590 0.150 0.173 0.820 2.778 ZZ Mic.... 6.6425 9.581 0.152 0.174 0.806 2.786 COMP.... 6.6453 10.088 0.328 0.497 0.346 2.680 ZZ Mic.... 6.6489 9.501 0.129 0.181 0.854 2.802 ZZ Mic.... 6.6509 9.484 0.130 0.173 0.846 2.784 ZZ Mic.... 6.6524 9.439 0.126 0.189 0.847 2.816 ZZ Mic.... 6.6546 9.394 0.113 0.181 0.904 2.830 ZZ Mic.... 6.6564 9.350 0.110 0.201 0.880 2.837 ZZ Mic.... 6.6581 9.314 0.100 0.194 0.915 2.843 COMP.... 6.6629 10.081 0.314 0.519 0.316 2.665 ZZ Mic.... 6.6690 9.244 0.089 0.200 0.971 2.875 ZZ Mic.... 6.6710 9.279 0.081 0.194 0.991 2.857 ZZ Mic.... 6.6726 9.308 0.107 0.191 0.938 2.835 ZZ Mic.... 6.6747 9.293 0.105 0.197 0.933 2.844 ZZ Mic.... 6.6764 9.323 0.101 0.197 0.945 2.835 ZZ Mic.... 6.6782 9.352 0.118 0.221 0.918 2.845 COMP.... 6.6812 10.169 0.318 0.512 0.338 2.650 COMP.... 7.5930 10.097 0.328 0.478 0.364 2.668 ZZ Mic.... 7.6008 9.298 0.084 0.210 0.930 2.849 ZZ Mic.... 7.6029 9.265 0.088 0.181 0.972 2.847 ZZ Mic.... 7.6053 9.247 0.074 0.194 0.990 2.870 ZZ Mic.... 7.6073 9.250 0.082 0.191 0.987 2.867 COMP.... 7.6100 10.113 0.310 0.504 0.359 2.676 ZZ Mic.... 7.6140 9.312 0.089 0.202 0.959 2.843 ZZ Mic.... 7.6160 9.337 0.111 0.172 0.957 2.842 ZZ Mic.... 7.6181 9.377 0.116 0.162 0.948 2.827 ZZ Mic.... 7.6291 9.499 0.143 0.148 0.918 2.796 COMP.... 7.6320 10.122 0.314 0.486 0.389 2.629 ZZ Mic.... 7.6372 9.562 0.141 0.169 0.885 2.785 ZZ Mic.... 7.6393 9.562 0.155 0.166 0.850 2.767 ZZ Mic.... 7.6413 9.579 0.157 0.159 0.855 2.788 ZZ Mic.... 7.6434 9.589 0.165 0.155 0.830 2.768 COMP.... 7.6572 10.134 0.315 0.484 0.361 2.630 ZZ Mic.... 7.6615 9.456 0.127 0.179 0.870 2.816 ZZ Mic.... 7.6636 9.410 0.120 0.179 0.886 2.810 ZZ Mic.... 7.6660 9.364 0.105 0.188 0.906 2.836 ZZ Mic.... 7.6680 9.328 0.085 0.204 0.928 2.867 COMP.... 7.6708 10.131 0.313 0.506 0.342 2.633 ZZ Mic.... 7.6753 9.264 0.084 0.184 0.998 2.848 ZZ Mic.... 7.6773 9.276 0.088 0.196 0.977 2.833 ZZ Mic.... 7.6794 9.301 0.092 0.181 0.986 2.856 ZZ Mic.... 7.6815 9.355 0.084 0.199 0.964 2.844 COMP.... 7.6844 10.117 0.322 0.513 0.326 2.667 ZZ Mic.... 7.6884 9.421 0.119 0.187 0.916 2.814 ZZ Mic.... 7.6904 9.454 0.127 0.174 0.916 2.793 ZZ Mic.... 7.6925 9.489 0.133 0.163 0.905 2.805 ZZ Mic.... 7.6945 9.513 0.132 0.175 0.887 2.795 COMP.... 7.7006 10.126 0.335 0.484 0.381 2.664 TABLE 1 (Continued) COMP..... 8.5899 10.152 0.323 ZZ Mic..... 8.5964 9.545 0.150 ZZ Mic..... 8.5980 9.522 0.147 ZZ Mic..... 8.5993 9.505 0.144 COMP..... 8.6010 10.155 0.327 ZZ Mic..... 8.6038 9.414 0.124 ZZ Mic..... 8.6052 9.387 0.110 ZZ Mic..... 8.6065 9.362 0.102 COMP..... 8.6398 10.161 0.329 ZZ Mic..... 8.6438 9.576 0.168 ZZ Mic..... 8.6451 9.585 0.163 ZZ Mic..... 8.6465 9.603 0.157 COMP..... 8.6487 10.158 0.321 standard deviation of the mean values were found for HD 199709: y ¼ 10:129 0:028 mag; n ¼ 16; b y ¼ 0:321 0:007 mag; n ¼ 16; m 1 ¼ 0:497 0:013 mag; n ¼ 12; c 1 ¼ 0:354 0:023 mag; n ¼ 12; β ¼ 2:655 0:017 mag; n ¼ 12: 3. ANALYSIS AND DISCUSSION The individual photometric observations of ZZ Mic and the comparison star are listed in Table 1 by Heliocentric Julian Date (HJD) and phase (variable) calculated from the revised light elements of HJD max ¼ HJD 2; 449; 996:6160 þ 0:067295E days: (1) We determined the period by applying the generalized leastsquares method developed by Vanicek (1971). All of the individual observations are displayed in Figure 1 according to the phase calculated from equation (1). In this figure we can see a larger dispersion in the upper panel, especially in the range between approximately 0.2 and 0.5 0.9 in phase. This is a sign of the existence of a second period. In order to discuss the variation in the physical parameters of ZZ Mic, a smooth freehand curve drawn through the data points has been used to yield the normal points tabulated in Table 2. It is on these normal points that our analysis is based. Intrinsic ðb yþ values have been calculated with the aid of the Crawford (1975, 1979) calibration of the A- and F-type stars at normal points. By comparing the intrinsic ðb yþ values with the observed ðb yþ values, we find an average color excess of

480 KIM & MOON FIG. 1. Observed light variations of ZZ Mic in the uvbyβ photometric system. Eðb yþ ¼ 0:012 mag. Normals for a restricted phase interval (ϕ ¼ 0:15 0:35) were used in order to eliminate any problems from averaging that might arise in portions of the more rapidly rising and descending branches of the pulsation curve. The negative color excesses are disconcerting. Either small errors were introduced by the application of the Crawfored calibrations to the pulsating variables, or the calibrations predicted ðb yþ 0 values that were too small for metal poor stars. Therefore, we have adopted the value of Eðb yþ ¼0:000 mag, derived from the photometry. Actually Eðb yþ values are positive for the range of light maximum (ϕ ¼ 0:5 0:95), and the mean value is þ0:005. The calibration of Crawford & Perry (1976) relating ½Fe=HŠ to δm 1 ðβþ is given by the formula ½Fe=HŠ ¼0:15 11δm 1 ðβþ: (2) Reddening-free color indices were used to calculate the δm 1 from the F-type star calibration of Crawford (1975) and were determined with respect to both ðb yþ and β. The values

A PHOTOMETRIC STUDY OF ZZ MICROSCOPIUM 481 for δm 1 near minimum light (ϕ ¼ 0:15 0:35) yield a range of values for ½Fe=HŠ of 0:078. Unlike SX Phe (½Fe=HŠ ¼ 1:0), ZZ Mic has almost the same metallicity as the Sun. However, the aforementioned estimation of ½Fe=HŠ ¼ 0:078 is different from 0.82 from Hintz et al. (1997). They derived the empirical relation between ½Fe=HŠ and the hk index. Although the fact that a different color system was adopted can be taken into account, the difference of ½Fe=HŠ for two cases is too big. Interestingly, if we use the relation between the period ratio and ½Fe=HŠ derived by Hintz et al. (1997), P 1 =P 0 ¼ 0:0044½Fe=HŠþ0:7726; (3) P 1 =P 0 ¼ 0:773 and 0.776 for ½Fe=HŠ ¼ 0:078 and 0:82, respectively. So ½Fe=HŠ ¼ 0:82 by Hintz et al. (1997) leads to good agreement with the observed period ratio of 0.777. It seems that the Crawford calibration is not appropriate for ZZ Mic. Spectropscpic estimation of ½Fe=HŠ will solve the problem. We have adopted Eðb yþ ¼0:000 mag for the color excess and ½Fe=HŠ ¼ 0:078. By utilizing Eðc 1 Þ¼0:2Eðb yþ and Eðm 1 Þ¼ 0:32Eðb yþ, we have calculated the intrinsic ðb yþ 0, ðc 1 Þ 0, and ðm 1 Þ 0 values calculated in Table 2. By plotting the ðb yþ 0 and ðc 1 Þ 0 values in a grid of unpublished model atmospheres computed by Kurucz, the effective temperatures, T eff, and surface gravity, log g, can be inferred. These values are given in Table 2 as a function of phase in the seventh and eighth columns. Recently Lorenz et al. (2006) published a new grid of uvby photometry for A-type stars. It is true that new model grids can give better results, but there is one problem. Because Kurucz TABLE 2 NORMALS, TEMPERATURES, AND SURFACE GRAVITIES OF ZZ MIC Phase y b y m 1 c 1 β T eff log g 0.00..... 9.499 0.129 0.178 0.902 2.802 7720 3.87 0.05..... 9.537 0.136 0.177 0.885 2.792 7670 3.87 0.10..... 9.564 0.144 0.175 0.867 2.782 7600 3.86 0.15..... 9.583 0.147 0.173 0.853 2.774 7590 3.89 0.20..... 9.594 0.153 0.172 0.840 2.768 7540 3.88 0.25..... 9.598 0.155 0.171 0.831 2.766 7530 3.90 0.30..... 9.598 0.156 0.170 0.823 2.767 7530 3.92 0.35..... 9.588 0.154 0.170 0.818 2.774 7560 3.96 0.40..... 9.565 0.151 0.172 0.820 2.782 7590 3.98 0.45..... 9.533 0.145 0.175 0.829 2.793 7650 4.00 0.50..... 9.489 0.135 0.178 0.847 2.805 7750 4.02 0.55..... 9.425 0.122 0.184 0.872 2.820 7860 4.03 0.60..... 9.354 0.104 0.188 0.913 2.837 8010 4.04 0.65..... 9.297 0.086 0.194 0.954 2.855 8150 4.03 0.70..... 9.247 0.077 0.196 0.989 2.869 8200 3.97 0.75..... 9.243 0.083 0.196 0.991 2.864 8130 3.92 0.80..... 9.278 0.093 0.193 0.976 2.852 8040 3.90 0.85..... 9.329 0.104 0.191 0.956 2.838 7940 3.88 0.90..... 9.384 0.115 0.187 0.937 2.825 7840 3.86 0.95..... 9.439 0.123 0.183 0.919 2.814 7760 3.86 grids have been widely adopted for many years, it would be difficult to compare the results with those from other grids. This is the reason why we did not use the new grids to estimate the effective temperature and surface gravity. It is necessary to determine the atmospheric parameters for all dwarf Cepheids using the new grids and same procedure for the comparison. The effective temperature of ZZ Mic varies from T eff ¼ 8200 K at light maximum to T eff ¼ 7530 K at light minimum. The effective surface gravity varies from log g ¼ 4:04 to log g ¼ 3:86. The mean values of the temperature and the surface gravity are T eff ¼ 7780 K and log g ¼ 3:94. The surface-gravity value of 3.94 is almost identical with the value one can estimate from the (log g, log P 0 ) diagram for dwarf Cepheids by Andreasen (1983, hereafter A83). The surface gravities for dwarf Cepheids are expected to be overestimated by about 0.1 in log g. The calibration of log g from uvbyβ photometry was based upon standard stars (ordinary rotational velocity), while the dwarf Cepheids are slow rotators (McNamara & Feltz 1978, hereafter MF; Breger 1980; A83), and therefore the log g value needs to be corrected. The corrected value of 3.84 is not in agreement with either 4.1 or 4.0 for Population I and extreme Population II stars from the theoretical period-gravity relation for dwarf Cepheids by A83. Hence, ZZ Mic is a very exceptional case that does not follow the period-gravity relation. The observed log g value for other dwarf Cepheids is also about 0.2 larger than that for ZZ Mic with respect to the period. However, the temperature of ZZ Mic is not so different from that of other SX Phe stars, such as SX Phe, CY Aqr, and Dy Peg. It is possible to gain some insight into the masses, luminosites, and ages of the dwarf Cepheids by comparing the log T eff and log P 0 values of the variables with standard evolutionary tracks. We utilized the evolutionary tracks of Schaller et al. 2.0 M Z=0.02 1.7 M 1.5 M FIG.2. Evolutionary sequences in the (log T eff, log L) plane. The plus marks the position of ZZ Mic. The three solid lines are models from Schaller et al. (1992). The dashed lines are the blue and red edges of the instability strip as defined by Breger (1995).

482 KIM & MOON (1992) for Z ¼ 0:02. Tracks for models of mass M ¼ 2:0, 1.7, and 1:5 M are shown in Figure 2 along with the position of ZZ Mic. From the evolutionary tracks, we estimate that M ¼ 1:75 M and that the age is 0.56 Gyr. These values of mass and age for ZZ Mic can be compared with 1:13 M for mass and 0.40 Gyr of age estimated for SX Phe (Kim et al. 1993). The Crawford calibration relating δc 1 to M V yields M V ¼ 2:0 mag, but as MF pointed out, this absolute magnitude requires a correction of 0:3 mag due to the effect of rotation on the c 1 index, which, if applied, yields M V ¼ 1:7 mag. This can be compared with 2:3 mag from the period luminosity relation of M V ¼ 3:25P 0 1:45 for dwarf Cepheids by MF. Again, a correction gives rather different results, as in the case of the surface-gravity correction. Using the Breger & Bregman (1975) equation for the Q- value, we tried to investigate the oscillation mode of ZZ Mic. For T eff ¼ 7780 K, log g ¼ 3:84, and M bol ¼ 2:3 mag, Q 1 ¼ 0:0259 and Q 2 ¼ 0:0202. So, if we assume radial oscillation, Q 1 and Q 2 are corresponding to the first and second overtone modes, respectively. And, the theoretical period ratio corresponding to this case is 0.82, which is much different from 0.777 by Derekas et al. (2006). But, the theoretical period ratio for the fundamental and first overtone modes is 0.766, which is close to 0.777. Pulsation modes determined using the Q-equation may be not so reliable because the same T eff, log g, and M bol were used for different oscillations. We found a radius of 1:7 R from the period-radius relation, log R ¼ 0:80 log P 0 þ 1:17, for dwarf Cepheids by MF. Using the Stefan Boltzmann law, a bolometric magnitude of M bol ¼ 2:25 mag was calculated. With this fact, a value of M V ¼ 2:25 mag from the P-L relation looks like a very reasonable estimate of absolute magnitude for ZZ Mic. However, the values of M V ¼ 2:0 and 0.7 mag from the Crawford calibration are even smaller than the bolometric magnitude, so the Crawford calibration looks inappropriate for the estimation of M V for ZZ Mic. Finally, we compared masses determined through different methods. The gravity mass of 1:2 M determined by adopting log g ¼ 4:0 and R ¼ 1:7 R can be compared with an evolutionary mass of 1:75 M and a pulsation mass of 1:0 M (taking a pulsation constant of Q 0 ¼ 0:033). Because the gravity masses are subject to uncertainty in calibration due to the rotational effect, we consider that the pulsation masses are more reliable than the gravity masses. Furthermore, M puls = M evol ¼ 0:59 for ZZ Mic. This is a typical value for dwarf Cepheids and is significantly different from that of RR Lyrae or classical Cepheids (see Fernley et al. 1987). This problem between observational and theoretical results makes it worthwhile to consider other explanations for the evolutionary stage of ZZ Mic. It is well known that the evolutionary mass and pulsation mass are not consistent. We think this is a matter for the theoreticians. However, we like to point out that the mass problem in SX Phe type stars is related to the existence of pulsating blue stragglers (PBS). PBS and SX Phe type stars are similar, and observational evidence of their binarity has increased. Hence, there is a strong possibility that the evolution of SX Phe type stars is different from that of normal stars. In this case, there is a possibility that the inconsistency of evolutionary mass and pulsation mass can be explained. 4. TIME-SERIES PHOTOMETRY Time-series observation in the BV system was done over 9 yr starting from 1994 on the 0.5 m telescope at the Sutherland site in the South African Astronomical Observatory (SAAO) using the modular photometer. We obtained 11 new times of maximum light from the observations (rightmost column of Table 3). We identified an additional three and two new times using the photometric data obtained by Churms & Evans (1961) and Balona & Martin (1978), respectively, while five and eight new times were obtained from Leung (1968) and Chambliss TABLE 3 TIMES OF MAXIMUM LIGHT OF ZZ MIC HJD E O C (days) 37,192.3140... 0 0.0017 37,249.2819... 848 0.0010 39,320.2161... 31,675 0.0026 39,321.2235... 31,690 0.0023 39,330.1563... 31,823 0.0003 39,330.2234... 31,824 0.0002 39,331.2287... 31,838 0.0022 40,449.5625... 48,485 0.0002 40,449.6303... 48,487 0.0004 40,450.5030... 48,499 0.0002 40,450.5704... 48,500 0.0000 40,450.6373... 48,501 0.0003 40,451.5105... 48,514 0.0004 40,451.5779... 48,515 0.0002 40,451.6463... 48,517 0.0010 43,356.3384... 91,754 0.0002 43,356.4064... 91,756 0.0006 49,996.6645... 190,599 0.0002 49,997.6062... 190,614 0.0010 49,997.6067... 190,614 0.0015 49,997.6736... 190,615 0.0012 49,997.6737... 190,615 0.0013 49,998.6139... 190,629 0.0010 50,405.5860... 196,687 0.0016 50,406.5941... 196,702 0.0020 52,237.2943... 223,953 0.0025 52,474.5707... 227,485 0.0019 52,477.5255... 227,529 0.0008 52,493.5164... 227,767 0.0031 52,495.5324... 227,797 0.0037 52,496.4069... 227,810 0.0049 52,496.4711... 227,811 0.0019 52,842.5112... 232,962 0.0020

A PHOTOMETRIC STUDY OF ZZ MICROSCOPIUM 483 (1971), respectively. In addition, we identified four new times in our uvbyβ data. We began our analysis by plotting the O C diagram with a total of 34 times of maximum light in Table 3. We calculated the expected times of maximum light by applying the following equation derived by Churms & Evans (1961), but with the revised period of 0.06717918 days: HJD max ¼ 2; 437; 192:313 þ 0:0671786E: (4) Figure 3 shows a plot of the differences between the observed time of maximum light and the calculated time of maximum light (O C) versus the calculated cycle. There is a sign that the residuals have varied with a long period of approximately 40 yr from their discovery through the present. Following is the result of a parabolic least-squares fit for all cycles: HJD max ¼ 2; 437; 192:3516ð0:0013Þ þ 0:067178882ð0:00000034ÞE þ 7:3ð13:8 10 13 ÞE 2 (5) This result means that the pulsation period of ZZ Mic is increasing at a rate of dp=dt ¼ 7:9ð15:0Þ 10 9 days yr 1 or dp=pdt ¼ 11:8ð22:1Þ0 10 8 yr 1. This value is larger than that for the fundamental radial period for main sequence (O C)(day) 5 4 3 2 1 0 1 2 3 x 10 3 0 0.5 1 1.5 2 Cycle Number x 10 5 FIG. 3. Difference between observed times of maximum light and times of maximum light calculated from equation (4) and their parabolic fitted curve. TABLE 4 COMPARISON OF PHYSICAL PARAMETERS FOR ZZ MIC AND SX PHE Parameter ZZ Mic SX Phe P 0... 0.0672 0.0550 Period ratio... 0.778 0.784 ½Fe=HŠ... 0.078 1.14 T eff... 7780 7640 log g... 3.84 3.80 Mass (M )... 1.75 1.1 Age (Gyr).... 0.56 0.60 M bol... 2.3 2.7 and postmain sequence stars based on the stellar evolutionary model by Breger & Pamyatnykh (1998). 5. CONCLUSION New photometric (uvbyβ) observations of ZZ Mic were carried out. The reddening in the direction of ZZ Mic is Eðb yþ ¼0:00. This is not surprising because the galactic latitude of ZZ Mic is b ¼ 41:8. Following galactic extinction estimates from Schlegal et al. (1998), EðB V Þ¼0:036. Hence, there is some possibility of extinction. However, EðB V Þ¼0:036 is the total extinction toward ZZ Mic, so we adopted no reddening, which is the result from the photometric calibration. The temperature and surface-gravity variations of ZZ Mic were determined from the Kurucz model atmosphere grids. The mean values T eff ¼ 7780 K and log g ¼ 3:84 indicate that the star is similar in these properties to other dwarf Cepheids of similar pulsation period. The ranges in temperature and surface gravity are 670 K and 0.18, respectively. The metal abundance, ½Fe=HŠ ¼ 0:078, implies that the star has almost the same solar abundance and is, therefore, a member of the metal-strong group of dwarf Cepheids. In this case, however, the problem is that ZZ Mic is a short-period pulsator. We present the comparison of physical and atmospheric parameters for ZZ Mic and SX Phe in Table 4. In many respects, ZZ Mic is similar to SX Phe except in its mass and metallicity. ZZ Mic is too metal strong and massive if it is a SX Phe type star. In addition, as a Population I high-amplitude δ star, the period is too short. Therefore, there is a possibility that ZZ Mic is an extreme case among dwarf Cepheids. To solve the problem, it is absolutely necessary to determine its metallicity using a spectroscopic method. We also investigated the variations of the O C diagram and found a sign that the period is increasing. We are grateful to Michael D. Joner and C. David Laney for sending us their unpublished data file. We deeply thank the anonymous reviewer for useful suggestions. This paper was (partially) supported by research funds of Chonbuk National University.

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